- #1
Karol
- 1,380
- 22
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