Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of dx/tan5x
Integral of dx/sqrt(4x-x^2)
Integral of (4x)/(1+x^2)
Integral of 2*x*exp(-x)
Graphing y =:
(4x)/(1+x^2)
Derivative of:
(4x)/(1+x^2)
Identical expressions
(4x)/(one +x^ two)
(4x) divide by (1 plus x squared )
(4x) divide by (one plus x to the power of two)
(4x)/(1+x2)
4x/1+x2
(4x)/(1+x²)
(4x)/(1+x to the power of 2)
4x/1+x^2
(4x) divide by (1+x^2)
(4x)/(1+x^2)dx
Similar expressions
arctg^4*x/(1+x^2)
(4x)/(1-x^2)

Solving integrals/ (4x)/(1+x^2)

Integral of (4x)/(1+x^2) dx

The solution

You have entered [src]

  1          
  /          
 |           
 |   4*x     
 |  ------ dx
 |       2   
 |  1 + x    
 |           
/            
0

\int\limits_{0}^{1} \frac{4 x}{x^{2} + 1}\, dx

Integral((4*x)/(1 + x^2), (x, 0, 1))

Detail solution

We have the integral:

  /         
 |          
 |  4*x     
 | ------ dx
 |      2   
 | 1 + x    
 |          
/

Rewrite the integrand

                             /0\   
                             |-|   
 4*x           2*x           \1/   
------ = 2*------------ + ---------
     2      2                 2    
1 + x      x  + 0*x + 1   (-x)  + 1

  /           
 |            
 |  4*x       
 | ------ dx  
 |      2    =
 | 1 + x      
 |            
/

    /               
   |                
   |     2*x        
2* | ------------ dx
   |  2             
   | x  + 0*x + 1   
   |                
  /

In the integral

    /               
   |                
   |     2*x        
2* | ------------ dx
   |  2             
   | x  + 0*x + 1   
   |                
  /

do replacement

     2
u = x

then

the integral =

    /                       
   |                        
   |   1                    
2* | ----- du = 2*log(1 + u)
   | 1 + u                  
   |                        
  /

do backward replacement

    /                               
   |                                
   |     2*x                /     2\
2* | ------------ dx = 2*log\1 + x /
   |  2                             
   | x  + 0*x + 1                   
   |                                
  /

In the integral

do replacement

v = -x

then

the integral =

True

do backward replacement

True

Solution is:

         /     2\
C + 2*log\1 + x /

The answer (Indefinite) [src]

  /                             
 |                              
 |  4*x                 /     2\
 | ------ dx = C + 2*log\1 + x /
 |      2                       
 | 1 + x                        
 |                              
/

\int \frac{4 x}{x^{2} + 1}\, dx = C + 2 \log{\left(x^{2} + 1 \right)}

Simplify

The graph

Plot the graph f(x)

The answer [src]

2*log(2)

2 \log{\left(2 \right)}

2*log(2)

2 \log{\left(2 \right)}

2*log(2)

Numerical answer [src]

1.38629436111989

1.38629436111989

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (4x)/(1+x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution