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

The integral of x(cosh(x))/((sinh(x))^2) is -xcsch(x)+ln(tanh(x/2))+C

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

integral

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

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

Solution steps

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

Apply Integration By Parts

: - x csch (x) - \int - csch (x) d x

= - x csch (x) - \int - csch (x) d x

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

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

Simplify

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

Add a constant to the solution

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

\frac{- 2}{( u ^{2} + u )}

5 x^{4} - 6 x^{2} + 3

\frac{22}{( 121 x ^{2} + 1 ) ^{2}}

\frac{2 ^{x}}{2 ^{x} ( 1 + 4 ^{x} )}

\frac{e ^{- x}}{x ^{\frac{1}{2}}}

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