Chapter 11.7, Problem 8P

Express the following integrals as $B$ functions, and then, by $(7.1),$ in terms of $\Gamma$ functions. When possible, use $\Gamma$ function formulas to write an exact answer in terms of $\pi ,\sqrt{2},$ etc. Compare your answers with computer results and reconcile any discrepancies.

${\displaystyle {\int }_0^2\frac{x^{2}dx}{\sqrt{2-x}}}$