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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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∫  cos⁡  x  +  x  sin⁡  xx2  +  x  cos⁡  x    dx\int \,\,\frac{{\cos \,\,x\,\, + \,\,x\,\,\sin \,\,x}}{{{x^2}\,\, + \,\,x\,\,\cos \,\,x}}\,\,\;dx is equal to
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Correct option: D
log⁡  ∣ xx  +  cos⁡  x ∣+c\log \,\,\left| {\,\frac{x}{{x\,\, + \,\,\cos \,\,x}}\,} \right| + c
Option D, \log \,\left| {\,\frac{x}{{x\,+\cos \,x}}\} \right| + c\log \,\left| {\,\frac{x}{{x\,+\cos \,x}}\} \right| + c, is correct because the integral simplifies to this form after algebraic manipulation and recognizing the derivative in the denominator.

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