100次までの正弦関数(sin x)積分リスト

100次まで(!)の正弦関数の積分結果を一覧にしました。


(余弦バージョンはこちら

量が量だけにMathJaxでTeXレンダリングすると恐ろしく時間がかかるのでテキスト形式で載せています。また、項数を節約するために倍角形式で表示しています。悪しからず…。

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

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

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

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

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

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

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

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

$ \displaystyle \int \sin^{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 \sin^{11}x\, dx$ = (-320166 cos(x) + 76230 cos(3 x) – 22869 cos(5 x) + 5445 cos(7 x) – 847 cos(9 x) + 63 cos(11 x))/709632 + C

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$ \displaystyle \int \sin^{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 \sin^{45}x\, dx$ = -(514589420475 cos(x))/2199023255552 + (628942625025 cos(3 x))/8796093022208 – (1584935415063 cos(5 x))/43980465111040 + (87084363465 cos(7 x))/4398046511104 – (428971123735 cos(9 x))/39582418599936 + (50139481995 cos(11 x))/8796093022208 – (323313211485 cos(13 x))/114349209288704 + (7184738033 cos(15 x))/5497558138880 – (613497555 cos(17 x))/1099511627776 + (3842432055 cos(19 x))/17592186044416 – (1369524845 cos(21 x))/17592186044416 + (5075297955 cos(23 x))/202310139510784 – (1595093643 cos(25 x))/219902325555200 + (886163135 cos(27 x))/474989023199232 – (215553195 cos(29 x))/510173395288064 + (11344905 cos(31 x))/136339441844224 – (61705 cos(33 x))/4398046511104 + (174537 cos(35 x))/87960930222080 – (148995 cos(37 x))/650910883643392 + (2365 cos(39 x))/114349209288704 – (495 cos(41 x))/360639813910528 + (45 cos(43 x))/756463999909888 – cos(45 x)/791648371998720 + C

$ \displaystyle \int \sin^{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 \sin^{47}x\, dx$ = -(8061900920775 cos(x))/35184372088832 + (2472316282371 cos(3 x))/35184372088832 – (6275879793711 cos(5 x))/175921860444160 + (697319977079 cos(7 x))/35184372088832 – (3486599885395 cos(9 x))/316659348799488 + (207665823895 cos(11 x))/35184372088832 – (1370594437707 cos(13 x))/457396837154816 + (250538768183 cos(15 x))/175921860444160 – (44212723797 cos(17 x))/70368744177664 + (17981251305 cos(19 x))/70368744177664 – (6698897545 cos(21 x))/70368744177664 + (2271800037 cos(23 x))/70368744177664 – (17417133617 cos(25 x))/1759218604441600 + (5178066751 cos(27 x))/1899956092796928 – (1362649145 cos(29 x))/2040693581152256 + (314457495 cos(31 x))/2181431069507584 – (1905803 cos(33 x))/70368744177664 + (1533939 cos(35 x))/351843720888320 – (1533939 cos(37 x))/2603643534573568 + (59455 cos(39 x))/914793674309632 – (16215 cos(41 x))/2885118511284224 + (1081 cos(43 x))/3025855999639552 – (47 cos(45 x))/3166593487994880 + cos(47 x)/3307330976350208 + C

$ \displaystyle \int \sin^{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 \sin^{49}x\, dx$ = -(15801325804719 cos(x))/70368744177664 + (1215486600363 cos(3 x))/17592186044416 – (3106243534261 cos(5 x))/87960930222080 + (697319977079 cos(7 x))/35184372088832 – (1178230306099 cos(9 x))/105553116266496 + (107111846009 cos(11 x))/17592186044416 – (722141155351 cos(13 x))/228698418577408 + (2166423466053 cos(15 x))/1407374883553280 – (196947587823 cos(17 x))/281474976710656 + (10365662517 cos(19 x))/35184372088832 – (4019338527 cos(21 x))/35184372088832 + (2854312867 cos(23 x))/70368744177664 – (23065933709 cos(25 x))/1759218604441600 + (1213996511 cos(27 x))/316659348799488 – (1027227817 cos(29 x))/1020346790576128 + (1027227817 cos(31 x))/4362862139015168 – (6833001 cos(33 x))/140737488355328 + (1533939 cos(35 x))/175921860444160 – (1747977 cos(37 x))/1301821767286784 + (158907 cos(39 x))/914793674309632 – (52969 cos(41 x))/2885118511284224 + (2303 cos(43 x))/1512927999819776 – (49 cos(45 x))/527765581332480 + (49 cos(47 x))/13229323905400832 – cos(49 x)/13792273858822144 + C

