What is the integral of (e^{7x}+e^{-2x}) ?

The integral of (e^{7x}+e^{-2x}) is 1/7 e^{7x}-1/2 e^{-2x}+C

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integral of (e^{7x}+e^{-2x})

\int (e^{7 x} + e^{- 2 x}) d x

\frac{1}{7} e^{7 x} - \frac{1}{2} e^{- 2 x} + C

Solution steps

\int e^{7 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^{7 x} d x + \int e^{- 2 x} d x

\int e^{7 x} d x = \frac{1}{7} e^{7 x}

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

= \frac{1}{7} e^{7 x} - \frac{1}{2} e^{- 2 x}

Add a constant to the solution

= \frac{1}{7} e^{7 x} - \frac{1}{2} e^{- 2 x} + C

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What is the integral of (e^{7x}+e^{-2x}) ?
The integral of (e^{7x}+e^{-2x}) is 1/7 e^{7x}-1/2 e^{-2x}+C