1,1,13,0,0.0009888,"\int \sqrt{1+2 x} \, dx","Int[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",1,1,9,0.1111,1,"{32}"
2,1,27,0,0.0044375,"\int x \sqrt{1+3 x} \, dx","Int[x*Sqrt[1 + 3*x],x]","\frac{2}{45} (3 x+1)^{5/2}-\frac{2}{27} (3 x+1)^{3/2}","\frac{2}{45} (3 x+1)^{5/2}-\frac{2}{27} (3 x+1)^{3/2}",1,"(-2*(1 + 3*x)^(3/2))/27 + (2*(1 + 3*x)^(5/2))/45","A",2,1,11,0.09091,1,"{43}"
3,1,34,0,0.0051121,"\int x^2 \sqrt{1+x} \, dx","Int[x^2*Sqrt[1 + x],x]","\frac{2}{7} (x+1)^{7/2}-\frac{4}{5} (x+1)^{5/2}+\frac{2}{3} (x+1)^{3/2}","\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))/3 - (4*(1 + x)^(5/2))/5 + (2*(1 + x)^(7/2))/7","A",2,1,11,0.09091,1,"{43}"
4,1,27,0,0.0046574,"\int \frac{x}{\sqrt{2-3 x}} \, dx","Int[x/Sqrt[2 - 3*x],x]","\frac{2}{27} (2-3 x)^{3/2}-\frac{4}{9} \sqrt{2-3 x}","\frac{2}{27} (2-3 x)^{3/2}-\frac{4}{9} \sqrt{2-3 x}",1,"(-4*Sqrt[2 - 3*x])/9 + (2*(2 - 3*x)^(3/2))/27","A",2,1,11,0.09091,1,"{43}"
5,1,14,0,0.0028358,"\int \frac{1+x}{\left(2+2 x+x^2\right)^3} \, dx","Int[(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*(2 + 2*x + x^2)^2)","A",1,1,14,0.07143,1,"{629}"
6,1,13,0,0.0063655,"\int \sin ^3(x) \, dx","Int[Sin[x]^3,x]","\frac{\cos ^3(x)}{3}-\cos (x)","\frac{\cos ^3(x)}{3}-\cos (x)",1,"-Cos[x] + Cos[x]^3/3","A",2,1,4,0.2500,1,"{2633}"
7,1,23,0,0.0037208,"\int \sqrt[3]{-1+z} z \, dz","Int[(-1 + z)^(1/3)*z,z]","\frac{3}{7} (z-1)^{7/3}+\frac{3}{4} (z-1)^{4/3}","\frac{3}{7} (z-1)^{7/3}+\frac{3}{4} (z-1)^{4/3}",1,"(3*(-1 + z)^(4/3))/4 + (3*(-1 + z)^(7/3))/7","A",2,1,9,0.1111,1,"{43}"
8,1,8,0,0.0130718,"\int \cot (x) \csc ^2(x) \, dx","Int[Cot[x]*Csc[x]^2,x]","-\frac{1}{2} \csc ^2(x)","-\frac{1}{2} \csc ^2(x)",1,"-Csc[x]^2/2","A",2,2,7,0.2857,1,"{2606, 30}"
9,1,16,0,0.0230421,"\int \cos (2 x) \sqrt{4-\sin (2 x)} \, dx","Int[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,"-(4 - Sin[2*x])^(3/2)/3","A",2,2,17,0.1176,1,"{2668, 32}"
10,1,6,0,0.0176402,"\int \frac{\sin (x)}{(3+\cos (x))^2} \, dx","Int[Sin[x]/(3 + Cos[x])^2,x]","\frac{1}{\cos (x)+3}","\frac{1}{\cos (x)+3}",1,"(3 + Cos[x])^(-1)","A",2,2,9,0.2222,1,"{2668, 32}"
11,1,12,0,0.027797,"\int \frac{\sin (x)}{\sqrt{\cos ^3(x)}} \, dx","Int[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",3,3,11,0.2727,1,"{3207, 2565, 30}"
12,1,10,0,0.0162841,"\int \frac{\sin \left(\sqrt{1+x}\right)}{\sqrt{1+x}} \, dx","Int[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",3,3,16,0.1875,1,"{3431, 15, 2638}"
13,1,9,0,0.0111279,"\int x^{-1+n} \sin \left(x^n\right) \, dx","Int[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",2,2,10,0.2000,1,"{3379, 2638}"
14,1,15,0,0.0027586,"\int \frac{x^5}{\sqrt{1-x^6}} \, dx","Int[x^5/Sqrt[1 - x^6],x]","-\frac{1}{3} \sqrt{1-x^6}","-\frac{1}{3} \sqrt{1-x^6}",1,"-Sqrt[1 - x^6]/3","A",1,1,15,0.06667,1,"{261}"
15,1,23,0,0.0037507,"\int t \sqrt[4]{1+t} \, dt","Int[t*(1 + t)^(1/4),t]","\frac{4}{9} (t+1)^{9/4}-\frac{4}{5} (t+1)^{5/4}","\frac{4}{9} (t+1)^{9/4}-\frac{4}{5} (t+1)^{5/4}",1,"(-4*(1 + t)^(5/4))/5 + (4*(1 + t)^(9/4))/9","A",2,1,9,0.1111,1,"{43}"
16,1,11,0,0.0011778,"\int \frac{1}{\left(1+x^2\right)^{3/2}} \, dx","Int[(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",1,1,9,0.1111,1,"{191}"
17,1,15,0,0.0030355,"\int x^2 \left(27+8 x^3\right)^{2/3} \, dx","Int[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",1,1,15,0.06667,1,"{261}"
18,1,15,0,0.0264653,"\int \frac{\cos (x)+\sin (x)}{\sqrt[3]{-\cos (x)+\sin (x)}} \, dx","Int[(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",1,1,17,0.05882,1,"{3145}"
19,1,32,0,0.1005739,"\int \frac{x}{\sqrt{1+x^2+\left(1+x^2\right)^{3/2}}} \, dx","Int[x/Sqrt[1 + x^2 + (1 + x^2)^(3/2)],x]","\frac{2 \sqrt{\left(x^2+1\right) \left(\sqrt{x^2+1}+1\right)}}{\sqrt{x^2+1}}","\frac{2 \sqrt{\left(x^2+1\right) \left(\sqrt{x^2+1}+1\right)}}{\sqrt{x^2+1}}",1,"(2*Sqrt[(1 + x^2)*(1 + Sqrt[1 + x^2])])/Sqrt[1 + x^2]","A",3,2,20,0.1000,1,"{6715, 1588}"
20,1,17,0,0.111079,"\int \frac{x}{\sqrt{1+x^2} \sqrt{1+\sqrt{1+x^2}}} \, dx","Int[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",1,1,26,0.03846,1,"{6686}"
21,1,16,0,0.0079128,"\int \frac{\sqrt[5]{1-2 x+x^2}}{1-x} \, dx","Int[(1 - 2*x + x^2)^(1/5)/(1 - x),x]","-\frac{5}{2} \sqrt[5]{x^2-2 x+1}","-\frac{5}{2} \sqrt[5]{x^2-2 x+1}",1,"(-5*(1 - 2*x + x^2)^(1/5))/2","A",2,2,20,0.1000,1,"{643, 629}"
22,1,8,0,0.0089634,"\int x \sin (x) \, dx","Int[x*Sin[x],x]","\sin (x)-x \cos (x)","\sin (x)-x \cos (x)",1,"-(x*Cos[x]) + Sin[x]","A",2,2,4,0.5000,1,"{3296, 2637}"
23,1,17,0,0.0207939,"\int x^2 \sin (x) \, dx","Int[x^2*Sin[x],x]","x^2 (-\cos (x))+2 x \sin (x)+2 \cos (x)","x^2 (-\cos (x))+2 x \sin (x)+2 \cos (x)",1,"2*Cos[x] - x^2*Cos[x] + 2*x*Sin[x]","A",3,2,6,0.3333,1,"{3296, 2638}"
24,1,23,0,0.0355037,"\int x^3 \cos (x) \, dx","Int[x^3*Cos[x],x]","x^3 \sin (x)+3 x^2 \cos (x)-6 x \sin (x)-6 \cos (x)","x^3 \sin (x)+3 x^2 \cos (x)-6 x \sin (x)-6 \cos (x)",1,"-6*Cos[x] + 3*x^2*Cos[x] - 6*x*Sin[x] + x^3*Sin[x]","A",4,2,6,0.3333,1,"{3296, 2638}"
