1,1,42,0,0.0408917,"\int x^3 \tan ^{-1}\left(a+b x^4\right) \, dx","Int[x^3*ArcTan[a + b*x^4],x]","\frac{\left(a+b x^4\right) \tan ^{-1}\left(a+b x^4\right)}{4 b}-\frac{\log \left(\left(a+b x^4\right)^2+1\right)}{8 b}","\frac{\left(a+b x^4\right) \tan ^{-1}\left(a+b x^4\right)}{4 b}-\frac{\log \left(\left(a+b x^4\right)^2+1\right)}{8 b}",1,"((a + b*x^4)*ArcTan[a + b*x^4])/(4*b) - Log[1 + (a + b*x^4)^2]/(8*b)","A",4,4,12,0.3333,1,"{6715, 5039, 4846, 260}"
2,1,45,0,0.0421264,"\int x^{-1+n} \tan ^{-1}\left(a+b x^n\right) \, dx","Int[x^(-1 + n)*ArcTan[a + b*x^n],x]","\frac{\left(a+b x^n\right) \tan ^{-1}\left(a+b x^n\right)}{b n}-\frac{\log \left(\left(a+b x^n\right)^2+1\right)}{2 b n}","\frac{\left(a+b x^n\right) \tan ^{-1}\left(a+b x^n\right)}{b n}-\frac{\log \left(\left(a+b x^n\right)^2+1\right)}{2 b n}",1,"((a + b*x^n)*ArcTan[a + b*x^n])/(b*n) - Log[1 + (a + b*x^n)^2]/(2*b*n)","A",4,4,14,0.2857,1,"{6715, 5039, 4846, 260}"
3,1,144,0,0.0801685,"\int x^5 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^5*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]],x]","\frac{5 d^3 \sqrt{-e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{96 e^{7/2}}+\frac{5 d^2 x \sqrt{d+e x^2}}{96 (-e)^{5/2}}+\frac{x^5 \sqrt{d+e x^2}}{36 \sqrt{-e}}+\frac{5 d x^3 \sqrt{d+e x^2}}{144 (-e)^{3/2}}+\frac{1}{6} x^6 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)","\frac{5 d^3 \sqrt{-e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{96 e^{7/2}}+\frac{5 d^2 x \sqrt{d+e x^2}}{96 (-e)^{5/2}}+\frac{x^5 \sqrt{d+e x^2}}{36 \sqrt{-e}}+\frac{5 d x^3 \sqrt{d+e x^2}}{144 (-e)^{3/2}}+\frac{1}{6} x^6 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)",1,"(5*d^2*x*Sqrt[d + e*x^2])/(96*(-e)^(5/2)) + (5*d*x^3*Sqrt[d + e*x^2])/(144*(-e)^(3/2)) + (x^5*Sqrt[d + e*x^2])/(36*Sqrt[-e]) + (x^6*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/6 + (5*d^3*Sqrt[-e]*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(96*e^(7/2))","A",6,4,25,0.1600,1,"{5151, 321, 217, 206}"
4,1,116,0,0.0419833,"\int x^3 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^3*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]],x]","-\frac{3 d^2 \sqrt{-e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{32 e^{5/2}}+\frac{x^3 \sqrt{d+e x^2}}{16 \sqrt{-e}}+\frac{3 d x \sqrt{d+e x^2}}{32 (-e)^{3/2}}+\frac{1}{4} x^4 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)","-\frac{3 d^2 \sqrt{-e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{32 e^{5/2}}+\frac{x^3 \sqrt{d+e x^2}}{16 \sqrt{-e}}+\frac{3 d x \sqrt{d+e x^2}}{32 (-e)^{3/2}}+\frac{1}{4} x^4 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)",1,"(3*d*x*Sqrt[d + e*x^2])/(32*(-e)^(3/2)) + (x^3*Sqrt[d + e*x^2])/(16*Sqrt[-e]) + (x^4*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/4 - (3*d^2*Sqrt[-e]*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(32*e^(5/2))","A",5,4,25,0.1600,1,"{5151, 321, 217, 206}"
5,1,88,0,0.0286042,"\int x \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]],x]","\frac{d \sqrt{-e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{4 e^{3/2}}+\frac{x \sqrt{d+e x^2}}{4 \sqrt{-e}}+\frac{1}{2} x^2 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)","\frac{d \sqrt{-e} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{4 e^{3/2}}+\frac{x \sqrt{d+e x^2}}{4 \sqrt{-e}}+\frac{1}{2} x^2 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)",1,"(x*Sqrt[d + e*x^2])/(4*Sqrt[-e]) + (x^2*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/2 + (d*Sqrt[-e]*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(4*e^(3/2))","A",4,4,23,0.1739,1,"{5151, 321, 217, 206}"
6,1,288,0,0.1668008,"\int \frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{x} \, dx","Int[ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/x,x]","\frac{\sqrt{d} \sqrt{-e} \sqrt{\frac{e x^2}{d}+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 \sqrt{e} \sqrt{d+e x^2}}-\frac{\sqrt{d} \sqrt{-e} \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{2 \sqrt{e} \sqrt{d+e x^2}}+\log (x) \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)+\frac{\sqrt{d} \sqrt{-e} \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{\sqrt{e} \sqrt{d+e x^2}}-\frac{\sqrt{d} \sqrt{-e} \log (x) \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e} \sqrt{d+e x^2}}","\frac{\sqrt{d} \sqrt{-e} \sqrt{\frac{e x^2}{d}+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{2 \sqrt{e} \sqrt{d+e x^2}}-\frac{\sqrt{d} \sqrt{-e} \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{2 \sqrt{e} \sqrt{d+e x^2}}+\log (x) \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)+\frac{\sqrt{d} \sqrt{-e} \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}\right)}{\sqrt{e} \sqrt{d+e x^2}}-\frac{\sqrt{d} \sqrt{-e} \log (x) \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e} \sqrt{d+e x^2}}",1,"-(Sqrt[d]*Sqrt[-e]*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]^2)/(2*Sqrt[e]*Sqrt[d + e*x^2]) + (Sqrt[d]*Sqrt[-e]*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[1 - E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(Sqrt[e]*Sqrt[d + e*x^2]) - (Sqrt[d]*Sqrt[-e]*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[x])/(Sqrt[e]*Sqrt[d + e*x^2]) + ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]*Log[x] + (Sqrt[d]*Sqrt[-e]*Sqrt[1 + (e*x^2)/d]*PolyLog[2, E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(2*Sqrt[e]*Sqrt[d + e*x^2])","A",8,8,25,0.3200,1,"{5149, 2327, 2325, 5659, 3716, 2190, 2279, 2391}"
7,1,57,0,0.0187291,"\int \frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{x^3} \, dx","Int[ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/x^3,x]","-\frac{\sqrt{-e} \sqrt{d+e x^2}}{2 d x}-\frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{2 x^2}","-\frac{\sqrt{-e} \sqrt{d+e x^2}}{2 d x}-\frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{2 x^2}",1,"-(Sqrt[-e]*Sqrt[d + e*x^2])/(2*d*x) - ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/(2*x^2)","A",2,2,25,0.08000,1,"{5151, 264}"
8,1,85,0,0.0281823,"\int \frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{x^5} \, dx","Int[ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/x^5,x]","-\frac{(-e)^{3/2} \sqrt{d+e x^2}}{6 d^2 x}-\frac{\sqrt{-e} \sqrt{d+e x^2}}{12 d x^3}-\frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{4 x^4}","-\frac{(-e)^{3/2} \sqrt{d+e x^2}}{6 d^2 x}-\frac{\sqrt{-e} \sqrt{d+e x^2}}{12 d x^3}-\frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{4 x^4}",1,"-(Sqrt[-e]*Sqrt[d + e*x^2])/(12*d*x^3) - ((-e)^(3/2)*Sqrt[d + e*x^2])/(6*d^2*x) - ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/(4*x^4)","A",3,3,25,0.1200,1,"{5151, 271, 264}"
9,1,113,0,0.0385326,"\int \frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{x^7} \, dx","Int[ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/x^7,x]","-\frac{4 (-e)^{5/2} \sqrt{d+e x^2}}{45 d^3 x}-\frac{2 (-e)^{3/2} \sqrt{d+e x^2}}{45 d^2 x^3}-\frac{\sqrt{-e} \sqrt{d+e x^2}}{30 d x^5}-\frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{6 x^6}","-\frac{4 (-e)^{5/2} \sqrt{d+e x^2}}{45 d^3 x}-\frac{2 (-e)^{3/2} \sqrt{d+e x^2}}{45 d^2 x^3}-\frac{\sqrt{-e} \sqrt{d+e x^2}}{30 d x^5}-\frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{6 x^6}",1,"-(Sqrt[-e]*Sqrt[d + e*x^2])/(30*d*x^5) - (2*(-e)^(3/2)*Sqrt[d + e*x^2])/(45*d^2*x^3) - (4*(-e)^(5/2)*Sqrt[d + e*x^2])/(45*d^3*x) - ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/(6*x^6)","A",4,3,25,0.1200,1,"{5151, 271, 264}"
10,1,141,0,0.0495252,"\int \frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{x^9} \, dx","Int[ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/x^9,x]","-\frac{2 (-e)^{7/2} \sqrt{d+e x^2}}{35 d^4 x}-\frac{(-e)^{5/2} \sqrt{d+e x^2}}{35 d^3 x^3}-\frac{3 (-e)^{3/2} \sqrt{d+e x^2}}{140 d^2 x^5}-\frac{\sqrt{-e} \sqrt{d+e x^2}}{56 d x^7}-\frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{8 x^8}","-\frac{2 (-e)^{7/2} \sqrt{d+e x^2}}{35 d^4 x}-\frac{(-e)^{5/2} \sqrt{d+e x^2}}{35 d^3 x^3}-\frac{3 (-e)^{3/2} \sqrt{d+e x^2}}{140 d^2 x^5}-\frac{\sqrt{-e} \sqrt{d+e x^2}}{56 d x^7}-\frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{8 x^8}",1,"-(Sqrt[-e]*Sqrt[d + e*x^2])/(56*d*x^7) - (3*(-e)^(3/2)*Sqrt[d + e*x^2])/(140*d^2*x^5) - ((-e)^(5/2)*Sqrt[d + e*x^2])/(35*d^3*x^3) - (2*(-e)^(7/2)*Sqrt[d + e*x^2])/(35*d^4*x) - ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/(8*x^8)","A",5,3,25,0.1200,1,"{5151, 271, 264}"
11,1,124,0,0.0670544,"\int x^6 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^6*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]],x]","-\frac{d^2 \left(d+e x^2\right)^{3/2}}{7 (-e)^{7/2}}+\frac{d^3 \sqrt{d+e x^2}}{7 (-e)^{7/2}}-\frac{\left(d+e x^2\right)^{7/2}}{49 (-e)^{7/2}}+\frac{3 d \left(d+e x^2\right)^{5/2}}{35 (-e)^{7/2}}+\frac{1}{7} x^7 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)","-\frac{d^2 \left(d+e x^2\right)^{3/2}}{7 (-e)^{7/2}}+\frac{d^3 \sqrt{d+e x^2}}{7 (-e)^{7/2}}-\frac{\left(d+e x^2\right)^{7/2}}{49 (-e)^{7/2}}+\frac{3 d \left(d+e x^2\right)^{5/2}}{35 (-e)^{7/2}}+\frac{1}{7} x^7 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)",1,"(d^3*Sqrt[d + e*x^2])/(7*(-e)^(7/2)) - (d^2*(d + e*x^2)^(3/2))/(7*(-e)^(7/2)) + (3*d*(d + e*x^2)^(5/2))/(35*(-e)^(7/2)) - (d + e*x^2)^(7/2)/(49*(-e)^(7/2)) + (x^7*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/7","A",4,3,25,0.1200,1,"{5151, 266, 43}"
12,1,99,0,0.0505896,"\int x^4 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^4*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]],x]","\frac{d^2 \sqrt{d+e x^2}}{5 (-e)^{5/2}}+\frac{\left(d+e x^2\right)^{5/2}}{25 (-e)^{5/2}}-\frac{2 d \left(d+e x^2\right)^{3/2}}{15 (-e)^{5/2}}+\frac{1}{5} x^5 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)","\frac{d^2 \sqrt{d+e x^2}}{5 (-e)^{5/2}}+\frac{\left(d+e x^2\right)^{5/2}}{25 (-e)^{5/2}}-\frac{2 d \left(d+e x^2\right)^{3/2}}{15 (-e)^{5/2}}+\frac{1}{5} x^5 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)",1,"(d^2*Sqrt[d + e*x^2])/(5*(-e)^(5/2)) - (2*d*(d + e*x^2)^(3/2))/(15*(-e)^(5/2)) + (d + e*x^2)^(5/2)/(25*(-e)^(5/2)) + (x^5*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/5","A",4,3,25,0.1200,1,"{5151, 266, 43}"
13,1,74,0,0.0362828,"\int x^2 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^2*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]],x]","-\frac{\left(d+e x^2\right)^{3/2}}{9 (-e)^{3/2}}+\frac{d \sqrt{d+e x^2}}{3 (-e)^{3/2}}+\frac{1}{3} x^3 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)","-\frac{\left(d+e x^2\right)^{3/2}}{9 (-e)^{3/2}}+\frac{d \sqrt{d+e x^2}}{3 (-e)^{3/2}}+\frac{1}{3} x^3 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)",1,"(d*Sqrt[d + e*x^2])/(3*(-e)^(3/2)) - (d + e*x^2)^(3/2)/(9*(-e)^(3/2)) + (x^3*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/3","A",4,3,25,0.1200,1,"{5151, 266, 43}"
14,1,43,0,0.0101861,"\int \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]],x]","\frac{\sqrt{d+e x^2}}{\sqrt{-e}}+x \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)","\frac{\sqrt{d+e x^2}}{\sqrt{-e}}+x \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)",1,"Sqrt[d + e*x^2]/Sqrt[-e] + x*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]","A",2,2,21,0.09524,1,"{5147, 261}"
15,1,59,0,0.0329614,"\int \frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{x^2} \, dx","Int[ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/x^2,x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{x}-\frac{\sqrt{-e} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{\sqrt{d}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{x}-\frac{\sqrt{-e} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{\sqrt{d}}",1,"-(ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/x) - (Sqrt[-e]*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/Sqrt[d]","A",4,4,25,0.1600,1,"{5151, 266, 63, 208}"
16,1,91,0,0.0460897,"\int \frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{x^4} \, dx","Int[ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/x^4,x]","-\frac{(-e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{6 d^{3/2}}-\frac{\sqrt{-e} \sqrt{d+e x^2}}{6 d x^2}-\frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{3 x^3}","-\frac{(-e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{6 d^{3/2}}-\frac{\sqrt{-e} \sqrt{d+e x^2}}{6 d x^2}-\frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{3 x^3}",1,"-(Sqrt[-e]*Sqrt[d + e*x^2])/(6*d*x^2) - ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/(3*x^3) - ((-e)^(3/2)*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(6*d^(3/2))","A",5,5,25,0.2000,1,"{5151, 266, 51, 63, 208}"
17,1,119,0,0.0599371,"\int \frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{x^6} \, dx","Int[ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/x^6,x]","-\frac{3 (-e)^{3/2} \sqrt{d+e x^2}}{40 d^2 x^2}-\frac{3 (-e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{40 d^{5/2}}-\frac{\sqrt{-e} \sqrt{d+e x^2}}{20 d x^4}-\frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{5 x^5}","-\frac{3 (-e)^{3/2} \sqrt{d+e x^2}}{40 d^2 x^2}-\frac{3 (-e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{40 d^{5/2}}-\frac{\sqrt{-e} \sqrt{d+e x^2}}{20 d x^4}-\frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{5 x^5}",1,"-(Sqrt[-e]*Sqrt[d + e*x^2])/(20*d*x^4) - (3*(-e)^(3/2)*Sqrt[d + e*x^2])/(40*d^2*x^2) - ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/(5*x^5) - (3*(-e)^(5/2)*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/(40*d^(5/2))","A",6,5,25,0.2000,1,"{5151, 266, 51, 63, 208}"
18,1,211,0,0.1202927,"\int x^{9/2} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^(9/2)*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]],x]","\frac{30 d^{11/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} \text{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right),\frac{1}{2}\right)}{847 e^{13/4} \sqrt{d+e x^2}}+\frac{60 d^2 \sqrt{x} \sqrt{d+e x^2}}{847 (-e)^{5/2}}+\frac{4 x^{9/2} \sqrt{d+e x^2}}{121 \sqrt{-e}}+\frac{36 d x^{5/2} \sqrt{d+e x^2}}{847 (-e)^{3/2}}+\frac{2}{11} x^{11/2} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)","\frac{30 d^{11/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} \text{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right),\frac{1}{2}\right)}{847 e^{13/4} \sqrt{d+e x^2}}+\frac{60 d^2 \sqrt{x} \sqrt{d+e x^2}}{847 (-e)^{5/2}}+\frac{4 x^{9/2} \sqrt{d+e x^2}}{121 \sqrt{-e}}+\frac{36 d x^{5/2} \sqrt{d+e x^2}}{847 (-e)^{3/2}}+\frac{2}{11} x^{11/2} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)",1,"(60*d^2*Sqrt[x]*Sqrt[d + e*x^2])/(847*(-e)^(5/2)) + (36*d*x^(5/2)*Sqrt[d + e*x^2])/(847*(-e)^(3/2)) + (4*x^(9/2)*Sqrt[d + e*x^2])/(121*Sqrt[-e]) + (2*x^(11/2)*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/11 + (30*d^(11/4)*Sqrt[-e]*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticF[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(847*e^(13/4)*Sqrt[d + e*x^2])","A",6,4,27,0.1481,1,"{5151, 321, 329, 220}"
19,1,181,0,0.0883095,"\int x^{5/2} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^(5/2)*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]],x]","-\frac{10 d^{7/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} \text{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right),\frac{1}{2}\right)}{147 e^{9/4} \sqrt{d+e x^2}}+\frac{4 x^{5/2} \sqrt{d+e x^2}}{49 \sqrt{-e}}+\frac{20 d \sqrt{x} \sqrt{d+e x^2}}{147 (-e)^{3/2}}+\frac{2}{7} x^{7/2} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)","-\frac{10 d^{7/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} \text{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right),\frac{1}{2}\right)}{147 e^{9/4} \sqrt{d+e x^2}}+\frac{4 x^{5/2} \sqrt{d+e x^2}}{49 \sqrt{-e}}+\frac{20 d \sqrt{x} \sqrt{d+e x^2}}{147 (-e)^{3/2}}+\frac{2}{7} x^{7/2} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)",1,"(20*d*Sqrt[x]*Sqrt[d + e*x^2])/(147*(-e)^(3/2)) + (4*x^(5/2)*Sqrt[d + e*x^2])/(49*Sqrt[-e]) + (2*x^(7/2)*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/7 - (10*d^(7/4)*Sqrt[-e]*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticF[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(147*e^(9/4)*Sqrt[d + e*x^2])","A",5,4,27,0.1481,1,"{5151, 321, 329, 220}"
20,1,153,0,0.0743981,"\int \sqrt{x} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[Sqrt[x]*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]],x]","\frac{2 d^{3/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} \text{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right),\frac{1}{2}\right)}{9 e^{5/4} \sqrt{d+e x^2}}+\frac{4 \sqrt{x} \sqrt{d+e x^2}}{9 \sqrt{-e}}+\frac{2}{3} x^{3/2} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)","\frac{2 d^{3/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} \text{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right),\frac{1}{2}\right)}{9 e^{5/4} \sqrt{d+e x^2}}+\frac{4 \sqrt{x} \sqrt{d+e x^2}}{9 \sqrt{-e}}+\frac{2}{3} x^{3/2} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)",1,"(4*Sqrt[x]*Sqrt[d + e*x^2])/(9*Sqrt[-e]) + (2*x^(3/2)*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/3 + (2*d^(3/4)*Sqrt[-e]*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticF[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(9*e^(5/4)*Sqrt[d + e*x^2])","A",4,4,27,0.1481,1,"{5151, 321, 329, 220}"
