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## Homework Statement

f(t)=te^t, find laplace

## Homework Equations

## The Attempt at a Solution

I started doing integration by parts and after doing it three times I wasn't sure if I was going in the right direction/making any progress. I'm not supposed to use a table to solve this (I have to do the integral out) so could anyone give me a hint as to how to start?

I can manipulate the original equation to

(0 to inf for all integrals)

∫ te^(t(1-s)) dt and then i set u=t, du=dt, dv=e^(t(1-s)), v=e^(t(1-s))/(1-s)

and then I end up with a longer expression and I need to integrate by parts again. is this is right direction?