What is the integral from 0 to infinity of r^4e^{-r} ?

The integral from 0 to infinity of r^4e^{-r} is 24

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integral from 0 to infinity of r^4e^{-r}

\int_{0}^{\infty} r^{4} e^{- r} d r

24

Solution steps

\int_{0}^{\infty} r^{4} e^{- r} d r

Compute the indefinite integral:

\int r^{4} e^{- r} d r = - e^{- r} r^{4} + 4 (- e^{- r} r^{3} - 3 (e^{- r} r^{2} - 2 (- e^{- r} r - e^{- r}))) + C

Compute the boundaries:

\int_{0}^{\infty} r^{4} e^{- r} d r = 0 - (- 24)

= 0 - (- 24)

Simplify

= 24

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What is the integral from 0 to infinity of r^4e^{-r} ?
The integral from 0 to infinity of r^4e^{-r} is 24