$(1)$ Compute the following integrals using integration by parts.

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(x6)e^{x}dx$

$($d$){\displaystyle \underset{0}{\overset{1}{}}}\frac{2x1}{e^x}dx$

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

$($c$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(4x-12)e^{-8x}dx$

$($e$){\displaystyle \underset{1}{\overset{9}{}}}ln(3x)dx$