Evaluate the integral: ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2\sqrt[\phantom{2}]{x^2-36}}{x^4}dx$

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

$x=6sin()$

$x=36tan()$

$x=2sin()$

$x=36sec()$

$x=6tan()$

$x=6sec()$

$($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 $?$

$$

$+C$

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

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