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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

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