Step-by-Step Solution
Key Concept: General
Let $I = \int \frac{dx}{x^2 + a^2}$<br>Put $x = at \Rightarrow dx = a \, dt$<br>$\therefore I = \int \frac{adt}{a^2t^2 + a^2} = \frac{1}{a} \int \frac{dt}{t^2 + 1}$<br>$= \frac{1}{a} \tan^{-1}(t) + C = \frac{1}{a} \tan^{-1} \left( \frac{x}{a} \right) + C$
Correct Answer: $\frac{1}{a} \tan^{-1} \left( \frac{x}{a} \right) + C$