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s;я7I@}tyGҶj^HX+ҖWvd%zVNGҿT c혷!s=pf[ gBWp']|q(g\g"!o&R׈z`M8 ΰ t&X#2ܓ 4Zqpw*ͅ*qA#샦7_:ߣ|hN9ebrwJӤYx>׶Df1QBv?Q0\Ӊ`&G `wp8^q7pK?8A'Opuç>`Ɓ`OXh*zTf\:`@b#?bszs>W)afIO'kŻ;.qD8&ۛC8 bXۿv/C'?G 'L# @e J^xD\0|Q.CnfN=,<4sӮ C:d%g'cV׮AS̟YZ>s<' [R/g7NI+Q?#nn[ }<8߄ۧt{gKKn?ɠǒ[0X7>Qx..? ]Xg"5`{SO06x<ޙ/l0lDcQ0W{q',e\~ (x"1)(x"2)=t 2 (x"1) 2    |:(x-1)x-2=t 2 x"t 2 x(1"t 2 )=2"t 2 x=2"t 2 1"t 2 dx="2t(1"t 2 )+2t(2"t 2 )(1"t 2 ) 2 dtdx="2t+2t 3 +4t"2t 3 (1"t 2 ) 2 dtdx=2t(1"t 2 ) 2 dtueEVuk[pѵ0X@YUirIDL(4# 1 DI$B ~X.\"ڥ8ޓ t _W1&!fQ ny[3~cܮ0XA@3c5k|m1b5Vfqԡi)j&wS[ ^{'q=ضThb ss}|Yu.~։Z+f!Ls+Xzh|onN&[|~VDd%1<  C A? 2:.l,ljqX`!:.l,lj`;N \yxle߻vm^ܶ^c~u;(2fdDY#,Zp`!YLH$&EMqcJ","p1"0{y6M|y>2D$@GdGd C- @-LDXT;BMl(dA"Rg#'cj\{`cBF[~VS-5:"l"NjmSal; ˶M:bئE9sy&185yc.TְZǰM5 TGNæ%Mk[x°m]]m]]Qiz ޮ}G76(isrhp3_ݴgh`7Y(mM1bxJ;b"mh%T?jpmǩJ?c_Cw``^\ہͷ'*10Hq6oH^/GMNioz?c d?V%П ~Q!rVq0BU ؏Ǜy?'̸Y8`c~_io=1nĶAs#lu3JփZ,傼dua?W+t~9 ߕBP-&y HpqYݴ r͒urkeII/ 䍁]w٨b?},uYY)Ըb=Hx3w;[ghd?Ot+VRMjq̍ 'bJ`DYW<0B=]Ѫ ֿUop|MN;2ApC)SRIƧ 7YOd~o8jJ&|F[B}&\ISF ܪ|`hRi˷TU"~g8L8Ӎh2v=VW<ʖ /A}Vߜ0_V('/!θ l_alG':'?`4柔x#9g;=!B',͕Ksgѹe0_s񦹾f/6'q+'gƪ dRU=CB] \#YJpL52pHsxs3>c/l- m߿n^$V K{0CS_wbNڡI>?>qmٖ?X.@oB}J@J78\\;P gzeŸHvb rVJ0a|V9"*(܇,گ|TG{9GYo::g:_t9,\B! W9fAaSC{?toV }݈.NЪ'vDJ_ V"FuaDd3*|#<  C A? 2WۙPw#C8[_`!SWۙPw#C84 ?7hXX!xkLU vw؅ݥ[C],5iSM66`.JM XĚ*V 3(w( ke1(3>u 73fRi.<y|ݏIw?hv?a/_y&Tp 㾲wR?b` n5])d)0Q 7_rxwQ~rX|GX!'mGK?i[D-"(a8[Oic8<0:<;@sO<'֨Dd%1<  C A? 2:.l,lj(e`!:.l,lj`;N \yxle߻vm^ܶ^c~u;(2fdDY#,\b})7pxBNP.1#$dFDyA"B UPPL)\ c CH*b/հz!NEϣMzWx쁋z/J%rUl|k%EpkgUf6j73Өn: L:M|Nd"@BuyW-uj=| JAy-WA3Jvl΃W\*W2+x:(7脔M|QN4_8Y\\"{Kd8 =Y{>4˦-ۯV'T>buNK]떳Wy>H{l=whiۦFu7W>>1n`5&>nFs>plg ],>!rPn\bsb>ךiMI|\ Vˇ^޾ lc_* ZscA߾[׮Gn1 cyy2F?`7nkŜU߯w~ (+AN_ӂ(m(' p!Dd$"2< K C A? 2IΗ}2pf^Dm[`!eIΗ}2pf^D@6 QT}3x}LSW_W?