Chapter 7.13, Problem 16MP

Given find the cosine transform of $f(x)$ and use it to write $f(x)$ as an integral. Use your result to evaluate $\begin{array}{ll}\hfill & {\displaystyle {\int }_0^{\infty }\frac{{\cos }^2\alpha {\sin }^2\alpha /2}{{\alpha }^2}}d\alpha \hfill \end{array}$.