Evaluate `int sin x cos x cos2x cos 4x cos 8x dx`

Explanation

f(x)
`=(2cos x cdot cos 2x cdot cos 4x cdot cos 8x cdot cos 16x)/(2 sin x)`
`=(sin 32x)/(2^(5)sinx)`
`therefore" "f'(x)=(1)/(32)xx(32 cos 32x xxsin x-cos x xx sin 32x)/(sin^(2)x)`
`therefore" "f'((pi)/(4))=(32xx(1)/(sqrt(2))-(1)/(sqrt(2))xx0)/(32xx((1)/(sqrt(2)))^(2))=sqrt(2)`