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{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 
0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1395 "RatFuncInt:=proc(f
f,x)\n  local f,a,b,c,d,i,v,m,A,eqns,vars,z;\n  # If you want to see w
hat the code does, then remove the\n  # comment symbol # from the foll
owing line:\n  # options trace;\n  f:=evala(Normal(ff));  # evala(Norm
al( .. )) is same as normal\n     # but also works with algebraic numb
ers\n  if type(f,polynom(anything,x)) then\n      # a polynomial, inte
grate it with the following formula.\n      RETURN( add( coeff(f,x,i)/
(i+1) * x^(i+1) ,i=0..degree(f,x)) )\n  fi;\n  v:=sqrfree(denom(f),x);
\n  v:=v[2];\n  m:=max(seq(i[2],i=v)); # = maximal pole order\n  d:=1;
\n  for i in v do\n     if i[2]=m then\n        d:=d*i[1]\n     fi\n  \+
od;\n  if m>1 then\n     A := add(c[i]*x^i,i=0..degree(d,x)-1)/d^(m-1)
;\n     eqns:=numer(normal( (f-diff(A,x))*d^m ));\n     eqns:=\{coeffs
(rem(eqns,d,x),x)\};\n     vars:=\{seq(c[i],i=0..degree(d,x)-1)\};\n  \+
   A:=subs( solve(eqns,vars) , A);\n     # Now integrate f-diff(A,x)\n
     # We don't need to normalize because this procedure\n     # alrea
dy does that in the beginning.\n     v:=RatFuncInt(f-diff(A,x), x);\n \+
    RETURN( v + A )\n  fi;\n  if m<>1 then\n     ERROR(`this can not h
appen`)\n  fi;\n  a,b := numer(f), denom(f);\n  v:=resultant(a-z*diff(
b,x),b,x);\n  v:=\{solve(v,z)\};\n  A := add(i*log(gcd(a-i*diff(b,x),b
)),i=v);\n  v:=RatFuncInt(f-diff(A,x), x);\n  v + A   # Note: if you d
on't use RETURN command then\n          # the last evaluated expressio
n will be returned.\nend;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%+RatFuncIntGR6$%#ffG%\"xG6.%\"fG%\"a
G%\"bG%\"cG%\"dG%\"iG%\"vG%\"mG%\"AG%%eqnsG%%varsG%\"zG6\"F6C1>8$-%&ev
alaG6#-%'NormalG6#9$@$-%%typeG6$F9-%(polynomG6$%)anythingG9%-%'RETURNG
6#-%$addG6$*&*&-%&coeffG6%F9FI8)\"\"\")FI,&FUFVFVFVFV\"\"\"FX!\"\"/FU;
\"\"!-%'degreeG6$F9FI>8*-%(sqrfreeG6$-%&denomG6#F9FI>F\\o&F\\o6#\"\"#>
8+-%$maxG6#-%$seqG6$&FUFeo/FUF\\o>8(FV?&FUF\\o%%trueG@$/F_pFho>Fbp*&Fb
pFV&FU6#FVFV@$2FVFhoC)>8,*&-FN6$*&&8'6#FUFV)FIFUFV/FU;Fgn,&-Fin6$FbpFI
FV!\"\"FVFY)Fbp,&FhoFVF]rFVFZ>8--%&numerG6#-%'normalG6#*&,&F9FV-%%diff
G6$F_qFIF]rFV)FbpFhoFV>Far<#-%'coeffsG6$-%$remG6%FarFbpFIFI>8.<#-F]p6$
FdqFhq>F_q-%%subsG6$-%&solveG6$FarFgsF_q>F\\o-F$6$FirFI-FK6#,&F\\oFVF_
qFV@$0FhoFV-%&ERRORG6#%4this~can~not~happenG>6$8%8&6$-FcrFboF`o>F\\o-%
*resultantG6%,&F`uFV*&8/FV-F[s6$FauFIFVF]rFauFI>F\\o<#-F`t6$F\\oFju>F_
q-FN6$*&FUFY-%$logG6#-%$gcdG6$,&F`uFV*&FUFVF[vFYF]rFauFVF`p>F\\oFctFgt
F6F6F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "RatFuncInt(x,x);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$)%\"xG\"\"#\"\"\"#\"\"\"F'" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "RatFuncInt(1/x,x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%#lnG6#%\"xG" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 35 "f:=(5*x^13-2079*x+120)/(x^4-3)^3*x;" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%\"fG*&*&,(*$)%\"xG\"#8\"\"\"\"\"&F*!%z?\"$?\"
\"\"\"F0F*F0F,*$),&*$)F*\"\"%F,F0!\"$F0\"\"$F,!\"\"" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 16 "RatFuncInt(f,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,,*$)%\"xG\"\"$\"\"\"#\"\"&F'*&-%%sqrtG6#F'F(-%#lnG6#,&
*$)F&\"\"#F(\"\"\"*$F,F(!\"\"F6#F*\"#7*&F,F(-F06#,&F3F6F7F6F6#!\"&F:*&
,&F3#F*F5F$!#XF(,&*$)F&\"\"%F(F6!\"$F6!\"\"F6*&,&F3F@F$\"#\")F(*$)FE\"
\"#F(FJF6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "evala(Normal( \+
 diff(%,x) - f ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "6 0 0" 0 }
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