How do you find the integral of $sin^3(x) cos^2(x) dx$ ?

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Answer 1 · 2015-10-12T22:48:22

$I = 1/5cos^5x-1/3cos^3x+C$

$I = int sin^3xcos^2xdx = int sin^2xcos^2xsinxdx$
$I = int (1-cos^2x)cos^2xsinxdx$
$cosx=t => -sinxdx=dt => sinxdx=-dt$

$I = int (1-t^2)t^2(-dt) = int (t^4-t^2)dt = t^5/5-t^3/3+C$

$I = 1/5cos^5x-1/3cos^3x+C$

How do you find the integral of sin^3(x) cos^2(x) dxsin^3(x) cos^2(x) dx?