Matematické Fórum

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1.st step is to get rid of the power using common trigonometric identities



where





Looking closer to using another trig identity :



For the integrand function in there holds therefore .

As for I tried to use Maclaurin expansion on nested trig function and switch the integral and sum order, getting to something like



there should be probably some discussion to verify the order interchange.

For each the integral on the right side is equal to zero.
For example by using integration by parts exhaustively for each there is possible to find primitive function
for the integrand in the shape like

for some finite set .

This gives and therefore .

As of similar approach should work as the integrand has only scaled variable when comparing to integrand in .

So I believe that the result should be .