呼啸大师收藏的积分公式.pdf

《呼啸大师收藏的积分公式.pdf》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。

1、ListofintegralsofrationalfunctionsThefollowingisalistofintegrals(antiderivativefunctions)ofrationalfunctions.Forothertypesoffunctions,seelistsofintegrals.MiscellaneousintegrandsAnyrationalfunctioncanbeintegratedusingpartialfractionsinintegration,bydecomposingtherationalfunctionintoasumoffunctio

2、nsoftheform:,andIntegrandsoftheformmnx(ax+b)[1]Moregenerally,(Cavalieri'squadratureformula)Integrandsoftheformm2nx/(ax+bx+c)ForIntegrandsoftheformmnpx(a+bx)Theresultingintegrandsareofthesameformastheoriginalintegrand,sothesereductionformulascanberepeatedlyappliedtodrivetheexponentsmandptoward0

3、.Thesereductionformulascanbeusedforintegrandshavingintegerand/orfractionalexponents.Integrandsoftheform(mnpA+Bx)(a+bx)(c+dx)(e+fx)Theresultingintegrandsareofthesameformastheoriginalintegrand,sothesereductionformulascanberepeatedlyappliedtodrivetheexponentsm,nandptoward0.Thesereductionformula

4、scanbeusedforintegrandshavingintegerand/orfractionalexponents.SpecialcasesofthesereductionsformulascanbeusedforintegrandsoftheformbysettingBto0.Integrandsoftheformmnnpnqx(A+Bx)(a+bx)(c+dx)Theresultingintegrandsareofthesameformastheoriginalintegrand,sothesereductionformulascanberepeatedlyappli

5、edtodrivetheexponentsm,pandqtoward0.Thesereductionformulascanbeusedforintegrandshavingintegerand/orfractionalexponents.Specialcasesofthesereductionsformulascanbeusedforintegrandsoftheformandbysettingmand/orBto0.Integrandsoftheform(m2p2d+ex)(a+bx+cx)whenb−4ac=0Theresultingintegrandsareofthesa

6、meformastheoriginalintegrand,sothesereductionformulascanberepeatedlyappliedtodrivetheexponentsmandptoward0.Thesereductionformulascanbeusedforintegrandshavingintegerand/orfractionalexponents.Specialcasesofthesereductionsformulascanbeusedforintegrandsoftheformwhenbysettingmto0.Integrandsofthefo

7、rm(m2pd+ex)(A+Bx)(a+bx+cx)Theresultingintegrandsareofthesameformastheoriginalintegrand,sothesereductionformulascanberepeatedlyappliedtodrivetheexponentsmandptoward0.Thesereductionformulascanbeusedforintegrandshavingintegerand/or