问题描述: 求∫(x^3+66)/x^2+7x+12)dx 1个回答 分类:数学 2014-11-26 问题解答: 我来补答 (x³+66)÷(x²+7x+12)=x-7余37x+150所以(x³+66)÷(x²+7x+12)=x-7+(37x+150)/(x+3)(x+4)令(37x+150)/(x+3)(x+4)=a/(x+3)+b/(x+4)=(ax+bx+4a+3b)/(x+3)(x+4)所以a=39,b=-2所以原式=∫[x-7+39/(x+3)-2/(x+4)]dx=x²/2-7x+39ln|x+3|-2ln|x+4|+C 展开全文阅读