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

The integral from 3 to infinity of xe^{-3x} is (10)/(9e^9)

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

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

\frac{10}{9 e ^{9}}

Decimal

0.00013 \dots

Solution steps

\int_{3}^{\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_{3}^{\infty} x e^{- 3 x} d x = 0 - (- \frac{10}{9 e ^{9}})

= 0 - (- \frac{10}{9 e ^{9}})

Simplify

= \frac{10}{9 e ^{9}}

What is the integral from 3 to infinity of xe^{-3x} ?
The integral from 3 to infinity of xe^{-3x} is (10)/(9e^9)