Consider the following function.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^3}{\sqrt[\phantom{2}]{64-x^2}}dx$

$($a$)$ Determine an appropriate trigonometric substitution.

the $x=8$ ste$(6),$ where $-\frac{}{2}\frac{}{2},$ slnce the integrand contains the expression $\sqrt[\phantom{2}]{8^2-x^2},$

Use $x=8$ tan $(0),$ where since the integrand contains the expression $\sqrt[\phantom{2}]{8^2-x^2},$

Use $x-8sec(8),$ where $08<mfrac><mrow><mi></mi></mrow><mrow><mn>2</mn></mrow></mfrac>$ or since the integrand contains the expression $\sqrt[\phantom{2}]{8^2-x^2}.$

$($b$)$ Apply the substitution to transform the integral into a trigenemetric integral. De not evaluate the integral.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^3}{\sqrt[\phantom{2}]{64-x^2}}dx={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}()d$