Mister Exam

Integral of atanx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1           
  /           
 |            
 |  atan(x) dx
 |            
/             
0             
$$\int\limits_{0}^{1} \operatorname{atan}{\left(x \right)}\, dx$$
Integral(atan(x), (x, 0, 1))
Detail solution
  1. Use integration by parts:

    Let and let .

    Then .

    To find :

    1. The integral of a constant is the constant times the variable of integration:

    Now evaluate the sub-integral.

  2. The integral of a constant times a function is the constant times the integral of the function:

    1. Let .

      Then let and substitute :

      1. The integral of is .

      Now substitute back in:

    So, the result is:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                    /     2\            
 |                  log\1 + x /            
 | atan(x) dx = C - ----------- + x*atan(x)
 |                       2                 
/                                          
$$x\,\arctan x-{{\log \left(x^2+1\right)}\over{2}}$$
The graph
The answer [src]
  log(2)   pi
- ------ + --
    2      4 
$$-{{2\,\log 2-\pi}\over{4}}$$
=
=
  log(2)   pi
- ------ + --
    2      4 
$$- \frac{\log{\left(2 \right)}}{2} + \frac{\pi}{4}$$
Numerical answer [src]
0.438824573117476
0.438824573117476
The graph
Integral of atanx dx

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