Question

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

Options

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

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

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

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

Answer 1

The standard form \[x^2+a^2\] produces an inverse tangent. Thus the answer usually involves \[\tan^{-1}\].