三角函數(shù)常用積分表

1、i.積分只有sin 的函數(shù)可編輯范本jsin.crax=cot)ex，.叫1.n-lI"1/n-2Ji1sinxax=-amxcosx%/sinxdxtJnnJ其中,1n-1a-1，,r-2smexdi=sin電工cosex-/sin-er.dr.JlienJjarsinexdr=/rnsinexdx=n>0)/'t?JiTT.t/tsin3-多。fsinct0Ird=lJH1=sinra*xcos2工c2c/nfn-1,/=cosct4/rcosexdx(CCJ其中q3(H27r26)tjr-(-24nMl其中一,g.)元(./,(2/|l)-(271)1其中,(其中

2、是Coversine函數(shù))fbinex丁tinex1dx=Jr"(n-1)工用一rdr1mIntanJsinexc2rdxcoserJsin71c(ln)sin'"-中口>1)Ccosex,11nIJi'nlXn2rdx.n-0("r1Jsmhi耍sincrdr1土silicajsin(?ij:sincTdx=Bin©Ic2)r2(ci+c2)中同I¥g|)2.積分只有cos的函數(shù)1-sinerccokexdr(n>0)/2Hcosctdxcosexc2tsinorcfcotscrIdx=Jx產(chǎn)InJCOtiCTc可

3、編輯范本Sill'cos17exc(n-l)cosncos"-2ex(n>1)dd11+cosCT1ex-tandr1COSCJ：1ex-cotc24 In c2CT s,1ICOSCJ：rextan+c21 COS CTCT31n 5T4cot+c2coserdx1IcosCTetanc21cosex1-cotcexfsin(6-Qa)Tsinfci+c2)COSCyXdr=-I7-I2(仃一仃)2(dIc3)（同川聞）3.積分只有tan的函數(shù)tanerdr=-Inccobntanner&*c(n1)-/tan"-2cjcdx(forn/1)tanc

4、i' + 1tailer - 1£1、Insiner4-cos廿22cI - n | sin tT cos ct|"tan(2JCd£tanerI1Insinex4cosex2ctan er 1tancjcdxsniexcober4.積分只有sec的函wtcexdx=-In|s<?ex+tan|(for n # 1(幻tsec71-1cihsincr九一2f9Tsecexdx=1/seeJc(n.-1)n-1Jfdxr/=xtan-/seerI125 .積分只有csc的函數(shù)esc er cot er可編輯范本(for n # 1)f,cscn_1er

5、cosern,2fn_9.escexdx=|esc/c(n-1)n-1J6 .積分只有cot的函數(shù)Jcotctdr=-hiyiner/(for ?i + 1)cotnexdr=；-"cotn-ierfcot?1-9exdrc(n-1)JrdrrtanerdrJ1+coter/tanrrI1dx1 cot sftailca*dxJtancjc17.積分只可編輯范本有sin和cos的函數(shù)dii)l=一fIntitn(二-土cosed'±Binexc/2dicoscw±siner/-2ctan干4J.rcost+sin,t)"sinx-co&t

6、7111(cOtiT+SillJ：)n-L2(n2)dr*s+smtcoscydrcosct|siIICT+1ilIsinctIcotier2c1coserdrcoaerbincj?12cbinexcoscj：sintu;dxcosarIsinct2cInbinsIcoaer2chi | sin ex cus 2上binC2,dicumurairiercosexdxsin(1Iwsex)19(7Ztan+4c2exUnyrcossdi/sincr(l|-cosch)19CTCOL1c2hi2certAH2csin2ersincitcosctdr=cos(ciIc2)r2(Q4仃)(for#同)

7、(forn/1)/sincrcos"erdx=：co&n+1J|1)f.msin,1-1ctcos1sinex.coscjcdx=彳Jcin+mex(forn*1)+iexnt_7小|/sinCTcosCTinI/also:.siii171excosmsinexcosctdx=Jcnm)fdx1/=-hiLan"JSillCTUOSCTcrdx1Jsincicos"exc(?i1)cos71-1exrdx1/一=,八一exm-'lf.4H/smexcosexdx?mJf-(for幾#1)Jsinccohi"-ex1/.一心(forn豐1J

8、sinexrayexcnijamrsin位di1J<?osraexc(n1)c。驢一1errexJSHICXCObex(forn+)fsin2exdx11/ttctI=tsmct-hitanI|-)/comercc42/1rsin2exdxxinu1/Jcosnexe(r?-1)cosn-1exn1Jmrsin"exdrsLHn_1ersin17_3erdx=F-J(forn1)JcobexcnL)Jcosexalso:also:ccoserdr1/.r/.n-l1/smexc(n1)binexrcos2exdi1/exIX/Icosex+Intan1/sincj:c21/他/

9、1)可編輯范本also:(for幾乎1)also:8 .積分只有sin和tan的函數(shù)/xincttsjidr=-(hi|xocer+tansincj;)r tan，ct dxJ sin2 exir t fm'i (&r)c(n - 1)(for n 1)9 .積分只有cos和tan的函數(shù)戶 t ann er dxcos' ex-r tail"+ i ex e(n + 1)(for n # 1)10 .積分只有sin和cot的函數(shù)cotn c上 dxsiny ex1c(n + 1)cotn+1 ex (for 花# 1)11.積分只有cos和cot的函數(shù)co尸 ex dr1-i-n_j-n-|-Lsmexcoscjcd&#