Question

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

Answer 1

\[\int\frac{dx}{a^2 - b^2 x^2}\]
\[ = \frac{1}{b^2}\int\frac{dx}{\left( \frac{a^2}{b^2} \right) - x^2} \]
\[ = \frac{1}{b^2} \times \frac{1}{2\frac{a}{b}} \log \left| \frac{\frac{a}{b} + x}{\frac{a}{b} - x} \right| + C \left[ \therefore \int\frac{dx}{a^2 - x^2} = \frac{1}{2a} \log \left| \frac{a + x}{a - x} \right| + C \right]\]

` = \text{1}/{2ab} \text{ log }|{a + bx}/{a - bx}| + c `