How do you evaluate the integral int xe^(-x^2)?

Feb 27, 2017

The answer is $= - \frac{1}{2} {e}^{- {x}^{2}} + C$

Explanation:

We perform this integral by substitution

Let $u = - {x}^{2}$

$\mathrm{du} = - 2 x \mathrm{dx}$

$x \mathrm{dx} = - \frac{\mathrm{du}}{2}$

Therefore,

$\int x {e}^{- {x}^{2}} \mathrm{dx} = \int - \frac{1}{2} {e}^{u} \mathrm{du}$

$= - \frac{1}{2} {e}^{u}$

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