1,1,127,0,0.0524512,"\int x^5 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^5*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","-\frac{5 d^2 x \sqrt{d+e x^2}}{96 e^{5/2}}+\frac{5 d^3 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{96 e^3}+\frac{5 d x^3 \sqrt{d+e x^2}}{144 e^{3/2}}-\frac{x^5 \sqrt{d+e x^2}}{36 \sqrt{e}}+\frac{1}{6} x^6 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)","-\frac{5 d^2 x \sqrt{d+e x^2}}{96 e^{5/2}}+\frac{5 d^3 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{96 e^3}+\frac{5 d x^3 \sqrt{d+e x^2}}{144 e^{3/2}}-\frac{x^5 \sqrt{d+e x^2}}{36 \sqrt{e}}+\frac{1}{6} x^6 \tanh ^{-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]) + (5*d^3*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(96*e^3) + (x^6*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/6","A",6,4,23,0.1739,1,"{6221, 321, 217, 206}"
2,1,101,0,0.0388202,"\int x^3 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^3*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","-\frac{3 d^2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{32 e^2}+\frac{3 d x \sqrt{d+e x^2}}{32 e^{3/2}}-\frac{x^3 \sqrt{d+e x^2}}{16 \sqrt{e}}+\frac{1}{4} x^4 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)","-\frac{3 d^2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{32 e^2}+\frac{3 d x \sqrt{d+e x^2}}{32 e^{3/2}}-\frac{x^3 \sqrt{d+e x^2}}{16 \sqrt{e}}+\frac{1}{4} x^4 \tanh ^{-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]) - (3*d^2*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(32*e^2) + (x^4*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/4","A",5,4,23,0.1739,1,"{6221, 321, 217, 206}"
3,1,75,0,0.0225233,"\int x \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","-\frac{x \sqrt{d+e x^2}}{4 \sqrt{e}}+\frac{1}{2} x^2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)+\frac{d \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{4 e}","-\frac{x \sqrt{d+e x^2}}{4 \sqrt{e}}+\frac{1}{2} x^2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)+\frac{d \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{4 e}",1,"-(x*Sqrt[d + e*x^2])/(4*Sqrt[e]) + (d*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(4*e) + (x^2*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/2","A",4,4,21,0.1905,1,"{6221, 321, 217, 206}"
4,1,238,0,0.1575959,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x} \, dx","Int[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x,x]","\frac{\sqrt{d} \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{d+e x^2}}-\frac{\sqrt{d} \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{2 \sqrt{d+e x^2}}+\frac{\sqrt{d} \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{d+e x^2}}-\frac{\sqrt{d} \log (x) \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d+e x^2}}+\log (x) \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)","\frac{\sqrt{d} \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{d+e x^2}}-\frac{\sqrt{d} \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{2 \sqrt{d+e x^2}}+\frac{\sqrt{d} \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{d+e x^2}}-\frac{\sqrt{d} \log (x) \sqrt{\frac{e x^2}{d}+1} \sinh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d+e x^2}}+\log (x) \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)",1,"-(Sqrt[d]*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]^2)/(2*Sqrt[d + e*x^2]) + (Sqrt[d]*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[1 - E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/Sqrt[d + e*x^2] - (Sqrt[d]*Sqrt[1 + (e*x^2)/d]*ArcSinh[(Sqrt[e]*x)/Sqrt[d]]*Log[x])/Sqrt[d + e*x^2] + ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]*Log[x] + (Sqrt[d]*Sqrt[1 + (e*x^2)/d]*PolyLog[2, E^(2*ArcSinh[(Sqrt[e]*x)/Sqrt[d]])])/(2*Sqrt[d + e*x^2])","A",8,8,23,0.3478,1,"{6219, 2327, 2325, 5659, 3716, 2190, 2279, 2391}"
5,1,53,0,0.0186087,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^3} \, dx","Int[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^3,x]","-\frac{\sqrt{e} \sqrt{d+e x^2}}{2 d x}-\frac{\tanh ^{-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{\tanh ^{-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) - ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/(2*x^2)","A",2,2,23,0.08696,1,"{6221, 264}"
6,1,79,0,0.0262587,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^5} \, dx","Int[ArcTanh[(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{\tanh ^{-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{\tanh ^{-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) - ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/(4*x^4)","A",3,3,23,0.1304,1,"{6221, 271, 264}"
7,1,105,0,0.0369368,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^7} \, dx","Int[ArcTanh[(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{\tanh ^{-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{\tanh ^{-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) - ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/(6*x^6)","A",4,3,23,0.1304,1,"{6221, 271, 264}"
8,1,131,0,0.048865,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^9} \, dx","Int[ArcTanh[(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{\tanh ^{-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{\tanh ^{-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) - ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/(8*x^8)","A",5,3,23,0.1304,1,"{6221, 271, 264}"
9,1,114,0,0.0639015,"\int x^6 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^6*ArcTanh[(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 \tanh ^{-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 \tanh ^{-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*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/7","A",4,3,23,0.1304,1,"{6221, 266, 43}"
10,1,91,0,0.0491054,"\int x^4 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^4*ArcTanh[(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 \tanh ^{-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 \tanh ^{-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*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/5","A",4,3,23,0.1304,1,"{6221, 266, 43}"
11,1,68,0,0.0347721,"\int x^2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^2*ArcTanh[(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 \tanh ^{-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 \tanh ^{-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*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/3","A",4,3,23,0.1304,1,"{6221, 266, 43}"
12,1,40,0,0.0086467,"\int \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","x \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)-\frac{\sqrt{d+e x^2}}{\sqrt{e}}","x \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)-\frac{\sqrt{d+e x^2}}{\sqrt{e}}",1,"-(Sqrt[d + e*x^2]/Sqrt[e]) + x*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]","A",2,2,19,0.1053,1,"{6217, 261}"
13,1,55,0,0.0310416,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^2} \, dx","Int[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^2,x]","-\frac{\tanh ^{-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{\tanh ^{-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,"-(ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x) - (Sqrt[e]*ArcTanh[Sqrt[d + e*x^2]/Sqrt[d]])/Sqrt[d]","A",4,4,23,0.1739,1,"{6221, 266, 63, 208}"
14,1,85,0,0.0447361,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^4} \, dx","Int[ArcTanh[(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{\tanh ^{-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{\tanh ^{-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) - ArcTanh[(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",5,5,23,0.2174,1,"{6221, 266, 51, 63, 208}"
15,1,111,0,0.0570099,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^6} \, dx","Int[ArcTanh[(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{\tanh ^{-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{\tanh ^{-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) - ArcTanh[(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",6,5,23,0.2174,1,"{6221, 266, 51, 63, 208}"
16,1,196,0,0.1150931,"\int x^{9/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^(9/2)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","-\frac{60 d^2 \sqrt{x} \sqrt{d+e x^2}}{847 e^{5/2}}+\frac{30 d^{11/4} \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)}{847 e^{11/4} \sqrt{d+e x^2}}+\frac{36 d x^{5/2} \sqrt{d+e x^2}}{847 e^{3/2}}-\frac{4 x^{9/2} \sqrt{d+e x^2}}{121 \sqrt{e}}+\frac{2}{11} x^{11/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)","-\frac{60 d^2 \sqrt{x} \sqrt{d+e x^2}}{847 e^{5/2}}+\frac{30 d^{11/4} \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)}{847 e^{11/4} \sqrt{d+e x^2}}+\frac{36 d x^{5/2} \sqrt{d+e x^2}}{847 e^{3/2}}-\frac{4 x^{9/2} \sqrt{d+e x^2}}{121 \sqrt{e}}+\frac{2}{11} x^{11/2} \tanh ^{-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)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/11 + (30*d^(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])/(847*e^(11/4)*Sqrt[d + e*x^2])","A",6,4,25,0.1600,1,"{6221, 321, 329, 220}"
17,1,168,0,0.0863851,"\int x^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^(5/2)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","-\frac{10 d^{7/4} \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)}{147 e^{7/4} \sqrt{d+e x^2}}+\frac{20 d \sqrt{x} \sqrt{d+e x^2}}{147 e^{3/2}}-\frac{4 x^{5/2} \sqrt{d+e x^2}}{49 \sqrt{e}}+\frac{2}{7} x^{7/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)","-\frac{10 d^{7/4} \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)}{147 e^{7/4} \sqrt{d+e x^2}}+\frac{20 d \sqrt{x} \sqrt{d+e x^2}}{147 e^{3/2}}-\frac{4 x^{5/2} \sqrt{d+e x^2}}{49 \sqrt{e}}+\frac{2}{7} x^{7/2} \tanh ^{-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)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/7 - (10*d^(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])/(147*e^(7/4)*Sqrt[d + e*x^2])","A",5,4,25,0.1600,1,"{6221, 321, 329, 220}"
18,1,142,0,0.0705534,"\int \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[Sqrt[x]*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","\frac{2 d^{3/4} \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)}{9 e^{3/4} \sqrt{d+e x^2}}-\frac{4 \sqrt{x} \sqrt{d+e x^2}}{9 \sqrt{e}}+\frac{2}{3} x^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)","\frac{2 d^{3/4} \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)}{9 e^{3/4} \sqrt{d+e x^2}}-\frac{4 \sqrt{x} \sqrt{d+e x^2}}{9 \sqrt{e}}+\frac{2}{3} x^{3/2} \tanh ^{-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)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/3 + (2*d^(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])/(9*e^(3/4)*Sqrt[d + e*x^2])","A",4,4,25,0.1600,1,"{6221, 321, 329, 220}"
19,1,113,0,0.0577945,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^{3/2}} \, dx","Int[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^(3/2),x]","\frac{2 \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)}{\sqrt[4]{d} \sqrt{d+e x^2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{\sqrt{x}}","\frac{2 \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)}{\sqrt[4]{d} \sqrt{d+e x^2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{\sqrt{x}}",1,"(-2*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/Sqrt[x] + (2*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])/(d^(1/4)*Sqrt[d + e*x^2])","A",3,3,25,0.1200,1,"{6221, 329, 220}"
20,1,145,0,0.0717091,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^{7/2}} \, dx","Int[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^(7/2),x]","-\frac{2 e^{5/4} \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)}{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 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{5 x^{5/2}}","-\frac{2 e^{5/4} \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)}{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 \tanh ^{-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*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(5*x^(5/2)) - (2*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])/(15*d^(5/4)*Sqrt[d + e*x^2])","A",4,4,25,0.1600,1,"{6221, 325, 329, 220}"
21,1,173,0,0.087056,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^{11/2}} \, dx","Int[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^(11/2),x]","\frac{20 e^{3/2} \sqrt{d+e x^2}}{189 d^2 x^{3/2}}+\frac{10 e^{9/4} \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)}{189 d^{9/4} \sqrt{d+e x^2}}-\frac{4 \sqrt{e} \sqrt{d+e x^2}}{63 d x^{7/2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{9 x^{9/2}}","\frac{20 e^{3/2} \sqrt{d+e x^2}}{189 d^2 x^{3/2}}+\frac{10 e^{9/4} \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)}{189 d^{9/4} \sqrt{d+e x^2}}-\frac{4 \sqrt{e} \sqrt{d+e x^2}}{63 d x^{7/2}}-\frac{2 \tanh ^{-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*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(9*x^(9/2)) + (10*e^(9/4)*(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",5,4,25,0.1600,1,"{6221, 325, 329, 220}"
22,1,201,0,0.1023987,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^{15/2}} \, dx","Int[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^(15/2),x]","-\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{30 e^{13/4} \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)}{1001 d^{13/4} \sqrt{d+e x^2}}-\frac{4 \sqrt{e} \sqrt{d+e x^2}}{143 d x^{11/2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{13 x^{13/2}}","-\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{30 e^{13/4} \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)}{1001 d^{13/4} \sqrt{d+e x^2}}-\frac{4 \sqrt{e} \sqrt{d+e x^2}}{143 d x^{11/2}}-\frac{2 \tanh ^{-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*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(13*x^(13/2)) - (30*e^(13/4)*(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",6,4,25,0.1600,1,"{6221, 325, 329, 220}"
23,1,297,0,0.1872175,"\int x^{7/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^(7/2)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","-\frac{28 d^2 \sqrt{x} \sqrt{d+e x^2}}{135 e^2 \left(\sqrt{d}+\sqrt{e} x\right)}-\frac{14 d^{9/4} \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^{9/4} \sqrt{d+e x^2}}+\frac{28 d^{9/4} \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^{9/4} \sqrt{d+e x^2}}+\frac{28 d x^{3/2} \sqrt{d+e x^2}}{405 e^{3/2}}-\frac{4 x^{7/2} \sqrt{d+e x^2}}{81 \sqrt{e}}+\frac{2}{9} x^{9/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)","-\frac{28 d^2 \sqrt{x} \sqrt{d+e x^2}}{135 e^2 \left(\sqrt{d}+\sqrt{e} x\right)}-\frac{14 d^{9/4} \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^{9/4} \sqrt{d+e x^2}}+\frac{28 d^{9/4} \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^{9/4} \sqrt{d+e x^2}}+\frac{28 d x^{3/2} \sqrt{d+e x^2}}{405 e^{3/2}}-\frac{4 x^{7/2} \sqrt{d+e x^2}}{81 \sqrt{e}}+\frac{2}{9} x^{9/2} \tanh ^{-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[x]*Sqrt[d + e*x^2])/(135*e^2*(Sqrt[d] + Sqrt[e]*x)) + (2*x^(9/2)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/9 + (28*d^(9/4)*(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])/(135*e^(9/4)*Sqrt[d + e*x^2]) - (14*d^(9/4)*(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])/(135*e^(9/4)*Sqrt[d + e*x^2])","A",7,6,25,0.2400,1,"{6221, 321, 329, 305, 220, 1196}"
24,1,269,0,0.1574952,"\int x^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Int[x^(3/2)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","\frac{6 d^{5/4} \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^{5/4} \sqrt{d+e x^2}}-\frac{12 d^{5/4} \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^{5/4} \sqrt{d+e x^2}}-\frac{4 x^{3/2} \sqrt{d+e x^2}}{25 \sqrt{e}}+\frac{12 d \sqrt{x} \sqrt{d+e x^2}}{25 e \left(\sqrt{d}+\sqrt{e} x\right)}+\frac{2}{5} x^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)","\frac{6 d^{5/4} \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^{5/4} \sqrt{d+e x^2}}-\frac{12 d^{5/4} \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^{5/4} \sqrt{d+e x^2}}-\frac{4 x^{3/2} \sqrt{d+e x^2}}{25 \sqrt{e}}+\frac{12 d \sqrt{x} \sqrt{d+e x^2}}{25 e \left(\sqrt{d}+\sqrt{e} x\right)}+\frac{2}{5} x^{5/2} \tanh ^{-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[x]*Sqrt[d + e*x^2])/(25*e*(Sqrt[d] + Sqrt[e]*x)) + (2*x^(5/2)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/5 - (12*d^(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])/(25*e^(5/4)*Sqrt[d + e*x^2]) + (6*d^(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])/(25*e^(5/4)*Sqrt[d + e*x^2])","A",6,6,25,0.2400,1,"{6221, 321, 329, 305, 220, 1196}"
25,1,232,0,0.1356356,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{\sqrt{x}} \, dx","Int[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/Sqrt[x],x]","-\frac{4 \sqrt{x} \sqrt{d+e x^2}}{\sqrt{d}+\sqrt{e} x}+2 \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)-\frac{2 \sqrt[4]{d} \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)}{\sqrt[4]{e} \sqrt{d+e x^2}}+\frac{4 \sqrt[4]{d} \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)}{\sqrt[4]{e} \sqrt{d+e x^2}}","-\frac{4 \sqrt{x} \sqrt{d+e x^2}}{\sqrt{d}+\sqrt{e} x}+2 \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)-\frac{2 \sqrt[4]{d} \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)}{\sqrt[4]{e} \sqrt{d+e x^2}}+\frac{4 \sqrt[4]{d} \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)}{\sqrt[4]{e} \sqrt{d+e x^2}}",1,"(-4*Sqrt[x]*Sqrt[d + e*x^2])/(Sqrt[d] + Sqrt[e]*x) + 2*Sqrt[x]*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]] + (4*d^(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])/(e^(1/4)*Sqrt[d + e*x^2]) - (2*d^(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])/(e^(1/4)*Sqrt[d + e*x^2])","A",5,5,25,0.2000,1,"{6221, 329, 305, 220, 1196}"
26,1,272,0,0.1617412,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^{5/2}} \, dx","Int[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^(5/2),x]","\frac{2 e^{3/4} \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 e^{3/4} \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 e \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 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{3 x^{3/2}}","\frac{2 e^{3/4} \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 e^{3/4} \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 e \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 \tanh ^{-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*e*Sqrt[x]*Sqrt[d + e*x^2])/(3*d*(Sqrt[d] + Sqrt[e]*x)) - (2*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(3*x^(3/2)) - (4*e^(3/4)*(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*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])/(3*d^(3/4)*Sqrt[d + e*x^2])","A",6,6,25,0.2400,1,"{6221, 325, 329, 305, 220, 1196}"
27,1,302,0,0.1811994,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^{9/2}} \, dx","Int[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^(9/2),x]","-\frac{12 e^2 \sqrt{x} \sqrt{d+e x^2}}{35 d^2 \left(\sqrt{d}+\sqrt{e} x\right)}+\frac{12 e^{3/2} \sqrt{d+e x^2}}{35 d^2 \sqrt{x}}-\frac{6 e^{7/4} \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^{7/4} \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{4 \sqrt{e} \sqrt{d+e x^2}}{35 d x^{5/2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{7 x^{7/2}}","-\frac{12 e^2 \sqrt{x} \sqrt{d+e x^2}}{35 d^2 \left(\sqrt{d}+\sqrt{e} x\right)}+\frac{12 e^{3/2} \sqrt{d+e x^2}}{35 d^2 \sqrt{x}}-\frac{6 e^{7/4} \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^{7/4} \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{4 \sqrt{e} \sqrt{d+e x^2}}{35 d x^{5/2}}-\frac{2 \tanh ^{-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*e^2*Sqrt[x]*Sqrt[d + e*x^2])/(35*d^2*(Sqrt[d] + Sqrt[e]*x)) - (2*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(7*x^(7/2)) + (12*e^(7/4)*(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*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])/(35*d^(7/4)*Sqrt[d + e*x^2])","A",7,6,25,0.2400,1,"{6221, 325, 329, 305, 220, 1196}"
28,1,44,0,0.0493132,"\int x^3 \tanh ^{-1}\left(a+b x^4\right) \, dx","Int[x^3*ArcTanh[a + b*x^4],x]","\frac{\log \left(1-\left(a+b x^4\right)^2\right)}{8 b}+\frac{\left(a+b x^4\right) \tanh ^{-1}\left(a+b x^4\right)}{4 b}","\frac{\log \left(1-\left(a+b x^4\right)^2\right)}{8 b}+\frac{\left(a+b x^4\right) \tanh ^{-1}\left(a+b x^4\right)}{4 b}",1,"((a + b*x^4)*ArcTanh[a + b*x^4])/(4*b) + Log[1 - (a + b*x^4)^2]/(8*b)","A",4,4,12,0.3333,1,"{6715, 6103, 5910, 260}"
29,1,47,0,0.0493811,"\int x^{-1+n} \tanh ^{-1}\left(a+b x^n\right) \, dx","Int[x^(-1 + n)*ArcTanh[a + b*x^n],x]","\frac{\log \left(1-\left(a+b x^n\right)^2\right)}{2 b n}+\frac{\left(a+b x^n\right) \tanh ^{-1}\left(a+b x^n\right)}{b n}","\frac{\log \left(1-\left(a+b x^n\right)^2\right)}{2 b n}+\frac{\left(a+b x^n\right) \tanh ^{-1}\left(a+b x^n\right)}{b n}",1,"((a + b*x^n)*ArcTanh[a + b*x^n])/(b*n) + Log[1 - (a + b*x^n)^2]/(2*b*n)","A",4,4,14,0.2857,1,"{6715, 6103, 5910, 260}"
30,0,0,0,0.0443373,"\int \frac{\left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^n}{1-c^2 x^2} \, dx","Int[(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2),x]","\int \frac{\left(a+b \tanh ^{-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 \tanh ^{-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*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2), x]","A",0,0,0,0,-1,"{}"
31,1,409,0,0.5062093,"\int \frac{\left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^3}{1-c^2 x^2} \, dx","Int[(a + b*ArcTanh[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{\sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}+\frac{3 b^2 \text{PolyLog}\left(3,\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}-1\right) \left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}+\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}-\frac{3 b \text{PolyLog}\left(2,\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}-1\right) \left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}+\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}\right)}{4 c}-\frac{3 b^3 \text{PolyLog}\left(4,\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}-1\right)}{4 c}-\frac{2 \tanh ^{-1}\left(1-\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tanh ^{-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{\sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}+\frac{3 b^2 \text{PolyLog}\left(3,\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}-1\right) \left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}+\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}-\frac{3 b \text{PolyLog}\left(2,\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}-1\right) \left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}+\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}\right)}{4 c}-\frac{3 b^3 \text{PolyLog}\left(4,\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}-1\right)}{4 c}-\frac{2 \tanh ^{-1}\left(1-\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{c}",1,"(-2*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3*ArcTanh[1 - 2/(1 - Sqrt[1 - c*x]/Sqrt[1 + c*x])])/c + (3*b*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*PolyLog[2, 1 - 2/(1 - Sqrt[1 - c*x]/Sqrt[1 + c*x])])/(2*c) - (3*b*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*PolyLog[2, -1 + 2/(1 - Sqrt[1 - c*x]/Sqrt[1 + c*x])])/(2*c) - (3*b^2*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[3, 1 - 2/(1 - Sqrt[1 - c*x]/Sqrt[1 + c*x])])/(2*c) + (3*b^2*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[3, -1 + 2/(1 - Sqrt[1 - c*x]/Sqrt[1 + c*x])])/(2*c) + (3*b^3*PolyLog[4, 1 - 2/(1 - Sqrt[1 - c*x]/Sqrt[1 + c*x])])/(4*c) - (3*b^3*PolyLog[4, -1 + 2/(1 - Sqrt[1 - c*x]/Sqrt[1 + c*x])])/(4*c)","A",9,7,40,0.1750,1,"{6681, 5914, 6052, 5948, 6058, 6062, 6610}"
