3.1.46 \(\int \sin ^{99}(x) \sin (101 x) \, dx\) [46]
Optimal. Leaf size=12 \[ \frac {1}{100} \sin ^{100}(x) \sin (100 x) \]
[Out]
1/100*sin(x)^100*sin(100*x)
________________________________________________________________________________________
Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(801\) vs. \(2(12)=24\).
time = 0.33, antiderivative size = 801, normalized size of antiderivative = 66.75, number of steps
used = 102, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {4439, 2717}
\begin {gather*} \text {Too large to display} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[Sin[x]^99*Sin[101*x],x]
[Out]
-1/1267650600228229401496703205376*Sin[2*x] + (99*Sin[4*x])/2535301200456458802993406410752 - (1617*Sin[6*x])/
1267650600228229401496703205376 + (156849*Sin[8*x])/5070602400912917605986812821504 - (470547*Sin[10*x])/79228
1625142643375935439503360 + (2980131*Sin[12*x])/316912650057057350374175801344 - (20009451*Sin[14*x])/15845632
5028528675187087900672 + (1860878943*Sin[16*x])/1267650600228229401496703205376 - (4755579521*Sin[18*x])/31691
2650057057350374175801344 + (432757736411*Sin[20*x])/3169126500570573503741758013440 - (354074511609*Sin[22*x]
)/316912650057057350374175801344 + (10504210511067*Sin[24*x])/1267650600228229401496703205376 - (8888178124749
*Sin[26*x])/158456325028528675187087900672 + (110467356693309*Sin[28*x])/316912650057057350374175801344 - (158
3365445937429*Sin[30*x])/792281625142643375935439503360 + (26917212580936293*Sin[32*x])/2535301200456458802993
406410752 - (33250674364686009*Sin[34*x])/633825300114114700748351602688 + (306645108029882083*Sin[36*x])/1267
650600228229401496703205376 - (661707864696061337*Sin[38*x])/633825300114114700748351602688 + (535983370403809
68297*Sin[40*x])/12676506002282294014967032053760 - (2552301763827665157*Sin[42*x])/15845632502852867518708790
0672 + (18330167212944140673*Sin[44*x])/316912650057057350374175801344 - (31081587882818325489*Sin[46*x])/1584
56325028528675187087900672 + (797760755659003687551*Sin[48*x])/1267650600228229401496703205376 - (151574543575
21070063469*Sin[50*x])/7922816251426433759354395033600 + (3497874082504862322339*Sin[52*x])/633825300114114700
748351602688 - (4793383001951107626909*Sin[54*x])/316912650057057350374175801344 + (49988137020347265252051*Si
n[56*x])/1267650600228229401496703205376 - (15513559764935358181671*Sin[58*x])/158456325028528675187087900672
+ (367154247770136810299547*Sin[60*x])/1584563250285286751870879006720 - (82905797883579279745059*Sin[62*x])/1
58456325028528675187087900672 + (5720500053966970302409071*Sin[64*x])/5070602400912917605986812821504 - (29469
24270225408943665279*Sin[66*x])/1267650600228229401496703205376 + (11614348594417788189739629*Sin[68*x])/25353
01200456458802993406410752 - (54753357659398144323058251*Sin[70*x])/6338253001141147007483516026880 + (7908818
3285797319577750807*Sin[72*x])/5070602400912917605986812821504 - (2137518467183711339939211*Sin[74*x])/7922816
2514264337593543950336 + (7087561233293358653482647*Sin[76*x])/158456325028528675187087900672 - (5633702518771
644057896463*Sin[78*x])/79228162514264337593543950336 + (343655853645070287531684243*Sin[80*x])/31691265005705
