1,1,13,13,0.0039059,"\int \sqrt{1+2 x} \, dx","Integrate[Sqrt[1 + 2*x],x]","\frac{1}{3} (2 x+1)^{3/2}","\frac{1}{3} (2 x+1)^{3/2}",1,"(1 + 2*x)^(3/2)/3","A",1
2,1,18,27,0.0066941,"\int x \sqrt{1+3 x} \, dx","Integrate[x*Sqrt[1 + 3*x],x]","\frac{2}{135} (3 x+1)^{3/2} (9 x-2)","\frac{2}{45} (3 x+1)^{5/2}-\frac{2}{27} (3 x+1)^{3/2}",1,"(2*(1 + 3*x)^(3/2)*(-2 + 9*x))/135","A",1
3,1,21,34,0.0071632,"\int x^2 \sqrt{1+x} \, dx","Integrate[x^2*Sqrt[1 + x],x]","\frac{2}{105} (x+1)^{3/2} \left(15 x^2-12 x+8\right)","\frac{2}{7} (x+1)^{7/2}-\frac{4}{5} (x+1)^{5/2}+\frac{2}{3} (x+1)^{3/2}",1,"(2*(1 + x)^(3/2)*(8 - 12*x + 15*x^2))/105","A",1
4,1,18,27,0.0064385,"\int \frac{x}{\sqrt{2-3 x}} \, dx","Integrate[x/Sqrt[2 - 3*x],x]","-\frac{2}{27} \sqrt{2-3 x} (3 x+4)","\frac{2}{27} (2-3 x)^{3/2}-\frac{4}{9} \sqrt{2-3 x}",1,"(-2*Sqrt[2 - 3*x]*(4 + 3*x))/27","A",1
5,1,14,14,0.005284,"\int \frac{1+x}{\left(2+2 x+x^2\right)^3} \, dx","Integrate[(1 + x)/(2 + 2*x + x^2)^3,x]","-\frac{1}{4 \left(x^2+2 x+2\right)^2}","-\frac{1}{4 \left(x^2+2 x+2\right)^2}",1,"-1/4*1/(2 + 2*x + x^2)^2","A",1
6,1,15,13,0.0019702,"\int \sin ^3(x) \, dx","Integrate[Sin[x]^3,x]","\frac{1}{12} \cos (3 x)-\frac{3 \cos (x)}{4}","\frac{\cos ^3(x)}{3}-\cos (x)",1,"(-3*Cos[x])/4 + Cos[3*x]/12","A",1
7,1,16,23,0.0056296,"\int \sqrt[3]{-1+z} z \, dz","Integrate[(-1 + z)^(1/3)*z,z]","\frac{3}{28} (z-1)^{4/3} (4 z+3)","\frac{3}{7} (z-1)^{7/3}+\frac{3}{4} (z-1)^{4/3}",1,"(3*(-1 + z)^(4/3)*(3 + 4*z))/28","A",1
8,1,8,8,0.0052287,"\int \cot (x) \csc ^2(x) \, dx","Integrate[Cot[x]*Csc[x]^2,x]","-\frac{1}{2} \csc ^2(x)","-\frac{1}{2} \csc ^2(x)",1,"-1/2*Csc[x]^2","A",1
9,1,16,16,0.0142256,"\int \cos (2 x) \sqrt{4-\sin (2 x)} \, dx","Integrate[Cos[2*x]*Sqrt[4 - Sin[2*x]],x]","-\frac{1}{3} (4-\sin (2 x))^{3/2}","-\frac{1}{3} (4-\sin (2 x))^{3/2}",1,"-1/3*(4 - Sin[2*x])^(3/2)","A",1
10,1,6,6,0.0154633,"\int \frac{\sin (x)}{(3+\cos (x))^2} \, dx","Integrate[Sin[x]/(3 + Cos[x])^2,x]","\frac{1}{\cos (x)+3}","\frac{1}{\cos (x)+3}",1,"(3 + Cos[x])^(-1)","A",1
11,1,12,12,0.0096757,"\int \frac{\sin (x)}{\sqrt{\cos ^3(x)}} \, dx","Integrate[Sin[x]/Sqrt[Cos[x]^3],x]","\frac{2 \cos (x)}{\sqrt{\cos ^3(x)}}","\frac{2 \cos (x)}{\sqrt{\cos ^3(x)}}",1,"(2*Cos[x])/Sqrt[Cos[x]^3]","A",1
12,1,10,10,0.0219933,"\int \frac{\sin \left(\sqrt{1+x}\right)}{\sqrt{1+x}} \, dx","Integrate[Sin[Sqrt[1 + x]]/Sqrt[1 + x],x]","-2 \cos \left(\sqrt{x+1}\right)","-2 \cos \left(\sqrt{x+1}\right)",1,"-2*Cos[Sqrt[1 + x]]","A",1
13,1,9,9,0.0179722,"\int x^{-1+n} \sin \left(x^n\right) \, dx","Integrate[x^(-1 + n)*Sin[x^n],x]","-\frac{\cos \left(x^n\right)}{n}","-\frac{\cos \left(x^n\right)}{n}",1,"-(Cos[x^n]/n)","A",1
14,1,15,15,0.0038504,"\int \frac{x^5}{\sqrt{1-x^6}} \, dx","Integrate[x^5/Sqrt[1 - x^6],x]","-\frac{1}{3} \sqrt{1-x^6}","-\frac{1}{3} \sqrt{1-x^6}",1,"-1/3*Sqrt[1 - x^6]","A",1
15,1,16,23,0.0058964,"\int t \sqrt[4]{1+t} \, dt","Integrate[t*(1 + t)^(1/4),t]","\frac{4}{45} (t+1)^{5/4} (5 t-4)","\frac{4}{9} (t+1)^{9/4}-\frac{4}{5} (t+1)^{5/4}",1,"(4*(1 + t)^(5/4)*(-4 + 5*t))/45","A",1
16,1,11,11,0.0027682,"\int \frac{1}{\left(1+x^2\right)^{3/2}} \, dx","Integrate[(1 + x^2)^(-3/2),x]","\frac{x}{\sqrt{x^2+1}}","\frac{x}{\sqrt{x^2+1}}",1,"x/Sqrt[1 + x^2]","A",1
17,1,15,15,0.0045326,"\int x^2 \left(27+8 x^3\right)^{2/3} \, dx","Integrate[x^2*(27 + 8*x^3)^(2/3),x]","\frac{1}{40} \left(8 x^3+27\right)^{5/3}","\frac{1}{40} \left(8 x^3+27\right)^{5/3}",1,"(27 + 8*x^3)^(5/3)/40","A",1
18,1,15,15,0.058816,"\int \frac{\cos (x)+\sin (x)}{\sqrt[3]{-\cos (x)+\sin (x)}} \, dx","Integrate[(Cos[x] + Sin[x])/(-Cos[x] + Sin[x])^(1/3),x]","\frac{3}{2} (\sin (x)-\cos (x))^{2/3}","\frac{3}{2} (\sin (x)-\cos (x))^{2/3}",1,"(3*(-Cos[x] + Sin[x])^(2/3))/2","A",1
19,1,37,32,0.0575154,"\int \frac{x}{\sqrt{1+x^2+\left(1+x^2\right)^{3/2}}} \, dx","Integrate[x/Sqrt[1 + x^2 + (1 + x^2)^(3/2)],x]","\frac{2 \left(x^2+\sqrt{x^2+1}+1\right)}{\sqrt{\left(x^2+1\right) \left(\sqrt{x^2+1}+1\right)}}","\frac{2 \sqrt{\left(x^2+1\right) \left(\sqrt{x^2+1}+1\right)}}{\sqrt{x^2+1}}",1,"(2*(1 + x^2 + Sqrt[1 + x^2]))/Sqrt[(1 + x^2)*(1 + Sqrt[1 + x^2])]","A",1
20,1,17,17,0.0155028,"\int \frac{x}{\sqrt{1+x^2} \sqrt{1+\sqrt{1+x^2}}} \, dx","Integrate[x/(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[1 + x^2]]),x]","2 \sqrt{\sqrt{x^2+1}+1}","2 \sqrt{\sqrt{x^2+1}+1}",1,"2*Sqrt[1 + Sqrt[1 + x^2]]","A",1
21,1,13,16,0.0081702,"\int \frac{\sqrt[5]{1-2 x+x^2}}{1-x} \, dx","Integrate[(1 - 2*x + x^2)^(1/5)/(1 - x),x]","-\frac{5}{2} \sqrt[5]{(x-1)^2}","-\frac{5}{2} \sqrt[5]{x^2-2 x+1}",1,"(-5*((-1 + x)^2)^(1/5))/2","A",1
22,1,8,8,0.0022371,"\int x \sin (x) \, dx","Integrate[x*Sin[x],x]","\sin (x)-x \cos (x)","\sin (x)-x \cos (x)",1,"-(x*Cos[x]) + Sin[x]","A",1
23,1,15,17,0.0169765,"\int x^2 \sin (x) \, dx","Integrate[x^2*Sin[x],x]","2 x \sin (x)-\left(x^2-2\right) \cos (x)","x^2 (-\cos (x))+2 x \sin (x)+2 \cos (x)",1,"-((-2 + x^2)*Cos[x]) + 2*x*Sin[x]","A",1
24,1,19,23,0.0159597,"\int x^3 \cos (x) \, dx","Integrate[x^3*Cos[x],x]","x \left(x^2-6\right) \sin (x)+3 \left(x^2-2\right) \cos (x)","x^3 \sin (x)+3 x^2 \cos (x)-6 x \sin (x)-6 \cos (x)",1,"3*(-2 + x^2)*Cos[x] + x*(-6 + x^2)*Sin[x]","A",1
25,1,20,24,0.0152703,"\int x^3 \sin (x) \, dx","Integrate[x^3*Sin[x],x]","3 \left(x^2-2\right) \sin (x)-x \left(x^2-6\right) \cos (x)","x^3 (-\cos (x))+3 x^2 \sin (x)-6 \sin (x)+6 x \cos (x)",1,"-(x*(-6 + x^2)*Cos[x]) + 3*(-2 + x^2)*Sin[x]","A",1
26,1,8,8,0.0014749,"\int \cos (x) \sin (x) \, dx","Integrate[Cos[x]*Sin[x],x]","-\frac{1}{2} \cos ^2(x)","\frac{\sin ^2(x)}{2}",1,"-1/2*Cos[x]^2","A",1
