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Resolución de integrales/ sqr(sin(x))*sqr(sin(x))/cos^3(x)

Integral de sqr(sin(x))*sqr(sin(x))/cos^3(x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
  /                 
 |                  
 |  sin(x)*sin(x)   
 |  ------------- dx
 |        81        
 |     cos  (x)     
 |                  
/                   
0
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)} \sin{\left(x \right)}}{\cos^{81}{\left(x \right)}}\, dx$$ 
Integral((sin(x)*sin(x))/cos(x)^81, (x, 0, 1))
Respuesta (Indefinida) [src] 
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 | sin(x)*sin(x)          340212685864987900195*log(1 + sin(x))   340212685864987900195*log(-1 + sin(x))                                                                                    - 675306851542052733640415353916219288522910*sin  (x) - 651634272201573798158562826772680644471930*sin  (x) - 471334679766267909595294953479074642546798*sin  (x) - 423138206006477030060483725542236950621690*sin  (x) - 219998946702561507267540370671220043857980*sin  (x) - 183278674117764655837822180587996783817780*sin  (x) - 67592827521963873520061232554287441286140*sin  (x) - 52013001206768719399943451095528437227156*sin  (x) - 13309153005670459691745651789948171689700*sin  (x) - 9389559960251275607823457051972789617900*sin  (x) - 1610466017759359066736073791565694157700*sin  (x) - 1029599217799588076866103913920036880300*sin  (x) - 112156463411265035482466005345855201755*sin  (x) - 63770763296437278131358376843813441425*sin  (x) - 4037640791930574553690093174935054075*sin  (x) - 1976183957651747501065861188470302425*sin (x) - 61761978539693729609200292143364625*sin  (x) - 24334266555867175125091681010702499*sin (x) - 254458679543808278381006718378825*sin  (x) + 6414924694381721303722858446525*sin  (x) + 6414924694381721303722858446525*sin(x) + 1645129532999397639511197852490935*sin (x) + 4919391917298196010448269380691805*sin  (x) + 251670076529935246843013462050145775*sin (x) + 566098266801909752379872595543726375*sin  (x) + 12371635384088485900368733976428222725*sin  (x) + 23324625637817735047876936498037796975*sin  (x) + 276869607161740690051451727581080329765*sin  (x) + 457853404979551461940052123741775446100*sin  (x) + 3321613731455682561936969912260315135100*sin  (x) + 4936957406516226265941098468664665946900*sin  (x) + 23441478500385305984432990632556605628700*sin  (x) + 31778438627038426341743853627782455058796*sin  (x) + 103093438806161793731524017808012524481540*sin  (x) + 128665191930189149828868104556896257067980*sin  (x) + 293199026473104431087337195212313668566980*sin  (x) + 338883026890723908708879932890888864797190*sin  (x) + 551950975838544779609279102131122881015698*sin  (x) + 592902335966441634657811024645127154455430*sin  (x) + 696874536950887358951996841236748284653410*sin  (x)                                                                                
 | ------------- dx = C - ------------------------------------- + -------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 |       81                      604462909807314587353088                604462909807314587353088                                                                                                38                                                       42                                                       34                                                       46                                                       30                                                       50                                                      26                                                      54                                                      22                                                      58                                                     18                                                     62                                                    14                                                    66                                                  10                                                  70                                                6                                                74                                              2                                              78                                            80                                               4                                               76                                                 8                                                 72                                                   12                                                   68                                                    16                                                    64                                                     20                                                     60                                                      24                                                      56                                                       28                                                       52                                                       32                                                       48                                                       36                                                       44                                                       40   
