1,1,18,12,0.00318,"\int \cot ^4(x) \, dx","Integrate[Cot[x]^4,x]","x+\frac{4 \cot (x)}{3}-\frac{1}{3} \cot (x) \csc ^2(x)","x-\frac{1}{3} \cot ^3(x)+\cot (x)",1,"x + (4*Cot[x])/3 - (Cot[x]*Csc[x]^2)/3","A",1
2,1,13,13,0.0042797,"\int \frac{1}{x^4 \left(1+x^2\right)} \, dx","Integrate[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*1/x^3 + x^(-1) + ArcTan[x]","A",1
3,1,14,19,0.0036681,"\int \frac{x+x^2}{\sqrt{x}} \, dx","Integrate[(x + x^2)/Sqrt[x],x]","\frac{2}{15} x^{3/2} (3 x+5)","\frac{2 x^{5/2}}{5}+\frac{2 x^{3/2}}{3}",1,"(2*x^(3/2)*(5 + 3*x))/15","A",1
4,1,2,2,0.0010375,"\int \cos (x) \, dx","Integrate[Cos[x],x]","\sin (x)","\sin (x)",1,"Sin[x]","A",1
5,1,9,9,0.0014037,"\int e^{x^2} x \, dx","Integrate[E^x^2*x,x]","\frac{e^{x^2}}{2}","\frac{e^{x^2}}{2}",1,"E^x^2/2","A",1
6,1,8,8,0.0050064,"\int \sec ^2(x) \tan (x) \, dx","Integrate[Sec[x]^2*Tan[x],x]","\frac{\sec ^2(x)}{2}","\frac{\sec ^2(x)}{2}",1,"Sec[x]^2/2","A",1
7,1,13,13,0.0018129,"\int x \sqrt{1+x^2} \, dx","Integrate[x*Sqrt[1 + x^2],x]","\frac{1}{3} \left(x^2+1\right)^{3/2}","\frac{1}{3} \left(x^2+1\right)^{3/2}",1,"(1 + x^2)^(3/2)/3","A",1
8,1,14,19,0.015033,"\int e^x \sin (x) \, dx","Integrate[E^x*Sin[x],x]","\frac{1}{2} e^x (\sin (x)-\cos (x))","\frac{1}{2} e^x \sin (x)-\frac{1}{2} e^x \cos (x)",1,"(E^x*(-Cos[x] + Sin[x]))/2","A",1
9,1,8,8,0.0051717,"\int \cot (x) \csc ^3(x) \, dx","Integrate[Cot[x]*Csc[x]^3,x]","-\frac{1}{3} \csc ^3(x)","-\frac{1}{3} \csc ^3(x)",1,"-1/3*Csc[x]^3","A",1
10,1,4,4,0.0057755,"\int \sin \left(e^x\right) \, dx","Integrate[Sin[E^x],x]","\text{Si}\left(e^x\right)","\text{Si}\left(e^x\right)",1,"SinIntegral[E^x]","A",1
11,1,2,2,0.0151695,"\int \frac{\sin (y)}{y} \, dy","Integrate[Sin[y]/y,y]","\text{Si}(y)","\text{Si}(y)",1,"SinIntegral[y]","A",1
12,1,8,8,0.0033145,"\int \left(e^x+\sin (x)\right) \, dx","Integrate[E^x + Sin[x],x]","e^x-\cos (x)","e^x-\cos (x)",1,"E^x - Cos[x]","A",1
13,1,7,7,0.0059823,"\int \left(e^{x^2}+2 e^{x^2} x^2\right) \, dx","Integrate[E^x^2 + 2*E^x^2*x^2,x]","e^{x^2} x","e^{x^2} x",1,"E^x^2*x","A",1
14,1,26,28,0.0150118,"\int \left(e^x+x\right)^2 \, dx","Integrate[(E^x + x)^2,x]","\frac{x^3}{3}+\frac{e^{2 x}}{2}+e^x (2 x-2)","\frac{x^3}{3}+2 e^x x-2 e^x+\frac{e^{2 x}}{2}",1,"E^(2*x)/2 + x^3/3 + E^x*(-2 + 2*x)","A",1
15,1,22,22,0.0022668,"\int \left(2 e^x+e^{2 x}+x^2\right) \, dx","Integrate[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",1
16,1,8,8,0.0015489,"\int \cos (x) \sin (x) \, dx","Integrate[Cos[x]*Sin[x],x]","-\frac{1}{2} \cos ^2(x)","\frac{\sin ^2(x)}{2}",1,"-1/2*Cos[x]^2","A",1
17,1,9,9,0.0007184,"\int e^{x^2} x \, dx","Integrate[E^x^2*x,x]","\frac{e^{x^2}}{2}","\frac{e^{x^2}}{2}",1,"E^x^2/2","A",1
18,1,13,13,0.0004895,"\int x \sqrt{1+x^2} \, dx","Integrate[x*Sqrt[1 + x^2],x]","\frac{1}{3} \left(x^2+1\right)^{3/2}","\frac{1}{3} \left(x^2+1\right)^{3/2}",1,"(1 + x^2)^(3/2)/3","A",1
19,1,6,6,0.0047817,"\int \frac{e^x}{1+e^x} \, dx","Integrate[E^x/(1 + E^x),x]","\log \left(e^x+1\right)","\log \left(e^x+1\right)",1,"Log[1 + E^x]","A",1
20,1,9,9,0.0006545,"\int x^{3/2} \, dx","Integrate[x^(3/2),x]","\frac{2 x^{5/2}}{5}","\frac{2 x^{5/2}}{5}",1,"(2*x^(5/2))/5","A",1
