Question

Evaluate $\int x.e^{-x^2}dx$.

Answer 1

$I={\int }^{}x{e}^{-x^2}dx$

Putting $-x^2=t$

$\Rightarrow$$-$$2xdx=dt$

$\Rightarrow$$xdx=\frac{-dt}{2}$

$\Rightarrow I=\frac{-1}{2}{\int }^{}{e}^{t}dt$

$=\frac{-1}{2}{e}^t+c$

$=\frac{-1}{2}{e}^{-x^2}+c$