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{SECT 0 {EXCHG {PARA 265 "" 0 "" {TEXT 315 35 "Matematick\351 v\375po
\350ty se syst\351m Maple" }}}{EXCHG {PARA 266 "" 0 "" {TEXT -1 77 "au
tor:  Ing. Vladim\355r \216\341k\n  email:  zakyn@centrum.cz\n        \+
         web:   " }{URLLINK 17 "www.vladimirzak.com/maple" 4 "www.vlad
imirzak.com/maple" "" }}{PARA 265 "" 0 "" {TEXT -1 0 "" }}{PARA 265 "
" 0 "" {TEXT -1 12 "            " }{TEXT 313 9 "recenzent" }{TEXT -1 
3 ":  " }{TEXT 312 31 "Prof. RNDr. Ji\370\355 H\370eb\355\350ek, CSc.
" }}{PARA 265 "" 0 "" {TEXT -1 48 "CENTRUM BIOSTATISTIKY A ANAL\335Z (
CBA LF a P\370F MU)" }}{PARA 265 "" 0 "" {TEXT -1 43 "L\351ka\370sk
\341 a P\370\355rodov\354deck\341 fakulta MU v Brn\354" }}{PARA 265 "
" 0 "" {TEXT -1 20 "hrebicek@cba.muni.cz" }}{PARA 265 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 265 "" 0 "" {TEXT -1 478 "Tento dokument je ur
\350en jen pro v\375ukov\351 \372\350ely a pro pou\236it\355 jen osoba
mi, kter\375m byl tento dokument poskytnut p\370\355mo autorem, pop
\370. si ho st\341hli z webov\351ho s\355dla autora. Jak\351koliv \350
\341sti dokumentu nen\355 mo\236n\351 pou\236\355t bez citace zdoje, t
edy n\341zvu dokumentu a jm\351na autora s kontaktn\355mi informacemi \+
(jak je zobrazeno v hlavi\350ce), kter\341 mus\355 b\375t autorovi sd
\354lena. Pro jin\351 pou\236it\355 ne\236 pro osobn\355 pot\370eby os
ob, tedy pro distribuci \350i kop\355rov\341n\355, je nutn\351 obdr
\236et p\355semn\375 souhlas autora. " }}{PARA 265 "" 0 "" {TEXT -1 0 
"" }}{PARA 265 "" 0 "" {TEXT -1 0 "" }{TEXT 314 59 "Soubor vznikl s po
dporou grantov\351ho projektu FRV\212 3323/2006" }{TEXT -1 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 53 "V\375po
\350et primitivn\355ch funkc\355 pomoc\355 knihovny \"student\"" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "Postup p\370i v\375po\350tu primit
ivn\355 funkce lze tak\351 vysv\354tlit p\370i pou\236it\355 roz\232i
\370uj\355c\355 knihovny " }{TEXT 256 7 "student" }{TEXT -1 28 ". Jsou
 v n\355 uvedeny p\370\355kazy " }{TEXT 257 8 "intparts" }{TEXT -1 2 "
, " }{TEXT 258 9 "changevar" }{TEXT -1 67 ", pro dva z\341kladn\355 po
stupy, metodu per partes a metodu substitu\350n\355." }}}{SECT 1 
{PARA 5 "" 0 "" {TEXT -1 17 "Metoda per partes" }}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 37 "Metoda vych\341z\355 z matematick\375ch vzorc\371" }}
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                           (2)" }}{PARA 0 "" 0 "" {TEXT -1 4 "kde " }
{TEXT 259 1 "F" }{TEXT -1 1 "," }{TEXT 260 1 "G" }{TEXT -1 34 " jsou p
rimitivn\355 funkce k funkc\355m " }{TEXT 261 1 "f" }{TEXT -1 2 ", " }
{TEXT 262 1 "g" }{TEXT -1 142 ". V obou p\370\355padech se po\350\355t
\341 integr\341l na lev\351 stran\354 a vol\355 se ten ze vzorc\371, v
e kter\351m v\375po\350et integr\341lu na prav\351 stran\354 a primiti
vn\355 funkce " }{TEXT 263 4 "G(x)" }{TEXT -1 8 ", pop\370. " }{TEXT 
264 4 "F(x)" }{TEXT -1 37 " nen\355 n\341ro\350n\375, anebo je m\351n
