Question

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

Options

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

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

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

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

Answer 1

For \[\sqrt{a^2-x^2}\], the answer usually involves \[\sin^{-1}\]. Specifically, the antiderivative is \[\sin^{-1}\left(\frac{x}{a}\right)+C\].