27,1,18,23,0.0028904,"\int x \cos (x) \sin (x) \, dx","Integrate[x*Cos[x]*Sin[x],x]","\frac{1}{8} \sin (2 x)-\frac{1}{4} x \cos (2 x)","-\frac{x}{4}+\frac{1}{2} x \sin ^2(x)+\frac{1}{4} \sin (x) \cos (x)",1,"-1/4*(x*Cos[2*x]) + Sin[2*x]/8","A",1
28,1,14,14,0.0019505,"\int \sin ^2(x) \, dx","Integrate[Sin[x]^2,x]","\frac{x}{2}-\frac{1}{4} \sin (2 x)","\frac{x}{2}-\frac{1}{2} \sin (x) \cos (x)",1,"x/2 - Sin[2*x]/4","A",1
29,1,15,13,0.0018799,"\int \sin ^3(x) \, dx","Integrate[Sin[x]^3,x]","\frac{1}{12} \cos (3 x)-\frac{3 \cos (x)}{4}","\frac{\cos ^3(x)}{3}-\cos (x)",1,"(-3*Cos[x])/4 + Cos[3*x]/12","A",1
30,1,22,24,0.0022079,"\int \sin ^4(x) \, dx","Integrate[Sin[x]^4,x]","\frac{3 x}{8}-\frac{1}{4} \sin (2 x)+\frac{1}{32} \sin (4 x)","\frac{3 x}{8}-\frac{1}{4} \sin ^3(x) \cos (x)-\frac{3}{8} \sin (x) \cos (x)",1,"(3*x)/8 - Sin[2*x]/4 + Sin[4*x]/32","A",1
31,1,23,21,0.0020186,"\int \sin ^5(x) \, dx","Integrate[Sin[x]^5,x]","-\frac{5 \cos (x)}{8}+\frac{5}{48} \cos (3 x)-\frac{1}{80} \cos (5 x)","-\frac{1}{5} \cos ^5(x)+\frac{2 \cos ^3(x)}{3}-\cos (x)",1,"(-5*Cos[x])/8 + (5*Cos[3*x])/48 - Cos[5*x]/80","A",1
32,1,30,34,0.0019974,"\int \sin ^6(x) \, dx","Integrate[Sin[x]^6,x]","\frac{5 x}{16}-\frac{15}{64} \sin (2 x)+\frac{3}{64} \sin (4 x)-\frac{1}{192} \sin (6 x)","\frac{5 x}{16}-\frac{1}{6} \sin ^5(x) \cos (x)-\frac{5}{24} \sin ^3(x) \cos (x)-\frac{5}{16} \sin (x) \cos (x)",1,"(5*x)/16 - (15*Sin[2*x])/64 + (3*Sin[4*x])/64 - Sin[6*x]/192","A",1
33,1,25,25,0.0111274,"\int x \sin ^2(x) \, dx","Integrate[x*Sin[x]^2,x]","\frac{x^2}{4}-\frac{1}{4} x \sin (2 x)-\frac{1}{8} \cos (2 x)","\frac{x^2}{4}+\frac{\sin ^2(x)}{4}-\frac{1}{2} x \sin (x) \cos (x)",1,"x^2/4 - Cos[2*x]/8 - (x*Sin[2*x])/4","A",1
34,1,31,33,0.0092534,"\int x \sin ^3(x) \, dx","Integrate[x*Sin[x]^3,x]","\frac{3 \sin (x)}{4}-\frac{1}{36} \sin (3 x)-\frac{3}{4} x \cos (x)+\frac{1}{12} x \cos (3 x)","\frac{\sin ^3(x)}{9}+\frac{2 \sin (x)}{3}-\frac{2}{3} x \cos (x)-\frac{1}{3} x \sin ^2(x) \cos (x)",1,"(-3*x*Cos[x])/4 + (x*Cos[3*x])/12 + (3*Sin[x])/4 - Sin[3*x]/36","A",1
35,1,29,41,0.0393999,"\int x^2 \sin ^2(x) \, dx","Integrate[x^2*Sin[x]^2,x]","\frac{1}{24} \left(4 x^3+\left(3-6 x^2\right) \sin (2 x)-6 x \cos (2 x)\right)","\frac{x^3}{6}-\frac{1}{2} x^2 \sin (x) \cos (x)-\frac{x}{4}+\frac{1}{2} x \sin ^2(x)+\frac{1}{4} \sin (x) \cos (x)",1,"(4*x^3 - 6*x*Cos[2*x] + (3 - 6*x^2)*Sin[2*x])/24","A",1
36,1,14,14,0.0017995,"\int \cos ^2(x) \, dx","Integrate[Cos[x]^2,x]","\frac{x}{2}+\frac{1}{4} \sin (2 x)","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"x/2 + Sin[2*x]/4","A",1
37,1,15,11,0.0017977,"\int \cos ^3(x) \, dx","Integrate[Cos[x]^3,x]","\frac{3 \sin (x)}{4}+\frac{1}{12} \sin (3 x)","\sin (x)-\frac{\sin ^3(x)}{3}",1,"(3*Sin[x])/4 + Sin[3*x]/12","A",1
38,1,22,24,0.0020487,"\int \cos ^4(x) \, dx","Integrate[Cos[x]^4,x]","\frac{3 x}{8}+\frac{1}{4} \sin (2 x)+\frac{1}{32} \sin (4 x)","\frac{3 x}{8}+\frac{1}{4} \sin (x) \cos ^3(x)+\frac{3}{8} \sin (x) \cos (x)",1,"(3*x)/8 + Sin[2*x]/4 + Sin[4*x]/32","A",1
39,1,62,84,0.0771387,"\int \left(a^2-x^2\right)^{5/2} \, dx","Integrate[(a^2 - x^2)^(5/2),x]","\frac{1}{48} \sqrt{a^2-x^2} \left(33 a^4 x-26 a^2 x^3+\frac{15 a^5 \sin ^{-1}\left(\frac{x}{a}\right)}{\sqrt{1-\frac{x^2}{a^2}}}+8 x^5\right)","\frac{5}{24} a^2 x \left(a^2-x^2\right)^{3/2}+\frac{1}{6} x \left(a^2-x^2\right)^{5/2}+\frac{5}{16} a^6 \tan ^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right)+\frac{5}{16} a^4 x \sqrt{a^2-x^2}",1,"(Sqrt[a^2 - x^2]*(33*a^4*x - 26*a^2*x^3 + 8*x^5 + (15*a^5*ArcSin[x/a])/Sqrt[1 - x^2/a^2]))/48","A",1
40,1,25,38,0.0075794,"\int \frac{x^5}{\sqrt{5+x^2}} \, dx","Integrate[x^5/Sqrt[5 + x^2],x]","\frac{1}{15} \sqrt{x^2+5} \left(3 x^4-20 x^2+200\right)","\frac{1}{5} \left(x^2+5\right)^{5/2}-\frac{10}{3} \left(x^2+5\right)^{3/2}+25 \sqrt{x^2+5}",1,"(Sqrt[5 + x^2]*(200 - 20*x^2 + 3*x^4))/15","A",1
41,1,34,172,0.0064389,"\int \frac{t^3}{\sqrt{4+t^3}} \, dt","Integrate[t^3/Sqrt[4 + t^3],t]","\frac{2}{5} t \left(\sqrt{t^3+4}-2 \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-\frac{t^3}{4}\right)\right)","\frac{2}{5} t \sqrt{t^3+4}-\frac{8\ 2^{2/3} \sqrt{2+\sqrt{3}} \left(t+2^{2/3}\right) \sqrt{\frac{t^2-2^{2/3} t+2 \sqrt[3]{2}}{\left(t+2^{2/3} \left(1+\sqrt{3}\right)\right)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{t+2^{2/3} \left(1-\sqrt{3}\right)}{t+2^{2/3} \left(1+\sqrt{3}\right)}\right),-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} \sqrt{\frac{t+2^{2/3}}{\left(t+2^{2/3} \left(1+\sqrt{3}\right)\right)^2}} \sqrt{t^3+4}}",1,"(2*t*(Sqrt[4 + t^3] - 2*Hypergeometric2F1[1/3, 1/2, 4/3, -1/4*t^3]))/5","C",1
42,1,6,6,0.0043082,"\int \tan ^2(x) \, dx","Integrate[Tan[x]^2,x]","\tan (x)-x","\tan (x)-x",1,"-x + Tan[x]","A",1
43,1,18,14,0.0032849,"\int \tan ^4(x) \, dx","Integrate[Tan[x]^4,x]","x-\frac{4 \tan (x)}{3}+\frac{1}{3} \tan (x) \sec ^2(x)","x+\frac{\tan ^3(x)}{3}-\tan (x)",1,"x - (4*Tan[x])/3 + (Sec[x]^2*Tan[x])/3","A",1
44,1,8,8,0.0023625,"\int \cot ^2(x) \, dx","Integrate[Cot[x]^2,x]","-x-\cot (x)","-x-\cot (x)",1,"-x - Cot[x]","A",1
45,1,18,12,0.0033657,"\int \cot ^4(x) \, dx","Integrate[Cot[x]^4,x]","x+\frac{4 \cot (x)}{3}-\frac{1}{3} \cot (x) \csc ^2(x)","x-\frac{1}{3} \cot ^3(x)+\cot (x)",1,"x + (4*Cot[x])/3 - (Cot[x]*Csc[x]^2)/3","A",1
46,1,26,22,0.0144705,"\int (2+3 x) \sin (5 x) \, dx","Integrate[(2 + 3*x)*Sin[5*x],x]","\frac{3}{25} \sin (5 x)-\frac{3}{5} x \cos (5 x)-\frac{2}{5} \cos (5 x)","\frac{3}{25} \sin (5 x)-\frac{1}{5} (3 x+2) \cos (5 x)",1,"(-2*Cos[5*x])/5 - (3*x*Cos[5*x])/5 + (3*Sin[5*x])/25","A",1
47,1,13,13,0.0022312,"\int x \sqrt{1+x^2} \, dx","Integrate[x*Sqrt[1 + x^2],x]","\frac{1}{3} \left(x^2+1\right)^{3/2}","\frac{1}{3} \left(x^2+1\right)^{3/2}",1,"(1 + x^2)^(3/2)/3","A",1
