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Graphing y =:
8/(x^2+4)
Identical expressions
eight /(x^ two + four)
8 divide by (x squared plus 4)
eight divide by (x to the power of two plus four)
8/(x2+4)
8/x2+4
8/(x²+4)
8/(x to the power of 2+4)
8/x^2+4
8 divide by (x^2+4)
8/(x^2+4)dx
Similar expressions
8/(x^2-4)

Solving integrals/ 8/(x^2+4)

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

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 /

  /           
 |            
 |   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)}

Simplify

The graph

Plot the graph f(x)

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

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution