What is the integral of xe^{-0.2x^2} ?

The integral of xe^{-0.2x^2} is -2.5e^{-0.2x^2}+C

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integral of xe^{-0.2x^2}

\int x e^{- 0.2 x^{2}} d x

- 2.5 e^{- 0.2 x^{2}} + C

Solution steps

\int x e^{- 0.2 x^{2}} d x

Apply u-substitution

: \int - \frac{e ^{u}}{0.4} d u

= \int - \frac{e ^{u}}{0.4} d u

Take the constant out:

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

= - \frac{1}{0.4} \cdot \int e^{u} d u

Simplify

= - 2.5 \cdot \int e^{u} d u

Use the common integral:

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

= - 2.5 e^{u}

Substitute back

u = - 0.2 x^{2}

= - 2.5 e^{- 0.2 x^{2}}

Add a constant to the solution

= - 2.5 e^{- 0.2 x^{2}} + C

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What is the integral of xe^{-0.2x^2} ?
The integral of xe^{-0.2x^2} is -2.5e^{-0.2x^2}+C