1,1,12,0,0.0099821,"\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}"
2,1,13,0,0.0048847,"\int \frac{1}{x^4 \left(1+x^2\right)} \, dx","Int[1/(x^4*(1 + x^2)),x]","-\frac{1}{3 x^3}+\frac{1}{x}+\tan ^{-1}(x)","-\frac{1}{3 x^3}+\frac{1}{x}+\tan ^{-1}(x)",1,"-1/(3*x^3) + x^(-1) + ArcTan[x]","A",3,2,11,0.1818,1,"{325, 203}"
3,1,19,0,0.002675,"\int \frac{x+x^2}{\sqrt{x}} \, dx","Int[(x + x^2)/Sqrt[x],x]","\frac{2 x^{5/2}}{5}+\frac{2 x^{3/2}}{3}","\frac{2 x^{5/2}}{5}+\frac{2 x^{3/2}}{3}",1,"(2*x^(3/2))/3 + (2*x^(5/2))/5","A",2,1,11,0.09091,1,"{14}"
4,1,2,0,0.0020616,"\int \cos (x) \, dx","Int[Cos[x],x]","\sin (x)","\sin (x)",1,"Sin[x]","A",1,1,2,0.5000,1,"{2637}"
5,1,9,0,0.0060194,"\int e^{x^2} x \, dx","Int[E^x^2*x,x]","\frac{e^{x^2}}{2}","\frac{e^{x^2}}{2}",1,"E^x^2/2","A",1,1,7,0.1429,1,"{2209}"
6,1,8,0,0.0106558,"\int \sec ^2(x) \tan (x) \, dx","Int[Sec[x]^2*Tan[x],x]","\frac{\sec ^2(x)}{2}","\frac{\sec ^2(x)}{2}",1,"Sec[x]^2/2","A",2,2,7,0.2857,1,"{2606, 30}"
7,1,13,0,0.0016729,"\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}"
8,1,19,0,0.0065227,"\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}"
9,1,8,0,0.0124362,"\int \cot (x) \csc ^3(x) \, dx","Int[Cot[x]*Csc[x]^3,x]","-\frac{1}{3} \csc ^3(x)","-\frac{1}{3} \csc ^3(x)",1,"-Csc[x]^3/3","A",2,2,7,0.2857,1,"{2606, 30}"
10,1,4,0,0.0117071,"\int \sin \left(e^x\right) \, dx","Int[Sin[E^x],x]","\text{Si}\left(e^x\right)","\text{Si}\left(e^x\right)",1,"SinIntegral[E^x]","A",2,2,4,0.5000,1,"{2282, 3299}"
11,1,2,0,0.0111784,"\int \frac{\sin (y)}{y} \, dy","Int[Sin[y]/y,y]","\text{Si}(y)","\text{Si}(y)",1,"SinIntegral[y]","A",1,1,6,0.1667,1,"{3299}"
12,1,8,0,0.00333,"\int \left(e^x+\sin (x)\right) \, dx","Int[E^x + Sin[x],x]","e^x-\cos (x)","e^x-\cos (x)",1,"E^x - Cos[x]","A",3,2,6,0.3333,1,"{2194, 2638}"
13,1,7,0,0.0199511,"\int \left(e^{x^2}+2 e^{x^2} x^2\right) \, dx","Int[E^x^2 + 2*E^x^2*x^2,x]","e^{x^2} x","e^{x^2} x",1,"E^x^2*x","A",4,2,16,0.1250,1,"{2204, 2212}"
14,1,28,0,0.0196767,"\int \left(e^x+x\right)^2 \, dx","Int[(E^x + x)^2,x]","\frac{x^3}{3}+2 e^x x-2 e^x+\frac{e^{2 x}}{2}","\frac{x^3}{3}+2 e^x x-2 e^x+\frac{e^{2 x}}{2}",1,"-2*E^x + E^(2*x)/2 + 2*E^x*x + x^3/3","A",5,3,7,0.4286,1,"{6742, 2194, 2176}"
15,1,22,0,0.004773,"\int \left(2 e^x+e^{2 x}+x^2\right) \, dx","Int[2*E^x + E^(2*x) + x^2,x]","\frac{x^3}{3}+2 e^x+\frac{e^{2 x}}{2}","\frac{x^3}{3}+2 e^x+\frac{e^{2 x}}{2}",1,"2*E^x + E^(2*x)/2 + x^3/3","A",3,1,14,0.07143,1,"{2194}"
16,1,8,0,0.0066878,"\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}"
17,1,9,0,0.0062455,"\int e^{x^2} x \, dx","Int[E^x^2*x,x]","\frac{e^{x^2}}{2}","\frac{e^{x^2}}{2}",1,"E^x^2/2","A",1,1,7,0.1429,1,"{2209}"
18,1,13,0,0.0019663,"\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}"
19,1,6,0,0.014687,"\int \frac{e^x}{1+e^x} \, dx","Int[E^x/(1 + E^x),x]","\log \left(e^x+1\right)","\log \left(e^x+1\right)",1,"Log[1 + E^x]","A",2,2,11,0.1818,1,"{2246, 31}"
20,1,9,0,0.0004782,"\int x^{3/2} \, dx","Int[x^(3/2),x]","\frac{2 x^{5/2}}{5}","\frac{2 x^{5/2}}{5}",1,"(2*x^(5/2))/5","A",1,1,5,0.2000,1,"{30}"
21,1,10,0,0.0030981,"\int \cos (3+2 x) \, dx","Int[Cos[3 + 2*x],x]","\frac{1}{2} \sin (2 x+3)","\frac{1}{2} \sin (2 x+3)",1,"Sin[3 + 2*x]/2","A",1,1,6,0.1667,1,"{2637}"
22,1,8,0,0.0032724,"\int 2 e^{2 x} y z \, dx","Int[2*E^(2*x)*y*z,x]","e^{2 x} y z","e^{2 x} y z",1,"E^(2*x)*y*z","A",2,2,9,0.2222,1,"{12, 2194}"
