100次までの余弦関数(cos x)積分リスト

100次まで(!)の余弦関数の積分結果を一覧にしました。


前回の記事で公開した正弦関数の積分リストの余弦バージョンです。

$ \displaystyle \int \cos^{1}x\, dx$ = sin(x) + C

$ \displaystyle \int \cos^{2}x\, dx$ = 1/2 (x + sin(x) cos(x)) + C

$ \displaystyle \int \cos^{3}x\, dx$ = 1/12 (9 sin(x) + sin(3 x)) + C

$ \displaystyle \int \cos^{4}x\, dx$ = 1/32 (12 x + 8 sin(2 x) + sin(4 x)) + C

$ \displaystyle \int \cos^{5}x\, dx$ = (5 sin(x))/8 + 5/48 sin(3 x) + 1/80 sin(5 x) + C

$ \displaystyle \int \cos^{6}x\, dx$ = 1/192 (60 x + 45 sin(2 x) + 9 sin(4 x) + sin(6 x)) + C

$ \displaystyle \int \cos^{7}x\, dx$ = (1225 sin(x) + 245 sin(3 x) + 49 sin(5 x) + 5 sin(7 x))/2240 + C

$ \displaystyle \int \cos^{8}x\, dx$ = (840 x + 672 sin(2 x) + 168 sin(4 x) + 32 sin(6 x) + 3 sin(8 x))/3072 + C

$ \displaystyle \int \cos^{9}x\, dx$ = (39690 sin(x) + 8820 sin(3 x) + 2268 sin(5 x) + 405 sin(7 x) + 35 sin(9 x))/80640 + C

$ \displaystyle \int \cos^{10}x\, dx$ = (2520 x + 2100 sin(2 x) + 600 sin(4 x) + 150 sin(6 x) + 25 sin(8 x) + 2 sin(10 x))/10240 + C

 


$ \displaystyle \int \cos^{11}x\, dx$ = (231 sin(x))/512 + 55/512 sin(3 x) + (33 sin(5 x))/1024 + (55 sin(7 x))/7168 + (11 sin(9 x))/9216 + sin(11 x)/11264 + C

$ \displaystyle \int \cos^{12}x\, dx$ = (231 x)/1024 + 99/512 sin(2 x) + (495 sin(4 x))/8192 + (55 sin(6 x))/3072 + (33 sin(8 x))/8192 + (3 sin(10 x))/5120 + sin(12 x)/24576 + C

$ \displaystyle \int \cos^{13}x\, dx$ = (429 sin(x))/1024 + (429 sin(3 x))/4096 + (143 sin(5 x))/4096 + (143 sin(7 x))/14336 + (13 sin(9 x))/6144 + (13 sin(11 x))/45056 + sin(13 x)/53248 + C

$ \displaystyle \int \cos^{14}x\, dx$ = (429 x)/2048 + (3003 sin(2 x))/16384 + (1001 sin(4 x))/16384 + (1001 sin(6 x))/49152 + (91 sin(8 x))/16384 + (91 sin(10 x))/81920 + (7 sin(12 x))/49152 + sin(14 x)/114688 + C

$ \displaystyle \int \cos^{15}x\, dx$ = (6435 sin(x))/16384 + (5005 sin(3 x))/49152 + (3003 sin(5 x))/81920 + (195 sin(7 x))/16384 + (455 sin(9 x))/147456 + (105 sin(11 x))/180224 + (15 sin(13 x))/212992 + sin(15 x)/245760 + C

$ \displaystyle \int \cos^{16}x\, dx$ = (6435 x)/32768 + (715 sin(2 x))/4096 + (1001 sin(4 x))/16384 + (91 sin(6 x))/4096 + (455 sin(8 x))/65536 + (7 sin(10 x))/4096 + (5 sin(12 x))/16384 + sin(14 x)/28672 + sin(16 x)/524288 + C

$ \displaystyle \int \cos^{17}x\, dx$ = (12155 sin(x))/32768 + (2431 sin(3 x))/24576 + (1547 sin(5 x))/40960 + (221 sin(7 x))/16384 + (595 sin(9 x))/147456 + (85 sin(11 x))/90112 + (17 sin(13 x))/106496 + (17 sin(15 x))/983040 + sin(17 x)/1114112 + C

$ \displaystyle \int \cos^{18}x\, dx$ = (12155 x)/65536 + (21879 sin(2 x))/131072 + (1989 sin(4 x))/32768 + (1547 sin(6 x))/65536 + (1071 sin(8 x))/131072 + (153 sin(10 x))/65536 + (17 sin(12 x))/32768 + (153 sin(14 x))/1835008 + (9 sin(16 x))/1048576 + sin(18 x)/2359296 + C

$ \displaystyle \int \cos^{19}x\, dx$ = (46189 sin(x))/131072 + (12597 sin(3 x))/131072 + (12597 sin(5 x))/327680 + (969 sin(7 x))/65536 + (323 sin(9 x))/65536 + (969 sin(11 x))/720896 + (969 sin(13 x))/3407872 + (57 sin(15 x))/1310720 + (19 sin(17 x))/4456448 + sin(19 x)/4980736 + C

$ \displaystyle \int \cos^{20}x\, dx$ = (46189 x)/262144 + (20995 sin(2 x))/131072 + (62985 sin(4 x))/1048576 + (1615 sin(6 x))/65536 + (4845 sin(8 x))/524288 + (969 sin(10 x))/327680 + (1615 sin(12 x))/2097152 + (285 sin(14 x))/1835008 + (95 sin(16 x))/4194304 + (5 sin(18 x))/2359296 + sin(20 x)/10485760 + C

 


$ \displaystyle \int \cos^{21}x\, dx$ = (88179 sin(x))/262144 + (146965 sin(3 x))/1572864 + (20349 sin(5 x))/524288 + (14535 sin(7 x))/917504 + (2261 sin(9 x))/393216 + (20349 sin(11 x))/11534336 + (5985 sin(13 x))/13631488 + (133 sin(15 x))/1572864 + (105 sin(17 x))/8912896 + (21 sin(19 x))/19922944 + sin(21 x)/22020096 + C

$ \displaystyle \int \cos^{22}x\, dx$ = (88179 x)/524288 + (323323 sin(2 x))/2097152 + (124355 sin(4 x))/2097152 + (53295 sin(6 x))/2097152 + (10659 sin(8 x))/1048576 + (74613 sin(10 x))/20971520 + (4389 sin(12 x))/4194304 + (1045 sin(14 x))/4194304 + (385 sin(16 x))/8388608 + (77 sin(18 x))/12582912 + (11 sin(20 x))/20971520 + sin(22 x)/46137344 + C

$ \displaystyle \int \cos^{23}x\, dx$ = (676039 sin(x))/2097152 + (572033 sin(3 x))/6291456 + (81719 sin(5 x))/2097152 + (245157 sin(7 x))/14680064 + (81719 sin(9 x))/12582912 + (9177 sin(11 x))/4194304 + (33649 sin(13 x))/54525952 + (1771 sin(15 x))/12582912 + (1771 sin(17 x))/71303168 + (253 sin(19 x))/79691776 + (23 sin(21 x))/88080384 + sin(23 x)/96468992 + C

$ \displaystyle \int \cos^{24}x\, dx$ = (676039 x)/4194304 + (156009 sin(2 x))/1048576 + (245157 sin(4 x))/4194304 + (81719 sin(6 x))/3145728 + (735471 sin(8 x))/67108864 + (43263 sin(10 x))/10485760 + (33649 sin(12 x))/25165824 + (759 sin(14 x))/2097152 + (5313 sin(16 x))/67108864 + (253 sin(18 x))/18874368 + (69 sin(20 x))/41943040 + (3 sin(22 x))/23068672 + sin(24 x)/201326592 + C

$ \displaystyle \int \cos^{25}x\, dx$ = (1300075 sin(x))/4194304 + (185725 sin(3 x))/2097152 + (81719 sin(5 x))/2097152 + (2042975 sin(7 x))/117440512 + (120175 sin(9 x))/16777216 + (10925 sin(11 x))/4194304 + (44275 sin(13 x))/54525952 + (1771 sin(15 x))/8388608 + (6325 sin(17 x))/142606336 + (575 sin(19 x))/79691776 + (25 sin(21 x))/29360128 + (25 sin(23 x))/385875968 + sin(25 x)/419430400 + C

$ \displaystyle \int \cos^{26}x\, dx$ = (1300075 x)/8388608 + (2414425 sin(2 x))/16777216 + (482885 sin(4 x))/8388608 + (5311735 sin(6 x))/201326592 + (1562275 sin(8 x))/134217728 + (312455 sin(10 x))/67108864 + (82225 sin(12 x))/50331648 + (16445 sin(14 x))/33554432 + (16445 sin(16 x))/134217728 + (7475 sin(18 x))/301989888 + (65 sin(20 x))/16777216 + (325 sin(22 x))/738197504 + (13 sin(24 x))/402653184 + sin(26 x)/872415232 + C

$ \displaystyle \int \cos^{27}x\, dx$ = (5014575 sin(x))/16777216 + (1448655 sin(3 x))/16777216 + (2607579 sin(5 x))/67108864 + (8436285 sin(7 x))/469762048 + (1562275 sin(9 x))/201326592 + (201825 sin(11 x))/67108864 + (34155 sin(13 x))/33554432 + (9867 sin(15 x))/33554432 + (40365 sin(17 x))/570425344 + (8775 sin(19 x))/637534208 + (975 sin(21 x))/469762048 + (351 sin(23 x))/1543503872 + (27 sin(25 x))/1677721600 + sin(27 x)/1811939328 + C

$ \displaystyle \int \cos^{28}x\, dx$ = (5014575 x)/33554432 + (2340135 sin(2 x))/16777216 + (30421755 sin(4 x))/536870912 + (1789515 sin(6 x))/67108864 + (6561555 sin(8 x))/536870912 + (345345 sin(10 x))/67108864 + (1036035 sin(12 x))/536870912 + (148005 sin(14 x))/234881024 + (94185 sin(16 x))/536870912 + (1365 sin(18 x))/33554432 + (4095 sin(20 x))/536870912 + (819 sin(22 x))/738197504 + (63 sin(24 x))/536870912 + (7 sin(26 x))/872415232 + sin(28 x)/3758096384 + C

$ \displaystyle \int \cos^{29}x\, dx$ = (9694845 sin(x))/33554432 + (22621305 sin(3 x))/268435456 + (10379187 sin(5 x))/268435456 + (2471235 sin(7 x))/134217728 + (3338335 sin(9 x))/402653184 + (910455 sin(11 x))/268435456 + (330165 sin(13 x))/268435456 + (26013 sin(15 x))/67108864 + (118755 sin(17 x))/1140850688 + (118755 sin(19 x))/5100273664 + (1131 sin(21 x))/268435456 + (1827 sin(23 x))/3087007744 + (203 sin(25 x))/3355443200 + (29 sin(27 x))/7247757312 + sin(29 x)/7784628224 + C

$ \displaystyle \int \cos^{30}x\, dx$ = (9694845 x)/67108864 + (145422675 sin(2 x))/1073741824 + (59879925 sin(4 x))/1073741824 + (28831075 sin(6 x))/1073741824 + (13656825 sin(8 x))/1073741824 + (6009003 sin(10 x))/1073741824 + (2384525 sin(12 x))/1073741824 + (5852925 sin(14 x))/7516192768 + (254475 sin(16 x))/1073741824 + (65975 sin(18 x))/1073741824 + (71253 sin(20 x))/5368709120 + (27405 sin(22 x))/11811160064 + (1015 sin(24 x))/3221225472 + (435 sin(26 x))/13958643712 + (15 sin(28 x))/7516192768 + sin(30 x)/16106127360 + C

 


$ \displaystyle \int \cos^{31}x\, dx$ = (300540195 sin(x))/1073741824 + (88394175 sin(3 x))/1073741824 + (41250615 sin(5 x))/1073741824 + (20160075 sin(7 x))/1073741824 + (9408035 sin(9 x))/1073741824 + (4032015 sin(11 x))/1073741824 + (1550775 sin(13 x))/1073741824 + (525915 sin(15 x))/1073741824 + (2629575 sin(17 x))/18253611008 + (736281 sin(19 x))/20401094656 + (8091 sin(21 x))/1073741824 + (31465 sin(23 x))/24696061952 + (899 sin(25 x))/5368709120 + (155 sin(27 x))/9663676416 + (31 sin(29 x))/31138512896 + sin(31 x)/33285996544 + C

$ \displaystyle \int \cos^{32}x\, dx$ = (300540195 x)/2147483648 + (17678835 sin(2 x))/134217728 + (29464725 sin(4 x))/536870912 + (3618475 sin(6 x))/134217728 + (28224105 sin(8 x))/2147483648 + (806403 sin(10 x))/134217728 + (1344005 sin(12 x))/536870912 + (876525 sin(14 x))/939524096 + (2629575 sin(16 x))/8589934592 + (11687 sin(18 x))/134217728 + (56637 sin(20 x))/2684354560 + (6293 sin(22 x))/1476395008 + (4495 sin(24 x))/6442450944 + (155 sin(26 x))/1744830464 + (31 sin(28 x))/3758096384 + sin(30 x)/2013265920 + sin(32 x)/68719476736 + C

$ \displaystyle \int \cos^{33}x\, dx$ = (583401555 sin(x))/2147483648 + (21607465 sin(3 x))/268435456 + (10235115 sin(5 x))/268435456 + (10235115 sin(7 x))/536870912 + (14784055 sin(9 x))/1610612736 + (12096045 sin(11 x))/2952790016 + (445005 sin(13 x))/268435456 + (642785 sin(15 x))/1073741824 + (3471039 sin(17 x))/18253611008 + (267003 sin(19 x))/5100273664 + (9889 sin(21 x))/805306368 + (29667 sin(23 x))/12348030976 + (1023 sin(25 x))/2684354560 + (341 sin(27 x))/7247757312 + (33 sin(29 x))/7784628224 + (33 sin(31 x))/133143986176 + sin(33 x)/141733920768 + C

$ \displaystyle \int \cos^{34}x\, dx$ = (583401555 x)/4294967296 + (1101980715 sin(2 x))/8589934592 + (57998985 sin(4 x))/1073741824 + (57998985 sin(6 x))/2147483648 + (57998985 sin(8 x))/4294967296 + (13708851 sin(10 x))/2147483648 + (2980185 sin(12 x))/1073741824 + (32782035 sin(14 x))/30064771072 + (6556407 sin(16 x))/17179869184 + (504339 sin(18 x))/4294967296 + (168113 sin(20 x))/5368709120 + (15283 sin(22 x))/2147483648 + (5797 sin(24 x))/4294967296 + (5797 sin(26 x))/27917287424 + (187 sin(28 x))/7516192768 + (187 sin(30 x))/85899345920 + (17 sin(32 x))/137438953472 + sin(34 x)/292057776128 + C

$ \displaystyle \int \cos^{35}x\, dx$ = (2268783825 sin(x))/8589934592 + (676654825 sin(3 x))/8589934592 + (81198579 sin(5 x))/2147483648 + (289994925 sin(7 x))/15032385536 + (61514075 sin(9 x))/6442450944 + (104306475 sin(11 x))/23622320128 + (8023575 sin(13 x))/4294967296 + (15298283 sin(15 x))/21474836480 + (1038345 sin(17 x))/4294967296 + (5883955 sin(19 x))/81604378624 + (840565 sin(21 x))/45097156608 + (202895 sin(23 x))/49392123904 + (40579 sin(25 x))/53687091200 + (6545 sin(27 x))/57982058496 + (6545 sin(29 x))/498216206336 + (595 sin(31 x))/532575944704 + (35 sin(33 x))/566935683072 + sin(35 x)/601295421440 + C

$ \displaystyle \int \cos^{36}x\, dx$ = (2268783825 x)/17179869184 + (1074687075 sin(2 x))/8589934592 + (3653936055 sin(4 x))/68719476736 + (57998985 sin(6 x))/2147483648 + (237268575 sin(8 x))/17179869184 + (14442435 sin(10 x))/2147483648 + (104306475 sin(12 x))/34359738368 + (5364333 sin(14 x))/4294967296 + (31773357 sin(16 x))/68719476736 + (5883955 sin(18 x))/38654705664 + (1513017 sin(20 x))/34359738368 + (23715 sin(22 x))/2147483648 + (40579 sin(24 x))/17179869184 + (11781 sin(26 x))/27917287424 + (8415 sin(28 x))/137438953472 + (119 sin(30 x))/17179869184 + (315 sin(32 x))/549755813888 + (9 sin(34 x))/292057776128 + sin(36 x)/1236950581248 + C

$ \displaystyle \int \cos^{37}x\, dx$ = (4418157975 sin(x))/17179869184 + (2650894785 sin(3 x))/34359738368 + (1287577467 sin(5 x))/34359738368 + (585262485 sin(7 x))/30064771072 + (42410325 sin(9 x))/4294967296 + (890616825 sin(11 x))/188978561024 + (35624673 sin(13 x))/17179869184 + (35624673 sin(15 x))/42949672960 + (2561251 sin(17 x))/8589934592 + (31100905 sin(19 x))/326417514496 + (3217335 sin(21 x))/120259084288 + (643467 sin(23 x))/98784247808 + (145299 sin(25 x))/107374182400 + (48433 sin(27 x))/206158430208 + (66045 sin(29 x))/1992864825344 + (3885 sin(31 x))/1065151889408 + (111 sin(33 x))/377957122048 + (37 sin(35 x))/2405181685760 + sin(37 x)/2542620639232 + C

