how to integrate (e^x)/ (((e^x)-5)((e^x)+4)) ? thxx?
回答 (1)
2016-03-23 11:14 am
Sol
1/[(x－5)(x－4)]
=[(x－4)－(x－5)]/[(x－5)(x－4)]
=1/(x－5)－1/(x－4)
∫(e^x)/[(e^x－5)][e^x+4]dx
=∫1/[(e^x－5)][e^x+4]d(e^x)
=∫1/(e^x－5)d(e^x)－∫1/(e^x+4)d(e^x)
=ln｜(e^x－5)｜－ln(e^x+4)+c
1/[(x－5)(x－4)]
=[(x－4)－(x－5)]/[(x－5)(x－4)]
=1/(x－5)－1/(x－4)
∫(e^x)/[(e^x－5)][e^x+4]dx
=∫1/[(e^x－5)][e^x+4]d(e^x)
=∫1/(e^x－5)d(e^x)－∫1/(e^x+4)d(e^x)
=ln｜(e^x－5)｜－ln(e^x+4)+c
收錄日期: 2021-04-30 20:14:53
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20160322232039AAdSB9n