21,1,10,10,0.0050046,"\int \cos (3+2 x) \, dx","Integrate[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
22,1,8,8,0.000767,"\int 2 e^{2 x} y z \, dx","Integrate[2*E^(2*x)*y*z,x]","e^{2 x} y z","e^{2 x} y z",1,"E^(2*x)*y*z","A",1
23,1,19,10,0.0224183,"\int e^x \cos ^2\left(e^x\right) \sin \left(e^x\right) \, dx","Integrate[E^x*Cos[E^x]^2*Sin[E^x],x]","-\frac{1}{4} \cos \left(e^x\right)-\frac{1}{12} \cos \left(3 e^x\right)","-\frac{1}{3} \cos ^3\left(e^x\right)",1,"-1/4*Cos[E^x] - Cos[3*E^x]/12","A",1
24,1,16,23,0.0049043,"\int x \sqrt{1+x} \, dx","Integrate[x*Sqrt[1 + x],x]","\frac{2}{15} (x+1)^{3/2} (3 x-2)","\frac{2}{5} (x+1)^{5/2}-\frac{2}{3} (x+1)^{3/2}",1,"(2*(1 + x)^(3/2)*(-2 + 3*x))/15","A",1
25,1,25,13,0.0037973,"\int \frac{1}{-1+x^4} \, dx","Integrate[(-1 + x^4)^(-1),x]","\frac{1}{4} \log (1-x)-\frac{1}{4} \log (x+1)-\frac{1}{2} \tan ^{-1}(x)","-\frac{1}{2} \tan ^{-1}(x)-\frac{1}{2} \tanh ^{-1}(x)",1,"-1/2*ArcTan[x] + Log[1 - x]/4 - Log[1 + x]/4","A",1
26,1,18,18,0.0075151,"\int \frac{e^x}{2+3 e^{2 x}} \, dx","Integrate[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",1
27,1,31,31,0.0087265,"\int \frac{e^{2 x}}{A+B e^{4 x}} \, dx","Integrate[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",1
28,1,8,8,0.00559,"\int \frac{e^{1+x}}{1+e^x} \, dx","Integrate[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",1
29,1,12,12,0.003394,"\int (10 e)^x \, dx","Integrate[(10*E)^x,x]","\frac{(10 e)^x}{\log (10 e)}","\frac{(10 e)^x}{1+\log (10)}",1,"(10*E)^x/Log[10*E]","A",1
30,1,20,20,0.0026091,"\int x^3 \sin \left(x^2\right) \, dx","Integrate[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,"-1/2*(x^2*Cos[x^2]) + Sin[x^2]/2","A",1
31,1,260,49,0.1179051,"\int \frac{x^7}{1+x^{12}} \, dx","Integrate[x^7/(1 + x^12),x]","\frac{1}{24} \left(-2 \log \left(x^2-\sqrt{2} x+1\right)-2 \log \left(x^2+\sqrt{2} x+1\right)+\log \left(2 x^2-\sqrt{6} x+\sqrt{2} x+2\right)+\log \left(2 x^2+\sqrt{2} \left(\sqrt{3}-1\right) x+2\right)+\log \left(2 x^2-\left(\sqrt{2}+\sqrt{6}\right) x+2\right)+\log \left(2 x^2+\left(\sqrt{2}+\sqrt{6}\right) x+2\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{-2 \sqrt{2} x+\sqrt{3}+1}{1-\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt{2} x-\sqrt{3}+1}{1+\sqrt{3}}\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt{2} x+\sqrt{3}-1}{1+\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt{2} x+\sqrt{3}+1}{\sqrt{3}-1}\right)\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,"(2*Sqrt[3]*ArcTan[(1 + Sqrt[3] - 2*Sqrt[2]*x)/(1 - Sqrt[3])] - 2*Sqrt[3]*ArcTan[(1 - Sqrt[3] + 2*Sqrt[2]*x)/(1 + Sqrt[3])] + 2*Sqrt[3]*ArcTan[(-1 + Sqrt[3] + 2*Sqrt[2]*x)/(1 + Sqrt[3])] - 2*Sqrt[3]*ArcTan[(1 + Sqrt[3] + 2*Sqrt[2]*x)/(-1 + Sqrt[3])] - 2*Log[1 - Sqrt[2]*x + x^2] - 2*Log[1 + Sqrt[2]*x + x^2] + Log[2 + Sqrt[2]*x - Sqrt[6]*x + 2*x^2] + Log[2 + Sqrt[2]*(-1 + Sqrt[3])*x + 2*x^2] + Log[2 - (Sqrt[2] + Sqrt[6])*x + 2*x^2] + Log[2 + (Sqrt[2] + Sqrt[6])*x + 2*x^2])/24","B",1
32,1,142,115,0.2978394,"\int x^{3 a} \sin \left(x^{2 a}\right) \, dx","Integrate[x^(3*a)*Sin[x^(2*a)],x]","-\frac{x^{a+1} \left(x^{4 a}\right)^{-\frac{a+1}{2 a}} \left((a+1) \left(-i x^{2 a}\right)^{\frac{a+1}{2 a}} \operatorname{Gamma}\left(\frac{a+1}{2 a},i x^{2 a}\right)+(a+1) \left(i x^{2 a}\right)^{\frac{a+1}{2 a}} \operatorname{Gamma}\left(\frac{a+1}{2 a},-i x^{2 a}\right)+4 a \left(x^{4 a}\right)^{\frac{a+1}{2 a}} \cos \left(x^{2 a}\right)\right)}{8 a^2}","\frac{i x^{3 a+1} \left(-i x^{2 a}\right)^{-\frac{3 a+1}{2 a}} \operatorname{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}} \operatorname{Gamma}\left(\frac{1}{2} \left(\frac{1}{a}+3\right),i x^{2 a}\right)}{4 a}",1,"-1/8*(x^(1 + a)*(4*a*(x^(4*a))^((1 + a)/(2*a))*Cos[x^(2*a)] + (1 + a)*(I*x^(2*a))^((1 + a)/(2*a))*Gamma[(1 + a)/(2*a), (-I)*x^(2*a)] + (1 + a)*((-I)*x^(2*a))^((1 + a)/(2*a))*Gamma[(1 + a)/(2*a), I*x^(2*a)]))/(a^2*(x^(4*a))^((1 + a)/(2*a)))","A",1
33,1,22,22,0.0166696,"\int \cos \left(\sqrt{x}\right) \, dx","Integrate[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",1
34,1,16,23,0.0051345,"\int x \sqrt{1+x} \, dx","Integrate[x*Sqrt[1 + x],x]","\frac{2}{15} (x+1)^{3/2} (3 x-2)","\frac{2}{5} (x+1)^{5/2}-\frac{2}{3} (x+1)^{3/2}",1,"(2*(1 + x)^(3/2)*(-2 + 3*x))/15","A",1
35,1,32,32,0.0134045,"\int \frac{1}{\sqrt[3]{x}+\sqrt{x}} \, dx","Integrate[(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
36,1,71,44,0.0373873,"\int \sqrt{\frac{1+x}{3+2 x}} \, dx","Integrate[Sqrt[(1 + x)/(3 + 2*x)],x]","\frac{2 (x+1) \sqrt{2 x+3}-\sqrt{2} \sqrt{x+1} \sinh ^{-1}\left(\sqrt{2} \sqrt{x+1}\right)}{4 \sqrt{\frac{x+1}{2 x+3}} \sqrt{2 x+3}}","\frac{1}{2} \sqrt{x+1} \sqrt{2 x+3}-\frac{\sinh ^{-1}\left(\sqrt{2} \sqrt{x+1}\right)}{2 \sqrt{2}}",1,"(2*(1 + x)*Sqrt[3 + 2*x] - Sqrt[2]*Sqrt[1 + x]*ArcSinh[Sqrt[2]*Sqrt[1 + x]])/(4*Sqrt[(1 + x)/(3 + 2*x)]*Sqrt[3 + 2*x])","A",1
37,1,26,35,0.0254571,"\int \frac{x^4}{\left(1-x^2\right)^{5/2}} \, dx","Integrate[x^4/(1 - x^2)^(5/2),x]","\frac{x \left(4 x^2-3\right)}{3 \left(1-x^2\right)^{3/2}}+\sin ^{-1}(x)","-\frac{x}{\sqrt{1-x^2}}+\frac{x^3}{3 \left(1-x^2\right)^{3/2}}+\sin ^{-1}(x)",1,"(x*(-3 + 4*x^2))/(3*(1 - x^2)^(3/2)) + ArcSin[x]","A",1
38,1,41,75,0.0201907,"\int \sqrt{x} (1+x)^{5/2} \, dx","Integrate[Sqrt[x]*(1 + x)^(5/2),x]","\frac{1}{192} \left(\sqrt{x} \sqrt{x+1} \left(48 x^3+136 x^2+118 x+15\right)-15 \sinh ^{-1}\left(\sqrt{x}\right)\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]*Sqrt[1 + x]*(15 + 118*x + 136*x^2 + 48*x^3) - 15*ArcSinh[Sqrt[x]])/192","A",1
39,1,26,35,0.0030135,"\int \frac{x^4}{\left(1-x^2\right)^{5/2}} \, dx","Integrate[x^4/(1 - x^2)^(5/2),x]","\frac{x \left(4 x^2-3\right)}{3 \left(1-x^2\right)^{3/2}}+\sin ^{-1}(x)","-\frac{x}{\sqrt{1-x^2}}+\frac{x^3}{3 \left(1-x^2\right)^{3/2}}+\sin ^{-1}(x)",1,"(x*(-3 + 4*x^2))/(3*(1 - x^2)^(3/2)) + ArcSin[x]","A",1
40,1,134,51,0.0277238,"\int \frac{\sqrt{A^2+B^2-B^2 y^2}}{1-y^2} \, dy","Integrate[Sqrt[A^2 + B^2 - B^2*y^2]/(1 - y^2),y]","i B \log \left(2 \sqrt{A^2-B^2 y^2+B^2}-2 i B y\right)+\frac{1}{2} A \log \left(A \sqrt{A^2-B^2 y^2+B^2}+A^2-B^2 y+B^2\right)-\frac{1}{2} A \log \left(A \sqrt{A^2-B^2 y^2+B^2}+A^2+B^2 y+B^2\right)-\frac{1}{2} A \log (1-y)+\frac{1}{2} A \log (y+1)","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,"-1/2*(A*Log[1 - y]) + (A*Log[1 + y])/2 + I*B*Log[(-2*I)*B*y + 2*Sqrt[A^2 + B^2 - B^2*y^2]] + (A*Log[A^2 + B^2 - B^2*y + A*Sqrt[A^2 + B^2 - B^2*y^2]])/2 - (A*Log[A^2 + B^2 + B^2*y + A*Sqrt[A^2 + B^2 - B^2*y^2]])/2","C",1