$ \displaystyle \int \cos^{38}x\, dx$ = (4418157975 x)/34359738368 + (16789000305 sin(2 x))/137438953472 + (7195285845 sin(4 x))/137438953472 + (3706662405 sin(6 x))/137438953472 + (483477705 sin(8 x))/34359738368 + (483477705 sin(10 x))/68719476736 + (225622929 sin(12 x))/68719476736 + (96695541 sin(14 x))/68719476736 + (75207643 sin(16 x))/137438953472 + (118183439 sin(18 x))/618475290624 + (4075291 sin(20 x))/68719476736 + (1111443 sin(22 x))/68719476736 + (131461 sin(24 x))/34359738368 + (2760681 sin(26 x))/3573412790272 + (35853 sin(28 x))/274877906944 + (4921 sin(30 x))/274877906944 + (2109 sin(32 x))/1099511627776 + (703 sin(34 x))/4672924418048 + (19 sin(36 x))/2473901162496 + sin(38 x)/5222680231936 + C

$ \displaystyle \int \cos^{39}x\, dx$ = (34461632205 sin(x))/137438953472 + (10393190665 sin(3 x))/137438953472 + (5102111781 sin(5 x))/137438953472 + (18855630495 sin(7 x))/962072674304 + (698356685 sin(9 x))/68719476736 + (3771126099 sin(11 x))/755914244096 + (2030606361 sin(13 x))/893353197568 + (977699359 sin(15 x))/1030792151040 + (24647883 sin(17 x))/68719476736 + (8365071 sin(19 x))/68719476736 + (52978783 sin(21 x))/1443109011456 + (15380937 sin(23 x))/1580547964928 + (15380937 sin(25 x))/6871947673600 + (1087541 sin(27 x))/2473901162496 + (575757 sin(29 x))/7971459301376 + (82251 sin(31 x))/8521215115264 + (9139 sin(33 x))/9070970929152 + (741 sin(35 x))/9620726743040 + (39 sin(37 x))/10170482556928 + sin(39 x)/10720238370816 + C

$ \displaystyle \int \cos^{40}x\, dx$ = (34461632205 x)/274877906944 + (8205150525 sin(2 x))/68719476736 + (14172532725 sin(4 x))/274877906944 + (1848591225 sin(6 x))/68719476736 + (31426050825 sin(8 x))/2199023255552 + (1257042033 sin(10 x))/171798691840 + (483477705 sin(12 x))/137438953472 + (53719745 sin(14 x))/34359738368 + (698356685 sin(16 x))/1099511627776 + (24081265 sin(18 x))/103079215104 + (52978783 sin(20 x))/687194767360 + (776815 sin(22 x))/34359738368 + (25634895 sin(24 x))/4398046511104 + (179265 sin(26 x))/137438953472 + (137085 sin(28 x))/549755813888 + (27417 sin(30 x))/687194767360 + (45695 sin(32 x))/8796093022208 + (1235 sin(34 x))/2336462209024 + (65 sin(36 x))/1649267441664 + (5 sin(38 x))/2611340115968 + sin(40 x)/21990232555520 + C

 


$ \displaystyle \int \cos^{41}x\, dx$ = (67282234305 sin(x))/274877906944 + (10194277925 sin(3 x))/137438953472 + (5052816015 sin(5 x))/137438953472 + (75792240225 sin(7 x))/3848290697216 + (5726524817 sin(9 x))/549755813888 + (3964517181 sin(11 x))/755914244096 + (2202509545 sin(13 x))/893353197568 + (440501909 sin(15 x))/412316860416 + (58078345 sin(17 x))/137438953472 + (10392967 sin(19 x))/68719476736 + (70068713 sin(21 x))/1443109011456 + (350343565 sin(23 x))/25288767438848 + (19109649 sin(25 x))/5497558138880 + (1873495 sin(27 x))/2473901162496 + (1124097 sin(29 x))/7971459301376 + (374699 sin(31 x))/17042430230528 + (50635 sin(33 x))/18141941858304 + (533 sin(35 x))/1924145348608 + (205 sin(37 x))/10170482556928 + (41 sin(39 x))/42880953483264 + sin(41 x)/45079976738816 + C

$ \displaystyle \int \cos^{42}x\, dx$ = (67282234305 x)/549755813888 + (128447901855 sin(2 x))/1099511627776 + (27923456925 sin(4 x))/549755813888 + (58949520175 sin(6 x))/2199023255552 + (63665481789 sin(8 x))/4398046511104 + (83254860801 sin(10 x))/10995116277760 + (3083513363 sin(12 x))/824633720832 + (6607528635 sin(14 x))/3848290697216 + (1594920705 sin(16 x))/2199023255552 + (1382264611 sin(18 x))/4947802324992 + (133767543 sin(20 x))/1374389534720 + (133767543 sin(22 x))/4398046511104 + (222945905 sin(24 x))/26388279066624 + (9079245 sin(26 x))/4398046511104 + (3372291 sin(28 x))/7696581394432 + (2622893 sin(30 x))/32985348833280 + (212667 sin(32 x))/17592186044416 + (55965 sin(34 x))/37383395344384 + (1435 sin(36 x))/9895604649984 + (861 sin(38 x))/83562883710976 + (21 sin(40 x))/43980465111040 + sin(42 x)/92358976733184 + C

$ \displaystyle \int \cos^{43}x\, dx$ = (263012370465 sin(x))/1099511627776 + (80047243185 sin(3 x))/1099511627776 + (80047243185 sin(5 x))/2199023255552 + (43454217729 sin(7 x))/2199023255552 + (23398424931 sin(9 x))/2199023255552 + (132591074609 sin(11 x))/24189255811072 + (18941582087 sin(13 x))/7146825580544 + (653158003 sin(15 x))/549755813888 + (268947413 sin(17 x))/549755813888 + (100912357 sin(19 x))/549755813888 + (273904969 sin(21 x))/4398046511104 + (1917334783 sin(23 x))/101155069755392 + (112784399 sin(25 x))/21990232555520 + (16112057 sin(27 x))/13194139533312 + (16112057 sin(29 x))/63771674411008 + (3048227 sin(31 x))/68169720922112 + (160433 sin(33 x))/24189255811072 + (1763 sin(35 x))/2199023255552 + (12341 sin(37 x))/162727720910848 + (301 sin(39 x))/57174604644352 + (43 sin(41 x))/180319906955264 + sin(43 x)/189115999977472 + C

$ \displaystyle \int \cos^{44}x\, dx$ = (263012370465 x)/2199023255552 + (125788525005 sin(2 x))/1099511627776 + (880519675035 sin(4 x))/17592186044416 + (58701311669 sin(6 x))/2199023255552 + (257382674241 sin(8 x))/17592186044416 + (85794224747 sin(10 x))/10995116277760 + (208357402957 sin(12 x))/52776558133248 + (7184738033 sin(14 x))/3848290697216 + (7184738033 sin(16 x))/8796093022208 + (1622360201 sin(18 x))/4947802324992 + (21090682613 sin(20 x))/175921860444160 + (1917334783 sin(22 x))/48378511622144 + (1240628389 sin(24 x))/105553116266496 + (13633279 sin(26 x))/4398046511104 + (177232627 sin(28 x))/246290604621824 + (4790071 sin(30 x))/32985348833280 + (1764763 sin(32 x))/70368744177664 + (135751 sin(34 x))/37383395344384 + (135751 sin(36 x))/316659348799488 + (3311 sin(38 x))/83562883710976 + (473 sin(40 x))/175921860444160 + (11 sin(42 x))/92358976733184 + sin(44 x)/387028092977152 + C

$ \displaystyle \int \cos^{45}x\, dx$ = (48723617986322528257515000 sin(x) + 14887772162487439189796250 sin(3 x) + 7503437169893669351657310 sin(5 x) + 4122767675765752391020500 sin(7 x) + 2256494242291543489735500 sin(9 x) + 1186857361205292354990750 sin(11 x) + 588706436459919550088250 sin(13 x) + 272113197297029480929680 sin(15 x) + 116177361274822833414000 sin(17 x) + 45477322341131306500875 sin(19 x) + 16209088915237276631625 sin(21 x) + 5223389266802805257250 sin(23 x) + 1510305696572696834382 sin(25 x) + 388453111258409679625 sin(27 x) + 87972139828325770875 sin(29 x) + 17325582716614243500 sin(31 x) + 2921252097517708500 sin(33 x) + 413148510934647345 sin(35 x) + 47660507194174875 sin(37 x) + 4306321773344250 sin(39 x) + 285785392785750 sin(41 x) + 12386047678875 sin(43 x) + 263012370465 sin(45 x))/208213314894141477145804800 + C

$ \displaystyle \int \cos^{46}x\, dx$ = (9419588158802421600 x + 9027105318852320700 sin(2 x) + 3971926340295021108 sin(4 x) + 2138729567851165212 sin(6 x) + 1188183093250647340 sin(8 x) + 645013679193208556 sin(10 x) + 333627765099935460 sin(12 x) + 162047771619968652 sin(14 x) + 73182864602566488 sin(16 x) + 30492860251069370 sin(18 x) + 11642728459499214 sin(20 x) + 4046937699825930 sin(22 x) + 1271894705659578 sin(24 x) + 358739532365522 sin(26 x) + 90031156771270 sin(28 x) + 19901624128386 sin(30 x) + 3827235409305 sin(32 x) + 630368185062 sin(34 x) + 87124058098 sin(36 x) + 9826021590 sin(38 x) + 868346094 sin(40 x) + 56386110 sin(42 x) + 2392138 sin(44 x) + 49742 sin(46 x))/80506487676363341824 + C

$ \displaystyle \int \cos^{47}x\, dx$ = (389965478738356756959603750 sin(x) + 119589413479762738800945150 sin(3 x) + 60714625305110313545095230 sin(5 x) + 33730347391727951969497350 sin(7 x) + 18739081884293306649720750 sin(9 x) + 10045087781235596981511750 sin(11 x) + 5099813796627303082921350 sin(13 x) + 2423782471085234368442190 sin(15 x) + 1069315796067015162548025 sin(17 x) + 434889199357398511084125 sin(19 x) + 162017544858638660992125 sin(21 x) + 54945080430320937206025 sin(23 x) + 16849824665298420743181 sin(25 x) + 4638340123080145850225 sin(27 x) + 1136435420355389636625 sin(29 x) + 245334693724364512125 sin(31 x) + 46093184881547271975 sin(33 x) + 7419878541907609635 sin(35 x) + 1002686289446974275 sin(37 x) + 110612381364156375 sin(39 x) + 9565150494904875 sin(41 x) + 608017318280775 sin(43 x) + 25260622885095 sin(45 x) + 514589420475 sin(47 x))/1701917530439069465365708800 + C

$ \displaystyle \int \cos^{48}x\, dx$ = (442720643463713815200 x + 425011817725165262592 sin(2 x) + 187985996301515404608 sin(4 x) + 102115849842798491392 sin(6 x) + 57440165536574151408 sin(8 x) + 31691125813282290432 sin(10 x) + 16725871957010097728 sin(12 x) + 8324397103028067072 sin(14 x) + 3869543965860703053 sin(16 x) + 1667682247913030272 sin(18 x) + 662167951377232608 sin(20 x) + 240788345955357312 sin(22 x) + 79705401554666888 sin(24 x) + 23861908157738112 sin(26 x) + 6414009147662688 sin(28 x) + 1534976548158592 sin(30 x) + 323784115627203 sin(32 x) + 59461071449472 sin(34 x) + 9359613098528 sin(36 x) + 1237256076672 sin(38 x) + 133567417368 sin(40 x) + 11307294592 sin(42 x) + 703912608 sin(44 x) + 28651392 sin(46 x) + 572033 sin(48 x))/3864311408465440407552 + C

$ \displaystyle \int \cos^{49}x\, dx$ = (24968189718687855292266896100 sin(x) + 7682519913442417013005198800 sin(3 x) + 3926621289092790917758212720 sin(5 x) + 2203716029592892862007160200 sin(7 x) + 1241173395977606324578745400 sin(9 x) + 677003670533239813406588400 sin(11 x) + 351101159159918414396965200 sin(13 x) + 171161815090460227018520535 sin(15 x) + 77800825041118285008418425 sin(17 x) + 32758242122576120003544600 sin(19 x) + 12702175516917271021782600 sin(21 x) + 4510192756006857101937300 sin(23 x) + 1457889334103838133491084 sin(25 x) + 426283431024514074120200 sin(27 x) + 111941802841981149437400 sin(29 x) + 26179937761431075271650 sin(31 x) + 5398523751248536585950 sin(33 x) + 969530796142594325640 sin(35 x) + 149299211222461099800 sin(37 x) + 19314932920388324100 sin(39 x) + 2041415674512587100 sin(41 x) + 169257922457059800 sin(43 x) + 10323532859083080 sin(45 x) + 411843066186825 sin(47 x) + 8061900920775 sin(49 x))/111191945322019205070559641600 + C

$ \displaystyle \int \cos^{50}x\, dx$ = (3099044504245996706400 x + 2979850484851919910000 sin(2 x) + 1324377993267519960000 sin(4 x) + 725254615360784740000 sin(6 x) + 412644867360446490000 sin(8 x) + 231081125721850034400 sin(10 x) + 124237164366586040000 sin(12 x) + 63227842579423252500 sin(14 x) + 30176924867452006875 sin(16 x) + 13411966607756447500 sin(18 x) + 5518066261476938400 sin(20 x) + 2090176614195810000 sin(22 x) + 724971167986835000 sin(24 x) + 228938263574790000 sin(26 x) + 65410932449940000 sin(28 x) + 16788805995484600 sin(30 x) + 3838903809943125 sin(32 x) + 774232701165000 sin(34 x) + 136040888060000 sin(36 x) + 20503770210000 sin(38 x) + 2597144226600 sin(40 x) + 268855510000 sin(42 x) + 21841260000 sin(44 x) + 1305727500 sin(46 x) + 51074375 sin(48 x) + 980628 sin(50 x))/27602224346181717196800 + C

 


$ \displaystyle \int \cos^{51}x\, dx$ = (199822342948637266508265220788 sin(x) + 61673562638468292132180623700 sin(3 x) + 31717832214069407382264320760 sin(5 x) + 17968230072009762802760575800 sin(7 x) + 10248546041072235080093069160 sin(9 x) + 5680279184054699208614633640 sin(11 x) + 3003993799259696696863508175 sin(13 x) + 1498962562458878957828861655 sin(15 x) + 700207425370064565075765825 sin(17 x) + 304300670574358886175783945 sin(19 x) + 122364290812969710843172380 sin(21 x) + 45293480148161526340304700 sin(23 x) + 15352105902850538401661172 sin(25 x) + 4738304291003252593105300 sin(27 x) + 1323457405418149862212170 sin(29 x) + 332165942036498667227130 sin(31 x) + 74293969719563193968550 sin(33 x) + 14661334888179580470870 sin(35 x) + 2521605509023515068700 sin(37 x) + 372134374266148377660 sin(39 x) + 46171497125280339540 sin(41 x) + 4683402726710771700 sin(43 x) + 372937624534376265 sin(45 x) + 21861302350039425 sin(47 x) + 838760171797431 sin(49 x) + 15801325804719 sin(51 x))/907326273827676713375766675456 + C

$ \displaystyle \int \cos^{52}x\, dx$ = (3099044504245996706400 x + 2984265078162811643200 sin(2 x) + 1332261195608398055000 sin(4 x) + 735040659646012720000 sin(6 x) + 422648379296457314000 sin(8 x) + 239955208890891894400 sin(10 x) + 131225504862206504750 sin(12 x) + 68169093434912470000 sin(14 x) + 33332681716335876875 sin(16 x) + 15237797356039258000 sin(18 x) + 6476063876316684650 sin(20 x) + 2545872776930392000 sin(22 x) + 921203965336655000 sin(24 x) + 305251018099720000 sin(26 x) + 92120396533665500 sin(28 x) + 25164596126269600 sin(30 x) + 6178807084575125 sin(32 x) + 1352406475420000 sin(34 x) + 261260341842500 sin(36 x) + 44001741784000 sin(38 x) + 6361121366600 sin(40 x) + 773388616000 sin(42 x) + 76899436250 sin(44 x) + 6004570000 sin(46 x) + 345262775 sin(48 x) + 12998128 sin(50 x) + 240350 sin(52 x))/28143444431400966553600 + C

$ \displaystyle \int \cos^{53}x\, dx$ = (3198296076026906447986991482584 sin(x) + 989948785436899614853116411276 sin(3 x) + 512042475225982559406784350660 sin(5 x) + 292595700129132891089591057520 sin(7 x) + 168845547386345503460301649680 sin(9 x) + 94975620404819345696419677945 sin(11 x) + 51140718679518109221149057355 sin(13 x) + 26071738934656290975487754730 sin(15 x) + 12488143859457215005065563190 sin(17 x) + 5586801200283490923318804585 sin(19 x) + 2322441168200215660530210915 sin(21 x) + 892837794639899842034497560 sin(23 x) + 315927219641810713335283752 sin(25 x) + 102383821180216434877175290 sin(27 x) + 30224323998533194820764110 sin(29 x) + 8078390746151729491264140 sin(31 x) + 1941318706439562901001460 sin(33 x) + 415996865665620621643170 sin(35 x) + 78702109720522820310870 sin(37 x) + 12985409407622494321080 sin(39 x) + 1839655821629964166920 sin(41 x) + 219261304322175961755 sin(43 x) + 21379220149327814865 sin(45 x) + 1637557288033619862 sin(47 x) + 92395189120744458 sin(49 x) + 3414301860419667 sin(51 x) + 61989816618513 sin(53 x))/14796397696266727941204810399744 + C

$ \displaystyle \int \cos^{54}x\, dx$ = (164249358725037825439200 x + 158383310199143617387800 sin(2 x) + 70999414916857483656600 sin(4 x) + 39444119398254157587000 sin(6 x) + 22903037069954026986000 sin(8 x) + 13169246315223565516950 sin(10 x) + 7316247952901980842750 sin(12 x) + 3873307739771636916750 sin(14 x) + 1936653869885818458375 sin(16 x) + 908553667353840758250 sin(18 x) + 397799173273843791450 sin(20 x) + 161784352766874269250 sin(22 x) + 60841978818311691000 sin(24 x) + 21060684975569431500 sin(26 x) + 6677778162985429500 sin(28 x) + 1929135913751346300 sin(30 x) + 504715791388433625 sin(32 x) + 118756656797278500 sin(34 x) + 24924236611774500 sin(36 x) + 4619824177468500 sin(38 x) + 747035398909800 sin(40 x) + 103754916515250 sin(42 x) + 12127198034250 sin(44 x) + 1159992855450 sin(46 x) + 87189005475 sin(48 x) + 4828929534 sin(50 x) + 175215150 sin(52 x) + 3124550 sin(54 x))/1519745999295652193894400 + C

