Question

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

Options

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

• \[\log\left|x+\sqrt{x^2+a^2}\right|+C\]

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

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

Answer 1

The standard radical form \[\sqrt{x^2+a^2}\] integrates to a logarithm. The positive sign inside the radical must remain \[x^2+a^2\].