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

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

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

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

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

Solution steps

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

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

\int 2 d x = 2 x

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

Simplify

= 2 e^{- x} + 2 x

Add a constant to the solution

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

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