1,0,0,12,0.0000341,"\int \cot ^4(x) \, dx","IntegrateAlgebraic[Cot[x]^4,x]","\int \cot ^4(x) \, dx","x-\frac{1}{3} \cot ^3(x)+\cot (x)",1,"Could not integrate","F",-1
2,1,17,13,0.0074595,"\int \frac{1}{x^4 \left(1+x^2\right)} \, dx","IntegrateAlgebraic[1/(x^4*(1 + x^2)),x]","\frac{3 x^2-1}{3 x^3}+\tan ^{-1}(x)","-\frac{1}{3 x^3}+\frac{1}{x}+\tan ^{-1}(x)",1,"(-1 + 3*x^2)/(3*x^3) + ArcTan[x]","A",1
3,1,19,19,0.0050369,"\int \frac{x+x^2}{\sqrt{x}} \, dx","IntegrateAlgebraic[(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",1
4,0,0,2,0.0000261,"\int \cos (x) \, dx","IntegrateAlgebraic[Cos[x],x]","\int \cos (x) \, dx","\sin (x)",1,"Could not integrate","F",-1
5,0,0,9,0.0000541,"\int e^{x^2} x \, dx","IntegrateAlgebraic[E^x^2*x,x]","\int e^{x^2} x \, dx","\frac{e^{x^2}}{2}",1,"Could not integrate","F",-1
6,0,0,8,0.0000291,"\int \sec ^2(x) \tan (x) \, dx","IntegrateAlgebraic[Sec[x]^2*Tan[x],x]","\int \sec ^2(x) \tan (x) \, dx","\frac{\sec ^2(x)}{2}",1,"Could not integrate","F",-1
7,1,13,13,0.0000852,"\int x \sqrt{1+x^2} \, dx","IntegrateAlgebraic[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
8,0,0,19,0.0000523,"\int e^x \sin (x) \, dx","IntegrateAlgebraic[E^x*Sin[x],x]","\int e^x \sin (x) \, dx","\frac{1}{2} e^x \sin (x)-\frac{1}{2} e^x \cos (x)",1,"Could not integrate","F",-1
9,0,0,8,0.0000309,"\int \cot (x) \csc ^3(x) \, dx","IntegrateAlgebraic[Cot[x]*Csc[x]^3,x]","\int \cot (x) \csc ^3(x) \, dx","-\frac{1}{3} \csc ^3(x)",1,"Could not integrate","F",-1
10,0,0,4,0.000025,"\int \sin \left(e^x\right) \, dx","IntegrateAlgebraic[Sin[E^x],x]","\int \sin \left(e^x\right) \, dx","\text{Si}\left(e^x\right)",1,"Could not integrate","F",-1
11,0,0,2,0.000035,"\int \frac{\sin (y)}{y} \, dy","IntegrateAlgebraic[Sin[y]/y,y]","\int \frac{\sin (y)}{y} \, dy","\text{Si}(y)",1,"Could not integrate","F",-1
12,0,0,8,0.0000354,"\int \left(e^x+\sin (x)\right) \, dx","IntegrateAlgebraic[E^x + Sin[x],x]","\int \left(e^x+\sin (x)\right) \, dx","e^x-\cos (x)",1,"Could not integrate","F",-1
13,0,0,7,0.0000636,"\int \left(e^{x^2}+2 e^{x^2} x^2\right) \, dx","IntegrateAlgebraic[E^x^2 + 2*E^x^2*x^2,x]","\int \left(e^{x^2}+2 e^{x^2} x^2\right) \, dx","e^{x^2} x",1,"Could not integrate","F",-1
14,0,0,28,0.0000489,"\int \left(e^x+x\right)^2 \, dx","IntegrateAlgebraic[(E^x + x)^2,x]","\int \left(e^x+x\right)^2 \, dx","\frac{x^3}{3}+2 e^x x-2 e^x+\frac{e^{2 x}}{2}",1,"Could not integrate","F",-1
15,0,0,22,0.000058,"\int \left(2 e^x+e^{2 x}+x^2\right) \, dx","IntegrateAlgebraic[2*E^x + E^(2*x) + x^2,x]","\int \left(2 e^x+e^{2 x}+x^2\right) \, dx","\frac{x^3}{3}+2 e^x+\frac{e^{2 x}}{2}",1,"Could not integrate","F",-1
16,0,0,8,0.000028,"\int \cos (x) \sin (x) \, dx","IntegrateAlgebraic[Cos[x]*Sin[x],x]","\int \cos (x) \sin (x) \, dx","\frac{\sin ^2(x)}{2}",1,"Could not integrate","F",-1
17,0,0,9,0.0000506,"\int e^{x^2} x \, dx","IntegrateAlgebraic[E^x^2*x,x]","\int e^{x^2} x \, dx","\frac{e^{x^2}}{2}",1,"Could not integrate","F",-1
18,1,13,13,0.0000836,"\int x \sqrt{1+x^2} \, dx","IntegrateAlgebraic[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
19,0,0,6,0.0000547,"\int \frac{e^x}{1+e^x} \, dx","IntegrateAlgebraic[E^x/(1 + E^x),x]","\int \frac{e^x}{1+e^x} \, dx","\log \left(e^x+1\right)",1,"Could not integrate","F",-1
