Logarithmic Forms of Inverse Hyperbolic Functions (Edexcel A-Level Further Mathematics): Flashcards

$\ln(x + \sqrt{x^2 + 1})$

$\ln(x + \sqrt{x^2 - 1})$

$\frac{1}{2} \ln\left(\frac{1 + x}{1 - x}\right)$

$x \in \mathbb{R}$ (all real numbers)

$x \geq 1$

$|x| < 1$

$\sinh^{-1}$: $x^2 + 1$; $\cosh^{-1}$: $x^2 - 1$

$\ln(2 + \sqrt{5})$

$\frac{1}{2} \ln(3)$

$x^2 - 1$