# Fourier Transform using Transform Pair and Properties

## Homework Statement

Finding the Fourier Transform using Transform Pair and Properties
x(t) = 2[u(t+1)- t$^{3}$e$^{6t}$u(t)]

## The Attempt at a Solution

For the first problem, I got
u(t) $\leftrightarrow$ ∏δ(ω)+$\frac{1}{jω}$
F(at-t$_{0}$) $\leftrightarrow$ $\frac{1}{|a|}$F($\frac{ω}{a}$)e$^{-jt_{0}(\frac{ω}{a})}$
The problem is I don't know what's next and where will I get the t$^{6}$ and e$^{6t}$. I don't even know what to do next. Please guide me.

Hopefully when I know already how to do this, I will be able to do other problems by myself.