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MathsJEE Main 28 Jan 2026, Shift 1·Q11·MCQ·Moderate

Indefinite Integration · Integration by parts

If ∫(1−5cos⁡2xsin⁡5xcos⁡2x)dx=f(x)+C\displaystyle\int\left(\frac{1 - 5\cos^2 x}{\sin^5 x\cos^2 x}\right)dx = f(x) + C where CC is the constant of integration, then f(π6)−f(π4)f\left(\dfrac{\pi}{6}\right) - f\left(\dfrac{\pi}{4}\right) is equal to
  1. (1)13(26+3)\dfrac{1}{\sqrt3}\left(26 + \sqrt3\right)
  2. (2)43(8−6)\dfrac{4}{\sqrt3}\left(8 - \sqrt6\right)
  3. (3)13(26−3)\dfrac{1}{\sqrt3}\left(26 - \sqrt3\right)
  4. (4)23(4+6)\dfrac{2}{\sqrt3}\left(4 + \sqrt6\right)

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