Find the indefinite integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}2x{e}^{x^2}dx.$

$\frac{e^{x^2}}{2}+C$

$2x{e}^{x^2}+C$

$e^{x^2}+C$

$2e^{x^2}+C$

$\frac{e^{x^2+1}}{x^2+1}+C$