48,1,11,13,0.0021841,"\int x \left(-1+x^2\right)^9 \, dx","Integrate[x*(-1 + x^2)^9,x]","\frac{1}{20} \left(x^2-1\right)^{10}","\frac{1}{20} \left(1-x^2\right)^{10}",1,"(-1 + x^2)^10/20","A",1
49,1,16,18,0.0043846,"\int \frac{3+2 x}{(7+6 x)^3} \, dx","Integrate[(3 + 2*x)/(7 + 6*x)^3,x]","-\frac{3 x+4}{9 (6 x+7)^2}","-\frac{(2 x+3)^2}{8 (6 x+7)^2}",1,"-1/9*(4 + 3*x)/(7 + 6*x)^2","A",1
50,1,43,11,0.0017869,"\int x^4 \left(1+x^5\right)^5 \, dx","Integrate[x^4*(1 + x^5)^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}","\frac{1}{30} \left(x^5+1\right)^6",1,"x^5/5 + x^10/2 + (2*x^15)/3 + x^20/2 + x^25/5 + x^30/30","B",1
51,1,140,56,0.0020738,"\int (1-x)^{20} x^4 \, dx","Integrate[(1 - x)^20*x^4,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}","-\frac{1}{25} (1-x)^{25}+\frac{1}{6} (1-x)^{24}-\frac{6}{23} (1-x)^{23}+\frac{2}{11} (1-x)^{22}-\frac{1}{21} (1-x)^{21}",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",1
52,1,4,4,0.0091311,"\int \frac{\sin \left(\frac{1}{x}\right)}{x^2} \, dx","Integrate[Sin[x^(-1)]/x^2,x]","\cos \left(\frac{1}{x}\right)","\cos \left(\frac{1}{x}\right)",1,"Cos[x^(-1)]","A",1
53,1,46,62,0.0349791,"\int \sin \left(\sqrt[4]{-1+x}\right) \, dx","Integrate[Sin[(-1 + x)^(1/4)],x]","12 \left(\sqrt{x-1}-2\right) \sin \left(\sqrt[4]{x-1}\right)-4 \left(\sqrt{x-1}-6\right) \sqrt[4]{x-1} \cos \left(\sqrt[4]{x-1}\right)","12 \sqrt{x-1} \sin \left(\sqrt[4]{x-1}\right)-24 \sin \left(\sqrt[4]{x-1}\right)-4 (x-1)^{3/4} \cos \left(\sqrt[4]{x-1}\right)+24 \sqrt[4]{x-1} \cos \left(\sqrt[4]{x-1}\right)",1,"-4*(-6 + Sqrt[-1 + x])*(-1 + x)^(1/4)*Cos[(-1 + x)^(1/4)] + 12*(-2 + Sqrt[-1 + x])*Sin[(-1 + x)^(1/4)]","A",1
54,1,10,10,0.0027144,"\int x \cos \left(x^2\right) \sin \left(x^2\right) \, dx","Integrate[x*Cos[x^2]*Sin[x^2],x]","-\frac{1}{4} \cos ^2\left(x^2\right)","\frac{1}{4} \sin ^2\left(x^2\right)",1,"-1/4*Cos[x^2]^2","A",1
55,1,16,16,0.013606,"\int \sqrt{1+3 \cos ^2(x)} \sin (2 x) \, dx","Integrate[Sqrt[1 + 3*Cos[x]^2]*Sin[2*x],x]","-\frac{2}{9} \left(4-3 \sin ^2(x)\right)^{3/2}","-\frac{2}{9} \left(4-3 \sin ^2(x)\right)^{3/2}",1,"(-2*(4 - 3*Sin[x]^2)^(3/2))/9","A",1
56,1,10,10,0.0008713,"\int \frac{1}{2+3 x} \, dx","Integrate[(2 + 3*x)^(-1),x]","\frac{1}{3} \log (3 x+2)","\frac{1}{3} \log (3 x+2)",1,"Log[2 + 3*x]/3","A",1
57,1,15,15,0.0009561,"\int \log ^2(x) \, dx","Integrate[Log[x]^2,x]","2 x+x \log ^2(x)-2 x \log (x)","2 x+x \log ^2(x)-2 x \log (x)",1,"2*x - 2*x*Log[x] + x*Log[x]^2","A",1
58,1,17,17,0.0008072,"\int x \log (x) \, dx","Integrate[x*Log[x],x]","\frac{1}{2} x^2 \log (x)-\frac{x^2}{4}","\frac{1}{2} x^2 \log (x)-\frac{x^2}{4}",1,"-1/4*x^2 + (x^2*Log[x])/2","A",1
59,1,28,28,0.0010709,"\int x \log ^2(x) \, dx","Integrate[x*Log[x]^2,x]","\frac{x^2}{4}+\frac{1}{2} x^2 \log ^2(x)-\frac{1}{2} x^2 \log (x)","\frac{x^2}{4}+\frac{1}{2} x^2 \log ^2(x)-\frac{1}{2} x^2 \log (x)",1,"x^2/4 - (x^2*Log[x])/2 + (x^2*Log[x]^2)/2","A",1
60,1,4,4,0.000722,"\int \frac{1}{1+t} \, dt","Integrate[(1 + t)^(-1),t]","\log (t+1)","\log (t+1)",1,"Log[1 + t]","A",1
61,1,3,3,0.0020434,"\int \cot (x) \, dx","Integrate[Cot[x],x]","\log (\sin (x))","\log (\sin (x))",1,"Log[Sin[x]]","A",1
62,1,21,28,0.0067592,"\int x^n \log (a x) \, dx","Integrate[x^n*Log[a*x],x]","\frac{x^{n+1} ((n+1) \log (a x)-1)}{(n+1)^2}","\frac{x^{n+1} \log (a x)}{n+1}-\frac{x^{n+1}}{(n+1)^2}",1,"(x^(1 + n)*(-1 + (1 + n)*Log[a*x]))/(1 + n)^2","A",1
63,1,28,28,0.0014115,"\int x^2 \log ^2(x) \, dx","Integrate[x^2*Log[x]^2,x]","\frac{2 x^3}{27}+\frac{1}{3} x^3 \log ^2(x)-\frac{2}{9} x^3 \log (x)","\frac{2 x^3}{27}+\frac{1}{3} x^3 \log ^2(x)-\frac{2}{9} x^3 \log (x)",1,"(2*x^3)/27 - (2*x^3*Log[x])/9 + (x^3*Log[x]^2)/3","A",1
64,1,3,3,0.0045992,"\int \frac{1}{x \log (x)} \, dx","Integrate[1/(x*Log[x]),x]","\log (\log (x))","\log (\log (x))",1,"Log[Log[x]]","A",1
65,1,12,12,0.0022486,"\int \frac{\log (1-t)}{1-t} \, dt","Integrate[Log[1 - t]/(1 - t),t]","-\frac{1}{2} \log ^2(1-t)","-\frac{1}{2} \log ^2(1-t)",1,"-1/2*Log[1 - t]^2","A",1
66,1,16,23,0.0183668,"\int \frac{\log (x)}{x \sqrt{1+\log (x)}} \, dx","Integrate[Log[x]/(x*Sqrt[1 + Log[x]]),x]","\frac{2}{3} (\log (x)-2) \sqrt{\log (x)+1}","\frac{2}{3} (\log (x)+1)^{3/2}-2 \sqrt{\log (x)+1}",1,"(2*(-2 + Log[x])*Sqrt[1 + Log[x]])/3","A",1
67,1,39,39,0.0015952,"\int x^3 \log ^3(x) \, dx","Integrate[x^3*Log[x]^3,x]","-\frac{3 x^4}{128}+\frac{1}{4} x^4 \log ^3(x)-\frac{3}{16} x^4 \log ^2(x)+\frac{3}{32} x^4 \log (x)","-\frac{3 x^4}{128}+\frac{1}{4} x^4 \log ^3(x)-\frac{3}{16} x^4 \log ^2(x)+\frac{3}{32} x^4 \log (x)",1,"(-3*x^4)/128 + (3*x^4*Log[x])/32 - (3*x^4*Log[x]^2)/16 + (x^4*Log[x]^3)/4","A",1
68,1,9,9,0.0016627,"\int e^{x^3} x^2 \, dx","Integrate[E^x^3*x^2,x]","\frac{e^{x^3}}{3}","\frac{e^{x^3}}{3}",1,"E^x^3/3","A",1
69,1,14,14,0.0035214,"\int \frac{2^{\sqrt{x}}}{\sqrt{x}} \, dx","Integrate[2^Sqrt[x]/Sqrt[x],x]","\frac{2^{\sqrt{x}+1}}{\log (2)}","\frac{2^{\sqrt{x}+1}}{\log (2)}",1,"2^(1 + Sqrt[x])/Log[2]","A",1
70,1,10,10,0.0079915,"\int e^{2 \sin (x)} \cos (x) \, dx","Integrate[E^(2*Sin[x])*Cos[x],x]","\frac{1}{2} e^{2 \sin (x)}","\frac{1}{2} e^{2 \sin (x)}",1,"E^(2*Sin[x])/2","A",1
71,1,14,19,0.0148729,"\int e^x \sin (x) \, dx","Integrate[E^x*Sin[x],x]","\frac{1}{2} e^x (\sin (x)-\cos (x))","\frac{1}{2} e^x \sin (x)-\frac{1}{2} e^x \cos (x)",1,"(E^x*(-Cos[x] + Sin[x]))/2","A",1
72,1,12,19,0.0097536,"\int e^x \cos (x) \, dx","Integrate[E^x*Cos[x],x]","\frac{1}{2} e^x (\sin (x)+\cos (x))","\frac{1}{2} e^x \sin (x)+\frac{1}{2} e^x \cos (x)",1,"(E^x*(Cos[x] + Sin[x]))/2","A",1
73,1,10,10,0.0031384,"\int \frac{1}{1+e^x} \, dx","Integrate[(1 + E^x)^(-1),x]","x-\log \left(e^x+1\right)","x-\log \left(e^x+1\right)",1,"x - Log[1 + E^x]","A",1