$ \displaystyle \int \cos^{55}x\, dx$ = (25594829708945481495133992684700 sin(x) + 7943223013121011498489859798700 sin(3 x) + 4130475966822925979214727095324 sin(5 x) + 2379306432501685471897884271500 sin(7 x) + 1387928752292649858607099158375 sin(9 x) + 791463503373494547470163982875 sin(11 x) + 433335221304040001103573945375 sin(13 x) + 225334315078100800573858451595 sin(15 x) + 110457997587304314006793358625 sin(17 x) + 50750971864437117246364516125 sin(19 x) + 21750416513330193105584792625 sin(21 x) + 8656520284569541737674215125 sin(23 x) + 3185599464721591359464111166 sin(25 x) + 1079132610000539078409251750 sin(27 x) + 334903223793270748471836750 sin(29 x) + 94717565919027060895635750 sin(31 x) + 24266483830494536262518250 sin(33 x) + 5592846749504455024313730 sin(35 x) + 1150115371519717543190250 sin(37 x) + 208940763074776836815250 sin(39 x) + 33124755121610961934125 sin(41 x) + 4512009833840695811625 sin(43 x) + 517377127613733119733 sin(45 x) + 48564811728448040025 sin(47 x) + 3583274962695538275 sin(49 x) + 194872889203197975 sin(51 x) + 6945155380407475 sin(53 x) + 121683714103007 sin(55 x))/120563240488099264706113269923840 + C

$ \displaystyle \int \cos^{56}x\, dx$ = (164249358725037825439200 x + 158585587734519279734400 sin(2 x) + 71363514480533675880480 sin(4 x) + 39902180139653238126720 sin(6 x) + 23380183675578069214875 sin(8 x) + 13603015956699967543200 sin(10 x) + 7668366838335766017000 sin(12 x) + 4131528255756412711200 sin(14 x) + 2108800880542335654675 sin(16 x) + 1013237660320641756000 sin(18 x) + 455956947144288790200 sin(20 x) + 191310607193407884000 sin(22 x) + 74531424052431821475 sin(24 x) + 26848092716823470400 sin(26 x) + 8903704217313906000 sin(28 x) + 2705621746656628800 sin(30 x) + 749426478122219625 sin(32 x) + 188091351371851200 sin(34 x) + 42479568486154800 sin(36 x) + 8562511005048000 sin(38 x) + 1525197272774175 sin(40 x) + 237154094892000 sin(42 x) + 31692410862840 sin(44 x) + 3566409406560 sin(46 x) + 328635482175 sin(48 x) + 23810570784 sin(50 x) + 1271932200 sin(52 x) + 44539040 sin(54 x) + 766935 sin(56 x))/1547377744737391324692480 + C

$ \displaystyle \int \cos^{57}x\, dx$ = (819286716496195757415668396380200 sin(x) + 254889200687705346751541278873840 sin(3 x) + 133200162940026665076611894121168 sin(5 x) + 77303665991979760981962259981035 sin(7 x) + 45549298143422418087014799652125 sin(9 x) + 26306546521334872478062023328500 sin(11 x) + 14627596197577412608680641543100 sin(13 x) + 7747208356494703714967895335790 sin(15 x) + 3879762531471910445492666185650 sin(17 x) + 1827034987119736220869122580500 sin(19 x) + 805323113980738431909344629500 sin(21 x) + 330882757700781660067100293425 sin(23 x) + 126219666596103052767059721687 sin(25 x) + 44521928252593669406370272200 sin(27 x) + 14459808293745337698139503000 sin(29 x) + 4304019184208656235663224500 sin(31 x) + 1168026755041137012102545100 sin(33 x) + 287291052792726867573048360 sin(35 x) + 63603827099022336984257400 sin(37 x) + 12571269244999073015050875 sin(39 x) + 2196374069186000312734125 sin(41 x) + 335074741717678187245020 sin(43 x) + 43946621898484154405556 sin(45 x) + 4854986870945467139730 sin(47 x) + 439323032218785051150 sin(49 x) + 31266272445490875100 sin(51 x) + 1641077078614100820 sin(53 x) + 56478626731524249 sin(55 x) + 956086325095055 sin(57 x))/3926916975898090336141975077519360 + C

$ \displaystyle \int \cos^{58}x\, dx$ = (164249358725037825439200 x + 158774380100869897924560 sin(2 x) + 71704558755231566804640 sin(4 x) + 40333814299817756327610 sin(6 x) + 23833617540801401466315 sin(8 x) + 14019775024000824391950 sin(10 x) + 8011300013714756795400 sin(12 x) + 4387140483700938245100 sin(14 x) + 2282498765168731384275 sin(16 x) + 1121227463591657522100 sin(18 x) + 517489598580765010200 sin(20 x) + 223461417568966708950 sin(22 x) + 89929594875315870675 sin(24 x) + 33600068414953182450 sin(26 x) + 11609325963970534800 sin(28 x) + 3693876443081533800 sin(30 x) + 1077380629232114025 sin(32 x) + 286566714680664600 sin(34 x) + 69101193610940400 sin(36 x) + 15002232823427850 sin(38 x) + 2908596159644175 sin(40 x) + 498616484510430 sin(42 x) + 74659152760920 sin(44 x) + 9613302278580 sin(46 x) + 1042952605695 sin(48 x) + 92706898284 sin(50 x) + 6482999880 sin(52 x) + 334440470 sin(54 x) + 11315655 sin(56 x) + 188370 sin(58 x))/1574524722715240295301120 + C

$ \displaystyle \int \cos^{59}x\, dx$ = (6556177149708637773710210776550520 sin(x) + 2044399326253231133737592607741560 sin(3 x) + 1073309646282946345212236119064319 sin(5 x) + 627258884191332279669488641011615 sin(7 x) + 373075545499419852613878864915405 sin(9 x) + 218031162954206407371747388586925 sin(11 x) + 122991938076731819543036988433650 sin(13 x) + 66260521594491556834897404579570 sin(15 x) + 33848254065297544513182884692350 sin(17 x) + 16307458436317440473962604365950 sin(19 x) + 7377183578334080214411654356025 sin(21 x) + 3121417017768078478844379732825 sin(23 x) + 1230730138434270943087212580371 sin(25 x) + 450525675137437683731322434675 sin(27 x) + 152529068698568244021889727100 sin(29 x) + 47562827873747086845535506300 sin(31 x) + 13598331552836782405113576900 sin(33 x) + 3546312605572632007169437380 sin(35 x) + 838655008074608920614393975 sin(37 x) + 178614645885068461899559575 sin(39 x) + 33980347265939853727233285 sin(41 x) + 5717623411368812597058405 sin(43 x) + 840539510047380997174398 sin(45 x) + 106290624514221201971070 sin(47 x) + 11328025741878450096690 sin(49 x) + 989435403479579420210 sin(51 x) + 68007015603043868505 sin(53 x) + 3449159643025191417 sin(55 x) + 114763327505375395 sin(57 x) + 1879204156221315 sin(59 x))/31956979527998252390672624768778240 + C

$ \displaystyle \int \cos^{60}x\, dx$ = (9690712164777231700912800 x + 9378108546558611323464000 sin(2 x) + 4249455435159370755944625 sin(4 x) + 2403732367362876387201000 sin(6 x) + 1431634718797007260024125 sin(8 x) + 850800061456507171671480 sin(10 x) + 492361146676219428050625 sin(12 x) + 273745193518824701310000 sin(14 x) + 144976895251745976680625 sin(16 x) + 72694967419678894290000 sin(18 x) + 34348372105798277552025 sin(20 x) + 15232094060220965655000 sin(22 x) + 6316483449575757583125 sin(24 x) + 2440716323986339245000 sin(26 x) + 875646603248345735625 sin(28 x) + 290584946855747325600 sin(30 x) + 88833713373020581875 sin(32 x) + 24904570457517660000 sin(34 x) + 6370266286008568125 sin(36 x) + 1477956517484265000 sin(38 x) + 308892912154211385 sin(40 x) + 57683083502187000 sin(42 x) + 9529810124050125 sin(44 x) + 1375920083538000 sin(46 x) + 170928343711125 sin(48 x) + 17900859268656 sin(50 x) + 1536818275125 sin(52 x) + 103852567000 sin(54 x) + 5179838625 sin(56 x) + 169533000 sin(58 x) + 2731365 sin(60 x))/94471483362914417718067200 + C

 


$ \displaystyle \int \cos^{61}x\, dx$ = (104927033006734800670863201288363376 sin(x) + 32789697814604625209644750402613555 sin(3 x) + 17289113393155166019630868394105329 sin(5 x) + 10170066701855980011547569643591370 sin(7 x) + 6102040021113588006928541786154822 sin(9 x) + 3605750921567120185912320146364213 sin(11 x) + 2061500007132968921259642495322575 sin(13 x) + 1128400003904361935847383260597620 sin(15 x) + 587176472619916844445470927460300 sin(17 x) + 288952632578748552398165956408095 sin(19 x) + 133904878512102987696711052969605 sin(21 x) + 58219512396566516389874370856350 sin(23 x) + 23666908760278667592907069827186 sin(25 x) + 8964738166772222573070859783025 sin(27 x) + 3153114803485402422252509302995 sin(29 x) + 1025978449380944406679638370680 sin(31 x) + 307595086371463023279195256200 sin(33 x) + 84588648752152331401778695455 sin(35 x) + 21228811462895372745620135925 sin(37 x) + 4833637071551561794387354026 sin(39 x) + 991693115110291731129686694 sin(41 x) + 181839971911994458749182265 sin(43 x) + 29506108649870798966848443 sin(45 x) + 4185263638279545952744460 sin(47 x) + 510928288309451064361012 sin(49 x) + 52595559090678786037163 sin(51 x) + 4439545702788179556265 sin(53 x) + 295041908774637638222 sin(55 x) + 14475740394830571010 sin(57 x) + 466167911019967541 sin(59 x) + 7391536347803839 sin(61 x))/519833533655438238888274696238792704 + C

$ \displaystyle \int \cos^{62}x\, dx$ = (591133442051411133755680800 x + 572660521987304535825815775 sin(2 x) + 260300237266956607193552625 sin(4 x) + 148013860406700815855157375 sin(6 x) + 88808316244020489513094425 sin(8 x) + 53284989746412293707856655 sin(10 x) + 31202921923574766585681825 sin(12 x) + 17595632663669981157339375 sin(14 x) + 9474571434283836007798125 sin(16 x) + 4842558733078405070652375 sin(18 x) + 2338601534511034643876025 sin(20 x) + 1063000697505015747216375 sin(22 x) + 453217351649425318580625 sin(24 x) + 180653070237882819294375 sin(26 x) + 67099711802642190023625 sin(28 x) + 23144538273954842355975 sin(30 x) + 7386554768283460326375 sin(32 x) + 2172516108318664801875 sin(34 x) + 586234505419322248125 sin(36 x) + 144398815019075164275 sin(38 x) + 32277382180734448485 sin(40 x) + 6502769303810969475 sin(42 x) + 1171167713379334125 sin(44 x) + 186707896335835875 sin(46 x) + 26025949186207425 sin(48 x) + 3123113902344891 sin(50 x) + 316104645986325 sin(52 x) + 26241126422875 sin(54 x) + 1715521582125 sin(56 x) + 82818283275 sin(58 x) + 2624841765 sin(60 x) + 40970475 sin(62 x))/5857231968500693898520166400 + C

$ \displaystyle \int \cos^{63}x\, dx$ = (839627810491391983594064608696601289 sin(x) + 262913758840738903953696998682774141 sin(3 x) + 139189637033332360916663116949703957 sin(5 x) + 82377540285033438093535314113090097 sin(7 x) + 49833326839094302056583091253597713 sin(9 x) + 29753067375675467812652803868855637 sin(11 x) + 17225460059601586628377939081969053 sin(13 x) + 9569700033111992571321077267760585 sin(15 x) + 5066311782235760773052335024108545 sin(17 x) + 2542911305332711761570555833666805 sin(19 x) + 1205143906608926889270399476726445 sin(21 x) + 537379638841796519887003204485705 sin(23 x) + 224722394424751271952746794603113 sin(25 x) + 87854434034367781216094425873645 sin(27 x) + 32006937736658726889821507477205 sin(29 x) + 10830075706364277526892246524545 sin(31 x) + 3391235827245379831653127699605 sin(33 x) + 978811506989191263363439190265 sin(35 x) + 259252777526866875161127136881 sin(37 x) + 62695116133948198568377150749 sin(39 x) + 13762342565988628954034008701 sin(41 x) + 2723482447240400025567941169 sin(43 x) + 481933107947889716458524569 sin(45 x) + 75505960819688717665648917 sin(47 x) + 10346297838266384053310493 sin(49 x) + 1220770608367860244336257 sin(51 x) + 121521082030112307991833 sin(53 x) + 9923909626496074458501 sin(55 x) + 638380151412028181541 sin(57 x) + 30331482603905756889 sin(59 x) + 946355089175272161 sin(61 x) + 14544636039226909 sin(63 x))/4225743563908723748382103982328250368 + C

$ \displaystyle \int \cos^{64}x\, dx$ = (1182266884102822267511361600 x + 1146440614887585229101926400 sin(2 x) + 522642045022281501502348800 sin(4 x) + 298652597155589429429913600 sin(6 x) + 180435944114835280280572800 sin(8 x) + 109236895896548926440130560 sin(10 x) + 64679740991377653813235200 sin(12 x) + 36959851995072945036134400 sin(14 x) + 20212419059805516816636000 sin(16 x) + 10517031055508561595648000 sin(18 x) + 5183393877357791072140800 sin(20 x) + 2410880873189670266112000 sin(22 x) + 1054760382020480741424000 sin(24 x) + 432722208008402355456000 sin(26 x) + 165966436922477300928000 sin(28 x) + 59324173197821673523200 sin(30 x) + 19697479382089227537000 sin(32 x) + 6053487061002211584000 sin(34 x) + 1715154667283959948800 sin(36 x) + 446046415021215590400 sin(38 x) + 105936023567538702720 sin(40 x) + 22843347400008345600 sin(42 x) + 4441761994446067200 sin(44 x) + 772480346860185600 sin(46 x) + 118975767708376800 sin(48 x) + 16030419228076032 sin(50 x) + 1860294008563200 sin(52 x) + 182175684454400 sin(54 x) + 14639117500800 sin(56 x) + 926840678400 sin(58 x) + 43352225280 sin(60 x) + 1331865600 sin(62 x) + 20160075 sin(64 x))/11900407809017282841437798400 + C

$ \displaystyle \int \cos^{65}x\, dx$ = (214995606019765523071813513438978208850 sin(x) + 67449601888553889591157180686738261600 sin(3 x) + 35844645575060067039872101736380904736 sin(5 x) + 21336098556583373238019108176417205200 sin(7 x) + 13006690711670945247200837717155233200 sin(9 x) + 7841354208949947852379452403643824800 sin(11 x) + 4593456015893756434234117088525080800 sin(13 x) + 2587646888953482791285219293202462184 sin(15 x) + 1392206001947713123001373364348527000 sin(17 x) + 711804572424394679429273599817292000 sin(19 x) + 344472423199845487165661753178468000 sin(21 x) + 157259149721668591966932539494518000 sin(23 x) + 67516594947169715484469703622979728 sin(25 x) + 27180593779053830710334019171892000 sin(27 x) + 10230113432615271573295195770492000 sin(29 x) + 3588789792893260592244685613035500 sin(31 x) + 1169630315927488146019139961700500 sin(33 x) + 352894175319836423484631942730208 sin(35 x) + 98182004262275634514802209821600 sin(37 x) + 25078046453579279427350860299600 sin(39 x) + 5851159480885731555299993636400 sin(41 x) + 1239780561841421156420153690400 sin(43 x) + 236935840707471598782518260832 sin(45 x) + 40509547233420296144427514200 sin(47 x) + 6135173104094803175471836200 sin(49 x) + 813045252469629088838728800 sin(51 x) + 92822882997012339211840800 sin(53 x) + 8944750543348461778595568 sin(55 x) + 707450790745132870035600 sin(57 x) + 44094800516645788509600 sin(59 x) + 2030908064388838034400 sin(61 x) + 61451087265733690525 sin(63 x) + 916312070471295267 sin(65 x))/1098693326616268174579347035405345095680 + C

$ \displaystyle \int \cos^{66}x\, dx$ = (1182266884102822267511361600 x + 1147494328688033377290439200 sin(2 x) + 524568835971672401047057920 sin(4 x) + 301141368798552674675162880 sin(6 x) + 183126508053173923788950400 sin(8 x) + 111803552285095658734306560 sin(10 x) + 66891014187664069328217600 sin(12 x) + 38701229637148497254183040 sin(14 x) + 21474462786466544208113760 sin(16 x) + 11362149622469071009584000 sin(18 x) + 5707498415007719390860800 sin(20 x) + 2712240982338379049376000 sin(22 x) + 1215485773566458759164800 sin(24 x) + 512211396218641483795200 sin(26 x) + 202393560815876574144000 sin(28 x) + 74773176634754401003200 sin(30 x) + 25750966443091439121000 sin(32 x) + 8240309261789260518720 sin(34 x) + 2441573114604225338880 sin(36 x) + 667231519173219475200 sin(38 x) + 167437343490638094720 sin(40 x) + 38389514380569580800 sin(42 x) + 7995171590002920960 sin(44 x) + 1502198388804896640 sin(46 x) + 252562594609010400 sin(48 x) + 37623117541756032 sin(50 x) + 4905230448729600 sin(52 x) + 551081445474560 sin(54 x) + 52268849043840 sin(56 x) + 4069877011200 sin(58 x) + 249791393280 sin(60 x) + 11331262800 sin(62 x) + 337758795 sin(64 x) + 4962480 sin(66 x))/12083491006079087192844533760 + C

