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Verified answer
InTegRaL∫sin² 4x dx
= ∫(1/2 - 1/2 cos 8x) dx
= 1/2 x - 1/2 . 1/8 ∫dsin 8x
= 1/2 x - 1/16 sin 8x + C
= (1/16)(8x - sin 8x) + C