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

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

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The solution

You have entered [src] 
  1               
  /               
 |                
 |       ___      
 |     \/ x       
 |  ----------- dx
 |     ________   
 |    /      3    
 |  \/  1 - x     
 |                
/                 
0
$$\int\limits_{0}^{1} \frac{\sqrt{x}}{\sqrt{- x^{3} + 1}}\, dx$$ 
Integral(sqrt(x)/(sqrt(1 - x^3)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                     //          / 3/2\              \
 |                      ||-2*I*acosh\x   /      | 3|    |
 |      ___             ||----------------  for |x | > 1|
 |    \/ x              ||       3                      |
 | ----------- dx = C + |<                              |
 |    ________          ||        / 3/2\                |
 |   /      3           ||  2*asin\x   /                |
 | \/  1 - x            ||  ------------     otherwise  |
 |                      \\       3                      /
/
$$-{{2\,\arctan \left({{\sqrt{1-x^3}}\over{x^{{{3}\over{2}}}}}\right) }\over{3}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  1                                             
  /                                             
 |                                              
 |  /              ___                          
 |  |         -I*\/ x                   3       
 |  |----------------------------  for x  > 1   
 |  |   __________    ___________               
 |  |  /      3/2    /       3/2                
 |  |\/  1 + x    *\/  -1 + x                   
 |  <                                         dx
 |  |             ___                           
 |  |           \/ x                            
 |  |        -----------           otherwise    
 |  |           ________                        
 |  |          /      3                         
 |  \        \/  1 - x                          
 |                                              
/                                               
0
$${{\pi}\over{3}}$$ 
=
= 
  1                                             
  /                                             
 |                                              
 |  /              ___                          
 |  |         -I*\/ x                   3       
 |  |----------------------------  for x  > 1   
 |  |   __________    ___________               
 |  |  /      3/2    /       3/2                
 |  |\/  1 + x    *\/  -1 + x                   
 |  <                                         dx
 |  |             ___                           
 |  |           \/ x                            
 |  |        -----------           otherwise    
 |  |           ________                        
 |  |          /      3                         
 |  \        \/  1 - x                          
 |                                              
/                                               
0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i \sqrt{x}}{\sqrt{x^{\frac{3}{2}} - 1} \sqrt{x^{\frac{3}{2}} + 1}} & \text{for}\: x^{3} > 1 \\\frac{\sqrt{x}}{\sqrt{- x^{3} + 1}} & \text{otherwise} \end{cases}\, dx$$
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Numerical answer [src] 
1.04719755089032
1.04719755089032
The graph
Integral of sqrt(x)/sqrt(1-x^3) dx

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

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