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[tex]\int_0^{\pi}\;\frac{k_1}{-k_2\left(2R\;(k_3\cos{\alpha}+k_4\sin{\alpha})-k_5\right)^{1.5}}[/tex]

All the [tex]k_i\;'s[/tex] are constants and so is R.

I tried writing out an infinite series for [tex]\left(2R\;(k_3\cos{\alpha}+k_4\sin{\alpha})-k_5\right)^{-1.5}[/tex] in Maple and then integrating. But the solution is nasty with the first 4 terms considered. It has got quite a few terms to deal with.

I then tried performing numerical integration by using the Simpson's rule, but the solution again has too many terms in it.

So is there any easier way to solve this or will I have to live with the multi-term solution that I get from both the methods I used?

Any sort of help will be highly appreciated.

Thanks