What is the integral from 1 to infinity of xe^{-9x} ?

The integral from 1 to infinity of xe^{-9x} is (10)/(81e^9)

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integral from 1 to infinity of xe^{-9x}

\int_{1}^{\infty} x e^{- 9 x} d x

\frac{10}{81 e ^{9}}

Decimal Notation

0.00001 \dots

Solution steps

\int_{1}^{\infty} x e^{- 9 x} d x

Compute the indefinite integral:

\int x e^{- 9 x} d x = \frac{1}{81} (- 9 e^{- 9 x} x - e^{- 9 x}) + C

Compute the boundaries:

\int_{1}^{\infty} x e^{- 9 x} d x = 0 - (- \frac{10}{81 e ^{9}})

= 0 - (- \frac{10}{81 e ^{9}})

Simplify

= \frac{10}{81 e ^{9}}

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What is the integral from 1 to infinity of xe^{-9x} ?
The integral from 1 to infinity of xe^{-9x} is (10)/(81e^9)