(--}< Zjg6U*$ͬ!laf٪ӹenqu[D`̲,fK)! c%KI׾WAJ9{}T0>)a?9WR^J%YTl2,URZp`!YLH$&EMqcJ","p1"0{y6M|y>2D$@GdGd C- @-LDXT;BMl(dA"Rg#'cj\{`cBF[~VS-5:"l"NjmSal; ˶M:bئE9sy&185yc.TְZǰM5 TGNæ%Mk[x°m]]m]]Qiz ޮ}G76(isrhp3_ݴgh`7Y(mM1bxJ;b"mh%T?jpmǩJ?c_Cw``^\ہͷ'*10Hq6oH^/GMNioz?c d?V%П ~Q!rVq0BU ؏Ǜy?'̸Y8`c~_io=1nĶAs#lu3JփZ,傼dua?W+t~9 ߕBP-&y HpqYݴ r͒urkeII/ 䍁]w٨b?},uYY)Ըb=Hx3w;[ghd?Ot+VRMjq̍ 'bJ`DYW<0B=]Ѫ ֿUop|MN;2ApC)SRIƧ 7YOd~o8jJ&|F[B}&\ISF ܪ|`hRi˷TU"~g8L8Ӎh2v=VW<ʖ /A}Vߜ0_V('/!θ l_alG':'?`4柔x#9g;=!B',͕Ksgѹe_1039002786FuuOle ObjInfo_1039004354 FRuRu  !"#$%&'()*+,-./01234569<=>?@ABCDEFGHIJKLMNOPQRSTUVY\]^_`abcdefghijklmnopqrsvyz{|}~ FMicrosoft Equation 3.0 DS Equation Equation.39q4hI cI 1) R(x; ax+b n )dx  +"  Ole CompObj fObjInfo Equation Native Notatie  ax+b=t n 2) R(x;R(x; ax+b n1 )dx  +" ;.....; ax+b nk )dx  +"  Notatie ax+b=t m  m=c.m.m.m.c(n 1 ,n 2 ,....,n k ) 3) (x; ax+bcx+d n )dx   +"  Notatie  ax+bcx+d=t n 4) (x; ax+bcx+d n1 ;.......; ax+bcx+d nk )  +" dxNotatie  ax+bcx+d=t m  m=c.m.m.m.c(n 1 ,n 2 ,....,n k )d FMicrosoft Equation 3.0 DS Equation Equation.39qӬ0hIcI 5) R(_1039508594F`zuuOle CompObj fObjInfo0_s񦹾f/6'q+'gƪ dRU=CB] \#YJpL52pHsxs3>c/l- m߿n^$V K{0CS_wbNڡI>?>qmٖ?X.@oB}J@J78\\;P gzeŸHvb rVJ0a|V9"*(܇,گ|TG{9GYo::g:_t9,\B! W9fAaSC{?toV }݈.NЪ'vDJ_ V"FuapDd'4<  C A? x; ax 2 +bx+c  )  +"  i) a>0 ax 2 +bx+c  =t+x a       sau(t"x a  )ii) c>0 ax 2 +bx+c  =tx+ c        sau(tx" c  ) iii) >0       (, radacini)  ax 2 +bx+c  =t(x-)     sau t(x-)                       APLICATIISa se calculeze primitivele urmatoarelor functii:1) I= 1-x1+x  +" dx               x"(-1,1) 1-x1+x=t 2  1-x=t 2 +t 2 xx(t 2 +1)=1"t 2 FMicrosoft Equation 3.0 DS Equation Equation.39qJ@I x=1"t 2 1+t 2 dx="2t(1+t 2 )+2t(1"t 2 )(1+t 2 ) 2 dtdx="2t"2tObjInfo:Equation Native ;_1039512566F u@uOle W 3 +2t"2t 3 (1+t 2 ) 2 dtdx="4t 3 (1+t 2 ) 2 dtI ' ="4t 4 (1+t 2 ) 2 dt="4[dt  +" "2t 2 +1(1+t 2 ) 2 dt  +" ]  +" I ' ="4[t"2t 2 (1+t 2 ) 2 dt+1(1+t 2 ) 2 dt  +"  +" ]I ' ="4[t"2t 2 +1"1(1+t 2 ) 2 dt+1(1+t 2 ) 2 dt  +"  +" ]I ' ="4[t"21(1+t 2 )dt+31(1+t 2 ) 2 dt  +"  +" ]I 