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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |      1      
 |  1*------ dy
 |         2   
 |    1 + y    
 |             
/              
0
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{y^{2} + 1}\, dy$$ 
Integral(1/(1 + y^2), (y, 0, 1))
Detail solution
We have the integral:
  /             
 |              
 |       1      
 | 1*1*------ dy
 |          2   
 |     1 + y    
 |              
/
Rewrite the integrand
    1              1        
1*------ = -----------------
       2     /        2    \
  1 + y    1*\(-y + 0)  + 1/
or
  /               
 |                
 |       1        
 | 1*1*------ dy  
 |          2    =
 |     1 + y      
 |                
/                 
  
  /                
 |                 
 |       1         
 | ------------- dy
 |         2       
 | (-y + 0)  + 1   
 |                 
/
In the integral
  /                
 |                 
 |       1         
 | ------------- dy
 |         2       
 | (-y + 0)  + 1   
 |                 
/
do replacement
v = -y
then
the integral =
  /                   
 |                    
 |   1                
 | ------ dv = atan(v)
 |      2             
 | 1 + v              
 |                    
/
do backward replacement
  /                          
 |                           
 |       1                   
 | ------------- dy = atan(y)
 |         2                 
 | (-y + 0)  + 1             
 |                           
/
Solution is:
C + atan(y)
The answer (Indefinite) [src] 
  /                         
 |                          
 |     1                    
 | 1*------ dy = C + atan(y)
 |        2                 
 |   1 + y                  
 |                          
/
$$\arctan y$$
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
Integral of 1/(1+y^2) dx

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

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