Group Abstract Group Abstract

Message Boards Message Boards

0
|
13.2K Views
|
3 Replies
|
3 Total Likes
View groups...
Share
Share this post:

Why can't Mathematica solve this integral in definite form?

M. R.
Posted 12 years ago

Hi guys, Could you help me out? Why can't Mathematica solve this integral in definite form? It's just stuck computing.

Integrate[(1/Sqrt[(x - 1) (x^2 - a^2)]) - (1/ Sqrt[(x + 1) (x^2 - a^2)]), {x, a, b}] ->And it stuck

Integrate[(1/Sqrt[(x - 1) (x^2 - a^2)]) - (1/ Sqrt[(x + 1) (x^2 - a^2)]] -> this gets solved

Am I doing something wrong?

Thanks, M.
POSTED BY: M. R.
3 Replies
Sort By:
POSTED BY: Marco Thiel
M. R.
M. R.
Posted 12 years ago

Wow thanks, Marco. Thank you for the detailed answer. This does indeed seem to be the problem (I should have checked that myself).
POSTED BY: M. R.

Even if you use Assumptions->1<a<b I believe Integrate will have trouble on attempting to find Limit of the antiderivative at the endpoints. I do eventually get a result for this.

Integrate[1/Sqrt[(x - 1)*(x^2 - a^2)] - 1/Sqrt[(x + 1)*(x^2 - a^2)], 
    {x, a, b}, Assumptions -> b > a > 1]

(2*((2*I)*Sqrt[(-1 + a^2)*(-1 + b)] - (2*I)*Sqrt[(-1 + a^2)*(1 + b)] + 
   Sqrt[(1 + a)*(-1 + b^2)]*EllipticF[ArcSin[Sqrt[(a + b)/a]/Sqrt[2]], 
     (2*a)/(-1 + a)] - Sqrt[(-1 + a)*(-1 + b^2)]*
    EllipticF[ArcSin[Sqrt[(a + b)/a]/Sqrt[2]], (2*a)/(1 + a)] - 
   Sqrt[(1 + a)*(-1 + b^2)]*EllipticK[(2*a)/(-1 + a)] + 
   Sqrt[(-1 + a)*(-1 + b^2)]*EllipticK[(2*a)/(1 + a)]))/
 Sqrt[(-1 + a^2)*(-1 + b^2)]
POSTED BY: Daniel Lichtblau
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Tag limit exceeded
Note: Only the first five people you tag will receive an email notification; the other tagged names will appear as links to their profiles.
Reply Preview
Attachments
Remove
or Discard