32,1,268,0,0.3111903,"\int \frac{\left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2}{1-c^2 x^2} \, dx","Int[(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2/(1 - c^2*x^2),x]","\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}-\frac{b \text{PolyLog}\left(2,\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}-1\right) \left(a+b \tanh ^{-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{\sqrt{1-c x}}{\sqrt{c x+1}}}\right)}{2 c}+\frac{b^2 \text{PolyLog}\left(3,\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}-1\right)}{2 c}-\frac{2 \tanh ^{-1}\left(1-\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{c}","\frac{b \text{PolyLog}\left(2,1-\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}-\frac{b \text{PolyLog}\left(2,\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}-1\right) \left(a+b \tanh ^{-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{\sqrt{1-c x}}{\sqrt{c x+1}}}\right)}{2 c}+\frac{b^2 \text{PolyLog}\left(3,\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}-1\right)}{2 c}-\frac{2 \tanh ^{-1}\left(1-\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{c}",1,"(-2*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*ArcTanh[1 - 2/(1 - Sqrt[1 - c*x]/Sqrt[1 + c*x])])/c + (b*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[2, 1 - 2/(1 - Sqrt[1 - c*x]/Sqrt[1 + c*x])])/c - (b*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[2, -1 + 2/(1 - Sqrt[1 - c*x]/Sqrt[1 + c*x])])/c - (b^2*PolyLog[3, 1 - 2/(1 - Sqrt[1 - c*x]/Sqrt[1 + c*x])])/(2*c) + (b^2*PolyLog[3, -1 + 2/(1 - Sqrt[1 - c*x]/Sqrt[1 + c*x])])/(2*c)","A",7,6,40,0.1500,1,"{6681, 5914, 6052, 5948, 6058, 6610}"
33,1,89,0,0.0506488,"\int \frac{a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)}{1-c^2 x^2} \, dx","Int[(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])/(1 - c^2*x^2),x]","\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}{2 c}-\frac{b \text{PolyLog}\left(2,\frac{\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{b \text{PolyLog}\left(2,-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}{2 c}-\frac{b \text{PolyLog}\left(2,\frac{\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) + (b*PolyLog[2, -(Sqrt[1 - c*x]/Sqrt[1 + c*x])])/(2*c) - (b*PolyLog[2, Sqrt[1 - c*x]/Sqrt[1 + c*x]])/(2*c)","A",2,3,38,0.07895,1,"{206, 6681, 5912}"
34,0,0,0,0.04332,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)} \, dx","Int[1/((1 - c^2*x^2)*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])),x]","\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \tanh ^{-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 \tanh ^{-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*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])), x]","A",0,0,0,0,-1,"{}"
35,0,0,0,0.0417539,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2} \, dx","Int[1/((1 - c^2*x^2)*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2),x]","\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \tanh ^{-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 \tanh ^{-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*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2), x]","A",0,0,0,0,-1,"{}"
36,1,37,0,0.0254027,"\int x^m \tanh ^{-1}(\tanh (a+b x)) \, dx","Int[x^m*ArcTanh[Tanh[a + b*x]],x]","\frac{x^{m+1} \tanh ^{-1}(\tanh (a+b x))}{m+1}-\frac{b x^{m+2}}{m^2+3 m+2}","\frac{x^{m+1} \tanh ^{-1}(\tanh (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)*ArcTanh[Tanh[a + b*x]])/(1 + m)","A",2,2,11,0.1818,1,"{2168, 30}"
37,1,23,0,0.0081557,"\int x^2 \tanh ^{-1}(\tanh (a+b x)) \, dx","Int[x^2*ArcTanh[Tanh[a + b*x]],x]","\frac{1}{3} x^3 \tanh ^{-1}(\tanh (a+b x))-\frac{b x^4}{12}","\frac{1}{3} x^3 \tanh ^{-1}(\tanh (a+b x))-\frac{b x^4}{12}",1,"-(b*x^4)/12 + (x^3*ArcTanh[Tanh[a + b*x]])/3","A",2,2,11,0.1818,1,"{2168, 30}"
38,1,23,0,0.0068111,"\int x \tanh ^{-1}(\tanh (a+b x)) \, dx","Int[x*ArcTanh[Tanh[a + b*x]],x]","\frac{1}{2} x^2 \tanh ^{-1}(\tanh (a+b x))-\frac{b x^3}{6}","\frac{1}{2} x^2 \tanh ^{-1}(\tanh (a+b x))-\frac{b x^3}{6}",1,"-(b*x^3)/6 + (x^2*ArcTanh[Tanh[a + b*x]])/2","A",2,2,9,0.2222,1,"{6239, 30}"
39,1,16,0,0.0032771,"\int \tanh ^{-1}(\tanh (a+b x)) \, dx","Int[ArcTanh[Tanh[a + b*x]],x]","\frac{\tanh ^{-1}(\tanh (a+b x))^2}{2 b}","\frac{\tanh ^{-1}(\tanh (a+b x))^2}{2 b}",1,"ArcTanh[Tanh[a + b*x]]^2/(2*b)","A",2,2,7,0.2857,1,"{2157, 30}"
40,1,21,0,0.0358928,"\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x} \, dx","Int[ArcTanh[Tanh[a + b*x]]/x,x]","b x-\log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)","b x-\log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)",1,"b*x - (b*x - ArcTanh[Tanh[a + b*x]])*Log[x]","A",2,2,11,0.1818,1,"{2158, 29}"
41,1,17,0,0.0080839,"\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^2} \, dx","Int[ArcTanh[Tanh[a + b*x]]/x^2,x]","b \log (x)-\frac{\tanh ^{-1}(\tanh (a+b x))}{x}","b \log (x)-\frac{\tanh ^{-1}(\tanh (a+b x))}{x}",1,"-(ArcTanh[Tanh[a + b*x]]/x) + b*Log[x]","A",2,2,11,0.1818,1,"{2168, 29}"
42,1,23,0,0.0089049,"\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^3} \, dx","Int[ArcTanh[Tanh[a + b*x]]/x^3,x]","-\frac{\tanh ^{-1}(\tanh (a+b x))}{2 x^2}-\frac{b}{2 x}","-\frac{\tanh ^{-1}(\tanh (a+b x))}{2 x^2}-\frac{b}{2 x}",1,"-b/(2*x) - ArcTanh[Tanh[a + b*x]]/(2*x^2)","A",2,2,11,0.1818,1,"{2168, 30}"
43,1,23,0,0.0081961,"\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^4} \, dx","Int[ArcTanh[Tanh[a + b*x]]/x^4,x]","-\frac{\tanh ^{-1}(\tanh (a+b x))}{3 x^3}-\frac{b}{6 x^2}","-\frac{\tanh ^{-1}(\tanh (a+b x))}{3 x^3}-\frac{b}{6 x^2}",1,"-b/(6*x^2) - ArcTanh[Tanh[a + b*x]]/(3*x^3)","A",2,2,11,0.1818,1,"{2168, 30}"
44,1,71,0,0.0321608,"\int x^m \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Int[x^m*ArcTanh[Tanh[a + b*x]]^2,x]","-\frac{2 b x^{m+2} \tanh ^{-1}(\tanh (a+b x))}{m^2+3 m+2}+\frac{x^{m+1} \tanh ^{-1}(\tanh (a+b x))^2}{m+1}+\frac{2 b^2 x^{m+3}}{m^3+6 m^2+11 m+6}","-\frac{2 b x^{m+2} \tanh ^{-1}(\tanh (a+b x))}{m^2+3 m+2}+\frac{x^{m+1} \tanh ^{-1}(\tanh (a+b x))^2}{m+1}+\frac{2 b^2 x^{m+3}}{m^3+6 m^2+11 m+6}",1,"(2*b^2*x^(3 + m))/(6 + 11*m + 6*m^2 + m^3) - (2*b*x^(2 + m)*ArcTanh[Tanh[a + b*x]])/(2 + 3*m + m^2) + (x^(1 + m)*ArcTanh[Tanh[a + b*x]]^2)/(1 + m)","A",3,2,13,0.1538,1,"{2168, 30}"
45,1,42,0,0.0234797,"\int x^3 \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Int[x^3*ArcTanh[Tanh[a + b*x]]^2,x]","-\frac{1}{10} b x^5 \tanh ^{-1}(\tanh (a+b x))+\frac{1}{4} x^4 \tanh ^{-1}(\tanh (a+b x))^2+\frac{b^2 x^6}{60}","-\frac{1}{10} b x^5 \tanh ^{-1}(\tanh (a+b x))+\frac{1}{4} x^4 \tanh ^{-1}(\tanh (a+b x))^2+\frac{b^2 x^6}{60}",1,"(b^2*x^6)/60 - (b*x^5*ArcTanh[Tanh[a + b*x]])/10 + (x^4*ArcTanh[Tanh[a + b*x]]^2)/4","A",3,2,13,0.1538,1,"{2168, 30}"
46,1,42,0,0.0221278,"\int x^2 \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Int[x^2*ArcTanh[Tanh[a + b*x]]^2,x]","-\frac{1}{6} b x^4 \tanh ^{-1}(\tanh (a+b x))+\frac{1}{3} x^3 \tanh ^{-1}(\tanh (a+b x))^2+\frac{b^2 x^5}{30}","-\frac{1}{6} b x^4 \tanh ^{-1}(\tanh (a+b x))+\frac{1}{3} x^3 \tanh ^{-1}(\tanh (a+b x))^2+\frac{b^2 x^5}{30}",1,"(b^2*x^5)/30 - (b*x^4*ArcTanh[Tanh[a + b*x]])/6 + (x^3*ArcTanh[Tanh[a + b*x]]^2)/3","A",3,2,13,0.1538,1,"{2168, 30}"
47,1,34,0,0.020971,"\int x \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Int[x*ArcTanh[Tanh[a + b*x]]^2,x]","\frac{x \tanh ^{-1}(\tanh (a+b x))^3}{3 b}-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{12 b^2}","\frac{x \tanh ^{-1}(\tanh (a+b x))^3}{3 b}-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{12 b^2}",1,"(x*ArcTanh[Tanh[a + b*x]]^3)/(3*b) - ArcTanh[Tanh[a + b*x]]^4/(12*b^2)","A",3,3,11,0.2727,1,"{2168, 2157, 30}"
48,1,16,0,0.0043591,"\int \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Int[ArcTanh[Tanh[a + b*x]]^2,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^3}{3 b}","\frac{\tanh ^{-1}(\tanh (a+b x))^3}{3 b}",1,"ArcTanh[Tanh[a + b*x]]^3/(3*b)","A",2,2,9,0.2222,1,"{2157, 30}"
49,1,49,0,0.033532,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x} \, dx","Int[ArcTanh[Tanh[a + b*x]]^2/x,x]","-b x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{1}{2} \tanh ^{-1}(\tanh (a+b x))^2+\log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2","-b x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{1}{2} \tanh ^{-1}(\tanh (a+b x))^2+\log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2",1,"-(b*x*(b*x - ArcTanh[Tanh[a + b*x]])) + ArcTanh[Tanh[a + b*x]]^2/2 + (b*x - ArcTanh[Tanh[a + b*x]])^2*Log[x]","A",3,3,13,0.2308,1,"{2159, 2158, 29}"
50,1,39,0,0.0243156,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^2} \, dx","Int[ArcTanh[Tanh[a + b*x]]^2/x^2,x]","-\frac{\tanh ^{-1}(\tanh (a+b x))^2}{x}-2 b \log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+2 b^2 x","-\frac{\tanh ^{-1}(\tanh (a+b x))^2}{x}-2 b \log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+2 b^2 x",1,"2*b^2*x - ArcTanh[Tanh[a + b*x]]^2/x - 2*b*(b*x - ArcTanh[Tanh[a + b*x]])*Log[x]","A",3,3,13,0.2308,1,"{2168, 2158, 29}"
51,1,36,0,0.0211679,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^3} \, dx","Int[ArcTanh[Tanh[a + b*x]]^2/x^3,x]","-\frac{\tanh ^{-1}(\tanh (a+b x))^2}{2 x^2}-\frac{b \tanh ^{-1}(\tanh (a+b x))}{x}+b^2 \log (x)","-\frac{\tanh ^{-1}(\tanh (a+b x))^2}{2 x^2}-\frac{b \tanh ^{-1}(\tanh (a+b x))}{x}+b^2 \log (x)",1,"-((b*ArcTanh[Tanh[a + b*x]])/x) - ArcTanh[Tanh[a + b*x]]^2/(2*x^2) + b^2*Log[x]","A",3,2,13,0.1538,1,"{2168, 29}"
52,1,31,0,0.0126636,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^4} \, dx","Int[ArcTanh[Tanh[a + b*x]]^2/x^4,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^3}{3 x^3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}","\frac{\tanh ^{-1}(\tanh (a+b x))^3}{3 x^3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"ArcTanh[Tanh[a + b*x]]^3/(3*x^3*(b*x - ArcTanh[Tanh[a + b*x]]))","A",1,1,13,0.07692,1,"{2167}"
53,1,64,0,0.0303805,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^5} \, dx","Int[ArcTanh[Tanh[a + b*x]]^2/x^5,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^3}{4 x^4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{b \tanh ^{-1}(\tanh (a+b x))^3}{12 x^3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","-\frac{b \tanh ^{-1}(\tanh (a+b x))}{6 x^3}-\frac{\tanh ^{-1}(\tanh (a+b x))^2}{4 x^4}-\frac{b^2}{12 x^2}",1,"(b*ArcTanh[Tanh[a + b*x]]^3)/(12*x^3*(b*x - ArcTanh[Tanh[a + b*x]])^2) + ArcTanh[Tanh[a + b*x]]^3/(4*x^4*(b*x - ArcTanh[Tanh[a + b*x]]))","A",2,2,13,0.1538,1,"{2171, 2167}"
54,1,110,0,0.0576198,"\int x^m \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Int[x^m*ArcTanh[Tanh[a + b*x]]^3,x]","\frac{6 b^2 x^{m+3} \tanh ^{-1}(\tanh (a+b x))}{m^3+6 m^2+11 m+6}-\frac{3 b x^{m+2} \tanh ^{-1}(\tanh (a+b x))^2}{m^2+3 m+2}+\frac{x^{m+1} \tanh ^{-1}(\tanh (a+b x))^3}{m+1}-\frac{6 b^3 x^{m+4}}{(m+1) \left(m^3+9 m^2+26 m+24\right)}","\frac{6 b^2 x^{m+3} \tanh ^{-1}(\tanh (a+b x))}{m^3+6 m^2+11 m+6}-\frac{3 b x^{m+2} \tanh ^{-1}(\tanh (a+b x))^2}{m^2+3 m+2}+\frac{x^{m+1} \tanh ^{-1}(\tanh (a+b x))^3}{m+1}-\frac{6 b^3 x^{m+4}}{(m+1) \left(m^3+9 m^2+26 m+24\right)}",1,"(-6*b^3*x^(4 + m))/((1 + m)*(24 + 26*m + 9*m^2 + m^3)) + (6*b^2*x^(3 + m)*ArcTanh[Tanh[a + b*x]])/(6 + 11*m + 6*m^2 + m^3) - (3*b*x^(2 + m)*ArcTanh[Tanh[a + b*x]]^2)/(2 + 3*m + m^2) + (x^(1 + m)*ArcTanh[Tanh[a + b*x]]^3)/(1 + m)","A",4,2,13,0.1538,1,"{2168, 30}"
55,1,61,0,0.04446,"\int x^3 \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Int[x^3*ArcTanh[Tanh[a + b*x]]^3,x]","\frac{1}{20} b^2 x^6 \tanh ^{-1}(\tanh (a+b x))-\frac{3}{20} b x^5 \tanh ^{-1}(\tanh (a+b x))^2+\frac{1}{4} x^4 \tanh ^{-1}(\tanh (a+b x))^3-\frac{1}{140} b^3 x^7","\frac{1}{20} b^2 x^6 \tanh ^{-1}(\tanh (a+b x))-\frac{3}{20} b x^5 \tanh ^{-1}(\tanh (a+b x))^2+\frac{1}{4} x^4 \tanh ^{-1}(\tanh (a+b x))^3-\frac{1}{140} b^3 x^7",1,"-(b^3*x^7)/140 + (b^2*x^6*ArcTanh[Tanh[a + b*x]])/20 - (3*b*x^5*ArcTanh[Tanh[a + b*x]]^2)/20 + (x^4*ArcTanh[Tanh[a + b*x]]^3)/4","A",4,2,13,0.1538,1,"{2168, 30}"
56,1,53,0,0.0286999,"\int x^2 \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Int[x^2*ArcTanh[Tanh[a + b*x]]^3,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^6}{60 b^3}-\frac{x \tanh ^{-1}(\tanh (a+b x))^5}{10 b^2}+\frac{x^2 \tanh ^{-1}(\tanh (a+b x))^4}{4 b}","\frac{\tanh ^{-1}(\tanh (a+b x))^6}{60 b^3}-\frac{x \tanh ^{-1}(\tanh (a+b x))^5}{10 b^2}+\frac{x^2 \tanh ^{-1}(\tanh (a+b x))^4}{4 b}",1,"(x^2*ArcTanh[Tanh[a + b*x]]^4)/(4*b) - (x*ArcTanh[Tanh[a + b*x]]^5)/(10*b^2) + ArcTanh[Tanh[a + b*x]]^6/(60*b^3)","A",4,3,13,0.2308,1,"{2168, 2157, 30}"
57,1,34,0,0.0139659,"\int x \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Int[x*ArcTanh[Tanh[a + b*x]]^3,x]","\frac{x \tanh ^{-1}(\tanh (a+b x))^4}{4 b}-\frac{\tanh ^{-1}(\tanh (a+b x))^5}{20 b^2}","\frac{x \tanh ^{-1}(\tanh (a+b x))^4}{4 b}-\frac{\tanh ^{-1}(\tanh (a+b x))^5}{20 b^2}",1,"(x*ArcTanh[Tanh[a + b*x]]^4)/(4*b) - ArcTanh[Tanh[a + b*x]]^5/(20*b^2)","A",3,3,11,0.2727,1,"{2168, 2157, 30}"
58,1,16,0,0.0044888,"\int \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Int[ArcTanh[Tanh[a + b*x]]^3,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^4}{4 b}","\frac{\tanh ^{-1}(\tanh (a+b x))^4}{4 b}",1,"ArcTanh[Tanh[a + b*x]]^4/(4*b)","A",2,2,9,0.2222,1,"{2157, 30}"
59,1,77,0,0.0809734,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x} \, dx","Int[ArcTanh[Tanh[a + b*x]]^3/x,x]","b x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2-\frac{1}{2} \tanh ^{-1}(\tanh (a+b x))^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{1}{3} \tanh ^{-1}(\tanh (a+b x))^3-\log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3","b x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2-\frac{1}{2} \tanh ^{-1}(\tanh (a+b x))^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{1}{3} \tanh ^{-1}(\tanh (a+b x))^3-\log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3",1,"b*x*(b*x - ArcTanh[Tanh[a + b*x]])^2 - ((b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^2)/2 + ArcTanh[Tanh[a + b*x]]^3/3 - (b*x - ArcTanh[Tanh[a + b*x]])^3*Log[x]","A",4,3,13,0.2308,1,"{2159, 2158, 29}"
60,1,68,0,0.0412704,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^2} \, dx","Int[ArcTanh[Tanh[a + b*x]]^3/x^2,x]","-3 b^2 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)-\frac{\tanh ^{-1}(\tanh (a+b x))^3}{x}+\frac{3}{2} b \tanh ^{-1}(\tanh (a+b x))^2+3 b \log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2","-3 b^2 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)-\frac{\tanh ^{-1}(\tanh (a+b x))^3}{x}+\frac{3}{2} b \tanh ^{-1}(\tanh (a+b x))^2+3 b \log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2",1,"-3*b^2*x*(b*x - ArcTanh[Tanh[a + b*x]]) + (3*b*ArcTanh[Tanh[a + b*x]]^2)/2 - ArcTanh[Tanh[a + b*x]]^3/x + 3*b*(b*x - ArcTanh[Tanh[a + b*x]])^2*Log[x]","A",4,4,13,0.3077,1,"{2168, 2159, 2158, 29}"
61,1,60,0,0.0396589,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^3} \, dx","Int[ArcTanh[Tanh[a + b*x]]^3/x^3,x]","-3 b^2 \log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)-\frac{\tanh ^{-1}(\tanh (a+b x))^3}{2 x^2}-\frac{3 b \tanh ^{-1}(\tanh (a+b x))^2}{2 x}+3 b^3 x","-3 b^2 \log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)-\frac{\tanh ^{-1}(\tanh (a+b x))^3}{2 x^2}-\frac{3 b \tanh ^{-1}(\tanh (a+b x))^2}{2 x}+3 b^3 x",1,"3*b^3*x - (3*b*ArcTanh[Tanh[a + b*x]]^2)/(2*x) - ArcTanh[Tanh[a + b*x]]^3/(2*x^2) - 3*b^2*(b*x - ArcTanh[Tanh[a + b*x]])*Log[x]","A",4,3,13,0.2308,1,"{2168, 2158, 29}"
62,1,55,0,0.0368214,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^4} \, dx","Int[ArcTanh[Tanh[a + b*x]]^3/x^4,x]","-\frac{b^2 \tanh ^{-1}(\tanh (a+b x))}{x}-\frac{b \tanh ^{-1}(\tanh (a+b x))^2}{2 x^2}-\frac{\tanh ^{-1}(\tanh (a+b x))^3}{3 x^3}+b^3 \log (x)","-\frac{b^2 \tanh ^{-1}(\tanh (a+b x))}{x}-\frac{b \tanh ^{-1}(\tanh (a+b x))^2}{2 x^2}-\frac{\tanh ^{-1}(\tanh (a+b x))^3}{3 x^3}+b^3 \log (x)",1,"-((b^2*ArcTanh[Tanh[a + b*x]])/x) - (b*ArcTanh[Tanh[a + b*x]]^2)/(2*x^2) - ArcTanh[Tanh[a + b*x]]^3/(3*x^3) + b^3*Log[x]","A",4,2,13,0.1538,1,"{2168, 29}"
63,1,31,0,0.0132947,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^5} \, dx","Int[ArcTanh[Tanh[a + b*x]]^3/x^5,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^4}{4 x^4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}","\frac{\tanh ^{-1}(\tanh (a+b x))^4}{4 x^4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"ArcTanh[Tanh[a + b*x]]^4/(4*x^4*(b*x - ArcTanh[Tanh[a + b*x]]))","A",1,1,13,0.07692,1,"{2167}"
64,1,64,0,0.0319722,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^6} \, dx","Int[ArcTanh[Tanh[a + b*x]]^3/x^6,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^4}{5 x^5 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{b \tanh ^{-1}(\tanh (a+b x))^4}{20 x^4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","\frac{\tanh ^{-1}(\tanh (a+b x))^4}{5 x^5 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{b \tanh ^{-1}(\tanh (a+b x))^4}{20 x^4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}",1,"(b*ArcTanh[Tanh[a + b*x]]^4)/(20*x^4*(b*x - ArcTanh[Tanh[a + b*x]])^2) + ArcTanh[Tanh[a + b*x]]^4/(5*x^5*(b*x - ArcTanh[Tanh[a + b*x]]))","A",2,2,13,0.1538,1,"{2171, 2167}"
65,1,154,0,0.0989838,"\int x^m \tanh ^{-1}(\tanh (a+b x))^4 \, dx","Int[x^m*ArcTanh[Tanh[a + b*x]]^4,x]","\frac{12 b^2 x^{m+3} \tanh ^{-1}(\tanh (a+b x))^2}{m^3+6 m^2+11 m+6}-\frac{24 b^3 x^{m+4} \tanh ^{-1}(\tanh (a+b x))}{(m+1) \left(m^3+9 m^2+26 m+24\right)}-\frac{4 b x^{m+2} \tanh ^{-1}(\tanh (a+b x))^3}{m^2+3 m+2}+\frac{x^{m+1} \tanh ^{-1}(\tanh (a+b x))^4}{m+1}+\frac{24 b^4 x^{m+5}}{(m+1) (m+2) (m+3) \left(m^2+9 m+20\right)}","\frac{12 b^2 x^{m+3} \tanh ^{-1}(\tanh (a+b x))^2}{m^3+6 m^2+11 m+6}-\frac{24 b^3 x^{m+4} \tanh ^{-1}(\tanh (a+b x))}{(m+1) \left(m^3+9 m^2+26 m+24\right)}-\frac{4 b x^{m+2} \tanh ^{-1}(\tanh (a+b x))^3}{m^2+3 m+2}+\frac{x^{m+1} \tanh ^{-1}(\tanh (a+b x))^4}{m+1}+\frac{24 b^4 x^{m+5}}{(m+1) (m+2) (m+3) \left(m^2+9 m+20\right)}",1,"(24*b^4*x^(5 + m))/((1 + m)*(2 + m)*(3 + m)*(20 + 9*m + m^2)) - (24*b^3*x^(4 + m)*ArcTanh[Tanh[a + b*x]])/((1 + m)*(24 + 26*m + 9*m^2 + m^3)) + (12*b^2*x^(3 + m)*ArcTanh[Tanh[a + b*x]]^2)/(6 + 11*m + 6*m^2 + m^3) - (4*b*x^(2 + m)*ArcTanh[Tanh[a + b*x]]^3)/(2 + 3*m + m^2) + (x^(1 + m)*ArcTanh[Tanh[a + b*x]]^4)/(1 + m)","A",5,2,13,0.1538,1,"{2168, 30}"
66,1,80,0,0.0632376,"\int x^6 \tanh ^{-1}(\tanh (a+b x))^4 \, dx","Int[x^6*ArcTanh[Tanh[a + b*x]]^4,x]","-\frac{1}{210} b^3 x^{10} \tanh ^{-1}(\tanh (a+b x))+\frac{1}{42} b^2 x^9 \tanh ^{-1}(\tanh (a+b x))^2-\frac{1}{14} b x^8 \tanh ^{-1}(\tanh (a+b x))^3+\frac{1}{7} x^7 \tanh ^{-1}(\tanh (a+b x))^4+\frac{b^4 x^{11}}{2310}","-\frac{1}{210} b^3 x^{10} \tanh ^{-1}(\tanh (a+b x))+\frac{1}{42} b^2 x^9 \tanh ^{-1}(\tanh (a+b x))^2-\frac{1}{14} b x^8 \tanh ^{-1}(\tanh (a+b x))^3+\frac{1}{7} x^7 \tanh ^{-1}(\tanh (a+b x))^4+\frac{b^4 x^{11}}{2310}",1,"(b^4*x^11)/2310 - (b^3*x^10*ArcTanh[Tanh[a + b*x]])/210 + (b^2*x^9*ArcTanh[Tanh[a + b*x]]^2)/42 - (b*x^8*ArcTanh[Tanh[a + b*x]]^3)/14 + (x^7*ArcTanh[Tanh[a + b*x]]^4)/7","A",5,2,13,0.1538,1,"{2168, 30}"
67,1,80,0,0.0564928,"\int x^5 \tanh ^{-1}(\tanh (a+b x))^4 \, dx","Int[x^5*ArcTanh[Tanh[a + b*x]]^4,x]","-\frac{1}{126} b^3 x^9 \tanh ^{-1}(\tanh (a+b x))+\frac{1}{28} b^2 x^8 \tanh ^{-1}(\tanh (a+b x))^2-\frac{2}{21} b x^7 \tanh ^{-1}(\tanh (a+b x))^3+\frac{1}{6} x^6 \tanh ^{-1}(\tanh (a+b x))^4+\frac{b^4 x^{10}}{1260}","-\frac{1}{126} b^3 x^9 \tanh ^{-1}(\tanh (a+b x))+\frac{1}{28} b^2 x^8 \tanh ^{-1}(\tanh (a+b x))^2-\frac{2}{21} b x^7 \tanh ^{-1}(\tanh (a+b x))^3+\frac{1}{6} x^6 \tanh ^{-1}(\tanh (a+b x))^4+\frac{b^4 x^{10}}{1260}",1,"(b^4*x^10)/1260 - (b^3*x^9*ArcTanh[Tanh[a + b*x]])/126 + (b^2*x^8*ArcTanh[Tanh[a + b*x]]^2)/28 - (2*b*x^7*ArcTanh[Tanh[a + b*x]]^3)/21 + (x^6*ArcTanh[Tanh[a + b*x]]^4)/6","A",5,2,13,0.1538,1,"{2168, 30}"
68,1,80,0,0.0547148,"\int x^4 \tanh ^{-1}(\tanh (a+b x))^4 \, dx","Int[x^4*ArcTanh[Tanh[a + b*x]]^4,x]","-\frac{1}{70} b^3 x^8 \tanh ^{-1}(\tanh (a+b x))+\frac{2}{35} b^2 x^7 \tanh ^{-1}(\tanh (a+b x))^2-\frac{2}{15} b x^6 \tanh ^{-1}(\tanh (a+b x))^3+\frac{1}{5} x^5 \tanh ^{-1}(\tanh (a+b x))^4+\frac{b^4 x^9}{630}","-\frac{1}{70} b^3 x^8 \tanh ^{-1}(\tanh (a+b x))+\frac{2}{35} b^2 x^7 \tanh ^{-1}(\tanh (a+b x))^2-\frac{2}{15} b x^6 \tanh ^{-1}(\tanh (a+b x))^3+\frac{1}{5} x^5 \tanh ^{-1}(\tanh (a+b x))^4+\frac{b^4 x^9}{630}",1,"(b^4*x^9)/630 - (b^3*x^8*ArcTanh[Tanh[a + b*x]])/70 + (2*b^2*x^7*ArcTanh[Tanh[a + b*x]]^2)/35 - (2*b*x^6*ArcTanh[Tanh[a + b*x]]^3)/15 + (x^5*ArcTanh[Tanh[a + b*x]]^4)/5","A",5,2,13,0.1538,1,"{2168, 30}"
69,1,72,0,0.0466606,"\int x^3 \tanh ^{-1}(\tanh (a+b x))^4 \, dx","Int[x^3*ArcTanh[Tanh[a + b*x]]^4,x]","-\frac{x^2 \tanh ^{-1}(\tanh (a+b x))^6}{10 b^2}-\frac{\tanh ^{-1}(\tanh (a+b x))^8}{280 b^4}+\frac{x \tanh ^{-1}(\tanh (a+b x))^7}{35 b^3}+\frac{x^3 \tanh ^{-1}(\tanh (a+b x))^5}{5 b}","-\frac{x^2 \tanh ^{-1}(\tanh (a+b x))^6}{10 b^2}-\frac{\tanh ^{-1}(\tanh (a+b x))^8}{280 b^4}+\frac{x \tanh ^{-1}(\tanh (a+b x))^7}{35 b^3}+\frac{x^3 \tanh ^{-1}(\tanh (a+b x))^5}{5 b}",1,"(x^3*ArcTanh[Tanh[a + b*x]]^5)/(5*b) - (x^2*ArcTanh[Tanh[a + b*x]]^6)/(10*b^2) + (x*ArcTanh[Tanh[a + b*x]]^7)/(35*b^3) - ArcTanh[Tanh[a + b*x]]^8/(280*b^4)","A",5,3,13,0.2308,1,"{2168, 2157, 30}"
70,1,53,0,0.0297045,"\int x^2 \tanh ^{-1}(\tanh (a+b x))^4 \, dx","Int[x^2*ArcTanh[Tanh[a + b*x]]^4,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^7}{105 b^3}-\frac{x \tanh ^{-1}(\tanh (a+b x))^6}{15 b^2}+\frac{x^2 \tanh ^{-1}(\tanh (a+b x))^5}{5 b}","\frac{\tanh ^{-1}(\tanh (a+b x))^7}{105 b^3}-\frac{x \tanh ^{-1}(\tanh (a+b x))^6}{15 b^2}+\frac{x^2 \tanh ^{-1}(\tanh (a+b x))^5}{5 b}",1,"(x^2*ArcTanh[Tanh[a + b*x]]^5)/(5*b) - (x*ArcTanh[Tanh[a + b*x]]^6)/(15*b^2) + ArcTanh[Tanh[a + b*x]]^7/(105*b^3)","A",4,3,13,0.2308,1,"{2168, 2157, 30}"
71,1,34,0,0.0139257,"\int x \tanh ^{-1}(\tanh (a+b x))^4 \, dx","Int[x*ArcTanh[Tanh[a + b*x]]^4,x]","\frac{x \tanh ^{-1}(\tanh (a+b x))^5}{5 b}-\frac{\tanh ^{-1}(\tanh (a+b x))^6}{30 b^2}","\frac{x \tanh ^{-1}(\tanh (a+b x))^5}{5 b}-\frac{\tanh ^{-1}(\tanh (a+b x))^6}{30 b^2}",1,"(x*ArcTanh[Tanh[a + b*x]]^5)/(5*b) - ArcTanh[Tanh[a + b*x]]^6/(30*b^2)","A",3,3,11,0.2727,1,"{2168, 2157, 30}"
72,1,16,0,0.0046208,"\int \tanh ^{-1}(\tanh (a+b x))^4 \, dx","Int[ArcTanh[Tanh[a + b*x]]^4,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^5}{5 b}","\frac{\tanh ^{-1}(\tanh (a+b x))^5}{5 b}",1,"ArcTanh[Tanh[a + b*x]]^5/(5*b)","A",2,2,9,0.2222,1,"{2157, 30}"
73,1,105,0,0.064792,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x} \, dx","Int[ArcTanh[Tanh[a + b*x]]^4/x,x]","-b x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3+\frac{1}{2} \tanh ^{-1}(\tanh (a+b x))^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2-\frac{1}{3} \tanh ^{-1}(\tanh (a+b x))^3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{1}{4} \tanh ^{-1}(\tanh (a+b x))^4+\log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4","-b x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3+\frac{1}{2} \tanh ^{-1}(\tanh (a+b x))^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2-\frac{1}{3} \tanh ^{-1}(\tanh (a+b x))^3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{1}{4} \tanh ^{-1}(\tanh (a+b x))^4+\log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4",1,"-(b*x*(b*x - ArcTanh[Tanh[a + b*x]])^3) + ((b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]]^2)/2 - ((b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^3)/3 + ArcTanh[Tanh[a + b*x]]^4/4 + (b*x - ArcTanh[Tanh[a + b*x]])^4*Log[x]","A",5,3,13,0.2308,1,"{2159, 2158, 29}"
74,1,95,0,0.0638568,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^2} \, dx","Int[ArcTanh[Tanh[a + b*x]]^4/x^2,x]","4 b^2 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{x}+\frac{4}{3} b \tanh ^{-1}(\tanh (a+b x))^3-2 b \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^2-4 b \log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3","4 b^2 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{x}+\frac{4}{3} b \tanh ^{-1}(\tanh (a+b x))^3-2 b \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^2-4 b \log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3",1,"4*b^2*x*(b*x - ArcTanh[Tanh[a + b*x]])^2 - 2*b*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^2 + (4*b*ArcTanh[Tanh[a + b*x]]^3)/3 - ArcTanh[Tanh[a + b*x]]^4/x - 4*b*(b*x - ArcTanh[Tanh[a + b*x]])^3*Log[x]","A",5,4,13,0.3077,1,"{2168, 2159, 2158, 29}"
