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Integral de cos4x/sin^34x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1            
  /            
 |             
 |  cos(4*x)   
 |  -------- dx
 |     34      
 |  sin  (x)   
 |             
/              
0              
$$\int\limits_{0}^{1} \frac{\cos{\left(4 x \right)}}{\sin^{34}{\left(x \right)}}\, dx$$
Integral(cos(4*x)/sin(x)^34, (x, 0, 1))
Respuesta (Indefinida) [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)
 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             
/                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              
$$\int \frac{\cos{\left(4 x \right)}}{\sin^{34}{\left(x \right)}}\, dx = C - \frac{\cot^{33}{\left(x \right)}}{33} - \frac{16 \cot^{31}{\left(x \right)}}{31} - \frac{120 \cot^{29}{\left(x \right)}}{29} - \frac{560 \cot^{27}{\left(x \right)}}{27} - \frac{364 \cot^{25}{\left(x \right)}}{5} - \frac{4368 \cot^{23}{\left(x \right)}}{23} - \frac{1144 \cot^{21}{\left(x \right)}}{3} - \frac{11440 \cot^{19}{\left(x \right)}}{19} - \frac{12870 \cot^{17}{\left(x \right)}}{17} - \frac{2288 \cot^{15}{\left(x \right)}}{3} - 616 \cot^{13}{\left(x \right)} - \frac{4368 \cot^{11}{\left(x \right)}}{11} - \frac{1820 \cot^{9}{\left(x \right)}}{9} - 80 \cot^{7}{\left(x \right)} - 24 \cot^{5}{\left(x \right)} - \frac{16 \cot^{3}{\left(x \right)}}{3} - \cot{\left(x \right)} - \frac{268435456 \cos{\left(x \right)}}{4508102925 \sin{\left(x \right)}} - \frac{134217728 \cos{\left(x \right)}}{4508102925 \sin^{3}{\left(x \right)}} - \frac{33554432 \cos{\left(x \right)}}{1502700975 \sin^{5}{\left(x \right)}} - \frac{16777216 \cos{\left(x \right)}}{901620585 \sin^{7}{\left(x \right)}} - \frac{14680064 \cos{\left(x \right)}}{901620585 \sin^{9}{\left(x \right)}} - \frac{7340032 \cos{\left(x \right)}}{500900325 \sin^{11}{\left(x \right)}} - \frac{20185088 \cos{\left(x \right)}}{1502700975 \sin^{13}{\left(x \right)}} - \frac{18743296 \cos{\left(x \right)}}{1502700975 \sin^{15}{\left(x \right)}} - \frac{1171456 \cos{\left(x \right)}}{100180065 \sin^{17}{\left(x \right)}} - \frac{585728 \cos{\left(x \right)}}{53036505 \sin^{19}{\left(x \right)}} - \frac{146432 \cos{\left(x \right)}}{13956975 \sin^{21}{\left(x \right)}} - \frac{46592 \cos{\left(x \right)}}{4652325 \sin^{23}{\left(x \right)}} - \frac{5824 \cos{\left(x \right)}}{606825 \sin^{25}{\left(x \right)}} - \frac{224 \cos{\left(x \right)}}{24273 \sin^{27}{\left(x \right)}} - \frac{8 \cos{\left(x \right)}}{899 \sin^{29}{\left(x \right)}} + \frac{8 \cos{\left(x \right)}}{31 \sin^{31}{\left(x \right)}}$$
Respuesta numérica [src]
6.3854596469311e+626
6.3854596469311e+626

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