What is the integral of ye^{-y^2} ?

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

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integral of ye^{-y^2}

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

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

Solution steps

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

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 = - y^{2}

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

Add a constant to the solution

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

y = - 3 - 7 x^{2}

\frac{d}{d x} (3^{4 x^{2} + 3 x})

\frac{\partial}{\partial x} (2 e^{x^{2}})

x \to 0 lim (\frac{14}{x})

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