1 =1(1+t 2 ) 2 dt=  +" 1+t 2 "t 2 (1+t 2 ) 2 dt  +"CompObjXfObjInfoZEquation Native [_1039512959 Fu vu FMicrosoft Equation 3.0 DS Equation Equation.39q0hIcI I 1 =11+t 2 dt  +" "tt(1+t 2 ) 2 dt  +" f(t)=t                 g ' (t)= t(1+t 2 ) 2 f ' (t)=1                 g(t)=-12(1+t 2 )I 1 =11+t 2 dt  +" +t2(1+t 2 )+1211+t 2 dt  +"  I 1  =32arctg t +t2(1+t 2 )I '  ="4t"72arctg t - 6t(1+t 2 ) I=-4 1-x1+x  "72arctg 1-x1+x  "6 1-x1+x  21+xI=-4 1-x1+x  "72arctg 1-x1+x  "3(1+x) 1-x1+x  FMicrosoft Equation 3.0 DS Equation Equation.39qOle tCompObjufObjInfowEquation Native x`DI)J 2) I=x-1 x 3 +1  +" dx       x"R\{-1}x=t 3 dx=3t 2 dtI=x x 3 +1  +" dx"1 x 3 +1  +" dxI ' =3t 5 t+1  +" dt"3t 2 t+1dt  +" t 5 t+1=t 4 "t 3 +t 2 "t+1"1t+1I ' =3(t 4 "t 3 +t 2 "t+1"1t+1)dt       +"          -3(t-1+11+t  +" )dtI ' =3[t 5 5"t 4 4+t 3 3"t 2 2+t"ln(t+1)]"         -3[t 2 2-t+ln(t+1)] FMicrosoft Equation 3.0 DS Eq_1039599280"F?ufuOle CompObj!#fObjInfo$uation Equation.39qVӬcIgI I=3[x x 23 5"x x 3 4+x3" x 23 2+ x 3 "ln( x 3 +1)]     -3[ x 23 2" x 329У[uFxNsa~F|99#p<*1gw̏~տ:rmW޶i]_fz,ѸDd%1< 9 C A? 2:.l,lj`!:.l,lj`;N \yxle߻vm^ܶ^c~u;(2fdDY#,Zp`!YLH$&EMqcJ","p1"0{y6M|y>2D$@GdGd C- @-LDXT;BMl(dA"Rg +ln( x 3 +1)]I=3(x x 23 5"x x 3 4+x3)+C3) I=dx(1+x) 1+x+x 2 +"            x"R\{-1}a>0! 1+x+x 2 =t+x | 2 1+x+x 2 =t 2 +2tx+x 2 x(1"2t)=t 2 "1x=t 2 "11"2tdx=2t(1"2t)+2(t 2 "1)(1"2t) 2 dtdx=2t"4t 2 +2t 2 "2(1"2t) 2 dtdx="2t 2 +2t"2(1"2t) 2 dt FMicrosoft Equation 3.0 DS Equation Equation.39qVfII 1+x=1+t 2 "11"2t=1ObjInfo)Equation Native 0_1039601451,F`Bu`BuOle "2t+t 2 "11"2t=t 2 "2t1"2t 1+x+x 2 =t+x=t+t 2 "11"2t=t"2t 2 +t 2 "11"2t=                   ="t 2 +t"11"2t1(1+x) 1+x+x 2 =1t 2 "2t1"2t."t 2 +t"11"2t=                              =(1"2t) 2 t(t"2)("t 2 +t"1)I ' =(1"2t) 2 t(t"2)("t 2 +t"1)  +" 2("t 2 +t"1)(1"2t) 2 dtI ' =21t(t"1)dt  +" 1t(t"1)=At+Bt"1=(A+B)t"At(t"1) #'cj\{`cBF[~VS-5:"l"NjmSal; ˶M:bئE9sy&185yc.TְZǰM5 TGNæ%Mk[x°m]]m]]Qiz ޮ}G76(isrhp3_ݴgh`7Y(mM1bxJ;b"mh%T?jpmǩJ?c_Cw``^\ہͷ'*10Hq6oH^/GMNioz?c d?V%П ~Q!rVq0BU ؏Ǜy?'