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Integrate the functionssin^3xcos^3x...

Integrate the functions`sin^3xcos^3x`

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`int sin^(3) x cos^(3) x dx`
`=int sin^(3) x. cos^(2) x. cos xdx`
`= int sin^(3) x(1-sin^(2)x) cos x dx`
` =int t^(3) (1-t^(2)) dt=int (t^(3)-t^(5)) dt`
`=(1)/(4) t^(4) -(1)/(6)t^(6)+c" "underset(rArr " cos x dx " =dt)(" Let "sin x =t)`
`=(1)/(4)sin^(4) x-(1)/(6) sin^(6) x+c`
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