1,1,9,13,0.320839,"\text{Not used}","int((2*x + 1)^(1/2),x)","\frac{{\left(2\,x+1\right)}^{3/2}}{3}","Not used",1,"(2*x + 1)^(3/2)/3","B"
2,1,14,27,0.085251,"\text{Not used}","int(x*(3*x + 1)^(1/2),x)","\frac{2\,{\left(3\,x+1\right)}^{3/2}\,\left(9\,x-2\right)}{135}","Not used",1,"(2*(3*x + 1)^(3/2)*(9*x - 2))/135","B"
3,1,19,34,0.068970,"\text{Not used}","int(x^2*(x + 1)^(1/2),x)","-\frac{2\,{\left(x+1\right)}^{3/2}\,\left(42\,x-15\,{\left(x+1\right)}^2+7\right)}{105}","Not used",1,"-(2*(x + 1)^(3/2)*(42*x - 15*(x + 1)^2 + 7))/105","B"
4,1,14,27,0.056862,"\text{Not used}","int(x/(2 - 3*x)^(1/2),x)","-\frac{2\,\sqrt{2-3\,x}\,\left(3\,x+4\right)}{27}","Not used",1,"-(2*(2 - 3*x)^(1/2)*(3*x + 4))/27","B"
5,1,12,14,0.064552,"\text{Not used}","int((x + 1)/(2*x + x^2 + 2)^3,x)","-\frac{1}{4\,{\left(x^2+2\,x+2\right)}^2}","Not used",1,"-1/(4*(2*x + x^2 + 2)^2)","B"
6,1,10,13,0.157537,"\text{Not used}","int(sin(x)^3,x)","\frac{\cos\left(x\right)\,\left({\cos\left(x\right)}^2-3\right)}{3}","Not used",1,"(cos(x)*(cos(x)^2 - 3))/3","B"
7,1,12,23,0.030899,"\text{Not used}","int(z*(z - 1)^(1/3),z)","\frac{3\,\left(4\,z+3\right)\,{\left(z-1\right)}^{4/3}}{28}","Not used",1,"(3*(4*z + 3)*(z - 1)^(4/3))/28","B"
8,1,6,8,0.418029,"\text{Not used}","int(cos(x)/sin(x)^3,x)","-\frac{{\mathrm{cot}\left(x\right)}^2}{2}","Not used",1,"-cot(x)^2/2","B"
9,1,12,16,0.170651,"\text{Not used}","int(cos(2*x)*(4 - sin(2*x))^(1/2),x)","-\frac{{\left(4-\sin\left(2\,x\right)\right)}^{3/2}}{3}","Not used",1,"-(4 - sin(2*x))^(3/2)/3","B"
10,1,6,6,0.043208,"\text{Not used}","int(sin(x)/(cos(x) + 3)^2,x)","\frac{1}{\cos\left(x\right)+3}","Not used",1,"1/(cos(x) + 3)","B"
11,1,9,12,0.199195,"\text{Not used}","int(sin(x)/(cos(x)^3)^(1/2),x)","\frac{2\,\left|\cos\left(x\right)\right|}{{\cos\left(x\right)}^{3/2}}","Not used",1,"(2*abs(cos(x)))/cos(x)^(3/2)","B"
12,1,8,10,0.170985,"\text{Not used}","int(sin((x + 1)^(1/2))/(x + 1)^(1/2),x)","-2\,\cos\left(\sqrt{x+1}\right)","Not used",1,"-2*cos((x + 1)^(1/2))","B"
13,1,9,9,0.207458,"\text{Not used}","int(x^(n - 1)*sin(x^n),x)","-\frac{\cos\left(x^n\right)}{n}","Not used",1,"-cos(x^n)/n","B"
14,1,11,15,0.353938,"\text{Not used}","int(x^5/(1 - x^6)^(1/2),x)","-\frac{\sqrt{1-x^6}}{3}","Not used",1,"-(1 - x^6)^(1/2)/3","B"
15,1,12,23,0.034017,"\text{Not used}","int(t*(t + 1)^(1/4),t)","\frac{4\,\left(5\,t-4\right)\,{\left(t+1\right)}^{5/4}}{45}","Not used",1,"(4*(5*t - 4)*(t + 1)^(5/4))/45","B"
16,1,9,11,0.072007,"\text{Not used}","int(1/(x^2 + 1)^(3/2),x)","\frac{x}{\sqrt{x^2+1}}","Not used",1,"x/(x^2 + 1)^(1/2)","B"
17,1,11,15,0.185328,"\text{Not used}","int(x^2*(8*x^3 + 27)^(2/3),x)","\frac{{\left(8\,x^3+27\right)}^{5/3}}{40}","Not used",1,"(8*x^3 + 27)^(5/3)/40","B"
18,1,15,15,0.239175,"\text{Not used}","int((cos(x) + sin(x))/(sin(x) - cos(x))^(1/3),x)","\frac{3\,2^{1/3}\,{\left(-\cos\left(x+\frac{\pi }{4}\right)\right)}^{2/3}}{2}","Not used",1,"(3*2^(1/3)*(-cos(x + pi/4))^(2/3))/2","B"
19,1,47,32,0.588935,"\text{Not used}","int(x/((x^2 + 1)^(3/2) + x^2 + 1)^(1/2),x)","\frac{2\,\left(x^2+1\right)\,\sqrt{\sqrt{x^2+1}+1}}{\left(\sqrt{\sqrt{x^2+1}+1}+1\right)\,\sqrt{{\left(x^2+1\right)}^{3/2}+x^2+1}}","Not used",1,"(2*(x^2 + 1)*((x^2 + 1)^(1/2) + 1)^(1/2))/((((x^2 + 1)^(1/2) + 1)^(1/2) + 1)*((x^2 + 1)^(3/2) + x^2 + 1)^(1/2))","B"
20,1,13,17,0.210050,"\text{Not used}","int(x/((x^2 + 1)^(1/2)*((x^2 + 1)^(1/2) + 1)^(1/2)),x)","2\,\sqrt{\sqrt{x^2+1}+1}","Not used",1,"2*((x^2 + 1)^(1/2) + 1)^(1/2)","B"
21,1,9,16,0.155708,"\text{Not used}","int(-(x^2 - 2*x + 1)^(1/5)/(x - 1),x)","-\frac{5\,{\left({\left(x-1\right)}^2\right)}^{1/5}}{2}","Not used",1,"-(5*((x - 1)^2)^(1/5))/2","B"
22,1,8,8,0.064298,"\text{Not used}","int(x*sin(x),x)","\sin\left(x\right)-x\,\cos\left(x\right)","Not used",1,"sin(x) - x*cos(x)","B"
23,1,15,17,0.032759,"\text{Not used}","int(x^2*sin(x),x)","2\,x\,\sin\left(x\right)-\cos\left(x\right)\,\left(x^2-2\right)","Not used",1,"2*x*sin(x) - cos(x)*(x^2 - 2)","B"
24,1,24,23,0.029955,"\text{Not used}","int(x^3*cos(x),x)","\cos\left(x\right)\,\left(3\,x^2-6\right)-\sin\left(x\right)\,\left(6\,x-x^3\right)","Not used",1,"cos(x)*(3*x^2 - 6) - sin(x)*(6*x - x^3)","B"
25,1,23,24,0.030161,"\text{Not used}","int(x^3*sin(x),x)","\cos\left(x\right)\,\left(6\,x-x^3\right)+\sin\left(x\right)\,\left(3\,x^2-6\right)","Not used",1,"cos(x)*(6*x - x^3) + sin(x)*(3*x^2 - 6)","B"
26,1,6,8,0.018810,"\text{Not used}","int(cos(x)*sin(x),x)","\frac{{\sin\left(x\right)}^2}{2}","Not used",1,"sin(x)^2/2","B"
27,1,18,23,0.094634,"\text{Not used}","int(x*cos(x)*sin(x),x)","\frac{\sin\left(2\,x\right)}{8}+\frac{x\,\left(2\,{\sin\left(x\right)}^2-1\right)}{4}","Not used",1,"sin(2*x)/8 + (x*(2*sin(x)^2 - 1))/4","B"
28,1,10,14,0.031521,"\text{Not used}","int(sin(x)^2,x)","\frac{x}{2}-\frac{\sin\left(2\,x\right)}{4}","Not used",1,"x/2 - sin(2*x)/4","B"
29,1,10,13,0.002041,"\text{Not used}","int(sin(x)^3,x)","\frac{\cos\left(x\right)\,\left({\cos\left(x\right)}^2-3\right)}{3}","Not used",1,"(cos(x)*(cos(x)^2 - 3))/3","B"
30,1,16,24,0.035605,"\text{Not used}","int(sin(x)^4,x)","\frac{3\,x}{8}-\frac{\sin\left(2\,x\right)}{4}+\frac{\sin\left(4\,x\right)}{32}","Not used",1,"(3*x)/8 - sin(2*x)/4 + sin(4*x)/32","B"
31,1,17,21,0.042792,"\text{Not used}","int(sin(x)^5,x)","-\frac{{\cos\left(x\right)}^5}{5}+\frac{2\,{\cos\left(x\right)}^3}{3}-\cos\left(x\right)","Not used",1,"(2*cos(x)^3)/3 - cos(x) - cos(x)^5/5","B"
32,1,22,34,0.039183,"\text{Not used}","int(sin(x)^6,x)","\frac{5\,x}{16}-\frac{15\,\sin\left(2\,x\right)}{64}+\frac{3\,\sin\left(4\,x\right)}{64}-\frac{\sin\left(6\,x\right)}{192}","Not used",1,"(5*x)/16 - (15*sin(2*x))/64 + (3*sin(4*x))/64 - sin(6*x)/192","B"
33,1,19,25,0.093290,"\text{Not used}","int(x*sin(x)^2,x)","\frac{{\sin\left(x\right)}^2}{4}-\frac{x\,\sin\left(2\,x\right)}{4}+\frac{x^2}{4}","Not used",1,"sin(x)^2/4 - (x*sin(2*x))/4 + x^2/4","B"