41,1,14,14,0.0018842,"\int \sin ^2(x) \, dx","Integrate[Sin[x]^2,x]","\frac{x}{2}-\frac{1}{4} \sin (2 x)","\frac{x}{2}-\frac{1}{2} \sin (x) \cos (x)",1,"x/2 - Sin[2*x]/4","A",1
42,1,99,49,0.1120127,"\int \csc (x) \sqrt{A^2+B^2 \sin ^2(x)} \, dx","Integrate[Csc[x]*Sqrt[A^2 + B^2*Sin[x]^2],x]","\sqrt{-B^2} \log \left(\sqrt{2 A^2-B^2 \cos (2 x)+B^2}+\sqrt{2} \sqrt{-B^2} \cos (x)\right)-\sqrt{A^2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{A^2} \cos (x)}{\sqrt{2 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,"-(Sqrt[A^2]*ArcTanh[(Sqrt[2]*Sqrt[A^2]*Cos[x])/Sqrt[2*A^2 + B^2 - B^2*Cos[2*x]]]) + Sqrt[-B^2]*Log[Sqrt[2]*Sqrt[-B^2]*Cos[x] + Sqrt[2*A^2 + B^2 - B^2*Cos[2*x]]]","B",1
43,1,6,9,0.0038388,"\int \frac{1}{1+\cos (x)} \, dx","Integrate[(1 + Cos[x])^(-1),x]","\tan \left(\frac{x}{2}\right)","\frac{\sin (x)}{\cos (x)+1}",1,"Tan[x/2]","A",1
44,1,7,11,0.0011941,"\int e^x x \, dx","Integrate[E^x*x,x]","e^x (x-1)","e^x x-e^x",1,"E^x*(-1 + x)","A",1
45,1,9,9,0.0237361,"\int \frac{e^x x}{(1+x)^2} \, dx","Integrate[(E^x*x)/(1 + x)^2,x]","\frac{e^x}{x+1}","\frac{e^x}{x+1}",1,"E^x/(1 + x)","A",1
46,1,7,7,0.0063692,"\int e^{x^2} \left(1+2 x^2\right) \, dx","Integrate[E^x^2*(1 + 2*x^2),x]","e^{x^2} x","e^{x^2} x",1,"E^x^2*x","A",1
47,1,11,11,0.0015467,"\int e^{x^2} \, dx","Integrate[E^x^2,x]","\frac{1}{2} \sqrt{\pi } \operatorname{Erfi}(x)","\frac{1}{2} \sqrt{\pi } \operatorname{Erfi}(x)",1,"(Sqrt[Pi]*Erfi[x])/2","A",1
48,1,2,2,0.0042867,"\int \frac{e^x}{x} \, dx","Integrate[E^x/x,x]","\operatorname{ExpIntegralEi}(x)","\operatorname{ExpIntegralEi}(x)",1,"ExpIntegralEi[x]","A",1
49,1,40,41,0.0091357,"\int \frac{x}{1+x^3} \, dx","Integrate[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{2 x-1}{\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",1
50,1,75,47,0.0134834,"\int \frac{1}{-1+x^6} \, dx","Integrate[(-1 + x^6)^(-1),x]","\frac{1}{12} \left(\log \left(x^2-x+1\right)-\log \left(x^2+x+1\right)+2 \log (1-x)-2 \log (x+1)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)\right)","-\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,"(-2*Sqrt[3]*ArcTan[(-1 + 2*x)/Sqrt[3]] - 2*Sqrt[3]*ArcTan[(1 + 2*x)/Sqrt[3]] + 2*Log[1 - x] - 2*Log[1 + x] + Log[1 - x + x^2] - Log[1 + x + x^2])/12","A",1
51,1,21,21,0.0041961,"\int \frac{1}{A^4-A^2 B^2+\left(-A^2+B^2\right) x^2} \, dx","Integrate[(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
52,1,17,17,0.0007812,"\int x \log (x) \, dx","Integrate[x*Log[x],x]","\frac{1}{2} x^2 \log (x)-\frac{x^2}{4}","\frac{1}{2} x^2 \log (x)-\frac{x^2}{4}",1,"-1/4*x^2 + (x^2*Log[x])/2","A",1
53,1,29,40,0.0126901,"\int x^2 \sin ^{-1}(x) \, dx","Integrate[x^2*ArcSin[x],x]","\frac{1}{9} \left(3 x^3 \sin ^{-1}(x)+\sqrt{1-x^2} \left(x^2+2\right)\right)","\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,"(Sqrt[1 - x^2]*(2 + x^2) + 3*x^3*ArcSin[x])/9","A",1