20,1,9,9,0.002022,"\int x^{3/2} \, dx","IntegrateAlgebraic[x^(3/2),x]","\frac{2 x^{5/2}}{5}","\frac{2 x^{5/2}}{5}",1,"(2*x^(5/2))/5","A",1
21,0,0,10,0.0000253,"\int \cos (3+2 x) \, dx","IntegrateAlgebraic[Cos[3 + 2*x],x]","\int \cos (3+2 x) \, dx","\frac{1}{2} \sin (2 x+3)",1,"Could not integrate","F",-1
22,0,0,8,0.0000511,"\int 2 e^{2 x} y z \, dx","IntegrateAlgebraic[2*E^(2*x)*y*z,x]","\int 2 e^{2 x} y z \, dx","e^{2 x} y z",1,"Could not integrate","F",-1
23,0,0,10,0.0000335,"\int e^x \cos ^2\left(e^x\right) \sin \left(e^x\right) \, dx","IntegrateAlgebraic[E^x*Cos[E^x]^2*Sin[E^x],x]","\int e^x \cos ^2\left(e^x\right) \sin \left(e^x\right) \, dx","-\frac{1}{3} \cos ^3\left(e^x\right)",1,"Could not integrate","F",-1
24,1,19,23,0.0054682,"\int x \sqrt{1+x} \, dx","IntegrateAlgebraic[x*Sqrt[1 + x],x]","\frac{2}{15} \sqrt{x+1} \left(3 x^2+x-2\right)","\frac{2}{5} (x+1)^{5/2}-\frac{2}{3} (x+1)^{3/2}",1,"(2*Sqrt[1 + x]*(-2 + x + 3*x^2))/15","A",1
25,1,13,13,0.0000836,"\int \frac{1}{-1+x^4} \, dx","IntegrateAlgebraic[(-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,"-1/2*ArcTan[x] - ArcTanh[x]/2","A",1
26,0,0,18,0.0000682,"\int \frac{e^x}{2+3 e^{2 x}} \, dx","IntegrateAlgebraic[E^x/(2 + 3*E^(2*x)),x]","\int \frac{e^x}{2+3 e^{2 x}} \, dx","\frac{\tan ^{-1}\left(\sqrt{\frac{3}{2}} e^x\right)}{\sqrt{6}}",1,"Could not integrate","F",-1
27,0,0,31,0.0000644,"\int \frac{e^{2 x}}{A+B e^{4 x}} \, dx","IntegrateAlgebraic[E^(2*x)/(A + B*E^(4*x)),x]","\int \frac{e^{2 x}}{A+B e^{4 x}} \, dx","\frac{\tan ^{-1}\left(\frac{\sqrt{B} e^{2 x}}{\sqrt{A}}\right)}{2 \sqrt{A} \sqrt{B}}",1,"Could not integrate","F",-1
28,0,0,8,0.0000571,"\int \frac{e^{1+x}}{1+e^x} \, dx","IntegrateAlgebraic[E^(1 + x)/(1 + E^x),x]","\int \frac{e^{1+x}}{1+e^x} \, dx","e \log \left(e^x+1\right)",1,"Could not integrate","F",-1
29,0,0,12,0.0000455,"\int (10 e)^x \, dx","IntegrateAlgebraic[(10*E)^x,x]","\int (10 e)^x \, dx","\frac{(10 e)^x}{1+\log (10)}",1,"Could not integrate","F",-1
30,0,0,20,0.0000301,"\int x^3 \sin \left(x^2\right) \, dx","IntegrateAlgebraic[x^3*Sin[x^2],x]","\int x^3 \sin \left(x^2\right) \, dx","\frac{\sin \left(x^2\right)}{2}-\frac{1}{2} x^2 \cos \left(x^2\right)",1,"Could not integrate","F",-1
31,1,169,49,0.00011,"\int \frac{x^7}{1+x^{12}} \, dx","IntegrateAlgebraic[x^7/(1 + x^12),x]","-\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{24} \log \left(-2 x^2+\sqrt{6} x-\sqrt{2} x-2\right)+\frac{1}{24} \log \left(-2 x^2+\sqrt{6} x+\sqrt{2} x-2\right)-\frac{1}{12} \log \left(-x^2+\sqrt{2} x-1\right)-\frac{1}{12} \log \left(x^2+\sqrt{2} x+1\right)+\frac{1}{24} \log \left(2 x^2+\sqrt{6} x-\sqrt{2} x+2\right)+\frac{1}{24} \log \left(2 x^2+\sqrt{6} x+\sqrt{2} x+2\right)","-\frac{1}{12} \log \left(x^4+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 x^4}{\sqrt{3}}\right)}{4 \sqrt{3}}+\frac{1}{24} \log \left(x^8-x^4+1\right)",1,"-1/4*ArcTan[1/Sqrt[3] - (2*x^4)/Sqrt[3]]/Sqrt[3] + Log[-2 - Sqrt[2]*x + Sqrt[6]*x - 2*x^2]/24 + Log[-2 + Sqrt[2]*x + Sqrt[6]*x - 2*x^2]/24 - Log[-1 + Sqrt[2]*x - x^2]/12 - Log[1 + Sqrt[2]*x + x^2]/12 + Log[2 - Sqrt[2]*x + Sqrt[6]*x + 2*x^2]/24 + Log[2 + Sqrt[2]*x + Sqrt[6]*x + 2*x^2]/24","B",1