$ \displaystyle \int \cos^{67}x\, dx$ = (1720348084532490968038094227856636683650 sin(x) + 540680826567354304240543900183514386290 sin(3 x) + 288363107502588962261623413431207672688 sin(5 x) + 172572516072977950388230228115201502960 sin(7 x) + 105965580044811022168211543579509694800 sin(9 x) + 64468569677612300200240589450470933200 sin(11 x) + 38185229732124208580142502982202014280 sin(13 x) + 21793521359309914165252062677647003272 sin(15 x) + 11904024271891969922196504823924833720 sin(17 x) + 6192423886847107976662808506937643000 sin(19 x) + 3056001398703767572898528873553642000 sin(21 x) + 1426133986061758200685980140991699600 sin(23 x) + 627498953867173608301831262036347824 sin(25 x) + 259603586115260949061041302260900400 sin(27 x) + 100708287717127092308162574152935500 sin(29 x) + 36530787710425956459379577589379500 sin(31 x) + 12354048207525868911717457148408340 sin(33 x) + 3882700865222415943682629389499764 sin(35 x) + 1130100043931680316248582358690160 sin(37 x) + 303437602507054947033363913436400 sin(39 x) + 74831495469219512683024704939600 sin(41 x) + 16864772551836786579303242170320 sin(43 x) + 3453262951090389632904949587256 sin(45 x) + 638060903616925296113456530680 sin(47 x) + 105520276108358511320663113800 sin(49 x) + 15465085331932902456767176200 sin(51 x) + 1984199627493278051056920720 sin(53 x) + 219415219612520464066204944 sin(55 x) + 20488687739709041636063280 sin(57 x) + 1570964758089070989044400 sin(59 x) + 94966107302515561837725 sin(61 x) + 4243906626705823642565 sin(63 x) + 124646208616534680411 sin(65 x) + 1804857108504066435 sin(67 x))/8922721561610905175371666832988863201280 + C

$ \displaystyle \int \cos^{68}x\, dx$ = (79211881234889091923261227200 x + 76948684628177975011168049280 sin(2 x) + 35268147121248238546785355920 sin(4 x) + 20334787529368353756705070080 sin(6 x) + 12441679212047742759036654720 sin(8 x) + 7656417976644764774791787520 sin(10 x) + 4625752527556212051436704960 sin(12 x) + 2707757577106075347182461440 sin(14 x) + 1523113637122167382790134560 sin(16 x) + 818624383776255337520279040 sin(18 x) + 418614741703766933959233600 sin(20 x) + 202964723250311240707507200 sin(22 x) + 93025498156392651990940800 sin(24 x) + 40194323262336595950259200 sin(26 x) + 16328943825324242104792800 sin(28 x) + 6220550028694949373254400 sin(30 x) + 2216070947722575714221880 sin(32 x) + 736134294053173939672320 sin(34 x) + 227289327971546227099680 sin(36 x) + 65004296381137351941120 sin(38 x) + 17153911545022356762240 sin(40 x) + 4158524010914510730240 sin(42 x) + 921491116054919991360 sin(44 x) + 185563428404652080640 sin(46 x) + 33726686340788057760 sin(48 x) + 5487732014772294144 sin(50 x) + 791499809822927040 sin(52 x) + 99958688793666560 sin(54 x) + 10882599183181440 sin(56 x) + 1000698775464960 sin(58 x) + 75573605438760 sin(60 x) + 4500661366080 sin(62 x) + 198182531745 sin(64 x) + 5736626880 sin(66 x) + 81880920 sin(68 x))/821677388413377929113428295680 + C

$ \displaystyle \int \cos^{69}x\, dx$ = (27531352035156939491863417206135957145740 sin(x) + 8667277492549406877068112824153912434770 sin(3 x) + 4638164712229142058539152268060742329958 sin(5 x) + 2789873511115273418670166777780897642080 sin(7 x) + 1724793595190924022368735586263403955360 sin(9 x) + 1058396069776248831908087746116179699880 sin(11 x) + 633449054894227724913095667938201358840 sin(13 x) + 365992787272220463283121941475405229552 sin(15 x) + 202773021676127616456449228861202623760 sin(17 x) + 107207745910105749370515022914654975720 sin(19 x) + 53887491330476434868777392470329220600 sin(21 x) + 25670411749111647612347642537850592800 sin(23 x) + 11557147076834094967601619491508905184 sin(25 x) + 4904653466249037216188958889143439700 sin(27 x) + 1957029215596906475425151083845411900 sin(29 x) + 732307706481423068223604921696992840 sin(31 x) + 256285941246320966835236660059137720 sin(33 x) + 83644972033139919945126690151169124 sin(35 x) + 25379275043201556536129719857187980 sin(37 x) + 7134155187832536310251089342571360 sin(39 x) + 1850767532098462856539639585545120 sin(41 x) + 441171330325796378593751296554360 sin(43 x) + 96146110585621900831932543771496 sin(45 x) + 19045817944327155704051200893840 sin(47 x) + 3405979895267083880662217524080 sin(49 x) + 545402009372833693308655747320 sin(51 x) + 77432577266356531156409832360 sin(53 x) + 9627980281799169856398172704 sin(55 x) + 1032239601362484097664521440 sin(57 x) + 93492040165775837235504855 sin(59 x) + 6955902105650409075529365 sin(61 x) + 408186655550432855803070 sin(63 x) + 17714644752934973535426 sin(65 x) + 505466158446344723355 sin(67 x) + 7113260368810144185 sin(69 x))/144863008882624107553092943876760367267840 + C

$ \displaystyle \int \cos^{70}x\, dx$ = (79211881234889091923261227200 x + 77011551200586617147615082000 sin(2 x) + 35383685686756013284039362000 sin(4 x) + 20485291713385060322338578000 sin(6 x) + 12606333362083114044516048000 sin(8 x) + 7815926684491530707599949760 sin(10 x) + 4765808953958250431463384000 sin(12 x) + 2820580809485495153315064000 sin(14 x) + 1607075112381270494330676000 sin(16 x) + 876586424935238451453096000 sin(18 x) + 455824940966323994755609920 sin(20 x) + 225209951070318179227080000 sin(22 x) + 105417423905255317936080000 sin(24 x) + 46626937496555236779420000 sin(26 x) + 19439218839671716791420000 sin(28 x) + 7620173785151312982236640 sin(30 x) + 2801534479835041537587000 sin(32 x) + 963423622024720166772000 sin(34 x) + 309022671215476279908000 sin(36 x) + 92164656327422750148000 sin(38 x) + 25470959566851378222720 sin(40 x) + 6497693767053923016000 sin(42 x) + 1523382749213599176000 sin(44 x) + 326602298557038504000 sin(46 x) + 63659770057727844000 sin(48 x) + 11204119530160100544 sin(50 x) + 1766097025561176000 sin(52 x) + 246873777766616000 sin(54 x) + 30229442175504000 sin(56 x) + 3192333333189000 sin(58 x) + 284854358961480 sin(60 x) + 20883750657000 sin(62 x) + 1207828862625 sin(64 x) + 51671823000 sin(66 x) + 1453683000 sin(68 x) + 20173560 sin(70 x))/833585756361397899100579430400 + C

 


$ \displaystyle \int \cos^{71}x\, dx$ = (220294516840041479330926168470049777732818 sin(x) + 69462235039652718707949692760826506492330 sin(3 x) + 37290252494971459516899308745285808748514 sin(5 x) + 22538064694762970037686395395502411880970 sin(7 x) + 14023684698963625801227090468312611837048 sin(9 x) + 8675405833726943677477512728734409539992 sin(11 x) + 5243377152252548376497397803081236535160 sin(13 x) + 3064733622324357733239564297304846781016 sin(15 x) + 1720839734460200866257509364796839101640 sin(17 x) + 923819225868107833464557658996197833512 sin(19 x) + 472429293559881231606098844248573219208 sin(21 x) + 229440683736297545414617847576781628200 sin(23 x) + 105542714518696870890724209885319548972 sin(25 x) + 45870794291950643055303416994753394300 sin(27 x) + 18791208144426677224034641168885183596 sin(29 x) + 7238359114456575856696455706420668444 sin(31 x) + 2615257955106688246591959520967840580 sin(33 x) + 883971287251694625667470953987512692 sin(35 x) + 278729685169453260345598949455522020 sin(37 x) + 81734718867872308045399412217959604 sin(39 x) + 22213616974543693475753150358887976 sin(41 x) + 5573796180883056502483960616367240 sin(43 x) + 1285603563560000005553771759024168 sin(45 x) + 271214599597042914983395773180360 sin(47 x) + 52028923188004151037631025875416 sin(49 x) + 9014332882781818517930929908984 sin(51 x) + 1399059577059868364012408476440 sin(53 x) + 192597811906942917643266621432 sin(55 x) + 23229999243161974715744877585 sin(57 x) + 2416889099875261515406051149 sin(59 x) + 212513348573234619089354721 sin(61 x) + 15355738288281582284352805 sin(63 x) + 875485531368090211687083 sin(65 x) + 36928331952580054354095 sin(67 x) + 1024512729119198195331 sin(69 x) + 14023284727082855679 sin(71 x))/1175459843504721329859382744599998408687616 + C

$ \displaystyle \int \cos^{72}x\, dx$ = (5624043567677125526551547131200 x + 5472042390172338350158262073600 sin(2 x) + 2520019521789892661257094376000 sin(4 x) + 1464626730612929068081046304000 sin(6 x) + 906237789566749860875147400600 sin(8 x) + 565846034461190157034238376960 sin(10 x) + 348040219609065374366297414400 sin(12 x) + 208130363885819825202436992000 sin(14 x) + 120029726900060865102541788000 sin(16 x) + 66386811915095392056714470400 sin(18 x) + 35069554989930826673438296320 sin(20 x) + 17636526687392678791284249600 sin(22 x) + 8420216734432268520144390000 sin(24 x) + 3806942573809251701415360000 sin(26 x) + 1626108327955666083890275200 sin(28 x) + 654694594784764906978045440 sin(30 x) + 247871150669712675117889800 sin(32 x) + 88034148961496177622336000 sin(34 x) + 29254146208398421164624000 sin(36 x) + 9070185044517787997452800 sin(38 x) + 2615776579802897788551120 sin(40 x) + 699288642887992725427200 sin(42 x) + 172630033314825790368000 sin(44 x) + 39182056198206590592000 sin(46 x) + 8135718613377618463200 sin(48 x) + 1536450466001805978624 sin(50 x) + 262111586941995436800 sin(52 x) + 40064087363267968000 sin(54 x) + 5432797560978859500 sin(56 x) + 645595041729052800 sin(58 x) + 66189794682322080 sin(60 x) + 5736236419267200 sin(62 x) + 408601399350375 sin(64 x) + 22969248624000 sin(66 x) + 955443535200 sin(68 x) + 26144933760 sin(70 x) + 353037300 sin(72 x))/60018174458020648735241718988800 + C

$ \displaystyle \int \cos^{73}x\, dx$ = (7050747629072558818945979289951322916145268 sin(x) + 2226551882865018574403993459984628289309032 sin(3 x) + 1198912552311933078525227247684030617320248 sin(5 x) + 727911192475102226247459400379590017658722 sin(7 x) + 455684242443763182284994909180718954144078 sin(9 x) + 284062904380527698047789034294474153232672 sin(11 x) + 173283453298318327431656638093766880594528 sin(13 x) + 102394767858097193482342558873589520351312 sin(15 x) + 58224475840878796293881062888903844905648 sin(17 x) + 31710355263453440544493576584803467019552 sin(19 x) + 16481674012311666665982983574472318724448 sin(21 x) + 8151262690871530796763323398244461977852 sin(23 x) + 3826102895715208333174621186931073989604 sin(25 x) + 1700490175873425925855387194191588439824 sin(27 x) + 713998917658821839050842087622025977776 sin(29 x) + 282587660959260752676449908128320455224 sin(31 x) + 105182714285007861630856998394246207176 sin(33 x) + 36730471655082110410775459756720897744 sin(35 x) + 12002832260751647873791489306250317936 sin(37 x) + 3660204343251189324150701409323585964 sin(39 x) + 1038389165415292478353408230372930036 sin(41 x) + 273128826187823522774593343674676064 sin(43 x) + 66353330655798934911341885751474976 sin(45 x) + 14823616423104017373810421284903984 sin(47 x) + 3030187231353815528738095485137616 sin(49 x) + 563488327652132678968374492492384 sin(51 x) + 94674139506692552531074600266016 sin(53 x) + 14254913050723594557235664244599 sin(55 x) + 1904502553335540973233914656161 sin(57 x) + 223023411484593395941105568364 sin(59 x) + 22536987752174473335864105636 sin(61 x) + 1925428925605942399842731714 sin(63 x) + 135230794106102977915375806 sin(65 x) + 7496803084773299415351324 sin(67 x) + 307584694843729982136276 sin(69 x) + 8303342701180504212599 sin(71 x) + 110628135069209194801 sin(73 x))/38137141589264292035437751269244392815198208 + C

$ \displaystyle \int \cos^{74}x\, dx$ = (410555180440430163438262940577600 x + 399751096744629369663571810562400 sin(2 x) + 184500506189828939844725451028800 sin(4 x) + 107625295277400214909423179766800 sin(6 x) + 66937683648139158053421733757400 sin(8 x) + 42075115435973185062150804076080 sin(10 x) + 26093094844014378333116777721600 sin(12 x) + 15757518314891799902466625507200 sin(14 x) + 9191885683686883276438864879200 sin(16 x) + 5151008402452552947183132009600 sin(18 x) + 2761817271102219878064147375360 sin(20 x) + 1412292922722726074010075362400 sin(22 x) + 686931591664455199263404002800 sin(24 x) + 317045349998979322736955693600 sin(26 x) + 138540825209638023380854588800 sin(28 x) + 57192494509619799395686125120 sin(30 x) + 22256513193602044576151440200 sin(32 x) + 8146174763671336576892030400 sin(34 x) + 2797676181462883268831606400 sin(36 x) + 899253058327355336410159200 sin(38 x) + 269775917498206600923047760 sin(40 x) + 75306906362389363147648800 sin(42 x) + 19493929536026830522041600 sin(44 x) + 4661591845571633385705600 sin(46 x) + 1025295474230919364888800 sin(48 x) + 206382056748417317319552 sin(50 x) + 37798911492384124051200 sin(52 x) + 6256069841910798309400 sin(54 x) + 928098273250503045900 sin(56 x) + 122194756979690056200 sin(58 x) + 14104071452382135840 sin(60 x) + 1405054556451730800 sin(62 x) + 118360574048922975 sin(64 x) + 8198134999059600 sin(66 x) + 448282444024800 sin(68 x) + 18144765591480 sin(70 x) + 483308063700 sin(72 x) + 6354671400 sin(74 x))/4441344909893528006407887205171200 + C

$ \displaystyle \int \cos^{75}x\, dx$ = (56416010545566349013614699155015919492627500 sin(x) + 17840960599879956525673024519107598472027500 sin(3 x) + 9634118723935176523863433240318103174894850 sin(5 x) + 5874462636545839343819166609950062911521250 sin(7 x) + 3698735734121454401663919717375965536883750 sin(9 x) + 2322461972587889973137810055096536499903750 sin(11 x) + 1429207367746393829623267726213253230710000 sin(13 x) + 853289732150809945686187990613246002927600 sin(15 x) + 491023503155836925266987974138057162810000 sin(17 x) + 271080164676178728058930650895926294810000 sin(19 x) + 143070086912427662031102287972849988927500 sin(21 x) + 71979360496314538040492455439756826727500 sin(23 x) + 34434926061436874998571590682379665906436 sin(25 x) + 15629505292954282406759073476025629042500 sin(27 x) + 6716126942860991379031750406143639005000 sin(29 x) + 2726510450936263694348251686486796845000 sin(31 x) + 1043479308383014500306121015815934595000 sin(33 x) + 375652551017885220110203565693736454200 sin(35 x) + 126909645614150412199393096518154207500 sin(37 x) + 40133819553192865396389269839074407500 sin(39 x) + 11847746562801257993383207496648542500 sin(41 x) + 3254978066327346007642134657139942500 sin(43 x) + 829416633197486686391773571893437200 sin(45 x) + 195275977470632547371624402172330000 sin(47 x) + 42294796963685390444545377429030000 sin(49 x) + 8385242971013879151315096614470000 sin(51 x) + 1512903507741890931782087007091875 sin(53 x) + 246719648954831444259848035002675 sin(55 x) + 36070124116203427523369595760625 sin(57 x) + 4680995110450887508092234410625 sin(59 x) + 532649395403283245858132748750 sin(61 x) + 52321438195813652169639448750 sin(63 x) + 4346704096267595718708508050 sin(65 x) + 296968432055280346558811250 sin(67 x) + 16020036189777603236264375 sin(69 x) + 639812365673155290354375 sin(71 x) + 16818466480116262723125 sin(73 x) + 218266320541953276229 sin(75 x))/309220066939980746233279064345224806609715200 + C

