求不定积分1/x^2-x-6与dx的积

问题描述:

求不定积分1/x^2-x-6与dx的积
1个回答 分类:数学 2014-11-02

问题解答:

我来补答
∫[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
 
 
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