What is the integral of e^{-2x}-1 ?

The integral of e^{-2x}-1 is -1/2 e^{-2x}-x+C

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integral of e^{-2x}-1

\int e^{- 2 x} - 1 d x

- \frac{1}{2} e^{- 2 x} - x + C

Solution steps

\int e^{- 2 x} - 1 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 e^{- 2 x} d x - \int 1 d x

\int e^{- 2 x} d x = - \frac{1}{2} e^{- 2 x}

\int 1 d x = x

= - \frac{1}{2} e^{- 2 x} - x

Add a constant to the solution

= - \frac{1}{2} e^{- 2 x} - x + C

What is the integral of e^{-2x}-1 ?
The integral of e^{-2x}-1 is -1/2 e^{-2x}-x+C