23,1,10,0,0.0274706,"\int e^x \cos ^2\left(e^x\right) \sin \left(e^x\right) \, dx","Int[E^x*Cos[E^x]^2*Sin[E^x],x]","-\frac{1}{3} \cos ^3\left(e^x\right)","-\frac{1}{3} \cos ^3\left(e^x\right)",1,"-Cos[E^x]^3/3","A",3,3,14,0.2143,1,"{2282, 2565, 30}"
24,1,23,0,0.0038989,"\int x \sqrt{1+x} \, dx","Int[x*Sqrt[1 + x],x]","\frac{2}{5} (x+1)^{5/2}-\frac{2}{3} (x+1)^{3/2}","\frac{2}{5} (x+1)^{5/2}-\frac{2}{3} (x+1)^{3/2}",1,"(-2*(1 + x)^(3/2))/3 + (2*(1 + x)^(5/2))/5","A",2,1,9,0.1111,1,"{43}"
25,1,13,0,0.0031654,"\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}"
26,1,18,0,0.0204306,"\int \frac{e^x}{2+3 e^{2 x}} \, dx","Int[E^x/(2 + 3*E^(2*x)),x]","\frac{\tan ^{-1}\left(\sqrt{\frac{3}{2}} e^x\right)}{\sqrt{6}}","\frac{\tan ^{-1}\left(\sqrt{\frac{3}{2}} e^x\right)}{\sqrt{6}}",1,"ArcTan[Sqrt[3/2]*E^x]/Sqrt[6]","A",2,2,15,0.1333,1,"{2249, 203}"
27,1,31,0,0.0347668,"\int \frac{e^{2 x}}{A+B e^{4 x}} \, dx","Int[E^(2*x)/(A + B*E^(4*x)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{B} e^{2 x}}{\sqrt{A}}\right)}{2 \sqrt{A} \sqrt{B}}","\frac{\tan ^{-1}\left(\frac{\sqrt{B} e^{2 x}}{\sqrt{A}}\right)}{2 \sqrt{A} \sqrt{B}}",1,"ArcTan[(Sqrt[B]*E^(2*x))/Sqrt[A]]/(2*Sqrt[A]*Sqrt[B])","A",2,2,17,0.1176,1,"{2249, 205}"
28,1,8,0,0.0340458,"\int \frac{e^{1+x}}{1+e^x} \, dx","Int[E^(1 + x)/(1 + E^x),x]","e \log \left(e^x+1\right)","e \log \left(e^x+1\right)",1,"E*Log[1 + E^x]","A",3,3,13,0.2308,1,"{2247, 2246, 31}"
29,1,12,0,0.0055997,"\int (10 e)^x \, dx","Int[(10*E)^x,x]","\frac{(10 e)^x}{1+\log (10)}","\frac{(10 e)^x}{1+\log (10)}",1,"(10*E)^x/(1 + Log[10])","A",1,1,5,0.2000,1,"{2194}"
30,1,20,0,0.0189159,"\int x^3 \sin \left(x^2\right) \, dx","Int[x^3*Sin[x^2],x]","\frac{\sin \left(x^2\right)}{2}-\frac{1}{2} x^2 \cos \left(x^2\right)","\frac{\sin \left(x^2\right)}{2}-\frac{1}{2} x^2 \cos \left(x^2\right)",1,"-(x^2*Cos[x^2])/2 + Sin[x^2]/2","A",3,3,8,0.3750,1,"{3379, 3296, 2637}"
31,1,49,0,0.0360088,"\int \frac{x^7}{1+x^{12}} \, dx","Int[x^7/(1 + x^12),x]","-\frac{1}{12} \log \left(x^4+1\right)+\frac{1}{24} \log \left(x^8-x^4+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}","-\frac{1}{12} \log \left(x^4+1\right)+\frac{1}{24} \log \left(x^8-x^4+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}",1,"-ArcTan[(1 - 2*x^4)/Sqrt[3]]/(4*Sqrt[3]) - Log[1 + x^4]/12 + Log[1 - x^4 + x^8]/24","A",7,7,11,0.6364,1,"{275, 292, 31, 634, 618, 204, 628}"
32,1,115,0,0.0560074,"\int x^{3 a} \sin \left(x^{2 a}\right) \, dx","Int[x^(3*a)*Sin[x^(2*a)],x]","\frac{i x^{3 a+1} \left(-i x^{2 a}\right)^{-\frac{3 a+1}{2 a}} \text{Gamma}\left(\frac{1}{2} \left(\frac{1}{a}+3\right),-i x^{2 a}\right)}{4 a}-\frac{i x^{3 a+1} \left(i x^{2 a}\right)^{-\frac{3 a+1}{2 a}} \text{Gamma}\left(\frac{1}{2} \left(\frac{1}{a}+3\right),i x^{2 a}\right)}{4 a}","\frac{i x^{3 a+1} \left(-i x^{2 a}\right)^{-\frac{3 a+1}{2 a}} \text{Gamma}\left(\frac{1}{2} \left(\frac{1}{a}+3\right),-i x^{2 a}\right)}{4 a}-\frac{i x^{3 a+1} \left(i x^{2 a}\right)^{-\frac{3 a+1}{2 a}} \text{Gamma}\left(\frac{1}{2} \left(\frac{1}{a}+3\right),i x^{2 a}\right)}{4 a}",1,"((I/4)*x^(1 + 3*a)*Gamma[(3 + a^(-1))/2, (-I)*x^(2*a)])/(a*((-I)*x^(2*a))^((1 + 3*a)/(2*a))) - ((I/4)*x^(1 + 3*a)*Gamma[(3 + a^(-1))/2, I*x^(2*a)])/(a*(I*x^(2*a))^((1 + 3*a)/(2*a)))","A",3,2,12,0.1667,1,"{3423, 2218}"
33,1,22,0,0.0100674,"\int \cos \left(\sqrt{x}\right) \, dx","Int[Cos[Sqrt[x]],x]","2 \sqrt{x} \sin \left(\sqrt{x}\right)+2 \cos \left(\sqrt{x}\right)","2 \sqrt{x} \sin \left(\sqrt{x}\right)+2 \cos \left(\sqrt{x}\right)",1,"2*Cos[Sqrt[x]] + 2*Sqrt[x]*Sin[Sqrt[x]]","A",3,3,6,0.5000,1,"{3362, 3296, 2638}"