34,1,25,33,0.119287,"\text{Not used}","int(x*sin(x)^3,x)","\frac{x\,{\cos\left(x\right)}^3}{3}-\frac{\sin\left(x\right)\,{\cos\left(x\right)}^2}{9}-x\,\cos\left(x\right)+\frac{7\,\sin\left(x\right)}{9}","Not used",1,"(7*sin(x))/9 + (x*cos(x)^3)/3 - (cos(x)^2*sin(x))/9 - x*cos(x)","B"
35,1,28,41,0.063468,"\text{Not used}","int(x^2*sin(x)^2,x)","\frac{\sin\left(2\,x\right)}{8}-\frac{x\,\cos\left(2\,x\right)}{4}-\frac{x^2\,\sin\left(2\,x\right)}{4}+\frac{x^3}{6}","Not used",1,"sin(2*x)/8 - (x*cos(2*x))/4 - (x^2*sin(2*x))/4 + x^3/6","B"
36,1,10,14,0.025700,"\text{Not used}","int(cos(x)^2,x)","\frac{x}{2}+\frac{\sin\left(2\,x\right)}{4}","Not used",1,"x/2 + sin(2*x)/4","B"
37,1,9,11,0.033380,"\text{Not used}","int(cos(x)^3,x)","\sin\left(x\right)-\frac{{\sin\left(x\right)}^3}{3}","Not used",1,"sin(x) - sin(x)^3/3","B"
38,1,16,24,0.028515,"\text{Not used}","int(cos(x)^4,x)","\frac{3\,x}{8}+\frac{\sin\left(2\,x\right)}{4}+\frac{\sin\left(4\,x\right)}{32}","Not used",1,"(3*x)/8 + sin(2*x)/4 + sin(4*x)/32","B"
39,1,37,84,0.214701,"\text{Not used}","int((a^2 - x^2)^(5/2),x)","\frac{x\,{\left(a^2-x^2\right)}^{5/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{2},\frac{1}{2};\ \frac{3}{2};\ \frac{x^2}{a^2}\right)}{{\left(1-\frac{x^2}{a^2}\right)}^{5/2}}","Not used",1,"(x*(a^2 - x^2)^(5/2)*hypergeom([-5/2, 1/2], 3/2, x^2/a^2))/(1 - x^2/a^2)^(5/2)","B"
40,1,20,38,0.028551,"\text{Not used}","int(x^5/(x^2 + 5)^(1/2),x)","\sqrt{x^2+5}\,\left(\frac{x^4}{5}-\frac{4\,x^2}{3}+\frac{40}{3}\right)","Not used",1,"(x^2 + 5)^(1/2)*(x^4/5 - (4*x^2)/3 + 40/3)","B"
41,1,301,172,0.075266,"\text{Not used}","int(t^3/(t^3 + 4)^(1/2),t)","\frac{2\,t\,\sqrt{t^3+4}}{5}-\frac{16\,\sqrt{-\frac{t-2^{2/3}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{2^{2/3}+2^{2/3}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}\,\sqrt{-\frac{t+2^{2/3}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{2^{2/3}-2^{2/3}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}\,\sqrt{\frac{t+2^{2/3}}{2^{2/3}+2^{2/3}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}\,\left(2^{2/3}+2^{2/3}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\right)\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{t+2^{2/3}}{2^{2/3}+2^{2/3}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}\right)\middle|\frac{2^{2/3}+2^{2/3}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{2^{2/3}-2^{2/3}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}\right)}{5\,\sqrt{t^3+\left(2^{2/3}+2^{2/3}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-2^{2/3}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\right)\,t^2+\left(2\,2^{1/3}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-2\,2^{1/3}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-2\,2^{1/3}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\right)\,t-4\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(2*t*(t^3 + 4)^(1/2))/5 - (16*(-(t - 2^(2/3)*((3^(1/2)*1i)/2 + 1/2))/(2^(2/3) + 2^(2/3)*((3^(1/2)*1i)/2 + 1/2)))^(1/2)*(-(t + 2^(2/3)*((3^(1/2)*1i)/2 - 1/2))/(2^(2/3) - 2^(2/3)*((3^(1/2)*1i)/2 - 1/2)))^(1/2)*((t + 2^(2/3))/(2^(2/3) + 2^(2/3)*((3^(1/2)*1i)/2 + 1/2)))^(1/2)*(2^(2/3) + 2^(2/3)*((3^(1/2)*1i)/2 + 1/2))*ellipticF(asin(((t + 2^(2/3))/(2^(2/3) + 2^(2/3)*((3^(1/2)*1i)/2 + 1/2)))^(1/2)), (2^(2/3) + 2^(2/3)*((3^(1/2)*1i)/2 + 1/2))/(2^(2/3) - 2^(2/3)*((3^(1/2)*1i)/2 - 1/2))))/(5*(t^2*(2^(2/3) + 2^(2/3)*((3^(1/2)*1i)/2 - 1/2) - 2^(2/3)*((3^(1/2)*1i)/2 + 1/2)) - 4*((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + t^3 - t*(2*2^(1/3)*((3^(1/2)*1i)/2 + 1/2) - 2*2^(1/3)*((3^(1/2)*1i)/2 - 1/2) + 2*2^(1/3)*((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2)))^(1/2))","B"
42,1,6,6,0.070422,"\text{Not used}","int(tan(x)^2,x)","\mathrm{tan}\left(x\right)-x","Not used",1,"tan(x) - x","B"
43,1,12,14,0.034128,"\text{Not used}","int(tan(x)^4,x)","\frac{{\mathrm{tan}\left(x\right)}^3}{3}-\mathrm{tan}\left(x\right)+x","Not used",1,"x - tan(x) + tan(x)^3/3","B"
44,1,8,8,0.057278,"\text{Not used}","int(cot(x)^2,x)","-x-\mathrm{cot}\left(x\right)","Not used",1,"- x - cot(x)","B"
45,1,10,12,0.021825,"\text{Not used}","int(cot(x)^4,x)","-\frac{{\mathrm{cot}\left(x\right)}^3}{3}+\mathrm{cot}\left(x\right)+x","Not used",1,"x + cot(x) - cot(x)^3/3","B"
46,1,20,22,0.102991,"\text{Not used}","int(sin(5*x)*(3*x + 2),x)","\frac{3\,\sin\left(5\,x\right)}{25}-\frac{2\,\cos\left(5\,x\right)}{5}-\frac{3\,x\,\cos\left(5\,x\right)}{5}","Not used",1,"(3*sin(5*x))/25 - (2*cos(5*x))/5 - (3*x*cos(5*x))/5","B"
47,1,9,13,0.024536,"\text{Not used}","int(x*(x^2 + 1)^(1/2),x)","\frac{{\left(x^2+1\right)}^{3/2}}{3}","Not used",1,"(x^2 + 1)^(3/2)/3","B"
48,1,9,13,0.097421,"\text{Not used}","int(x*(x^2 - 1)^9,x)","\frac{{\left(x^2-1\right)}^{10}}{20}","Not used",1,"(x^2 - 1)^10/20","B"
49,1,14,18,0.041561,"\text{Not used}","int((2*x + 3)/(6*x + 7)^3,x)","-\frac{3\,x+4}{9\,{\left(6\,x+7\right)}^2}","Not used",1,"-(3*x + 4)/(9*(6*x + 7)^2)","B"
50,1,31,11,0.025207,"\text{Not used}","int(x^4*(x^5 + 1)^5,x)","\frac{x^{30}}{30}+\frac{x^{25}}{5}+\frac{x^{20}}{2}+\frac{2\,x^{15}}{3}+\frac{x^{10}}{2}+\frac{x^5}{5}","Not used",1,"x^5/5 + x^10/2 + (2*x^15)/3 + x^20/2 + x^25/5 + x^30/30","B"
51,1,106,56,0.463879,"\text{Not used}","int(x^4*(x - 1)^20,x)","\frac{x^{25}}{25}-\frac{5\,x^{24}}{6}+\frac{190\,x^{23}}{23}-\frac{570\,x^{22}}{11}+\frac{1615\,x^{21}}{7}-\frac{3876\,x^{20}}{5}+2040\,x^{19}-\frac{12920\,x^{18}}{3}+7410\,x^{17}-\frac{20995\,x^{16}}{2}+\frac{184756\,x^{15}}{15}-\frac{83980\,x^{14}}{7}+9690\,x^{13}-6460\,x^{12}+\frac{38760\,x^{11}}{11}-\frac{7752\,x^{10}}{5}+\frac{1615\,x^9}{3}-\frac{285\,x^8}{2}+\frac{190\,x^7}{7}-\frac{10\,x^6}{3}+\frac{x^5}{5}","Not used",1,"x^5/5 - (10*x^6)/3 + (190*x^7)/7 - (285*x^8)/2 + (1615*x^9)/3 - (7752*x^10)/5 + (38760*x^11)/11 - 6460*x^12 + 9690*x^13 - (83980*x^14)/7 + (184756*x^15)/15 - (20995*x^16)/2 + 7410*x^17 - (12920*x^18)/3 + 2040*x^19 - (3876*x^20)/5 + (1615*x^21)/7 - (570*x^22)/11 + (190*x^23)/23 - (5*x^24)/6 + x^25/25","B"
52,1,4,4,0.095510,"\text{Not used}","int(sin(1/x)/x^2,x)","\cos\left(\frac{1}{x}\right)","Not used",1,"cos(1/x)","B"
