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2*x/(x^2+1)

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

Limits of integration:

from to
v

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
                           /0\   
                           |-|   
 2*x         2*x           \1/   
------ = ------------ + ---------
 2        2                 2    
x  + 1   x  + 0*x + 1   (-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                 
 |                              
/                               
In the integral
0
do replacement
v = -x
then
the integral =
True
do backward replacement
True
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]
log(2)
$$\log{\left(2 \right)}$$
=
=
log(2)
$$\log{\left(2 \right)}$$
log(2)
Numerical answer [src]
0.693147180559945
0.693147180559945
The graph
Integral of 2*x/(x^2+1) dx

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