∫sin^4xdx/cos^2x
=∫[1-cos²x]²dx/cos²x
=∫[1-2cos²x+cos^4x]dx/cos²x
=∫[cos²x-2+1/cos²x]dx
=∫(1/2)(cos2x+1)-2+1/cos²xdx
=(1/4)sin2x-3x/2+tanx+C