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8/(x^2+4)

Integral of 8/(x^2+4) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1          
  /          
 |           
 |    8      
 |  ------ dx
 |   2       
 |  x  + 4   
 |           
/            
0            
$$\int\limits_{0}^{1} \frac{8}{x^{2} + 4}\, dx$$
Integral(8/(x^2 + 4), (x, 0, 1))
Detail solution
We have the integral:
  /         
 |          
 |   8      
 | ------ dx
 |  2       
 | x  + 4   
 |          
/           
Rewrite the integrand
            /8\    
            |-|    
  8         \4/    
------ = ----------
 2            2    
x  + 4   /-x \     
         |---|  + 1
         \ 2 /     
or
  /           
 |            
 |   8        
 | ------ dx  
 |  2        =
 | x  + 4     
 |            
/             
  
    /             
   |              
   |     1        
2* | ---------- dx
   |      2       
   | /-x \        
   | |---|  + 1   
   | \ 2 /        
   |              
  /               
In the integral
    /             
   |              
   |     1        
2* | ---------- dx
   |      2       
   | /-x \        
   | |---|  + 1   
   | \ 2 /        
   |              
  /               
do replacement
    -x 
v = ---
     2 
then
the integral =
    /                     
   |                      
   |   1                  
2* | ------ dv = 2*atan(v)
   |      2               
   | 1 + v                
   |                      
  /                       
do backward replacement
    /                         
   |                          
   |     1                 /x\
2* | ---------- dx = 4*atan|-|
   |      2                \2/
   | /-x \                    
   | |---|  + 1               
   | \ 2 /                    
   |                          
  /                           
Solution is:
          /x\
C + 4*atan|-|
          \2/
The answer (Indefinite) [src]
  /                         
 |                          
 |   8                   /x\
 | ------ dx = C + 4*atan|-|
 |  2                    \2/
 | x  + 4                   
 |                          
/                           
$$\int \frac{8}{x^{2} + 4}\, dx = C + 4 \operatorname{atan}{\left(\frac{x}{2} \right)}$$
The graph
The answer [src]
4*atan(1/2)
$$4 \operatorname{atan}{\left(\frac{1}{2} \right)}$$
=
=
4*atan(1/2)
$$4 \operatorname{atan}{\left(\frac{1}{2} \right)}$$
4*atan(1/2)
Numerical answer [src]
1.85459043600322
1.85459043600322
The graph
Integral of 8/(x^2+4) dx

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