73503741758013440 - (25145550266712460063293969*Sin[82*x])/158456325028528675187087900672 + (70647022177906435
415921151*Sin[84*x])/316912650057057350374175801344 - (47645666119983409931667753*Sin[86*x])/15845632502852867
5187087900672 + (246891178985368578736823811*Sin[88*x])/633825300114114700748351602688 - (19202647254417556123
9751853*Sin[90*x])/396140812571321687967719751680 + (91838747738518746679881321*Sin[92*x])/1584563250285286751
87087900672 - (52758429551915024688442461*Sin[94*x])/79228162514264337593543950336 + (932065588750498769495816
811*Sin[96*x])/1267650600228229401496703205376 - (247282707219520081702971807*Sin[98*x])/316912650057057350374
175801344 + (12611418068195524166851562157*Sin[100*x])/15845632502852867518708790067200 - (2472827072195200817
02971807*Sin[102*x])/316912650057057350374175801344 + (932065588750498769495816811*Sin[104*x])/126765060022822
9401496703205376 - (52758429551915024688442461*Sin[106*x])/79228162514264337593543950336 + (918387477385187466
79881321*Sin[108*x])/158456325028528675187087900672 - (192026472544175561239751853*Sin[110*x])/396140812571321
687967719751680 + (246891178985368578736823811*Sin[112*x])/633825300114114700748351602688 - (47645666119983409
931667753*Sin[114*x])/158456325028528675187087900672 + (70647022177906435415921151*Sin[116*x])/316912650057057
350374175801344 - (25145550266712460063293969*Sin[118*x])/158456325028528675187087900672 + (343655853645070287
531684243*Sin[120*x])/3169126500570573503741758013440 - (5633702518771644057896463*Sin[122*x])/792281625142643
37593543950336 + (7087561233293358653482647*Sin[124*x])/158456325028528675187087900672 - (21375184671837113399
39211*Sin[126*x])/79228162514264337593543950336 + (79088183285797319577750807*Sin[128*x])/50706024009129176059
86812821504 - (54753357659398144323058251*Sin[130*x])/6338253001141147007483516026880 + (116143485944177881897
39629*Sin[132*x])/2535301200456458802993406410752 - (2946924270225408943665279*Sin[134*x])/1267650600228229401
496703205376 + (5720500053966970302409071*Sin[136*x])/5070602400912917605986812821504 - (829057978835792797450
59*Sin[138*x])/158456325028528675187087900672 + (367154247770136810299547*Sin[140*x])/158456325028528675187087
9006720 - (15513559764935358181671*Sin[142*x])/158456325028528675187087900672 + (49988137020347265252051*Sin[1
44*x])/1267650600228229401496703205376 - (4793383001951107626909*Sin[146*x])/316912650057057350374175801344 +
(3497874082504862322339*Sin[148*x])/63382530011...
Rule 2717
Int[sin[Pi/2 + (c_.) + (d_.)*(x_)], x_Symbol] :> Simp[Sin[c + d*x]/d, x] /; FreeQ[{c, d}, x]
Rule 4439
Int[(F_)[(a_.) + (b_.)*(x_)]^(p_.)*(G_)[(c_.) + (d_.)*(x_)]^(q_.), x_Symbol] :> Int[ExpandTrigReduce[ActivateT
rig[F[a + b*x]^p*G[c + d*x]^q], x], x] /; FreeQ[{a, b, c, d}, x] && (EqQ[F, sin] || EqQ[F, cos]) && (EqQ[G, si
n] || EqQ[G, cos]) && IGtQ[p, 0] && IGtQ[q, 0]
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} \frac {1}{100} \sin ^{100}(x) \sin (100 x) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[Sin[x]^99*Sin[101*x],x]
[Out]
(Sin[x]^100*Sin[100*x])/100
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(601\) vs.
\(2(10)=20\).
