What is the integral of y^2e^{-y} ?

The integral of y^2e^{-y} is -e^{-y}y^2+2(-e^{-y}y-e^{-y})+C

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integral of y^2e^{-y}

\int y^{2} e^{- y} d y

- e^{- y} y^{2} + 2 (- e^{- y} y - e^{- y}) + C

Solution steps

\int y^{2} e^{- y} d y

Apply Integration By Parts

= - e^{- y} y^{2} - \int - 2 e^{- y} y d y

\int - 2 e^{- y} y d y = - 2 (- e^{- y} y - e^{- y})

= - e^{- y} y^{2} - (- 2 (- e^{- y} y - e^{- y}))

Simplify

= - e^{- y} y^{2} + 2 (- e^{- y} y - e^{- y})

Add a constant to the solution

= - e^{- y} y^{2} + 2 (- e^{- y} y - e^{- y}) + C

What is the integral of y^2e^{-y} ?
The integral of y^2e^{-y} is -e^{-y}y^2+2(-e^{-y}y-e^{-y})+C