What is the integral from 1 to infinity of xe^{-13x} ?

The integral from 1 to infinity of xe^{-13x} is (14)/(169e^{13)}

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integral from 1 to infinity of xe^{-13x}

\int_{1}^{\infty} x e^{- 13 x} d x

\frac{14}{169 e ^{13}}

Decimal

1.87246 E - 7

Solution steps

\int_{1}^{\infty} x e^{- 13 x} d x

Compute the indefinite integral:

\int x e^{- 13 x} d x = \frac{1}{169} (- 13 e^{- 13 x} x - e^{- 13 x}) + C

Compute the boundaries:

\int_{1}^{\infty} x e^{- 13 x} d x = 0 - (- \frac{14}{169 e ^{13}})

= 0 - (- \frac{14}{169 e ^{13}})

Simplify

= \frac{14}{169 e ^{13}}

What is the integral from 1 to infinity of xe^{-13x} ?
The integral from 1 to infinity of xe^{-13x} is (14)/(169e^{13)}