If ∫₀^π (5^(cos x)(1 + cos x cos 3x + cos ²x + cos ³x cos 3x)dx)/(1 + 5^(cos x)) = (kπ)/16, then k is equal to _ _ _ _ _ _ _.

Integral Calculus: JEE Main 2023 Mathematics question

JEE Main 2023 · 1 Feb, Evening shift · Q29

JEE Main 20231 Feb, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

\int\limits_0^\pi {{{{5^{\cos x}}(1 + \cos x\cos 3x + {{\cos }^2}x + {{\cos }^3}x\cos 3x)dx} \over {1 + {5^{\cos x}}}} = {{k\pi } \over {16}}}

, then k is equal to _____________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2023 Integral Calculus Question with Answer (1 Feb Evening shift, Q29) | JEE Arc

JEE Main 2023 · 1 Feb, Evening shift · Q29

JEE Main 20231 Feb, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

\int\limits_0^\pi {{{{5^{\cos x}}(1 + \cos x\cos 3x + {{\cos }^2}x + {{\cos }^3}x\cos 3x)dx} \over {1 + {5^{\cos x}}}} = {{k\pi } \over {16}}}

, then k is equal to _____________.

Your answerType your answer. Integers and decimals are accepted.