21,1,122,0,0.0607988,"\int \frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{x^{3/2}} \, dx","Int[ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/x^(3/2),x]","\frac{2 \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} \text{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right),\frac{1}{2}\right)}{\sqrt[4]{d} \sqrt[4]{e} \sqrt{d+e x^2}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{\sqrt{x}}","\frac{2 \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} \text{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right),\frac{1}{2}\right)}{\sqrt[4]{d} \sqrt[4]{e} \sqrt{d+e x^2}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{\sqrt{x}}",1,"(-2*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/Sqrt[x] + (2*Sqrt[-e]*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticF[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(d^(1/4)*e^(1/4)*Sqrt[d + e*x^2])","A",3,3,27,0.1111,1,"{5151, 329, 220}"
22,1,156,0,0.0749551,"\int \frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{x^{7/2}} \, dx","Int[ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/x^(7/2),x]","-\frac{2 \sqrt{-e} e^{3/4} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} \text{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right),\frac{1}{2}\right)}{15 d^{5/4} \sqrt{d+e x^2}}-\frac{4 \sqrt{-e} \sqrt{d+e x^2}}{15 d x^{3/2}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{5 x^{5/2}}","-\frac{2 \sqrt{-e} e^{3/4} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} \text{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right),\frac{1}{2}\right)}{15 d^{5/4} \sqrt{d+e x^2}}-\frac{4 \sqrt{-e} \sqrt{d+e x^2}}{15 d x^{3/2}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{5 x^{5/2}}",1,"(-4*Sqrt[-e]*Sqrt[d + e*x^2])/(15*d*x^(3/2)) - (2*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/(5*x^(5/2)) - (2*Sqrt[-e]*e^(3/4)*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticF[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(15*d^(5/4)*Sqrt[d + e*x^2])","A",4,4,27,0.1481,1,"{5151, 325, 329, 220}"
23,1,186,0,0.0903199,"\int \frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{x^{11/2}} \, dx","Int[ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/x^(11/2),x]","\frac{10 \sqrt{-e} e^{7/4} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} \text{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right),\frac{1}{2}\right)}{189 d^{9/4} \sqrt{d+e x^2}}-\frac{20 (-e)^{3/2} \sqrt{d+e x^2}}{189 d^2 x^{3/2}}-\frac{4 \sqrt{-e} \sqrt{d+e x^2}}{63 d x^{7/2}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{9 x^{9/2}}","\frac{10 \sqrt{-e} e^{7/4} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} \text{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right),\frac{1}{2}\right)}{189 d^{9/4} \sqrt{d+e x^2}}-\frac{20 (-e)^{3/2} \sqrt{d+e x^2}}{189 d^2 x^{3/2}}-\frac{4 \sqrt{-e} \sqrt{d+e x^2}}{63 d x^{7/2}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{9 x^{9/2}}",1,"(-4*Sqrt[-e]*Sqrt[d + e*x^2])/(63*d*x^(7/2)) - (20*(-e)^(3/2)*Sqrt[d + e*x^2])/(189*d^2*x^(3/2)) - (2*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/(9*x^(9/2)) + (10*Sqrt[-e]*e^(7/4)*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticF[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(189*d^(9/4)*Sqrt[d + e*x^2])","A",5,4,27,0.1481,1,"{5151, 325, 329, 220}"
24,1,216,0,0.1080087,"\int \frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{x^{15/2}} \, dx","Int[ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/x^(15/2),x]","-\frac{30 \sqrt{-e} e^{11/4} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} \text{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right),\frac{1}{2}\right)}{1001 d^{13/4} \sqrt{d+e x^2}}-\frac{60 (-e)^{5/2} \sqrt{d+e x^2}}{1001 d^3 x^{3/2}}-\frac{36 (-e)^{3/2} \sqrt{d+e x^2}}{1001 d^2 x^{7/2}}-\frac{4 \sqrt{-e} \sqrt{d+e x^2}}{143 d x^{11/2}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{13 x^{13/2}}","-\frac{30 \sqrt{-e} e^{11/4} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} \text{EllipticF}\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right),\frac{1}{2}\right)}{1001 d^{13/4} \sqrt{d+e x^2}}-\frac{60 (-e)^{5/2} \sqrt{d+e x^2}}{1001 d^3 x^{3/2}}-\frac{36 (-e)^{3/2} \sqrt{d+e x^2}}{1001 d^2 x^{7/2}}-\frac{4 \sqrt{-e} \sqrt{d+e x^2}}{143 d x^{11/2}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{13 x^{13/2}}",1,"(-4*Sqrt[-e]*Sqrt[d + e*x^2])/(143*d*x^(11/2)) - (36*(-e)^(3/2)*Sqrt[d + e*x^2])/(1001*d^2*x^(7/2)) - (60*(-e)^(5/2)*Sqrt[d + e*x^2])/(1001*d^3*x^(3/2)) - (2*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/(13*x^(13/2)) - (30*Sqrt[-e]*e^(11/4)*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticF[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(1001*d^(13/4)*Sqrt[d + e*x^2])","A",6,4,27,0.1481,1,"{5151, 325, 329, 220}"
25,1,326,0,0.191851,"\int x^{7/2} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^(7/2)*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]],x]","-\frac{28 d^2 \sqrt{-e} \sqrt{x} \sqrt{d+e x^2}}{135 e^{5/2} \left(\sqrt{d}+\sqrt{e} x\right)}-\frac{14 d^{9/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{135 e^{11/4} \sqrt{d+e x^2}}+\frac{28 d^{9/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{135 e^{11/4} \sqrt{d+e x^2}}+\frac{4 x^{7/2} \sqrt{d+e x^2}}{81 \sqrt{-e}}+\frac{28 d x^{3/2} \sqrt{d+e x^2}}{405 (-e)^{3/2}}+\frac{2}{9} x^{9/2} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)","-\frac{28 d^2 \sqrt{-e} \sqrt{x} \sqrt{d+e x^2}}{135 e^{5/2} \left(\sqrt{d}+\sqrt{e} x\right)}-\frac{14 d^{9/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{135 e^{11/4} \sqrt{d+e x^2}}+\frac{28 d^{9/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{135 e^{11/4} \sqrt{d+e x^2}}+\frac{4 x^{7/2} \sqrt{d+e x^2}}{81 \sqrt{-e}}+\frac{28 d x^{3/2} \sqrt{d+e x^2}}{405 (-e)^{3/2}}+\frac{2}{9} x^{9/2} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)",1,"(28*d*x^(3/2)*Sqrt[d + e*x^2])/(405*(-e)^(3/2)) + (4*x^(7/2)*Sqrt[d + e*x^2])/(81*Sqrt[-e]) - (28*d^2*Sqrt[-e]*Sqrt[x]*Sqrt[d + e*x^2])/(135*e^(5/2)*(Sqrt[d] + Sqrt[e]*x)) + (2*x^(9/2)*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/9 + (28*d^(9/4)*Sqrt[-e]*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticE[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(135*e^(11/4)*Sqrt[d + e*x^2]) - (14*d^(9/4)*Sqrt[-e]*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticF[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(135*e^(11/4)*Sqrt[d + e*x^2])","A",7,6,27,0.2222,1,"{5151, 321, 329, 305, 220, 1196}"
26,1,296,0,0.1612983,"\int x^{3/2} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^(3/2)*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]],x]","\frac{6 d^{5/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{25 e^{7/4} \sqrt{d+e x^2}}-\frac{12 d^{5/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{25 e^{7/4} \sqrt{d+e x^2}}+\frac{12 d \sqrt{-e} \sqrt{x} \sqrt{d+e x^2}}{25 e^{3/2} \left(\sqrt{d}+\sqrt{e} x\right)}+\frac{4 x^{3/2} \sqrt{d+e x^2}}{25 \sqrt{-e}}+\frac{2}{5} x^{5/2} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)","\frac{6 d^{5/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{25 e^{7/4} \sqrt{d+e x^2}}-\frac{12 d^{5/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{25 e^{7/4} \sqrt{d+e x^2}}+\frac{12 d \sqrt{-e} \sqrt{x} \sqrt{d+e x^2}}{25 e^{3/2} \left(\sqrt{d}+\sqrt{e} x\right)}+\frac{4 x^{3/2} \sqrt{d+e x^2}}{25 \sqrt{-e}}+\frac{2}{5} x^{5/2} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)",1,"(4*x^(3/2)*Sqrt[d + e*x^2])/(25*Sqrt[-e]) + (12*d*Sqrt[-e]*Sqrt[x]*Sqrt[d + e*x^2])/(25*e^(3/2)*(Sqrt[d] + Sqrt[e]*x)) + (2*x^(5/2)*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/5 - (12*d^(5/4)*Sqrt[-e]*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticE[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(25*e^(7/4)*Sqrt[d + e*x^2]) + (6*d^(5/4)*Sqrt[-e]*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticF[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(25*e^(7/4)*Sqrt[d + e*x^2])","A",6,6,27,0.2222,1,"{5151, 321, 329, 305, 220, 1196}"
27,1,260,0,0.1389345,"\int \frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{\sqrt{x}} \, dx","Int[ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/Sqrt[x],x]","-\frac{2 \sqrt[4]{d} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{e^{3/4} \sqrt{d+e x^2}}+\frac{4 \sqrt[4]{d} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{e^{3/4} \sqrt{d+e x^2}}-\frac{4 \sqrt{-e} \sqrt{x} \sqrt{d+e x^2}}{\sqrt{e} \left(\sqrt{d}+\sqrt{e} x\right)}+2 \sqrt{x} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)","-\frac{2 \sqrt[4]{d} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{e^{3/4} \sqrt{d+e x^2}}+\frac{4 \sqrt[4]{d} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{e^{3/4} \sqrt{d+e x^2}}-\frac{4 \sqrt{-e} \sqrt{x} \sqrt{d+e x^2}}{\sqrt{e} \left(\sqrt{d}+\sqrt{e} x\right)}+2 \sqrt{x} \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)",1,"(-4*Sqrt[-e]*Sqrt[x]*Sqrt[d + e*x^2])/(Sqrt[e]*(Sqrt[d] + Sqrt[e]*x)) + 2*Sqrt[x]*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]] + (4*d^(1/4)*Sqrt[-e]*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticE[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(e^(3/4)*Sqrt[d + e*x^2]) - (2*d^(1/4)*Sqrt[-e]*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticF[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(e^(3/4)*Sqrt[d + e*x^2])","A",5,5,27,0.1852,1,"{5151, 329, 305, 220, 1196}"
28,1,298,0,0.1660539,"\int \frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{x^{5/2}} \, dx","Int[ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/x^(5/2),x]","\frac{2 \sqrt{-e} \sqrt[4]{e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{3 d^{3/4} \sqrt{d+e x^2}}-\frac{4 \sqrt{-e} \sqrt[4]{e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{3 d^{3/4} \sqrt{d+e x^2}}+\frac{4 \sqrt{-e^2} \sqrt{x} \sqrt{d+e x^2}}{3 d \left(\sqrt{d}+\sqrt{e} x\right)}-\frac{4 \sqrt{-e} \sqrt{d+e x^2}}{3 d \sqrt{x}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{3 x^{3/2}}","\frac{2 \sqrt{-e} \sqrt[4]{e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{3 d^{3/4} \sqrt{d+e x^2}}-\frac{4 \sqrt{-e} \sqrt[4]{e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{3 d^{3/4} \sqrt{d+e x^2}}+\frac{4 \sqrt{-e^2} \sqrt{x} \sqrt{d+e x^2}}{3 d \left(\sqrt{d}+\sqrt{e} x\right)}-\frac{4 \sqrt{-e} \sqrt{d+e x^2}}{3 d \sqrt{x}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{3 x^{3/2}}",1,"(-4*Sqrt[-e]*Sqrt[d + e*x^2])/(3*d*Sqrt[x]) + (4*Sqrt[-e^2]*Sqrt[x]*Sqrt[d + e*x^2])/(3*d*(Sqrt[d] + Sqrt[e]*x)) - (2*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/(3*x^(3/2)) - (4*Sqrt[-e]*e^(1/4)*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticE[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(3*d^(3/4)*Sqrt[d + e*x^2]) + (2*Sqrt[-e]*e^(1/4)*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticF[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(3*d^(3/4)*Sqrt[d + e*x^2])","A",6,6,27,0.2222,1,"{5151, 325, 329, 305, 220, 1196}"
29,1,331,0,0.1936369,"\int \frac{\tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{x^{9/2}} \, dx","Int[ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]]/x^(9/2),x]","-\frac{12 e^{3/2} \sqrt{-e} \sqrt{x} \sqrt{d+e x^2}}{35 d^2 \left(\sqrt{d}+\sqrt{e} x\right)}-\frac{6 e^{5/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{35 d^{7/4} \sqrt{d+e x^2}}+\frac{12 e^{5/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{35 d^{7/4} \sqrt{d+e x^2}}-\frac{12 (-e)^{3/2} \sqrt{d+e x^2}}{35 d^2 \sqrt{x}}-\frac{4 \sqrt{-e} \sqrt{d+e x^2}}{35 d x^{5/2}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{7 x^{7/2}}","-\frac{12 e^{3/2} \sqrt{-e} \sqrt{x} \sqrt{d+e x^2}}{35 d^2 \left(\sqrt{d}+\sqrt{e} x\right)}-\frac{6 e^{5/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{35 d^{7/4} \sqrt{d+e x^2}}+\frac{12 e^{5/4} \sqrt{-e} \left(\sqrt{d}+\sqrt{e} x\right) \sqrt{\frac{d+e x^2}{\left(\sqrt{d}+\sqrt{e} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)|\frac{1}{2}\right)}{35 d^{7/4} \sqrt{d+e x^2}}-\frac{12 (-e)^{3/2} \sqrt{d+e x^2}}{35 d^2 \sqrt{x}}-\frac{4 \sqrt{-e} \sqrt{d+e x^2}}{35 d x^{5/2}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{-e} x}{\sqrt{d+e x^2}}\right)}{7 x^{7/2}}",1,"(-4*Sqrt[-e]*Sqrt[d + e*x^2])/(35*d*x^(5/2)) - (12*(-e)^(3/2)*Sqrt[d + e*x^2])/(35*d^2*Sqrt[x]) - (12*Sqrt[-e]*e^(3/2)*Sqrt[x]*Sqrt[d + e*x^2])/(35*d^2*(Sqrt[d] + Sqrt[e]*x)) - (2*ArcTan[(Sqrt[-e]*x)/Sqrt[d + e*x^2]])/(7*x^(7/2)) + (12*Sqrt[-e]*e^(5/4)*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticE[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(35*d^(7/4)*Sqrt[d + e*x^2]) - (6*Sqrt[-e]*e^(5/4)*(Sqrt[d] + Sqrt[e]*x)*Sqrt[(d + e*x^2)/(Sqrt[d] + Sqrt[e]*x)^2]*EllipticF[2*ArcTan[(e^(1/4)*Sqrt[x])/d^(1/4)], 1/2])/(35*d^(7/4)*Sqrt[d + e*x^2])","A",7,6,27,0.2222,1,"{5151, 325, 329, 305, 220, 1196}"
30,1,50,0,0.1460135,"\int \frac{\tan ^{-1}\left(1+x+x^2\right)}{x^2} \, dx","Int[ArcTan[1 + x + x^2]/x^2,x]","-\frac{1}{2} \log \left(x^2+1\right)+\frac{1}{4} \log \left(x^2+2 x+2\right)-\frac{\tan ^{-1}\left(x^2+x+1\right)}{x}+\frac{\log (x)}{2}+\frac{1}{2} \tan ^{-1}(x+1)","-\frac{1}{2} \log \left(x^2+1\right)+\frac{1}{4} \log \left(x^2+2 x+2\right)-\frac{\tan ^{-1}\left(x^2+x+1\right)}{x}+\frac{\log (x)}{2}+\frac{1}{2} \tan ^{-1}(x+1)",1,"ArcTan[1 + x]/2 - ArcTan[1 + x + x^2]/x + Log[x]/2 - Log[1 + x^2]/2 + Log[2 + 2*x + x^2]/4","A",8,7,11,0.6364,1,"{5205, 6742, 260, 634, 617, 204, 628}"
31,0,0,0,0.046276,"\int \frac{\left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^n}{1-c^2 x^2} \, dx","Int[(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2),x]","\int \frac{\left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^n}{1-c^2 x^2} \, dx","\text{Int}\left(\frac{\left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^n}{1-c^2 x^2},x\right)",0,"Defer[Int][(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2), x]","A",0,0,0,0,-1,"{}"
32,1,431,0,0.4846252,"\int \frac{\left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^3}{1-c^2 x^2} \, dx","Int[(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3/(1 - c^2*x^2),x]","\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}-\frac{3 b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}+\frac{3 i b \text{PolyLog}\left(2,1-\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}-\frac{3 i b \text{PolyLog}\left(2,-1+\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}-\frac{3 i b^3 \text{PolyLog}\left(4,1-\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right)}{4 c}+\frac{3 i b^3 \text{PolyLog}\left(4,-1+\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right)}{4 c}-\frac{2 \tanh ^{-1}\left(1-\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{c}","\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}-\frac{3 b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}+\frac{3 i b \text{PolyLog}\left(2,1-\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}-\frac{3 i b \text{PolyLog}\left(2,-1+\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}-\frac{3 i b^3 \text{PolyLog}\left(4,1-\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right)}{4 c}+\frac{3 i b^3 \text{PolyLog}\left(4,-1+\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right)}{4 c}-\frac{2 \tanh ^{-1}\left(1-\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{c}",1,"(-2*(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3*ArcTanh[1 - 2/(1 + (I*Sqrt[1 - c*x])/Sqrt[1 + c*x])])/c + (((3*I)/2)*b*(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*PolyLog[2, 1 - 2/(1 + (I*Sqrt[1 - c*x])/Sqrt[1 + c*x])])/c - (((3*I)/2)*b*(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*PolyLog[2, -1 + 2/(1 + (I*Sqrt[1 - c*x])/Sqrt[1 + c*x])])/c + (3*b^2*(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[3, 1 - 2/(1 + (I*Sqrt[1 - c*x])/Sqrt[1 + c*x])])/(2*c) - (3*b^2*(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[3, -1 + 2/(1 + (I*Sqrt[1 - c*x])/Sqrt[1 + c*x])])/(2*c) - (((3*I)/4)*b^3*PolyLog[4, 1 - 2/(1 + (I*Sqrt[1 - c*x])/Sqrt[1 + c*x])])/c + (((3*I)/4)*b^3*PolyLog[4, -1 + 2/(1 + (I*Sqrt[1 - c*x])/Sqrt[1 + c*x])])/c","A",9,7,40,0.1750,1,"{6681, 4850, 4988, 4884, 4994, 4998, 6610}"
