Use $u-$substitution to evaluate the following indefinite integrals.

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

$($b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^3}{\sqrt[\phantom{2}]{2x^2+1}}dx$

$($c$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1-6x^2}{4x^3-2x+3}dx$

$($d$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^4+3x^3-2x^2+x-8}{x^2+2}dx$