${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^2}{\sqrt[\phantom{2}]{x^2-7}}dx$

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

Use $x=\sqrt[\phantom{2}]{7}sin(),$ where $-\frac{}{2}\frac{}{2},$ since the integrand contains the expression $\sqrt[\phantom{2}]{x^2-7}.$

Use $x=\sqrt[\phantom{2}]{7}tan(),$ where since the integrand contains the expression $\sqrt[\phantom{2}]{x^2-7}.$

Use $x=\frac{r}{b}ar(7)sec(0),$ where $00<mfrac><mrow><mi></mi></mrow><mrow><mn>2</mn></mrow></mfrac>$ or since the integrand contains the expression

$($b$)$ Apply the substitution to transform the integral into a trigonometric integral. Do not evaluate the integr $$