test gauleg.for on interval -1.0 to 1.0 ordinates, weights x( 1 )= 0.000000000000000 w( 1 )= 2.00000000000000 sum= 2.00000000000000 x( 1 )= -0.577350269189626 w( 1 )= 1.00000000000000 x( 2 )= 0.577350269189626 w( 2 )= 1.00000000000000 sum= 2.00000000000000 x( 1 )= -0.774596669241483 w( 1 )= 0.555555555555553 x( 2 )= 0.000000000000000 w( 2 )= 0.888888888888889 x( 3 )= 0.774596669241483 w( 3 )= 0.555555555555553 sum= 1.99999999999999 x( 1 )= -0.861136311594053 w( 1 )= 0.347854845137448 x( 2 )= -0.339981043584856 w( 2 )= 0.652145154862546 x( 3 )= 0.339981043584856 w( 3 )= 0.652145154862546 x( 4 )= 0.861136311594053 w( 4 )= 0.347854845137448 sum= 1.99999999999999 x( 1 )= -0.906179845938664 w( 1 )= 0.236926885056182 x( 2 )= -0.538469310105683 w( 2 )= 0.478628670499366 x( 3 )= 0.000000000000000 w( 3 )= 0.568888888888889 x( 4 )= 0.538469310105683 w( 4 )= 0.478628670499366 x( 5 )= 0.906179845938664 w( 5 )= 0.236926885056182 sum= 1.99999999999999 x( 1 )= -0.932469514203152 w( 1 )= 0.171324492379163 x( 2 )= -0.661209386466264 w( 2 )= 0.360761573048139 x( 3 )= -0.238619186083197 w( 3 )= 0.467913934572689 x( 4 )= 0.238619186083197 w( 4 )= 0.467913934572689 x( 5 )= 0.661209386466264 w( 5 )= 0.360761573048139 x( 6 )= 0.932469514203152 w( 6 )= 0.171324492379163 sum= 1.99999999999998 x( 1 )= -0.949107912342758 w( 1 )= 0.129484966168863 x( 2 )= -0.741531185599394 w( 2 )= 0.279705391489277 x( 3 )= -0.405845151377397 w( 3 )= 0.381830050505119 x( 4 )= 0.000000000000000 w( 4 )= 0.417959183673469 x( 5 )= 0.405845151377397 w( 5 )= 0.381830050505119 x( 6 )= 0.741531185599394 w( 6 )= 0.279705391489277 x( 7 )= 0.949107912342758 w( 7 )= 0.129484966168863 sum= 1.99999999999999 x( 1 )= -0.960289856497536 w( 1 )= 0.101228536290371 x( 2 )= -0.796666477413627 w( 2 )= 0.222381034453374 x( 3 )= -0.525532409916329 w( 3 )= 0.313706645877887 x( 4 )= -0.183434642495650 w( 4 )= 0.362683783378362 x( 5 )= 0.183434642495650 w( 5 )= 0.362683783378362 x( 6 )= 0.525532409916329 w( 6 )= 0.313706645877887 x( 7 )= 0.796666477413627 w( 7 )= 0.222381034453374 x( 8 )= 0.960289856497536 w( 8 )= 0.101228536290371 sum= 1.99999999999999 x( 1 )= -0.968160239507626 w( 1 )= 0.0812743883615689 x( 2 )= -0.836031107326636 w( 2 )= 0.180648160694857 x( 3 )= -0.613371432700590 w( 3 )= 0.260610696402936 x( 4 )= -0.324253423403809 w( 4 )= 0.312347077040002 x( 5 )= 0.000000000000000 w( 5 )= 0.330239355001260 x( 6 )= 0.324253423403809 w( 6 )= 0.312347077040002 x( 7 )= 0.613371432700590 w( 7 )= 0.260610696402936 x( 8 )= 0.836031107326636 w( 8 )= 0.180648160694857 x( 9 )= 0.968160239507626 w( 9 )= 0.0812743883615689 sum= 1.99999999999999 x( 1 )= -0.973906528517172 w( 1 )= 0.0666713443086836 x( 2 )= -0.865063366688985 w( 2 )= 0.149451349150581 x( 3 )= -0.679409568299024 w( 3 )= 0.219086362515982 x( 4 )= -0.433395394129247 w( 4 )= 0.269266719309992 x( 5 )= -0.148874338981631 w( 5 )= 0.295524224714753 x( 6 )= 0.148874338981631 w( 6 )= 0.295524224714753 x( 7 )= 0.433395394129247 w( 7 )= 0.269266719309992 x( 8 )= 0.679409568299024 w( 8 )= 0.219086362515982 x( 9 )= 0.865063366688985 w( 9 )= 0.149451349150581 x( 10 )= 0.973906528517172 w( 10 )= 0.0666713443086836 sum= 1.99999999999998 x( 1 )= -0.978228658146057 w( 1 )= 0.0556685671161698 x( 2 )= -0.887062599768095 w( 2 )= 0.125580369464905 x( 3 )= -0.730152005574049 w( 3 )= 0.186290210927734 x( 4 )= -0.519096129206812 w( 4 )= 0.233193764591978 x( 5 )= -0.269543155952345 w( 5 )= 0.262804544510247 x( 6 )= 0.000000000000000 w( 6 )= 0.272925086777901 x( 7 )= 0.269543155952345 w( 7 )= 0.262804544510247 x( 8 )= 0.519096129206812 w( 8 )= 0.233193764591978 x( 9 )= 0.730152005574049 w( 9 )= 0.186290210927734 x( 10 )= 0.887062599768095 w( 10 )= 0.125580369464905 x( 11 )= 0.978228658146057 w( 11 )= 0.0556685671161698 sum= 1.99999999999997 x( 1 )= -0.981560634246719 w( 1 )= 0.0471753363865084 x( 2 )= -0.904117256370475 w( 2 )= 0.106939325995318 x( 3 )= -0.769902674194305 w( 3 )= 0.160078328543346 x( 4 )= -0.587317954286617 w( 4 )= 0.203167426723066 x( 5 )= -0.367831498998180 w( 5 )= 0.233492536538355 x( 6 )= -0.125233408511469 w( 6 )= 0.249147045813403 x( 7 )= 0.125233408511469 w( 7 )= 0.249147045813403 x( 8 )= 0.367831498998180 w( 8 )= 0.233492536538355 x( 9 )= 0.587317954286617 w( 9 )= 0.203167426723066 x( 10 )= 0.769902674194305 w( 10 )= 0.160078328543346 x( 11 )= 0.904117256370475 w( 11 )= 0.106939325995318 x( 12 )= 0.981560634246719 w( 12 )= 0.0471753363865084 sum= 1.99999999999999 x( 1 )= -0.984183054718588 w( 1 )= 0.0404840047653125 x( 2 )= -0.917598399222978 w( 2 )= 0.0921214998377285 x( 3 )= -0.801578090733310 w( 3 )= 0.138873510219787 x( 4 )= -0.642349339440340 w( 4 )= 0.178145980761946 x( 5 )= -0.448492751036447 w( 5 )= 0.207816047536888 x( 6 )= -0.230458315955135 w( 6 )= 0.226283180262897 x( 7 )= 0.000000000000000 w( 7 )= 0.232551553230874 x( 8 )= 0.230458315955135 w( 8 )= 0.226283180262897 x( 9 )= 0.448492751036447 w( 9 )= 0.207816047536888 x( 10 )= 0.642349339440340 w( 10 )= 0.178145980761946 x( 11 )= 0.801578090733310 w( 11 )= 0.138873510219787 x( 12 )= 0.917598399222978 w( 12 )= 0.0921214998377285 x( 13 )= 0.984183054718588 w( 13 )= 0.0404840047653125 sum= 1.99999999999999 x( 1 )= -0.986283808696812 w( 1 )= 0.0351194603317491 x( 2 )= -0.928434883663574 w( 2 )= 0.0801580871597602 x( 3 )= -0.827201315069765 w( 3 )= 0.121518570687903 x( 4 )= -0.687292904811685 w( 4 )= 0.157203167158194 x( 5 )= -0.515248636358154 w( 5 )= 0.185538397477936 x( 6 )= -0.319112368927890 w( 6 )= 0.205198463721296 x( 7 )= -0.108054948707344 w( 7 )= 0.215263853463158 x( 8 )= 0.108054948707344 w( 8 )= 0.215263853463158 x( 9 )= 0.319112368927890 w( 9 )= 0.205198463721296 x( 10 )= 0.515248636358154 w( 10 )= 0.185538397477936 x( 11 )= 0.687292904811685 w( 11 )= 0.157203167158194 x( 12 )= 0.827201315069765 w( 12 )= 0.121518570687903 x( 13 )= 0.928434883663574 w( 13 )= 0.0801580871597602 x( 14 )= 0.986283808696812 w( 14 )= 0.0351194603317491 sum= 1.99999999999999 x( 1 )= -0.987992518020485 w( 1 )= 0.0307532419961149 x( 2 )= -0.937273392400706 w( 2 )= 0.0703660474881081 x( 3 )= -0.848206583410427 w( 3 )= 0.107159220467172 x( 4 )= -0.724417731360170 w( 4 )= 0.139570677926154 x( 5 )= -0.570972172608539 w( 5 )= 0.166269205816992 x( 6 )= -0.394151347077563 w( 6 )= 0.186161000015562 x( 7 )= -0.201194093997435 w( 7 )= 0.198431485327112 x( 8 )= 0.000000000000000 w( 8 )= 0.202578241925561 x( 9 )= 0.201194093997435 w( 9 )= 0.198431485327112 x( 10 )= 0.394151347077563 w( 10 )= 0.186161000015562 x( 11 )= 0.570972172608539 w( 11 )= 0.166269205816992 x( 12 )= 0.724417731360170 w( 12 )= 0.139570677926154 x( 13 )= 0.848206583410427 w( 13 )= 0.107159220467172 x( 14 )= 0.937273392400706 w( 14 )= 0.0703660474881081 x( 15 )= 0.987992518020485 w( 15 )= 0.0307532419961149 sum= 1.99999999999999 test gauleg on integral(sin(x), 0.500000000000000 .. 