Mister Exam

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Integral of d{x}:
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Integral of e^3
Integral of 1/(1+4x^2)
Integral of (x^2-1)e^x
Graphing y =:
2/(x^2+1)
Identical expressions
two /(x^ two + one)
2 divide by (x squared plus 1)
two divide by (x to the power of two plus one)
2/(x2+1)
2/x2+1
2/(x²+1)
2/(x to the power of 2+1)
2/x^2+1
2 divide by (x^2+1)
2/(x^2+1)dx
Similar expressions
(x^2+2)/(x^2+1)
tan(x^2)/x^2+1
2/(x^2-1)
x^2/((x^2+1)(x^2+9))

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

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

The solution

You have entered [src]

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

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

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

Detail solution

We have the integral:

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

Rewrite the integrand

            /2\   
            |-|   
  2         \1/   
------ = ---------
 2           2    
x  + 1   (-x)  + 1

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

    /            
   |             
   |     1       
2* | --------- dx
   |     2       
   | (-x)  + 1   
   |             
  /

In the integral

    /            
   |             
   |     1       
2* | --------- dx
   |     2       
   | (-x)  + 1   
   |             
  /

do replacement

v = -x

then

the integral =

    /                     
   |                      
   |   1                  
2* | ------ dv = 2*atan(v)
   |      2               
   | 1 + v                
   |                      
  /

do backward replacement

    /                        
   |                         
   |     1                   
2* | --------- dx = 2*atan(x)
   |     2                   
   | (-x)  + 1               
   |                         
  /

Solution is:

C + 2*atan(x)

The answer (Indefinite) [src]

  /                         
 |                          
 |   2                      
 | ------ dx = C + 2*atan(x)
 |  2                       
 | x  + 1                   
 |                          
/

$$\int \frac{2}{x^{2} + 1}\, dx = C + 2 \operatorname{atan}{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

pi
--
2

$$\frac{\pi}{2}$$

pi
--
2

$$\frac{\pi}{2}$$

pi/2

Numerical answer [src]

1.5707963267949

1.5707963267949

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^2+1) dx

Limits of integration:

The graph:

Piecewise:

The solution