33,1,283,0,0.2952757,"\int \frac{\left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2}{1-c^2 x^2} \, dx","Int[(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2/(1 - c^2*x^2),x]","\frac{i b \text{PolyLog}\left(2,1-\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}-\frac{i b \text{PolyLog}\left(2,-1+\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right)}{2 c}-\frac{b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right)}{2 c}-\frac{2 \tanh ^{-1}\left(1-\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{c}","\frac{i b \text{PolyLog}\left(2,1-\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}-\frac{i b \text{PolyLog}\left(2,-1+\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right)}{2 c}-\frac{b^2 \text{PolyLog}\left(3,-1+\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right)}{2 c}-\frac{2 \tanh ^{-1}\left(1-\frac{2}{1+\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{c}",1,"(-2*(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*ArcTanh[1 - 2/(1 + (I*Sqrt[1 - c*x])/Sqrt[1 + c*x])])/c + (I*b*(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[2, 1 - 2/(1 + (I*Sqrt[1 - c*x])/Sqrt[1 + c*x])])/c - (I*b*(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[2, -1 + 2/(1 + (I*Sqrt[1 - c*x])/Sqrt[1 + c*x])])/c + (b^2*PolyLog[3, 1 - 2/(1 + (I*Sqrt[1 - c*x])/Sqrt[1 + c*x])])/(2*c) - (b^2*PolyLog[3, -1 + 2/(1 + (I*Sqrt[1 - c*x])/Sqrt[1 + c*x])])/(2*c)","A",7,6,40,0.1500,1,"{6681, 4850, 4988, 4884, 4994, 6610}"
34,1,98,0,0.0666915,"\int \frac{a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)}{1-c^2 x^2} \, dx","Int[(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])/(1 - c^2*x^2),x]","-\frac{i b \text{PolyLog}\left(2,-\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}\right)}{2 c}+\frac{i b \text{PolyLog}\left(2,\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}\right)}{2 c}-\frac{a \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}{c}","-\frac{i b \text{PolyLog}\left(2,-\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}\right)}{2 c}+\frac{i b \text{PolyLog}\left(2,\frac{i \sqrt{1-c x}}{\sqrt{c x+1}}\right)}{2 c}-\frac{a \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}{c}",1,"-((a*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])/c) - ((I/2)*b*PolyLog[2, ((-I)*Sqrt[1 - c*x])/Sqrt[1 + c*x]])/c + ((I/2)*b*PolyLog[2, (I*Sqrt[1 - c*x])/Sqrt[1 + c*x]])/c","A",4,4,38,0.1053,1,"{206, 6681, 4848, 2391}"
35,0,0,0,0.0436831,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)} \, dx","Int[1/((1 - c^2*x^2)*(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])),x]","\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)} \, dx","\text{Int}\left(\frac{1}{\left(1-c^2 x^2\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)},x\right)",0,"Defer[Int][1/((1 - c^2*x^2)*(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])), x]","A",0,0,0,0,-1,"{}"
36,0,0,0,0.0411422,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2} \, dx","Int[1/((1 - c^2*x^2)*(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2),x]","\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(1-c^2 x^2\right) \left(a+b \tan ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2},x\right)",0,"Defer[Int][1/((1 - c^2*x^2)*(a + b*ArcTan[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2), x]","A",0,0,0,0,-1,"{}"
37,1,37,0,0.0242773,"\int x^m \tan ^{-1}(\tan (a+b x)) \, dx","Int[x^m*ArcTan[Tan[a + b*x]],x]","\frac{x^{m+1} \tan ^{-1}(\tan (a+b x))}{m+1}-\frac{b x^{m+2}}{m^2+3 m+2}","\frac{x^{m+1} \tan ^{-1}(\tan (a+b x))}{m+1}-\frac{b x^{m+2}}{m^2+3 m+2}",1,"-((b*x^(2 + m))/(2 + 3*m + m^2)) + (x^(1 + m)*ArcTan[Tan[a + b*x]])/(1 + m)","A",2,2,11,0.1818,1,"{2168, 30}"
38,1,23,0,0.008892,"\int x^2 \tan ^{-1}(\tan (a+b x)) \, dx","Int[x^2*ArcTan[Tan[a + b*x]],x]","\frac{1}{3} x^3 \tan ^{-1}(\tan (a+b x))-\frac{b x^4}{12}","\frac{1}{3} x^3 \tan ^{-1}(\tan (a+b x))-\frac{b x^4}{12}",1,"-(b*x^4)/12 + (x^3*ArcTan[Tan[a + b*x]])/3","A",2,2,11,0.1818,1,"{2168, 30}"
39,1,23,0,0.0070475,"\int x \tan ^{-1}(\tan (a+b x)) \, dx","Int[x*ArcTan[Tan[a + b*x]],x]","\frac{1}{2} x^2 \tan ^{-1}(\tan (a+b x))-\frac{b x^3}{6}","\frac{1}{2} x^2 \tan ^{-1}(\tan (a+b x))-\frac{b x^3}{6}",1,"-(b*x^3)/6 + (x^2*ArcTan[Tan[a + b*x]])/2","A",2,2,9,0.2222,1,"{5171, 30}"
40,1,16,0,0.002841,"\int \tan ^{-1}(\tan (a+b x)) \, dx","Int[ArcTan[Tan[a + b*x]],x]","\frac{\tan ^{-1}(\tan (a+b x))^2}{2 b}","\frac{\tan ^{-1}(\tan (a+b x))^2}{2 b}",1,"ArcTan[Tan[a + b*x]]^2/(2*b)","A",2,2,7,0.2857,1,"{2157, 30}"
41,1,21,0,0.0313861,"\int \frac{\tan ^{-1}(\tan (a+b x))}{x} \, dx","Int[ArcTan[Tan[a + b*x]]/x,x]","b x-\log (x) \left(b x-\tan ^{-1}(\tan (a+b x))\right)","b x-\log (x) \left(b x-\tan ^{-1}(\tan (a+b x))\right)",1,"b*x - (b*x - ArcTan[Tan[a + b*x]])*Log[x]","A",2,2,11,0.1818,1,"{2158, 29}"
42,1,36,0,0.0210559,"\int x^m \tan ^{-1}(\cot (a+b x)) \, dx","Int[x^m*ArcTan[Cot[a + b*x]],x]","\frac{x^{m+1} \tan ^{-1}(\cot (a+b x))}{m+1}+\frac{b x^{m+2}}{m^2+3 m+2}","\frac{x^{m+1} \tan ^{-1}(\cot (a+b x))}{m+1}+\frac{b x^{m+2}}{m^2+3 m+2}",1,"(b*x^(2 + m))/(2 + 3*m + m^2) + (x^(1 + m)*ArcTan[Cot[a + b*x]])/(1 + m)","A",2,2,11,0.1818,1,"{2168, 30}"
43,1,23,0,0.0083937,"\int x^2 \tan ^{-1}(\cot (a+b x)) \, dx","Int[x^2*ArcTan[Cot[a + b*x]],x]","\frac{1}{3} x^3 \tan ^{-1}(\cot (a+b x))+\frac{b x^4}{12}","\frac{1}{3} x^3 \tan ^{-1}(\cot (a+b x))+\frac{b x^4}{12}",1,"(b*x^4)/12 + (x^3*ArcTan[Cot[a + b*x]])/3","A",2,2,11,0.1818,1,"{2168, 30}"
44,1,23,0,0.0071134,"\int x \tan ^{-1}(\cot (a+b x)) \, dx","Int[x*ArcTan[Cot[a + b*x]],x]","\frac{1}{2} x^2 \tan ^{-1}(\cot (a+b x))+\frac{b x^3}{6}","\frac{1}{2} x^2 \tan ^{-1}(\cot (a+b x))+\frac{b x^3}{6}",1,"(b*x^3)/6 + (x^2*ArcTan[Cot[a + b*x]])/2","A",2,2,9,0.2222,1,"{5173, 30}"
45,1,16,0,0.0030273,"\int \tan ^{-1}(\cot (a+b x)) \, dx","Int[ArcTan[Cot[a + b*x]],x]","-\frac{\tan ^{-1}(\cot (a+b x))^2}{2 b}","-\frac{\tan ^{-1}(\cot (a+b x))^2}{2 b}",1,"-ArcTan[Cot[a + b*x]]^2/(2*b)","A",2,2,7,0.2857,1,"{2157, 30}"
46,1,19,0,0.0327329,"\int \frac{\tan ^{-1}(\cot (a+b x))}{x} \, dx","Int[ArcTan[Cot[a + b*x]]/x,x]","\log (x) \left(\tan ^{-1}(\cot (a+b x))+b x\right)-b x","\log (x) \left(\tan ^{-1}(\cot (a+b x))+b x\right)-b x",1,"-(b*x) + (b*x + ArcTan[Cot[a + b*x]])*Log[x]","A",2,2,11,0.1818,1,"{2158, 29}"
47,1,16,0,0.0028136,"\int \tan ^{-1}(\tan (a+b x)) \, dx","Int[ArcTan[Tan[a + b*x]],x]","\frac{\tan ^{-1}(\tan (a+b x))^2}{2 b}","\frac{\tan ^{-1}(\tan (a+b x))^2}{2 b}",1,"ArcTan[Tan[a + b*x]]^2/(2*b)","A",2,2,7,0.2857,1,"{2157, 30}"
48,1,403,0,0.5165257,"\int x^2 \tan ^{-1}(c+d \tan (a+b x)) \, dx","Int[x^2*ArcTan[c + d*Tan[a + b*x]],x]","\frac{i x \text{PolyLog}\left(3,-\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)}{4 b^2}-\frac{i x \text{PolyLog}\left(3,-\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,-\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)}{8 b^3}+\frac{\text{PolyLog}\left(4,-\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)}{8 b^3}+\frac{x^2 \text{PolyLog}\left(2,-\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)}{4 b}-\frac{x^2 \text{PolyLog}\left(2,-\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)}{4 b}+\frac{1}{6} i x^3 \log \left(1+\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)-\frac{1}{6} i x^3 \log \left(1+\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)+\frac{1}{3} x^3 \tan ^{-1}(d \tan (a+b x)+c)","\frac{i x \text{PolyLog}\left(3,-\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)}{4 b^2}-\frac{i x \text{PolyLog}\left(3,-\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,-\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)}{8 b^3}+\frac{\text{PolyLog}\left(4,-\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)}{8 b^3}+\frac{x^2 \text{PolyLog}\left(2,-\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)}{4 b}-\frac{x^2 \text{PolyLog}\left(2,-\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)}{4 b}+\frac{1}{6} i x^3 \log \left(1+\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)-\frac{1}{6} i x^3 \log \left(1+\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)+\frac{1}{3} x^3 \tan ^{-1}(d \tan (a+b x)+c)",1,"(x^3*ArcTan[c + d*Tan[a + b*x]])/3 + (I/6)*x^3*Log[1 + ((1 + I*c + d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c - d)] - (I/6)*x^3*Log[1 + ((c + I*(1 - d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 + d))] + (x^2*PolyLog[2, -(((1 + I*c + d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c - d))])/(4*b) - (x^2*PolyLog[2, -(((c + I*(1 - d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 + d)))])/(4*b) + ((I/4)*x*PolyLog[3, -(((1 + I*c + d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c - d))])/b^2 - ((I/4)*x*PolyLog[3, -(((c + I*(1 - d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 + d)))])/b^2 - PolyLog[4, -(((1 + I*c + d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c - d))]/(8*b^3) + PolyLog[4, -(((c + I*(1 - d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 + d)))]/(8*b^3)","A",11,6,15,0.4000,1,"{5175, 2190, 2531, 6609, 2282, 6589}"
49,1,305,0,0.4053538,"\int x \tan ^{-1}(c+d \tan (a+b x)) \, dx","Int[x*ArcTan[c + d*Tan[a + b*x]],x]","\frac{i \text{PolyLog}\left(3,-\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)}{8 b^2}-\frac{i \text{PolyLog}\left(3,-\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)}{8 b^2}+\frac{x \text{PolyLog}\left(2,-\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)}{4 b}-\frac{x \text{PolyLog}\left(2,-\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)}{4 b}+\frac{1}{4} i x^2 \log \left(1+\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)-\frac{1}{4} i x^2 \log \left(1+\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)+\frac{1}{2} x^2 \tan ^{-1}(d \tan (a+b x)+c)","\frac{i \text{PolyLog}\left(3,-\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)}{8 b^2}-\frac{i \text{PolyLog}\left(3,-\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)}{8 b^2}+\frac{x \text{PolyLog}\left(2,-\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)}{4 b}-\frac{x \text{PolyLog}\left(2,-\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)}{4 b}+\frac{1}{4} i x^2 \log \left(1+\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)-\frac{1}{4} i x^2 \log \left(1+\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)+\frac{1}{2} x^2 \tan ^{-1}(d \tan (a+b x)+c)",1,"(x^2*ArcTan[c + d*Tan[a + b*x]])/2 + (I/4)*x^2*Log[1 + ((1 + I*c + d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c - d)] - (I/4)*x^2*Log[1 + ((c + I*(1 - d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 + d))] + (x*PolyLog[2, -(((1 + I*c + d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c - d))])/(4*b) - (x*PolyLog[2, -(((c + I*(1 - d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 + d)))])/(4*b) + ((I/8)*PolyLog[3, -(((1 + I*c + d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c - d))])/b^2 - ((I/8)*PolyLog[3, -(((c + I*(1 - d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 + d)))])/b^2","A",9,5,13,0.3846,1,"{5175, 2190, 2531, 2282, 6589}"
50,1,198,0,0.2339398,"\int \tan ^{-1}(c+d \tan (a+b x)) \, dx","Int[ArcTan[c + d*Tan[a + b*x]],x]","\frac{\text{PolyLog}\left(2,-\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)}{4 b}-\frac{\text{PolyLog}\left(2,-\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)}{4 b}+\frac{1}{2} i x \log \left(1+\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)-\frac{1}{2} i x \log \left(1+\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)+x \tan ^{-1}(d \tan (a+b x)+c)","\frac{\text{PolyLog}\left(2,-\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)}{4 b}-\frac{\text{PolyLog}\left(2,-\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)}{4 b}+\frac{1}{2} i x \log \left(1+\frac{(i c+d+1) e^{2 i a+2 i b x}}{i c-d+1}\right)-\frac{1}{2} i x \log \left(1+\frac{(c+i (1-d)) e^{2 i a+2 i b x}}{c+i (d+1)}\right)+x \tan ^{-1}(d \tan (a+b x)+c)",1,"x*ArcTan[c + d*Tan[a + b*x]] + (I/2)*x*Log[1 + ((1 + I*c + d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c - d)] - (I/2)*x*Log[1 + ((c + I*(1 - d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 + d))] + PolyLog[2, -(((1 + I*c + d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c - d))]/(4*b) - PolyLog[2, -(((c + I*(1 - d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 + d)))]/(4*b)","A",7,4,11,0.3636,1,"{5167, 2190, 2279, 2391}"
51,0,0,0,0.1316172,"\int \frac{\tan ^{-1}(c+d \tan (a+b x))}{x} \, dx","Int[ArcTan[c + d*Tan[a + b*x]]/x,x]","\int \frac{\tan ^{-1}(c+d \tan (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tan ^{-1}(d \tan (a+b x)+c)}{x},x\right)",0,"Defer[Int][ArcTan[c + d*Tan[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
52,1,154,0,0.2376965,"\int x^2 \tan ^{-1}(c+(1+i c) \tan (a+b x)) \, dx","Int[x^2*ArcTan[c + (1 + I*c)*Tan[a + b*x]],x]","-\frac{i x \text{PolyLog}\left(3,i c e^{2 i a+2 i b x}\right)}{4 b^2}+\frac{\text{PolyLog}\left(4,i c e^{2 i a+2 i b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,i c e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} i x^3 \log \left(1-i c e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \tan ^{-1}(c+(1+i c) \tan (a+b x))-\frac{b x^4}{12}","-\frac{i x \text{PolyLog}\left(3,i c e^{2 i a+2 i b x}\right)}{4 b^2}+\frac{\text{PolyLog}\left(4,i c e^{2 i a+2 i b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,i c e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} i x^3 \log \left(1-i c e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \tan ^{-1}(c+(1+i c) \tan (a+b x))-\frac{b x^4}{12}",1,"-(b*x^4)/12 + (x^3*ArcTan[c + (1 + I*c)*Tan[a + b*x]])/3 - (I/6)*x^3*Log[1 - I*c*E^((2*I)*a + (2*I)*b*x)] - (x^2*PolyLog[2, I*c*E^((2*I)*a + (2*I)*b*x)])/(4*b) - ((I/4)*x*PolyLog[3, I*c*E^((2*I)*a + (2*I)*b*x)])/b^2 + PolyLog[4, I*c*E^((2*I)*a + (2*I)*b*x)]/(8*b^3)","A",7,7,21,0.3333,1,"{5171, 2184, 2190, 2531, 6609, 2282, 6589}"
53,1,123,0,0.206246,"\int x \tan ^{-1}(c+(1+i c) \tan (a+b x)) \, dx","Int[x*ArcTan[c + (1 + I*c)*Tan[a + b*x]],x]","-\frac{i \text{PolyLog}\left(3,i c e^{2 i a+2 i b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,i c e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} i x^2 \log \left(1-i c e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \tan ^{-1}(c+(1+i c) \tan (a+b x))-\frac{b x^3}{6}","-\frac{i \text{PolyLog}\left(3,i c e^{2 i a+2 i b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,i c e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} i x^2 \log \left(1-i c e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \tan ^{-1}(c+(1+i c) \tan (a+b x))-\frac{b x^3}{6}",1,"-(b*x^3)/6 + (x^2*ArcTan[c + (1 + I*c)*Tan[a + b*x]])/2 - (I/4)*x^2*Log[1 - I*c*E^((2*I)*a + (2*I)*b*x)] - (x*PolyLog[2, I*c*E^((2*I)*a + (2*I)*b*x)])/(4*b) - ((I/8)*PolyLog[3, I*c*E^((2*I)*a + (2*I)*b*x)])/b^2","A",6,6,19,0.3158,1,"{5171, 2184, 2190, 2531, 2282, 6589}"
54,1,85,0,0.1247726,"\int \tan ^{-1}(c+(1+i c) \tan (a+b x)) \, dx","Int[ArcTan[c + (1 + I*c)*Tan[a + b*x]],x]","-\frac{\text{PolyLog}\left(2,i c e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} i x \log \left(1-i c e^{2 i a+2 i b x}\right)+x \tan ^{-1}(c+(1+i c) \tan (a+b x))-\frac{b x^2}{2}","-\frac{\text{PolyLog}\left(2,i c e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} i x \log \left(1-i c e^{2 i a+2 i b x}\right)+x \tan ^{-1}(c+(1+i c) \tan (a+b x))-\frac{b x^2}{2}",1,"-(b*x^2)/2 + x*ArcTan[c + (1 + I*c)*Tan[a + b*x]] - (I/2)*x*Log[1 - I*c*E^((2*I)*a + (2*I)*b*x)] - PolyLog[2, I*c*E^((2*I)*a + (2*I)*b*x)]/(4*b)","A",5,5,17,0.2941,1,"{5163, 2184, 2190, 2279, 2391}"
55,0,0,0,0.1195289,"\int \frac{\tan ^{-1}(c+(1+i c) \tan (a+b x))}{x} \, dx","Int[ArcTan[c + (1 + I*c)*Tan[a + b*x]]/x,x]","\int \frac{\tan ^{-1}(c+(1+i c) \tan (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tan ^{-1}(c+(1+i c) \tan (a+b x))}{x},x\right)",0,"Defer[Int][ArcTan[c + (1 + I*c)*Tan[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
56,1,155,0,0.2442379,"\int x^2 \tan ^{-1}(c+(-1+i c) \tan (a+b x)) \, dx","Int[x^2*ArcTan[c + (-1 + I*c)*Tan[a + b*x]],x]","\frac{i x \text{PolyLog}\left(3,-i c e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,-i c e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{x^2 \text{PolyLog}\left(2,-i c e^{2 i a+2 i b x}\right)}{4 b}+\frac{1}{6} i x^3 \log \left(1+i c e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \tan ^{-1}(c-(1-i c) \tan (a+b x))+\frac{b x^4}{12}","\frac{i x \text{PolyLog}\left(3,-i c e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,-i c e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{x^2 \text{PolyLog}\left(2,-i c e^{2 i a+2 i b x}\right)}{4 b}+\frac{1}{6} i x^3 \log \left(1+i c e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \tan ^{-1}(c-(1-i c) \tan (a+b x))+\frac{b x^4}{12}",1,"(b*x^4)/12 + (x^3*ArcTan[c - (1 - I*c)*Tan[a + b*x]])/3 + (I/6)*x^3*Log[1 + I*c*E^((2*I)*a + (2*I)*b*x)] + (x^2*PolyLog[2, (-I)*c*E^((2*I)*a + (2*I)*b*x)])/(4*b) + ((I/4)*x*PolyLog[3, (-I)*c*E^((2*I)*a + (2*I)*b*x)])/b^2 - PolyLog[4, (-I)*c*E^((2*I)*a + (2*I)*b*x)]/(8*b^3)","A",7,7,21,0.3333,1,"{5171, 2184, 2190, 2531, 6609, 2282, 6589}"
