What is the integral from 4 to infinity of xe^{-4x} ?

The integral from 4 to infinity of xe^{-4x} is (17)/(16e^{16)}

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integral from 4 to infinity of xe^{-4x}

\int_{4}^{\infty} x e^{- 4 x} d x

\frac{17}{16 e ^{16}}

Decimal Notation

1.19569 E - 7

Solution steps

\int_{4}^{\infty} x e^{- 4 x} d x

Compute the indefinite integral:

\int x e^{- 4 x} d x = \frac{1}{16} (- 4 e^{- 4 x} x - e^{- 4 x}) + C

Compute the boundaries:

\int_{4}^{\infty} x e^{- 4 x} d x = 0 - (- \frac{17}{16 e ^{16}})

= 0 - (- \frac{17}{16 e ^{16}})

Simplify

= \frac{17}{16 e ^{16}}

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What is the integral from 4 to infinity of xe^{-4x} ?
The integral from 4 to infinity of xe^{-4x} is (17)/(16e^{16)}