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1/sqrt(1+x^3)
Solving integrals/ 1/sqrt(1+x^3)

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

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |       1        
 |  ----------- dx
 |     ________   
 |    /      3    
 |  \/  1 + x     
 |                
/                 
0
∫011x3+1 dx\int\limits_{0}^{1} \frac{1}{\sqrt{x^{3} + 1}}\, dx 
Integral(1/(sqrt(1 + x^3)), (x, 0, 1))
The answer (Indefinite) [src] 
                                       _                       
  /                                   |_  /1/3, 1/2 |  3  pi*I\
 |                      x*Gamma(1/3)* |   |         | x *e    |
 |      1                            2  1 \  4/3    |         /
 | ----------- dx = C + ---------------------------------------
 |    ________                        3*Gamma(4/3)             
 |   /      3                                                  
 | \/  1 + x                                                   
 |                                                             
/
∫1x3+1 dx=C+xΓ(13)2F1(13,1243|x3eiπ)3Γ(43)\int \frac{1}{\sqrt{x^{3} + 1}}\, dx = C + \frac{x \Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {x^{3} e^{i \pi}} \right)}}{3 \Gamma\left(\frac{4}{3}\right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
             _                 
            |_  /1/3, 1/2 |   \
Gamma(1/3)* |   |         | -1|
           2  1 \  4/3    |   /
-------------------------------
          3*Gamma(4/3)
Γ(13)2F1(13,1243|−1)3Γ(43)\frac{\Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {-1} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} 
=
= 
             _                 
            |_  /1/3, 1/2 |   \
Gamma(1/3)* |   |         | -1|
           2  1 \  4/3    |   /
-------------------------------
          3*Gamma(4/3)
Γ(13)2F1(13,1243|−1)3Γ(43)\frac{\Gamma\left(\frac{1}{3}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{4}{3} \end{matrix}\middle| {-1} \right)}}{3 \Gamma\left(\frac{4}{3}\right)} 
gamma(1/3)*hyper((1/3, 1/2), (4/3,), -1)/(3*gamma(4/3))
Numerical answer [src] 
0.909604242638896
0.909604242638896
The graph
Integral of 1/sqrt(1+x^3) dx

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

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