Question

Evaluate \[\int \frac{dx}{x^2-a^2}\].

Options

• \[\sin^{-1}\left(\frac{x}{a}\right)+C\]

• \[\frac{1}{2a}\log\left|\frac{x-a}{x+a}\right|+C\]

• \[\frac{1}{2a}\log\left|\frac{a+x}{a-x}\right|+C\]

• \[\frac{1}{a}\tan^{-1}\left(\frac{x}{a}\right)+C\]

Answer 1

The denominator has the standard form \[x^2-a^2\]. Its integral is a logarithmic expression with the ratio \[\frac{x-a}{x+a}\].