\(\int \frac{dx}{x^2 - a^2} = \frac{1}{2a} \ln \left| \frac{x - a}{x + a} \right| + c;\)

\(\int \frac{dx}{\sqrt{a^2 - x^2}} = \sin^{-1}\frac{x}{a} + c\)

\(\int \frac{dx}{\sqrt{x^2 - a^2}} = \ln \left| x + \sqrt{x^2 - a^2} \right| + c\)

\(\int \frac{dx}{\sqrt{x^2 + a^2}} = \ln \left| x + \sqrt{x^2 + a^2} \right| + c\)

\(\int \sqrt{a^2 - x^2} = \dfrac{x \sqrt{a^2 - x^2}}{2} + \dfrac{a^2}{3} sin^{-1}\frac{x}{a} + c\)