## integral solution

### integral solution

*snip*

Hmm ... I seem to remember this question being asked a little while ago. If
you posted this before, go look at the original thread in which you posted
it -- I seem to remember at least two solutions being given in that thread.
If you can't find it, look at HELP SUBS.

--
Steve Lord
XXXX@XXXXX.COM

Dear All,

I am trying to evaluate the definite integral of the following function, but
encountered the problem of Hypergeometric2F1Regularized.

Input : Integrate[x^n*Sqrt[(C + x)/(L - x)], {x, 0, L}, Assumptions ->
C ≥ 0 && L ≥ 0 && n ≥ 0]

Output : \!\(If[C > 0 && L > 0, L\^n\ \@\(C\ L\)\ \@π\ Gamma[1 + n]\
Hypergeometric2F1Regularized[\(-\(1\/2\)\),
1 + n, 3\/2 + n, \(-\(L\/C\)\)], Integrate[x\^n\ \@\(\(C +
x\)\/\(L - \x\)\), {x, 0, L},
Assumptions -> C ≤ 0 || L ≤ 0]]\)

Here, for n = 0, 1, 2.... two conditions apply

1. L>= C >= 0, OR
2. C>= L >= 0

However, suppose I put n = 0, 1, 2,...10 individually in the integration, I'll
get a closed-form solution without the complexity of
Hypergeometric2F1Regularized.

Could anyone suggest any possibility of avoiding the presence of
"Hypergeometric2F1Regularized", in order to make the integral more
approachable in calculation? Many thanks in advance.

Cheers,

Jeffrey M.L.Tan