54,1,7,7,0.000976,"\int \frac{1}{1+2 x+x^2} \, dx","Integrate[(1 + 2*x + x^2)^(-1),x]","-\frac{1}{x+1}","-\frac{1}{x+1}",1,"-(1 + x)^(-1)","A",1
55,1,8,8,0.0154532,"\int \frac{\log (x)}{(1+\log (x))^2} \, dx","Integrate[Log[x]/(1 + Log[x])^2,x]","\frac{x}{\log (x)+1}","\frac{x}{\log (x)+1}",1,"x/(1 + Log[x])","A",1
56,1,3,3,0.0115532,"\int \frac{1}{x \left(1+\log ^2(x)\right)} \, dx","Integrate[1/(x*(1 + Log[x]^2)),x]","\tan ^{-1}(\log (x))","\tan ^{-1}(\log (x))",1,"ArcTan[Log[x]]","A",1
57,0,0,2,0.0016182,"\int \frac{1}{\log (x)} \, dx","Integrate[Log[x]^(-1),x]","\int \frac{1}{\log (x)} \, dx","\operatorname{LogIntegral}(x)",1,"Integrate[Log[x]^(-1), x]","F",-1
58,1,14,14,0.0048778,"\int x (\cos (x)+\sin (x)) \, dx","Integrate[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",1
59,1,13,17,0.0103967,"\int e^{-x} \left(e^x+x\right) \, dx","Integrate[(E^x + x)/E^x,x]","e^{-x} (-x-1)+x","-e^{-x} x+x-e^{-x}",1,"(-1 - x)/E^x + x","A",1
60,1,29,38,0.0283074,"\int \left(1+e^x\right)^2 x \, dx","Integrate[(1 + E^x)^2*x,x]","\frac{1}{4} \left(2 x^2+8 e^x (x-1)+e^{2 x} (2 x-1)\right)","\frac{x^2}{2}+2 e^x x+\frac{1}{2} e^{2 x} x-2 e^x-\frac{e^{2 x}}{4}",1,"(8*E^x*(-1 + x) + 2*x^2 + E^(2*x)*(-1 + 2*x))/4","A",1
61,1,7,7,0.0024684,"\int x \cos (x) \, dx","Integrate[x*Cos[x],x]","x \sin (x)+\cos (x)","x \sin (x)+\cos (x)",1,"Cos[x] + x*Sin[x]","A",1
62,1,22,22,0.0126571,"\int \cos \left(\sqrt{x}\right) \, dx","Integrate[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",1
63,1,7,7,0.0020537,"\int x \cos (x) \, dx","Integrate[x*Cos[x],x]","x \sin (x)+\cos (x)","x \sin (x)+\cos (x)",1,"Cos[x] + x*Sin[x]","A",1
64,1,28,28,0.0011649,"\int x \log ^2(x) \, dx","Integrate[x*Log[x]^2,x]","\frac{x^2}{4}+\frac{1}{2} x^2 \log ^2(x)-\frac{1}{2} x^2 \log (x)","\frac{x^2}{4}+\frac{1}{2} x^2 \log ^2(x)-\frac{1}{2} x^2 \log (x)",1,"x^2/4 - (x^2*Log[x])/2 + (x^2*Log[x]^2)/2","A",1
65,1,11,11,0.0036173,"\int \cos (x) \left(1+\sin ^3(x)\right) \, dx","Integrate[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",1
66,1,3,3,0.0096686,"\int \frac{1}{x \left(1+\log ^2(x)\right)} \, dx","Integrate[1/(x*(1 + Log[x]^2)),x]","\tan ^{-1}(\log (x))","\tan ^{-1}(\log (x))",1,"ArcTan[Log[x]]","A",1
67,1,3,3,0.059426,"\int \frac{1}{\sqrt{1-x^2} \left(1+\sin ^{-1}(x)^2\right)} \, dx","Integrate[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",1
68,1,16,16,0.0222709,"\int \frac{\sin (x)}{\cos (x)+\sin (x)} \, dx","Integrate[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",1
69,1,127,53,0.057242,"\int -\frac{\sqrt{A^2+B^2 \left(1-y^2\right)}}{1-y^2} \, dy","Integrate[-(Sqrt[A^2 + B^2*(1 - y^2)]/(1 - y^2)),y]","\frac{1}{2} \left(-2 i B \log \left(2 \left(\sqrt{A^2-B^2 y^2+B^2}-i B y\right)\right)-A \log \left(A \sqrt{A^2-B^2 y^2+B^2}+A^2-B^2 y+B^2\right)+A \log \left(A \sqrt{A^2-B^2 y^2+B^2}+A^2+B^2 (y+1)\right)+A \log (1-y)-A \log (y+1)\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,"(A*Log[1 - y] - A*Log[1 + y] - (2*I)*B*Log[2*((-I)*B*y + Sqrt[A^2 + B^2 - B^2*y^2])] - A*Log[A^2 + B^2 - B^2*y + A*Sqrt[A^2 + B^2 - B^2*y^2]] + A*Log[A^2 + B^2*(1 + y) + A*Sqrt[A^2 + B^2 - B^2*y^2]])/2","C",1
