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I want mathematica to evaluate a certain expression (see attached) assuming that n is an integer. The answer is far from what it produces. Maple produces the right answer but I don't have access to it.

The expression is

[tex]\frac{\int_{-\pi}^{\pi}|\sin(x)|\cos(nx)\dx}{\int_{-\pi}^{\pi}\cos^2(nx)\dx}[/tex]

The expression is

[tex]\frac{\int_{-\pi}^{\pi}|\sin(x)|\cos(nx)\dx}{\int_{-\pi}^{\pi}\cos^2(nx)\dx}[/tex]

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