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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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∫  1  +  tan⁡2  x1  −  tan⁡2  x    dx\int \,\,\frac{{1\,\, + \,\,{{\tan }^2}\,\,x}}{{1\,\, - \,\,{{\tan }^2}\,\,x}}\,\,\;dx is equal to
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Correct option: D
12  log⁡  (1  +  tan⁡  x1  −  tan⁡  x)  +  c\frac{1}{2}\,\,\log \,\,\left( {\frac{{1\,\, + \,\,\tan \,\,x}}{{1\,\, - \,\,\tan \,\,x}}} \right)\,\, + \,\,c
The correct answer is (1/2)log((1 + tan x)/(1 - tan x)) + c because the integral simplifies to a standard form after trigonometric manipulation and substitution.

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