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x*dx/(x^2+1)
Solving integrals/ 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     \            
         |------------|      /0\   
         | 2          |      |-|   
  x      \x  + 0*x + 1/      \1/   
------ = -------------- + ---------
 2             2              2    
x  + 1                    (-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
In the integral
0
do replacement
v = -x
then
the integral =
True
do backward replacement
True
Solution is:
       /     2\
    log\1 + x /
C + -----------
         2
The answer (Indefinite) [src] 
  /                           
 |                    /     2\
 |   x             log\1 + x /
 | ------ dx = C + -----------
 |  2                   2     
 | x  + 1                     
 |                            
/
$$\int \frac{x}{x^{2} + 1}\, dx = C + \frac{\log{\left(x^{2} + 1 \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
log(2)
------
  2
$$\frac{\log{\left(2 \right)}}{2}$$ 
=
= 
log(2)
------
  2
$$\frac{\log{\left(2 \right)}}{2}$$ 
log(2)/2
Numerical answer [src] 
0.346573590279973
0.346573590279973
The graph
Integral of x*dx/(x^2+1) dx

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

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