What is the integral of e^t-e^{-t} ?

The integral of e^t-e^{-t} is 2cosh(t)+C

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integral of e^t-e^{-t}

\int e^{t} - e^{- t} d t

2 cosh (t) + C

Solution steps

\int e^{t} - e^{- t} d t

Rewrite using trig identities

= \int 2 sinh (t) d t

Take the constant out:

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

= 2 \cdot \int sinh (t) d t

Use the common integral:

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

= 2 cosh (t)

Add a constant to the solution

= 2 cosh (t) + C