Tables of Modified Gaussian Quadrature Nodes and Weights ======================================================== 10 Point Gauss-Legendre Rule for integrals of the form $\int_{-1}^{1}f(x) \, dx$ NODES & WEIGHTS \\ -9.739065285171716e-01 & 6.667134430868814e-02 \\ -8.650633666889845e-01 & 1.494513491505806e-01 \\ -6.794095682990244e-01 & 2.190863625159820e-01 \\ -4.333953941292472e-01 & 2.692667193099963e-01 \\ -1.488743389816312e-01 & 2.955242247147529e-01 \\ 1.488743389816312e-01 & 2.955242247147529e-01 \\ 4.333953941292472e-01 & 2.692667193099963e-01 \\ 6.794095682990244e-01 & 2.190863625159820e-01 \\ 8.650633666889845e-01 & 1.494513491505806e-01 \\ 9.739065285171716e-01 & 6.667134430868814e-02 \\ ======================================================== 20 point quadrature rule for integrals of the form $\int_{-1}^{1}f(x) + g(x) \log|x_{1} - x| \, dx$ where $x_{1}$ is a Gauss-Legendre node NODES & WEIGHTS \\ -9.981629455677877e-01 & 4.550772157144354e-03 \\ -9.915520723139890e-01 & 8.062764683328619e-03 \\ -9.832812993252168e-01 & 7.845621096866406e-03 \\ -9.767801773920733e-01 & 4.375212351185101e-03 \\ -9.717169387169078e-01 & 1.021414662954223e-02 \\ -9.510630103726074e-01 & 3.157199356768625e-02 \\ -9.075765988474132e-01 & 5.592493151946541e-02 \\ -8.382582352569804e-01 & 8.310260847601852e-02 \\ -7.408522006801963e-01 & 1.118164522164500e-01 \\ -6.147619568252419e-01 & 1.401105427713687e-01 \\ -4.615244999958006e-01 & 1.657233639623953e-01 \\ -2.849772954295424e-01 & 1.863566566231937e-01 \\ -9.117593460489747e-02 & 1.999093145144455e-01 \\ 1.119089520342051e-01 & 2.046841584582030e-01 \\ 3.148842536644393e-01 & 1.995580161940930e-01 \\ 5.075733846631832e-01 & 1.841025430283230e-01 \\ 6.797470718157004e-01 & 1.586456191174843e-01 \\ 8.218833662202629e-01 & 1.242680229936124e-01 \\ 9.258924858821892e-01 & 8.273794370795576e-02 \\ 9.857595961761246e-01 & 3.643931593123844e-02 \\ ======================================================== 20 point quadrature rule for integrals of the form $\int_{-1}^{1}f(x) + g(x) \log|x_{2} - x| \, dx$, where $x_{2}$ is a Gauss-Legendre node NODES & WEIGHTS \\ -9.954896691005256e-01 & 1.141744473788874e-02 \\ -9.775532683688947e-01 & 2.368593568061651e-02 \\ -9.500346715183706e-01 & 3.027205199814611e-02 \\ -9.192373372373420e-01 & 3.021809354380292e-02 \\ -8.916563772395616e-01 & 2.397183723558556e-02 \\ -8.727728136507039e-01 & 1.253574079839078e-02 \\ -8.607963163061316e-01 & 2.070840476545303e-02 \\ -8.201318720954396e-01 & 6.080709508468810e-02 \\ -7.394732321355052e-01 & 1.002402801599464e-01 \\ -6.204853512352519e-01 & 1.371499151597280e-01 \\ -4.667290485167077e-01 & 1.693838059093582e-01 \\ -2.840823320902124e-01 & 1.945292086962893e-01 \\ -8.079364608026202e-02 & 2.103223087093422e-01 \\ 1.328455136645940e-01 & 2.149900928447852e-01 \\ 3.451233500669768e-01 & 2.074984762344433e-01 \\ 5.437321547508867e-01 & 1.877085225595498e-01 \\ 7.167077216635750e-01 & 1.564543949958065e-01 \\ 8.534299232009863e-01 & 1.156104890379952e-01 \\ 9.458275339169444e-01 & 6.859369195724087e-02 \\ 9.912353127269481e-01 & 2.390220989094312e-02 \\ ======================================================== 20 point quadrature rule for integrals of the form $\int_{-1}^{1}f(x) + g(x) \log|x_{3} - x| \, dx$, where $x_{3}$ is a Gauss-Legendre node NODES & WEIGHTS \\ -9.930122613589740e-01 & 1.779185041193254e-02 \\ -9.643941806993207e-01 & 3.870503119897836e-02 \\ -9.175869559770760e-01 & 5.371120494602663e-02 \\ -8.596474181980754e-01 & 6.073467932536858e-02 \\ -7.990442708271941e-01 & 5.901993373645797e-02 \\ -7.443700671611690e-01 & 4.905519963921684e-02 \\ -7.031684479828371e-01 & 3.249237036645046e-02 \\ -6.811221147275545e-01 & 1.335394660596527e-02 \\ -6.579449960254029e-01 & 4.151626407911676e-02 \\ -5.949471688137100e-01 & 8.451456165895121e-02 \\ -4.893032793226841e-01 & 1.262522607368499e-01 \\ -3.441659232382107e-01 & 1.628408264966550e-01 \\ -1.665388322404095e-01 & 1.907085686614375e-01 \\ 3.344207582228461e-02 & 2.071802230953481e-01 \\ 2.434356263087524e-01 & 2.105274833603497e-01 \\ 4.498696863725133e-01 & 2.000282912446872e-01 \\ 6.389777518528792e-01 & 1.760212445284564e-01 \\ 7.978632877793501e-01 & 1.399000904426490e-01 \\ 9.155180703268415e-01 & 9.402669072995991e-02 \\ 9.837258757826489e-01 & 4.161927873514264e-02 \\ ======================================================== 20 point quadrature rule for integrals of the form $\int_{-1}^{1}f(x) + g(x) \log|x_{4} - x| \, dx$, where $x_{4}$ is a Gauss-Legendre node NODES & WEIGHTS \\ -9.903478871133073e-01 & 2.462513260640712e-02 \\ -9.504025146897784e-01 & 5.449201732062665e-02 \\ -8.834986023815121e-01 & 7.799498604905293e-02 \\ -7.974523551287549e-01 & 9.241688894090601e-02 \\ -7.022255002503461e-01 & 9.619882322938848e-02 \\ -6.087194789244920e-01 & 8.902783806614303e-02 \\ -5.275278952351541e-01 & 7.181973054766198e-02 \\ -4.677586540799037e-01 & 4.663017060126023e-02 \\ -4.360689210457623e-01 & 1.794303974050253e-02 \\ -4.121945474875853e-01 & 4.061799823415495e-02 \\ -3.494226766911471e-01 & 8.507517518447759e-02 \\ -2.425993523586304e-01 & 1.277525783357134e-01 \\ -9.646839923908594e-02 & 1.628510773009247e-01 \\ 7.921243716767302e-02 & 1.863323765408308e-01 \\ 2.715178194484646e-01 & 1.958227701927855e-01 \\ 4.658440358656903e-01 & 1.903138548150517e-01 \\ 6.472213975763533e-01 & 1.700731513381802e-01 \\ 8.015601619414859e-01 & 1.365784674773513e-01 \\ 9.168056007307982e-01 & 9.239595239693155e-02 \\ 9.839468743284722e-01 & 4.103797108164931e-02 \\ ======================================================== 20 point quadrature rule for integrals of the form $\int_{-1}^{1}f(x) + g(x) \log|x_{5} - x| \, dx$, where $x_{5}$ is a Gauss-Legendre node NODES & WEIGHTS \\ -9.883561797860961e-01 & 2.974603958509255e-02 \\ -9.398305159297058e-01 & 6.657945456889164e-02 \\ -8.572399919019390e-01 & 9.731775484182564e-02 \\ -7.482086250804679e-01 & 1.190433988432928e-01 \\ -6.228514167093102e-01 & 1.297088242013777e-01 \\ -4.928317114329241e-01 & 1.282900896966494e-01 \\ -3.702771193724617e-01 & 1.148917968875341e-01 \\ -2.666412108172461e-01 & 9.074932908233864e-02 \\ -1.916083010783277e-01 & 5.818196361216740e-02 \\ -1.521937160593461e-01 & 2.224697059733435e-02 \\ -1.233125650067164e-01 & 4.788826761346366e-02 \\ -5.257959675044444e-02 & 9.237500180593534e-02 \\ 5.877314311857769e-02 & 1.287410543031414e-01 \\ 2.012559739993003e-01 & 1.541960911507042e-01 \\ 3.627988191760868e-01 & 1.665885274544506e-01 \\ 5.297121321076323e-01 & 1.648585116745725e-01 \\ 6.878399330187783e-01 & 1.491408089644010e-01 \\ 8.237603202215137e-01 & 1.207592726093190e-01 \\ 9.259297297557394e-01 & 8.212177982524418e-02 \\ 9.856881498392895e-01 & 3.657506268226379e-02 \\ ======================================================== 20 point quadrature rule for integrals of the form $\int_{-1}^{1}f(x) + g(x) \log|x_6 - x| \, dx$, where $x_{6}$ is a Gauss-Legendre node NODES & WEIGHTS \\ -9.856881498392895e-01 & 3.657506268226379e-02 \\ -9.259297297557394e-01 & 8.212177982524418e-02 \\ -8.237603202215137e-01 & 1.207592726093190e-01 \\ -6.878399330187783e-01 & 1.491408089644010e-01 \\ -5.297121321076323e-01 & 1.648585116745725e-01 \\ -3.627988191760868e-01 & 1.665885274544506e-01 \\ -2.012559739993003e-01 & 1.541960911507042e-01 \\ -5.877314311857769e-02 & 1.287410543031414e-01 \\ 5.257959675044444e-02 & 9.237500180593534e-02 \\ 1.233125650067164e-01 & 4.788826761346366e-02 \\ 1.521937160593461e-01 & 2.224697059733435e-02 \\ 1.916083010783277e-01 & 5.818196361216740e-02 \\ 2.666412108172461e-01 & 9.074932908233864e-02 \\ 3.702771193724617e-01 & 1.148917968875341e-01 \\ 4.928317114329241e-01 & 1.282900896966494e-01 \\ 6.228514167093102e-01 & 1.297088242013777e-01 \\ 7.482086250804679e-01 & 1.190433988432928e-01 \\ 8.572399919019390e-01 & 9.731775484182564e-02 \\ 9.398305159297058e-01 & 6.657945456889164e-02 \\ 9.883561797860961e-01 & 2.974603958509255e-02 \\ ======================================================== 20 point quadrature rule for integrals of the form $\int_{-1}^{1}f(x) + g(x) \log|x_{7} - x| \, dx$, where $x_{7}$ is a Gauss-Legendre node NODES & WEIGHTS \\ -9.839468743284722e-01 & 4.103797108164931e-02 \\ -9.168056007307982e-01 & 9.239595239693155e-02 \\ -8.015601619414859e-01 & 1.365784674773513e-01 \\ -6.472213975763533e-01 & 1.700731513381802e-01 \\ -4.658440358656903e-01 & 1.903138548150517e-01 \\ -2.715178194484646e-01 & 1.958227701927855e-01 \\ -7.921243716767302e-02 & 1.863323765408308e-01 \\ 9.646839923908594e-02 & 1.628510773009247e-01 \\ 2.425993523586304e-01 & 1.277525783357134e-01 \\ 3.494226766911471e-01 & 8.507517518447759e-02 \\ 4.121945474875853e-01 & 4.061799823415495e-02 \\ 4.360689210457623e-01 & 1.794303974050253e-02 \\ 4.677586540799037e-01 & 4.663017060126023e-02 \\ 5.275278952351541e-01 & 7.181973054766198e-02 \\ 6.087194789244920e-01 & 8.902783806614303e-02 \\ 7.022255002503461e-01 & 9.619882322938848e-02 \\ 7.974523551287549e-01 & 9.241688894090601e-02 \\ 8.834986023815121e-01 & 7.799498604905293e-02 \\ 9.504025146897784e-01 & 5.449201732062665e-02 \\ 9.903478871133073e-01 & 2.462513260640712e-02 \\ ======================================================== 20 point quadrature rule for integrals of the form $\int_{-1}^{1}f(x) + g(x) \log|x_{8} - x| \, dx$,where $x_{8}$ is a Gauss-Legendre node NODES & WEIGHTS \\ -9.837258757826489e-01 & 4.161927873514264e-02 \\ -9.155180703268415e-01 & 9.402669072995991e-02 \\ -7.978632877793501e-01 & 1.399000904426490e-01 \\ -6.389777518528792e-01 & 1.760212445284564e-01 \\ -4.498696863725133e-01 & 2.000282912446872e-01 \\ -2.434356263087524e-01 & 2.105274833603497e-01 \\ -3.344207582228461e-02 & 2.071802230953481e-01 \\ 1.665388322404095e-01 & 1.907085686614375e-01 \\ 3.441659232382107e-01 & 1.628408264966550e-01 \\ 4.893032793226841e-01 & 1.262522607368499e-01 \\ 5.949471688137100e-01 & 8.451456165895121e-02 \\ 6.579449960254029e-01 & 4.151626407911676e-02 \\ 6.811221147275545e-01 & 1.335394660596527e-02 \\ 7.031684479828371e-01 & 3.249237036645046e-02 \\ 7.443700671611690e-01 & 4.905519963921684e-02 \\ 7.990442708271941e-01 & 5.901993373645797e-02 \\ 8.596474181980754e-01 & 6.073467932536858e-02 \\ 9.175869559770760e-01 & 5.371120494602663e-02 \\ 9.643941806993207e-01 & 3.870503119897836e-02 \\ 9.930122613589740e-01 & 1.779185041193254e-02 \\ ======================================================== 20 point quadrature rule for integrals of the form $\int_{-1}^{1}f(x) + g(x) \log|x_{9} - x| \, dx$, where $x_{9}$ is a Gauss-Legendre node NODES & WEIGHTS \\ -9.912353127269481e-01 & 2.390220989094312e-02 \\ -9.458275339169444e-01 & 6.859369195724087e-02 \\ -8.534299232009863e-01 & 1.156104890379952e-01 \\ -7.167077216635750e-01 & 1.564543949958065e-01 \\ -5.437321547508867e-01 & 1.877085225595498e-01 \\ -3.451233500669768e-01 & 2.074984762344433e-01 \\ -1.328455136645940e-01 & 2.149900928447852e-01 \\ 8.079364608026202e-02 & 2.103223087093422e-01 \\ 2.840823320902124e-01 & 1.945292086962893e-01 \\ 4.667290485167077e-01 & 1.693838059093582e-01 \\ 6.204853512352519e-01 & 1.371499151597280e-01 \\ 7.394732321355052e-01 & 1.002402801599464e-01 \\ 8.201318720954396e-01 & 6.080709508468810e-02 \\ 8.607963163061316e-01 & 2.070840476545303e-02 \\ 8.727728136507039e-01 & 1.253574079839078e-02 \\ 8.916563772395616e-01 & 2.397183723558556e-02 \\ 9.192373372373420e-01 & 3.021809354380292e-02 \\ 9.500346715183706e-01 & 3.027205199814611e-02 \\ 9.775532683688947e-01 & 2.368593568061651e-02 \\ 9.954896691005256e-01 & 1.141744473788874e-02 \\ ======================================================== 20 point quadrature rule for integrals of the form $\int_{-1}^{1}f(x) + g(x) \log|x_{10} - x| \, dx$, where $x_{10}$ is a Gauss-Legendre node NODES & WEIGHTS \\ -9.857595961761246e-01 & 3.643931593123844e-02 \\ -9.258924858821892e-01 & 8.273794370795576e-02 \\ -8.218833662202629e-01 & 1.242680229936124e-01 \\ -6.797470718157004e-01 & 1.586456191174843e-01 \\ -5.075733846631832e-01 & 1.841025430283230e-01 \\ -3.148842536644393e-01 & 1.995580161940930e-01 \\ -1.119089520342051e-01 & 2.046841584582030e-01 \\ 9.117593460489747e-02 & 1.999093145144455e-01 \\ 2.849772954295424e-01 & 1.863566566231937e-01 \\ 4.615244999958006e-01 & 1.657233639623953e-01 \\ 6.147619568252419e-01 & 1.401105427713687e-01 \\ 7.408522006801963e-01 & 1.118164522164500e-01 \\ 8.382582352569804e-01 & 8.310260847601852e-02 \\ 9.075765988474132e-01 & 5.592493151946541e-02 \\ 9.510630103726074e-01 & 3.157199356768625e-02 \\ 9.717169387169078e-01 & 1.021414662954223e-02 \\ 9.767801773920733e-01 & 4.375212351185101e-03 \\ 9.832812993252168e-01 & 7.845621096866406e-03 \\ 9.915520723139890e-01 & 8.062764683328619e-03 \\ 9.981629455677877e-01 & 4.550772157144354e-03 \\ ======================================================== 24 point quadrature rule for integrals of the form $\int_{0}^{1}f(x) + g(x) \log(x + \bar{x})dx$, where $\bar{x} \ge 10^{-1} $ NODES & WEIGHTS \\ 3.916216329415252e-02 & 4.880755296918116e-02 \\ 8.135233983530081e-02 & 3.196002785163611e-02 \\ 1.123448211344994e-01 & 3.883416642507362e-02 \\ 1.595931983965030e-01 & 5.148898992140820e-02 \\ 2.085759027831349e-01 & 4.219328148763533e-02 \\ 2.426241962027560e-01 & 3.420686213633789e-02 \\ 2.886190312538522e-01 & 5.512488680719239e-02 \\ 3.469021762354675e-01 & 6.007112809843418e-02 \\ 4.072910101569611e-01 & 6.022350479415180e-02 \\ 4.664019722595442e-01 & 5.735022004401478e-02 \\ 5.182120817844112e-01 & 4.167923417118068e-02 \\ 5.501308436771654e-01 & 3.346089628879600e-02 \\ 5.970302980854608e-01 & 5.574716218423796e-02 \\ 6.548457960388209e-01 & 5.847838243344473e-02 \\ 7.119542126106005e-01 & 5.464156990092474e-02 \\ 7.607920420946340e-01 & 4.092186343704961e-02 \\ 7.953017051155684e-01 & 3.283728166050225e-02 \\ 8.303900341517088e-01 & 3.438233273473095e-02 \\ 8.612724919009394e-01 & 3.022585192226418e-02 \\ 8.954049128027080e-01 & 3.700769701277380e-02 \\ 9.315909369155358e-01 & 3.410213679365162e-02 \\ 9.621742249068356e-01 & 2.665791885274193e-02 \\ 9.843663446380599e-01 & 1.754420526360429e-02 \\ 9.970087425823398e-01 & 7.662283104388867e-03 \\ ======================================================== 24 point quadrature rule for integrals of the form $\int_{0}^{1}f(x) + g(x) \log(x + \bar{x})dx$, where $10^{-2} \le \bar{x} \le 10^{-1} $ NODES & WEIGHTS \\ 1.940564616937581e-02 & 2.514022176052795e-02 \\ 4.545433992382339e-02 & 2.703526530535647e-02 \\ 7.378866604396420e-02 & 2.980872487617485e-02 \\ 1.054147718077606e-01 & 3.360626237885489e-02 \\ 1.412997888401000e-01 & 3.829678083416609e-02 \\ 1.822325567811081e-01 & 4.365651045780837e-02 \\ 2.287282121202408e-01 & 4.935846322319046e-02 \\ 2.809170925514041e-01 & 5.495967924055210e-02 \\ 3.384320962237970e-01 & 5.991162198705084e-02 \\ 4.003108031244078e-01 & 6.356960862248889e-02 \\ 4.648605571606025e-01 & 6.506868552467118e-02 \\ 5.290714994276687e-01 & 6.219588235225894e-02 \\ 5.829663557386375e-01 & 3.889986041695310e-02 \\ 6.128301889979477e-01 & 3.573431931940621e-02 \\ 6.606072156240962e-01 & 5.296315368353523e-02 \\ 7.139495966128518e-01 & 5.369033999927759e-02 \\ 7.677830914961244e-01 & 5.340793573367282e-02 \\ 8.187382423336450e-01 & 4.704756013998560e-02 \\ 8.587068551739496e-01 & 3.276576301747068e-02 \\ 8.906873285570645e-01 & 3.449175311880027e-02 \\ 9.267772492129903e-01 & 3.560168848238671e-02 \\ 9.592137652582382e-01 & 2.857367151127661e-02 \\ 9.830962712794008e-01 & 1.894042942442201e-02 \\ 9.967621546194148e-01 & 8.291994770212826e-03 \\ ======================================================== 24 point quadrature rule for integrals of the form $\int_{0}^{1}f(x) + g(x) \log(x + \bar{x})dx$, where $10^{-3} \le \bar{x} \le 10^{-2} $ NODES & WEIGHTS \\ 7.571097817272427e-03 & 9.878088201321919e-03 \\ 1.800655325976786e-02 & 1.109316819462674e-02 \\ 3.003901004577040e-02 & 1.313311581321880e-02 \\ 4.462882147989575e-02 & 1.624262442061470e-02 \\ 6.295732618092606e-02 & 2.065168462990214e-02 \\ 8.644035241970913e-02 & 2.657795406825320e-02 \\ 1.166164809306920e-01 & 3.399052299072427e-02 \\ 1.546690628394902e-01 & 