Determine the indefinite integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}21x^6{e}^{x^7}dx.$

Possibilities:

$($a$)3e^x+C$

$($b$)\frac{1}{3}{e}^{x^7}+C$

$($c$)147x^{12}{e}^{x^7}+126x^5{e}^{x^7}+C$

$($d$)3e^{x^7}+C$

$($e$)\frac{1}{3}{e}^x+C$