求不定积分1/x^2-x-6与dx的积

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/28 03:37:13
求不定积分1/x^2-x-6与dx的积求不定积分1/x^2-x-6与dx的积求不定积分1/x^2-x-6与dx的积∫[1/(x^2-x-6)]dx=∫[1/(x-3)(x+2)]dx=∫(1/5)[1

求不定积分1/x^2-x-6与dx的积
求不定积分1/x^2-x-6与dx的积

求不定积分1/x^2-x-6与dx的积
∫[1/(x^2-x-6)] dx
=∫[1/(x-3)(x+2)] dx
=∫(1/5)[1/(x-3) -1/(x+2)] dx
=(1/5)∫[1/(x-3) -1/(x+2)]dx
=(1/5)[∫1/(x-3) d(x-3) -∫1/(x+2) d(x+2)]
=(1/5)(ln|x-3|-ln|x+2|) +C