Mister Exam

Other calculators


x/(x^3+1)

Integral of x/(x^3+1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 oo          
  /          
 |           
 |    x      
 |  ------ dx
 |   3       
 |  x  + 1   
 |           
/            
0            
$$\int\limits_{0}^{\infty} \frac{x}{x^{3} + 1}\, dx$$
Integral(x/(x^3 + 1), (x, 0, oo))
The answer (Indefinite) [src]
                                                            /    ___           \
  /                                                 ___     |2*\/ 3 *(-1/2 + x)|
 |                                 /     2    \   \/ 3 *atan|------------------|
 |   x             log(1 + x)   log\1 + x  - x/             \        3         /
 | ------ dx = C - ---------- + --------------- + ------------------------------
 |  3                  3               6                        3               
 | x  + 1                                                                       
 |                                                                              
/                                                                               
$$\int \frac{x}{x^{3} + 1}\, dx = C - \frac{\log{\left(x + 1 \right)}}{3} + \frac{\log{\left(x^{2} - x + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x - \frac{1}{2}\right)}{3} \right)}}{3}$$
The graph
The answer [src]
       ___
2*pi*\/ 3 
----------
    9     
$$\frac{2 \sqrt{3} \pi}{9}$$
=
=
       ___
2*pi*\/ 3 
----------
    9     
$$\frac{2 \sqrt{3} \pi}{9}$$
2*pi*sqrt(3)/9
The graph
Integral of x/(x^3+1) dx

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