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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 18 "Substitucni metoda" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Pro integraci substituci existuje \+
v baliku " }{TEXT 256 7 "student" }{TEXT -1 8 " prikaz " }{TEXT 257 9 
"changevar" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
14 "with(student):" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Priklad 1" 
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "i1:=Int((1+ln(x))^4/x, x);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i1G-%$IntG6$*&*$),&\"\"\"F,-%#l
nG6#%\"xGF,\"\"%\"\"\"F2F0!\"\"F0" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "i1=changevar((1+ln(x))=t, i1, t);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#/-%$IntG6$*&*$),&\"\"\"F+-%#lnG6#%\"xGF+\"\"%\"\"\"F1
F/!\"\"F/-F%6$*$)%\"tGF0F1F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 14 "value(rhs(%));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$)%\"tG\"\"
&\"\"\"#\"\"\"F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "subs(t=
ln(x)+1, %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$),&\"\"\"F'-%#lnG6
#%\"xGF'\"\"&\"\"\"#F'F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 
"testeq(diff(%,x)=integrand(i1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%
%trueG" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Priklad 2" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "assume(x>-1);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 18 "additionally(x>1);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 24 "i2:=Int(sqrt(1-x^2), x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#i2G-%$IntG6$*$-%%sqrtG6#,&\"\"\"F-*$)%#x|irG\"\"#\"
\"\"!\"\"F2F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "i2=changev
ar(x=sin(t), i2, t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*$-%
%sqrtG6#,&\"\"\"F,*$)%#x|irG\"\"#\"\"\"!\"\"F1F/-F%6$*&-F)6#,&F,F,*$)-
%$sinG6#%\"tGF0F1F2F1-%$cosGF=F,F>" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "value(rhs(%));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*
&-%$sinG6#%\"tG\"\"\"-%%sqrtG6#,&F)F)*$)F%\"\"#\"\"\"!\"\"F1#F)F0-%'ar
csinG6#F%F3" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 24 "i2=subs(t=arcsin(x), %);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#/-%$IntG6$*$-%%sqrtG6#,&\"\"\"F,*$)%#x|irG\"\"#\"
\"\"!\"\"F1F/,&*&-%$sinG6#-%'arcsinG6#F/F,-F)6#,&F,F,*$)F5F0F1F2F1#F,F
0-F96#F5F@" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "combine(%);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*$-%%sqrtG6#,&\"\"\"F,*$)%
#x|irG\"\"#\"\"\"!\"\"F1F/,&*&F/F,F(F1#F,F0-%'arcsinG6#F/F5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "value(i2);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#,&*&%#x|irG\"\"\"-%%sqrtG6#,&F&F&*$)F%\"\"#\"\"\"!\"
\"F.#F&F--%'arcsinG6#F%F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
33 "rationalize(simplify(diff(%,x)));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#*$-%%sqrtG6#,&\"\"\"F(*$)%#x|irG\"\"#\"\"\"!\"\"F-" }}}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 9 "Priklad 3" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "restart; with(student):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "i3:=Int(cos(x)^5 *sin(x)^2, x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#i3G-%$IntG6$*&)-%$cosG6#%\"xG\"\"&\"\"\")-%$sinGF,\"
\"#F/F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "i3=changevar(sin
(x)=t, i3, t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&)-%$cosG
6#%\"xG\"\"&\"\"\")-%$sinGF+\"\"#F.F,-F%6$*&),&\"\"\"F8*$)%\"tGF2F.!\"
\"F2F.F:F.F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "value(rhs(%
));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"tG\"\"(\"\"\"#\"\"\"F'*
$)F&\"\"&F(#!\"#F-*$)F&\"\"$F(#F*F2" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "i3=subs(t=sin(x), %);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/-%$IntG6$*&)-%$cosG6#%\"xG\"\"&\"\"\")-%$sinGF+\"\"#F.F,,(*$)F0
\"\"(F.#\"\"\"F6*$)F0F-F.#!\"#F-*$)F0\"\"$F.#F8F?" }}}}{SECT 1 {PARA 
3 "" 0 "" {TEXT -1 9 "Priklad 4" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 21 "i4:=Int(1/sin(x), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i4
G-%$IntG6$*&\"\"\"F)-%$sinG6#%\"xG!\"\"F-" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 30 "i4=changevar(cos(x)=t, i4, t);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/-%$IntG6$*&\"\"\"F(-%$sinG6#%\"xG!\"\"F,-F%6$,$*&F(F(,
&\"\"\"F3*$)%\"tG\"\"#F(!\"\"F-F8F6" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$I
ntG6$*&\"\"\"F(-%$sinG6#%\"xG!\"\"F,-F%6$*&F(F(,&!\"\"\"\"\"*$)%\"tG\"
\"#F(F3F-F6" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 7 "rhs(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#-%$IntG6$*&\"\"\"F',&!\"\"\"\"\"*$)%\"tG\"\"#F'F*!\"\"F-" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 46 "Integral resime rozkladem na parcialni zl
