Fourier Transform

Find the Fourier cosine integral of $f(x)=\begin{cases}x^2, & 01\end{cases}$.

Find the Fourier cosine integral representation of $f(x)=e^{-kx}$ ($x>0$, $k>0$) and hence evaluate $\displaystyle\int_0^\infty\frac{\cos\omega x}{k^2+\omega^2}\,d\omega$.

Find the Fourier cosine integral representation of $f(x)=e^{-kx}$ ($x>0$, $k>0$) and hence show that $\displaystyle\int_0^\infty\frac{\cos\omega x}{k^2+\omega^2}\,d\omega=\frac{\pi}{2k}e^{-kx}$, $x>0$, $k>0$.