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Similar expressions
(arctg(x))dx/(1-x^2)

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

The solution

You have entered [src]

 oo           
  /           
 |            
 |  atan(x)   
 |  ------- dx
 |        2   
 |   1 + x    
 |            
/             
o

$$\int\limits_{o}^{\infty} \frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}\, dx$$

Integral(atan(x)/(1 + x^2), (x, o, oo))

Detail solution

Let $u = \operatorname{atan}{\left(x \right)}$ .

Then let $du = \frac{dx}{x^{2} + 1}$ and substitute $du$ :

$\int u\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int u\, du = \frac{u^{2}}{2}$
Now substitute $u$ back in:

$\frac{\operatorname{atan}^{2}{\left(x \right)}}{2}$
Add the constant of integration:

$\frac{\operatorname{atan}^{2}{\left(x \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\operatorname{atan}^{2}{\left(x \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                         
 |                      2   
 | atan(x)          atan (x)
 | ------- dx = C + --------
 |       2             2    
 |  1 + x                   
 |                          
/

$$\int \frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}\, dx = C + \frac{\operatorname{atan}^{2}{\left(x \right)}}{2}$$

Simplify

The answer [src]

      2        2
  atan (o)   pi 
- -------- + ---
     2        8

$$- \frac{\operatorname{atan}^{2}{\left(o \right)}}{2} + \frac{\pi^{2}}{8}$$

      2        2
  atan (o)   pi 
- -------- + ---
     2        8

$$- \frac{\operatorname{atan}^{2}{\left(o \right)}}{2} + \frac{\pi^{2}}{8}$$

-atan(o)^2/2 + pi^2/8

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

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

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The solution