What is the integral of (cosh(x))/(sinh(x)) ?

The integral of (cosh(x))/(sinh(x)) is ln|sinh(x)|+C

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integral of (cosh(x))/(sinh(x))

\int \frac{cosh ( x )}{sinh ( x )} d x

ln ∣ sinh (x) ∣ + C

Solution steps

\int \frac{cosh ( x )}{sinh ( 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 = sinh (x)

= ln ∣ sinh (x) ∣

Add a constant to the solution

= ln ∣ sinh (x) ∣ + C

x \to 0 + lim (\frac{2}{3 x ^{\frac{1}{3}}})

f (x) = - 4 x^{2}

\frac{\partial}{\partial y} (x e^{2 x - 3 y})

x \to 0 lim (\frac{sin ( 4 x ) cos ( 3 x )}{7 x})

x \to 0 lim (x^{x^{3}})

What is the integral of (cosh(x))/(sinh(x)) ?
The integral of (cosh(x))/(sinh(x)) is ln|sinh(x)|+C