\354 n\341ro\350n\375." }}{PARA 0 "" 0 "" {TEXT -1 52 "P\370\355kaz ur
\350en\375 pro v\375po\350et metodou per partes m\341 tvar" }}{PARA 0 
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jJNk;B:<j:>:ccs_jVAv]YQ<>Z:f?=J<Jr?:AB:;B:;:::Ja@Na`><::::s:?JR@Vs?:;S
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`;K;AFXbZMK:>::::::::::::::::::::::::::::::fb:FHemj^HMmqnG;Ka<jj:gmlB:
;:::::JJ<J;vyyuy:>:;B::::::F\\:>Z:n[;Z:::::::::::::yay=J:B::::::::::::
:::::::jysy:>:<:::::::::::::::::::vYxI:;Z:::::::::1:" }{TEXT -1 29 " p
\370i u\236it\355 vztahu (1), pop\370. " }{OLE 1 4098 1 "[xm]Br=WfoRrB
:::wk;nyyI;G:;:j::>:B>N:F:nyyyyy]::yyyyyy:::::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::::::::::fyyyyyq:nY^:f:nYnyyyYyA:::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::_lqvGcMJ<j\\nGcMsFI>:::::::JEf:yyyxIN:<j;tV;J:>R<:T><::[GhicPmDMI
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C:yayA:<::::::A:Su:B:nyyM;:^:f:<J=j=B:KJ:F;N;;j?>:S:UJ:n;v;;JBB:wA_J:V
<^<f<nYvY:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::F:D:<::JB<MlQZ:B:::::::=Jyyy;d:yayYZHQ:>:;`:Z@o<fc[_hb_ds?h_?
^on_j>^?GhoGfnGgioGSZ::RSPN]v;fbk;n_>WdG_dnBwmcf]]:>::::::yayYZ:J<j:>:
yayQ:>:F^BB:cc:N_=j:F;HjDA:?J<K:f:NZ;F:<j<j:Djyyyy=j<JQ@jFB:E:Qb:>Z:f:
^[<b:;u;aZ:n^@v;sjyyiyAZ:fc:><<JZyIGxyyyy;s;nr;j?<:G;Sj`@@J:<Jbf:<j>D:
Dj<JDDJj@J=@JHB:qi:;fyB:>l;B:;B:DJ:<Kd`ppPps<LaPpu<Lcxpp@Pq<jUQv]YQZQv
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`a\\wgfsW;\\:vu@N[Ryp?yR;`q?>>::UK:^:>X=j>>:_c<B:=J:<jX`a=^Jn>ny:fc[;P
pdPOsgZ;R;Lncp^ojCXontpZlPpDnjHqnHp[xPlPPb@pmPpsF\\?^dcgg_WH:jBHjc`qpD
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J[Dwer==D:cYKcYCcy]?tQ=\\JrJyTJvk?_xdveB_xIHb:B><NtyrZxQ^LYBxjZdliLniP
Ntyo\\RJYB==j:FZ<NZ<NZ:NZ:FZ;F:AB:=J<b<=B:?j;i`<bZKK;<j;]Q:DZ<H??B;GVI
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:=K?AZ:B:=J:^``Q<mWjIxWCJ:<jPF:C:[Q:VZ:>Z:>::::WTJWTLB::::^=N:[Sj_Q:>^
cQ<>:SB:GOv]XCf::B:::::c\\_;<<nGZ\\CUrJ:J::E<==v?ZnA<I\\JOXBweZ:RK:B>H
^;kAQ^dZID:<[:kZxQ^>\\IFBvExo\\RJZ:FZ<b:?B:F:V:=J<b<=B:?j;i@DRNj;]ADrN
N::X@>?Vjr[<H?;J::::::::::::::::::::::::::::::j\\<jrfH=MtFGYMq>>WD:==n
HE]:>::::::;C:?jyyiy=J:>Z::::::jB<J:<JA@:<::::::::::::vYxI:;Z:::::::::
:::::::::::yay=J:B:::::::::::::::::::jysy:>:<::::::::3:" }{TEXT -1 
144 " p\370i u\236it\355 druh\351ho vztahu. k(x) je tedy v\236dy ta fu
nkce, kterou chceme derivovat.\nP\370\355kaz pro v\375po\350et metodou
 per partes m\371\236e m\355t i obecn\354j\232\355 tvar" }}{PARA 0 "" 
0 "" {TEXT 276 23 "intparts(Z(x,y),k(x))  " }{TEXT -1 25 "            \+
            ," }}{PARA 0 "" 0 "" {TEXT -1 4 "kde " }{TEXT 277 7 "Z(x,y
) " }{TEXT -1 36 "je v\375raz pro v\375po\350et hodnoty funkce " }
{TEXT 278 1 "Z" }{TEXT -1 19 " dvou prom\354nn\375ch a " }{OLE 1 4098 
1 "[xm]Br=WfoRrB:::wk;nyyI;G:;:j::>:B>N:F:nyyyyy]::yyyyyy:::::::::::::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::fyyyyyq:nY^:
f:nYnyyyYyA:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:::::::::::::::::::::_lqvGcMJ<j\\nGcMsFI>:::::::JEf:yyyxIN:<j;tV;J:>R<
