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### How to force correct answers for Integrals of Cos[mx]*Cos[nx]? [duplicate]

This is a big problem if you do anything with a Fourier Series. This statement: Assuming[Element[{m, n}, Integers], Integrate[Cos[m*x]*Cos[n*x], {x, 0, 2 Pi}]] ...
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### Why does Assuming for Integrate not work as expected?

I'm trying to perform the following integral with Mathematica 7: ...
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### How to get a difference of two contour integrals depending on integer parameter?

I have two following functions: ...
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### Is this result wrong because of calculation time? (and more questions about Assumptions)

I am confused with the Integrate Given by Mathematica. First let's see a one-dimensional case: ...
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### Need help understandig the output of DSolve

I give Mathematica (10) the following command: DSolve[I D[P[x], {x, 2}] f[x] - (P'[x])^2 f[x] + 2 I P'[x] f'[x] == 0, P, x] And I have the following output: ...