75,1,87,0,0.062113,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^3} \, dx","Int[ArcTanh[Tanh[a + b*x]]^4/x^3,x]","3 b^2 \tanh ^{-1}(\tanh (a+b x))^2-6 b^3 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+6 b^2 \log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{2 x^2}-\frac{2 b \tanh ^{-1}(\tanh (a+b x))^3}{x}","3 b^2 \tanh ^{-1}(\tanh (a+b x))^2-6 b^3 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+6 b^2 \log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{2 x^2}-\frac{2 b \tanh ^{-1}(\tanh (a+b x))^3}{x}",1,"-6*b^3*x*(b*x - ArcTanh[Tanh[a + b*x]]) + 3*b^2*ArcTanh[Tanh[a + b*x]]^2 - (2*b*ArcTanh[Tanh[a + b*x]]^3)/x - ArcTanh[Tanh[a + b*x]]^4/(2*x^2) + 6*b^2*(b*x - ArcTanh[Tanh[a + b*x]])^2*Log[x]","A",5,4,13,0.3077,1,"{2168, 2159, 2158, 29}"
76,1,77,0,0.0582334,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^4} \, dx","Int[ArcTanh[Tanh[a + b*x]]^4/x^4,x]","-\frac{2 b^2 \tanh ^{-1}(\tanh (a+b x))^2}{x}-4 b^3 \log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)-\frac{2 b \tanh ^{-1}(\tanh (a+b x))^3}{3 x^2}-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{3 x^3}+4 b^4 x","-\frac{2 b^2 \tanh ^{-1}(\tanh (a+b x))^2}{x}-4 b^3 \log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)-\frac{2 b \tanh ^{-1}(\tanh (a+b x))^3}{3 x^2}-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{3 x^3}+4 b^4 x",1,"4*b^4*x - (2*b^2*ArcTanh[Tanh[a + b*x]]^2)/x - (2*b*ArcTanh[Tanh[a + b*x]]^3)/(3*x^2) - ArcTanh[Tanh[a + b*x]]^4/(3*x^3) - 4*b^3*(b*x - ArcTanh[Tanh[a + b*x]])*Log[x]","A",5,3,13,0.2308,1,"{2168, 2158, 29}"
77,1,74,0,0.05442,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^5} \, dx","Int[ArcTanh[Tanh[a + b*x]]^4/x^5,x]","-\frac{b^2 \tanh ^{-1}(\tanh (a+b x))^2}{2 x^2}-\frac{b^3 \tanh ^{-1}(\tanh (a+b x))}{x}-\frac{b \tanh ^{-1}(\tanh (a+b x))^3}{3 x^3}-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{4 x^4}+b^4 \log (x)","-\frac{b^2 \tanh ^{-1}(\tanh (a+b x))^2}{2 x^2}-\frac{b^3 \tanh ^{-1}(\tanh (a+b x))}{x}-\frac{b \tanh ^{-1}(\tanh (a+b x))^3}{3 x^3}-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{4 x^4}+b^4 \log (x)",1,"-((b^3*ArcTanh[Tanh[a + b*x]])/x) - (b^2*ArcTanh[Tanh[a + b*x]]^2)/(2*x^2) - (b*ArcTanh[Tanh[a + b*x]]^3)/(3*x^3) - ArcTanh[Tanh[a + b*x]]^4/(4*x^4) + b^4*Log[x]","A",5,2,13,0.1538,1,"{2168, 29}"
78,1,31,0,0.0131038,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^6} \, dx","Int[ArcTanh[Tanh[a + b*x]]^4/x^6,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^5}{5 x^5 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}","\frac{\tanh ^{-1}(\tanh (a+b x))^5}{5 x^5 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"ArcTanh[Tanh[a + b*x]]^5/(5*x^5*(b*x - ArcTanh[Tanh[a + b*x]]))","A",1,1,13,0.07692,1,"{2167}"
79,1,64,0,0.0313652,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^7} \, dx","Int[ArcTanh[Tanh[a + b*x]]^4/x^7,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^5}{6 x^6 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{b \tanh ^{-1}(\tanh (a+b x))^5}{30 x^5 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","\frac{\tanh ^{-1}(\tanh (a+b x))^5}{6 x^6 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{b \tanh ^{-1}(\tanh (a+b x))^5}{30 x^5 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}",1,"(b*ArcTanh[Tanh[a + b*x]]^5)/(30*x^5*(b*x - ArcTanh[Tanh[a + b*x]])^2) + ArcTanh[Tanh[a + b*x]]^5/(6*x^6*(b*x - ArcTanh[Tanh[a + b*x]]))","A",2,2,13,0.1538,1,"{2171, 2167}"
80,1,98,0,0.0531644,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^8} \, dx","Int[ArcTanh[Tanh[a + b*x]]^4/x^8,x]","\frac{b^2 \tanh ^{-1}(\tanh (a+b x))^5}{105 x^5 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{\tanh ^{-1}(\tanh (a+b x))^5}{7 x^7 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{b \tanh ^{-1}(\tanh (a+b x))^5}{21 x^6 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","\frac{b^2 \tanh ^{-1}(\tanh (a+b x))^5}{105 x^5 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{\tanh ^{-1}(\tanh (a+b x))^5}{7 x^7 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{b \tanh ^{-1}(\tanh (a+b x))^5}{21 x^6 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}",1,"(b^2*ArcTanh[Tanh[a + b*x]]^5)/(105*x^5*(b*x - ArcTanh[Tanh[a + b*x]])^3) + (b*ArcTanh[Tanh[a + b*x]]^5)/(21*x^6*(b*x - ArcTanh[Tanh[a + b*x]])^2) + ArcTanh[Tanh[a + b*x]]^5/(7*x^7*(b*x - ArcTanh[Tanh[a + b*x]]))","A",3,2,13,0.1538,1,"{2171, 2167}"
81,1,132,0,0.0754094,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^9} \, dx","Int[ArcTanh[Tanh[a + b*x]]^4/x^9,x]","\frac{b^2 \tanh ^{-1}(\tanh (a+b x))^5}{56 x^6 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{b^3 \tanh ^{-1}(\tanh (a+b x))^5}{280 x^5 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}+\frac{\tanh ^{-1}(\tanh (a+b x))^5}{8 x^8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{3 b \tanh ^{-1}(\tanh (a+b x))^5}{56 x^7 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","-\frac{b^3 \tanh ^{-1}(\tanh (a+b x))}{70 x^5}-\frac{b^2 \tanh ^{-1}(\tanh (a+b x))^2}{28 x^6}-\frac{b \tanh ^{-1}(\tanh (a+b x))^3}{14 x^7}-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{8 x^8}-\frac{b^4}{280 x^4}",1,"(b^3*ArcTanh[Tanh[a + b*x]]^5)/(280*x^5*(b*x - ArcTanh[Tanh[a + b*x]])^4) + (b^2*ArcTanh[Tanh[a + b*x]]^5)/(56*x^6*(b*x - ArcTanh[Tanh[a + b*x]])^3) + (3*b*ArcTanh[Tanh[a + b*x]]^5)/(56*x^7*(b*x - ArcTanh[Tanh[a + b*x]])^2) + ArcTanh[Tanh[a + b*x]]^5/(8*x^8*(b*x - ArcTanh[Tanh[a + b*x]]))","A",4,2,13,0.1538,1,"{2171, 2167}"
82,1,80,0,0.0554779,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^{10}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^4/x^10,x]","-\frac{b^3 \tanh ^{-1}(\tanh (a+b x))}{126 x^6}-\frac{b^2 \tanh ^{-1}(\tanh (a+b x))^2}{42 x^7}-\frac{b \tanh ^{-1}(\tanh (a+b x))^3}{18 x^8}-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{9 x^9}-\frac{b^4}{630 x^5}","-\frac{b^3 \tanh ^{-1}(\tanh (a+b x))}{126 x^6}-\frac{b^2 \tanh ^{-1}(\tanh (a+b x))^2}{42 x^7}-\frac{b \tanh ^{-1}(\tanh (a+b x))^3}{18 x^8}-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{9 x^9}-\frac{b^4}{630 x^5}",1,"-b^4/(630*x^5) - (b^3*ArcTanh[Tanh[a + b*x]])/(126*x^6) - (b^2*ArcTanh[Tanh[a + b*x]]^2)/(42*x^7) - (b*ArcTanh[Tanh[a + b*x]]^3)/(18*x^8) - ArcTanh[Tanh[a + b*x]]^4/(9*x^9)","A",5,2,13,0.1538,1,"{2168, 30}"
83,1,80,0,0.0561019,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^{11}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^4/x^11,x]","-\frac{b^3 \tanh ^{-1}(\tanh (a+b x))}{210 x^7}-\frac{b^2 \tanh ^{-1}(\tanh (a+b x))^2}{60 x^8}-\frac{2 b \tanh ^{-1}(\tanh (a+b x))^3}{45 x^9}-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{10 x^{10}}-\frac{b^4}{1260 x^6}","-\frac{b^3 \tanh ^{-1}(\tanh (a+b x))}{210 x^7}-\frac{b^2 \tanh ^{-1}(\tanh (a+b x))^2}{60 x^8}-\frac{2 b \tanh ^{-1}(\tanh (a+b x))^3}{45 x^9}-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{10 x^{10}}-\frac{b^4}{1260 x^6}",1,"-b^4/(1260*x^6) - (b^3*ArcTanh[Tanh[a + b*x]])/(210*x^7) - (b^2*ArcTanh[Tanh[a + b*x]]^2)/(60*x^8) - (2*b*ArcTanh[Tanh[a + b*x]]^3)/(45*x^9) - ArcTanh[Tanh[a + b*x]]^4/(10*x^10)","A",5,2,13,0.1538,1,"{2168, 30}"
84,1,34,0,0.0137937,"\int x \tanh ^{-1}(\tanh (a+b x))^6 \, dx","Int[x*ArcTanh[Tanh[a + b*x]]^6,x]","\frac{x \tanh ^{-1}(\tanh (a+b x))^7}{7 b}-\frac{\tanh ^{-1}(\tanh (a+b x))^8}{56 b^2}","\frac{x \tanh ^{-1}(\tanh (a+b x))^7}{7 b}-\frac{\tanh ^{-1}(\tanh (a+b x))^8}{56 b^2}",1,"(x*ArcTanh[Tanh[a + b*x]]^7)/(7*b) - ArcTanh[Tanh[a + b*x]]^8/(56*b^2)","A",3,3,11,0.2727,1,"{2168, 2157, 30}"
85,1,53,0,0.0256857,"\int \frac{x^m}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Int[x^m/ArcTanh[Tanh[a + b*x]],x]","-\frac{x^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{b x}{b x-\tanh ^{-1}(\tanh (a+b x))}\right)}{(m+1) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}","-\frac{x^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{b x}{b x-\tanh ^{-1}(\tanh (a+b x))}\right)}{(m+1) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"-((x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (b*x)/(b*x - ArcTanh[Tanh[a + b*x]])])/((1 + m)*(b*x - ArcTanh[Tanh[a + b*x]])))","A",1,1,13,0.07692,1,"{2164}"
86,1,81,0,0.058285,"\int \frac{x^3}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Int[x^3/ArcTanh[Tanh[a + b*x]],x]","\frac{x^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{2 b^2}+\frac{x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{b^3}+\frac{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^4}+\frac{x^3}{3 b}","\frac{x^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{2 b^2}+\frac{x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{b^3}+\frac{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^4}+\frac{x^3}{3 b}",1,"x^3/(3*b) + (x^2*(b*x - ArcTanh[Tanh[a + b*x]]))/(2*b^2) + (x*(b*x - ArcTanh[Tanh[a + b*x]])^2)/b^3 + ((b*x - ArcTanh[Tanh[a + b*x]])^3*Log[ArcTanh[Tanh[a + b*x]]])/b^4","A",5,4,13,0.3077,1,"{2159, 2158, 2157, 29}"
87,1,56,0,0.0346303,"\int \frac{x^2}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Int[x^2/ArcTanh[Tanh[a + b*x]],x]","\frac{x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^2}+\frac{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}+\frac{x^2}{2 b}","\frac{x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^2}+\frac{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}+\frac{x^2}{2 b}",1,"x^2/(2*b) + (x*(b*x - ArcTanh[Tanh[a + b*x]]))/b^2 + ((b*x - ArcTanh[Tanh[a + b*x]])^2*Log[ArcTanh[Tanh[a + b*x]]])/b^3","A",4,4,13,0.3077,1,"{2159, 2158, 2157, 29}"
88,1,31,0,0.0150204,"\int \frac{x}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Int[x/ArcTanh[Tanh[a + b*x]],x]","\frac{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^2}+\frac{x}{b}","\frac{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^2}+\frac{x}{b}",1,"x/b + ((b*x - ArcTanh[Tanh[a + b*x]])*Log[ArcTanh[Tanh[a + b*x]]])/b^2","A",3,3,11,0.2727,1,"{2158, 2157, 29}"
89,1,12,0,0.0043055,"\int \frac{1}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(-1),x]","\frac{\log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b}","\frac{\log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b}",1,"Log[ArcTanh[Tanh[a + b*x]]]/b","A",2,2,9,0.2222,1,"{2157, 29}"
90,1,44,0,0.0265642,"\int \frac{1}{x \tanh ^{-1}(\tanh (a+b x))} \, dx","Int[1/(x*ArcTanh[Tanh[a + b*x]]),x]","\frac{\log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b x-\tanh ^{-1}(\tanh (a+b x))}-\frac{\log (x)}{b x-\tanh ^{-1}(\tanh (a+b x))}","\frac{\log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b x-\tanh ^{-1}(\tanh (a+b x))}-\frac{\log (x)}{b x-\tanh ^{-1}(\tanh (a+b x))}",1,"-(Log[x]/(b*x - ArcTanh[Tanh[a + b*x]])) + Log[ArcTanh[Tanh[a + b*x]]]/(b*x - ArcTanh[Tanh[a + b*x]])","A",4,3,13,0.2308,1,"{2160, 2157, 29}"
91,1,65,0,0.0443764,"\int \frac{1}{x^2 \tanh ^{-1}(\tanh (a+b x))} \, dx","Int[1/(x^2*ArcTanh[Tanh[a + b*x]]),x]","\frac{1}{x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{b \log (x)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}+\frac{b \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","\frac{1}{x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{b \log (x)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}+\frac{b \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}",1,"1/(x*(b*x - ArcTanh[Tanh[a + b*x]])) - (b*Log[x])/(b*x - ArcTanh[Tanh[a + b*x]])^2 + (b*Log[ArcTanh[Tanh[a + b*x]]])/(b*x - ArcTanh[Tanh[a + b*x]])^2","A",5,4,13,0.3077,1,"{2163, 2160, 2157, 29}"
92,1,92,0,0.0681549,"\int \frac{1}{x^3 \tanh ^{-1}(\tanh (a+b x))} \, dx","Int[1/(x^3*ArcTanh[Tanh[a + b*x]]),x]","-\frac{b^2 \log (x)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{b^2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{1}{2 x^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{b}{x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","-\frac{b^2 \log (x)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{b^2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{1}{2 x^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{b}{x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}",1,"b/(x*(b*x - ArcTanh[Tanh[a + b*x]])^2) + 1/(2*x^2*(b*x - ArcTanh[Tanh[a + b*x]])) - (b^2*Log[x])/(b*x - ArcTanh[Tanh[a + b*x]])^3 + (b^2*Log[ArcTanh[Tanh[a + b*x]]])/(b*x - ArcTanh[Tanh[a + b*x]])^3","A",6,4,13,0.3077,1,"{2163, 2160, 2157, 29}"
93,1,65,0,0.0360839,"\int \frac{x^m}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[x^m/ArcTanh[Tanh[a + b*x]]^2,x]","-\frac{x^m \, _2F_1\left(1,m;m+1;\frac{b x}{b x-\tanh ^{-1}(\tanh (a+b x))}\right)}{b \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{x^m}{b \tanh ^{-1}(\tanh (a+b x))}","-\frac{x^m \, _2F_1\left(1,m;m+1;\frac{b x}{b x-\tanh ^{-1}(\tanh (a+b x))}\right)}{b \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{x^m}{b \tanh ^{-1}(\tanh (a+b x))}",1,"-(x^m/(b*ArcTanh[Tanh[a + b*x]])) - (x^m*Hypergeometric2F1[1, m, 1 + m, (b*x)/(b*x - ArcTanh[Tanh[a + b*x]])])/(b*(b*x - ArcTanh[Tanh[a + b*x]]))","A",2,2,13,0.1538,1,"{2168, 2164}"
94,1,98,0,0.0806588,"\int \frac{x^4}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[x^4/ArcTanh[Tanh[a + b*x]]^2,x]","\frac{2 x^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}+\frac{4 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{b^4}+\frac{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^5}-\frac{x^4}{b \tanh ^{-1}(\tanh (a+b x))}+\frac{4 x^3}{3 b^2}","\frac{2 x^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}+\frac{4 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{b^4}+\frac{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^5}-\frac{x^4}{b \tanh ^{-1}(\tanh (a+b x))}+\frac{4 x^3}{3 b^2}",1,"(4*x^3)/(3*b^2) + (2*x^2*(b*x - ArcTanh[Tanh[a + b*x]]))/b^3 + (4*x*(b*x - ArcTanh[Tanh[a + b*x]])^2)/b^4 - x^4/(b*ArcTanh[Tanh[a + b*x]]) + (4*(b*x - ArcTanh[Tanh[a + b*x]])^3*Log[ArcTanh[Tanh[a + b*x]]])/b^5","A",6,5,13,0.3846,1,"{2168, 2159, 2158, 2157, 29}"
95,1,75,0,0.0529525,"\int \frac{x^3}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[x^3/ArcTanh[Tanh[a + b*x]]^2,x]","\frac{3 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}+\frac{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^4}-\frac{x^3}{b \tanh ^{-1}(\tanh (a+b x))}+\frac{3 x^2}{2 b^2}","\frac{3 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}+\frac{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^4}-\frac{x^3}{b \tanh ^{-1}(\tanh (a+b x))}+\frac{3 x^2}{2 b^2}",1,"(3*x^2)/(2*b^2) + (3*x*(b*x - ArcTanh[Tanh[a + b*x]]))/b^3 - x^3/(b*ArcTanh[Tanh[a + b*x]]) + (3*(b*x - ArcTanh[Tanh[a + b*x]])^2*Log[ArcTanh[Tanh[a + b*x]]])/b^4","A",5,5,13,0.3846,1,"{2168, 2159, 2158, 2157, 29}"
96,1,50,0,0.0340511,"\int \frac{x^2}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[x^2/ArcTanh[Tanh[a + b*x]]^2,x]","\frac{2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}-\frac{x^2}{b \tanh ^{-1}(\tanh (a+b x))}+\frac{2 x}{b^2}","\frac{2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}-\frac{x^2}{b \tanh ^{-1}(\tanh (a+b x))}+\frac{2 x}{b^2}",1,"(2*x)/b^2 - x^2/(b*ArcTanh[Tanh[a + b*x]]) + (2*(b*x - ArcTanh[Tanh[a + b*x]])*Log[ArcTanh[Tanh[a + b*x]]])/b^3","A",4,4,13,0.3077,1,"{2168, 2158, 2157, 29}"
97,1,28,0,0.0140836,"\int \frac{x}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[x/ArcTanh[Tanh[a + b*x]]^2,x]","\frac{\log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^2}-\frac{x}{b \tanh ^{-1}(\tanh (a+b x))}","\frac{\log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^2}-\frac{x}{b \tanh ^{-1}(\tanh (a+b x))}",1,"-(x/(b*ArcTanh[Tanh[a + b*x]])) + Log[ArcTanh[Tanh[a + b*x]]]/b^2","A",3,3,11,0.2727,1,"{2168, 2157, 29}"
98,1,14,0,0.0048739,"\int \frac{1}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(-2),x]","-\frac{1}{b \tanh ^{-1}(\tanh (a+b x))}","-\frac{1}{b \tanh ^{-1}(\tanh (a+b x))}",1,"-(1/(b*ArcTanh[Tanh[a + b*x]]))","A",2,2,9,0.2222,1,"{2157, 30}"
99,1,70,0,0.0459563,"\int \frac{1}{x \tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[1/(x*ArcTanh[Tanh[a + b*x]]^2),x]","-\frac{1}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))}+\frac{\log (x)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}-\frac{\log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","-\frac{1}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))}+\frac{\log (x)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}-\frac{\log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}",1,"-(1/((b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]])) + Log[x]/(b*x - ArcTanh[Tanh[a + b*x]])^2 - Log[ArcTanh[Tanh[a + b*x]]]/(b*x - ArcTanh[Tanh[a + b*x]])^2","A",5,4,13,0.3077,1,"{2163, 2160, 2157, 29}"
100,1,102,0,0.0716322,"\int \frac{1}{x^2 \tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[1/(x^2*ArcTanh[Tanh[a + b*x]]^2),x]","-\frac{2 b}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))}+\frac{1}{x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))}+\frac{2 b \log (x)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}-\frac{2 b \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}","-\frac{2 b}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))}+\frac{1}{x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))}+\frac{2 b \log (x)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}-\frac{2 b \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}",1,"(-2*b)/((b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]]) + 1/(x*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]) + (2*b*Log[x])/(b*x - ArcTanh[Tanh[a + b*x]])^3 - (2*b*Log[ArcTanh[Tanh[a + b*x]]])/(b*x - ArcTanh[Tanh[a + b*x]])^3","A",6,5,13,0.3846,1,"{2171, 2163, 2160, 2157, 29}"
101,1,143,0,0.0961146,"\int \frac{1}{x^3 \tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[1/(x^3*ArcTanh[Tanh[a + b*x]]^2),x]","-\frac{3 b^2}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))}+\frac{3 b^2 \log (x)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}-\frac{3 b^2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}+\frac{1}{2 x^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))}+\frac{3 b}{2 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))}","-\frac{3 b^2}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))}+\frac{3 b^2 \log (x)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}-\frac{3 b^2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}+\frac{1}{2 x^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))}+\frac{3 b}{2 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))}",1,"(-3*b^2)/((b*x - ArcTanh[Tanh[a + b*x]])^3*ArcTanh[Tanh[a + b*x]]) + (3*b)/(2*x*(b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]]) + 1/(2*x^2*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]) + (3*b^2*Log[x])/(b*x - ArcTanh[Tanh[a + b*x]])^4 - (3*b^2*Log[ArcTanh[Tanh[a + b*x]]])/(b*x - ArcTanh[Tanh[a + b*x]])^4","A",7,5,13,0.3846,1,"{2171, 2163, 2160, 2157, 29}"
102,1,94,0,0.0606245,"\int \frac{x^m}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[x^m/ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{m x^{m-1} \, _2F_1\left(1,m-1;m;\frac{b x}{b x-\tanh ^{-1}(\tanh (a+b x))}\right)}{2 b^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{m x^{m-1}}{2 b^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{x^m}{2 b \tanh ^{-1}(\tanh (a+b x))^2}","-\frac{m x^{m-1} \, _2F_1\left(1,m-1;m;\frac{b x}{b x-\tanh ^{-1}(\tanh (a+b x))}\right)}{2 b^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{m x^{m-1}}{2 b^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{x^m}{2 b \tanh ^{-1}(\tanh (a+b x))^2}",1,"-x^m/(2*b*ArcTanh[Tanh[a + b*x]]^2) - (m*x^(-1 + m))/(2*b^2*ArcTanh[Tanh[a + b*x]]) - (m*x^(-1 + m)*Hypergeometric2F1[1, -1 + m, m, (b*x)/(b*x - ArcTanh[Tanh[a + b*x]])])/(2*b^2*(b*x - ArcTanh[Tanh[a + b*x]]))","A",3,2,13,0.1538,1,"{2168, 2164}"
103,1,92,0,0.0727309,"\int \frac{x^4}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[x^4/ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{2 x^3}{b^2 \tanh ^{-1}(\tanh (a+b x))}+\frac{6 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^4}+\frac{6 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^5}-\frac{x^4}{2 b \tanh ^{-1}(\tanh (a+b x))^2}+\frac{3 x^2}{b^3}","-\frac{2 x^3}{b^2 \tanh ^{-1}(\tanh (a+b x))}+\frac{6 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^4}+\frac{6 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^5}-\frac{x^4}{2 b \tanh ^{-1}(\tanh (a+b x))^2}+\frac{3 x^2}{b^3}",1,"(3*x^2)/b^3 + (6*x*(b*x - ArcTanh[Tanh[a + b*x]]))/b^4 - x^4/(2*b*ArcTanh[Tanh[a + b*x]]^2) - (2*x^3)/(b^2*ArcTanh[Tanh[a + b*x]]) + (6*(b*x - ArcTanh[Tanh[a + b*x]])^2*Log[ArcTanh[Tanh[a + b*x]]])/b^5","A",6,5,13,0.3846,1,"{2168, 2159, 2158, 2157, 29}"
104,1,71,0,0.0483379,"\int \frac{x^3}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[x^3/ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{3 x^2}{2 b^2 \tanh ^{-1}(\tanh (a+b x))}+\frac{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^4}-\frac{x^3}{2 b \tanh ^{-1}(\tanh (a+b x))^2}+\frac{3 x}{b^3}","-\frac{3 x^2}{2 b^2 \tanh ^{-1}(\tanh (a+b x))}+\frac{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^4}-\frac{x^3}{2 b \tanh ^{-1}(\tanh (a+b x))^2}+\frac{3 x}{b^3}",1,"(3*x)/b^3 - x^3/(2*b*ArcTanh[Tanh[a + b*x]]^2) - (3*x^2)/(2*b^2*ArcTanh[Tanh[a + b*x]]) + (3*(b*x - ArcTanh[Tanh[a + b*x]])*Log[ArcTanh[Tanh[a + b*x]]])/b^4","A",5,4,13,0.3077,1,"{2168, 2158, 2157, 29}"
105,1,47,0,0.0287172,"\int \frac{x^2}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[x^2/ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{x}{b^2 \tanh ^{-1}(\tanh (a+b x))}+\frac{\log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}-\frac{x^2}{2 b \tanh ^{-1}(\tanh (a+b x))^2}","-\frac{x}{b^2 \tanh ^{-1}(\tanh (a+b x))}+\frac{\log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}-\frac{x^2}{2 b \tanh ^{-1}(\tanh (a+b x))^2}",1,"-x^2/(2*b*ArcTanh[Tanh[a + b*x]]^2) - x/(b^2*ArcTanh[Tanh[a + b*x]]) + Log[ArcTanh[Tanh[a + b*x]]]/b^3","A",4,3,13,0.2308,1,"{2168, 2157, 29}"
106,1,34,0,0.0144834,"\int \frac{x}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[x/ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{1}{2 b^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{x}{2 b \tanh ^{-1}(\tanh (a+b x))^2}","-\frac{1}{2 b^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{x}{2 b \tanh ^{-1}(\tanh (a+b x))^2}",1,"-x/(2*b*ArcTanh[Tanh[a + b*x]]^2) - 1/(2*b^2*ArcTanh[Tanh[a + b*x]])","A",3,3,11,0.2727,1,"{2168, 2157, 30}"
107,1,16,0,0.004478,"\int \frac{1}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(-3),x]","-\frac{1}{2 b \tanh ^{-1}(\tanh (a+b x))^2}","-\frac{1}{2 b \tanh ^{-1}(\tanh (a+b x))^2}",1,"-1/(2*b*ArcTanh[Tanh[a + b*x]]^2)","A",2,2,9,0.2222,1,"{2157, 30}"
108,1,97,0,0.0663209,"\int \frac{1}{x \tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[1/(x*ArcTanh[Tanh[a + b*x]]^3),x]","\frac{1}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{1}{2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^2}-\frac{\log (x)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{\log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}","\frac{1}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{1}{2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^2}-\frac{\log (x)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{\log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}",1,"-1/(2*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^2) + 1/((b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]]) - Log[x]/(b*x - ArcTanh[Tanh[a + b*x]])^3 + Log[ArcTanh[Tanh[a + b*x]]]/(b*x - ArcTanh[Tanh[a + b*x]])^3","A",6,4,13,0.3077,1,"{2163, 2160, 2157, 29}"
