{VERSION 3 0 "IBM INTEL LINUX" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Map le Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 34 "Integrace racionalni lome ne funkce" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Maple umoznuje rozlo zit racionalni lomenou funkci " }{XPPEDIT 18 0 "f;" "6#%\"fG" }{TEXT -1 30 " na parcialni zlomky prikazem " }{TEXT 256 29 "convert(f, parfr ac, promenna)" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "convert((12*x+7)/(x^2-9*x+18), parfrac, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"\"F%,&%\"xG\"\"\"!\"$F(!\"\"#!#V\"\"$*&F%F%,&F' F(!\"'F(F*#\"#zF-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "i1:=In t(x/(x^3-1), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i1G-%$IntG6$*&% \"xG\"\"\",&*$)F)\"\"$F*\"\"\"!\"\"F/!\"\"F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(student):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "convert(integrand(i1), parfrac, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"\"F%,&%\"xG\"\"\"!\"\"F(!\"\"#F(\"\"$*&F&F%, (*$)F'\"\"#F%F(F'F(F(F(F*#F)F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "int(%,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(-%#lnG6#,&%\"xG \"\"\"!\"\"F)#F)\"\"$-F%6#,(*$)F(\"\"#\"\"\"F)F(F)F)F)#F*\"\"'*&-%%sqr tG6#F,F3-%'arctanG6#,$*&,&F(F2F)F)F)F7F3F+F)F+" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 40 "i2:=Int((x^7+7*x-1)/(x^9+2*x^6+x^3), x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i2G-%$IntG6$*&,(*$)%\"xG\"\"(\"\"\" \"\"\"F,F-!\"\"F/F.,(*$)F,\"\"*F.F/*$)F,\"\"'F.\"\"#*$)F,\"\"$F.F/!\" \"F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "convert(integrand(i 2), parfrac, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,.*&\"\"\"F%*$)%\" xG\"\"$F%!\"\"!\"\"*&F%F%*$)F(\"\"#F%F*\"\"(*&F%F%*$),&F(\"\"\"F5F5\" \"#F%F*F5*&F%F%F4F*#\"#J\"\"**&,&F5F5F(F9F%,(*$)F(\"\"#F%F5F(F+F5F5F*# F+F:*&,&F0F5F(F5F%*$)F=\"\"#F%F*#F+\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "int(%,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,0*&\"\" \"F%*$)%\"xG\"\"#F%!\"\"#\"\"\"\"\"#*&F%F%F(F*!\"(*&F%F%,&F(F,F,F,F*! \"\"-%#lnG6#F1#\"#J\"\"*-F46#,(*$)F(F-F%F,F(F2F,F,#!#J\"#=*&-%%sqrtG6# \"\"$F%-%'arctanG6#,$*&,&F(F-F2F,F,FBF%#F,FEF,#F/FE*&,&F(\"#:!\"*F,F%F ;F*#F2F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "normal(diff(%,x ), expanded);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*$)%\"xG\"\"(\"\" \"\"\"\"F'F(!\"\"F*F),(*$)F'\"\"*F)F**$)F'\"\"'F)\"\"#*$)F'\"\"$F)F*! \"\"" }}}{EXCHG {PARA 18 "" 0 "" {TEXT -1 27 " Trigonometricke substit uce" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "i3:=Int(x^3*sqrt(4-x ^2), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i3G-%$IntG6$*&)%\"xG\" \"$\"\"\"-%%sqrtG6#,&\"\"%\"\"\"*$)F*\"\"#F,!\"\"F,F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "changevar(x=2*sin(t), i3, t);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$,$*()-%$sinG6#%\"tG\"\"$\"\" \"-%%sqrtG6#,&\"\"%\"\"\"*$)F)\"\"#F.!\"%F.-%$cosGF+F4\"#;F," }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(%);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,&*&)-%$sinG6#%\"tG\"\"#\"\"\"),&\"\"\"F.*$F%F+!\"\"# \"\"$F*F+#!#K\"\"&*$F,F+#!#k\"#:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "subs(sin(t)=x/2, %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&)%\"xG\"\"#\"\"\"),&\"\"\"F+*$F%F(#!\"\"\"\"%#\"\"$F'F(#!\")\" \"&*$F)F(#!#k\"#:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "i3=sim plify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&)%\"xG\"\"$\" \"\"-%%sqrtG6#,&\"\"%\"\"\"*$)F)\"\"#F+!\"\"F+F),(*&F3F+F,F+#!\"%\"#:* &)F)F0F+F,F+#F1\"\"&*$F,F+#!#KF:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(rhs(%),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,, *&%\"xG\"\"\"-%%sqrtG6#,&\"\"%F&*$)F%\"\"#\"\"\"!\"\"F/#!\")\"#:*&*$)F %\"\"$F/F/*$-F(6#F*F/!\"\"#F+F3*&F6F/F'F/#F+\"\"&*&*$)F%F?F/F/*$-F(6#F *F/F;#F0F?*&F%F/*$-F(6#F*F/F;#\"#KF3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "rationalize(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*& )%\"xG\"\"$\"\"\"-%%sqrtG6#,&\"\"%\"\"\"*$)F%\"\"#F'!\"\"F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "i4:=Int(1/(9+x^2), x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i4G-%$IntG6$*&\"\"\"F),&\"\"*\"\"\" *$)%\"xG\"\"#F)F,!\"\"F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "changevar(x=tan(t), i4, t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$Int G6$*&,&\"\"\"F(*$)-%$tanG6#%\"tG\"\"#\"\"\"F(F0,&\"\"*F(F)F(!\"\"F." } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%'arctanG6#,$-%$tanG6#%\"tG#\"\"\"\"\"$F," }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "i4=subs(tan(t)=x, %);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&\"\"\"F(,&\"\"*\"\"\"*$)% \"xG\"\"#F(F+!\"\"F.,$-%'arctanG6#,$F.#F+\"\"$F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "normal(diff(rhs(%), x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\"\"\"F$,&\"\"*\"\"\"*$)%\"xG\"\"#F$F'!\"\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Nakreslete graf primitivni funkce \+ k funkci " }{XPPEDIT 18 0 "1/(2-cos(x));" "6#*&\"\"\"\"\"\",&\"\"#F%-% $cosG6#%\"xG!\"\"F," }{TEXT -1 14 " na intervalu " }{XPPEDIT 18 0 "0 . . 2*Pi;" "6#;\"\"!*&\"\"#\"\"\"%#PiGF'" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=x->1/(2-cos(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%&arrowGF(*&\"\"\"F- ,&\"\"#\"\"\"-%$cosG6#9$!\"\"!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "i:=int(f(x), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> 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