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integral cos^4 x dx = integral (1 + cos 2x/2)^2 dx = integral (1/4 + cos 2x/2 + cos^2 2x/4) dx = integral [1/4 + cos 2x/2 + 1/4(1 + cos 4x/2)] dx = 3/8 integral dx + 1/4 integral 2 cos 2x dx + 1/32 integral 4 cos 4x dx = 3x/8 + sin 2x/4 + sin 4x/32 + C
integral cos^4 x dx = integral (1 + cos 2x/2)^2 dx = integral (1/4 + cos 2x/2 + cos^2 2x/4) dx = integral [1/4 + cos 2x/2 + 1/4(1 + cos 4x/2)] dx = 3/8 integral dx + 1/4 integral 2 cos 2x dx + 1/32 integral 4 cos 4x dx = 3x/8 + sin 2x/4 + sin 4x/32 + C
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