NVAMediumJEE Main 2023 · 1 February, Shift 2Properties of Definite Integrals

Mathematics Question from JEE Main 2023 · 1 February, Shift 2

If 0π5cosx(1+cosxcos3x+cos2x+cos3xcos3x)1+5cosxdx=kπ16\int_0^\pi \frac{5^{\cos x} (1 + \cos x \cos 3x + \cos^2 x + \cos^3 x \cos 3x)}{1 + 5^{\cos x}} \, dx = \frac{k \pi}{16}, then kk is equal to _____.

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