Mister Exam

Other calculators

Integral of (arctg^3xdx)/(1+x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1            
  /            
 |             
 |      3      
 |  atan (x)   
 |  -------- dx
 |        2    
 |   1 + x     
 |             
/              
0              
$$\int\limits_{0}^{1} \frac{\operatorname{atan}^{3}{\left(x \right)}}{x^{2} + 1}\, dx$$
Integral(atan(x)^3/(1 + x^2), (x, 0, 1))
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]
  /                          
 |                           
 |     3                 4   
 | atan (x)          atan (x)
 | -------- dx = C + --------
 |       2              4    
 |  1 + x                    
 |                           
/                            
$$\int \frac{\operatorname{atan}^{3}{\left(x \right)}}{x^{2} + 1}\, dx = C + \frac{\operatorname{atan}^{4}{\left(x \right)}}{4}$$
The graph
The answer [src]
  4 
pi  
----
1024
$$\frac{\pi^{4}}{1024}$$
=
=
  4 
pi  
----
1024
$$\frac{\pi^{4}}{1024}$$
pi^4/1024
Numerical answer [src]
0.095126065462893
0.095126065462893

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