例8求∫ sec xdx 解 I sec' xdx=」 seed(tanx) secx tanx- secxtan xdx secx tan x- secxlsecx-1lx secx tanx- sec'x-secx dx secxtanx-sec'xdx+Inlsecx+tan x, 把sec3xdx移到等式左端,整理得 sec xdx=-lsecx x +Inlsecx+ tan x+C xdx 3 求 sec  xdx 3 sec sec tan )  = xd( x x x x x x  = − d 2 sec tan sec tan x x x( x ) x  = sec tan − sec sec −1 d 2 x x ( x x) x  = sec tan − sec − sec d 3 sec tan sec ln sec tan , 3 = x x − x x + x + x  d (sec tan ln sec tan ) . 2 1 sec3 x x = x x + x + x + C  d 3 sec d , x x 把 移到等式左端 整理得  例8 解