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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 50 "Demonstration of pmint -
 The Poor Man's Integrator" }}{PARA 0 "" 0 "" {TEXT -1 153 "This works
heet contains examples illustrating the scope of the poor man's integr
ator, a 95-line heuristic parallel integrator available for download a
t  " }{TEXT 256 47 "http://www.inria.fr/cafe/Manuel.Bronstein/pmint" }
}{PARA 0 "" 0 "" {TEXT -1 149 "Some of the examples involving Airy, Be
ssel,  Whittaker, Lambert W and Wright omega functions cannot be integ
rated by Maple's built-in int function. " }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 
"read(\"pmint.maple\"):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 18 "Rational functions" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "f := (x^7-24*x^4-4*x^2+8*x-8
)/(x^8+6*x^6+12*x^4+8*x^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*
&,,*$)%\"xG\"\"(\"\"\"F+*&\"#CF+)F)\"\"%F+!\"\"*&F/F+)F)\"\"#F+F0*&\"
\")F+F)F+F+F5F0F+,**$)F)F5F+F+*&\"\"'F+)F)F:F+F+*&\"#7F+F.F+F+*&F5F+F2
F+F+F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "pmint(f,x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(,*\"\"%\"\"\"*&\"\")F')%\"xG\"\"#F
'F'*&\"\"$F')F+F.F'F'*&\"\"'F'F+F'F'F'F+!\"\",(*$)F+F&F'F'*&F&F'F*F'F'
F&F'F2F'-%#lnG6#F+F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "nor
mal(f-diff(%,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f := 1/(1+x^2);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"fG*&\"\"\"F&,&F&F&*$)%\"xG\"\"#F&F&!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "pmint(f,x);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,&*&^##\"\"\"\"\"#F'-%#lnG6#,&%\"xGF'^#F'F'F'F'*&^
##!\"\"F(F'-F*6#,&F-F'^#F2F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "normal(f-diff(%,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#\"\"!" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 23 "Trigonometric funct
ions" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "f := (x-tan(x))/tan(
x)^2 + tan(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&*&,&%\"xG\"
\"\"-%$tanG6#F(!\"\"F)F*!\"#F)F*F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "pmint(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&,&
%\"xG!\"\"*&#\"\"\"\"\"#F**&)F&F+F*-%$tanG6#F&F*F*F'F*F.F'F**&#F*F+F*-
%#lnG6#,&F*F**$)F.F+F*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 20 "normal(f-diff(%,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }
}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 17 "Log-Exp functions" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "f := (1+x+x*exp(x))*(x+log(x)+exp(x
)-1)/(x+log(x)+exp(x))^2/x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*
*,(\"\"\"F'%\"xGF'*&F(F'-%$expG6#F(F'F'F',*F(F'-%#lnGF,F'F*F'F'!\"\"F'
,(F(F'F.F'F*F'!\"#F(F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "p
mint(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"\"F%,(%\"xGF%-%#
lnG6#F'F%-%$expGF*F%!\"\"F%-F)6#F&F%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "normal(f-diff(%,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f := log(x^2-1)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG-%#lnG6#,&*$)%\"xG\"\"#\"\"
\"F-F-!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "normal(pmint
(f,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&\"\"#\"\"\"%\"xGF&!\"\"
*&F'F&-%#lnG6#,&*$)F'F%F&F&F&F(F&F&-F+6#,&F'F&F&F(F(-F+6#,&F'F&F&F&F&
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "normal(f-diff(%,x));" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}}{SECT 1 {PARA 3 "" 0 "" 
{TEXT -1 29 "Liouvillian special functions" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 51 "f := exp(-x^2)*erf(x)/(erf(x)^3-erf(x)^2-erf(x)+1);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*(-%$expG6#,$*$)%\"xG\"\"#\"
\"\"!\"\"F.-%$erfG6#F,F.,**$)F0\"\"$F.F.*$)F0F-F.F/F0F/F.F.F/" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "pmint(f,x);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,(*&#\"\"\"\"\"%F&*&%#PiG#F&\"\"#,&-%$erfG6#%\"xGF
&F&!\"\"F1F&F1*&#F&\"\")F&*&F)F*-%#lnG6#,&F-F&F&F&F&F&F1*&#F&F4F&*&F)F
*-F76#F,F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "normal(f-
