What is the integral from 0 to 5 of xe^{-x} ?

The integral from 0 to 5 of xe^{-x} is -6/(e^5)+1

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integral from 0 to 5 of xe^{-x}

\int_{0}^{5} x e^{- x} d x

- \frac{6}{e ^{5}} + 1

Decimal

0.95957 \dots

Solution steps

\int_{0}^{5} x e^{- x} d x

Apply Integration By Parts

= [- e^{- x} x - \int - e^{- x} d x]_{0}^{5}

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

= [- e^{- x} x - e^{- x}]_{0}^{5}

Compute the boundaries:

- \frac{6}{e ^{5}} + 1

= - \frac{6}{e ^{5}} + 1

What is the integral from 0 to 5 of xe^{-x} ?
The integral from 0 to 5 of xe^{-x} is -6/(e^5)+1