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1/(x³+1)
Solving integrals/ 1/(x³+1)

Integral of 1/(x³+1) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |    1      
 |  ------ dx
 |   3       
 |  x  + 1   
 |           
/            
0
$$\int\limits_{0}^{1} \frac{1}{x^{3} + 1}\, dx$$ 
Integral(1/(x^3 + 1), (x, 0, 1))
The answer (Indefinite) [src] 
                                                            /    ___           \
  /                                                 ___     |2*\/ 3 *(-1/2 + x)|
 |                    /     2    \                \/ 3 *atan|------------------|
 |   1             log\1 + x  - x/   log(1 + x)             \        3         /
 | ------ dx = C - --------------- + ---------- + ------------------------------
 |  3                     6              3                      3               
 | x  + 1                                                                       
 |                                                                              
/
$$\int \frac{1}{x^{3} + 1}\, dx = C + \frac{\log{\left(x + 1 \right)}}{3} - \frac{\log{\left(x^{2} - x + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x - \frac{1}{2}\right)}{3} \right)}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
              ___
log(2)   pi*\/ 3 
------ + --------
  3         9
$$\frac{\log{\left(2 \right)}}{3} + \frac{\sqrt{3} \pi}{9}$$ 
=
= 
              ___
log(2)   pi*\/ 3 
------ + --------
  3         9
$$\frac{\log{\left(2 \right)}}{3} + \frac{\sqrt{3} \pi}{9}$$ 
log(2)/3 + pi*sqrt(3)/9
Numerical answer [src] 
0.835648848264721
0.835648848264721
The graph
Integral of 1/(x³+1) dx

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

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