Question

\[ \int \frac{a^x}{\sqrt{1 - a^2 x}} \, dx \] is equal to :

• A. \( \sin^{-1} (a^x) + C \)
• B. \( \log_e (1 - a^2 x) + C \)
• C. \( \cos^{-1} (a^x) + C \)
• D. \( \sin^{-1} (a^x) \, \frac{a}{x} + C \)

Hint:

For integrals involving square roots and powers, use standard trigonometric integrals and simplifications.

Answer 1

The Correct Option is A

This is a standard integral: \[ \int \frac{a^x}{\sqrt{1 - a^2 x}} \, dx = \sin^{-1} (a^x) + C \] Thus, the correct answer is (A).