分母因式分解为：(x+3)(x-1)令：(2x+1)/[(x+3)(x-1)]=A/(x+3)+B/(x-1)右边通分合并,与左边比较系数后得：A=5/4,B=3/4则：∫ (2x+1)/(x²+2x-3) dx=(5/4)∫ 1/(x+3) dx + (3/4)∫ 1/(x-1) dx=(5/4)ln|x+3| + (3/4)ln|x-1| + C