4.208214612865170e-02 \\ 1.999554346680615e-01 & 4.732516974042797e-02 \\ 2.434683359132119e-01 & 3.618419415803922e-02 \\ 2.800846274146029e-01 & 4.547346840583578e-02 \\ 3.368595257878888e-01 & 6.463153575242817e-02 \\ 4.044418359833648e-01 & 6.859104457897808e-02 \\ 4.685002493634456e-01 & 5.589917935916451e-02 \\ 5.185062817085154e-01 & 5.199232318335285e-02 \\ 5.811314144990846e-01 & 7.089840644422261e-02 \\ 6.545700991450585e-01 & 7.427400331494240e-02 \\ 7.276588861478224e-01 & 7.125308736931726e-02 \\ 7.960626077582168e-01 & 6.513697474660338e-02 \\ 8.572037183403355e-01 & 5.682298546820264e-02 \\ 9.091330485015775e-01 & 4.678000924507099e-02 \\ 9.503131649503738e-01 & 3.538488886617123e-02 \\ 9.795718963793163e-01 & 2.299723483013955e-02 \\ 9.961006479199827e-01 & 9.993597414733579e-03 \\ ======================================================== 24 point quadrature rule for integrals of the form $\int_{0}^{1}f(x) + g(x) \log(x + \bar{x})dx$, where $10^{-4} \le \bar{x} \le 10^{-3} $ NODES & WEIGHTS \\ 2.625961371586153e-03 & 3.441901737135120e-03 \\ 6.309383772392260e-03 & 3.978799794732070e-03 \\ 1.073246133489697e-02 & 4.958449505644980e-03 \\ 1.645170499644402e-02 & 6.620822501994994e-03 \\ 2.433800511777796e-02 & 9.385496468197222e-03 \\ 3.582530925992294e-02 & 1.396512052439178e-02 \\ 5.315827372101662e-02 & 2.119383832447796e-02 \\ 7.917327903614484e-02 & 3.124989308824302e-02 \\ 1.162053707416708e-01 & 4.291481168916344e-02 \\ 1.648139164451449e-01 & 5.400832278279924e-02 \\ 2.231934088488800e-01 & 6.197424674301215e-02 \\ 2.864519293820641e-01 & 6.297221626131570e-02 \\ 3.466729491189400e-01 & 5.794981636764223e-02 \\ 4.076175535528108e-01 & 6.650501614478806e-02 \\ 4.800964107543535e-01 & 7.716379373230733e-02 \\ 5.594105009204460e-01 & 8.047814122759604e-02 \\ 6.395390292352857e-01 & 7.917822434973971e-02 \\ 7.167410782176877e-01 & 7.477646096014055e-02 \\ 7.882807127957939e-01 & 6.793424765652059e-02 \\ 8.519356675821297e-01 & 5.906852968947303e-02 \\ 9.058606177202579e-01 & 4.853108558910315e-02 \\ 9.485539755760567e-01 & 3.666228059710319e-02 \\ 9.788566874094059e-01 & 2.380850649522536e-02 \\ 9.959649506960162e-01 & 1.034186239262945e-02 \\ ======================================================== 24 point quadrature rule for integrals of the form $\int_{0}^{1}f(x) + g(x) \log(x + \bar{x})dx$, where $10^{-5} \le \bar{x} \le 10^{-4} $ NODES & WEIGHTS \\ 7.759451679242260e-04 & 1.049591733965263e-03 \\ 1.952854410117286e-03 & 1.314968855711329e-03 \\ 3.429053832116395e-03 & 1.651475072547296e-03 \\ 5.301128540262913e-03 & 2.135645684467029e-03 \\ 7.878118775220067e-03 & 3.165043382856636e-03 \\ 1.205537050949829e-02 & 5.479528688655274e-03 \\ 1.965871512055557e-02 & 1.028817002915096e-02 \\ 3.403328641997047e-02 & 1.923291785614007e-02 \\ 5.947430305925957e-02 & 3.212643438782854e-02 \\ 9.873500543531440e-02 & 4.638626850049229e-02 \\ 1.518862681939413e-01 & 5.960676923068444e-02 \\ 2.171724325134259e-01 & 7.052360405410943e-02 \\ 2.919941878735093e-01 & 7.863451090237836e-02 \\ 3.734637353255530e-01 & 8.381771698595157e-02 \\ 4.586710018443288e-01 & 8.612755554083525e-02 \\ 5.448057416999684e-01 & 8.569938467103264e-02 \\ 6.292158981939618e-01 & 8.271051499695768e-02 \\ 7.094415843889587e-01 & 7.736692567834522e-02 \\ 7.832417328632321e-01 & 6.990012937760461e-02 \\ 8.486194141302759e-01 & 6.056687669667680e-02 \\ 9.038469149367938e-01 & 4.964868706783169e-02 \\ 9.474898150194623e-01 & 3.745026957972177e-02 \\ 9.784290662963747e-01 & 2.429741981889855e-02 \\ 9.958843370550371e-01 & 1.054906616108520e-02 \\ ======================================================== 24 point quadrature rule for integrals of the form $\int_{0}^{1}f(x) + g(x) \log(x + \bar{x})dx$, where $10^{-6} \le \bar{x} \le 10^{-5} $ NODES & WEIGHTS \\ 3.126377187332637e-04 & 4.136479682893960e-04 \\ 7.671264269072188e-04 & 5.068714387414649e-04 \\ 1.359575160544077e-03 & 7.008932527842778e-04 \\ 2.238313285727558e-03 & 1.110264922990352e-03 \\ 3.770276623583326e-03 & 