̸Y8`c~_io=1nĶAs#lu3JփZ,傼dua?W+t~9 ߕBP-&y HpqYݴ r͒urkeI FMicrosoft Equation 3.0 DS Equation Equation.39qVӠ0hIcI A+B=0"A=1!A="1                  B=1I ' =2["1tdt+1t"1dt  +"  +" ]I ' =2["lnt+ln(t"1)]I ' =2["ln( 1+x+x 2 "x)+ln( 1+x+x 2 "x"1)]4)I=x 2 +x+1x x 2 "x+1  +" dxc>0 x 2 "x+1  =tx+1  | 2 x 2 "x+1=t 2 x 2 +2tx+1x 2 "x=t 2 x 2 +2tx   |:xx-1=t 2 x+2tx(1"t 2 )=2t"1x=2t"1(1"t 2 ) FMicrosoft Equation 3.0 DS EqOle CompObj02fObjInfo3Equation Native uation Equation.39qx0hIcI dx=2(1"t 2 )"(2t"1)("2t)(1"t 2 ) 2 dtdx=2"2t 2 +4t 2 "2t(1"t 2 ) 2 dtdx=2t 2 "2t+2(1"t 2 ) 2 dt x 2 "x+1  =t2t"11"t 2 +1=2t 2 "t+1"t 2 1"t 2 =                   =t 2 "t+11"t 2 I=x 2 x x 2 "x+1  dx+  +" xx x 2 "x+1  dx+  +"       +dxx x 2 "x+1  +" I=x x 2 "x+1  dx+  +" dx x 2 "x+1  +dxx x 2 "x+1  +"  +" x x 2 "x+1  =(2t"1)(1"t 2 )(1"t 2 )(t 2 "t+1)=2t"1t 2 "t+1 FMicrosoft Equation 3.0 DS Equation Equation.39qI/ 䍁]w٨b?},uYY)Ըb=Hx3w;[ghd?Ot+VRMjq̍ 'bJ`DYW<0B=]Ѫ ֿUop|MN;2ApC)SRIƧ 7YOd~o8jJ&|F[B}&\ISF ܪ|`hRi˷TU"~g8L8Ӎh2v=VW<ʖ /A}Vߜ0_V('/!θ l_alG':'?`4柔x#9g;=!B',͕Ksgѹe0_s񦹾f/6'q+'gƪ dRU=CB] \#YJpL52pHsxs3>c/l- m߿n^$V K{0CS_wbNڡI>?>qmٖ?X.@oB}J@J78\\;P gzeŸHvb rVJ0a|V9"*(܇,گ|TG{9GYo::g:_t9,\B! W9fAaSC{?toV }݈.NЪ'vDJ_ V"FuapDd'4< K C A? 2u;Vʏښ|M`!u;Vʏښ|~?Thqbx}ltfII 1 x 2 "x+1  =1"t 2 t 2 "t+11x x 2 "x+1  =(1"t 2 )(2t"1)(1"t 2 )(t 2 "t+1)=(1"t 2 ) 2 c5ƚ?bBFURf_0&>>XCΝ;3X{;w2'$ |spƆ\@S<vZ D<*O\jVst<39z.u,dgSȱ>#i˫N bCKôn^´kU^5z{w)Z4E(z\"{ƴe_S}ZhhJRgeZKiL-xTƂ) Xb}%uV-]ԾJL$tBɊ<*,+rֆ_gj]SEkzO:AןT(ϸprb_DfĴcWv,zD2Vݞ^u@*3w{Pۣ8/+EYƷL3ZT{3fԗFDnQDnلQ٨ZTlwsy˫G~yڕ+:w{OHC=d$蕔m4Y/&)L)׷S2)7F &wWSn5ZeIIzT\P!o3%"{"WbSCrB皈/Ԕi<\ ~_]+炐G \(\! 