I=\int cos^4xdx=cos^3xsinx+\int 3cos^2xsin^2xdx=cos^3xsinx+\int 3cos^2x(1-cos^2x)dx=cos^3xsinx+3\int cos^2xdx-3\int cos^4xdx=cos^3xsinx+3{\int cos^2xdx}-3I