70,1,35,16,0.0976533,"\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","Integrate[((-A^2 - B^2)*Cos[z]^2)/(B*(1 - ((A^2 + B^2)*Sin[z]^2)/B^2)),z]","-\frac{B \left(A^2+B^2\right) \left(A \tanh ^{-1}\left(\frac{A \tan (z)}{B}\right)+B z\right)}{A^2 B+B^3}","-A \tanh ^{-1}\left(\frac{A \tan (z)}{B}\right)-B z",1,"-((B*(A^2 + B^2)*(B*z + A*ArcTanh[(A*Tan[z])/B]))/(A^2*B + B^3))","B",1
71,1,35,16,0.0192355,"\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","Integrate[(-A^2 - B^2)/(B*(1 + w^2)^2*(1 - ((A^2 + B^2)*w^2)/(B^2*(1 + w^2)))),w]","-\frac{B \left(A^2+B^2\right) \left(A \tanh ^{-1}\left(\frac{A w}{B}\right)+B \tan ^{-1}(w)\right)}{A^2 B+B^3}","-A \tanh ^{-1}\left(\frac{A w}{B}\right)-B \tan ^{-1}(w)",1,"-((B*(A^2 + B^2)*(B*ArcTan[w] + A*ArcTanh[(A*w)/B]))/(A^2*B + B^3))","B",1
72,1,35,16,0.0130743,"\int -\frac{B \left(A^2+B^2\right)}{\left(1+w^2\right) \left(B^2-A^2 w^2\right)} \, dw","Integrate[-((B*(A^2 + B^2))/((1 + w^2)*(B^2 - A^2*w^2))),w]","-\frac{B \left(A^2+B^2\right) \left(A \tanh ^{-1}\left(\frac{A w}{B}\right)+B \tan ^{-1}(w)\right)}{A^2 B+B^3}","-A \tanh ^{-1}\left(\frac{A w}{B}\right)-B \tan ^{-1}(w)",1,"-((B*(A^2 + B^2)*(B*ArcTan[w] + A*ArcTanh[(A*w)/B]))/(A^2*B + B^3))","B",1
73,1,26,35,0.0208842,"\int \frac{x^4}{\left(1-x^2\right)^{5/2}} \, dx","Integrate[x^4/(1 - x^2)^(5/2),x]","\frac{x \left(4 x^2-3\right)}{3 \left(1-x^2\right)^{3/2}}+\sin ^{-1}(x)","-\frac{x}{\sqrt{1-x^2}}+\frac{x^3}{3 \left(1-x^2\right)^{3/2}}+\sin ^{-1}(x)",1,"(x*(-3 + 4*x^2))/(3*(1 - x^2)^(3/2)) + ArcSin[x]","A",1
74,1,18,14,0.0068382,"\int \tan ^4(y) \, dy","Integrate[Tan[y]^4,y]","y-\frac{4 \tan (y)}{3}+\frac{1}{3} \tan (y) \sec ^2(y)","y+\frac{\tan ^3(y)}{3}-\tan (y)",1,"y - (4*Tan[y])/3 + (Sec[y]^2*Tan[y])/3","A",1
75,1,13,13,0.0041691,"\int \frac{z^4}{1+z^2} \, dz","Integrate[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",1
76,1,7,7,0.0053713,"\int e^{x^2} \left(1+2 x^2\right) \, dx","Integrate[E^x^2*(1 + 2*x^2),x]","e^{x^2} x","e^{x^2} x",1,"E^x^2*x","A",1
77,1,20,24,0.0733762,"\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","Integrate[(E^x^2*(1 + 4*x^2 + x^3 + 5*x^4 + 2*x^6))/(1 + x^2)^2,x]","\frac{1}{2} e^{x^2} \left(\frac{1}{x^2+1}+2 x\right)","e^{x^2} x+\frac{e^{x^2}}{2 \left(x^2+1\right)}",1,"(E^x^2*(2*x + (1 + x^2)^(-1)))/2","A",1
78,1,9,9,0.0028805,"\int e^{-1-x} \, dx","Integrate[E^(-1 - x),x]","-e^{-x-1}","-e^{-x-1}",1,"-E^(-1 - x)","A",1
79,1,25,25,0.0020066,"\int \left(\frac{1}{x}+x\right) \log (x) \, dx","Integrate[(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,"-1/4*x^2 + (x^2*Log[x])/2 + Log[x]^2/2","A",1
80,1,8,8,0.0033439,"\int \frac{x}{1+x^4} \, dx","Integrate[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
81,1,16,16,0.0037728,"\int \frac{x^5}{1+x^4} \, dx","Integrate[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
82,1,14,14,0.0024624,"\int \frac{1}{1+\tan ^2(x)} \, dx","Integrate[(1 + Tan[x]^2)^(-1),x]","\frac{x}{2}+\frac{1}{4} \sin (2 x)","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"x/2 + Sin[2*x]/4","A",1
