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x*dx/(x^2-1)

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1          
  /          
 |           
 |    x      
 |  ------ dx
 |   2       
 |  x  - 1   
 |           
/            
0            
$$\int\limits_{0}^{1} \frac{x}{x^{2} - 1}\, dx$$
Integral(x/(x^2 - 1), (x, 0, 1))
Detail solution
We have the integral:
  /         
 |          
 |   x      
 | ------ dx
 |  2       
 | x  - 1   
 |          
/           
Rewrite the integrand
         /    2*x     \
         |------------|
         | 2          |
  x      \x  + 0*x - 1/
------ = --------------
 2             2       
x  - 1                 
or
  /           
 |            
 |   x        
 | ------ dx  
 |  2        =
 | x  - 1     
 |            
/             
  
  /               
 |                
 |     2*x        
 | ------------ dx
 |  2             
 | x  + 0*x - 1   
 |                
/                 
------------------
        2         
In the integral
  /               
 |                
 |     2*x        
 | ------------ dx
 |  2             
 | x  + 0*x - 1   
 |                
/                 
------------------
        2         
do replacement
     2
u = x 
then
the integral =
  /                       
 |                        
 |   1                    
 | ------ du              
 | -1 + u                 
 |                        
/              log(-1 + u)
------------ = -----------
     2              2     
do backward replacement
  /                              
 |                               
 |     2*x                       
 | ------------ dx               
 |  2                            
 | x  + 0*x - 1                  
 |                      /      2\
/                    log\-1 + x /
------------------ = ------------
        2                 2      
Solution is:
       /      2\
    log\-1 + x /
C + ------------
         2      
The answer (Indefinite) [src]
  /                            
 |                    /      2\
 |   x             log\-1 + x /
 | ------ dx = C + ------------
 |  2                   2      
 | x  - 1                      
 |                             
/                              
$$\int \frac{x}{x^{2} - 1}\, dx = C + \frac{\log{\left(x^{2} - 1 \right)}}{2}$$
The graph
The answer [src]
      pi*I
-oo - ----
       2  
$$-\infty - \frac{i \pi}{2}$$
=
=
      pi*I
-oo - ----
       2  
$$-\infty - \frac{i \pi}{2}$$
-oo - pi*i/2
Numerical answer [src]
-21.6989048028269
-21.6989048028269
The graph
Integral of x*dx/(x^2-1) dx

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