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

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

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integral of u^2e^{-u}

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

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

Solution steps

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

Apply Integration By Parts

: - e^{- u} u^{2} - \int - 2 e^{- u} u d u

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

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

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

Simplify

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

Add a constant to the solution

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

\int \frac{1}{4 x + 3} d x

\frac{d}{d x} (3 x^{5} + 7 x)

\frac{d}{d x} (4 x^{2} - 3 x)

\int 21 - x^{2} - 4 x d x

\frac{d}{d x} (2 x^{2} + 4 x y - x - 2 y)

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