:T><::[tImcPmDMIX:A:;b;B:F:YLpfF>:::::::::J?NZ;vyyyyy=J:B:::::::c:;:=j
[vGUMrvC?MoJ::::::::JCNZ;F:VZ:>:yayA:<::::::=J:FG>:N:YLpJbNHEms>@[;;B:
::::::JFNZ;vYxY<jysy;Z::::::j;JyI:<:wyyN::C:EJ:<J=j=B:K:M:OJ:V;^;f;;JA
jA>:[Z:F<N<;JyKDjDJE>:i:wAyA::::::::::::::::::::::::::::::::::::::::::
::::::::::::::::::::::::::j:b:<Z:::>mEP<>:::::::=Jyyy;d:yayYZHQ:>:;`:Z
@o<fc[_hb_ds?h_?^on_j>^?GhoGfnGgioGSZ::RSPN]v;fbk;n_>WdG_dnBwmcf]]:>::
::::yayYZ:J<j:>:yayQ:>:fyEJ>H:sw:F:MZ=nu;J;nL;J:f:NZ;F:<j<j:Djyyyy=j<J
Q@jFB:E:Qb:B:E:Sb:;h:;i<aZ:n^@v;sjyyiyAZ:fc:><;B:;xy>ryyY;g<>j<>Z:V[:B
:G;Sj`@@J:<J:=j<B:Mb:>Z<f:^\\<>r;vj>^=<jwEJ:uI<:[V:<Z:b:;B>cTTUUSaEBWT
SiEB_tUUURWE:iWkIxW;XkIxW;CjOxW;JR^:f_;j@JSd:;B:C:KSDKSD[T:oU:[T:Hj<<:
c:wLH>:qAB:>L=Z:>Z<:VH::>RXQJJ::f?=J<JrAZ:N\\:>:_;<j=B:meSkuSkESkmkHJk
@Jb@Jwna;>RHj<<:c:SU:s:qAB:>L;J:@J:D:aTXDpql`q?B<JQPJ?LrUQv]?RXQJJ:>@j
P>:C:[q:F;;JSd:<j:>Z:fass:EB:^<Od:wf:s:qQZqI<:[V:R:D:jq:<JPPJ?HsUQv]?R
XQJJ::f?=J<Jr?Z:F[:>:_c<B:=Z:Nxs?j>nLn>N^;fc[_HRSeTOgR:ER:PZ>WdGSGV\\Q
GghGbf_g<GfmGg]Wbi_f_?d[wf_WH]R;cTTUUSa=:WmBHjc`qpDpqR>ErJYUW_UTEeV;cM
EM:@K<pNd<l\\\\QtDqjN<KRBYSKYFKYSJ[Dw[r=ItQ=DN_yAwRJ[Dwer==D:cYKcYCcy]
?tQ=\\JrJyTJvk?_xdveB_xIHb:B><NtyrZxQ^LYBxjZdliLniPNtyo\\RJYB==j:FZ<NZ
<NZ:NZ:FZ;F:AB:=J<<ZDFZ:N:AVX;b:Cb[ukXHZIF:=B:?Z`c:DRNN:AFX;b:DrNNZ:Vj
ac:DRNj;]ADrNj;M`<Jv>ZEFZ;FZ;f[<^Z@X_\\NX;j?<:G;Sjysy=J:>:^=<jw?<IZ:>:
sg:bu=b:?bBaTXaEWEUUB:OB:=K?AJ:<Z::ccs_jVAv]YQ<>Z:f?;J<JrGZ:J:<J::::nc
;ocC[:JHJ;n_;q\\;JJ`XCJ:^[:nNkIt_j<@::<::::JdRSZZ:W=fg\\CUrJ:J::E<==Kj
Q:LYBvB<Os[ni<<Z?;ZJrJ@>YVKd<xb:B><>=tYKLBxjZjirQE\\;;FZ<b:?B:F:=B:F:C
ZDFZ:N:AVX;J<fA:=B:?Z`[<@?Vjrc:DrNB:AvSbZK;AFXbZM;AFSJv>:=Z;f;V?<J:>::
:ED:]mtFFcmnvGWMJnc:FFJufF<J::::::>^:N:yyyxI:;J:<::::::aB:;JS@Z:>Z::::
:::::::::yay=J:B:::::::::::::::::::jysy:>:<:::::::::::::::::::vYxI:;Z:
::::::::1:" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 67 "Je\232t\354
 p\370ipome\362me, \236e tento p\370\355kaz je sou\350\341st\355 roz
\232i\370uj\355c\355 knihovny " }{TEXT 266 8 "student." }{TEXT -1 42 "
 Proto je nutn\351 knihovnu nahr\341t do pam\354ti." }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 64 "restart:with(student):            # nahr
\341n\355 roz\232i\370uj\355c\355 knihovny" }}}{SECT 1 {PARA 20 "" 0 "
" {TEXT -1 9 "P\370\355klad 1" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "V
ypo\350t\354te n\341sleduj\355c\355 integr\341l metodou per partes" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "i0:=Int(x*sin(x),x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i0G-%$IntG6$*&%\"xG\"\"\"-%$sinG6#F
)F*F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "i0=intparts(i0,x);
                 # v\375po\350et - za nederivovanou slo\236ku vol\355m
e x " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&%\"xG\"\"\"-%$sinG
6#F(F)F(,&*&F(F)-%$cosGF,F)!\"\"-F%6$,$F/F1F(F1" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 27 "Pou\236ili jsme vzorec (1) pro" }{TEXT 267 7 " f(x)=
x" }{TEXT -1 2 ", " }{TEXT 268 11 "g(x)=sin(x)" }{TEXT -1 99 ". Vid
