/* nint_test.mac load nint with default fpprec and default fpprintprec. Then run test via: batch("nint_test.mac",test) */ /* 1 */ nint(x,x,0,1); 0.5; /* 2 */ quad1d(sin(sin(x)),x,0,2); 1.2470560582440029; /* 3 */ quad(cos(cos(x)),x,0,1); 0.65978105360122186; /* 4 */ nint(log(1/x)/sqrt(x),x,0,1); 3.9999999999999973; /* 5 */ mdefint(log(1/x)/sqrt(x),x,0,1); 4; /* 6 */ ndefint(log(1/x)/sqrt(x),x,0,1); 4.0; /* 7 */ ndefint(log(1/x)/sqrt(%i*x),x,0,1); 2.8284271247461903-2.8284271247461903*%i; /* 8 (%i23) quad(log(1/x)/sqrt(%i*x),x,0,1,singular,complex); (%o23) 2.82842712474623-2.828427124746158*%i (%i24) ?print(%)$ ((MPLUS SIMP (1708 "c:/work2/quad1d.mac" SRC $QAGS 1596)) 2.8284271247462298 ((MTIMES SIMP) -2.8284271247461579 $%I)) */ quad(log(1/x)/sqrt(%i*x),x,0,1,singular,complex); 2.8284271247462298-2.8284271247461579*%i; /* 9 */ mdefint(exp(exp(-x)),x,0,5); gamma_incomplete(0,-%e^-5)-gamma_incomplete(0,-1); /* 10 */ ndefint(exp(exp(-x)),x,0,5); 6.3111528374568113; /* 11 */ nint(exp(exp(-x)),x,0,5); 6.3111528374568113; /* 12 */ nint(x^x,x,1,5); 1241.0332840494043; /* 13 */ mdefint(1/(1+x^2),x,0,inf); %pi/2; /* 14 */ nint(1/(1+x^2),x,0,inf); 1.5707963267948966; /* 15 */ mdefint(exp (%i*x^2),x,minf,inf); sqrt(%pi)*(%i/sqrt(2)+1/sqrt(2)); /* 16 */ ndefint(exp (%i*x^2),x,minf,inf); 1.2533141373155003*%i+1.2533141373155003; /* 17 */ nint(exp(%i*x)*exp(-x^2),x,1,inf); 0.12973820125290061*%i+0.034019860790064659; /* 18 */ ndefint(2^(%i*x)*exp(-x^2),x,1,inf); 0.10826106510905262*%i+0.083661720679270316; /* 19 */ quad(2^(%i*x)*exp(-x^2),x,1,inf); 0.10826106510905262*%i+0.083661720679270316; /* 20 */ nint (x,x,0,5); 12.5; /* 21 */ nint(1/sqrt(x),x,0,5); 4.4721359549995778; /* 22 */ nint(sin(x),x,0,5); 0.7163378145367737; /* 23 */ nint(1/sqrt(x),x,0,1); 1.9999999999999996; /* 24 */ nint(1/x^(1/5),x,0,1); 1.25; /* 25 */ nint(1/x^(4/5),x,0,1); 4.9999999999999742; /* 26 */ nint(1/sqrt(1-x),x,0,1); 2.0000000000001306; /* 27 */ nint(1/(1-x)^(1/5),x,0,1); 1.2500000000000009; /* 28 */ nint(1/(1-x)^(4/5),x,0,1); 5.0000000000679909; /* 29 */ nint(log(x),x,0,1); -1.0; /* 30 */ nint(log(log(x)),x,0,1); 3.1415926535897927*%i-0.57721566490005427; /* 31 */ nint(sqrt(log(x)),x,0,1); 0.88622692545258752*%i; /* 32 */ nint (log(x)^2,x,0,1); 1.9999999999999993; /* 33 */ nint(1/(sqrt(1-x)*x^(1/5)),x,0,1); 2.2992878184833088; /* 34 */ nint(1/(sqrt(1-x)*x^(4/5)),x,0,1); 6.2686531232173621; /* 35 */ nint(log(2*x)/sqrt(1-x),x,0,1); 0.15888308336231891; /* 36 */ nint(cos(x),x,1,10^4); -1.1470853736961486; /* 