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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 46 "Zakladni integracni metod
y - metoda per partes" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "K naznac
eni postupu vypoctu metodou per partes pouzijeme proceduru " }{TEXT 
256 9 "intparts " }{TEXT -1 9 "z baliku " }{TEXT 257 7 "student" }
{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(stude
nt):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "Int(u(x)*Diff(v(x),
 x), x)=intparts(Int(u(x)*Diff(v(x),x),x), u(x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/-%$IntG6$*&-%\"uG6#%\"xG\"\"\"-%%DiffG6$-%\"vGF*F+F,F+
,&*&F(\"\"\"F0F,F,-F%6$*&-%%diffG6$F(F+F,F0F4F+!\"\"" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 53 "Reste nasledujici integraly za pomoci programu \+
Maple." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "i1:=Int(x*cos(x),
 x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i1G-%$IntG6$*&%\"xG\"\"\"-%
$cosG6#F)F*F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "i1=intpart
s(Int(x*cos(x), x), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*
&%\"xG\"\"\"-%$cosG6#F(F)F(,&*&F(\"\"\"-%$sinGF,F)F)-F%6$F0F(!\"\"" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "i1=value(rhs(%));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&%\"xG\"\"\"-%$cosG6#F(F)F(,&*&F(
\"\"\"-%$sinGF,F)F)F*F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Kontro
la vysledku primym vypoctem:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 13 "i1=value(i1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&%\"
xG\"\"\"-%$cosG6#F(F)F(,&*&F(\"\"\"-%$sinGF,F)F)F*F)" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 28 "i2:=Int((x^2+1)*exp(-x), x);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%#i2G-%$IntG6$*&,&*$)%\"xG\"\"#\"\"\"\"\"\"F/F
/F/-%$expG6#,$F,!\"\"F/F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
23 "i2=intparts(i2, x^2+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$Int
G6$*&,&*$)%\"xG\"\"#\"\"\"\"\"\"F.F.F.-%$expG6#,$F+!\"\"F.F+,&F'F3-F%6
$,$*&F+F.F/F-!\"#F+F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "si
mplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&,&*$)%\"xG\"
\"#\"\"\"\"\"\"F.F.F.-%$expG6#,$F+!\"\"F.F+,(*&F/F-F*F-F3F/F3-F%6$*&F+
F.F/F-F+F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Pouzijeme metodu pe
r partes jeste jednou" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "i2
=intparts(rhs(%), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&,
&*$)%\"xG\"\"#\"\"\"\"\"\"F.F.F.-%$expG6#,$F+!\"\"F.F+,**&F/F-F*F-F3F/
F3*&F+F.F/F-!\"#-F%6$,$F/F3F+F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 17 "i2=value(rhs(%));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6
$*&,&*$)%\"xG\"\"#\"\"\"\"\"\"F.F.F.-%$expG6#,$F+!\"\"F.F+,(*&F/F-F*F-
F3F/!\"$*&F+F.F/F-!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "i
2=value(i2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&,&*$)%\"xG
\"\"#\"\"\"\"\"\"F.F.F.-%$expG6#,$F+!\"\"F.F+,(*&F/F-F*F-F3F/!\"$*&F+F
.F/F-!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "i3:=Int(arccot
(x), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i3G-%$IntG6$-%'arccotG6
#%\"xGF+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "i3=intparts(i3,
 arccot(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$-%'arccotG6#
%\"xGF*,&*&F'\"\"\"F*F-F--F%6$,$*&F*\"\"\",&*$)F*\"\"#F2F-F-F-!\"\"!\"
\"F*F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "i3=value(rhs(%));
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$-%'arccotG6#%\"xGF*,&*&F
'\"\"\"F*F-F--%#lnG6#,&*$)F*\"\"#\"\"\"F-F-F-#F-F4" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 26 "i4:=Int(exp(x)*sin(x), x);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%#i4G-%$IntG6$*&-%$expG6#%\"xG\"\"\"-%$sinGF+F-F,
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "i4=intparts(i4, exp(x))
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&-%$expG6#%\"xG\"\"\"-
%$sinGF*F,F+,&*&F(\"\"\"-%$cosGF*F,!\"\"-F%6$,$F0F4F+F4" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 71 "Pouzijeme znovu metodu per partes a pravo
u stranu rovnice zjednodusime." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 38 "i4=simplify(intparts(rhs(%), exp(x)));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/-%$IntG6$*&-%$expG6#%\"xG\"\"\"-%$sinGF*F,F+,(*&F(\"\"
\"-%$cosGF*F,!\"\"F'F,F$F4" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "Ze \+
ziskane rovnice jiz snadno vypocitame, ze" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 25 "simplify(isolate(%, i4));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/-%$IntG6$*&-%$expG6#%\"xG\"\"\"-%$sinGF*F,F+,&*&F(\"\"
\"-%$cosGF*F,#!\"\"\"\"#F'#F,F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}}{MARK "26 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }