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What is the integral of cos6x cos 5x?
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Verified answer
∫cos(6x)*cos(5x) dx
Note that cos(6x + 5x) = cos(6x)cos(5x) - sin(6x)sin(5x)
cos(6x - 5x) = cos(6x)cos(5x) + sin(6x)sin(5x)
Adding the two, we get that cos(11x) + cos(x) = 2cos(6x)cos(5x)
So we get that the integral is actually:
1/2 * ∫(cos(11x) + cos(x)) dx = 1/2 * (1/11*sin(11x) + sin(x)) + C