32,0,0,115,0.0000376,"\int x^{3 a} \sin \left(x^{2 a}\right) \, dx","IntegrateAlgebraic[x^(3*a)*Sin[x^(2*a)],x]","\int x^{3 a} \sin \left(x^{2 a}\right) \, dx","\frac{i x^{3 a+1} \left(-i x^{2 a}\right)^{-\frac{3 a+1}{2 a}} \Gamma \left(\frac{1}{2} \left(3+\frac{1}{a}\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}} \Gamma \left(\frac{1}{2} \left(3+\frac{1}{a}\right),i x^{2 a}\right)}{4 a}",1,"Could not integrate","F",-1
33,0,0,22,0.0000663,"\int \cos \left(\sqrt{x}\right) \, dx","IntegrateAlgebraic[Cos[Sqrt[x]],x]","\int \cos \left(\sqrt{x}\right) \, dx","2 \sqrt{x} \sin \left(\sqrt{x}\right)+2 \cos \left(\sqrt{x}\right)",1,"Could not integrate","F",-1
34,1,19,23,0.0000862,"\int x \sqrt{1+x} \, dx","IntegrateAlgebraic[x*Sqrt[1 + x],x]","\frac{2}{15} \sqrt{x+1} \left(3 x^2+x-2\right)","\frac{2}{5} (x+1)^{5/2}-\frac{2}{3} (x+1)^{3/2}",1,"(2*Sqrt[1 + x]*(-2 + x + 3*x^2))/15","A",1
35,1,32,32,0.0001001,"\int \frac{1}{\sqrt[3]{x}+\sqrt{x}} \, dx","IntegrateAlgebraic[(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",1
36,1,56,44,0.0663767,"\int \sqrt{\frac{1+x}{3+2 x}} \, dx","IntegrateAlgebraic[Sqrt[(1 + x)/(3 + 2*x)],x]","\frac{1}{2} \sqrt{\frac{x+1}{2 x+3}} (2 x+3)-\frac{\tanh ^{-1}\left(\sqrt{2} \sqrt{\frac{x+1}{2 x+3}}\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)/(3 + 2*x)]*(3 + 2*x))/2 - ArcTanh[Sqrt[2]*Sqrt[(1 + x)/(3 + 2*x)]]/(2*Sqrt[2])","A",1
37,1,52,35,0.0844899,"\int \frac{x^4}{\left(1-x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[x^4/(1 - x^2)^(5/2),x]","2 \tan ^{-1}\left(\frac{x}{\sqrt{1-x^2}-1}\right)+\frac{\sqrt{1-x^2} \left(4 x^3-3 x\right)}{3 \left(x^2-1\right)^2}","-\frac{x}{\sqrt{1-x^2}}+\frac{x^3}{3 \left(1-x^2\right)^{3/2}}+\sin ^{-1}(x)",1,"(Sqrt[1 - x^2]*(-3*x + 4*x^3))/(3*(-1 + x^2)^2) + 2*ArcTan[x/(-1 + Sqrt[1 - x^2])]","A",1
38,1,180,75,0.1059828,"\int \sqrt{x} (1+x)^{5/2} \, dx","IntegrateAlgebraic[Sqrt[x]*(1 + x)^(5/2),x]","\frac{\sqrt{x} \left(\frac{x^7}{4}-\frac{7}{4} \sqrt{x+1} x^6+\frac{167 x^6}{24}-\frac{455}{24} \sqrt{x+1} x^5+\frac{4255 x^5}{96}-\frac{2303}{32} \sqrt{x+1} x^4+\frac{8007 x^4}{64}-\frac{8339}{64} \sqrt{x+1} x^3+\frac{35303 x^3}{192}-\frac{2845}{24} \sqrt{x+1} x^2+\frac{3407 x^2}{24}-\frac{577}{12} \sqrt{x+1} x+\frac{607 x}{12}-5 \sqrt{x+1}+5\right)}{\left(\sqrt{x+1}-1\right)^7}-\frac{5}{32} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x+1}-1}\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,"(Sqrt[x]*(5 + (607*x)/12 + (3407*x^2)/24 + (35303*x^3)/192 + (8007*x^4)/64 + (4255*x^5)/96 + (167*x^6)/24 + x^7/4 - 5*Sqrt[1 + x] - (577*x*Sqrt[1 + x])/12 - (2845*x^2*Sqrt[1 + x])/24 - (8339*x^3*Sqrt[1 + x])/64 - (2303*x^4*Sqrt[1 + x])/32 - (455*x^5*Sqrt[1 + x])/24 - (7*x^6*Sqrt[1 + x])/4))/(-1 + Sqrt[1 + x])^7 - (5*ArcTanh[Sqrt[x]/(-1 + Sqrt[1 + x])])/32","B",1
39,1,52,35,0.0001046,"\int \frac{x^4}{\left(1-x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[x^4/(1 - x^2)^(5/2),x]","2 \tan ^{-1}\left(\frac{x}{\sqrt{1-x^2}-1}\right)+\frac{\sqrt{1-x^2} \left(4 x^3-3 x\right)}{3 \left(x^2-1\right)^2}","-\frac{x}{\sqrt{1-x^2}}+\frac{x^3}{3 \left(1-x^2\right)^{3/2}}+\sin ^{-1}(x)",1,"(Sqrt[1 - x^2]*(-3*x + 4*x^3))/(3*(-1 + x^2)^2) + 2*ArcTan[x/(-1 + Sqrt[1 - x^2])]","A",1
