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

The integral of ((e^x-e^{-x})/(e^x+e^{-x)}) is ln|e^x+e^{-x}|+C

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

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

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

Solution steps

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

Apply u-substitution

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

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

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

Add a constant to the solution

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

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