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

The integral of 4e^{-2x}+4 is -2e^{-2x}+4x+C

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integral of 4e^{-2x}+4

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

- 2 e^{- 2 x} + 4 x + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 e^{- 2 x} d x + \int 4 d x

\int 4 e^{- 2 x} d x = - 2 e^{- 2 x}

\int 4 d x = 4 x

= - 2 e^{- 2 x} + 4 x

Add a constant to the solution

= - 2 e^{- 2 x} + 4 x + C

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