Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 1/(1+x^2)
Integral of x^-1
Integral of -e^-x
Integral of sin(5*x)
Derivative of:
1/(1+x^2)
Graphing y =:
1/(1+x^2)
Limit of the function:
1/(1+x^2)
Identical expressions
one /(one +x^ two)
1 divide by (1 plus x squared )
one divide by (one plus x to the power of two)
1/(1+x2)
1/1+x2
1/(1+x²)
1/(1+x to the power of 2)
1/1+x^2
1 divide by (1+x^2)
1/(1+x^2)dx
Similar expressions
(1/(1+x^2))
1/(1+(x^2))
1/(1-x^2)

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

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

The solution

You have entered [src]

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

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

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

Detail solution

We have the integral:

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

Rewrite the integrand

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

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

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

In the integral

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

do replacement

v = -x

then

the integral =

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

do backward replacement

  /                          
 |                           
 |       1                   
 | ------------- dx = atan(x)
 |         2                 
 | (-x + 0)  + 1             
 |                           
/

Solution is:

C + atan(x)

The answer (Indefinite) [src]

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

$$\arctan x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

pi
--
4

$${{\pi}\over{4}}$$

pi
--
4

$$\frac{\pi}{4}$$

Упростить

Numerical answer [src]

0.785398163397448

0.785398163397448

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 1/(1+x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution