What is the integral from 5 to infinity of xe^{-x/2} ?

The integral from 5 to infinity of xe^{-x/2} is (14)/(e^{5/2)}

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integral from 5 to infinity of xe^{-x/2}

\int_{5}^{\infty} x e^{- \frac{x}{2}} d x

\frac{14}{e ^{\frac{5}{2}}}

Decimal

1.14918 \dots

Solution steps

\int_{5}^{\infty} x e^{- \frac{x}{2}} d x

Compute the indefinite integral:

\int x e^{- \frac{x}{2}} d x = - 2 e^{- \frac{x}{2}} x - 4 e^{- \frac{x}{2}} + C

Compute the boundaries:

\int_{5}^{\infty} x e^{- \frac{x}{2}} d x = 0 - (- \frac{14}{e ^{\frac{5}{2}}})

= 0 - (- \frac{14}{e ^{\frac{5}{2}}})

Simplify

= \frac{14}{e ^{\frac{5}{2}}}

What is the integral from 5 to infinity of xe^{-x/2} ?
The integral from 5 to infinity of xe^{-x/2} is (14)/(e^{5/2)}