34,1,23,0,0.0039135,"\int x \sqrt{1+x} \, dx","Int[x*Sqrt[1 + x],x]","\frac{2}{5} (x+1)^{5/2}-\frac{2}{3} (x+1)^{3/2}","\frac{2}{5} (x+1)^{5/2}-\frac{2}{3} (x+1)^{3/2}",1,"(-2*(1 + x)^(3/2))/3 + (2*(1 + x)^(5/2))/5","A",2,1,9,0.1111,1,"{43}"
35,1,32,0,0.0136464,"\int \frac{1}{\sqrt[3]{x}+\sqrt{x}} \, dx","Int[(x^(1/3) + Sqrt[x])^(-1),x]","2 \sqrt{x}-3 \sqrt[3]{x}+6 \sqrt[6]{x}-6 \log \left(\sqrt[6]{x}+1\right)","2 \sqrt{x}-3 \sqrt[3]{x}+6 \sqrt[6]{x}-6 \log \left(\sqrt[6]{x}+1\right)",1,"6*x^(1/6) - 3*x^(1/3) + 2*Sqrt[x] - 6*Log[1 + x^(1/6)]","A",4,3,13,0.2308,1,"{1593, 266, 43}"
36,1,44,0,0.0162064,"\int \sqrt{\frac{1+x}{3+2 x}} \, dx","Int[Sqrt[(1 + x)/(3 + 2*x)],x]","\frac{1}{2} \sqrt{x+1} \sqrt{2 x+3}-\frac{\sinh ^{-1}\left(\sqrt{2} \sqrt{x+1}\right)}{2 \sqrt{2}}","\frac{1}{2} \sqrt{x+1} \sqrt{2 x+3}-\frac{\sinh ^{-1}\left(\sqrt{2} \sqrt{x+1}\right)}{2 \sqrt{2}}",1,"(Sqrt[1 + x]*Sqrt[3 + 2*x])/2 - ArcSinh[Sqrt[2]*Sqrt[1 + x]]/(2*Sqrt[2])","A",4,4,15,0.2667,1,"{1958, 50, 54, 215}"
37,1,35,0,0.0086468,"\int \frac{x^4}{\left(1-x^2\right)^{5/2}} \, dx","Int[x^4/(1 - x^2)^(5/2),x]","\frac{x^3}{3 \left(1-x^2\right)^{3/2}}-\frac{x}{\sqrt{1-x^2}}+\sin ^{-1}(x)","\frac{x^3}{3 \left(1-x^2\right)^{3/2}}-\frac{x}{\sqrt{1-x^2}}+\sin ^{-1}(x)",1,"x^3/(3*(1 - x^2)^(3/2)) - x/Sqrt[1 - x^2] + ArcSin[x]","A",3,2,15,0.1333,1,"{288, 216}"
38,1,75,0,0.0130271,"\int \sqrt{x} (1+x)^{5/2} \, dx","Int[Sqrt[x]*(1 + x)^(5/2),x]","\frac{1}{4} x^{3/2} (x+1)^{5/2}+\frac{5}{24} x^{3/2} (x+1)^{3/2}+\frac{5}{32} x^{3/2} \sqrt{x+1}+\frac{5}{64} \sqrt{x} \sqrt{x+1}-\frac{5}{64} \sinh ^{-1}\left(\sqrt{x}\right)","\frac{1}{4} x^{3/2} (x+1)^{5/2}+\frac{5}{24} x^{3/2} (x+1)^{3/2}+\frac{5}{32} x^{3/2} \sqrt{x+1}+\frac{5}{64} \sqrt{x} \sqrt{x+1}-\frac{5}{64} \sinh ^{-1}\left(\sqrt{x}\right)",1,"(5*Sqrt[x]*Sqrt[1 + x])/64 + (5*x^(3/2)*Sqrt[1 + x])/32 + (5*x^(3/2)*(1 + x)^(3/2))/24 + (x^(3/2)*(1 + x)^(5/2))/4 - (5*ArcSinh[Sqrt[x]])/64","A",6,3,13,0.2308,1,"{50, 54, 215}"
39,1,35,0,0.0076016,"\int \frac{x^4}{\left(1-x^2\right)^{5/2}} \, dx","Int[x^4/(1 - x^2)^(5/2),x]","\frac{x^3}{3 \left(1-x^2\right)^{3/2}}-\frac{x}{\sqrt{1-x^2}}+\sin ^{-1}(x)","\frac{x^3}{3 \left(1-x^2\right)^{3/2}}-\frac{x}{\sqrt{1-x^2}}+\sin ^{-1}(x)",1,"x^3/(3*(1 - x^2)^(3/2)) - x/Sqrt[1 - x^2] + ArcSin[x]","A",3,2,15,0.1333,1,"{288, 216}"
40,1,51,0,0.0285577,"\int \frac{\sqrt{A^2+B^2-B^2 y^2}}{1-y^2} \, dy","Int[Sqrt[A^2 + B^2 - B^2*y^2]/(1 - y^2),y]","B \tan ^{-1}\left(\frac{B y}{\sqrt{A^2-B^2 y^2+B^2}}\right)+A \tanh ^{-1}\left(\frac{A y}{\sqrt{A^2-B^2 y^2+B^2}}\right)","B \tan ^{-1}\left(\frac{B y}{\sqrt{A^2-B^2 y^2+B^2}}\right)+A \tanh ^{-1}\left(\frac{A y}{\sqrt{A^2-B^2 y^2+B^2}}\right)",1,"B*ArcTan[(B*y)/Sqrt[A^2 + B^2 - B^2*y^2]] + A*ArcTanh[(A*y)/Sqrt[A^2 + B^2 - B^2*y^2]]","A",5,5,29,0.1724,1,"{402, 217, 203, 377, 206}"
41,1,14,0,0.0057409,"\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}"
42,1,57,0,0.0846305,"\int \csc (x) \sqrt{A^2+B^2 \sin ^2(x)} \, dx","Int[Csc[x]*Sqrt[A^2 + B^2*Sin[x]^2],x]","-B \tan ^{-1}\left(\frac{B \cos (x)}{\sqrt{A^2-B^2 \cos ^2(x)+B^2}}\right)-A \tanh ^{-1}\left(\frac{A \cos (x)}{\sqrt{A^2-B^2 \cos ^2(x)+B^2}}\right)","-B \tan ^{-1}\left(\frac{B \cos (x)}{\sqrt{A^2+B^2 \sin ^2(x)}}\right)-A \tanh ^{-1}\left(\frac{A \cos (x)}{\sqrt{A^2+B^2 \sin ^2(x)}}\right)",1,"-(B*ArcTan[(B*Cos[x])/Sqrt[A^2 + B^2 - B^2*Cos[x]^2]]) - A*ArcTanh[(A*Cos[x])/Sqrt[A^2 + B^2 - B^2*Cos[x]^2]]","A",6,6,19,0.3158,1,"{3186, 402, 217, 203, 377, 206}"