37 */ nint(sin(x),x,1,10^4); 1.4924576741271545; /* 38 */ nint((x-2)^2*sin(4000*x),x,2,3); -1.5862464665268553E-4; /* 39 */ nint(exp(%i*x),x,1,10^4); 1.4924576741271545*%i-1.1470853736961486; /* 40 */ nint(2^(%i*x),x,1,10^4); 0.47915862215533017*%i+0.37574425579319543; /* 41 */ nint(bessel_j(1,x),x,1,10^4,real,strong_osc); 0.77229384691157477; /* 42 */ quad (bessel_j(0,x),x,1,10^4,real,strong_osc); 0.083917750245353973; /* 43 */ quad (bessel_y(2,x),x,1,10^4,strong_osc,real); -0.93245297359761448; /* 44 */ ndefint(bessel_j(1,%i*x),x,1,700); 1.5295933476718737E+302*%i; /* 45 */ quad(bessel_j(1,%i*x),x,1,700,strong_osc); 1.5295933476718754E+302*%i; /* 46 */ quad(bessel_j(1,%i*x),x,1,800,strong_osc); false; /* 47 */ ndefint(bessel_j(1,x),x,1,inf); 0.76519768655796661; /* 48 */ nint(bessel_j(1,x),x,1,inf,real); 0.76519768655796661; /* 49 */ nint(bessel_i(1,%i*x),x,1,10); 1.0111334510093148*%i; /* 50 */ ndefint(bessel_i(2,%i*x),x,1,10); -0.94043657301912076; /* 51 */ quad(bessel_i(2,%i*x),x,1,10); -0.94043657301912331; /* 52 45.5 sec */ nint(bessel_k(2.0,%i*y),y,1,10^4,strong_osc); 1.5028185767244386*%i-1.4646937058354936; /* 53 */ ndefint(cos(x)*exp(-x^2),x,1,inf); 0.034019860790064659; /* 54 */ quad(cos(x)*exp(-x^2),x,1,inf,real); 0.034019860790064652; /* 55 */ ndefint(sin(x)*exp(-x^2),x,1,inf); 0.12973820125290061; /* 56 */ quad(sin(x)*exp(-x^2),x,1,inf); 0.12973820125290059; /* 57 */ quad(sin(x+sqrt(x))/(1+x),x,0,1,real); 0.52463649764169618; /* 58 */ ndefint(sin(sqrt(2)*x) + sin(sqrt(3)*x) + sin(sqrt(5)*x),x,1,10^4); -0.2540764606112777; /* 59 */ ndefint(sin(sqrt(2)*x) * sin(sqrt(3)*x) * sin(sqrt(5)*x),x,1,10^4); 0.13467278340822891; /* 60 */ quad(bessel_j(1,x)*bessel_j(2,sqrt(2)*x),x,1,100,strong_osc,real); 0.48023984378250428; /* 61 */ nint(bessel_y(1,x)*bessel_y(2,sqrt(2)*x),x,1,10^3,strong_osc,real); 0.4473705233554845; /* 62 */ ndefint(bessel_j(1,x),x,1,inf); 0.76519768655796661; /* 63 */ ndefint(bessel_i(1,%i*x),x,1,inf); 0.76519768655796661*%i; /* 64 */ qagi(bessel_i(1,%i*x)/x^4,x,1,inf); 0.16334064796529954*%i; /* 65 */ /* (%i7) qagi(bessel_k(1,%i*x)/x^10,x,1,inf); (%o7) -0.11914744615379*%i-0.082794805550016 (%i8) p()$ ((MPLUS SIMP (2212 "c:/work2/quad1d.mac" SRC $QAGI 2101)) -0.082794805550016254 ((MTIMES SIMP) -0.11914744615378614 $%I)) */ qagi(bessel_k(1,%i*x)/x^10,x,1,inf); -0.11914744615378614*%i-0.082794805550016254; /* 66 */ quad(bessel_j(2,sqrt(2)*x)^2,x,1,10^3,real,strong_osc); 1.6206625540514363; /* 67 */ ndefint( (sin(sqrt(2)*x)*sin(sqrt(3)*x))^3,x,1,10^4); -1.0454081930987682; /* 