加a -m-9c tan ∫nom点西+-rc intantanC= 2 3 sin 1 1 1 1 1 1 1 1 2 tan (tan ) tan ln cot 8 4 sin 4 2 2 4 sin 8 2 4 cos 2 x x x x dx dx d dx ccx x C x x x + = + = + − +     解法二 原式= 2 3 sec 1 1 1 2 ( ) (tan ) 2sin (cos 1) 4 2 4 2 sin cos tan 2 2 2 x dx x x d d x x x x x = = +    = 2 2 1 tan 1 1 1 2 (tan ) [ln tan tan ] 4 2 4 2 2 2 tan 2 x x x x d C x + = + +  解法三 令 tan 2 x = t ，则 2 2 2 2 2 1 2 sin ,cos , 1 1 1 t t x x dx dt t t t − = = = + + + ，于是 1 1 1 1 2 ( ) [ln ] sin 2 2sin 2sin (cos 1) 4 4 2 dx dx t dt t t C x x x x t = = + = + + + +    = 1 1 2 ln tan tan 4 2 8 2 x x + + C