What is the integral of xe^{-7x^2} ?

The integral of xe^{-7x^2} is -1/14 e^{-7x^2}+C

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integral of xe^{-7x^2}

\int x e^{- 7 x^{2}} d x

- \frac{1}{14} e^{- 7 x^{2}} + C

Solution steps

\int x e^{- 7 x^{2}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{14} d u

= \int - \frac{e ^{u}}{14} d u

Take the constant out:

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

= - \frac{1}{14} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{14} e^{u}

Substitute back

u = - 7 x^{2}

= - \frac{1}{14} e^{- 7 x^{2}}

Add a constant to the solution

= - \frac{1}{14} e^{- 7 x^{2}} + C

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What is the integral of xe^{-7x^2} ?
The integral of xe^{-7x^2} is -1/14 e^{-7x^2}+C