{VERSION 2 3 "IBM INTEL NT" "2.3" } {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 "Hyperlink" -1 17 "" 0 1 0 128 128 1 0 0 1 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 " Help Heading" -1 26 "" 1 14 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 "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 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 "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {SECT 0 {PARA 0 "" 0 "" {TEXT 26 8 "Bug fix:" }{TEXT -1 40 " \+ Integrals involving fractional powers\n" }}{PARA 0 "" 0 "" {TEXT -1 156 "Maple has trouble with some integrals involving products of half- integer powers of linear terms. In some cases this produces an error \+ message in Release 4:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "f1: = (2*x-3)^(-3/2)*x^(1/2);\nint(f1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1G*&,&%\"xG\"\"#!\"$\"\"\"#F)F(F'#F*F(" }}{PARA 8 "" 1 "" {TEXT -1 32 "Error, (in int) division by zero" }}}{PARA 0 "" 0 "" {TEXT -1 47 "In other cases the antiderivative is incorrect." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "f2:=(2*x+3)^(1/2)*x^(-5/2); \nF2:=int(f2,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f2G*&,&%\"xG\" \"#\"\"$\"\"\"#F*F(F'#!\"&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#F2G ,&*&%\"xG#!\"$\"\"#,&F'F*\"\"$\"\"\"#F-F*#!\"#F,*&F'#!\"\"F*F+F.#F0\" \"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "simplify(diff(F2,x) \+ - f2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&%\"xG#!\"$\"\"#,&F%F(\" \"$\"\"\"#!\"\"F(#F-F*" }}}{PARA 0 "" 0 "" {TEXT -1 200 "A work-around is to express the integrand as a single square root. Note that this \+ is not quite equivalent to the original integrand (although it is when at least one of the linear terms is positive)." }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 55 "f1p:= sqrt((2*x-3)^(-3)*x);\nF1p:= simplify(in t(f1p,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$f1pG*$*&,&%\"xG\"\"#! \"$\"\"\"F*F(F+#F+F)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$F1pG,$*(,2* &*&%\"xG\"\"\",&F*\"\"#!\"$F+F+#F+F-F*F+\"\")*$F)F/!#7*(F-F/F*F--%#lnG 6#\"\"%F+F7*(F-F/F*F--F56#,(*&F-F/F*F+F7*$F-F/F.F1F7F+!\"%*(F-F/F*F+F4 F+F2*(F-F/F*F+F9F+\"#7*&F-F/F4F+\"\"**&F-F/F9F+!\"*F+*&F,F.F*F+F/F)#! \"\"F-#FHF7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "normal(diff( F1p,x)-f1p);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "f2p:= sqrt((2*x+3)/x^5);\nF2p:= sim plify(int(f2p,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$f2pG*$*&,&%\" xG\"\"#\"\"$\"\"\"F+F(!\"&#F+F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ F2pG,$*(,&%\"xG\"\"#\"\"$\"\"\"F+F(F+*&F'F+F(!\"&#F+F)#!\"#\"\"*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "normal(diff(F2p,x)-f2p);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{PARA 0 "" 0 "" {TEXT -1 217 "In general it is prudent to check the correctness of integrals, e ither by comparing definite integrals to their floating-point approxim ations or by comparing the derivative of an indefinite integral to the integrand. " }}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 9 "See also:" } {TEXT -1 1 " " }{HYPERLNK 17 "Errors in symbolic integration" 2 "Error s_in_symbolic_integration" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "Error: d ivision by zero" 2 "Error:division_by_zero" "" }{TEXT -1 2 ", " } {HYPERLNK 17 "int" 2 "int" "" }}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 22 " Maple Advisor Database" }{TEXT -1 18 " R. Israel, 1998" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{MARK "1 0 2" 23 }{VIEWOPTS 1 1 0 1 1 1803 }