53,1,41,62,0.225527,"\text{Not used}","int(sin((x - 1)^(1/4)),x)","4\,\cos\left({\left(x-1\right)}^{1/4}\right)\,\left(6\,{\left(x-1\right)}^{1/4}-{\left(x-1\right)}^{3/4}\right)+4\,\sin\left({\left(x-1\right)}^{1/4}\right)\,\left(3\,\sqrt{x-1}-6\right)","Not used",1,"4*cos((x - 1)^(1/4))*(6*(x - 1)^(1/4) - (x - 1)^(3/4)) + 4*sin((x - 1)^(1/4))*(3*(x - 1)^(1/2) - 6)","B"
54,1,8,10,0.050130,"\text{Not used}","int(x*cos(x^2)*sin(x^2),x)","\frac{{\sin\left(x^2\right)}^2}{4}","Not used",1,"sin(x^2)^2/4","B"
55,1,12,16,0.192887,"\text{Not used}","int(sin(2*x)*(3*cos(x)^2 + 1)^(1/2),x)","-\frac{2\,{\left(3\,{\cos\left(x\right)}^2+1\right)}^{3/2}}{9}","Not used",1,"-(2*(3*cos(x)^2 + 1)^(3/2))/9","B"
56,1,6,10,0.074063,"\text{Not used}","int(1/(3*x + 2),x)","\frac{\ln\left(x+\frac{2}{3}\right)}{3}","Not used",1,"log(x + 2/3)/3","B"
57,1,12,15,0.079473,"\text{Not used}","int(log(x)^2,x)","x\,\left({\ln\left(x\right)}^2-2\,\ln\left(x\right)+2\right)","Not used",1,"x*(log(x)^2 - 2*log(x) + 2)","B"
58,1,9,17,0.032349,"\text{Not used}","int(x*log(x),x)","\frac{x^2\,\left(\ln\left(x\right)-\frac{1}{2}\right)}{2}","Not used",1,"(x^2*(log(x) - 1/2))/2","B"
59,1,17,28,0.030323,"\text{Not used}","int(x*log(x)^2,x)","\frac{x^2\,\left(2\,{\ln\left(x\right)}^2-2\,\ln\left(x\right)+1\right)}{4}","Not used",1,"(x^2*(2*log(x)^2 - 2*log(x) + 1))/4","B"
60,1,4,4,0.015419,"\text{Not used}","int(1/(t + 1),t)","\ln\left(t+1\right)","Not used",1,"log(t + 1)","B"
61,1,3,3,0.022953,"\text{Not used}","int(cot(x),x)","\ln\left(\sin\left(x\right)\right)","Not used",1,"log(sin(x))","B"
62,1,38,28,0.205118,"\text{Not used}","int(x^n*log(a*x),x)","\left\{\begin{array}{cl} \frac{{\ln\left(a\,x\right)}^2}{2} & \text{\ if\ \ }n=-1\\ \frac{x^{n+1}\,\left(\ln\left(a\,x\right)-\frac{1}{n+1}\right)}{n+1} & \text{\ if\ \ }n\neq -1 \end{array}\right.","Not used",1,"piecewise(n == -1, log(a*x)^2/2, n ~= -1, (x^(n + 1)*(log(a*x) - 1/(n + 1)))/(n + 1))","B"
63,1,17,28,0.029269,"\text{Not used}","int(x^2*log(x)^2,x)","\frac{2\,x^3\,\left(\frac{9\,{\ln\left(x\right)}^2}{2}-3\,\ln\left(x\right)+1\right)}{27}","Not used",1,"(2*x^3*((9*log(x)^2)/2 - 3*log(x) + 1))/27","B"
64,1,3,3,0.069592,"\text{Not used}","int(1/(x*log(x)),x)","\ln\left(\ln\left(x\right)\right)","Not used",1,"log(log(x))","B"
65,1,10,12,0.345653,"\text{Not used}","int(-log(1 - t)/(t - 1),t)","-\frac{{\ln\left(1-t\right)}^2}{2}","Not used",1,"-log(1 - t)^2/2","B"
66,1,13,23,0.168173,"\text{Not used}","int(log(x)/(x*(log(x) + 1)^(1/2)),x)","\sqrt{\ln\left(x\right)+1}\,\left(\frac{2\,\ln\left(x\right)}{3}-\frac{4}{3}\right)","Not used",1,"(log(x) + 1)^(1/2)*((2*log(x))/3 - 4/3)","B"
67,1,23,39,0.036237,"\text{Not used}","int(x^3*log(x)^3,x)","\frac{3\,x^4\,\left(\frac{32\,{\ln\left(x\right)}^3}{3}-8\,{\ln\left(x\right)}^2+4\,\ln\left(x\right)-1\right)}{128}","Not used",1,"(3*x^4*(4*log(x) - 8*log(x)^2 + (32*log(x)^3)/3 - 1))/128","B"
68,1,6,9,0.075717,"\text{Not used}","int(x^2*exp(x^3),x)","\frac{{\mathrm{e}}^{x^3}}{3}","Not used",1,"exp(x^3)/3","B"
69,1,11,14,0.104910,"\text{Not used}","int(2^(x^(1/2))/x^(1/2),x)","\frac{2\,2^{\sqrt{x}}}{\ln\left(2\right)}","Not used",1,"(2*2^(x^(1/2)))/log(2)","B"
70,1,7,10,0.100568,"\text{Not used}","int(exp(2*sin(x))*cos(x),x)","\frac{{\mathrm{e}}^{2\,\sin\left(x\right)}}{2}","Not used",1,"exp(2*sin(x))/2","B"
71,1,11,19,0.018429,"\text{Not used}","int(exp(x)*sin(x),x)","-\frac{{\mathrm{e}}^x\,\left(\cos\left(x\right)-\sin\left(x\right)\right)}{2}","Not used",1,"-(exp(x)*(cos(x) - sin(x)))/2","B"
72,1,9,19,0.019254,"\text{Not used}","int(exp(x)*cos(x),x)","\frac{{\mathrm{e}}^x\,\left(\cos\left(x\right)+\sin\left(x\right)\right)}{2}","Not used",1,"(exp(x)*(cos(x) + sin(x)))/2","B"
73,1,9,10,0.044682,"\text{Not used}","int(1/(exp(x) + 1),x)","x-\ln\left({\mathrm{e}}^x+1\right)","Not used",1,"x - log(exp(x) + 1)","B"
74,1,6,11,0.017852,"\text{Not used}","int(x*exp(x),x)","{\mathrm{e}}^x\,\left(x-1\right)","Not used",1,"exp(x)*(x - 1)","B"
75,1,9,16,0.020677,"\text{Not used}","int(x*exp(-x),x)","-{\mathrm{e}}^{-x}\,\left(x+1\right)","Not used",1,"-exp(-x)*(x + 1)","B"
76,1,11,19,0.022327,"\text{Not used}","int(x^2*exp(x),x)","{\mathrm{e}}^x\,\left(x^2-2\,x+2\right)","Not used",1,"exp(x)*(x^2 - 2*x + 2)","B"
77,1,16,32,0.075155,"\text{Not used}","int(x^2*exp(-2*x),x)","-\frac{{\mathrm{e}}^{-2\,x}\,\left(4\,x^2+4\,x+2\right)}{8}","Not used",1,"-(exp(-2*x)*(4*x + 4*x^2 + 2))/8","B"
78,1,11,24,0.023760,"\text{Not used}","int(exp(x^(1/2)),x)","2\,{\mathrm{e}}^{\sqrt{x}}\,\left(\sqrt{x}-1\right)","Not used",1,"2*exp(x^(1/2))*(x^(1/2) - 1)","B"
79,1,13,26,0.108663,"\text{Not used}","int(x^3*exp(-x^2),x)","-\frac{{\mathrm{e}}^{-x^2}\,\left(x^2+1\right)}{2}","Not used",1,"-(exp(-x^2)*(x^2 + 1))/2","B"
80,1,27,41,0.031617,"\text{Not used}","int(exp(a*x)*cos(b*x),x)","\frac{{\mathrm{e}}^{a\,x}\,\left(a\,\cos\left(b\,x\right)+b\,\sin\left(b\,x\right)\right)}{a^2+b^2}","Not used",1,"(exp(a*x)*(a*cos(b*x) + b*sin(b*x)))/(a^2 + b^2)","B"
81,1,29,42,0.020546,"\text{Not used}","int(exp(a*x)*sin(b*x),x)","-\frac{{\mathrm{e}}^{a\,x}\,\left(b\,\cos\left(b\,x\right)-a\,\sin\left(b\,x\right)\right)}{a^2+b^2}","Not used",1,"-(exp(a*x)*(b*cos(b*x) - a*sin(b*x)))/(a^2 + b^2)","B"
82,1,13,15,0.104823,"\text{Not used}","int(acot(x),x)","\frac{\ln\left(x^2+1\right)}{2}+x\,\mathrm{acot}\left(x\right)","Not used",1,"log(x^2 + 1)/2 + x*acot(x)","B"
83,1,21,19,0.609447,"\text{Not used}","int(acos(1/x),x)","x\,\mathrm{acos}\left(\frac{1}{x}\right)-\ln\left(x+\sqrt{x^2-1}\right)\,\mathrm{sign}\left(x\right)","Not used",1,"x*acos(1/x) - log(x + (x^2 - 1)^(1/2))*sign(x)","B"
84,1,20,17,0.208685,"\text{Not used}","int(asin(1/x),x)","x\,\mathrm{asin}\left(\frac{1}{x}\right)+\ln\left(x+\sqrt{x^2-1}\right)\,\mathrm{sign}\left(x\right)","Not used",1,"x*asin(1/x) + log(x + (x^2 - 1)^(1/2))*sign(x)","B"
85,1,22,25,0.031517,"\text{Not used}","int(asin(x)^2,x)","2\,\mathrm{asin}\left(x\right)\,\sqrt{1-x^2}+x\,\left({\mathrm{asin}\left(x\right)}^2-2\right)","Not used",1,"2*asin(x)*(1 - x^2)^(1/2) + x*(asin(x)^2 - 2)","B"
