What is the integral of (2e^x-3e^{-2x}) ?

The integral of (2e^x-3e^{-2x}) is 2e^x+3/2 e^{-2x}+C

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integral of (2e^x-3e^{-2x})

\int (2 e^{x} - 3 e^{- 2 x}) d x

2 e^{x} + \frac{3}{2} e^{- 2 x} + C

Solution steps

\int 2 e^{x} - 3 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 2 e^{x} d x - \int 3 e^{- 2 x} d x

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

\int 3 e^{- 2 x} d x = - \frac{3}{2} e^{- 2 x}

= 2 e^{x} - (- \frac{3}{2} e^{- 2 x})

Simplify

= 2 e^{x} + \frac{3}{2} e^{- 2 x}

Add a constant to the solution

= 2 e^{x} + \frac{3}{2} e^{- 2 x} + C

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What is the integral of (2e^x-3e^{-2x}) ?
The integral of (2e^x-3e^{-2x}) is 2e^x+3/2 e^{-2x}+C