Evaluate the integrals. Show your work. $($Please answer all A through H problems$)$

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^2}{\sqrt[\phantom{2}]{4-x^2}}dx($Hint: Trig. substitution.$)$

$($b$){\displaystyle \underset{1}{\overset{}{}}}\frac{1}{1+t^2}dt($Hint: Derivative of $ta{n}^{-1}t)$

$($c$),{\displaystyle \underset{\frac{}{4}}{\overset{\frac{}{2}}{}}}ta{n}^3(2x)se{c}^3(2x)dx$

$($d$),{\displaystyle \underset{0}{\overset{}{}}}\sqrt[\phantom{2}]{1+cos(x)}dx($Hint: Half$-$angle identity.$)$

$($e$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{ln(x)}{x}dx($Hint: Integration by parts.$)$

$($f$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^2{e}^{x}dx($Hint: Two integrations by parts.$)$

$($g$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xsinh(x^2)dx($Hint: Substitution.$)$

$($h$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2x^2}{x^2-4x+3}dx($Hint: Polynomial division and partial fractions.$)$