Evaluate: ∫ (√(tan x) + √(cot x)) dx

Evaluate: ∫ (√(tan x) + √(cot x)) dx

• A. √2 sin⁻¹(sin x - cos x) + C
• B. √2 cos⁻¹(sin x + cos x) + C
• C. tan⁻¹(√tan x) + C
• D. log|sin x + cos x| + C

Answer: A) √2 sin⁻¹(sin x - cos x) + C

Explanation: Simplify to (sin x + cos x) / √(sin x cos x). Let sin x - cos x = t, then (cos x + sin x)dx = dt. Integral becomes √2 ∫ dt / √(1 - t²), yielding √2 sin⁻¹ t.