40,1,111,51,0.1447209,"\int \frac{\sqrt{A^2+B^2-B^2 y^2}}{1-y^2} \, dy","IntegrateAlgebraic[Sqrt[A^2 + B^2 - B^2*y^2]/(1 - y^2),y]","\sqrt{-B^2} \log \left(\sqrt{A^2-B^2 y^2+B^2}-\sqrt{-B^2} y\right)+\frac{A \sqrt{-B^2} \tan ^{-1}\left(-\frac{\sqrt{-B^2} y \sqrt{A^2-B^2 y^2+B^2}}{A B}-\frac{B y^2}{A}+\frac{B}{A}\right)}{B}","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,"(A*Sqrt[-B^2]*ArcTan[B/A - (B*y^2)/A - (Sqrt[-B^2]*y*Sqrt[A^2 + B^2 - B^2*y^2])/(A*B)])/B + Sqrt[-B^2]*Log[-(Sqrt[-B^2]*y) + Sqrt[A^2 + B^2 - B^2*y^2]]","B",1
41,0,0,14,0.0000274,"\int \sin ^2(x) \, dx","IntegrateAlgebraic[Sin[x]^2,x]","\int \sin ^2(x) \, dx","\frac{x}{2}-\frac{1}{2} \sin (x) \cos (x)",1,"Could not integrate","F",-1
42,0,0,49,0.0000365,"\int \csc (x) \sqrt{A^2+B^2 \sin ^2(x)} \, dx","IntegrateAlgebraic[Csc[x]*Sqrt[A^2 + B^2*Sin[x]^2],x]","\int \csc (x) \sqrt{A^2+B^2 \sin ^2(x)} \, dx","-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,"Could not integrate","F",-1
43,0,0,9,0.0000327,"\int \frac{1}{1+\cos (x)} \, dx","IntegrateAlgebraic[(1 + Cos[x])^(-1),x]","\int \frac{1}{1+\cos (x)} \, dx","\frac{\sin (x)}{\cos (x)+1}",1,"Could not integrate","F",-1
44,0,0,11,0.0000475,"\int e^x x \, dx","IntegrateAlgebraic[E^x*x,x]","\int e^x x \, dx","e^x x-e^x",1,"Could not integrate","F",-1
45,0,0,9,0.0000528,"\int \frac{e^x x}{(1+x)^2} \, dx","IntegrateAlgebraic[(E^x*x)/(1 + x)^2,x]","\int \frac{e^x x}{(1+x)^2} \, dx","\frac{e^x}{x+1}",1,"Could not integrate","F",-1
46,0,0,7,0.0000736,"\int e^{x^2} \left(1+2 x^2\right) \, dx","IntegrateAlgebraic[E^x^2*(1 + 2*x^2),x]","\int e^{x^2} \left(1+2 x^2\right) \, dx","e^{x^2} x",1,"Could not integrate","F",-1
47,0,0,11,0.0000479,"\int e^{x^2} \, dx","IntegrateAlgebraic[E^x^2,x]","\int e^{x^2} \, dx","\frac{1}{2} \sqrt{\pi } \text{erfi}(x)",1,"Could not integrate","F",-1
48,0,0,2,0.0000483,"\int \frac{e^x}{x} \, dx","IntegrateAlgebraic[E^x/x,x]","\int \frac{e^x}{x} \, dx","\text{Ei}(x)",1,"Could not integrate","F",-1
49,1,44,41,0.00013,"\int \frac{x}{1+x^3} \, dx","IntegrateAlgebraic[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}{\sqrt{3}}-\frac{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/Sqrt[3] - (2*x)/Sqrt[3]]/Sqrt[3]) - Log[1 + x]/3 + Log[1 - x + x^2]/6","A",1
50,1,69,47,0.0000974,"\int \frac{1}{-1+x^6} \, dx","IntegrateAlgebraic[(-1 + x^6)^(-1),x]","-\frac{1}{6} \tanh ^{-1}\left(\frac{x}{x^2+1}\right)+\frac{\tan ^{-1}\left(\frac{1}{\sqrt{3}}-\frac{2 x}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 x}{\sqrt{3}}+\frac{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/Sqrt[3] - (2*x)/Sqrt[3]]/(2*Sqrt[3]) - ArcTan[1/Sqrt[3] + (2*x)/Sqrt[3]]/(2*Sqrt[3]) - ArcTanh[x]/3 - ArcTanh[x/(1 + x^2)]/6","A",1
51,1,21,21,0.0078921,"\int \frac{1}{A^4-A^2 B^2+\left(-A^2+B^2\right) x^2} \, dx","IntegrateAlgebraic[(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
52,0,0,17,0.0000321,"\int x \log (x) \, dx","IntegrateAlgebraic[x*Log[x],x]","\int x \log (x) \, dx","\frac{1}{2} x^2 \log (x)-\frac{x^2}{4}",1,"Could not integrate","F",-1
53,0,0,40,0.000033,"\int x^2 \sin ^{-1}(x) \, dx","IntegrateAlgebraic[x^2*ArcSin[x],x]","\int x^2 \sin ^{-1}(x) \, dx","\frac{1}{3} x^3 \sin ^{-1}(x)-\frac{1}{9} \left(1-x^2\right)^{3/2}+\frac{\sqrt{1-x^2}}{3}",1,"Could not integrate","F",-1
54,1,7,7,0.002485,"\int \frac{1}{1+2 x+x^2} \, dx","IntegrateAlgebraic[(1 + 2*x + x^2)^(-1),x]","\frac{1}{-x-1}","-\frac{1}{x+1}",1,"(-1 - x)^(-1)","A",1
55,0,0,8,0.0000326,"\int \frac{\log (x)}{(1+\log (x))^2} \, dx","IntegrateAlgebraic[Log[x]/(1 + Log[x])^2,x]","\int \frac{\log (x)}{(1+\log (x))^2} \, dx","\frac{x}{\log (x)+1}",1,"Could not integrate","F",-1
56,0,0,3,0.0000312,"\int \frac{1}{x \left(1+\log ^2(x)\right)} \, dx","IntegrateAlgebraic[1/(x*(1 + Log[x]^2)),x]","\int \frac{1}{x \left(1+\log ^2(x)\right)} \, dx","\tan ^{-1}(\log (x))",1,"Could not integrate","F",-1
57,0,0,2,0.0000327,"\int \frac{1}{\log (x)} \, dx","IntegrateAlgebraic[Log[x]^(-1),x]","\int \frac{1}{\log (x)} \, dx","\text{li}(x)",1,"Could not integrate","F",-1
58,0,0,14,0.0000391,"\int x (\cos (x)+\sin (x)) \, dx","IntegrateAlgebraic[x*(Cos[x] + Sin[x]),x]","\int x (\cos (x)+\sin (x)) \, dx","x \sin (x)+\sin (x)-x \cos (x)+\cos (x)",1,"Could not integrate","F",-1
59,0,0,17,0.0000571,"\int e^{-x} \left(e^x+x\right) \, dx","IntegrateAlgebraic[(E^x + x)/E^x,x]","\int e^{-x} \left(e^x+x\right) \, dx","-e^{-x} x+x-e^{-x}",1,"Could not integrate","F",-1
60,0,0,38,0.0000534,"\int \left(1+e^x\right)^2 x \, dx","IntegrateAlgebraic[(1 + E^x)^2*x,x]","\int \left(1+e^x\right)^2 x \, dx","\frac{x^2}{2}+2 e^x x+\frac{1}{2} e^{2 x} x-2 e^x-\frac{e^{2 x}}{4}",1,"Could not integrate","F",-1
61,0,0,7,0.0000265,"\int x \cos (x) \, dx","IntegrateAlgebraic[x*Cos[x],x]","\int x \cos (x) \, dx","x \sin (x)+\cos (x)",1,"Could not integrate","F",-1
62,0,0,22,0.0000297,"\int \cos \left(\sqrt{x}\right) \, dx","IntegrateAlgebraic[Cos[Sqrt[x]],x]","\int \cos \left(\sqrt{x}\right) \, dx","2 \sqrt{x} \sin \left(\sqrt{x}\right)+2 \cos \left(\sqrt{x}\right)",1,"Could not integrate","F",-1
63,0,0,7,0.0000267,"\int x \cos (x) \, dx","IntegrateAlgebraic[x*Cos[x],x]","\int x \cos (x) \, dx","x \sin (x)+\cos (x)",1,"Could not integrate","F",-1
64,0,0,28,0.0000265,"\int x \log ^2(x) \, dx","IntegrateAlgebraic[x*Log[x]^2,x]","\int x \log ^2(x) \, dx","\frac{x^2}{4}+\frac{1}{2} x^2 \log ^2(x)-\frac{1}{2} x^2 \log (x)",1,"Could not integrate","F",-1
65,0,0,11,0.0000317,"\int \cos (x) \left(1+\sin ^3(x)\right) \, dx","IntegrateAlgebraic[Cos[x]*(1 + Sin[x]^3),x]","\int \cos (x) \left(1+\sin ^3(x)\right) \, dx","\frac{\sin ^4(x)}{4}+\sin (x)",1,"Could not integrate","F",-1
66,0,0,3,0.0000297,"\int \frac{1}{x \left(1+\log ^2(x)\right)} \, dx","IntegrateAlgebraic[1/(x*(1 + Log[x]^2)),x]","\int \frac{1}{x \left(1+\log ^2(x)\right)} \, dx","\tan ^{-1}(\log (x))",1,"Could not integrate","F",-1
67,0,0,3,0.0000335,"\int \frac{1}{\sqrt{1-x^2} \left(1+\sin ^{-1}(x)^2\right)} \, dx","IntegrateAlgebraic[1/(Sqrt[1 - x^2]*(1 + ArcSin[x]^2)),x]","\int \frac{1}{\sqrt{1-x^2} \left(1+\sin ^{-1}(x)^2\right)} \, dx","\tan ^{-1}\left(\sin ^{-1}(x)\right)",1,"Could not integrate","F",-1
68,0,0,16,0.0000308,"\int \frac{\sin (x)}{\cos (x)+\sin (x)} \, dx","IntegrateAlgebraic[Sin[x]/(Cos[x] + Sin[x]),x]","\int \frac{\sin (x)}{\cos (x)+\sin (x)} \, dx","\frac{x}{2}-\frac{1}{2} \log (\sin (x)+\cos (x))",1,"Could not integrate","F",-1
69,1,113,53,0.1167136,"\int -\frac{\sqrt{A^2+B^2 \left(1-y^2\right)}}{1-y^2} \, dy","IntegrateAlgebraic[-(Sqrt[A^2 + B^2*(1 - y^2)]/(1 - y^2)),y]","-\sqrt{-B^2} \log \left(\sqrt{A^2-B^2 y^2+B^2}-\sqrt{-B^2} y\right)-\frac{A \sqrt{-B^2} \tan ^{-1}\left(-\frac{\sqrt{-B^2} y \sqrt{A^2-B^2 y^2+B^2}}{A B}-\frac{B y^2}{A}+\frac{B}{A}\right)}{B}","-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,"-((A*Sqrt[-B^2]*ArcTan[B/A - (B*y^2)/A - (Sqrt[-B^2]*y*Sqrt[A^2 + B^2 - B^2*y^2])/(A*B)])/B) - Sqrt[-B^2]*Log[-(Sqrt[-B^2]*y) + Sqrt[A^2 + B^2 - B^2*y^2]]","B",1
