What is the integral from 1 to infinity of xe^{-12x} ?

The integral from 1 to infinity of xe^{-12x} is (13)/(144e^{12)}

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integral from 1 to infinity of xe^{-12x}

\int_{1}^{\infty} x e^{- 12 x} d x

\frac{13}{144 e ^{12}}

Decimal Notation

5.54686 E - 7

Solution steps

\int_{1}^{\infty} x e^{- 12 x} d x

Compute the indefinite integral:

\int x e^{- 12 x} d x = \frac{1}{144} (- 12 e^{- 12 x} x - e^{- 12 x}) + C

Compute the boundaries:

\int_{1}^{\infty} x e^{- 12 x} d x = 0 - (- \frac{13}{144 e ^{12}})

= 0 - (- \frac{13}{144 e ^{12}})

Simplify

= \frac{13}{144 e ^{12}}

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What is the integral from 1 to infinity of xe^{-12x} ?
The integral from 1 to infinity of xe^{-12x} is (13)/(144e^{12)}