What is the integral of e^{x/a}+e^{-x/a} ?

The integral of e^{x/a}+e^{-x/a} is ae^{x/a}-ae^{-x/a}+C

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integral of e^{x/a}+e^{-x/a}

\int e^{\frac{x}{a}} + e^{- \frac{x}{a}} d x

a e^{\frac{x}{a}} - a e^{- \frac{x}{a}} + C

Solution steps

\int e^{\frac{x}{a}} + e^{- \frac{x}{a}} 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^{\frac{x}{a}} d x + \int e^{- \frac{x}{a}} d x

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

\int e^{- \frac{x}{a}} d x = - a e^{- \frac{x}{a}}

= a e^{\frac{x}{a}} - a e^{- \frac{x}{a}}

Add a constant to the solution

= a e^{\frac{x}{a}} - a e^{- \frac{x}{a}} + C

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