What is the integral from 0 to infinity of 3xe^{-x} ?

The integral from 0 to infinity of 3xe^{-x} is 3

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integral from 0 to infinity of 3xe^{-x}

\int_{0}^{\infty} 3 x e^{- x} d x

3

Solution steps

\int_{0}^{\infty} 3 x e^{- x} d x

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- 3)

Simplify

= 3

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What is the integral from 0 to infinity of 3xe^{-x} ?
The integral from 0 to infinity of 3xe^{-x} is 3