74,1,7,11,0.001131,"\int e^x x \, dx","Integrate[E^x*x,x]","e^x (x-1)","e^x x-e^x",1,"E^x*(-1 + x)","A",1
75,1,11,16,0.0054515,"\int e^{-x} x \, dx","Integrate[x/E^x,x]","e^{-x} (-x-1)","-e^{-x} x-e^{-x}",1,"(-1 - x)/E^x","A",1
76,1,12,19,0.0050177,"\int e^x x^2 \, dx","Integrate[E^x*x^2,x]","e^x \left(x^2-2 x+2\right)","e^x x^2-2 e^x x+2 e^x",1,"E^x*(2 - 2*x + x^2)","A",1
77,1,19,32,0.0076142,"\int e^{-2 x} x^2 \, dx","Integrate[x^2/E^(2*x),x]","-\frac{1}{4} e^{-2 x} \left(2 x^2+2 x+1\right)","-\frac{1}{2} e^{-2 x} x^2-\frac{1}{2} e^{-2 x} x-\frac{e^{-2 x}}{4}",1,"-1/4*(1 + 2*x + 2*x^2)/E^(2*x)","A",1
78,1,16,24,0.0065069,"\int e^{\sqrt{x}} \, dx","Integrate[E^Sqrt[x],x]","2 e^{\sqrt{x}} \left(\sqrt{x}-1\right)","2 e^{\sqrt{x}} \sqrt{x}-2 e^{\sqrt{x}}",1,"2*E^Sqrt[x]*(-1 + Sqrt[x])","A",1
79,1,16,26,0.002956,"\int e^{-x^2} x^3 \, dx","Integrate[x^3/E^x^2,x]","-\frac{1}{2} e^{-x^2} \left(x^2+1\right)","-\frac{1}{2} e^{-x^2} x^2-\frac{e^{-x^2}}{2}",1,"-1/2*(1 + x^2)/E^x^2","A",1
80,1,28,41,0.0322692,"\int e^{a x} \cos (b x) \, dx","Integrate[E^(a*x)*Cos[b*x],x]","\frac{e^{a x} (a \cos (b x)+b \sin (b x))}{a^2+b^2}","\frac{b e^{a x} \sin (b x)}{a^2+b^2}+\frac{a e^{a x} \cos (b x)}{a^2+b^2}",1,"(E^(a*x)*(a*Cos[b*x] + b*Sin[b*x]))/(a^2 + b^2)","A",1
81,1,29,42,0.0314728,"\int e^{a x} \sin (b x) \, dx","Integrate[E^(a*x)*Sin[b*x],x]","\frac{e^{a x} (a \sin (b x)-b \cos (b x))}{a^2+b^2}","\frac{a e^{a x} \sin (b x)}{a^2+b^2}-\frac{b e^{a x} \cos (b x)}{a^2+b^2}",1,"(E^(a*x)*(-(b*Cos[b*x]) + a*Sin[b*x]))/(a^2 + b^2)","A",1
82,1,15,15,0.0018721,"\int \cot ^{-1}(x) \, dx","Integrate[ArcCot[x],x]","\frac{1}{2} \log \left(x^2+1\right)+x \cot ^{-1}(x)","\frac{1}{2} \log \left(x^2+1\right)+x \cot ^{-1}(x)",1,"x*ArcCot[x] + Log[1 + x^2]/2","A",1
83,1,64,19,0.0741563,"\int \sec ^{-1}(x) \, dx","Integrate[ArcSec[x],x]","x \sec ^{-1}(x)-\frac{\sqrt{x^2-1} \left(\log \left(\frac{x}{\sqrt{x^2-1}}+1\right)-\log \left(1-\frac{x}{\sqrt{x^2-1}}\right)\right)}{2 \sqrt{1-\frac{1}{x^2}} x}","x \sec ^{-1}(x)-\tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)",1,"x*ArcSec[x] - (Sqrt[-1 + x^2]*(-Log[1 - x/Sqrt[-1 + x^2]] + Log[1 + x/Sqrt[-1 + x^2]]))/(2*Sqrt[1 - x^(-2)]*x)","B",1
84,1,64,17,0.0479399,"\int \csc ^{-1}(x) \, dx","Integrate[ArcCsc[x],x]","\frac{\sqrt{x^2-1} \left(\log \left(\frac{x}{\sqrt{x^2-1}}+1\right)-\log \left(1-\frac{x}{\sqrt{x^2-1}}\right)\right)}{2 \sqrt{1-\frac{1}{x^2}} x}+x \csc ^{-1}(x)","\tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)+x \csc ^{-1}(x)",1,"x*ArcCsc[x] + (Sqrt[-1 + x^2]*(-Log[1 - x/Sqrt[-1 + x^2]] + Log[1 + x/Sqrt[-1 + x^2]]))/(2*Sqrt[1 - x^(-2)]*x)","B",1
85,1,25,25,0.0075466,"\int \sin ^{-1}(x)^2 \, dx","Integrate[ArcSin[x]^2,x]","2 \sqrt{1-x^2} \sin ^{-1}(x)-2 x+x \sin ^{-1}(x)^2","2 \sqrt{1-x^2} \sin ^{-1}(x)-2 x+x \sin ^{-1}(x)^2",1,"-2*x + 2*Sqrt[1 - x^2]*ArcSin[x] + x*ArcSin[x]^2","A",1
86,1,22,22,0.0023434,"\int \frac{\sin ^{-1}(x)}{x^2} \, dx","Integrate[ArcSin[x]/x^2,x]","-\tanh ^{-1}\left(\sqrt{1-x^2}\right)-\frac{\sin ^{-1}(x)}{x}","-\tanh ^{-1}\left(\sqrt{1-x^2}\right)-\frac{\sin ^{-1}(x)}{x}",1,"-(ArcSin[x]/x) - ArcTanh[Sqrt[1 - x^2]]","A",1
87,1,16,16,0.0037164,"\int \frac{1}{\sqrt{a^2-x^2}} \, dx","Integrate[1/Sqrt[a^2 - x^2],x]","\tan ^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right)","\tan ^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right)",1,"ArcTan[x/Sqrt[a^2 - x^2]]","A",1
88,1,14,10,0.0062886,"\int \frac{1}{\sqrt{1-2 x-x^2}} \, dx","Integrate[1/Sqrt[1 - 2*x - x^2],x]","-\sin ^{-1}\left(\frac{-x-1}{\sqrt{2}}\right)","\sin ^{-1}\left(\frac{x+1}{\sqrt{2}}\right)",1,"-ArcSin[(-1 - x)/Sqrt[2]]","A",1
89,1,10,10,0.0023162,"\int \frac{1}{a^2+x^2} \, dx","Integrate[(a^2 + x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{a}","\frac{\tan ^{-1}\left(\frac{x}{a}\right)}{a}",1,"ArcTan[x/a]/a","A",1
90,1,24,24,0.0053071,"\int \frac{1}{a+b x^2} \, dx","Integrate[(a + b*x^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}",1,"ArcTan[(Sqrt[b]*x)/Sqrt[a]]/(Sqrt[a]*Sqrt[b])","A",1
91,1,19,19,0.0063852,"\int \frac{1}{2-x+x^2} \, dx","Integrate[(2 - x + x^2)^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{2 x-1}{\sqrt{7}}\right)}{\sqrt{7}}","-\frac{2 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{7}}\right)}{\sqrt{7}}",1,"(2*ArcTan[(-1 + 2*x)/Sqrt[7]])/Sqrt[7]","A",1
92,1,21,21,0.002767,"\int x \tan ^{-1}(x) \, dx","Integrate[x*ArcTan[x],x]","\frac{1}{2} x^2 \tan ^{-1}(x)-\frac{x}{2}+\frac{1}{2} \tan ^{-1}(x)","\frac{1}{2} x^2 \tan ^{-1}(x)-\frac{x}{2}+\frac{1}{2} \tan ^{-1}(x)",1,"-1/2*x + ArcTan[x]/2 + (x^2*ArcTan[x])/2","A",1
93,1,30,40,0.0133279,"\int x^2 \cos ^{-1}(x) \, dx","Integrate[x^2*ArcCos[x],x]","\frac{1}{3} x^3 \cos ^{-1}(x)-\frac{1}{9} \sqrt{1-x^2} \left(x^2+2\right)","\frac{1}{3} x^3 \cos ^{-1}(x)+\frac{1}{9} \left(1-x^2\right)^{3/2}-\frac{\sqrt{1-x^2}}{3}",1,"-1/9*(Sqrt[1 - x^2]*(2 + x^2)) + (x^3*ArcCos[x])/3","A",1
94,1,26,35,0.0090013,"\int x \tan ^{-1}(x)^2 \, dx","Integrate[x*ArcTan[x]^2,x]","\frac{1}{2} \left(\log \left(x^2+1\right)+\left(x^2+1\right) \tan ^{-1}(x)^2-2 x \tan ^{-1}(x)\right)","\frac{1}{2} \log \left(x^2+1\right)+\frac{1}{2} x^2 \tan ^{-1}(x)^2+\frac{1}{2} \tan ^{-1}(x)^2-x \tan ^{-1}(x)",1,"(-2*x*ArcTan[x] + (1 + x^2)*ArcTan[x]^2 + Log[1 + x^2])/2","A",1
95,1,18,22,0.0065102,"\int \tan ^{-1}\left(\sqrt{x}\right) \, dx","Integrate[ArcTan[Sqrt[x]],x]","(x+1) \tan ^{-1}\left(\sqrt{x}\right)-\sqrt{x}","-\sqrt{x}+x \tan ^{-1}\left(\sqrt{x}\right)+\tan ^{-1}\left(\sqrt{x}\right)",1,"-Sqrt[x] + (1 + x)*ArcTan[Sqrt[x]]","A",1
96,1,8,8,0.0069104,"\int \frac{\tan ^{-1}\left(\sqrt{x}\right)}{\sqrt{x} (1+x)} \, dx","Integrate[ArcTan[Sqrt[x]]/(Sqrt[x]*(1 + x)),x]","\tan ^{-1}\left(\sqrt{x}\right)^2","\tan ^{-1}\left(\sqrt{x}\right)^2",1,"ArcTan[Sqrt[x]]^2","A",1