$ \displaystyle \int \cos^{76}x\, dx$ = (410555180440430163438262940577600 x + 400028124531701184888563890819200 sin(2 x) + 185013007595911798010960799503880 sin(4 x) + 108300297129314223225928272880320 sin(6 x) + 67687685705821389516205170550200 sin(8 x) + 42816396539496320810250712534080 sin(10 x) + 26760247837185200506406695333800 sin(12 x) + 16311008205522407927714557155840 sin(14 x) + 9618176034234680761722986148960 sin(16 x) + 5457121154175705396722261644800 sin(18 x) + 2967309627583039809467729769360 sin(20 x) + 1541459546796384316606612867200 sin(22 x) + 763022475664210236720273369264 sin(24 x) + 359069400312569523162481585536 sin(26 x) + 160298839425254251411822136400 sin(28 x) + 67748943455201796823109733120 sin(30 x) + 27052529504681273037005622600 sin(32 x) + 10184481695880008672755057920 sin(34 x) + 3607003933957503071600749680 sin(36 x) + 1199004077769807115213545600 sin(38 x) + 373138337995603766027663760 sin(40 x) + 108417919030199641460822400 sin(42 x) + 29322119010440357576904240 sin(44 x) + 7356654234978621430556160 sin(46 x) + 1705675881093833597810400 sin(48 x) + 363877521300017834199552 sin(50 x) + 71069828378909733242100 sin(52 x) + 12634636156250619243040 sin(54 x) + 2030566525111706664060 sin(56 x) + 292618953695974197600 sin(58 x) + 37438013193455522340 sin(60 x) + 4200618591131054400 sin(62 x) + 406934926015820895 sin(64 x) + 33346780108850880 sin(66 x) + 2247638365179900 sin(68 x) + 119639458968480 sin(70 x) + 4715519216100 sin(72 x) + 122348606688 sin(74 x) + 1567485612 sin(76 x))/4500562842025441713159992367906816 + C

$ \displaystyle \int \cos^{77}x\, dx$ = (902808438663057714714498114143291192096595000 sin(x) + 285889338909968276326257736145375544163921750 sin(3 x) + 154798617653690139864461505912861880010708850 sin(5 x) + 94774663869606208080282554640527681639209500 sin(7 x) + 59999464206856643358318413144520108531282500 sin(9 x) + 37933545552268869561250897566576762831761250 sin(11 x) + 23538251342689913932878762079773273346887750 sin(13 x) + 14191177621100006081271833369834321322181600 sin(15 x) + 8258945674357325191228288506849761470356000 sin(17 x) + 4618489357370872639831608704488353453817500 sin(19 x) + 2473068645200535300823339549244978380032500 sin(21 x) + 1264490750763404136420977091266128076051400 sin(23 x) + 615881377430646249974452371510796498217976 sin(25 x) + 285130267329002893506690912736479860286100 sin(27 x) + 125219863661078043667544805528382502077500 sin(29 x) + 52062739013208075503351962155169785810000 sin(31 x) + 20452194444307084205999971909992318062000 sin(33 x) + 7575659778860685272222438574823685159700 sin(35 x) + 2640165925776483487474391821951355425500 sin(37 x) + 863714759095754987060587952362512385000 sin(39 x) + 264577361095475173795740253286739015000 sin(41 x) + 75681431197077782271804770126206741500 sin(43 x) + 20154144336999584277118137326869627700 sin(45 x) + 4979747399670453218780047657977396000 sin(47 x) + 1137260096134651609731109037536140000 sin(49 x) + 239019738342025430231476960707656875 sin(51 x) + 46000025114880365818133301872039625 sin(53 x) + 8059508532524493845821702476754050 sin(55 x) + 1276774721701314159916766168744750 sin(57 x) + 181396209214792889120776848500625 sin(59 x) + 22884625111203379454296152661875 sin(61 x) + 2532357608677380765010549319500 sin(63 x) + 241986935087047652734485861300 sin(65 x) + 19563620373952857497191021125 sin(67 x) + 1301134172180704240928924375 sin(69 x) + 68350405695065544441641250 sin(71 x) + 2659111673616248578277550 sin(73 x) + 68110579710170577619039 sin(75 x) + 861577581086657669325 sin(77 x))/5012620032500740517886839569385749496620646400 + C

$ \displaystyle \int \cos^{78}x\, dx$ = (410555180440430163438262940577600 x + 400291300929419409352306367063160 sin(2 x) + 185500846772169970187654170102440 sin(4 x) + 108944941755083950745130226885560 sin(6 x) + 68407289009006201630663165718840 sin(8 x) + 43531911187549401037694741821080 sin(10 x) + 27408981118086659912622615220680 sin(12 x) + 16853969755842107648134403148120 sin(14 x) + 10040662833267638598888580598880 sin(16 x) + 5764084219098088825287888862320 sin(18 x) + 3176128039094865271076999985360 sin(20 x) + 1674685693340928961113327265008 sin(22 x) + 842815675733670130756380388272 sin(24 x) + 403953075351640713557791783728 sin(26 x) + 184010969634574880299910542992 sin(28 x) + 79510912805063219882677395120 sin(30 x) + 32527191602071317224731661640 sin(32 x) + 12573536249540173044854255760 sin(34 x) + 4583335825855774579703208240 sin(36 x) + 1572142415765410881241209360 sin(38 x) + 506283150839708588874287760 sin(40 x) + 152688569300864495057324880 sin(42 x) + 43007659609334410679335920 sin(44 x) + 11279708761494438705520080 sin(46 x) + 2745325941951027409809120 sin(48 x) + 617698336938981167207052 sin(50 x) + 127925691082037519835780 sin(52 x) + 24264244436435848319020 sin(54 x) + 4190626437849261649980 sin(56 x) + 654519747899377580220 sin(58 x) + 91696003328898308340 sin(60 x) + 11409180137697024540 sin(62 x) + 1245368254466928735 sin(64 x) + 117408454966579140 sin(66 x) + 9366186173804460 sin(68 x) + 614768976658980 sin(70 x) + 31876909900836 sin(72 x) + 1224290991924 sin(74 x) + 30962930076 sin(76 x) + 386782164 sin(78 x))/4559011710103694202941290970087424 + C

$ \displaystyle \int \cos^{79}x\, dx$ = (7223624956020696407093824013292667089583140250 sin(x) + 2290417668982172031517553955434260296697093250 sin(3 x) + 1243369591733179102823815004378598446778422050 sin(5 x) + 764197257377535328978092278438673463966804250 sin(7 x) + 486307345603886118440604177188246749797057250 sin(9 x) + 309468310838836620825839021847066113507218250 sin(11 x) + 193547070658402836436227080553181816808862250 sin(13 x) + 117775451507028108980342436251510637462414050 sin(15 x) + 69279677357075358223730844853829786742596500 sin(17 x) + 39216315754219885911821863843145325041190500 sin(19 x) + 21288857123719366637846154657707462165217700 sin(21 x) + 11052782598759671170032658300548887006494100 sin(23 x) + 5475378456616329410385409188887294793986308 sin(25 x) + 2582725687083174250181796787210988110370900 sin(27 x) + 1157773583864871215598736490818718808097300 sin(29 x) + 492308415426411513964272114864264595818500 sin(31 x) + 198202089327516323803797864425872759355500 sin(33 x) + 75406208420844556274226856691347079875100 sin(35 x) + 27056281679426984310882888933987535649500 sin(37 x) + 9136345443248486227534117645244813211500 sin(39 x) + 2896890018590983437998622668004452969500 sin(41 x) + 860342098544558176973285191908299223500 sin(43 x) + 238675549918812913611943633884237849100 sin(45 x) + 61663895875681147893663248875866921500 sin(47 x) + 14786750541617418117358023965131353625 sin(49 x) + 3278510301082594967197027937970300125 sin(51 x) + 669198500564028818347249270357574125 sin(53 x) + 125122867541008373362620012829408025 sin(55 x) + 21305751438871394845028175559187125 sin(57 x) + 3281431135389920060877589308673625 sin(59 x) + 453406175615937432299245361151625 sin(61 x) + 55649450125899765332502951771125 sin(63 x) + 5993017705866128574269548652275 sin(65 x) + 557518514857715907031822661375 sin(67 x) + 43893937127458244149391443375 sin(69 x) + 2843832546286027085735220275 sin(71 x) + 145574701359991292780966575 sin(73 x) + 5520495168456812661304187 sin(75 x) + 137874504706713602929675 sin(77 x) + 1701063429324939500975 sin(79 x))/40615075135134205221852341126305047203387801600 + C

$ \displaystyle \int \cos^{80}x\, dx$ = (32433859254793982911622772305630400 x + 31642789516872178450363680298176000 sin(2 x) + 14691295132833511423383137281296000 sin(4 x) + 8655336667405789675791615762624000 sin(6 x) + 5458763466375242352345848577564000 sin(8 x) + 3493608618480155105501343089640960 sin(10 x) + 2215150392152272258922953045968000 sin(12 x) + 1373527902732715929544931371968000 sin(14 x) + 826262878987649426366872778449500 sin(16 x) + 479644664446345245237912542592000 sin(18 x) + 267641722761060646842755198766336 sin(20 x) + 143123915915005693498799571532800 sin(22 x) + 73167514706549384977751704036800 sin(24 x) + 35681110219739612993504459443200 sin(26 x) + 16566229744879106032698499027200 sin(28 x) + 7309221366225447995033034722304 sin(30 x) + 3059104924480516738992620559000 sin(32 x) + 1212276874097542237124010624000 sin(34 x) + 454023235413926259306023136000 sin(36 x) + 160386441769772344946641536000 sin(38 x) + 53328491888449304694758310720 sin(40 x) + 16652144227462702480798848000 sin(42 x) + 4871118436039309596655968000 sin(44 x) + 1331237336557326846291072000 sin(46 x) + 338876170959579945898313250 sin(48 x) + 80079045937525353369201408 sin(50 x) + 17499791507326344704808000 sin(52 x) + 3521240524415030111968000 sin(54 x) + 649136252137434647742000 sin(56 x) + 109000390164007017312000 sin(58 x) + 16557678315389637391680 sin(60 x) + 2256839388740068704000 sin(62 x) + 273289144730242694625 sin(64 x) + 29041934848875936000 sin(66 x) + 2666409757587576000 sin(68 x) + 207218129732520192 sin(70 x) + 13254083590347600 sin(72 x) + 669915070905600 sin(74 x) + 25087912574400 sin(76 x) + 618851462400 sin(78 x) + 7542252198 sin(80 x))/364720936808295536235303277606993920 + C

 


$ \displaystyle \int \cos^{81}x\, dx$ = (462382471575139406116512969280128670973219348100 sin(x) + 146788086214329970195718402946072593959752174000 sin(3 x) + 79880028311984216339065363463676713922283741200 sin(5 x) + 49276640841808445144228633305514855991019191000 sin(7 x) + 31512715995131820474951150681798389386849309800 sin(9 x) + 20178102732060691371312594507712802690393629200 sin(11 x) + 12714516451462137770794351694712649813095822000 sin(13 x) + 7805300377147590131515421457031932246372712950 sin(15 x) + 4638203705507871686794878296795686028756894250 sin(17 x) + 2655981911364507576438330308901950736467105760 sin(19 x) + 1460666055829780543904926752514704933500583840 sin(21 x) + 769414393957158647709116934853063635539605200 sin(23 x) + 387320302467490428695834713620372411248993712 sin(25 x) + 185956249469988546013089368679191143946704800 sin(27 x) + 84991915901957147362722350951178899020155360 sin(29 x) + 36914691584144982207081021092850743007602040 sin(31 x) + 15209402433658884216101962438574867533701000 sin(33 x) + 5933914644067899654755051355345465559946400 sin(35 x) + 2188181991971900697241326770981722297644000 sin(37 x) + 761188094643216738271128201529539294992400 sin(39 x) + 249265513599677932284707715734783159775600 sin(41 x) + 76668312510028471295371465454809524012000 sin(43 x) + 22094536621055824002934210679569446602400 sin(45 x) + 5949659130005058990151831998155336352375 sin(47 x) + 1492551850823875081045938388234258632825 sin(49 x) + 347641310471158069976237580622596187800 sin(51 x) + 74893157564189220932644818129058317000 sin(53 x) + 14858482062200107468455201885497666100 sin(55 x) + 2701198747641260320352267823069115500 sin(57 x) + 447365603725574348455436123723795400 sin(59 x) + 67037699565434715342317719763736600 sin(61 x) + 9015210920395761983865478186922250 sin(63 x) + 1077265456662675878788561882399350 sin(65 x) + 112984678794794565746279180889000 sin(67 x) + 10239577653093459195170035910520 sin(69 x) + 785616224681373629874053904180 sin(71 x) + 49616395616774175165502425900 sin(73 x) + 2476579063264625495440462968 sin(75 x) + 91604519025898526462946600 sin(77 x) + 2232135431960185613179395 sin(79 x) + 26876802183334044115405 sin(81 x))/2631856868756696498376031704984567058779529543680 + C

$ \displaystyle \int \cos^{82}x\, dx$ = (97301577764381948734868316916891200 x + 94984873531896664241180976037917600 sin(2 x) + 44179010945068215926130686529264000 sin(4 x) + 26105779194813036683622678403656000 sin(6 x) + 16533660156714923232961029655648800 sin(8 x) + 10639050883451341906427097343634880 sin(10 x) + 6790883542628516110485381283171200 sin(12 x) + 4244302214142822569053363301982000 sin(14 x) + 2576897772872427988353827719060500 sin(16 x) + 1511780026751824419834245595182160 sin(18 x) + 853711073930442025318162218455808 sin(20 x) + 462675582025239559175927076435840 sin(22 x) + 240067518975360148629018766075200 sin(24 x) + 119007829919409304448573405404800 sin(26 x) + 56258246870993489375689246191360 sin(28 x) + 25316211091947070219060160786112 sin(30 x) + 10826011322214207659466516125640 sin(32 x) + 4391891002926656251304874696000 sin(34 x) + 1687280159316455508975884064000 sin(36 x) + 612749110488607526943873686400 sin(38 x) + 209941908347736021526671476160 sin(40 x) + 67723196241205168234410153600 sin(42 x) + 20522180679153081283154592000 sin(44 x) + 5827630111335589657852323000 sin(46 x) + 1546563375700598793814654950 sin(48 x) + 382422943809602610834169224 sin(50 x) + 87812386638255478951588800 sin(52 x) + 18652957946034660561612000 sin(54 x) + 3649491772050259675098000 sin(56 x) + 654391628091770700362400 sin(58 x) + 106914688533303382031040 sin(60 x) + 15807279218633564547600 sin(62 x) + 2097712567541269267875 sin(64 x) + 247396076761623894000 sin(66 x) + 25612770300026944320 sin(68 x) + 2291668921581358176 sin(70 x) + 173611281937981680 sin(72 x) + 10828146482618400 sin(74 x) + 533832671361600 sin(76 x) + 19505424530520 sin(78 x) + 469575034994 sin(80 x) + 5586853480 sin(82 x))/1107670993269638295233143287547166720 + C

$ \displaystyle \int \cos^{83}x\, dx$ = (3699596802184826212237697845959124755324631926900 sin(x) + 1175840844105254842649190788250574534638061310100 sin(3 x) + 641367733148320823263194975409404291620760714600 sin(5 x) + 397037168139436700115311175253440751955709013800 sin(7 x) + 255101175664468990895344861394722801981204342200 sin(9 x) + 164310815273245984464506458113041959496597767800 sin(11 x) + 104274171231098413217859867648661243526687044950 sin(13 x) + 64550677428775208182484679972980769802234837350 sin(15 x) + 38730406457265124909490807983788461881340902410 sin(17 x) + 22422866896311388105494678306403846352355259290 sin(19 x) + 12484526623587293011117916126642434599113550960 sin(21 x) + 6667290264114296759834096307173277214128729840 sin(23 x) + 3407726134991751677248538112555230576110239696 sin(25 x) + 1663704678699676744784639819260971156686817360 sin(27 x) + 774483212498125381192849571035279676388690840 sin(29 x) + 343192051718184591666101422818689296328435160 sin(31 x) + 144520790848932487399622647226678982675401640 sin(33 x) + 57738330484440340002270549134145356274676200 sin(35 x) + 21846935858977425946805072645352296968796400 sin(37 x) + 7814940065569478554321612787387475712671600 sin(39 x) + 2637772846679233910152613600148880472648400 sin(41 x) + 838361912510454188498117500822512398283600 sin(43 x) + 250344182207982847954298975940055785598575 sin(45 x) + 70063592729239062193429009632977969455575 sin(47 x) + 18328323886498530184180872649814274013425 sin(49 x) + 4468098857902626761317725173337808092825 sin(51 x) + 1011645024430783417656843435472711266300 sin(53 x) + 211925637528978344410326885691911846300 sin(55 x) + 40897930049451961201992907765105794900 sin(57 x) + 7234510901562163583355632526603818100 sin(59 x) + 1166218970470403419174815079425205650 sin(61 x) + 170152843919469600840682956793718850 sin(63 x) + 22286131324171694081004212636183550 sin(65 x) + 2594504840724465878087057590481070 sin(67 x) + 265189663353988121787693148073580 sin(69 x) + 23429048362900359031179036129420 sin(71 x) + 1752858202071575860077672882180 sin(73 x) + 107981982068544335684109806244 sin(75 x) + 5258862763078457906693659395 sin(77 x) + 189841740626836033199911755 sin(79 x) + 4515958298560688534415245 sin(81 x) + 53098072606098965203605 sin(83 x))/21311621473834713108801037220850640573531800207360 + C

