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

= \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

\frac{\partial}{\partial x} (sin^{2} (k x))

y^{^{'}} - \frac{9}{x} y = \frac{( y ^{5} )}{x ^{8}}

y = sin (5 x)

\int (x^{2} + 1)^{3} d x

\int \frac{1}{2 t} d t

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