What is the integral from 0 to infinity of xe^{-6x} ?

The integral from 0 to infinity of xe^{-6x} is 1/36

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integral from 0 to infinity of xe^{-6x}

\int_{0}^{\infty} x e^{- 6 x} d x

\frac{1}{36}

Decimal Notation

0.02777 \dots

Solution steps

\int_{0}^{\infty} x e^{- 6 x} d x

Compute the indefinite integral:

\int x e^{- 6 x} d x = \frac{1}{36} (- 6 e^{- 6 x} x - e^{- 6 x}) + C

Compute the boundaries:

\int_{0}^{\infty} x e^{- 6 x} d x = 0 - (- \frac{1}{36})

= 0 - (- \frac{1}{36})

Simplify

= \frac{1}{36}

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What is the integral from 0 to infinity of xe^{-6x} ?
The integral from 0 to infinity of xe^{-6x} is 1/36