Question

\[\int\frac{1}{\sqrt{a^2 - b^2 x^2}} dx\]

Answer 1

\[\int\frac{dx}{\sqrt{a^2 - b^2 x^2}}\]
\[ = \int\frac{dx}{\sqrt{b^2 \left( \frac{a^2}{b^2} - x^2 \right)}}\]
\[ = \frac{1}{b}\int\frac{dx}{\sqrt{\left( \frac{a}{b} \right)^2 - x^2}}\]
\[ = \frac{1}{b} \sin^{- 1} \left( \frac{xb}{a} \right) + C\]