What is the integral of sech(x)tanh(x) ?

The integral of sech(x)tanh(x) is -sech(x)+C

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integral of sech(x)tanh(x)

\int sech (x) tanh (x) d x

- sech (x) + C

Solution steps

\int sech (x) tanh (x) d x

Apply u-substitution

: \int - 1 d u

= \int - 1 d u

Integral of a constant:

\int a d x = a x

= (- 1) u

Substitute back

u = sech (x)

= (- 1) sech (x)

Simplify

= - sech (x)

Add a constant to the solution

= - sech (x) + C

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What is the integral of sech(x)tanh(x) ?
The integral of sech(x)tanh(x) is -sech(x)+C