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Integral of (x)/(x^2+4) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1          
  /          
 |           
 |    x      
 |  ------ dx
 |   2       
 |  x  + 4   
 |           
/            
0            
$$\int\limits_{0}^{1} \frac{x}{x^{2} + 4}\, dx$$
Integral(x/(x^2 + 4), (x, 0, 1))
Detail solution
We have the integral:
  /         
 |          
 |   x      
 | ------ dx
 |  2       
 | x  + 4   
 |          
/           
Rewrite the integrand
         /    2*x     \             
         |------------|      /0\    
         | 2          |      |-|    
  x      \x  + 0*x + 4/      \4/    
------ = -------------- + ----------
 2             2               2    
x  + 4                    /-x \     
                          |---|  + 1
                          \ 2 /     
or
  /           
 |            
 |   x        
 | ------ dx  
 |  2        =
 | x  + 4     
 |            
/             
  
  /               
 |                
 |     2*x        
 | ------------ dx
 |  2             
 | x  + 0*x + 4   
 |                
/                 
------------------
        2         
In the integral
  /               
 |                
 |     2*x        
 | ------------ dx
 |  2             
 | x  + 0*x + 4   
 |                
/                 
------------------
        2         
do replacement
     2
u = x 
then
the integral =
  /                     
 |                      
 |   1                  
 | ----- du             
 | 4 + u                
 |                      
/             log(4 + u)
----------- = ----------
     2            2     
do backward replacement
  /                             
 |                              
 |     2*x                      
 | ------------ dx              
 |  2                           
 | x  + 0*x + 4                 
 |                      /     2\
/                    log\4 + x /
------------------ = -----------
        2                 2     
In the integral
0
do replacement
    -x 
v = ---
     2 
then
the integral =
True
do backward replacement
True
Solution is:
       /     2\
    log\4 + x /
C + -----------
         2     
The answer (Indefinite) [src]
  /                           
 |                    /     2\
 |   x             log\4 + x /
 | ------ dx = C + -----------
 |  2                   2     
 | x  + 4                     
 |                            
/                             
$$\int \frac{x}{x^{2} + 4}\, dx = C + \frac{\log{\left(x^{2} + 4 \right)}}{2}$$
The graph
The answer [src]
log(5)   log(4)
------ - ------
  2        2   
$$- \frac{\log{\left(4 \right)}}{2} + \frac{\log{\left(5 \right)}}{2}$$
=
=
log(5)   log(4)
------ - ------
  2        2   
$$- \frac{\log{\left(4 \right)}}{2} + \frac{\log{\left(5 \right)}}{2}$$
log(5)/2 - log(4)/2
Numerical answer [src]
0.111571775657105
0.111571775657105

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