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arctg(x)/(x^2+1)

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 oo           
  /           
 |            
 |  atan(x)   
 |  ------- dx
 |    2       
 |   x  + 1   
 |            
/             
1             
$$\int\limits_{1}^{\infty} \frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}\, dx$$
Integral(atan(x)/(x^2 + 1), (x, 1, oo))
Detail solution
  1. Let .

    Then let and substitute :

    1. The integral of is when :

    Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                         
 |                      2   
 | atan(x)          atan (x)
 | ------- dx = C + --------
 |   2                 2    
 |  x  + 1                  
 |                          
/                           
$$\int \frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}\, dx = C + \frac{\operatorname{atan}^{2}{\left(x \right)}}{2}$$
The graph
The answer [src]
    2
3*pi 
-----
  32 
$$\frac{3 \pi^{2}}{32}$$
=
=
    2
3*pi 
-----
  32 
$$\frac{3 \pi^{2}}{32}$$
3*pi^2/32
The graph
Integral of arctg(x)/(x^2+1) dx

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