Evaluate the integral: ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{-30}{x^2\sqrt[\phantom{2}]{x^2+25}}dx$

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

$x=-30sec()$

$x=25tan()$

$x=25sin()$

$x=25sec()$

$x=5sin()$

$x=5tan()$

$($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 inteoral in terms of $?$

$$

$+C$

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

$$

$+c$