restart; Digits:=64; NiM+SSdEaWdpdHNHNiIiI2s= This integral is to find the length of a Bezier curve with control points x0=6,y0=8,x1=1,y1=10,x2=7,y2=3,x3=4,y3=4. The polynomial was factored first to make it easier for Maple to interate it. q:=factor((-15+2*33*t+3*(-20)*t^2)^2+(6+2*(-27)*t+3*17*t^2)^2,complex); NiM+SSJxRzYiLCQqKiwmSSJ0R0YlIiIiXiQkIVtvYyRmbUV0Q1ZsYls/SXMsQj8yJDRbR3IkUXVfc2okUiplOyMhI2skIltvciVlXzpSJCpvYUF4OT8hKT1GbGdoM3JoNCFIdShbc1pMdVAqISNsRipGKiwmRilGKl4kRiwkIVtvciVlXzpSJCpvYUF4OT8hKT1GbGdoM3JoNCFIdShbc1pMdVAqRjFGKkYqLCZGKUYqXiQkIVtvUT9xI3B5YClRbSNcOSwlb2dremwxaVQjb0dvLGBfKT5SaCcpRi4kIltvR21vK3ZmKFswdFhuYCwnKlJ0Yy9YNyhSLC1bO1ZWSl1YdEYxRipGKiwmRilGKl4kRjgkIVtvR21vK3ZmKFswdFhuYCwnKlJ0Yy9YNyhSLC1bO1ZWSl1YdEYxRipGKiQiJSxpIiIh This value of the integral is wrong since the value of sqrt(q) is always positive for t between 0 and 1. The correct value of the integral is: 7.237223368328592885826619210956022413967067986017504163362886516 int(sqrt(q),t=0..1); NiNeJCQhW295YCwhKlxPPyg0QSkzLFpJMy9pclheKT4qPUxdKEdNenpoUSMhI2kkIiIhRig= This is a plot of sqrt(q). sqrt(q); NiMqJCoqLCZJInRHNiIkIiUsaSIiIV4kJCFbb25hbHNtbkMiKjQuXVcpSFpoUl4tckxTYGtVZ1cqSDMyVjghI2ckIltveWQ8NSNmRzh2LU9IIkg0dj8jRzBwTicpR1BcJz5DKlxZXCJlISNoIiIiRjIsJkYmRjJeJCQhW29jJGZtRXRDVmxiWz9JcyxCPzIkNFtHciRRdV9zaiRSKmU7IyEjayQhW29yJWVfOlIkKm9hQXg5PyEpPUZsZ2gzcmg0IUh1KFtzWkx1UCohI2xGMkYyLCZGJkYyXiQkIVtvUT9xI3B5YClRbSNcOSwlb2dremwxaVQjb0dvLGBfKT5SaCcpRjckIltvR21vK3ZmKFswdFhuYCwnKlJ0Yy9YNyhSLC1bO1ZWSl1YdEY6RjJGMiwmRiZGMl4kRj0kIVtvR21vK3ZmKFswdFhuYCwnKlJ0Yy9YNyhSLC1bO1ZWSl1YdEY6RjJGMiNGMiIiIw== f1:=proc(t) ((6201.*t+(-1343.0708299446042645340337102513961472984450030991246766726\
55467+581.4946499241964937288635690528220750929129360275132859210175778*\
I))*(t+(-.21658939363725274383712848093072023017230204855654324732666593\
56-0.9377433477248774290096171086160652718802014772254689339155258471e-1\
*I))*(t+(-.8661391985253016828682416206657964606840114492663885378692702\
038+0.7345503143431648020139712450456733996015367457305487597500686628e-\
1*I))*(t+(-.866139198525301682868241620665796460684011449266388537869270\
2038-0.7345503143431648020139712450456733996015367457305487597500686628e\
-1*I)))^(1/2) end proc; NiM+SSNmMUc2ImYqNiNJInRHRiVGJUYlRiUqJCoqLCgqJiQiJSxpIiIhIiIiOSRGMEYwJCJbb25hbHNtbkMiKjQuXVcpSFpoUl4tckxTYGtVZ1cqSDMyVjghI2chIiIqJiQiW295ZDw1I2ZHOHYtT0giSDR2PyNHMHBOJylHUFwnPkMqXFlcImUhI2hGMF4jRjBGMEYwRjAsKEYxRjAkIltvYyRmbUV0Q1ZsYls/SXMsQj8yJDRbR3IkUXVfc2okUiplOyMhI2tGNSomJCJbb3IlZV86UiQqb2FBeDk/ISk9RmxnaDNyaDQhSHUoW3NaTHVQKiEjbEYwRjpGMEY1RjAsKEYxRjAkIltvUT9xI3B5YClRbSNcOSwlb2dremwxaVQjb0dvLGBfKT5SaCcpRj5GNSomJCJbb0dtbyt2ZihbMHRYbmAsJypSdGMvWDcoUiwtWztWVkpdWHRGQkYwRjpGMEYwRjAsKEYxRjBGREY1RkZGNUYwI0YwIiIjRiVGJUYl plot(Re(f1(t)),t=0..1); 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N"=cxf'\_$3M6&RFgn7$$"[olmmmmmmmmmmmmmmmmmmmmmmmm;a8H'pQ)F[o$"[oh+*\$oI*fTH#))>S4$*4yHg2!\;E#oJI*f&z%)QFgn7$$"[olmmmmmmmmmmmmmmmmmmmmmmmmmTge)*R%)F[o$"[o[98*f*)*R9mk(3#*)HtNW6&z7R"[w0QVqT^KQFgn7$$"[olmmmmmmmmmmmmmmmmmmmmmmmm;H2)3I\)F[o$"[o[/PB_E!3mu?VANk%>Ix8'4\?Z)ok-&fZdz$Fgn7$$"[olmmmmmmmmmmmmmmmmmmmmmmmmm;a<.Y&)F[o$"[ov\/^"H'Q*fur,R%32e@lSHr"e()G!ft'>Yex$Fgn7$$"[oILLLLLLLLLLLLLLLLLLLLLLLL3FWch)f)F[o$"[o'y<_sjk)*z<MUsB=U6^[ksUG0&pS>j$GRx$Fgn7$$"[o+++++++++++++++++++++++++]PM&*>^')F[o$"[o&=)4r@Tr`&e-q'y>%>e*o=R!)fi:v@u*)oo!z$Fgn7$$"[olmmmmmmmmmmmmmmmmmmmmmmmm"zWU$y.()F[o$"[o#GZ</H*[*4@i%oh3#[fsdEdvodyYx!yVyEQFgn7$$"[oKLLLLLLLLLLLLLLLLLLLLLLLLLe9tOc()F[o$"[ozEiUdOc#p5%*egS8lI\#GFfq6QP8[h4f#)QFgn7$$"[olmmmmmmmmmmmmmmmmmmmmmmmm;H#e0I&))F[o$"[oQvN'y:n!yopczxi*e_fdfyG2&3HPidDfOSFgn7$$"[o******************************************************\Qk\*)F[o$"[o85YR8rSpL[45k-Rc+=il&HbU")znx3Q`D%Fgn7$$"[oKLLLLLLLLLLLLLLLLLLLLLLLLL$3dg6<*F[o$"[oor;cGTu@wr=sY^U4&)*>\N\$GhIl&R$oCw\Fgn7$$"[olmmmmmmmmmmmmmmmmmmmmmmmmmmmxGp$*F[o$"[oF+J")e^RB^k4MWLfl^8B\D0W!3LGr3ra$eFgn7$$"[o)**************************************************\7oK0e*F[o$"[o<)f"e<:7'=>(zSc9=*G>RciO6sQu_(yPgCpFgn7$$"[o+++++++++++++++++++++++++++]oi"o*F[o$"[oyNAP8W:X7FLs)4cYkbU\"[a6*=1h0u6!)