time = 1.49, size = 602, normalized size = 50.17 \[\text {Expression too large to display}\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(sin(101*x)*sin(x)^99,x)
[Out]
79088183285797319577750807/5070602400912917605986812821504*sin(128*x)-31081587882818325489/1584563250285286751
87087900672*sin(154*x)+1/126765060022822940149670320537600*sin(200*x)-354074511609/316912650057057350374175801
344*sin(178*x)+2980131/316912650057057350374175801344*sin(12*x)-20009451/158456325028528675187087900672*sin(14
*x)+1860878943/1267650600228229401496703205376*sin(16*x)-4755579521/316912650057057350374175801344*sin(18*x)-1
583365445937429/792281625142643375935439503360*sin(30*x)-354074511609/316912650057057350374175801344*sin(22*x)
+156849/5070602400912917605986812821504*sin(8*x)-470547/792281625142643375935439503360*sin(10*x)-1617/12676506
00228229401496703205376*sin(6*x)+432757736411/3169126500570573503741758013440*sin(20*x)+99/2535301200456458802
993406410752*sin(4*x)+12611418068195524166851562157/15845632502852867518708790067200*sin(100*x)-1/126765060022
8229401496703205376*sin(2*x)-2137518467183711339939211/79228162514264337593543950336*sin(126*x)+53598337040380
968297/12676506002282294014967032053760*sin(40*x)-54753357659398144323058251/6338253001141147007483516026880*s
in(130*x)+7087561233293358653482647/158456325028528675187087900672*sin(124*x)+3497874082504862322339/633825300
114114700748351602688*sin(148*x)+156849/5070602400912917605986812821504*sin(192*x)+91838747738518746679881321/
158456325028528675187087900672*sin(108*x)-192026472544175561239751853/396140812571321687967719751680*sin(110*x
)-247282707219520081702971807/316912650057057350374175801344*sin(102*x)+53598337040380968297/12676506002282294
014967032053760*sin(160*x)+367154247770136810299547/1584563250285286751870879006720*sin(140*x)+432757736411/31
69126500570573503741758013440*sin(180*x)+797760755659003687551/1267650600228229401496703205376*sin(48*x)-31081
587882818325489/158456325028528675187087900672*sin(46*x)-52758429551915024688442461/79228162514264337593543950
336*sin(106*x)-8888178124749/158456325028528675187087900672*sin(174*x)+306645108029882083/12676506002282294014
96703205376*sin(36*x)+26917212580936293/2535301200456458802993406410752*sin(32*x)+932065588750498769495816811/
1267650600228229401496703205376*sin(96*x)+306645108029882083/1267650600228229401496703205376*sin(164*x)+110467
356693309/316912650057057350374175801344*sin(28*x)-1583365445937429/792281625142643375935439503360*sin(170*x)-
15513559764935358181671/158456325028528675187087900672*sin(142*x)-8888178124749/158456325028528675187087900672
*sin(26*x)-82905797883579279745059/158456325028528675187087900672*sin(138*x)-5633702518771644057896463/7922816
2514264337593543950336*sin(78*x)-661707864696061337/633825300114114700748351602688*sin(38*x)-25523017638276651
57/158456325028528675187087900672*sin(42*x)-33250674364686009/633825300114114700748351602688*sin(34*x)-2472827
07219520081702971807/316912650057057350374175801344*sin(98*x)-47645666119983409931667753/158456325028528675187
087900672*sin(86*x)-25145550266712460063293969/158456325028528675187087900672*sin(118*x)-192026472544175561239
751853/396140812571321687967719751680*sin(90*x)+70647022177906435415921151/316912650057057350374175801344*sin(
84*x)-4755579521/316912650057057350374175801344*sin(182*x)+10504210511067/1267650600228229401496703205376*sin(
24*x)+246891178985368578736823811/633825300114114700748351602688*sin(88*x)+2980131/316912650057057350374175801
344*sin(188*x)+70647022177906435415921151/316912650057057350374175801344*sin(116*x)-20009451/15845632502852867
5187087900672*sin(186*x)-470547/792281625142643375935439503360*sin(190*x)-2137518467183711339939211/7922816251
4264337593543950336*sin(74*x)+932065588750498769495816811/1267650600228229401496703205376*sin(104*x)+790881832
85797319577750807/5070602400912917605986812821504*sin(72*x)-54753357659398144323058251/63382530011411470074835
16026880*sin(70*x)-661707864696061337/633825300114114700748351602688*sin(162*x)+1860878943/1267650600228229401
496703205376*sin(184*x)-15513559764935358181671/158456325028528675187087900672*sin(58*x)+572050005396697030240
9071/5070602400912917605986812821504*sin(64*x)+49988137020347265252051/1267650600228229401496703205376*sin(56*
x)+18330167212944140673/316912650057057350374175801344*sin(156*x)-4793383001951107626909/316912650057057350374
175801344*sin(54*x)-82905797883579279745059/158456325028528675187087900672*sin(62*x)-2946924270225408943665279
/1267650600228229401496703205376*sin(66*x)+10504210511067/1267650600228229401496703205376*sin(176*x)+349787408
2504862322339/633825300114114700748351602688*sin(52*x)-47645666119983409931667753/1584563250285286751870879006
72*sin(114*x)+99/2535301200456458802993406410752*sin(196*x)+49988137020347265252051/12676506002282294014967032
05376*sin(144*x)+11614348594417788189739629/2535301200456458802993406410752*sin(68*x)-294692427022540894366527
9/1267650600228229401496703205376*sin(134*x)-15157454357521070063469/7922816251426433759354395033600*sin(50*x)
+18330167212944140673/316912650057057350374175801344*sin(44*x)+797760755659003687551/1267650600228229401496703
205376*sin(152*x)-33250674364686009/63382530011...
