=∫(cos²x)²dx
=∫[(1+cos2x)/2]²dx
=∫(cos²2x+2cos2x+1)/4 dx
=1/4*∫cos²2xdx+1/2*∫cos2xdx+∫dx/4
=1/4*∫(1+cos4x)/2 dx+1/4*sin2x+x/4
=x/8+1/32*sin4x+1/4*sin2x+x/4+C
=1/32*sin4x+1/4*sin2x+3x/8+C