\(Fgn7$$"[o)**************************************************\(=5s#y*F[o$"[omEk!3c-wnoHn()\c=`Xm'*3$fyLvgehC+,")Fgn7$$"[o+++++++++++++++++++++++++]P40O"*)*F[o$"[o)pTxm$ot]q`[%pzop)[-"\Xi&>*\7fp(zKz()Fgn7$$"""F+$"[odX^s0[]c(zTl'e6gb")HL1o'*f*z800)H$o[*Fgn-%&COLORG6&%$RGBG$"#5!""$F+FjblF[cl-%+AXESLABELSG6$Q"t6"Q!F`cl-%%VIEWG6$;F[clFhbl;$"1"))H?/(HEN!#:$"0xcUd7.k"!#8 This is a plot of the same polynomial not factored. q1:=expand((-15+2*33*t+3*(-20)*t^2)^2+(6+2*(-27)*t+3*17*t^2)^2); NiM+SSNxMUc2IiwsIiRoIyIiIkkidEdGJSElR0UqJEYpIiIjIiUlbyoqJEYpIiIkISZHTSIqJEYpIiIlIiUsaQ== f2:=proc(t) 261-2628*t+9684*t^2-13428*t^3+6201*t^4 end proc; NiM+SSNmMkc2ImYqNiNJInRHRiVGJUYlRiUsLCIkaCMiIiI5JCElR0UqJEYsIiIjIiUlbyoqJEYsIiIkISZHTSIqJEYsIiIlIiUsaUYlRiVGJQ== plot(sqrt(f2(t)),t=0..1); -%%PLOTG6%-%'CURVESG6$7eo7$$""!F+$"[o,m6/8lOM\[g`))o'))4iu98_P47NS@W\bh"!#i7$$"[oLLLLLLLLLLLLLLLLLLLLLLLLLLL3x&)*3"!#l$"[oU\yZ^FjA'*)=_bC`m2!H[dSQ>Ys;.lG/G:F.7$$"[ommmmmmmmmmmmmmmmmmmmmmmmmmm;arz@F2$"[oo:7O<`F,,2c]f=Qw3.ry&Q(3>K;zKf%GW"F.7$$"[o++++++++++++++++++++++++++D"y%*z7$F2$"[o!ykgCVONzTcd&)QVdNP`NDe.g7x5VvV1P"F.7$$"[oLLLLLLLLLLLLLLLLLLLLLLLLLL$e9ui2%F2$"[o-^K*o_N?uWN\6KjMkWft<38!p4a+0\G+8F.7$$"[o++++++++++++++++++++++++++voMrU^F2$"[o)fszdPwD^T@a*z3t#yK-rV9ZZ')*\Ob1VB7F.7$$"[ommmmmmmmmmmmmmmmmmmmmmmmmmm"z_"4iF2$"[o#ynuo)oTLzEa4)yix;@!*ygA=0q(y8!=r!\6F.7$$"[olmmmmmmmmmmmmmmmmmmmmmmmmmmm6m#G(F2$"[oE=&3a.dq*=PNM=*p$ptjkt%f$yGQjjV/&o2"F.7$$"[olmmmmmmmmmmmmmmmmmmmmmmmmmmT&phN)F2$"[oA(GmY&HQyK8InN()3vzHe!fs%>gw%3W`/u+"F.7$$"[o++++++++++++++++++++++++++v=ddC%*F2$"[o4d9gv0O*H=?&=")3Vl2oy'*3pm9.[I3f.7%*!#j7$$"[oLLLLLLLLLLLLLLLLLLLLLLLLLLe*=)H\5!#k$"[o_[oB@y5jWWb:$z(p%oL,P)Q(GVk!*GcO55y)Fgn7$$"[o++++++++++++++++++++++++++v=JN[6F[o$"[omS/+deZq_J%>tv*Hklz["z*Hk_'e!4(H>cA)Fgn7$$"[ommmmmmmmmmmmmmmmmmmmmmmmmm"z/3uC"F[o$"[oy"Hrn;9lC>q9!o\MSoh?&z6BIMBb'z"Q4q(Fgn7$$"[o++++++++++++++++++++++++++DJ$RDX"F[o$"[onl_v[mS)HJZCReP/H:t!*H*o@IG>RU]8BnFgn7$$"[ommmmmmmmmmmmmmmmmmmmmmmmmm"zR'ok;F[o$"[oI^ELrhXy$\Z!e#y:mu65o!ooXb2:i>>_!