How do I integrate e^x (sinx)^2

How do I integrate (e^x)*(sinx)^2 ??

I know I need integration by parts.

If I choose e^x as my 'u' i get
e^x (sinx)^2 - integral of e^x 2sin(x)cos(x) dx
and I don't know how to solve that integral either

Maybe I picked the wrong 'u' though..

Thanks!

Use an identity first. There is the half-angle identity

sin²(x) = ½ - ½cos(2x).

The integrand is then (1/2)e^x - (1/2)e^x cos(2x). The first term can be integrated straight away. The second term requires integration by parts.

With e^x cos(2x), integrate by parts twice until you get the same integral---with integrand e^x cos(2x)---on both sides of the equation with different coefficients. Then solve algebraically.

You can choose u = e^x each time you integrate by parts.