Integrating $e^{ \cos(x)\sin(x)}$ from $0$ to $2\pi$ So i'm trying to find out how, or if its even possible, to integrate $e^{\sin(x)\cos(x)}$ analytically from $0$ to $2\pi$.
I know that i can integrate $e^{\cos(x)+\sin(x)}$ or $e^{\cos(x)^2}$ and these just give me Bessel functions.. but i don't know how to do the one in the title.. and google searches are coming up short.
Does anyone have any idea?
Cheers

You can use $\cos(x)\sin(x)=\frac 12 \sin(2x)$ and maybe $u=2x$ to get to a form you know.
