What is the integral from 0 to infinity of y^5e^{-y} ?

The integral from 0 to infinity of y^5e^{-y} is 120

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integral from 0 to infinity of y^5e^{-y}

\int_{0}^{\infty} y^{5} e^{- y} d y

120

Solution steps

\int_{0}^{\infty} y^{5} e^{- y} d y

Compute the indefinite integral:

\int y^{5} e^{- y} d y = - e^{- y} y^{5} - 5 (e^{- y} y^{4} - 4 (- e^{- y} y^{3} - 3 (e^{- y} y^{2} - 2 (- e^{- y} y - e^{- y})))) + C

Compute the boundaries:

\int_{0}^{\infty} y^{5} e^{- y} d y = 0 - (- 120)

= 0 - (- 120)

Simplify

= 120

What is the integral from 0 to infinity of y^5e^{-y} ?
The integral from 0 to infinity of y^5e^{-y} is 120