If ∫ (1-5cos² x)/(sin⁵ xcos² x) dx=f(x)+C, where C is the constan… | JEE Main 2026 Mathematics PYQ

MCQMediumJEE Main 2026 · 28 January, Shift 1Indefinite Integrals

If $\int \frac{1-5\cos^2 x}{\sin^5 x\cos^2 x}\,dx=f(x)+C,$ where $C$ is the constant of integration, then $f\!\left(\frac{\pi}{6}\right)-f\!\left(\frac{\pi}{4}\right)$ is equal to:

A
$\dfrac{1}{\sqrt{3}}(26-\sqrt{3})$
B
$\dfrac{1}{\sqrt{3}}(26+\sqrt{3})$
C
$\dfrac{4}{\sqrt{3}}(8-\sqrt{6})$
D
$\dfrac{2}{\sqrt{3}}(4+\sqrt{6})$

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