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Integral of cos^2(x)sin^3(x) (integrate cosine squared times sine cubed).
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We compute the integral of cosine squared times sine cubed by splitting off a factor of sin^2(x) and applying the Pythagorean identity sin^2(x)=1-cos^2(x). This sets us up with two terms that have powers of cosine next to sin(x)dx, so we have the perfect differential to allow us to use an explicit u-substitution or apply the chain rule backwards.
Using the power rule, we obtain a final answer of 1/5*cos^5(x)-1/3*cos^3(x)+C for the integral of cos^2(x)sin^3(x).
Using the power rule, we obtain a final answer of 1/5*cos^5(x)-1/3*cos^3(x)+C for the integral of cos^2(x)sin^3(x).
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