Evaluate `int cos^(3)x sqrt(sinx)dx`.

Explanation

[ Here, the power of cos x is 3, which is an odd positive integer. Therefore, put `dz=cos x dx`.
Now, `int cos^(3)x sqrt(sinx)dx=int cos^(2)x sqrt(sinx)cos x dx`
`=int(1-sin^(2)x)sqrt(sinx)cosx dx`
`=int (1-z^(2))sqrt(z) dz`
`=int (sqrt(z)-z^(5//2))dz`
`=(z^(3//2))/(3//2)-(z^(7//2))/(7//2)+c=(2)/(3)z^(3//2)-(2)/(7)z^(7//2)+c`
`=(2)/(3)"sin"^(3//2)x-(2)/(7)"sin"^(7//2)x+c`