68 */ quad(sin(x)*(sin(x^2)*(sin(x^3)+1/x)+1/x),x,0,10,real,strong_osc); 2.5281885572727916; /* 69 */ quad(bessel_y(2/3,x)*sin(x+sqrt(x))^4,x,0,10^3,real,strong_osc); -0.38748316840429553; /* 70 */ noutL; [qag,-0.38748316840429553,1.5011056557384735E-9,16151,0]; /* 71 */ ndefint(1/sqrt(x) + cos(x),x,0,5000); 140.43338979854272; /* 72 */ quad(1/sqrt(x) + cos(x),x,0,5000,real); 140.43338979854312; /* 73 */ quad(1/sqrt(x) + bessel_y(0,x),x,0,5000,real,strong_osc); 141.42800610978355; /* 74 */ ndefint(sin(x)/sqrt(x),x,0,5000); 1.2511281929995333; /* 75 */ quad(sin(x)/sqrt(x),x,0,5000,real,singular); 1.2511281929995182; /* 76 */ quad(bessel_j(1,x)/sqrt(x),x,0,5000,real,strong_osc); 0.95607163870946721; /* 77 */ ndefint(sin(x)/x^10,x,1,inf); 0.099212566918873923; /* 78 */ quad(sin(x)/x^10,x,1,inf,real); 0.099212566918934583; /* 79 */ ndefint(sin (10^3*sqrt(x)),x,0,1); -0.0011231043935003419; /* 80 */ quad(sin (10^3*sqrt(x)),x,0,1,real); -0.00112310439350074; /* 81 */ quad(airy_ai(10*log(x)),x,0,1,real); 0.063922501876800611; /* 82 */ quad(bessel_j(0,x)/(1+x),x,0,1,real,strong_osc); 0.64654342647715979; /* 83 */ quad( exp (sin(x)) - sin (sin (x)),x,0,2,real); 2.9894750989770067; /* 84 */ /* (%i55) quad(log(-3+%i*x),x,-2,3); (%o55) 2.449536971144524*%i+6.02070929514083 (%i56) p()$ ((MPLUS SIMP (514 "c:/work2/quad1d.mac" SRC $QUADPACK1 413)) 6.0207092951408301 ((MTIMES SIMP) 2.4495369711445236 $%I)) */ quad(log(-3+%i*x),x,-2,3); 2.4495369711445236*%i+6.0207092951408301; /* 85 */ quad(sqrt(-1+%i*x),x,-2,3); 1.3582889377520364*%i+2.6513350744758153; /* 86 */ ndefint(airy_ai(-x),x,0,10); 0.76569840313421289; /* 87 */ quad(airy_ai(-x),x,0,100); 0.66422602599798353; /* 88 */ ndefint(airy_bi(-x),x,0,10); 0.015040424806140021; /* 89 */ quad(airy_bi(-x),x,0,10); 0.015040424806140207; /* 90 */ ndefint((x-x^2)^(-1),x,-1/2,1/2); 1.0986122886681098; /* 91 */ quad((x-x^2)^(-1),x,-1/2,1/2,principal_val(0)); 1.0986122886681096; /* 92 */ (ex:1/(32*((x-1)^2+1/1024)*(x-2)),ndefint(ex,x,0,5)); -3.1301203374159172; /* 93 */ quad(ex,x,0,5,principal_val(2)); -3.1301203374159403; /* 94 */ ndefint(1,[x,0,1],[y,0,1]); 1.0; /* 95 */ quad(1,[x,0,1],[y,0,1]); 1.0; /* 96 */ ndefint(expintegral_si(x),x,1,10^4); 15706.476913115124; /* 97 */ quad(expintegral_si(x),x,1,10^4,real); 15706.47691311513; /* 98 */ ndefint(expintegral_ci(x),x,1,10^4); 0.50416228355032844; /* 99 */ quad(expintegral_ci(x),x,1,10^4); 0.50416228355038983; /* 100 */ nint(fresnel_c(x/10),x,0,10); 