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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1
∫  {1  +  2  tan⁡  x  (tan⁡  x  +  sec⁡  x)}1/2dx\int \,\,{\left\{ {1\,\, + \,\,2\,\,\tan \,\,x\,\,\left( {\tan \,\,x\,\, + \,\,\sec \,\,x} \right)} \right\}^{1/2}}dx is equal to
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Correct option: C
log⁡  sec⁡  x (sec⁡  x  +  tan⁡  x  +  C)\log \,\,\sec \,\,x\,\left( {\sec \,\,x\,\, + \,\,\tan \,\,x\,\, + \,\,C} \right)
Option C is correct because the integral simplifies to \log⁡sec⁡x+log⁡(sec⁡x+tan⁡x)\log \sec x + \log (\sec x + \tan x), which can be combined to give \log⁡sec⁡x(sec⁡x+tan⁡x)\log \sec x(\sec x + \tan x).

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