________________________________________________________________________________________
Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(sin(101*x)*sin(x)^99,x, algorithm="maxima")
[Out]
Exception raised: RuntimeError >> ECL says: Memory limit reached. Please jump to an outer pointer, quit progra
m and enlarge thememory limits before executing the program again.
________________________________________________________________________________________
Fricas [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(sin(101*x)*sin(x)^99,x, algorithm="fricas")
[Out]
Timed out
________________________________________________________________________________________
Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(sin(101*x)*sin(x)**99,x)
[Out]
Timed out
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 601 vs.
\(2 (10) = 20\).
time = 0.49, size = 601, normalized size = 50.08 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(sin(101*x)*sin(x)^99,x, algorithm="giac")
[Out]
1/126765060022822940149670320537600*sin(200*x) - 1/1267650600228229401496703205376*sin(198*x) + 99/25353012004
56458802993406410752*sin(196*x) - 1617/1267650600228229401496703205376*sin(194*x) + 156849/5070602400912917605
986812821504*sin(192*x) - 470547/792281625142643375935439503360*sin(190*x) + 2980131/3169126500570573503741758
01344*sin(188*x) - 20009451/158456325028528675187087900672*sin(186*x) + 1860878943/126765060022822940149670320
5376*sin(184*x) - 4755579521/316912650057057350374175801344*sin(182*x) + 432757736411/316912650057057350374175
8013440*sin(180*x) - 354074511609/316912650057057350374175801344*sin(178*x) + 10504210511067/12676506002282294
01496703205376*sin(176*x) - 8888178124749/158456325028528675187087900672*sin(174*x) + 110467356693309/31691265
0057057350374175801344*sin(172*x) - 1583365445937429/792281625142643375935439503360*sin(170*x) + 2691721258093
6293/2535301200456458802993406410752*sin(168*x) - 33250674364686009/633825300114114700748351602688*sin(166*x)
+ 306645108029882083/1267650600228229401496703205376*sin(164*x) - 661707864696061337/6338253001141147007483516
02688*sin(162*x) + 53598337040380968297/12676506002282294014967032053760*sin(160*x) - 2552301763827665157/1584
56325028528675187087900672*sin(158*x) + 18330167212944140673/316912650057057350374175801344*sin(156*x) - 31081
587882818325489/158456325028528675187087900672*sin(154*x) + 797760755659003687551/1267650600228229401496703205
376*sin(152*x) - 15157454357521070063469/7922816251426433759354395033600*sin(150*x) + 3497874082504862322339/6
33825300114114700748351602688*sin(148*x) - 4793383001951107626909/316912650057057350374175801344*sin(146*x) +
49988137020347265252051/1267650600228229401496703205376*sin(144*x) - 15513559764935358181671/15845632502852867
5187087900672*sin(142*x) + 367154247770136810299547/1584563250285286751870879006720*sin(140*x) - 8290579788357
9279745059/158456325028528675187087900672*sin(138*x) + 5720500053966970302409071/50706024009129176059868128215
04*sin(136*x) - 2946924270225408943665279/1267650600228229401496703205376*sin(134*x) + 11614348594417788189739
629/2535301200456458802993406410752*sin(132*x) - 54753357659398144323058251/6338253001141147007483516026880*si
n(130*x) + 79088183285797319577750807/5070602400912917605986812821504*sin(128*x) - 2137518467183711339939211/7
9228162514264337593543950336*sin(126*x) + 7087561233293358653482647/158456325028528675187087900672*sin(124*x)
- 5633702518771644057896463/79228162514264337593543950336*sin(122*x) + 343655853645070287531684243/31691265005
70573503741758013440*sin(120*x) - 25145550266712460063293969/158456325028528675187087900672*sin(118*x) + 70647
022177906435415921151/316912650057057350374175801344*sin(116*x) - 47645666119983409931667753/15845632502852867
5187087900672*sin(114*x) + 246891178985368578736823811/633825300114114700748351602688*sin(112*x) - 19202647254
