Hey there, I've been struggling with this one for quite a while; so much so that I created an account on here so that I could ask for some help

I(n) = integral of ((e^sinx)(cosx)(sin^n x))

I need to show that it comes down to I(n) = e - n I(n-1)

The integral doesn't have any limits, but I'm pretty sure I need to integrate by parts, but I've tried all the different combinations for u and dv/dx and haven't gotten anywhere.

Thanks for the help :)