1.00000000000000 ) 2 integral (0.5,1.0) sin(x) dx = 0.337275337402820 3 integral (0.5,1.0) sin(x) dx = 0.337280258658711 4 integral (0.5,1.0) sin(x) dx = 0.337280256021483 5 integral (0.5,1.0) sin(x) dx = 0.337280256022231 6 integral (0.5,1.0) sin(x) dx = 0.337280256022230 7 integral (0.5,1.0) sin(x) dx = 0.337280256022231 8 integral (0.5,1.0) sin(x) dx = 0.337280256022231 9 integral (0.5,1.0) sin(x) dx = 0.337280256022231 10 integral (0.5,1.0) sin(x) dx = 0.337280256022230 Maple says 0.3372802560 test gauleg on integral(exp(x), 0.500000000000000 .. 5.00000000000000 ) 2 integral (0.5,5.0) exp(x) dx = 138.621353525362 3 integral (0.5,5.0) exp(x) dx = 146.426441517713 4 integral (0.5,5.0) exp(x) dx = 146.756900639624 5 integral (0.5,5.0) exp(x) dx = 146.764332896365 6 integral (0.5,5.0) exp(x) dx = 146.764436833358 7 integral (0.5,5.0) exp(x) dx = 146.764437824972 8 integral (0.5,5.0) exp(x) dx = 146.764437831838 9 integral (0.5,5.0) exp(x) dx = 146.764437831875 10 integral (0.5,5.0) exp(x) dx = 146.764437831875 11 integral (0.5,5.0) exp(x) dx = 146.764437831874 12 integral (0.5,5.0) exp(x) dx = 146.764437831875 13 integral (0.5,5.0) exp(x) dx = 146.764437831875 14 integral (0.5,5.0) exp(x) dx = 146.764437831875 15 integral (0.5,5.0) exp(x) dx = 146.764437831875 Maple says 146.7644378 test gauleg on integral(mess(x), 0.500000000000000 .. 5.00000000000000 ) 2 integral (0.5,5.0) mess(x) dx = 3.13565070117053E+11 3 integral (0.5,5.0) mess(x) dx = 3.33875441481890E+14 4 integral (0.5,5.0) mess(x) dx = 8.29976580337804E+15 5 integral (0.5,5.0) mess(x) dx = 4.20268820138059E+16 6 integral (0.5,5.0) mess(x) dx = 1.00860131815889E+17 7 integral (0.5,5.0) mess(x) dx = 1.64709518288182E+17 8 integral (0.5,5.0) mess(x) dx = 2.17390643607277E+17 9 integral (0.5,5.0) mess(x) dx = 2.53750719708527E+17 10 integral (0.5,5.0) mess(x) dx = 2.75736214225415E+17 11 integral (0.5,5.0) mess(x) dx = 2.87665034143842E+17 12 integral (0.5,5.0) mess(x) dx = 2.93554910945554E+17 13 integral (0.5,5.0) mess(x) dx = 2.96226282472342E+17 14 integral (0.5,5.0) mess(x) dx = 2.97346996889230E+17 15 integral (0.5,5.0) mess(x) dx = 2.97784295593256E+17 16 integral (0.5,5.0) mess(x) dx = 2.97943724837075E+17 17 integral (0.5,5.0) mess(x) dx = 2.97998245704575E+17 18 integral (0.5,5.0) mess(x) dx = 2.98015794531122E+17 19 integral (0.5,5.0) mess(x) dx = 2.98021127189697E+17 20 integral (0.5,5.0) mess(x) dx = 2.98022661227586E+17 21 integral (0.5,5.0) mess(x) dx = 2.98023080021823E+17 22 integral (0.5,5.0) mess(x) dx = 2.98023188769469E+17 23 integral (0.5,5.0) mess(x) dx = 2.98023215684548E+17 24 integral (0.5,5.0) mess(x) dx = 2.98023222046057E+17 25 integral (0.5,5.0) mess(x) dx = 2.98023223484466E+17 26 integral (0.5,5.0) mess(x) dx = 2.98023223796129E+17 27 integral (0.5,5.0) mess(x) dx = 2.98023223860937E+17 28 integral (0.5,5.0) mess(x) dx = 2.98023223873887E+17 29 integral (0.5,5.0) mess(x) dx = 2.98023223876384E+17 30 integral (0.5,5.0) mess(x) dx = 2.98023223876840E+17 mess(x) = ((x^x)^x)*(x*(log(x)+1)+x*log(x))) Maple says 2.980232239E+17 Done.