∫sin^3 xcos^2 xdx=?


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Question Number 167490 by mathlove last updated on 18/Mar/22

$\int {s i n}^{3} {x c o s}^{2} x d x = ?$
	Answered by nimnim last updated on 18/Mar/22

	$I = \int {s i n}^{2} {c o s}^{2} x s i n x d x$ $= \int (1 - {c o s}^{2} x) {c o s}^{2} x s i n x d x$ $= \int {c o s}^{2} x s i n x d x - \int {c o s}^{4} x s i n x d x$ $= - \frac{1}{3} {c o s}^{3} x + \frac{1}{5} {c o s}^{5} x + C$
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