86,1,20,22,0.021347,"\text{Not used}","int(asin(x)/x^2,x)","-\mathrm{atanh}\left(\frac{1}{\sqrt{1-x^2}}\right)-\frac{\mathrm{asin}\left(x\right)}{x}","Not used",1,"- atanh(1/(1 - x^2)^(1/2)) - asin(x)/x","B"
87,1,14,16,0.162753,"\text{Not used}","int(1/(a^2 - x^2)^(1/2),x)","\mathrm{atan}\left(\frac{x}{\sqrt{a^2-x^2}}\right)","Not used",1,"atan(x/(a^2 - x^2)^(1/2))","B"
88,1,11,10,0.089740,"\text{Not used}","int(1/(1 - x^2 - 2*x)^(1/2),x)","\mathrm{asin}\left(\frac{\sqrt{8}\,\left(2\,x+2\right)}{8}\right)","Not used",1,"asin((8^(1/2)*(2*x + 2))/8)","B"
89,1,10,10,0.036294,"\text{Not used}","int(1/(a^2 + x^2),x)","\frac{\mathrm{atan}\left(\frac{x}{a}\right)}{a}","Not used",1,"atan(x/a)/a","B"
90,1,16,24,0.101055,"\text{Not used}","int(1/(a + b*x^2),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{\sqrt{a}\,\sqrt{b}}","Not used",1,"atan((b^(1/2)*x)/a^(1/2))/(a^(1/2)*b^(1/2))","B"
91,1,16,19,0.076039,"\text{Not used}","int(1/(x^2 - x + 2),x)","\frac{2\,\sqrt{7}\,\mathrm{atan}\left(\frac{\sqrt{7}\,\left(2\,x-1\right)}{7}\right)}{7}","Not used",1,"(2*7^(1/2)*atan((7^(1/2)*(2*x - 1))/7))/7","B"
92,1,14,21,0.023419,"\text{Not used}","int(x*atan(x),x)","\mathrm{atan}\left(x\right)\,\left(\frac{x^2}{2}+\frac{1}{2}\right)-\frac{x}{2}","Not used",1,"atan(x)*(x^2/2 + 1/2) - x/2","B"
93,1,24,40,0.029461,"\text{Not used}","int(x^2*acos(x),x)","\frac{x^3\,\mathrm{acos}\left(x\right)}{3}-\frac{\sqrt{1-x^2}\,\left(x^2+2\right)}{9}","Not used",1,"(x^3*acos(x))/3 - ((1 - x^2)^(1/2)*(x^2 + 2))/9","B"
94,1,29,35,0.124137,"\text{Not used}","int(x*atan(x)^2,x)","\frac{\ln\left(x^2+1\right)}{2}+\frac{{\mathrm{atan}\left(x\right)}^2}{2}+\frac{x^2\,{\mathrm{atan}\left(x\right)}^2}{2}-x\,\mathrm{atan}\left(x\right)","Not used",1,"log(x^2 + 1)/2 + atan(x)^2/2 + (x^2*atan(x)^2)/2 - x*atan(x)","B"
95,1,16,22,0.057270,"\text{Not used}","int(atan(x^(1/2)),x)","\mathrm{atan}\left(\sqrt{x}\right)+x\,\mathrm{atan}\left(\sqrt{x}\right)-\sqrt{x}","Not used",1,"atan(x^(1/2)) + x*atan(x^(1/2)) - x^(1/2)","B"
96,1,6,8,0.660788,"\text{Not used}","int(atan(x^(1/2))/(x^(1/2)*(x + 1)),x)","{\mathrm{atan}\left(\sqrt{x}\right)}^2","Not used",1,"atan(x^(1/2))^2","B"
97,1,17,23,0.077523,"\text{Not used}","int((1 - x^2)^(1/2),x)","\frac{\mathrm{asin}\left(x\right)}{2}+\frac{x\,\sqrt{1-x^2}}{2}","Not used",1,"asin(x)/2 + (x*(1 - x^2)^(1/2))/2","B"
98,0,-1,22,0.000000,"\text{Not used}","int((x*exp(atan(x)))/(x^2 + 1)^(3/2),x)","\int \frac{x\,{\mathrm{e}}^{\mathrm{atan}\left(x\right)}}{{\left(x^2+1\right)}^{3/2}} \,d x","Not used",1,"int((x*exp(atan(x)))/(x^2 + 1)^(3/2), x)","F"
99,0,-1,20,0.000000,"\text{Not used}","int(exp(atan(x))/(x^2 + 1)^(3/2),x)","\int \frac{{\mathrm{e}}^{\mathrm{atan}\left(x\right)}}{{\left(x^2+1\right)}^{3/2}} \,d x","Not used",1,"int(exp(atan(x))/(x^2 + 1)^(3/2), x)","F"
100,1,17,19,0.027646,"\text{Not used}","int(x^2/(x^2 + 1)^2,x)","\frac{\mathrm{atan}\left(x\right)}{2}-\frac{x}{2\,\left(x^2+1\right)}","Not used",1,"atan(x)/2 - x/(2*(x^2 + 1))","B"
101,1,3,4,0.099680,"\text{Not used}","int(exp(x)/(exp(2*x) + 1),x)","\mathrm{atan}\left({\mathrm{e}}^x\right)","Not used",1,"atan(exp(x))","B"
102,1,22,27,0.135638,"\text{Not used}","int(acot(exp(x))*exp(-x),x)","\frac{\ln\left({\mathrm{e}}^{2\,x}+1\right)}{2}-x-\mathrm{acot}\left({\mathrm{e}}^x\right)\,{\mathrm{e}}^{-x}","Not used",1,"log(exp(2*x) + 1)/2 - x - acot(exp(x))*exp(-x)","B"
103,1,49,42,0.069972,"\text{Not used}","int(((a + x)/(a - x))^(1/2),x)","2\,a\,\mathrm{atan}\left(\sqrt{\frac{a+x}{a-x}}\right)-\frac{2\,a\,\sqrt{\frac{a+x}{a-x}}}{\frac{a+x}{a-x}+1}","Not used",1,"2*a*atan(((a + x)/(a - x))^(1/2)) - (2*a*((a + x)/(a - x))^(1/2))/((a + x)/(a - x) + 1)","B"
104,0,-1,71,0.000000,"\text{Not used}","int((-(a - x)*(b - x))^(1/2),x)","\int \sqrt{-\left(a-x\right)\,\left(b-x\right)} \,d x","Not used",1,"int((-(a - x)*(b - x))^(1/2), x)","F"
105,0,-1,32,0.000000,"\text{Not used}","int(1/(-(a - x)*(b - x))^(1/2),x)","\int \frac{1}{\sqrt{-\left(a-x\right)\,\left(b-x\right)}} \,d x","Not used",1,"int(1/(-(a - x)*(b - x))^(1/2), x)","F"
106,1,13,15,0.050938,"\text{Not used}","int((5*x + 3)/(2*x + x^2 - 3),x)","2\,\ln\left(x-1\right)+3\,\ln\left(x+3\right)","Not used",1,"2*log(x - 1) + 3*log(x + 3)","B"
107,1,13,19,0.038021,"\text{Not used}","int((2*x + 5)/(2*x + x^2 - 3),x)","\frac{7\,\ln\left(x-1\right)}{4}+\frac{\ln\left(x+3\right)}{4}","Not used",1,"(7*log(x - 1))/4 + log(x + 3)/4","B"
108,1,19,23,0.041452,"\text{Not used}","int(-(3*x + x^3)/(2*x - x^2 + 3),x)","2\,x+\ln\left(x+1\right)+9\,\ln\left(x-3\right)+\frac{x^2}{2}","Not used",1,"2*x + log(x + 1) + 9*log(x - 3) + x^2/2","B"
109,1,19,23,0.188843,"\text{Not used}","int((5*x + 2*x^2 - 1)/(x^2 - 2*x + x^3),x)","2\,\ln\left(x-1\right)+\mathrm{atanh}\left(\frac{135}{11\,\left(11\,x-5\right)}+\frac{16}{11}\right)","Not used",1,"2*log(x - 1) + atanh(135/(11*(11*x - 5)) + 16/11)","B"
110,1,18,24,0.050294,"\text{Not used}","int((2*x + x^2 + 3)/((x - 1)*(x + 1)^2),x)","\frac{3\,\ln\left(x-1\right)}{2}-\frac{\ln\left(x+1\right)}{2}+\frac{1}{x+1}","Not used",1,"(3*log(x - 1))/2 - log(x + 1)/2 + 1/(x + 1)","B"
111,1,57,28,0.186334,"\text{Not used}","int((2*x + 3*x^2 - 2)/(x^3 - 1),x)","\ln\left(x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)+\ln\left(x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)+\ln\left(x-1\right)-\frac{\sqrt{3}\,\ln\left(x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,2{}\mathrm{i}}{3}+\frac{\sqrt{3}\,\ln\left(x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,2{}\mathrm{i}}{3}","Not used",1,"log(x - (3^(1/2)*1i)/2 + 1/2) + log(x + (3^(1/2)*1i)/2 + 1/2) + log(x - 1) - (3^(1/2)*log(x - (3^(1/2)*1i)/2 + 1/2)*2i)/3 + (3^(1/2)*log(x + (3^(1/2)*1i)/2 + 1/2)*2i)/3","B"
