求不定积分3-x^2/x^3-xdx
问题描述:
求不定积分3-x^2/x^3-xdx
答
思路:利用待定系数法x^3-x=x(x-1)(x+1)设3-x^2/x^3= a/x +b/(x-1) +c/(x+1)=[(a+b+c)x²+(b-c)x-a]/[x(x-1)(x+1)]所以有a+b+c=-1b-c=0-a=3解得:a=-3 n=c=1所以3-x^2/x^3= -3/x +1/(x-1) +1/(x+1)三项分别积分....