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

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

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

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

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

Solution steps

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

Apply u-substitution

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

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

Simplify

\frac{1}{e ^{- u}} : e^{u}

= \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

\frac{\partial}{\partial x} (2 x ln (y))

\frac{d}{d x} (2 x^{2} - e^{x})

\frac{d}{d x} (e^{π} - e^{π x} + 2 π^{2})

y^{^{''}} + 2 y = sin (2 t)

tan (4 x)

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