Differentiating & Integrating Hyperbolic Functions (Edexcel A-Level Further Mathematics): Flashcards

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

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

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

$\frac{1}{\sqrt{1 - x^2}}$

$\frac{-1}{\sqrt{1 - x^2}}$

$\frac{1}{\sqrt{1 + x^2}}$

$\frac{1}{1 + x^2}$

$x \geq 1$

$|x| < 1$

$1$