integrals.wolfram.com   Use one of Mathematica's 2500+ functions FREE online

Wolfram Mathematica Online Integrator
The world's only full-power integration solver
∫

An image showing the results of your requested integral.


Integrate[x^2*Sqrt[(a^2 - x^2)^3], x] ==
-(Sqrt[(a^2 - x^2)^3]*(x*Sqrt[a^2 - x^2]* (3*a^4 - 14*a^2*x^2 + 8*x^4) - 3*a^6*ArcTan[x/Sqrt[a^2 - x^2]]))/ (48*(a^2 - x^2)^(3/2))



           2        2    2 3
Integrate[x  Sqrt[(a  - x ) ], x] == 

         2    2 3           2    2
-(Sqrt[(a  - x ) ] (x Sqrt[a  - x ] 
 
            4       2  2      4
        (3 a  - 14 a  x  + 8 x ) - 
 
          6              x
       3 a  ArcTan[-------------])) / 
                         2    2
                   Sqrt[a  - x ]
 
        2    2 3/2
  (48 (a  - x )   )

Time to compute: 0.23 second

Spread the word: