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Find the integrals of the functions s...

Find the integrals of the functions `s in^3(2x+1)`

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` int sin^(3) (2x +1) dx`
` = int sin^(2) (2x+1) sin(2x+1) dx`
`=int {1-cos^(2) (2x+1))} sin (2x+1)dx`
`= int (1-t^(2)) (dt)/(-2) =-(1)/(2) [t-(t^(3))/(3)]+c`
` underset( rArr sin (2x+1 )dx =(dt)/(-2))underset(rArr -2 sin (2x+1) dx=dt)(" Let " cos (2x+1)=t)`
`= -(1)/(2) cos (2x+1) +(1)/(6) cos^(3) (2x+1)+c`
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