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Condition Generation in Integrate


Greetings!

Integrate[
 Cos[\[Pi] x]^2*Sin[\[Pi] x (m + 1)]*Sin[\[Pi] x (n + 1)], {x, 0, 1}]

When I evaluate this I get an answer, however, there are some special cases (for example, m & n are both integers and m == n+2)in which this integral must yield different result. My question is, why doesn't it take in consideration all cases and doesn't generate conditional expressions?

Thank you.



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