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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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5  
What makes you think there's a closed-form solution for problems like this? –  Ted Shifrin Dec 13 '13 at 14:24
    
I found this article on a math forum, but no one solution. –  Iloveyou Dec 13 '13 at 14:27
3  
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
3  
Is a series solution okay? Can you post a link to the forum you found it in? –  Brian Rushton Jan 4 at 4:19
2  
Series solution seams to be the only way. Otherwise, you should use numerical methods. –  metacompactness Jan 4 at 23:51

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