57,1,124,0,0.2078786,"\int x \tan ^{-1}(c+(-1+i c) \tan (a+b x)) \, dx","Int[x*ArcTan[c + (-1 + I*c)*Tan[a + b*x]],x]","\frac{i \text{PolyLog}\left(3,-i c e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{x \text{PolyLog}\left(2,-i c e^{2 i a+2 i b x}\right)}{4 b}+\frac{1}{4} i x^2 \log \left(1+i c e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \tan ^{-1}(c-(1-i c) \tan (a+b x))+\frac{b x^3}{6}","\frac{i \text{PolyLog}\left(3,-i c e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{x \text{PolyLog}\left(2,-i c e^{2 i a+2 i b x}\right)}{4 b}+\frac{1}{4} i x^2 \log \left(1+i c e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \tan ^{-1}(c-(1-i c) \tan (a+b x))+\frac{b x^3}{6}",1,"(b*x^3)/6 + (x^2*ArcTan[c - (1 - I*c)*Tan[a + b*x]])/2 + (I/4)*x^2*Log[1 + I*c*E^((2*I)*a + (2*I)*b*x)] + (x*PolyLog[2, (-I)*c*E^((2*I)*a + (2*I)*b*x)])/(4*b) + ((I/8)*PolyLog[3, (-I)*c*E^((2*I)*a + (2*I)*b*x)])/b^2","A",6,6,19,0.3158,1,"{5171, 2184, 2190, 2531, 2282, 6589}"
58,1,86,0,0.128898,"\int \tan ^{-1}(c+(-1+i c) \tan (a+b x)) \, dx","Int[ArcTan[c + (-1 + I*c)*Tan[a + b*x]],x]","\frac{\text{PolyLog}\left(2,-i c e^{2 i a+2 i b x}\right)}{4 b}+\frac{1}{2} i x \log \left(1+i c e^{2 i a+2 i b x}\right)+x \tan ^{-1}(c-(1-i c) \tan (a+b x))+\frac{b x^2}{2}","\frac{\text{PolyLog}\left(2,-i c e^{2 i a+2 i b x}\right)}{4 b}+\frac{1}{2} i x \log \left(1+i c e^{2 i a+2 i b x}\right)+x \tan ^{-1}(c-(1-i c) \tan (a+b x))+\frac{b x^2}{2}",1,"(b*x^2)/2 + x*ArcTan[c - (1 - I*c)*Tan[a + b*x]] + (I/2)*x*Log[1 + I*c*E^((2*I)*a + (2*I)*b*x)] + PolyLog[2, (-I)*c*E^((2*I)*a + (2*I)*b*x)]/(4*b)","A",5,5,17,0.2941,1,"{5163, 2184, 2190, 2279, 2391}"
59,0,0,0,0.1363241,"\int \frac{\tan ^{-1}(c+(-1+i c) \tan (a+b x))}{x} \, dx","Int[ArcTan[c + (-1 + I*c)*Tan[a + b*x]]/x,x]","\int \frac{\tan ^{-1}(c+(-1+i c) \tan (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tan ^{-1}(c+(-1+i c) \tan (a+b x))}{x},x\right)",0,"Defer[Int][ArcTan[c + (-1 + I*c)*Tan[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
60,1,16,0,0.0030392,"\int \tan ^{-1}(\cot (a+b x)) \, dx","Int[ArcTan[Cot[a + b*x]],x]","-\frac{\tan ^{-1}(\cot (a+b x))^2}{2 b}","-\frac{\tan ^{-1}(\cot (a+b x))^2}{2 b}",1,"-ArcTan[Cot[a + b*x]]^2/(2*b)","A",2,2,7,0.2857,1,"{2157, 30}"
61,1,399,0,0.5114813,"\int x^2 \tan ^{-1}(c+d \cot (a+b x)) \, dx","Int[x^2*ArcTan[c + d*Cot[a + b*x]],x]","\frac{i x \text{PolyLog}\left(3,\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)}{4 b^2}-\frac{i x \text{PolyLog}\left(3,\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)}{8 b^3}+\frac{\text{PolyLog}\left(4,\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)}{8 b^3}+\frac{x^2 \text{PolyLog}\left(2,\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)}{4 b}-\frac{x^2 \text{PolyLog}\left(2,\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)}{4 b}+\frac{1}{6} i x^3 \log \left(1-\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)-\frac{1}{6} i x^3 \log \left(1-\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)+\frac{1}{3} x^3 \tan ^{-1}(d \cot (a+b x)+c)","\frac{i x \text{PolyLog}\left(3,\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)}{4 b^2}-\frac{i x \text{PolyLog}\left(3,\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)}{8 b^3}+\frac{\text{PolyLog}\left(4,\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)}{8 b^3}+\frac{x^2 \text{PolyLog}\left(2,\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)}{4 b}-\frac{x^2 \text{PolyLog}\left(2,\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)}{4 b}+\frac{1}{6} i x^3 \log \left(1-\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)-\frac{1}{6} i x^3 \log \left(1-\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)+\frac{1}{3} x^3 \tan ^{-1}(d \cot (a+b x)+c)",1,"(x^3*ArcTan[c + d*Cot[a + b*x]])/3 + (I/6)*x^3*Log[1 - ((1 + I*c - d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c + d)] - (I/6)*x^3*Log[1 - ((c + I*(1 + d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 - d))] + (x^2*PolyLog[2, ((1 + I*c - d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c + d)])/(4*b) - (x^2*PolyLog[2, ((c + I*(1 + d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 - d))])/(4*b) + ((I/4)*x*PolyLog[3, ((1 + I*c - d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c + d)])/b^2 - ((I/4)*x*PolyLog[3, ((c + I*(1 + d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 - d))])/b^2 - PolyLog[4, ((1 + I*c - d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c + d)]/(8*b^3) + PolyLog[4, ((c + I*(1 + d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 - d))]/(8*b^3)","A",11,6,15,0.4000,1,"{5177, 2190, 2531, 6609, 2282, 6589}"
62,1,303,0,0.4004498,"\int x \tan ^{-1}(c+d \cot (a+b x)) \, dx","Int[x*ArcTan[c + d*Cot[a + b*x]],x]","\frac{i \text{PolyLog}\left(3,\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)}{8 b^2}-\frac{i \text{PolyLog}\left(3,\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)}{8 b^2}+\frac{x \text{PolyLog}\left(2,\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)}{4 b}-\frac{x \text{PolyLog}\left(2,\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)}{4 b}+\frac{1}{4} i x^2 \log \left(1-\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)-\frac{1}{4} i x^2 \log \left(1-\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)+\frac{1}{2} x^2 \tan ^{-1}(d \cot (a+b x)+c)","\frac{i \text{PolyLog}\left(3,\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)}{8 b^2}-\frac{i \text{PolyLog}\left(3,\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)}{8 b^2}+\frac{x \text{PolyLog}\left(2,\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)}{4 b}-\frac{x \text{PolyLog}\left(2,\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)}{4 b}+\frac{1}{4} i x^2 \log \left(1-\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)-\frac{1}{4} i x^2 \log \left(1-\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)+\frac{1}{2} x^2 \tan ^{-1}(d \cot (a+b x)+c)",1,"(x^2*ArcTan[c + d*Cot[a + b*x]])/2 + (I/4)*x^2*Log[1 - ((1 + I*c - d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c + d)] - (I/4)*x^2*Log[1 - ((c + I*(1 + d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 - d))] + (x*PolyLog[2, ((1 + I*c - d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c + d)])/(4*b) - (x*PolyLog[2, ((c + I*(1 + d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 - d))])/(4*b) + ((I/8)*PolyLog[3, ((1 + I*c - d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c + d)])/b^2 - ((I/8)*PolyLog[3, ((c + I*(1 + d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 - d))])/b^2","A",9,5,13,0.3846,1,"{5177, 2190, 2531, 2282, 6589}"
63,1,198,0,0.2499618,"\int \tan ^{-1}(c+d \cot (a+b x)) \, dx","Int[ArcTan[c + d*Cot[a + b*x]],x]","\frac{\text{PolyLog}\left(2,\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)}{4 b}-\frac{\text{PolyLog}\left(2,\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)}{4 b}+\frac{1}{2} i x \log \left(1-\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)-\frac{1}{2} i x \log \left(1-\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)+x \tan ^{-1}(d \cot (a+b x)+c)","\frac{\text{PolyLog}\left(2,\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)}{4 b}-\frac{\text{PolyLog}\left(2,\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)}{4 b}+\frac{1}{2} i x \log \left(1-\frac{(i c-d+1) e^{2 i a+2 i b x}}{i c+d+1}\right)-\frac{1}{2} i x \log \left(1-\frac{(c+i (d+1)) e^{2 i a+2 i b x}}{c+i (1-d)}\right)+x \tan ^{-1}(d \cot (a+b x)+c)",1,"x*ArcTan[c + d*Cot[a + b*x]] + (I/2)*x*Log[1 - ((1 + I*c - d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c + d)] - (I/2)*x*Log[1 - ((c + I*(1 + d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 - d))] + PolyLog[2, ((1 + I*c - d)*E^((2*I)*a + (2*I)*b*x))/(1 + I*c + d)]/(4*b) - PolyLog[2, ((c + I*(1 + d))*E^((2*I)*a + (2*I)*b*x))/(c + I*(1 - d))]/(4*b)","A",7,4,11,0.3636,1,"{5169, 2190, 2279, 2391}"
64,0,0,0,0.1343237,"\int \frac{\tan ^{-1}(c+d \cot (a+b x))}{x} \, dx","Int[ArcTan[c + d*Cot[a + b*x]]/x,x]","\int \frac{\tan ^{-1}(c+d \cot (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tan ^{-1}(d \cot (a+b x)+c)}{x},x\right)",0,"Defer[Int][ArcTan[c + d*Cot[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
65,1,154,0,0.2558708,"\int x^2 \tan ^{-1}(c+(1-i c) \cot (a+b x)) \, dx","Int[x^2*ArcTan[c + (1 - I*c)*Cot[a + b*x]],x]","\frac{i x \text{PolyLog}\left(3,i c e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,i c e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{x^2 \text{PolyLog}\left(2,i c e^{2 i a+2 i b x}\right)}{4 b}+\frac{1}{6} i x^3 \log \left(1-i c e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \tan ^{-1}(c+(1-i c) \cot (a+b x))+\frac{b x^4}{12}","\frac{i x \text{PolyLog}\left(3,i c e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,i c e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{x^2 \text{PolyLog}\left(2,i c e^{2 i a+2 i b x}\right)}{4 b}+\frac{1}{6} i x^3 \log \left(1-i c e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \tan ^{-1}(c+(1-i c) \cot (a+b x))+\frac{b x^4}{12}",1,"(b*x^4)/12 + (x^3*ArcTan[c + (1 - I*c)*Cot[a + b*x]])/3 + (I/6)*x^3*Log[1 - I*c*E^((2*I)*a + (2*I)*b*x)] + (x^2*PolyLog[2, I*c*E^((2*I)*a + (2*I)*b*x)])/(4*b) + ((I/4)*x*PolyLog[3, I*c*E^((2*I)*a + (2*I)*b*x)])/b^2 - PolyLog[4, I*c*E^((2*I)*a + (2*I)*b*x)]/(8*b^3)","A",7,7,21,0.3333,1,"{5173, 2184, 2190, 2531, 6609, 2282, 6589}"
66,1,123,0,0.2223631,"\int x \tan ^{-1}(c+(1-i c) \cot (a+b x)) \, dx","Int[x*ArcTan[c + (1 - I*c)*Cot[a + b*x]],x]","\frac{i \text{PolyLog}\left(3,i c e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{x \text{PolyLog}\left(2,i c e^{2 i a+2 i b x}\right)}{4 b}+\frac{1}{4} i x^2 \log \left(1-i c e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \tan ^{-1}(c+(1-i c) \cot (a+b x))+\frac{b x^3}{6}","\frac{i \text{PolyLog}\left(3,i c e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{x \text{PolyLog}\left(2,i c e^{2 i a+2 i b x}\right)}{4 b}+\frac{1}{4} i x^2 \log \left(1-i c e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \tan ^{-1}(c+(1-i c) \cot (a+b x))+\frac{b x^3}{6}",1,"(b*x^3)/6 + (x^2*ArcTan[c + (1 - I*c)*Cot[a + b*x]])/2 + (I/4)*x^2*Log[1 - I*c*E^((2*I)*a + (2*I)*b*x)] + (x*PolyLog[2, I*c*E^((2*I)*a + (2*I)*b*x)])/(4*b) + ((I/8)*PolyLog[3, I*c*E^((2*I)*a + (2*I)*b*x)])/b^2","A",6,6,19,0.3158,1,"{5173, 2184, 2190, 2531, 2282, 6589}"
67,1,85,0,0.1314527,"\int \tan ^{-1}(c+(1-i c) \cot (a+b x)) \, dx","Int[ArcTan[c + (1 - I*c)*Cot[a + b*x]],x]","\frac{\text{PolyLog}\left(2,i c e^{2 i a+2 i b x}\right)}{4 b}+\frac{1}{2} i x \log \left(1-i c e^{2 i a+2 i b x}\right)+x \tan ^{-1}(c+(1-i c) \cot (a+b x))+\frac{b x^2}{2}","\frac{\text{PolyLog}\left(2,i c e^{2 i a+2 i b x}\right)}{4 b}+\frac{1}{2} i x \log \left(1-i c e^{2 i a+2 i b x}\right)+x \tan ^{-1}(c+(1-i c) \cot (a+b x))+\frac{b x^2}{2}",1,"(b*x^2)/2 + x*ArcTan[c + (1 - I*c)*Cot[a + b*x]] + (I/2)*x*Log[1 - I*c*E^((2*I)*a + (2*I)*b*x)] + PolyLog[2, I*c*E^((2*I)*a + (2*I)*b*x)]/(4*b)","A",5,5,17,0.2941,1,"{5165, 2184, 2190, 2279, 2391}"
68,0,0,0,0.1214139,"\int \frac{\tan ^{-1}(c+(1-i c) \cot (a+b x))}{x} \, dx","Int[ArcTan[c + (1 - I*c)*Cot[a + b*x]]/x,x]","\int \frac{\tan ^{-1}(c+(1-i c) \cot (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tan ^{-1}(c+(1-i c) \cot (a+b x))}{x},x\right)",0,"Defer[Int][ArcTan[c + (1 - I*c)*Cot[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
69,1,155,0,0.2612754,"\int x^2 \tan ^{-1}(c+(-1-i c) \cot (a+b x)) \, dx","Int[x^2*ArcTan[c + (-1 - I*c)*Cot[a + b*x]],x]","-\frac{i x \text{PolyLog}\left(3,-i c e^{2 i a+2 i b x}\right)}{4 b^2}+\frac{\text{PolyLog}\left(4,-i c e^{2 i a+2 i b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,-i c e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} i x^3 \log \left(1+i c e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \tan ^{-1}(c-(1+i c) \cot (a+b x))-\frac{b x^4}{12}","-\frac{i x \text{PolyLog}\left(3,-i c e^{2 i a+2 i b x}\right)}{4 b^2}+\frac{\text{PolyLog}\left(4,-i c e^{2 i a+2 i b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,-i c e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} i x^3 \log \left(1+i c e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \tan ^{-1}(c-(1+i c) \cot (a+b x))-\frac{b x^4}{12}",1,"-(b*x^4)/12 + (x^3*ArcTan[c - (1 + I*c)*Cot[a + b*x]])/3 - (I/6)*x^3*Log[1 + I*c*E^((2*I)*a + (2*I)*b*x)] - (x^2*PolyLog[2, (-I)*c*E^((2*I)*a + (2*I)*b*x)])/(4*b) - ((I/4)*x*PolyLog[3, (-I)*c*E^((2*I)*a + (2*I)*b*x)])/b^2 + PolyLog[4, (-I)*c*E^((2*I)*a + (2*I)*b*x)]/(8*b^3)","A",7,7,21,0.3333,1,"{5173, 2184, 2190, 2531, 6609, 2282, 6589}"
70,1,124,0,0.2237224,"\int x \tan ^{-1}(c+(-1-i c) \cot (a+b x)) \, dx","Int[x*ArcTan[c + (-1 - I*c)*Cot[a + b*x]],x]","-\frac{i \text{PolyLog}\left(3,-i c e^{2 i a+2 i b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,-i c e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} i x^2 \log \left(1+i c e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \tan ^{-1}(c-(1+i c) \cot (a+b x))-\frac{b x^3}{6}","-\frac{i \text{PolyLog}\left(3,-i c e^{2 i a+2 i b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,-i c e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} i x^2 \log \left(1+i c e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \tan ^{-1}(c-(1+i c) \cot (a+b x))-\frac{b x^3}{6}",1,"-(b*x^3)/6 + (x^2*ArcTan[c - (1 + I*c)*Cot[a + b*x]])/2 - (I/4)*x^2*Log[1 + I*c*E^((2*I)*a + (2*I)*b*x)] - (x*PolyLog[2, (-I)*c*E^((2*I)*a + (2*I)*b*x)])/(4*b) - ((I/8)*PolyLog[3, (-I)*c*E^((2*I)*a + (2*I)*b*x)])/b^2","A",6,6,19,0.3158,1,"{5173, 2184, 2190, 2531, 2282, 6589}"
71,1,86,0,0.1335806,"\int \tan ^{-1}(c+(-1-i c) \cot (a+b x)) \, dx","Int[ArcTan[c + (-1 - I*c)*Cot[a + b*x]],x]","-\frac{\text{PolyLog}\left(2,-i c e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} i x \log \left(1+i c e^{2 i a+2 i b x}\right)+x \tan ^{-1}(c-(1+i c) \cot (a+b x))-\frac{b x^2}{2}","-\frac{\text{PolyLog}\left(2,-i c e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} i x \log \left(1+i c e^{2 i a+2 i b x}\right)+x \tan ^{-1}(c-(1+i c) \cot (a+b x))-\frac{b x^2}{2}",1,"-(b*x^2)/2 + x*ArcTan[c - (1 + I*c)*Cot[a + b*x]] - (I/2)*x*Log[1 + I*c*E^((2*I)*a + (2*I)*b*x)] - PolyLog[2, (-I)*c*E^((2*I)*a + (2*I)*b*x)]/(4*b)","A",5,5,17,0.2941,1,"{5165, 2184, 2190, 2279, 2391}"
72,0,0,0,0.1188174,"\int \frac{\tan ^{-1}(c+(-1-i c) \cot (a+b x))}{x} \, dx","Int[ArcTan[c + (-1 - I*c)*Cot[a + b*x]]/x,x]","\int \frac{\tan ^{-1}(c+(-1-i c) \cot (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tan ^{-1}(c+(-1-i c) \cot (a+b x))}{x},x\right)",0,"Defer[Int][ArcTan[c + (-1 - I*c)*Cot[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
73,1,39,0,0.0317576,"\int \tan ^{-1}(\sinh (x)) \, dx","Int[ArcTan[Sinh[x]],x]","i \text{PolyLog}\left(2,-i e^x\right)-i \text{PolyLog}\left(2,i e^x\right)-2 x \tan ^{-1}\left(e^x\right)+x \tan ^{-1}(\sinh (x))","i \text{PolyLog}\left(2,-i e^x\right)-i \text{PolyLog}\left(2,i e^x\right)-2 x \tan ^{-1}\left(e^x\right)+x \tan ^{-1}(\sinh (x))",1,"-2*x*ArcTan[E^x] + x*ArcTan[Sinh[x]] + I*PolyLog[2, (-I)*E^x] - I*PolyLog[2, I*E^x]","A",6,4,3,1.333,1,"{5203, 4180, 2279, 2391}"
74,1,74,0,0.061271,"\int x \tan ^{-1}(\sinh (x)) \, dx","Int[x*ArcTan[Sinh[x]],x]","i x \text{PolyLog}\left(2,-i e^x\right)-i x \text{PolyLog}\left(2,i e^x\right)-i \text{PolyLog}\left(3,-i e^x\right)+i \text{PolyLog}\left(3,i e^x\right)+x^2 \left(-\tan ^{-1}\left(e^x\right)\right)+\frac{1}{2} x^2 \tan ^{-1}(\sinh (x))","i x \text{PolyLog}\left(2,-i e^x\right)-i x \text{PolyLog}\left(2,i e^x\right)-i \text{PolyLog}\left(3,-i e^x\right)+i \text{PolyLog}\left(3,i e^x\right)+x^2 \left(-\tan ^{-1}\left(e^x\right)\right)+\frac{1}{2} x^2 \tan ^{-1}(\sinh (x))",1,"-(x^2*ArcTan[E^x]) + (x^2*ArcTan[Sinh[x]])/2 + I*x*PolyLog[2, (-I)*E^x] - I*x*PolyLog[2, I*E^x] - I*PolyLog[3, (-I)*E^x] + I*PolyLog[3, I*E^x]","A",8,5,5,1.000,1,"{5205, 4180, 2531, 2282, 6589}"
75,1,108,0,0.0878868,"\int x^2 \tan ^{-1}(\sinh (x)) \, dx","Int[x^2*ArcTan[Sinh[x]],x]","i x^2 \text{PolyLog}\left(2,-i e^x\right)-i x^2 \text{PolyLog}\left(2,i e^x\right)-2 i x \text{PolyLog}\left(3,-i e^x\right)+2 i x \text{PolyLog}\left(3,i e^x\right)+2 i \text{PolyLog}\left(4,-i e^x\right)-2 i \text{PolyLog}\left(4,i e^x\right)-\frac{2}{3} x^3 \tan ^{-1}\left(e^x\right)+\frac{1}{3} x^3 \tan ^{-1}(\sinh (x))","i x^2 \text{PolyLog}\left(2,-i e^x\right)-i x^2 \text{PolyLog}\left(2,i e^x\right)-2 i x \text{PolyLog}\left(3,-i e^x\right)+2 i x \text{PolyLog}\left(3,i e^x\right)+2 i \text{PolyLog}\left(4,-i e^x\right)-2 i \text{PolyLog}\left(4,i e^x\right)-\frac{2}{3} x^3 \tan ^{-1}\left(e^x\right)+\frac{1}{3} x^3 \tan ^{-1}(\sinh (x))",1,"(-2*x^3*ArcTan[E^x])/3 + (x^3*ArcTan[Sinh[x]])/3 + I*x^2*PolyLog[2, (-I)*E^x] - I*x^2*PolyLog[2, I*E^x] - (2*I)*x*PolyLog[3, (-I)*E^x] + (2*I)*x*PolyLog[3, I*E^x] + (2*I)*PolyLog[4, (-I)*E^x] - (2*I)*PolyLog[4, I*E^x]","A",10,6,7,0.8571,1,"{5205, 4180, 2531, 6609, 2282, 6589}"
