例7计算广义积分xmx 2 解 dx_ lim Ji+6 x 2 dx I xIn x E→0+ :Inx 2 d(n x) lim [ inar n 6→0+1+6Iny E→>0+ E =lim[n(n2)-ln(n(1+)] E→)0+ oo 故原广义积分发散 上页例7 计算广义积分 解 . ln 2 1 x x dx  2 1 x ln x dx  → + + = 2 0 1 ln lim   x x d x  → + + = 2 0 1 ln (ln ) lim   x d x   2 1 0 lim ln(ln )   + → + = x lim ln(ln 2) ln(ln( 1 )) 0   = − + → + = . 故原广义积分发散