(x^2-x+3)/(x^3+x)的不定积分怎么求_数学解答

(x^2-x+3)/(x^3+x)的不定积分怎么求

人气：285 ℃　时间：2020-05-15 02:08:07

解答

令(x²-x+3)/(x³+x)=(Ax+B)/(x²+1)+C/xx²-x+3=(Ax+B)x+C(x²+1)当x=0,C=3当x=1,3=A+B+6→A+B=-3...(1)当x=-1,5=A-B+6→A-B=-1...(2)(1)+(2):2A=-4→A=-2-2+B=-3→B=-1∴∫(x²-x+3)/(x&s...