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Identical expressions
two *x/(x^ two - four)
2 multiply by x divide by (x squared minus 4)
two multiply by x divide by (x to the power of two minus four)
2*x/(x2-4)
2*x/x2-4
2*x/(x²-4)
2*x/(x to the power of 2-4)
2x/(x^2-4)
2x/(x2-4)
2x/x2-4
2x/x^2-4
2*x divide by (x^2-4)
2*x/(x^2-4)dx
Similar expressions
2*x/(x^2+4)

Solving integrals/ 2*x/(x^2-4)

Integral of 2*x/(x^2-4) dx

The solution

You have entered [src]

  2          
  /          
 |           
 |   2*x     
 |  ------ dx
 |   2       
 |  x  - 4   
 |           
/            
0

$$\int\limits_{0}^{2} \frac{2 x}{x^{2} - 4}\, dx$$

Integral((2*x)/(x^2 - 4), (x, 0, 2))

Detail solution

We have the integral:

  /         
 |          
 |  2*x     
 | ------ dx
 |  2       
 | x  - 4   
 |          
/

Rewrite the integrand

 2*x         2*x     
------ = ------------
 2        2          
x  - 4   x  + 0*x - 4

  /           
 |            
 |  2*x       
 | ------ dx  
 |  2        =
 | x  - 4     
 |            
/

  /               
 |                
 |     2*x        
 | ------------ dx
 |  2             
 | x  + 0*x - 4   
 |                
/

In the integral

  /               
 |                
 |     2*x        
 | ------------ dx
 |  2             
 | x  + 0*x - 4   
 |                
/

do replacement

     2
u = x

then

the integral =

  /                       
 |                        
 |   1                    
 | ------ du = log(-4 + u)
 | -4 + u                 
 |                        
/

do backward replacement

  /                              
 |                               
 |     2*x              /      2\
 | ------------ dx = log\-4 + x /
 |  2                            
 | x  + 0*x - 4                  
 |                               
/

Solution is:

       /      2\
C + log\-4 + x /

The answer (Indefinite) [src]

  /                            
 |                             
 |  2*x               /      2\
 | ------ dx = C + log\-4 + x /
 |  2                          
 | x  - 4                      
 |                             
/

$$\int \frac{2 x}{x^{2} - 4}\, dx = C + \log{\left(x^{2} - 4 \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-oo - pi*I

$$-\infty - i \pi$$

-oo - pi*I

$$-\infty - i \pi$$

-oo - pi*i

Numerical answer [src]

-43.3978096056539

-43.3978096056539

The graph

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

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Identical expressions

Similar expressions

Integral of 2*x/(x^2-4) dx

Limits of integration:

The graph:

Piecewise:

The solution