Find `intsin^(5)x cos^(3)x dx`.

Explanation

[Here, powers of both cos x and sin x are odd positive integers, therefore, put `z=cosx or z=sin x`, but the power of `cosx` is greater. Therefore, it is convenient to put `z=cosx`.]
`intsin^(3)x cos^(5)x dx`
`=intsin^(2)x cos^(5)xsin x dx`
`=int(1-cos^(2)x)cos^(5)x sinx dx`
`=int(1-z^(2))z^(5)(-dz)`
`= -int(z^(5)-z^(7))dz`
`= -((z^(6))/(6)-(z^(8))/(8))+c= -(cos^(6)x)/(6)+(cos^(8)x)/(8)+c`