Evaluate the integral: ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{-17}{x^2\sqrt[\phantom{2}]{x^2+81}}dx$

$($A$)$ Which trig substitution is correct for this integral?

$x=81sin()$

$x=9tan()$

$x=81tan()$

$x=-17sec()$

$x=81sec()$

$x=9sin()$

$($B$)$ Which integral do you obtain after substituting for $x$ and simplifying?

Note: to enter $,$ type the word theta.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$

$d$

$($C$)$ What is the value of the above integral in terms of $?$

$1+C$

$($D$)$ What is the value of the original integral in terms of $x?$

$+C$