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

\int \frac{( x - 1 ) ^{2}}{x ^{2}} d x

3 cos (8 x), 3 - 3 cos (8 x), [0, \frac{π}{8}]

\frac{d}{d x} (\frac{4}{3} x^{3} - 4 x + 3)

f (x) = \frac{1}{x - 4}

\int_{0}^{\frac{π}{3}} sin (x) ln (cos (x)) d x

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