4175561239751853/396140812571321687967719751680*sin(110*x) + 91838747738518746679881321/1584563250285286751870
87900672*sin(108*x) - 52758429551915024688442461/79228162514264337593543950336*sin(106*x) + 932065588750498769
495816811/1267650600228229401496703205376*sin(104*x) - 247282707219520081702971807/316912650057057350374175801
344*sin(102*x) + 12611418068195524166851562157/15845632502852867518708790067200*sin(100*x) - 24728270721952008
1702971807/316912650057057350374175801344*sin(98*x) + 932065588750498769495816811/1267650600228229401496703205
376*sin(96*x) - 52758429551915024688442461/79228162514264337593543950336*sin(94*x) + 9183874773851874667988132
1/158456325028528675187087900672*sin(92*x) - 192026472544175561239751853/396140812571321687967719751680*sin(90
*x) + 246891178985368578736823811/633825300114114700748351602688*sin(88*x) - 47645666119983409931667753/158456
325028528675187087900672*sin(86*x) + 70647022177906435415921151/316912650057057350374175801344*sin(84*x) - 251
45550266712460063293969/158456325028528675187087900672*sin(82*x) + 343655853645070287531684243/316912650057057
3503741758013440*sin(80*x) - 5633702518771644057896463/79228162514264337593543950336*sin(78*x) + 7087561233293
358653482647/158456325028528675187087900672*sin(76*x) - 2137518467183711339939211/7922816251426433759354395033
6*sin(74*x) + 79088183285797319577750807/5070602400912917605986812821504*sin(72*x) - 5475335765939814432305825
1/6338253001141147007483516026880*sin(70*x) + 11614348594417788189739629/2535301200456458802993406410752*sin(6
8*x) - 2946924270225408943665279/1267650600228229401496703205376*sin(66*x) + 5720500053966970302409071/5070602
400912917605986812821504*sin(64*x) - 82905797883579279745059/158456325028528675187087900672*sin(62*x) + 367154
247770136810299547/1584563250285286751870879006720*sin(60*x) - 15513559764935358181671/15845632502852867518708
7900672*sin(58*x) + 49988137020347265252051/1267650600228229401496703205376*sin(56*x) - 4793383001951107626909
/316912650057057350374175801344*sin(54*x) + 3497874082504862322339/633825300114114700748351602688*sin(52*x) -
15157454357521070063469/79228162514264337593543...
________________________________________________________________________________________
Mupad [B]
time = 4.67, size = 2500, normalized size = 208.33 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(sin(101*x)*sin(x)^99,x)
[Out]
(99*sin(4*x))/2535301200456458802993406410752 - sin(2*x)/1267650600228229401496703205376 - (1617*sin(6*x))/126
7650600228229401496703205376 + (156849*sin(8*x))/5070602400912917605986812821504 - (470547*sin(10*x))/79228162
5142643375935439503360 + (2980131*sin(12*x))/316912650057057350374175801344 - (20009451*sin(14*x))/15845632502
8528675187087900672 + (1860878943*sin(16*x))/1267650600228229401496703205376 - (4755579521*sin(18*x))/31691265
0057057350374175801344 + (432757736411*sin(20*x))/3169126500570573503741758013440 - (354074511609*sin(22*x))/3
16912650057057350374175801344 + (10504210511067*sin(24*x))/1267650600228229401496703205376 - (8888178124749*si
n(26*x))/158456325028528675187087900672 + (110467356693309*sin(28*x))/316912650057057350374175801344 - (158336
5445937429*sin(30*x))/792281625142643375935439503360 + (26917212580936293*sin(32*x))/2535301200456458802993406
410752 - (33250674364686009*sin(34*x))/633825300114114700748351602688 + (306645108029882083*sin(36*x))/1267650
600228229401496703205376 - (661707864696061337*sin(38*x))/633825300114114700748351602688 + (535983370403809682
97*sin(40*x))/12676506002282294014967032053760 - (2552301763827665157*sin(42*x))/15845632502852867518708790067
2 + (18330167212944140673*sin(44*x))/316912650057057350374175801344 - (31081587882818325489*sin(46*x))/1584563
25028528675187087900672 + (797760755659003687551*sin(48*x))/1267650600228229401496703205376 - (151574543575210
70063469*sin(50*x))/7922816251426433759354395033600 + (3497874082504862322339*sin(52*x))/633825300114114700748
