What is the integral from 0 to infinity of xe^{-5x} ?

The integral from 0 to infinity of xe^{-5x} is 1/25

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integral from 0 to infinity of xe^{-5x}

\int_{0}^{\infty} x e^{- 5 x} d x

\frac{1}{25}

Decimal

0.04

Solution steps

\int_{0}^{\infty} x e^{- 5 x} d x

Compute the indefinite integral:

\int x e^{- 5 x} d x = \frac{1}{25} (- 5 e^{- 5 x} x - e^{- 5 x}) + C

Compute the boundaries:

\int_{0}^{\infty} x e^{- 5 x} d x = 0 - (- \frac{1}{25})

= 0 - (- \frac{1}{25})

Simplify

= \frac{1}{25}

What is the integral from 0 to infinity of xe^{-5x} ?
The integral from 0 to infinity of xe^{-5x} is 1/25