4.6158351419303214; /* 101 */ nint(fresnel_s(x/10),x,0,10^4); 4996.8169011381633; /* 102 */ ndefint(bessel_j(1,x)+fresnel_s(x/10),x,1,10); 2.2104951645345574; /* 103 */ quad(bessel_j(1,x)+fresnel_s(x/10),x,1,10); 2.2104951645345574; /* 104 */ quad(1+sin(5*x*y+y^2),[x,-1,1], [y,-sqrt(1-x^2),sqrt(1-x^2)]); 3.4367788501465104; /* 105 */ nint(1+sin(5*x*y+y^2),[x,-1,1], [y,-sqrt(1-x^2),sqrt(1-x^2)]); 3.4367788501465104; /* 106 */ quad (bessel_j(3,y)/(x+1),[x,0,5],[y,0,5]); 1.9431031898821471; /* 107 */ ndefint(exp(y-x),[x,0,inf],[y,0,1]); 1.7182818284590453; /* 108 */ quad(exp(y-x),[x,0,inf],[y,0,1]); 1.7182818284582178; /* 109 */ ndefint (1/sqrt(x),[x,0,1],[y,0,1]); 2.0; /* 110 */ quad (1/sqrt(x),[x,0,1],[y,0,1],real); 1.9999999999999996; /* 111 */ ndefint(log(y),[x,0,1],[y,0,1]); -1.0; /* 112 */ quad(log(y),[x,0,1],[y,0,1],real); -1.0; /* 113 */ ndefint(log(y)/x^(4/5),[x,0,1],[y,0,1]); -5.0; /* 114 */ quad(log(y)/x^(4/5),[x,0,1],[y,0,1]); -5.0000000000000044; /* 115 */ ndefint(1/sqrt(x+y),[x,0,1],[y,0,1]); 1.1045694996615869; /* 116 */ quad(1/sqrt(x+y),[x,0,1],[y,0,1]); 1.1045694996605762; /* 117 */ ndefint(log(x*y),[x,0,1],[y,0,1]); -2.0; /* 118 */ quad(log(x*y),[x,0,1],[y,0,1]); -1.9999999999999996; /* 119 */ ndefint (log(x+y),[x,0,1],[y,0,1]); -0.11370563888010939; /* 120 */ quad (log(x+y),[x,0,1],[y,0,1]); -0.11370563745101407; /* 121 */ quad(log(x+y)/sqrt(1-x*y),[x,0,1],[y,0,1],real); -0.034122929212114322; /* 122 */ nint(log(2-sin(x)-sin(y)),[x,0,4],[y,0,4],real); -2.4190761836102923; /* 123 */ ndefint(sin(x)*cos(y),[x,1,10],[y,1,10]); -1.9111115453273582; /* 124 */ quad(sin(x)*cos(y),[x,1,10],[y,1,10],real); -1.9111115453273597; /* 125 */ ndefint(sin(x+y),[x,1,10],[y,1,10]); -3.8222230906547163; /* 126 */ quad(sin(x+y),[x,1,10],[y,1,10],real); -3.8222230906547243; /* 127 */ ndefint(exp(%i*(x+y)),[x,1,10],[y,1,10]); 0.016916170709851974-3.8222230906547163*%i; /* 128 */ quad(exp(%i*(x+y)),[x,1,10],[y,1,10]); 0.016916170709853937-3.8222230906547243*%i; /* 129 */ ndefint(2^(%i*(x*y)),[x,1,10],[y,1,10]); 0.061314144038472462*%i-0.95975928150581102; /* 130 */ quad(2^(%i*(x*y)),[x,1,10],[y,1,10]); 0.061314144038471685*%i-0.95975928150581014; /* 131 */ ndefint(2^(%i*(x+y)),[x,1,10],[y,1,10]); 0.0040783349141081246*%i+9.5217361897768536E-4; /* 132 */ quad(2^(%i*(x+y)),[x,1,10],[y,1,10]); 0.0040783349141092547*%i+9.5217361897653729E-4; /* 133 */ ndefint(exp(-x^4),x,0,1); 0.84483859475710243; /* 134 */ quad(exp(-x^4),x,0,1); 0.84483859475710243; /* 135 */ (e: