I need help solving the integral of t * e^-3t dt

Question

I know that I have to solve using integration by parts and so I've let u=t to rid of dt and dv=e^-3t which I believe would yield -(1/3) * e^-3t as v. Am I doing this correctly?

Thanks. I appreciate the help. (:

Answer 1

Good work. So,

∫ u dv = uv - ∫ v du
= -1/3 t e^-3t - ∫ (-1/3) e^-3t dt

and you're almost done

Answer 2

Awesome, thanks for the help!