25,1,24,0,0.0358987,"\int x^3 \sin (x) \, dx","Int[x^3*Sin[x],x]","x^3 (-\cos (x))+3 x^2 \sin (x)-6 \sin (x)+6 x \cos (x)","x^3 (-\cos (x))+3 x^2 \sin (x)-6 \sin (x)+6 x \cos (x)",1,"6*x*Cos[x] - x^3*Cos[x] - 6*Sin[x] + 3*x^2*Sin[x]","A",4,2,6,0.3333,1,"{3296, 2637}"
26,1,8,0,0.006863,"\int \cos (x) \sin (x) \, dx","Int[Cos[x]*Sin[x],x]","\frac{\sin ^2(x)}{2}","\frac{\sin ^2(x)}{2}",1,"Sin[x]^2/2","A",2,2,5,0.4000,1,"{2564, 30}"
27,1,23,0,0.0127059,"\int x \cos (x) \sin (x) \, dx","Int[x*Cos[x]*Sin[x],x]","-\frac{x}{4}+\frac{1}{2} x \sin ^2(x)+\frac{1}{4} \sin (x) \cos (x)","-\frac{x}{4}+\frac{1}{2} x \sin ^2(x)+\frac{1}{4} \sin (x) \cos (x)",1,"-x/4 + (Cos[x]*Sin[x])/4 + (x*Sin[x]^2)/2","A",3,3,6,0.5000,1,"{3443, 2635, 8}"
28,1,14,0,0.0051129,"\int \sin ^2(x) \, dx","Int[Sin[x]^2,x]","\frac{x}{2}-\frac{1}{2} \sin (x) \cos (x)","\frac{x}{2}-\frac{1}{2} \sin (x) \cos (x)",1,"x/2 - (Cos[x]*Sin[x])/2","A",2,2,4,0.5000,1,"{2635, 8}"
29,1,13,0,0.0056728,"\int \sin ^3(x) \, dx","Int[Sin[x]^3,x]","\frac{\cos ^3(x)}{3}-\cos (x)","\frac{\cos ^3(x)}{3}-\cos (x)",1,"-Cos[x] + Cos[x]^3/3","A",2,1,4,0.2500,1,"{2633}"
30,1,24,0,0.0092784,"\int \sin ^4(x) \, dx","Int[Sin[x]^4,x]","\frac{3 x}{8}-\frac{1}{4} \sin ^3(x) \cos (x)-\frac{3}{8} \sin (x) \cos (x)","\frac{3 x}{8}-\frac{1}{4} \sin ^3(x) \cos (x)-\frac{3}{8} \sin (x) \cos (x)",1,"(3*x)/8 - (3*Cos[x]*Sin[x])/8 - (Cos[x]*Sin[x]^3)/4","A",3,2,4,0.5000,1,"{2635, 8}"
31,1,21,0,0.0066113,"\int \sin ^5(x) \, dx","Int[Sin[x]^5,x]","-\frac{1}{5} \cos ^5(x)+\frac{2 \cos ^3(x)}{3}-\cos (x)","-\frac{1}{5} \cos ^5(x)+\frac{2 \cos ^3(x)}{3}-\cos (x)",1,"-Cos[x] + (2*Cos[x]^3)/3 - Cos[x]^5/5","A",2,1,4,0.2500,1,"{2633}"
32,1,34,0,0.0156523,"\int \sin ^6(x) \, dx","Int[Sin[x]^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)","\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 - (5*Cos[x]*Sin[x])/16 - (5*Cos[x]*Sin[x]^3)/24 - (Cos[x]*Sin[x]^5)/6","A",4,2,4,0.5000,1,"{2635, 8}"
33,1,25,0,0.0139333,"\int x \sin ^2(x) \, dx","Int[x*Sin[x]^2,x]","\frac{x^2}{4}+\frac{\sin ^2(x)}{4}-\frac{1}{2} x \sin (x) \cos (x)","\frac{x^2}{4}+\frac{\sin ^2(x)}{4}-\frac{1}{2} x \sin (x) \cos (x)",1,"x^2/4 - (x*Cos[x]*Sin[x])/2 + Sin[x]^2/4","A",2,2,6,0.3333,1,"{3310, 30}"
34,1,33,0,0.0219208,"\int x \sin ^3(x) \, dx","Int[x*Sin[x]^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)","\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,"(-2*x*Cos[x])/3 + (2*Sin[x])/3 - (x*Cos[x]*Sin[x]^2)/3 + Sin[x]^3/9","A",3,3,6,0.5000,1,"{3310, 3296, 2637}"
35,1,41,0,0.0313716,"\int x^2 \sin ^2(x) \, dx","Int[x^2*Sin[x]^2,x]","\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)","\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,"-x/4 + x^3/6 + (Cos[x]*Sin[x])/4 - (x^2*Cos[x]*Sin[x])/2 + (x*Sin[x]^2)/2","A",4,4,8,0.5000,1,"{3311, 30, 2635, 8}"
36,1,14,0,0.0060605,"\int \cos ^2(x) \, dx","Int[Cos[x]^2,x]","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"x/2 + (Cos[x]*Sin[x])/2","A",2,2,4,0.5000,1,"{2635, 8}"
37,1,11,0,0.0060146,"\int \cos ^3(x) \, dx","Int[Cos[x]^3,x]","\sin (x)-\frac{\sin ^3(x)}{3}","\sin (x)-\frac{\sin ^3(x)}{3}",1,"Sin[x] - Sin[x]^3/3","A",2,1,4,0.2500,1,"{2633}"
38,1,24,0,0.0112994,"\int \cos ^4(x) \, dx","Int[Cos[x]^4,x]","\frac{3 x}{8}+\frac{1}{4} \sin (x) \cos ^3(x)+\frac{3}{8} \sin (x) \cos (x)","\frac{3 x}{8}+\frac{1}{4} \sin (x) \cos ^3(x)+\frac{3}{8} \sin (x) \cos (x)",1,"(3*x)/8 + (3*Cos[x]*Sin[x])/8 + (Cos[x]^3*Sin[x])/4","A",3,2,4,0.5000,1,"{2635, 8}"
39,1,84,0,0.0145512,"\int \left(a^2-x^2\right)^{5/2} \, dx","Int[(a^2 - x^2)^(5/2),x]","\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}","\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,"(5*a^4*x*Sqrt[a^2 - x^2])/16 + (5*a^2*x*(a^2 - x^2)^(3/2))/24 + (x*(a^2 - x^2)^(5/2))/6 + (5*a^6*ArcTan[x/Sqrt[a^2 - x^2]])/16","A",5,3,13,0.2308,1,"{195, 217, 203}"
40,1,38,0,0.0129593,"\int \frac{x^5}{\sqrt{5+x^2}} \, dx","Int[x^5/Sqrt[5 + x^2],x]","\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}","\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,"25*Sqrt[5 + x^2] - (10*(5 + x^2)^(3/2))/3 + (5 + x^2)^(5/2)/5","A",3,2,13,0.1538,1,"{266, 43}"
41,1,172,0,0.0288655,"\int \frac{t^3}{\sqrt{4+t^3}} \, dt","Int[t^3/Sqrt[4 + t^3],t]","\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}} \text{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}}","\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}} \text{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])/5 - (8*2^(2/3)*Sqrt[2 + Sqrt[3]]*(2^(2/3) + t)*Sqrt[(2*2^(1/3) - 2^(2/3)*t + t^2)/(2^(2/3)*(1 + Sqrt[3]) + t)^2]*EllipticF[ArcSin[(2^(2/3)*(1 - Sqrt[3]) + t)/(2^(2/3)*(1 + Sqrt[3]) + t)], -7 - 4*Sqrt[3]])/(5*3^(1/4)*Sqrt[(2^(2/3) + t)/(2^(2/3)*(1 + Sqrt[3]) + t)^2]*Sqrt[4 + t^3])","A",2,2,13,0.1538,1,"{321, 218}"
42,1,6,0,0.0043751,"\int \tan ^2(x) \, dx","Int[Tan[x]^2,x]","\tan (x)-x","\tan (x)-x",1,"-x + Tan[x]","A",2,2,4,0.5000,1,"{3473, 8}"
