(完整word版)三角函数常用积分表

1、1.积分只有sin的函数1COSCXCjsinnexdx=sin11_1excosex十jsinn_2CJCdxJncnJ其中(其中CV5E是Coversine函数)rsinexxcoserIisinexdx=-Jc2csillexdr=其中,n0)fsinexIdxfx+1)|1)!中丹U/IJlfsinexdr=-coser+JT71_1COSCTdx其中smex.dx1/7TCJC1sinex一十13n(鼻千百f.sin(,-3)Tsin(ci+C2)T/sinciTsmc9Tdx=-；-rJ2(e：i-c2)2(C1Ic2)中,同)2.积分只有cos的函数coscrdx=-smcxcf

2、cosexJ-dx=Inexcosex,COSCJCdx=产(?l)rn-1cbinurcoxCTdxco占iCTsinexn+一cos-2exdrno(0)cosexrcosCTdr=-c2TsinCT+/Tncosexdx=sinexncxnccJsinerdx/dr1/ex?r.=_tank干：1sinexc24)T)l(E(-ir7=1G 产21(21dr1+sinex二！/尹办,/idrcosexJcosuCTcn1/dx1=tanJ1Icosexcfdx1/=-C(JICOSCTCfTdrT/1一tA】JI+COSCTCfrdrxJIcoscxccoyexdx1I,=x-J1+co

3、sexcfCO&CTdx1=一工J1cosexjcosccosc2dx=cosuxcxnLJcos-iexexCJCCT2exln|COS2CT2.exotT*?nsmTex-tan:21ex-cotc2sin-C2)Tsin&+/江门?i2(C-C2)12(C+C2)(同#)3.积分只有tan的函数drsincrn2fdr二=ik_+/5/tanexdx=-Incosexf11/tan-erdr=-Ttan11-ex-Jc(n-1)fdxT1/=十nsinCT+Jtanex+122cx1/=+InsinexJtanex122cftanexdrT1-Jtan77-3exdr(f

4、orn*1)cosex-COSCTJtanex122crtanexdxx1/=+Insinex-JtanCT122c-cosexsmCTIcosex4.积分只有sec的函数/secexdx=-In|seccTtanex,sec71-1cj?sinCTn2r7tstIsecCTdx=+/secexdxJcn-1)n-lJfdxxI=TtanJsecr+125.积分只有csc的函数r“.csc-1CTcosexn2fn_2,/cscexdx=；p/escCTaxJc(n-1)n1J6.积分只有cot的函数/cotexdj;=-In|sinCTf.r/8俨-2CXdx(forn1jfdxJ1|cot

5、CJ?=ltanexdrtanex|1dr1coter=/tanerdxtanex1(forn丰1)CSCCTdx=-In|cscCT-cotCTc(forn卢1)d.rcoscrsinCTdrCOSCEsinexdxCOST+sincoisc上d上cosCT+sinexCOSCTd.TcosexsinexsinCTdxCO5CT-ksinex7.积分只有sin和cos的函数二11)CX7T-土)1LU2cI4sinxcosrn1I(cosx+sinz)n-1-2(n-2)dxcosx+siniIn|sinCE+cosex2c-InIsinCJCcoser2c111Insinex+2cCOSC

6、TsinexdrcosCTbinCT-ln|sincr-2cCOSCTcosCTdrsinCT(1+cos)12一tan4cerT+Imtan2cfj：cosexdx2CTsinc2：(1Hcoserr)Intan2eersinercosexdx=-sin2er2cf.COS(C1+c2)xISHICOS呼dx=+)cos(ci-c2)x2(CC2)(br同)fnj1*n+1/sinexcosCTdx=sinexe(n+1)(forn/1)sincxcoserdx=c(n+1)coser.(forR,1)rimSinCTCOSCT.sin71-1cxcosm+1cxn1dx=：1n+in)*1

7、7-2Tiltsinercosexaalso:sinnercosnierdr=d.rn+77iJsinn+1cxcos*icxm1c(nIm)sincxcos；!-2erdrsinexcosex-Intancxcd.rsinexcos7?CJCc(n1)cosn-1exsinCTCOS-2CT(forn1)dxsinnCJ-coscx1c(n-1)sinCEdx?一2SltlexCOSClsinexdrcosnerc(n1)cos?,_1cx(forTL#1jsin2erdr111/7TCXsinexdIntan(|7TCTCOMCXsin2exdxdrcos11exc(nIJcos71-1e

8、xcos71-2cxsinUEdr*八一1smcxcosexcnjsinTcx也coyex(forn71)also:also:coscirdx*T1SillCTc(n1)sin-1CTcos2exdrHill(rciosexhitancos2exdxcosexcsin71-1ex)+Jamn2cx(forn#1)8 .积分只有sin和tan的函数JsinCJ:tanexdx=-(In|secex+tancxsinex)9 .积分只有cos和tan的函数10 .积分只有sn和co上的函数11.积分只有cos和cot的函数12 .积分只有tan和cot的函数tan?n(cT)T1_lz、ftanm-2(cr).also:also:rtanexdrJsin2e