Question

Integrate:

$\int 2x^3{e}^{x^2}.dx$

Answer 1

$\int 2x^3{e}^{x^2}dx=\int 2x.x^2{e}^{x^2}Let,x^2=t\Rightarrow 2xdx=dt\therefore \int 2x^3{e}^{x^2}dx=\int t.e^{t}dt=t\int e^{t}dt+\int [\frac{dt}{dt}.\int e^{t}dt]dt=t.e^t+e^t+C=x^2{e}^{x^2}+e^{x^2}+C$