What is the integral from 1 to infinity of xe^{-15x} ?

The integral from 1 to infinity of xe^{-15x} is (16)/(225e^{15)}

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integral from 1 to infinity of xe^{-15x}

\int_{1}^{\infty} x e^{- 15 x} d x

\frac{16}{225 e ^{15}}

Solution steps

\int_{1}^{\infty} x e^{- 15 x} d x

Compute the indefinite integral:

\int x e^{- 15 x} d x = \frac{1}{225} (- 15 e^{- 15 x} x - e^{- 15 x}) + C

Compute the boundaries:

\int_{1}^{\infty} x e^{- 15 x} d x = 0 - (- \frac{16}{225 e ^{15}})

= 0 - (- \frac{16}{225 e ^{15}})

Simplify

= \frac{16}{225 e ^{15}}

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What is the integral from 1 to infinity of xe^{-15x} ?
The integral from 1 to infinity of xe^{-15x} is (16)/(225e^{15)}