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ListofintegralsofrationalfunctionsThefollowingisalistofintegrals(antiderivativefunctions)ofrationalfunctions.Forothertypesoffunctions,seelistsofintegrals.MiscellaneousintegrandsAnyrationalfunctioncanbeintegratedusingpartialfractionsinintegration,bydecomposingtherationalfunctionintoasumoffunctionsoftheform:,andIntegrandsoftheformxm(ax+b)nMoregenerally,[1](Cavalieri'squadratureformula)Integrandsoftheformxm/(ax2+bx+c)nForIntegrandsoftheformxm(a+bxn)pTheresultingintegrandsareofthesameformastheoriginalintegrand,sothesereductionformulascanberepeatedlyappliedtodrivetheexponentsmandptoward0.Thesereductionformulascanbeusedforintegrandshavingintegerand/orfractionalexponents.Integrandsoftheform(A+Bx)(a+bx)m(c+dx)n(e+fx)pTheresultingintegrandsareofthesameformastheoriginalintegrand,sothesereductionformulascanberepeatedlyappliedtodrivetheexponentsm,nandptoward0.Thesereductionformulascanbeusedforintegrandshavingintegerand/orfractionalexponents.SpecialcasesofthesereductionsformulascanbeusedforintegrandsoftheformbysettingBto0.Integrandsoftheformxm(A+Bxn)(a+bxn)p(c+dxn)qTheresultingintegrandsareofthesameformastheoriginalintegrand,sothesereductionformulascanberepeatedlyappliedtodrivetheexponentsm,pandqtoward0.Thesereductionformulascanbeusedforintegrandshavingintegerand/orfractionalexponents.Specialcasesofthesereductionsformulascanbeusedforintegrandsoftheformandbysettingmand/orBto0.Integrandsoftheform(d+ex)m(a+bx+cx2)pwhenb2−4ac=0Theresultingintegrandsareofthesameformastheoriginalintegrand,sothesereductionformulascanberepeatedlyappliedtodrivetheexponentsmandptoward0.Thesereductionformulascanbeusedforintegrandshavingintegerand/orfractionalexponents.Specialcasesofthesereductionsformulascanbeusedforintegrandsoftheformwhenbysettingmto0.Integrandsoftheform(d+ex)m(A+Bx)(a+bx+cx2)pTheresultingintegrandsareofthesa
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