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

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

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integral of xe^{-y^2}

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

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

Solution steps

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

Take the constant out:

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

= e^{- y^{2}} \cdot \int x d x

Apply the Power Rule

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Add a constant to the solution

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

in t e g r a l \frac{x ^{- 1}}{2}

\int \frac{2 t + 3}{t} d t

\int sin (\frac{π}{4})

\int \frac{10 x ^{2}}{8 + 9 x} d x

\int \frac{x ^{3}}{1 - 16 x ^{8}} d x

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