*eFgn7$$"[o++++++++++++++++++++++++++D1J:w=F[o$"[oW<j$*[A-^eQ#f$pQfn\hiRU4+r9'eVOW[F&Fgn7$$"[ommmmmmmmmmmmmmmmmmmmmmmmm;HdG"\)>F[o$"[oWI"Gnw&y"y")3*e<_^RfxR%f:D^%*fuJL_90&Fgn7$$"[oLLLLLLLLLLLLLLLLLLLLLLLLLLL3En$4#F[o$"[oUWCZ.;+zJ]"G'fQWC42E+$4<(y<(pR-`X*[Fgn7$$"[ommmmmmmmmmmmmmmmmmmmmmmmm;HK/dT@F[o$"[otM$)HM-mNi)p)f()QZ'4')4s;O+DP![%>*>eY[Fgn7$$"[o++++++++++++++++++++++++++Dc#o%*=#F[o$"[oX^vWRqV!zn0w>B![N'3\JNq_@!)*[>=kK6[Fgn7$$"[oLLLLLLLLLLLLLLLLLLLLLLLLL$3-3mtB#F[o$"[o,;5H23Al0;A#>%>N,RH:jVrbuv1I5D^)y%Fgn7$$"[ommmmmmmmmmmmmmmmmmmmmmmmmm;/RE&G#F[o$"[o)[qfW#=tj*ptE,x+sa<YD+kHe&*[nh!3xxZFgn7$$"[o+++++++++++++++++++++++++]P4b=RBF[o$"[o/#GO2!3!)4%y="*[t?X49OnAG76uv>!3"\&zZFgn7$$"[oLLLLLLLLLLLLLLLLLLLLLLLLLLe9r5$R#F[o$"[o;AE%4E%z%\Qy*eccsv_1\4vzb^mT1dNF&z%Fgn7$$"[ommmmmmmmmmmmmmmmmmmmmmmmm;z>(GqW#F[o$"[opEI0i"[6e"[b4"))=%)4[*=K4">N>$)=w'32C[Fgn7$$"[o+++++++++++++++++++++++++++D.&4]#F[o$"[o]"RDV@J#3WpZ20xybqT9F-1[*)o)3l7"*\'[Fgn7$$"[o+++++++++++++++++++++++++++]jB4EF[o$"[o/"*Rvvs$p;a<)[(37p7Ss!G@+G>(p1$e[sz\Fgn7$$"[o+++++++++++++++++++++++++++vB_<FF[o$"[o9i_WtpySagB>1T,B')H!p5e*z<+^*\[E58&Fgn7$$"[o+++++++++++++++++++++++++++v'Hi#HF[o$"[oJ7WkRJ#[QB7B(f(Q<k+F%p%))G(*zyeaJ,o\&Fgn7$$"[ommmmmmmmmmmmmmmmmmmmmmmmmm"z*ev:JF[o$"[oKwzgT2(Hf')*RYg7cO08N/)zjs9()*3+1#)zeFgn7$$"[oLLLLLLLLLLLLLLLLLLLLLLLLLLL347TLF[o$"[oQw#\DA&3%*H29T'o"=6+R[ZtQcurHy1PrejFgn7$$"[oLLLLLLLLLLLLLLLLLLLLLLLLLLLLY.KNF[o$"[oS**[6-ES<*Hc:sF&4maaF=$Qc')*Ha$eEx7w'Fgn7$$"[o***************************************************\7o7Tv$F[o$"[o^Z>Iy@Fm53r8FU(yTU7g4eL;M<K*>As1sFgn7$$"[oLLLLLLLLLLLLLLLLLLLLLLLLLLL$Q*o]RF[o$"[oYl9vD<MGI5'3JhR:=uGF$>9SdZ<ZWRIpvFgn7$$"[o***************************************************\7=lj;%F[o$"[oM)[]wT)4H&\.z#*y@'QSkZ[-'e'=22uyM7CzFgn7$$"[o***************************************************\PaR<P%F[o$"[o*[(\@:$>sHz'>Z**oTO)H)[gsUJ?">(>wJW9#)Fgn7$$"[oLLLLLLLLLLLLLLLLLLLLLLLLLL$e9Ege%F[o$"[o9Q8[(3^[r#*zig;jj+r"*GCy--i4**frtNY)Fgn7$$"[oLLLLLLLLLLLLLLLLLLLLLLLLLLeR"3Gy%F[o$"