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{SECT 0 {EXCHG {PARA 256 "> " 0 "" {MPLTEXT 1 0 14 "with(student);" }}
{PARA 267 "" 1 "" {XPPMATH 20 "6#7@%\"DG%%DiffG%*DoubleintG%$IntG%&Lim
itG%(LineintG%(ProductG%$SumG%*TripleintG%*changevarG%/completesquareG
%)distanceG%'equateG%*integrandG%*interceptG%)intpartsG%(leftboxG%(lef
tsumG%)makeprocG%*middleboxG%*middlesumG%)midpointG%(powsubsG%)rightbo
xG%)rightsumG%,showtangentG%(simpsonG%&slopeG%(summandG%*trapezoidG" }
}}{SECT 1 {PARA 300 "" 0 "" {TEXT 260 13 "Beispiel    1" }{TEXT -1 0 "
" }}{PARA 278 "" 0 "" {TEXT -1 13 "Funktions Def" }}{PARA 278 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 278 "> " 0 "" {MPLTEXT 1 0 28 "f:=x->(sin
(x)/(2+cos(x)^2));" }}{PARA 279 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG
6\"6$%)operatorG%&arrowGF(*&-%$sinG6#9$\"\"\",&\"\"#F1*$)-%$cosGF/F3F1
F1!\"\"F(F(F(" }}}{EXCHG {PARA 278 "" 0 "" {TEXT -1 15 "Echtes Integra
l" }}{PARA 278 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 278 "> " 0 "" 
{MPLTEXT 1 0 19 "J:= Int(f(x)  , x);" }}{PARA 280 "" 1 "" {XPPMATH 20 
"6#>%\"JG-%$IntG6$*&-%$sinG6#%\"xG\"\"\",&\"\"#F-*$)-%$cosGF+F/F-F-!\"
\"F," }}}{EXCHG {PARA 278 "" 0 "" {TEXT -1 12 "Substitution" }}{PARA 
281 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 282 "> " 0 "" {MPLTEXT 1 0 
36 "changevar( u = cos(x)  ,  J  , u  );" }}{PARA 283 "" 1 "" 
{XPPMATH 20 "6#-%$IntG6$,$*&\"\"\"F(,&\"\"#F(*$)%\"uGF*F(F(!\"\"F.F-" 
}}}{EXCHG {PARA 284 "" 0 "" {TEXT 257 8 "Integral" }}{PARA 285 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 286 "> " 0 "" {MPLTEXT 1 0 13 "int(f(x
), x);" }}{PARA 287 "" 1 "" {XPPMATH 20 "6#,$*&-%%sqrtG6#\"\"#\"\"\"-%
'arctanG6#,$*&-%$cosG6#%\"xGF)F%F)#F)F(F)#!\"\"F(" }}}{EXCHG {PARA 
288 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 278 "" 0 "" {TEXT 259 
13 "Beispiel    2" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 278 "" 0 "
" {TEXT -1 13 "Funktions Def" }}{PARA 278 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 278 "> " 0 "" {MPLTEXT 1 0 22 "f:=x->((x^7)/(1+x^4));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrow
GF(*&9$\"\"(,&\"\"\"F0*$)F-\"\"%F0F0!\"\"F(F(F(" }}}{EXCHG {PARA 278 "
" 0 "" {TEXT -1 15 "Echtes Integral" }}{PARA 278 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 278 "> " 0 "" {MPLTEXT 1 0 19 "J:= Int(f(x)  , x);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"JG-%$IntG6$*&%\"xG\"\"(,&\"\"\"F
,*$)F)\"\"%F,F,!\"\"F)" }}}{EXCHG {PARA 278 "" 0 "" {TEXT -1 12 "Subst
itution" }}{PARA 291 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 292 "> " 0 
"" {MPLTEXT 1 0 33 "changevar( u = x^4  ,  J  , u  );" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#-%$IntG6$*&%\"uG\"\"\",&\"\"%F(*&F*F(F'F(F(!\"\"F'
" }}}{EXCHG {PARA 294 "" 0 "" {TEXT 258 8 "Integral" }}{PARA 295 "" 0 
"" {TEXT -1 0 "" }}}{EXCHG {PARA 296 "> " 0 "" {MPLTEXT 1 0 13 "int(f(
x), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"xG\"\"%\"\"\"#F(F'*
&#F(F'F(-%#lnG6#,&F(F(F$F(F(!\"\"" }}}{EXCHG {PARA 298 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 
278 "" 0 "" {TEXT 264 13 "Beispiel    3" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 278 "" 0 "" {TEXT -1 13 "Funktions Def" }}{PARA 278 "" 0 "
" {TEXT -1 0 "" }}{EXCHG {PARA 278 "> " 0 "" {MPLTEXT 1 0 30 "f:=x->(1
/(1+x)/sqrt(1+x+x^2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%
\"xG6\"6$%)operatorG%&arrowGF(*&\"\"\"F-*&,&9$F-F-F-F--%%sqrtG6#,(F-F-
F0F-*$)F0\"\"#F-F-F-!\"\"F(F(F(" }}}{EXCHG {PARA 278 "" 0 "" {TEXT -1 