112,1,53,49,0.101276,"\text{Not used}","int((2*x^2 - x - x^3 + x^4 + 2)/((x^2 + 2)^2*(x - 1)),x)","\frac{\ln\left(x-1\right)}{3}+\ln\left(x-\sqrt{2}\,1{}\mathrm{i}\right)\,\left(\frac{1}{3}+\frac{\sqrt{2}\,1{}\mathrm{i}}{12}\right)-\ln\left(x+\sqrt{2}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{3}+\frac{\sqrt{2}\,1{}\mathrm{i}}{12}\right)+\frac{1}{2\,\left(x^2+2\right)}","Not used",1,"log(x - 1)/3 + log(x - 2^(1/2)*1i)*((2^(1/2)*1i)/12 + 1/3) - log(x + 2^(1/2)*1i)*((2^(1/2)*1i)/12 - 1/3) + 1/(2*(x^2 + 2))","B"
113,1,21,21,0.325779,"\text{Not used}","int(1/(cos(x) + sin(x)),x)","-\sqrt{2}\,\mathrm{atanh}\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}\,\mathrm{tan}\left(\frac{x}{2}\right)}{2}\right)","Not used",1,"-2^(1/2)*atanh(2^(1/2)/2 - (2^(1/2)*tan(x/2))/2)","B"
114,1,87,16,0.157284,"\text{Not used}","int(x/((4 - x^2)^(1/2) - x^2 + 4),x)","-\frac{\ln\left(x-\sqrt{3}\right)}{2}-\frac{\ln\left(\frac{\sqrt{3}\,x\,1{}\mathrm{i}+\sqrt{4-x^2}\,1{}\mathrm{i}+4{}\mathrm{i}}{x+\sqrt{3}}\right)}{2}-\frac{\ln\left(x+\sqrt{3}\right)}{2}-\frac{\ln\left(\frac{-\sqrt{3}\,x\,1{}\mathrm{i}+\sqrt{4-x^2}\,1{}\mathrm{i}+4{}\mathrm{i}}{x-\sqrt{3}}\right)}{2}","Not used",1,"- log(x - 3^(1/2))/2 - log((3^(1/2)*x*1i + (4 - x^2)^(1/2)*1i + 4i)/(x + 3^(1/2)))/2 - log(x + 3^(1/2))/2 - log(((4 - x^2)^(1/2)*1i - 3^(1/2)*x*1i + 4i)/(x - 3^(1/2)))/2","B"
115,1,9,11,0.046853,"\text{Not used}","int((2*x + 3)/((x - 2)*(x + 5)),x)","\ln\left(x^2+3\,x-10\right)","Not used",1,"log(3*x + x^2 - 10)","B"
116,1,19,23,0.111094,"\text{Not used}","int(x/((x + 1)*(x + 2)*(x + 3)),x)","2\,\ln\left(x+2\right)-\frac{\ln\left(x+1\right)}{2}-\frac{3\,\ln\left(x+3\right)}{2}","Not used",1,"2*log(x + 2) - log(x + 1)/2 - (3*log(x + 3))/2","B"
117,1,18,30,0.040842,"\text{Not used}","int(x/(x^3 - 3*x + 2),x)","-\frac{4\,\mathrm{atanh}\left(\frac{2\,x}{3}+\frac{1}{3}\right)}{9}-\frac{1}{3\,\left(x-1\right)}","Not used",1,"- (4*atanh((2*x)/3 + 1/3))/9 - 1/(3*(x - 1))","B"
118,1,30,27,0.095296,"\text{Not used}","int((2*x + x^4 - 6)/(x^2 - 2*x + x^3),x)","3\,\ln\left(x\right)-x+\frac{x^2}{2}+\mathrm{atan}\left(\frac{192{}\mathrm{i}}{7\,\left(28\,x-40\right)}+\frac{9}{7}{}\mathrm{i}\right)\,2{}\mathrm{i}","Not used",1,"atan(192i/(7*(28*x - 40)) + 9i/7)*2i - x + 3*log(x) + x^2/2","B"
119,1,15,23,0.085853,"\text{Not used}","int((8*x^3 + 7)/((2*x + 1)^3*(x + 1)),x)","\ln\left(x+1\right)+\frac{6\,x}{{\left(2\,x+1\right)}^2}","Not used",1,"log(x + 1) + (6*x)/(2*x + 1)^2","B"
120,1,14,16,0.044465,"\text{Not used}","int((x + 4*x^2 + 1)/(x^3 - 1),x)","\ln\left(x^2+x+1\right)+2\,\ln\left(x-1\right)","Not used",1,"log(x + x^2 + 1) + 2*log(x - 1)","B"
121,1,12,18,0.038282,"\text{Not used}","int(x^4/(5*x^2 + x^4 + 4),x)","x-\frac{8\,\mathrm{atan}\left(\frac{x}{2}\right)}{3}+\frac{\mathrm{atan}\left(x\right)}{3}","Not used",1,"x - (8*atan(x/2))/3 + atan(x)/3","B"
122,1,11,11,0.103002,"\text{Not used}","int((x + 2)/(x + x^2),x)","2\,\ln\left(x\right)-\ln\left(x+1\right)","Not used",1,"2*log(x) - log(x + 1)","B"
123,1,20,24,0.034621,"\text{Not used}","int(1/(x*(x^2 + 1)^2),x)","\ln\left(x\right)-\frac{\ln\left(x^2+1\right)}{2}+\frac{1}{2\,\left(x^2+1\right)}","Not used",1,"log(x) - log(x^2 + 1)/2 + 1/(2*(x^2 + 1))","B"
124,1,45,46,0.088039,"\text{Not used}","int(1/((x + 1)*(x + 2)^2*(x + 3)^3),x)","\frac{\ln\left(x+1\right)}{8}+2\,\ln\left(x+2\right)-\frac{17\,\ln\left(x+3\right)}{8}+\frac{\frac{9\,x^2}{4}+\frac{25\,x}{2}+17}{x^3+8\,x^2+21\,x+18}","Not used",1,"log(x + 1)/8 + 2*log(x + 2) - (17*log(x + 3))/8 + ((25*x)/2 + (9*x^2)/4 + 17)/(21*x + 8*x^2 + x^3 + 18)","B"
125,1,10,10,0.027615,"\text{Not used}","int(x/(x + 1)^2,x)","\ln\left(x+1\right)+\frac{1}{x+1}","Not used",1,"log(x + 1) + 1/(x + 1)","B"
126,1,13,17,0.110478,"\text{Not used}","int(-1/(x - x^3),x)","\frac{\ln\left(x^2-1\right)}{2}-\ln\left(x\right)","Not used",1,"log(x^2 - 1)/2 - log(x)","B"
127,1,14,20,0.044970,"\text{Not used}","int(x^2/(x + x^2 - 6),x)","x+\frac{4\,\ln\left(x-2\right)}{5}-\frac{9\,\ln\left(x+3\right)}{5}","Not used",1,"x + (4*log(x - 2))/5 - (9*log(x + 3))/5","B"
128,1,12,16,0.037085,"\text{Not used}","int((x + 2)/(x^2 - 4*x + 4),x)","\ln\left(x-2\right)-\frac{4}{x-2}","Not used",1,"log(x - 2) - 4/(x - 2)","B"
129,1,14,14,0.081564,"\text{Not used}","int(1/((x^2 - 4*x + 4)*(x^2 - 4*x + 5)),x)","-\mathrm{atan}\left(x-2\right)-\frac{1}{x-2}","Not used",1,"- atan(x - 2) - 1/(x - 2)","B"
130,1,17,21,0.063137,"\text{Not used}","int((x - 3)/(2*x + 3*x^2 + x^3),x)","4\,\ln\left(x+1\right)-\frac{5\,\ln\left(x+2\right)}{2}-\frac{3\,\ln\left(x\right)}{2}","Not used",1,"4*log(x + 1) - (5*log(x + 2))/2 - (3*log(x))/2","B"
131,1,17,21,0.087243,"\text{Not used}","int(1/(x^2 - 1)^2,x)","\frac{\mathrm{atanh}\left(x\right)}{2}-\frac{x}{2\,\left(x^2-1\right)}","Not used",1,"atanh(x)/2 - x/(2*(x^2 - 1))","B"
132,1,16,22,0.158916,"\text{Not used}","int((x + 1)/(x^3 - 1),x)","\frac{2\,\ln\left(x-1\right)}{3}-\frac{\ln\left(x^2+x+1\right)}{3}","Not used",1,"(2*log(x - 1))/3 - log(x + x^2 + 1)/3","B"
133,1,10,10,0.030061,"\text{Not used}","int((x^4 + 1)/(x*(x^2 + 1)^2),x)","\ln\left(x\right)+\frac{1}{x^2+1}","Not used",1,"log(x) + 1/(x^2 + 1)","B"
134,1,16,31,0.039515,"\text{Not used}","int(-1/(2*x^3 - x^4),x)","\frac{\frac{x}{4}+\frac{1}{4}}{x^2}-\frac{\mathrm{atanh}\left(x-1\right)}{4}","Not used",1,"(x/4 + 1/4)/x^2 - atanh(x - 1)/4","B"
135,1,24,18,0.039361,"\text{Not used}","int(-(x^3 - 1)/(x*(x^2 + 1)),x)","\ln\left(x\right)-x+\ln\left(x-\mathrm{i}\right)\,\left(-\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)+\ln\left(x+1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)","Not used",1,"log(x) - log(x - 1i)*(1/2 + 1i/2) - log(x + 1i)*(1/2 - 1i/2) - x","B"
136,1,9,13,0.028754,"\text{Not used}","int(1/(x^4 - 1),x)","-\frac{\mathrm{atan}\left(x\right)}{2}-\frac{\mathrm{atanh}\left(x\right)}{2}","Not used",1,"- atan(x)/2 - atanh(x)/2","B"
137,1,33,85,0.115439,"\text{Not used}","int(1/(x^4 + 1),x)","\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,x\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(\frac{1}{4}+\frac{1}{4}{}\mathrm{i}\right)+\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,x\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(\frac{1}{4}-\frac{1}{4}{}\mathrm{i}\right)","Not used",1,"2^(1/2)*atan(2^(1/2)*x*(1/2 - 1i/2))*(1/4 + 1i/4) + 2^(1/2)*atan(2^(1/2)*x*(1/2 + 1i/2))*(1/4 - 1i/4)","B"
