$(2)$ Compute the following integrals, which require some combination of substitution and$/$or integration by parts.

$($a$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^3{e}^{x^4}dx$

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

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