Calculate the following integrals:

$($a$){\displaystyle \underset{1}{\overset{e}{}}}\frac{1}{x(1+lnx{)}^2}dx$

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

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

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

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

$($f$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(1+a{x}^2{)}^{2}dx$