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Resolución de integrales/ cos(x)/ 1/sin/ sin(2x)/ cos(x)^3*1/sin(2x)^6

Integral de cos(x)^3*1/sin(2x)^6 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1             
  /             
 |              
 |      3       
 |   cos (x)    
 |  --------- dx
 |     6        
 |  sin (2*x)   
 |              
/               
0
∫01cos⁡3(x)sin⁡6(2x) dx\int\limits_{0}^{1} \frac{\cos^{3}{\left(x \right)}}{\sin^{6}{\left(2 x \right)}}\, dx 
Integral(cos(x)^3/sin(2*x)^6, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                  
 |                                                                                                                                                                   
 |     3                                                                  6            2             4             8                  4            2             6   
 |  cos (x)           7*log(-1 + sin(x))   7*log(1 + sin(x))   8 - 525*sin (x) + 24*sin (x) + 168*sin (x) + 315*sin (x)    8 - 175*sin (x) + 56*sin (x) + 105*sin (x)
 | --------- dx = C - ------------------ + ----------------- - -------------------------------------------------------- + -------------------------------------------
 |    6                      256                  256                   /        7            5            9   \             /        5            3            7   \
 | sin (2*x)                                                         64*\- 80*sin (x) + 40*sin (x) + 40*sin (x)/          64*\- 48*sin (x) + 24*sin (x) + 24*sin (x)/
 |                                                                                                                                                                   
/
∫cos⁡3(x)sin⁡6(2x) dx=C−7log⁡(sin⁡(x)−1)256+7log⁡(sin⁡(x)+1)256−315sin⁡8(x)−525sin⁡6(x)+168sin⁡4(x)+24sin⁡2(x)+864(40sin⁡9(x)−80sin⁡7(x)+40sin⁡5(x))+105sin⁡6(x)−175sin⁡4(x)+56sin⁡2(x)+864(24sin⁡7(x)−48sin⁡5(x)+24sin⁡3(x))\int \frac{\cos^{3}{\left(x \right)}}{\sin^{6}{\left(2 x \right)}}\, dx = C - \frac{7 \log{\left(\sin{\left(x \right)} - 1 \right)}}{256} + \frac{7 \log{\left(\sin{\left(x \right)} + 1 \right)}}{256} - \frac{315 \sin^{8}{\left(x \right)} - 525 \sin^{6}{\left(x \right)} + 168 \sin^{4}{\left(x \right)} + 24 \sin^{2}{\left(x \right)} + 8}{64 \left(40 \sin^{9}{\left(x \right)} - 80 \sin^{7}{\left(x \right)} + 40 \sin^{5}{\left(x \right)}\right)} + \frac{105 \sin^{6}{\left(x \right)} - 175 \sin^{4}{\left(x \right)} + 56 \sin^{2}{\left(x \right)} + 8}{64 \left(24 \sin^{7}{\left(x \right)} - 48 \sin^{5}{\left(x \right)} + 24 \sin^{3}{\left(x \right)}\right)}
Simplificar
Respuesta numérica [src] 
1.09548049849947e+93
1.09548049849947e+93

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

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