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1/(1+x^2)

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

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/
or
  /               
 |                
 |       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                  
 |                          
/                           
$$\arctan x$$
The graph
The answer [src]
pi
--
4 
$${{\pi}\over{4}}$$
=
=
pi
--
4 
$$\frac{\pi}{4}$$
Numerical answer [src]
0.785398163397448
0.785398163397448
The graph
Integral of 1/(1+x^2) dx

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