 |    cos  (x)                                                                                             5698764637629617753676613712609280 - 748147546532769485874063802947811726589952000*sin  (x) - 748147546532769485874063802947811726589952000*sin  (x) - 505664942518195976618438380648520969355264000*sin  (x) - 505664942518195976618438380648520969355264000*sin  (x) - 229234773941582176067025399227329506107719680*sin  (x) - 229234773941582176067025399227329506107719680*sin  (x) - 68574505025259625319195632247491732596326400*sin  (x) - 68574505025259625319195632247491732596326400*sin  (x) - 13174412295493228509599160875133879661363200*sin  (x) - 13174412295493228509599160875133879661363200*sin  (x) - 1558263819897048533393449135768523400806400*sin  (x) - 1558263819897048533393449135768523400806400*sin  (x) - 106245260447526036367735168347853868236800*sin  (x) - 106245260447526036367735168347853868236800*sin  (x) - 3749832721677389518861241235806607114240*sin  (x) - 3749832721677389518861241235806607114240*sin  (x) - 56303794619780623406324943480579686400*sin (x) - 56303794619780623406324943480579686400*sin  (x) - 227950585505184710147064548504371200*sin (x) - 227950585505184710147064548504371200*sin  (x) + 5698764637629617753676613712609280*sin  (x) + 4445036417351101847867758695835238400*sin (x) + 4445036417351101847867758695835238400*sin  (x) + 520810100232970766508505727195362099200*sin (x) + 520810100232970766508505727195362099200*sin  (x) + 21874024209784772193357240542205208166400*sin  (x) + 21874024209784772193357240542205208166400*sin  (x) + 438261699346044900016907569434897206476800*sin  (x) + 438261699346044900016907569434897206476800*sin  (x) + 4830617841680850453519692320882422542499840*sin  (x) + 4830617841680850453519692320882422542499840*sin  (x) + 31838163047441968898197972114906875848294400*sin  (x) + 31838163047441968898197972114906875848294400*sin  (x) + 132250831120143563115591576477305484292915200*sin  (x) + 132250831120143563115591576477305484292915200*sin  (x) + 358179334283722150104727186292702353293312000*sin  (x) + 358179334283722150104727186292702353293312000*sin  (x) + 646127426551028192345782375273110127509504000*sin  (x) + 646127426551028192345782375273110127509504000*sin  (x) + 785554923859407960167766993095202312919449600*sin  (x)
 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            
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$$\int \frac{\sin{\left(x \right)} \sin{\left(x \right)}}{\cos^{81}{\left(x \right)}}\, dx = C + \frac{6414924694381721303722858446525 \sin^{79}{\left(x \right)} - 254458679543808278381006718378825 \sin^{77}{\left(x \right)} + 4919391917298196010448269380691805 \sin^{75}{\left(x \right)} - 61761978539693729609200292143364625 \sin^{73}{\left(x \right)} + 566098266801909752379872595543726375 \sin^{71}{\left(x \right)} - 4037640791930574553690093174935054075 \sin^{69}{\left(x \right)} + 23324625637817735047876936498037796975 \sin^{67}{\left(x \right)} - 112156463411265035482466005345855201755 \sin^{65}{\left(x \right)} + 457853404979551461940052123741775446100 \sin^{63}{\left(x \right)} - 1610466017759359066736073791565694157700 \sin^{61}{\left(x \right)} + 4936957406516226265941098468664665946900 \sin^{59}{\left(x \right)} - 13309153005670459691745651789948171689700 \sin^{57}{\left(x \right)} + 31778438627038426341743853627782455058796 \sin^{55}{\left(x \right)} - 67592827521963873520061232554287441286140 \sin^{53}{\left(x \right)} + 128665191930189149828868104556896257067980 \sin^{51}{\left(x \right)} - 219998946702561507267540370671220043857980 \sin^{49}{\left(x \right)} + 338883026890723908708879932890888864797190 \sin^{47}{\left(x \right)} - 471334679766267909595294953479074642546798 \sin^{45}{\left(x \right)} + 592902335966441634657811024645127154455430 \sin^{43}{\left(x \right)} - 675306851542052733640415353916219288522910 \sin^{41}{\left(x \right)} + 696874536950887358951996841236748284653410 \sin^{39}{\left(x \right)} - 651634272201573798158562826772680644471930 \sin^{37}{\left(x \right)} + 551950975838544779609279102131122881015698 \sin^{35}{\left(x \right)} - 423138206006477030060483725542236950621690 \sin^{33}{\left(x \right)} + 293199026473104431087337195212313668566980 \sin^{31}{\left(x \right)} - 183278674117764655837822180587996783817780 \sin^{29}{\left(x \right)} + 103093438806161793731524017808012524481540 \sin^{27}{\left(x \right)} - 52013001206768719399943451095528437227156 \sin^{25}{\left(x \right)} + 23441478500385305984432990632556605628700 \sin^{23}{\left(x \right)} - 9389559960251275607823457051972789617900 \sin^{21}{\left(x \right)} + 3321613731455682561936969912260315135100 \sin^{19}{\left(x \right)} - 1029599217799588076866103913920036880300 \sin^{17}{\left(x \right)} + 276869607161740690051451727581080329765 \sin^{15}{\left(x \right)} - 63770763296437278131358376843813441425 \sin^{13}{\left(x \right)} + 12371635384088485900368733976428222725 \sin^{11}{\left(x \right)} - 1976183957651747501065861188470302425 \sin^{9}{\left(x \right)} + 251670076529935246843013462050145775 \sin^{7}{\left(x \right)} - 24334266555867175125091681010702499 \sin^{5}{\left(x \right)} + 1645129532999397639511197852490935 \sin^{3}{\left(x \right)} + 6414924694381721303722858446525 \sin{\left(x \right)}}{5698764637629617753676613712609280 \sin^{80}{\left(x \right)} - 227950585505184710147064548504371200 \sin^{78}{\left(x \right)} + 4445036417351101847867758695835238400 \sin^{76}{\left(x \right)} - 56303794619780623406324943480579686400 \sin^{74}{\left(x \right)} + 520810100232970766508505727195362099200 \sin^{72}{\left(x \right)} - 3749832721677389518861241235806607114240 \sin^{70}{\left(x \right)} + 21874024209784772193357240542205208166400 \sin^{68}{\left(x \right)} - 106245260447526036367735168347853868236800 \sin^{66}{\left(x \right)} + 438261699346044900016907569434897206476800 \sin^{64}{\left(x \right)} - 1558263819897048533393449135768523400806400 \sin^{62}{\left(x \right)} + 4830617841680850453519692320882422542499840 \sin^{60}{\left(x \right)} - 13174412295493228509599160875133879661363200 \sin^{58}{\left(x \right)} + 31838163047441968898197972114906875848294400 \sin^{56}{\left(x \right)} - 68574505025259625319195632247491732596326400 \sin^{54}{\left(x \right)} + 132250831120143563115591576477305484292915200 \sin^{52}{\left(x \right)} - 229234773941582176067025399227329506107719680 \sin^{50}{\left(x \right)} + 358179334283722150104727186292702353293312000 \sin^{48}{\left(x \right)} - 505664942518195976618438380648520969355264000 \sin^{46}{\left(x \right)} + 646127426551028192345782375273110127509504000 \sin^{44}{\left(x \right)} - 748147546532769485874063802947811726589952000 \sin^{42}{\left(x \right)} + 785554923859407960167766993095202312919449600 \sin^{40}{\left(x \right)} - 748147546532769485874063802947811726589952000 \sin^{38}{\left(x \right)} + 646127426551028192345782375273110127509504000 \sin^{36}{\left(x \right)} - 505664942518195976618438380648520969355264000 \sin^{34}{\left(x \right)} + 358179334283722150104727186292702353293312000 \sin^{32}{\left(x \right)} - 229234773941582176067025399227329506107719680 \sin^{30}{\left(x \right)} + 132250831120143563115591576477305484292915200 \sin^{28}{\left(x \right)} - 68574505025259625319195632247491732596326400 \sin^{26}{\left(x \right)} + 31838163047441968898197972114906875848294400 \sin^{24}{\left(x \right)} - 13174412295493228509599160875133879661363200 \sin^{22}{\left(x \right)} + 4830617841680850453519692320882422542499840 \sin^{20}{\left(x \right)} - 1558263819897048533393449135768523400806400 \sin^{18}{\left(x \right)} + 438261699346044900016907569434897206476800 \sin^{16}{\left(x \right)} - 106245260447526036367735168347853868236800 \sin^{14}{\left(x \right)} + 21874024209784772193357240542205208166400 \sin^{12}{\left(x \right)} - 3749832721677389518861241235806607114240 \sin^{10}{\left(x \right)} + 520810100232970766508505727195362099200 \sin^{8}{\left(x \right)} - 56303794619780623406324943480579686400 \sin^{6}{\left(x \right)} + 4445036417351101847867758695835238400 \sin^{4}{\left(x \right)} - 227950585505184710147064548504371200 \sin^{2}{\left(x \right)} + 5698764637629617753676613712609280} + \frac{340212685864987900195 \log{\left(\sin{\left(x \right)} - 1 \right)}}{604462909807314587353088} - \frac{340212685864987900195 \log{\left(\sin{\left(x \right)} + 1 \right)}}{604462909807314587353088}$$
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  340212685864987900195*log(1 + sin(1))   340212685864987900195*log(1 - sin(1))                                                                                    - 675306851542052733640415353916219288522910*sin  (1) - 651634272201573798158562826772680644471930*sin  (1) - 471334679766267909595294953479074642546798*sin  (1) - 423138206006477030060483725542236950621690*sin  (1) - 219998946702561507267540370671220043857980*sin  (1) - 183278674117764655837822180587996783817780*sin  (1) - 67592827521963873520061232554287441286140*sin  (1) - 52013001206768719399943451095528437227156*sin  (1) - 13309153005670459691745651789948171689700*sin  (1) - 9389559960251275607823457051972789617900*sin  (1) - 1610466017759359066736073791565694157700*sin  (1) - 1029599217799588076866103913920036880300*sin  (1) - 112156463411265035482466005345855201755*sin  (1) - 63770763296437278131358376843813441425*sin  (1) - 4037640791930574553690093174935054075*sin  (1) - 1976183957651747501065861188470302425*sin (1) - 61761978539693729609200292143364625*sin  (1) - 24334266555867175125091681010702499*sin (1) - 254458679543808278381006718378825*sin  (1) + 6414924694381721303722858446525*sin  (1) + 6414924694381721303722858446525*sin(1) + 1645129532999397639511197852490935*sin (1) + 4919391917298196010448269380691805*sin  (1) + 251670076529935246843013462050145775*sin (1) + 566098266801909752379872595543726375*sin  (1) + 12371635384088485900368733976428222725*sin  (1) + 23324625637817735047876936498037796975*sin  (1) + 276869607161740690051451727581080329765*sin  (1) + 457853404979551461940052123741775446100*sin  (1) + 3321613731455682561936969912260315135100*sin  (1) + 4936957406516226265941098468664665946900*sin  (1) + 23441478500385305984432990632556605628700*sin  (1) + 31778438627038426341743853627782455058796*sin  (1) + 103093438806161793731524017808012524481540*sin  (1) + 128665191930189149828868104556896257067980*sin  (1) + 293199026473104431087337195212313668566980*sin  (1) + 338883026890723908708879932890888864797190*sin  (1) + 551950975838544779609279102131122881015698*sin  (1) + 592902335966441634657811024645127154455430*sin  (1) + 696874536950887358951996841236748284653410*sin  (1)                                                                                
- ------------------------------------- + ------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
         604462909807314587353088                604462909807314587353088                                                                                               38                                                       42                                                       34                                                       46                                                       30                                                       50                                                      26                                                      54                                                      22                                                      58                                                     18                                                     62                                                    14                                                    66                                                  10                                                  70                                                6                                                74                                              2                                              