[oyU=e<rHAEaj80Pl%QWP#*GUiJrnTps(GT')Fgn7$$"[ommmmmmmmmmmmmmmmmmmmmmmmmm;/T1&*\F[o$"[ohRjuj:ZjIU<">N<\P]t<<(=AvLIoc[5w()Fgn7$$"[ommmmmmmmmmmmmmmmmmmmmmmmmm"zRQb@&F[o$"[onMDZEna"R-k&Hu=be%=![%*y2U&z(eW0,2_))Fgn7$$"[o***************************************************\(=>Y2aF[o$"[oZtV!GXAMFjE-fv`7"ewPGj$QLgNh!f@>k))Fgn7$$"[ommmmmmmmmmmmmmmmmmmmmmmmmm;zXu9cF[o$"[o,:Qc-`b;wsFncU$z6Dj;(*eS2SwiTRI.#))Fgn7$$"[o******************************************************\y))GeF[o$"[oDPV4*HUjAm$>;`(4$)zTa](*yk=0d(4Bfv7()Fgn7$$"[o****************************************************\i_QQgF[o$"[o!eov([YU.0-'3!fDE6$48qj0+wF7&f7%>la)Fgn7$$"[o***************************************************\7y%3TiF[o$"[oYw-G'pD)3jo-fj['y"f1gZ%='=.<\C3[()G$)Fgn7$$"[o****************************************************\P![hY'F[o$"[oSmJT5v%4@B3<'[B%[w#)z%o!\)[[I)GCC!3B!)Fgn7$$"[oKLLLLLLLLLLLLLLLLLLLLLLLLLL$Qx$omF[o$"[o/8jG'eesAZTs5lrhA*Q***RsC@!QV$eN(e#p(Fgn7$$"[o*****************************************************\P+V)oF[o$"[o)yDp$QOw-'GlfjS"=G(H_-wigos37z'**[%G(Fgn7$$"[ommmmmmmmmmmmmmmmmmmmmmmmmm"zpe*zqF[o$"[ozVc7;*=W^2P'[!\!fv8u29]&*4*=@=jTu#poFgn7$$"[o*****************************************************\#\'QH(F[o$"[o'H#eUeJ]1l^#3#)fO]hYFT@%pFz&fe^teBP'Fgn7$$"[oKLLLLLLLLLLLLLLLLLLLLLLLLLe9S8&\(F[o$"[o!*[mB!ROh(o^x/Ra,)o,3BT**e]`M$=0`.teFgn7$$"[o***************************************************\i?=bq(F[o$"[omHr@#H)=C())H_K.)))f>CK'G<v2A&R;lacL`Fgn7$$"[oKLLLLLLLLLLLLLLLLLLLLLLLLLL3s?6zF[o$"[oG(4\/nET7TT3oq!>[i]Y&\<sog"o&)R]&H"[Fgn7$$"[o***************************************************\7`Wl7)F[o$"[o:WAPLEPXiCfEAy')*p;-Y<Hy#3Vd&=EHuJ%Fgn7$$"[oILLLLLLLLLLLLLLLLLLLLLLLL$e*[ACI#)F[o$"[ojBJM["eB+j[5&*yXi0&[3())Hev_$o5"[qd6%Fgn7$$"[olmmmmmmmmmmmmmmmmmmmmmmmmmmm*RRL)F[o$"[oZE>()*4BJ/USJ,>L@*4kYN"=cxf'\_$3M6&RFgn7$$"[olmmmmmmmmmmmmmmmmmmmmmmmm;a8H'pQ)F[o$"[o(3!*\$oI*fTH#))>S4$*4yHg2!