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Identical expressions
x/(sqrt(one +x^ three))
x divide by ( square root of (1 plus x cubed ))
x divide by ( square root of (one plus x to the power of three))
x/(√(1+x^3))
x/(sqrt(1+x3))
x/sqrt1+x3
x/(sqrt(1+x³))
x/(sqrt(1+x to the power of 3))
x/sqrt1+x^3
x divide by (sqrt(1+x^3))
x/(sqrt(1+x^3))dx
Similar expressions
x/(sqrt(1-x^3))

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

The solution

You have entered [src]

 oo               
  /               
 |                
 |       x        
 |  ----------- dx
 |     ________   
 |    /      3    
 |  \/  1 + x     
 |                
/                 
0

\int\limits_{0}^{\infty} \frac{x}{\sqrt{x^{3} + 1}}\, dx

Integral(x/sqrt(1 + x^3), (x, 0, oo))

The answer (Indefinite) [src]

                                        _                       
  /                      2             |_  /1/2, 2/3 |  3  pi*I\
 |                      x *Gamma(2/3)* |   |         | x *e    |
 |      x                             2  1 \  5/3    |         /
 | ----------- dx = C + ----------------------------------------
 |    ________                        3*Gamma(5/3)              
 |   /      3                                                   
 | \/  1 + x                                                    
 |                                                              
/

\int \frac{x}{\sqrt{x^{3} + 1}}\, dx = C + \frac{x^{2} \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}

Simplify

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

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

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The solution