Evaluate the integral: ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{\sqrt[\phantom{2}]{9x^2-25}}{x^3}dx$

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

$x=\frac{25}{9}sec()$

$x=\frac{1}{9}sec()$

$x=\frac{3}{5}sec()$

$x=\frac{5}{3}sin()$

$x=\frac{5}{3}sec()$

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

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

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

$d$

$($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 $x?$

Note: WAMAP does not recognize the inverse secant $($arcsec$)$ function. You will need to use another inverse trig function when you fill in your answer below.