Read the two statements and choose the correct option.

I. $\int \frac{dx}{x^{2} + a^{2}} = \frac{1}{a}\tan^{-1}\frac{x}{a} + C$.

II. $\int \frac{dx}{\sqrt{a^{2} - x^{2}}} = \frac{1}{a}\sin^{-1}\frac{x}{a} + C$.

Explanation

1. 01

   I: $\frac{d}{dx}\left(\frac{1}{a}\tan^{-1}\frac{x}{a}\right) = \frac{1}{a} \cdot \frac{1/a}{1 + x^{2}/a^{2}} = \frac{1}{x^{2} + a^{2}}$. True.

2. 02

   II: $\frac{d}{dx}\sin^{-1}\frac{x}{a} = \frac{1}{\sqrt{a^{2} - x^{2}}}$ already, so the extra $\frac{1}{a}$ is wrong. False.