What is the integral of xe^{-3x^2+9} ?

The integral of xe^{-3x^2+9} is -1/6 e^{-3x^2+9}+C

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integral of xe^{-3x^2+9}

\int x e^{- 3 x^{2} + 9} d x

- \frac{1}{6} e^{- 3 x^{2} + 9} + C

Solution steps

\int x e^{- 3 x^{2} + 9} d x

Apply u-substitution

: \int - \frac{e ^{u}}{6} d u

= \int - \frac{e ^{u}}{6} d u

Take the constant out:

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

= - \frac{1}{6} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{6} e^{u}

Substitute back

u = - 3 x^{2} + 9

= - \frac{1}{6} e^{- 3 x^{2} + 9}

Add a constant to the solution

= - \frac{1}{6} e^{- 3 x^{2} + 9} + C

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What is the integral of xe^{-3x^2+9} ?
The integral of xe^{-3x^2+9} is -1/6 e^{-3x^2+9}+C