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

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

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integral of 4sech(x)tanh(x)

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

- 4 sech (x) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply u-substitution

: \int - 1 d u

= 4 \cdot \int - 1 d u

Integral of a constant:

\int a d x = a x

= 4 (- 1) u

Substitute back

u = sech (x)

= 4 (- 1) sech (x)

Simplify

= - 4 sech (x)

Add a constant to the solution

= - 4 sech (x) + C

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\frac{\partial}{\partial x} (e^{x} - e^{- x})

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