Evaluate the following integral by using integration by parts

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

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

b$.($:$2x^2-x+3\}))$

c$.\frac{e^{2x}}{2}(x^2-2x+\frac{1}{2})+c$

d$.e^{2x}(3x^2-3x+\frac{3}{2})+c$

e$.\frac{c^{2x}}{2}(3x^2-3x+\frac{3}{2})+c$