Evaluate each of the following integrals:

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{e^{\sqrt[\phantom{2}]{x1}}}{\sqrt[\phantom{2}]{x1}}dx$

$($b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}sin\sqrt[\phantom{2}]{7-2cos}d$

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

$($d$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2xln(x^{2}1)}{x^{2}1}dx$

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

$($f$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\sqrt[\phantom{2}]{44co{t}^{2}2t}dt$