$ \displaystyle \int \sin^{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 \sin^{51}x\, dx$ = -(61989816618513 cos(x))/281474976710656 + (57397978350475 cos(3 x))/844424930131968 – (4919826715755 cos(5 x))/140737488355328 + (2787093952275 cos(7 x))/140737488355328 – (14307082288345 cos(9 x))/1266637395197952 + (881081313945 cos(11 x))/140737488355328 – (48459472266975 cos(13 x))/14636698788954112 + (5580181654985 cos(15 x))/3377699720527872 – (14771069086725 cos(17 x))/19140298416324608 + (377606277405 cos(19 x))/1125899906842624 – (113881258265 cos(21 x))/844424930131968 + (14051154075 cos(23 x))/281474976710656 – (4762601697 cos(25 x))/281474976710656 + (39688347475 cos(27 x))/7599824371187712 – (23813008485 cos(29 x))/16325548649218048 + (6388855935 cos(31 x))/17451448556060672 – (138286925 cos(33 x))/1688849860263936 + (9096615 cos(35 x))/562949953421312 – (28943775 cos(37 x))/10414574138294272 + (4502365 cos(39 x))/10977524091715584 – (587265 cos(41 x))/11540474045136896 + (62475 cos(43 x))/12103423998558208 – (4165 cos(45 x))/10133099161583616 + (1275 cos(47 x))/52917295621603328 – (51 cos(49 x))/55169095435288576 + cos(51 x)/57420895248973824 + C

$ \displaystyle \int \sin^{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 \sin^{53}x\, dx$ = -(121683714103007 cos(x))/562949953421312 + (225984040477013 cos(3 x))/3377699720527872 – (38962765599485 cos(5 x))/1125899906842624 + (5566109371355 cos(7 x))/281474976710656 – (28907858348005 cos(9 x))/2533274790395904 + (28907858348005 cos(11 x))/4503599627370496 – (15565769879695 cos(13 x))/4503599627370496 + (11903235790355 cos(15 x))/6755399441055744 – (32308782859535 cos(17 x))/38280596832649216 + (1700462255765 cos(19 x))/4503599627370496 – (2120653701205 cos(21 x))/13510798882111488 + (33969281255 cos(23 x))/562949953421312 – (12019899521 cos(25 x))/562949953421312 + (420696483235 cos(27 x))/60798594969501696 – (133391567855 cos(29 x))/65302194596872192 + (19055938265 cos(31 x))/34902897112121344 – (443161355 cos(33 x))/3377699720527872 + (63308765 cos(35 x))/2251799813685248 – (443161355 cos(37 x))/83316593106354176 + (1482145 cos(39 x))/1688849860263936 – (2869685 cos(41 x))/23080948090273792 + (2869685 cos(43 x))/193654783976931328 – (58565 cos(45 x))/40532396646334464 + (11713 cos(47 x))/105834591243206656 – (689 cos(49 x))/110338190870577152 + (53 cos(51 x))/229683580995895296 – cos(53 x)/238690780250636288 + C

