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Derivative of:
arctg(x)/(x^2+1)
Identical expressions
arctg(x)/(x^ two + one)
arctg(x) divide by (x squared plus 1)
arctg(x) divide by (x to the power of two plus one)
arctg(x)/(x2+1)
arctgx/x2+1
arctg(x)/(x²+1)
arctg(x)/(x to the power of 2+1)
arctgx/x^2+1
arctg(x) divide by (x^2+1)
arctg(x)/(x^2+1)dx
Similar expressions
arctgx/x^2+1
arctg(x)/(x^2-1)

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

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

The solution

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 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

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    
 |  x  + 1                  
 |                          
/

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

Simplify

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Plot the graph f(x)

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

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

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Identical expressions

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

Limits of integration:

The graph:

Piecewise:

The solution