43,1,9,0,0.0075139,"\int \frac{1}{1+\cos (x)} \, dx","Int[(1 + Cos[x])^(-1),x]","\frac{\sin (x)}{\cos (x)+1}","\frac{\sin (x)}{\cos (x)+1}",1,"Sin[x]/(1 + Cos[x])","A",1,1,6,0.1667,1,"{2648}"
44,1,11,0,0.007018,"\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}"
45,1,9,0,0.0256603,"\int \frac{e^x x}{(1+x)^2} \, dx","Int[(E^x*x)/(1 + x)^2,x]","\frac{e^x}{x+1}","\frac{e^x}{x+1}",1,"E^x/(1 + x)","A",1,1,10,0.1000,1,"{2197}"
46,1,7,0,0.031599,"\int e^{x^2} \left(1+2 x^2\right) \, dx","Int[E^x^2*(1 + 2*x^2),x]","e^{x^2} x","e^{x^2} x",1,"E^x^2*x","A",5,3,13,0.2308,1,"{2226, 2204, 2212}"
47,1,11,0,0.0018481,"\int e^{x^2} \, dx","Int[E^x^2,x]","\frac{1}{2} \sqrt{\pi } \text{Erfi}(x)","\frac{1}{2} \sqrt{\pi } \text{Erfi}(x)",1,"(Sqrt[Pi]*Erfi[x])/2","A",1,1,5,0.2000,1,"{2204}"
48,1,2,0,0.0099006,"\int \frac{e^x}{x} \, dx","Int[E^x/x,x]","\text{ExpIntegralEi}(x)","\text{ExpIntegralEi}(x)",1,"ExpIntegralEi[x]","A",1,1,7,0.1429,1,"{2178}"
49,1,41,0,0.0220315,"\int \frac{x}{1+x^3} \, dx","Int[x/(1 + x^3),x]","\frac{1}{6} \log \left(x^2-x+1\right)-\frac{1}{3} \log (x+1)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{1}{6} \log \left(x^2-x+1\right)-\frac{1}{3} \log (x+1)-\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[(1 - 2*x)/Sqrt[3]]/Sqrt[3]) - Log[1 + x]/3 + Log[1 - x + x^2]/6","A",6,6,9,0.6667,1,"{292, 31, 634, 618, 204, 628}"
50,1,73,0,0.1048977,"\int \frac{1}{-1+x^6} \, dx","Int[(-1 + x^6)^(-1),x]","\frac{1}{12} \log \left(x^2-x+1\right)-\frac{1}{12} \log \left(x^2+x+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{1}{3} \tanh ^{-1}(x)","-\frac{\tan ^{-1}\left(\frac{\sqrt{3} x}{1-x^2}\right)}{2 \sqrt{3}}-\frac{1}{6} \tanh ^{-1}\left(\frac{x}{x^2+1}\right)-\frac{1}{3} \tanh ^{-1}(x)",1,"ArcTan[(1 - 2*x)/Sqrt[3]]/(2*Sqrt[3]) - ArcTan[(1 + 2*x)/Sqrt[3]]/(2*Sqrt[3]) - ArcTanh[x]/3 + Log[1 - x + x^2]/12 - Log[1 + x + x^2]/12","A",10,6,7,0.8571,1,"{210, 634, 618, 204, 628, 206}"
51,1,21,0,0.0094333,"\int \frac{1}{A^4-A^2 B^2+\left(-A^2+B^2\right) x^2} \, dx","Int[(A^4 - A^2*B^2 + (-A^2 + B^2)*x^2)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{x}{A}\right)}{A \left(A^2-B^2\right)}","\frac{\tanh ^{-1}\left(\frac{x}{A}\right)}{A \left(A^2-B^2\right)}",1,"ArcTanh[x/A]/(A*(A^2 - B^2))","A",1,1,27,0.03704,1,"{208}"
52,1,17,0,0.0039045,"\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}"
53,1,40,0,0.0241101,"\int x^2 \sin ^{-1}(x) \, dx","Int[x^2*ArcSin[x],x]","-\frac{1}{9} \left(1-x^2\right)^{3/2}+\frac{\sqrt{1-x^2}}{3}+\frac{1}{3} x^3 \sin ^{-1}(x)","-\frac{1}{9} \left(1-x^2\right)^{3/2}+\frac{\sqrt{1-x^2}}{3}+\frac{1}{3} x^3 \sin ^{-1}(x)",1,"Sqrt[1 - x^2]/3 - (1 - x^2)^(3/2)/9 + (x^3*ArcSin[x])/3","A",4,3,6,0.5000,1,"{4627, 266, 43}"
54,1,7,0,0.0010104,"\int \frac{1}{1+2 x+x^2} \, dx","Int[(1 + 2*x + x^2)^(-1),x]","-\frac{1}{x+1}","-\frac{1}{x+1}",1,"-(1 + x)^(-1)","A",2,2,10,0.2000,1,"{27, 32}"
55,1,8,0,0.0441281,"\int \frac{\log (x)}{(1+\log (x))^2} \, dx","Int[Log[x]/(1 + Log[x])^2,x]","\frac{x}{\log (x)+1}","\frac{x}{\log (x)+1}",1,"x/(1 + Log[x])","A",7,4,9,0.4444,1,"{2360, 2297, 2299, 2178}"
56,1,3,0,0.0196644,"\int \frac{1}{x \left(1+\log ^2(x)\right)} \, dx","Int[1/(x*(1 + Log[x]^2)),x]","\tan ^{-1}(\log (x))","\tan ^{-1}(\log (x))",1,"ArcTan[Log[x]]","A",2,1,12,0.08333,1,"{203}"
57,1,2,0,0.001793,"\int \frac{1}{\log (x)} \, dx","Int[Log[x]^(-1),x]","\text{LogIntegral}(x)","\text{LogIntegral}(x)",1,"LogIntegral[x]","A",1,1,4,0.2500,1,"{2298}"
