X 例1计算反常积分 1+x +oo d x +∞a℃ 解 1+x2J∞1+x2J01+x2 b im dx+ lim dx 1+x b-→+∞01+y lim arctan]+ lim arctanxlo b→)+ =-lim arctan a+ lim arctan= = a→-0 b→+0 2)2例1 计算反常积分 . 1 2 + − + x dx 解 + − + 2 1 x dx − + = 0 2 1 x dx + + + 0 2 1 x dx + = →− 0 2 1 1 lim a a dx x + + →+ b b dx x 0 2 1 1 lim 0 lim arctan a a x →− = b b arctan x 0 lim →+ + a a lim arctan →− = − b b lim arctan →+ + . 2 2 = + = − −