What is the integral from 5 to infinity of xe^{-3x} ?

The integral from 5 to infinity of xe^{-3x} is (16)/(9e^{15)}

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integral from 5 to infinity of xe^{-3x}

\int_{5}^{\infty} x e^{- 3 x} d x

\frac{16}{9 e ^{15}}

Decimal

5.43826 E - 7

Solution steps

\int_{5}^{\infty} x e^{- 3 x} d x

Compute the indefinite integral:

\int x e^{- 3 x} d x = \frac{1}{9} (- 3 e^{- 3 x} x - e^{- 3 x}) + C

Compute the boundaries:

\int_{5}^{\infty} x e^{- 3 x} d x = 0 - (- \frac{16}{9 e ^{15}})

= 0 - (- \frac{16}{9 e ^{15}})

Simplify

= \frac{16}{9 e ^{15}}

What is the integral from 5 to infinity of xe^{-3x} ?
The integral from 5 to infinity of xe^{-3x} is (16)/(9e^{15)}