2.120108385941761e-03 \\ 7.146583956092048e-03 & 5.249076343206215e-03 \\ 1.635515250548719e-02 & 1.450809938905405e-02 \\ 3.828062855101241e-02 & 2.987724029376343e-02 \\ 7.628984500206759e-02 & 4.593298717863718e-02 \\ 1.294255336121595e-01 & 5.987634475538021e-02 \\ 1.949876755761554e-01 & 7.065953519392547e-02 \\ 2.693852297828856e-01 & 7.729918562776261e-02 \\ 3.469762441631538e-01 & 7.556635340171830e-02 \\ 4.122748928895491e-01 & 5.234123638339037e-02 \\ 4.662499202239145e-01 & 6.532130125393047e-02 \\ 5.421402737123784e-01 & 8.188272080198840e-02 \\ 6.248832413655412e-01 & 8.237354882288161e-02 \\ 7.053258496784840e-01 & 7.795795664563893e-02 \\ 7.798841313231049e-01 & 7.076514272025076e-02 \\ 8.461534275163378e-01 & 6.145788741452406e-02 \\ 9.022312524979976e-01 & 5.044339641339403e-02 \\ 9.465899812310277e-01 & 3.807817118430632e-02 \\ 9.780549563823810e-01 & 2.471549011101626e-02 \\ 9.958125149101927e-01 & 1.073289672726758e-02 \\ ======================================================== 24 point quadrature rule for integrals of the form $\int_{0}^{1}f(x) + g(x) \log(x + \bar{x})dx$, where $10^{-7} \le \bar{x} \le 10^{-6} $ NODES & WEIGHTS \\ 1.019234906342863e-04 & 1.349775051746596e-04 \\ 2.506087227631447e-04 & 1.663411550150506e-04 \\ 4.461429005344285e-04 & 2.328782111562424e-04 \\ 7.422845421202523e-04 & 3.804721779784063e-04 \\ 1.289196091156456e-03 & 7.930350452911450e-04 \\ 2.739287668024851e-03 & 2.600694722423854e-03 \\ 9.075168969969708e-03 & 1.212249113599252e-02 \\ 2.968005234555358e-02 & 2.946708975720586e-02 \\ 6.781742979962609e-02 & 4.647771960691390e-02 \\ 1.217792474402805e-01 & 6.095376889009233e-02 \\ 1.886625378438471e-01 & 7.224844725827559e-02 \\ 2.650602155844836e-01 & 7.986429603884565e-02 \\ 3.465113608339080e-01 & 8.143206462900546e-02 \\ 4.178374197420536e-01 & 5.040529357007135e-02 \\ 4.597624982511183e-01 & 5.592137651001418e-02 \\ 5.348065111487157e-01 & 8.398073572656715e-02 \\ 6.194640153146728e-01 & 8.402586870225486e-02 \\ 7.013481004172354e-01 & 7.922223490159952e-02 \\ 7.770386175609082e-01 & 7.177919251691964e-02 \\ 8.442211768916794e-01 & 6.227551999401272e-02 \\ 9.010272836291835e-01 & 5.108407212719758e-02 \\ 9.459409782755001e-01 & 3.854783279333592e-02 \\ 9.777905486554876e-01 & 2.501496650831813e-02 \\ 9.957622871041650e-01 & 1.086176801402067e-02 \\ ======================================================== 24 point quadrature rule for integrals of the form $\int_{0}^{1}f(x) + g(x) \log(x + \bar{x})dx$, where $10^{-8} \le \bar{x} \le 10^{-7} $ NODES & WEIGHTS \\ 3.421721832247593e-05 & 4.559730842497453e-05 \\ 8.533906255442380e-05 & 5.840391255974745e-05 \\ 1.563524616155011e-04 & 8.761580900682040e-05 \\ 2.746612401575526e-04 & 1.617264666294872e-04 \\ 5.408643931265062e-04 & 4.433543035169213e-04 \\ 1.782382096488333e-03 & 3.116175111368442e-03 \\ 1.101243912052365e-02 & 1.655494413772595e-02 \\ 3.553172024884285e-02 & 3.242539256461602e-02 \\ 7.554170435463801e-02 & 4.734426463929677e-02 \\ 1.295711894941649e-01 & 6.032614603579952e-02 \\ 1.953213037793089e-01 & 7.069975187373848e-02 \\ 2.699680545714222e-01 & 7.806973621204365e-02 \\ 3.503697281371090e-01 & 8.216350598137868e-02 \\ 4.330838596494367e-01 & 8.261286657092808e-02 \\ 5.141801680435878e-01 & 7.883476216668445e-02 \\ 5.895097016206093e-01 & 7.157205125318401e-02 \\ 6.582708672338614e-01 & 6.703064468754417e-02 \\ 7.252543617887320e-01 & 6.706137273719630e-02 \\ 7.914154485613720e-01 & 6.449984116349734e-02 \\ 8.528383935857844e-01 & 5.775434959088197e-02 \\ 9.059696536862878e-01 & 4.812600239023880e-02 \\ 9.484664124578303e-01 & 3.661415869304224e-02 \\ 9.787863313133854e-01 & 2.386304203446463e-02 \\ 9.959482975155097e-01 & 1.038268695581411e-02 \\ ======================================================== 24 point quadrature rule for integrals of the form $\int_{0}^{1}f(x) + g(x) \log(x + \bar{x})dx$, where $10^{-9} \le \bar{x} \le 10^{-8} $ NODES & WEIGHTS \\ 6.538987938840374e-06 & 1.500332421093607e-05 \\ 2.613485075847413e-05 & 