58,1,14,0,0.0214771,"\int x (\cos (x)+\sin (x)) \, dx","Int[x*(Cos[x] + Sin[x]),x]","x \sin (x)+\sin (x)-x \cos (x)+\cos (x)","x \sin (x)+\sin (x)-x \cos (x)+\cos (x)",1,"Cos[x] - x*Cos[x] + Sin[x] + x*Sin[x]","A",6,4,7,0.5714,1,"{14, 3296, 2638, 2637}"
59,1,17,0,0.0313499,"\int e^{-x} \left(e^x+x\right) \, dx","Int[(E^x + x)/E^x,x]","-e^{-x} x+x-e^{-x}","-e^{-x} x+x-e^{-x}",1,"-E^(-x) + x - x/E^x","A",4,3,11,0.2727,1,"{6742, 2176, 2194}"
60,1,38,0,0.0326818,"\int \left(1+e^x\right)^2 x \, dx","Int[(1 + E^x)^2*x,x]","\frac{x^2}{2}+2 e^x x+\frac{1}{2} e^{2 x} x-2 e^x-\frac{e^{2 x}}{4}","\frac{x^2}{2}+2 e^x x+\frac{1}{2} e^{2 x} x-2 e^x-\frac{e^{2 x}}{4}",1,"-2*E^x - E^(2*x)/4 + 2*E^x*x + (E^(2*x)*x)/2 + x^2/2","A",6,3,9,0.3333,1,"{2183, 2176, 2194}"
61,1,7,0,0.0087321,"\int x \cos (x) \, dx","Int[x*Cos[x],x]","x \sin (x)+\cos (x)","x \sin (x)+\cos (x)",1,"Cos[x] + x*Sin[x]","A",2,2,4,0.5000,1,"{3296, 2638}"
62,1,22,0,0.0117688,"\int \cos \left(\sqrt{x}\right) \, dx","Int[Cos[Sqrt[x]],x]","2 \sqrt{x} \sin \left(\sqrt{x}\right)+2 \cos \left(\sqrt{x}\right)","2 \sqrt{x} \sin \left(\sqrt{x}\right)+2 \cos \left(\sqrt{x}\right)",1,"2*Cos[Sqrt[x]] + 2*Sqrt[x]*Sin[Sqrt[x]]","A",3,3,6,0.5000,1,"{3362, 3296, 2638}"
63,1,7,0,0.0090752,"\int x \cos (x) \, dx","Int[x*Cos[x],x]","x \sin (x)+\cos (x)","x \sin (x)+\cos (x)",1,"Cos[x] + x*Sin[x]","A",2,2,4,0.5000,1,"{3296, 2638}"
64,1,28,0,0.0097481,"\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}"
65,1,11,0,0.0120964,"\int \cos (x) \left(1+\sin ^3(x)\right) \, dx","Int[Cos[x]*(1 + Sin[x]^3),x]","\frac{\sin ^4(x)}{4}+\sin (x)","\frac{\sin ^4(x)}{4}+\sin (x)",1,"Sin[x] + Sin[x]^4/4","A",2,1,9,0.1111,1,"{3223}"
66,1,3,0,0.0190214,"\int \frac{1}{x \left(1+\log ^2(x)\right)} \, dx","Int[1/(x*(1 + Log[x]^2)),x]","\tan ^{-1}(\log (x))","\tan ^{-1}(\log (x))",1,"ArcTan[Log[x]]","A",2,1,12,0.08333,1,"{203}"
67,1,3,0,0.0469675,"\int \frac{1}{\sqrt{1-x^2} \left(1+\sin ^{-1}(x)^2\right)} \, dx","Int[1/(Sqrt[1 - x^2]*(1 + ArcSin[x]^2)),x]","\tan ^{-1}\left(\sin ^{-1}(x)\right)","\tan ^{-1}\left(\sin ^{-1}(x)\right)",1,"ArcTan[ArcSin[x]]","A",2,2,20,0.1000,1,"{6696, 203}"
68,1,16,0,0.0411408,"\int \frac{\sin (x)}{\cos (x)+\sin (x)} \, dx","Int[Sin[x]/(Cos[x] + Sin[x]),x]","\frac{x}{2}-\frac{1}{2} \log (\sin (x)+\cos (x))","\frac{x}{2}-\frac{1}{2} \log (\sin (x)+\cos (x))",1,"x/2 - Log[Cos[x] + Sin[x]]/2","A",2,2,10,0.2000,1,"{3097, 3133}"
69,1,53,0,0.0648788,"\int -\frac{\sqrt{A^2+B^2 \left(1-y^2\right)}}{1-y^2} \, dy","Int[-(Sqrt[A^2 + B^2*(1 - y^2)]/(1 - y^2)),y]","-B \tan ^{-1}\left(\frac{B y}{\sqrt{A^2-B^2 y^2+B^2}}\right)-A \tanh ^{-1}\left(\frac{A y}{\sqrt{A^2-B^2 y^2+B^2}}\right)","-B \tan ^{-1}\left(\frac{B y}{\sqrt{A^2-B^2 y^2+B^2}}\right)-A \tanh ^{-1}\left(\frac{A y}{\sqrt{A^2-B^2 y^2+B^2}}\right)",1,"-(B*ArcTan[(B*y)/Sqrt[A^2 + B^2 - B^2*y^2]]) - A*ArcTanh[(A*y)/Sqrt[A^2 + B^2 - B^2*y^2]]","A",6,6,30,0.2000,1,"{1974, 402, 217, 203, 377, 206}"
70,1,16,0,0.0859799,"\int \frac{\left(-A^2-B^2\right) \cos ^2(z)}{B \left(1-\frac{\left(A^2+B^2\right) \sin ^2(z)}{B^2}\right)} \, dz","Int[((-A^2 - B^2)*Cos[z]^2)/(B*(1 - ((A^2 + B^2)*Sin[z]^2)/B^2)),z]","-A \tanh ^{-1}\left(\frac{A \tan (z)}{B}\right)-B z","-A \tanh ^{-1}\left(\frac{A \tan (z)}{B}\right)-B z",1,"-(B*z) - A*ArcTanh[(A*Tan[z])/B]","A",5,5,39,0.1282,1,"{12, 3191, 391, 203, 206}"
