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

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

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integral of e^{-y^2}y

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

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

Solution steps

\int e^{- y^{2}} y 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^{^{'}} = 5 - y

\int_{0}^{5} \frac{x}{1 + 4 x} d x

\int \frac{2 x ^{3} - 3 x ^{2} - 3 x + 2}{x - 2} d x

\int_{0}^{2} x - 1 d x

x^{^{''}} + 2 x = 0, x (0) = 1, x (1) = 0

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