$ \displaystyle \int \cos^{84}x\, dx$ = (8076030954443701744994070304101969600 x + 7888216281084545890459324483076342400 sin(2 x) + 3675191676414390698964003452342386800 sin(4 x) + 2177891363801120414200890934721414400 sin(6 x) + 1384854834590929828595131735665247200 sin(8 x) + 895735893012005676367914994983479040 sin(10 x) + 575385903497295312944667618305359800 sin(12 x) + 362342143310250109609469987037777600 sin(14 x) + 221934562777528192135800367060638780 sin(16 x) + 131516777942238928673066884184082240 sin(18 x) + 75116313555471080415193970389754664 sin(20 x) + 41230223563894932646418645840002560 sin(22 x) + 21696768881617549432760429369507520 sin(24 x) + 10924247269066178735375880521710080 sin(26 x) + 5253113801579017070454983363118240 sin(28 x) + 2408445158150847592536085939581696 sin(30 x) + 1051099449408505684242580609407960 sin(32 x) + 435949522386778030553253772197120 sin(34 x) + 171554210198500613875123012207200 sin(36 x) + 63944278520925164101857757785600 sin(38 x) + 22535201381971207026219225929280 sin(40 x) + 7494700384026705284608056998400 sin(42 x) + 2347416810622000731897836034300 sin(44 x) + 690878526203130650190667461600 sin(46 x) + 190602219665888948316490960050 sin(48 x) + 49158303818306880998641250592 sin(50 x) + 11816899956323769470827223700 sin(52 x) + 2638663651009494417533078400 sin(54 x) + 545234070744308795459641200 sin(56 x) + 103803669612321052850985600 sin(58 x) + 18117584927706035613343320 sin(60 x) + 2882161102065476279630400 sin(62 x) + 415040935728178805470425 sin(64 x) + 53661858356774633434560 sin(66 x) + 6167790995341356861480 sin(68 x) + 622500612516827111808 sin(70 x) + 54313621818597807120 sin(72 x) + 4013596412185127040 sin(74 x) + 244248465873108060 sin(76 x) + 11752379491203680 sin(78 x) + 419215975753302 sin(80 x) + 9855209538720 sin(82 x) + 114530496340 sin(84 x))/93044363434649616799584036153962004480 + C

$ \displaystyle \int \cos^{85}x\, dx$ = (59201742847808127095055076272546348520975560735000 sin(x) + 18836918178848040439335706086719292711219496597500 sin(3 x) + 10297515271103595440170185994073213348799991473300 sin(5 x) + 6395972218076767354142972667126219471304342530000 sin(7 x) + 4127896963439615810120641934102737389281526030000 sin(9 x) + 2673751442227932967919052161862000354420988451250 sin(11 x) + 1708346682867768787979676969980901325352185713750 sin(13 x) + 1066008330109487723699318429268082427019763885380 sin(15 x) + 645506774287752081824846799729807698022348373500 sin(17 x) + 377634529897085732079718067048409766656798947250 sin(19 x) + 212737511451458000012563547205168844289140107750 sin(21 x) + 115104354022044908219358054526468166958375324000 sin(23 x) + 59686839576522196043928940274452220393688440736 sin(25 x) + 29606567250259025815440942596454474401631171000 sin(27 x) + 14024163434333222754682551756215277348141081000 sin(29 x) + 6333493163892423179534055631839157512063714000 sin(31 x) + 2722718941026172676563946874088019947404894000 sin(33 x) + 1112425167333550550710412579984533864225428120 sin(35 x) + 431268064429267493075591939515492747539765000 sin(37 x) + 158381323909507664950837734611148701329740000 sin(39 x) + 55001179847784891777352476943941302784660000 sin(41 x) + 18027276243714379499699103998341226421425625 sin(43 x) + 5565343742931311004522492618975086310614475 sin(45 x) + 1614703213616434527424320875911533745826250 sin(47 x) + 439211078208795623816606318059396781913750 sin(49 x) + 111702471447565669032943129333445202320625 sin(51 x) + 26482374280842065915111209497428764126875 sin(53 x) + 5833000880559499193769949520472621293400 sin(55 x) + 1189084686548452393096172066812432065000 sin(57 x) + 223373253264045435426258311985951221250 sin(59 x) + 38474575623966505495607483784690003750 sin(61 x) + 6041053058074534968422281881251197500 sin(63 x) + 858758927024749278588028993580939460 sin(65 x) + 109621622656340736661865444977928250 sin(67 x) + 12441528037224442726727811654750750 sin(69 x) + 1240108970124213142859110154103000 sin(71 x) + 106872578143182578810642924673000 sin(73 x) + 7801698204452328253176933501129 sin(75 x) + 469077573620269856492119618875 sin(77 x) + 22302545951689273819014023250 sin(79 x) + 786212017038577702678316750 sin(81 x) + 18268265456145953504573625 sin(83 x) + 209863810776486386280915 sin(85 x))/345045300052562021761540602623296085476229146214400 + C

$ \displaystyle \int \cos^{85}x\, dx$ = (59201742847808127095055076272546348520975560735000 sin(x) + 18836918178848040439335706086719292711219496597500 sin(3 x) + 10297515271103595440170185994073213348799991473300 sin(5 x) + 6395972218076767354142972667126219471304342530000 sin(7 x) + 4127896963439615810120641934102737389281526030000 sin(9 x) + 2673751442227932967919052161862000354420988451250 sin(11 x) + 1708346682867768787979676969980901325352185713750 sin(13 x) + 1066008330109487723699318429268082427019763885380 sin(15 x) + 645506774287752081824846799729807698022348373500 sin(17 x) + 377634529897085732079718067048409766656798947250 sin(19 x) + 212737511451458000012563547205168844289140107750 sin(21 x) + 115104354022044908219358054526468166958375324000 sin(23 x) + 59686839576522196043928940274452220393688440736 sin(25 x) + 29606567250259025815440942596454474401631171000 sin(27 x) + 14024163434333222754682551756215277348141081000 sin(29 x) + 6333493163892423179534055631839157512063714000 sin(31 x) + 2722718941026172676563946874088019947404894000 sin(33 x) + 1112425167333550550710412579984533864225428120 sin(35 x) + 431268064429267493075591939515492747539765000 sin(37 x) + 158381323909507664950837734611148701329740000 sin(39 x) + 55001179847784891777352476943941302784660000 sin(41 x) + 18027276243714379499699103998341226421425625 sin(43 x) + 5565343742931311004522492618975086310614475 sin(45 x) + 1614703213616434527424320875911533745826250 sin(47 x) + 439211078208795623816606318059396781913750 sin(49 x) + 111702471447565669032943129333445202320625 sin(51 x) + 26482374280842065915111209497428764126875 sin(53 x) + 5833000880559499193769949520472621293400 sin(55 x) + 1189084686548452393096172066812432065000 sin(57 x) + 223373253264045435426258311985951221250 sin(59 x) + 38474575623966505495607483784690003750 sin(61 x) + 6041053058074534968422281881251197500 sin(63 x) + 858758927024749278588028993580939460 sin(65 x) + 109621622656340736661865444977928250 sin(67 x) + 12441528037224442726727811654750750 sin(69 x) + 1240108970124213142859110154103000 sin(71 x) + 106872578143182578810642924673000 sin(73 x) + 7801698204452328253176933501129 sin(75 x) + 469077573620269856492119618875 sin(77 x) + 22302545951689273819014023250 sin(79 x) + 786212017038577702678316750 sin(81 x) + 18268265456145953504573625 sin(83 x) + 209863810776486386280915 sin(85 x))/345045300052562021761540602623296085476229146214400

$ \displaystyle \int \cos^{86}x\, dx$ = (8076030954443701744994070304101969600 x + 7892484796388163068971477797190561200 sin(2 x) + 3683159571647809432186689638688928560 sin(4 x) + 2188544093297973720574699640380377840 sin(6 x) + 1396943038275302374834914664072581600 sin(8 x) + 908012974878946543642694531647178040 sin(10 x) + 586811106214285181265686942220965400 sin(12 x) + 372205901655918029259950003351583768 sin(14 x) + 229891880434537606307616178540684092 sin(16 x) + 137542150687330191807975491434597320 sin(18 x) + 79411128510043469232529245998088264 sin(20 x) + 44117293616690816240294025554493480 sin(22 x) + 23529223262235101994823480295729856 sin(24 x) + 12023174524109145524827382788477344 sin(26 x) + 5875987549376650068524660761285920 sin(28 x) + 2742127523042436698644841688600096 sin(30 x) + 1220014364065490904058086344504280 sin(32 x) + 516711965957149088777542451790048 sin(34 x) + 208002448955427957413181934144992 sin(36 x) + 79457641791122734156139108968800 sin(38 x) + 28756098933930132361269391817280 sin(40 x) + 9842117194648706016505893032700 sin(42 x) + 3179760939809581943794211595180 sin(44 x) + 967753329507264069850412224620 sin(46 x) + 276844857943620318489545785650 sin(48 x) + 74259561895465214841901693092 sin(50 x) + 18626980408561508739607448100 sin(52 x) + 4356150973854067123230948180 sin(54 x) + 946608259911950199816785520 sin(56 x) + 190409707453553201112571800 sin(58 x) + 35299699190019451895755320 sin(60 x) + 6001256619053001848014200 sin(62 x) + 930194775953215286442201 sin(64 x) + 130553652765363548974344 sin(66 x) + 16456342785550027181640 sin(68 x) + 1844557103435277772008 sin(70 x) + 181601965176468978960 sin(72 x) + 15460707846104791452 sin(74 x) + 1115099786171300748 sin(76 x) + 66250456339132940 sin(78 x) + 3112973249670102 sin(80 x) + 108465966887460 sin(82 x) + 2491375149796 sin(84 x) + 28295769684 sin(86 x))/94139003004469024056049730696949792768 + C

$ \displaystyle \int \cos^{87}x\, dx$ = (473676523905982784336651027808565868874486278227500 sin(x) + 150874744651535257233155512561246906382243777509500 sin(3 x) + 82653120983014967005989541663987435670272678113900 sin(5 x) + 51501184807045800110115063954764207636492094265500 sin(7 x) + 33380397560122277849148652563273097542170801838750 sin(9 x) + 21737513067908941604918695825062814911506403423750 sin(11 x) + 13978893019055288601316945930578856358476425586350 sin(13 x) + 8789343192373325251285556853082914912976680662790 sin(15 x) + 5369055796246148909156335634236169743221049273650 sin(17 x) + 3172381528069968819213525027180259182935972510250 sin(19 x) + 1807194415461375535460262052520676747951180107250 sin(21 x) + 990028244991883988991273993989588131486298667450 sin(23 x) + 520471991652876154212555471125954903409939870888 sin(25 x) + 262096032183872007481956133932823294439703313800 sin(27 x) + 126217470908999004792142965805937496133269729000 sin(29 x) + 58036573556297519426020904452046710906549941000 sin(31 x) + 25442295882255680233225325790089164175194620600 sin(33 x) + 10617838703086562570399890060407234323231103960 sin(35 x) + 4211958683438871813018265019603567233714169400 sin(37 x) + 1585698731046380312186363509618762593075135000 sin(39 x) + 565630340037885660139647959223765924968874375 sin(41 x) + 190836998445698095710800724704118521375902875 sin(43 x) + 60785118023444578633810601202052566067880175 sin(45 x) + 18241326304272825280708484641454326749490875 sin(47 x) + 5146112462790052750259896627541136597995625 sin(49 x) + 1361475050542068516763843069122136451473125 sin(51 x) + 336882505767552263716767638127795488531625 sin(53 x) + 77728844480554312319797091409255758045325 sin(55 x) + 16667003689787474376564678469820922777750 sin(57 x) + 3308634352163522310648432805130459478750 sin(59 x) + 605434642199173555293665373734550183750 sin(61 x) + 101610512436813678168862781242645141950 sin(63 x) + 15550110810168247104384668546445288930 sin(65 x) + 2155132628274916976087427410488153050 sin(67 x) + 268290386648865547004566400042189250 sin(69 x) + 29703749350854966070571534039258250 sin(71 x) + 2888994799877674782206272488749775 sin(73 x) + 243008451479422520774881521275907 sin(75 x) + 17319259291374744116043187293975 sin(77 x) + 1016915483785157310458536999875 sin(79 x) + 47228879023531703425176027625 sin(81 x) + 1626735308677279083248444325 sin(83 x) + 36940911250400592040935945 sin(85 x) + 414847067813984717066925 sin(87 x))/2792459637634687990070142551462954366179714950758400 + C

$ \displaystyle \int \cos^{88}x\, dx$ = (8076030954443701744994070304101969600 x + 7896563599900508372883090964010814720 sin(2 x) + 3690785160823063696021444689700706880 sin(4 x) + 2198765627724378372097881942800421120 sin(6 x) + 1408584230260929894625205619606519780 sin(8 x) + 919891742211219523020542445457319040 sin(10 x) + 597929632437292689963352589547257376 sin(12 x) + 381871025758270961657267200046987904 sin(14 x) + 237751431902385045839500492336946796 sin(16 x) + 143548034356157008808755014241175424 sin(18 x) + 83736353374424921805107091640685664 sin(20 x) + 47058446524470203989646960591459712 sin(22 x) + 25419964417236136976550367105208148 sin(24 x) + 13173098969255973817807477690148352 sin(26 x) + 6537880399766203754404450134396288 sin(28 x) + 3102722901583961103785162775645696 sin(30 x) + 1405921314780232375152651882714456 sin(32 x) + 607379700117207429188416628212224 sin(34 x) + 249809392790141765230719742248576 sin(36 x) + 97669837782611817984943057119744 sin(38 x) + 36244666364641104330349962603030 sin(40 x) + 12745377183170498226057129706560 sin(42 x) + 4239681253079442591725615460240 sin(44 x) + 1331606571376022202722386685760 sin(46 x) + 394096797778565394555706353690 sin(48 x) + 109661717642731240224196550592 sin(50 x) + 28620503230932603904666682160 sin(52 x) + 6987165108021105178604072640 sin(54 x) + 1590827770129805196914320110 sin(56 x) + 336651318383633787537843840 sin(58 x) + 65965461034630944855388320 sin(60 x) + 11916341348191396490005632 sin(62 x) + 1974623998076123678236953 sin(64 x) + 298408349177973826227072 sin(66 x) + 40845486708749811055968 sin(68 x) + 5022591494023484903808 sin(70 x) + 549345944658818661354 sin(72 x) + 52790000687934526016 sin(74 x) + 4387872329324467984 sin(76 x) + 309062369813400896 sin(78 x) + 17936655390956302 sin(80 x) + 823490634878912 sin(82 x) + 28042455174448 sin(84 x) + 629662185152 sin(86 x) + 6992632738 sin(88 x))/95221060510267518585429612658983698432 + C

$ \displaystyle \int \cos^{89}x\, dx$ = (15159562609532483372648940570794546453958811352889000 sin(x) + 4833483730575574408670676703731594521552084779182000 sin(3 x) + 2653274047847868505185179977793088056511569942614800 sin(5 x) + 1658296279904917815740737486120680035319731214134250 sin(7 x) + 1079208690096851276910638681443617165842999679039750 sin(9 x) + 706391142608848108523327136944913054006327062644200 sin(11 x) + 457076621688078187868035206258473152592329275828600 sin(13 x) + 289481860402449518983088963963699663308475208024780 sin(15 x) + 178315685375537717020659683684631868075697825142900 sin(17 x) + 106363742153829515415832092022411991483749579909800 sin(19 x) + 61239730330992751300024537831085692066401273281400 sin(21 x) + 33948111379137286046752732928101851036809401492950 sin(23 x) + 18081836166151017620691455643810038552237428584666 sin(25 x) + 9237208769425807213635481810375498621832658280800 sin(27 x) + 4518728077153360980603681049260252686425444173600 sin(29 x) + 2113598616733023684475915329492698837198998081200 sin(31 x) + 943927052381017532212542414910052784223496907600 sin(33 x) + 401930228755788110490501931510086991991940618720 sin(35 x) + 162944687333427612361014296558143375131867818400 sin(37 x) + 62801598243091892264140926798451092498740721675 sin(39 x) + 22976194479179960584441802487238204572710020125 sin(41 x) + 7966376098489457792491449488175614270453368500 sin(43 x) + 2613182740101517000588405818841022392530143100 sin(45 x) + 809465241771120722960738973921342981415782750 sin(47 x) + 236303517784115987448166035865236770972309250 sin(49 x) + 64867632332894584789692637296339505757104500 sin(51 x) + 16703889378308491273242669556245809481433500 sin(53 x) + 4024118804774318352190279484004672284163525 sin(55 x) + 904242028950730031073759028489394036455875 sin(57 x) + 188884271736845118721774675671627888513000 sin(59 x) + 36538268958930695096999035621724739089400 sin(61 x) + 6517059668113369593324389394518155217700 sin(63 x) + 1066427945691278660725809173648425399260 sin(65 x) + 159168350103175919511314802037078417800 sin(67 x) + 21520285090082673395677675490979048600 sin(69 x) + 2614259984534690958277745790277384425 sin(71 x) + 282515158146062493208097338066505775 sin(73 x) + 26827455667853739192443714704201524 sin(75 x) + 2203788800754688323585190145471100 sin(77 x) + 153428334229756782021753744304950 sin(79 x) + 8802351782244579360725160348650 sin(81 x) + 399546368373107833129021007700 sin(83 x) + 13453285425950486876149591740 sin(85 x) + 298727602195870267626101175 sin(87 x) + 3281063172710606398620225 sin(89 x))/90374148272540811314997340756437432214543502042726400 + C

$ \displaystyle \int \cos^{90}x\, dx$ = (718766754945489455304472257065075294400 x + 703141390707544032363070686259312788000 sin(2 x) + 329130012671616355574203299951167688000 sin(4 x) + 196563757567770879023482526359725147000 sin(6 x) + 126362415579281279372238766945537594500 sin(8 x) + 82893744620008519268188631116272661992 sin(10 x) + 54178918052293149848489301383184746400 sin(12 x) + 34829304462188453474028836603475908400 sin(14 x) + 21850459874863510905876581454067433100 sin(16 x) + 13308099018435389358311662778608971600 sin(18 x) + 7839680149041938458350870436853285088 sin(20 x) + 4454363721046555942244812748212093800 sin(22 x) + 2435573145718438483040292350630589300 sin(24 x) + 1279160431968835065363336566113678200 sin(26 x) + 644226077117476255679355946129891200 sin(28 x) + 310660130521094105516489422911525312 sin(30 x) + 143234691326324126518873197039125400 sin(32 x) + 63055879293562044311913817292366400 sin(34 x) + 26467899950384067982778639357289600 sin(36 x) + 10578453434117316644432910137864100 sin(38 x) + 4019812304964580324884505852388358 sin(40 x) + 1450148739164711516913602399851500 sin(42 x) + 495844616376536366705872190994000 sin(44 x) + 160420317062997059816605708851000 sin(46 x) + 49017319102582434943962855482250 sin(48 x) + 14116987901543741263861302378888 sin(50 x) + 3823669529128857330406636614000 sin(52 x) + 971652647834184938899628851500 sin(54 x) + 231028956383274892517230734750 sin(56 x) + 51244074202441215674837758500 sin(58 x) + 10567666857747877365833208864 sin(60 x) + 2018442311539280481589534800 sin(62 x) + 355521088964305084825429425 sin(64 x) + 57457953772008902598049200 sin(66 x) + 8471090727369890330911200 sin(68 x) + 1131495690012978208485996 sin(70 x) + 135810525207319057945850 sin(72 x) + 14503167490827743828100 sin(74 x) + 1361108933825305064400 sin(76 x) + 110517392062738445400 sin(78 x) + 7606196983141410654 sin(80 x) + 431434882764685800 sin(82 x) + 19363798788562800 sin(84 x) + 644777655221700 sin(86 x) + 14160081294450 sin(88 x) + 153837920236 sin(90 x))/8569895445924076672688665139308532858880 + C