109,1,131,0,0.0932824,"\int \frac{1}{x^2 \tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[1/(x^2*ArcTanh[Tanh[a + b*x]]^3),x]","\frac{3 b}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))}-\frac{3 b}{2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^2}+\frac{1}{x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^2}-\frac{3 b \log (x)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}+\frac{3 b \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}","\frac{3 b}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))}-\frac{3 b}{2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^2}+\frac{1}{x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^2}-\frac{3 b \log (x)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}+\frac{3 b \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}",1,"(-3*b)/(2*(b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]]^2) + 1/(x*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^2) + (3*b)/((b*x - ArcTanh[Tanh[a + b*x]])^3*ArcTanh[Tanh[a + b*x]]) - (3*b*Log[x])/(b*x - ArcTanh[Tanh[a + b*x]])^4 + (3*b*Log[ArcTanh[Tanh[a + b*x]]])/(b*x - ArcTanh[Tanh[a + b*x]])^4","A",7,5,13,0.3846,1,"{2171, 2163, 2160, 2157, 29}"
110,1,170,0,0.1207833,"\int \frac{1}{x^3 \tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[1/(x^3*ArcTanh[Tanh[a + b*x]]^3),x]","\frac{6 b^2}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4 \tanh ^{-1}(\tanh (a+b x))}-\frac{3 b^2}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))^2}-\frac{6 b^2 \log (x)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^5}+\frac{6 b^2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^5}+\frac{1}{2 x^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^2}+\frac{2 b}{x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^2}","\frac{6 b^2}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4 \tanh ^{-1}(\tanh (a+b x))}-\frac{3 b^2}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))^2}-\frac{6 b^2 \log (x)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^5}+\frac{6 b^2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^5}+\frac{1}{2 x^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^2}+\frac{2 b}{x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^2}",1,"(-3*b^2)/((b*x - ArcTanh[Tanh[a + b*x]])^3*ArcTanh[Tanh[a + b*x]]^2) + (2*b)/(x*(b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]]^2) + 1/(2*x^2*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^2) + (6*b^2)/((b*x - ArcTanh[Tanh[a + b*x]])^4*ArcTanh[Tanh[a + b*x]]) - (6*b^2*Log[x])/(b*x - ArcTanh[Tanh[a + b*x]])^5 + (6*b^2*Log[ArcTanh[Tanh[a + b*x]]])/(b*x - ArcTanh[Tanh[a + b*x]])^5","A",8,5,13,0.3846,1,"{2171, 2163, 2160, 2157, 29}"
111,1,101,0,0.0645386,"\int x^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx","Int[x^4*Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{32 x^2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^3}-\frac{16 x^3 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{15 b^2}+\frac{256 \tanh ^{-1}(\tanh (a+b x))^{11/2}}{3465 b^5}-\frac{128 x \tanh ^{-1}(\tanh (a+b x))^{9/2}}{315 b^4}+\frac{2 x^4 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b}","\frac{32 x^2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^3}-\frac{16 x^3 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{15 b^2}+\frac{256 \tanh ^{-1}(\tanh (a+b x))^{11/2}}{3465 b^5}-\frac{128 x \tanh ^{-1}(\tanh (a+b x))^{9/2}}{315 b^4}+\frac{2 x^4 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b}",1,"(2*x^4*ArcTanh[Tanh[a + b*x]]^(3/2))/(3*b) - (16*x^3*ArcTanh[Tanh[a + b*x]]^(5/2))/(15*b^2) + (32*x^2*ArcTanh[Tanh[a + b*x]]^(7/2))/(35*b^3) - (128*x*ArcTanh[Tanh[a + b*x]]^(9/2))/(315*b^4) + (256*ArcTanh[Tanh[a + b*x]]^(11/2))/(3465*b^5)","A",6,3,15,0.2000,1,"{2168, 2157, 30}"
112,1,80,0,0.0487165,"\int x^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx","Int[x^3*Sqrt[ArcTanh[Tanh[a + b*x]]],x]","-\frac{4 x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b^2}-\frac{32 \tanh ^{-1}(\tanh (a+b x))^{9/2}}{315 b^4}+\frac{16 x \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^3}+\frac{2 x^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b}","-\frac{4 x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b^2}-\frac{32 \tanh ^{-1}(\tanh (a+b x))^{9/2}}{315 b^4}+\frac{16 x \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^3}+\frac{2 x^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b}",1,"(2*x^3*ArcTanh[Tanh[a + b*x]]^(3/2))/(3*b) - (4*x^2*ArcTanh[Tanh[a + b*x]]^(5/2))/(5*b^2) + (16*x*ArcTanh[Tanh[a + b*x]]^(7/2))/(35*b^3) - (32*ArcTanh[Tanh[a + b*x]]^(9/2))/(315*b^4)","A",5,3,15,0.2000,1,"{2168, 2157, 30}"
113,1,59,0,0.0297581,"\int x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx","Int[x^2*Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{16 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{105 b^3}-\frac{8 x \tanh ^{-1}(\tanh (a+b x))^{5/2}}{15 b^2}+\frac{2 x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b}","\frac{16 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{105 b^3}-\frac{8 x \tanh ^{-1}(\tanh (a+b x))^{5/2}}{15 b^2}+\frac{2 x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b}",1,"(2*x^2*ArcTanh[Tanh[a + b*x]]^(3/2))/(3*b) - (8*x*ArcTanh[Tanh[a + b*x]]^(5/2))/(15*b^2) + (16*ArcTanh[Tanh[a + b*x]]^(7/2))/(105*b^3)","A",4,3,15,0.2000,1,"{2168, 2157, 30}"
114,1,38,0,0.0140504,"\int x \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx","Int[x*Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{2 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b}-\frac{4 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{15 b^2}","\frac{2 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b}-\frac{4 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{15 b^2}",1,"(2*x*ArcTanh[Tanh[a + b*x]]^(3/2))/(3*b) - (4*ArcTanh[Tanh[a + b*x]]^(5/2))/(15*b^2)","A",3,3,13,0.2308,1,"{2168, 2157, 30}"
115,1,18,0,0.0047037,"\int \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx","Int[Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b}","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b}",1,"(2*ArcTanh[Tanh[a + b*x]]^(3/2))/(3*b)","A",2,2,11,0.1818,1,"{2157, 30}"
116,1,63,0,0.0595282,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x} \, dx","Int[Sqrt[ArcTanh[Tanh[a + b*x]]]/x,x]","2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}-2 \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))} \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)","2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}-2 \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))} \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)",1,"-2*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]*Sqrt[b*x - ArcTanh[Tanh[a + b*x]]] + 2*Sqrt[ArcTanh[Tanh[a + b*x]]]","A",2,2,15,0.1333,1,"{2159, 2161}"
117,1,66,0,0.0315191,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^2} \, dx","Int[Sqrt[ArcTanh[Tanh[a + b*x]]]/x^2,x]","\frac{b \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}-\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x}","\frac{b \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}-\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x}",1,"(b*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]] - Sqrt[ArcTanh[Tanh[a + b*x]]]/x","A",2,2,15,0.1333,1,"{2168, 2161}"
118,1,125,0,0.0716427,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^3} \, dx","Int[Sqrt[ArcTanh[Tanh[a + b*x]]]/x^3,x]","\frac{b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{b^2 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}-\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{2 x^2}-\frac{b}{4 x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","\frac{b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{b^2 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}-\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{2 x^2}-\frac{b}{4 x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(b^2*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(4*(b*x - ArcTanh[Tanh[a + b*x]])^(3/2)) - b/(4*x*Sqrt[ArcTanh[Tanh[a + b*x]]]) + b^2/(4*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]]) - Sqrt[ArcTanh[Tanh[a + b*x]]]/(2*x^2)","A",4,3,15,0.2000,1,"{2168, 2163, 2161}"
119,1,179,0,0.1205675,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^4} \, dx","Int[Sqrt[ArcTanh[Tanh[a + b*x]]]/x^4,x]","\frac{b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{b^3}{24 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{b^2}{24 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{b^3 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}-\frac{b}{12 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{3 x^3}","\frac{b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{b^3}{24 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{b^2}{24 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{b^3 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}-\frac{b}{12 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{3 x^3}",1,"(b^3*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(8*(b*x - ArcTanh[Tanh[a + b*x]])^(5/2)) + b^2/(24*x*ArcTanh[Tanh[a + b*x]]^(3/2)) - b^3/(24*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(3/2)) - b/(12*x^2*Sqrt[ArcTanh[Tanh[a + b*x]]]) + b^3/(8*(b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]]) - Sqrt[ArcTanh[Tanh[a + b*x]]]/(3*x^3)","A",6,3,15,0.2000,1,"{2168, 2163, 2161}"
120,1,101,0,0.0672489,"\int x^4 \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx","Int[x^4*ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{32 x^2 \tanh ^{-1}(\tanh (a+b x))^{9/2}}{105 b^3}-\frac{16 x^3 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^2}+\frac{256 \tanh ^{-1}(\tanh (a+b x))^{13/2}}{15015 b^5}-\frac{128 x \tanh ^{-1}(\tanh (a+b x))^{11/2}}{1155 b^4}+\frac{2 x^4 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b}","\frac{32 x^2 \tanh ^{-1}(\tanh (a+b x))^{9/2}}{105 b^3}-\frac{16 x^3 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^2}+\frac{256 \tanh ^{-1}(\tanh (a+b x))^{13/2}}{15015 b^5}-\frac{128 x \tanh ^{-1}(\tanh (a+b x))^{11/2}}{1155 b^4}+\frac{2 x^4 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b}",1,"(2*x^4*ArcTanh[Tanh[a + b*x]]^(5/2))/(5*b) - (16*x^3*ArcTanh[Tanh[a + b*x]]^(7/2))/(35*b^2) + (32*x^2*ArcTanh[Tanh[a + b*x]]^(9/2))/(105*b^3) - (128*x*ArcTanh[Tanh[a + b*x]]^(11/2))/(1155*b^4) + (256*ArcTanh[Tanh[a + b*x]]^(13/2))/(15015*b^5)","A",6,3,15,0.2000,1,"{2168, 2157, 30}"
121,1,80,0,0.0460745,"\int x^3 \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx","Int[x^3*ArcTanh[Tanh[a + b*x]]^(3/2),x]","-\frac{12 x^2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^2}-\frac{32 \tanh ^{-1}(\tanh (a+b x))^{11/2}}{1155 b^4}+\frac{16 x \tanh ^{-1}(\tanh (a+b x))^{9/2}}{105 b^3}+\frac{2 x^3 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b}","-\frac{12 x^2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^2}-\frac{32 \tanh ^{-1}(\tanh (a+b x))^{11/2}}{1155 b^4}+\frac{16 x \tanh ^{-1}(\tanh (a+b x))^{9/2}}{105 b^3}+\frac{2 x^3 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b}",1,"(2*x^3*ArcTanh[Tanh[a + b*x]]^(5/2))/(5*b) - (12*x^2*ArcTanh[Tanh[a + b*x]]^(7/2))/(35*b^2) + (16*x*ArcTanh[Tanh[a + b*x]]^(9/2))/(105*b^3) - (32*ArcTanh[Tanh[a + b*x]]^(11/2))/(1155*b^4)","A",5,3,15,0.2000,1,"{2168, 2157, 30}"
122,1,59,0,0.0292661,"\int x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx","Int[x^2*ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{16 \tanh ^{-1}(\tanh (a+b x))^{9/2}}{315 b^3}-\frac{8 x \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^2}+\frac{2 x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b}","\frac{16 \tanh ^{-1}(\tanh (a+b x))^{9/2}}{315 b^3}-\frac{8 x \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^2}+\frac{2 x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b}",1,"(2*x^2*ArcTanh[Tanh[a + b*x]]^(5/2))/(5*b) - (8*x*ArcTanh[Tanh[a + b*x]]^(7/2))/(35*b^2) + (16*ArcTanh[Tanh[a + b*x]]^(9/2))/(315*b^3)","A",4,3,15,0.2000,1,"{2168, 2157, 30}"
123,1,38,0,0.0141962,"\int x \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx","Int[x*ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{2 x \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b}-\frac{4 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^2}","\frac{2 x \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b}-\frac{4 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^2}",1,"(2*x*ArcTanh[Tanh[a + b*x]]^(5/2))/(5*b) - (4*ArcTanh[Tanh[a + b*x]]^(7/2))/(35*b^2)","A",3,3,13,0.2308,1,"{2168, 2157, 30}"
124,1,18,0,0.0047478,"\int \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b}","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b}",1,"(2*ArcTanh[Tanh[a + b*x]]^(5/2))/(5*b)","A",2,2,11,0.1818,1,"{2157, 30}"
125,1,91,0,0.0497527,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(3/2)/x,x]","-2 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{2}{3} \tanh ^{-1}(\tanh (a+b x))^{3/2}+2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)","-2 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{2}{3} \tanh ^{-1}(\tanh (a+b x))^{3/2}+2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)",1,"2*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^(3/2) - 2*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]] + (2*ArcTanh[Tanh[a + b*x]]^(3/2))/3","A",3,2,15,0.1333,1,"{2159, 2161}"
126,1,81,0,0.0474029,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^2} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(3/2)/x^2,x]","-\frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x}+3 b \sqrt{\tanh ^{-1}(\tanh (a+b x))}-3 b \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))} \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)","-\frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x}+3 b \sqrt{\tanh ^{-1}(\tanh (a+b x))}-3 b \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))} \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)",1,"-3*b*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]*Sqrt[b*x - ArcTanh[Tanh[a + b*x]]] + 3*b*Sqrt[ArcTanh[Tanh[a + b*x]]] - ArcTanh[Tanh[a + b*x]]^(3/2)/x","A",3,3,15,0.2000,1,"{2168, 2159, 2161}"
127,1,92,0,0.0490936,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^3} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(3/2)/x^3,x]","\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}-\frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{2 x^2}-\frac{3 b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{4 x}","\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}-\frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{2 x^2}-\frac{3 b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{4 x}",1,"(3*b^2*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(4*Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]) - (3*b*Sqrt[ArcTanh[Tanh[a + b*x]]])/(4*x) - ArcTanh[Tanh[a + b*x]]^(3/2)/(2*x^2)","A",3,2,15,0.1333,1,"{2168, 2161}"
128,1,146,0,0.0935789,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^4} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(3/2)/x^4,x]","\frac{b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{b^2}{8 x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{b^3 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}-\frac{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{4 x^2}-\frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 x^3}","\frac{b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{b^2}{8 x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{b^3 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}-\frac{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{4 x^2}-\frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 x^3}",1,"(b^3*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(8*(b*x - ArcTanh[Tanh[a + b*x]])^(3/2)) - b^2/(8*x*Sqrt[ArcTanh[Tanh[a + b*x]]]) + b^3/(8*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]]) - (b*Sqrt[ArcTanh[Tanh[a + b*x]]])/(4*x^2) - ArcTanh[Tanh[a + b*x]]^(3/2)/(3*x^3)","A",5,3,15,0.2000,1,"{2168, 2163, 2161}"
129,1,101,0,0.0647503,"\int x^4 \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx","Int[x^4*ArcTanh[Tanh[a + b*x]]^(5/2),x]","\frac{32 x^2 \tanh ^{-1}(\tanh (a+b x))^{11/2}}{231 b^3}-\frac{16 x^3 \tanh ^{-1}(\tanh (a+b x))^{9/2}}{63 b^2}+\frac{256 \tanh ^{-1}(\tanh (a+b x))^{15/2}}{45045 b^5}-\frac{128 x \tanh ^{-1}(\tanh (a+b x))^{13/2}}{3003 b^4}+\frac{2 x^4 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{7 b}","\frac{32 x^2 \tanh ^{-1}(\tanh (a+b x))^{11/2}}{231 b^3}-\frac{16 x^3 \tanh ^{-1}(\tanh (a+b x))^{9/2}}{63 b^2}+\frac{256 \tanh ^{-1}(\tanh (a+b x))^{15/2}}{45045 b^5}-\frac{128 x \tanh ^{-1}(\tanh (a+b x))^{13/2}}{3003 b^4}+\frac{2 x^4 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{7 b}",1,"(2*x^4*ArcTanh[Tanh[a + b*x]]^(7/2))/(7*b) - (16*x^3*ArcTanh[Tanh[a + b*x]]^(9/2))/(63*b^2) + (32*x^2*ArcTanh[Tanh[a + b*x]]^(11/2))/(231*b^3) - (128*x*ArcTanh[Tanh[a + b*x]]^(13/2))/(3003*b^4) + (256*ArcTanh[Tanh[a + b*x]]^(15/2))/(45045*b^5)","A",6,3,15,0.2000,1,"{2168, 2157, 30}"
130,1,80,0,0.0468241,"\int x^3 \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx","Int[x^3*ArcTanh[Tanh[a + b*x]]^(5/2),x]","-\frac{4 x^2 \tanh ^{-1}(\tanh (a+b x))^{9/2}}{21 b^2}-\frac{32 \tanh ^{-1}(\tanh (a+b x))^{13/2}}{3003 b^4}+\frac{16 x \tanh ^{-1}(\tanh (a+b x))^{11/2}}{231 b^3}+\frac{2 x^3 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{7 b}","-\frac{4 x^2 \tanh ^{-1}(\tanh (a+b x))^{9/2}}{21 b^2}-\frac{32 \tanh ^{-1}(\tanh (a+b x))^{13/2}}{3003 b^4}+\frac{16 x \tanh ^{-1}(\tanh (a+b x))^{11/2}}{231 b^3}+\frac{2 x^3 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{7 b}",1,"(2*x^3*ArcTanh[Tanh[a + b*x]]^(7/2))/(7*b) - (4*x^2*ArcTanh[Tanh[a + b*x]]^(9/2))/(21*b^2) + (16*x*ArcTanh[Tanh[a + b*x]]^(11/2))/(231*b^3) - (32*ArcTanh[Tanh[a + b*x]]^(13/2))/(3003*b^4)","A",5,3,15,0.2000,1,"{2168, 2157, 30}"
131,1,59,0,0.02927,"\int x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx","Int[x^2*ArcTanh[Tanh[a + b*x]]^(5/2),x]","\frac{16 \tanh ^{-1}(\tanh (a+b x))^{11/2}}{693 b^3}-\frac{8 x \tanh ^{-1}(\tanh (a+b x))^{9/2}}{63 b^2}+\frac{2 x^2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{7 b}","\frac{16 \tanh ^{-1}(\tanh (a+b x))^{11/2}}{693 b^3}-\frac{8 x \tanh ^{-1}(\tanh (a+b x))^{9/2}}{63 b^2}+\frac{2 x^2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{7 b}",1,"(2*x^2*ArcTanh[Tanh[a + b*x]]^(7/2))/(7*b) - (8*x*ArcTanh[Tanh[a + b*x]]^(9/2))/(63*b^2) + (16*ArcTanh[Tanh[a + b*x]]^(11/2))/(693*b^3)","A",4,3,15,0.2000,1,"{2168, 2157, 30}"
132,1,38,0,0.0142888,"\int x \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx","Int[x*ArcTanh[Tanh[a + b*x]]^(5/2),x]","\frac{2 x \tanh ^{-1}(\tanh (a+b x))^{7/2}}{7 b}-\frac{4 \tanh ^{-1}(\tanh (a+b x))^{9/2}}{63 b^2}","\frac{2 x \tanh ^{-1}(\tanh (a+b x))^{7/2}}{7 b}-\frac{4 \tanh ^{-1}(\tanh (a+b x))^{9/2}}{63 b^2}",1,"(2*x*ArcTanh[Tanh[a + b*x]]^(7/2))/(7*b) - (4*ArcTanh[Tanh[a + b*x]]^(9/2))/(63*b^2)","A",3,3,13,0.2308,1,"{2168, 2157, 30}"
133,1,18,0,0.0046375,"\int \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(5/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{7 b}","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{7 b}",1,"(2*ArcTanh[Tanh[a + b*x]]^(7/2))/(7*b)","A",2,2,11,0.1818,1,"{2157, 30}"
134,1,121,0,0.0702375,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(5/2)/x,x]","2 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2-\frac{2}{3} \tanh ^{-1}(\tanh (a+b x))^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{2}{5} \tanh ^{-1}(\tanh (a+b x))^{5/2}-2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2} \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)","2 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2-\frac{2}{3} \tanh ^{-1}(\tanh (a+b x))^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{2}{5} \tanh ^{-1}(\tanh (a+b x))^{5/2}-2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2} \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)",1,"-2*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^(5/2) + 2*(b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]] - (2*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(3/2))/3 + (2*ArcTanh[Tanh[a + b*x]]^(5/2))/5","A",4,2,15,0.1333,1,"{2159, 2161}"
135,1,110,0,0.0689825,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^2} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(5/2)/x^2,x]","-\frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x}+\frac{5}{3} b \tanh ^{-1}(\tanh (a+b x))^{3/2}-5 b \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}+5 b \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)","-\frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x}+\frac{5}{3} b \tanh ^{-1}(\tanh (a+b x))^{3/2}-5 b \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}+5 b \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)",1,"5*b*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^(3/2) - 5*b*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]] + (5*b*ArcTanh[Tanh[a + b*x]]^(3/2))/3 - ArcTanh[Tanh[a + b*x]]^(5/2)/x","A",4,3,15,0.2000,1,"{2168, 2159, 2161}"
136,1,110,0,0.0667365,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^3} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(5/2)/x^3,x]","\frac{15}{4} b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}-\frac{15}{4} b^2 \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))} \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)-\frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{2 x^2}-\frac{5 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{4 x}","\frac{15}{4} b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}-\frac{15}{4} b^2 \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))} \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)-\frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{2 x^2}-\frac{5 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{4 x}",1,"(-15*b^2*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]*Sqrt[b*x - ArcTanh[Tanh[a + b*x]]])/4 + (15*b^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/4 - (5*b*ArcTanh[Tanh[a + b*x]]^(3/2))/(4*x) - ArcTanh[Tanh[a + b*x]]^(5/2)/(2*x^2)","A",4,3,15,0.2000,1,"{2168, 2159, 2161}"
137,1,113,0,0.0675483,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^4} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(5/2)/x^4,x]","-\frac{5 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{8 x}+\frac{5 b^3 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{8 \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}-\frac{5 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{12 x^2}-\frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{3 x^3}","-\frac{5 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{8 x}+\frac{5 b^3 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{8 \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}-\frac{5 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{12 x^2}-\frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{3 x^3}",1,"(5*b^3*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(8*Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]) - (5*b^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/(8*x) - (5*b*ArcTanh[Tanh[a + b*x]]^(3/2))/(12*x^2) - ArcTanh[Tanh[a + b*x]]^(5/2)/(3*x^3)","A",4,2,15,0.1333,1,"{2168, 2161}"
138,1,167,0,0.1169213,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^5} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(5/2)/x^5,x]","-\frac{5 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{32 x^2}+\frac{5 b^4}{64 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{5 b^3}{64 x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{5 b^4 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{64 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}-\frac{5 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{24 x^3}-\frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{4 x^4}","-\frac{5 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{32 x^2}+\frac{5 b^4}{64 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{5 b^3}{64 x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{5 b^4 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{64 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}-\frac{5 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{24 x^3}-\frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{4 x^4}",1,"(5*b^4*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(64*(b*x - ArcTanh[Tanh[a + b*x]])^(3/2)) - (5*b^3)/(64*x*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (5*b^4)/(64*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]]) - (5*b^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/(32*x^2) - (5*b*ArcTanh[Tanh[a + b*x]]^(3/2))/(24*x^3) - ArcTanh[Tanh[a + b*x]]^(5/2)/(4*x^4)","A",6,3,15,0.2000,1,"{2168, 2163, 2161}"