43,1,14,0,0.0091532,"\int \tan ^4(x) \, dx","Int[Tan[x]^4,x]","x+\frac{\tan ^3(x)}{3}-\tan (x)","x+\frac{\tan ^3(x)}{3}-\tan (x)",1,"x - Tan[x] + Tan[x]^3/3","A",3,2,4,0.5000,1,"{3473, 8}"
44,1,8,0,0.0054236,"\int \cot ^2(x) \, dx","Int[Cot[x]^2,x]","-x-\cot (x)","-x-\cot (x)",1,"-x - Cot[x]","A",2,2,4,0.5000,1,"{3473, 8}"
45,1,12,0,0.0102067,"\int \cot ^4(x) \, dx","Int[Cot[x]^4,x]","x-\frac{1}{3} \cot ^3(x)+\cot (x)","x-\frac{1}{3} \cot ^3(x)+\cot (x)",1,"x + Cot[x] - Cot[x]^3/3","A",3,2,4,0.5000,1,"{3473, 8}"
46,1,22,0,0.0112121,"\int (2+3 x) \sin (5 x) \, dx","Int[(2 + 3*x)*Sin[5*x],x]","\frac{3}{25} \sin (5 x)-\frac{1}{5} (3 x+2) \cos (5 x)","\frac{3}{25} \sin (5 x)-\frac{1}{5} (3 x+2) \cos (5 x)",1,"-((2 + 3*x)*Cos[5*x])/5 + (3*Sin[5*x])/25","A",2,2,10,0.2000,1,"{3296, 2637}"
47,1,13,0,0.0019292,"\int x \sqrt{1+x^2} \, dx","Int[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",1,1,11,0.09091,1,"{261}"
48,1,13,0,0.0014274,"\int x \left(-1+x^2\right)^9 \, dx","Int[x*(-1 + x^2)^9,x]","\frac{1}{20} \left(1-x^2\right)^{10}","\frac{1}{20} \left(1-x^2\right)^{10}",1,"(1 - x^2)^10/20","A",1,1,9,0.1111,1,"{261}"
49,1,18,0,0.0015898,"\int \frac{3+2 x}{(7+6 x)^3} \, dx","Int[(3 + 2*x)/(7 + 6*x)^3,x]","-\frac{(2 x+3)^2}{8 (6 x+7)^2}","-\frac{(2 x+3)^2}{8 (6 x+7)^2}",1,"-(3 + 2*x)^2/(8*(7 + 6*x)^2)","A",1,1,13,0.07692,1,"{37}"
50,1,11,0,0.0018053,"\int x^4 \left(1+x^5\right)^5 \, dx","Int[x^4*(1 + x^5)^5,x]","\frac{1}{30} \left(x^5+1\right)^6","\frac{1}{30} \left(x^5+1\right)^6",1,"(1 + x^5)^6/30","A",1,1,11,0.09091,1,"{261}"
51,1,56,0,0.0252189,"\int (1-x)^{20} x^4 \, dx","Int[(1 - x)^20*x^4,x]","-\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}","-\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,"-(1 - x)^21/21 + (2*(1 - x)^22)/11 - (6*(1 - x)^23)/23 + (1 - x)^24/6 - (1 - x)^25/25","A",2,1,11,0.09091,1,"{43}"
52,1,4,0,0.0082888,"\int \frac{\sin \left(\frac{1}{x}\right)}{x^2} \, dx","Int[Sin[x^(-1)]/x^2,x]","\cos \left(\frac{1}{x}\right)","\cos \left(\frac{1}{x}\right)",1,"Cos[x^(-1)]","A",2,2,8,0.2500,1,"{3379, 2638}"
53,1,62,0,0.0426793,"\int \sin \left(\sqrt[4]{-1+x}\right) \, dx","Int[Sin[(-1 + x)^(1/4)],x]","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)","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,"24*(-1 + x)^(1/4)*Cos[(-1 + x)^(1/4)] - 4*(-1 + x)^(3/4)*Cos[(-1 + x)^(1/4)] - 24*Sin[(-1 + x)^(1/4)] + 12*Sqrt[-1 + x]*Sin[(-1 + x)^(1/4)]","A",5,3,8,0.3750,1,"{3361, 3296, 2637}"
54,1,10,0,0.0071152,"\int x \cos \left(x^2\right) \sin \left(x^2\right) \, dx","Int[x*Cos[x^2]*Sin[x^2],x]","\frac{1}{4} \sin ^2\left(x^2\right)","\frac{1}{4} \sin ^2\left(x^2\right)",1,"Sin[x^2]^2/4","A",1,1,10,0.1000,1,"{3441}"
55,1,16,0,0.0305212,"\int \sqrt{1+3 \cos ^2(x)} \sin (2 x) \, dx","Int[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",3,2,17,0.1176,1,"{12, 261}"
56,1,10,0,0.0008861,"\int \frac{1}{2+3 x} \, dx","Int[(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",1,1,7,0.1429,1,"{31}"
57,1,15,0,0.0035862,"\int \log ^2(x) \, dx","Int[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",2,2,4,0.5000,1,"{2296, 2295}"
58,1,17,0,0.003479,"\int x \log (x) \, dx","Int[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,"-x^2/4 + (x^2*Log[x])/2","A",1,1,4,0.2500,1,"{2304}"
59,1,28,0,0.0093492,"\int x \log ^2(x) \, dx","Int[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",2,2,6,0.3333,1,"{2305, 2304}"
60,1,4,0,0.0004936,"\int \frac{1}{1+t} \, dt","Int[(1 + t)^(-1),t]","\log (t+1)","\log (t+1)",1,"Log[1 + t]","A",1,1,5,0.2000,1,"{31}"
61,1,3,0,0.0025934,"\int \cot (x) \, dx","Int[Cot[x],x]","\log (\sin (x))","\log (\sin (x))",1,"Log[Sin[x]]","A",1,1,2,0.5000,1,"{3475}"
62,1,28,0,0.0098877,"\int x^n \log (a x) \, dx","Int[x^n*Log[a*x],x]","\frac{x^{n+1} \log (a x)}{n+1}-\frac{x^{n+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 + n)^2) + (x^(1 + n)*Log[a*x])/(1 + n)","A",1,1,8,0.1250,1,"{2304}"
63,1,28,0,0.0173121,"\int x^2 \log ^2(x) \, dx","Int[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",2,2,8,0.2500,1,"{2305, 2304}"
64,1,3,0,0.0118875,"\int \frac{1}{x \log (x)} \, dx","Int[1/(x*Log[x]),x]","\log (\log (x))","\log (\log (x))",1,"Log[Log[x]]","A",2,2,8,0.2500,1,"{2302, 29}"
65,1,12,0,0.0154553,"\int \frac{\log (1-t)}{1-t} \, dt","Int[Log[1 - t]/(1 - t),t]","-\frac{1}{2} \log ^2(1-t)","-\frac{1}{2} \log ^2(1-t)",1,"-Log[1 - t]^2/2","A",2,2,14,0.1429,1,"{2390, 2301}"
66,1,23,0,0.0383046,"\int \frac{\log (x)}{x \sqrt{1+\log (x)}} \, dx","Int[Log[x]/(x*Sqrt[1 + Log[x]]),x]","\frac{2}{3} (\log (x)+1)^{3/2}-2 \sqrt{\log (x)+1}","\frac{2}{3} (\log (x)+1)^{3/2}-2 \sqrt{\log (x)+1}",1,"-2*Sqrt[1 + Log[x]] + (2*(1 + Log[x])^(3/2))/3","A",3,2,14,0.1429,1,"{2365, 43}"
67,1,39,0,0.0303477,"\int x^3 \log ^3(x) \, dx","Int[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",3,2,8,0.2500,1,"{2305, 2304}"
