I have the integral with $\sin()$ sum expression in $\cos()$ argument: $$\int_0^{2\pi}e^{-\sin^2x}\cos\Bigl(6x-\frac{\sin(2x)}{2}\Bigr)dx.$$ Can anyone please explain an algorithm for solving it?
I've tried so far: Weierstrass substitution (if I can use it with $\int \cos(f(x))dx$), Euler formula, integration by parts, formula of $\cos(x-y)$ and $\sin(2x)$ formula and everything not seems to work or I make actions not in the right order. Need some fresh view on the problem.
Thanks!