78                                            80                                               4                                               76                                                 8                                                 72                                                   12                                                   68                                                    16                                                    64                                                     20                                                     60                                                      24                                                      56                                                       28                                                       52                                                       32                                                       48                                                       36                                                       44                                                       40   
                                                                                  5698764637629617753676613712609280 - 748147546532769485874063802947811726589952000*sin  (1) - 748147546532769485874063802947811726589952000*sin  (1) - 505664942518195976618438380648520969355264000*sin  (1) - 505664942518195976618438380648520969355264000*sin  (1) - 229234773941582176067025399227329506107719680*sin  (1) - 229234773941582176067025399227329506107719680*sin  (1) - 68574505025259625319195632247491732596326400*sin  (1) - 68574505025259625319195632247491732596326400*sin  (1) - 13174412295493228509599160875133879661363200*sin  (1) - 13174412295493228509599160875133879661363200*sin  (1) - 1558263819897048533393449135768523400806400*sin  (1) - 1558263819897048533393449135768523400806400*sin  (1) - 106245260447526036367735168347853868236800*sin  (1) - 106245260447526036367735168347853868236800*sin  (1) - 3749832721677389518861241235806607114240*sin  (1) - 3749832721677389518861241235806607114240*sin  (1) - 56303794619780623406324943480579686400*sin (1) - 56303794619780623406324943480579686400*sin  (1) - 227950585505184710147064548504371200*sin (1) - 227950585505184710147064548504371200*sin  (1) + 5698764637629617753676613712609280*sin  (1) + 4445036417351101847867758695835238400*sin (1) + 4445036417351101847867758695835238400*sin  (1) + 520810100232970766508505727195362099200*sin (1) + 520810100232970766508505727195362099200*sin  (1) + 21874024209784772193357240542205208166400*sin  (1) + 21874024209784772193357240542205208166400*sin  (1) + 438261699346044900016907569434897206476800*sin  (1) + 438261699346044900016907569434897206476800*sin  (1) + 4830617841680850453519692320882422542499840*sin  (1) + 4830617841680850453519692320882422542499840*sin  (1) + 31838163047441968898197972114906875848294400*sin  (1) + 31838163047441968898197972114906875848294400*sin  (1) + 132250831120143563115591576477305484292915200*sin  (1) + 132250831120143563115591576477305484292915200*sin  (1) + 358179334283722150104727186292702353293312000*sin  (1) + 358179334283722150104727186292702353293312000*sin  (1) + 646127426551028192345782375273110127509504000*sin  (1) + 646127426551028192345782375273110127509504000*sin  (1) + 785554923859407960167766993095202312919449600*sin  (1)
$$\frac{340212685864987900195 \log{\left(1 - \sin{\left(1 \right)} \right)}}{604462909807314587353088} - \frac{340212685864987900195 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{604462909807314587353088} + \frac{- 423138206006477030060483725542236950621690 \sin^{33}{\left(1 \right)} - 183278674117764655837822180587996783817780 \sin^{29}{\left(1 \right)} - 651634272201573798158562826772680644471930 \sin^{37}{\left(1 \right)} - 52013001206768719399943451095528437227156 \sin^{25}{\left(1 \right)} - 675306851542052733640415353916219288522910 \sin^{41}{\left(1 \right)} - 9389559960251275607823457051972789617900 \sin^{21}{\left(1 \right)} - 471334679766267909595294953479074642546798 \sin^{45}{\left(1 \right)} - 1029599217799588076866103913920036880300 \sin^{17}{\left(1 \right)} - 219998946702561507267540370671220043857980 \sin^{49}{\left(1 \right)} - 67592827521963873520061232554287441286140 \sin^{53}{\left(1 \right)} - 63770763296437278131358376843813441425 \sin^{13}{\left(1 \right)} - 13309153005670459691745651789948171689700 \sin^{57}{\left(1 \right)} - 1976183957651747501065861188470302425 \sin^{9}{\left(1 \right)} - 1610466017759359066736073791565694157700 \sin^{61}{\left(1 \right)} - 24334266555867175125091681010702499 \sin^{5}{\left(1 \right)} - 112156463411265035482466005345855201755 \sin^{65}{\left(1 \right)} - 4037640791930574553690093174935054075 \sin^{69}{\left(1 \right)} - 61761978539693729609200292143364625 \sin^{73}{\left(1 \right)} - 254458679543808278381006718378825 \sin^{77}{\left(1 \right)} + 6414924694381721303722858446525 \sin^{79}{\left(1 \right)} + 4919391917298196010448269380691805 \sin^{75}{\left(1 \right)} + 566098266801909752379872595543726375 \sin^{71}{\left(1 \right)} + 6414924694381721303722858446525 \sin{\left(1 \right)} + 23324625637817735047876936498037796975 \sin^{67}{\left(1 \right)} + 1645129532999397639511197852490935 \sin^{3}{\left(1 \right)} + 457853404979551461940052123741775446100 \sin^{63}{\left(1 \right)} + 251670076529935246843013462050145775 \sin^{7}{\left(1 \right)} + 4936957406516226265941098468664665946900 \sin^{59}{\left(1 \right)} + 12371635384088485900368733976428222725 \sin^{11}{\left(1 \right)} + 31778438627038426341743853627782455058796 \sin^{55}{\left(1 \right)} + 128665191930189149828868104556896257067980 \sin^{51}{\left(1 \right)} + 276869607161740690051451727581080329765 \sin^{15}{\left(1 \right)} + 338883026890723908708879932890888864797190 \sin^{47}{\left(1 \right)} + 3321613731455682561936969912260315135100 \sin^{19}{\left(1 \right)} + 592902335966441634657811024645127154455430 \sin^{43}{\left(1 \right)} + 23441478500385305984432990632556605628700 \sin^{23}{\left(1 \right)} + 696874536950887358951996841236748284653410 \sin^{39}{\left(1 \right)} + 103093438806161793731524017808012524481540 \sin^{27}{\left(1 \right)} + 551950975838544779609279102131122881015698 \sin^{35}{\left(1 \right)} + 293199026473104431087337195212313668566980 \sin^{31}{\left(1 \right)}}{- 505664942518195976618438380648520969355264000 \sin^{34}{\left(1 \right)} - 229234773941582176067025399227329506107719680 \sin^{30}{\left(1 \right)} - 748147546532769485874063802947811726589952000 \sin^{38}{\left(1 \right)} - 68574505025259625319195632247491732596326400 \sin^{26}{\left(1 \right)} - 748147546532769485874063802947811726589952000 \sin^{42}{\left(1 \right)} - 13174412295493228509599160875133879661363200 \sin^{22}{\left(1 \right)} - 505664942518195976618438380648520969355264000 \sin^{46}{\left(1 \right)} - 1558263819897048533393449135768523400806400 \sin^{18}{\left(1 \right)} - 229234773941582176067025399227329506107719680 \sin^{50}{\left(1 \right)} - 106245260447526036367735168347853868236800 \sin^{14}{\left(1 \right)} - 68574505025259625319195632247491732596326400 \sin^{54}{\left(1 \right)} - 3749832721677389518861241235806607114240 \sin^{10}{\left(1 \right)} - 13174412295493228509599160875133879661363200 \sin^{58}{\left(1 \right)} - 1558263819897048533393449135768523400806400 \sin^{62}{\left(1 \right)} - 56303794619780623406324943480579686400 \sin^{6}{\left(1 \right)} - 106245260447526036367735168347853868236800 \sin^{66}{\left(1 \right)} - 227950585505184710147064548504371200 \sin^{2}{\left(1 \right)} - 3749832721677389518861241235806607114240 \sin^{70}{\left(1 \right)} - 56303794619780623406324943480579686400 \sin^{74}{\left(1 \right)} - 227950585505184710147064548504371200 \sin^{78}{\left(1 \right)} + 5698764637629617753676613712609280 \sin^{80}{\left(1 \right)} + 4445036417351101847867758695835238400 \sin^{76}{\left(1 \right)} + 520810100232970766508505727195362099200 \sin^{72}{\left(1 \right)} + 5698764637629617753676613712609280 + 21874024209784772193357240542205208166400 \sin^{68}{\left(1 \right)} + 4445036417351101847867758695835238400 \sin^{4}{\left(1 \right)} + 438261699346044900016907569434897206476800 \sin^{64}{\left(1 \right)} + 520810100232970766508505727195362099200 \sin^{8}{\left(1 \right)} + 4830617841680850453519692320882422542499840 \sin^{60}{\left(1 \right)} + 31838163047441968898197972114906875848294400 \sin^{56}{\left(1 \right)} + 21874024209784772193357240542205208166400 \sin^{12}{\left(1 \right)} + 132250831120143563115591576477305484292915200 \sin^{52}{\left(1 \right)} + 438261699346044900016907569434897206476800 \sin^{16}{\left(1 \right)} + 358179334283722150104727186292702353293312000 \sin^{48}{\left(1 \right)} + 4830617841680850453519692320882422542499840 \sin^{20}{\left(1 \right)} + 646127426551028192345782375273110127509504000 \sin^{44}{\left(1 \right)} + 31838163047441968898197972114906875848294400 \sin^{24}{\left(1 \right)} + 785554923859407960167766993095202312919449600 \sin^{40}{\left(1 \right)} + 132250831120143563115591576477305484292915200 \sin^{28}{\left(1 \right)} + 646127426551028192345782375273110127509504000 \sin^{36}{\left(1 \right)} + 358179334283722150104727186292702353293312000 \sin^{32}{\left(1 \right)}}$$ 
=
= 
                                                                                                                                                                                                                   41                                                    37                                                    45                                                    33                                                    49                                                    29                                                   53                                                   25                                                   57                                                  21                                                  61                                                  17                                                 65                                                13                                               69                                               9                                             73                                             5                                           77                                         79                                                                                     3                                            75                                              7                                              71                                                11                                                67                                                 15                                                 63                                                  19                                                  59                                                   23                                                   55                                                    27                                                    51                                                    31                                                    47                                                    35                                                    43                                                    39                                                                                   
