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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  3             
  /             
 |              
 |      1       
 |  --------- dx
 |     3        
 |  sin (2*x)   
 |              
/               
2
$$\int\limits_{2}^{3} \frac{1}{\sin^{3}{\left(2 x \right)}}\, dx$$ 
Integral(1/(sin(2*x)^3), (x, 2, 3))
Respuesta (Indefinida) [src] 
  /                                                                                
 |                                                                                 
 |     1              log(1 + cos(2*x))   log(-1 + cos(2*x))         cos(2*x)      
 | --------- dx = C - ----------------- + ------------------ + --------------------
 |    3                       8                   8              /          2     \
 | sin (2*x)                                                   2*\-2 + 2*cos (2*x)/
 |                                                                                 
/
$$\int \frac{1}{\sin^{3}{\left(2 x \right)}}\, dx = C + \frac{\log{\left(\cos{\left(2 x \right)} - 1 \right)}}{8} - \frac{\log{\left(\cos{\left(2 x \right)} + 1 \right)}}{8} + \frac{\cos{\left(2 x \right)}}{2 \left(2 \cos^{2}{\left(2 x \right)} - 2\right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
  log(1 - cos(4))   log(1 + cos(6))   log(1 - cos(6))   log(1 + cos(4))         cos(6)               cos(4)      
- --------------- - --------------- + --------------- + --------------- + ------------------ - ------------------
         8                 8                 8                 8            /          2   \     /          2   \
                                                                          2*\-2 + 2*cos (6)/   2*\-2 + 2*cos (4)/
$$\frac{\cos{\left(6 \right)}}{2 \left(-2 + 2 \cos^{2}{\left(6 \right)}\right)} + \frac{\log{\left(1 - \cos{\left(6 \right)} \right)}}{8} - \frac{\cos{\left(4 \right)}}{2 \left(-2 + 2 \cos^{2}{\left(4 \right)}\right)} + \frac{\log{\left(\cos{\left(4 \right)} + 1 \right)}}{8} - \frac{\log{\left(\cos{\left(6 \right)} + 1 \right)}}{8} - \frac{\log{\left(1 - \cos{\left(4 \right)} \right)}}{8}$$ 
=
= 
  log(1 - cos(4))   log(1 + cos(6))   log(1 - cos(6))   log(1 + cos(4))         cos(6)               cos(4)      
- --------------- - --------------- + --------------- + --------------- + ------------------ - ------------------
         8                 8                 8                 8            /          2   \     /          2   \
                                                                          2*\-2 + 2*cos (6)/   2*\-2 + 2*cos (4)/
$$\frac{\cos{\left(6 \right)}}{2 \left(-2 + 2 \cos^{2}{\left(6 \right)}\right)} + \frac{\log{\left(1 - \cos{\left(6 \right)} \right)}}{8} - \frac{\cos{\left(4 \right)}}{2 \left(-2 + 2 \cos^{2}{\left(4 \right)}\right)} + \frac{\log{\left(\cos{\left(4 \right)} + 1 \right)}}{8} - \frac{\log{\left(\cos{\left(6 \right)} + 1 \right)}}{8} - \frac{\log{\left(1 - \cos{\left(4 \right)} \right)}}{8}$$ 
-log(1 - cos(4))/8 - log(1 + cos(6))/8 + log(1 - cos(6))/8 + log(1 + cos(4))/8 + cos(6)/(2*(-2 + 2*cos(6)^2)) - cos(4)/(2*(-2 + 2*cos(4)^2))
Respuesta numérica [src] 
-4.04233004739611
-4.04233004739611

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

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