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atan(x)/(one +x^ two)
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atan(x)/(1+x2)
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Similar expressions
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Solving integrals/ atan(x)/(1+x^2)

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

The solution

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  1           
  /           
 |            
 |  atan(x)   
 |  ------- dx
 |        2   
 |   1 + x    
 |            
/             
0

$$\int\limits_{0}^{1} \frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}\, dx$$

Integral(atan(x)/(1 + x^2), (x, 0, 1))

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 graph

Plot the graph f(x)

Numerical answer [src]

0.308425137534042

0.308425137534042

The graph

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution