A student using the trig substitution $x=2tan()$ to solve ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^2}{\sqrt[\phantom{2}]{4x^2}}dx$ rewrites the integration using the substitution to get which of the following integral?

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{ta{n}^2()}{sec()}d$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{ta{n}^2()}{4se{c}^2()}d$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}4ta{n}^2()d$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}2\frac{ta{n}^2()}{sec()}d$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}4ta{n}^2()sec()d$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}8ta{n}^2()se{c}^2()d$