What is the integral of (x^2-2x)e^{-x} ?

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

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integral of (x^2-2x)e^{-x}

\int (x^{2} - 2 x) e^{- x} d x

- e^{- x} x^{2} + C

Solution steps

\int (x^{2} - 2 x) e^{- x} d x

Apply Integration By Parts

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

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

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

Simplify

- e^{- x} (x^{2} - 2 x) - 2 e^{- x} x : - e^{- x} x^{2}

= - e^{- x} x^{2}

Add a constant to the solution

= - e^{- x} x^{2} + C

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