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

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

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

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

e^{3 + x} + e^{x - 3} + C

Solution steps

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

\int e^{x + 3} d x = e^{3 + x}

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

= e^{3 + x} + e^{x - 3}

Add a constant to the solution

= e^{3 + x} + e^{x - 3} + C

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