- #1

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## Homework Statement

$$\int \tanh=?$$

## Homework Equations

$$\cosh^2-\sinh^2=1$$

$$(\tanh)'={\rm sech}^2=\frac{1}{\cosh^2},~~(\coth)'=-{\rm csch}^2=-\frac{1}{\sinh^2}$$

$$({\rm sech})'=\left( \frac{1}{\cosh} \right)'=-{\rm sech}\cdot\tanh=-\frac{\sinh}{{\rm cosh}^2}$$

$$({\rm csch})'=\left( \frac{1}{\sinh}\right)'=-{\rm csch}\cdot\coth=-\frac{\rm cosh}{\sinh^2}$$

## The Attempt at a Solution

$$\int \tanh=\int \frac{\sinh}{\sqrt{1+\sinh^2}}$$

That's as far as i can go