 


$ \displaystyle \int \cos^{91}x\, dx$ = (25674715590128696833261065 sin(x))/154742504910672534362390528 + (8194058167062350053168425 sin(3 x))/154742504910672534362390528 + (18026927967537170116970535 sin(5 x))/618970019642690137449562112 + (79097745163683501533646225 sin(7 x))/4332790137498830962146934784 + (7382456215277126809806981 sin(9 x))/618970019642690137449562112 + (4855840184380142233188549 sin(11 x))/618970019642690137449562112 + (20543939241608294063490015 sin(13 x))/4023305127677485893422153728 + (1007815887324180463491963 sin(15 x))/309485009821345068724781056 + (10638056588421904892415165 sin(17 x))/5261245166962866168321277952 + (376658462939340173224269 sin(19 x))/309485009821345068724781056 + (3067076055363198553397619 sin(21 x))/4332790137498830962146934784 + (5649876944090102598364035 sin(23 x))/14236310451781873161339928576 + (662399365858839614980611 sin(25 x))/3094850098213450687247810560 + (68610103808354385732455 sin(27 x))/618970019642690137449562112 + (123498186855037894318419 sin(29 x))/2243766321204751748254662656 + (2024560440246522857679 sin(31 x))/77371252455336267181195264 + (920254745566601298945 sin(33 x))/77371252455336267181195264 + (2795821560340436327271 sin(35 x))/541598767187353870268366848 + (2644696070592304633905 sin(37 x))/1237940039285380274899124224 + (13548981407803652970621 sin(39 x))/16093220510709943573688614912 + (390547135923386892723 sin(41 x))/1237940039285380274899124224 + (138948564498948825075 sin(43 x))/1237940039285380274899124224 + (23430542248842350895 sin(45 x))/618970019642690137449562112 + (351458133732635263425 sin(47 x))/29091590923206436460129419264 + (110458270601685368505 sin(49 x))/30329530962491816735028543488 + (10890252031152078585 sin(51 x))/10522490333925732336642555904 + (18150420051920130975 sin(53 x))/65610822082125154569653583872 + (85892398751303235 sin(55 x))/1237940039285380274899124224 + (20159666847745425 sin(57 x))/1237940039285380274899124224 + (260462895672870891 sin(59 x))/73038462317837436219048329216 + (13708573456466889 sin(61 x))/18878585599102049192211644416 + (296722369187595 sin(63 x))/2166395068749415481073467392 + (95864150045223 sin(65 x))/4023305127677485893422153728 + (78875566492905 sin(67 x))/20735495658030119604560330752 + (15775113298581 sin(69 x))/28472620903563746322679857152 + (6426898010533 sin(71 x))/87893742789261999517837819904 + (783768050065 sin(73 x))/90369622867832760067636068352 + (5665793133 sin(75 x))/6189700196426901374495621120 + (367908645 sin(77 x))/4332790137498830962146934784 + (333281949 sin(79 x))/48898631551772520858515406848 + (2583581 sin(81 x))/5570730176784211237046059008 + (1336335 sin(83 x))/51374511630343281408313655296 + (24297 sin(85 x))/21044980667851464673285111808 + (1365 sin(87 x))/35900261139276027972074602496 + (91 sin(89 x))/110176663496398844466022055936 + sin(91 x)/112652543574969605015820304384 + C

$ \displaystyle \int \cos^{92}x\, dx$ = (25674715590128696833261065 x)/309485009821345068724781056 + (12564222522828936748191585 sin(2 x))/154742504910672534362390528 + (188463337842434051222873775 sin(4 x))/4951760157141521099596496896 + (14102698750114112676541575 sin(6 x))/618970019642690137449562112 + (72769925550588821410954527 sin(8 x))/4951760157141521099596496896 + (29964086991418926463334217 sin(10 x))/3094850098213450687247810560 + (31500706837132717564018023 sin(12 x))/4951760157141521099596496896 + (1273613483981107179138195 sin(14 x))/309485009821345068724781056 + (12877647449142305922397305 sin(16 x))/4951760157141521099596496896 + (1482880615355780681973023 sin(18 x))/928455029464035206174343168 + (23514249757784522242715079 sin(20 x))/24758800785707605497982484480 + (3712776277544924564639223 sin(22 x))/6808670216069591511945183232 + (1493645628897383445544515 sin(24 x))/4951760157141521099596496896 + (99316723694610894032295 sin(26 x))/618970019642690137449562112 + (405779756809410224189091 sin(28 x))/4951760157141521099596496896 + (15521630041890008575539 sin(30 x))/386856262276681335905976320 + (46564890125670025726617 sin(32 x))/2475880078570760549798248448 + (652169329491176830905 sin(34 x))/77371252455336267181195264 + (107173159813050059212055 sin(36 x))/29710560942849126597578981376 + (34625174708831557591587 sin(38 x))/23520860746422225223083360256 + (28329688398134910756753 sin(40 x))/49517601571415210995964968960 + (261752629122781691427 sin(42 x))/1237940039285380274899124224 + (8083537075850611058775 sin(44 x))/108938723457113464191122931712 + (351458133732635263425 sin(46 x))/14236310451781873161339928576 + (76986067389053438655 sin(48 x))/9903520314283042199192993792 + (7156451334757080213 sin(50 x))/3094850098213450687247810560 + (6422456326064046345 sin(52 x))/9903520314283042199192993792 + (635402832867828025 sin(54 x))/3713820117856140824697372672 + (419513067260226225 sin(56 x))/9903520314283042199192993792 + (12151412982710001 sin(58 x))/1237940039285380274899124224 + (105099063166246149 sin(60 x))/49517601571415210995964968960 + (4094768694788811 sin(62 x))/9594035304461697130468212736 + (1574911036457235 sin(64 x))/19807040628566084398385987584 + (46516359726585 sin(66 x))/3404335108034795755972591616 + (21342800345139 sin(68 x))/9903520314283042199192993792 + (1919722782367 sin(70 x))/6189700196426901374495621120 + (3605333030299 sin(72 x))/89131682828547379792736944128 + (217188736765 sin(74 x))/45803781453559070171267596288 + (93080887185 sin(76 x))/188166885971377801784666882048 + (28078699 sin(78 x))/618970019642690137449562112 + (178267089 sin(80 x))/49517601571415210995964968960 + (6147141 sin(82 x))/25377770805350295635432046592 + (133055 sin(84 x))/9903520314283042199192993792 + (31395 sin(86 x))/53231421689271351820662341632 + (2093 sin(88 x))/108938723457113464191122931712 + (23 sin(90 x))/55707301767842112370460590080 + sin(92 x)/227780967228509970581438857216 + C
$ \displaystyle \int \cos^{93}x\, dx$ = (50803160635786570329644235 sin(x))/309485009821345068724781056 + (129830299402565679731313045 sin(3 x))/2475880078570760549798248448 + (71539144568760680668274535 sin(5 x))/2475880078570760549798248448 + (157386118051273497470203977 sin(7 x))/8665580274997661924293869568 + (14744233281491852704180329 sin(9 x))/1237940039285380274899124224 + (19487133497915805322308267 sin(11 x))/2475880078570760549798248448 + (165824475614340154723792989 sin(13 x))/32186441021419887147377229824 + (2047215748325187095355469 sin(15 x))/618970019642690137449562112 + (21774931141276990014235443 sin(17 x))/10522490333925732336642555904 + (3110704448753855716319349 sin(19 x))/2475880078570760549798248448 + (12788451622654740167090657 sin(21 x))/17331160549995323848587739136 + (517673453990521715909217 sin(23 x))/1237940039285380274899124224 + (1412634340550406716294643 sin(25 x))/6189700196426901374495621120 + (889436436642848673222553 sin(27 x))/7427640235712281649394745344 + (4330534781687312392575381 sin(29 x))/71800522278552055944149204992 + (139694670377010077179851 sin(31 x))/4797017652230848565234106368 + (2082989312980910241739 sin(33 x))/154742504910672534362390528 + (206215941985110113932161 sin(35 x))/34662321099990647697175478272 + (12432977791202065081149 sin(37 x))/4951760157141521099596496896 + (32526679271932675313309 sin(39 x))/32186441021419887147377229824 + (959104849299798580407 sin(41 x))/2475880078570760549798248448 + (699319951678238910201 sin(43 x))/4951760157141521099596496896 + (242115603238037625915 sin(45 x))/4951760157141521099596496896 + (933874469632430842815 sin(47 x))/58183181846412872920258838528 + (302522715514731118095 sin(49 x))/60659061924983633470057086976 + (123249995209705270335 sin(51 x))/84179922671405858693140447232 + (106366434222074411385 sin(53 x))/262443288328500618278614335488 + (261342590226227055 sin(55 x))/2475880078570760549798248448 + (63883744277522169 sin(57 x))/2475880078570760549798248448 + (1724861095493098563 sin(59 x))/292153849271349744876193316864 + (380813488615359423 sin(61 x))/302057369585632787075386310656 + (1084938714003873 sin(63 x))/4332790137498830962146934784 + (370801838963349 sin(65 x))/8046610255354971786844307456 + (2595612872743443 sin(67 x))/331767930528481913672965292032 + (18112167120593 sin(69 x))/14855280471424563298789490688 + (30481451983437 sin(71 x))/175787485578523999035675639808 + (4039710503829 sin(73 x))/180739245735665520135272136704 + (192367166849 sin(75 x))/74276402357122816493947453440 + (9258312843 sin(77 x))/34662321099990647697175478272 + (2368405611 sin(79 x))/97797263103545041717030813696 + (63520457 sin(81 x))/33424381060705267422276354048 + (51971283 sin(83 x))/410996093042746251266509242368 + (583947 sin(85 x))/84179922671405858693140447232 + (64883 sin(87 x))/215401566835656167832447614976 + (2139 sin(89 x))/220353326992797688932044111872 + (93 sin(91 x))/450610174299878420063281217536 + sin(93 x)/460513694614161462262474211328 + C

$ \displaystyle \int \cos^{94}x\, dx$ = (50803160635786570329644235 x)/618970019642690137449562112 + (795916183293989601831093015 sin(2 x))/9903520314283042199192993792 + (373593310525750221267655905 sin(4 x))/9903520314283042199192993792 + (224155986315450132760593543 sin(6 x))/9903520314283042199192993792 + (145042108792350085903913469 sin(8 x))/9903520314283042199192993792 + (479754667543927207220636859 sin(10 x))/49517601571415210995964968960 + (63363824015235668878197321 sin(12 x))/9903520314283042199192993792 + (41236774359121625777874447 sin(14 x))/9903520314283042199192993792 + (26241583683077398222283739 sin(16 x))/9903520314283042199192993792 + (16244789899047913185223267 sin(18 x))/9903520314283042199192993792 + (48734369697143739555669801 sin(20 x))/49517601571415210995964968960 + (62178333751528219433095953 sin(22 x))/108938723457113464191122931712 + (3161610190755672174564201 sin(24 x))/9903520314283042199192993792 + (1702405487329977324765339 sin(26 x))/9903520314283042199192993792 + (881104479390925032255597 sin(28 x))/9903520314283042199192993792 + (2188549835906491209150999 sin(30 x))/49517601571415210995964968960 + (104216658852690057578619 sin(32 x))/4951760157141521099596496896 + (190042142613728928525717 sin(34 x))/19807040628566084398385987584 + (82838882677779276536851 sin(36 x))/19807040628566084398385987584 + (655180253906072459882367 sin(38 x))/376333771942755603569333764096 + (68451668318544883868307 sin(40 x))/99035203142830421991929937920 + (5177016931654655082477 sin(42 x))/19807040628566084398385987584 + (20482980033937983152409 sin(44 x))/217877446914226928382245863424 + (14630700024241416537435 sin(46 x))/455561934457019941162877714432 + (206066197524526993485 sin(48 x))/19807040628566084398385987584 + (315968169537608056677 sin(50 x))/99035203142830421991929937920 + (18312169994276547015 sin(52 x))/19807040628566084398385987584 + (5004226635072569905 sin(54 x))/19807040628566084398385987584 + (1286801134732946547 sin(56 x))/19807040628566084398385987584 + (310607170452780201 sin(58 x))/19807040628566084398385987584 + (350945764018076331 sin(60 x))/99035203142830421991929937920 + (14804163742698009 sin(62 x))/19807040628566084398385987584 + (5809228810425801 sin(64 x))/39614081257132168796771975168 + (5809228810425801 sin(66 x))/217877446914226928382245863424 + (88593903426973 sin(68 x))/19807040628566084398385987584 + (68220392534359 sin(70 x))/99035203142830421991929937920 + (5753527081211 sin(72 x))/59421121885698253195157962752 + (9041256841903 sin(74 x))/732860503256945122740281540608 + (531838637759 sin(76 x))/376333771942755603569333764096 + (2854232403 sin(78 x))/19807040628566084398385987584 + (1279483491 sin(80 x))/99035203142830421991929937920 + (814216767 sin(82 x))/812088665771209460333825490944 + (1306929 sin(84 x))/19807040628566084398385987584 + (3049501 sin(86 x))/851702747028341629130597466112 + (33511 sin(88 x))/217877446914226928382245863424 + (1457 sin(90 x))/297105609428491265975789813760 + (47 sin(92 x))/455561934457019941162877714432 + sin(94 x)/930930909542605966724141416448 + C

$ \displaystyle \int \cos^{95}x\, dx$ = (1608766753466574727105400775 sin(x))/9903520314283042199192993792 + (514367601448496681455468275 sin(3 x))/9903520314283042199192993792 + (1419654579997850840817092439 sin(5 x))/49517601571415210995964968960 + (1252636394115750741897434505 sin(7 x))/69324642199981295394350956544 + (117769233634814172315143415 sin(9 x))/9903520314283042199192993792 + (78176146512303747317256435 sin(11 x))/9903520314283042199192993792 + (668840364605265393714305055 sin(13 x))/128745764085679548589508919296 + (166196696659490188741130347 sin(15 x))/49517601571415210995964968960 + (356135778556050404445279315 sin(17 x))/168359845342811717386280894464 + (243671848485718697778349005 sin(19 x))/188166885971377801784666882048 + (53215691048605232848145185 sin(21 x))/69324642199981295394350956544 + (4352941566982447196863755 sin(23 x))/9903520314283042199192993792 + (60070593624357771316719819 sin(25 x))/247588007857076054979824844800 + (3829637116306961741503085 sin(27 x))/29710560942849126597578981376 + (18901112219192424079031355 sin(29 x))/287202089114208223776596819968 + (9900582591005555469968805 sin(31 x))/307009129742774308174982807552 + (300017654272895620302085 sin(33 x))/19807040628566084398385987584 + (4721816312633418762600507 sin(35 x))/693246421999812953943509565440 + (58007571408272957771505 sin(37 x))/19807040628566084398385987584 + (309662309060083998451865 sin(39 x))/257491528171359097179017838592 + (9329854361925055907445 sin(41 x))/19807040628566084398385987584 + (3481007340293574954345 sin(43 x))/19807040628566084398385987584 + (6177406676901931426917 sin(45 x))/99035203142830421991929937920 + (416516782230426901725 sin(47 x))/19807040628566084398385987584 + (6525429588276688127025 sin(49 x))/970544990799738135520913391616 + (685319089179743501925 sin(51 x))/336719690685623434772561788928 + (611230538998149609825 sin(53 x))/1049773153314002473114457341952 + (15558595538134717341 sin(55 x))/99035203142830421991929937920 + (15012679905217709715 sin(57 x))/376333771942755603569333764096 + (11113282527239083815 sin(59 x))/1168615397085398979504773267456 + (2564603660132096265 sin(61 x))/1208229478342531148301545242624 + (61319637443383455 sin(63 x))/138649284399962590788701913088 + (110375347398090219 sin(65 x))/1287457640856795485895089192960 + (20439879147794485 sin(67 x))/1327071722113927654691861168128 + (151727628880765 sin(69 x))/59421121885698253195157962752 + (546585072715045 sin(71 x))/1406299884628191992285405118464 + (78083581816435 sin(73 x))/1445913965885324161082177093632 + (10104934117421 sin(75 x))/1485528047142456329878949068800 + (106817485385 sin(77 x))/138649284399962590788701913088 + (121550931645 sin(79 x))/1564756209656720667472493019136 + (3683361565 sin(81 x))/534790096971284278756421664768 + (869107785 sin(83 x))/1643984372170985005066036969472 + (57940519 sin(85 x))/1683598453428117173862808944640 + (3183545 sin(87 x))/1723212534685249342659580919808 + (138415 sin(89 x))/1762826615942381511456352894976 + (4465 sin(91 x))/1802440697199513680253124870144 + (95 sin(93 x))/1842054778456645849049896845312 + sin(95 x)/1881668859713778017846668820480 + C