71,1,16,0,0.1243708,"\int -\frac{A^2+B^2}{B \left(1+w^2\right)^2 \left(1-\frac{\left(A^2+B^2\right) w^2}{B^2 \left(1+w^2\right)}\right)} \, dw","Int[-((A^2 + B^2)/(B*(1 + w^2)^2*(1 - ((A^2 + B^2)*w^2)/(B^2*(1 + w^2))))),w]","-A \tanh ^{-1}\left(\frac{A w}{B}\right)-B \tan ^{-1}(w)","-A \tanh ^{-1}\left(\frac{A w}{B}\right)-B \tan ^{-1}(w)",1,"-(B*ArcTan[w]) - A*ArcTanh[(A*w)/B]","A",6,5,45,0.1111,1,"{12, 6688, 391, 203, 208}"
72,1,16,0,0.0186529,"\int -\frac{B \left(A^2+B^2\right)}{\left(1+w^2\right) \left(B^2-A^2 w^2\right)} \, dw","Int[-((B*(A^2 + B^2))/((1 + w^2)*(B^2 - A^2*w^2))),w]","-A \tanh ^{-1}\left(\frac{A w}{B}\right)-B \tan ^{-1}(w)","-A \tanh ^{-1}\left(\frac{A w}{B}\right)-B \tan ^{-1}(w)",1,"-(B*ArcTan[w]) - A*ArcTanh[(A*w)/B]","A",4,4,31,0.1290,1,"{12, 391, 203, 208}"
73,1,35,0,0.0080682,"\int \frac{x^4}{\left(1-x^2\right)^{5/2}} \, dx","Int[x^4/(1 - x^2)^(5/2),x]","\frac{x^3}{3 \left(1-x^2\right)^{3/2}}-\frac{x}{\sqrt{1-x^2}}+\sin ^{-1}(x)","\frac{x^3}{3 \left(1-x^2\right)^{3/2}}-\frac{x}{\sqrt{1-x^2}}+\sin ^{-1}(x)",1,"x^3/(3*(1 - x^2)^(3/2)) - x/Sqrt[1 - x^2] + ArcSin[x]","A",3,2,15,0.1333,1,"{288, 216}"
74,1,14,0,0.0094383,"\int \tan ^4(y) \, dy","Int[Tan[y]^4,y]","y+\frac{\tan ^3(y)}{3}-\tan (y)","y+\frac{\tan ^3(y)}{3}-\tan (y)",1,"y - Tan[y] + Tan[y]^3/3","A",3,2,4,0.5000,1,"{3473, 8}"
75,1,13,0,0.0053858,"\int \frac{z^4}{1+z^2} \, dz","Int[z^4/(1 + z^2),z]","\frac{z^3}{3}-z+\tan ^{-1}(z)","\frac{z^3}{3}-z+\tan ^{-1}(z)",1,"-z + z^3/3 + ArcTan[z]","A",3,2,11,0.1818,1,"{302, 203}"
76,1,7,0,0.0298354,"\int e^{x^2} \left(1+2 x^2\right) \, dx","Int[E^x^2*(1 + 2*x^2),x]","e^{x^2} x","e^{x^2} x",1,"E^x^2*x","A",5,3,13,0.2308,1,"{2226, 2204, 2212}"
77,1,24,0,0.3570296,"\int \frac{e^{x^2} \left(1+4 x^2+x^3+5 x^4+2 x^6\right)}{\left(1+x^2\right)^2} \, dx","Int[(E^x^2*(1 + 4*x^2 + x^3 + 5*x^4 + 2*x^6))/(1 + x^2)^2,x]","e^{x^2} x+\frac{e^{x^2}}{2 \left(x^2+1\right)}","e^{x^2} x+\frac{e^{x^2}}{2 \left(x^2+1\right)}",1,"E^x^2*x + E^x^2/(2*(1 + x^2))","A",10,6,33,0.1818,1,"{6742, 2204, 2212, 6715, 2177, 2178}"
78,1,9,0,0.003023,"\int e^{-1-x} \, dx","Int[E^(-1 - x),x]","-e^{-x-1}","-e^{-x-1}",1,"-E^(-1 - x)","A",1,1,7,0.1429,1,"{2194}"
79,1,25,0,0.0449937,"\int \left(\frac{1}{x}+x\right) \log (x) \, dx","Int[(x^(-1) + x)*Log[x],x]","-\frac{x^2}{4}+\frac{1}{2} x^2 \log (x)+\frac{\log ^2(x)}{2}","-\frac{x^2}{4}+\frac{1}{2} x^2 \log (x)+\frac{\log ^2(x)}{2}",1,"-x^2/4 + (x^2*Log[x])/2 + Log[x]^2/2","A",5,5,8,0.6250,1,"{1593, 14, 2351, 2301, 2304}"
80,1,8,0,0.0031274,"\int \frac{x}{1+x^4} \, dx","Int[x/(1 + x^4),x]","\frac{1}{2} \tan ^{-1}\left(x^2\right)","\frac{1}{2} \tan ^{-1}\left(x^2\right)",1,"ArcTan[x^2]/2","A",2,2,9,0.2222,1,"{275, 203}"
81,1,16,0,0.0082944,"\int \frac{x^5}{1+x^4} \, dx","Int[x^5/(1 + x^4),x]","\frac{x^2}{2}-\frac{1}{2} \tan ^{-1}\left(x^2\right)","\frac{x^2}{2}-\frac{1}{2} \tan ^{-1}\left(x^2\right)",1,"x^2/2 - ArcTan[x^2]/2","A",3,3,11,0.2727,1,"{275, 321, 203}"
82,1,14,0,0.0153262,"\int \frac{1}{1+\tan ^2(x)} \, dx","Int[(1 + Tan[x]^2)^(-1),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",3,3,8,0.3750,1,"{3657, 2635, 8}"
83,1,35,0,0.0110509,"\int \frac{x^4}{\left(1-x^2\right)^{5/2}} \, dx","Int[x^4/(1 - x^2)^(5/2),x]","\frac{x^3}{3 \left(1-x^2\right)^{3/2}}-\frac{x}{\sqrt{1-x^2}}+\sin ^{-1}(x)","\frac{x^3}{3 \left(1-x^2\right)^{3/2}}-\frac{x}{\sqrt{1-x^2}}+\sin ^{-1}(x)",1,"x^3/(3*(1 - x^2)^(3/2)) - x/Sqrt[1 - x^2] + ArcSin[x]","A",3,2,15,0.1333,1,"{288, 216}"
84,1,17,0,0.0050743,"\int -\frac{x^2}{\left(1-x^2\right)^{3/2}} \, dx","Int[-(x^2/(1 - x^2)^(3/2)),x]","\sin ^{-1}(x)-\frac{x}{\sqrt{1-x^2}}","\sin ^{-1}(x)-\frac{x}{\sqrt{1-x^2}}",1,"-(x/Sqrt[1 - x^2]) + ArcSin[x]","A",2,2,16,0.1250,1,"{288, 216}"