97,1,20,23,0.0059604,"\int \sqrt{1-x^2} \, dx","Integrate[Sqrt[1 - x^2],x]","\frac{1}{2} \left(\sqrt{1-x^2} x+\sin ^{-1}(x)\right)","\frac{1}{2} \sqrt{1-x^2} x+\frac{1}{2} \sin ^{-1}(x)",1,"(x*Sqrt[1 - x^2] + ArcSin[x])/2","A",1
98,1,37,22,0.0111623,"\int \frac{e^{\tan ^{-1}(x)} x}{\left(1+x^2\right)^{3/2}} \, dx","Integrate[(E^ArcTan[x]*x)/(1 + x^2)^(3/2),x]","\frac{1}{2} (1-i x)^{-\frac{1}{2}+\frac{i}{2}} (1+i x)^{-\frac{1}{2}-\frac{i}{2}} (x-1)","-\frac{(1-x) e^{\tan ^{-1}(x)}}{2 \sqrt{x^2+1}}",1,"(-1 + x)/(2*(1 - I*x)^(1/2 - I/2)*(1 + I*x)^(1/2 + I/2))","C",0
99,1,20,20,0.0066011,"\int \frac{e^{\tan ^{-1}(x)}}{\left(1+x^2\right)^{3/2}} \, dx","Integrate[E^ArcTan[x]/(1 + x^2)^(3/2),x]","\frac{(x+1) e^{\tan ^{-1}(x)}}{2 \sqrt{x^2+1}}","\frac{(x+1) e^{\tan ^{-1}(x)}}{2 \sqrt{x^2+1}}",1,"(E^ArcTan[x]*(1 + x))/(2*Sqrt[1 + x^2])","A",1
100,1,19,19,0.0089385,"\int \frac{x^2}{\left(1+x^2\right)^2} \, dx","Integrate[x^2/(1 + x^2)^2,x]","\frac{1}{2} \tan ^{-1}(x)-\frac{x}{2 \left(x^2+1\right)}","\frac{1}{2} \tan ^{-1}(x)-\frac{x}{2 \left(x^2+1\right)}",1,"-1/2*x/(1 + x^2) + ArcTan[x]/2","A",1
101,1,4,4,0.0026749,"\int \frac{e^x}{1+e^{2 x}} \, dx","Integrate[E^x/(1 + E^(2*x)),x]","\tan ^{-1}\left(e^x\right)","\tan ^{-1}\left(e^x\right)",1,"ArcTan[E^x]","A",1
102,1,27,27,0.0201666,"\int e^{-x} \cot ^{-1}\left(e^x\right) \, dx","Integrate[ArcCot[E^x]/E^x,x]","-x+\frac{1}{2} \log \left(e^{2 x}+1\right)-e^{-x} \cot ^{-1}\left(e^x\right)","-x+\frac{1}{2} \log \left(e^{2 x}+1\right)-e^{-x} \cot ^{-1}\left(e^x\right)",1,"-x - ArcCot[E^x]/E^x + Log[1 + E^(2*x)]/2","A",1
103,1,83,42,0.0545166,"\int \sqrt{\frac{a+x}{a-x}} \, dx","Integrate[Sqrt[(a + x)/(a - x)],x]","\frac{\sqrt{x-a} \sqrt{\frac{a+x}{a-x}} \left(2 a^{3/2} \sqrt{\frac{a+x}{a}} \sinh ^{-1}\left(\frac{\sqrt{x-a}}{\sqrt{2} \sqrt{a}}\right)+\sqrt{x-a} (a+x)\right)}{a+x}","2 a \tan ^{-1}\left(\sqrt{\frac{a+x}{a-x}}\right)-(a-x) \sqrt{\frac{a+x}{a-x}}",1,"(Sqrt[-a + x]*Sqrt[(a + x)/(a - x)]*(Sqrt[-a + x]*(a + x) + 2*a^(3/2)*Sqrt[(a + x)/a]*ArcSinh[Sqrt[-a + x]/(Sqrt[2]*Sqrt[a])]))/(a + x)","A",1
104,1,106,71,0.1674342,"\int \sqrt{(b-x) (-a+x)} \, dx","Integrate[Sqrt[(b - x)*(-a + x)],x]","\frac{(a-x) \left((a-b)^{5/2} \sqrt{b-x} \sqrt{\frac{a-x}{a-b}} \sinh ^{-1}\left(\frac{\sqrt{b-x}}{\sqrt{a-b}}\right)-(a-x) (b-x) (a+b-2 x)\right)}{4 (x-a) \sqrt{(a-x) (x-b)}}","-\frac{1}{4} (a+b-2 x) \sqrt{x (a+b)-a b-x^2}-\frac{1}{8} (a-b)^2 \tan ^{-1}\left(\frac{a+b-2 x}{2 \sqrt{x (a+b)-a b-x^2}}\right)",1,"((a - x)*(-((a + b - 2*x)*(a - x)*(b - x)) + (a - b)^(5/2)*Sqrt[(a - x)/(a - b)]*Sqrt[b - x]*ArcSinh[Sqrt[b - x]/Sqrt[a - b]]))/(4*(-a + x)*Sqrt[(a - x)*(-b + x)])","A",1
105,1,72,32,0.0296264,"\int \frac{1}{\sqrt{(b-x) (-a+x)}} \, dx","Integrate[1/Sqrt[(b - x)*(-a + x)],x]","-\frac{2 \sqrt{a-b} \sqrt{b-x} \sqrt{\frac{a-x}{a-b}} \sinh ^{-1}\left(\frac{\sqrt{b-x}}{\sqrt{a-b}}\right)}{\sqrt{(a-x) (x-b)}}","-\tan ^{-1}\left(\frac{a+b-2 x}{2 \sqrt{x (a+b)-a b-x^2}}\right)",1,"(-2*Sqrt[a - b]*Sqrt[(a - x)/(a - b)]*Sqrt[b - x]*ArcSinh[Sqrt[b - x]/Sqrt[a - b]])/Sqrt[(a - x)*(-b + x)]","B",1
106,1,15,15,0.0042623,"\int \frac{3+5 x}{-3+2 x+x^2} \, dx","Integrate[(3 + 5*x)/(-3 + 2*x + x^2),x]","2 \log (1-x)+3 \log (x+3)","2 \log (1-x)+3 \log (x+3)",1,"2*Log[1 - x] + 3*Log[3 + x]","A",1
107,1,19,19,0.0039043,"\int \frac{5+2 x}{-3+2 x+x^2} \, dx","Integrate[(5 + 2*x)/(-3 + 2*x + x^2),x]","\frac{7}{4} \log (1-x)+\frac{1}{4} \log (x+3)","\frac{7}{4} \log (1-x)+\frac{1}{4} \log (x+3)",1,"(7*Log[1 - x])/4 + Log[3 + x]/4","A",1
108,1,23,23,0.0049427,"\int \frac{3 x+x^3}{-3-2 x+x^2} \, dx","Integrate[(3*x + x^3)/(-3 - 2*x + x^2),x]","\frac{x^2}{2}+2 x+9 \log (3-x)+\log (x+1)","\frac{x^2}{2}+2 x+9 \log (3-x)+\log (x+1)",1,"2*x + x^2/2 + 9*Log[3 - x] + Log[1 + x]","A",1
109,1,23,23,0.0061965,"\int \frac{-1+5 x+2 x^2}{-2 x+x^2+x^3} \, dx","Integrate[(-1 + 5*x + 2*x^2)/(-2*x + x^2 + x^3),x]","2 \log (1-x)+\frac{\log (x)}{2}-\frac{1}{2} \log (x+2)","2 \log (1-x)+\frac{\log (x)}{2}-\frac{1}{2} \log (x+2)",1,"2*Log[1 - x] + Log[x]/2 - Log[2 + x]/2","A",1
110,1,22,24,0.011426,"\int \frac{3+2 x+x^2}{(-1+x) (1+x)^2} \, dx","Integrate[(3 + 2*x + x^2)/((-1 + x)*(1 + x)^2),x]","\frac{1}{x+1}+\frac{3}{2} \log (x-1)-\frac{1}{2} \log (x+1)","\frac{1}{x+1}+\frac{3}{2} \log (1-x)-\frac{1}{2} \log (x+1)",1,"(1 + x)^(-1) + (3*Log[-1 + x])/2 - Log[1 + x]/2","A",1
111,1,28,28,0.0118036,"\int \frac{-2+2 x+3 x^2}{-1+x^3} \, dx","Integrate[(-2 + 2*x + 3*x^2)/(-1 + x^3),x]","\log \left(1-x^3\right)+\frac{4 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}","\log \left(1-x^3\right)+\frac{4 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"(4*ArcTan[(1 + 2*x)/Sqrt[3]])/Sqrt[3] + Log[1 - x^3]","A",1
112,1,61,49,0.0321715,"\int \frac{2-x+2 x^2-x^3+x^4}{(-1+x) \left(2+x^2\right)^2} \, dx","Integrate[(2 - x + 2*x^2 - x^3 + x^4)/((-1 + x)*(2 + x^2)^2),x]","\frac{1}{2 \left((x-1)^2+2 (x-1)+3\right)}+\frac{1}{3} \log \left((x-1)^2+2 (x-1)+3\right)+\frac{1}{3} \log (x-1)-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{3 \sqrt{2}}","\frac{1}{2 \left(x^2+2\right)}+\frac{1}{3} \log \left(x^2+2\right)+\frac{1}{3} \log (1-x)-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{3 \sqrt{2}}",1,"1/(2*(3 + 2*(-1 + x) + (-1 + x)^2)) - ArcTan[x/Sqrt[2]]/(3*Sqrt[2]) + Log[3 + 2*(-1 + x) + (-1 + x)^2]/3 + Log[-1 + x]/3","A",1
113,1,24,21,0.0225122,"\int \frac{1}{\cos (x)+\sin (x)} \, dx","Integrate[(Cos[x] + Sin[x])^(-1),x]","(-1-i) (-1)^{3/4} \tanh ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right)-1}{\sqrt{2}}\right)","-\frac{\tanh ^{-1}\left(\frac{\cos (x)-\sin (x)}{\sqrt{2}}\right)}{\sqrt{2}}",1,"(-1 - I)*(-1)^(3/4)*ArcTanh[(-1 + Tan[x/2])/Sqrt[2]]","C",1