diff(%,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 14 "Airy functions" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 57 "f := (x - AiryAi(x) * AiryAi(1,x)) / (x^2 - AiryAi(
x)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*&,&%\"xG\"\"\"*&-%'Ai
ryAiG6#F'F(-F+6$F(F'F(!\"\"F(,&*$)F'\"\"#F(F(*$)F*F3F(F/F/" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "pmint(f,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*&#\"\"\"\"\"#F&-%#lnG6#,&-%'AiryAiG6#%\"xGF&F/!\"\"F
&F&*&F%F&-F)6#,&F,F&F/F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 20 "normal(diff(%,x)-f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Maple has trouble with such inte
grands" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "int(f,x);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#-%$intG6$*&,&%\"xG\"\"\"*&-%'AiryAiG6#F(F)-F,6$F)F
(F)!\"\"F),&*$)F(\"\"#F)F)*$)F+F4F)F0F0F(" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 19 "f := x^2*AiryAi(x);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"fG*&)%\"xG\"\"#\"\"\"-%'AiryAiG6#F'F)" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 11 "pmint(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#,&-%'AiryAiG6#%\"xG!\"\"*&-F%6$\"\"\"F'F,F'F,F," }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 20 "normal(diff(%,x)-f);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Compare w
ith Maple's answer" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "int(f,x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"\"#F&*(\"\"$#\"\"&\"\"'%#
PiG!\"\",&*&#F'\"#FF&*,F-F&F)F%-%&GAMMAG6##F'F)F.%\"xGF)-%*hypergeomG6
%7#F&7$F7F',$*&\"\"*F.F8F)F&F&F&F&*&#F'F@F&*,F8#F+F'F)#F&F,F-F&*$)F8#F
)F'F&#F.F)-%(BesselIG6$#\"\"%F),$*(F'F&F)F.F8FHF&F&F&F.F&F&F&" }}}}
{SECT 1 {PARA 3 "" 0 "" {TEXT -1 16 "Bessel functions" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 35 "f := BesselJ(nu+1,x)/BesselJ(nu,x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*&-%(BesselJG6$,&%#nuG\"\"\"F+F+
%\"xGF+-F'6$F*F,!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "pm
int(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%#lnG6#-%(BesselJG6$%#
nuG%\"xG!\"\"*&F*\"\"\"-F%6#F+F.F." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "normal(diff(%,x)-f);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Maple has trouble wit
h such integrands" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "int(f,x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$intG6$*&-%(BesselJG6$,&%#nuG\"\"\"F
,F,%\"xGF,-F(6$F+F-!\"\"F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
50 "f := normal(nu*BesselJ(nu,x)/x - BesselJ(nu+1,x));" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"fG,$*&,&*&-%(BesselJG6$,&%#nuG\"\"\"F.F.%\"xGF
.F/F.F.*&F-F.-F*6$F-F/F.!\"\"F.F/F3F3" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "pmint(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%(Bes
selJG6$%#nuG%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "normal
(diff(%,x)-f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 27 "Compare with Maple's answer" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 9 "int(f,x);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,
(*&#\"\"\"\"\"#F&**%\"xGF&-%(BesselJG6$,&%#nuGF&F&F&F)F&%#PiGF&,&*&-%$
cotG6#,$*(F'!\"\"F/F&F.F&F&F&-%'AngerJG6$F.F)F&F&-%'WeberEGF:F&F&F&F&*
&F%F&**F)F&-F+F:F&F/F&,&*&-%$tanG6#,$*(F'F7F/F&F-F&F&F&-F9F,F&F&-F<F,F
7F&F&F&*&F.F&,&**F)F&,&F.F&F'F7F&F?F&-%)LommelS1G6%!\"#,&F&F7F.F&F)F&F
&*&F%F&*,F)F&-F+6$FQF)F&F/F&F.F7F0F&F&F&F&F&" }}}}{SECT 1 {PARA 3 "" 
0 "" {TEXT -1 19 "Whittaker functions" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "f := WhittakerW(mu+1,nu,x)/WhittakerW(mu,nu,x)/x;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*(-%+WhittakerWG6%,&%#muG\"\"\"F
+F+%#nuG%\"xGF+-F'6%F*F,F-!\"\"F-F0" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "pmint(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&\"
\"#!\"\"%\"xG\"\"\"F(*&%#muGF(-%#lnG6#F'F(F&-F,6#-%+WhittakerWG6%F*%#n
uGF'F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "normal(diff(%,x)-
f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 38 "Maple has trouble with such integrands" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 9 "int(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$i
ntG6$*(-%+WhittakerWG6%,&%#muG\"\"\"F,F,%#nuG%\"xGF,-F(6%F+F-F.!\"\"F.
