Verified answer

int [ sin x cos^2 x dx ]

Let u = cos x

du = - sin x dx

int [ - du * u^2 ]

= - int [ u^2 du ]

= - ( 1 / 3 )u^3 + C

= ( - 1 / 3 )(cos^3 x ) + C

( - 1 / 3 )cos^3 ( pi / 2 ) - ( - 1 / 3 )cos^3 ( 0 )

= 0 + ( 1 / 3 )

= 1 / 3

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