$ \displaystyle \int \cos^{96}x\, dx$ = (1608766753466574727105400775 x)/19807040628566084398385987584 + (98495923681627024108493925 sin(2 x))/1237940039285380274899124224 + (185172336521458805323968579 sin(4 x))/4951760157141521099596496896 + (27836364313683349819942989 sin(6 x))/1237940039285380274899124224 + (289069937103634786591715655 sin(8 x))/19807040628566084398385987584 + (11999129464679179820788197 sin(10 x))/1237940039285380274899124224 + (31849541171679304462585955 sin(12 x))/4951760157141521099596496896 + (5211743100820249821150429 sin(14 x))/1237940039285380274899124224 + (213681467133630242667167589 sin(16 x))/79228162514264337593543950336 + (6247996115018428148162795 sin(18 x))/3713820117856140824697372672 + (5041486520394179954034807 sin(20 x))/4951760157141521099596496896 + (8117647787075374502259435 sin(22 x))/13617340432139183023890366464 + (6674510402706419035191091 sin(24 x))/19807040628566084398385987584 + (227253191517116411034249 sin(26 x))/1237940039285380274899124224 + (476498627374598926362135 sin(28 x))/4951760157141521099596496896 + (60003530854579124060417 sin(30 x))/1237940039285380274899124224 + (29701747773016666409906415 sin(32 x))/1267650600228229401496703205376 + (26879409749336349692223 sin(34 x))/2475880078570760549798248448 + (143085342807073295836379 sin(36 x))/29710560942849126597578981376 + (5058005048168341172535 sin(38 x))/2475880078570760549798248448 + (32787773900479482189021 sin(40 x))/39614081257132168796771975168 + (791975214987427106015 sin(42 x))/2475880078570760549798248448 + (12829998482796319117443 sin(44 x))/108938723457113464191122931712 + (2349154651779607725729 sin(46 x))/56945241807127492645359714304 + (2175143196092229375675 sin(48 x))/158456325028528675187087900672 + (10726733569769898291 sin(50 x))/2475880078570760549798248448 + (12823018300660481325 sin(52 x))/9903520314283042199192993792 + (2716580173325109377 sin(54 x))/7427640235712281649394745344 + (3860403404198839641 sin(56 x))/39614081257132168796771975168 + (60507890347944195 sin(58 x))/2475880078570760549798248448 + (56991192447379917 sin(60 x))/9903520314283042199192993792 + (3141613303550955 sin(62 x))/2475880078570760549798248448 + (331126042194270657 sin(64 x))/1267650600228229401496703205376 + (4087975829558897 sin(66 x))/81704042592835098143342198784 + (87976524309015 sin(68 x))/9903520314283042199192993792 + (3603857622297 sin(70 x))/2475880078570760549798248448 + (78083581816435 sin(72 x))/356526731314189519170947776512 + (2755891122933 sin(74 x))/91607562907118140342535192576 + (37105021239 sin(76 x))/9903520314283042199192993792 + (3116690555 sin(78 x))/7427640235712281649394745344 + (6630050817 sin(80 x))/158456325028528675187087900672 + (372474765 sin(82 x))/101511083221401182541728186368 + (8277217 sin(84 x))/29710560942849126597578981376 + (1910127 sin(86 x))/106462843378542703641324683264 + (415245 sin(88 x))/435754893828453856764491726848 + (893 sin(90 x))/22282920707136844948184236032 + (285 sin(92 x))/227780967228509970581438857216 + (3 sin(94 x))/116366363692825745840517677056 + sin(96 x)/3802951800684688204490109616128 + C

$ \displaystyle \int \cos^{97}x\, dx$ = (3184701532372607112841303575 sin(x))/19807040628566084398385987584 + (127388061294904284513652143 sin(3 x))/2475880078570760549798248448 + (352190522403558904243626513 sin(5 x))/12379400392853802748991242240 + (623106308867834984431031523 sin(7 x))/34662321099990647697175478272 + (58783614044135375889719955 sin(9 x))/4951760157141521099596496896 + (19594538014711791963239985 sin(11 x))/2475880078570760549798248448 + (168513026926521410883863871 sin(13 x))/32186441021419887147377229824 + (168513026926521410883863871 sin(15 x))/49517601571415210995964968960 + (363633373894072518223074669 sin(17 x))/168359845342811717386280894464 + (62695409292081468659150805 sin(19 x))/47041721492844450446166720512 + (13814242725373882924897635 sin(21 x))/17331160549995323848587739136 + (2282353145931337178896131 sin(23 x))/4951760157141521099596496896 + (31840697167009310479354221 sin(25 x))/123794003928538027489912422400 + (342373087817304413756497 sin(27 x))/2475880078570760549798248448 + (5135596317259566206347455 sin(29 x))/71800522278552055944149204992 + (87305137393412625507906735 sin(31 x))/2456073037942194465399862460416 + (1343155959898655777044719 sin(33 x))/79228162514264337593543950336 + (1343155959898655777044719 sin(35 x))/173311605499953238485877391360 + (16796222168962617623391 sin(37 x))/4951760157141521099596496896 + (182782417721063780019255 sin(39 x))/128745764085679548589508919296 + (5621092379544909459765 sin(41 x))/9903520314283042199192993792 + (1071929244471354827211 sin(43 x))/4951760157141521099596496896 + (1947589754039503840989 sin(45 x))/24758800785707605497982484480 + (538695038351352126231 sin(47 x))/19807040628566084398385987584 + (8670776302230667785225 sin(49 x))/970544990799738135520913391616 + (234345305465693723925 sin(51 x))/84179922671405858693140447232 + (215597681028438226011 sin(53 x))/262443288328500618278614335488 + (11347246369917801369 sin(55 x))/49517601571415210995964968960 + (11347246369917801369 sin(57 x))/188166885971377801784666882048 + (4364325526891462065 sin(59 x))/292153849271349744876193316864 + (1049647911530857965 sin(61 x))/302057369585632787075386310656 + (209929582306171593 sin(63 x))/277298568799925181577403826176 + (396533655467213009 sin(65 x))/2574915281713590971790178385920 + (9671552572371049 sin(67 x))/331767930528481913672965292032 + (25331462997305 sin(69 x))/4951760157141521099596496896 + (582623648938015 sin(71 x))/703149942314095996142702559232 + (89107146308167 sin(73 x))/722956982942662080541088546816 + (2072259216469 sin(75 x))/123794003928538027489912422400 + (71457214361 sin(77 x))/34662321099990647697175478272 + (357286071805 sin(79 x))/1564756209656720667472493019136 + (4014450245 sin(81 x))/178263365657094759585473888256 + (802890049 sin(83 x))/410996093042746251266509242368 + (61760773 sin(85 x))/420899613357029293465702236160 + (2685251 sin(87 x))/287202089114208223776596819968 + (433105 sin(89 x))/881413307971190755728176447488 + (9215 sin(91 x))/450610174299878420063281217536 + (97 sin(93 x))/153504564871387154087491403776 + (97 sin(95 x))/7526675438855112071386675281920 + sin(97 x)/7685131763883640746573763182592 + C
$ \displaystyle \int \cos^{98}x\, dx$ = (3184701532372607112841303575 x)/39614081257132168796771975168 + (6242015003450309941168955007 sin(2 x))/79228162514264337593543950336 + (367177353144135878892291471 sin(4 x))/9903520314283042199192993792 + (442495784558317597639428183 sin(6 x))/19807040628566084398385987584 + (576079417632526683719255559 sin(8 x))/39614081257132168796771975168 + (192026472544175561239751853 sin(10 x))/19807040628566084398385987584 + (64008824181391853746583951 sin(12 x))/9903520314283042199192993792 + (168513026926521410883863871 sin(14 x))/39614081257132168796771975168 + (434586227336818375437333141 sin(16 x))/158456325028528675187087900672 + (204805003687466130953225963 sin(18 x))/118842243771396506390315925504 + (10413813746820311743384371 sin(20 x))/9903520314283042199192993792 + (135379578708664052663996823 sin(22 x))/217877446914226928382245863424 + (14055803253905010932327539 sin(24 x))/39614081257132168796771975168 + (3871449531472596063246543 sin(26 x))/19807040628566084398385987584 + (1027119263451913241269491 sin(28 x))/9903520314283042199192993792 + (16776281303047916274068353 sin(30 x))/316912650057057350374175801344 + (65814642035034133075191231 sin(32 x))/2535301200456458802993406410752 + (3871449531472596063246543 sin(34 x))/316912650057057350374175801344 + (327436030025045438185031 sin(36 x))/59421121885698253195157962752 + (94277247035075002325721 sin(38 x))/39614081257132168796771975168 + (77881204072453262790813 sin(40 x))/79228162514264337593543950336 + (15364319170756085856691 sin(42 x))/39614081257132168796771975168 + (31810632649311896069487 sin(44 x))/217877446914226928382245863424 + (95431897947935688208461 sin(46 x))/1822247737828079764651510857728 + (5664907184124036286347 sin(48 x))/316912650057057350374175801344 + (459316798712759698893 sin(50 x))/79228162514264337593543950336 + (35332061439443053761 sin(52 x))/19807040628566084398385987584 + (61779452458441363009 sin(54 x))/118842243771396506390315925504 + (11347246369917801369 sin(56 x))/79228162514264337593543950336 + (1474841040121942353 sin(58 x))/39614081257132168796771975168 + (180465781280744001 sin(60 x))/19807040628566084398385987584 + (331824178483948647 sin(62 x))/158456325028528675187087900672 + (1142949948111378673 sin(64 x))/2535301200456458802993406410752 + (473906076046181401 sin(66 x))/5229058725941446281173900722176 + (335865397623091 sin(68 x))/19807040628566084398385987584 + (116524729787603 sin(70 x))/39614081257132168796771975168 + (335865397623091 sin(72 x))/713053462628379038341895553024 + (101540701606981 sin(74 x))/1465721006513890245480563081216 + (184284394931 sin(76 x))/19807040628566084398385987584 + (269338731053 sin(78 x))/237684487542793012780631851008 + (39341612401 sin(80 x))/316912650057057350374175801344 + (39341612401 sin(82 x))/3248354663084837841335301963776 + (61760773 sin(84 x))/59421121885698253195157962752 + (131577299 sin(86 x))/1703405494056683258261194932224 + (4244429 sin(88 x))/871509787656907713528983453696 + (90307 sin(90 x))/356526731314189519170947776512 + (4753 sin(92 x))/455561934457019941162877714432 + (4753 sin(94 x))/14894894552681695467586262663168 + (49 sin(96 x))/7605903601369376408980219232256 + sin(98 x)/15528719852795810168334614265856 + C

$ \displaystyle \int \cos^{99}x\, dx$ = (12611418068195524166851562157 sin(x))/79228162514264337593543950336 + (4038950884585494667815206181 sin(3 x))/79228162514264337593543950336 + (2796196766251496308487450433 sin(5 x))/99035203142830421991929937920 + (354235169848572308622399381 sin(7 x))/19807040628566084398385987584 + (704097065995310391212423461 sin(9 x))/59421121885698253195157962752 + (1728238252897580051157766677 sin(11 x))/217877446914226928382245863424 + (2715802968839054366105061921 sin(13 x))/514983056342718194358035677184 + (682921214386428875687237793 sin(15 x))/198070406285660843983859875840 + (1483587465736035143734344171 sin(17 x))/673439381371246869545123577856 + (1030967560935210862595052729 sin(19 x))/752667543885511207138667528192 + (16364564459289061311032583 sin(21 x))/19807040628566084398385987584 + (9552799923134526880780959 sin(23 x))/19807040628566084398385987584 + (134663663432573814416170293 sin(25 x))/495176015714152109959649689600 + (26362727761932439859250269 sin(27 x))/178263365657094759585473888256 + (711793649572175876199757263 sin(29 x))/9190466851654663160851098238976 + (383273503615787010261407757 sin(31 x))/9824292151768777861599449841664 + (65814642035034133075191231 sin(33 x))/3486039150627630854115933814784 + (13892642988205499305850601 sin(35 x))/1584563250285286751870879006720 + (154608109566674873038083 sin(37 x))/39614081257132168796771975168 + (856693244796985890698943 sin(39 x))/514983056342718194358035677184 + (26864944958790498314601 sin(41 x))/39614081257132168796771975168 + (10462633329840125285313 sin(43 x))/39614081257132168796771975168 + (116638986380810285588119 sin(45 x))/1188422437713965063903159255040 + (2753645554312338423969 sin(47 x))/79228162514264337593543950336 + (928007409644147146743 sin(49 x))/79228162514264337593543950336 + (5052484785840356687823 sin(51 x))/1346878762742493739090247155712 + (2393282266977011062653 sin(53 x))/2099546306628004946228914683904 + (714876521304821486247 sin(55 x))/2178774469142269283822458634240 + (67210613114128515801 sin(57 x))/752667543885511207138667528192 + (53598337040380968297 sin(59 x))/2337230794170797959009546534912 + (53598337040380968297 sin(61 x))/9665835826740249186412361940992 + (1796064204175023629 sin(63 x))/1426106925256758076683791106048 + (2759805972268938747 sin(65 x))/10299661126854363887160713543680 + (565261464199662153 sin(67 x))/10616573776911421237534889345024 + (390104530158497 sin(69 x))/39614081257132168796771975168 + (4750096337812287 sin(71 x))/2812599769256383984570810236928 + (773271496853163 sin(73 x))/2891827931770648322164354187264 + (38515438540579 sin(75 x))/990352031428304219919299379200 + (4501804504743 sin(77 x))/871509787656907713528983453696 + (3894819627699 sin(79 x))/6259024838626882669889972076544 + (432757736411 sin(81 x))/6417481163655411345077059977216 + (42800215689 sin(83 x))/6575937488683940020264147877888 + (1860878943 sin(85 x))/3367196906856234347725617889280 + (46688719 sin(87 x))/1148808356456832895106387279872 + (8940393 sin(89 x))/3525653231884763022912705789952 + (67221 sin(91 x))/514983056342718194358035677184 + (52283 sin(93 x))/9824292151768777861599449841664 + (4851 sin(95 x))/30106701755420448285546701127680 + (99 sin(97 x))/30740527055534562986295052730368 + sin(99 x)/31374352355648677687043404333056 + C

$ \displaystyle \int \cos^{100}x\, dx$ = (12611418068195524166851562157 x)/158456325028528675187087900672 + (6182067680488002042574295175 sin(2 x))/79228162514264337593543950336 + (23301639718762469237395420275 sin(4 x))/633825300114114700748351602688 + (439653579599291872403687175 sin(6 x))/19807040628566084398385987584 + (2295968693462968666997033025 sin(8 x))/158456325028528675187087900672 + (192026472544175561239751853 sin(10 x))/19807040628566084398385987584 + (2057426491544738156140198425 sin(12 x))/316912650057057350374175801344 + (170163093285655035470241975 sin(14 x))/39614081257132168796771975168 + (1766175554447660885398028775 sin(16 x))/633825300114114700748351602688 + (69848750740867944620261025 sin(18 x))/39614081257132168796771975168 + (343655853645070287531684243 sin(20 x))/316912650057057350374175801344 + (12803869360844645586128325 sin(22 x))/19807040628566084398385987584 + (59063010277444655445688725 sin(24 x))/158456325028528675187087900672 + (4110612436891752576806175 sin(26 x))/19807040628566084398385987584 + (282457797449276141349110025 sin(28 x))/2535301200456458802993406410752 + (18251119219799381441019417 sin(30 x))/316912650057057350374175801344 + (290358714860444704743490725 sin(32 x))/10141204801825835211973625643008 + (4333712162096189623037175 sin(34 x))/316912650057057350374175801344 + (15890277927686028617802975 sin(36 x))/2535301200456458802993406410752 + (109086576162604315454025 sin(38 x))/39614081257132168796771975168 + (367154247770136810299547 sin(40 x))/316912650057057350374175801344 + (18468523529684950216275 sin(42 x))/39614081257132168796771975168 + (113609402318971057391025 sin(44 x))/633825300114114700748351602688 + (119834575048777690672725 sin(46 x))/1822247737828079764651510857728 + (29148950687540519352825 sin(48 x))/1267650600228229401496703205376 + (15157454357521070063469 sin(50 x))/1980704062856608439838598758400 + (1534155299344237860675 sin(52 x))/633825300114114700748351602688 + (28779248039646597675 sin(54 x))/39614081257132168796771975168 + (65464882903371930975 sin(56 x))/316912650057057350374175801344 + (2200260141230745825 sin(58 x))/39614081257132168796771975168 + (17866112346793656099 sin(60 x))/1267650600228229401496703205376 + (533635374754888175 sin(62 x))/158456325028528675187087900672 + (7666127700747052075 sin(64 x))/10141204801825835211973625643008 + (25189904821731825 sin(66 x))/158456325028528675187087900672 + (39584136148435725 sin(68 x))/1267650600228229401496703205376 + (226195063705347 sin(70 x))/39614081257132168796771975168 + (306853768592525 sin(72 x))/316912650057057350374175801344 + (222204453118725 sin(74 x))/1465721006513890245480563081216 + (13821329619825 sin(76 x))/633825300114114700748351602688 + (226970840775 sin(78 x))/79228162514264337593543950336 + (432757736411 sin(80 x))/1267650600228229401496703205376 + (118889488025 sin(82 x))/3248354663084837841335301963776 + (2215332075 sin(84 x))/633825300114114700748351602688 + (500236275 sin(86 x))/1703405494056683258261194932224 + (6773025 sin(88 x))/316912650057057350374175801344 + (52283 sin(90 x))/39614081257132168796771975168 + (3921225 sin(92 x))/58311927610498552468848347447296 + (40425 sin(94 x))/14894894552681695467586262663168 + (825 sin(96 x))/10141204801825835211973625643008 + (25 sin(98 x))/15528719852795810168334614265856 + sin(100 x)/63382530011411470074835160268800 + C

 


この記事だけで12万文字以上あるみたいです。普段の記事の文字数は数千くらいなのでボリューム的には数十倍ということになりますが、大して中身はありませんね…。

 

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