test gauleg.java on interval -1.0 to 1.0 ordinates, weights x[1]=0.0, w[1]=2.0 integral(1.0, -1.0..1.0)=2.0 x[1]=-0.5773502691896257, w[1]=0.9999999999999996 x[2]=0.5773502691896257, w[2]=0.9999999999999996 integral(1.0, -1.0..1.0)=1.9999999999999991 x[1]=-0.7745966692414834, w[1]=0.5555555555555527 x[2]=0.0, w[2]=0.8888888888888888 x[3]=0.7745966692414834, w[3]=0.5555555555555527 integral(1.0, -1.0..1.0)=1.9999999999999942 x[1]=-0.8611363115940526, w[1]=0.3478548451374476 x[2]=-0.3399810435848563, w[2]=0.6521451548625464 x[3]=0.3399810435848563, w[3]=0.6521451548625464 x[4]=0.8611363115940526, w[4]=0.3478548451374476 integral(1.0, -1.0..1.0)=1.999999999999988 x[1]=-0.906179845938664, w[1]=0.23692688505618173 x[2]=-0.5384693101056831, w[2]=0.47862867049936647 x[3]=0.0, w[3]=0.5688888888888889 x[4]=0.5384693101056831, w[4]=0.47862867049936647 x[5]=0.906179845938664, w[5]=0.23692688505618173 integral(1.0, -1.0..1.0)=1.9999999999999851 x[1]=-0.932469514203152, w[1]=0.17132449237916234 x[2]=-0.6612093864662646, w[2]=0.3607615730481386 x[3]=-0.2386191860831969, w[3]=0.4679139345726895 x[4]=0.2386191860831969, w[4]=0.4679139345726895 x[5]=0.6612093864662646, w[5]=0.3607615730481386 x[6]=0.932469514203152, w[6]=0.17132449237916234 integral(1.0, -1.0..1.0)=1.999999999999981 x[1]=-0.9491079123427585, w[1]=0.12948496616886246 x[2]=-0.7415311855993945, w[2]=0.2797053914892767 x[3]=-0.4058451513773972, w[3]=0.38183005050511903 x[4]=0.0, w[4]=0.4179591836734694 x[5]=0.4058451513773972, w[5]=0.38183005050511903 x[6]=0.7415311855993945, w[6]=0.2797053914892767 x[7]=0.9491079123427585, w[7]=0.12948496616886246 integral(1.0, -1.0..1.0)=1.9999999999999856 x[1]=-0.9602898564975362, w[1]=0.10122853629036972 x[2]=-0.7966664774136268, w[2]=0.22238103445337445 x[3]=-0.525532409916329, w[3]=0.3137066458778874 x[4]=-0.18343464249564978, w[4]=0.362683783378362 x[5]=0.18343464249564978, w[5]=0.362683783378362 x[6]=0.525532409916329, w[6]=0.3137066458778874 x[7]=0.7966664774136268, w[7]=0.22238103445337445 x[8]=0.9602898564975362, w[8]=0.10122853629036972 integral(1.0, -1.0..1.0)=1.9999999999999873 x[1]=-0.9681602395076261, w[1]=0.08127438836156874 x[2]=-0.8360311073266359, w[2]=0.18064816069485756 x[3]=-0.6133714327005905, w[3]=0.26061069640293555 x[4]=-0.3242534234038089, w[4]=0.3123470770400019 x[5]=0.0, w[5]=0.3302393550012598 x[6]=0.3242534234038089, w[6]=0.3123470770400019 x[7]=0.6133714327005905, w[7]=0.26061069640293555 x[8]=0.8360311073266359, w[8]=0.18064816069485756 x[9]=0.9681602395076261, w[9]=0.08127438836156874 integral(1.0, -1.0..1.0)=1.9999999999999871 x[1]=-0.9739065285171716, w[1]=0.06667134430868286 x[2]=-0.8650633666889845, w[2]=0.14945134915058053 x[3]=-0.6794095682990244, w[3]=0.21908636251598207 x[4]=-0.43339539412924716, w[4]=0.26926671930999174 x[5]=-0.1488743389816312, w[5]=0.2955242247147529 x[6]=0.1488743389816312, w[6]=0.2955242247147529 x[7]=0.43339539412924716, w[7]=0.26926671930999174 x[8]=0.6794095682990244, w[8]=0.21908636251598207 x[9]=0.8650633666889845, w[9]=0.14945134915058053 x[10]=0.9739065285171716, w[10]=0.06667134430868286 