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

The integral of xe^{-x^2} is -1/2 e^{-x^2}+C

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integral of xe^{-x^2}

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

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

Solution steps

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

Apply u-substitution

: \int - \frac{e ^{u}}{2} d u

= \int - \frac{e ^{u}}{2} d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

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

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

Substitute back

u = - x^{2}

= - \frac{1}{2} e^{- x^{2}}

Add a constant to the solution

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

\int \frac{y + 1}{y} d y

f (x) = \frac{1}{x + 2}

\frac{\partial}{\partial x} (\frac{x}{3 + y})

\int \frac{1}{x ^{2} + 5 x + 4} d x

x \to 5 lim (x - 9)

What is the integral of xe^{-x^2} ?
The integral of xe^{-x^2} is -1/2 e^{-x^2}+C