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

  • #1
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. :)
 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
Gold Member
5,002
6
Try by parts with [itex]u=x^2[/itex] and [itex]dv=x\sqrt{1-x^2}dx[/itex]....and post your work if you get stuck
 
  • #3
got it! Thank you very much.
 

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

  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
6
Views
11K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
7
Views
2K
Replies
11
Views
849
Replies
5
Views
48K
Replies
3
Views
12K
Replies
6
Views
1K
Replies
2
Views
1K
Replies
3
Views
1K
Top