83,1,26,35,0.0030478,"\int \frac{x^4}{\left(1-x^2\right)^{5/2}} \, dx","Integrate[x^4/(1 - x^2)^(5/2),x]","\frac{x \left(4 x^2-3\right)}{3 \left(1-x^2\right)^{3/2}}+\sin ^{-1}(x)","-\frac{x}{\sqrt{1-x^2}}+\frac{x^3}{3 \left(1-x^2\right)^{3/2}}+\sin ^{-1}(x)",1,"(x*(-3 + 4*x^2))/(3*(1 - x^2)^(3/2)) + ArcSin[x]","A",1
84,1,32,17,0.0079973,"\int -\frac{x^2}{\left(1-x^2\right)^{3/2}} \, dx","Integrate[-(x^2/(1 - x^2)^(3/2)),x]","\frac{\sqrt{1-x^2} x+x^2 \sin ^{-1}(x)-\sin ^{-1}(x)}{x^2-1}","\sin ^{-1}(x)-\frac{x}{\sqrt{1-x^2}}",1,"(x*Sqrt[1 - x^2] - ArcSin[x] + x^2*ArcSin[x])/(-1 + x^2)","A",1
85,1,14,19,0.0145245,"\int e^x \sin (x) \, dx","Integrate[E^x*Sin[x],x]","\frac{1}{2} e^x (\sin (x)-\cos (x))","\frac{1}{2} e^x \sin (x)-\frac{1}{2} e^x \cos (x)",1,"(E^x*(-Cos[x] + Sin[x]))/2","A",1
86,1,2,2,0.0001519,"\int \frac{1}{x} \, dx","Integrate[x^(-1),x]","\log (x)","\log (x)",1,"Log[x]","A",1
87,1,73,45,0.1928517,"\int \frac{\sec (2 t)}{1+\sec ^2(t)+3 \tan (t)} \, dt","Integrate[Sec[2*t]/(1 + Sec[t]^2 + 3*Tan[t]),t]","-\frac{\cos (t) (\log (\cos (t)-\sin (t))+3 \log (\sin (t)+\cos (t))-4 \log (\sin (t)+2 \cos (t)))+\sin (t) (\log (\cos (t)-\sin (t))+3 \log (\sin (t)+\cos (t))-4 \log (\sin (t)+2 \cos (t))-6)}{12 (\sin (t)+\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,"-1/12*(Cos[t]*(Log[Cos[t] - Sin[t]] + 3*Log[Cos[t] + Sin[t]] - 4*Log[2*Cos[t] + Sin[t]]) + (-6 + Log[Cos[t] - Sin[t]] + 3*Log[Cos[t] + Sin[t]] - 4*Log[2*Cos[t] + Sin[t]])*Sin[t])/(Cos[t] + Sin[t])","A",1
88,1,14,14,0.0018822,"\int \cos ^2(x) \, dx","Integrate[Cos[x]^2,x]","\frac{x}{2}+\frac{1}{4} \sin (2 x)","\frac{x}{2}+\frac{1}{2} \sin (x) \cos (x)",1,"x/2 + Sin[2*x]/4","A",1
89,1,14,17,0.0036064,"\int \frac{1+x^2}{\sqrt{x}} \, dx","Integrate[(1 + x^2)/Sqrt[x],x]","\frac{2}{5} \sqrt{x} \left(x^2+5\right)","\frac{2 x^{5/2}}{5}+2 \sqrt{x}",1,"(2*Sqrt[x]*(5 + x^2))/5","A",1
90,1,25,23,0.0053208,"\int \frac{x}{\sqrt{5+2 x+x^2}} \, dx","Integrate[x/Sqrt[5 + 2*x + x^2],x]","\sqrt{x^2+2 x+5}-\sinh ^{-1}\left(\frac{1}{4} (2 x+2)\right)","\sqrt{x^2+2 x+5}-\sinh ^{-1}\left(\frac{x+1}{2}\right)",1,"Sqrt[5 + 2*x + x^2] - ArcSinh[(2 + 2*x)/4]","A",1
91,1,8,8,0.0012453,"\int \cos (x) \sin ^2(x) \, dx","Integrate[Cos[x]*Sin[x]^2,x]","\frac{\sin ^3(x)}{3}","\frac{\sin ^3(x)}{3}",1,"Sin[x]^3/3","A",1
92,1,6,6,0.0045462,"\int \frac{e^x}{1+e^x} \, dx","Integrate[E^x/(1 + E^x),x]","\log \left(e^x+1\right)","\log \left(e^x+1\right)",1,"Log[1 + E^x]","A",1
93,1,12,12,0.0082988,"\int \frac{e^{2 x}}{1+e^x} \, dx","Integrate[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",1
94,1,8,12,0.009319,"\int \frac{1}{1-\cos (x)} \, dx","Integrate[(1 - Cos[x])^(-1),x]","-\cot \left(\frac{x}{2}\right)","-\frac{\sin (x)}{1-\cos (x)}",1,"-Cot[x/2]","A",1
95,1,8,8,0.005212,"\int \sec ^2(x) \tan (x) \, dx","Integrate[Sec[x]^2*Tan[x],x]","\frac{\sec ^2(x)}{2}","\frac{\sec ^2(x)}{2}",1,"Sec[x]^2/2","A",1
96,1,17,17,0.0007221,"\int x \log (x) \, dx","Integrate[x*Log[x],x]","\frac{1}{2} x^2 \log (x)-\frac{x^2}{4}","\frac{1}{2} x^2 \log (x)-\frac{x^2}{4}",1,"-1/4*x^2 + (x^2*Log[x])/2","A",1
