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

The integral from 3 to infinity of xe^{-x} is 4/(e^3)

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

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

\frac{4}{e ^{3}}

Decimal Notation

0.19914 \dots

Solution steps

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

Compute the indefinite integral:

\int x e^{- x} d x = - e^{- x} x - e^{- x} + C

Compute the boundaries:

\int_{3}^{\infty} x e^{- x} d x = 0 - (- \frac{4}{e ^{3}})

= 0 - (- \frac{4}{e ^{3}})

Simplify

= \frac{4}{e ^{3}}

\int \frac{1}{x ^{4} x ^{2} - 2} d x

\frac{d}{d x} (\frac{cos ( 3 x ^{3} )}{tan ( 3 x ^{2} + 2 x )})

- \frac{3}{2} x^{2} + 4 x + 4

\int x^{- \frac{1}{5}} d x

What is the integral from 3 to infinity of xe^{-x} ?
The integral from 3 to infinity of xe^{-x} is 4/(e^3)