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

Integral of 1÷(x^2+1) dx

Limits of integration:

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v

The graph:

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Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |    1      
 |  ------ dx
 |   2       
 |  x  + 1   
 |           
/            
0
∫011x2+1 dx\int\limits_{0}^{1} \frac{1}{x^{2} + 1}\, dx 
Integral(1/(x^2 + 1), (x, 0, 1))
Detail solution
We have the integral:
  /         
 |          
 |   1      
 | ------ dx
 |  2       
 | x  + 1   
 |          
/
Rewrite the integrand
  1            1      
------ = -------------
 2         /    2    \
x  + 1   1*\(-x)  + 1/
or
  /           
 |            
 |   1        
 | ------ dx  
 |  2        =
 | x  + 1     
 |            
/             
  
  /            
 |             
 |     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                     
 | x  + 1                 
 |                        
/
∫1x2+1 dx=C+atan⁡(x)\int \frac{1}{x^{2} + 1}\, dx = C + \operatorname{atan}{\left(x \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
pi
--
4
π4\frac{\pi}{4} 
=
= 
pi
--
4
π4\frac{\pi}{4} 
pi/4
Numerical answer [src] 
0.785398163397448
0.785398163397448
The graph
Integral of 1÷(x^2+1) dx

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

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