What is the integral of sech(4x)tanh(4x) ?

The integral of sech(4x)tanh(4x) is -1/4 sech(4x)+C

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integral of sech(4x)tanh(4x)

\int sech (4 x) tanh (4 x) d x

- \frac{1}{4} sech (4 x) + C

Solution steps

\int sech (4 x) tanh (4 x) d x

Apply u-substitution

: \int - \frac{1}{4} d u

= \int - \frac{1}{4} d u

Integral of a constant:

\int a d x = a x

= (- \frac{1}{4}) u

Substitute back

u = sech (4 x)

= (- \frac{1}{4}) sech (4 x)

Simplify

= - \frac{1}{4} sech (4 x)

Add a constant to the solution

= - \frac{1}{4} sech (4 x) + C

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What is the integral of sech(4x)tanh(4x) ?
The integral of sech(4x)tanh(4x) is -1/4 sech(4x)+C