114,1,16,16,0.0313091,"\int \frac{x}{4-x^2+\sqrt{4-x^2}} \, dx","Integrate[x/(4 - x^2 + Sqrt[4 - x^2]),x]","-\log \left(\sqrt{4-x^2}+1\right)","-\log \left(\sqrt{4-x^2}+1\right)",1,"-Log[1 + Sqrt[4 - x^2]]","A",1
115,1,9,11,0.0042303,"\int \frac{3+2 x}{(-2+x) (5+x)} \, dx","Integrate[(3 + 2*x)/((-2 + x)*(5 + x)),x]","\log (x-2)+\log (x+5)","\log (2-x)+\log (x+5)",1,"Log[-2 + x] + Log[5 + x]","A",1
116,1,23,23,0.0069563,"\int \frac{x}{(1+x) (2+x) (3+x)} \, dx","Integrate[x/((1 + x)*(2 + x)*(3 + x)),x]","-\frac{1}{2} \log (x+1)+2 \log (x+2)-\frac{3}{2} \log (x+3)","-\frac{1}{2} \log (x+1)+2 \log (x+2)-\frac{3}{2} \log (x+3)",1,"-1/2*Log[1 + x] + 2*Log[2 + x] - (3*Log[3 + x])/2","A",1
117,1,28,30,0.0103039,"\int \frac{x}{2-3 x+x^3} \, dx","Integrate[x/(2 - 3*x + x^3),x]","-\frac{1}{3 (x-1)}+\frac{2}{9} \log (1-x)-\frac{2}{9} \log (x+2)","\frac{1}{3 (1-x)}+\frac{2}{9} \log (1-x)-\frac{2}{9} \log (x+2)",1,"-1/3*1/(-1 + x) + (2*Log[1 - x])/9 - (2*Log[2 + x])/9","A",1
118,1,27,27,0.006205,"\int \frac{-6+2 x+x^4}{-2 x+x^2+x^3} \, dx","Integrate[(-6 + 2*x + x^4)/(-2*x + x^2 + x^3),x]","\frac{x^2}{2}-x-\log (1-x)+3 \log (x)+\log (x+2)","\frac{x^2}{2}-x-\log (1-x)+3 \log (x)+\log (x+2)",1,"-x + x^2/2 - Log[1 - x] + 3*Log[x] + Log[2 + x]","A",1
119,1,24,23,0.0125152,"\int \frac{7+8 x^3}{(1+x) (1+2 x)^3} \, dx","Integrate[(7 + 8*x^3)/((1 + x)*(1 + 2*x)^3),x]","\frac{6 x+(2 x+1)^2 \log (x+1)}{(2 x+1)^2}","\frac{3}{2 x+1}-\frac{3}{(2 x+1)^2}+\log (x+1)",1,"(6*x + (1 + 2*x)^2*Log[1 + x])/(1 + 2*x)^2","A",1
120,1,16,16,0.0048255,"\int \frac{1+x+4 x^2}{-1+x^3} \, dx","Integrate[(1 + x + 4*x^2)/(-1 + x^3),x]","\log \left(x^2+x+1\right)+2 \log (1-x)","\log \left(x^2+x+1\right)+2 \log (1-x)",1,"2*Log[1 - x] + Log[1 + x + x^2]","A",1
121,1,18,18,0.0080777,"\int \frac{x^4}{4+5 x^2+x^4} \, dx","Integrate[x^4/(4 + 5*x^2 + x^4),x]","x+\frac{8}{3} \tan ^{-1}\left(\frac{2}{x}\right)+\frac{1}{3} \tan ^{-1}(x)","x-\frac{8}{3} \tan ^{-1}\left(\frac{x}{2}\right)+\frac{1}{3} \tan ^{-1}(x)",1,"x + (8*ArcTan[2/x])/3 + ArcTan[x]/3","A",1
122,1,11,11,0.0024106,"\int \frac{2+x}{x+x^2} \, dx","Integrate[(2 + x)/(x + x^2),x]","2 \log (x)-\log (x+1)","2 \log (x)-\log (x+1)",1,"2*Log[x] - Log[1 + x]","A",1
123,1,24,24,0.0097808,"\int \frac{1}{x \left(1+x^2\right)^2} \, dx","Integrate[1/(x*(1 + x^2)^2),x]","\frac{1}{2 \left(x^2+1\right)}-\frac{1}{2} \log \left(x^2+1\right)+\log (x)","\frac{1}{2 \left(x^2+1\right)}-\frac{1}{2} \log \left(x^2+1\right)+\log (x)",1,"1/(2*(1 + x^2)) + Log[x] - Log[1 + x^2]/2","A",1
124,1,44,46,0.0206564,"\int \frac{1}{(1+x) (2+x)^2 (3+x)^3} \, dx","Integrate[1/((1 + x)*(2 + x)^2*(3 + x)^3),x]","\frac{1}{8} \left(\frac{8}{x+2}+\frac{10}{x+3}+\frac{2}{(x+3)^2}+\log (-x-1)+16 \log (x+2)-17 \log (x+3)\right)","\frac{1}{x+2}+\frac{5}{4 (x+3)}+\frac{1}{4 (x+3)^2}+\frac{1}{8} \log (x+1)+2 \log (x+2)-\frac{17}{8} \log (x+3)",1,"(8/(2 + x) + 2/(3 + x)^2 + 10/(3 + x) + Log[-1 - x] + 16*Log[2 + x] - 17*Log[3 + x])/8","A",1
125,1,10,10,0.0028316,"\int \frac{x}{(1+x)^2} \, dx","Integrate[x/(1 + x)^2,x]","\frac{1}{x+1}+\log (x+1)","\frac{1}{x+1}+\log (x+1)",1,"(1 + x)^(-1) + Log[1 + x]","A",1
126,1,17,17,0.0028084,"\int \frac{1}{-x+x^3} \, dx","Integrate[(-x + x^3)^(-1),x]","\frac{1}{2} \log \left(1-x^2\right)-\log (x)","\frac{1}{2} \log \left(1-x^2\right)-\log (x)",1,"-Log[x] + Log[1 - x^2]/2","A",1
127,1,20,20,0.0034354,"\int \frac{x^2}{-6+x+x^2} \, dx","Integrate[x^2/(-6 + x + x^2),x]","x+\frac{4}{5} \log (2-x)-\frac{9}{5} \log (x+3)","x+\frac{4}{5} \log (2-x)-\frac{9}{5} \log (x+3)",1,"x + (4*Log[2 - x])/5 - (9*Log[3 + x])/5","A",1
128,1,12,16,0.0036925,"\int \frac{2+x}{4-4 x+x^2} \, dx","Integrate[(2 + x)/(4 - 4*x + x^2),x]","\log (x-2)-\frac{4}{x-2}","\frac{4}{2-x}+\log (2-x)",1,"-4/(-2 + x) + Log[-2 + x]","A",1
129,1,14,14,0.0081541,"\int \frac{1}{\left(4-4 x+x^2\right) \left(5-4 x+x^2\right)} \, dx","Integrate[1/((4 - 4*x + x^2)*(5 - 4*x + x^2)),x]","\tan ^{-1}(2-x)-\frac{1}{x-2}","\frac{1}{2-x}+\tan ^{-1}(2-x)",1,"-(-2 + x)^(-1) + ArcTan[2 - x]","A",1
130,1,21,21,0.0054553,"\int \frac{-3+x}{2 x+3 x^2+x^3} \, dx","Integrate[(-3 + x)/(2*x + 3*x^2 + x^3),x]","-\frac{3 \log (x)}{2}+4 \log (x+1)-\frac{5}{2} \log (x+2)","-\frac{3 \log (x)}{2}+4 \log (x+1)-\frac{5}{2} \log (x+2)",1,"(-3*Log[x])/2 + 4*Log[1 + x] - (5*Log[2 + x])/2","A",1
131,1,27,21,0.0081153,"\int \frac{1}{\left(-1+x^2\right)^2} \, dx","Integrate[(-1 + x^2)^(-2),x]","\frac{1}{4} \left(-\frac{2 x}{x^2-1}-\log (1-x)+\log (x+1)\right)","\frac{x}{2 \left(1-x^2\right)}+\frac{1}{2} \tanh ^{-1}(x)",1,"((-2*x)/(-1 + x^2) - Log[1 - x] + Log[1 + x])/4","A",1
132,1,22,22,0.0031829,"\int \frac{1+x}{-1+x^3} \, dx","Integrate[(1 + x)/(-1 + x^3),x]","\frac{2}{3} \log (1-x)-\frac{1}{3} \log \left(x^2+x+1\right)","\frac{2}{3} \log (1-x)-\frac{1}{3} \log \left(x^2+x+1\right)",1,"(2*Log[1 - x])/3 - Log[1 + x + x^2]/3","A",1
133,1,10,10,0.0052817,"\int \frac{1+x^4}{x \left(1+x^2\right)^2} \, dx","Integrate[(1 + x^4)/(x*(1 + x^2)^2),x]","\frac{1}{x^2+1}+\log (x)","\frac{1}{x^2+1}+\log (x)",1,"(1 + x^2)^(-1) + Log[x]","A",1
134,1,31,31,0.0021808,"\int \frac{1}{-2 x^3+x^4} \, dx","Integrate[(-2*x^3 + x^4)^(-1),x]","\frac{1}{4 x^2}+\frac{1}{4 x}+\frac{1}{8} \log (2-x)-\frac{\log (x)}{8}","\frac{1}{4 x^2}+\frac{1}{4 x}+\frac{1}{8} \log (2-x)-\frac{\log (x)}{8}",1,"1/(4*x^2) + 1/(4*x) + Log[2 - x]/8 - Log[x]/8","A",1
135,1,18,18,0.0053033,"\int \frac{1-x^3}{x \left(1+x^2\right)} \, dx","Integrate[(1 - x^3)/(x*(1 + x^2)),x]","-\frac{1}{2} \log \left(x^2+1\right)-x+\log (x)+\tan ^{-1}(x)","-\frac{1}{2} \log \left(x^2+1\right)-x+\log (x)+\tan ^{-1}(x)",1,"-x + ArcTan[x] + Log[x] - Log[1 + x^2]/2","A",1
