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Solving integrals/ sh(x-y)shx/(chx)^2

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

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The solution

You have entered [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))
The answer (Indefinite) [src] 
  /                               /                      
 |                               |                       
 | sinh(x - y)*sinh(x)           | sinh(x)*sinh(x - y)   
 | ------------------- dx = C +  | ------------------- dx
 |           2                   |           2           
 |       cosh (x)                |       cosh (x)        
 |                               |                       
/                               /
−e2 y+1ey−2 x+ey−log⁡(e−2 x+1) e−y (e2 y−1)2+x e−y-{{e^{2\,y}+1}\over{e^{y-2\,x}+e^{y}}}-{{\log \left(e^ {- 2\,x }+1 \right)\,e^ {- y }\,\left(e^{2\,y}-1\right)}\over{2}}+x\,e^ {- y }
Simplify
The answer [src] 
  1                       
  /                       
 |                        
 |  sinh(x)*sinh(x - y)   
 |  ------------------- dx
 |            2           
 |        cosh (x)        
 |                        
/                         
0
−(e2+1) log⁡(e−1 (e2+1)2) sinh⁡y−2 cosh⁡ye2+1-{{\left(e^2+1\right)\,\log \left({{e^ {- 1 }\,\left(e^2+1\right) }\over{2}}\right)\,\sinh y-2\,\cosh y}\over{e^2+1}} 
=
= 
  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
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    Use the examples entering the upper and lower limits of integration.

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