What is the integral of (sinh(x))/(1+cosh(x)) ?

The integral of (sinh(x))/(1+cosh(x)) is ln|1+cosh(x)|+C

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integral of (sinh(x))/(1+cosh(x))

\int \frac{sinh ( x )}{1 + cosh ( x )} d x

ln ∣ 1 + cosh (x) ∣ + C

Solution steps

\int \frac{sinh ( x )}{1 + cosh ( 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 = 1 + cosh (x)

= ln ∣ 1 + cosh (x) ∣

Add a constant to the solution

= ln ∣ 1 + cosh (x) ∣ + C

\frac{d y}{d x} = \frac{2 y}{x ^{2} - 1}

x sin^{2} (x)

3 x^{2} e^{x} + e^{x} x^{3}

x \to 0 lim (4 x^{2} - 2 x - 6)

x^{x^{3}}

What is the integral of (sinh(x))/(1+cosh(x)) ?
The integral of (sinh(x))/(1+cosh(x)) is ln|1+cosh(x)|+C