Question:medium
\(\int \frac{\sec x \sqrt{\sec x}}{\sqrt{\sin x} + \sqrt{\cos x}} dx = \)
\(\int \frac{\sec x \sqrt{\sec x}}{\sqrt{\sin x} + \sqrt{\cos x}} dx = \)
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When an integrand involves roots of \(\sin x\) and \(\cos x\), dividing by a power of \(\cos x\) to convert to \(\tan x\) is a standard winning strategy.
Updated On: Jun 24, 2026
- \(2(\sqrt{\tan x} - \log_e(\sqrt{\tan x} + 1)) + C\)
- \(2(\sqrt{\tan x} + \log_e(\sqrt{\tan x} + 1)) + C\)
- \(2\sqrt{\tan x} - \log_e(\sqrt{\tan x} + 1) + C\)
- \(2\sqrt{\tan x} + \log_e(\sqrt{\tan x} + 1) + C\)
- \(\sqrt{\tan x} - \log_e(\sqrt{\tan x} + 1) + C\)
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The Correct Option is A
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