85,1,19,0,0.007656,"\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}"
86,1,2,0,0.0002056,"\int \frac{1}{x} \, dx","Int[x^(-1),x]","\log (x)","\log (x)",1,"Log[x]","A",1,1,3,0.3333,1,"{29}"
87,1,45,0,0.1230938,"\int \frac{\sec (2 t)}{1+\sec ^2(t)+3 \tan (t)} \, dt","Int[Sec[2*t]/(1 + Sec[t]^2 + 3*Tan[t]),t]","-\frac{1}{2 (\tan (t)+1)}-\frac{1}{12} \log (\cos (t)-\sin (t))-\frac{1}{4} \log (\sin (t)+\cos (t))+\frac{1}{3} \log (\sin (t)+2 \cos (t))","-\frac{1}{2 (\tan (t)+1)}-\frac{1}{12} \log (\cos (t)-\sin (t))-\frac{1}{4} \log (\sin (t)+\cos (t))+\frac{1}{3} \log (\sin (t)+2 \cos (t))",1,"-Log[Cos[t] - Sin[t]]/12 - Log[Cos[t] + Sin[t]]/4 + Log[2*Cos[t] + Sin[t]]/3 - 1/(2*(1 + Tan[t]))","A",4,2,17,0.1176,1,"{709, 800}"
88,1,14,0,0.0064947,"\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}"
89,1,17,0,0.0032497,"\int \frac{1+x^2}{\sqrt{x}} \, dx","Int[(1 + x^2)/Sqrt[x],x]","\frac{2 x^{5/2}}{5}+2 \sqrt{x}","\frac{2 x^{5/2}}{5}+2 \sqrt{x}",1,"2*Sqrt[x] + (2*x^(5/2))/5","A",2,1,11,0.09091,1,"{14}"
90,1,23,0,0.0098206,"\int \frac{x}{\sqrt{5+2 x+x^2}} \, dx","Int[x/Sqrt[5 + 2*x + x^2],x]","\sqrt{x^2+2 x+5}-\sinh ^{-1}\left(\frac{x+1}{2}\right)","\sqrt{x^2+2 x+5}-\sinh ^{-1}\left(\frac{x+1}{2}\right)",1,"Sqrt[5 + 2*x + x^2] - ArcSinh[(1 + x)/2]","A",3,3,14,0.2143,1,"{640, 619, 215}"
91,1,8,0,0.0127217,"\int \cos (x) \sin ^2(x) \, dx","Int[Cos[x]*Sin[x]^2,x]","\frac{\sin ^3(x)}{3}","\frac{\sin ^3(x)}{3}",1,"Sin[x]^3/3","A",2,2,7,0.2857,1,"{2564, 30}"
92,1,6,0,0.0164506,"\int \frac{e^x}{1+e^x} \, dx","Int[E^x/(1 + E^x),x]","\log \left(e^x+1\right)","\log \left(e^x+1\right)",1,"Log[1 + E^x]","A",2,2,11,0.1818,1,"{2246, 31}"
93,1,12,0,0.0264504,"\int \frac{e^{2 x}}{1+e^x} \, dx","Int[E^(2*x)/(1 + E^x),x]","e^x-\log \left(e^x+1\right)","e^x-\log \left(e^x+1\right)",1,"E^x - Log[1 + E^x]","A",3,2,13,0.1538,1,"{2248, 43}"
94,1,12,0,0.0090661,"\int \frac{1}{1-\cos (x)} \, dx","Int[(1 - Cos[x])^(-1),x]","-\frac{\sin (x)}{1-\cos (x)}","-\frac{\sin (x)}{1-\cos (x)}",1,"-(Sin[x]/(1 - Cos[x]))","A",1,1,8,0.1250,1,"{2648}"
95,1,8,0,0.0119479,"\int \sec ^2(x) \tan (x) \, dx","Int[Sec[x]^2*Tan[x],x]","\frac{\sec ^2(x)}{2}","\frac{\sec ^2(x)}{2}",1,"Sec[x]^2/2","A",2,2,7,0.2857,1,"{2606, 30}"
96,1,17,0,0.0042968,"\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}"
97,1,8,0,0.007369,"\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}"
98,1,24,0,0.0092363,"\int \frac{1+x}{\sqrt{2 x-x^2}} \, dx","Int[(1 + x)/Sqrt[2*x - x^2],x]","-\sqrt{2 x-x^2}-2 \sin ^{-1}(1-x)","-\sqrt{2 x-x^2}-2 \sin ^{-1}(1-x)",1,"-Sqrt[2*x - x^2] - 2*ArcSin[1 - x]","A",3,3,17,0.1765,1,"{640, 619, 216}"
99,1,20,0,0.0226488,"\int \frac{2 e^x}{2+3 e^{2 x}} \, dx","Int[(2*E^x)/(2 + 3*E^(2*x)),x]","\sqrt{\frac{2}{3}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} e^x\right)","\sqrt{\frac{2}{3}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} e^x\right)",1,"Sqrt[2/3]*ArcTan[Sqrt[3/2]*E^x]","A",3,3,16,0.1875,1,"{12, 2249, 203}"
100,1,35,0,0.0088799,"\int \frac{x^4}{\left(1-x^2\right)^{5/2}} \, dx","Int[x^4/(1 - x^2)^(5/2),x]","\frac{x^3}{3 \left(1-x^2\right)^{3/2}}-\frac{x}{\sqrt{1-x^2}}+\sin ^{-1}(x)","\frac{x^3}{3 \left(1-x^2\right)^{3/2}}-\frac{x}{\sqrt{1-x^2}}+\sin ^{-1}(x)",1,"x^3/(3*(1 - x^2)^(3/2)) - x/Sqrt[1 - x^2] + ArcSin[x]","A",3,2,15,0.1333,1,"{288, 216}"
