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x/sqrt(x^3-1)

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1               
  /               
 |                
 |       x        
 |  ----------- dx
 |     ________   
 |    /  3        
 |  \/  x  - 1    
 |                
/                 
0                 
$$\int\limits_{0}^{1} \frac{x}{\sqrt{x^{3} - 1}}\, dx$$
Integral(x/(sqrt(x^3 - 1*1)), (x, 0, 1))
The answer (Indefinite) [src]
                                          _                 
  /                        2             |_  /1/2, 2/3 |  3\
 |                      I*x *Gamma(2/3)* |   |         | x |
 |      x                               2  1 \  5/3    |   /
 | ----------- dx = C - ------------------------------------
 |    ________                      3*Gamma(5/3)            
 |   /  3                                                   
 | \/  x  - 1                                               
 |                                                          
/                                                           
$$\int {{{x}\over{\sqrt{x^3-1}}}}{\;dx}$$
The graph
The answer [src]
                _                 
               |_  /1/2, 2/3 |  \ 
-I*Gamma(2/3)* |   |         | 1| 
              2  1 \  5/3    |  / 
----------------------------------
           3*Gamma(5/3)           
$$\int_{0}^{1}{{{x}\over{\sqrt{x^3-1}}}\;dx}$$
=
=
                _                 
               |_  /1/2, 2/3 |  \ 
-I*Gamma(2/3)* |   |         | 1| 
              2  1 \  5/3    |  / 
----------------------------------
           3*Gamma(5/3)           
$$- \frac{i \Gamma\left(\frac{2}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{2}{3} \\ \frac{5}{3} \end{matrix}\middle| {1} \right)}}{3 \Gamma\left(\frac{5}{3}\right)}$$
Numerical answer [src]
(0.0 - 0.862369852689889j)
(0.0 - 0.862369852689889j)
The graph
Integral of x/sqrt(x^3-1) dx

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