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

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

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

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

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

Solution steps

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

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 = y^{2}

= \frac{1}{2} e^{y^{2}}

Add a constant to the solution

= \frac{1}{2} e^{y^{2}} + C

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