76,1,299,0,0.209102,"\int (e+f x)^3 \tan ^{-1}(\tanh (a+b x)) \, dx","Int[(e + f*x)^3*ArcTan[Tanh[a + b*x]],x]","\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,-i e^{2 a+2 b x}\right)}{8 b^3}-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,i e^{2 a+2 b x}\right)}{8 b^3}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(3,-i e^{2 a+2 b x}\right)}{8 b^2}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(3,i e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 i f^3 \text{PolyLog}\left(5,-i e^{2 a+2 b x}\right)}{16 b^4}+\frac{3 i f^3 \text{PolyLog}\left(5,i e^{2 a+2 b x}\right)}{16 b^4}+\frac{i (e+f x)^3 \text{PolyLog}\left(2,-i e^{2 a+2 b x}\right)}{4 b}-\frac{i (e+f x)^3 \text{PolyLog}\left(2,i e^{2 a+2 b x}\right)}{4 b}-\frac{(e+f x)^4 \tan ^{-1}\left(e^{2 a+2 b x}\right)}{4 f}+\frac{(e+f x)^4 \tan ^{-1}(\tanh (a+b x))}{4 f}","\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,-i e^{2 a+2 b x}\right)}{8 b^3}-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,i e^{2 a+2 b x}\right)}{8 b^3}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(3,-i e^{2 a+2 b x}\right)}{8 b^2}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(3,i e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 i f^3 \text{PolyLog}\left(5,-i e^{2 a+2 b x}\right)}{16 b^4}+\frac{3 i f^3 \text{PolyLog}\left(5,i e^{2 a+2 b x}\right)}{16 b^4}+\frac{i (e+f x)^3 \text{PolyLog}\left(2,-i e^{2 a+2 b x}\right)}{4 b}-\frac{i (e+f x)^3 \text{PolyLog}\left(2,i e^{2 a+2 b x}\right)}{4 b}-\frac{(e+f x)^4 \tan ^{-1}\left(e^{2 a+2 b x}\right)}{4 f}+\frac{(e+f x)^4 \tan ^{-1}(\tanh (a+b x))}{4 f}",1,"-((e + f*x)^4*ArcTan[E^(2*a + 2*b*x)])/(4*f) + ((e + f*x)^4*ArcTan[Tanh[a + b*x]])/(4*f) + ((I/4)*(e + f*x)^3*PolyLog[2, (-I)*E^(2*a + 2*b*x)])/b - ((I/4)*(e + f*x)^3*PolyLog[2, I*E^(2*a + 2*b*x)])/b - (((3*I)/8)*f*(e + f*x)^2*PolyLog[3, (-I)*E^(2*a + 2*b*x)])/b^2 + (((3*I)/8)*f*(e + f*x)^2*PolyLog[3, I*E^(2*a + 2*b*x)])/b^2 + (((3*I)/8)*f^2*(e + f*x)*PolyLog[4, (-I)*E^(2*a + 2*b*x)])/b^3 - (((3*I)/8)*f^2*(e + f*x)*PolyLog[4, I*E^(2*a + 2*b*x)])/b^3 - (((3*I)/16)*f^3*PolyLog[5, (-I)*E^(2*a + 2*b*x)])/b^4 + (((3*I)/16)*f^3*PolyLog[5, I*E^(2*a + 2*b*x)])/b^4","A",12,6,15,0.4000,1,"{5183, 4180, 2531, 6609, 2282, 6589}"
77,1,229,0,0.1518098,"\int (e+f x)^2 \tan ^{-1}(\tanh (a+b x)) \, dx","Int[(e + f*x)^2*ArcTan[Tanh[a + b*x]],x]","-\frac{i f (e+f x) \text{PolyLog}\left(3,-i e^{2 a+2 b x}\right)}{4 b^2}+\frac{i f (e+f x) \text{PolyLog}\left(3,i e^{2 a+2 b x}\right)}{4 b^2}+\frac{i f^2 \text{PolyLog}\left(4,-i e^{2 a+2 b x}\right)}{8 b^3}-\frac{i f^2 \text{PolyLog}\left(4,i e^{2 a+2 b x}\right)}{8 b^3}+\frac{i (e+f x)^2 \text{PolyLog}\left(2,-i e^{2 a+2 b x}\right)}{4 b}-\frac{i (e+f x)^2 \text{PolyLog}\left(2,i e^{2 a+2 b x}\right)}{4 b}-\frac{(e+f x)^3 \tan ^{-1}\left(e^{2 a+2 b x}\right)}{3 f}+\frac{(e+f x)^3 \tan ^{-1}(\tanh (a+b x))}{3 f}","-\frac{i f (e+f x) \text{PolyLog}\left(3,-i e^{2 a+2 b x}\right)}{4 b^2}+\frac{i f (e+f x) \text{PolyLog}\left(3,i e^{2 a+2 b x}\right)}{4 b^2}+\frac{i f^2 \text{PolyLog}\left(4,-i e^{2 a+2 b x}\right)}{8 b^3}-\frac{i f^2 \text{PolyLog}\left(4,i e^{2 a+2 b x}\right)}{8 b^3}+\frac{i (e+f x)^2 \text{PolyLog}\left(2,-i e^{2 a+2 b x}\right)}{4 b}-\frac{i (e+f x)^2 \text{PolyLog}\left(2,i e^{2 a+2 b x}\right)}{4 b}-\frac{(e+f x)^3 \tan ^{-1}\left(e^{2 a+2 b x}\right)}{3 f}+\frac{(e+f x)^3 \tan ^{-1}(\tanh (a+b x))}{3 f}",1,"-((e + f*x)^3*ArcTan[E^(2*a + 2*b*x)])/(3*f) + ((e + f*x)^3*ArcTan[Tanh[a + b*x]])/(3*f) + ((I/4)*(e + f*x)^2*PolyLog[2, (-I)*E^(2*a + 2*b*x)])/b - ((I/4)*(e + f*x)^2*PolyLog[2, I*E^(2*a + 2*b*x)])/b - ((I/4)*f*(e + f*x)*PolyLog[3, (-I)*E^(2*a + 2*b*x)])/b^2 + ((I/4)*f*(e + f*x)*PolyLog[3, I*E^(2*a + 2*b*x)])/b^2 + ((I/8)*f^2*PolyLog[4, (-I)*E^(2*a + 2*b*x)])/b^3 - ((I/8)*f^2*PolyLog[4, I*E^(2*a + 2*b*x)])/b^3","A",10,6,15,0.4000,1,"{5183, 4180, 2531, 6609, 2282, 6589}"
78,1,159,0,0.0973901,"\int (e+f x) \tan ^{-1}(\tanh (a+b x)) \, dx","Int[(e + f*x)*ArcTan[Tanh[a + b*x]],x]","-\frac{i f \text{PolyLog}\left(3,-i e^{2 a+2 b x}\right)}{8 b^2}+\frac{i f \text{PolyLog}\left(3,i e^{2 a+2 b x}\right)}{8 b^2}+\frac{i (e+f x) \text{PolyLog}\left(2,-i e^{2 a+2 b x}\right)}{4 b}-\frac{i (e+f x) \text{PolyLog}\left(2,i e^{2 a+2 b x}\right)}{4 b}-\frac{(e+f x)^2 \tan ^{-1}\left(e^{2 a+2 b x}\right)}{2 f}+\frac{(e+f x)^2 \tan ^{-1}(\tanh (a+b x))}{2 f}","-\frac{i f \text{PolyLog}\left(3,-i e^{2 a+2 b x}\right)}{8 b^2}+\frac{i f \text{PolyLog}\left(3,i e^{2 a+2 b x}\right)}{8 b^2}+\frac{i (e+f x) \text{PolyLog}\left(2,-i e^{2 a+2 b x}\right)}{4 b}-\frac{i (e+f x) \text{PolyLog}\left(2,i e^{2 a+2 b x}\right)}{4 b}-\frac{(e+f x)^2 \tan ^{-1}\left(e^{2 a+2 b x}\right)}{2 f}+\frac{(e+f x)^2 \tan ^{-1}(\tanh (a+b x))}{2 f}",1,"-((e + f*x)^2*ArcTan[E^(2*a + 2*b*x)])/(2*f) + ((e + f*x)^2*ArcTan[Tanh[a + b*x]])/(2*f) + ((I/4)*(e + f*x)*PolyLog[2, (-I)*E^(2*a + 2*b*x)])/b - ((I/4)*(e + f*x)*PolyLog[2, I*E^(2*a + 2*b*x)])/b - ((I/8)*f*PolyLog[3, (-I)*E^(2*a + 2*b*x)])/b^2 + ((I/8)*f*PolyLog[3, I*E^(2*a + 2*b*x)])/b^2","A",8,5,13,0.3846,1,"{5183, 4180, 2531, 2282, 6589}"
79,1,74,0,0.0424545,"\int \tan ^{-1}(\tanh (a+b x)) \, dx","Int[ArcTan[Tanh[a + b*x]],x]","\frac{i \text{PolyLog}\left(2,-i e^{2 a+2 b x}\right)}{4 b}-\frac{i \text{PolyLog}\left(2,i e^{2 a+2 b x}\right)}{4 b}-x \tan ^{-1}\left(e^{2 a+2 b x}\right)+x \tan ^{-1}(\tanh (a+b x))","\frac{i \text{PolyLog}\left(2,-i e^{2 a+2 b x}\right)}{4 b}-\frac{i \text{PolyLog}\left(2,i e^{2 a+2 b x}\right)}{4 b}-x \tan ^{-1}\left(e^{2 a+2 b x}\right)+x \tan ^{-1}(\tanh (a+b x))",1,"-(x*ArcTan[E^(2*a + 2*b*x)]) + x*ArcTan[Tanh[a + b*x]] + ((I/4)*PolyLog[2, (-I)*E^(2*a + 2*b*x)])/b - ((I/4)*PolyLog[2, I*E^(2*a + 2*b*x)])/b","A",6,4,7,0.5714,1,"{5179, 4180, 2279, 2391}"
80,0,0,0,0.0378732,"\int \frac{\tan ^{-1}(\tanh (a+b x))}{e+f x} \, dx","Int[ArcTan[Tanh[a + b*x]]/(e + f*x),x]","\int \frac{\tan ^{-1}(\tanh (a+b x))}{e+f x} \, dx","\text{Int}\left(\frac{\tan ^{-1}(\tanh (a+b x))}{e+f x},x\right)",0,"Defer[Int][ArcTan[Tanh[a + b*x]]/(e + f*x), x]","A",0,0,0,0,-1,"{}"
81,1,355,0,0.4613607,"\int x^2 \tan ^{-1}(c+d \tanh (a+b x)) \, dx","Int[x^2*ArcTan[c + d*Tanh[a + b*x]],x]","-\frac{i x \text{PolyLog}\left(3,-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{4 b^2}+\frac{i x \text{PolyLog}\left(3,-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{4 b^2}+\frac{i \text{PolyLog}\left(4,-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{8 b^3}-\frac{i \text{PolyLog}\left(4,-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{4 b}-\frac{i x^2 \text{PolyLog}\left(2,-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{4 b}+\frac{1}{6} i x^3 \log \left(1+\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)-\frac{1}{6} i x^3 \log \left(1+\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)+\frac{1}{3} x^3 \tan ^{-1}(d \tanh (a+b x)+c)","-\frac{i x \text{PolyLog}\left(3,-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{4 b^2}+\frac{i x \text{PolyLog}\left(3,-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{4 b^2}+\frac{i \text{PolyLog}\left(4,-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{8 b^3}-\frac{i \text{PolyLog}\left(4,-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{4 b}-\frac{i x^2 \text{PolyLog}\left(2,-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{4 b}+\frac{1}{6} i x^3 \log \left(1+\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)-\frac{1}{6} i x^3 \log \left(1+\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)+\frac{1}{3} x^3 \tan ^{-1}(d \tanh (a+b x)+c)",1,"(x^3*ArcTan[c + d*Tanh[a + b*x]])/3 + (I/6)*x^3*Log[1 + ((I - c - d)*E^(2*a + 2*b*x))/(I - c + d)] - (I/6)*x^3*Log[1 + ((I + c + d)*E^(2*a + 2*b*x))/(I + c - d)] + ((I/4)*x^2*PolyLog[2, -(((I - c - d)*E^(2*a + 2*b*x))/(I - c + d))])/b - ((I/4)*x^2*PolyLog[2, -(((I + c + d)*E^(2*a + 2*b*x))/(I + c - d))])/b - ((I/4)*x*PolyLog[3, -(((I - c - d)*E^(2*a + 2*b*x))/(I - c + d))])/b^2 + ((I/4)*x*PolyLog[3, -(((I + c + d)*E^(2*a + 2*b*x))/(I + c - d))])/b^2 + ((I/8)*PolyLog[4, -(((I - c - d)*E^(2*a + 2*b*x))/(I - c + d))])/b^3 - ((I/8)*PolyLog[4, -(((I + c + d)*E^(2*a + 2*b*x))/(I + c - d))])/b^3","A",11,6,15,0.4000,1,"{5199, 2190, 2531, 6609, 2282, 6589}"
82,1,267,0,0.3734045,"\int x \tan ^{-1}(c+d \tanh (a+b x)) \, dx","Int[x*ArcTan[c + d*Tanh[a + b*x]],x]","-\frac{i \text{PolyLog}\left(3,-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{8 b^2}+\frac{i \text{PolyLog}\left(3,-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{4 b}-\frac{i x \text{PolyLog}\left(2,-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{4 b}+\frac{1}{4} i x^2 \log \left(1+\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)-\frac{1}{4} i x^2 \log \left(1+\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)+\frac{1}{2} x^2 \tan ^{-1}(d \tanh (a+b x)+c)","-\frac{i \text{PolyLog}\left(3,-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{8 b^2}+\frac{i \text{PolyLog}\left(3,-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{4 b}-\frac{i x \text{PolyLog}\left(2,-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{4 b}+\frac{1}{4} i x^2 \log \left(1+\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)-\frac{1}{4} i x^2 \log \left(1+\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)+\frac{1}{2} x^2 \tan ^{-1}(d \tanh (a+b x)+c)",1,"(x^2*ArcTan[c + d*Tanh[a + b*x]])/2 + (I/4)*x^2*Log[1 + ((I - c - d)*E^(2*a + 2*b*x))/(I - c + d)] - (I/4)*x^2*Log[1 + ((I + c + d)*E^(2*a + 2*b*x))/(I + c - d)] + ((I/4)*x*PolyLog[2, -(((I - c - d)*E^(2*a + 2*b*x))/(I - c + d))])/b - ((I/4)*x*PolyLog[2, -(((I + c + d)*E^(2*a + 2*b*x))/(I + c - d))])/b - ((I/8)*PolyLog[3, -(((I - c - d)*E^(2*a + 2*b*x))/(I - c + d))])/b^2 + ((I/8)*PolyLog[3, -(((I + c + d)*E^(2*a + 2*b*x))/(I + c - d))])/b^2","A",9,5,13,0.3846,1,"{5199, 2190, 2531, 2282, 6589}"
83,1,174,0,0.2306351,"\int \tan ^{-1}(c+d \tanh (a+b x)) \, dx","Int[ArcTan[c + d*Tanh[a + b*x]],x]","\frac{i \text{PolyLog}\left(2,-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{4 b}-\frac{i \text{PolyLog}\left(2,-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{4 b}+\frac{1}{2} i x \log \left(1+\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)-\frac{1}{2} i x \log \left(1+\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)+x \tan ^{-1}(d \tanh (a+b x)+c)","\frac{i \text{PolyLog}\left(2,-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{4 b}-\frac{i \text{PolyLog}\left(2,-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{4 b}+\frac{1}{2} i x \log \left(1+\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)-\frac{1}{2} i x \log \left(1+\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)+x \tan ^{-1}(d \tanh (a+b x)+c)",1,"x*ArcTan[c + d*Tanh[a + b*x]] + (I/2)*x*Log[1 + ((I - c - d)*E^(2*a + 2*b*x))/(I - c + d)] - (I/2)*x*Log[1 + ((I + c + d)*E^(2*a + 2*b*x))/(I + c - d)] + ((I/4)*PolyLog[2, -(((I - c - d)*E^(2*a + 2*b*x))/(I - c + d))])/b - ((I/4)*PolyLog[2, -(((I + c + d)*E^(2*a + 2*b*x))/(I + c - d))])/b","A",7,4,11,0.3636,1,"{5191, 2190, 2279, 2391}"
84,0,0,0,0.1260241,"\int \frac{\tan ^{-1}(c+d \tanh (a+b x))}{x} \, dx","Int[ArcTan[c + d*Tanh[a + b*x]]/x,x]","\int \frac{\tan ^{-1}(c+d \tanh (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tan ^{-1}(d \tanh (a+b x)+c)}{x},x\right)",0,"Defer[Int][ArcTan[c + d*Tanh[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
85,1,142,0,0.2280856,"\int x^2 \tan ^{-1}(c+(i+c) \tanh (a+b x)) \, dx","Int[x^2*ArcTan[c + (I + c)*Tanh[a + b*x]],x]","-\frac{i x \text{PolyLog}\left(3,-i c e^{2 a+2 b x}\right)}{4 b^2}+\frac{i \text{PolyLog}\left(4,-i c e^{2 a+2 b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,-i c e^{2 a+2 b x}\right)}{4 b}+\frac{1}{6} i x^3 \log \left(1+i c e^{2 a+2 b x}\right)+\frac{1}{3} x^3 \tan ^{-1}(c+(c+i) \tanh (a+b x))-\frac{1}{12} i b x^4","-\frac{i x \text{PolyLog}\left(3,-i c e^{2 a+2 b x}\right)}{4 b^2}+\frac{i \text{PolyLog}\left(4,-i c e^{2 a+2 b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,-i c e^{2 a+2 b x}\right)}{4 b}+\frac{1}{6} i x^3 \log \left(1+i c e^{2 a+2 b x}\right)+\frac{1}{3} x^3 \tan ^{-1}(c+(c+i) \tanh (a+b x))-\frac{1}{12} i b x^4",1,"(-I/12)*b*x^4 + (x^3*ArcTan[c + (I + c)*Tanh[a + b*x]])/3 + (I/6)*x^3*Log[1 + I*c*E^(2*a + 2*b*x)] + ((I/4)*x^2*PolyLog[2, (-I)*c*E^(2*a + 2*b*x)])/b - ((I/4)*x*PolyLog[3, (-I)*c*E^(2*a + 2*b*x)])/b^2 + ((I/8)*PolyLog[4, (-I)*c*E^(2*a + 2*b*x)])/b^3","A",7,7,19,0.3684,1,"{5195, 2184, 2190, 2531, 6609, 2282, 6589}"
86,1,113,0,0.1949718,"\int x \tan ^{-1}(c+(i+c) \tanh (a+b x)) \, dx","Int[x*ArcTan[c + (I + c)*Tanh[a + b*x]],x]","-\frac{i \text{PolyLog}\left(3,-i c e^{2 a+2 b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,-i c e^{2 a+2 b x}\right)}{4 b}+\frac{1}{4} i x^2 \log \left(1+i c e^{2 a+2 b x}\right)+\frac{1}{2} x^2 \tan ^{-1}(c+(c+i) \tanh (a+b x))-\frac{1}{6} i b x^3","-\frac{i \text{PolyLog}\left(3,-i c e^{2 a+2 b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,-i c e^{2 a+2 b x}\right)}{4 b}+\frac{1}{4} i x^2 \log \left(1+i c e^{2 a+2 b x}\right)+\frac{1}{2} x^2 \tan ^{-1}(c+(c+i) \tanh (a+b x))-\frac{1}{6} i b x^3",1,"(-I/6)*b*x^3 + (x^2*ArcTan[c + (I + c)*Tanh[a + b*x]])/2 + (I/4)*x^2*Log[1 + I*c*E^(2*a + 2*b*x)] + ((I/4)*x*PolyLog[2, (-I)*c*E^(2*a + 2*b*x)])/b - ((I/8)*PolyLog[3, (-I)*c*E^(2*a + 2*b*x)])/b^2","A",6,6,17,0.3529,1,"{5195, 2184, 2190, 2531, 2282, 6589}"
87,1,79,0,0.1176914,"\int \tan ^{-1}(c+(i+c) \tanh (a+b x)) \, dx","Int[ArcTan[c + (I + c)*Tanh[a + b*x]],x]","\frac{i \text{PolyLog}\left(2,-i c e^{2 a+2 b x}\right)}{4 b}+\frac{1}{2} i x \log \left(1+i c e^{2 a+2 b x}\right)+x \tan ^{-1}(c+(c+i) \tanh (a+b x))-\frac{1}{2} i b x^2","\frac{i \text{PolyLog}\left(2,-i c e^{2 a+2 b x}\right)}{4 b}+\frac{1}{2} i x \log \left(1+i c e^{2 a+2 b x}\right)+x \tan ^{-1}(c+(c+i) \tanh (a+b x))-\frac{1}{2} i b x^2",1,"(-I/2)*b*x^2 + x*ArcTan[c + (I + c)*Tanh[a + b*x]] + (I/2)*x*Log[1 + I*c*E^(2*a + 2*b*x)] + ((I/4)*PolyLog[2, (-I)*c*E^(2*a + 2*b*x)])/b","A",5,5,15,0.3333,1,"{5187, 2184, 2190, 2279, 2391}"
88,0,0,0,0.1119503,"\int \frac{\tan ^{-1}(c+(i+c) \tanh (a+b x))}{x} \, dx","Int[ArcTan[c + (I + c)*Tanh[a + b*x]]/x,x]","\int \frac{\tan ^{-1}(c+(i+c) \tanh (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tan ^{-1}(c+(c+i) \tanh (a+b x))}{x},x\right)",0,"Defer[Int][ArcTan[c + (I + c)*Tanh[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
89,1,145,0,0.2203341,"\int x^2 \tan ^{-1}(c-(i-c) \tanh (a+b x)) \, dx","Int[x^2*ArcTan[c - (I - c)*Tanh[a + b*x]],x]","\frac{i x \text{PolyLog}\left(3,i c e^{2 a+2 b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,i c e^{2 a+2 b x}\right)}{8 b^3}-\frac{i x^2 \text{PolyLog}\left(2,i c e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} i x^3 \log \left(1-i c e^{2 a+2 b x}\right)+\frac{1}{3} x^3 \tan ^{-1}(c-(-c+i) \tanh (a+b x))+\frac{1}{12} i b x^4","\frac{i x \text{PolyLog}\left(3,i c e^{2 a+2 b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,i c e^{2 a+2 b x}\right)}{8 b^3}-\frac{i x^2 \text{PolyLog}\left(2,i c e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} i x^3 \log \left(1-i c e^{2 a+2 b x}\right)+\frac{1}{3} x^3 \tan ^{-1}(c-(-c+i) \tanh (a+b x))+\frac{1}{12} i b x^4",1,"(I/12)*b*x^4 + (x^3*ArcTan[c - (I - c)*Tanh[a + b*x]])/3 - (I/6)*x^3*Log[1 - I*c*E^(2*a + 2*b*x)] - ((I/4)*x^2*PolyLog[2, I*c*E^(2*a + 2*b*x)])/b + ((I/4)*x*PolyLog[3, I*c*E^(2*a + 2*b*x)])/b^2 - ((I/8)*PolyLog[4, I*c*E^(2*a + 2*b*x)])/b^3","A",7,7,22,0.3182,1,"{5195, 2184, 2190, 2531, 6609, 2282, 6589}"
90,1,116,0,0.1969857,"\int x \tan ^{-1}(c-(i-c) \tanh (a+b x)) \, dx","Int[x*ArcTan[c - (I - c)*Tanh[a + b*x]],x]","\frac{i \text{PolyLog}\left(3,i c e^{2 a+2 b x}\right)}{8 b^2}-\frac{i x \text{PolyLog}\left(2,i c e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} i x^2 \log \left(1-i c e^{2 a+2 b x}\right)+\frac{1}{2} x^2 \tan ^{-1}(c-(-c+i) \tanh (a+b x))+\frac{1}{6} i b x^3","\frac{i \text{PolyLog}\left(3,i c e^{2 a+2 b x}\right)}{8 b^2}-\frac{i x \text{PolyLog}\left(2,i c e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} i x^2 \log \left(1-i c e^{2 a+2 b x}\right)+\frac{1}{2} x^2 \tan ^{-1}(c-(-c+i) \tanh (a+b x))+\frac{1}{6} i b x^3",1,"(I/6)*b*x^3 + (x^2*ArcTan[c - (I - c)*Tanh[a + b*x]])/2 - (I/4)*x^2*Log[1 - I*c*E^(2*a + 2*b*x)] - ((I/4)*x*PolyLog[2, I*c*E^(2*a + 2*b*x)])/b + ((I/8)*PolyLog[3, I*c*E^(2*a + 2*b*x)])/b^2","A",6,6,20,0.3000,1,"{5195, 2184, 2190, 2531, 2282, 6589}"
