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

The integral of (cosh(x))/(sinh^2(x)) is -csch(x)+C

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

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

- csch (x) + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = sinh (x)

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

Use the Hyperbolic identity:

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

= - csch (x)

Add a constant to the solution

= - csch (x) + C

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

\int e^{y} 2^{e^{y}} 3^{e^{y}} d y

\frac{d}{d x} ((x - 2)^{- 1})

x^{2} - 6 x + 3

f (x) = ln (x^{2} - 3 x + 1), (3, 0)

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