Question

Evaluate the integral: \[ \int \frac{dx}{a^2 + x^2} \] The correct answer is:

• A. \(\frac{1}{a} \tan^{-1} \left( \frac{x}{a} \right) + c\)
• B. \(\tan^{-1} \left( \frac{a}{x} \right) + c\)
• C. \(\frac{1}{a} \tan^{-1} \left( \frac{a}{x} \right) + c\)
• D. \(\frac{1}{a} \tan^{-1} x + c\)

Hint:

For integrals of the form \(\int \frac{dx}{a^2 + x^2}\), the result is \(\frac{1}{a} \tan^{-1} \left( \frac{x}{a} \right) + c\).

Answer 1

The Correct Option is A

The integral is of the standard form: \[ \int \frac{dx}{a^2 + x^2}. \] This is a well-known integral with the result: \[ \int \frac{dx}{a^2 + x^2} = \frac{1}{a} \tan^{-1} \left( \frac{x}{a} \right) + c. \] Thus, the correct answer is \( (A) \).