91,1,82,0,0.118922,"\int \tan ^{-1}(c-(i-c) \tanh (a+b x)) \, dx","Int[ArcTan[c - (I - c)*Tanh[a + b*x]],x]","-\frac{i \text{PolyLog}\left(2,i c e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} i x \log \left(1-i c e^{2 a+2 b x}\right)+x \tan ^{-1}(c-(-c+i) \tanh (a+b x))+\frac{1}{2} i b x^2","-\frac{i \text{PolyLog}\left(2,i c e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} i x \log \left(1-i c e^{2 a+2 b x}\right)+x \tan ^{-1}(c-(-c+i) \tanh (a+b x))+\frac{1}{2} i b x^2",1,"(I/2)*b*x^2 + x*ArcTan[c - (I - c)*Tanh[a + b*x]] - (I/2)*x*Log[1 - I*c*E^(2*a + 2*b*x)] - ((I/4)*PolyLog[2, I*c*E^(2*a + 2*b*x)])/b","A",5,5,18,0.2778,1,"{5187, 2184, 2190, 2279, 2391}"
92,0,0,0,0.1156691,"\int \frac{\tan ^{-1}(c-(i-c) \tanh (a+b x))}{x} \, dx","Int[ArcTan[c - (I - c)*Tanh[a + b*x]]/x,x]","\int \frac{\tan ^{-1}(c-(i-c) \tanh (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tan ^{-1}(c-(-c+i) \tanh (a+b x))}{x},x\right)",0,"Defer[Int][ArcTan[c - (I - c)*Tanh[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
93,1,299,0,0.2085548,"\int (e+f x)^3 \tan ^{-1}(\coth (a+b x)) \, dx","Int[(e + f*x)^3*ArcTan[Coth[a + b*x]],x]","-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,-i e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,i e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(3,-i e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(3,i e^{2 a+2 b x}\right)}{8 b^2}+\frac{3 i f^3 \text{PolyLog}\left(5,-i e^{2 a+2 b x}\right)}{16 b^4}-\frac{3 i f^3 \text{PolyLog}\left(5,i e^{2 a+2 b x}\right)}{16 b^4}-\frac{i (e+f x)^3 \text{PolyLog}\left(2,-i e^{2 a+2 b x}\right)}{4 b}+\frac{i (e+f x)^3 \text{PolyLog}\left(2,i e^{2 a+2 b x}\right)}{4 b}+\frac{(e+f x)^4 \tan ^{-1}\left(e^{2 a+2 b x}\right)}{4 f}+\frac{(e+f x)^4 \tan ^{-1}(\coth (a+b x))}{4 f}","-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,-i e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,i e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(3,-i e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(3,i e^{2 a+2 b x}\right)}{8 b^2}+\frac{3 i f^3 \text{PolyLog}\left(5,-i e^{2 a+2 b x}\right)}{16 b^4}-\frac{3 i f^3 \text{PolyLog}\left(5,i e^{2 a+2 b x}\right)}{16 b^4}-\frac{i (e+f x)^3 \text{PolyLog}\left(2,-i e^{2 a+2 b x}\right)}{4 b}+\frac{i (e+f x)^3 \text{PolyLog}\left(2,i e^{2 a+2 b x}\right)}{4 b}+\frac{(e+f x)^4 \tan ^{-1}\left(e^{2 a+2 b x}\right)}{4 f}+\frac{(e+f x)^4 \tan ^{-1}(\coth (a+b x))}{4 f}",1,"((e + f*x)^4*ArcTan[E^(2*a + 2*b*x)])/(4*f) + ((e + f*x)^4*ArcTan[Coth[a + b*x]])/(4*f) - ((I/4)*(e + f*x)^3*PolyLog[2, (-I)*E^(2*a + 2*b*x)])/b + ((I/4)*(e + f*x)^3*PolyLog[2, I*E^(2*a + 2*b*x)])/b + (((3*I)/8)*f*(e + f*x)^2*PolyLog[3, (-I)*E^(2*a + 2*b*x)])/b^2 - (((3*I)/8)*f*(e + f*x)^2*PolyLog[3, I*E^(2*a + 2*b*x)])/b^2 - (((3*I)/8)*f^2*(e + f*x)*PolyLog[4, (-I)*E^(2*a + 2*b*x)])/b^3 + (((3*I)/8)*f^2*(e + f*x)*PolyLog[4, I*E^(2*a + 2*b*x)])/b^3 + (((3*I)/16)*f^3*PolyLog[5, (-I)*E^(2*a + 2*b*x)])/b^4 - (((3*I)/16)*f^3*PolyLog[5, I*E^(2*a + 2*b*x)])/b^4","A",12,6,15,0.4000,1,"{5185, 4180, 2531, 6609, 2282, 6589}"
94,1,229,0,0.1529202,"\int (e+f x)^2 \tan ^{-1}(\coth (a+b x)) \, dx","Int[(e + f*x)^2*ArcTan[Coth[a + b*x]],x]","\frac{i f (e+f x) \text{PolyLog}\left(3,-i e^{2 a+2 b x}\right)}{4 b^2}-\frac{i f (e+f x) \text{PolyLog}\left(3,i e^{2 a+2 b x}\right)}{4 b^2}-\frac{i f^2 \text{PolyLog}\left(4,-i e^{2 a+2 b x}\right)}{8 b^3}+\frac{i f^2 \text{PolyLog}\left(4,i e^{2 a+2 b x}\right)}{8 b^3}-\frac{i (e+f x)^2 \text{PolyLog}\left(2,-i e^{2 a+2 b x}\right)}{4 b}+\frac{i (e+f x)^2 \text{PolyLog}\left(2,i e^{2 a+2 b x}\right)}{4 b}+\frac{(e+f x)^3 \tan ^{-1}\left(e^{2 a+2 b x}\right)}{3 f}+\frac{(e+f x)^3 \tan ^{-1}(\coth (a+b x))}{3 f}","\frac{i f (e+f x) \text{PolyLog}\left(3,-i e^{2 a+2 b x}\right)}{4 b^2}-\frac{i f (e+f x) \text{PolyLog}\left(3,i e^{2 a+2 b x}\right)}{4 b^2}-\frac{i f^2 \text{PolyLog}\left(4,-i e^{2 a+2 b x}\right)}{8 b^3}+\frac{i f^2 \text{PolyLog}\left(4,i e^{2 a+2 b x}\right)}{8 b^3}-\frac{i (e+f x)^2 \text{PolyLog}\left(2,-i e^{2 a+2 b x}\right)}{4 b}+\frac{i (e+f x)^2 \text{PolyLog}\left(2,i e^{2 a+2 b x}\right)}{4 b}+\frac{(e+f x)^3 \tan ^{-1}\left(e^{2 a+2 b x}\right)}{3 f}+\frac{(e+f x)^3 \tan ^{-1}(\coth (a+b x))}{3 f}",1,"((e + f*x)^3*ArcTan[E^(2*a + 2*b*x)])/(3*f) + ((e + f*x)^3*ArcTan[Coth[a + b*x]])/(3*f) - ((I/4)*(e + f*x)^2*PolyLog[2, (-I)*E^(2*a + 2*b*x)])/b + ((I/4)*(e + f*x)^2*PolyLog[2, I*E^(2*a + 2*b*x)])/b + ((I/4)*f*(e + f*x)*PolyLog[3, (-I)*E^(2*a + 2*b*x)])/b^2 - ((I/4)*f*(e + f*x)*PolyLog[3, I*E^(2*a + 2*b*x)])/b^2 - ((I/8)*f^2*PolyLog[4, (-I)*E^(2*a + 2*b*x)])/b^3 + ((I/8)*f^2*PolyLog[4, I*E^(2*a + 2*b*x)])/b^3","A",10,6,15,0.4000,1,"{5185, 4180, 2531, 6609, 2282, 6589}"
95,1,159,0,0.1001055,"\int (e+f x) \tan ^{-1}(\coth (a+b x)) \, dx","Int[(e + f*x)*ArcTan[Coth[a + b*x]],x]","\frac{i f \text{PolyLog}\left(3,-i e^{2 a+2 b x}\right)}{8 b^2}-\frac{i f \text{PolyLog}\left(3,i e^{2 a+2 b x}\right)}{8 b^2}-\frac{i (e+f x) \text{PolyLog}\left(2,-i e^{2 a+2 b x}\right)}{4 b}+\frac{i (e+f x) \text{PolyLog}\left(2,i e^{2 a+2 b x}\right)}{4 b}+\frac{(e+f x)^2 \tan ^{-1}\left(e^{2 a+2 b x}\right)}{2 f}+\frac{(e+f x)^2 \tan ^{-1}(\coth (a+b x))}{2 f}","\frac{i f \text{PolyLog}\left(3,-i e^{2 a+2 b x}\right)}{8 b^2}-\frac{i f \text{PolyLog}\left(3,i e^{2 a+2 b x}\right)}{8 b^2}-\frac{i (e+f x) \text{PolyLog}\left(2,-i e^{2 a+2 b x}\right)}{4 b}+\frac{i (e+f x) \text{PolyLog}\left(2,i e^{2 a+2 b x}\right)}{4 b}+\frac{(e+f x)^2 \tan ^{-1}\left(e^{2 a+2 b x}\right)}{2 f}+\frac{(e+f x)^2 \tan ^{-1}(\coth (a+b x))}{2 f}",1,"((e + f*x)^2*ArcTan[E^(2*a + 2*b*x)])/(2*f) + ((e + f*x)^2*ArcTan[Coth[a + b*x]])/(2*f) - ((I/4)*(e + f*x)*PolyLog[2, (-I)*E^(2*a + 2*b*x)])/b + ((I/4)*(e + f*x)*PolyLog[2, I*E^(2*a + 2*b*x)])/b + ((I/8)*f*PolyLog[3, (-I)*E^(2*a + 2*b*x)])/b^2 - ((I/8)*f*PolyLog[3, I*E^(2*a + 2*b*x)])/b^2","A",8,5,13,0.3846,1,"{5185, 4180, 2531, 2282, 6589}"
96,1,73,0,0.043107,"\int \tan ^{-1}(\coth (a+b x)) \, dx","Int[ArcTan[Coth[a + b*x]],x]","-\frac{i \text{PolyLog}\left(2,-i e^{2 a+2 b x}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,i e^{2 a+2 b x}\right)}{4 b}+x \tan ^{-1}\left(e^{2 a+2 b x}\right)+x \tan ^{-1}(\coth (a+b x))","-\frac{i \text{PolyLog}\left(2,-i e^{2 a+2 b x}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,i e^{2 a+2 b x}\right)}{4 b}+x \tan ^{-1}\left(e^{2 a+2 b x}\right)+x \tan ^{-1}(\coth (a+b x))",1,"x*ArcTan[E^(2*a + 2*b*x)] + x*ArcTan[Coth[a + b*x]] - ((I/4)*PolyLog[2, (-I)*E^(2*a + 2*b*x)])/b + ((I/4)*PolyLog[2, I*E^(2*a + 2*b*x)])/b","A",6,4,7,0.5714,1,"{5181, 4180, 2279, 2391}"
97,0,0,0,0.0432478,"\int \frac{\tan ^{-1}(\coth (a+b x))}{e+f x} \, dx","Int[ArcTan[Coth[a + b*x]]/(e + f*x),x]","\int \frac{\tan ^{-1}(\coth (a+b x))}{e+f x} \, dx","\text{Int}\left(\frac{\tan ^{-1}(\coth (a+b x))}{e+f x},x\right)",0,"Defer[Int][ArcTan[Coth[a + b*x]]/(e + f*x), x]","A",0,0,0,0,-1,"{}"
98,1,351,0,0.4649252,"\int x^2 \tan ^{-1}(c+d \coth (a+b x)) \, dx","Int[x^2*ArcTan[c + d*Coth[a + b*x]],x]","-\frac{i x \text{PolyLog}\left(3,\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{4 b^2}+\frac{i x \text{PolyLog}\left(3,\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{4 b^2}+\frac{i \text{PolyLog}\left(4,\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{8 b^3}-\frac{i \text{PolyLog}\left(4,\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{4 b}-\frac{i x^2 \text{PolyLog}\left(2,\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{4 b}+\frac{1}{6} i x^3 \log \left(1-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)-\frac{1}{6} i x^3 \log \left(1-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)+\frac{1}{3} x^3 \tan ^{-1}(d \coth (a+b x)+c)","-\frac{i x \text{PolyLog}\left(3,\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{4 b^2}+\frac{i x \text{PolyLog}\left(3,\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{4 b^2}+\frac{i \text{PolyLog}\left(4,\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{8 b^3}-\frac{i \text{PolyLog}\left(4,\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{4 b}-\frac{i x^2 \text{PolyLog}\left(2,\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{4 b}+\frac{1}{6} i x^3 \log \left(1-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)-\frac{1}{6} i x^3 \log \left(1-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)+\frac{1}{3} x^3 \tan ^{-1}(d \coth (a+b x)+c)",1,"(x^3*ArcTan[c + d*Coth[a + b*x]])/3 + (I/6)*x^3*Log[1 - ((I - c - d)*E^(2*a + 2*b*x))/(I - c + d)] - (I/6)*x^3*Log[1 - ((I + c + d)*E^(2*a + 2*b*x))/(I + c - d)] + ((I/4)*x^2*PolyLog[2, ((I - c - d)*E^(2*a + 2*b*x))/(I - c + d)])/b - ((I/4)*x^2*PolyLog[2, ((I + c + d)*E^(2*a + 2*b*x))/(I + c - d)])/b - ((I/4)*x*PolyLog[3, ((I - c - d)*E^(2*a + 2*b*x))/(I - c + d)])/b^2 + ((I/4)*x*PolyLog[3, ((I + c + d)*E^(2*a + 2*b*x))/(I + c - d)])/b^2 + ((I/8)*PolyLog[4, ((I - c - d)*E^(2*a + 2*b*x))/(I - c + d)])/b^3 - ((I/8)*PolyLog[4, ((I + c + d)*E^(2*a + 2*b*x))/(I + c - d)])/b^3","A",11,6,15,0.4000,1,"{5201, 2190, 2531, 6609, 2282, 6589}"
99,1,265,0,0.3704374,"\int x \tan ^{-1}(c+d \coth (a+b x)) \, dx","Int[x*ArcTan[c + d*Coth[a + b*x]],x]","-\frac{i \text{PolyLog}\left(3,\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{8 b^2}+\frac{i \text{PolyLog}\left(3,\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{4 b}-\frac{i x \text{PolyLog}\left(2,\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{4 b}+\frac{1}{4} i x^2 \log \left(1-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)-\frac{1}{4} i x^2 \log \left(1-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)+\frac{1}{2} x^2 \tan ^{-1}(d \coth (a+b x)+c)","-\frac{i \text{PolyLog}\left(3,\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{8 b^2}+\frac{i \text{PolyLog}\left(3,\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{4 b}-\frac{i x \text{PolyLog}\left(2,\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{4 b}+\frac{1}{4} i x^2 \log \left(1-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)-\frac{1}{4} i x^2 \log \left(1-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)+\frac{1}{2} x^2 \tan ^{-1}(d \coth (a+b x)+c)",1,"(x^2*ArcTan[c + d*Coth[a + b*x]])/2 + (I/4)*x^2*Log[1 - ((I - c - d)*E^(2*a + 2*b*x))/(I - c + d)] - (I/4)*x^2*Log[1 - ((I + c + d)*E^(2*a + 2*b*x))/(I + c - d)] + ((I/4)*x*PolyLog[2, ((I - c - d)*E^(2*a + 2*b*x))/(I - c + d)])/b - ((I/4)*x*PolyLog[2, ((I + c + d)*E^(2*a + 2*b*x))/(I + c - d)])/b - ((I/8)*PolyLog[3, ((I - c - d)*E^(2*a + 2*b*x))/(I - c + d)])/b^2 + ((I/8)*PolyLog[3, ((I + c + d)*E^(2*a + 2*b*x))/(I + c - d)])/b^2","A",9,5,13,0.3846,1,"{5201, 2190, 2531, 2282, 6589}"
100,1,174,0,0.2276233,"\int \tan ^{-1}(c+d \coth (a+b x)) \, dx","Int[ArcTan[c + d*Coth[a + b*x]],x]","\frac{i \text{PolyLog}\left(2,\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{4 b}-\frac{i \text{PolyLog}\left(2,\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{4 b}+\frac{1}{2} i x \log \left(1-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)-\frac{1}{2} i x \log \left(1-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)+x \tan ^{-1}(d \coth (a+b x)+c)","\frac{i \text{PolyLog}\left(2,\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)}{4 b}-\frac{i \text{PolyLog}\left(2,\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)}{4 b}+\frac{1}{2} i x \log \left(1-\frac{(-c-d+i) e^{2 a+2 b x}}{-c+d+i}\right)-\frac{1}{2} i x \log \left(1-\frac{(c+d+i) e^{2 a+2 b x}}{c-d+i}\right)+x \tan ^{-1}(d \coth (a+b x)+c)",1,"x*ArcTan[c + d*Coth[a + b*x]] + (I/2)*x*Log[1 - ((I - c - d)*E^(2*a + 2*b*x))/(I - c + d)] - (I/2)*x*Log[1 - ((I + c + d)*E^(2*a + 2*b*x))/(I + c - d)] + ((I/4)*PolyLog[2, ((I - c - d)*E^(2*a + 2*b*x))/(I - c + d)])/b - ((I/4)*PolyLog[2, ((I + c + d)*E^(2*a + 2*b*x))/(I + c - d)])/b","A",7,4,11,0.3636,1,"{5193, 2190, 2279, 2391}"
101,0,0,0,0.1211009,"\int \frac{\tan ^{-1}(c+d \coth (a+b x))}{x} \, dx","Int[ArcTan[c + d*Coth[a + b*x]]/x,x]","\int \frac{\tan ^{-1}(c+d \coth (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tan ^{-1}(d \coth (a+b x)+c)}{x},x\right)",0,"Defer[Int][ArcTan[c + d*Coth[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
102,1,142,0,0.2359109,"\int x^2 \tan ^{-1}(c+(i+c) \coth (a+b x)) \, dx","Int[x^2*ArcTan[c + (I + c)*Coth[a + b*x]],x]","-\frac{i x \text{PolyLog}\left(3,i c e^{2 a+2 b x}\right)}{4 b^2}+\frac{i \text{PolyLog}\left(4,i c e^{2 a+2 b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,i c e^{2 a+2 b x}\right)}{4 b}+\frac{1}{6} i x^3 \log \left(1-i c e^{2 a+2 b x}\right)+\frac{1}{3} x^3 \tan ^{-1}(c+(c+i) \coth (a+b x))-\frac{1}{12} i b x^4","-\frac{i x \text{PolyLog}\left(3,i c e^{2 a+2 b x}\right)}{4 b^2}+\frac{i \text{PolyLog}\left(4,i c e^{2 a+2 b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,i c e^{2 a+2 b x}\right)}{4 b}+\frac{1}{6} i x^3 \log \left(1-i c e^{2 a+2 b x}\right)+\frac{1}{3} x^3 \tan ^{-1}(c+(c+i) \coth (a+b x))-\frac{1}{12} i b x^4",1,"(-I/12)*b*x^4 + (x^3*ArcTan[c + (I + c)*Coth[a + b*x]])/3 + (I/6)*x^3*Log[1 - I*c*E^(2*a + 2*b*x)] + ((I/4)*x^2*PolyLog[2, I*c*E^(2*a + 2*b*x)])/b - ((I/4)*x*PolyLog[3, I*c*E^(2*a + 2*b*x)])/b^2 + ((I/8)*PolyLog[4, I*c*E^(2*a + 2*b*x)])/b^3","A",7,7,19,0.3684,1,"{5197, 2184, 2190, 2531, 6609, 2282, 6589}"
103,1,113,0,0.2059654,"\int x \tan ^{-1}(c+(i+c) \coth (a+b x)) \, dx","Int[x*ArcTan[c + (I + c)*Coth[a + b*x]],x]","-\frac{i \text{PolyLog}\left(3,i c e^{2 a+2 b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,i c e^{2 a+2 b x}\right)}{4 b}+\frac{1}{4} i x^2 \log \left(1-i c e^{2 a+2 b x}\right)+\frac{1}{2} x^2 \tan ^{-1}(c+(c+i) \coth (a+b x))-\frac{1}{6} i b x^3","-\frac{i \text{PolyLog}\left(3,i c e^{2 a+2 b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,i c e^{2 a+2 b x}\right)}{4 b}+\frac{1}{4} i x^2 \log \left(1-i c e^{2 a+2 b x}\right)+\frac{1}{2} x^2 \tan ^{-1}(c+(c+i) \coth (a+b x))-\frac{1}{6} i b x^3",1,"(-I/6)*b*x^3 + (x^2*ArcTan[c + (I + c)*Coth[a + b*x]])/2 + (I/4)*x^2*Log[1 - I*c*E^(2*a + 2*b*x)] + ((I/4)*x*PolyLog[2, I*c*E^(2*a + 2*b*x)])/b - ((I/8)*PolyLog[3, I*c*E^(2*a + 2*b*x)])/b^2","A",6,6,17,0.3529,1,"{5197, 2184, 2190, 2531, 2282, 6589}"
104,1,79,0,0.1224231,"\int \tan ^{-1}(c+(i+c) \coth (a+b x)) \, dx","Int[ArcTan[c + (I + c)*Coth[a + b*x]],x]","\frac{i \text{PolyLog}\left(2,i c e^{2 a+2 b x}\right)}{4 b}+\frac{1}{2} i x \log \left(1-i c e^{2 a+2 b x}\right)+x \tan ^{-1}(c+(c+i) \coth (a+b x))-\frac{1}{2} i b x^2","\frac{i \text{PolyLog}\left(2,i c e^{2 a+2 b x}\right)}{4 b}+\frac{1}{2} i x \log \left(1-i c e^{2 a+2 b x}\right)+x \tan ^{-1}(c+(c+i) \coth (a+b x))-\frac{1}{2} i b x^2",1,"(-I/2)*b*x^2 + x*ArcTan[c + (I + c)*Coth[a + b*x]] + (I/2)*x*Log[1 - I*c*E^(2*a + 2*b*x)] + ((I/4)*PolyLog[2, I*c*E^(2*a + 2*b*x)])/b","A",5,5,15,0.3333,1,"{5189, 2184, 2190, 2279, 2391}"
105,0,0,0,0.1098866,"\int \frac{\tan ^{-1}(c+(i+c) \coth (a+b x))}{x} \, dx","Int[ArcTan[c + (I + c)*Coth[a + b*x]]/x,x]","\int \frac{\tan ^{-1}(c+(i+c) \coth (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tan ^{-1}(c+(c+i) \coth (a+b x))}{x},x\right)",0,"Defer[Int][ArcTan[c + (I + c)*Coth[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
106,1,145,0,0.2312046,"\int x^2 \tan ^{-1}(c-(i-c) \coth (a+b x)) \, dx","Int[x^2*ArcTan[c - (I - c)*Coth[a + b*x]],x]","\frac{i x \text{PolyLog}\left(3,-i c e^{2 a+2 b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,-i c e^{2 a+2 b x}\right)}{8 b^3}-\frac{i x^2 \text{PolyLog}\left(2,-i c e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} i x^3 \log \left(1+i c e^{2 a+2 b x}\right)+\frac{1}{3} x^3 \tan ^{-1}(c-(-c+i) \coth (a+b x))+\frac{1}{12} i b x^4","\frac{i x \text{PolyLog}\left(3,-i c e^{2 a+2 b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,-i c e^{2 a+2 b x}\right)}{8 b^3}-\frac{i x^2 \text{PolyLog}\left(2,-i c e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} i x^3 \log \left(1+i c e^{2 a+2 b x}\right)+\frac{1}{3} x^3 \tan ^{-1}(c-(-c+i) \coth (a+b x))+\frac{1}{12} i b x^4",1,"(I/12)*b*x^4 + (x^3*ArcTan[c - (I - c)*Coth[a + b*x]])/3 - (I/6)*x^3*Log[1 + I*c*E^(2*a + 2*b*x)] - ((I/4)*x^2*PolyLog[2, (-I)*c*E^(2*a + 2*b*x)])/b + ((I/4)*x*PolyLog[3, (-I)*c*E^(2*a + 2*b*x)])/b^2 - ((I/8)*PolyLog[4, (-I)*c*E^(2*a + 2*b*x)])/b^3","A",7,7,22,0.3182,1,"{5197, 2184, 2190, 2531, 6609, 2282, 6589}"
107,1,116,0,0.2013362,"\int x \tan ^{-1}(c-(i-c) \coth (a+b x)) \, dx","Int[x*ArcTan[c - (I - c)*Coth[a + b*x]],x]","\frac{i \text{PolyLog}\left(3,-i c e^{2 a+2 b x}\right)}{8 b^2}-\frac{i x \text{PolyLog}\left(2,-i c e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} i x^2 \log \left(1+i c e^{2 a+2 b x}\right)+\frac{1}{2} x^2 \tan ^{-1}(c-(-c+i) \coth (a+b x))+\frac{1}{6} i b x^3","\frac{i \text{PolyLog}\left(3,-i c e^{2 a+2 b x}\right)}{8 b^2}-\frac{i x \text{PolyLog}\left(2,-i c e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} i x^2 \log \left(1+i c e^{2 a+2 b x}\right)+\frac{1}{2} x^2 \tan ^{-1}(c-(-c+i) \coth (a+b x))+\frac{1}{6} i b x^3",1,"(I/6)*b*x^3 + (x^2*ArcTan[c - (I - c)*Coth[a + b*x]])/2 - (I/4)*x^2*Log[1 + I*c*E^(2*a + 2*b*x)] - ((I/4)*x*PolyLog[2, (-I)*c*E^(2*a + 2*b*x)])/b + ((I/8)*PolyLog[3, (-I)*c*E^(2*a + 2*b*x)])/b^2","A",6,6,20,0.3000,1,"{5197, 2184, 2190, 2531, 2282, 6589}"