136,1,25,13,0.0037309,"\int \frac{1}{-1+x^4} \, dx","Integrate[(-1 + x^4)^(-1),x]","\frac{1}{4} \log (1-x)-\frac{1}{4} \log (x+1)-\frac{1}{2} \tan ^{-1}(x)","-\frac{1}{2} \tan ^{-1}(x)-\frac{1}{2} \tanh ^{-1}(x)",1,"-1/2*ArcTan[x] + Log[1 - x]/4 - Log[1 + x]/4","A",1
137,1,64,85,0.0197685,"\int \frac{1}{1+x^4} \, dx","Integrate[(1 + x^4)^(-1),x]","\frac{-\log \left(x^2-\sqrt{2} x+1\right)+\log \left(x^2+\sqrt{2} x+1\right)-2 \tan ^{-1}\left(1-\sqrt{2} x\right)+2 \tan ^{-1}\left(\sqrt{2} x+1\right)}{4 \sqrt{2}}","-\frac{\log \left(x^2-\sqrt{2} x+1\right)}{4 \sqrt{2}}+\frac{\log \left(x^2+\sqrt{2} x+1\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} x\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} x+1\right)}{2 \sqrt{2}}",1,"(-2*ArcTan[1 - Sqrt[2]*x] + 2*ArcTan[1 + Sqrt[2]*x] - Log[1 - Sqrt[2]*x + x^2] + Log[1 + Sqrt[2]*x + x^2])/(4*Sqrt[2])","A",1
138,1,15,23,0.0088855,"\int \frac{x^2}{\left(2+2 x+x^2\right)^2} \, dx","Integrate[x^2/(2 + 2*x + x^2)^2,x]","\frac{1}{x^2+2 x+2}+\tan ^{-1}(x+1)","\tan ^{-1}(x+1)-\frac{x (x+2)}{2 \left(x^2+2 x+2\right)}",1,"(2 + 2*x + x^2)^(-1) + ArcTan[1 + x]","A",1
139,1,11,11,0.0065881,"\int \frac{-1+4 x^5}{\left(1+x+x^5\right)^2} \, dx","Integrate[(-1 + 4*x^5)/(1 + x + x^5)^2,x]","-\frac{x}{x^5+x+1}","-\frac{x}{x^5+x+1}",1,"-(x/(1 + x + x^5))","A",1
140,1,23,45,0.0295966,"\int \frac{1}{5-\cos (x)+2 \sin (x)} \, dx","Integrate[(5 - Cos[x] + 2*Sin[x])^(-1),x]","\frac{\tan ^{-1}\left(\frac{3 \tan \left(\frac{x}{2}\right)+1}{\sqrt{5}}\right)}{\sqrt{5}}","\frac{x}{2 \sqrt{5}}+\frac{\tan ^{-1}\left(\frac{\sin (x)+2 \cos (x)}{2 \sin (x)-\cos (x)+2 \sqrt{5}+5}\right)}{\sqrt{5}}",1,"ArcTan[(1 + 3*Tan[x/2])/Sqrt[5]]/Sqrt[5]","A",1
141,1,31,37,0.0257803,"\int \frac{1}{1+a \cos (x)} \, dx","Integrate[(1 + a*Cos[x])^(-1),x]","\frac{2 \tanh ^{-1}\left(\frac{(a-1) \tan \left(\frac{x}{2}\right)}{\sqrt{a^2-1}}\right)}{\sqrt{a^2-1}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-a} \tan \left(\frac{x}{2}\right)}{\sqrt{a+1}}\right)}{\sqrt{1-a^2}}",1,"(2*ArcTanh[((-1 + a)*Tan[x/2])/Sqrt[-1 + a^2]])/Sqrt[-1 + a^2]","A",1
142,1,20,56,0.0154156,"\int \frac{1}{1+2 \cos (x)} \, dx","Integrate[(1 + 2*Cos[x])^(-1),x]","\frac{2 \tanh ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right)}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{\log \left(\sin \left(\frac{x}{2}\right)+\sqrt{3} \cos \left(\frac{x}{2}\right)\right)}{\sqrt{3}}-\frac{\log \left(\sqrt{3} \cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)}{\sqrt{3}}",1,"(2*ArcTanh[Tan[x/2]/Sqrt[3]])/Sqrt[3]","A",1
143,1,20,31,0.0129997,"\int \frac{1}{1+\frac{\cos (x)}{2}} \, dx","Integrate[(1 + Cos[x]/2)^(-1),x]","\frac{4 \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right)}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{2 x}{\sqrt{3}}-\frac{4 \tan ^{-1}\left(\frac{\sin (x)}{\cos (x)+\sqrt{3}+2}\right)}{\sqrt{3}}",1,"(4*ArcTan[Tan[x/2]/Sqrt[3]])/Sqrt[3]","A",1
144,1,18,36,0.0352425,"\int \frac{\sin ^2(x)}{1+\sin ^2(x)} \, dx","Integrate[Sin[x]^2/(1 + Sin[x]^2),x]","x-\frac{\tan ^{-1}\left(\sqrt{2} \tan (x)\right)}{\sqrt{2}}","-\frac{x}{\sqrt{2}}+x-\frac{\tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\sin ^2(x)+\sqrt{2}+1}\right)}{\sqrt{2}}",1,"x - ArcTan[Sqrt[2]*Tan[x]]/Sqrt[2]","A",1
145,1,15,15,0.0495551,"\int \frac{1}{b^2 \cos ^2(x)+a^2 \sin ^2(x)} \, dx","Integrate[(b^2*Cos[x]^2 + a^2*Sin[x]^2)^(-1),x]","\frac{\tan ^{-1}\left(\frac{a \tan (x)}{b}\right)}{a b}","\frac{\tan ^{-1}\left(\frac{a \tan (x)}{b}\right)}{a b}",1,"ArcTan[(a*Tan[x])/b]/(a*b)","A",1
146,1,17,17,0.0341192,"\int \frac{1}{(b \cos (x)+a \sin (x))^2} \, dx","Integrate[(b*Cos[x] + a*Sin[x])^(-2),x]","\frac{\sin (x)}{b (a \sin (x)+b \cos (x))}","\frac{\sin (x)}{b (a \sin (x)+b \cos (x))}",1,"Sin[x]/(b*(b*Cos[x] + a*Sin[x]))","A",1
147,1,22,30,0.0425313,"\int \frac{\sin (x)}{1+\cos (x)+\sin (x)} \, dx","Integrate[Sin[x]/(1 + Cos[x] + Sin[x]),x]","\frac{x}{2}-\log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)","\frac{x}{2}-\frac{1}{2} \log \left(\tan \left(\frac{x}{2}\right)+1\right)-\frac{1}{2} \log (\sin (x)+\cos (x)+1)",1,"x/2 - Log[Cos[x/2] + Sin[x/2]]","A",1
148,1,29,29,0.0093187,"\int \sqrt{3-x^2} \, dx","Integrate[Sqrt[3 - x^2],x]","\frac{1}{2} \sqrt{3-x^2} x+\frac{3}{2} \sin ^{-1}\left(\frac{x}{\sqrt{3}}\right)","\frac{1}{2} \sqrt{3-x^2} x+\frac{3}{2} \sin ^{-1}\left(\frac{x}{\sqrt{3}}\right)",1,"(x*Sqrt[3 - x^2])/2 + (3*ArcSin[x/Sqrt[3]])/2","A",1
149,1,13,13,0.0018487,"\int \frac{x}{\sqrt{3-x^2}} \, dx","Integrate[x/Sqrt[3 - x^2],x]","-\sqrt{3-x^2}","-\sqrt{3-x^2}",1,"-Sqrt[3 - x^2]","A",1
150,1,33,37,0.0085776,"\int \frac{\sqrt{3-x^2}}{x} \, dx","Integrate[Sqrt[3 - x^2]/x,x]","\sqrt{3-x^2}-\sqrt{3} \tanh ^{-1}\left(\sqrt{1-\frac{x^2}{3}}\right)","\sqrt{3-x^2}-\sqrt{3} \tanh ^{-1}\left(\frac{\sqrt{3-x^2}}{\sqrt{3}}\right)",1,"Sqrt[3 - x^2] - Sqrt[3]*ArcTanh[Sqrt[1 - x^2/3]]","A",1
151,1,31,22,0.0164678,"\int \frac{\sqrt{x+x^2}}{x} \, dx","Integrate[Sqrt[x + x^2]/x,x]","\sqrt{x (x+1)} \left(\frac{\sinh ^{-1}\left(\sqrt{x}\right)}{\sqrt{x} \sqrt{x+1}}+1\right)","\sqrt{x^2+x}+\tanh ^{-1}\left(\frac{x}{\sqrt{x^2+x}}\right)",1,"Sqrt[x*(1 + x)]*(1 + ArcSinh[Sqrt[x]]/(Sqrt[x]*Sqrt[1 + x]))","A",1
152,1,27,27,0.0088255,"\int \sqrt{5+x^2} \, dx","Integrate[Sqrt[5 + x^2],x]","\frac{1}{2} \sqrt{x^2+5} x+\frac{5}{2} \sinh ^{-1}\left(\frac{x}{\sqrt{5}}\right)","\frac{1}{2} \sqrt{x^2+5} x+\frac{5}{2} \sinh ^{-1}\left(\frac{x}{\sqrt{5}}\right)",1,"(x*Sqrt[5 + x^2])/2 + (5*ArcSinh[x/Sqrt[5]])/2","A",1
