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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy
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Application +4 | -1
∫{1+2tan⁡x(tan⁡x+sec⁡x)}12dx\int\{1+2 \tan x(\tan x+\sec x)\}^{\frac{1}{2}} d x is equal to
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Correct option: C
log⁡∣sec⁡x(sec⁡x+tan⁡x)∣+C\log |\sec x(\sec x+\tan x)|+C
Option C (log⁡∣sec⁡x(sec⁡x+tan⁡x)∣+C\log |\sec x(\sec x+\tan x)|+C) is correct because the integral simplifies to ∫(sec⁡x+tan⁡x)dx\int (\sec x + \tan x) dx, which evaluates to log⁡∣sec⁡x(sec⁡x+tan⁡x)∣+C\log |\sec x(\sec x+\tan x)|+C.

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