`int((cos^-1 2x)^4)/(sqrt[1-4x^2]) dx`

Put `u = cos^-1 2x`

`du=(-2)/(sqrt[1-4x^2]) dx`

So

`int((cos^-1 2x)^4)/(sqrt[1-4x^2]) dx`

` = - 1/2 intu^4 du`

`=(-1/2) ((u^5)/(5))+K`

`=(-(cos^-1 2x)^5)/(10)+K`