_0^ /4 ^2x ^2x ( ^3x + ^3x)^2 dx is equal to

JEE Main 2024 Mathematics question

is equal to

Answer: (C)

Divide by cos⁶x: ∫tan²x sec²x/(1 + tan³x)² dx; with t = 1 + tan³x, dt = 3tan²x sec²x dx, so the integral is

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Question ID VK-011730