PROBLEMS, SECTION $7$

Express the following integrals as $B$ functions, and then, by $(7\mathrm{.}1),$ in terms of $$ functions. When possible, use $$ function formulas to write an exact answer in terms of $,\sqrt[\phantom{2}]{2},$ etc. Compare your answers with computer results and reconcile any discrepancies.

${\displaystyle \underset{0}{\overset{1}{}}}\frac{x^{4}dx}{\sqrt[\phantom{2}]{1-x^2}}$

${\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}\sqrt[\phantom{2}]{si{n}^{3}xcosx}dx$

${\displaystyle \underset{0}{\overset{1}{}}}\frac{dx}{\sqrt[\phantom{2}]{1-x^3}}$