\355me, \236e v\375po\350et integr\341lu na prav\351 stran\354 je ji
\236 snadn\375. Stejn\354 tak v\375po\350et primitivn\355 funkce " }
{TEXT 269 5 "G(x) " }{TEXT -1 11 "byl snadn\375." }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 23 "i0=intparts(i0,sin(x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/-%$IntG6$*&%\"xG\"\"\"-%$sinG6#F(F)F(,&*&#F)\"\"#F)*&F
*F))F(F0F)F)F)-F%6$,$*&F/F)*&-%$cosGF,F)F2F)F)F)F(!\"\"" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 32 "Pou\236ili jsme zde vzorec (2) pro " }
{TEXT 271 6 "f(x)=x" }{TEXT -1 3 " a " }{TEXT 270 11 "g(x)=sin(x)" }
{TEXT -1 93 ". Vid\355me, \236e v\375po\350et integr\341lu na prav\351
 stran\354 je n\341ro\350n\354j\232\355 ne\236 v\375po\350et p\371vodn
\355ho integr\341lu." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "i0=
intparts(i0,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&%\"xG\"
\"\"-%$sinG6#F(F)F(,(F*F)*&F(F)-%$cosGF,F)!\"\"-F%6$\"\"!F(F1" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Op\354t jsme pou\236ili vzorec (2)
 pro " }{TEXT 273 13 "f(x)=x sin(x)" }{TEXT -1 3 " a " }{TEXT 272 6 "g
(x)=1" }{TEXT -1 28 ". V\375po\350et primitivn\355 funkce " }{TEXT 
274 4 "F(x)" }{TEXT -1 167 " je n\341ro\350n\375, ve skute\350nosti se
 jedn\341 o v\375po\350et p\371vodn\355ho integr\341lu. Porovnejme pos
ledn\355 variantu s v\375sledkem p\370\355kazu pro v\375po\350et primi
tivn\355 funkce bez pou\236it\355 p\370\355kazu " }{TEXT 275 8 "intpar
ts" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "i0=in
t(integrand(i0),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&%\"
xG\"\"\"-%$sinG6#F(F)F(,&F*F)*&F(F)-%$cosGF,F)!\"\"" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 15 "Pomoc\355 p\370\355kazu " }{TEXT 279 9 "integra
nd" }{TEXT -1 24 " z roz\232i\370uj\355c\355 knihovny " }{TEXT 280 7 "
student" }{TEXT -1 38 " z\355sk\341me integrand z dan\351ho integr\341
lu." }}{PARA 0 "" 0 "" {TEXT -1 29 "D\341le uk\341\236eme pou\236it
\355 p\370\355kazu " }{TEXT 281 8 "intparts" }{TEXT -1 19 " v obecn
\354j\232\355m tvaru" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "int
parts(x^3+2*x+sin(i0^2),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%
\"xG\"\"$\"\"\"F(*&\"\"#F(F&F(F(-%$sinG6#*$),&*&F&F(-%$cosG6#F&F(!\"\"
-%$IntG6$,$F2F5F&F5F*F(F(" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{SECT 1 {PARA 20 "" 0 "" {TEXT -1 9 "P\370\355klad 2" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "i1:=Int(x^3*ln(x),x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i1G-%$IntG6$*&)%\"xG\"\"$\"\"\"-%#l
nG6#F*F,F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "intparts(%,ln
(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&#\"\"\"\"\"%F&*&-%#lnG6#%
\"xGF&)F,F'F&F&F&-%$IntG6$,$*&F'!\"\"F,\"\"$F&F,F3" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 117 "V\375po\350et integr\341lu na prav\351 stran\354
 n\341m ne\350in\355 \236\341dn\351 pot\355\236e. Pro v\375po\350et v
\375sledn\351 primitivn\355 funkce po pou\236it\355 p\370\355kazu " }
{TEXT 283 8 "intparts" }{TEXT -1 18 " se u\236\355v\341 p\370\355kazu \+
