Question

Evaluate :$\int {2x}^3{e}^{x^2}dx$

Answer 1

Let, $x^2=t$

So, $2x.dx=dt$

$⟹\int t.e^{t}dt$

Solving By parts, we get

$⟹t.e^t-e^t+C$

$⟹x^2{e}^{x^2}-e^{x^2}+C$

$⟹e^{x^2}(x^2-1)+C$