3v?x `~;dwCâ kI礭BKھcm; ,v3e-`Os&ʍ&ߌbXD`#?e0>UT-黮Đ F3Ni,bv{;3;3U0x;}>|hK ƞ&Τ9^jљ)!ja\Iew)7߸N_w@ u0?cq_Ĥi K_ R`ex~1<0'6_VxcIgI 11"t 2 =A1"t+B1+t1=A(1+t)+B(1"t)A"B=0A+B=1 FMicrosoft Equation 3.0 DS Equation Equation.39q  I=2 x"2x"1  +c6)I=lnxx 1"4lnx"ln 2 x  dx ;x"e -2- 6  ,e -2+ 6  ()  +" \{0}lnx=tx=e t   !dx=e t dtI ' =te t  (4hI cI 2A=1A=12    !B=12 I ' =214"11"tdt"14"1(1"t) 2 dt"  +" 14dt1+t"  +" 34dt(1+t) 2 +"  +" []        +dt1-t  +" +dt1+t+2dt2t-1  +"  +" I ' =12ln(1"t)+12(1"t)"12ln(1+t)+32(1+t)"ln(1"t)+       +ln(1+t)+ln(2t-1)I ' ="12ln(1"t)+12ln(1+t)+ln(2t"1)+12(1"t)+32(1+t)t= x 2 "x+1  "1xI ' ="12[lnx" x 2 "x+1  "1x"ln FMicrosoft Equation 3.0 DS Equation Equation.39qR?b` n5])d)0Q 7_rxwQ~rX|GX!'mGK?i[D-"(a8[Oic8<0:<;@sO<' x 2 "x+1  "1)+3x2(x+ x 2 "x+1  "1)]Oh+'0p1-4t-t 2  e t dt=  +" t 1-4t-t 2  dt  +" c>0! 1-4t-t 2 =zt+1  | 2 1-4t-t 2 =z 2 t 2 +2zt+1-4t-t 2 =z 2 t 2 +2zt  |:tϪ2jU Y~JcjY1tOS s=2#/tILa0Y9"*֩&R=N_l+|&Wm%mX.\Nrm[ȶMmZ FM Jlؤ.6۱J櫓m͊nUU*D&\GymuAiL-}yL/ o۱E&3*&?.j6͙Ӓ,C,XCVPvDw4Z>gː5Nn}{"۟m{Z פ|uYFc%id;57,`r)lsP._h9Zȟ4/Q?礜xMGo΄X?Q?֏Carq1Xax=4_NBU4&mwZX~ȕS@|qZ {pߝKO.h|^F1Ʉ-2bùTd~%췴Uoz|Ǟ~擤Dw)SUc`WDIץ;'y O;屍LewN꧃T?RcC3*@Q8O@2G hcЀzczqŽe~zP"9|WG>ze^pTP=/XJ0Oa<֟qkG3N#t[[T?awCiF>C~RC i);ˑ5zd7zmyW?^~VρZTv.[3igY)XTl/G}P[zgګ?%Z?zL@~`E> Vo\Մ;:Z +2]Qn<`=kfSt{_d_Xs );j%0*^S}W/z|,j|55N~vν'U~zܝ3 }ޙYiegԤEGy71ʙ~ 7tVQt0\Iz}3?/w#p="7,x"bOxJވ@x~|^'/yaNx2b ֻxrɟޅ,/ͣ!\x XhګNo yEt̴ޔ֛9t^>ݳR}ZQNwʈea<- k ǭg$VNGŲ̓"=}LHrB!2 ~yyYd*"Rv> 3K]̕pdgYy3q0F1pMv&nt*Ď ZJل F)sSAiÄr' .ʝ(,Qn&PoqܕrMV@%p/Pn:hwZmŤzuG  \PGԠ\S).vMq-U +Y1b=jN-:{kyp?@VP ˀkePv$Wq4WR^:ˀ뮀YrfKfo}4){)w+c ɦAV_kGZ|+x; ގ鶭Z t&rt&I[38 w'[Vpro't[m33NښI#\wzA#k=?CL||/ݢ{0TӒD3- (h[yeR5^EG2ʅp`='j7p$*7>]Bk拿e.Ee"K66>xO oq $<ű $#؃pv؃d{0ű $#؃p {aA7. 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HB  C D(r   (r   (r   H  C A  ?(r  HB  C DH  C A  ?H  C A ?H  C A ?H  C A ?H  C A ?H  C A ?B S  ?%)+-/13568:<mALp$"4(C$ 24P!14 "P/4 /4 xp0"D54 @(#0044t `'L14`'`148 &.4 tRtZJtH/ /tHMKE4 tM =t8'x74%14'444&24l/4L,4X4$=IJTU^_knx~CCAlexCC:\DOS\AutoRecovery save of INTEGRAREA UNOR EXPRESII IRATIONALE.asdAlexCC:\DOS\AutoRecovery save of INTEGRAREA UNOR EXPRESII IRATIONALE.asdAlexCC:\DOS\AutoRecovery