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x/(sqrt1+x^2)
Solving integrals/ x/(sqrt1+x^2)

Integral of x/(sqrt1+x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1              
  /              
 |               
 |      x        
 |  ---------- dx
 |    ___    2   
 |  \/ 1  + x    
 |               
/                
0
∫01xx2+1 dx\int\limits_{0}^{1} \frac{x}{x^{2} + \sqrt{1}}\, dx 
Integral(x/(sqrt(1) + x^2), (x, 0, 1))
Detail solution
We have the integral:
  /             
 |              
 |     x        
 | ---------- dx
 |   ___    2   
 | \/ 1  + x    
 |              
/
Rewrite the integrand
             /    2*x     \            
             |------------|      /0\   
             | 2          |      |-|   
    x        \x  + 0*x + 1/      \1/   
---------- = -------------- + ---------
  ___    2         2              2    
\/ 1  + x                     (-x)  + 1
or
  /               
 |                
 |     x          
 | ---------- dx  
 |   ___    2    =
 | \/ 1  + x      
 |                
/                 
  
  /               
 |                
 |     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       
 | \/ 1  + x                          
 |                                    
/
∫xx2+1 dx=C+log⁡(x2+1)2\int \frac{x}{x^{2} + \sqrt{1}}\, dx = C + \frac{\log{\left(x^{2} + \sqrt{1} \right)}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.01.0
Plot the graph f(x)
The answer [src] 
log(2)
------
  2
log⁡(2)2\frac{\log{\left(2 \right)}}{2} 
=
= 
log(2)
------
  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/(sqrt1+x^2) dx

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

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