MathsJEE Main 22 Jan 2026, Shift 1·Q23·Numerical·Moderate

Indefinite Integration · Integration by substitution

\int(\sin x)^{\frac{-11}{2}}(\cos x)^{\frac{-5}{2}}\,dx = -\frac{p_1}{q_1}(\cot x)^{\frac92} - \frac{p_2}{q_2}(\cot x)^{\frac52} - \frac{p_3}{q_3}(\cot x)^{\frac12} + \frac{p_4}{q_4}(\cot x)^{\frac{-3}{2}} + C,

where

p_i

and

q_i

are positive integers with

\gcd(p_i, q_i) = 1

for

i = 1, 2, 3, 4

and

C

is the constant of integration, then

\dfrac{15p_1p_2p_3p_4}{q_1q_2q_3q_4}

is equal to .

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