In Inx 例5、 dx=「 n In x dhn x In x. In In x-「h In x in hnx-Inx +c 例6、∫ Xian XaX x(secx-I)dx 2 xtanx- tan x d =x tan x+In cosx-=+c x arctan x 例7、 arctan xdx 1+x 1+ⅹ arctan (arctan arctan xdx-arctan xd arctan xarctanx Ix--(arctan)2 1+x xarctanx--In(1+x)--(arctan x)+例 5、  =  dx ln ln x d ln x x ln lnx  =    dx x 1 ln x 1 ln x ln ln x - ln x = ln x ln ln x -ln x + c 例 6、  xtan xdx =  x(sec x −1)dx 2 2 =  − 2 x xdtanx 2 2 x xtanx tan x dx 2 = −  − c 2 x x tan x ln cos x - 2 = + + 例 7、   + + − = + arctan xdx 1 x x 1 1 dx 1 x x arctan x 2 2 2 2  + = − )dx 1 x arctan x (arctan x 2 =  −  arctanxdx arctan xdarctan x 2 2 (arctan x) 2 1 dx 1 x x xarctan x − + = −  (arctan x) c 2 1 ln(1 x ) 2 1 xarctan x 2 2 = − + − +