omky." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "integrand(%);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\"\"\"F$,&!\"\"\"\"\"*$)%\"tG\"\"#F$
F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "convert(%, 'parf
rac', t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"\"F%,&%\"tG\"\"\"
!\"\"F(!\"\"#F(\"\"#*&F%F%,&F'F(F(F(F*#F)F," }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 10 "int(%, t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%
#lnG6#,&%\"tG\"\"\"!\"\"F)#F)\"\"#-F%6#,&F(F)F)F)#F*F," }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "subs(t=cos(x), %);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,&-%#lnG6#,&-%$cosG6#%\"xG\"\"\"!\"\"F,#F,\"\"#-F%
6#,&F(F,F,F,#F-F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "v:=%;" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG,&-%#lnG6#,&-%$cosG6#%\"xG\"\"
\"!\"\"F.#F.\"\"#-F'6#,&F*F.F.F.#F/F1" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "diff(v,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%$
sinG6#%\"xG\"\"\",&-%$cosGF'\"\"\"!\"\"F-!\"\"#F.\"\"#*&F%F),&F+F-F-F-
F/#F-F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "testeq(%=integra
nd(i4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 9 "Priklad 5" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "i5:=Int(1/(1+sin(x)^2), x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#i5G-%$IntG6$*&\"\"\"F),&\"\"\"F+*$)-%$sinG6#%\"xG\"
\"#F)F+!\"\"F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "i5=change
var(tan(x)=t, i5, t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&
\"\"\"F(,&\"\"\"F**$)-%$sinG6#%\"xG\"\"#F(F*!\"\"F0-F%6$*&F(F(*&,&F*F*
*&*$)%\"tGF1F(F(,&*$F:F(F*F*F*F2F*\"\"\"F<\"\"\"F2F;" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 17 "simplify(rhs(%));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%$IntG6$*&\"\"\"F',&*$)%\"tG\"\"#F'F,\"\"\"F-!\"\"F+" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(%);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,$*&-%%sqrtG6#\"\"#\"\"\"-%'arctanG6#*&%\"tG\"\"\"
F%F)F/#F/F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "i5=subs(t=ta
n(x), %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&\"\"\"F(,&\"
\"\"F**$)-%$sinG6#%\"xG\"\"#F(F*!\"\"F0,$*&-%%sqrtG6#F1F(-%'arctanG6#*
&-%$tanGF/F*F5F(F*#F*F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "
v:=diff(rhs(%), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG*&,&\"\"
\"F'*$)-%$tanG6#%\"xG\"\"#\"\"\"F'F/,&F'F'F(F.!\"\"" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 24 "testeq(v=integrand(i5));" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#%%trueG" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "P
riklad 6" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assume(x>1);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "i6:=Int(1/x*sqrt((x+1)/(x-1
)), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i6G-%$IntG6$*&*$-%%sqrtG
6#*&,&%#x|irG\"\"\"F0F0\"\"\",&F/F0!\"\"F0!\"\"F1F1F/F4F/" }}}{EXCHG 
{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 44 "simplify(changevar((x+1)/(x-1)=t^2, i6, t));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#,$-%$IntG6$*&*$)%\"tG\"\"#\"\"\"F,*&,&*$F)F,\"\"\"F0F
0\"\"\",&!\"\"F0F/F0\"\"\"!\"\"F*!\"%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 39 "(-4)*convert(integrand(%), parfrac, t);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,(*&\"\"\"F%,&%\"tG\"\"\"!\"\"F(!\"\"F)*&F%F%,&F
'F(F(F(F*F(*&F%F%,&*$)F'\"\"#F%F(F(F(F*!\"#" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 10 "int(%, t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(-%
#lnG6#,&%\"tG\"\"\"!\"\"F)F*-F%6#,&F(F)F)F)F)-%'arctanG6#F(!\"#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "subs(t=sqrt((x+1)/(x-1)), %)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(-%#lnG6#,&*$-%%sqrtG6#*&,&%#x|i
rG\"\"\"F/F/\"\"\",&F.F/!\"\"F/!\"\"F0F/F2F/F2-F%6#,&F(F/F/F/F/-%'arct
anG6#F(!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "v:=simplify(
diff(%,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG,$*&*$-%%sqrtG6#,
&%#x|irG\"\"\"F-F-\"\"\"F.**F,\"\"\",&*$F(F.F-*$-F)6#,&F,F-!\"\"F-F.F-
\"\"\",&F2F-F3F7\"\"\"-F)6#F6F.!\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 15 "rationalize(v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
*&*$-%%sqrtG6#,&%#x|irG\"\"\"F*F*\"\"\"F+*&-F&6#,&F)F*!\"\"F*F+F)\"\"
\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#*&*$-%%sqrtG6#,&%#x|irG\"\"\"F*F*\"\"
\"F+*&-F&6#,&F)F*!\"\"F*F+F)\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "testeq(%=integrand(i6));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%%trueG" }}}}}{MARK "8 0 0" 9 }{VIEWOPTS 1 1 0 1 1 
1803 }