方法一:∫tan^4x dx 令y=tanx,dy=secx dx=(1+y) dx 原式=∫y^4/(1+y) dy =∫[y+1/(1+y)-1] dy =y/3+arctany-y+C =(1/3)tanx+arctan(tanx)-tanx+C 方法二:∫tan^4x dx =(1/3)tanx-∫tanx dx =(1/3)tanx-∫(secx-1) dx =(1/3)tanx-tanx+x+C