F1F." }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 22 "The Lambert W function
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "pmint(LambertW(x),x);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,(*$)%\"xG\"\"#\"\"\"F)*&F&F)-%)Lam
bertWG6#F'F)!\"\"*&F&F))F+F(F)F)F)F'F.F+F." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 30 "normal(LambertW(x)-diff(%,x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "pmi
nt(sin(LambertW(x)),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#**,**&#\"\"
\"\"\"#F'*&)%\"xGF(F'-%)LambertWG6#F+F'F'!\"\"*&F*F'-%$tanG6#,$*&#F'F(
F'F,F'F'F'F'*(F*F'F1F'F,F'F'*&F6F'*(F*F')F1F(F'F,F'F'F'F'F+F/F,F/,&F'F
'*$F:F'F'F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "normal(conve
rt(sin(LambertW(x))-diff(%,x), tan));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "f := ((x^2 + 2)
 * LambertW(x^2)^2 + x^2 * (2 * LambertW(x^2) + 1))/x/(1 + LambertW(x^
2))^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*(,&*&,&*$)%\"xG\"\"#
\"\"\"F-F,F-F-)-%)LambertWG6#F)F,F-F-*&F*F-,&*&F,F-F/F-F-F-F-F-F-F-F+!
\"\",&F-F-F/F-!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "pmint
(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&**,,*&)%\"xG\"\"#\"\"\"-%)
LambertWG6#*$F'F*F*F**&)F+F)F*F'F*F**&F)!\"\"F(\"\"%F**&)F(F3F*F+F*F**
&#F*F)F**&F5F*F0F*F*F*F*F(!\"#F+F2,&F*F*F+F*F9F*-%#lnG6#F:F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "normal(f-diff(%,x));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 78 "Maple cannot integrate LambertW functions whose arguments
 are not linear in x:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "int(f,x);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$intG6$*(,&*&,&*$)%\"xG\"\"#\"\"\"
F.F-F.F.)-%)LambertWG6#F*F-F.F.*&F+F.,&*&F-F.F0F.F.F.F.F.F.F.F,!\"\",&
F.F.F0F.!\"$F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Example with a \+
parameter a" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 152 "f := (2*LambertW(x^
2)*cos(LambertW(x^2))*(a*x + LambertW(x^2)) + a*x*(1+LambertW(x^2)) + \+
2*LambertW(x^2)) / (1+LambertW(x^2)) / (a*x+LambertW(x^2)) / x;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG**,(**\"\"#\"\"\"-%)LambertWG6#*
$)%\"xGF(F)F)-%$cosG6#F*F),&*&%\"aGF)F/F)F)F*F)F)F)*(F5F)F/F),&F)F)F*F
)F)F)*&F(F)F*F)F)F)F7!\"\"F3F9F/F9" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "pmint(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(\"
\"#\"\"\"-%$tanG6#,$*&#F&F%F&-%)LambertWG6#*$)%\"xGF%F&F&F&F&,&F&F&*$)
F'F%F&F&!\"\"F&-%#lnG6#,&*&%\"aGF&F2F&F&F-F&F&" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 34 "normal(convert(f-diff(%,x), tan));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
45 "Again, Maple cannot integrate such integrands" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 9 "int(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$intG
6$**,(**\"\"#\"\"\"-%)LambertWG6#*$)%\"xGF)F*F*-%$cosG6#F+F*,&*&%\"aGF
*F0F*F*F+F*F*F**(F6F*F0F*,&F*F*F+F*F*F**&F)F*F+F*F*F*F8!\"\"F4F:F0F:F0
" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 25 "The Wright omega function" 
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "omega := proc(z) LambertW(
exp(z)); end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&omegaGf*6#%\"zG6\"
F(F(-%)LambertWG6#-%$expG6#9$F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "normal(pmint(omega(x),x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*&#\"\"\"\"\"#F&*$)-%)LambertWG6#-%$expG6#%\"xGF'F&F&
F&F0F&-%#lnG6#F*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "no
rmal(omega(x)-diff(%,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "f := (1 + omega(x) * (2 + c
os(omega(x)) * (x + omega(x)))) / (1 + omega(x)) / (x + omega(x));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*(,&\"\"\"F'*&-%)LambertWG6#-%$e
xpG6#%\"xGF',&\"\"#F'*&-%$cosG6#F)F',&F/F'F)F'F'F'F'F'F',&F'F'F)F'!\"
\"F6F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "pmint(f,x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(\"\"#\"\"\"-%$tanG6#,$*&#F&F%F&-%)
LambertWG6#-%$expG6#%\"xGF&F&F&,&F&F&*$)F'F%F&F&!\"\"F&-%#lnG6#,&F3F&F
-F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "normal(convert(f-d
iff(%,x), tan));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 29 "This one is also beyond Maple" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 9 "int(f,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#-%$intG6$*(,&\"\"\"F(*&-%)LambertWG6#-%$expG6#%\"xGF(,&\"\"#F(*&-%$co
sG6#F*F(,&F0F(F*F(F(F(F(F(F(,&F(F(F*F(!\"\"F7F9F0" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}}}{MARK "8" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 
1 2 33 1 1 }