save of INTEGRAREA UNOR EXPRESII IRATIONALE.asdAlex:C:\WINDOWS\Desktop\INTEGRAREA UNOR EXPRESII IRATIONALE.docAlexCC:\DOS\AutoRecovery save of INTEGRAREA UNOR EXPRESII IRATIONALE.asdAlex:C:\WINDOWS\Desktop\INTEGRAREA UNOR EXPRESII IRATIONALE.docAlex:C:\WINDOWS\Desktop\INTEGRAREA UNOR EXPRESII IRATIONALE.docAlex:C:\WINDOWS\Desktop\INTEGRAREA UNOR EXPRESII IRATIONALE.docAlex:C:\WINDOWS\Desktop\INTEGRAREA UNOR EXPRESII IRATIONALE.docAlex:C:\WINDOWS\Desktop\INTEGRAREA UNOR EXPRESII IRATIONALE.doc@,BC0@10 @10 @10 @10 @10 @0 @0| @11111*1,1.10020416181:1F1\1^1`1b0d0f1h1j1l1x111100111111°1İ1ư0Ȱ0ʰ1̰1ΰ1а1ܰ1111000 @0 @GTimes New Roman5Symbol3& Arial"hLQf. !>0dF#INTEGRAREA UNOR EXPRESII IRATIONALEAlexAlexp(  G Lbjbjَ C]vvv6T> > > > ,j < & '''[#]#]#]#]#]#]#$L'@)#v'5'''#  +   ' Hv [#`'[# N [#v[#  ~Uu > 4[#C WRoot Entry   C A ?D Fg<l~UuEADataH    ?߫WordDocumentA ?FH   C A ObjectPool(r  %uu ?$   l]"%&'()*+,-./01256789:;<=>?@ABCDdP^opqrstuvwxyz{|}~SummaryInformation(EODocumentSummaryInformation8VCompObjG^j0TableC4 CompObj?A.fObjInfoB0Equation Native 1D1Tablen):!?`Equation Native  _1040036442/S;FuuOle %CompObj:<&fObjInfoQEquation Native n_1040048150IXrF@Uu Uu_1040048660HZUF@ 56u`<6u_1040048188nF@[Uu@[Uu_1040049864jFUu $Uuf_1040050717Y[fF $UuKUu_1040052939ive`]F`&u&uEquation Native hOleObj CompObjmofObjInfoNativep      !"#$%&'(),_1040045773>ROFݙu@ݙu_1040048081KF@ݙu`|ݙuOle mCompObjJLkfEquation Native POleObj CompObjikfObjInfoNativelEquation Native OleObj CompObjegfObjInfoNativeh_1040052768bFUuUuOleObj CompObjacfObjInfoNatived  !"#$%&'()*+,-./01234567;<=tA@BKFZGJHILRMNOQTRSUYVWX[^\]_Pahbce fgiqjkmnopsruyvwxz>|}~  , 8 DPX`h$INTEGRAREA UNOR EXPRESII IRATIONALENTEAlexRARlexNormalRAlexlR16xMicrosoft Word 8.0R@fI}<@X[l@l5u. ՜.+,D՜.