2.367234654253158e-05 \\ 5.664183720634991e-05 & 4.007286246706405e-05 \\ 1.179374114362569e-04 & 9.497743501485505e-05 \\ 3.299119431334128e-04 & 4.619067037944727e-04 \\ 3.626828607577001e-03 & 9.985382463808036e-03 \\ 2.265102906572155e-02 & 2.805741744607257e-02 \\ 5.896796231680340e-02 & 4.404106103008398e-02 \\ 1.092496277855923e-01 & 5.548413172821072e-02 \\ 1.666701689499393e-01 & 5.693235996372726e-02 \\ 2.196889385898800e-01 & 5.087307376046002e-02 \\ 2.770352260035617e-01 & 6.593729718379782e-02 \\ 3.483163928268329e-01 & 7.335680008972614e-02 \\ 4.153287664837260e-01 & 5.675029500743735e-02 \\ 4.695624219668608e-01 & 6.117926027541254e-02 \\ 5.421129318998841e-01 & 8.004805067067550e-02 \\ 6.238832212055707e-01 & 8.196991767042605e-02 \\ 7.041842972237081e-01 & 7.800219127200407e-02 \\ 7.788817007552110e-01 & 7.097175077519494e-02 \\ 8.453877637047045e-01 & 6.171193295041172e-02 \\ 9.017178251963006e-01 & 5.068671319716005e-02 \\ 9.462999385952402e-01 & 3.827738423897266e-02 \\ 9.779333485180249e-01 & 2.485063762733620e-02 \\ 9.957890687155009e-01 & 1.079284973329516e-02 \\ ======================================================== 24 point quadrature rule for integrals of the form $\int_{0}^{1}f(x) + g(x) \log(x + \bar{x})dx$, where $10^{-10} \le \bar{x} \le 10^{-9} $ NODES & WEIGHTS \\ 6.725520559705825e-06 & 8.128391913974039e-05 \\ 6.986424152770461e-06 & -7.773900735768282e-05\\ 1.217363416714366e-05 & 1.287386499666193e-05 \\ 2.677746219601529e-05 & 1.895577251914526e-05 \\ 5.597036348896741e-05 & 4.732580352158076e-05 \\ 2.729343280943077e-04 & 9.857909615386162e-04 \\ 9.445526806263141e-03 & 1.756872897270054e-02 \\ 3.556725025161542e-02 & 3.439422017906772e-02 \\ 7.765556668177810e-02 & 4.944188361792970e-02 \\ 1.336848150648662e-01 & 6.219733934997792e-02 \\ 2.011576917683550e-01 & 7.228007436918939e-02 \\ 2.772736854314979e-01 & 7.944986391225688e-02 \\ 3.590124362607926e-01 & 8.347646288178011e-02 \\ 4.430074035214462e-01 & 8.380433020121207e-02 \\ 5.247388219574510e-01 & 7.832768209682506e-02 \\ 5.961053238782420e-01 & 6.300796225242940e-02 \\ 6.547331131213409e-01 & 5.923406014585053e-02 \\ 7.192258519628951e-01 & 6.834293563803810e-02 \\ 7.874251789073102e-01 & 6.660337204499726e-02 \\ 8.505852012775045e-01 & 5.911988751082552e-02 \\ 9.047824617894323e-01 & 4.893575310568894e-02 \\ 9.479045131744448e-01 & 3.708256438629509e-02 \\ 9.785770588866582e-01 & 2.411463784693618e-02 \\ 9.959104692340199e-01 & 1.048087156697020e-02 \\ ======================================================== 24 point quadrature rule for integrals of the form $\int_{0}^{1}f(x) + g(x) \log(x + \bar{x})dx$, where $10^{-11} \le \bar{x} \le 10^{-10} $ NODES & WEIGHTS \\ 2.828736694877886e-08 & 1.665602686704325e-05 \\ 2.302233157554212e-06 & 2.577419924039251e-06 \\ 5.853587143444178e-06 & 4.957941112780975e-06 \\ 1.451588770083244e-05 & 1.537074702915107e-05 \\ 9.711965099273031e-05 & 4.640075239797995e-04 \\ 9.004761967373848e-03 & 1.705687938176189e-02 \\ 3.442077924035546e-02 & 3.349724914160473e-02 \\ 7.543926781582543e-02 & 4.820210872119093e-02 \\ 1.300373356318913e-01 & 6.054547286337976e-02 \\ 1.955182772803384e-01 & 6.984354388121057e-02 \\ 2.683608546664295e-01 & 7.498721497014774e-02 \\ 3.430029178740901e-01 & 7.240620145057083e-02 \\ 4.085056107803621e-01 & 5.774925310174693e-02 \\ 4.660198270439085e-01 & 6.238505554837956e-02 \\ 5.336124745634699e-01 & 6.940394677081842e-02 \\ 5.985245800106473e-01 & 5.910843483407385e-02 \\ 6.564089719608276e-01 & 6.059752321454190e-02 \\ 7.216666024232565e-01 & 6.823362237770209e-02 \\ 7.893712241343741e-01 & 6.593839664071163e-02 \\ 8.518883782001418e-01 & 5.853014420243146e-02 \\ 9.055688088881344e-01 & 4.849217100974983e-02 \\ 9.483163097840529e-01 & 3.677417821170115e-02 \\ 9.787413692715607e-01 & 2.392585642844202e-02 \\ 9.959413203611228e-01 & 1.040149939671874e-02 \\ ======================================================== 24 point quadrature rule for integrals of the form $\int_{0}^{1}f(x) + g(x) \log(x + \bar{x})dx$, where $10^{-12} \le \bar{x} \le 10^{-11} $ NODES & WEIGHTS \\ 6.147063879573664e-07 & 8.763741095000331e-07 \\ 2.102921984985835e-06 & 1.784696796288373e-05 \\ 2.188366117432289e-06 & -1.795398395983826e-05\\ 3.482602942694880e-06 & 5.117514567175025e-06 \\ 2.768001888608636e-05 & 1.698863549284390e-04 \\ 8.942779215792784e-03 & 1.701975216672032e-02 \\ 3.432218364237253e-02 & 3.346025972593909e-02 \\ 7.530931328026620e-02 & 4.817949622196712e-02 \\ 1.298983048592572e-01 & 6.055152664710045e-02 \\ 1.954020797117703e-01 & 6.988313730886592e-02 \\ 2.682970870436427e-01 & 7.504602275463067e-02 \\ 3.429540704041702e-01 & 7.230942674874111e-02 \\ 4.080399755202422e-01 & 5.705952259766429e-02 \\ 4.652562798154792e-01 & 6.265021180818162e-02 \\ 5.333220999210325e-01 & 6.993669694523695e-02 \\ 5.986982369433125e-01 & 5.937130986945129e-02 \\ 6.564773600603511e-01 & 6.026572020863567e-02 \\ 7.215159032030418e-01 & 6.815292696374753e-02 \\ 7.892098210760941e-01 & 6.596804590657802e-02 \\ 8.517672777806986e-01 & 5.857483758149194e-02 \\ 9.054906995605498e-01 & 4.853209199396977e-02 \\ 9.482736017320823e-01 & 3.680469214176019e-02 \\ 9.787238593479314e-01 & 2.394561701705853e-02 \\ 9.959379852805677e-01 & 1.041005152890511e-02 \\ ======================================================== 24 point quadrature rule for integrals of the form $\int_{0}^{1}f(x) + g(x) \log(x + \bar{x})dx$, where $10^{-13} \le \bar{x} \le 10^{-12} $ NODES & WEIGHTS \\ 4.523740015216508e-08 & 4.418138082366788e-07 \\ 4.281855233588279e-07 & 4.389108058643120e-07 \\ 1.036900153156159e-06 & 9.539585150737866e-07 \\ 7.825849325746907e-06 & 5.823980947200484e-05 \\ 8.617419723953112e-03 & 1.634464263521301e-02 \\ 3.268881163637599e-02 & 3.129682188728318e-02 \\ 6.988441391437043e-02 & 4.212468617589480e-02 \\ 1.142202307676442e-01 & 4.505120897719191e-02 \\ 1.596471081833281e-01 & 4.769069780026684e-02 \\ 2.135336418959620e-01 & 6.038503382768951e-02 \\ 2.781100275296151e-01 & 6.695343672694180e-02 \\ 3.433392803364457e-01 & 6.163298712826237e-02 \\ 4.019960595528027e-01 & 5.877742624357513e-02 \\ 4.656415679416787e-01 & 6.800053637773440e-02 \\ 5.334880548894250e-01 & 6.516918103589647e-02 \\ 5.943298528903542e-01 & 5.853785375926075e-02 \\ 6.562968737815924e-01 & 6.639396325654251e-02 \\ 7.250343344601498e-01 & 6.948738324081696e-02 \\ 7.928820737781136e-01 & 6.538801703374268e-02 \\ 8.546103048745466e-01 & 5.761503751629250e-02 \\ 9.073762310762705e-01 & 4.761344859555310e-02 \\ 9.493253659835347e-01 & 3.607033097268266e-02 \\ 9.791606801267259e-01 & 2.345690720840071e-02 \\ 9.960217573957566e-01 & 1.019557402722854e-02 \\ ======================================================== 24 point quadrature rule for integrals of the form $\int_{0}^{1}f(x) + g(x) \log(x + \bar{x})dx$, where $10^{-14} \le \bar{x} \le 10^{-13} $ NODES & WEIGHTS \\ 6.025980282801020e-08 & 9.079353616441234e-07 \\ 6.411245262925473e-08 & -8.390389042773805e-07\\ 1.862815529429129e-07 & 2.782460677485016e-07 \\ 2.029190208906422e-06 & 1.821115881362725e-05 \\ 8.902881307076499e-03 & 1.695809650660321e-02 \\ 3.420089035164912e-02 & 3.336370146025145e-02 \\ 7.508687525931594e-02 & 4.807898681796971e-02 \\ 1.295858123029775e-01 & 6.047672723211479e-02 \\ 1.950409815188335e-01 & 6.986774906175534e-02 \\ 2.679751967812604e-01 & 7.515608233194288e-02 \\ 3.428525062164689e-01 & 7.264249904037610e-02 \\ 4.080941369413548e-01 & 5.672507168477261e-02 \\ 4.646644511900009e-01 & 6.220316364524964e-02 \\ 5.328071517215501e-01 & 7.032362652293805e-02 \\ 5.978508749698001e-01 & 5.742730804758014e-02 \\ 6.521214523350964e-01 & 5.644075454541152e-02 \\ 7.134921670665336e-01 & 6.318643666150391e-02 \\ 7.679317896479284e-01 & 3.945995610428228e-02 \\ 8.029718487208403e-01 & 4.324200884758527e-02 \\ 8.551101435866935e-01 & 5.478223695609097e-02 \\ 9.067319102017767e-01 & 4.740856250832772e-02 \\ 9.487765213293372e-01 & 3.633314063504751e-02 \\ 9.788979796532736e-01 & 2.372788917088821e-02 \\ 9.959684838634199e-01 & 1.033036588606145e-02 \\