108,1,82,0,0.1206852,"\int \tan ^{-1}(c-(i-c) \coth (a+b x)) \, dx","Int[ArcTan[c - (I - c)*Coth[a + b*x]],x]","-\frac{i \text{PolyLog}\left(2,-i c e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} i x \log \left(1+i c e^{2 a+2 b x}\right)+x \tan ^{-1}(c-(-c+i) \coth (a+b x))+\frac{1}{2} i b x^2","-\frac{i \text{PolyLog}\left(2,-i c e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} i x \log \left(1+i c e^{2 a+2 b x}\right)+x \tan ^{-1}(c-(-c+i) \coth (a+b x))+\frac{1}{2} i b x^2",1,"(I/2)*b*x^2 + x*ArcTan[c - (I - c)*Coth[a + b*x]] - (I/2)*x*Log[1 + I*c*E^(2*a + 2*b*x)] - ((I/4)*PolyLog[2, (-I)*c*E^(2*a + 2*b*x)])/b","A",5,5,18,0.2778,1,"{5189, 2184, 2190, 2279, 2391}"
109,0,0,0,0.1119698,"\int \frac{\tan ^{-1}(c-(i-c) \coth (a+b x))}{x} \, dx","Int[ArcTan[c - (I - c)*Coth[a + b*x]]/x,x]","\int \frac{\tan ^{-1}(c-(i-c) \coth (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tan ^{-1}(c-(-c+i) \coth (a+b x))}{x},x\right)",0,"Defer[Int][ArcTan[c - (I - c)*Coth[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
110,1,31,0,0.0255403,"\int \tan ^{-1}\left(e^x\right) \, dx","Int[ArcTan[E^x],x]","\frac{1}{2} i \text{PolyLog}\left(2,-i e^x\right)-\frac{1}{2} i \text{PolyLog}\left(2,i e^x\right)","\frac{1}{2} i \text{PolyLog}\left(2,-i e^x\right)-\frac{1}{2} i \text{PolyLog}\left(2,i e^x\right)",1,"(I/2)*PolyLog[2, (-I)*E^x] - (I/2)*PolyLog[2, I*E^x]","A",4,3,4,0.7500,1,"{2282, 4848, 2391}"
111,1,63,0,0.0427798,"\int x \tan ^{-1}\left(e^x\right) \, dx","Int[x*ArcTan[E^x],x]","\frac{1}{2} i x \text{PolyLog}\left(2,-i e^x\right)-\frac{1}{2} i x \text{PolyLog}\left(2,i e^x\right)-\frac{1}{2} i \text{PolyLog}\left(3,-i e^x\right)+\frac{1}{2} i \text{PolyLog}\left(3,i e^x\right)","\frac{1}{2} i x \text{PolyLog}\left(2,-i e^x\right)-\frac{1}{2} i x \text{PolyLog}\left(2,i e^x\right)-\frac{1}{2} i \text{PolyLog}\left(3,-i e^x\right)+\frac{1}{2} i \text{PolyLog}\left(3,i e^x\right)",1,"(I/2)*x*PolyLog[2, (-I)*E^x] - (I/2)*x*PolyLog[2, I*E^x] - (I/2)*PolyLog[3, (-I)*E^x] + (I/2)*PolyLog[3, I*E^x]","A",7,4,6,0.6667,1,"{5143, 2531, 2282, 6589}"
112,1,91,0,0.0661729,"\int x^2 \tan ^{-1}\left(e^x\right) \, dx","Int[x^2*ArcTan[E^x],x]","\frac{1}{2} i x^2 \text{PolyLog}\left(2,-i e^x\right)-\frac{1}{2} i x^2 \text{PolyLog}\left(2,i e^x\right)-i x \text{PolyLog}\left(3,-i e^x\right)+i x \text{PolyLog}\left(3,i e^x\right)+i \text{PolyLog}\left(4,-i e^x\right)-i \text{PolyLog}\left(4,i e^x\right)","\frac{1}{2} i x^2 \text{PolyLog}\left(2,-i e^x\right)-\frac{1}{2} i x^2 \text{PolyLog}\left(2,i e^x\right)-i x \text{PolyLog}\left(3,-i e^x\right)+i x \text{PolyLog}\left(3,i e^x\right)+i \text{PolyLog}\left(4,-i e^x\right)-i \text{PolyLog}\left(4,i e^x\right)",1,"(I/2)*x^2*PolyLog[2, (-I)*E^x] - (I/2)*x^2*PolyLog[2, I*E^x] - I*x*PolyLog[3, (-I)*E^x] + I*x*PolyLog[3, I*E^x] + I*PolyLog[4, (-I)*E^x] - I*PolyLog[4, I*E^x]","A",9,5,8,0.6250,1,"{5143, 2531, 6609, 2282, 6589}"
113,1,45,0,0.027565,"\int \tan ^{-1}\left(e^{a+b x}\right) \, dx","Int[ArcTan[E^(a + b*x)],x]","\frac{i \text{PolyLog}\left(2,-i e^{a+b x}\right)}{2 b}-\frac{i \text{PolyLog}\left(2,i e^{a+b x}\right)}{2 b}","\frac{i \text{PolyLog}\left(2,-i e^{a+b x}\right)}{2 b}-\frac{i \text{PolyLog}\left(2,i e^{a+b x}\right)}{2 b}",1,"((I/2)*PolyLog[2, (-I)*E^(a + b*x)])/b - ((I/2)*PolyLog[2, I*E^(a + b*x)])/b","A",4,3,8,0.3750,1,"{2282, 4848, 2391}"
114,1,91,0,0.0579984,"\int x \tan ^{-1}\left(e^{a+b x}\right) \, dx","Int[x*ArcTan[E^(a + b*x)],x]","-\frac{i \text{PolyLog}\left(3,-i e^{a+b x}\right)}{2 b^2}+\frac{i \text{PolyLog}\left(3,i e^{a+b x}\right)}{2 b^2}+\frac{i x \text{PolyLog}\left(2,-i e^{a+b x}\right)}{2 b}-\frac{i x \text{PolyLog}\left(2,i e^{a+b x}\right)}{2 b}","-\frac{i \text{PolyLog}\left(3,-i e^{a+b x}\right)}{2 b^2}+\frac{i \text{PolyLog}\left(3,i e^{a+b x}\right)}{2 b^2}+\frac{i x \text{PolyLog}\left(2,-i e^{a+b x}\right)}{2 b}-\frac{i x \text{PolyLog}\left(2,i e^{a+b x}\right)}{2 b}",1,"((I/2)*x*PolyLog[2, (-I)*E^(a + b*x)])/b - ((I/2)*x*PolyLog[2, I*E^(a + b*x)])/b - ((I/2)*PolyLog[3, (-I)*E^(a + b*x)])/b^2 + ((I/2)*PolyLog[3, I*E^(a + b*x)])/b^2","A",7,4,10,0.4000,1,"{5143, 2531, 2282, 6589}"
115,1,133,0,0.0899561,"\int x^2 \tan ^{-1}\left(e^{a+b x}\right) \, dx","Int[x^2*ArcTan[E^(a + b*x)],x]","-\frac{i x \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^2}+\frac{i x \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^2}+\frac{i \text{PolyLog}\left(4,-i e^{a+b x}\right)}{b^3}-\frac{i \text{PolyLog}\left(4,i e^{a+b x}\right)}{b^3}+\frac{i x^2 \text{PolyLog}\left(2,-i e^{a+b x}\right)}{2 b}-\frac{i x^2 \text{PolyLog}\left(2,i e^{a+b x}\right)}{2 b}","-\frac{i x \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^2}+\frac{i x \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^2}+\frac{i \text{PolyLog}\left(4,-i e^{a+b x}\right)}{b^3}-\frac{i \text{PolyLog}\left(4,i e^{a+b x}\right)}{b^3}+\frac{i x^2 \text{PolyLog}\left(2,-i e^{a+b x}\right)}{2 b}-\frac{i x^2 \text{PolyLog}\left(2,i e^{a+b x}\right)}{2 b}",1,"((I/2)*x^2*PolyLog[2, (-I)*E^(a + b*x)])/b - ((I/2)*x^2*PolyLog[2, I*E^(a + b*x)])/b - (I*x*PolyLog[3, (-I)*E^(a + b*x)])/b^2 + (I*x*PolyLog[3, I*E^(a + b*x)])/b^2 + (I*PolyLog[4, (-I)*E^(a + b*x)])/b^3 - (I*PolyLog[4, I*E^(a + b*x)])/b^3","A",9,5,12,0.4167,1,"{5143, 2531, 6609, 2282, 6589}"
116,1,196,0,0.1481497,"\int \tan ^{-1}\left(a+b f^{c+d x}\right) \, dx","Int[ArcTan[a + b*f^(c + d*x)],x]","\frac{i \text{PolyLog}\left(2,1-\frac{2}{1-i \left(a+b f^{c+d x}\right)}\right)}{2 d \log (f)}-\frac{i \text{PolyLog}\left(2,1-\frac{2 b f^{c+d x}}{(-a+i) \left(1-i \left(a+b f^{c+d x}\right)\right)}\right)}{2 d \log (f)}-\frac{\log \left(\frac{2}{1-i \left(a+b f^{c+d x}\right)}\right) \tan ^{-1}\left(a+b f^{c+d x}\right)}{d \log (f)}+\frac{\log \left(\frac{2 b f^{c+d x}}{(-a+i) \left(1-i \left(a+b f^{c+d x}\right)\right)}\right) \tan ^{-1}\left(a+b f^{c+d x}\right)}{d \log (f)}","\frac{i \text{PolyLog}\left(2,1-\frac{2}{1-i \left(a+b f^{c+d x}\right)}\right)}{2 d \log (f)}-\frac{i \text{PolyLog}\left(2,1-\frac{2 b f^{c+d x}}{(-a+i) \left(1-i \left(a+b f^{c+d x}\right)\right)}\right)}{2 d \log (f)}-\frac{\log \left(\frac{2}{1-i \left(a+b f^{c+d x}\right)}\right) \tan ^{-1}\left(a+b f^{c+d x}\right)}{d \log (f)}+\frac{\log \left(\frac{2 b f^{c+d x}}{(-a+i) \left(1-i \left(a+b f^{c+d x}\right)\right)}\right) \tan ^{-1}\left(a+b f^{c+d x}\right)}{d \log (f)}",1,"-((ArcTan[a + b*f^(c + d*x)]*Log[2/(1 - I*(a + b*f^(c + d*x)))])/(d*Log[f])) + (ArcTan[a + b*f^(c + d*x)]*Log[(2*b*f^(c + d*x))/((I - a)*(1 - I*(a + b*f^(c + d*x))))])/(d*Log[f]) + ((I/2)*PolyLog[2, 1 - 2/(1 - I*(a + b*f^(c + d*x)))])/(d*Log[f]) - ((I/2)*PolyLog[2, 1 - (2*b*f^(c + d*x))/((I - a)*(1 - I*(a + b*f^(c + d*x))))])/(d*Log[f])","A",6,6,12,0.5000,1,"{2282, 5047, 4856, 2402, 2315, 2447}"
117,1,250,0,0.1509293,"\int x \tan ^{-1}\left(a+b f^{c+d x}\right) \, dx","Int[x*ArcTan[a + b*f^(c + d*x)],x]","-\frac{i \text{PolyLog}\left(3,\frac{b f^{c+d x}}{-a+i}\right)}{2 d^2 \log ^2(f)}+\frac{i \text{PolyLog}\left(3,-\frac{b f^{c+d x}}{a+i}\right)}{2 d^2 \log ^2(f)}+\frac{i x \text{PolyLog}\left(2,\frac{b f^{c+d x}}{-a+i}\right)}{2 d \log (f)}-\frac{i x \text{PolyLog}\left(2,-\frac{b f^{c+d x}}{a+i}\right)}{2 d \log (f)}+\frac{1}{4} i x^2 \log \left(-i a-i b f^{c+d x}+1\right)-\frac{1}{4} i x^2 \log \left(i a+i b f^{c+d x}+1\right)+\frac{1}{4} i x^2 \log \left(1-\frac{b f^{c+d x}}{-a+i}\right)-\frac{1}{4} i x^2 \log \left(1+\frac{b f^{c+d x}}{a+i}\right)","\frac{i \text{PolyLog}\left(3,\frac{i b f^{c+d x}}{1-i a}\right)}{2 d^2 \log ^2(f)}-\frac{i \text{PolyLog}\left(3,-\frac{i b f^{c+d x}}{1+i a}\right)}{2 d^2 \log ^2(f)}-\frac{i x \text{PolyLog}\left(2,\frac{i b f^{c+d x}}{1-i a}\right)}{2 d \log (f)}+\frac{i x \text{PolyLog}\left(2,-\frac{i b f^{c+d x}}{1+i a}\right)}{2 d \log (f)}-\frac{1}{4} i x^2 \log \left(1-\frac{i b f^{c+d x}}{1-i a}\right)+\frac{1}{4} i x^2 \log \left(1+\frac{i b f^{c+d x}}{1+i a}\right)+\frac{1}{2} x^2 \tan ^{-1}\left(a+b f^{c+d x}\right)",1,"(I/4)*x^2*Log[1 - I*a - I*b*f^(c + d*x)] - (I/4)*x^2*Log[1 + I*a + I*b*f^(c + d*x)] + (I/4)*x^2*Log[1 - (b*f^(c + d*x))/(I - a)] - (I/4)*x^2*Log[1 + (b*f^(c + d*x))/(I + a)] + ((I/2)*x*PolyLog[2, (b*f^(c + d*x))/(I - a)])/(d*Log[f]) - ((I/2)*x*PolyLog[2, -((b*f^(c + d*x))/(I + a))])/(d*Log[f]) - ((I/2)*PolyLog[3, (b*f^(c + d*x))/(I - a)])/(d^2*Log[f]^2) + ((I/2)*PolyLog[3, -((b*f^(c + d*x))/(I + a))])/(d^2*Log[f]^2)","A",9,5,14,0.3571,0,"{5143, 2532, 2531, 2282, 6589}"
118,1,313,0,0.2010919,"\int x^2 \tan ^{-1}\left(a+b f^{c+d x}\right) \, dx","Int[x^2*ArcTan[a + b*f^(c + d*x)],x]","-\frac{i x \text{PolyLog}\left(3,\frac{b f^{c+d x}}{-a+i}\right)}{d^2 \log ^2(f)}+\frac{i x \text{PolyLog}\left(3,-\frac{b f^{c+d x}}{a+i}\right)}{d^2 \log ^2(f)}+\frac{i \text{PolyLog}\left(4,\frac{b f^{c+d x}}{-a+i}\right)}{d^3 \log ^3(f)}-\frac{i \text{PolyLog}\left(4,-\frac{b f^{c+d x}}{a+i}\right)}{d^3 \log ^3(f)}+\frac{i x^2 \text{PolyLog}\left(2,\frac{b f^{c+d x}}{-a+i}\right)}{2 d \log (f)}-\frac{i x^2 \text{PolyLog}\left(2,-\frac{b f^{c+d x}}{a+i}\right)}{2 d \log (f)}+\frac{1}{6} i x^3 \log \left(-i a-i b f^{c+d x}+1\right)-\frac{1}{6} i x^3 \log \left(i a+i b f^{c+d x}+1\right)+\frac{1}{6} i x^3 \log \left(1-\frac{b f^{c+d x}}{-a+i}\right)-\frac{1}{6} i x^3 \log \left(1+\frac{b f^{c+d x}}{a+i}\right)","\frac{i x \text{PolyLog}\left(3,\frac{i b f^{c+d x}}{1-i a}\right)}{d^2 \log ^2(f)}-\frac{i x \text{PolyLog}\left(3,-\frac{i b f^{c+d x}}{1+i a}\right)}{d^2 \log ^2(f)}-\frac{i \text{PolyLog}\left(4,\frac{i b f^{c+d x}}{1-i a}\right)}{d^3 \log ^3(f)}+\frac{i \text{PolyLog}\left(4,-\frac{i b f^{c+d x}}{1+i a}\right)}{d^3 \log ^3(f)}-\frac{i x^2 \text{PolyLog}\left(2,\frac{i b f^{c+d x}}{1-i a}\right)}{2 d \log (f)}+\frac{i x^2 \text{PolyLog}\left(2,-\frac{i b f^{c+d x}}{1+i a}\right)}{2 d \log (f)}-\frac{1}{6} i x^3 \log \left(1-\frac{i b f^{c+d x}}{1-i a}\right)+\frac{1}{6} i x^3 \log \left(1+\frac{i b f^{c+d x}}{1+i a}\right)+\frac{1}{3} x^3 \tan ^{-1}\left(a+b f^{c+d x}\right)",1,"(I/6)*x^3*Log[1 - I*a - I*b*f^(c + d*x)] - (I/6)*x^3*Log[1 + I*a + I*b*f^(c + d*x)] + (I/6)*x^3*Log[1 - (b*f^(c + d*x))/(I - a)] - (I/6)*x^3*Log[1 + (b*f^(c + d*x))/(I + a)] + ((I/2)*x^2*PolyLog[2, (b*f^(c + d*x))/(I - a)])/(d*Log[f]) - ((I/2)*x^2*PolyLog[2, -((b*f^(c + d*x))/(I + a))])/(d*Log[f]) - (I*x*PolyLog[3, (b*f^(c + d*x))/(I - a)])/(d^2*Log[f]^2) + (I*x*PolyLog[3, -((b*f^(c + d*x))/(I + a))])/(d^2*Log[f]^2) + (I*PolyLog[4, (b*f^(c + d*x))/(I - a)])/(d^3*Log[f]^3) - (I*PolyLog[4, -((b*f^(c + d*x))/(I + a))])/(d^3*Log[f]^3)","A",11,6,16,0.3750,0,"{5143, 2532, 2531, 6609, 2282, 6589}"
119,1,25,0,0.0211932,"\int e^{-x} \tan ^{-1}\left(e^x\right) \, dx","Int[ArcTan[E^x]/E^x,x]","x-\frac{1}{2} \log \left(e^{2 x}+1\right)-e^{-x} \tan ^{-1}\left(e^x\right)","x-\frac{1}{2} \log \left(e^{2 x}+1\right)-e^{-x} \tan ^{-1}\left(e^x\right)",1,"x - ArcTan[E^x]/E^x - Log[1 + E^(2*x)]/2","A",5,6,10,0.6000,1,"{2194, 5207, 2282, 36, 29, 31}"
120,1,45,0,0.0317409,"\int \frac{\tan ^{-1}(x)}{(-1+x)^3} \, dx","Int[ArcTan[x]/(-1 + x)^3,x]","\frac{1}{8} \log \left(x^2+1\right)+\frac{1}{4 (1-x)}-\frac{1}{4} \log (1-x)-\frac{\tan ^{-1}(x)}{2 (1-x)^2}","\frac{1}{8} \log \left(x^2+1\right)+\frac{1}{4 (1-x)}-\frac{1}{4} \log (1-x)-\frac{\tan ^{-1}(x)}{2 (1-x)^2}",1,"1/(4*(1 - x)) - ArcTan[x]/(2*(1 - x)^2) - Log[1 - x]/4 + Log[1 + x^2]/8","A",5,4,8,0.5000,1,"{4862, 710, 801, 260}"
121,1,64,0,0.067086,"\int \frac{\tan ^{-1}(1+2 x)}{(4+3 x)^3} \, dx","Int[ArcTan[1 + 2*x]/(4 + 3*x)^3,x]","-\frac{5}{578} \log \left(2 x^2+2 x+1\right)-\frac{1}{34 (3 x+4)}+\frac{5}{289} \log (3 x+4)-\frac{\tan ^{-1}(2 x+1)}{6 (3 x+4)^2}+\frac{8}{867} \tan ^{-1}(2 x+1)","-\frac{5}{578} \log \left(2 x^2+2 x+1\right)-\frac{1}{34 (3 x+4)}+\frac{5}{289} \log (3 x+4)-\frac{\tan ^{-1}(2 x+1)}{6 (3 x+4)^2}+\frac{8}{867} \tan ^{-1}(2 x+1)",1,"-1/(34*(4 + 3*x)) + (8*ArcTan[1 + 2*x])/867 - ArcTan[1 + 2*x]/(6*(4 + 3*x)^2) + (5*Log[4 + 3*x])/289 - (5*Log[1 + 2*x + 2*x^2])/578","A",9,8,14,0.5714,1,"{5045, 1982, 709, 800, 634, 617, 204, 628}"
122,1,30,0,0.0110627,"\int \tan ^{-1}\left(\sqrt{1+x}\right) \, dx","Int[ArcTan[Sqrt[1 + x]],x]","-\sqrt{x+1}+x \tan ^{-1}\left(\sqrt{x+1}\right)+2 \tan ^{-1}\left(\sqrt{x+1}\right)","-\sqrt{x+1}+x \tan ^{-1}\left(\sqrt{x+1}\right)+2 \tan ^{-1}\left(\sqrt{x+1}\right)",1,"-Sqrt[1 + x] + 2*ArcTan[Sqrt[1 + x]] + x*ArcTan[Sqrt[1 + x]]","A",4,4,8,0.5000,1,"{5203, 80, 63, 203}"
123,1,5,0,0.0245949,"\int \frac{1}{\left(1+x^2\right) \left(2+\tan ^{-1}(x)\right)} \, dx","Int[1/((1 + x^2)*(2 + ArcTan[x])),x]","\log \left(\tan ^{-1}(x)+2\right)","\log \left(\tan ^{-1}(x)+2\right)",1,"Log[2 + ArcTan[x]]","A",1,1,14,0.07143,1,"{4882}"
124,1,17,0,0.0393312,"\int \frac{1}{\left(a+a x^2\right) \left(b-2 b \tan ^{-1}(x)\right)} \, dx","Int[1/((a + a*x^2)*(b - 2*b*ArcTan[x])),x]","-\frac{\log \left(1-2 \tan ^{-1}(x)\right)}{2 a b}","-\frac{\log \left(1-2 \tan ^{-1}(x)\right)}{2 a b}",1,"-Log[1 - 2*ArcTan[x]]/(2*a*b)","A",1,1,19,0.05263,1,"{4882}"
125,1,18,0,0.1508042,"\int \frac{x+x^3+(1+x)^2 \tan ^{-1}(x)}{(1+x)^2 \left(1+x^2\right)} \, dx","Int[(x + x^3 + (1 + x)^2*ArcTan[x])/((1 + x)^2*(1 + x^2)),x]","\frac{1}{x+1}+\log (x+1)+\frac{1}{2} \tan ^{-1}(x)^2","\frac{1}{x+1}+\log (x+1)+\frac{1}{2} \tan ^{-1}(x)^2",1,"(1 + x)^(-1) + ArcTan[x]^2/2 + Log[1 + x]","A",5,3,26,0.1154,1,"{6725, 43, 4884}"
126,1,68,0,0.0279441,"\int -x^3 \tan ^{-1}\left(\sqrt{x}-\sqrt{1+x}\right) \, dx","Int[-(x^3*ArcTan[Sqrt[x] - Sqrt[1 + x]]),x]","\frac{\pi  x^4}{16}+\frac{x^{7/2}}{56}-\frac{x^{5/2}}{40}+\frac{x^{3/2}}{24}-\frac{1}{8} x^4 \tan ^{-1}\left(\sqrt{x}\right)-\frac{\sqrt{x}}{8}+\frac{1}{8} \tan ^{-1}\left(\sqrt{x}\right)","\frac{\pi  x^4}{16}+\frac{x^{7/2}}{56}-\frac{x^{5/2}}{40}+\frac{x^{3/2}}{24}-\frac{1}{8} x^4 \tan ^{-1}\left(\sqrt{x}\right)-\frac{\sqrt{x}}{8}+\frac{1}{8} \tan ^{-1}\left(\sqrt{x}\right)",1,"-Sqrt[x]/8 + x^(3/2)/24 - x^(5/2)/40 + x^(7/2)/56 + (Pi*x^4)/16 + ArcTan[Sqrt[x]]/8 - (x^4*ArcTan[Sqrt[x]])/8","A",9,6,21,0.2857,1,"{5159, 30, 5033, 50, 63, 203}"
127,1,59,0,0.0259393,"\int -x^2 \tan ^{-1}\left(\sqrt{x}-\sqrt{1+x}\right) \, dx","Int[-(x^2*ArcTan[Sqrt[x] - Sqrt[1 + x]]),x]","\frac{\pi  x^3}{12}+\frac{x^{5/2}}{30}-\frac{x^{3/2}}{18}-\frac{1}{6} x^3 \tan ^{-1}\left(\sqrt{x}\right)+\frac{\sqrt{x}}{6}-\frac{1}{6} \tan ^{-1}\left(\sqrt{x}\right)","\frac{\pi  x^3}{12}+\frac{x^{5/2}}{30}-\frac{x^{3/2}}{18}-\frac{1}{6} x^3 \tan ^{-1}\left(\sqrt{x}\right)+\frac{\sqrt{x}}{6}-\frac{1}{6} \tan ^{-1}\left(\sqrt{x}\right)",1,"Sqrt[x]/6 - x^(3/2)/18 + x^(5/2)/30 + (Pi*x^3)/12 - ArcTan[Sqrt[x]]/6 - (x^3*ArcTan[Sqrt[x]])/6","A",8,6,21,0.2857,1,"{5159, 30, 5033, 50, 63, 203}"
128,1,50,0,0.0176926,"\int -x \tan ^{-1}\left(\sqrt{x}-\sqrt{1+x}\right) \, dx","Int[-(x*ArcTan[Sqrt[x] - Sqrt[1 + x]]),x]","\frac{\pi  x^2}{8}+\frac{x^{3/2}}{12}-\frac{1}{4} x^2 \tan ^{-1}\left(\sqrt{x}\right)-\frac{\sqrt{x}}{4}+\frac{1}{4} \tan ^{-1}\left(\sqrt{x}\right)","\frac{\pi  x^2}{8}+\frac{x^{3/2}}{12}-\frac{1}{4} x^2 \tan ^{-1}\left(\sqrt{x}\right)-\frac{\sqrt{x}}{4}+\frac{1}{4} \tan ^{-1}\left(\sqrt{x}\right)",1,"-Sqrt[x]/4 + x^(3/2)/12 + (Pi*x^2)/8 + ArcTan[Sqrt[x]]/4 - (x^2*ArcTan[Sqrt[x]])/4","A",7,6,19,0.3158,1,"{5159, 30, 5033, 50, 63, 203}"
129,1,37,0,0.0100762,"\int -\tan ^{-1}\left(\sqrt{x}-\sqrt{1+x}\right) \, dx","Int[-ArcTan[Sqrt[x] - Sqrt[1 + x]],x]","\frac{\pi  x}{4}+\frac{\sqrt{x}}{2}-\frac{1}{2} x \tan ^{-1}\left(\sqrt{x}\right)-\frac{1}{2} \tan ^{-1}\left(\sqrt{x}\right)","\frac{\pi  x}{4}+\frac{\sqrt{x}}{2}-\frac{1}{2} x \tan ^{-1}\left(\sqrt{x}\right)-\frac{1}{2} \tan ^{-1}\left(\sqrt{x}\right)",1,"Sqrt[x]/2 + (Pi*x)/4 - ArcTan[Sqrt[x]]/2 - (x*ArcTan[Sqrt[x]])/2","A",6,6,18,0.3333,1,"{5159, 8, 5027, 50, 63, 203}"
130,1,42,0,0.0422181,"\int -\frac{\tan ^{-1}\left(\sqrt{x}-\sqrt{1+x}\right)}{x} \, dx","Int[-(ArcTan[Sqrt[x] - Sqrt[1 + x]]/x),x]","-\frac{1}{2} i \text{PolyLog}\left(2,-i \sqrt{x}\right)+\frac{1}{2} i \text{PolyLog}\left(2,i \sqrt{x}\right)+\frac{1}{4} \pi  \log (x)","-\frac{1}{2} i \text{PolyLog}\left(2,-i \sqrt{x}\right)+\frac{1}{2} i \text{PolyLog}\left(2,i \sqrt{x}\right)+\frac{1}{4} \pi  \log (x)",1,"(Pi*Log[x])/4 - (I/2)*PolyLog[2, (-I)*Sqrt[x]] + (I/2)*PolyLog[2, I*Sqrt[x]]","A",6,5,21,0.2381,1,"{5159, 29, 5031, 4848, 2391}"