139,1,221,0,0.1740423,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^6} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(5/2)/x^6,x]","-\frac{b^3}{64 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{16 x^3}+\frac{3 b^5}{128 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{b^5}{128 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{b^4}{128 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{3 b^5 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{128 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}-\frac{b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{8 x^4}-\frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 x^5}","-\frac{b^3}{64 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{16 x^3}+\frac{3 b^5}{128 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{b^5}{128 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{b^4}{128 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{3 b^5 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{128 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}-\frac{b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{8 x^4}-\frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 x^5}",1,"(3*b^5*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(128*(b*x - ArcTanh[Tanh[a + b*x]])^(5/2)) + b^4/(128*x*ArcTanh[Tanh[a + b*x]]^(3/2)) - b^5/(128*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(3/2)) - b^3/(64*x^2*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (3*b^5)/(128*(b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]]) - (b^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/(16*x^3) - (b*ArcTanh[Tanh[a + b*x]]^(3/2))/(8*x^4) - ArcTanh[Tanh[a + b*x]]^(5/2)/(5*x^5)","A",8,3,15,0.2000,1,"{2168, 2163, 2161}"
140,1,99,0,0.0653643,"\int \frac{x^4}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[x^4/Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{32 x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b^3}-\frac{16 x^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b^2}+\frac{256 \tanh ^{-1}(\tanh (a+b x))^{9/2}}{315 b^5}-\frac{128 x \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^4}+\frac{2 x^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b}","\frac{32 x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b^3}-\frac{16 x^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b^2}+\frac{256 \tanh ^{-1}(\tanh (a+b x))^{9/2}}{315 b^5}-\frac{128 x \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^4}+\frac{2 x^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b}",1,"(2*x^4*Sqrt[ArcTanh[Tanh[a + b*x]]])/b - (16*x^3*ArcTanh[Tanh[a + b*x]]^(3/2))/(3*b^2) + (32*x^2*ArcTanh[Tanh[a + b*x]]^(5/2))/(5*b^3) - (128*x*ArcTanh[Tanh[a + b*x]]^(7/2))/(35*b^4) + (256*ArcTanh[Tanh[a + b*x]]^(9/2))/(315*b^5)","A",6,3,15,0.2000,1,"{2168, 2157, 30}"
141,1,76,0,0.0481367,"\int \frac{x^3}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[x^3/Sqrt[ArcTanh[Tanh[a + b*x]]],x]","-\frac{4 x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{b^2}-\frac{32 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^4}+\frac{16 x \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b^3}+\frac{2 x^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b}","-\frac{4 x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{b^2}-\frac{32 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^4}+\frac{16 x \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b^3}+\frac{2 x^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b}",1,"(2*x^3*Sqrt[ArcTanh[Tanh[a + b*x]]])/b - (4*x^2*ArcTanh[Tanh[a + b*x]]^(3/2))/b^2 + (16*x*ArcTanh[Tanh[a + b*x]]^(5/2))/(5*b^3) - (32*ArcTanh[Tanh[a + b*x]]^(7/2))/(35*b^4)","A",5,3,15,0.2000,1,"{2168, 2157, 30}"
142,1,57,0,0.0307876,"\int \frac{x^2}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[x^2/Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{16 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{15 b^3}-\frac{8 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b^2}+\frac{2 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b}","\frac{16 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{15 b^3}-\frac{8 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b^2}+\frac{2 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b}",1,"(2*x^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/b - (8*x*ArcTanh[Tanh[a + b*x]]^(3/2))/(3*b^2) + (16*ArcTanh[Tanh[a + b*x]]^(5/2))/(15*b^3)","A",4,3,15,0.2000,1,"{2168, 2157, 30}"
143,1,36,0,0.0145474,"\int \frac{x}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[x/Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{2 x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b}-\frac{4 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b^2}","\frac{2 x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b}-\frac{4 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b^2}",1,"(2*x*Sqrt[ArcTanh[Tanh[a + b*x]]])/b - (4*ArcTanh[Tanh[a + b*x]]^(3/2))/(3*b^2)","A",3,3,13,0.2308,1,"{2168, 2157, 30}"
144,1,16,0,0.0044057,"\int \frac{1}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[1/Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b}","\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b}",1,"(2*Sqrt[ArcTanh[Tanh[a + b*x]]])/b","A",2,2,11,0.1818,1,"{2157, 30}"
145,1,49,0,0.0157421,"\int \frac{1}{x \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[1/(x*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}",1,"(2*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]","A",1,1,15,0.06667,1,"{2161}"
146,1,94,0,0.0528121,"\int \frac{1}{x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[1/(x^2*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","\frac{b}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{1}{x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{b \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}","\frac{b}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{1}{x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{b \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}",1,"(b*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(b*x - ArcTanh[Tanh[a + b*x]])^(3/2) - 1/(x*Sqrt[ArcTanh[Tanh[a + b*x]]]) + b/((b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",3,3,15,0.2000,1,"{2168, 2163, 2161}"
147,1,158,0,0.0962233,"\int \frac{1}{x^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[1/(x^3*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","\frac{3 b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}-\frac{1}{2 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{b}{4 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}","\frac{3 b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{3 b^2 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}-\frac{1}{2 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{b}{4 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(3*b^2*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(4*(b*x - ArcTanh[Tanh[a + b*x]])^(5/2)) + b/(4*x*ArcTanh[Tanh[a + b*x]]^(3/2)) - b^2/(4*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(3/2)) - 1/(2*x^2*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (3*b^2)/(4*(b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",5,3,15,0.2000,1,"{2168, 2163, 2161}"
148,1,212,0,0.1506565,"\int \frac{1}{x^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[1/(x^4*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","\frac{5 b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{5 b^3}{24 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{5/2}}-\frac{b^2}{8 x \tanh ^{-1}(\tanh (a+b x))^{5/2}}+\frac{5 b^3 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{7/2}}+\frac{b}{12 x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}-\frac{1}{3 x^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","\frac{5 b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{5 b^3}{24 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{5/2}}-\frac{b^2}{8 x \tanh ^{-1}(\tanh (a+b x))^{5/2}}+\frac{5 b^3 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{7/2}}+\frac{b}{12 x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}-\frac{1}{3 x^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(5*b^3*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(8*(b*x - ArcTanh[Tanh[a + b*x]])^(7/2)) - b^2/(8*x*ArcTanh[Tanh[a + b*x]]^(5/2)) + b^3/(8*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(5/2)) + b/(12*x^2*ArcTanh[Tanh[a + b*x]]^(3/2)) - (5*b^3)/(24*(b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]]^(3/2)) - 1/(3*x^3*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (5*b^3)/(8*(b*x - ArcTanh[Tanh[a + b*x]])^3*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",7,3,15,0.2000,1,"{2168, 2163, 2161}"
149,1,95,0,0.0671925,"\int \frac{x^4}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[x^4/ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{16 x^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^2}-\frac{32 x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{b^3}+\frac{128 x \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b^4}-\frac{256 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^5}-\frac{2 x^4}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","\frac{16 x^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^2}-\frac{32 x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{b^3}+\frac{128 x \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b^4}-\frac{256 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^5}-\frac{2 x^4}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(-2*x^4)/(b*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (16*x^3*Sqrt[ArcTanh[Tanh[a + b*x]]])/b^2 - (32*x^2*ArcTanh[Tanh[a + b*x]]^(3/2))/b^3 + (128*x*ArcTanh[Tanh[a + b*x]]^(5/2))/(5*b^4) - (256*ArcTanh[Tanh[a + b*x]]^(7/2))/(35*b^5)","A",6,3,15,0.2000,1,"{2168, 2157, 30}"
150,1,74,0,0.0486649,"\int \frac{x^3}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[x^3/ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{12 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^2}-\frac{16 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}{b^3}+\frac{32 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b^4}-\frac{2 x^3}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","\frac{12 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^2}-\frac{16 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}{b^3}+\frac{32 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b^4}-\frac{2 x^3}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(-2*x^3)/(b*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (12*x^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/b^2 - (16*x*ArcTanh[Tanh[a + b*x]]^(3/2))/b^3 + (32*ArcTanh[Tanh[a + b*x]]^(5/2))/(5*b^4)","A",5,3,15,0.2000,1,"{2168, 2157, 30}"
151,1,55,0,0.0300588,"\int \frac{x^2}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[x^2/ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{8 x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^2}-\frac{16 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b^3}-\frac{2 x^2}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","\frac{8 x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^2}-\frac{16 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b^3}-\frac{2 x^2}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(-2*x^2)/(b*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (8*x*Sqrt[ArcTanh[Tanh[a + b*x]]])/b^2 - (16*ArcTanh[Tanh[a + b*x]]^(3/2))/(3*b^3)","A",4,3,15,0.2000,1,"{2168, 2157, 30}"
152,1,34,0,0.0148316,"\int \frac{x}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[x/ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^2}-\frac{2 x}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","\frac{4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^2}-\frac{2 x}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(-2*x)/(b*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (4*Sqrt[ArcTanh[Tanh[a + b*x]]])/b^2","A",3,3,13,0.2308,1,"{2168, 2157, 30}"
153,1,16,0,0.0048986,"\int \frac{1}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(-3/2),x]","-\frac{2}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","-\frac{2}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"-2/(b*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",2,2,11,0.1818,1,"{2157, 30}"
154,1,78,0,0.0357063,"\int \frac{1}{x \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[1/(x*ArcTanh[Tanh[a + b*x]]^(3/2)),x]","-\frac{2}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}","-\frac{2}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}",1,"(-2*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(b*x - ArcTanh[Tanh[a + b*x]])^(3/2) - 2/((b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",2,2,15,0.1333,1,"{2163, 2161}"
155,1,124,0,0.074482,"\int \frac{1}{x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[1/(x^2*ArcTanh[Tanh[a + b*x]]^(3/2)),x]","-\frac{3 b}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{b}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}-\frac{1}{x \tanh ^{-1}(\tanh (a+b x))^{3/2}}-\frac{3 b \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}","-\frac{3 b}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{b}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}-\frac{1}{x \tanh ^{-1}(\tanh (a+b x))^{3/2}}-\frac{3 b \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}",1,"(-3*b*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(b*x - ArcTanh[Tanh[a + b*x]])^(5/2) - 1/(x*ArcTanh[Tanh[a + b*x]]^(3/2)) + b/((b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(3/2)) - (3*b)/((b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",4,3,15,0.2000,1,"{2168, 2163, 2161}"
156,1,191,0,0.1279173,"\int \frac{1}{x^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[1/(x^3*ArcTanh[Tanh[a + b*x]]^(3/2)),x]","-\frac{15 b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{5 b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}-\frac{3 b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{5/2}}-\frac{15 b^2 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{7/2}}-\frac{1}{2 x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{3 b}{4 x \tanh ^{-1}(\tanh (a+b x))^{5/2}}","-\frac{15 b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{5 b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}-\frac{3 b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{5/2}}-\frac{15 b^2 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{7/2}}-\frac{1}{2 x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{3 b}{4 x \tanh ^{-1}(\tanh (a+b x))^{5/2}}",1,"(-15*b^2*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(4*(b*x - ArcTanh[Tanh[a + b*x]])^(7/2)) + (3*b)/(4*x*ArcTanh[Tanh[a + b*x]]^(5/2)) - (3*b^2)/(4*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(5/2)) - 1/(2*x^2*ArcTanh[Tanh[a + b*x]]^(3/2)) + (5*b^2)/(4*(b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]]^(3/2)) - (15*b^2)/(4*(b*x - ArcTanh[Tanh[a + b*x]])^3*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",6,3,15,0.2000,1,"{2168, 2163, 2161}"
157,1,245,0,0.1828594,"\int \frac{1}{x^4 \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[1/(x^4*ArcTanh[Tanh[a + b*x]]^(3/2)),x]","-\frac{35 b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{35 b^3}{24 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}-\frac{7 b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}+\frac{5 b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{7/2}}-\frac{5 b^2}{8 x \tanh ^{-1}(\tanh (a+b x))^{7/2}}-\frac{35 b^3 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{9/2}}+\frac{b}{4 x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}-\frac{1}{3 x^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}","-\frac{35 b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{35 b^3}{24 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}-\frac{7 b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}+\frac{5 b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{7/2}}-\frac{5 b^2}{8 x \tanh ^{-1}(\tanh (a+b x))^{7/2}}-\frac{35 b^3 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{9/2}}+\frac{b}{4 x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}-\frac{1}{3 x^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(-35*b^3*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(8*(b*x - ArcTanh[Tanh[a + b*x]])^(9/2)) - (5*b^2)/(8*x*ArcTanh[Tanh[a + b*x]]^(7/2)) + (5*b^3)/(8*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(7/2)) + b/(4*x^2*ArcTanh[Tanh[a + b*x]]^(5/2)) - (7*b^3)/(8*(b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]]^(5/2)) - 1/(3*x^3*ArcTanh[Tanh[a + b*x]]^(3/2)) + (35*b^3)/(24*(b*x - ArcTanh[Tanh[a + b*x]])^3*ArcTanh[Tanh[a + b*x]]^(3/2)) - (35*b^3)/(8*(b*x - ArcTanh[Tanh[a + b*x]])^4*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",8,3,15,0.2000,1,"{2168, 2163, 2161}"
158,1,99,0,0.0660405,"\int \frac{x^4}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[x^4/ArcTanh[Tanh[a + b*x]]^(5/2),x]","-\frac{16 x^3}{3 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{32 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^3}-\frac{128 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b^4}+\frac{256 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{15 b^5}-\frac{2 x^4}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}","-\frac{16 x^3}{3 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{32 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^3}-\frac{128 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b^4}+\frac{256 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{15 b^5}-\frac{2 x^4}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(-2*x^4)/(3*b*ArcTanh[Tanh[a + b*x]]^(3/2)) - (16*x^3)/(3*b^2*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (32*x^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/b^3 - (128*x*ArcTanh[Tanh[a + b*x]]^(3/2))/(3*b^4) + (256*ArcTanh[Tanh[a + b*x]]^(5/2))/(15*b^5)","A",6,3,15,0.2000,1,"{2168, 2157, 30}"
159,1,76,0,0.0485976,"\int \frac{x^3}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[x^3/ArcTanh[Tanh[a + b*x]]^(5/2),x]","-\frac{4 x^2}{b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{16 x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^3}-\frac{32 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b^4}-\frac{2 x^3}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}","-\frac{4 x^2}{b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{16 x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^3}-\frac{32 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b^4}-\frac{2 x^3}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(-2*x^3)/(3*b*ArcTanh[Tanh[a + b*x]]^(3/2)) - (4*x^2)/(b^2*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (16*x*Sqrt[ArcTanh[Tanh[a + b*x]]])/b^3 - (32*ArcTanh[Tanh[a + b*x]]^(3/2))/(3*b^4)","A",5,3,15,0.2000,1,"{2168, 2157, 30}"
160,1,59,0,0.0296099,"\int \frac{x^2}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[x^2/ArcTanh[Tanh[a + b*x]]^(5/2),x]","-\frac{8 x}{3 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{16 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{3 b^3}-\frac{2 x^2}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}","-\frac{8 x}{3 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{16 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{3 b^3}-\frac{2 x^2}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(-2*x^2)/(3*b*ArcTanh[Tanh[a + b*x]]^(3/2)) - (8*x)/(3*b^2*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (16*Sqrt[ArcTanh[Tanh[a + b*x]]])/(3*b^3)","A",4,3,15,0.2000,1,"{2168, 2157, 30}"
161,1,38,0,0.0140306,"\int \frac{x}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[x/ArcTanh[Tanh[a + b*x]]^(5/2),x]","-\frac{4}{3 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{2 x}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}","-\frac{4}{3 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{2 x}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(-2*x)/(3*b*ArcTanh[Tanh[a + b*x]]^(3/2)) - 4/(3*b^2*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",3,3,13,0.2308,1,"{2168, 2157, 30}"
162,1,18,0,0.0045551,"\int \frac{1}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(-5/2),x]","-\frac{2}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}","-\frac{2}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"-2/(3*b*ArcTanh[Tanh[a + b*x]]^(3/2))","A",2,2,11,0.1818,1,"{2157, 30}"
163,1,108,0,0.0540267,"\int \frac{1}{x \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[1/(x*ArcTanh[Tanh[a + b*x]]^(5/2)),x]","\frac{2}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{2}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}","\frac{2}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{2}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}",1,"(2*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(b*x - ArcTanh[Tanh[a + b*x]])^(5/2) - 2/(3*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(3/2)) + 2/((b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",3,2,15,0.1333,1,"{2163, 2161}"
164,1,155,0,0.0998613,"\int \frac{1}{x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[1/(x^2*ArcTanh[Tanh[a + b*x]]^(5/2)),x]","\frac{5 b}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{5 b}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{b}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{5/2}}-\frac{1}{x \tanh ^{-1}(\tanh (a+b x))^{5/2}}+\frac{5 b \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{7/2}}","\frac{5 b}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{5 b}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{b}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{5/2}}-\frac{1}{x \tanh ^{-1}(\tanh (a+b x))^{5/2}}+\frac{5 b \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{7/2}}",1,"(5*b*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(b*x - ArcTanh[Tanh[a + b*x]])^(7/2) - 1/(x*ArcTanh[Tanh[a + b*x]]^(5/2)) + b/((b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(5/2)) - (5*b)/(3*(b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]]^(3/2)) + (5*b)/((b*x - ArcTanh[Tanh[a + b*x]])^3*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",5,3,15,0.2000,1,"{2168, 2163, 2161}"
165,1,224,0,0.1519803,"\int \frac{1}{x^3 \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[1/(x^3*ArcTanh[Tanh[a + b*x]]^(5/2)),x]","\frac{35 b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{35 b^2}{12 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{7 b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}-\frac{5 b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{7/2}}+\frac{35 b^2 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{9/2}}-\frac{1}{2 x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}+\frac{5 b}{4 x \tanh ^{-1}(\tanh (a+b x))^{7/2}}","\frac{35 b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{35 b^2}{12 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{7 b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}-\frac{5 b^2}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{7/2}}+\frac{35 b^2 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{9/2}}-\frac{1}{2 x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}+\frac{5 b}{4 x \tanh ^{-1}(\tanh (a+b x))^{7/2}}",1,"(35*b^2*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(4*(b*x - ArcTanh[Tanh[a + b*x]])^(9/2)) + (5*b)/(4*x*ArcTanh[Tanh[a + b*x]]^(7/2)) - (5*b^2)/(4*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(7/2)) - 1/(2*x^2*ArcTanh[Tanh[a + b*x]]^(5/2)) + (7*b^2)/(4*(b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]]^(5/2)) - (35*b^2)/(12*(b*x - ArcTanh[Tanh[a + b*x]])^3*ArcTanh[Tanh[a + b*x]]^(3/2)) + (35*b^2)/(4*(b*x - ArcTanh[Tanh[a + b*x]])^4*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",7,3,15,0.2000,1,"{2168, 2163, 2161}"
