$\displaystyle \int e^{sin(x)}cos(x) dx$

So I do;

$\displaystyle u = e^{sin(x)}$

$\displaystyle du = cos e^{sin(x)}$

dv = cos(x)

v = sin(x)

$\displaystyle

sin(x)e^{sin(x)} - \int sin(x)cose^{sin(x)}$

How do I proceed? It didn't become any simpler after using integration by parts.