Edit: Excuse me for being boring. xp I'll have to remember to use that.
Integration by parts should work fine.
u = e^x ... du = e^x
dv = cosxdx ... v = sinx
Doesn't look like it helps, does it? But, if we use integration by parts again for (e^x)sinxdx
Now some simple algebra, add to both sides
I trust you can take it from there.