166,1,278,0,0.2215214,"\int \frac{1}{x^4 \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[1/(x^4*ArcTanh[Tanh[a + b*x]]^(5/2)),x]","\frac{105 b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^5 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{35 b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{21 b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))^{5/2}}-\frac{15 b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}+\frac{35 b^3}{24 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{9/2}}-\frac{35 b^2}{24 x \tanh ^{-1}(\tanh (a+b x))^{9/2}}+\frac{105 b^3 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{11/2}}+\frac{5 b}{12 x^2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}-\frac{1}{3 x^3 \tanh ^{-1}(\tanh (a+b x))^{5/2}}","\frac{105 b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^5 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{35 b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{21 b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))^{5/2}}-\frac{15 b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}+\frac{35 b^3}{24 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{9/2}}-\frac{35 b^2}{24 x \tanh ^{-1}(\tanh (a+b x))^{9/2}}+\frac{105 b^3 \tan ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{11/2}}+\frac{5 b}{12 x^2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}-\frac{1}{3 x^3 \tanh ^{-1}(\tanh (a+b x))^{5/2}}",1,"(105*b^3*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(8*(b*x - ArcTanh[Tanh[a + b*x]])^(11/2)) - (35*b^2)/(24*x*ArcTanh[Tanh[a + b*x]]^(9/2)) + (35*b^3)/(24*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(9/2)) + (5*b)/(12*x^2*ArcTanh[Tanh[a + b*x]]^(7/2)) - (15*b^3)/(8*(b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]]^(7/2)) - 1/(3*x^3*ArcTanh[Tanh[a + b*x]]^(5/2)) + (21*b^3)/(8*(b*x - ArcTanh[Tanh[a + b*x]])^3*ArcTanh[Tanh[a + b*x]]^(5/2)) - (35*b^3)/(8*(b*x - ArcTanh[Tanh[a + b*x]])^4*ArcTanh[Tanh[a + b*x]]^(3/2)) + (105*b^3)/(8*(b*x - ArcTanh[Tanh[a + b*x]])^5*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",9,3,15,0.2000,1,"{2168, 2163, 2161}"
167,1,27,0,0.0097488,"\int x^{7/2} \tanh ^{-1}(\tanh (a+b x)) \, dx","Int[x^(7/2)*ArcTanh[Tanh[a + b*x]],x]","\frac{2}{9} x^{9/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{99} b x^{11/2}","\frac{2}{9} x^{9/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{99} b x^{11/2}",1,"(-4*b*x^(11/2))/99 + (2*x^(9/2)*ArcTanh[Tanh[a + b*x]])/9","A",2,2,13,0.1538,1,"{2168, 30}"
168,1,27,0,0.0090049,"\int x^{5/2} \tanh ^{-1}(\tanh (a+b x)) \, dx","Int[x^(5/2)*ArcTanh[Tanh[a + b*x]],x]","\frac{2}{7} x^{7/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{63} b x^{9/2}","\frac{2}{7} x^{7/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{63} b x^{9/2}",1,"(-4*b*x^(9/2))/63 + (2*x^(7/2)*ArcTanh[Tanh[a + b*x]])/7","A",2,2,13,0.1538,1,"{2168, 30}"
169,1,27,0,0.0098923,"\int x^{3/2} \tanh ^{-1}(\tanh (a+b x)) \, dx","Int[x^(3/2)*ArcTanh[Tanh[a + b*x]],x]","\frac{2}{5} x^{5/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{35} b x^{7/2}","\frac{2}{5} x^{5/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{35} b x^{7/2}",1,"(-4*b*x^(7/2))/35 + (2*x^(5/2)*ArcTanh[Tanh[a + b*x]])/5","A",2,2,13,0.1538,1,"{2168, 30}"
170,1,27,0,0.0080778,"\int \sqrt{x} \tanh ^{-1}(\tanh (a+b x)) \, dx","Int[Sqrt[x]*ArcTanh[Tanh[a + b*x]],x]","\frac{2}{3} x^{3/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{15} b x^{5/2}","\frac{2}{3} x^{3/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{15} b x^{5/2}",1,"(-4*b*x^(5/2))/15 + (2*x^(3/2)*ArcTanh[Tanh[a + b*x]])/3","A",2,2,13,0.1538,1,"{2168, 30}"
171,1,25,0,0.007859,"\int \frac{\tanh ^{-1}(\tanh (a+b x))}{\sqrt{x}} \, dx","Int[ArcTanh[Tanh[a + b*x]]/Sqrt[x],x]","2 \sqrt{x} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{3} b x^{3/2}","2 \sqrt{x} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{3} b x^{3/2}",1,"(-4*b*x^(3/2))/3 + 2*Sqrt[x]*ArcTanh[Tanh[a + b*x]]","A",2,2,13,0.1538,1,"{2168, 30}"
172,1,23,0,0.0082348,"\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^{3/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]/x^(3/2),x]","4 b \sqrt{x}-\frac{2 \tanh ^{-1}(\tanh (a+b x))}{\sqrt{x}}","4 b \sqrt{x}-\frac{2 \tanh ^{-1}(\tanh (a+b x))}{\sqrt{x}}",1,"4*b*Sqrt[x] - (2*ArcTanh[Tanh[a + b*x]])/Sqrt[x]","A",2,2,13,0.1538,1,"{2168, 30}"
173,1,27,0,0.0086571,"\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^{5/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]/x^(5/2),x]","-\frac{2 \tanh ^{-1}(\tanh (a+b x))}{3 x^{3/2}}-\frac{4 b}{3 \sqrt{x}}","-\frac{2 \tanh ^{-1}(\tanh (a+b x))}{3 x^{3/2}}-\frac{4 b}{3 \sqrt{x}}",1,"(-4*b)/(3*Sqrt[x]) - (2*ArcTanh[Tanh[a + b*x]])/(3*x^(3/2))","A",2,2,13,0.1538,1,"{2168, 30}"
174,1,27,0,0.0087224,"\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^{7/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]/x^(7/2),x]","-\frac{2 \tanh ^{-1}(\tanh (a+b x))}{5 x^{5/2}}-\frac{4 b}{15 x^{3/2}}","-\frac{2 \tanh ^{-1}(\tanh (a+b x))}{5 x^{5/2}}-\frac{4 b}{15 x^{3/2}}",1,"(-4*b)/(15*x^(3/2)) - (2*ArcTanh[Tanh[a + b*x]])/(5*x^(5/2))","A",2,2,13,0.1538,1,"{2168, 30}"
175,1,48,0,0.0231425,"\int x^{7/2} \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Int[x^(7/2)*ArcTanh[Tanh[a + b*x]]^2,x]","-\frac{8}{99} b x^{11/2} \tanh ^{-1}(\tanh (a+b x))+\frac{2}{9} x^{9/2} \tanh ^{-1}(\tanh (a+b x))^2+\frac{16 b^2 x^{13/2}}{1287}","-\frac{8}{99} b x^{11/2} \tanh ^{-1}(\tanh (a+b x))+\frac{2}{9} x^{9/2} \tanh ^{-1}(\tanh (a+b x))^2+\frac{16 b^2 x^{13/2}}{1287}",1,"(16*b^2*x^(13/2))/1287 - (8*b*x^(11/2)*ArcTanh[Tanh[a + b*x]])/99 + (2*x^(9/2)*ArcTanh[Tanh[a + b*x]]^2)/9","A",3,2,15,0.1333,1,"{2168, 30}"
176,1,48,0,0.0220721,"\int x^{5/2} \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Int[x^(5/2)*ArcTanh[Tanh[a + b*x]]^2,x]","-\frac{8}{63} b x^{9/2} \tanh ^{-1}(\tanh (a+b x))+\frac{2}{7} x^{7/2} \tanh ^{-1}(\tanh (a+b x))^2+\frac{16}{693} b^2 x^{11/2}","-\frac{8}{63} b x^{9/2} \tanh ^{-1}(\tanh (a+b x))+\frac{2}{7} x^{7/2} \tanh ^{-1}(\tanh (a+b x))^2+\frac{16}{693} b^2 x^{11/2}",1,"(16*b^2*x^(11/2))/693 - (8*b*x^(9/2)*ArcTanh[Tanh[a + b*x]])/63 + (2*x^(7/2)*ArcTanh[Tanh[a + b*x]]^2)/7","A",3,2,15,0.1333,1,"{2168, 30}"
177,1,48,0,0.0228219,"\int x^{3/2} \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Int[x^(3/2)*ArcTanh[Tanh[a + b*x]]^2,x]","-\frac{8}{35} b x^{7/2} \tanh ^{-1}(\tanh (a+b x))+\frac{2}{5} x^{5/2} \tanh ^{-1}(\tanh (a+b x))^2+\frac{16}{315} b^2 x^{9/2}","-\frac{8}{35} b x^{7/2} \tanh ^{-1}(\tanh (a+b x))+\frac{2}{5} x^{5/2} \tanh ^{-1}(\tanh (a+b x))^2+\frac{16}{315} b^2 x^{9/2}",1,"(16*b^2*x^(9/2))/315 - (8*b*x^(7/2)*ArcTanh[Tanh[a + b*x]])/35 + (2*x^(5/2)*ArcTanh[Tanh[a + b*x]]^2)/5","A",3,2,15,0.1333,1,"{2168, 30}"
178,1,48,0,0.0217704,"\int \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Int[Sqrt[x]*ArcTanh[Tanh[a + b*x]]^2,x]","-\frac{8}{15} b x^{5/2} \tanh ^{-1}(\tanh (a+b x))+\frac{2}{3} x^{3/2} \tanh ^{-1}(\tanh (a+b x))^2+\frac{16}{105} b^2 x^{7/2}","-\frac{8}{15} b x^{5/2} \tanh ^{-1}(\tanh (a+b x))+\frac{2}{3} x^{3/2} \tanh ^{-1}(\tanh (a+b x))^2+\frac{16}{105} b^2 x^{7/2}",1,"(16*b^2*x^(7/2))/105 - (8*b*x^(5/2)*ArcTanh[Tanh[a + b*x]])/15 + (2*x^(3/2)*ArcTanh[Tanh[a + b*x]]^2)/3","A",3,2,15,0.1333,1,"{2168, 30}"
179,1,46,0,0.0208972,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{\sqrt{x}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^2/Sqrt[x],x]","-\frac{8}{3} b x^{3/2} \tanh ^{-1}(\tanh (a+b x))+2 \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^2+\frac{16}{15} b^2 x^{5/2}","-\frac{8}{3} b x^{3/2} \tanh ^{-1}(\tanh (a+b x))+2 \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^2+\frac{16}{15} b^2 x^{5/2}",1,"(16*b^2*x^(5/2))/15 - (8*b*x^(3/2)*ArcTanh[Tanh[a + b*x]])/3 + 2*Sqrt[x]*ArcTanh[Tanh[a + b*x]]^2","A",3,2,15,0.1333,1,"{2168, 30}"
180,1,44,0,0.0217644,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^{3/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^2/x^(3/2),x]","8 b \sqrt{x} \tanh ^{-1}(\tanh (a+b x))-\frac{2 \tanh ^{-1}(\tanh (a+b x))^2}{\sqrt{x}}-\frac{16}{3} b^2 x^{3/2}","8 b \sqrt{x} \tanh ^{-1}(\tanh (a+b x))-\frac{2 \tanh ^{-1}(\tanh (a+b x))^2}{\sqrt{x}}-\frac{16}{3} b^2 x^{3/2}",1,"(-16*b^2*x^(3/2))/3 + 8*b*Sqrt[x]*ArcTanh[Tanh[a + b*x]] - (2*ArcTanh[Tanh[a + b*x]]^2)/Sqrt[x]","A",3,2,15,0.1333,1,"{2168, 30}"
181,1,48,0,0.0230305,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^{5/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^2/x^(5/2),x]","-\frac{2 \tanh ^{-1}(\tanh (a+b x))^2}{3 x^{3/2}}-\frac{8 b \tanh ^{-1}(\tanh (a+b x))}{3 \sqrt{x}}+\frac{16 b^2 \sqrt{x}}{3}","-\frac{2 \tanh ^{-1}(\tanh (a+b x))^2}{3 x^{3/2}}-\frac{8 b \tanh ^{-1}(\tanh (a+b x))}{3 \sqrt{x}}+\frac{16 b^2 \sqrt{x}}{3}",1,"(16*b^2*Sqrt[x])/3 - (8*b*ArcTanh[Tanh[a + b*x]])/(3*Sqrt[x]) - (2*ArcTanh[Tanh[a + b*x]]^2)/(3*x^(3/2))","A",3,2,15,0.1333,1,"{2168, 30}"
182,1,48,0,0.023184,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^{7/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^2/x^(7/2),x]","-\frac{8 b \tanh ^{-1}(\tanh (a+b x))}{15 x^{3/2}}-\frac{2 \tanh ^{-1}(\tanh (a+b x))^2}{5 x^{5/2}}-\frac{16 b^2}{15 \sqrt{x}}","-\frac{8 b \tanh ^{-1}(\tanh (a+b x))}{15 x^{3/2}}-\frac{2 \tanh ^{-1}(\tanh (a+b x))^2}{5 x^{5/2}}-\frac{16 b^2}{15 \sqrt{x}}",1,"(-16*b^2)/(15*Sqrt[x]) - (8*b*ArcTanh[Tanh[a + b*x]])/(15*x^(3/2)) - (2*ArcTanh[Tanh[a + b*x]]^2)/(5*x^(5/2))","A",3,2,15,0.1333,1,"{2168, 30}"
183,1,69,0,0.0385126,"\int x^{7/2} \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Int[x^(7/2)*ArcTanh[Tanh[a + b*x]]^3,x]","\frac{16}{429} b^2 x^{13/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{33} b x^{11/2} \tanh ^{-1}(\tanh (a+b x))^2+\frac{2}{9} x^{9/2} \tanh ^{-1}(\tanh (a+b x))^3-\frac{32 b^3 x^{15/2}}{6435}","\frac{16}{429} b^2 x^{13/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{33} b x^{11/2} \tanh ^{-1}(\tanh (a+b x))^2+\frac{2}{9} x^{9/2} \tanh ^{-1}(\tanh (a+b x))^3-\frac{32 b^3 x^{15/2}}{6435}",1,"(-32*b^3*x^(15/2))/6435 + (16*b^2*x^(13/2)*ArcTanh[Tanh[a + b*x]])/429 - (4*b*x^(11/2)*ArcTanh[Tanh[a + b*x]]^2)/33 + (2*x^(9/2)*ArcTanh[Tanh[a + b*x]]^3)/9","A",4,2,15,0.1333,1,"{2168, 30}"
184,1,69,0,0.0377565,"\int x^{5/2} \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Int[x^(5/2)*ArcTanh[Tanh[a + b*x]]^3,x]","\frac{16}{231} b^2 x^{11/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{21} b x^{9/2} \tanh ^{-1}(\tanh (a+b x))^2+\frac{2}{7} x^{7/2} \tanh ^{-1}(\tanh (a+b x))^3-\frac{32 b^3 x^{13/2}}{3003}","\frac{16}{231} b^2 x^{11/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{21} b x^{9/2} \tanh ^{-1}(\tanh (a+b x))^2+\frac{2}{7} x^{7/2} \tanh ^{-1}(\tanh (a+b x))^3-\frac{32 b^3 x^{13/2}}{3003}",1,"(-32*b^3*x^(13/2))/3003 + (16*b^2*x^(11/2)*ArcTanh[Tanh[a + b*x]])/231 - (4*b*x^(9/2)*ArcTanh[Tanh[a + b*x]]^2)/21 + (2*x^(7/2)*ArcTanh[Tanh[a + b*x]]^3)/7","A",4,2,15,0.1333,1,"{2168, 30}"
185,1,69,0,0.0374426,"\int x^{3/2} \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Int[x^(3/2)*ArcTanh[Tanh[a + b*x]]^3,x]","\frac{16}{105} b^2 x^{9/2} \tanh ^{-1}(\tanh (a+b x))-\frac{12}{35} b x^{7/2} \tanh ^{-1}(\tanh (a+b x))^2+\frac{2}{5} x^{5/2} \tanh ^{-1}(\tanh (a+b x))^3-\frac{32 b^3 x^{11/2}}{1155}","\frac{16}{105} b^2 x^{9/2} \tanh ^{-1}(\tanh (a+b x))-\frac{12}{35} b x^{7/2} \tanh ^{-1}(\tanh (a+b x))^2+\frac{2}{5} x^{5/2} \tanh ^{-1}(\tanh (a+b x))^3-\frac{32 b^3 x^{11/2}}{1155}",1,"(-32*b^3*x^(11/2))/1155 + (16*b^2*x^(9/2)*ArcTanh[Tanh[a + b*x]])/105 - (12*b*x^(7/2)*ArcTanh[Tanh[a + b*x]]^2)/35 + (2*x^(5/2)*ArcTanh[Tanh[a + b*x]]^3)/5","A",4,2,15,0.1333,1,"{2168, 30}"
186,1,69,0,0.0369685,"\int \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Int[Sqrt[x]*ArcTanh[Tanh[a + b*x]]^3,x]","\frac{16}{35} b^2 x^{7/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{5} b x^{5/2} \tanh ^{-1}(\tanh (a+b x))^2+\frac{2}{3} x^{3/2} \tanh ^{-1}(\tanh (a+b x))^3-\frac{32}{315} b^3 x^{9/2}","\frac{16}{35} b^2 x^{7/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{5} b x^{5/2} \tanh ^{-1}(\tanh (a+b x))^2+\frac{2}{3} x^{3/2} \tanh ^{-1}(\tanh (a+b x))^3-\frac{32}{315} b^3 x^{9/2}",1,"(-32*b^3*x^(9/2))/315 + (16*b^2*x^(7/2)*ArcTanh[Tanh[a + b*x]])/35 - (4*b*x^(5/2)*ArcTanh[Tanh[a + b*x]]^2)/5 + (2*x^(3/2)*ArcTanh[Tanh[a + b*x]]^3)/3","A",4,2,15,0.1333,1,"{2168, 30}"
187,1,65,0,0.0357662,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{\sqrt{x}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^3/Sqrt[x],x]","\frac{16}{5} b^2 x^{5/2} \tanh ^{-1}(\tanh (a+b x))-4 b x^{3/2} \tanh ^{-1}(\tanh (a+b x))^2+2 \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^3-\frac{32}{35} b^3 x^{7/2}","\frac{16}{5} b^2 x^{5/2} \tanh ^{-1}(\tanh (a+b x))-4 b x^{3/2} \tanh ^{-1}(\tanh (a+b x))^2+2 \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^3-\frac{32}{35} b^3 x^{7/2}",1,"(-32*b^3*x^(7/2))/35 + (16*b^2*x^(5/2)*ArcTanh[Tanh[a + b*x]])/5 - 4*b*x^(3/2)*ArcTanh[Tanh[a + b*x]]^2 + 2*Sqrt[x]*ArcTanh[Tanh[a + b*x]]^3","A",4,2,15,0.1333,1,"{2168, 30}"
188,1,63,0,0.0359327,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^{3/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^3/x^(3/2),x]","-16 b^2 x^{3/2} \tanh ^{-1}(\tanh (a+b x))+12 b \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^2-\frac{2 \tanh ^{-1}(\tanh (a+b x))^3}{\sqrt{x}}+\frac{32}{5} b^3 x^{5/2}","-16 b^2 x^{3/2} \tanh ^{-1}(\tanh (a+b x))+12 b \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^2-\frac{2 \tanh ^{-1}(\tanh (a+b x))^3}{\sqrt{x}}+\frac{32}{5} b^3 x^{5/2}",1,"(32*b^3*x^(5/2))/5 - 16*b^2*x^(3/2)*ArcTanh[Tanh[a + b*x]] + 12*b*Sqrt[x]*ArcTanh[Tanh[a + b*x]]^2 - (2*ArcTanh[Tanh[a + b*x]]^3)/Sqrt[x]","A",4,2,15,0.1333,1,"{2168, 30}"
189,1,65,0,0.0382775,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^{5/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^3/x^(5/2),x]","16 b^2 \sqrt{x} \tanh ^{-1}(\tanh (a+b x))-\frac{2 \tanh ^{-1}(\tanh (a+b x))^3}{3 x^{3/2}}-\frac{4 b \tanh ^{-1}(\tanh (a+b x))^2}{\sqrt{x}}-\frac{32}{3} b^3 x^{3/2}","16 b^2 \sqrt{x} \tanh ^{-1}(\tanh (a+b x))-\frac{2 \tanh ^{-1}(\tanh (a+b x))^3}{3 x^{3/2}}-\frac{4 b \tanh ^{-1}(\tanh (a+b x))^2}{\sqrt{x}}-\frac{32}{3} b^3 x^{3/2}",1,"(-32*b^3*x^(3/2))/3 + 16*b^2*Sqrt[x]*ArcTanh[Tanh[a + b*x]] - (4*b*ArcTanh[Tanh[a + b*x]]^2)/Sqrt[x] - (2*ArcTanh[Tanh[a + b*x]]^3)/(3*x^(3/2))","A",4,2,15,0.1333,1,"{2168, 30}"
190,1,69,0,0.0376807,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^{7/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^3/x^(7/2),x]","-\frac{16 b^2 \tanh ^{-1}(\tanh (a+b x))}{5 \sqrt{x}}-\frac{4 b \tanh ^{-1}(\tanh (a+b x))^2}{5 x^{3/2}}-\frac{2 \tanh ^{-1}(\tanh (a+b x))^3}{5 x^{5/2}}+\frac{32 b^3 \sqrt{x}}{5}","-\frac{16 b^2 \tanh ^{-1}(\tanh (a+b x))}{5 \sqrt{x}}-\frac{4 b \tanh ^{-1}(\tanh (a+b x))^2}{5 x^{3/2}}-\frac{2 \tanh ^{-1}(\tanh (a+b x))^3}{5 x^{5/2}}+\frac{32 b^3 \sqrt{x}}{5}",1,"(32*b^3*Sqrt[x])/5 - (16*b^2*ArcTanh[Tanh[a + b*x]])/(5*Sqrt[x]) - (4*b*ArcTanh[Tanh[a + b*x]]^2)/(5*x^(3/2)) - (2*ArcTanh[Tanh[a + b*x]]^3)/(5*x^(5/2))","A",4,2,15,0.1333,1,"{2168, 30}"
191,1,143,0,0.1272888,"\int \frac{x^{7/2}}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Int[x^(7/2)/ArcTanh[Tanh[a + b*x]],x]","\frac{2 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{5 b^2}+\frac{2 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{3 b^3}+\frac{2 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{b^4}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{7/2}}{b^{9/2}}+\frac{2 x^{7/2}}{7 b}","\frac{2 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{5 b^2}+\frac{2 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{3 b^3}+\frac{2 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{b^4}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{7/2}}{b^{9/2}}+\frac{2 x^{7/2}}{7 b}",1,"(2*x^(7/2))/(7*b) + (2*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]]))/(5*b^2) + (2*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2)/(3*b^3) + (2*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^3)/b^4 - (2*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^(7/2))/b^(9/2)","A",5,2,15,0.1333,1,"{2159, 2162}"
192,1,116,0,0.0791174,"\int \frac{x^{5/2}}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Int[x^(5/2)/ArcTanh[Tanh[a + b*x]],x]","\frac{2 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{3 b^2}+\frac{2 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{b^3}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}{b^{7/2}}+\frac{2 x^{5/2}}{5 b}","\frac{2 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{3 b^2}+\frac{2 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{b^3}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}{b^{7/2}}+\frac{2 x^{5/2}}{5 b}",1,"(2*x^(5/2))/(5*b) + (2*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]]))/(3*b^2) + (2*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^2)/b^3 - (2*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^(5/2))/b^(7/2)","A",4,2,15,0.1333,1,"{2159, 2162}"
193,1,89,0,0.0556897,"\int \frac{x^{3/2}}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Int[x^(3/2)/ArcTanh[Tanh[a + b*x]],x]","\frac{2 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^2}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}{b^{5/2}}+\frac{2 x^{3/2}}{3 b}","\frac{2 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^2}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}{b^{5/2}}+\frac{2 x^{3/2}}{3 b}",1,"(2*x^(3/2))/(3*b) + (2*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]]))/b^2 - (2*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^(3/2))/b^(5/2)","A",3,2,15,0.1333,1,"{2159, 2162}"
194,1,64,0,0.03323,"\int \frac{\sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Int[Sqrt[x]/ArcTanh[Tanh[a + b*x]],x]","\frac{2 \sqrt{x}}{b}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}{b^{3/2}}","\frac{2 \sqrt{x}}{b}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}{b^{3/2}}",1,"(2*Sqrt[x])/b - (2*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]*Sqrt[b*x - ArcTanh[Tanh[a + b*x]]])/b^(3/2)","A",2,2,15,0.1333,1,"{2159, 2162}"
195,1,53,0,0.017706,"\int \frac{1}{\sqrt{x} \tanh ^{-1}(\tanh (a+b x))} \, dx","Int[1/(Sqrt[x]*ArcTanh[Tanh[a + b*x]]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\sqrt{b} \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\sqrt{b} \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}",1,"(-2*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(Sqrt[b]*Sqrt[b*x - ArcTanh[Tanh[a + b*x]]])","A",1,1,15,0.06667,1,"{2162}"
196,1,76,0,0.035544,"\int \frac{1}{x^{3/2} \tanh ^{-1}(\tanh (a+b x))} \, dx","Int[1/(x^(3/2)*ArcTanh[Tanh[a + b*x]]),x]","\frac{2}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}","\frac{2}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}",1,"(-2*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(b*x - ArcTanh[Tanh[a + b*x]])^(3/2) + 2/(Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]]))","A",2,2,15,0.1333,1,"{2163, 2162}"
197,1,101,0,0.0572352,"\int \frac{1}{x^{5/2} \tanh ^{-1}(\tanh (a+b x))} \, dx","Int[1/(x^(5/2)*ArcTanh[Tanh[a + b*x]]),x]","-\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}+\frac{2}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{2 b}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","-\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}+\frac{2}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{2 b}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}",1,"(-2*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(b*x - ArcTanh[Tanh[a + b*x]])^(5/2) + (2*b)/(Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^2) + 2/(3*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",3,2,15,0.1333,1,"{2163, 2162}"
198,1,128,0,0.0840996,"\int \frac{1}{x^{7/2} \tanh ^{-1}(\tanh (a+b x))} \, dx","Int[1/(x^(7/2)*ArcTanh[Tanh[a + b*x]]),x]","-\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{7/2}}+\frac{2 b^2}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{2 b}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}+\frac{2}{5 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}","-\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{7/2}}+\frac{2 b^2}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{2 b}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}+\frac{2}{5 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"(-2*b^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(b*x - ArcTanh[Tanh[a + b*x]])^(7/2) + (2*b^2)/(Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^3) + (2*b)/(3*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) + 2/(5*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",4,2,15,0.1333,1,"{2163, 2162}"
199,1,135,0,0.1033772,"\int \frac{x^{7/2}}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[x^(7/2)/ArcTanh[Tanh[a + b*x]]^2,x]","\frac{7 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{3 b^3}+\frac{7 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{b^4}-\frac{7 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}{b^{9/2}}-\frac{x^{7/2}}{b \tanh ^{-1}(\tanh (a+b x))}+\frac{7 x^{5/2}}{5 b^2}","\frac{7 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{3 b^3}+\frac{7 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{b^4}-\frac{7 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}{b^{9/2}}-\frac{x^{7/2}}{b \tanh ^{-1}(\tanh (a+b x))}+\frac{7 x^{5/2}}{5 b^2}",1,"(7*x^(5/2))/(5*b^2) + (7*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]]))/(3*b^3) + (7*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^2)/b^4 - (7*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^(5/2))/b^(9/2) - x^(7/2)/(b*ArcTanh[Tanh[a + b*x]])","A",5,3,15,0.2000,1,"{2168, 2159, 2162}"
200,1,108,0,0.0764184,"\int \frac{x^{5/2}}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[x^(5/2)/ArcTanh[Tanh[a + b*x]]^2,x]","\frac{5 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}{b^{7/2}}-\frac{x^{5/2}}{b \tanh ^{-1}(\tanh (a+b x))}+\frac{5 x^{3/2}}{3 b^2}","\frac{5 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}{b^{7/2}}-\frac{x^{5/2}}{b \tanh ^{-1}(\tanh (a+b x))}+\frac{5 x^{3/2}}{3 b^2}",1,"(5*x^(3/2))/(3*b^2) + (5*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]]))/b^3 - (5*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^(3/2))/b^(7/2) - x^(5/2)/(b*ArcTanh[Tanh[a + b*x]])","A",4,3,15,0.2000,1,"{2168, 2159, 2162}"
201,1,83,0,0.0536394,"\int \frac{x^{3/2}}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[x^(3/2)/ArcTanh[Tanh[a + b*x]]^2,x]","-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}{b^{5/2}}-\frac{x^{3/2}}{b \tanh ^{-1}(\tanh (a+b x))}+\frac{3 \sqrt{x}}{b^2}","-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}{b^{5/2}}-\frac{x^{3/2}}{b \tanh ^{-1}(\tanh (a+b x))}+\frac{3 \sqrt{x}}{b^2}",1,"(3*Sqrt[x])/b^2 - (3*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]*Sqrt[b*x - ArcTanh[Tanh[a + b*x]]])/b^(5/2) - x^(3/2)/(b*ArcTanh[Tanh[a + b*x]])","A",3,3,15,0.2000,1,"{2168, 2159, 2162}"
202,1,73,0,0.0341577,"\int \frac{\sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[Sqrt[x]/ArcTanh[Tanh[a + b*x]]^2,x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{b^{3/2} \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}-\frac{\sqrt{x}}{b \tanh ^{-1}(\tanh (a+b x))}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{b^{3/2} \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}-\frac{\sqrt{x}}{b \tanh ^{-1}(\tanh (a+b x))}",1,"-(ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]/(b^(3/2)*Sqrt[b*x - ArcTanh[Tanh[a + b*x]]])) - Sqrt[x]/(b*ArcTanh[Tanh[a + b*x]])","A",2,2,15,0.1333,1,"{2168, 2162}"
