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  • Identical expressions

  • (one * two)*sqrt((a^ three - three *x^ two)/(a-x))
  • (1 multiply by 2) multiply by square root of ((a cubed minus 3 multiply by x squared ) divide by (a minus x))
  • (one multiply by two) multiply by square root of ((a to the power of three minus three multiply by x to the power of two) divide by (a minus x))
  • (1*2)*√((a^3-3*x^2)/(a-x))
  • (1*2)*sqrt((a3-3*x2)/(a-x))
  • 1*2*sqrta3-3*x2/a-x
  • (1*2)*sqrt((a³-3*x²)/(a-x))
  • (1*2)*sqrt((a to the power of 3-3*x to the power of 2)/(a-x))
  • (12)sqrt((a^3-3x^2)/(a-x))
  • (12)sqrt((a3-3x2)/(a-x))
  • 12sqrta3-3x2/a-x
  • 12sqrta^3-3x^2/a-x
  • (1*2)*sqrt((a^3-3*x^2) divide by (a-x))
  • (1*2)*sqrt((a^3-3*x^2)/(a-x))dx

  • Similar expressions

  • (1*2)*sqrt((a^3-3*x^2)/(a+x))
  • (1*2)*sqrt((a^3+3*x^2)/(a-x))
Solving integrals/ (1*2)*sqrt((a^3-3*x^2)/(a-x))

Integral of (1*2)*sqrt((a^3-3*x^2)/(a-x)) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src] 
     ____________                     
    /    2                            
  \/  - x  + a*x                      
         /                            
        |                             
        |               ___________   
        |              /  3      2    
        |             /  a  - 3*x     
        |        2*  /   ---------  dx
        |          \/      a - x      
        |                             
       /                              
    ____________                      
   /    2                             
-\/  - x  + a*x
$$\int\limits_{- \sqrt{a x - x^{2}}}^{\sqrt{a x - x^{2}}} 2 \sqrt{\frac{a^{3} - 3 x^{2}}{a - x}}\, dx$$ 
Integral(2*sqrt((a^3 - 3*x^2)/(a - x)), (x, -sqrt(-x^2 + a*x), sqrt(-x^2 + a*x)))
The answer (Indefinite) [src] 
  /                                /                   
 |                                |                    
 |        ___________             |      ___________   
 |       /  3      2              |     /  3      2    
 |      /  a  - 3*x               |    /  a  - 3*x     
 | 2*  /   ---------  dx = C + 2* |   /   ---------  dx
 |   \/      a - x                | \/      a - x      
 |                                |                    
/                                /
$$\int 2 \sqrt{\frac{a^{3} - 3 x^{2}}{a - x}}\, dx = C + 2 \int \sqrt{\frac{a^{3} - 3 x^{2}}{a - x}}\, dx$$
Simplify

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

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