How do you evaluate the integral $\int x e^{- x^{2}}$ $int xe^(-x^2)$ ?

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Answer 1 · 2017-02-27T10:14:25

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

We perform this integral by substitution

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

$d u = - 2 x d x$ $du=-2xdx$

$x d x = - \frac{d u}{2}$ $xdx=-(du)/2$

Therefore,

$\int x e^{- x^{2}} d x = \int - \frac{1}{2} e^{u} d u$ $intxe^(-x^2)dx=int-1/2e^(u)du$

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

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

How do you evaluate the integral ∫xe−x2int xe^(-x^2)?