Evaluate the following integral by using substitution method

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x{e}^{x^2}dx=$

a$.\frac{x^2}{2}{e}^{x^3}+c$

b$.x+e^{x^3}+c$

c$.e^{x^2}+c$

d$.e^x+c$

e$.\frac{e^{x^2}}{2}+c$