What is the integral from infinity to 0 of xe^{-4x} ?

The integral from infinity to 0 of xe^{-4x} is -1/16

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integral from infinity to 0 of xe^{-4x}

\int_{\infty}^{0} x e^{- 4 x} d x

- \frac{1}{16}

Decimal Notation

- 0.0625

Solution steps

\int_{\infty}^{0} x e^{- 4 x} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{\infty} x e^{- 4 x} d x

\int_{0}^{\infty} x e^{- 4 x} d x = \frac{1}{16}

= - \frac{1}{16}

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What is the integral from infinity to 0 of xe^{-4x} ?
The integral from infinity to 0 of xe^{-4x} is -1/16