What is the integral of e^{4x}+e^{-2x} ?

The integral of e^{4x}+e^{-2x} is 1/4 e^{4x}-1/2 e^{-2x}+C

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integral of e^{4x}+e^{-2x}

\int e^{4 x} + e^{- 2 x} d x

\frac{1}{4} e^{4 x} - \frac{1}{2} e^{- 2 x} + C

Solution steps

\int e^{4 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^{4 x} d x + \int e^{- 2 x} d x

\int e^{4 x} d x = \frac{1}{4} e^{4 x}

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

= \frac{1}{4} e^{4 x} - \frac{1}{2} e^{- 2 x}

Add a constant to the solution

= \frac{1}{4} e^{4 x} - \frac{1}{2} e^{- 2 x} + C

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What is the integral of e^{4x}+e^{-2x} ?
The integral of e^{4x}+e^{-2x} is 1/4 e^{4x}-1/2 e^{-2x}+C