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$ \displaystyle \int \sin^{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 \sin^{91}x\, dx$ = (-121291147796655550540005678132125255251432769867897400 cos(x) + 38709940786166665065959258978337847420670032936563000 cos(3 x) – 21290467432391665786277592438085816081368518115109650 cos(5 x) + 13345336728758624326675458816875948855668313104223250 cos(7 x) – 8718953329455634560094633093692286585703297894759190 cos(9 x) + 5734926521513599202629090216706691176692543535055510 cos(11 x) – 3732792410452638534255620851110864079504022419266900 cos(13 x) + 2380535537232060046374339335236739733721433165494740 cos(15 x) – 1478110300895723558206289129722158658193046736745100 cos(17 x) + 889695099773598199150005610138983536845384112356620 cos(19 x) – 517475721296888748485207344672674097961090759227830 cos(21 x) + 290117967317477673635871394610538109840886123594550 cos(23 x) – 156463620994667269505690641783062621996946861138578 cos(25 x) + 81031065486880412644190068720041847550207884770450 cos(27 x) – 40236115276244066968149551364434572576654949679120 cos(29 x) + 19128644967394720361907163763419714831524484273680 cos(31 x) – 8694838621543054709957801710645324923420220124400 cos(33 x) + 3773678258873788370716379245844705647035442475760 cos(35 x) – 1561741847000132011529582627081001492438654402975 cos(37 x) + 615455662782300544188581082624820706487659072415 cos(39 x) – 230625292705562731636075838056750996444377789885 cos(41 x) + 82051692128844776094056832352714255937343712125 cos(43 x) – 27672335384630002917995637577778141218084546050 cos(45 x) + 8831596399350000931275203482269619537686557250 cos(47 x) – 2662352967034373458582670670748334286288017550 cos(49 x) + 756575863871408530483724971057728798837439950 cos(51 x) – 202229397575690959406027114905367760695542125 cos(53 x) + 50721046913753622944425729691084765883041325 cos(55 x) – 11904655392275032412276309244706950740685375 cos(57 x) + 2606917757088024046891693482061250907960255 cos(59 x) – 530830535524394887891664936813162393683020 cos(61 x) + 100125734901014496479256527970324384708300 cos(63 x) – 17418323112957551458521549836257614854580 cos(65 x) + 2780744951908016433487759231369296155700 cos(67 x) – 405021547343124132703651888047267048765 cos(69 x) + 53453547980078458828390155282190173885 cos(71 x) – 6340130147987922781182260315796027975 cos(73 x) + 669151085498484380278995185137026567 cos(75 x) – 62073384554590387780982855764102650 cos(77 x) + 4982509944143591811459383359173690 cos(79 x) – 339033837715197031098442106265910 cos(81 x) + 19015192393664976816904729682550 cos(83 x) – 843989822820424104707536130295 cos(85 x) + 27795092963865187485525211575 cos(87 x) – 603788536293700701932757405 cos(89 x) + 6489213830472088210604445 cos(91 x))/731026443804552340414645156340960562802085216523386880 + C