\;E#oJI*f&z%)QFgn7$$"[olmmmmmmmmmmmmmmmmmmmmmmmmmTge)*R%)F[o$"[o398*f*)*R9mk(3#*)HtNW6&z7R"[w0QVqT^KQFgn7$$"[olmmmmmmmmmmmmmmmmmmmmmmmm;H2)3I\)F[o$"[og/PB_E!3mu?VANk%>Ix8'4\?Z)ok-&fZdz$Fgn7$$"[olmmmmmmmmmmmmmmmmmmmmmmmmm;a<.Y&)F[o$"[oB\/^"H'Q*fur,R%32e@lSHr"e()G!ft'>Yex$Fgn7$$"[oILLLLLLLLLLLLLLLLLLLLLLLL3FWch)f)F[o$"[o*)z@DPY')*z<MUsB=U6^[ksUG0&pS>j$GRx$Fgn7$$"[o+++++++++++++++++++++++++]PM&*>^')F[o$"[o&=)4r@Tr`&e-q'y>%>e*o=R!)fi:v@u*)oo!z$Fgn7$$"[olmmmmmmmmmmmmmmmmmmmmmmmm"zWU$y.()F[o$"[ovsuT!H*[*4@i%oh3#[fsdEdvodyYx!yVyEQFgn7$$"[oKLLLLLLLLLLLLLLLLLLLLLLLLLe9tOc()F[o$"[o5CiUdOc#p5%*egS8lI\#GFfq6QP8[h4f#)QFgn7$$"[olmmmmmmmmmmmmmmmmmmmmmmmm;H#e0I&))F[o$"[oTwN'y:n!yopczxi*e_fdfyG2&3HPidDfOSFgn7$$"[o******************************************************\Qk\*)F[o$"[o#fg%R8rSpL[45k-Rc+=il&HbU")znx3Q`D%Fgn7$$"[oKLLLLLLLLLLLLLLLLLLLLLLLLL$3dg6<*F[o$"[o")o;cGTu@wr=sY^U4&)*>\N\$GhIl&R$oCw\Fgn7$$"[olmmmmmmmmmmmmmmmmmmmmmmmmmmmxGp$*F[o$"[ox.J")e^RB^k4MWLfl^8B\D0W!3LGr3ra$eFgn7$$"[o)**************************************************\7oK0e*F[o$"[oh*f"e<:7'=>(zSc9=*G>RciO6sQu_(yPgCpFgn7$$"[o+++++++++++++++++++++++++++]oi"o*F[o$"[ozNAP8W:X7FLs)4cYkbU\"[a6*=1h0u6!)\(Fgn7$$"[o)**************************************************\(=5s#y*F[o$"[o8Ik!3c-wnoHn()\c=`Xm'*3$fyLvgehC+,")Fgn7$$"[o+++++++++++++++++++++++++]P40O"*)*F[o$"[o+<unOot]q`[%pzop)[-"\Xi&>*\7fp(zKz()Fgn7$$"""F+$"[ofX^s0[]c(zTl'e6gb")HL1o'*f*z800)H$o[*Fgn-%&COLORG6&%$RGBG$"#5!""$F+FjblF[cl-%+AXESLABELSG6$Q"t6"Q!F`cl-%%VIEWG6$;F[clFhbl;$"1"))H?/(HEN!#:$"0xcUd7.k"!#8 Maple failed to integrate this in a reasonable time when the polynomial is not factored. int(sqrt(q1),t=0..1); Warning, computation interrupted Try to evaluate the basic elliptic integrals I(-e1), I(0), and I(e1) for this example to see if Maple can succeed. First I(-e1). q2:=evalf(solve(q1,t)); NiM+SSNxMkc2IjYmXiQkIltvUT9xI3B5YClRbSNcOSwlb2dremwxaVQjb0dvLGBfKT5SaCcpISNrJCJbb0dtbyt2ZihbMHRYbmAsJypSdGMvWDcoUiwtWztWVkpdWHQhI2xeJCQiW29jJGZtRXRDVmxiWz9JcyxCPzIkNFtHciRRdV9zaiRSKmU7I0YqJCJbb3IlZV86UiQqb2FBeDk/ISk9RmxnaDNyaDQhSHUoW3NaTHVQKkYtXiRGLyQhW29yJWVfOlIkKm9hQXg5PyEpPUZsZ2gzcmg0IUh1KFtzWkx1UCpGLV4kRigkIVtvR21vK3ZmKFswdFhuYCwnKlJ0Yy9YNyhSLC1bO1ZWSl1YdEYt