DTube: Integral of ∫cos^3(x)dx

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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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