What is the integral of sech^8(x)tanh(x) ?

The integral of sech^8(x)tanh(x) is -1/8 sech^8(x)+C

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integral of sech^8(x)tanh(x)

\int sech^{8} (x) tanh (x) d x

- \frac{1}{8} sech^{8} (x) + C

Solution steps

\int sech^{8} (x) tanh (x) d x

Apply u-substitution

= \int - \frac{1}{8} d u

Integral of a constant:

\int a d x = a x

= (- \frac{1}{8}) u

Substitute back

u = sech^{8} (x)

= (- \frac{1}{8}) sech^{8} (x)

Simplify

= - \frac{1}{8} sech^{8} (x)

Add a constant to the solution

= - \frac{1}{8} sech^{8} (x) + C

What is the integral of sech^8(x)tanh(x) ?
The integral of sech^8(x)tanh(x) is -1/8 sech^8(x)+C