How should I attack this ? $$ \int_0^{\pi} \cos(ax)^m \cos(x)^n dx$$
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Are $n$ and $m$ assumed to be integers or are they any real numbers? – andraiamatrix Jan 27 '14 at 23:19
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both $n, m$ are positive integers. $a$ is a real constant. – user1318806 Jan 27 '14 at 23:21
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Is this from a class/textbook? What methods have you been learning that might relate? Or what methods are in that section of the book? (As an added note, Wolfram was unable to compute this integral so I doubt it's going to have a simple answer). – andraiamatrix Jan 27 '14 at 23:50
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No its not from any textbooks. The power reduction formula seems to be the way to go. Here is the link http://math.stackexchange.com/questions/125539/power-reduction-formula. Express $\cos(ax)^m$ as a binomial series of $\cos(ax(m-k))$. You are right it seems like a mess. – user1318806 Jan 27 '14 at 23:58
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The result seems to be zero for any $m \neq n$ if $a$ is an integer? – Bennett Gardiner Jan 28 '14 at 13:01