• Support PF! Buy your school textbooks, materials and every day products Here!

Integrate (x^2)(sqrt(x^2-a^2))^(-1)

  • Thread starter coverband
  • Start date
  • #1
171
0
Anyone know how to integrate this?

Thanks
 

Answers and Replies

  • #2
296
15
Yes. Start by factoring out 1/a, then make the trig substitution [tex]x = a \sec \theta[/tex]. After simplification, you will obtain an integral in terms of secant cubed, for which there is an entire http://en.wikipedia.org/wiki/Integral_of_secant_cubed" [Broken] devoted to explaining how to integrate that. Do so, back-substitute, and simplify. Or alternatively, simply look this up in your handy table of integrals, and find that the solution is:

<< complete solution deleted by berkeman >>
 
Last edited by a moderator:
  • #3
Fredrik
Staff Emeritus
Science Advisor
Gold Member
10,851
407
[itex]y=\sqrt{x^2-a^2}[/itex] simplifies it a bit.
 

Related Threads on Integrate (x^2)(sqrt(x^2-a^2))^(-1)

Replies
5
Views
48K
  • Last Post
Replies
2
Views
2K
Replies
3
Views
12K
Replies
2
Views
1K
  • Last Post
Replies
8
Views
21K
  • Last Post
Replies
6
Views
53K
  • Last Post
Replies
6
Views
11K
Replies
25
Views
3K
  • Last Post
Replies
1
Views
7K
  • Last Post
Replies
5
Views
14K
Top