What is the integral of xe^{-(x^2)/2} ?

The integral of xe^{-(x^2)/2} is -e^{-(x^2)/2}+C

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integral of xe^{-(x^2)/2}

\int x e^{- \frac{x ^{2}}{2}} d x

- e^{- \frac{x ^{2}}{2}} + C

Solution steps

\int x e^{- \frac{x ^{2}}{2}} d x

Apply u-substitution

: \int - e^{u} d u

= \int - e^{u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= - e^{u}

Substitute back

u = - \frac{x ^{2}}{2}

= - e^{- \frac{x ^{2}}{2}}

Add a constant to the solution

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

\int \frac{1}{6 x ^{4}} d x

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\int 1.3 y ln (x^{1.3} y^{2}) - 1.3 y d x

\frac{d}{d x} (3 x + 2 y)

x \to 3 lim (\frac{9 - x ^{2}}{x - 3})

What is the integral of xe^{-(x^2)/2} ?
The integral of xe^{-(x^2)/2} is -e^{-(x^2)/2}+C