In this video, I work through the steps to solving the integral of cos3(x) or [cos(x)]3.
Note that because cos(x) is a function of x, not a mere polynomial, we can't just use the power formula as a method of integration. We must change the integrand cos3(x) into a form that we can integrate.
We can do this by writing cos3(x) as cos2(x)cos(x). Then by recognising that cos2(x) = 1 - sin2(x), we have:
cos3(x) = [1 - sin2(x)]cos(x)
Then we can simply use a u-substitution where u = sin(x) to complete the integral.
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