70,0,0,16,0.0000706,"\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","IntegrateAlgebraic[((-A^2 - B^2)*Cos[z]^2)/(B*(1 - ((A^2 + B^2)*Sin[z]^2)/B^2)),z]","\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","-A \tanh ^{-1}\left(\frac{A \tan (z)}{B}\right)-B z",1,"Could not integrate","F",-1
71,1,16,16,0.0265066,"\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","IntegrateAlgebraic[(-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",1
72,1,16,16,0.0195252,"\int -\frac{B \left(A^2+B^2\right)}{\left(1+w^2\right) \left(B^2-A^2 w^2\right)} \, dw","IntegrateAlgebraic[-((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",1
73,1,52,35,0.000123,"\int \frac{x^4}{\left(1-x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[x^4/(1 - x^2)^(5/2),x]","2 \tan ^{-1}\left(\frac{x}{\sqrt{1-x^2}-1}\right)+\frac{\sqrt{1-x^2} \left(4 x^3-3 x\right)}{3 \left(x^2-1\right)^2}","-\frac{x}{\sqrt{1-x^2}}+\frac{x^3}{3 \left(1-x^2\right)^{3/2}}+\sin ^{-1}(x)",1,"(Sqrt[1 - x^2]*(-3*x + 4*x^3))/(3*(-1 + x^2)^2) + 2*ArcTan[x/(-1 + Sqrt[1 - x^2])]","A",1
74,0,0,14,0.0000289,"\int \tan ^4(y) \, dy","IntegrateAlgebraic[Tan[y]^4,y]","\int \tan ^4(y) \, dy","y+\frac{\tan ^3(y)}{3}-\tan (y)",1,"Could not integrate","F",-1
75,1,13,13,0.0067629,"\int \frac{z^4}{1+z^2} \, dz","IntegrateAlgebraic[z^4/(1 + z^2),z]","\frac{1}{3} z \left(z^2-3\right)+\tan ^{-1}(z)","\frac{z^3}{3}-z+\tan ^{-1}(z)",1,"(z*(-3 + z^2))/3 + ArcTan[z]","A",1
76,0,0,7,0.0000629,"\int e^{x^2} \left(1+2 x^2\right) \, dx","IntegrateAlgebraic[E^x^2*(1 + 2*x^2),x]","\int e^{x^2} \left(1+2 x^2\right) \, dx","e^{x^2} x",1,"Could not integrate","F",-1
77,0,0,24,0.0000851,"\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","IntegrateAlgebraic[(E^x^2*(1 + 4*x^2 + x^3 + 5*x^4 + 2*x^6))/(1 + x^2)^2,x]","\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","e^{x^2} x+\frac{e^{x^2}}{2 \left(x^2+1\right)}",1,"Could not integrate","F",-1
78,0,0,9,0.0000571,"\int e^{-1-x} \, dx","IntegrateAlgebraic[E^(-1 - x),x]","\int e^{-1-x} \, dx","-e^{-x-1}",1,"Could not integrate","F",-1
79,0,0,25,0.0000343,"\int \left(\frac{1}{x}+x\right) \log (x) \, dx","IntegrateAlgebraic[(x^(-1) + x)*Log[x],x]","\int \left(\frac{1}{x}+x\right) \log (x) \, dx","-\frac{x^2}{4}+\frac{1}{2} x^2 \log (x)+\frac{\log ^2(x)}{2}",1,"Could not integrate","F",-1
80,1,8,8,0.0046978,"\int \frac{x}{1+x^4} \, dx","IntegrateAlgebraic[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",1
81,1,16,16,0.0061179,"\int \frac{x^5}{1+x^4} \, dx","IntegrateAlgebraic[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",1
82,0,0,14,0.000031,"\int \frac{1}{1+\tan ^2(x)} \, dx","IntegrateAlgebraic[(1 + Tan[x]^2)^(-1),x]","\int \frac{1}{1+\tan ^2(x)} \, dx","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"Could not integrate","F",-1
83,1,52,35,0.0001033,"\int \frac{x^4}{\left(1-x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[x^4/(1 - x^2)^(5/2),x]","2 \tan ^{-1}\left(\frac{x}{\sqrt{1-x^2}-1}\right)+\frac{\sqrt{1-x^2} \left(4 x^3-3 x\right)}{3 \left(x^2-1\right)^2}","-\frac{x}{\sqrt{1-x^2}}+\frac{x^3}{3 \left(1-x^2\right)^{3/2}}+\sin ^{-1}(x)",1,"(Sqrt[1 - x^2]*(-3*x + 4*x^3))/(3*(-1 + x^2)^2) + 2*ArcTan[x/(-1 + Sqrt[1 - x^2])]","A",1