138,1,15,23,0.081388,"\text{Not used}","int(x^2/(2*x + x^2 + 2)^2,x)","\mathrm{atan}\left(x+1\right)+\frac{1}{x^2+2\,x+2}","Not used",1,"atan(x + 1) + 1/(2*x + x^2 + 2)","B"
139,1,11,11,0.061860,"\text{Not used}","int((4*x^5 - 1)/(x + x^5 + 1)^2,x)","-\frac{x}{x^5+x+1}","Not used",1,"-x/(x + x^5 + 1)","B"
140,1,21,45,0.100408,"\text{Not used}","int(1/(2*sin(x) - cos(x) + 5),x)","\frac{\sqrt{20}\,\mathrm{atan}\left(\frac{3\,\sqrt{20}\,\mathrm{tan}\left(\frac{x}{2}\right)}{10}+\frac{\sqrt{20}}{10}\right)}{10}","Not used",1,"(20^(1/2)*atan((3*20^(1/2)*tan(x/2))/10 + 20^(1/2)/10))/10","B"
141,1,28,37,0.318502,"\text{Not used}","int(1/(a*cos(x) + 1),x)","\frac{2\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{a-1}}{\sqrt{a+1}}\right)}{\sqrt{a-1}\,\sqrt{a+1}}","Not used",1,"(2*atanh((tan(x/2)*(a - 1)^(1/2))/(a + 1)^(1/2)))/((a - 1)^(1/2)*(a + 1)^(1/2))","B"
142,1,15,56,0.238567,"\text{Not used}","int(1/(2*cos(x) + 1),x)","\frac{2\,\sqrt{3}\,\mathrm{atanh}\left(\frac{\sqrt{3}\,\mathrm{tan}\left(\frac{x}{2}\right)}{3}\right)}{3}","Not used",1,"(2*3^(1/2)*atanh((3^(1/2)*tan(x/2))/3))/3","B"
143,1,32,31,0.219278,"\text{Not used}","int(1/(cos(x)/2 + 1),x)","\frac{4\,\sqrt{3}\,\left(\frac{x}{2}-\mathrm{atan}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)\right)}{3}+\frac{4\,\sqrt{3}\,\mathrm{atan}\left(\frac{\sqrt{3}\,\mathrm{tan}\left(\frac{x}{2}\right)}{3}\right)}{3}","Not used",1,"(4*3^(1/2)*(x/2 - atan(tan(x/2))))/3 + (4*3^(1/2)*atan((3^(1/2)*tan(x/2))/3))/3","B"
144,1,26,36,0.207798,"\text{Not used}","int(sin(x)^2/(sin(x)^2 + 1),x)","x-\frac{\sqrt{2}\,\left(x-\mathrm{atan}\left(\mathrm{tan}\left(x\right)\right)\right)}{2}-\frac{\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,\mathrm{tan}\left(x\right)\right)}{2}","Not used",1,"x - (2^(1/2)*(x - atan(tan(x))))/2 - (2^(1/2)*atan(2^(1/2)*tan(x)))/2","B"
145,1,15,15,0.455354,"\text{Not used}","int(1/(b^2*cos(x)^2 + a^2*sin(x)^2),x)","\frac{\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(x\right)}{b}\right)}{a\,b}","Not used",1,"atan((a*tan(x))/b)/(a*b)","B"
146,1,29,17,0.633979,"\text{Not used}","int(1/(b*cos(x) + a*sin(x))^2,x)","\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)}{b\,\left(-b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)+b\right)}","Not used",1,"(2*tan(x/2))/(b*(b + 2*a*tan(x/2) - b*tan(x/2)^2))","B"
147,1,34,30,0.313615,"\text{Not used}","int(sin(x)/(cos(x) + sin(x) + 1),x)","-\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)+\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)+\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)","Not used",1,"log(tan(x/2) - 1i)*(1/2 - 1i/2) - log(tan(x/2) + 1) + log(tan(x/2) + 1i)*(1/2 + 1i/2)","B"
148,1,22,29,0.037039,"\text{Not used}","int((3 - x^2)^(1/2),x)","\frac{3\,\mathrm{asin}\left(\frac{\sqrt{3}\,x}{3}\right)}{2}+\frac{x\,\sqrt{3-x^2}}{2}","Not used",1,"(3*asin((3^(1/2)*x)/3))/2 + (x*(3 - x^2)^(1/2))/2","B"
149,1,11,13,0.169091,"\text{Not used}","int(x/(3 - x^2)^(1/2),x)","-\sqrt{3-x^2}","Not used",1,"-(3 - x^2)^(1/2)","B"
150,1,35,37,0.208816,"\text{Not used}","int((3 - x^2)^(1/2)/x,x)","\sqrt{3}\,\ln\left(\sqrt{\frac{3}{x^2}-1}-\sqrt{3}\,\sqrt{\frac{1}{x^2}}\right)+\sqrt{3-x^2}","Not used",1,"3^(1/2)*log((3/x^2 - 1)^(1/2) - 3^(1/2)*(1/x^2)^(1/2)) + (3 - x^2)^(1/2)","B"
151,1,21,22,0.084824,"\text{Not used}","int((x + x^2)^(1/2)/x,x)","\frac{\ln\left(x+\sqrt{x\,\left(x+1\right)}+\frac{1}{2}\right)}{2}+\sqrt{x^2+x}","Not used",1,"log(x + (x*(x + 1))^(1/2) + 1/2)/2 + (x + x^2)^(1/2)","B"
152,1,20,27,0.088049,"\text{Not used}","int((x^2 + 5)^(1/2),x)","\frac{5\,\mathrm{asinh}\left(\frac{\sqrt{5}\,x}{5}\right)}{2}+\frac{x\,\sqrt{x^2+5}}{2}","Not used",1,"(5*asinh((5^(1/2)*x)/5))/2 + (x*(x^2 + 5)^(1/2))/2","B"
153,1,23,27,0.052582,"\text{Not used}","int(x/(x + x^2 + 1)^(1/2),x)","\sqrt{x^2+x+1}-\frac{\ln\left(x+\sqrt{x^2+x+1}+\frac{1}{2}\right)}{2}","Not used",1,"(x + x^2 + 1)^(1/2) - log(x + (x + x^2 + 1)^(1/2) + 1/2)/2","B"
154,1,11,14,0.171280,"\text{Not used}","int(1/(x + x^2)^(1/2),x)","\ln\left(x+\sqrt{x\,\left(x+1\right)}+\frac{1}{2}\right)","Not used",1,"log(x + (x*(x + 1))^(1/2) + 1/2)","B"
155,1,73,68,0.084682,"\text{Not used}","int((2 - x^2 - x)^(1/2)/x^2,x)","\frac{\sqrt{2}\,\ln\left(\frac{2}{x}+\frac{\sqrt{2}\,\sqrt{-x^2-x+2}}{x}-\frac{1}{2}\right)}{4}-\frac{\sqrt{-x^2-x+2}}{x}+\ln\left(x\,1{}\mathrm{i}+\sqrt{-x^2-x+2}+\frac{1}{2}{}\mathrm{i}\right)\,1{}\mathrm{i}","Not used",1,"log(x*1i + (2 - x^2 - x)^(1/2) + 1i/2)*1i - (2 - x^2 - x)^(1/2)/x + (2^(1/2)*log(2/x + (2^(1/2)*(2 - x^2 - x)^(1/2))/x - 1/2))/4","B"
156,1,13,13,0.030596,"\text{Not used}","int(log(t)/(t + 1),t)","\mathrm{polylog}\left(2,-t\right)+\ln\left(t+1\right)\,\ln\left(t\right)","Not used",1,"polylog(2, -t) + log(t + 1)*log(t)","B"
157,1,2,15,0.098924,"\text{Not used}","int(log(exp(cos(x))),x)","\sin\left(x\right)","Not used",1,"sin(x)","B"
158,1,2,2,0.007025,"\text{Not used}","int(exp(t)/t,t)","\mathrm{ei}\left(t\right)","Not used",1,"ei(t)","B"
159,1,4,4,0.014191,"\text{Not used}","int(exp(a*t)/t,t)","\mathrm{ei}\left(a\,t\right)","Not used",1,"ei(a*t)","B"
160,1,14,11,0.024387,"\text{Not used}","int(exp(t)/t^2,t)","-\frac{{\mathrm{e}}^t}{t}-\mathrm{expint}\left(-t\right)","Not used",1,"- exp(t)/t - expint(-t)","B"
161,1,9,14,0.016922,"\text{Not used}","int(exp(1/t),t)","t\,\mathrm{expint}\left(2,-\frac{1}{t}\right)","Not used",1,"t*expint(2, -1/t)","B"
162,1,14,15,0.028414,"\text{Not used}","int(-exp(-t)/(a - t + 1),t)","{\mathrm{e}}^{-a-1}\,\mathrm{ei}\left(a-t+1\right)","Not used",1,"exp(- a - 1)*ei(a - t + 1)","B"
163,1,10,13,0.118105,"\text{Not used}","int((t*exp(t^2))/(t^2 + 1),t)","\frac{{\mathrm{e}}^{-1}\,\mathrm{ei}\left(t^2+1\right)}{2}","Not used",1,"(exp(-1)*ei(t^2 + 1))/2","B"
164,1,17,19,0.125515,"\text{Not used}","int(exp(t)/(t + 1)^2,t)","\mathrm{ei}\left(t+1\right)\,{\mathrm{e}}^{-1}-\frac{{\mathrm{e}}^t}{t+1}","Not used",1,"ei(t + 1)*exp(-1) - exp(t)/(t + 1)","B"