97,1,8,8,0.0014788,"\int \cos (x) \sin (x) \, dx","Integrate[Cos[x]*Sin[x],x]","-\frac{1}{2} \cos ^2(x)","\frac{\sin ^2(x)}{2}",1,"-1/2*Cos[x]^2","A",1
98,1,27,24,0.0321697,"\int \frac{1+x}{\sqrt{2 x-x^2}} \, dx","Integrate[(1 + x)/Sqrt[2*x - x^2],x]","-\sqrt{-((x-2) x)}-4 \sin ^{-1}\left(\sqrt{1-\frac{x}{2}}\right)","-\sqrt{2 x-x^2}-2 \sin ^{-1}(1-x)",1,"-Sqrt[-((-2 + x)*x)] - 4*ArcSin[Sqrt[1 - x/2]]","A",1
99,1,20,20,0.0060995,"\int \frac{2 e^x}{2+3 e^{2 x}} \, dx","Integrate[(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",1
100,1,26,35,0.0033569,"\int \frac{x^4}{\left(1-x^2\right)^{5/2}} \, dx","Integrate[x^4/(1 - x^2)^(5/2),x]","\frac{x \left(4 x^2-3\right)}{3 \left(1-x^2\right)^{3/2}}+\sin ^{-1}(x)","-\frac{x}{\sqrt{1-x^2}}+\frac{x^3}{3 \left(1-x^2\right)^{3/2}}+\sin ^{-1}(x)",1,"(x*(-3 + 4*x^2))/(3*(1 - x^2)^(3/2)) + ArcSin[x]","A",1
101,1,18,20,0.0084013,"\int \frac{e^{6 x}}{1+e^{4 x}} \, dx","Integrate[E^(6*x)/(1 + E^(4*x)),x]","\frac{1}{2} \left(e^{2 x}-\tan ^{-1}\left(e^{2 x}\right)\right)","\frac{e^{2 x}}{2}-\frac{1}{2} \tan ^{-1}\left(e^{2 x}\right)",1,"(E^(2*x) - ArcTan[E^(2*x)])/2","A",1
102,1,33,33,0.0132515,"\int \log \left(2+3 x^2\right) \, dx","Integrate[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",1
103,1,21,21,0.0000782,"\int \frac{1}{r \sqrt{-a^2+2 H r^2}} \, dx","Integrate[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
104,1,26,26,0.0000913,"\int \frac{1}{r \sqrt{-a^2-e^2+2 H r^2}} \, dx","Integrate[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
105,1,27,27,0.0000751,"\int \frac{1}{r \sqrt{-a^2+2 H r^2-2 K r^4}} \, dx","Integrate[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
106,1,32,32,0.0000831,"\int \frac{1}{r \sqrt{-a^2-e^2+2 H r^2-2 K r^4}} \, dx","Integrate[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
107,1,25,24,0.0001125,"\int \frac{1}{r \sqrt{-a^2-2 K r+2 H r^2}} \, dx","Integrate[1/(r*Sqrt[-a^2 - 2*K*r + 2*H*r^2]),x]","\frac{x}{r \sqrt{-a^2+2 H r^2-2 K r}}","\frac{x}{r \sqrt{-a^2-2 r (K-H r)}}",1,"x/(r*Sqrt[-a^2 - 2*K*r + 2*H*r^2])","A",1
108,1,30,29,0.0000818,"\int \frac{1}{r \sqrt{-a^2-e^2-2 K r+2 H r^2}} \, dx","Integrate[1/(r*Sqrt[-a^2 - e^2 - 2*K*r + 2*H*r^2]),x]","\frac{x}{r \sqrt{-a^2-e^2+2 H r^2-2 K r}}","\frac{x}{r \sqrt{-a^2-e^2-2 r (K-H r)}}",1,"x/(r*Sqrt[-a^2 - e^2 - 2*K*r + 2*H*r^2])","A",1
109,1,19,19,0.0001044,"\int \frac{r}{\sqrt{-a^2+2 e r^2}} \, dx","Integrate[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
110,1,24,24,0.0000726,"\int \frac{r}{\sqrt{-a^2-e^2+2 e r^2}} \, dx","Integrate[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
111,1,25,25,0.0000755,"\int \frac{r}{\sqrt{-a^2+2 e r^2-2 K r^4}} \, dx","Integrate[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
112,1,30,30,0.0000853,"\int \frac{r}{\sqrt{-a^2-e^2+2 e r^2-2 K r^4}} \, dx","Integrate[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
113,1,28,27,0.0000747,"\int \frac{r}{\sqrt{-a^2-e^2-2 K r+2 H r^2}} \, dx","Integrate[r/Sqrt[-a^2 - e^2 - 2*K*r + 2*H*r^2],x]","\frac{r x}{\sqrt{-a^2-e^2+2 H r^2-2 K r}}","\frac{r x}{\sqrt{-a^2-e^2-2 r (K-H r)}}",1,"(r*x)/Sqrt[-a^2 - e^2 - 2*K*r + 2*H*r^2]","A",1