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

The integral of 1/(sinh(x)) is ln(tanh(x/2))+C

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integral of 1/(sinh(x))

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

ln (tanh (\frac{x}{2})) + C

Solution steps

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

Use the Hyperbolic identity:

\frac{1}{sinh ( x )} = csch (x)

= \int csch (x) d x

Use the common integral:

\int csch (x) d x = ln (tanh (\frac{x}{2}))

= ln (tanh (\frac{x}{2}))

Add a constant to the solution

= ln (tanh (\frac{x}{2})) + C

\int 2 x^{2} - 5 d x

(x^{2} \cdot 6^{x})^{3}

\frac{d}{d x} (ln (3 x^{2} + 5 y^{2}))

\frac{d}{d x} (\frac{x + 5}{x + 2})

What is the integral of 1/(sinh(x)) ?
The integral of 1/(sinh(x)) is ln(tanh(x/2))+C