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4tx=∫xexd∫tettd2vuvuuv′+′=′)(xvuxvuuvdd′+′=∫∫xvuuvxvudd∫∫′−=′uvvuvudd∫∫−=——1xexIxd11∫=∫=xexdvduxxe=∫−xexduvvudCexexx+−=?xeu=∫⋅=xxexd221uvd∫xxexd2d21xex∫=)d(2122∫−=xxexex)d(2122∫−=xexexxxvd∫−=xexd2vdxex2−=2dxex∫+uvdxexIxd222∫=xex2−=xxexd2∫+1Ixex2−=Cexexx+−+2nxu=xexnexxnxnd1∫−−∫=xexIxnndvd1−−=nxnnnIexI2xxxIdcos11∫=?=u∫xxxdcos∫+=xxxxxdsin2cos222vxxxdd21d2==,cosxu=u.xxxIdcos11∫=uvd∫=xxsindvdxxsin=∫−xxdsinuvvudCxxx++=cossinvd∫−=xxcosd2vd∫=xxxIdsin222xxcos2−=2dcosxx∫+uvdxxcos2−=xxxdcos2∫+1Ixxcos2−=Cxxx+++)cossin(2,dsin∫xxxnnxu=).()()(,d)(xxxfxxfψϕ=∫1uxxvd)(d)1(ψ=,d)(∫xxψ;v.dd)2(∫∫vuuv3xxxIdln)1(1∫=u∫=2dln2xxvdxxln22=xxlnd22∫−uvd∫−xxd21xxln212=Cxxx+−=2241ln21xxxIdarctan22∫=)2d(tanrca2xx∫=vudxxarctan212=∫+−xxxd12122xxarctan212=∫+−−xxd)111(212xxarctan212=Cxx+−−)arctan(212∫∫xxxxexnxndsind)1(αnxu=12∫xxxndln)2(xuln=3(1)xxvndd=∫xxxndarcsin)3(xuarcsin=3(2)3u“”(“LIATE”).LuIATE∫+.d1arctan2xxxx,1)1(22xxx+=′+QAILIATEu42arctand1xxxx∴+∫2arctand1xx=+∫u221arctan1d(arctan)xxxx=+−+∫22211arctan1d1xxxxx=+−+⋅+∫2211arctand1xxxx=+−+∫txtan=21d1xx+∫221secd1tanttt=+∫secdtt=∫Ctt++=)tanln(secCxx+++=)1ln(22arctand1xxxx∴+∫xxarctan12+=.)1ln(2Cxx+++−5xxeIxdcos∫=xexcos=∫−xexcosd∫=xexdcosvduvdxexcos=∫+xxexdsinxexcos=xexsin+∫−xxexdcosxexsin+xexcos=I−CxxeIx++=)cos(sin21xeu=:∫=)d(sinxeIx∫−=xxexxedsinsinu∫⋅−=xexxexxdsinsin∫+=xexexxcosdsinu∫−+=xxexexexxxdcoscossinu()Ixexexx−+=cossinI∴.)cos(sin2Cxxex+−=4ºu.LIATE,.∫xxexdcosβα5vud,u5º“”.“”(1)“”“+1”.u.xxd1∫)1d(1xxxx∫−⋅=xxd1∫+xx1⋅=1(2).(3).6xxxIdsectan2∫=∫=xxsecdtanvudxxsectan=∫−xxdsec3uvxxsectan=∫+−xxxdsec1tan2xxsectan=I−Cxx++−tanseclnCxxxxI++−=]tanseclnsec[tan2177xxInndsin∫=,2≥n.xx22sin1cos−=)cosd(sin1∫−=−xxInnvudxxn1sincos−−=∫+dcosxuvxxnn22sin1−−xxn1sincos−−=∫−−+xxnndsin)1(2∫−−xxnndsin)1(xxJnndcos∫=xxn1sincos−−=xxInndsin∫=∫−−+xxnndsin)1(2∫−−xxnndsin)1(xxn1sincos−−=21−−+nInnIn1−−Nnn∈≥,2xxnInn1sincos1−−=21−−+nInnxxnJnn1cossin1−=21−−+nJnn.vud∫+=nnaxxI)(d228.11+−nnIInInIxaxxnnd)(21222∫+++naxx)(22+=xaxnnd)(2122∫+++222)(aax−+naxx)(22+=uvCaxaxaxI+=+=∫arctand1221naxx)(22+=xaxnnd)(2122∫+++222)(aax−+nInaxx)(22+=nIn2+122+−nIan∫+=nnaxxI)(d22:nnnIannaxxanI22221212)(21−++=+6º∫−+−22d)]([)(1nnIxxfxf∫+−xxfxfxfnd)]([)()(122xxfInnd)]([1∫=∫+−xxfxfxfnd)]([)()(1⎪⎩⎪⎨⎧=++––⎪⎩⎪⎨⎧=∫−+−1d)]([)(1nnIxxfxf++––xxInndsin1)1(∫=∫+−=xxxxndsinsinsin12222dsincos−+=∫nnIxxx21)d(sincos11−−+−=∫nnIxxnuxxxInnd11)2(2∫+=∫+−+=xxxxxnd1122222d1−−+=∫nnIxxx212d111−−−+−=∫nnIxxnu7º2(1)1234(2)56(3)78.9xexd∫∫text=ttd2tet(2=)te−C+Cxex+−=)1(2∫=xxtandcoslnvudxxxIdcoscosln2∫=10xxcoslntan⋅=∫+xxdtan2xxcoslntan⋅=∫−+xxd)1(sec2xxcoslntan⋅=Cxx+−+tan11)(xf,cosxx.d)(xxfx′∫′=xxxfcos)(∫xxfd)(1cosCxx+=xxfxd)(′∫)(dxfx∫=)(xfx=xxfd)(∫−(x=)′xxcosCxx+−cos−−=xsinCxx+cos2)(xf′.2′=xxxfcos)(2cossinxxxx−−=)()(′=′xf2cossinxxxx−−L==′∫xxfxd)(xxxxxxdcos2sin2cos2⎟⎠⎞+⎜⎝⎛+−∫L=xexeIxxd1∫−=1−xxee12(1),∫−=xexeIxxd1∫−−=)1(d1xxeex∫=x2)1(d−xevud12−=xex∫−−xexd12∫−=xexeIxxd112−=xex∫−−xexd12uuuxd12d2+=,1−=xeu∫+−uuud1422112−+u412−=xexI12−=xexCuu+−−arctan412−=xexICeexx+−+−−1arctan414(2),1−xe.d1∫−=xexeIxx,)1ln(2tx+=tttxd12d2+=,1−=xet∫−=xexeIxxd1∫+⋅++=ttttttd12)1ln()1(222∫−=xexeIxxd1∫+⋅++=ttttttd12)1ln()1(222∫+=ttd)1ln(22)1ln(22tt+=∫+−tttd1422+11−vud)1ln(22tt+=t4−Ct++arctan412−=xexICeexx+−+−−1arctan41413.dxI∫=23)1(2x+xearctan(1),,tantx=∫=teIt3secttdsec2⋅ttetdcos∫=−=tetsinttetdsin∫tetsin=ttetdcos∫−tetcos+CettIt++=)cos(sin21.dxI∫=23)1(2x+xearctantx21x+txtan=CettIt++=)cos(sin211⎢⎣⎡=2121xx+211x++Cex+⎥⎦⎤arctan(2)xeIxdarctan∫=23)1(2x+xexIarctan2d11∫+=xxexxexarctan2arctan2d111∫+++=xexarctan211+=xd∫+23)1(2x+xexarctan)1(11arctan2xexx++=I−CexxIx+++=arctan2121xvuvuxvudd∫∫′−=′xvuvd∫′,1.:v′2.:“”,u3.:;;.??∫xxxdsincos∫′−=xxxxxdsin)sin1(sinsin∫−−=xxxxdsinsincos12∫+=xxxdsincos1,1dsincosdsincos=−∴∫∫xxxxxx0=1∫=xxsinsindCx+=sinln,0..1-1xxxdcos)6(2∫+xxxdcos)6(2∫+xxsind)6(2∫+=()()6dsinsin622+−+=∫xxxx()xxxxxdsin2sin62∫−+=()xxxxcosd2sin62∫++=()xxxxxxdcos2cos2sin62∫−++=()cxxxxx+−++=sin2cos2sin622-1xxxde2∫−xxxde2∫−∫−−=xxde222deexxxx∫−−+−=xxxxxde2e2∫−−+−=∫−−−−=xxxxde2e2xxxxxxde2e2e2∫−−−+−−=Cxxxxx+−−−=−−−e2e2e23-1xxIdarcsin∫=vud∫−−xxxd12xxarcsin=)1d()1(212212∫−−+−xxxxarcsin=xxarcsin=Cx+−+21LIATEu.d)1(2xxexIx∫+=xexxId)1(2∫+=xxxeexxxxd])1([)1(22′+⋅−+=∫AExxxeexxxxd])1(2)1(1[)1(322+++−⋅−+=∫])1(111[])1(1)1([])1([222′+−+=′+−+=′+xxxxxx6-1(1)22312(1)(1)(1)xxxxeededxxxx=+−+++∫∫22312(1)(1)(1)xxxxeededxxxx=+−+++∫∫I2233(2)[]2(1)(1)(1)(1)xxxxxeeeedxdxxxxx−=+−−++++∫∫.1xeCx=++xexxIxd)1(1)1(2∫+−+=(2)xxexxexxd)1(d12∫∫+−+=∫∫+++=)1(1dd1xexxexx∫∫+−+++=xxexexxexxxd11d1.1Cxex++=6-2vud.0d22+=∫axaxI22axx+=∫+−xaxxd22222axx+=∫+−+−xaxaaxd22222)(22axx+=∫+−xaxd22∫++22d2axxa22axx+=I−Caxxa++++)(ln2222221axxI+=Caxxa++++)(ln22227-1∫=xxInndtan)2(1tan21≥−−=−−nInxnn2−nIxxxInnd)1(sectan22−=∫−)d(tantan2xxn∫−=1tan1−=−nxn2−−nI2−−nI∫=xxInndtan)2(1tan21≥−−=−−nInxnnxxxnnd)tan(tan2−+=∫2−+nnII∫−=xn2tanxxdsec2Cnxn+−=−1tan1∫−=xxntandtan2=0I,Cx+=1ICx+−coslnL,,32II12-1∫=xxId)ln(sin,lnxt=texexttdd,==∫−=ttetettdcossintteItdsin∫=∴tetsintetcostsin−te+−∫+Ittet−−=)cos(sinCtteIt+−=∴)cos(sin21Cxxx+−=)]cos(ln)[sin(ln21