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  • Identical expressions

  • x^ three /sqrt(nine - twenty-five *x^ eight)
  • x cubed divide by square root of (9 minus 25 multiply by x to the power of 8)
  • x to the power of three divide by square root of (nine minus twenty minus five multiply by x to the power of eight)
  • x^3/√(9-25*x^8)
  • x3/sqrt(9-25*x8)
  • x3/sqrt9-25*x8
  • x³/sqrt(9-25*x⁸)
  • x to the power of 3/sqrt(9-25*x to the power of 8)
  • x^3/sqrt(9-25x^8)
  • x3/sqrt(9-25x8)
  • x3/sqrt9-25x8
  • x^3/sqrt9-25x^8
  • x^3 divide by sqrt(9-25*x^8)
  • x^3/sqrt(9-25*x^8)dx

  • Similar expressions

  • x^3/sqrt(9+25*x^8)
Solving integrals/ x^3/sqrt(9-25*x^8)

Integral of x^3/sqrt(9-25*x^8) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                  
  /                  
 |                   
 |         3         
 |        x          
 |  -------------- dx
 |     ___________   
 |    /         8    
 |  \/  9 - 25*x     
 |                   
/                    
0
$$\int\limits_{0}^{1} \frac{x^{3}}{\sqrt{9 - 25 x^{8}}}\, dx$$ 
Integral(x^3/sqrt(9 - 25*x^8), (x, 0, 1))
The answer (Indefinite) [src] 
                           //        /   4\                  \
                           ||        |5*x |                  |
  /                        ||-I*acosh|----|          | 8|    |
 |                         ||        \ 3  /       25*|x |    |
 |        3                ||---------------  for ------- > 1|
 |       x                 ||       20               9       |
 | -------------- dx = C + |<                                |
 |    ___________          ||      /   4\                    |
 |   /         8           ||      |5*x |                    |
 | \/  9 - 25*x            ||  asin|----|                    |
 |                         ||      \ 3  /                    |
/                          ||  ----------        otherwise   |
                           \\      20                        /
$$\int \frac{x^{3}}{\sqrt{9 - 25 x^{8}}}\, dx = C + \begin{cases} - \frac{i \operatorname{acosh}{\left(\frac{5 x^{4}}{3} \right)}}{20} & \text{for}\: \frac{25 \left|{x^{8}}\right|}{9} > 1 \\\frac{\operatorname{asin}{\left(\frac{5 x^{4}}{3} \right)}}{20} & \text{otherwise} \end{cases}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  1                                       
  /                                       
 |                                        
 |  /           3                 8       
 |  |       -I*x              25*x        
 |  |-------------------  for ----- > 1   
 |  |       ____________        9         
 |  |      /          8                   
 |  |     /       25*x                    
 |  |3*  /   -1 + -----                   
 |  |  \/           9                     
 |  <                                   dx
 |  |         3                           
 |  |        x                            
 |  |------------------     otherwise     
 |  |       ___________                   
 |  |      /         8                    
 |  |     /      25*x                     
 |  |3*  /   1 - -----                    
 |  \  \/          9                      
 |                                        
/                                         
0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i x^{3}}{3 \sqrt{\frac{25 x^{8}}{9} - 1}} & \text{for}\: \frac{25 x^{8}}{9} > 1 \\\frac{x^{3}}{3 \sqrt{1 - \frac{25 x^{8}}{9}}} & \text{otherwise} \end{cases}\, dx$$ 
=
= 
  1                                       
  /                                       
 |                                        
 |  /           3                 8       
 |  |       -I*x              25*x        
 |  |-------------------  for ----- > 1   
 |  |       ____________        9         
 |  |      /          8                   
 |  |     /       25*x                    
 |  |3*  /   -1 + -----                   
 |  |  \/           9                     
 |  <                                   dx
 |  |         3                           
 |  |        x                            
 |  |------------------     otherwise     
 |  |       ___________                   
 |  |      /         8                    
 |  |     /      25*x                     
 |  |3*  /   1 - -----                    
 |  \  \/          9                      
 |                                        
/                                         
0
$$\int\limits_{0}^{1} \begin{cases} - \frac{i x^{3}}{3 \sqrt{\frac{25 x^{8}}{9} - 1}} & \text{for}\: \frac{25 x^{8}}{9} > 1 \\\frac{x^{3}}{3 \sqrt{1 - \frac{25 x^{8}}{9}}} & \text{otherwise} \end{cases}\, dx$$ 
Integral(Piecewise((-i*x^3/(3*sqrt(-1 + 25*x^8/9)), 25*x^8/9 > 1), (x^3/(3*sqrt(1 - 25*x^8/9)), True)), (x, 0, 1))
Numerical answer [src] 
(0.0789597690179029 - 0.0488269922453112j)
(0.0789597690179029 - 0.0488269922453112j)

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

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