Integrals
Oswaal
CBSE
Grade 12
Question:
$\int \frac{dx}{\sqrt{x^2 - a^2}}$ is equal to:
(a) $\log|x + \sqrt{x^2 - a^2}| + C$
(b) $\sin^{-1}\left(\frac{x}{a}\right) + C$
(c) $\frac{1}{a} \sec^{-1}\left(\frac{x}{a}\right) + C$
(d) $\log|x - \sqrt{x^2 - a^2}| + C$
Step-by-Step Solution
Key Concept: Standard logarithmic integral formula.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: $\log|x + \sqrt{x^2 - a^2}| + C$
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