dx 7计算广义积分(1) ∞1+x +0 dx dx dx 解 1+ 1+ 1+ 而 dx -o1 a→-Ja1+x lim arctan x lim arctan a= 同理/ar lim +x2b)+00Jo1+x lim [arctan x]= lim arctan b b→+00 →+00 故∫ dx丌 1+x2223 例17 计算广义积分 2 (1) 1 dx x + − +  0 2 2 2 1 1 1 0 dx dx dx x x x + + − − = + + + + 解    0 0 2 2 lim 1 1 a a dx dx x x − →− = + + 而   2 2 0 0 lim 1 1 b b dx dx x x + →+ = + + 同理  0 lim [arctan ] a x →− a = lim arctan ( ) a 2 2 a   →− = − = − − = lim[arctan ] lim arctan b b 0 2 b x b  →+ →+ = = = 2 1 2 2 dx x    + − = + = + 故 