153,1,27,27,0.005117,"\int \frac{x}{\sqrt{1+x+x^2}} \, dx","Integrate[x/Sqrt[1 + x + x^2],x]","\sqrt{x^2+x+1}-\frac{1}{2} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)","\sqrt{x^2+x+1}-\frac{1}{2} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"Sqrt[1 + x + x^2] - ArcSinh[(1 + 2*x)/Sqrt[3]]/2","A",1
154,1,29,14,0.0057856,"\int \frac{1}{\sqrt{x+x^2}} \, dx","Integrate[1/Sqrt[x + x^2],x]","\frac{2 \sqrt{x} \sqrt{x+1} \sinh ^{-1}\left(\sqrt{x}\right)}{\sqrt{x (x+1)}}","2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2+x}}\right)",1,"(2*Sqrt[x]*Sqrt[1 + x]*ArcSinh[Sqrt[x]])/Sqrt[x*(1 + x)]","B",1
155,1,68,68,0.0332141,"\int \frac{\sqrt{2-x-x^2}}{x^2} \, dx","Integrate[Sqrt[2 - x - x^2]/x^2,x]","-\frac{\sqrt{-x^2-x+2}}{x}+\frac{\tanh ^{-1}\left(\frac{4-x}{2 \sqrt{2} \sqrt{-x^2-x+2}}\right)}{2 \sqrt{2}}+\sin ^{-1}\left(\frac{1}{3} (-2 x-1)\right)","-\frac{\sqrt{-x^2-x+2}}{x}+\frac{\tanh ^{-1}\left(\frac{4-x}{2 \sqrt{2} \sqrt{-x^2-x+2}}\right)}{2 \sqrt{2}}+\sin ^{-1}\left(\frac{1}{3} (-2 x-1)\right)",1,"-(Sqrt[2 - x - x^2]/x) + ArcSin[(-1 - 2*x)/3] + ArcTanh[(4 - x)/(2*Sqrt[2]*Sqrt[2 - x - x^2])]/(2*Sqrt[2])","A",1
156,1,13,13,0.0021388,"\int \frac{\log (t)}{1+t} \, dt","Integrate[Log[t]/(1 + t),t]","\operatorname{PolyLog}(2,-t)+\log (t) \log (t+1)","\operatorname{PolyLog}(2,-t)+\log (t) \log (t+1)",1,"Log[t]*Log[1 + t] + PolyLog[2, -t]","A",1
157,1,15,15,0.0106672,"\int \log \left(e^{\cos (x)}\right) \, dx","Integrate[Log[E^Cos[x]],x]","\sin (x)+x \left(\log \left(e^{\cos (x)}\right)-\cos (x)\right)","\sin (x)-x \cos (x)+x \log \left(e^{\cos (x)}\right)",1,"x*(-Cos[x] + Log[E^Cos[x]]) + Sin[x]","A",1
158,1,2,2,0.0054594,"\int \frac{e^t}{t} \, dt","Integrate[E^t/t,t]","\operatorname{ExpIntegralEi}(t)","\operatorname{ExpIntegralEi}(t)",1,"ExpIntegralEi[t]","A",1
159,1,4,4,0.007657,"\int \frac{e^{a t}}{t} \, dt","Integrate[E^(a*t)/t,t]","\operatorname{ExpIntegralEi}(a t)","\operatorname{ExpIntegralEi}(a t)",1,"ExpIntegralEi[a*t]","A",1
160,1,11,11,0.0088923,"\int \frac{e^t}{t^2} \, dt","Integrate[E^t/t^2,t]","\text{Ei}(t)-\frac{e^t}{t}","\text{Ei}(t)-\frac{e^t}{t}",1,"-(E^t/t) + ExpIntegralEi[t]","A",1
161,1,14,14,0.002178,"\int e^{\frac{1}{t}} \, dt","Integrate[E^t^(-1),t]","e^{\frac{1}{t}} t-\text{Ei}\left(\frac{1}{t}\right)","e^{\frac{1}{t}} t-\text{Ei}\left(\frac{1}{t}\right)",1,"E^t^(-1)*t - ExpIntegralEi[t^(-1)]","A",1
162,1,15,15,0.0142142,"\int \frac{e^{-t}}{-1-a+t} \, dt","Integrate[1/(E^t*(-1 - a + t)),t]","e^{-a-1} \text{Ei}(a-t+1)","e^{-a-1} \text{Ei}(a-t+1)",1,"E^(-1 - a)*ExpIntegralEi[1 + a - t]","A",1
163,1,13,13,0.0214668,"\int \frac{e^{t^2} t}{1+t^2} \, dt","Integrate[(E^t^2*t)/(1 + t^2),t]","\frac{\text{Ei}\left(t^2+1\right)}{2 e}","\frac{\text{Ei}\left(t^2+1\right)}{2 e}",1,"ExpIntegralEi[1 + t^2]/(2*E)","A",1
164,1,19,19,0.0234563,"\int \frac{e^t}{(1+t)^2} \, dt","Integrate[E^t/(1 + t)^2,t]","\frac{\text{Ei}(t+1)}{e}-\frac{e^t}{t+1}","\frac{\text{Ei}(t+1)}{e}-\frac{e^t}{t+1}",1,"-(E^t/(1 + t)) + ExpIntegralEi[1 + t]/E","A",1
165,1,18,18,0.0096293,"\int e^t \log (1+t) \, dt","Integrate[E^t*Log[1 + t],t]","e^t \log (t+1)-\frac{\text{Ei}(t+1)}{e}","e^t \log (t+1)-\frac{\text{Ei}(t+1)}{e}",1,"-(ExpIntegralEi[1 + t]/E) + E^t*Log[1 + t]","A",1
166,1,11,16,0.0048423,"\int e^{-t} t \, dt","Integrate[t/E^t,t]","e^{-t} (-t-1)","-e^{-t} t-e^{-t}",1,"(-1 - t)/E^t","A",1
167,1,16,26,0.005693,"\int e^{-t} t^2 \, dt","Integrate[t^2/E^t,t]","e^{-t} \left(-t^2-2 t-2\right)","-e^{-t} t^2-2 e^{-t} t-2 e^{-t}",1,"(-2 - 2*t - t^2)/E^t","A",1
168,1,21,36,0.0064384,"\int e^{-t} t^3 \, dt","Integrate[t^3/E^t,t]","e^{-t} \left(-t^3-3 t^2-6 t-6\right)","-e^{-t} t^3-3 e^{-t} t^2-6 e^{-t} t-6 e^{-t}",1,"(-6 - 6*t - 3*t^2 - t^3)/E^t","A",1
169,1,39,48,0.1338586,"\int \frac{\text{b1} \cos (x)+\text{a1} \sin (x)}{b \cos (x)+a \sin (x)} \, dx","Integrate[(b1*Cos[x] + a1*Sin[x])/(b*Cos[x] + a*Sin[x]),x]","\frac{x (a \text{a1}+b \text{b1})+(a \text{b1}-\text{a1} b) \log (a \sin (x)+b \cos (x))}{a^2+b^2}","\frac{x (a \text{a1}+b \text{b1})}{a^2+b^2}-\frac{(\text{a1} b-a \text{b1}) \log (a \sin (x)+b \cos (x))}{a^2+b^2}",1,"((a*a1 + b*b1)*x + (-(a1*b) + a*b1)*Log[b*Cos[x] + a*Sin[x]])/(a^2 + b^2)","A",1
170,1,2,2,0.0022727,"\int \frac{1}{\log (t)} \, dt","Integrate[Log[t]^(-1),t]","\operatorname{LogIntegral}(t)","\operatorname{LogIntegral}(t)",1,"LogIntegral[t]","A",1
171,1,10,10,0.0013862,"\int \frac{1}{\log ^2(t)} \, dt","Integrate[Log[t]^(-2),t]","\text{li}(t)-\frac{t}{\log (t)}","\text{li}(t)-\frac{t}{\log (t)}",1,"-(t/Log[t]) + LogIntegral[t]","A",1
172,1,22,22,0.0127559,"\int \log ^{-1-n}(t) \, dt","Integrate[Log[t]^(-1 - n),t]","(-\log (t))^n \log ^{-n}(t) (-\operatorname{Gamma}(-n,-\log (t)))","(-\log (t))^n \log ^{-n}(t) (-\operatorname{Gamma}(-n,-\log (t)))",1,"-((Gamma[-n, -Log[t]]*(-Log[t])^n)/Log[t]^n)","A",1
173,1,10,12,0.0164565,"\int \frac{e^{2 t}}{-1+t} \, dt","Integrate[E^(2*t)/(-1 + t),t]","e^2 \text{Ei}(2 (t-1))","e^2 \text{Ei}(-2 (1-t))",1,"E^2*ExpIntegralEi[2*(-1 + t)]","A",1
174,1,22,22,0.0384273,"\int \frac{e^{2 x}}{2-3 x+x^2} \, dx","Integrate[E^(2*x)/(2 - 3*x + x^2),x]","e^4 \text{Ei}(2 x-4)-e^2 \text{Ei}(2 x-2)","e^4 \text{Ei}(2 x-4)-e^2 \text{Ei}(2 x-2)",1,"E^4*ExpIntegralEi[-4 + 2*x] - E^2*ExpIntegralEi[-2 + 2*x]","A",1
175,1,17,103,0.0022295,"\int \frac{1}{\sqrt{1+t^3}} \, dt","Integrate[1/Sqrt[1 + t^3],t]","t \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-t^3\right)","\frac{2 \sqrt{2+\sqrt{3}} (t+1) \sqrt{\frac{t^2-t+1}{\left(t+\sqrt{3}+1\right)^2}} \operatorname{EllipticF}\left(\sin ^{-1}\left(\frac{t-\sqrt{3}+1}{t+\sqrt{3}+1}\right),-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{t+1}{\left(t+\sqrt{3}+1\right)^2}} \sqrt{t^3+1}}",1,"t*Hypergeometric2F1[1/3, 1/2, 4/3, -t^3]","C",1