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JEE Main 2018

JEE Main 2018 Mathematics question on Indefinite Integration

The integral
∫sin⁡2xcos⁡2x(sin⁡5x+cos⁡3xsin⁡2x+sin⁡3xcos⁡2x+cos⁡5x)2 dx\int \frac{\sin^2 x \cos^2 x}{\left(\sin^5 x + \cos^3 x \sin^2 x + \sin^3 x \cos^2 x + \cos^5 x\right)^2} \, dx
is equal to
  1. A.
    −13(1+tan⁡3x)+C\dfrac{-1}{3(1+ \tan^3 x)} + C
  2. B.
    13(1+tan⁡3x)+C\dfrac{1}{3(1+ \tan^3 x)} + C
  3. C.
    −11+cot⁡3x+C\dfrac{-1}{1+ \cot^3 x} + C
  4. D.
    11+cot⁡3x+C\dfrac{1}{1+ \cot^3 x} + C
Show answer

Correct option: B

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