203,1,97,0,0.0537793,"\int \frac{1}{\sqrt{x} \tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[1/(Sqrt[x]*ArcTanh[Tanh[a + b*x]]^2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\sqrt{b} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}-\frac{1}{b \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{1}{b \sqrt{x} \tanh ^{-1}(\tanh (a+b x))}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\sqrt{b} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}-\frac{1}{b \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{1}{b \sqrt{x} \tanh ^{-1}(\tanh (a+b x))}",1,"ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]/(Sqrt[b]*(b*x - ArcTanh[Tanh[a + b*x]])^(3/2)) - 1/(b*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])) - 1/(b*Sqrt[x]*ArcTanh[Tanh[a + b*x]])","A",3,3,15,0.2000,1,"{2168, 2163, 2162}"
204,1,120,0,0.0799972,"\int \frac{1}{x^{3/2} \tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[1/(x^(3/2)*ArcTanh[Tanh[a + b*x]]^2),x]","-\frac{1}{b x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{1}{b x^{3/2} \tanh ^{-1}(\tanh (a+b x))}+\frac{3 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}-\frac{3}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","-\frac{1}{b x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{1}{b x^{3/2} \tanh ^{-1}(\tanh (a+b x))}+\frac{3 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}-\frac{3}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}",1,"(3*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(b*x - ArcTanh[Tanh[a + b*x]])^(5/2) - 3/(Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^2) - 1/(b*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])) - 1/(b*x^(3/2)*ArcTanh[Tanh[a + b*x]])","A",4,3,15,0.2000,1,"{2168, 2163, 2162}"
205,1,145,0,0.10639,"\int \frac{1}{x^{5/2} \tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[1/(x^(5/2)*ArcTanh[Tanh[a + b*x]]^2),x]","\frac{5 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{7/2}}-\frac{5}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}-\frac{1}{b x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{1}{b x^{5/2} \tanh ^{-1}(\tanh (a+b x))}-\frac{5 b}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}","\frac{5 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{7/2}}-\frac{5}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}-\frac{1}{b x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{1}{b x^{5/2} \tanh ^{-1}(\tanh (a+b x))}-\frac{5 b}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}",1,"(5*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(b*x - ArcTanh[Tanh[a + b*x]])^(7/2) - (5*b)/(Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^3) - 5/(3*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) - 1/(b*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])) - 1/(b*x^(5/2)*ArcTanh[Tanh[a + b*x]])","A",5,3,15,0.2000,1,"{2168, 2163, 2162}"
206,1,172,0,0.1368524,"\int \frac{1}{x^{7/2} \tanh ^{-1}(\tanh (a+b x))^2} \, dx","Int[1/(x^(7/2)*ArcTanh[Tanh[a + b*x]]^2),x]","\frac{7 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{9/2}}-\frac{7 b^2}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}-\frac{7 b}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}-\frac{7}{5 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}-\frac{1}{b x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{1}{b x^{7/2} \tanh ^{-1}(\tanh (a+b x))}","\frac{7 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{9/2}}-\frac{7 b^2}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}-\frac{7 b}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}-\frac{7}{5 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}-\frac{1}{b x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{1}{b x^{7/2} \tanh ^{-1}(\tanh (a+b x))}",1,"(7*b^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(b*x - ArcTanh[Tanh[a + b*x]])^(9/2) - (7*b^2)/(Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^4) - (7*b)/(3*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3) - 7/(5*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) - 1/(b*x^(7/2)*(b*x - ArcTanh[Tanh[a + b*x]])) - 1/(b*x^(7/2)*ArcTanh[Tanh[a + b*x]])","A",6,3,15,0.2000,1,"{2168, 2163, 2162}"
207,1,135,0,0.0970262,"\int \frac{x^{7/2}}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[x^(7/2)/ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{7 x^{5/2}}{4 b^2 \tanh ^{-1}(\tanh (a+b x))}+\frac{35 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{4 b^4}-\frac{35 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}{4 b^{9/2}}-\frac{x^{7/2}}{2 b \tanh ^{-1}(\tanh (a+b x))^2}+\frac{35 x^{3/2}}{12 b^3}","-\frac{7 x^{5/2}}{4 b^2 \tanh ^{-1}(\tanh (a+b x))}+\frac{35 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{4 b^4}-\frac{35 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}{4 b^{9/2}}-\frac{x^{7/2}}{2 b \tanh ^{-1}(\tanh (a+b x))^2}+\frac{35 x^{3/2}}{12 b^3}",1,"(35*x^(3/2))/(12*b^3) + (35*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]]))/(4*b^4) - (35*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^(3/2))/(4*b^(9/2)) - x^(7/2)/(2*b*ArcTanh[Tanh[a + b*x]]^2) - (7*x^(5/2))/(4*b^2*ArcTanh[Tanh[a + b*x]])","A",5,3,15,0.2000,1,"{2168, 2159, 2162}"
208,1,110,0,0.0711217,"\int \frac{x^{5/2}}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[x^(5/2)/ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{5 x^{3/2}}{4 b^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{15 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}{4 b^{7/2}}-\frac{x^{5/2}}{2 b \tanh ^{-1}(\tanh (a+b x))^2}+\frac{15 \sqrt{x}}{4 b^3}","-\frac{5 x^{3/2}}{4 b^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{15 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right) \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}{4 b^{7/2}}-\frac{x^{5/2}}{2 b \tanh ^{-1}(\tanh (a+b x))^2}+\frac{15 \sqrt{x}}{4 b^3}",1,"(15*Sqrt[x])/(4*b^3) - (15*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]*Sqrt[b*x - ArcTanh[Tanh[a + b*x]]])/(4*b^(7/2)) - x^(5/2)/(2*b*ArcTanh[Tanh[a + b*x]]^2) - (5*x^(3/2))/(4*b^2*ArcTanh[Tanh[a + b*x]])","A",4,3,15,0.2000,1,"{2168, 2159, 2162}"
209,1,98,0,0.0528765,"\int \frac{x^{3/2}}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[x^(3/2)/ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{3 \sqrt{x}}{4 b^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 b^{5/2} \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}-\frac{x^{3/2}}{2 b \tanh ^{-1}(\tanh (a+b x))^2}","-\frac{3 \sqrt{x}}{4 b^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 b^{5/2} \sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}-\frac{x^{3/2}}{2 b \tanh ^{-1}(\tanh (a+b x))^2}",1,"(-3*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(4*b^(5/2)*Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]) - x^(3/2)/(2*b*ArcTanh[Tanh[a + b*x]]^2) - (3*Sqrt[x])/(4*b^2*ArcTanh[Tanh[a + b*x]])","A",3,2,15,0.1333,1,"{2168, 2162}"
210,1,125,0,0.0706845,"\int \frac{\sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[Sqrt[x]/ArcTanh[Tanh[a + b*x]]^3,x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 b^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}-\frac{1}{4 b^2 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{1}{4 b^2 \sqrt{x} \tanh ^{-1}(\tanh (a+b x))}-\frac{\sqrt{x}}{2 b \tanh ^{-1}(\tanh (a+b x))^2}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 b^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{3/2}}-\frac{1}{4 b^2 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{1}{4 b^2 \sqrt{x} \tanh ^{-1}(\tanh (a+b x))}-\frac{\sqrt{x}}{2 b \tanh ^{-1}(\tanh (a+b x))^2}",1,"ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]]/(4*b^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^(3/2)) - 1/(4*b^2*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])) - Sqrt[x]/(2*b*ArcTanh[Tanh[a + b*x]]^2) - 1/(4*b^2*Sqrt[x]*ArcTanh[Tanh[a + b*x]])","A",4,3,15,0.2000,1,"{2168, 2163, 2162}"
211,1,152,0,0.0974084,"\int \frac{1}{\sqrt{x} \tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[1/(Sqrt[x]*ArcTanh[Tanh[a + b*x]]^3),x]","\frac{1}{4 b^2 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{1}{4 b^2 x^{3/2} \tanh ^{-1}(\tanh (a+b x))}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \sqrt{b} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}+\frac{3}{4 b \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}-\frac{1}{2 b \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^2}","\frac{1}{4 b^2 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{1}{4 b^2 x^{3/2} \tanh ^{-1}(\tanh (a+b x))}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \sqrt{b} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{5/2}}+\frac{3}{4 b \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}-\frac{1}{2 b \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^2}",1,"(-3*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(4*Sqrt[b]*(b*x - ArcTanh[Tanh[a + b*x]])^(5/2)) + 3/(4*b*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^2) + 1/(4*b^2*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])) - 1/(2*b*Sqrt[x]*ArcTanh[Tanh[a + b*x]]^2) + 1/(4*b^2*x^(3/2)*ArcTanh[Tanh[a + b*x]])","A",5,3,15,0.2000,1,"{2168, 2163, 2162}"
212,1,176,0,0.1280145,"\int \frac{1}{x^{3/2} \tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[1/(x^(3/2)*ArcTanh[Tanh[a + b*x]]^3),x]","\frac{3}{4 b^2 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{3}{4 b^2 x^{5/2} \tanh ^{-1}(\tanh (a+b x))}+\frac{5}{4 b x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}-\frac{1}{2 b x^{3/2} \tanh ^{-1}(\tanh (a+b x))^2}-\frac{15 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{7/2}}+\frac{15}{4 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}","\frac{3}{4 b^2 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{3}{4 b^2 x^{5/2} \tanh ^{-1}(\tanh (a+b x))}+\frac{5}{4 b x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}-\frac{1}{2 b x^{3/2} \tanh ^{-1}(\tanh (a+b x))^2}-\frac{15 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{7/2}}+\frac{15}{4 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}",1,"(-15*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(4*(b*x - ArcTanh[Tanh[a + b*x]])^(7/2)) + 15/(4*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^3) + 5/(4*b*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) + 3/(4*b^2*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])) - 1/(2*b*x^(3/2)*ArcTanh[Tanh[a + b*x]]^2) + 3/(4*b^2*x^(5/2)*ArcTanh[Tanh[a + b*x]])","A",6,3,15,0.2000,1,"{2168, 2163, 2162}"
213,1,201,0,0.1586714,"\int \frac{1}{x^{5/2} \tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[1/(x^(5/2)*ArcTanh[Tanh[a + b*x]]^3),x]","\frac{5}{4 b^2 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{5}{4 b^2 x^{7/2} \tanh ^{-1}(\tanh (a+b x))}-\frac{35 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{9/2}}+\frac{35}{12 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{7}{4 b x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}-\frac{1}{2 b x^{5/2} \tanh ^{-1}(\tanh (a+b x))^2}+\frac{35 b}{4 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}","\frac{5}{4 b^2 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{5}{4 b^2 x^{7/2} \tanh ^{-1}(\tanh (a+b x))}-\frac{35 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{9/2}}+\frac{35}{12 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{7}{4 b x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}-\frac{1}{2 b x^{5/2} \tanh ^{-1}(\tanh (a+b x))^2}+\frac{35 b}{4 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}",1,"(-35*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(4*(b*x - ArcTanh[Tanh[a + b*x]])^(9/2)) + (35*b)/(4*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^4) + 35/(12*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3) + 7/(4*b*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) + 5/(4*b^2*x^(7/2)*(b*x - ArcTanh[Tanh[a + b*x]])) - 1/(2*b*x^(5/2)*ArcTanh[Tanh[a + b*x]]^2) + 5/(4*b^2*x^(7/2)*ArcTanh[Tanh[a + b*x]])","A",7,3,15,0.2000,1,"{2168, 2163, 2162}"
214,1,228,0,0.2020595,"\int \frac{1}{x^{7/2} \tanh ^{-1}(\tanh (a+b x))^3} \, dx","Int[1/(x^(7/2)*ArcTanh[Tanh[a + b*x]]^3),x]","\frac{7}{4 b^2 x^{9/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{7}{4 b^2 x^{9/2} \tanh ^{-1}(\tanh (a+b x))}-\frac{63 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{11/2}}+\frac{63 b^2}{4 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^5}+\frac{21 b}{4 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}+\frac{63}{20 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{9}{4 b x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}-\frac{1}{2 b x^{7/2} \tanh ^{-1}(\tanh (a+b x))^2}","\frac{7}{4 b^2 x^{9/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{7}{4 b^2 x^{9/2} \tanh ^{-1}(\tanh (a+b x))}-\frac{63 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{b x-\tanh ^{-1}(\tanh (a+b x))}}\right)}{4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^{11/2}}+\frac{63 b^2}{4 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^5}+\frac{21 b}{4 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}+\frac{63}{20 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{9}{4 b x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}-\frac{1}{2 b x^{7/2} \tanh ^{-1}(\tanh (a+b x))^2}",1,"(-63*b^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[b*x - ArcTanh[Tanh[a + b*x]]]])/(4*(b*x - ArcTanh[Tanh[a + b*x]])^(11/2)) + (63*b^2)/(4*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^5) + (21*b)/(4*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^4) + 63/(20*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3) + 9/(4*b*x^(7/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) + 7/(4*b^2*x^(9/2)*(b*x - ArcTanh[Tanh[a + b*x]])) - 1/(2*b*x^(7/2)*ArcTanh[Tanh[a + b*x]]^2) + 7/(4*b^2*x^(9/2)*ArcTanh[Tanh[a + b*x]])","A",8,3,15,0.2000,1,"{2168, 2163, 2162}"
215,1,142,0,0.0775207,"\int x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx","Int[x^(3/2)*Sqrt[ArcTanh[Tanh[a + b*x]]],x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{8 b^{5/2}}-\frac{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{8 b^2}-\frac{x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{12 b}+\frac{1}{3} x^{5/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{8 b^{5/2}}-\frac{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{8 b^2}-\frac{x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{12 b}+\frac{1}{3} x^{5/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}",1,"-(ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^3)/(8*b^(5/2)) + (x^(5/2)*Sqrt[ArcTanh[Tanh[a + b*x]]])/3 - (x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])/(12*b) - (Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/(8*b^2)","A",4,2,17,0.1176,1,"{2169, 2165}"
216,1,104,0,0.0506659,"\int \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx","Int[Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]],x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{4 b^{3/2}}+\frac{1}{2} x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}-\frac{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{4 b}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{4 b^{3/2}}+\frac{1}{2} x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}-\frac{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{4 b}",1,"-(ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^2)/(4*b^(3/2)) + (x^(3/2)*Sqrt[ArcTanh[Tanh[a + b*x]]])/2 - (Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])/(4*b)","A",3,2,17,0.1176,1,"{2169, 2165}"
217,1,61,0,0.0293383,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{x}} \, dx","Int[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[x],x]","\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{\sqrt{b}}","\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{\sqrt{b}}",1,"-((ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]]))/Sqrt[b]) + Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]]","A",2,2,17,0.1176,1,"{2169, 2165}"
218,1,49,0,0.0285149,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^{3/2}} \, dx","Int[Sqrt[ArcTanh[Tanh[a + b*x]]]/x^(3/2),x]","2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right)-\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{x}}","2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right)-\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{x}}",1,"2*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]] - (2*Sqrt[ArcTanh[Tanh[a + b*x]]])/Sqrt[x]","A",2,2,17,0.1176,1,"{2168, 2165}"
219,1,35,0,0.0141844,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^{5/2}} \, dx","Int[Sqrt[ArcTanh[Tanh[a + b*x]]]/x^(5/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"(2*ArcTanh[Tanh[a + b*x]]^(3/2))/(3*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",1,1,17,0.05882,1,"{2167}"
220,1,72,0,0.033482,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^{7/2}} \, dx","Int[Sqrt[ArcTanh[Tanh[a + b*x]]]/x^(7/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{5 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{4 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{15 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{5 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{4 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{15 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}",1,"(4*b*ArcTanh[Tanh[a + b*x]]^(3/2))/(15*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) + (2*ArcTanh[Tanh[a + b*x]]^(3/2))/(5*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",2,2,17,0.1176,1,"{2171, 2167}"
221,1,110,0,0.0543659,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^{9/2}} \, dx","Int[Sqrt[ArcTanh[Tanh[a + b*x]]]/x^(9/2),x]","\frac{16 b^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{105 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{8 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{35 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}+\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{7 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}","\frac{16 b^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{105 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{8 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{35 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}+\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{7 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"(16*b^2*ArcTanh[Tanh[a + b*x]]^(3/2))/(105*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3) + (8*b*ArcTanh[Tanh[a + b*x]]^(3/2))/(35*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) + (2*ArcTanh[Tanh[a + b*x]]^(3/2))/(7*x^(7/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",3,2,17,0.1176,1,"{2171, 2167}"
222,1,148,0,0.0778354,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^{11/2}} \, dx","Int[Sqrt[ArcTanh[Tanh[a + b*x]]]/x^(11/2),x]","\frac{32 b^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{315 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}+\frac{16 b^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{105 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{4 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{21 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}+\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{9 x^{9/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}","\frac{32 b^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{315 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}+\frac{16 b^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{105 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{4 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{21 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}+\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{9 x^{9/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"(32*b^3*ArcTanh[Tanh[a + b*x]]^(3/2))/(315*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^4) + (16*b^2*ArcTanh[Tanh[a + b*x]]^(3/2))/(105*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3) + (4*b*ArcTanh[Tanh[a + b*x]]^(3/2))/(21*x^(7/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) + (2*ArcTanh[Tanh[a + b*x]]^(3/2))/(9*x^(9/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",4,2,17,0.1176,1,"{2171, 2167}"
223,1,177,0,0.1037112,"\int x^{3/2} \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx","Int[x^(3/2)*ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}{64 b^{5/2}}+\frac{3 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{64 b^2}+\frac{x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{32 b}-\frac{1}{8} x^{5/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{1}{4} x^{5/2} \tanh ^{-1}(\tanh (a+b x))^{3/2}","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}{64 b^{5/2}}+\frac{3 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{64 b^2}+\frac{x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{32 b}-\frac{1}{8} x^{5/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{1}{4} x^{5/2} \tanh ^{-1}(\tanh (a+b x))^{3/2}",1,"(3*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^4)/(64*b^(5/2)) - (x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])/8 + (x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/(32*b) + (3*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^3*Sqrt[ArcTanh[Tanh[a + b*x]]])/(64*b^2) + (x^(5/2)*ArcTanh[Tanh[a + b*x]]^(3/2))/4","A",5,2,17,0.1176,1,"{2169, 2165}"
224,1,139,0,0.070956,"\int \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx","Int[Sqrt[x]*ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{8 b^{3/2}}-\frac{1}{4} x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{1}{3} x^{3/2} \tanh ^{-1}(\tanh (a+b x))^{3/2}+\frac{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{8 b}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{8 b^{3/2}}-\frac{1}{4} x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{1}{3} x^{3/2} \tanh ^{-1}(\tanh (a+b x))^{3/2}+\frac{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{8 b}",1,"(ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^3)/(8*b^(3/2)) - (x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])/4 + (Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/(8*b) + (x^(3/2)*ArcTanh[Tanh[a + b*x]]^(3/2))/3","A",4,2,17,0.1176,1,"{2169, 2165}"
225,1,101,0,0.0476427,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{\sqrt{x}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(3/2)/Sqrt[x],x]","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{4 \sqrt{b}}-\frac{3}{4} \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{1}{2} \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{3/2}","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{4 \sqrt{b}}-\frac{3}{4} \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{1}{2} \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{3/2}",1,"(3*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^2)/(4*Sqrt[b]) - (3*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])/4 + (Sqrt[x]*ArcTanh[Tanh[a + b*x]]^(3/2))/2","A",3,2,17,0.1176,1,"{2169, 2165}"
226,1,81,0,0.056096,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{3/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(3/2)/x^(3/2),x]","-\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{\sqrt{x}}+3 b \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}-3 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)","-\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{\sqrt{x}}+3 b \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}-3 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)",1,"-3*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]]) + 3*b*Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]] - (2*ArcTanh[Tanh[a + b*x]]^(3/2))/Sqrt[x]","A",3,3,17,0.1765,1,"{2168, 2169, 2165}"
