JEE AdvancedHardQuestion 330012
Question
∫√(tan x) dx is of the form:
- ARequires splitting into ∫√(tan x)(1+tan²x)/... with substitution tan x = t²Correct
- BSimple power rule gives answer
- C∫tan^(1/2) x dx = (2/3)tan^(3/2) x + C
- Dln|tan x| + C
Correct answer
Requires splitting into ∫√(tan x)(1+tan²x)/... with substitution tan x = t²
Explanation
∫√(tan x) dx is a non-trivial integral. Standard approach: let tan x = t² → sec²x dx = 2t dt. Then ∫t·2t/(1+t⁴) dt = 2∫t²/(1+t⁴) dt, which is solved by decomposing 1+t⁴ = (t²+√2t+1)(t²−√2t+1). This is a JEE Advanced-level technique.