68,1,9,0,0.0124797,"\int e^{x^3} x^2 \, dx","Int[E^x^3*x^2,x]","\frac{e^{x^3}}{3}","\frac{e^{x^3}}{3}",1,"E^x^3/3","A",1,1,9,0.1111,1,"{2209}"
69,1,14,0,0.0087419,"\int \frac{2^{\sqrt{x}}}{\sqrt{x}} \, dx","Int[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",1,1,13,0.07692,1,"{2209}"
70,1,10,0,0.0089844,"\int e^{2 \sin (x)} \cos (x) \, dx","Int[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",2,2,9,0.2222,1,"{4334, 2194}"
71,1,19,0,0.0069675,"\int e^x \sin (x) \, dx","Int[E^x*Sin[x],x]","\frac{1}{2} e^x \sin (x)-\frac{1}{2} e^x \cos (x)","\frac{1}{2} e^x \sin (x)-\frac{1}{2} e^x \cos (x)",1,"-(E^x*Cos[x])/2 + (E^x*Sin[x])/2","A",1,1,6,0.1667,1,"{4432}"
72,1,19,0,0.0070147,"\int e^x \cos (x) \, dx","Int[E^x*Cos[x],x]","\frac{1}{2} e^x \sin (x)+\frac{1}{2} e^x \cos (x)","\frac{1}{2} e^x \sin (x)+\frac{1}{2} e^x \cos (x)",1,"(E^x*Cos[x])/2 + (E^x*Sin[x])/2","A",1,1,6,0.1667,1,"{4433}"
73,1,10,0,0.0061695,"\int \frac{1}{1+e^x} \, dx","Int[(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",4,4,7,0.5714,1,"{2282, 36, 29, 31}"
74,1,11,0,0.005418,"\int e^x x \, dx","Int[E^x*x,x]","e^x x-e^x","e^x x-e^x",1,"-E^x + E^x*x","A",2,2,5,0.4000,1,"{2176, 2194}"
75,1,16,0,0.0068846,"\int e^{-x} x \, dx","Int[x/E^x,x]","-e^{-x} x-e^{-x}","-e^{-x} x-e^{-x}",1,"-E^(-x) - x/E^x","A",2,2,7,0.2857,1,"{2176, 2194}"
76,1,19,0,0.0145115,"\int e^x x^2 \, dx","Int[E^x*x^2,x]","e^x x^2-2 e^x x+2 e^x","e^x x^2-2 e^x x+2 e^x",1,"2*E^x - 2*E^x*x + E^x*x^2","A",3,2,7,0.2857,1,"{2176, 2194}"
77,1,32,0,0.0176593,"\int e^{-2 x} x^2 \, dx","Int[x^2/E^(2*x),x]","-\frac{1}{2} e^{-2 x} x^2-\frac{1}{2} e^{-2 x} x-\frac{e^{-2 x}}{4}","-\frac{1}{2} e^{-2 x} x^2-\frac{1}{2} e^{-2 x} x-\frac{e^{-2 x}}{4}",1,"-1/(4*E^(2*x)) - x/(2*E^(2*x)) - x^2/(2*E^(2*x))","A",3,2,9,0.2222,1,"{2176, 2194}"
78,1,24,0,0.0077448,"\int e^{\sqrt{x}} \, dx","Int[E^Sqrt[x],x]","2 e^{\sqrt{x}} \sqrt{x}-2 e^{\sqrt{x}}","2 e^{\sqrt{x}} \sqrt{x}-2 e^{\sqrt{x}}",1,"-2*E^Sqrt[x] + 2*E^Sqrt[x]*Sqrt[x]","A",3,3,7,0.4286,1,"{2207, 2176, 2194}"
79,1,26,0,0.0199832,"\int e^{-x^2} x^3 \, dx","Int[x^3/E^x^2,x]","-\frac{1}{2} e^{-x^2} x^2-\frac{e^{-x^2}}{2}","-\frac{1}{2} e^{-x^2} x^2-\frac{e^{-x^2}}{2}",1,"-1/(2*E^x^2) - x^2/(2*E^x^2)","A",2,2,11,0.1818,1,"{2212, 2209}"
80,1,41,0,0.011306,"\int e^{a x} \cos (b x) \, dx","Int[E^(a*x)*Cos[b*x],x]","\frac{b e^{a x} \sin (b x)}{a^2+b^2}+\frac{a e^{a x} \cos (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,"(a*E^(a*x)*Cos[b*x])/(a^2 + b^2) + (b*E^(a*x)*Sin[b*x])/(a^2 + b^2)","A",1,1,10,0.1000,1,"{4433}"
81,1,42,0,0.0113484,"\int e^{a x} \sin (b x) \, dx","Int[E^(a*x)*Sin[b*x],x]","\frac{a e^{a x} \sin (b x)}{a^2+b^2}-\frac{b e^{a x} \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,"-((b*E^(a*x)*Cos[b*x])/(a^2 + b^2)) + (a*E^(a*x)*Sin[b*x])/(a^2 + b^2)","A",1,1,10,0.1000,1,"{4432}"
82,1,15,0,0.0033438,"\int \cot ^{-1}(x) \, dx","Int[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",2,2,2,1.000,1,"{4847, 260}"
83,1,19,0,0.0091662,"\int \sec ^{-1}(x) \, dx","Int[ArcSec[x],x]","x \sec ^{-1}(x)-\tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)","x \sec ^{-1}(x)-\tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)",1,"x*ArcSec[x] - ArcTanh[Sqrt[1 - x^(-2)]]","A",4,4,2,2.000,1,"{5214, 266, 63, 206}"
84,1,17,0,0.0090909,"\int \csc ^{-1}(x) \, dx","Int[ArcCsc[x],x]","\tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)+x \csc ^{-1}(x)","\tanh ^{-1}\left(\sqrt{1-\frac{1}{x^2}}\right)+x \csc ^{-1}(x)",1,"x*ArcCsc[x] + ArcTanh[Sqrt[1 - x^(-2)]]","A",4,4,2,2.000,1,"{5215, 266, 63, 206}"
85,1,25,0,0.0337108,"\int \sin ^{-1}(x)^2 \, dx","Int[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",3,3,4,0.7500,1,"{4619, 4677, 8}"
86,1,22,0,0.0155042,"\int \frac{\sin ^{-1}(x)}{x^2} \, dx","Int[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",4,4,6,0.6667,1,"{4627, 266, 63, 206}"
87,1,16,0,0.0022237,"\int \frac{1}{\sqrt{a^2-x^2}} \, dx","Int[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",2,2,13,0.1538,1,"{217, 203}"
88,1,10,0,0.0086627,"\int \frac{1}{\sqrt{1-2 x-x^2}} \, dx","Int[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",2,2,14,0.1429,1,"{619, 216}"
89,1,10,0,0.0018177,"\int \frac{1}{a^2+x^2} \, dx","Int[(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",1,1,9,0.1111,1,"{203}"
90,1,24,0,0.0042678,"\int \frac{1}{a+b x^2} \, dx","Int[(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",1,1,9,0.1111,1,"{205}"
91,1,19,0,0.0087962,"\int \frac{1}{2-x+x^2} \, dx","Int[(2 - x + x^2)^(-1),x]","-\frac{2 \tan ^{-1}\left(\frac{1-2 x}{\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",2,2,10,0.2000,1,"{618, 204}"
92,1,21,0,0.0075216,"\int x \tan ^{-1}(x) \, dx","Int[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,"-x/2 + ArcTan[x]/2 + (x^2*ArcTan[x])/2","A",3,3,4,0.7500,1,"{4852, 321, 203}"
