What is the integral of xe^{-9x^2} ?

The integral of xe^{-9x^2} is -1/18 e^{-9x^2}+C

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integral of xe^{-9x^2}

\int x e^{- 9 x^{2}} d x

- \frac{1}{18} e^{- 9 x^{2}} + C

Solution steps

\int x e^{- 9 x^{2}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{18} d u

= \int - \frac{e ^{u}}{18} d u

Take the constant out:

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

= - \frac{1}{18} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= - \frac{1}{18} e^{u}

Substitute back

u = - 9 x^{2}

= - \frac{1}{18} e^{- 9 x^{2}}

Add a constant to the solution

= - \frac{1}{18} e^{- 9 x^{2}} + C

y^{^{'}} + e^{x + y} = 0

t \to 0 lim (sin (8 t))

\frac{x y d y}{d x} + y^{2} = 2 x

sin (e^{4 x})

\frac{d}{d x} (\frac{1 - x e ^{x}}{x + e ^{x}})

What is the integral of xe^{-9x^2} ?
The integral of xe^{-9x^2} is -1/18 e^{-9x^2}+C