" }{TEXT 282 5 "value" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&#\"\"
\"\"\"%F&*&-%#lnG6#%\"xGF&)F,F'F&F&F&*&\"#;!\"\"F,F'F0" }}}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 20 "" 0 "" {TEXT 
-1 9 "P\370\355klad 3" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "i2:
=Int(x^2*exp(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i2G-%$IntG6$
*&)%\"xG\"\"#\"\"\"-%$expG6#F*F,F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "i2=intparts(%,x^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#/-%$IntG6$*&)%\"xG\"\"#\"\"\"-%$expG6#F)F+F),&F'F+-F%6$,$*(F*F+F)F+F
,F+F+F)!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Metodu per partes
 opakujeme pro pravou stranu, tzn. u\236ijeme p\370\355kazu " }{TEXT 
306 3 "rhs" }{TEXT -1 43 " pro z\355sk\341n\355 prav\351 strany p\370e
dchoz\355 rovnice" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "intpar
ts(rhs(%),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&)%\"xG\"\"#\"\"\"
-%$expG6#F&F(F(*(F'F(F&F(F)F(!\"\"-%$IntG6$,$*&F'F(F)F(F(F&F(" }}}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 20 "" 0 "
" {TEXT -1 9 "P\370\355klad 4" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 24 "i3:=Int(x^3*cos(x^2),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i
3G-%$IntG6$*&)%\"xG\"\"$\"\"\"-%$cosG6#*$)F*\"\"#F,F,F*" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 10 "Za funkci " }{TEXT 284 4 "k(x)" }{TEXT 
-1 8 " vol\355me " }{TEXT 285 3 "x^2" }{TEXT -1 31 ". Jin\351 volby by
 nevedly k c\355li." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "intp
arts(i3,x);               # tato volba nevede k c\355li" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,&*&%\"xG\"\"\",&*&#F&\"\"#F&*&-%$sinG6#*$)F%F*F
&F&F%F&F&F&*&#F&\"\"%F&*(F*F)%#PiGF)-%)FresnelSG6#*(F*F)F5#!\"\"F*F%F&
F&F&F;F&F&-%$IntG6$F'F%F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
66 "i3=intparts(i3,x^2);             # jedin\341 volba, kter\341 vede \+
k c\355li" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&)%\"xG\"\"$\"
\"\"-%$cosG6#*$)F)\"\"#F+F+F),&*&#F+F1F+*&F0F+-%$sinGF.F+F+F+-F%6$*&F6
F+F)F+F)!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 106 "V\375po\350et i
ntegr\341lu na prav\351 stran\354 lze ji\236 snadno prov\351st substit
u\350n\355 metodou ( viz. n\341sleduj\355c\355 odstavec)." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "intparts(i3,x^3);             # op
\354t nevede k c\355li" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&#\"\"\"
\"\"#F&**)%\"xG\"\"$F&F'F%%#PiGF%-%)FresnelCG6#*(F'F%F,#!\"\"F'F*F&F&F
&F&-%$IntG6$,$*&#F+F'F&**)F*F'F&F'F%F,F%F-F&F&F&F*F2" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{SECT 1 {PARA 20 "" 0 "" {TEXT -1 9 "P\370\355klad 5" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "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 23 "i4=intpart
s(i4,sin(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&-%$expG6#
