What is the integral of (4x+10)e^{-2x} ?

The integral of (4x+10)e^{-2x} is -2e^{-2x}x-6e^{-2x}+C

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integral of (4x+10)e^{-2x}

\int (4 x + 10) e^{- 2 x} d x

- 2 e^{- 2 x} x - 6 e^{- 2 x} + C

Solution steps

\int (4 x + 10) e^{- 2 x} d x

Apply Integration By Parts

: - e^{- 2 x} (2 x + 5) - \int - 2 e^{- 2 x} d x

= - e^{- 2 x} (2 x + 5) - \int - 2 e^{- 2 x} d x

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

= - e^{- 2 x} (2 x + 5) - e^{- 2 x}

Simplify

- e^{- 2 x} (2 x + 5) - e^{- 2 x} : - 2 e^{- 2 x} x - 6 e^{- 2 x}

= - 2 e^{- 2 x} x - 6 e^{- 2 x}

Add a constant to the solution

= - 2 e^{- 2 x} x - 6 e^{- 2 x} + C

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What is the integral of (4x+10)e^{-2x} ?
The integral of (4x+10)e^{-2x} is -2e^{-2x}x-6e^{-2x}+C