What is the integral of 1/(sinh^2(x)) ?

The integral of 1/(sinh^2(x)) is -coth(x)+C

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integral of 1/(sinh^2(x))

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

- coth (x) + C

Solution steps

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

Use the Hyperbolic identity:

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

= \int csch^{2} (x) d x

Use the common integral:

\int csch^{2} (x) d x = - coth (x)

= - coth (x)

Add a constant to the solution

= - coth (x) + C

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What is the integral of 1/(sinh^2(x)) ?
The integral of 1/(sinh^2(x)) is -coth(x)+C