∫x/(x^2+5x+6)dx

来源：学生作业帮编辑：拍题作业网作业帮分类：综合作业时间：2024/04/27 19:00:33

∫x/(x^2+5x+6)dx

∫ x/(x+2)(x+3)dx
=∫ x ×[1/(x+2) -1/(x+3)] dx
=∫ x/(x+2)-x/(x+3) dx
=∫ 1-2/(x+2)-1+3/(x+3) dx
=∫ 3/(x+3)-2/(x+2) dx
=3ln|x+3|-2ln|x+2| +C
再问：请问=∫ 1-2/(x+2)-1+3/(x+3) dx这一步是什么意思？
再答： x/(x+2)
=[(x+2)-2]/(x+2)
=(x+2)/(x+2) -2/(x+2)
=1-2/(x+2) 能看懂吗

实际上用待定系数法
直接可把x/(x+2)(x+3) 化成3/(x+3) -2/(x+2)

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