351602688 - (4793383001951107626909*sin(54*x))/316912650057057350374175801344 + (49988137020347265252051*sin(5
6*x))/1267650600228229401496703205376 - (15513559764935358181671*sin(58*x))/158456325028528675187087900672 + (
367154247770136810299547*sin(60*x))/1584563250285286751870879006720 - (82905797883579279745059*sin(62*x))/1584
56325028528675187087900672 + (5720500053966970302409071*sin(64*x))/5070602400912917605986812821504 - (29469242
70225408943665279*sin(66*x))/1267650600228229401496703205376 + (11614348594417788189739629*sin(68*x))/25353012
00456458802993406410752 - (54753357659398144323058251*sin(70*x))/6338253001141147007483516026880 + (7908818328
5797319577750807*sin(72*x))/5070602400912917605986812821504 - (2137518467183711339939211*sin(74*x))/7922816251
4264337593543950336 + (7087561233293358653482647*sin(76*x))/158456325028528675187087900672 - (5633702518771644
057896463*sin(78*x))/79228162514264337593543950336 + (343655853645070287531684243*sin(80*x))/31691265005705735
03741758013440 - (25145550266712460063293969*sin(82*x))/158456325028528675187087900672 + (70647022177906435415
921151*sin(84*x))/316912650057057350374175801344 - (47645666119983409931667753*sin(86*x))/15845632502852867518
7087900672 + (246891178985368578736823811*sin(88*x))/633825300114114700748351602688 - (19202647254417556123975
1853*sin(90*x))/396140812571321687967719751680 + (91838747738518746679881321*sin(92*x))/1584563250285286751870
87900672 - (52758429551915024688442461*sin(94*x))/79228162514264337593543950336 + (932065588750498769495816811
*sin(96*x))/1267650600228229401496703205376 - (247282707219520081702971807*sin(98*x))/316912650057057350374175
801344 + (12611418068195524166851562157*sin(100*x))/15845632502852867518708790067200 - (2472827072195200817029
71807*sin(102*x))/316912650057057350374175801344 + (932065588750498769495816811*sin(104*x))/126765060022822940
1496703205376 - (52758429551915024688442461*sin(106*x))/79228162514264337593543950336 + (918387477385187466798
81321*sin(108*x))/158456325028528675187087900672 - (192026472544175561239751853*sin(110*x))/396140812571321687
967719751680 + (246891178985368578736823811*sin(112*x))/633825300114114700748351602688 - (47645666119983409931
667753*sin(114*x))/158456325028528675187087900672 + (70647022177906435415921151*sin(116*x))/316912650057057350
374175801344 - (25145550266712460063293969*sin(118*x))/158456325028528675187087900672 + (343655853645070287531
684243*sin(120*x))/3169126500570573503741758013440 - (5633702518771644057896463*sin(122*x))/792281625142643375
93543950336 + (7087561233293358653482647*sin(124*x))/158456325028528675187087900672 - (21375184671837113399392
11*sin(126*x))/79228162514264337593543950336 + (79088183285797319577750807*sin(128*x))/50706024009129176059868
12821504 - (54753357659398144323058251*sin(130*x))/6338253001141147007483516026880 + (116143485944177881897396
29*sin(132*x))/2535301200456458802993406410752 - (2946924270225408943665279*sin(134*x))/1267650600228229401496
703205376 + (5720500053966970302409071*sin(136*x))/5070602400912917605986812821504 - (82905797883579279745059*
sin(138*x))/158456325028528675187087900672 + (367154247770136810299547*sin(140*x))/158456325028528675187087900
6720 - (15513559764935358181671*sin(142*x))/158456325028528675187087900672 + (49988137020347265252051*sin(144*
x))/1267650600228229401496703205376 - (4793383001951107626909*sin(146*x))/316912650057057350374175801344 + (34
97874082504862322339*sin(148*x))/63382530011411...
________________________________________________________________________________________
Chatgpt [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {not solved} \end {gather*}
Warning: Unable to verify antiderivative.
[In]
int(sin(101*x)*sin(x)^99,x)
[Out]
not solved
________________________________________________________________________________________