$ \displaystyle \int \sin^{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 \sin^{93}x\, dx$ = (-1940882770200321658872357280600835028065942694888889200 cos(x) + 620004218258436085473114131303044522854398360867284050 cos(3 x) – 341634977407709679750491460105759226878954198845238150 cos(5 x) + 214741985799131798700308917780762942609628353559863980 cos(7 x) – 140822086548014534659679704252744326199342340787623220 cos(9 x) + 93060749502009605072305818544645726054810148282730030 cos(11 x) – 60914946335858246571277103285392195138925075291017770 cos(13 x) + 39105891474871960761807523096794989471902517470776840 cos(15 x) – 24467322473582991492681712311898469348730452107384440 cos(17 x) + 14855160073246816263413896760795499247443488779483410 cos(19 x) – 8724459090637019075338320319832277335800144203823590 cos(21 x) + 4944296156313033299067293974357722388204579473831060 cos(23 x) – 2698412478530163936101133321598621371189617950124748 cos(25 x) + 1415833707870765028201211927999276645377268677534590 cos(27 x) – 713119182426710932802306290473349627490755450358010 cos(29 x) + 344315609413104966514328947741554866967440716926240 cos(31 x) – 159156950767673820500370427503431566693463457896160 cos(33 x) + 70341688062498697453288715726963058493986081838035 cos(35 x) – 29686824691657454434548044267304575622202026222705 cos(37 x) + 11948543271389713595257099402069751493629098355370 cos(39 x) – 4580202426200716569277657688525463532141041342630 cos(41 x) + 1669800200523243455147053042396766116710790038045 cos(43 x) – 578111180535422452265082776353147689360418451175 cos(45 x) + 189775098777585485849935987374285563680623686100 cos(47 x) – 58967197981767723542334234651222389864545617900 cos(49 x) + 17311176313819609471306183266344699421018566475 cos(51 x) – 4792005642827811254528023333743906197960942025 cos(53 x) + 1248040781670142488894276347363277781287124950 cos(55 x) – 305076635519368163951934218244356790981297210 cos(57 x) + 69805670839177461243239185530488418275381565 cos(59 x) – 14906341888800296705763019605509875139494935 cos(61 x) + 2960640961226920957432785334753284113990040 cos(63 x) – 544850186632802396255887466668325898290280 cos(65 x) + 92502550342509362050906267661973240194805 cos(67 x) – 14415766925805270056600350533830504957895 cos(69 x) + 2050198387936579114885793583306708709230 cos(71 x) – 264268846505771297033471660102746245570 cos(73 x) + 30621628245906832830862589186508691947 cos(75 x) – 3158074723603836846574827761786610705 cos(77 x) + 286337066491016116792772137365403620 cos(79 x) – 22469759865124437716248473387692380 cos(81 x) + 1495112718298258040812809154767045 cos(83 x) – 82018741321054472827140224617095 cos(85 x) + 3561477911769926023145297109810 cos(87 x) – 114772902206686096066294918590 cos(89 x) + 2440226539989264823196428035 cos(91 x) – 25674715590128696833261065 cos(93 x))/11823558134577976984097739050384231711407639154204344320 + C

$ \displaystyle \int \sin^{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 \sin^{95}x\, dx$ = (-15528782802356296960392752178566078127921217040223603750 cos(x) + 4964984977624122157404485390425888925253722455037478750 cos(3 x) – 2740671707648515430887275935515090686740054795180688270 cos(5 x) + 1727314101459148380811308362719594970634488316290349750 cos(7 x) – 1136779365917559190790348238712895835374834191062879750 cos(9 x) + 754603112538757130078670271667050923310567464736422750 cos(11 x) – 496619142440036743726988127507375393973621322946192750 cos(13 x) + 320846064146108587159375359953249799985382018339782710 cos(15 x) – 202213905974438185184480268878098613436165137609106750 cos(17 x) + 123793000610390135528449139673295827062029073162361750 cos(19 x) – 73381401018638487562840951431953684021990961267015750 cos(21 x) + 42017206036464336651678275064574806547595414078460750 cos(23 x) – 23193497732128313831726407835645293214272668571310334 cos(25 x) + 12321985741112492169253556075403540717965139647781750 cos(27 x) – 6291202953471227926237355104127058052887651944751750 cos(29 x) + 3082786086263166986896645588658266542044794117320750 cos(31 x) – 1447975282941790554451454746187973678839221479347625 cos(33 x) + 651111522834923840529159650703427285034076295987965 cos(35 x) – 279961956992903371234896655707861854744381699749125 cos(37 x) + 114963329450204866947969426549764933081026239506625 cos(39 x) – 45028678536450399823236231632834758581234093809625 cos(41 x) + 16800386632912232087739301792230562099570657852125 cos(43 x) – 5962803890665357293362710921813894738831744596405 cos(45 x) + 2010235054539564565487878270015172784292991510625 cos(47 x) – 642728214716731527741022304018456604501840823125 cos(49 x) + 194562099915593991878628024880150575684548645625 cos(51 x) – 55660039802472325060637594063112938785839770625 cos(53 x) + 15018090739430714616361125379938109301488403565 cos(55 x) – 3813457943992102049399177728054459887266215125 cos(57 x) + 909085395849316865397162553265018722850387625 cos(59 x) – 202910611683895441582973230678320698542898625 cos(61 x) + 42278140308659749431694442478082894191076125 cos(63 x) – 8195454890601736043682307311136068720116295 cos(65 x) + 1472373045575215154337617399734230145957875 cos(67 x) – 244094364925689610245437455099100013592875 cos(69 x) + 37154699701059490987639130701492060443375 cos(71 x) – 5162394674706896008067276477115335208375 cos(73 x) + 650259282163080391290670276254684576051 cos(75 x) – 73647608218409890285110647416341502875 cos(77 x) + 7425839152532817396709104999203355375 cos(79 x) – 658407736307623540224488546506245875 cos(81 x) + 50537049747722018046200758883043375 cos(83 x) – 3289862846322296076733069009641255 cos(85 x) + 176606253591887815158715969318875 cos(87 x) – 7505981466777840702886316233875 cos(89 x) + 236806930359173279885459817375 cos(91 x) – 4930091663849180615323002375 cos(93 x) + 50803160635786570329644235 cos(95 x))/95594725343396409658662571045659745751806444225481932800 + C

