Three Formulae

\[ \int\sqrt{a^2 - x^2}dx = \frac x2\sqrt{a^2 - x^2} + \frac {a^2}2\arcsin(\frac xa) + C \] \[ \int \frac 1{\sqrt{x^2 \pm a^2}}dx = \ln|x + \sqrt{x^2 \pm a^2}| + C \] \[ \int \sqrt{x^2 \pm a^2}dx = \frac x2 \sqrt{x^2 \pm a^2} \pm\frac {a^2}2\ln|x + \sqrt{x^2 \pm a^2}| + C \]