How would I go about finding the indefinite integral of $\sqrt{1+x^2}\cos^3{x}\sin^3{x}$? I'm aware that any definite integral of it that is symmetric about zero will be zero because the function is odd, but how would I go about finding its indefinite integral?
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Do you have some reason to think it has an indefinite integral in closed form? Or do you want an integral as an infinite series or something? – GEdgar Oct 04 '15 at 22:29
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I found it on a practice test, and while I thought the goal of the problem was to be able to identity the parity, some part of me thought it would have a closed for. But now it has my interest, and any kind of solution would be interesting to see... – Bob Oct 04 '15 at 22:32
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1If by absurd the indefinite integral were to have a closed form, it could only be expressed in terms of “incomplete” Bessel functions, or $($ generalized $)$ hypergeometric series. – Lucian Oct 05 '15 at 02:24