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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫  cosec  xcos⁡2  (1  +  log⁡  tan⁡  x2)  dx\int \,\,\frac{{\mathrm{cosec}\,\,x}}{{{{\cos }^2}\,\,\left( {1\,\, + \,\,\log \,\,\tan \,\,\frac{x}{2}} \right)}}\,\,dx
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Correct option: B
tan⁡  [1+  log⁡  tan⁡  x2]  +  c\tan \,\,\left[ {1 + \,\,\log \,\,\tan \,\,\frac{x}{2}} \right]\,\, + \,\,c
Option B is correct because after the trigonometric simplification and substitution, the integral is a standard form, resulting in tan[1 + log tan(x/2)] + c.

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