+,X hp   Damage Inc.F  $INTEGRAREA UNOR EXPRESII IRATIONALE Title 6> _PID_GUIDAN{8B18E1CA-D81A-11D4-B04D-C16749CB903C}  FMicrosoft Word Document MSWordDocWord.Document.89qx+ x 2 "x+1  "1x         -ln2 x 2 "x+1  "1"xx+x2(x" x 2 "x+1  "1)+3x2(x+ x 2 "x+1  "1)]Oh+'0pEquation Native Ole -CompObjqs+fObjInfot*Equation Native 4lnx"ln 2 x  "1lnx()+   +2(1"2lnx" 1"4lnx"ln 2 x  )( 1"4t"ln 2 x  "1)ln 3 x+c FMicrosoft Equation 3.0 DS Eqc FMicrosoft Equation 3.0 DS Equation Equation.39qJYI I ' ="t 2 4(1"2t" 1"4t"t 2 )+arctg 1"4t"t 2 "1t()+      +2(1"2t" 1"4t"t 2 )( 1"4t"t 2 "1)t 3 +c3I="ln 2 x4(1"2lnx" 1"4lnx"ln 2 x  )   +arctg 1"uation Equation.39q40hIcI I 1 =1(z 2 +1) 2 dz=  +" z 2 +1"z 2 (z 2 +1) 2 dz=  +"     =1z 2 +1dz"z 2 (z 2 +1) 2 dz  +"  +" f(z)=z           g ' (z)=z(z 2 +1) 2 f ' (z)=1          g(z)="12(z 2 +1)I 1 =arctg(z)+z2(z 2 +1)"12arctg(z)I 1 =12arctg(z)+z2(z 2 +1)+c1I '' ="12(z 2 +1)+arctg(z)+z(z 2 +1)+c2z= 1"4t"t 2 "1t FMicrosoft Equation 3.0 DS Equation Equation.39qL+I I "4"t=z 2 t+2z"4"2z=t(z 2 +1)t="4"2zz 2 +1dt="2(z 2 +1)"2z("4"2z)(z 2 +1) 2 dzdt="2z 2 "2+8z+4z 2 (z 2 +1) 2 dzdt=2z 2 +8z"2(z 2 +1) 2 dz 1"4t"t 2 =z"4"2zz 2 +1+1="4z"2z 2 +z 2 +1z 2 +1=                   ="z 2 "4z+1z 2 +1I '' ="4"2zz 2 +1.z 2 +1"z 2 "4z+1.2("z 2 "4z+1)(z 2 +1) 2 +" dzI '' =z+2(z 2 +1) 2 +" dz=z(z 2 +1) 2 +" dz+2dz(z 2 +1) 2 +" FMicrosoft Equation 3.0 DS Equation Equation.39qII x"1=2"t 2 1"t 2 "1=11"t 2  x 2 "3x+2  =t1"t 2 I ' =(1"t 2 ) 2 t  +" 2t(1"t 2 ) 2 dt=2dt=2t+c  +" t= x"2x"1  I=2 x"2x"1  +c6)I=lnxx 1"4lnx"ln 2 x  dx ;x"e -2- 6  ,e -2+ 6  ()  +" \{0}lnx=tx=e t   !dx=e t dtI ' =te t  1-4t-t 2  e t dt=  +" t 1-4t-t 2  dt  +" c>0! 1-4t-t 2 =zt+1  | 2 1-4t-t 2 =z 2 t 2 +2zt+1-4t-t 2 =z 2 t 2 +2zt  |:t FMicrosoft Equation 3.0 DS Equation Equation.39qcII 5)I=dx(x"1) x 2 "3x+2       ,x"(-",1)*"  +" (2,")=1>0x 1 =1;x 2 =2 x 2 "3x+2  =t(x"1)  | 2 x 2 "3x+2=t 2 (x"1) 2 (x"1)(x"2)=t 2 (x"1) 2    |:(x-1)x-2=t 2 x"t 2 x(1"t 2 )=2"t 2 x=2"t 2 1"t 2 dx="2t(1"t 2 )+2t(2"t 2 )(1"t 2 ) 2 dtdx="2t+2t 3 +4t"2t 3 (1"t 2 ) 2 dtdx=2t(1"t 2 ) 2 dt FMicrosoft Equation 3.0 DS Equation Equation.39q