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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫  dxsin⁡  x−cos⁡  x+2\int \,\,\frac{{dx}}{{\sin \,\,x - \cos \,\,x + \sqrt 2 }} equals
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Correct option: C
12  cot⁡  (x2  +  π8)  +  c\frac{1}{{\sqrt 2 }}\,\,\cot \,\,\left( {\frac{x}{2}\,\, + \,\,\frac{\pi }{8}} \right)\,\, + \,\,c
Option D (−12cot⁡(x2+π8)+,c- \frac{1}{{\sqrt 2 }}\cot \left( {\frac{x}{2} + \frac{\pi }{8}} \right)\\ + \\,c) is the correct result after simplifying the integral using trigonometric identities and substitution.

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