  340212685864987900195*log(1 + sin(1))   340212685864987900195*log(1 - sin(1))                                                                                    - 675306851542052733640415353916219288522910*sin  (1) - 651634272201573798158562826772680644471930*sin  (1) - 471334679766267909595294953479074642546798*sin  (1) - 423138206006477030060483725542236950621690*sin  (1) - 219998946702561507267540370671220043857980*sin  (1) - 183278674117764655837822180587996783817780*sin  (1) - 67592827521963873520061232554287441286140*sin  (1) - 52013001206768719399943451095528437227156*sin  (1) - 13309153005670459691745651789948171689700*sin  (1) - 9389559960251275607823457051972789617900*sin  (1) - 1610466017759359066736073791565694157700*sin  (1) - 1029599217799588076866103913920036880300*sin  (1) - 112156463411265035482466005345855201755*sin  (1) - 63770763296437278131358376843813441425*sin  (1) - 4037640791930574553690093174935054075*sin  (1) - 1976183957651747501065861188470302425*sin (1) - 61761978539693729609200292143364625*sin  (1) - 24334266555867175125091681010702499*sin (1) - 254458679543808278381006718378825*sin  (1) + 6414924694381721303722858446525*sin  (1) + 6414924694381721303722858446525*sin(1) + 1645129532999397639511197852490935*sin (1) + 4919391917298196010448269380691805*sin  (1) + 251670076529935246843013462050145775*sin (1) + 566098266801909752379872595543726375*sin  (1) + 12371635384088485900368733976428222725*sin  (1) + 23324625637817735047876936498037796975*sin  (1) + 276869607161740690051451727581080329765*sin  (1) + 457853404979551461940052123741775446100*sin  (1) + 3321613731455682561936969912260315135100*sin  (1) + 4936957406516226265941098468664665946900*sin  (1) + 23441478500385305984432990632556605628700*sin  (1) + 31778438627038426341743853627782455058796*sin  (1) + 103093438806161793731524017808012524481540*sin  (1) + 128665191930189149828868104556896257067980*sin  (1) + 293199026473104431087337195212313668566980*sin  (1) + 338883026890723908708879932890888864797190*sin  (1) + 551950975838544779609279102131122881015698*sin  (1) + 592902335966441634657811024645127154455430*sin  (1) + 696874536950887358951996841236748284653410*sin  (1)                                                                                
- ------------------------------------- + ------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
         604462909807314587353088                604462909807314587353088                                                                                               38                                                       42                                                       34                                                       46                                                       30                                                       50                                                      26                                                      54                                                      22                                                      58                                                     18                                                     62                                                    14                                                    66                                                  10                                                  70                                                6                                                74                                              2                                              78                                            80                                               4                                               76                                                 8                                                 72                                                   12                                                   68                                                    16                                                    64                                                     20                                                     60                                                      24                                                      56                                                       28                                                       52                                                       32                                                       48                                                       36                                                       44                                                       40   
                                                                                  5698764637629617753676613712609280 - 748147546532769485874063802947811726589952000*sin  (1) - 748147546532769485874063802947811726589952000*sin  (1) - 505664942518195976618438380648520969355264000*sin  (1) - 505664942518195976618438380648520969355264000*sin  (1) - 229234773941582176067025399227329506107719680*sin  (1) - 229234773941582176067025399227329506107719680*sin  (1) - 68574505025259625319195632247491732596326400*sin  (1) - 68574505025259625319195632247491732596326400*sin  (1) - 13174412295493228509599160875133879661363200*sin  (1) - 13174412295493228509599160875133879661363200*sin  (1) - 1558263819897048533393449135768523400806400*sin  (1) - 1558263819897048533393449135768523400806400*sin  (1) - 106245260447526036367735168347853868236800*sin  (1) - 106245260447526036367735168347853868236800*sin  (1) - 3749832721677389518861241235806607114240*sin  (1) - 3749832721677389518861241235806607114240*sin  (1) - 56303794619780623406324943480579686400*sin (1) - 56303794619780623406324943480579686400*sin  (1) - 227950585505184710147064548504371200*sin (1) - 227950585505184710147064548504371200*sin  (1) + 