Anyone has any idea how to perform the Fourier transform in this case?

Question

Anyone has any idea how to perform the Fourier transform in this case? I'm pretty new to the subject....

$$ f(t) = t^2 e^{-5|t|}$$

Answer 1

$$ \int_{-\infty}^{\infty}t^2 e^{-5|t|}e^{-ixt}dt = -\frac{d^2}{dx^2}\int_{-\infty}^{\infty}e^{-5|t|}e^{-ixt}dt \\ = -\frac{d^2}{dx^2}\left[\int_{-\infty}^{0}e^{5t}e^{-ixt}dt+\int_{0}^{\infty}e^{-5t}e^{-ixt}dt\right] \\ = -\frac{d^2}{dx^2}\left[\frac{1}{5-ix}+\frac{1}{5+ix}\right] \\ = -\frac{d^2}{dx^2}\left[\frac{10}{25+x^2}\right] $$