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Resolución de integrales/ (x-y)/ sh(x-y)shx/(chx)^2

Integral de sh(x-y)shx/(chx)^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                       
  /                       
 |                        
 |  sinh(x - y)*sinh(x)   
 |  ------------------- dx
 |            2           
 |        cosh (x)        
 |                        
/                         
0
∫01sinh⁡(x)sinh⁡(x−y)cosh⁡2(x) dx\int\limits_{0}^{1} \frac{\sinh{\left(x \right)} \sinh{\left(x - y \right)}}{\cosh^{2}{\left(x \right)}}\, dx 
Integral((sinh(x - y)*sinh(x))/cosh(x)^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                               /                      
 |                               |                       
 | sinh(x - y)*sinh(x)           | sinh(x)*sinh(x - y)   
 | ------------------- dx = C +  | ------------------- dx
 |           2                   |           2           
 |       cosh (x)                |       cosh (x)        
 |                               |                       
/                               /
∫sinh⁡(x)sinh⁡(x−y)cosh⁡2(x) dx=C+∫sinh⁡(x)sinh⁡(x−y)cosh⁡2(x) dx\int \frac{\sinh{\left(x \right)} \sinh{\left(x - y \right)}}{\cosh^{2}{\left(x \right)}}\, dx = C + \int \frac{\sinh{\left(x \right)} \sinh{\left(x - y \right)}}{\cosh^{2}{\left(x \right)}}\, dx
Simplificar
Respuesta [src] 
  1                       
  /                       
 |                        
 |  sinh(x)*sinh(x - y)   
 |  ------------------- dx
 |            2           
 |        cosh (x)        
 |                        
/                         
0
∫01sinh⁡(x)sinh⁡(x−y)cosh⁡2(x) dx\int\limits_{0}^{1} \frac{\sinh{\left(x \right)} \sinh{\left(x - y \right)}}{\cosh^{2}{\left(x \right)}}\, dx 
=
= 
  1                       
  /                       
 |                        
 |  sinh(x)*sinh(x - y)   
 |  ------------------- dx
 |            2           
 |        cosh (x)        
 |                        
/                         
0
∫01sinh⁡(x)sinh⁡(x−y)cosh⁡2(x) dx\int\limits_{0}^{1} \frac{\sinh{\left(x \right)} \sinh{\left(x - y \right)}}{\cosh^{2}{\left(x \right)}}\, dx 
Integral(sinh(x)*sinh(x - y)/cosh(x)^2, (x, 0, 1))

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

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