integral(1.0, -1.0..1.0)=1.9999999999999802 x[1]=-0.978228658146057, w[1]=0.055668567116169604 x[2]=-0.8870625997680953, w[2]=0.12558036946490472 x[3]=-0.7301520055740494, w[3]=0.18629021092773426 x[4]=-0.5190961292068118, w[4]=0.23319376459197813 x[5]=-0.26954315595234496, w[5]=0.2628045445102466 x[6]=0.0, w[6]=0.2729250867779006 x[7]=0.26954315595234496, w[7]=0.2628045445102466 x[8]=0.5190961292068118, w[8]=0.23319376459197813 x[9]=0.7301520055740494, w[9]=0.18629021092773426 x[10]=0.8870625997680953, w[10]=0.12558036946490472 x[11]=0.978228658146057, w[11]=0.055668567116169604 integral(1.0, -1.0..1.0)=1.9999999999999671 x[1]=-0.9815606342467192, w[1]=0.047175336386507824 x[2]=-0.9041172563704748, w[2]=0.10693932599531818 x[3]=-0.7699026741943047, w[3]=0.16007832854334633 x[4]=-0.5873179542866175, w[4]=0.20316742672306584 x[5]=-0.3678314989981802, w[5]=0.23349253653835458 x[6]=-0.1252334085114689, w[6]=0.24914704581340288 x[7]=0.1252334085114689, w[7]=0.24914704581340288 x[8]=0.3678314989981802, w[8]=0.23349253653835458 x[9]=0.5873179542866175, w[9]=0.20316742672306584 x[10]=0.7699026741943047, w[10]=0.16007832854334633 x[11]=0.9041172563704748, w[11]=0.10693932599531818 x[12]=0.9815606342467192, w[12]=0.047175336386507824 integral(1.0, -1.0..1.0)=1.9999999999999911 x[1]=-0.9841830547185881, w[1]=0.0404840047653123 x[2]=-0.917598399222978, w[2]=0.09212149983772838 x[3]=-0.8015780907333099, w[3]=0.1388735102197872 x[4]=-0.6423493394403402, w[4]=0.17814598076194568 x[5]=-0.44849275103644687, w[5]=0.2078160475368879 x[6]=-0.2304583159551348, w[6]=0.22628318026289715 x[7]=0.0, w[7]=0.2325515532308739 x[8]=0.2304583159551348, w[8]=0.22628318026289715 x[9]=0.44849275103644687, w[9]=0.2078160475368879 x[10]=0.6423493394403402, w[10]=0.17814598076194568 x[11]=0.8015780907333099, w[11]=0.1388735102197872 x[12]=0.917598399222978, w[12]=0.09212149983772838 x[13]=0.9841830547185881, w[13]=0.0404840047653123 integral(1.0, -1.0..1.0)=1.9999999999999911 x[1]=-0.9862838086968123, w[1]=0.03511946033174906 x[2]=-0.9284348836635736, w[2]=0.08015808715976037 x[3]=-0.827201315069765, w[3]=0.12151857068790312 x[4]=-0.6872929048116855, w[4]=0.1572031671581936 x[5]=-0.5152486363581541, w[5]=0.18553839747793643 x[6]=-0.31911236892788974, w[6]=0.2051984637212955 x[7]=-0.10805494870734365, w[7]=0.21526385346315777 x[8]=0.10805494870734365, w[8]=0.21526385346315777 x[9]=0.31911236892788974, w[9]=0.2051984637212955 x[10]=0.5152486363581541, w[10]=0.18553839747793643 x[11]=0.6872929048116855, w[11]=0.1572031671581936 x[12]=0.827201315069765, w[12]=0.12151857068790312 x[13]=0.9284348836635736, w[13]=0.08015808715976037 x[14]=0.9862838086968123, w[14]=0.03511946033174906 integral(1.0, -1.0..1.0)=1.9999999999999918 x[1]=-0.9879925180204855, w[1]=0.03075324199611479 x[2]=-0.937273392400706, w[2]=0.07036604748810828 x[3]=-0.8482065834104272, w[3]=0.10715922046717204 x[4]=-0.7244177313601701, w[4]=0.13957067792615427 x[5]=-0.5709721726085388, w[5]=0.16626920581699137 x[6]=-0.3941513470775634, w[6]=0.18616100001556224 x[7]=-0.20119409399743451, w[7]=0.19843148532711158 x[8]=0.0, w[8]=0.2025782419255613 