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1÷(1+x^2)
Solving integrals/ 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      
 |  ------ dx
 |       2   
 |  1 + x    
 |           
/            
0
$$\int\limits_{0}^{1} \frac{1}{x^{2} + 1}\, dx$$ 
Integral(1/(1 + x^2), (x, 0, 1))
Detail solution
We have the integral:
  /         
 |          
 |   1      
 | ------ dx
 |      2   
 | 1 + x    
 |          
/
Rewrite the integrand
  1            1      
------ = -------------
     2     /    2    \
1 + x    1*\(-x)  + 1/
or
  /           
 |            
 |   1        
 | ------ dx  
 |      2    =
 | 1 + x      
 |            
/             
  
  /            
 |             
 |     1       
 | --------- dx
 |     2       
 | (-x)  + 1   
 |             
/
In the integral
  /            
 |             
 |     1       
 | --------- dx
 |     2       
 | (-x)  + 1   
 |             
/
do replacement
v = -x
then
the integral =
  /                   
 |                    
 |   1                
 | ------ dv = atan(v)
 |      2             
 | 1 + v              
 |                    
/
do backward replacement
  /                      
 |                       
 |     1                 
 | --------- dx = atan(x)
 |     2                 
 | (-x)  + 1             
 |                       
/
Solution is:
C + atan(x)
The answer (Indefinite) [src] 
  /                       
 |                        
 |   1                    
 | ------ dx = C + atan(x)
 |      2                 
 | 1 + x                  
 |                        
/
$$\int \frac{1}{x^{2} + 1}\, dx = C + \operatorname{atan}{\left(x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
pi
--
4
$$\frac{\pi}{4}$$ 
=
= 
pi
--
4
$$\frac{\pi}{4}$$ 
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.

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