$ \displaystyle \int \sin^{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 \sin^{97}x\, dx$ = (-1987895474658100654426332044192220804157969131040325002500 cos(x) + 636126551890592209416426254141510657330550121932904000800 cos(3 x) – 351740563986562751089082752290011775229833596833488094560 cos(5 x) + 222253653068432507556288552271161286546323426570610609200 cos(7 x) – 146771280328210146499435836405483868473987168490025874000 cos(9 x) + 97847520218806764332957224270322578982658112326683916000 cos(11 x) – 64729897990902936404879394517290321480835366616113975200 cos(13 x) + 42074433694086908663171606436238708962542988300474083880 cos(15 x) – 26703587948259493114396839998231997948363196908969619800 cos(17 x) + 16477713071521284317413658075134082218590720415698132000 cos(19 x) – 9854709754638637352060952892392538276009462330938108000 cos(21 x) + 5698593032030168555756985802992206916127210826151166800 cos(23 x) – 3180001750988638321933898307112372515163446828232552752 cos(25 x) + 1709678360746579742975214143608802427507229477544383200 cos(27 x) – 884316393489610211883731453590759876296842833212612000 cos(29 x) + 439483852812880881510765732480085301425749512876832375 cos(31 x) – 209599991341527805028211349336656066833818998448950825 cos(33 x) + 95817138898984139441468045411042773409745827862377520 cos(35 x) – 41936908311979746387250031976999358269291739907494800 cos(37 x) + 17552778365873875750319583519784799275608533671689000 cos(39 x) – 7017388593779905787773576868461155171690792358671000 cos(41 x) + 2676399370650940812081085131227045228272767318190800 cos(43 x) – 972550757222454548615380230783912209710385870553840 cos(45 x) + 336254251167338008829785718090182412931782348861700 cos(47 x) – 110455338306296382548224271388304259210188498717500 cos(49 x) + 34418515593058968170829820655179069642602457470000 cos(51 x) – 10156709129725325701731667831075483947364196883600 cos(53 x) + 2833187283554959274693570500247371837948960183320 cos(55 x) – 745575600935515598603571184275624167881305311400 cos(57 x) + 184692782500323290397234061293831280179202098000 cos(59 x) – 42963396800759993470699187115664010184869382000 cos(61 x) + 9359882874451284291830894335912516504560829650 cos(63 x) – 1903976174461030479876711839271093100927758510 cos(65 x) + 360417768736707626332686624106650313972491600 cos(67 x) – 63247748835409667271581990086813962902454000 cos(69 x) + 10244353684608608079199899802793810892651000 cos(71 x) – 1523857929233480299291137392099707889430600 cos(73 x) + 206961169923802905764191683020053350564528 cos(75 x) – 25487828808350111547314246677346471744400 cos(77 x) + 2823019013583081975177210866161792756500 cos(79 x) – 278425096221053028762796077936056963500 cos(81 x) + 24152538467368455507134117604091688400 cos(83 x) – 1814172572662064983793784399221366640 cos(85 x) + 115595703655378953240233638631046600 cos(87 x) – 6075163838358081993415685973723000 cos(89 x) + 252835904425470796078557891822000 cos(91 x) – 7812586520447484700559853363600 cos(93 x) + 159335646140705280077207535705 cos(95 x) – 1608766753466574727105400775 cos(97 x))/12363584477745935649187025855238660450566966786495663308800 + C

$ \displaystyle \int \sin^{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 \sin^{99}x\, dx$ = (-15904786569080852664516310502145270286981433023123449264900 cos(x) + 5093689816241580265106530814412537542889478549889209241700 cos(3 x) – 2821120513610721377597463220290020792984941966092485118480 cos(5 x) + 1786963128567438069367665382124406701755960544559929926800 cos(7 x) – 1183954994647561848428782413670903205690163159152875383600 cos(9 x) + 792564913772334791096953516589612889759530709846139719600 cos(11 x) – 526925025090398405069952612677709668466501186216389593800 cos(13 x) + 344504197690681530332284807586947023009092588415159980040 cos(15 x) – 220119314954492255688985221886183189143740700508672198200 cos(17 x) + 136862767638966192877094290503719610020684449825641857400 cos(19 x) – 82552145560011354433802905383195955250571572910704612400 cos(21 x) + 48189741420990234697993285466028144939571003716227425200 cos(23 x) – 27172796130287396855513633224070063662700036934182432016 cos(25 x) + 14776505832166867778571493669761792409169626198776454800 cos(27 x) – 7738558011242562220243260693431283524629782685997151975 cos(29 x) + 3898082571419950696549334790983996415632371923715686975 cos(31 x) – 1886399922073750245253902144029904601504370986040557425 cos(33 x) + 876029643982223461442004023389580431146379532536531785 cos(35 x) – 389965501295743353265121027899972211003157820525006200 cos(37 x) + 166217179482057832105200230026483881835979940595385400 cos(39 x) – 67761010450873750370412637327869735800730498430871400 cos(41 x) + 26389728603370091447894079850257817185413875740028200 cos(43 x) – 9806553468659750031871750660404448114579724194751220 cos(45 x) + 3472737529706090436818471889359196869488302214113300 cos(47 x) – 1170348941340552265248806577164075723804386460465100 cos(49 x) + 374817634808412163380336746934900068407940761848300 cos(51 x) – 113896917826588005952714046238410547103108116311400 cos(53 x) + 32784024281135957321454172931433874124837967835560 cos(55 x) – 8922327795810730625047132084353348558491664660600 cos(57 x) + 2291359444665403252130748145241570097514379446200 cos(59 x) – 554058226374011442113582543316609162923558964450 cos(61 x) + 125838425312067266590170912738379388561317820850 cos(63 x) – 26773128387220315255769946537583907434997074830 cos(65 x) + 5319961673777818442299189160947710432596973150 cos(67 x) – 983954264025158966553611245779148651439605800 cos(69 x) + 168747748677057088713005408348205278250205800 cos(71 x) – 26717945553519392510469476887243715606993400 cos(73 x) + 3885874380121058006503530048428243082151224 cos(75 x) – 516128533369089758833113495216266052824100 cos(77 x) + 62176200791298396491487289211801642261700 cos(79 x) – 6737887328549483296059665086052578516700 cos(81 x) + 650327004172192946223685402850831423100 cos(83 x) – 55219581939940679832803977940275200120 cos(85 x) + 4060765202603473550923046208684185400 cos(87 x) – 253373109701053453691349524376421800 cos(89 x) + 13042340522494943538768136303933800 cos(91 x) – 531744170047956927431855019560025 cos(93 x) + 16099470802320128350893928427265 cos(95 x) – 321786182667875487762449652975 cos(97 x) + 3184701532372607112841303575 cos(99 x))/99917948024232459532205351809683868131112629539842503475200 + C

$ \displaystyle \int \sin^{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

 


Pythonのスクリプトで効率よくWolframAlpha(外部リンク)から情報を収集できるようになったので作成してみましたが、どの程度の需要があるかは全く不明ですね…。暇で暇で死にそうな人は検算してみて下さい(笑)

 

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