93,1,40,0,0.0215891,"\int x^2 \cos ^{-1}(x) \, dx","Int[x^2*ArcCos[x],x]","\frac{1}{3} x^3 \cos ^{-1}(x)+\frac{1}{9} \left(1-x^2\right)^{3/2}-\frac{\sqrt{1-x^2}}{3}","\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,"-Sqrt[1 - x^2]/3 + (1 - x^2)^(3/2)/9 + (x^3*ArcCos[x])/3","A",4,3,6,0.5000,1,"{4628, 266, 43}"
94,1,35,0,0.0557313,"\int x \tan ^{-1}(x)^2 \, dx","Int[x*ArcTan[x]^2,x]","\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)","\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,"-(x*ArcTan[x]) + ArcTan[x]^2/2 + (x^2*ArcTan[x]^2)/2 + Log[1 + x^2]/2","A",5,5,6,0.8333,1,"{4852, 4916, 4846, 260, 4884}"
95,1,22,0,0.0051936,"\int \tan ^{-1}\left(\sqrt{x}\right) \, dx","Int[ArcTan[Sqrt[x]],x]","-\sqrt{x}+x \tan ^{-1}\left(\sqrt{x}\right)+\tan ^{-1}\left(\sqrt{x}\right)","-\sqrt{x}+x \tan ^{-1}\left(\sqrt{x}\right)+\tan ^{-1}\left(\sqrt{x}\right)",1,"-Sqrt[x] + ArcTan[Sqrt[x]] + x*ArcTan[Sqrt[x]]","A",4,4,6,0.6667,1,"{5027, 50, 63, 203}"
96,1,8,0,0.0304373,"\int \frac{\tan ^{-1}\left(\sqrt{x}\right)}{\sqrt{x} (1+x)} \, dx","Int[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",1,3,17,0.1765,1,"{63, 203, 6686}"
97,1,23,0,0.0025152,"\int \sqrt{1-x^2} \, dx","Int[Sqrt[1 - x^2],x]","\frac{1}{2} \sqrt{1-x^2} x+\frac{1}{2} \sin ^{-1}(x)","\frac{1}{2} \sqrt{1-x^2} x+\frac{1}{2} \sin ^{-1}(x)",1,"(x*Sqrt[1 - x^2])/2 + ArcSin[x]/2","A",2,2,11,0.1818,1,"{195, 216}"
98,1,22,0,0.0412641,"\int \frac{e^{\tan ^{-1}(x)} x}{\left(1+x^2\right)^{3/2}} \, dx","Int[(E^ArcTan[x]*x)/(1 + x^2)^(3/2),x]","-\frac{(1-x) e^{\tan ^{-1}(x)}}{2 \sqrt{x^2+1}}","-\frac{(1-x) e^{\tan ^{-1}(x)}}{2 \sqrt{x^2+1}}",1,"-(E^ArcTan[x]*(1 - x))/(2*Sqrt[1 + x^2])","A",1,1,15,0.06667,1,"{5077}"
99,1,20,0,0.0230173,"\int \frac{e^{\tan ^{-1}(x)}}{\left(1+x^2\right)^{3/2}} \, dx","Int[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",1,1,14,0.07143,1,"{5069}"
100,1,19,0,0.0036853,"\int \frac{x^2}{\left(1+x^2\right)^2} \, dx","Int[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,"-x/(2*(1 + x^2)) + ArcTan[x]/2","A",2,2,11,0.1818,1,"{288, 203}"
101,1,4,0,0.0162207,"\int \frac{e^x}{1+e^{2 x}} \, dx","Int[E^x/(1 + E^(2*x)),x]","\tan ^{-1}\left(e^x\right)","\tan ^{-1}\left(e^x\right)",1,"ArcTan[E^x]","A",2,2,13,0.1538,1,"{2249, 203}"
102,1,27,0,0.0180276,"\int e^{-x} \cot ^{-1}\left(e^x\right) \, dx","Int[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",5,6,10,0.6000,1,"{2194, 5208, 2282, 36, 29, 31}"
103,1,42,0,0.0132306,"\int \sqrt{\frac{a+x}{a-x}} \, dx","Int[Sqrt[(a + x)/(a - x)],x]","2 a \tan ^{-1}\left(\sqrt{\frac{a+x}{a-x}}\right)-(a-x) \sqrt{\frac{a+x}{a-x}}","2 a \tan ^{-1}\left(\sqrt{\frac{a+x}{a-x}}\right)-(a-x) \sqrt{\frac{a+x}{a-x}}",1,"-((a - x)*Sqrt[(a + x)/(a - x)]) + 2*a*ArcTan[Sqrt[(a + x)/(a - x)]]","A",3,3,15,0.2000,1,"{1959, 288, 203}"
104,1,71,0,0.0222152,"\int \sqrt{(b-x) (-a+x)} \, dx","Int[Sqrt[(b - x)*(-a + x)],x]","-\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)","-\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 + b - 2*x)*Sqrt[-(a*b) + (a + b)*x - x^2])/4 - ((a - b)^2*ArcTan[(a + b - 2*x)/(2*Sqrt[-(a*b) + (a + b)*x - x^2])])/8","A",4,4,15,0.2667,1,"{1981, 612, 621, 204}"
105,1,32,0,0.0120996,"\int \frac{1}{\sqrt{(b-x) (-a+x)}} \, dx","Int[1/Sqrt[(b - x)*(-a + x)],x]","-\tan ^{-1}\left(\frac{a+b-2 x}{2 \sqrt{x (a+b)-a b-x^2}}\right)","-\tan ^{-1}\left(\frac{a+b-2 x}{2 \sqrt{x (a+b)-a b-x^2}}\right)",1,"-ArcTan[(a + b - 2*x)/(2*Sqrt[-(a*b) + (a + b)*x - x^2])]","A",3,3,15,0.2000,1,"{1981, 621, 204}"
106,1,15,0,0.004191,"\int \frac{3+5 x}{-3+2 x+x^2} \, dx","Int[(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",3,2,16,0.1250,1,"{632, 31}"
107,1,19,0,0.0044599,"\int \frac{5+2 x}{-3+2 x+x^2} \, dx","Int[(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",3,2,16,0.1250,1,"{632, 31}"
108,1,23,0,0.0267258,"\int \frac{3 x+x^3}{-3-2 x+x^2} \, dx","Int[(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",6,4,18,0.2222,1,"{1593, 1628, 632, 31}"
109,1,23,0,0.033277,"\int \frac{-1+5 x+2 x^2}{-2 x+x^2+x^3} \, dx","Int[(-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",3,2,23,0.08696,1,"{1594, 1628}"
110,1,24,0,0.0143797,"\int \frac{3+2 x+x^2}{(-1+x) (1+x)^2} \, dx","Int[(3 + 2*x + x^2)/((-1 + x)*(1 + x)^2),x]","\frac{1}{x+1}+\frac{3}{2} \log (1-x)-\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",2,1,19,0.05263,1,"{893}"
111,1,28,0,0.0276238,"\int \frac{-2+2 x+3 x^2}{-1+x^3} \, dx","Int[(-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",5,5,18,0.2778,1,"{1871, 1586, 618, 204, 260}"
112,1,49,0,0.0672271,"\int \frac{2-x+2 x^2-x^3+x^4}{(-1+x) \left(2+x^2\right)^2} \, dx","Int[(2 - x + 2*x^2 - x^3 + x^4)/((-1 + x)*(2 + x^2)^2),x]","\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}}","\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*(2 + x^2)) - ArcTan[x/Sqrt[2]]/(3*Sqrt[2]) + Log[1 - x]/3 + Log[2 + x^2]/3","A",6,5,31,0.1613,1,"{1647, 1629, 635, 203, 260}"