84,1,41,17,0.0628468,"\int -\frac{x^2}{\left(1-x^2\right)^{3/2}} \, dx","IntegrateAlgebraic[-(x^2/(1 - x^2)^(3/2)),x]","\frac{\sqrt{1-x^2} x}{x^2-1}+2 \tan ^{-1}\left(\frac{x}{\sqrt{1-x^2}-1}\right)","\sin ^{-1}(x)-\frac{x}{\sqrt{1-x^2}}",1,"(x*Sqrt[1 - x^2])/(-1 + x^2) + 2*ArcTan[x/(-1 + Sqrt[1 - x^2])]","B",1
85,0,0,19,0.0000395,"\int e^x \sin (x) \, dx","IntegrateAlgebraic[E^x*Sin[x],x]","\int e^x \sin (x) \, dx","\frac{1}{2} e^x \sin (x)-\frac{1}{2} e^x \cos (x)",1,"Could not integrate","F",-1
86,1,2,2,0.0000876,"\int \frac{1}{x} \, dx","IntegrateAlgebraic[x^(-1),x]","\log (x)","\log (x)",1,"Log[x]","A",1
87,0,0,45,0.0000557,"\int \frac{\sec (2 t)}{1+\sec ^2(t)+3 \tan (t)} \, dt","IntegrateAlgebraic[Sec[2*t]/(1 + Sec[t]^2 + 3*Tan[t]),t]","\int \frac{\sec (2 t)}{1+\sec ^2(t)+3 \tan (t)} \, dt","-\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,"Could not integrate","F",-1
88,0,0,14,0.0000284,"\int \cos ^2(x) \, dx","IntegrateAlgebraic[Cos[x]^2,x]","\int \cos ^2(x) \, dx","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"Could not integrate","F",-1
89,1,17,17,0.0049017,"\int \frac{1+x^2}{\sqrt{x}} \, dx","IntegrateAlgebraic[(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",1
90,1,31,23,0.0608471,"\int \frac{x}{\sqrt{5+2 x+x^2}} \, dx","IntegrateAlgebraic[x/Sqrt[5 + 2*x + x^2],x]","\sqrt{x^2+2 x+5}+\log \left(\sqrt{x^2+2 x+5}-x-1\right)","\sqrt{x^2+2 x+5}-\sinh ^{-1}\left(\frac{x+1}{2}\right)",1,"Sqrt[5 + 2*x + x^2] + Log[-1 - x + Sqrt[5 + 2*x + x^2]]","A",1
91,0,0,8,0.0000343,"\int \cos (x) \sin ^2(x) \, dx","IntegrateAlgebraic[Cos[x]*Sin[x]^2,x]","\int \cos (x) \sin ^2(x) \, dx","\frac{\sin ^3(x)}{3}",1,"Could not integrate","F",-1
92,0,0,6,0.0000604,"\int \frac{e^x}{1+e^x} \, dx","IntegrateAlgebraic[E^x/(1 + E^x),x]","\int \frac{e^x}{1+e^x} \, dx","\log \left(e^x+1\right)",1,"Could not integrate","F",-1
93,0,0,12,0.00006,"\int \frac{e^{2 x}}{1+e^x} \, dx","IntegrateAlgebraic[E^(2*x)/(1 + E^x),x]","\int \frac{e^{2 x}}{1+e^x} \, dx","e^x-\log \left(e^x+1\right)",1,"Could not integrate","F",-1
94,0,0,12,0.0000301,"\int \frac{1}{1-\cos (x)} \, dx","IntegrateAlgebraic[(1 - Cos[x])^(-1),x]","\int \frac{1}{1-\cos (x)} \, dx","-\frac{\sin (x)}{1-\cos (x)}",1,"Could not integrate","F",-1
95,0,0,8,0.0000633,"\int \sec ^2(x) \tan (x) \, dx","IntegrateAlgebraic[Sec[x]^2*Tan[x],x]","\int \sec ^2(x) \tan (x) \, dx","\frac{\sec ^2(x)}{2}",1,"Could not integrate","F",-1
96,0,0,17,0.0000267,"\int x \log (x) \, dx","IntegrateAlgebraic[x*Log[x],x]","\int x \log (x) \, dx","\frac{1}{2} x^2 \log (x)-\frac{x^2}{4}",1,"Could not integrate","F",-1
97,0,0,8,0.0000444,"\int \cos (x) \sin (x) \, dx","IntegrateAlgebraic[Cos[x]*Sin[x],x]","\int \cos (x) \sin (x) \, dx","\frac{\sin ^2(x)}{2}",1,"Could not integrate","F",-1
98,1,36,24,0.143489,"\int \frac{1+x}{\sqrt{2 x-x^2}} \, dx","IntegrateAlgebraic[(1 + x)/Sqrt[2*x - x^2],x]","-\sqrt{2 x-x^2}-4 \tan ^{-1}\left(\frac{\sqrt{2 x-x^2}}{x}\right)","-\sqrt{2 x-x^2}-2 \sin ^{-1}(1-x)",1,"-Sqrt[2*x - x^2] - 4*ArcTan[Sqrt[2*x - x^2]/x]","A",1
99,0,0,20,0.0000688,"\int \frac{2 e^x}{2+3 e^{2 x}} \, dx","IntegrateAlgebraic[(2*E^x)/(2 + 3*E^(2*x)),x]","\int \frac{2 e^x}{2+3 e^{2 x}} \, dx","\sqrt{\frac{2}{3}} \tan ^{-1}\left(\sqrt{\frac{3}{2}} e^x\right)",1,"Could not integrate","F",-1
