Question

∫[0,π,e^(3t)sin(3t),]dt

Answer 1

it looks like you have to integrate by parts two times letting u = e^(3t) and dv = sin(3t) and then in the second sub, keep the e expression in u and the cos value for dv. The integral part of the second resulting \[uv - \int\limits_{a}^{b} v du\] should look like a form of the original integral, in which case you can do some algebra with the initegral expressions and solve the integral.