113,1,21,0,0.009178,"\int \frac{1}{\cos (x)+\sin (x)} \, dx","Int[(Cos[x] + Sin[x])^(-1),x]","-\frac{\tanh ^{-1}\left(\frac{\cos (x)-\sin (x)}{\sqrt{2}}\right)}{\sqrt{2}}","-\frac{\tanh ^{-1}\left(\frac{\cos (x)-\sin (x)}{\sqrt{2}}\right)}{\sqrt{2}}",1,"-(ArcTanh[(Cos[x] - Sin[x])/Sqrt[2]]/Sqrt[2])","A",2,2,7,0.2857,1,"{3074, 206}"
114,1,16,0,0.0450431,"\int \frac{x}{4-x^2+\sqrt{4-x^2}} \, dx","Int[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",3,2,22,0.09091,1,"{2155, 31}"
115,1,11,0,0.004397,"\int \frac{3+2 x}{(-2+x) (5+x)} \, dx","Int[(3 + 2*x)/((-2 + x)*(5 + x)),x]","\log (2-x)+\log (x+5)","\log (2-x)+\log (x+5)",1,"Log[2 - x] + Log[5 + x]","A",2,1,16,0.06250,1,"{72}"
116,1,23,0,0.0076509,"\int \frac{x}{(1+x) (2+x) (3+x)} \, dx","Int[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,"-Log[1 + x]/2 + 2*Log[2 + x] - (3*Log[3 + x])/2","A",2,1,17,0.05882,1,"{148}"
117,1,30,0,0.0165808,"\int \frac{x}{2-3 x+x^3} \, dx","Int[x/(2 - 3*x + x^3),x]","\frac{1}{3 (1-x)}+\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 - x)) + (2*Log[1 - x])/9 - (2*Log[2 + x])/9","A",2,1,12,0.08333,1,"{2074}"
118,1,27,0,0.0307892,"\int \frac{-6+2 x+x^4}{-2 x+x^2+x^3} \, dx","Int[(-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",3,2,21,0.09524,1,"{1594, 1628}"
119,1,23,0,0.0263759,"\int \frac{7+8 x^3}{(1+x) (1+2 x)^3} \, dx","Int[(7 + 8*x^3)/((1 + x)*(1 + 2*x)^3),x]","\frac{3}{2 x+1}-\frac{3}{(2 x+1)^2}+\log (x+1)","\frac{3}{2 x+1}-\frac{3}{(2 x+1)^2}+\log (x+1)",1,"-3/(1 + 2*x)^2 + 3/(1 + 2*x) + Log[1 + x]","A",2,1,20,0.05000,1,"{1620}"
120,1,16,0,0.0167353,"\int \frac{1+x+4 x^2}{-1+x^3} \, dx","Int[(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",3,3,16,0.1875,1,"{1875, 31, 628}"
121,1,18,0,0.0120354,"\int \frac{x^4}{4+5 x^2+x^4} \, dx","Int[x^4/(4 + 5*x^2 + x^4),x]","x-\frac{8}{3} \tan ^{-1}\left(\frac{x}{2}\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[x/2])/3 + ArcTan[x]/3","A",4,3,16,0.1875,1,"{1122, 1166, 203}"
122,1,11,0,0.0051985,"\int \frac{2+x}{x+x^2} \, dx","Int[(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",2,1,11,0.09091,1,"{631}"
123,1,24,0,0.0095761,"\int \frac{1}{x \left(1+x^2\right)^2} \, dx","Int[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",3,2,11,0.1818,1,"{266, 44}"
124,1,46,0,0.0128362,"\int \frac{1}{(1+x) (2+x)^2 (3+x)^3} \, dx","Int[1/((1 + x)*(2 + x)^2*(3 + x)^3),x]","\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)","\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,"(2 + x)^(-1) + 1/(4*(3 + x)^2) + 5/(4*(3 + x)) + Log[1 + x]/8 + 2*Log[2 + x] - (17*Log[3 + x])/8","A",2,1,16,0.06250,1,"{88}"
125,1,10,0,0.0036734,"\int \frac{x}{(1+x)^2} \, dx","Int[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",2,1,7,0.1429,1,"{43}"
126,1,17,0,0.007101,"\int \frac{1}{-x+x^3} \, dx","Int[(-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",5,5,9,0.5556,1,"{1593, 266, 36, 31, 29}"
127,1,20,0,0.0075442,"\int \frac{x^2}{-6+x+x^2} \, dx","Int[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",4,3,12,0.2500,1,"{703, 632, 31}"
128,1,16,0,0.0052333,"\int \frac{2+x}{4-4 x+x^2} \, dx","Int[(2 + x)/(4 - 4*x + x^2),x]","\frac{4}{2-x}+\log (2-x)","\frac{4}{2-x}+\log (2-x)",1,"4/(2 - x) + Log[2 - x]","A",3,2,14,0.1429,1,"{27, 43}"
129,1,14,0,0.0103845,"\int \frac{1}{\left(4-4 x+x^2\right) \left(5-4 x+x^2\right)} \, dx","Int[1/((4 - 4*x + x^2)*(5 - 4*x + x^2)),x]","\frac{1}{2-x}+\tan ^{-1}(2-x)","\frac{1}{2-x}+\tan ^{-1}(2-x)",1,"(2 - x)^(-1) + ArcTan[2 - x]","A",4,4,21,0.1905,1,"{27, 693, 618, 204}"
130,1,21,0,0.0179242,"\int \frac{-3+x}{2 x+3 x^2+x^3} \, dx","Int[(-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",3,2,18,0.1111,1,"{1594, 800}"
131,1,21,0,0.0027293,"\int \frac{1}{\left(-1+x^2\right)^2} \, dx","Int[(-1 + x^2)^(-2),x]","\frac{x}{2 \left(1-x^2\right)}+\frac{1}{2} \tanh ^{-1}(x)","\frac{x}{2 \left(1-x^2\right)}+\frac{1}{2} \tanh ^{-1}(x)",1,"x/(2*(1 - x^2)) + ArcTanh[x]/2","A",2,2,7,0.2857,1,"{199, 207}"
132,1,22,0,0.0106187,"\int \frac{1+x}{-1+x^3} \, dx","Int[(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",3,3,11,0.2727,1,"{1861, 31, 628}"
133,1,10,0,0.0149757,"\int \frac{1+x^4}{x \left(1+x^2\right)^2} \, dx","Int[(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",3,2,16,0.1250,1,"{1252, 894}"
134,1,31,0,0.0090875,"\int \frac{1}{-2 x^3+x^4} \, dx","Int[(-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",3,2,11,0.1818,1,"{1593, 44}"
135,1,18,0,0.0251952,"\int \frac{1-x^3}{x \left(1+x^2\right)} \, dx","Int[(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",5,4,18,0.2222,1,"{1802, 635, 203, 260}"
136,1,13,0,0.0030568,"\int \frac{1}{-1+x^4} \, dx","Int[(-1 + x^4)^(-1),x]","-\frac{1}{2} \tan ^{-1}(x)-\frac{1}{2} \tanh ^{-1}(x)","-\frac{1}{2} \tan ^{-1}(x)-\frac{1}{2} \tanh ^{-1}(x)",1,"-ArcTan[x]/2 - ArcTanh[x]/2","A",3,3,7,0.4286,1,"{212, 206, 203}"
