Question

∫e^x(3x^2)

Answer 1

Integration by parts 2 times,
You can let
\(u=3x^2 \\ du=6xdx\)\[dv=e^x dx \\ v=e^x\]

Answer 2

Then
\[\int\limits e^x(3x^2)dx \\ =3x^2e^x-6\int\limits e^x xdx\]

Answer 3

Use Integration by parts one more time for
\[3x^2e^x-6\int\limits\limits e^x xdx\]