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Resolución de integrales/ sinh^2(x)/ sinh2x/sqrt(1-sinh^2(x))

Integral de sinh2x/sqrt(1-sinh^2(x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1/2                    
   /                     
  |                      
  |      sinh(2*x)       
  |  ----------------- dx
  |     ______________   
  |    /         2       
  |  \/  1 - sinh (x)    
  |                      
 /                       
-1/2
$$\int\limits_{- \frac{1}{2}}^{\frac{1}{2}} \frac{\sinh{\left(2 x \right)}}{\sqrt{1 - \sinh^{2}{\left(x \right)}}}\, dx$$ 
Integral(sinh(2*x)/sqrt(1 - sinh(x)^2), (x, -1/2, 1/2))
Respuesta (Indefinida) [src] 
  /                             /                                    
 |                             |                                     
 |     sinh(2*x)               |             sinh(2*x)               
 | ----------------- dx = C +  | --------------------------------- dx
 |    ______________           |   _______________________________   
 |   /         2               | \/ -(1 + sinh(x))*(-1 + sinh(x))    
 | \/  1 - sinh (x)            |                                     
 |                            /                                      
/
$$\int \frac{\sinh{\left(2 x \right)}}{\sqrt{1 - \sinh^{2}{\left(x \right)}}}\, dx = C + \int \frac{\sinh{\left(2 x \right)}}{\sqrt{- \left(\sinh{\left(x \right)} - 1\right) \left(\sinh{\left(x \right)} + 1\right)}}\, dx$$
Simplificar
Respuesta [src] 
  1/2                                    
   /                                     
  |                                      
  |              sinh(2*x)               
  |  --------------------------------- dx
  |    _______________________________   
  |  \/ -(1 + sinh(x))*(-1 + sinh(x))    
  |                                      
 /                                       
-1/2
$$\int\limits_{- \frac{1}{2}}^{\frac{1}{2}} \frac{\sinh{\left(2 x \right)}}{\sqrt{- \left(\sinh{\left(x \right)} - 1\right) \left(\sinh{\left(x \right)} + 1\right)}}\, dx$$ 
=
= 
  1/2                                    
   /                                     
  |                                      
  |              sinh(2*x)               
  |  --------------------------------- dx
  |    _______________________________   
  |  \/ -(1 + sinh(x))*(-1 + sinh(x))    
  |                                      
 /                                       
-1/2
$$\int\limits_{- \frac{1}{2}}^{\frac{1}{2}} \frac{\sinh{\left(2 x \right)}}{\sqrt{- \left(\sinh{\left(x \right)} - 1\right) \left(\sinh{\left(x \right)} + 1\right)}}\, dx$$ 
Integral(sinh(2*x)/sqrt(-(1 + sinh(x))*(-1 + sinh(x))), (x, -1/2, 1/2))
Respuesta numérica [src] 
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    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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