165,0,-1,18,0.000000,"\text{Not used}","int(log(t + 1)*exp(t),t)","\int \ln\left(t+1\right)\,{\mathrm{e}}^t \,d t","Not used",1,"int(log(t + 1)*exp(t), t)","F"
166,1,9,16,0.017073,"\text{Not used}","int(t*exp(-t),t)","-{\mathrm{e}}^{-t}\,\left(t+1\right)","Not used",1,"-exp(-t)*(t + 1)","B"
167,1,14,26,0.029660,"\text{Not used}","int(t^2*exp(-t),t)","-{\mathrm{e}}^{-t}\,\left(t^2+2\,t+2\right)","Not used",1,"-exp(-t)*(2*t + t^2 + 2)","B"
168,1,19,36,0.023333,"\text{Not used}","int(t^3*exp(-t),t)","-{\mathrm{e}}^{-t}\,\left(t^3+3\,t^2+6\,t+6\right)","Not used",1,"-exp(-t)*(6*t + 3*t^2 + t^3 + 6)","B"
169,1,2034,48,10.613330,"\text{Not used}","int((b1*cos(x) + a1*sin(x))/(b*cos(x) + a*sin(x)),x)","\frac{2\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{\left(\frac{{\left(a\,a_{1}+b\,b_{1}\right)}^3\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{{\left(a^2+b^2\right)}^3}+\frac{\left(\frac{\left(a\,a_{1}+b\,b_{1}\right)\,\left(32\,a^2\,a_{1}\,b^2-\frac{\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{2\,\left(a^2+b^2\right)}-64\,a_{1}\,b^4+128\,a\,b^3\,b_{1}+32\,a^3\,b\,b_{1}\right)}{a^2+b^2}-\frac{\left(a\,a_{1}+b\,b_{1}\right)\,\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{2\,{\left(a^2+b^2\right)}^2}\right)\,\left(2\,a\,b_{1}-2\,a_{1}\,b\right)}{2\,\left(a^2+b^2\right)}-\frac{\left(a\,a_{1}+b\,b_{1}\right)\,\left(32\,b^3\,{b_{1}}^2-\frac{\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(32\,a^2\,a_{1}\,b^2-\frac{\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{2\,\left(a^2+b^2\right)}-64\,a_{1}\,b^4+128\,a\,b^3\,b_{1}+32\,a^3\,b\,b_{1}\right)}{2\,\left(a^2+b^2\right)}+64\,a^2\,{a_{1}}^2\,b-96\,a^2\,b\,{b_{1}}^2+192\,a\,a_{1}\,b^2\,b_{1}\right)}{a^2+b^2}\right)\,\left(a^4\,{a_{1}}^2-4\,a^4\,{b_{1}}^2+18\,a^3\,a_{1}\,b\,b_{1}-13\,a^2\,{a_{1}}^2\,b^2+13\,a^2\,b^2\,{b_{1}}^2-18\,a\,a_{1}\,b^3\,b_{1}+4\,{a_{1}}^2\,b^4-b^4\,{b_{1}}^2\right)}{{\left(a^2+b^2\right)}^2\,{\left(a^2\,{a_{1}}^2+4\,a^2\,{b_{1}}^2-6\,a\,a_{1}\,b\,b_{1}+4\,{a_{1}}^2\,b^2+b^2\,{b_{1}}^2\right)}^2}-\frac{\left(\frac{\left(\frac{\left(a\,a_{1}+b\,b_{1}\right)\,\left(32\,a^2\,a_{1}\,b^2-\frac{\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{2\,\left(a^2+b^2\right)}-64\,a_{1}\,b^4+128\,a\,b^3\,b_{1}+32\,a^3\,b\,b_{1}\right)}{a^2+b^2}-\frac{\left(a\,a_{1}+b\,b_{1}\right)\,\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{2\,{\left(a^2+b^2\right)}^2}\right)\,\left(a\,a_{1}+b\,b_{1}\right)}{a^2+b^2}-32\,a_{1}\,b^2\,{b_{1}}^2-64\,{a_{1}}^3\,b^2+\frac{\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(32\,b^3\,{b_{1}}^2-\frac{\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(32\,a^2\,a_{1}\,b^2-\frac{\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{2\,\left(a^2+b^2\right)}-64\,a_{1}\,b^4+128\,a\,b^3\,b_{1}+32\,a^3\,b\,b_{1}\right)}{2\,\left(a^2+b^2\right)}+64\,a^2\,{a_{1}}^2\,b-96\,a^2\,b\,{b_{1}}^2+192\,a\,a_{1}\,b^2\,b_{1}\right)}{2\,\left(a^2+b^2\right)}+32\,a\,b\,{b_{1}}^3-\frac{{\left(a\,a_{1}+b\,b_{1}\right)}^2\,\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(96\,a^4\,b+96\,a^2\,b^3\right)}{2\,{\left(a^2+b^2\right)}^3}+64\,a\,{a_{1}}^2\,b\,b_{1}\right)\,\left(4\,a^4\,a_{1}\,b_{1}-6\,a^3\,{a_{1}}^2\,b+12\,a^3\,b\,{b_{1}}^2-28\,a^2\,a_{1}\,b^2\,b_{1}+12\,a\,{a_{1}}^2\,b^3-6\,a\,b^3\,{b_{1}}^2+4\,a_{1}\,b^4\,b_{1}\right)}{{\left(a^2+b^2\right)}^2\,{\left(a^2\,{a_{1}}^2+4\,a^2\,{b_{1}}^2-6\,a\,a_{1}\,b\,b_{1}+4\,{a_{1}}^2\,b^2+b^2\,{b_{1}}^2\right)}^2}\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}{32\,b_{1}\,b^2+32\,a\,a_{1}\,b}+\frac{\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(32\,{a_{1}}^2\,b^2\,b_{1}+\frac{\left(\frac{\left(a\,a_{1}+b\,b_{1}\right)\,\left(\frac{\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{2\,\left(a^2+b^2\right)}-32\,b^4\,b_{1}+64\,a^2\,b^2\,b_{1}-64\,a\,a_{1}\,b^3+32\,a^3\,a_{1}\,b\right)}{a^2+b^2}+\frac{\left(a\,a_{1}+b\,b_{1}\right)\,\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{2\,{\left(a^2+b^2\right)}^2}\right)\,\left(a\,a_{1}+b\,b_{1}\right)}{a^2+b^2}-\frac{\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(\frac{\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(\frac{\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{2\,\left(a^2+b^2\right)}-32\,b^4\,b_{1}+64\,a^2\,b^2\,b_{1}-64\,a\,a_{1}\,b^3+32\,a^3\,a_{1}\,b\right)}{2\,\left(a^2+b^2\right)}-32\,a\,{a_{1}}^2\,b^2-32\,a\,b^2\,{b_{1}}^2+64\,a_{1}\,b^3\,b_{1}+64\,a^2\,a_{1}\,b\,b_{1}\right)}{2\,\left(a^2+b^2\right)}+\frac{{\left(a\,a_{1}+b\,b_{1}\right)}^2\,\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{2\,{\left(a^2+b^2\right)}^3}-32\,a\,a_{1}\,b\,{b_{1}}^2\right)\,\left(4\,a^4\,a_{1}\,b_{1}-6\,a^3\,{a_{1}}^2\,b+12\,a^3\,b\,{b_{1}}^2-28\,a^2\,a_{1}\,b^2\,b_{1}+12\,a\,{a_{1}}^2\,b^3-6\,a\,b^3\,{b_{1}}^2+4\,a_{1}\,b^4\,b_{1}\right)}{\left(32\,b_{1}\,b^2+32\,a\,a_{1}\,b\right)\,{\left(a^2+b^2\right)}^2\,{\left(a^2\,{a_{1}}^2+4\,a^2\,{b_{1}}^2-6\,a\,a_{1}\,b\,b_{1}+4\,{a_{1}}^2\,b^2+b^2\,{b_{1}}^2\right)}^2}-\frac{\left(a^4+2\,a^2\,b^2+b^4\right)\,\left(\frac{\left(\frac{\left(a\,a_{1}+b\,b_{1}\right)\,\left(\frac{\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{2\,\left(a^2+b^2\right)}-32\,b^4\,b_{1}+64\,a^2\,b^2\,b_{1}-64\,a\,a_{1}\,b^3+32\,a^3\,a_{1}\,b\right)}{a^2+b^2}+\frac{\left(a\,a_{1}+b\,b_{1}\right)\,\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{2\,{\left(a^2+b^2\right)}^2}\right)\,\left(2\,a\,b_{1}-2\,a_{1}\,b\right)}{2\,\left(a^2+b^2\right)}-\frac{{\left(a\,a_{1}+b\,b_{1}\right)}^3\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{{\left(a^2+b^2\right)}^3}+\frac{\left(a\,a_{1}+b\,b_{1}\right)\,\left(\frac{\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(\frac{\left(2\,a\,b_{1}-2\,a_{1}\,b\right)\,\left(96\,a^3\,b^2+96\,a\,b^4\right)}{2\,\left(a^2+b^2\right)}-32\,b^4\,b_{1}+64\,a^2\,b^2\,b_{1}-64\,a\,a_{1}\,b^3+32\,a^3\,a_{1}\,b\right)}{2\,\left(a^2+b^2\right)}-32\,a\,{a_{1}}^2\,b^2-32\,a\,b^2\,{b_{1}}^2+64\,a_{1}\,b^3\,b_{1}+64\,a^2\,a_{1}\,b\,b_{1}\right)}{a^2+b^2}\right)\,\left(a^4\,{a_{1}}^2-4\,a^4\,{b_{1}}^2+18\,a^3\,a_{1}\,b\,b_{1}-13\,a^2\,{a_{1}}^2\,b^2+13\,a^2\,b^2\,{b_{1}}^2-18\,a\,a_{1}\,b^3\,b_{1}+4\,{a_{1}}^2\,b^4-b^4\,{b_{1}}^2\right)}{\left(32\,b_{1}\,b^2+32\,a\,a_{1}\,b\right)\,{\left(a^2+b^2\right)}^2\,{\left(a^2\,{a_{1}}^2+4\,a^2\,{b_{1}}^2-6\,a\,a_{1}\,b\,b_{1}+4\,{a_{1}}^2\,b^2+b^2\,{b_{1}}^2\right)}^2}\right)\,\left(a\,a_{1}+b\,b_{1}\right)}{a^2+b^2}-\frac{\ln\left(\frac{1}{\cos\left(x\right)+1}\right)\,\left(2\,a\,b_{1}-2\,a_{1}\,b\right)}{2\,\left(a^2+b^2\right)}+\frac{\ln\left(-b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)+b\right)\,\left(a\,b_{1}-a_{1}\,b\right)}{a^2+b^2}","Not