Evaluate `intsin^(5)x cos^(2)x dx`

Answer

` -(cos^(3))/(3)+(cos^(5)x)/(5) +C`

Explanation

[Here, power of `sinx` is odd positive integer. Therefore, put `z= cos x.`]
Let ` z=cos x.` Then `dz= -sinx dx`. Now,
`=intsin^(3)x cos^(2)x dx=int sin^(2)x cos^(2)x sinx dx`
`= int (1-cos^(2)x)cos^(2)x sinx dx`
`int(1-z^(2))z^(2)(-dz)`
`=-int(z^(2)-z^(4))dz`
`=-((z^(3))/(3)-(z^(5))/(5))+C= - (cos^(3))/(3)+(cos^(5)x)/(5) +C`