100,1,52,35,0.0001004,"\int \frac{x^4}{\left(1-x^2\right)^{5/2}} \, dx","IntegrateAlgebraic[x^4/(1 - x^2)^(5/2),x]","2 \tan ^{-1}\left(\frac{x}{\sqrt{1-x^2}-1}\right)+\frac{\sqrt{1-x^2} \left(4 x^3-3 x\right)}{3 \left(x^2-1\right)^2}","-\frac{x}{\sqrt{1-x^2}}+\frac{x^3}{3 \left(1-x^2\right)^{3/2}}+\sin ^{-1}(x)",1,"(Sqrt[1 - x^2]*(-3*x + 4*x^3))/(3*(-1 + x^2)^2) + 2*ArcTan[x/(-1 + Sqrt[1 - x^2])]","A",1
101,0,0,20,0.0000659,"\int \frac{e^{6 x}}{1+e^{4 x}} \, dx","IntegrateAlgebraic[E^(6*x)/(1 + E^(4*x)),x]","\int \frac{e^{6 x}}{1+e^{4 x}} \, dx","\frac{e^{2 x}}{2}-\frac{1}{2} \tan ^{-1}\left(e^{2 x}\right)",1,"Could not integrate","F",-1
102,0,0,33,0.0000283,"\int \log \left(2+3 x^2\right) \, dx","IntegrateAlgebraic[Log[2 + 3*x^2],x]","\int \log \left(2+3 x^2\right) \, dx","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,"Could not integrate","F",-1
103,1,21,21,0.0039989,"\int \frac{1}{r \sqrt{-a^2+2 H r^2}} \, dx","IntegrateAlgebraic[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
104,1,26,26,0.0045,"\int \frac{1}{r \sqrt{-a^2-e^2+2 H r^2}} \, dx","IntegrateAlgebraic[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
105,0,0,27,0.000147,"\int \frac{1}{r \sqrt{-a^2+2 H r^2-2 K r^4}} \, dx","IntegrateAlgebraic[1/(r*Sqrt[-a^2 + 2*H*r^2 - 2*K*r^4]),x]","\int \frac{1}{r \sqrt{-a^2+2 H r^2-2 K r^4}} \, dx","\frac{x}{r \sqrt{-a^2+2 H r^2-2 K r^4}}",1,"Could not integrate","F",-1
106,0,0,32,0.0001093,"\int \frac{1}{r \sqrt{-a^2-e^2+2 H r^2-2 K r^4}} \, dx","IntegrateAlgebraic[1/(r*Sqrt[-a^2 - e^2 + 2*H*r^2 - 2*K*r^4]),x]","\int \frac{1}{r \sqrt{-a^2-e^2+2 H r^2-2 K r^4}} \, dx","\frac{x}{r \sqrt{-a^2-e^2+2 H r^2-2 K r^4}}",1,"Could not integrate","F",-1
107,0,0,24,0.0000381,"\int \frac{1}{r \sqrt{-a^2-2 K r+2 H r^2}} \, dx","IntegrateAlgebraic[1/(r*Sqrt[-a^2 - 2*K*r + 2*H*r^2]),x]","\int \frac{1}{r \sqrt{-a^2-2 K r+2 H r^2}} \, dx","\frac{x}{r \sqrt{-a^2-2 r (K-H r)}}",1,"Could not integrate","F",-1
108,0,0,29,0.0000408,"\int \frac{1}{r \sqrt{-a^2-e^2-2 K r+2 H r^2}} \, dx","IntegrateAlgebraic[1/(r*Sqrt[-a^2 - e^2 - 2*K*r + 2*H*r^2]),x]","\int \frac{1}{r \sqrt{-a^2-e^2-2 K r+2 H r^2}} \, dx","\frac{x}{r \sqrt{-a^2-e^2-2 r (K-H r)}}",1,"Could not integrate","F",-1
109,1,19,19,0.003628,"\int \frac{r}{\sqrt{-a^2+2 e r^2}} \, dx","IntegrateAlgebraic[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
110,1,24,24,0.0041381,"\int \frac{r}{\sqrt{-a^2-e^2+2 e r^2}} \, dx","IntegrateAlgebraic[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
111,0,0,25,0.0000432,"\int \frac{r}{\sqrt{-a^2+2 e r^2-2 K r^4}} \, dx","IntegrateAlgebraic[r/Sqrt[-a^2 + 2*E*r^2 - 2*K*r^4],x]","\int \frac{r}{\sqrt{-a^2+2 e r^2-2 K r^4}} \, dx","\frac{r x}{\sqrt{-a^2-2 K r^4+2 e r^2}}",1,"Could not integrate","F",-1
112,0,0,30,0.0000396,"\int \frac{r}{\sqrt{-a^2-e^2+2 e r^2-2 K r^4}} \, dx","IntegrateAlgebraic[r/Sqrt[-a^2 - e^2 + 2*E*r^2 - 2*K*r^4],x]","\int \frac{r}{\sqrt{-a^2-e^2+2 e r^2-2 K r^4}} \, dx","\frac{r x}{\sqrt{-a^2-e^2-2 K r^4+2 e r^2}}",1,"Could not integrate","F",-1
113,0,0,27,0.0000404,"\int \frac{r}{\sqrt{-a^2-e^2-2 K r+2 H r^2}} \, dx","IntegrateAlgebraic[r/Sqrt[-a^2 - e^2 - 2*K*r + 2*H*r^2],x]","\int \frac{r}{\sqrt{-a^2-e^2-2 K r+2 H r^2}} \, dx","\frac{r x}{\sqrt{-a^2-e^2-2 r (K-H r)}}",1,"Could not integrate","F",-1