Integration by parts [ x^3 * sqrt (1 - x^2)

[amcloughlan]

I have tried pretty much every method I can think of to solve this integral but I haven't managed to get much luck. I used a derivative value (U) of x^3 and managed to get a x^5 term inside the next part and there is no easy way to get a derivative for the square root of 1-x^2.

I tried subbing in x=sinx but that didn't work either after using the pythagorean identity to get cosx after removing the square root. I worked it out got jibberish as an answer.

I'd rather know how I could go about doing this rather than get an answer! Thanks. :)

 

[gabbagabbahey]

Try by parts with $u=x^2$ and $dv=x\sqrt{1-x^2}dx$...and post your work if you get stuck

 

[amcloughlan]

got it! Thank you very much.