used",1,"(2*atan((tan(x/2)*(((((a*a1 + b*b1)^3*(96*a^4*b + 96*a^2*b^3))/(a^2 + b^2)^3 + ((((a*a1 + b*b1)*(32*a^2*a1*b^2 - ((2*a*b1 - 2*a1*b)*(96*a^4*b + 96*a^2*b^3))/(2*(a^2 + b^2)) - 64*a1*b^4 + 128*a*b^3*b1 + 32*a^3*b*b1))/(a^2 + b^2) - ((a*a1 + b*b1)*(2*a*b1 - 2*a1*b)*(96*a^4*b + 96*a^2*b^3))/(2*(a^2 + b^2)^2))*(2*a*b1 - 2*a1*b))/(2*(a^2 + b^2)) - ((a*a1 + b*b1)*(32*b^3*b1^2 - ((2*a*b1 - 2*a1*b)*(32*a^2*a1*b^2 - ((2*a*b1 - 2*a1*b)*(96*a^4*b + 96*a^2*b^3))/(2*(a^2 + b^2)) - 64*a1*b^4 + 128*a*b^3*b1 + 32*a^3*b*b1))/(2*(a^2 + b^2)) + 64*a^2*a1^2*b - 96*a^2*b*b1^2 + 192*a*a1*b^2*b1))/(a^2 + b^2))*(a^4*a1^2 + 4*a1^2*b^4 - 4*a^4*b1^2 - b^4*b1^2 - 13*a^2*a1^2*b^2 + 13*a^2*b^2*b1^2 - 18*a*a1*b^3*b1 + 18*a^3*a1*b*b1))/((a^2 + b^2)^2*(a^2*a1^2 + 4*a^2*b1^2 + 4*a1^2*b^2 + b^2*b1^2 - 6*a*a1*b*b1)^2) - ((((((a*a1 + b*b1)*(32*a^2*a1*b^2 - ((2*a*b1 - 2*a1*b)*(96*a^4*b + 96*a^2*b^3))/(2*(a^2 + b^2)) - 64*a1*b^4 + 128*a*b^3*b1 + 32*a^3*b*b1))/(a^2 + b^2) - ((a*a1 + b*b1)*(2*a*b1 - 2*a1*b)*(96*a^4*b + 96*a^2*b^3))/(2*(a^2 + b^2)^2))*(a*a1 + b*b1))/(a^2 + b^2) - 32*a1*b^2*b1^2 - 64*a1^3*b^2 + ((2*a*b1 - 2*a1*b)*(32*b^3*b1^2 - ((2*a*b1 - 2*a1*b)*(32*a^2*a1*b^2 - ((2*a*b1 - 2*a1*b)*(96*a^4*b + 96*a^2*b^3))/(2*(a^2 + b^2)) - 64*a1*b^4 + 128*a*b^3*b1 + 32*a^3*b*b1))/(2*(a^2 + b^2)) + 64*a^2*a1^2*b - 96*a^2*b*b1^2 + 192*a*a1*b^2*b1))/(2*(a^2 + b^2)) + 32*a*b*b1^3 - ((a*a1 + b*b1)^2*(2*a*b1 - 2*a1*b)*(96*a^4*b + 96*a^2*b^3))/(2*(a^2 + b^2)^3) + 64*a*a1^2*b*b1)*(12*a*a1^2*b^3 - 6*a^3*a1^2*b - 6*a*b^3*b1^2 + 12*a^3*b*b1^2 + 4*a^4*a1*b1 + 4*a1*b^4*b1 - 28*a^2*a1*b^2*b1))/((a^2 + b^2)^2*(a^2*a1^2 + 4*a^2*b1^2 + 4*a1^2*b^2 + b^2*b1^2 - 6*a*a1*b*b1)^2))*(a^4 + b^4 + 2*a^2*b^2))/(32*b^2*b1 + 32*a*a1*b) + ((a^4 + b^4 + 2*a^2*b^2)*(32*a1^2*b^2*b1 + ((((a*a1 + b*b1)*(((2*a*b1 - 2*a1*b)*(96*a*b^4 + 96*a^3*b^2))/(2*(a^2 + b^2)) - 32*b^4*b1 + 64*a^2*b^2*b1 - 64*a*a1*b^3 + 32*a^3*a1*b))/(a^2 + b^2) + ((a*a1 + b*b1)*(2*a*b1 - 2*a1*b)*(96*a*b^4 + 96*a^3*b^2))/(2*(a^2 + b^2)^2))*(a*a1 + b*b1))/(a^2 + b^2) - ((2*a*b1 - 2*a1*b)*(((2*a*b1 - 2*a1*b)*(((2*a*b1 - 2*a1*b)*(96*a*b^4 + 96*a^3*b^2))/(2*(a^2 + b^2)) - 32*b^4*b1 + 64*a^2*b^2*b1 - 64*a*a1*b^3 + 32*a^3*a1*b))/(2*(a^2 + b^2)) - 32*a*a1^2*b^2 - 32*a*b^2*b1^2 + 64*a1*b^3*b1 + 64*a^2*a1*b*b1))/(2*(a^2 + b^2)) + ((a*a1 + b*b1)^2*(2*a*b1 - 2*a1*b)*(96*a*b^4 + 96*a^3*b^2))/(2*(a^2 + b^2)^3) - 32*a*a1*b*b1^2)*(12*a*a1^2*b^3 - 6*a^3*a1^2*b - 6*a*b^3*b1^2 + 12*a^3*b*b1^2 + 4*a^4*a1*b1 + 4*a1*b^4*b1 - 28*a^2*a1*b^2*b1))/((32*b^2*b1 + 32*a*a1*b)*(a^2 + b^2)^2*(a^2*a1^2 + 4*a^2*b1^2 + 4*a1^2*b^2 + b^2*b1^2 - 6*a*a1*b*b1)^2) - ((a^4 + b^4 + 2*a^2*b^2)*(((((a*a1 + b*b1)*(((2*a*b1 - 2*a1*b)*(96*a*b^4 + 96*a^3*b^2))/(2*(a^2 + b^2)) - 32*b^4*b1 + 64*a^2*b^2*b1 - 64*a*a1*b^3 + 32*a^3*a1*b))/(a^2 + b^2) + ((a*a1 + b*b1)*(2*a*b1 - 2*a1*b)*(96*a*b^4 + 96*a^3*b^2))/(2*(a^2 + b^2)^2))*(2*a*b1 - 2*a1*b))/(2*(a^2 + b^2)) - ((a*a1 + b*b1)^3*(96*a*b^4 + 96*a^3*b^2))/(a^2 + b^2)^3 + ((a*a1 + b*b1)*(((2*a*b1 - 2*a1*b)*(((2*a*b1 - 2*a1*b)*(96*a*b^4 + 96*a^3*b^2))/(2*(a^2 + b^2)) - 32*b^4*b1 + 64*a^2*b^2*b1 - 64*a*a1*b^3 + 32*a^3*a1*b))/(2*(a^2 + b^2)) - 32*a*a1^2*b^2 - 32*a*b^2*b1^2 + 64*a1*b^3*b1 + 64*a^2*a1*b*b1))/(a^2 + b^2))*(a^4*a1^2 + 4*a1^2*b^4 - 4*a^4*b1^2 - b^4*b1^2 - 13*a^2*a1^2*b^2 + 13*a^2*b^2*b1^2 - 18*a*a1*b^3*b1 + 18*a^3*a1*b*b1))/((32*b^2*b1 + 32*a*a1*b)*(a^2 + b^2)^2*(a^2*a1^2 + 4*a^2*b1^2 + 4*a1^2*b^2 + b^2*b1^2 - 6*a*a1*b*b1)^2))*(a*a1 + b*b1))/(a^2 + b^2) - (log(1/(cos(x) + 1))*(2*a*b1 - 2*a1*b))/(2*(a^2 + b^2)) + (log(b + 2*a*tan(x/2) - b*tan(x/2)^2)*(a*b1 - a1*b))/(a^2 + b^2)","B"
170,1,2,2,0.009298,"\text{Not used}","int(1/log(t),t)","\mathrm{logint}\left(t\right)","Not used",1,"logint(t)","B"
171,1,10,10,0.033526,"\text{Not used}","int(1/log(t)^2,t)","\mathrm{logint}\left(t\right)-\frac{t}{\ln\left(t\right)}","Not used",1,"logint(t) - t/log(t)","B"
172,1,22,22,0.062249,"\text{Not used}","int(1/log(t)^(n + 1),t)","-\frac{{\left(-\ln\left(t\right)\right)}^n\,\Gamma \left(-n,-\ln\left(t\right)\right)}{{\ln\left(t\right)}^n}","Not used",1,"-((-log(t))^n*igamma(-n, -log(t)))/log(t)^n","B"
173,1,9,12,0.015130,"\text{Not used}","int(exp(2*t)/(t - 1),t)","{\mathrm{e}}^2\,\mathrm{ei}\left(2\,t-2\right)","Not used",1,"exp(2)*ei(2*t - 2)","B"
174,0,-1,22,0.000000,"\text{Not used}","int(exp(2*x)/(x^2 - 3*x + 2),x)","\int \frac{{\mathrm{e}}^{2\,x}}{x^2-3\,x+2} \,d x","Not used",1,"int(exp(2*x)/(x^2 - 3*x + 2), x)","F"
175,1,155,103,0.285296,"\text{Not used}","int(1/(t^3 + 1)^(1/2),t)","\frac{\left(3+\sqrt{3}\,1{}\mathrm{i}\right)\,\sqrt{\frac{t-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{t+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-t+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\mathrm{F}\left(\mathrm{asin}\left(\sqrt{\frac{t+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{t^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,t-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"((3^(1/2)*1i + 3)*((t + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((t + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - t + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticF(asin(((t + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(t^3 - t*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)","B"