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2*x/(x^2-1)

Integral of 2*x/(x^2-1) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  1          
  /          
 |           
 |   2*x     
 |  ------ dx
 |   2       
 |  x  - 1   
 |           
/            
0            
$$\int\limits_{0}^{1} \frac{2 x}{x^{2} - 1}\, dx$$
Integral((2*x)/(x^2 - 1), (x, 0, 1))
Detail solution
We have the integral:
  /         
 |          
 |  2*x     
 | ------ dx
 |  2       
 | x  - 1   
 |          
/           
Rewrite the integrand
 2*x         2*x     
------ = ------------
 2        2          
x  - 1   x  + 0*x - 1
or
  /           
 |            
 |  2*x       
 | ------ dx  
 |  2        =
 | x  - 1     
 |            
/             
  
  /               
 |                
 |     2*x        
 | ------------ dx
 |  2             
 | x  + 0*x - 1   
 |                
/                 
In the integral
  /               
 |                
 |     2*x        
 | ------------ dx
 |  2             
 | x  + 0*x - 1   
 |                
/                 
do replacement
     2
u = x 
then
the integral =
  /                       
 |                        
 |   1                    
 | ------ du = log(-1 + u)
 | -1 + u                 
 |                        
/                         
do backward replacement
  /                              
 |                               
 |     2*x              /      2\
 | ------------ dx = log\-1 + x /
 |  2                            
 | x  + 0*x - 1                  
 |                               
/                                
Solution is:
       /      2\
C + log\-1 + x /
The answer (Indefinite) [src]
  /                            
 |                             
 |  2*x               /      2\
 | ------ dx = C + log\-1 + x /
 |  2                          
 | x  - 1                      
 |                             
/                              
$$\int \frac{2 x}{x^{2} - 1}\, dx = C + \log{\left(x^{2} - 1 \right)}$$
The graph
The answer [src]
-oo - pi*I
$$-\infty - i \pi$$
=
=
-oo - pi*I
$$-\infty - i \pi$$
-oo - pi*i
Numerical answer [src]
-43.3978096056539
-43.3978096056539
The graph
Integral of 2*x/(x^2-1) dx

    Use the examples entering the upper and lower limits of integration.