Fourier Transform
$ X(\omega)=\int_{-\infty}^{\infty}x(t)e^{-j\omega t}dt $
$ x(t)=t^2 u(t) $
$ X(\omega)=\int_{-\infty}^{\infty}t^2 u(t) e^{-j\omega t}dt \; = \int_{0}^{\infty}t^2 e^{-j\omega t}dt $
Integration by Parts
$ u=t^2 \; \; \; \; \; \; \; \; \; \; \; \; dv = e^{-j \omega t} $
$ du=2t dt \; \; \; \; \; \; \; \; v = \frac{1}{-j\omega}e^{-j \omega t} $