137,1,85,0,0.0394903,"\int \frac{1}{1+x^4} \, dx","Int[(1 + x^4)^(-1),x]","-\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}}","-\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,"-ArcTan[1 - Sqrt[2]*x]/(2*Sqrt[2]) + ArcTan[1 + Sqrt[2]*x]/(2*Sqrt[2]) - Log[1 - Sqrt[2]*x + x^2]/(4*Sqrt[2]) + Log[1 + Sqrt[2]*x + x^2]/(4*Sqrt[2])","A",9,6,7,0.8571,1,"{211, 1165, 628, 1162, 617, 204}"
138,1,23,0,0.0072044,"\int \frac{x^2}{\left(2+2 x+x^2\right)^2} \, dx","Int[x^2/(2 + 2*x + x^2)^2,x]","\tan ^{-1}(x+1)-\frac{x (x+2)}{2 \left(x^2+2 x+2\right)}","\tan ^{-1}(x+1)-\frac{x (x+2)}{2 \left(x^2+2 x+2\right)}",1,"-(x*(2 + x))/(2*(2 + 2*x + x^2)) + ArcTan[1 + x]","A",3,3,14,0.2143,1,"{722, 617, 204}"
139,1,11,0,0.0064788,"\int \frac{-1+4 x^5}{\left(1+x+x^5\right)^2} \, dx","Int[(-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",1,1,16,0.06250,1,"{1588}"
140,1,45,0,0.0242,"\int \frac{1}{5-\cos (x)+2 \sin (x)} \, dx","Int[(5 - Cos[x] + 2*Sin[x])^(-1),x]","\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}}","\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,"x/(2*Sqrt[5]) + ArcTan[(2*Cos[x] + Sin[x])/(5 + 2*Sqrt[5] - Cos[x] + 2*Sin[x])]/Sqrt[5]","A",3,3,12,0.2500,1,"{3124, 618, 204}"
141,1,37,0,0.0183064,"\int \frac{1}{1+a \cos (x)} \, dx","Int[(1 + a*Cos[x])^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-a} \tan \left(\frac{x}{2}\right)}{\sqrt{a+1}}\right)}{\sqrt{1-a^2}}","\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*ArcTan[(Sqrt[1 - a]*Tan[x/2])/Sqrt[1 + a]])/Sqrt[1 - a^2]","A",2,2,8,0.2500,1,"{2659, 205}"
142,1,56,0,0.0154401,"\int \frac{1}{1+2 \cos (x)} \, dx","Int[(1 + 2*Cos[x])^(-1),x]","\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}}","\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,"-(Log[Sqrt[3]*Cos[x/2] - Sin[x/2]]/Sqrt[3]) + Log[Sqrt[3]*Cos[x/2] + Sin[x/2]]/Sqrt[3]","A",2,2,8,0.2500,1,"{2659, 206}"
143,1,31,0,0.0114407,"\int \frac{1}{1+\frac{\cos (x)}{2}} \, dx","Int[(1 + Cos[x]/2)^(-1),x]","\frac{2 x}{\sqrt{3}}-\frac{4 \tan ^{-1}\left(\frac{\sin (x)}{\cos (x)+\sqrt{3}+2}\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,"(2*x)/Sqrt[3] - (4*ArcTan[Sin[x]/(2 + Sqrt[3] + Cos[x])])/Sqrt[3]","A",1,1,10,0.1000,1,"{2657}"
144,1,36,0,0.0377339,"\int \frac{\sin ^2(x)}{1+\sin ^2(x)} \, dx","Int[Sin[x]^2/(1 + Sin[x]^2),x]","-\frac{x}{\sqrt{2}}+x-\frac{\tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\sin ^2(x)+\sqrt{2}+1}\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 - x/Sqrt[2] - ArcTan[(Cos[x]*Sin[x])/(1 + Sqrt[2] + Sin[x]^2)]/Sqrt[2]","A",3,3,13,0.2308,1,"{3171, 3181, 203}"
145,1,15,0,0.0230196,"\int \frac{1}{b^2 \cos ^2(x)+a^2 \sin ^2(x)} \, dx","Int[(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",2,1,19,0.05263,1,"{205}"
146,1,17,0,0.0122878,"\int \frac{1}{(b \cos (x)+a \sin (x))^2} \, dx","Int[(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",1,1,11,0.09091,1,"{3075}"
147,1,30,0,0.0290074,"\int \frac{\sin (x)}{1+\cos (x)+\sin (x)} \, dx","Int[Sin[x]/(1 + Cos[x] + Sin[x]),x]","\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)","\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[1 + Cos[x] + Sin[x]]/2 - Log[1 + Tan[x/2]]/2","A",3,3,11,0.2727,1,"{3137, 3124, 31}"
148,1,29,0,0.003629,"\int \sqrt{3-x^2} \, dx","Int[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",2,2,11,0.1818,1,"{195, 216}"
149,1,13,0,0.0021519,"\int \frac{x}{\sqrt{3-x^2}} \, dx","Int[x/Sqrt[3 - x^2],x]","-\sqrt{3-x^2}","-\sqrt{3-x^2}",1,"-Sqrt[3 - x^2]","A",1,1,13,0.07692,1,"{261}"
150,1,37,0,0.0195136,"\int \frac{\sqrt{3-x^2}}{x} \, dx","Int[Sqrt[3 - x^2]/x,x]","\sqrt{3-x^2}-\sqrt{3} \tanh ^{-1}\left(\frac{\sqrt{3-x^2}}{\sqrt{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[3 - x^2]/Sqrt[3]]","A",4,4,15,0.2667,1,"{266, 50, 63, 206}"
151,1,22,0,0.0070825,"\int \frac{\sqrt{x+x^2}}{x} \, dx","Int[Sqrt[x + x^2]/x,x]","\sqrt{x^2+x}+\tanh ^{-1}\left(\frac{x}{\sqrt{x^2+x}}\right)","\sqrt{x^2+x}+\tanh ^{-1}\left(\frac{x}{\sqrt{x^2+x}}\right)",1,"Sqrt[x + x^2] + ArcTanh[x/Sqrt[x + x^2]]","A",3,3,13,0.2308,1,"{664, 620, 206}"
152,1,27,0,0.0032337,"\int \sqrt{5+x^2} \, dx","Int[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",2,2,9,0.2222,1,"{195, 215}"
153,1,27,0,0.0109699,"\int \frac{x}{\sqrt{1+x+x^2}} \, dx","Int[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",3,3,12,0.2500,1,"{640, 619, 215}"
154,1,14,0,0.0031101,"\int \frac{1}{\sqrt{x+x^2}} \, dx","Int[1/Sqrt[x + x^2],x]","2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2+x}}\right)","2 \tanh ^{-1}\left(\frac{x}{\sqrt{x^2+x}}\right)",1,"2*ArcTanh[x/Sqrt[x + x^2]]","A",2,2,9,0.2222,1,"{620, 206}"
155,1,68,0,0.0367591,"\int \frac{\sqrt{2-x-x^2}}{x^2} \, dx","Int[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",6,6,18,0.3333,1,"{732, 843, 619, 216, 724, 206}"
156,1,13,0,0.0153927,"\int \frac{\log (t)}{1+t} \, dt","Int[Log[t]/(1 + t),t]","\text{PolyLog}(2,-t)+\log (t) \log (t+1)","\text{PolyLog}(2,-t)+\log (t) \log (t+1)",1,"Log[t]*Log[1 + t] + PolyLog[2, -t]","A",2,2,8,0.2500,1,"{2317, 2391}"
