Evaluate the integral: ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{25}{x^2\sqrt[\phantom{2}]{x^2+16}}dx$

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

$x=16sec()$

$x=16sin()$

$x=16tan()$

$x=4tan()$

$x=25sec()$

$x=4sin()$

$($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 $x?$

$$

$+C$