Problem #$2$: By making an appropriate substitution, which of the following integrals is equal to

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}ta{n}^9(x)se{c}^3(x)dx$

$($A$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{u}^8(1+u^2{)}^{2}du$

$($B$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{u}^8(1-u^2{)}^{3}du$

$($C$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{u}^8(1+u^2)du$

$($D$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(u^2-1{)}^4{u}^{2}du$

$($E$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(u^2+1{)}^4$udu

$($F$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(u^2+1{)}^4{u}^{3}du$

$($G$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(u^2-1{)}^4{u}^{3}du$

$($H$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{u}^8(1-u^2{)}^{2}du$

Problem #$2$: $$