5698764637629617753676613712609280*sin  (1) + 4445036417351101847867758695835238400*sin (1) + 4445036417351101847867758695835238400*sin  (1) + 520810100232970766508505727195362099200*sin (1) + 520810100232970766508505727195362099200*sin  (1) + 21874024209784772193357240542205208166400*sin  (1) + 21874024209784772193357240542205208166400*sin  (1) + 438261699346044900016907569434897206476800*sin  (1) + 438261699346044900016907569434897206476800*sin  (1) + 4830617841680850453519692320882422542499840*sin  (1) + 4830617841680850453519692320882422542499840*sin  (1) + 31838163047441968898197972114906875848294400*sin  (1) + 31838163047441968898197972114906875848294400*sin  (1) + 132250831120143563115591576477305484292915200*sin  (1) + 132250831120143563115591576477305484292915200*sin  (1) + 358179334283722150104727186292702353293312000*sin  (1) + 358179334283722150104727186292702353293312000*sin  (1) + 646127426551028192345782375273110127509504000*sin  (1) + 646127426551028192345782375273110127509504000*sin  (1) + 785554923859407960167766993095202312919449600*sin  (1)
$$\frac{340212685864987900195 \log{\left(1 - \sin{\left(1 \right)} \right)}}{604462909807314587353088} - \frac{340212685864987900195 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{604462909807314587353088} + \frac{- 423138206006477030060483725542236950621690 \sin^{33}{\left(1 \right)} - 183278674117764655837822180587996783817780 \sin^{29}{\left(1 \right)} - 651634272201573798158562826772680644471930 \sin^{37}{\left(1 \right)} - 52013001206768719399943451095528437227156 \sin^{25}{\left(1 \right)} - 675306851542052733640415353916219288522910 \sin^{41}{\left(1 \right)} - 9389559960251275607823457051972789617900 \sin^{21}{\left(1 \right)} - 471334679766267909595294953479074642546798 \sin^{45}{\left(1 \right)} - 1029599217799588076866103913920036880300 \sin^{17}{\left(1 \right)} - 219998946702561507267540370671220043857980 \sin^{49}{\left(1 \right)} - 67592827521963873520061232554287441286140 \sin^{53}{\left(1 \right)} - 63770763296437278131358376843813441425 \sin^{13}{\left(1 \right)} - 13309153005670459691745651789948171689700 \sin^{57}{\left(1 \right)} - 1976183957651747501065861188470302425 \sin^{9}{\left(1 \right)} - 1610466017759359066736073791565694157700 \sin^{61}{\left(1 \right)} - 24334266555867175125091681010702499 \sin^{5}{\left(1 \right)} - 112156463411265035482466005345855201755 \sin^{65}{\left(1 \right)} - 4037640791930574553690093174935054075 \sin^{69}{\left(1 \right)} - 61761978539693729609200292143364625 \sin^{73}{\left(1 \right)} - 254458679543808278381006718378825 \sin^{77}{\left(1 \right)} + 6414924694381721303722858446525 \sin^{79}{\left(1 \right)} + 4919391917298196010448269380691805 \sin^{75}{\left(1 \right)} + 566098266801909752379872595543726375 \sin^{71}{\left(1 \right)} + 6414924694381721303722858446525 \sin{\left(1 \right)} + 23324625637817735047876936498037796975 \sin^{67}{\left(1 \right)} + 1645129532999397639511197852490935 \sin^{3}{\left(1 \right)} + 457853404979551461940052123741775446100 \sin^{63}{\left(1 \right)} + 251670076529935246843013462050145775 \sin^{7}{\left(1 \right)} + 4936957406516226265941098468664665946900 \sin^{59}{\left(1 \right)} + 12371635384088485900368733976428222725 \sin^{11}{\left(1 \right)} + 31778438627038426341743853627782455058796 \sin^{55}{\left(1 \right)} + 128665191930189149828868104556896257067980 \sin^{51}{\left(1 \right)} + 276869607161740690051451727581080329765 \sin^{15}{\left(1 \right)} + 338883026890723908708879932890888864797190 \sin^{47}{\left(1 \right)} + 3321613731455682561936969912260315135100 \sin^{19}{\left(1 \right)} + 592902335966441634657811024645127154455430 \sin^{43}{\left(1 \right)} + 23441478500385305984432990632556605628700 \sin^{23}{\left(1 \right)} + 696874536950887358951996841236748284653410 \sin^{39}{\left(1 \right)} + 103093438806161793731524017808012524481540 \sin^{27}{\left(1 \right)} + 551950975838544779609279102131122881015698 \sin^{35}{\left(1 \right)} + 293199026473104431087337195212313668566980 \sin^{31}{\left(1 \right)}}{- 505664942518195976618438380648520969355264000 \sin^{34}{\left(1 \right)} - 229234773941582176067025399227329506107719680 \sin^{30}{\left(1 \right)} - 748147546532769485874063802947811726589952000 \sin^{38}{\left(1 \right)} - 68574505025259625319195632247491732596326400 \sin^{26}{\left(1 \right)} - 748147546532769485874063802947811726589952000 \sin^{42}{\left(1 \right)} - 13174412295493228509599160875133879661363200 \sin^{22}{\left(1 \right)} - 505664942518195976618438380648520969355264000 \sin^{46}{\left(1 \right)} - 1558263819897048533393449135768523400806400 \sin^{18}{\left(1 \right)} - 229234773941582176067025399227329506107719680 \sin^{50}{\left(1 \right)} - 106245260447526036367735168347853868236800 \sin^{14}{\left(1 \right)} - 68574505025259625319195632247491732596326400 \sin^{54}{\left(1 \right)} - 3749832721677389518861241235806607114240 \sin^{10}{\left(1 \right)} - 13174412295493228509599160875133879661363200 \sin^{58}{\left(1 \right)} - 1558263819897048533393449135768523400806400 \sin^{62}{\left(1 \right)} - 56303794619780623406324943480579686400 \sin^{6}{\left(1 \right)} - 106245260447526036367735168347853868236800 \sin^{66}{\left(1 \right)} - 227950585505184710147064548504371200 \sin^{2}{\left(1 \right)} - 3749832721677389518861241235806607114240 \sin^{70}{\left(1 \right)} - 56303794619780623406324943480579686400 \sin^{74}{\left(1 \right)} - 227950585505184710147064548504371200 \sin^{78}{\left(1 \right)} + 5698764637629617753676613712609280 \sin^{80}{\left(1 \right)} + 4445036417351101847867758695835238400 \sin^{76}{\left(1 \right)} + 520810100232970766508505727195362099200 \sin^{72}{\left(1 \right)} + 5698764637629617753676613712609280 + 21874024209784772193357240542205208166400 \sin^{68}{\left(1 \right)} + 4445036417351101847867758695835238400 \sin^{4}{\left(1 \right)} + 438261699346044900016907569434897206476800 \sin^{64}{\left(1 \right)} + 520810100232970766508505727195362099200 \sin^{8}{\left(1 \right)} + 4830617841680850453519692320882422542499840 \sin^{60}{\left(1 \right)} + 31838163047441968898197972114906875848294400 \sin^{56}{\left(1 \right)} + 21874024209784772193357240542205208166400 \sin^{12}{\left(1 \right)} + 132250831120143563115591576477305484292915200 \sin^{52}{\left(1 \right)} + 438261699346044900016907569434897206476800 \sin^{16}{\left(1 \right)} + 358179334283722150104727186292702353293312000 \sin^{48}{\left(1 \right)} + 4830617841680850453519692320882422542499840 \sin^{20}{\left(1 \right)} + 646127426551028192345782375273110127509504000 \sin^{44}{\left(1 \right)} + 31838163047441968898197972114906875848294400 \sin^{24}{\left(1 \right)} + 785554923859407960167766993095202312919449600 \sin^{40}{\left(1 \right)} + 132250831120143563115591576477305484292915200 \sin^{28}{\left(1 \right)} + 646127426551028192345782375273110127509504000 \sin^{36}{\left(1 \right)} + 358179334283722150104727186292702353293312000 \sin^{32}{\left(1 \right)}}$$ 
-340212685864987900195*log(1 + sin(1))/604462909807314587353088 + 340212685864987900195*log(1 - sin(1))/604462909807314587353088 + (-675306851542052733640415353916219288522910*sin(1)^41 - 651634272201573798158562826772680644471930*sin(1)^37 - 471334679766267909595294953479074642546798*sin(1)^45 - 423138206006477030060483725542236950621690*sin(1)^33 - 219998946702561507267540370671220043857980*sin(1)^49 - 183278674117764655837822180587996783817780*sin(1)^29 - 67592827521963873520061232554287441286140*sin(1)^53 - 52013001206768719399943451095528437227156*sin(1)^25 - 13309153005670459691745651789948171689700*sin(1)^57 - 9389559960251275607823457051972789617900*sin(1)^21 - 1610466017759359066736073791565694157700*sin(1)^61 - 1029599217799588076866103913920036880300*sin(1)^17 - 112156463411265035482466005345855201755*sin(1)^65 - 63770763296437278131358376843813441425*sin(1)^13 - 4037640791930574553690093174935054075*sin(1)^69 - 1976183957651747501065861188470302425*sin(1)^9 - 61761978539693729609200292143364625*sin(1)^73 - 24334266555867175125091681010702499*sin(1)^5 - 254458679543808278381006718378825*sin(1)^77 + 6414924694381721303722858446525*sin(1)^79 + 6414924694381721303722858446525*sin(1) + 1645129532999397639511197852490935*sin(1)^3 + 4919391917298196010448269380691805*sin(1)^75 + 251670076529935246843013462050145775*sin(1)^7 + 566098266801909752379872595543726375*sin(1)^71 + 12371635384088485900368733976428222725*sin(1)^11 + 23324625637817735047876936498037796975*sin(1)^67 + 276869607161740690051451727581080329765*sin(1)^15 + 457853404979551461940052123741775446100*sin(1)^63 + 3321613731455682561936969912260315135100*sin(1)^19 + 4936957406516226265941098468664665946900*sin(1)^59 + 23441478500385305984432990632556605628700*sin(1)^23 + 31778438627038426341743853627782455058796*sin(1)^55 + 103093438806161793731524017808012524481540*sin(1)^27 + 128665191930189149828868104556896257067980*sin(1)^51 + 293199026473104431087337195212313668566980*sin(1)^31 + 338883026890723908708879932890888864797190*sin(1)^47 + 551950975838544779609279102131122881015698*sin(1)^35 + 592902335966441634657811024645127154455430*sin(1)^43 + 696874536950887358951996841236748284653410*sin(1)^39)/(5698764637629617753676613712609280 - 748147546532769485874063802947811726589952000*sin(1)^38 - 748147546532769485874063802947811726589952000*sin(1)^42 - 505664942518195976618438380648520969355264000*sin(1)^34 - 505664942518195976618438380648520969355264000*sin(1)^46 - 229234773941582176067025399227329506107719680*sin(1)^30 - 229234773941582176067025399227329506107719680*sin(1)^50 - 68574505025259625319195632247491732596326400*sin(1)^26 - 68574505025259625319195632247491732596326400*sin(1)^54 - 13174412295493228509599160875133879661363200*sin(1)^22 - 13174412295493228509599160875133879661363200*sin(1)^58 - 1558263819897048533393449135768523400806400*sin(1)^18 - 1558263819897048533393449135768523400806400*sin(1)^62 - 106245260447526036367735168347853868236800*sin(1)^14 - 106245260447526036367735168347853868236800*sin(1)^66 - 3749832721677389518861241235806607114240*sin(1)^10 - 3749832721677389518861241235806607114240*sin(1)^70 - 56303794619780623406324943480579686400*sin(1)^6 - 56303794619780623406324943480579686400*sin(1)^74 - 227950585505184710147064548504371200*sin(1)^2 - 227950585505184710147064548504371200*sin(1)^78 + 5698764637629617753676613712609280*sin(1)^80 + 4445036417351101847867758695835238400*sin(1)^4 + 4445036417351101847867758695835238400*sin(1)^76 + 520810100232970766508505727195362099200*sin(1)^8 + 520810100232970766508505727195362099200*sin(1)^72 + 21874024209784772193357240542205208166400*sin(1)^12 + 21874024209784772193357240542205208166400*sin(1)^68 + 438261699346044900016907569434897206476800*sin(1)^16 + 438261699346044900016907569434897206476800*sin(1)^64 + 4830617841680850453519692320882422542499840*sin(1)^20 + 4830617841680850453519692320882422542499840*sin(1)^60 + 31838163047441968898197972114906875848294400*sin(1)^24 + 31838163047441968898197972114906875848294400*sin(1)^56 + 132250831120143563115591576477305484292915200*sin(1)^28 + 132250831120143563115591576477305484292915200*sin(1)^52 + 358179334283722150104727186292702353293312000*sin(1)^32 + 358179334283722150104727186292702353293312000*sin(1)^48 + 646127426551028192345782375273110127509504000*sin(1)^36 + 646127426551028192345782375273110127509504000*sin(1)^44 + 785554923859407960167766993095202312919449600*sin(1)^40)
Respuesta numérica [src] 
2.56264893374785e+19
2.56264893374785e+19

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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