(2x^2-3x-3)/[(x-1)(x^2-2x+5)]求不定积分

题目

(2x^2-3x-3)/[(x-1)(x^2-2x+5)]求不定积分

答案

设(2x²-3x-3)/[(x-1)(x²-2x+5)]=[a/(x-1)]+[(bx+c)/(x²-2x+5)]则2x²-3x-3=a(x²-2x+5)+(bx+c)(x-1)整理得2x²-3x-3=(a+b)x²-(2a+b-c)x+(5a-c)∴a+b=22a+b-c=35a-c=-3解得a=-1b=3c=...