x*x^(0.5)/(1+x)^(0.5),ndefint(e,x,0,1)); 0.30747679967138353; /* 136 */ quad(e,x,0,1); 0.30747679966905256; /* 137 */ nint(e,x,0,1); 0.30747679966905256; /* 138 */ quad(ee,[x,0,1],[y,0,1]); 0.17570102933166901; /* 139 */ ndefint(exp(sqrt(x^3)),x,0,1); 4.1086505480261029E-33*%i+1.5623940622173118; /* 140 */ quad(exp(sqrt(x^3)),x,0,1,real); 1.5623940622145414; /* 141 */ ndefint(exp(sqrt(x^3)),x,1,2); 2.2597578014143566E-32*%i+7.4022422870366364; /* 142 */ quad(exp(sqrt(x^3)),x,1,2,real); 7.4022422870366364; /* 143 */ ndefint(x^(1/3)*sin(x),x,0,1); 0.39140213472340452; /* 144 */ quad(x^(1/3)*sin(x),x,0,1); 0.39140213472073826; /* 145 */ ndefint(x^(1/3)*sin(x),x,1,2); 1.091879396853239; /* 146 */ quad(x^(1/3)*sin(x),x,1,2); 1.091879396853239; /* 147 */ ndefint(exp(x^2),x,1,2); 14.989976019600048; /* 148 */ quad(exp(x^2),x,1,2); 14.98997601960005; /* 149 */ ndefint(exp(x^3),x,0,1); 3.0814879110195774E-33*%i+1.3419044179774198; /* 150 */ quad(exp(x^3),x,0,1); 1.3419044179774198; /* 151 */ ndefint(exp(x^3),x,1,2); 2.8144256253978805E-31*%i+275.51098376331163; /* 152 */ quad(exp(x^3),x,1,2); 275.51098376331163; /* 153 */ quad(exp(x^5),x,1,2); 1.0132394896940144E+12; /* 154 */ ndefint(exp(x^5),x,1,2); 1.0512336862202133E-20*%i+1.0132394896940183E+12; /* 155 */ ndefint(exp(y)/y^(4/5),y,0,1); 6.1629758220391547E-32*%i+6.1244675181765533; /* 156 */ quad(exp(y)/y^(4/5),y,0,1); 6.1244675181765302; /* 157 */ ndefint(exp(y)/y^(4/5),y,1,2); 3.0814879110195774E-32*%i+3.3192819565021714; /* 158 */ quad(exp(y)/y^(4/5),y,1,2); 3.3192819565021709; /* 159 */ ndefint(exp(-x),x,1,2); 0.23254415793482963; /* 160 */ quad(exp(-x),x,1,2); 0.23254415793482963; /* 161 */ /* overflow test */ quad(%e^x^(3/2),x,0,100); false; /* 162 */ quad(1/sqrt(sin(x)),x,1,5,points(%pi)); 3.2093097893775431-2.9116804492994262*%i; /* 163 */ quad(1/sqrt(sin(x)),x,0,10,points(%pi,2*%pi,3*%pi)); 10.488230217166814-6.7694655217253867*%i; /* 164 */ nint(sqrt(log(x-7)),x,0,20,points(7,8)); 8.5606525646854674*%i+25.881678170889444; /* 165 */ quad(sqrt(log(x-7)),x,0,20,points(7,8)); 8.5606525646854674*%i+25.881678170889444; /* 166 */ ndefint(sin(x)^2/x,x,minf,inf); 0.0; /* 167 */ quad(sin(x)^2/x,x,minf,inf); 0.0; /* 168 */ ndefint(sin(x)/x,x,0,inf); 1.5707963267948966; /* 169 */ ndefint(sin(x)^3/x,x,0,inf); 0.78539816339744828; /* 170 */ ndefint(sin(x)^2/x^2,x,0,inf); 1.5707963267948966; /* 171 */ ndefint(sin(x)^4/x^2,x,0,inf); 0.78539816339744828; /* 172 */ ndefint(sin(x)^3/x^3,x,0,inf); 1.1780972450961724; /* 173 */ ndefint(sin(x)*cos(x)/x,x,0,inf); 