131,1,41,0,0.0221297,"\int -\frac{\tan ^{-1}\left(\sqrt{x}-\sqrt{1+x}\right)}{x^2} \, dx","Int[-(ArcTan[Sqrt[x] - Sqrt[1 + x]]/x^2),x]","\frac{1}{2 \sqrt{x}}-\frac{\pi }{4 x}+\frac{\tan ^{-1}\left(\sqrt{x}\right)}{2 x}+\frac{1}{2} \tan ^{-1}\left(\sqrt{x}\right)","\frac{1}{2 \sqrt{x}}-\frac{\pi }{4 x}+\frac{\tan ^{-1}\left(\sqrt{x}\right)}{2 x}+\frac{1}{2} \tan ^{-1}\left(\sqrt{x}\right)",1,"-Pi/(4*x) + 1/(2*Sqrt[x]) + ArcTan[Sqrt[x]]/2 + ArcTan[Sqrt[x]]/(2*x)","A",6,6,21,0.2857,1,"{5159, 30, 5033, 51, 63, 203}"
132,1,50,0,0.0242087,"\int -\frac{\tan ^{-1}\left(\sqrt{x}-\sqrt{1+x}\right)}{x^3} \, dx","Int[-(ArcTan[Sqrt[x] - Sqrt[1 + x]]/x^3),x]","\frac{1}{12 x^{3/2}}-\frac{\pi }{8 x^2}+\frac{\tan ^{-1}\left(\sqrt{x}\right)}{4 x^2}-\frac{1}{4 \sqrt{x}}-\frac{1}{4} \tan ^{-1}\left(\sqrt{x}\right)","\frac{1}{12 x^{3/2}}-\frac{\pi }{8 x^2}+\frac{\tan ^{-1}\left(\sqrt{x}\right)}{4 x^2}-\frac{1}{4 \sqrt{x}}-\frac{1}{4} \tan ^{-1}\left(\sqrt{x}\right)",1,"-Pi/(8*x^2) + 1/(12*x^(3/2)) - 1/(4*Sqrt[x]) - ArcTan[Sqrt[x]]/4 + ArcTan[Sqrt[x]]/(4*x^2)","A",7,6,21,0.2857,1,"{5159, 30, 5033, 51, 63, 203}"
133,1,59,0,0.0245805,"\int -\frac{\tan ^{-1}\left(\sqrt{x}-\sqrt{1+x}\right)}{x^4} \, dx","Int[-(ArcTan[Sqrt[x] - Sqrt[1 + x]]/x^4),x]","-\frac{1}{18 x^{3/2}}+\frac{1}{30 x^{5/2}}-\frac{\pi }{12 x^3}+\frac{\tan ^{-1}\left(\sqrt{x}\right)}{6 x^3}+\frac{1}{6 \sqrt{x}}+\frac{1}{6} \tan ^{-1}\left(\sqrt{x}\right)","-\frac{1}{18 x^{3/2}}+\frac{1}{30 x^{5/2}}-\frac{\pi }{12 x^3}+\frac{\tan ^{-1}\left(\sqrt{x}\right)}{6 x^3}+\frac{1}{6 \sqrt{x}}+\frac{1}{6} \tan ^{-1}\left(\sqrt{x}\right)",1,"-Pi/(12*x^3) + 1/(30*x^(5/2)) - 1/(18*x^(3/2)) + 1/(6*Sqrt[x]) + ArcTan[Sqrt[x]]/6 + ArcTan[Sqrt[x]]/(6*x^3)","A",8,6,21,0.2857,1,"{5159, 30, 5033, 51, 63, 203}"
134,1,63,0,0.1065234,"\int \frac{\tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)^m}{\sqrt{d-\frac{c^2 d x^2}{a}}} \, dx","Int[ArcTan[(c*x)/Sqrt[a - c^2*x^2]]^m/Sqrt[d - (c^2*d*x^2)/a],x]","\frac{\sqrt{a-c^2 x^2} \tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)^{m+1}}{c (m+1) \sqrt{d-\frac{c^2 d x^2}{a}}}","\frac{\sqrt{a-c^2 x^2} \tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)^{m+1}}{c (m+1) \sqrt{d-\frac{c^2 d x^2}{a}}}",1,"(Sqrt[a - c^2*x^2]*ArcTan[(c*x)/Sqrt[a - c^2*x^2]]^(1 + m))/(c*(1 + m)*Sqrt[d - (c^2*d*x^2)/a])","A",2,2,39,0.05128,1,"{5157, 5155}"
135,1,59,0,0.0981454,"\int \frac{\tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)^2}{\sqrt{d-\frac{c^2 d x^2}{a}}} \, dx","Int[ArcTan[(c*x)/Sqrt[a - c^2*x^2]]^2/Sqrt[d - (c^2*d*x^2)/a],x]","\frac{\sqrt{a-c^2 x^2} \tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)^3}{3 c \sqrt{d-\frac{c^2 d x^2}{a}}}","\frac{\sqrt{a-c^2 x^2} \tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)^3}{3 c \sqrt{d-\frac{c^2 d x^2}{a}}}",1,"(Sqrt[a - c^2*x^2]*ArcTan[(c*x)/Sqrt[a - c^2*x^2]]^3)/(3*c*Sqrt[d - (c^2*d*x^2)/a])","A",2,2,39,0.05128,1,"{5157, 5155}"
136,1,59,0,0.0621355,"\int \frac{\tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)}{\sqrt{d-\frac{c^2 d x^2}{a}}} \, dx","Int[ArcTan[(c*x)/Sqrt[a - c^2*x^2]]/Sqrt[d - (c^2*d*x^2)/a],x]","\frac{\sqrt{a-c^2 x^2} \tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)^2}{2 c \sqrt{d-\frac{c^2 d x^2}{a}}}","\frac{\sqrt{a-c^2 x^2} \tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)^2}{2 c \sqrt{d-\frac{c^2 d x^2}{a}}}",1,"(Sqrt[a - c^2*x^2]*ArcTan[(c*x)/Sqrt[a - c^2*x^2]]^2)/(2*c*Sqrt[d - (c^2*d*x^2)/a])","A",2,2,37,0.05405,1,"{5157, 5155}"
137,1,55,0,0.1079994,"\int \frac{1}{\sqrt{d-\frac{c^2 d x^2}{a}} \tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)} \, dx","Int[1/(Sqrt[d - (c^2*d*x^2)/a]*ArcTan[(c*x)/Sqrt[a - c^2*x^2]]),x]","\frac{\sqrt{a-c^2 x^2} \log \left(\tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)\right)}{c \sqrt{d-\frac{c^2 d x^2}{a}}}","\frac{\sqrt{a-c^2 x^2} \log \left(\tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)\right)}{c \sqrt{d-\frac{c^2 d x^2}{a}}}",1,"(Sqrt[a - c^2*x^2]*Log[ArcTan[(c*x)/Sqrt[a - c^2*x^2]]])/(c*Sqrt[d - (c^2*d*x^2)/a])","A",2,2,39,0.05128,1,"{5157, 5153}"
138,1,57,0,0.0985449,"\int \frac{1}{\sqrt{d-\frac{c^2 d x^2}{a}} \tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)^2} \, dx","Int[1/(Sqrt[d - (c^2*d*x^2)/a]*ArcTan[(c*x)/Sqrt[a - c^2*x^2]]^2),x]","-\frac{\sqrt{a-c^2 x^2}}{c \sqrt{d-\frac{c^2 d x^2}{a}} \tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)}","-\frac{\sqrt{a-c^2 x^2}}{c \sqrt{d-\frac{c^2 d x^2}{a}} \tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)}",1,"-(Sqrt[a - c^2*x^2]/(c*Sqrt[d - (c^2*d*x^2)/a]*ArcTan[(c*x)/Sqrt[a - c^2*x^2]]))","A",2,2,39,0.05128,1,"{5157, 5155}"
139,1,59,0,0.1010098,"\int \frac{1}{\sqrt{d-\frac{c^2 d x^2}{a}} \tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)^3} \, dx","Int[1/(Sqrt[d - (c^2*d*x^2)/a]*ArcTan[(c*x)/Sqrt[a - c^2*x^2]]^3),x]","-\frac{\sqrt{a-c^2 x^2}}{2 c \sqrt{d-\frac{c^2 d x^2}{a}} \tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)^2}","-\frac{\sqrt{a-c^2 x^2}}{2 c \sqrt{d-\frac{c^2 d x^2}{a}} \tan ^{-1}\left(\frac{c x}{\sqrt{a-c^2 x^2}}\right)^2}",1,"-Sqrt[a - c^2*x^2]/(2*c*Sqrt[d - (c^2*d*x^2)/a]*ArcTan[(c*x)/Sqrt[a - c^2*x^2]]^2)","A",2,2,39,0.05128,1,"{5157, 5155}"
140,1,72,0,0.1076592,"\int \frac{\tan ^{-1}\left(\frac{e x}{\sqrt{-\frac{a e^2}{b}-e^2 x^2}}\right)^m}{\sqrt{a+b x^2}} \, dx","Int[ArcTan[(e*x)/Sqrt[-((a*e^2)/b) - e^2*x^2]]^m/Sqrt[a + b*x^2],x]","\frac{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}} \tan ^{-1}\left(\frac{e x}{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}}}\right)^{m+1}}{e (m+1) \sqrt{a+b x^2}}","\frac{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}} \tan ^{-1}\left(\frac{e x}{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}}}\right)^{m+1}}{e (m+1) \sqrt{a+b x^2}}",1,"(Sqrt[-((a*e^2)/b) - e^2*x^2]*ArcTan[(e*x)/Sqrt[-((a*e^2)/b) - e^2*x^2]]^(1 + m))/(e*(1 + m)*Sqrt[a + b*x^2])","A",2,2,40,0.05000,1,"{5157, 5155}"
141,1,68,0,0.0979628,"\int \frac{\tan ^{-1}\left(\frac{e x}{\sqrt{-\frac{a e^2}{b}-e^2 x^2}}\right)^2}{\sqrt{a+b x^2}} \, dx","Int[ArcTan[(e*x)/Sqrt[-((a*e^2)/b) - e^2*x^2]]^2/Sqrt[a + b*x^2],x]","\frac{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}} \tan ^{-1}\left(\frac{e x}{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}}}\right)^3}{3 e \sqrt{a+b x^2}}","\frac{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}} \tan ^{-1}\left(\frac{e x}{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}}}\right)^3}{3 e \sqrt{a+b x^2}}",1,"(Sqrt[-((a*e^2)/b) - e^2*x^2]*ArcTan[(e*x)/Sqrt[-((a*e^2)/b) - e^2*x^2]]^3)/(3*e*Sqrt[a + b*x^2])","A",2,2,40,0.05000,1,"{5157, 5155}"
142,1,68,0,0.0618708,"\int \frac{\tan ^{-1}\left(\frac{e x}{\sqrt{-\frac{a e^2}{b}-e^2 x^2}}\right)}{\sqrt{a+b x^2}} \, dx","Int[ArcTan[(e*x)/Sqrt[-((a*e^2)/b) - e^2*x^2]]/Sqrt[a + b*x^2],x]","\frac{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}} \tan ^{-1}\left(\frac{e x}{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}}}\right)^2}{2 e \sqrt{a+b x^2}}","\frac{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}} \tan ^{-1}\left(\frac{e x}{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}}}\right)^2}{2 e \sqrt{a+b x^2}}",1,"(Sqrt[-((a*e^2)/b) - e^2*x^2]*ArcTan[(e*x)/Sqrt[-((a*e^2)/b) - e^2*x^2]]^2)/(2*e*Sqrt[a + b*x^2])","A",2,2,38,0.05263,1,"{5157, 5155}"
143,1,64,0,0.1076276,"\int \frac{1}{\sqrt{a+b x^2} \tan ^{-1}\left(\frac{e x}{\sqrt{-\frac{a e^2}{b}-e^2 x^2}}\right)} \, dx","Int[1/(Sqrt[a + b*x^2]*ArcTan[(e*x)/Sqrt[-((a*e^2)/b) - e^2*x^2]]),x]","\frac{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}} \log \left(\tan ^{-1}\left(\frac{e x}{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}}}\right)\right)}{e \sqrt{a+b x^2}}","\frac{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}} \log \left(\tan ^{-1}\left(\frac{e x}{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}}}\right)\right)}{e \sqrt{a+b x^2}}",1,"(Sqrt[-((a*e^2)/b) - e^2*x^2]*Log[ArcTan[(e*x)/Sqrt[-((a*e^2)/b) - e^2*x^2]]])/(e*Sqrt[a + b*x^2])","A",2,2,40,0.05000,1,"{5157, 5153}"
144,1,66,0,0.1014191,"\int \frac{1}{\sqrt{a+b x^2} \tan ^{-1}\left(\frac{e x}{\sqrt{-\frac{a e^2}{b}-e^2 x^2}}\right)^2} \, dx","Int[1/(Sqrt[a + b*x^2]*ArcTan[(e*x)/Sqrt[-((a*e^2)/b) - e^2*x^2]]^2),x]","-\frac{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}}}{e \sqrt{a+b x^2} \tan ^{-1}\left(\frac{e x}{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}}}\right)}","-\frac{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}}}{e \sqrt{a+b x^2} \tan ^{-1}\left(\frac{e x}{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}}}\right)}",1,"-(Sqrt[-((a*e^2)/b) - e^2*x^2]/(e*Sqrt[a + b*x^2]*ArcTan[(e*x)/Sqrt[-((a*e^2)/b) - e^2*x^2]]))","A",2,2,40,0.05000,1,"{5157, 5155}"
145,1,68,0,0.1002362,"\int \frac{1}{\sqrt{a+b x^2} \tan ^{-1}\left(\frac{e x}{\sqrt{-\frac{a e^2}{b}-e^2 x^2}}\right)^3} \, dx","Int[1/(Sqrt[a + b*x^2]*ArcTan[(e*x)/Sqrt[-((a*e^2)/b) - e^2*x^2]]^3),x]","-\frac{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}}}{2 e \sqrt{a+b x^2} \tan ^{-1}\left(\frac{e x}{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}}}\right)^2}","-\frac{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}}}{2 e \sqrt{a+b x^2} \tan ^{-1}\left(\frac{e x}{\sqrt{e^2 \left(-x^2\right)-\frac{a e^2}{b}}}\right)^2}",1,"-Sqrt[-((a*e^2)/b) - e^2*x^2]/(2*e*Sqrt[a + b*x^2]*ArcTan[(e*x)/Sqrt[-((a*e^2)/b) - e^2*x^2]]^2)","A",2,2,40,0.05000,1,"{5157, 5155}"
146,1,101,0,0.2664208,"\int \frac{\tan ^{-1}(c (a+b x)) \log (d (a+b x))}{a+b x} \, dx","Int[(ArcTan[c*(a + b*x)]*Log[d*(a + b*x)])/(a + b*x),x]","\frac{i \log (d (a+b x)) \text{PolyLog}(2,-i c (a+b x))}{2 b}-\frac{i \log (d (a+b x)) \text{PolyLog}(2,i c (a+b x))}{2 b}-\frac{i \text{PolyLog}(3,-i c (a+b x))}{2 b}+\frac{i \text{PolyLog}(3,i c (a+b x))}{2 b}","\frac{i \log (d (a+b x)) \text{PolyLog}(2,-i c (a+b x))}{2 b}-\frac{i \log (d (a+b x)) \text{PolyLog}(2,i c (a+b x))}{2 b}-\frac{i \text{PolyLog}(3,-i c (a+b x))}{2 b}+\frac{i \text{PolyLog}(3,i c (a+b x))}{2 b}",1,"((I/2)*Log[d*(a + b*x)]*PolyLog[2, (-I)*c*(a + b*x)])/b - ((I/2)*Log[d*(a + b*x)]*PolyLog[2, I*c*(a + b*x)])/b - ((I/2)*PolyLog[3, (-I)*c*(a + b*x)])/b + ((I/2)*PolyLog[3, I*c*(a + b*x)])/b","A",9,7,24,0.2917,1,"{4848, 2391, 5209, 2444, 2433, 2374, 6589}"
147,1,48,0,0.0753947,"\int e^{c (a+b x)} \tan ^{-1}(\sinh (a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcTan[Sinh[a*c + b*c*x]],x]","\frac{e^{a c+b c x} \tan ^{-1}(\sinh (c (a+b x)))}{b c}-\frac{\log \left(e^{2 c (a+b x)}+1\right)}{b c}","\frac{e^{a c+b c x} \tan ^{-1}(\sinh (c (a+b x)))}{b c}-\frac{\log \left(e^{2 c (a+b x)}+1\right)}{b c}",1,"(E^(a*c + b*c*x)*ArcTan[Sinh[c*(a + b*x)]])/(b*c) - Log[1 + E^(2*c*(a + b*x))]/(b*c)","A",5,5,20,0.2500,1,"{2194, 5207, 2282, 12, 260}"
148,1,103,0,0.1549342,"\int e^{c (a+b x)} \tan ^{-1}(\cosh (a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcTan[Cosh[a*c + b*c*x]],x]","-\frac{\left(1-\sqrt{2}\right) \log \left(e^{2 c (a+b x)}+3-2 \sqrt{2}\right)}{2 b c}-\frac{\left(1+\sqrt{2}\right) \log \left(e^{2 c (a+b x)}+3+2 \sqrt{2}\right)}{2 b c}+\frac{e^{a c+b c x} \tan ^{-1}(\cosh (c (a+b x)))}{b c}","-\frac{\left(1-\sqrt{2}\right) \log \left(e^{2 c (a+b x)}+3-2 \sqrt{2}\right)}{2 b c}-\frac{\left(1+\sqrt{2}\right) \log \left(e^{2 c (a+b x)}+3+2 \sqrt{2}\right)}{2 b c}+\frac{e^{a c+b c x} \tan ^{-1}(\cosh (c (a+b x)))}{b c}",1,"(E^(a*c + b*c*x)*ArcTan[Cosh[c*(a + b*x)]])/(b*c) - ((1 - Sqrt[2])*Log[3 - 2*Sqrt[2] + E^(2*c*(a + b*x))])/(2*b*c) - ((1 + Sqrt[2])*Log[3 + 2*Sqrt[2] + E^(2*c*(a + b*x))])/(2*b*c)","A",8,7,20,0.3500,1,"{2194, 5207, 2282, 12, 1247, 632, 31}"
149,1,180,0,0.1818309,"\int e^{c (a+b x)} \tan ^{-1}(\tanh (a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcTan[Tanh[a*c + b*c*x]],x]","-\frac{\log \left(e^{2 c (a+b x)}-\sqrt{2} e^{a c+b c x}+1\right)}{2 \sqrt{2} b c}+\frac{\log \left(e^{2 c (a+b x)}+\sqrt{2} e^{a c+b c x}+1\right)}{2 \sqrt{2} b c}+\frac{\tan ^{-1}\left(1-\sqrt{2} e^{a c+b c x}\right)}{\sqrt{2} b c}-\frac{\tan ^{-1}\left(\sqrt{2} e^{a c+b c x}+1\right)}{\sqrt{2} b c}+\frac{e^{a c+b c x} \tan ^{-1}(\tanh (c (a+b x)))}{b c}","-\frac{\log \left(e^{2 c (a+b x)}-\sqrt{2} e^{a c+b c x}+1\right)}{2 \sqrt{2} b c}+\frac{\log \left(e^{2 c (a+b x)}+\sqrt{2} e^{a c+b c x}+1\right)}{2 \sqrt{2} b c}+\frac{\tan ^{-1}\left(1-\sqrt{2} e^{a c+b c x}\right)}{\sqrt{2} b c}-\frac{\tan ^{-1}\left(\sqrt{2} e^{a c+b c x}+1\right)}{\sqrt{2} b c}+\frac{e^{a c+b c x} \tan ^{-1}(\tanh (c (a+b x)))}{b c}",1,"ArcTan[1 - Sqrt[2]*E^(a*c + b*c*x)]/(Sqrt[2]*b*c) - ArcTan[1 + Sqrt[2]*E^(a*c + b*c*x)]/(Sqrt[2]*b*c) + (E^(a*c + b*c*x)*ArcTan[Tanh[c*(a + b*x)]])/(b*c) - Log[1 + E^(2*c*(a + b*x)) - Sqrt[2]*E^(a*c + b*c*x)]/(2*Sqrt[2]*b*c) + Log[1 + E^(2*c*(a + b*x)) + Sqrt[2]*E^(a*c + b*c*x)]/(2*Sqrt[2]*b*c)","A",13,10,20,0.5000,1,"{2194, 5207, 12, 2249, 297, 1162, 617, 204, 1165, 628}"
150,1,180,0,0.1791357,"\int e^{c (a+b x)} \tan ^{-1}(\coth (a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcTan[Coth[a*c + b*c*x]],x]","\frac{\log \left(e^{2 c (a+b x)}-\sqrt{2} e^{a c+b c x}+1\right)}{2 \sqrt{2} b c}-\frac{\log \left(e^{2 c (a+b x)}+\sqrt{2} e^{a c+b c x}+1\right)}{2 \sqrt{2} b c}-\frac{\tan ^{-1}\left(1-\sqrt{2} e^{a c+b c x}\right)}{\sqrt{2} b c}+\frac{\tan ^{-1}\left(\sqrt{2} e^{a c+b c x}+1\right)}{\sqrt{2} b c}+\frac{e^{a c+b c x} \tan ^{-1}(\coth (c (a+b x)))}{b c}","\frac{\log \left(e^{2 c (a+b x)}-\sqrt{2} e^{a c+b c x}+1\right)}{2 \sqrt{2} b c}-\frac{\log \left(e^{2 c (a+b x)}+\sqrt{2} e^{a c+b c x}+1\right)}{2 \sqrt{2} b c}-\frac{\tan ^{-1}\left(1-\sqrt{2} e^{a c+b c x}\right)}{\sqrt{2} b c}+\frac{\tan ^{-1}\left(\sqrt{2} e^{a c+b c x}+1\right)}{\sqrt{2} b c}+\frac{e^{a c+b c x} \tan ^{-1}(\coth (c (a+b x)))}{b c}",1,"-(ArcTan[1 - Sqrt[2]*E^(a*c + b*c*x)]/(Sqrt[2]*b*c)) + ArcTan[1 + Sqrt[2]*E^(a*c + b*c*x)]/(Sqrt[2]*b*c) + (E^(a*c + b*c*x)*ArcTan[Coth[c*(a + b*x)]])/(b*c) + Log[1 + E^(2*c*(a + b*x)) - Sqrt[2]*E^(a*c + b*c*x)]/(2*Sqrt[2]*b*c) - Log[1 + E^(2*c*(a + b*x)) + Sqrt[2]*E^(a*c + b*c*x)]/(2*Sqrt[2]*b*c)","A",13,10,20,0.5000,1,"{2194, 5207, 12, 2249, 297, 1162, 617, 204, 1165, 628}"
151,1,103,0,0.1453893,"\int e^{c (a+b x)} \tan ^{-1}(\text{sech}(a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcTan[Sech[a*c + b*c*x]],x]","\frac{\left(1-\sqrt{2}\right) \log \left(e^{2 c (a+b x)}+3-2 \sqrt{2}\right)}{2 b c}+\frac{\left(1+\sqrt{2}\right) \log \left(e^{2 c (a+b x)}+3+2 \sqrt{2}\right)}{2 b c}+\frac{e^{a c+b c x} \tan ^{-1}(\text{sech}(c (a+b x)))}{b c}","\frac{\left(1-\sqrt{2}\right) \log \left(e^{2 c (a+b x)}+3-2 \sqrt{2}\right)}{2 b c}+\frac{\left(1+\sqrt{2}\right) \log \left(e^{2 c (a+b x)}+3+2 \sqrt{2}\right)}{2 b c}+\frac{e^{a c+b c x} \tan ^{-1}(\text{sech}(c (a+b x)))}{b c}",1,"(E^(a*c + b*c*x)*ArcTan[Sech[c*(a + b*x)]])/(b*c) + ((1 - Sqrt[2])*Log[3 - 2*Sqrt[2] + E^(2*c*(a + b*x))])/(2*b*c) + ((1 + Sqrt[2])*Log[3 + 2*Sqrt[2] + E^(2*c*(a + b*x))])/(2*b*c)","A",8,7,20,0.3500,1,"{2194, 5207, 2282, 12, 1247, 632, 31}"
152,1,47,0,0.0793913,"\int e^{c (a+b x)} \tan ^{-1}(\text{csch}(a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcTan[Csch[a*c + b*c*x]],x]","\frac{\log \left(e^{2 c (a+b x)}+1\right)}{b c}+\frac{e^{a c+b c x} \tan ^{-1}(\text{csch}(c (a+b x)))}{b c}","\frac{\log \left(e^{2 c (a+b x)}+1\right)}{b c}+\frac{e^{a c+b c x} \tan ^{-1}(\text{csch}(c (a+b x)))}{b c}",1,"(E^(a*c + b*c*x)*ArcTan[Csch[c*(a + b*x)]])/(b*c) + Log[1 + E^(2*c*(a + b*x))]/(b*c)","A",5,5,20,0.2500,1,"{2194, 5207, 2282, 12, 260}"
153,1,163,0,0.5716651,"\int \frac{\left(a+b \tan ^{-1}\left(c x^n\right)\right) \left(d+e \log \left(f x^m\right)\right)}{x} \, dx","Int[((a + b*ArcTan[c*x^n])*(d + e*Log[f*x^m]))/x,x]","\frac{i b d \text{PolyLog}\left(2,-i c x^n\right)}{2 n}-\frac{i b d \text{PolyLog}\left(2,i c x^n\right)}{2 n}+\frac{i b e \log \left(f x^m\right) \text{PolyLog}\left(2,-i c x^n\right)}{2 n}-\frac{i b e \log \left(f x^m\right) \text{PolyLog}\left(2,i c x^n\right)}{2 n}-\frac{i b e m \text{PolyLog}\left(3,-i c x^n\right)}{2 n^2}+\frac{i b e m \text{PolyLog}\left(3,i c x^n\right)}{2 n^2}+a d \log (x)+\frac{a e \log ^2\left(f x^m\right)}{2 m}","\frac{i b d \text{PolyLog}\left(2,-i c x^n\right)}{2 n}-\frac{i b d \text{PolyLog}\left(2,i c x^n\right)}{2 n}+\frac{i b e \log \left(f x^m\right) \text{PolyLog}\left(2,-i c x^n\right)}{2 n}-\frac{i b e \log \left(f x^m\right) \text{PolyLog}\left(2,i c x^n\right)}{2 n}-\frac{i b e m \text{PolyLog}\left(3,-i c x^n\right)}{2 n^2}+\frac{i b e m \text{PolyLog}\left(3,i c x^n\right)}{2 n^2}+a d \log (x)+\frac{a e \log ^2\left(f x^m\right)}{2 m}",1,"a*d*Log[x] + (a*e*Log[f*x^m]^2)/(2*m) + ((I/2)*b*d*PolyLog[2, (-I)*c*x^n])/n + ((I/2)*b*e*Log[f*x^m]*PolyLog[2, (-I)*c*x^n])/n - ((I/2)*b*d*PolyLog[2, I*c*x^n])/n - ((I/2)*b*e*Log[f*x^m]*PolyLog[2, I*c*x^n])/n - ((I/2)*b*e*m*PolyLog[3, (-I)*c*x^n])/n^2 + ((I/2)*b*e*m*PolyLog[3, I*c*x^n])/n^2","A",13,9,24,0.3750,1,"{2301, 6742, 5031, 4848, 2391, 5007, 5005, 2374, 6589}"