x[9]=0.20119409399743451, w[9]=0.19843148532711158 x[10]=0.3941513470775634, w[10]=0.18616100001556224 x[11]=0.5709721726085388, w[11]=0.16626920581699137 x[12]=0.7244177313601701, w[12]=0.13957067792615427 x[13]=0.8482065834104272, w[13]=0.10715922046717204 x[14]=0.937273392400706, w[14]=0.07036604748810828 x[15]=0.9879925180204855, w[15]=0.03075324199611479 integral(1.0, -1.0..1.0)=1.9999999999999905 integral (0.5,1.0) sin(x) dx = 0.33727533740281995 integral (0.5,1.0) sin(x) dx = 0.33728025865871103 integral (0.5,1.0) sin(x) dx = 0.3372802560214835 integral (0.5,1.0) sin(x) dx = 0.33728025602223066 integral (0.5,1.0) sin(x) dx = 0.3372802560222298 integral (0.5,1.0) sin(x) dx = 0.33728025602223066 integral (0.5,1.0) sin(x) dx = 0.3372802560222309 integral (0.5,1.0) sin(x) dx = 0.3372802560222309 integral (0.5,1.0) sin(x) dx = 0.3372802560222297 -cos(1.0)+cos(0.5) = 0.33728025602223294 Maple says 0.3372802560 integral (0.5,5.0) exp(x) dx = 138.6213535253615 integral (0.5,5.0) exp(x) dx = 146.42644151771293 integral (0.5,5.0) exp(x) dx = 146.75690063962443 integral (0.5,5.0) exp(x) dx = 146.76433289636498 integral (0.5,5.0) exp(x) dx = 146.7644368333577 integral (0.5,5.0) exp(x) dx = 146.7644378249716 integral (0.5,5.0) exp(x) dx = 146.76443783183822 integral (0.5,5.0) exp(x) dx = 146.76443783187455 integral (0.5,5.0) exp(x) dx = 146.7644378318743 exp(5.0)-exp(0.5) = 146.76443783187648 Maple says 146.7644378 integral (0.5,5.0) mess(x) dx = 3.135650701170534E11 integral (0.5,5.0) mess(x) dx = 3.338754414818903E14 integral (0.5,5.0) mess(x) dx = 8.299765803378176E15 integral (0.5,5.0) mess(x) dx = 4.2026882013805928E16 integral (0.5,5.0) mess(x) dx = 1.00860131815889264E17 integral (0.5,5.0) mess(x) dx = 1.64709518288182112E17 integral (0.5,5.0) mess(x) dx = 2.17390643607271136E17 integral (0.5,5.0) mess(x) dx = 2.53750719708526048E17 integral (0.5,5.0) mess(x) dx = 2.7573621422540656E17 integral (0.5,5.0) mess(x) dx = 2.876650341438408E17 integral (0.5,5.0) mess(x) dx = 2.9355491094555046E17 integral (0.5,5.0) mess(x) dx = 2.962262824723401E17 integral (0.5,5.0) mess(x) dx = 2.9734699688922963E17 integral (0.5,5.0) mess(x) dx = 2.9778429559325523E17 integral (0.5,5.0) mess(x) dx = 2.9794372483707981E17 integral (0.5,5.0) mess(x) dx = 2.9799824570457549E17 integral (0.5,5.0) mess(x) dx = 2.9801579453112448E17 integral (0.5,5.0) mess(x) dx = 2.9802112718969357E17 integral (0.5,5.0) mess(x) dx = 2.980226612275849E17 integral (0.5,5.0) mess(x) dx = 2.9802308002182432E17 integral (0.5,5.0) mess(x) dx = 2.9802318876946918E17 integral (0.5,5.0) mess(x) dx = 2.9802321568454925E17 integral (0.5,5.0) mess(x) dx = 2.9802322204606118E17 integral (0.5,5.0) mess(x) dx = 2.9802322348446931E17 integral (0.5,5.0) mess(x) dx = 2.9802322379612653E17 integral (0.5,5.0) mess(x) dx = 2.9802322386094227E17 integral (0.5,5.0) mess(x) dx = 2.9802322387388614E17 integral (0.5,5.0) mess(x) dx = 2.9802322387637837E17 integral (0.5,5.0) mess(x) dx = 2.9802322387683904E17 ((5.0**5.0)**5.0)-(0.5**0.5)**0.5 = 2.9802322387695315E17 Maple says 2.980232239E17 Done.