101,1,20,0,0.0239091,"\int \frac{e^{6 x}}{1+e^{4 x}} \, dx","Int[E^(6*x)/(1 + E^(4*x)),x]","\frac{e^{2 x}}{2}-\frac{1}{2} \tan ^{-1}\left(e^{2 x}\right)","\frac{e^{2 x}}{2}-\frac{1}{2} \tan ^{-1}\left(e^{2 x}\right)",1,"E^(2*x)/2 - ArcTan[E^(2*x)]/2","A",3,3,15,0.2000,1,"{2248, 321, 203}"
102,1,33,0,0.0111443,"\int \log \left(2+3 x^2\right) \, dx","Int[Log[2 + 3*x^2],x]","x \log \left(3 x^2+2\right)-2 x+2 \sqrt{\frac{2}{3}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","x \log \left(3 x^2+2\right)-2 x+2 \sqrt{\frac{2}{3}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"-2*x + 2*Sqrt[2/3]*ArcTan[Sqrt[3/2]*x] + x*Log[2 + 3*x^2]","A",3,3,8,0.3750,1,"{2448, 321, 203}"
103,1,21,0,0.0161468,"\int \frac{1}{r \sqrt{-a^2+2 H r^2}} \, dx","Int[1/(r*Sqrt[-a^2 + 2*H*r^2]),x]","\frac{x}{r \sqrt{2 H r^2-a^2}}","\frac{x}{r \sqrt{2 H r^2-a^2}}",1,"x/(r*Sqrt[-a^2 + 2*H*r^2])","A",1,1,20,0.05000,1,"{8}"
104,1,26,0,0.0194002,"\int \frac{1}{r \sqrt{-a^2-e^2+2 H r^2}} \, dx","Int[1/(r*Sqrt[-a^2 - e^2 + 2*H*r^2]),x]","\frac{x}{r \sqrt{-a^2-e^2+2 H r^2}}","\frac{x}{r \sqrt{-a^2-e^2+2 H r^2}}",1,"x/(r*Sqrt[-a^2 - e^2 + 2*H*r^2])","A",1,1,25,0.04000,1,"{8}"
105,1,27,0,0.0227884,"\int \frac{1}{r \sqrt{-a^2+2 H r^2-2 K r^4}} \, dx","Int[1/(r*Sqrt[-a^2 + 2*H*r^2 - 2*K*r^4]),x]","\frac{x}{r \sqrt{-a^2+2 H r^2-2 K r^4}}","\frac{x}{r \sqrt{-a^2+2 H r^2-2 K r^4}}",1,"x/(r*Sqrt[-a^2 + 2*H*r^2 - 2*K*r^4])","A",1,1,26,0.03846,1,"{8}"
106,1,32,0,0.0256325,"\int \frac{1}{r \sqrt{-a^2-e^2+2 H r^2-2 K r^4}} \, dx","Int[1/(r*Sqrt[-a^2 - e^2 + 2*H*r^2 - 2*K*r^4]),x]","\frac{x}{r \sqrt{-a^2-e^2+2 H r^2-2 K r^4}}","\frac{x}{r \sqrt{-a^2-e^2+2 H r^2-2 K r^4}}",1,"x/(r*Sqrt[-a^2 - e^2 + 2*H*r^2 - 2*K*r^4])","A",1,1,31,0.03226,1,"{8}"
107,1,24,0,0.0265996,"\int \frac{1}{r \sqrt{-a^2-2 K r+2 H r^2}} \, dx","Int[1/(r*Sqrt[-a^2 - 2*K*r + 2*H*r^2]),x]","\frac{x}{r \sqrt{-a^2-2 r (K-H r)}}","\frac{x}{r \sqrt{-a^2-2 r (K-H r)}}",1,"x/(r*Sqrt[-a^2 - 2*r*(K - H*r)])","A",1,1,24,0.04167,1,"{8}"
108,1,29,0,0.0316036,"\int \frac{1}{r \sqrt{-a^2-e^2-2 K r+2 H r^2}} \, dx","Int[1/(r*Sqrt[-a^2 - e^2 - 2*K*r + 2*H*r^2]),x]","\frac{x}{r \sqrt{-a^2-e^2-2 r (K-H r)}}","\frac{x}{r \sqrt{-a^2-e^2-2 r (K-H r)}}",1,"x/(r*Sqrt[-a^2 - e^2 - 2*r*(K - H*r)])","A",1,1,29,0.03448,1,"{8}"
109,1,19,0,0.0094807,"\int \frac{r}{\sqrt{-a^2+2 e r^2}} \, dx","Int[r/Sqrt[-a^2 + 2*E*r^2],x]","\frac{r x}{\sqrt{2 e r^2-a^2}}","\frac{r x}{\sqrt{2 e r^2-a^2}}",1,"(r*x)/Sqrt[-a^2 + 2*E*r^2]","A",1,1,18,0.05556,1,"{8}"
110,1,24,0,0.0111275,"\int \frac{r}{\sqrt{-a^2-e^2+2 e r^2}} \, dx","Int[r/Sqrt[-a^2 - e^2 + 2*E*r^2],x]","\frac{r x}{\sqrt{-a^2-e^2+2 e r^2}}","\frac{r x}{\sqrt{-a^2-e^2+2 e r^2}}",1,"(r*x)/Sqrt[-a^2 - e^2 + 2*E*r^2]","A",1,1,23,0.04348,1,"{8}"
111,1,25,0,0.0127465,"\int \frac{r}{\sqrt{-a^2+2 e r^2-2 K r^4}} \, dx","Int[r/Sqrt[-a^2 + 2*E*r^2 - 2*K*r^4],x]","\frac{r x}{\sqrt{-a^2-2 K r^4+2 e r^2}}","\frac{r x}{\sqrt{-a^2-2 K r^4+2 e r^2}}",1,"(r*x)/Sqrt[-a^2 + 2*E*r^2 - 2*K*r^4]","A",1,1,24,0.04167,1,"{8}"
112,1,30,0,0.0153597,"\int \frac{r}{\sqrt{-a^2-e^2+2 e r^2-2 K r^4}} \, dx","Int[r/Sqrt[-a^2 - e^2 + 2*E*r^2 - 2*K*r^4],x]","\frac{r x}{\sqrt{-a^2-e^2-2 K r^4+2 e r^2}}","\frac{r x}{\sqrt{-a^2-e^2-2 K r^4+2 e r^2}}",1,"(r*x)/Sqrt[-a^2 - e^2 + 2*E*r^2 - 2*K*r^4]","A",1,1,29,0.03448,1,"{8}"
113,1,27,0,0.0056563,"\int \frac{r}{\sqrt{-a^2-e^2-2 K r+2 H r^2}} \, dx","Int[r/Sqrt[-a^2 - e^2 - 2*K*r + 2*H*r^2],x]","\frac{r x}{\sqrt{-a^2-e^2-2 r (K-H r)}}","\frac{r x}{\sqrt{-a^2-e^2-2 r (K-H r)}}",1,"(r*x)/Sqrt[-a^2 - e^2 - 2*r*(K - H*r)]","A",1,1,27,0.03704,1,"{8}"