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Resolución de integrales/ a*sinh(x)*tanh(x)/(a^2+(b+cosh(x))^2)

Integral de a*sinh(x)*tanh(x)/(a^2+(b+cosh(x))^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                       
  /                       
 |                        
 |   a*sinh(x)*tanh(x)    
 |  ------------------- dx
 |   2                2   
 |  a  + (b + cosh(x))    
 |                        
/                         
-oo
∫−∞∞asinh⁡(x)tanh⁡(x)a2+(b+cosh⁡(x))2 dx\int\limits_{-\infty}^{\infty} \frac{a \sinh{\left(x \right)} \tanh{\left(x \right)}}{a^{2} + \left(b + \cosh{\left(x \right)}\right)^{2}}\, dx 
Integral(((a*sinh(x))*tanh(x))/(a^2 + (b + cosh(x))^2), (x, -oo, oo))
Respuesta (Indefinida) [src] 
  /                                 /                                   
 |                                 |                                    
 |  a*sinh(x)*tanh(x)              |         sinh(x)*tanh(x)            
 | ------------------- dx = C + a* | -------------------------------- dx
 |  2                2             |  2    2       2                    
 | a  + (b + cosh(x))              | a  + b  + cosh (x) + 2*b*cosh(x)   
 |                                 |                                    
/                                 /
∫asinh⁡(x)tanh⁡(x)a2+(b+cosh⁡(x))2 dx=C+a∫sinh⁡(x)tanh⁡(x)a2+b2+2bcosh⁡(x)+cosh⁡2(x) dx\int \frac{a \sinh{\left(x \right)} \tanh{\left(x \right)}}{a^{2} + \left(b + \cosh{\left(x \right)}\right)^{2}}\, dx = C + a \int \frac{\sinh{\left(x \right)} \tanh{\left(x \right)}}{a^{2} + b^{2} + 2 b \cosh{\left(x \right)} + \cosh^{2}{\left(x \right)}}\, dx
Simplificar
Respuesta [src] 
   oo                                    
    /                                    
   |                                     
   |          sinh(x)*tanh(x)            
a* |  -------------------------------- dx
   |   2    2       2                    
   |  a  + b  + cosh (x) + 2*b*cosh(x)   
   |                                     
  /                                      
  -oo
a∫−∞∞sinh⁡(x)tanh⁡(x)a2+b2+2bcosh⁡(x)+cosh⁡2(x) dxa \int\limits_{-\infty}^{\infty} \frac{\sinh{\left(x \right)} \tanh{\left(x \right)}}{a^{2} + b^{2} + 2 b \cosh{\left(x \right)} + \cosh^{2}{\left(x \right)}}\, dx 
=
= 
   oo                                    
    /                                    
   |                                     
   |          sinh(x)*tanh(x)            
a* |  -------------------------------- dx
   |   2    2       2                    
   |  a  + b  + cosh (x) + 2*b*cosh(x)   
   |                                     
  /                                      
  -oo
a∫−∞∞sinh⁡(x)tanh⁡(x)a2+b2+2bcosh⁡(x)+cosh⁡2(x) dxa \int\limits_{-\infty}^{\infty} \frac{\sinh{\left(x \right)} \tanh{\left(x \right)}}{a^{2} + b^{2} + 2 b \cosh{\left(x \right)} + \cosh^{2}{\left(x \right)}}\, dx 
a*Integral(sinh(x)*tanh(x)/(a^2 + b^2 + cosh(x)^2 + 2*b*cosh(x)), (x, -oo, oo))

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

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