换元：x=tany
dx=sec^2ydy
原积分＝∫cos^4ydy＝1/4∫(1＋cos2y)^2dy
＝1/4∫[1＋2cos2y＋(cos2y)^2]dy
＝y/4＋sin(2y)/4＋1/8∫(1＋cos4y)dy
＝3/8y +1/4sin(2y)＋1/32sin4y