Evaluate the following integral:

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x{e}^{2x}dx$

$($b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{3x+2}{(x-1)(x+4)}dx$

$($c$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^2}{\sqrt[\phantom{2}]{3-x^2}}dx$

$($d$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xcosxdx$

$($e$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x-5}{(x+3)(x-2)}dx$

$($f$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{e}^{3x}sin(2x)dx$

$($g$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x-1}{(x+1)(x^2+3x+4)}dx$

$($h$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\sqrt[\phantom{2}]{x}ln(5x)dx$

$($i$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{\sqrt[\phantom{2}]{x^2-7}}dx$