Determine the indefinite integral: $I=\int \frac{\sin^5x\arcsin^5x}{e^{5x}\ln^5x}dx$ [closed]

Determine the indefinite integral: $$I = \int{\sin^{5}\left(x\right)\arcsin^{5}\left(x\right) \over {\rm e}^{5x}\ln^{5}\left(x\right)}\,{\rm d}x$$

I have not seen this ever, so do not know how solve. Please help me come up with a method of solving the problem.

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closed as off-topic by Carl Mummert, kjetil b halvorsen, Fabian, Harish Chandra Rajpoot, yoknapatawphaDec 31 '15 at 0:34

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What makes you think there's a closed-form solution for problems like this? – Ted Shifrin Dec 13 '13 at 14:24
What article? Even if you make all the exponents $5$ equal to $1$, I expect one could prove that there is no elementary antiderivative using differential algebra. – Ted Shifrin Dec 13 '13 at 14:31
Is a series solution okay? Can you post a link to the forum you found it in? – Brian Rushton Jan 4 '14 at 4:19
Series solution seams to be the only way. Otherwise, you should use numerical methods. – whatever Jan 4 '14 at 23:51
I think posting a question with no definite solution has become a good way to gain reputation.. – Apurv Jan 10 '14 at 5:20