15 "Echtes Integral" }}{PARA 278 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 278 "> " 0 "" {MPLTEXT 1 0 19 "J:= Int(f(x)  , x);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"JG-%$IntG6$*&\"\"\"F)*&,&%\"xGF)F)F)F)-%%sqr
tG6#,(F)F)F,F)*$)F,\"\"#F)F)F)!\"\"F," }}}{EXCHG {PARA 278 "" 0 "" 
{TEXT -1 12 "Substitution" }}{PARA 299 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 299 "> " 0 "" {MPLTEXT 1 0 45 "changevar( sqrt(1+x+x^2) =
 t+x  ,  J  , t  );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$,$*&\"
\"\"F(*&,&*&,&!\"\"F(*$)%\"tG\"\"#F(F(F(,&F-F(*&F1F(F0F(F(F-F-F(F(F(F2
F(F-!\"#F0" }}}{EXCHG {PARA 299 "" 0 "" {TEXT 263 12 "Vereinfachen" }}
{PARA 299 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*(%\"xG\"\"
\")%\"tG\"\"#F&-%$IntG6$*&F&F&*&F(F&,&F(F&F)!\"\"F&F0F(F&F&*&F%F&F(F&F
&*(F)F&F%F&-%#lnG6#F/F&F&**F)F&F%F&F3F&F(F&F0*&\"\"%F&F%F&F0" }}}
{PARA 299 "> " 0 "" {MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }}}{SECT 1 {PARA 
278 "" 0 "" {TEXT 266 13 "Beispiel    4" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 278 "" 0 "" {TEXT -1 13 "Funktions Def" }}{PARA 278 "" 0 "
" {TEXT -1 0 "" }}{EXCHG {PARA 278 "> " 0 "" {MPLTEXT 1 0 28 "f:=x->(1
/((x+2)*sqrt(x+1)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"x
G6\"6$%)operatorG%&arrowGF(*&\"\"\"F-*&,&9$F-\"\"#F-F--%%sqrtG6#,&F0F-
F-F-F-!\"\"F(F(F(" }}}{EXCHG {PARA 278 "" 0 "" {TEXT -1 15 "Echtes Int
egral" }}{PARA 278 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 278 "> " 0 "
" {MPLTEXT 1 0 19 "J:= Int(f(x)  , x);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"JG-%$IntG6$*&\"\"\"F)*&,&%\"xGF)\"\"#F)F)-%%sqrtG6#,&F,F)F)F
)F)!\"\"F," }}}{EXCHG {PARA 278 "" 0 "" {TEXT -1 12 "Substitution" }}
{PARA 299 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 299 "> " 0 "" 
{MPLTEXT 1 0 39 "changevar( sqrt(x+1) = u  ,  J  , u  );" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#-%$IntG6$,$*&\"\"\"F(,&*$)%\"uG\"\"#F(F(F(F(!\"
\"F-F," }}}{EXCHG {PARA 299 "" 0 "" {TEXT 265 8 "Integral" }}{PARA 
299 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 299 "> " 0 "" {MPLTEXT 1 0 
13 "int(f(x), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%'arctanG6#*$-
%%sqrtG6#,&%\"xG\"\"\"F-F-F-\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 
278 "" 0 "" {TEXT 268 13 "Beispiel    5" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 278 "" 0 "" {TEXT -1 13 "Funktions Def" }}{PARA 278 "" 0 "
" {TEXT -1 0 "" }}{EXCHG {PARA 278 "> " 0 "" {MPLTEXT 1 0 47 "f:=x->( \+
 ((1+x)^(1/2)-1)  / ((1+x)^(1/3)+1)  );" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*&,&*$-%%sqrtG6#,&9$\"
\"\"F4F4F4F4F4!\"\"F4,&*$)F2#F4\"\"$F4F4F4F4F5F(F(F(" }}}{EXCHG {PARA 
278 "" 0 "" {TEXT -1 15 "Echtes Integral" }}{PARA 278 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 278 "> " 0 "" {MPLTEXT 1 0 19 "J:= Int(f(x)  ,
 x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"JG-%$IntG6$*&,&*$-%%sqrtG6
#,&%\"xG\"\"\"F0F0F0F0F0!\"\"F0,&*$)F.#F0\"\"$F0F0F0F0F1F/" }}}{EXCHG 
{PARA 278 "" 0 "" {TEXT -1 12 "Substitution" }}{PARA 299 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 299 "> " 0 "" {MPLTEXT 1 0 41 "changevar
( (x+1)^(1/3) = u  ,  J  , u  );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%
$IntG6$,$*(,&*$)%\"uG#\"\"$\"\"#\"\"\"F/F/!\"\"F/F+F.,&F+F/F/F/F0F-F+
" }}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }}{EXCHG 
{PARA 12 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}}}{MARK "6 0 0" 13 }
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