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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫  sin⁡  x    dx3+4  cos⁡2  x\int \,\,\frac{{\sin \,\,x\;\,\,dx}}{{3 + 4\,\,{{\cos }^2}\,\,x}} is equal to
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Correct option: C
−  12 3  tan⁡−1  (2  cos⁡  x3)  +  c- \,\,\frac{1}{{2\,\sqrt 3 }}\,\,{\tan ^{ - 1}}\,\,\left( {\frac{{2\,\,\cos \,\,x}}{{\sqrt 3 }}} \right)\,\, + \,\,c
Option C (− 123tan⁡−1(2cos⁡,x3)+,c- \,\frac{{1}}{{2\sqrt 3 }}\tan ^{ - 1}\left( {\frac{{2\cos \\,x}}{{\sqrt 3 }}} \right)\\ + \\,c) is the correct result of the integration after substitution and applying the standard integral formula.

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