q3:=1/((q2[1]-t)^(3/2)*(q2[2]-t)^(1/2)*(q2[3]-t)^(1/2)*(q2[4]-t)^(1/2)); NiM+SSNxM0c2IioqLCZeJCQiW29RP3EjcHlgKVFtI1w5LCVvZ2t6bDFpVCNvR28sYF8pPlJoJykhI2skIltvR21vK3ZmKFswdFhuYCwnKlJ0Yy9YNyhSLC1bO1ZWSl1YdCEjbCIiIkkidEdGJSEiIiMhIiQiIiMsJl4kJCJbb2MkZm1FdENWbGJbP0lzLEI/MiQ0W0dyJFF1X3NqJFIqZTsjRiskIltvciVlXzpSJCpvYUF4OT8hKT1GbGdoM3JoNCFIdShbc1pMdVAqRi5GL0YwRjEjRjFGNCwmXiRGNyQhW29yJWVfOlIkKm9hQXg5PyEpPUZsZ2gzcmg0IUh1KFtzWkx1UCpGLkYvRjBGMUY7LCZeJEYpJCFbb0dtbyt2ZihbMHRYbmAsJypSdGMvWDcoUiwtWztWVkpdWHRGLkYvRjBGMUY7 q4:=int(q3,t=0..1); Error, (in gcdex) invalid arguments
Maple failed to evaluate this integral. Try I(0). q5:=1/((q2[1]-t)^(1/2)*(q2[2]-t)^(1/2)*(q2[3]-t)^(1/2)*(q2[4]-t)^(1/2)); NiM+SSNxNUc2IioqLCZeJCQiW29RP3EjcHlgKVFtI1w5LCVvZ2t6bDFpVCNvR28sYF8pPlJoJykhI2skIltvR21vK3ZmKFswdFhuYCwnKlJ0Yy9YNyhSLC1bO1ZWSl1YdCEjbCIiIkkidEdGJSEiIiNGMSIiIywmXiQkIltvYyRmbUV0Q1ZsYls/SXMsQj8yJDRbR3IkUXVfc2okUiplOyNGKyQiW29yJWVfOlIkKm9hQXg5PyEpPUZsZ2gzcmg0IUh1KFtzWkx1UCpGLkYvRjBGMUYyLCZeJEY2JCFbb3IlZV86UiQqb2FBeDk/ISk9RmxnaDNyaDQhSHUoW3NaTHVQKkYuRi9GMEYxRjIsJl4kRikkIVtvR21vK3ZmKFswdFhuYCwnKlJ0Yy9YNyhSLC1bO1ZWSl1YdEYuRi9GMEYxRjI= q6:=int(q5,t=0..1); NiM+SSNxNkc2IiQiW29PJHA2KnA5YWg2ITRQKXllSV05XldwU1BwKCl5XyZSMFdUPyIhI2k= Maple got the correct answer. Now try I(e1). q7:=(q2[1]-t)^(1/2)/((q2[2]-t)^(1/2)*(q2[3]-t)^(1/2)*(q2[4]-t)^(1/2)); NiM+SSNxN0c2IioqLCZeJCQiW29RP3EjcHlgKVFtI1w5LCVvZ2t6bDFpVCNvR28sYF8pPlJoJykhI2skIltvR21vK3ZmKFswdFhuYCwnKlJ0Yy9YNyhSLC1bO1ZWSl1YdCEjbCIiIkkidEdGJSEiIiNGLyIiIywmXiQkIltvYyRmbUV0Q1ZsYls/SXMsQj8yJDRbR3IkUXVfc2okUiplOyNGKyQiW29yJWVfOlIkKm9hQXg5PyEpPUZsZ2gzcmg0IUh1KFtzWkx1UCpGLkYvRjBGMSNGMUYzLCZeJEY2JCFbb3IlZV86UiQqb2FBeDk/ISk9RmxnaDNyaDQhSHUoW3NaTHVQKkYuRi9GMEYxRjosJl4kRikkIVtvR21vK3ZmKFswdFhuYCwnKlJ0Yy9YNyhSLC1bO1ZWSl1YdEYuRi9GMEYxRjo= q8:=int(q7,t=0..1); NiM+SSNxOEc2Il4kJCJbbzorW2xQL3o6TG4mWyFcJClROEkjXDFQIypwWShcLDMxcVNlUiEjaiQhW29fJHpJOStHIik+QyszMUUrbHhmKnkyPXZNQVBmWk0kPkgnbyEjaw== Maple got the wrong answer this time.