157,1,15,0,0.0098554,"\int \log \left(e^{\cos (x)}\right) \, dx","Int[Log[E^Cos[x]],x]","\sin (x)-x \cos (x)+x \log \left(e^{\cos (x)}\right)","\sin (x)-x \cos (x)+x \log \left(e^{\cos (x)}\right)",1,"-(x*Cos[x]) + x*Log[E^Cos[x]] + Sin[x]","A",3,3,5,0.6000,1,"{2548, 3296, 2637}"
158,1,2,0,0.009748,"\int \frac{e^t}{t} \, dt","Int[E^t/t,t]","\text{ExpIntegralEi}(t)","\text{ExpIntegralEi}(t)",1,"ExpIntegralEi[t]","A",1,1,7,0.1429,1,"{2178}"
159,1,4,0,0.0120414,"\int \frac{e^{a t}}{t} \, dt","Int[E^(a*t)/t,t]","\text{ExpIntegralEi}(a t)","\text{ExpIntegralEi}(a t)",1,"ExpIntegralEi[a*t]","A",1,1,9,0.1111,1,"{2178}"
160,1,11,0,0.0196118,"\int \frac{e^t}{t^2} \, dt","Int[E^t/t^2,t]","\text{ExpIntegralEi}(t)-\frac{e^t}{t}","\text{ExpIntegralEi}(t)-\frac{e^t}{t}",1,"-(E^t/t) + ExpIntegralEi[t]","A",2,2,7,0.2857,1,"{2177, 2178}"
161,1,14,0,0.0120688,"\int e^{\frac{1}{t}} \, dt","Int[E^t^(-1),t]","e^{\frac{1}{t}} t-\text{ExpIntegralEi}\left(\frac{1}{t}\right)","e^{\frac{1}{t}} t-\text{ExpIntegralEi}\left(\frac{1}{t}\right)",1,"E^t^(-1)*t - ExpIntegralEi[t^(-1)]","A",2,2,5,0.4000,1,"{2206, 2210}"
162,1,15,0,0.0153825,"\int \frac{e^{-t}}{-1-a+t} \, dt","Int[1/(E^t*(-1 - a + t)),t]","e^{-a-1} \text{ExpIntegralEi}(a-t+1)","e^{-a-1} \text{ExpIntegralEi}(a-t+1)",1,"E^(-1 - a)*ExpIntegralEi[1 + a - t]","A",1,1,14,0.07143,1,"{2178}"
163,1,13,0,0.0654647,"\int \frac{e^{t^2} t}{1+t^2} \, dt","Int[(E^t^2*t)/(1 + t^2),t]","\frac{\text{ExpIntegralEi}\left(t^2+1\right)}{2 e}","\frac{\text{ExpIntegralEi}\left(t^2+1\right)}{2 e}",1,"ExpIntegralEi[1 + t^2]/(2*E)","A",2,2,14,0.1429,1,"{6715, 2178}"
164,1,19,0,0.0233803,"\int \frac{e^t}{(1+t)^2} \, dt","Int[E^t/(1 + t)^2,t]","\frac{\text{ExpIntegralEi}(t+1)}{e}-\frac{e^t}{t+1}","\frac{\text{ExpIntegralEi}(t+1)}{e}-\frac{e^t}{t+1}",1,"-(E^t/(1 + t)) + ExpIntegralEi[1 + t]/E","A",2,2,9,0.2222,1,"{2177, 2178}"
165,1,18,0,0.0199313,"\int e^t \log (1+t) \, dt","Int[E^t*Log[1 + t],t]","e^t \log (t+1)-\frac{\text{ExpIntegralEi}(t+1)}{e}","e^t \log (t+1)-\frac{\text{ExpIntegralEi}(t+1)}{e}",1,"-(ExpIntegralEi[1 + t]/E) + E^t*Log[1 + t]","A",2,3,8,0.3750,1,"{2194, 2554, 2178}"
166,1,16,0,0.0086752,"\int e^{-t} t \, dt","Int[t/E^t,t]","-e^{-t} t-e^{-t}","-e^{-t} t-e^{-t}",1,"-E^(-t) - t/E^t","A",2,2,7,0.2857,1,"{2176, 2194}"
167,1,26,0,0.0205438,"\int e^{-t} t^2 \, dt","Int[t^2/E^t,t]","-e^{-t} t^2-2 e^{-t} t-2 e^{-t}","-e^{-t} t^2-2 e^{-t} t-2 e^{-t}",1,"-2/E^t - (2*t)/E^t - t^2/E^t","A",3,2,9,0.2222,1,"{2176, 2194}"
168,1,36,0,0.0338808,"\int e^{-t} t^3 \, dt","Int[t^3/E^t,t]","-e^{-t} t^3-3 e^{-t} t^2-6 e^{-t} t-6 e^{-t}","-e^{-t} t^3-3 e^{-t} t^2-6 e^{-t} t-6 e^{-t}",1,"-6/E^t - (6*t)/E^t - (3*t^2)/E^t - t^3/E^t","A",4,2,9,0.2222,1,"{2176, 2194}"
169,1,48,0,0.0343966,"\int \frac{\text{b1} \cos (x)+\text{a1} \sin (x)}{b \cos (x)+a \sin (x)} \, dx","Int[(b1*Cos[x] + a1*Sin[x])/(b*Cos[x] + a*Sin[x]),x]","\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}","\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)/(a^2 + b^2) - ((a1*b - a*b1)*Log[b*Cos[x] + a*Sin[x]])/(a^2 + b^2)","A",1,1,21,0.04762,1,"{3133}"
170,1,2,0,0.001934,"\int \frac{1}{\log (t)} \, dt","Int[Log[t]^(-1),t]","\text{LogIntegral}(t)","\text{LogIntegral}(t)",1,"LogIntegral[t]","A",1,1,4,0.2500,1,"{2298}"
171,1,10,0,0.0041417,"\int \frac{1}{\log ^2(t)} \, dt","Int[Log[t]^(-2),t]","\text{LogIntegral}(t)-\frac{t}{\log (t)}","\text{LogIntegral}(t)-\frac{t}{\log (t)}",1,"-(t/Log[t]) + LogIntegral[t]","A",2,2,4,0.5000,1,"{2297, 2298}"
172,1,22,0,0.0174485,"\int \log ^{-1-n}(t) \, dt","Int[Log[t]^(-1 - n),t]","(-\log (t))^n \log ^{-n}(t) (-\text{Gamma}(-n,-\log (t)))","(-\log (t))^n \log ^{-n}(t) (-\text{Gamma}(-n,-\log (t)))",1,"-((Gamma[-n, -Log[t]]*(-Log[t])^n)/Log[t]^n)","A",2,2,8,0.2500,1,"{2299, 2181}"
173,1,12,0,0.0148496,"\int \frac{e^{2 t}}{-1+t} \, dt","Int[E^(2*t)/(-1 + t),t]","e^2 \text{ExpIntegralEi}(-2 (1-t))","e^2 \text{ExpIntegralEi}(-2 (1-t))",1,"E^2*ExpIntegralEi[-2*(1 - t)]","A",1,1,11,0.09091,1,"{2178}"
174,1,22,0,0.0559034,"\int \frac{e^{2 x}}{2-3 x+x^2} \, dx","Int[E^(2*x)/(2 - 3*x + x^2),x]","e^4 \text{ExpIntegralEi}(2 x-4)-e^2 \text{ExpIntegralEi}(2 x-2)","e^4 \text{ExpIntegralEi}(2 x-4)-e^2 \text{ExpIntegralEi}(2 x-2)",1,"E^4*ExpIntegralEi[-4 + 2*x] - E^2*ExpIntegralEi[-2 + 2*x]","A",4,2,16,0.1250,1,"{2268, 2178}"
175,1,103,0,0.0084795,"\int \frac{1}{\sqrt{1+t^3}} \, dt","Int[1/Sqrt[1 + t^3],t]","\frac{2 \sqrt{2+\sqrt{3}} (t+1) \sqrt{\frac{t^2-t+1}{\left(t+\sqrt{3}+1\right)^2}} \text{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}}","\frac{2 \sqrt{2+\sqrt{3}} (t+1) \sqrt{\frac{t^2-t+1}{\left(t+\sqrt{3}+1\right)^2}} \text{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,"(2*Sqrt[2 + Sqrt[3]]*(1 + t)*Sqrt[(1 - t + t^2)/(1 + Sqrt[3] + t)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + t)/(1 + Sqrt[3] + t)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + t)/(1 + Sqrt[3] + t)^2]*Sqrt[1 + t^3])","A",1,1,9,0.1111,1,"{218}"