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

x^{2} y^{^{''}} + 2 x y^{^{'}} - 12 y = 0, y (1) = 0, y^{^{'}} (1) = - 2

n = 1 \sum \infty \frac{1}{n ^{0}}

x \frac{d y}{d x} + 4 y = x^{3} - x

(1.3) (4.2)

y \frac{d y}{d t} = 2 t + 7

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