%\"xG\"\"\"-%$sinGF*F,F+,&F'F,-F%6$*&-%$cosGF*F,F(F,F+!\"\"" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "Integr\341l na prav\351 stran\354 \+
op\354t po\350\355t\341me metodou per partes" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 27 "i4=intparts(rhs(%),cos(x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/-%$IntG6$*&-%$expG6#%\"xG\"\"\"-%$sinGF*F,F+,(F'F,*&-%
$cosGF*F,F(F,!\"\"-F%6$,$F'F3F+F," }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$I
ntG6$*&-%$expG6#%\"xG\"\"\"-%$sinGF*F,F+,(F'F,*&-%$cosGF*F,F(F,!\"\"F$
F3" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 100 "Vid\355me, \236e na obou s
tran\341ch rovnice vystupuje hledan\375 integr\341l. Rovnici proto \+
\370e\232\355me pomoc\355 p\370\355kazu " }{TEXT 286 5 "solve" }{TEXT 
-1 46 " vzhledem k nezn\341m\351, kterou je tento integr\341l." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "i4=solve(%,i4);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&-%$expG6#%\"xG\"\"\"-%$sinGF*F,F+,&
*&#F,\"\"#F,F'F,F,*&#F,F2F,*&-%$cosGF*F,F(F,F,!\"\"" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 37 "Elegantn\354j\232\355 je v\232ak pou\236it\355 \+
p\370\355kazu " }{TEXT 287 20 "isolate( odkud , co)" }{TEXT -1 61 ", p
omoc\355 kter\351ho vyj\341d\370\355me danou prom\354nnou (v\375raz) z
 rovnice." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "isolate(%%,i4)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&-%$expG6#%\"xG\"\"\"-
%$sinGF*F,F+,&*&#F,\"\"#F,F'F,F,*&#F,F2F,*&-%$cosGF*F,F(F,F,!\"\"" }}}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 20 "" 0 "
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0 21 "i5:=Int(arctan(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i5G-
%$IntG6$-%'arctanG6#%\"xGF+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
26 "i5=intparts(i5,arctan(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$
IntG6$-%'arctanG6#%\"xGF*,&*&F'\"\"\"F*F-F--F%6$*&,&F-F-*$)F*\"\"#F-F-
!\"\"F*F-F*F5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 105 "V\375po\350et i
ntegr\341lu na prav\351 stran\354 lze ji\236 snadno prov\351st substit
u\350n\355 metodou (viz. n\341sleduj\355c\355 odstavec)." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 18 "Metoda subst
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". Tedy ozna\350\355me " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "
i2p:=Int(1/((cos(x))^2*sqrt(1+2*(tan(x))^2)),x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$i2pG-%$IntG6$*&\"\"\"F)*&)-%$cosG6#%\"xG\"\"#F),&F)F
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i2=i2p;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&\"\"\"F(*$,&F(F
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1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "i2p1:=changevar(t=t
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-1 42 "Je ohl\341\232ena chyba, nebo\235 v relaci p\370\355kazu " }
{TEXT 299 9 "changevar" }{TEXT -1 15 " nov\341 prom\354nn\341 " }
{TEXT 296 1 "t" }{TEXT -1 67 " nevystupuje pouze na prav\351 stran\354
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