0.78539816339744828; /* 174 */ ndefint(sin(2*x)*cos(x)/x,x,0,inf); 1.5707963267948966; /* 175 */ ndefint(sin(x)*cos(2*x)/x,x,0,inf); 0.0; /* 176 */ ndefint(sin(x)/sqrt(x),x,0,inf); 1.2533141373155003; /* 177 */ ndefint(sin(x)*sin(2*x)/x^2,x,0,inf); 1.5707963267948966; /* 178 */ ndefint(sin(x)^2*cos(x)/x^2,x,0,inf); 0.78539816339744828; /* 179 */ ndefint(log(1+x)/x,x,0,1); 0.82246703342411309; /* 180 */ quad(log(1+x)/x,x,0,1); 0.82246703342411298; /* 181 */ ndefint(log(x)*log(1-x),x,0,1); 0.35506593315177354; /* 182 */ quad(log(x)*log(1-x),x,0,1); 0.35506593315177354; /* 183 */ ndefint(cos(x*y*log(2)),[x,1,10],[y,1,10]); -0.95975928150581102; /* 184 */ quad(cos(x*y*log(2)),[x,1,10],[y,1,10]); -0.95975928150581014; /* 185 */ ndefint(sin(x*y*log(2)),[x,1,10],[y,1,10]); 0.061314144038472462-2.7785295798670222E-34*%i; /* 186 */ quad(sin(x*y*log(2)),[x,1,10],[y,1,10]); 0.061314144038471685; /* 187 */ ndefint(sqrt(x),x,-1,0); 0.66666666666666663*%i; /* 188 */ quad(sqrt(x),x,-1,0); 0.66666666666666663*%i; /* 189 */ ndefint(log(x),x,-1,-1/2); 1.5707963267948966*%i-0.15342640972002736; /* 190 */ quad(log(x),x,-1,-1/2); 1.5707963267948963*%i-0.15342640972002733; /* 191 */ ndefint(sqrt(x^2 - 2*x*y + y^2),[x,-1,1],[y,-1,1]); 2.6666666666666665; /* 192 */ quad(sqrt(x^2 - 2*x*y + y^2),[x,-1,1],[y,-1,1]); 2.6666666601445783; /* 193 */ quad(hankel_1(0,x),x,0,10); 0.24129031832499795*%i+1.0670113039567373; /* 194 */ quad(hankel_2(0,x),x,0,10); 1.0670113039567373-0.24129031832499795*%i; /* 195 */ quad(hankel_1(1/2,x),x,0,10); 1.2168725181302213-0.87392790545876686*%i; /* 196 */ quad(hankel_2(1/2,x),x,0,10); 0.87392790545876686*%i+1.2168725181302213; /* 197 */ ndefint(exp(-abs(x)),x,minf,inf); 2.0; /* 198 */ quad(exp(-abs(x)),x,minf,inf); 2.0000000000000004; /* 199 */ ndefint(exp(-abs(x)),x,1,inf); 0.36787944117144233; /* 200 */ quad(exp(-abs(x)),x,1,inf); 0.36787944117144228; /* 201 */ ndefint(exp(-abs(x)),x,inf,minf); -2.0; /* 202 */ quad(exp(-abs(x)),x,inf,minf); -2.0000000000000004; /* 203 */ ndefint(exp(-x),x,inf,1); -0.36787944117144233; /* 204 */ quad(exp(-x),x,inf,1); -0.36787944117144228; /* 205 */ ndefint(sin(1/x),x,-1,1); 0.0; /* 206 */ ndefint(sin(x),x,-1,1); 0.0; /* 207 */ quad(sin(x),x,-1,1); 0.0; /* 208 */ ndefint(sin(1/x),x,0,1); 0.5040670619069284; /* 209 */ ndefint(exp(%i*x),x,-1,1); 1.682941969615793; /* 210 */ quad(exp(%i*x),x,-1,1); 1.682941969615793; /* 211 */ ndefint(exp(x),x,1,inf); false; /* 212 */ quad(exp(x),x,1,inf); false; /* 213 */ ndefint(exp(-x),x,minf,0); false; /* 214 */ quad(exp(-x),x,minf,0); false; /* 215 */ ndefint(cos(x)/x^3,x,minf,-1); -0.018117621980605673; /* 216 */ quad(cos(x)/x^3,x,minf,-1); -0.018117622501279095; /* 217 */ ndefint(cos(x)/x^2,x,minf,-1); -0.084410950559573886; /* 218 */ ndefint(sin(x)/x^3,x,minf,-1); 0.37853001712416129; /* 219 */ quad(sin(x)/x^3,x,minf,-1); 0.37853001687655274; /* 220 */ ndefint(sin(x)/x^2,x,minf,-1); -0.5040670619069284; /* 221 */ qagi(bessel_j(1,x)/x^3,x,minf,-1); 0.22830936708465363; /* 222 */ ndefint(1/x^4,x,1,inf); 0.33333333333333331; /* 223 */ quad(1/x^4,x,1,inf); 0.33333333333333337; /* 224 */ ndefint(1/x^3,x,1,inf); 0.5; /* 225 */ quad(1/x^3,x,1,inf); 0.5; /* 226 */ ndefint(1/x^2,x,1,inf); 1.0; /* 227 */ quad(1/x^2,x,1,inf); 1.0; /* 228 */ ndefint(1/x^4,x,minf,-1); 0.33333333333333331; /* 229 */ quad(1/x^4,x,minf,-1); 0.33333333333333337; /* 230 */ ndefint(1/x^2,x,minf,-1); 1.0; /* 231 */ quad(1/x^2,x,minf,-1); 1.0; /* 232 */ ndefint(1/x^3,x,minf,-1); -0.5; /* 233 */ quad(1/x^3,x,minf,-1); -0.5; /* 234 */ ndefint(x*y,[x,0,1],[y,0,1]); 0.25; /* 235 */ quad(x*y,[x,0,1],[y,0,1]); 0.24999999999999997; /* 236 */ ndefint(exp(-abs(x) - abs(y)),[x,minf,inf],[y,minf,inf]); 4.0; /* 237 */ quad(exp(-abs(x) - abs(y)),[x,minf,inf],[y,minf,inf]); 3.9999999999961493; /* 238 */ ndefint(4^(-16)/((x - %pi/4)^2 + 16^(-16)),x,0,1); 3.1415926522084017; /* 239 */ quad(4^(-16)/((x - %pi/4)^2 + 16^(-16)),x,0,1); 3.1415926288388865; /* 240 */ ndefint(sqrt(x^2 - 2*x*y + y^2),[x,-1,1],[y,-x,x]); 0.0; /* 241 */ quad(sqrt(x^2 - 2*x*y + y^2),[x,-1,1],[y,-x,x]); 0.0; /* 242 */ quad(log(sin(x)),x,1,2); -0.045502182913370805; /* 243 */ ndefint(cos(x*y),[x,1,10],[y,1,10]); -0.80838665118150876; /* 244 */ quad(cos(x*y),[x,1,10],[y,1,10]); -0.80838665118151076; /* 245 */ ndefint(sin(x*y),[x,1,10],[y,1,10]); -0.4231679637672684; /* 246 */ quad(sin(x*y),[x,1,10],[y,1,10]); -0.42316796376726901; /* 247 */ ndefint(((-%pi)/2+acos(y)+acos(x))/(2*%pi), [x,0,1],[y,0,sqrt(1-x^2)]); 0.079577471545947673; /* 248 */ quad(((-%pi)/2+acos(y)+acos(x))/(2*%pi), [x,0,1],[y,0,sqrt(1-x^2)]); 0.079577471546450007; /* 249 */ nint(((-%pi)/2+acos(y)+acos(x))/(2*%pi), [x,0,1],[y,0,sqrt(1-x^2)]); 0.079577471546450007; /* 250 */ noutL; [[qags21,0.079577471546450007,2.4892906088319779E-13,21,0],[qags21,0.0,0.0, 21,0]]; /* 251 (orig. 2nd 105) */ ndefint (bessel_j(3,y)/(x+1),[x,0,5],[y,0,5]); 1.9431031898821141; /* 252 (orig. 2nd 137) */ (ee:x^1.5*y^0.75/(x+1)^0.5,ndefint(ee,[x,0,1],[y,0,1])); 0.17570102838364771;