What is the integral of sech^3(x)tanh(x) ?

The integral of sech^3(x)tanh(x) is -1/3 sech^3(x)+C

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integral of sech^3(x)tanh(x)

\int sech^{3} (x) tanh (x) d x

- \frac{1}{3} sech^{3} (x) + C

Solution steps

\int sech^{3} (x) tanh (x) d x

Apply u-substitution

= \int - \frac{1}{3} d u

Integral of a constant:

\int a d x = a x

= (- \frac{1}{3}) u

Substitute back

u = sech^{3} (x)

= (- \frac{1}{3}) sech^{3} (x)

Simplify

= - \frac{1}{3} sech^{3} (x)

Add a constant to the solution

= - \frac{1}{3} sech^{3} (x) + C

What is the integral of sech^3(x)tanh(x) ?
The integral of sech^3(x)tanh(x) is -1/3 sech^3(x)+C