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

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

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

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

2 sinh (x) + C

Solution steps

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

Rewrite using trig identities

= \int 2 cosh (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int cosh (x) d x

Use the common integral:

\int cosh (x) d x = sinh (x)

= 2 sinh (x)

Add a constant to the solution

= 2 sinh (x) + C

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