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

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

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

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

- 2 e^{x} x + C

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

= - 2 e^{x} x

Add a constant to the solution

= - 2 e^{x} x + C

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