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Integral of cos4x/sin³4x dx

Limits of integration:

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The solution

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  1            
  /            
 |             
 |  cos(4*x)   
 |  -------- dx
 |     34      
 |  sin  (x)   
 |             
/              
0              
01cos(4x)sin34(x)dx\int\limits_{0}^{1} \frac{\cos{\left(4 x \right)}}{\sin^{34}{\left(x \right)}}\, dx
Integral(cos(4*x)/(sin(x)^34), (x, 0, 1))
The answer (Indefinite) [src]
  /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            
 |                                                                              17               19              11              23              15              9              21             27             25             29            3            31         33                                                                                                                                                                                                                                                                                                                          
 | cos(4*x)                          13            7            5      12870*cot  (x)   11440*cot  (x)   4368*cot  (x)   4368*cot  (x)   2288*cot  (x)   1820*cot (x)   1144*cot  (x)   560*cot  (x)   364*cot  (x)   120*cot  (x)   16*cot (x)   16*cot  (x)   cot  (x)    268435456*cos(x)    134217728*cos(x)     33554432*cos(x)       20185088*cos(x)       18743296*cos(x)      16777216*cos(x)     14680064*cos(x)      7340032*cos(x)       1171456*cos(x)       585728*cos(x)       146432*cos(x)       46592*cos(x)       5824*cos(x)       224*cos(x)       8*cos(x)       8*cos(x) 
 | -------- dx = C - cot(x) - 616*cot  (x) - 80*cot (x) - 24*cot (x) - -------------- - -------------- - ------------- - ------------- - ------------- - ------------ - ------------- - ------------ - ------------ - ------------ - ---------- - ----------- - -------- - ----------------- - ------------------ - ------------------ - ------------------- - ------------------- - ----------------- - ----------------- - ------------------ - ------------------ - ----------------- - ----------------- - ---------------- - --------------- - -------------- - ------------ + -----------
 |    34                                                                     17               19               11              23              3              9               3              27             5              29            3             31          33      4508102925*sin(x)                 3                    5                    13                    15                   7                   9                   11                   17                  19                  21                 23                25               27             29            31   
 | sin  (x)                                                                                                                                                                                                                                                                                    4508102925*sin (x)   1502700975*sin (x)   1502700975*sin  (x)   1502700975*sin  (x)   901620585*sin (x)   901620585*sin (x)   500900325*sin  (x)   100180065*sin  (x)   53036505*sin  (x)   13956975*sin  (x)   4652325*sin  (x)   606825*sin  (x)   24273*sin  (x)   899*sin  (x)   31*sin  (x)
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9917826435tan28x+99178264350tan26x+501401225325tan24x+1640949464700tan22x+3818363177475tan20x+6618496174290tan18x+8759774348325tan16x+8957363243400tan14x+7091245901025tan12x+4316410548450tan10x+1985548852287tan8x+668534967100tan6x+155607276825tan4x+22395091950tan2x+150270097549589132175tan33x+2(1502700975tan28x+12622688190tan26x+58605338025tan24x+182327718300tan22x+410237366175tan20x+694247850450tan18x+902522205585tan16x+910106425800tan14x+712517530725tan12x+429772478850tan10x+196200479475tan8x+65637978588tan6x+15193976525tan4x+2176325550tan2x+145422675)1502700975tan31x145422675tan28x+678639150tan26x+2646692685tan24x+7561979100tan22x+16174233075tan20x+26466926850tan18x+33592637925tan16x+33272708040tan14x+25688487825tan12x+15322957650tan10x+6931814175tan8x+2301471900tan6x+529338537tan4x+75404350tan2x+5014575145422675tan29x-{{9917826435\,\tan ^{28}x+99178264350\,\tan ^{26}x+501401225325\, \tan ^{24}x+1640949464700\,\tan ^{22}x+3818363177475\,\tan ^{20}x+ 6618496174290\,\tan ^{18}x+8759774348325\,\tan ^{16}x+8957363243400 \,\tan ^{14}x+7091245901025\,\tan ^{12}x+4316410548450\,\tan ^{10}x+ 1985548852287\,\tan ^8x+668534967100\,\tan ^6x+155607276825\,\tan ^4 x+22395091950\,\tan ^2x+1502700975}\over{49589132175\,\tan ^{33}x}}+ {{2\,\left(1502700975\,\tan ^{28}x+12622688190\,\tan ^{26}x+ 58605338025\,\tan ^{24}x+182327718300\,\tan ^{22}x+410237366175\, \tan ^{20}x+694247850450\,\tan ^{18}x+902522205585\,\tan ^{16}x+ 910106425800\,\tan ^{14}x+712517530725\,\tan ^{12}x+429772478850\, \tan ^{10}x+196200479475\,\tan ^8x+65637978588\,\tan ^6x+15193976525 \,\tan ^4x+2176325550\,\tan ^2x+145422675\right)}\over{1502700975\, \tan ^{31}x}}-{{145422675\,\tan ^{28}x+678639150\,\tan ^{26}x+ 2646692685\,\tan ^{24}x+7561979100\,\tan ^{22}x+16174233075\,\tan ^{ 20}x+26466926850\,\tan ^{18}x+33592637925\,\tan ^{16}x+33272708040\, \tan ^{14}x+25688487825\,\tan ^{12}x+15322957650\,\tan ^{10}x+ 6931814175\,\tan ^8x+2301471900\,\tan ^6x+529338537\,\tan ^4x+ 75404350\,\tan ^2x+5014575}\over{145422675\,\tan ^{29}x}}
Numerical answer [src]
6.3854596469311e+626
6.3854596469311e+626

    Use the examples entering the upper and lower limits of integration.