227,1,70,0,0.0422076,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{5/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(3/2)/x^(5/2),x]","2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right)-\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 x^{3/2}}-\frac{2 b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{x}}","2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right)-\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 x^{3/2}}-\frac{2 b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{x}}",1,"2*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]] - (2*b*Sqrt[ArcTanh[Tanh[a + b*x]]])/Sqrt[x] - (2*ArcTanh[Tanh[a + b*x]]^(3/2))/(3*x^(3/2))","A",3,2,17,0.1176,1,"{2168, 2165}"
228,1,35,0,0.0140935,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{7/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(3/2)/x^(7/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"(2*ArcTanh[Tanh[a + b*x]]^(5/2))/(5*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",1,1,17,0.05882,1,"{2167}"
229,1,72,0,0.0330791,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{9/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(3/2)/x^(9/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{7 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{4 b \tanh ^{-1}(\tanh (a+b x))^{5/2}}{35 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{7 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{4 b \tanh ^{-1}(\tanh (a+b x))^{5/2}}{35 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}",1,"(4*b*ArcTanh[Tanh[a + b*x]]^(5/2))/(35*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) + (2*ArcTanh[Tanh[a + b*x]]^(5/2))/(7*x^(7/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",2,2,17,0.1176,1,"{2171, 2167}"
230,1,110,0,0.0522912,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{11/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(3/2)/x^(11/2),x]","\frac{16 b^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{315 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{9 x^{9/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{8 b \tanh ^{-1}(\tanh (a+b x))^{5/2}}{63 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","\frac{16 b^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{315 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{9 x^{9/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{8 b \tanh ^{-1}(\tanh (a+b x))^{5/2}}{63 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}",1,"(16*b^2*ArcTanh[Tanh[a + b*x]]^(5/2))/(315*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3) + (8*b*ArcTanh[Tanh[a + b*x]]^(5/2))/(63*x^(7/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) + (2*ArcTanh[Tanh[a + b*x]]^(5/2))/(9*x^(9/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",3,2,17,0.1176,1,"{2171, 2167}"
231,1,148,0,0.0755237,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{13/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(3/2)/x^(13/2),x]","\frac{32 b^3 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{1155 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}+\frac{16 b^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{231 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{4 b \tanh ^{-1}(\tanh (a+b x))^{5/2}}{33 x^{9/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}+\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{11 x^{11/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}","\frac{32 b^3 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{1155 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}+\frac{16 b^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{231 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{4 b \tanh ^{-1}(\tanh (a+b x))^{5/2}}{33 x^{9/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}+\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{11 x^{11/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"(32*b^3*ArcTanh[Tanh[a + b*x]]^(5/2))/(1155*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])^4) + (16*b^2*ArcTanh[Tanh[a + b*x]]^(5/2))/(231*x^(7/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3) + (4*b*ArcTanh[Tanh[a + b*x]]^(5/2))/(33*x^(9/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) + (2*ArcTanh[Tanh[a + b*x]]^(5/2))/(11*x^(11/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",4,2,17,0.1176,1,"{2171, 2167}"
232,1,174,0,0.0975145,"\int \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx","Int[Sqrt[x]*ArcTanh[Tanh[a + b*x]]^(5/2),x]","-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}{64 b^{3/2}}+\frac{5}{32} x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2-\frac{5}{24} x^{3/2} \tanh ^{-1}(\tanh (a+b x))^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{1}{4} x^{3/2} \tanh ^{-1}(\tanh (a+b x))^{5/2}-\frac{5 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{64 b}","-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}{64 b^{3/2}}+\frac{5}{32} x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2-\frac{5}{24} x^{3/2} \tanh ^{-1}(\tanh (a+b x))^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{1}{4} x^{3/2} \tanh ^{-1}(\tanh (a+b x))^{5/2}-\frac{5 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{64 b}",1,"(-5*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^4)/(64*b^(3/2)) + (5*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/32 - (5*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^3*Sqrt[ArcTanh[Tanh[a + b*x]]])/(64*b) - (5*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(3/2))/24 + (x^(3/2)*ArcTanh[Tanh[a + b*x]]^(5/2))/4","A",5,2,17,0.1176,1,"{2169, 2165}"
233,1,136,0,0.069098,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{\sqrt{x}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(5/2)/Sqrt[x],x]","-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{8 \sqrt{b}}+\frac{5}{8} \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2-\frac{5}{12} \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{1}{3} \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{5/2}","-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{8 \sqrt{b}}+\frac{5}{8} \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2-\frac{5}{12} \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+\frac{1}{3} \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{5/2}",1,"(-5*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^3)/(8*Sqrt[b]) + (5*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/8 - (5*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(3/2))/12 + (Sqrt[x]*ArcTanh[Tanh[a + b*x]]^(5/2))/3","A",4,2,17,0.1176,1,"{2169, 2165}"
234,1,121,0,0.0660079,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{3/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(5/2)/x^(3/2),x]","-\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{\sqrt{x}}+\frac{5}{2} b \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{3/2}-\frac{15}{4} b \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}+\frac{15}{4} \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2","-\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{\sqrt{x}}+\frac{5}{2} b \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{3/2}-\frac{15}{4} b \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}+\frac{15}{4} \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2",1,"(15*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^2)/4 - (15*b*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])/4 + (5*b*Sqrt[x]*ArcTanh[Tanh[a + b*x]]^(3/2))/2 - (2*ArcTanh[Tanh[a + b*x]]^(5/2))/Sqrt[x]","A",4,3,17,0.1765,1,"{2168, 2169, 2165}"
235,1,106,0,0.0632354,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{5/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(5/2)/x^(5/2),x]","5 b^2 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}-5 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)-\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{3 x^{3/2}}-\frac{10 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 \sqrt{x}}","5 b^2 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}-5 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)-\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{3 x^{3/2}}-\frac{10 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 \sqrt{x}}",1,"-5*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]]) + 5*b^2*Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]] - (10*b*ArcTanh[Tanh[a + b*x]]^(3/2))/(3*Sqrt[x]) - (2*ArcTanh[Tanh[a + b*x]]^(5/2))/(3*x^(3/2))","A",4,3,17,0.1765,1,"{2168, 2169, 2165}"
236,1,93,0,0.0587725,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{7/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(5/2)/x^(7/2),x]","2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right)-\frac{2 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{x}}-\frac{2 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 x^{3/2}}-\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 x^{5/2}}","2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right)-\frac{2 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{x}}-\frac{2 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 x^{3/2}}-\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 x^{5/2}}",1,"2*b^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]] - (2*b^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/Sqrt[x] - (2*b*ArcTanh[Tanh[a + b*x]]^(3/2))/(3*x^(3/2)) - (2*ArcTanh[Tanh[a + b*x]]^(5/2))/(5*x^(5/2))","A",4,2,17,0.1176,1,"{2168, 2165}"
237,1,35,0,0.0131392,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{9/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(5/2)/x^(9/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{7 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{7 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"(2*ArcTanh[Tanh[a + b*x]]^(7/2))/(7*x^(7/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",1,1,17,0.05882,1,"{2167}"
238,1,72,0,0.0327222,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{11/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(5/2)/x^(11/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{9 x^{9/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{4 b \tanh ^{-1}(\tanh (a+b x))^{7/2}}{63 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{9 x^{9/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{4 b \tanh ^{-1}(\tanh (a+b x))^{7/2}}{63 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}",1,"(4*b*ArcTanh[Tanh[a + b*x]]^(7/2))/(63*x^(7/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) + (2*ArcTanh[Tanh[a + b*x]]^(7/2))/(9*x^(9/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",2,2,17,0.1176,1,"{2171, 2167}"
239,1,110,0,0.057208,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{13/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(5/2)/x^(13/2),x]","\frac{16 b^2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{693 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{11 x^{11/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{8 b \tanh ^{-1}(\tanh (a+b x))^{7/2}}{99 x^{9/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","\frac{16 b^2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{693 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{11 x^{11/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{8 b \tanh ^{-1}(\tanh (a+b x))^{7/2}}{99 x^{9/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}",1,"(16*b^2*ArcTanh[Tanh[a + b*x]]^(7/2))/(693*x^(7/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3) + (8*b*ArcTanh[Tanh[a + b*x]]^(7/2))/(99*x^(9/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) + (2*ArcTanh[Tanh[a + b*x]]^(7/2))/(11*x^(11/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",3,2,17,0.1176,1,"{2171, 2167}"
240,1,148,0,0.0786454,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{15/2}} \, dx","Int[ArcTanh[Tanh[a + b*x]]^(5/2)/x^(15/2),x]","\frac{16 b^2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{429 x^{9/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{32 b^3 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{3003 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}+\frac{2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{13 x^{13/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{12 b \tanh ^{-1}(\tanh (a+b x))^{7/2}}{143 x^{11/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","\frac{16 b^2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{429 x^{9/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{32 b^3 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{3003 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}+\frac{2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{13 x^{13/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{12 b \tanh ^{-1}(\tanh (a+b x))^{7/2}}{143 x^{11/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}",1,"(32*b^3*ArcTanh[Tanh[a + b*x]]^(7/2))/(3003*x^(7/2)*(b*x - ArcTanh[Tanh[a + b*x]])^4) + (16*b^2*ArcTanh[Tanh[a + b*x]]^(7/2))/(429*x^(9/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3) + (12*b*ArcTanh[Tanh[a + b*x]]^(7/2))/(143*x^(11/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) + (2*ArcTanh[Tanh[a + b*x]]^(7/2))/(13*x^(13/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",4,2,17,0.1176,1,"{2171, 2167}"
241,1,145,0,0.0808685,"\int \frac{x^{5/2}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[x^(5/2)/Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{5 x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{12 b^2}+\frac{5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{8 b^{7/2}}+\frac{5 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{8 b^3}+\frac{x^{5/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{3 b}","\frac{5 x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{12 b^2}+\frac{5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{8 b^{7/2}}+\frac{5 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{8 b^3}+\frac{x^{5/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{3 b}",1,"(5*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^3)/(8*b^(7/2)) + (x^(5/2)*Sqrt[ArcTanh[Tanh[a + b*x]]])/(3*b) + (5*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])/(12*b^2) + (5*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/(8*b^3)","A",4,2,17,0.1176,1,"{2169, 2165}"
242,1,107,0,0.0515712,"\int \frac{x^{3/2}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[x^(3/2)/Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{4 b^{5/2}}+\frac{3 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{4 b^2}+\frac{x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{2 b}","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{4 b^{5/2}}+\frac{3 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{4 b^2}+\frac{x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{2 b}",1,"(3*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^2)/(4*b^(5/2)) + (x^(3/2)*Sqrt[ArcTanh[Tanh[a + b*x]]])/(2*b) + (3*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])/(4*b^2)","A",3,2,17,0.1176,1,"{2169, 2165}"
243,1,63,0,0.0283892,"\int \frac{\sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[Sqrt[x]/Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^{3/2}}+\frac{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^{3/2}}+\frac{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b}",1,"(ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]]))/b^(3/2) + (Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]])/b","A",2,2,17,0.1176,1,"{2169, 2165}"
244,1,30,0,0.0120342,"\int \frac{1}{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[1/(Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right)}{\sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right)}{\sqrt{b}}",1,"(2*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]])/Sqrt[b]","A",1,1,17,0.05882,1,"{2165}"
245,1,33,0,0.0133372,"\int \frac{1}{x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[1/(x^(3/2)*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}","\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"(2*Sqrt[ArcTanh[Tanh[a + b*x]]])/(Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]]))","A",1,1,17,0.05882,1,"{2167}"
246,1,72,0,0.0316608,"\int \frac{1}{x^{5/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[1/(x^(5/2)*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{4 b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{3 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}","\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}+\frac{4 b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{3 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}",1,"(4*b*Sqrt[ArcTanh[Tanh[a + b*x]]])/(3*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^2) + (2*Sqrt[ArcTanh[Tanh[a + b*x]]])/(3*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",2,2,17,0.1176,1,"{2171, 2167}"
247,1,110,0,0.0558492,"\int \frac{1}{x^{7/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[1/(x^(7/2)*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","\frac{16 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{15 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{8 b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{15 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}+\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{5 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}","\frac{16 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{15 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{8 b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{15 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}+\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{5 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"(16*b^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/(15*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^3) + (8*b*Sqrt[ArcTanh[Tanh[a + b*x]]])/(15*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) + (2*Sqrt[ArcTanh[Tanh[a + b*x]]])/(5*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",3,2,17,0.1176,1,"{2171, 2167}"
248,1,148,0,0.0830278,"\int \frac{1}{x^{9/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Int[1/(x^(9/2)*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","\frac{16 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{35 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{32 b^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{35 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}+\frac{12 b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{35 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}+\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{7 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}","\frac{16 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{35 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}+\frac{32 b^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{35 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4}+\frac{12 b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{35 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}+\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{7 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"(32*b^3*Sqrt[ArcTanh[Tanh[a + b*x]]])/(35*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^4) + (16*b^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/(35*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3) + (12*b*Sqrt[ArcTanh[Tanh[a + b*x]]])/(35*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2) + (2*Sqrt[ArcTanh[Tanh[a + b*x]]])/(7*x^(7/2)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",4,2,17,0.1176,1,"{2171, 2167}"
249,1,166,0,0.1074176,"\int \frac{x^{7/2}}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[x^(7/2)/ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{7 x^{5/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{3 b^2}+\frac{35 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{12 b^3}+\frac{35 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{8 b^4}+\frac{35 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{8 b^{9/2}}-\frac{2 x^{7/2}}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","\frac{7 x^{5/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{3 b^2}+\frac{35 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{12 b^3}+\frac{35 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{8 b^4}+\frac{35 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{8 b^{9/2}}-\frac{2 x^{7/2}}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(35*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^3)/(8*b^(9/2)) - (2*x^(7/2))/(b*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (7*x^(5/2)*Sqrt[ArcTanh[Tanh[a + b*x]]])/(3*b^2) + (35*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])/(12*b^3) + (35*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/(8*b^4)","A",5,3,17,0.1765,1,"{2168, 2169, 2165}"
250,1,128,0,0.076284,"\int \frac{x^{5/2}}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[x^(5/2)/ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{5 x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{2 b^2}+\frac{15 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{4 b^3}+\frac{15 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{4 b^{7/2}}-\frac{2 x^{5/2}}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","\frac{5 x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{2 b^2}+\frac{15 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{4 b^3}+\frac{15 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{4 b^{7/2}}-\frac{2 x^{5/2}}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(15*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^2)/(4*b^(7/2)) - (2*x^(5/2))/(b*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (5*x^(3/2)*Sqrt[ArcTanh[Tanh[a + b*x]]])/(2*b^2) + (15*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])/(4*b^3)","A",4,3,17,0.1765,1,"{2168, 2169, 2165}"
251,1,86,0,0.0487386,"\int \frac{x^{3/2}}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[x^(3/2)/ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{3 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^2}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^{5/2}}-\frac{2 x^{3/2}}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","\frac{3 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^2}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^{5/2}}-\frac{2 x^{3/2}}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(3*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]]))/b^(5/2) - (2*x^(3/2))/(b*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (3*Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]])/b^2","A",3,3,17,0.1765,1,"{2168, 2169, 2165}"
252,1,52,0,0.0258759,"\int \frac{\sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[Sqrt[x]/ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right)}{b^{3/2}}-\frac{2 \sqrt{x}}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right)}{b^{3/2}}-\frac{2 \sqrt{x}}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(2*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]])/b^(3/2) - (2*Sqrt[x])/(b*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",2,2,17,0.1176,1,"{2168, 2165}"
253,1,33,0,0.0128226,"\int \frac{1}{\sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[1/(Sqrt[x]*ArcTanh[Tanh[a + b*x]]^(3/2)),x]","-\frac{2 \sqrt{x}}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","-\frac{2 \sqrt{x}}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(-2*Sqrt[x])/((b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",1,1,17,0.05882,1,"{2167}"
254,1,68,0,0.032766,"\int \frac{1}{x^{3/2} \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[1/(x^(3/2)*ArcTanh[Tanh[a + b*x]]^(3/2)),x]","\frac{2}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{4 b \sqrt{x}}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","\frac{2}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{4 b \sqrt{x}}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(-4*b*Sqrt[x])/((b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]]) + 2/(Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",2,2,17,0.1176,1,"{2171, 2167}"
255,1,110,0,0.0540588,"\int \frac{1}{x^{5/2} \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[1/(x^(5/2)*ArcTanh[Tanh[a + b*x]]^(3/2)),x]","-\frac{16 b^2 \sqrt{x}}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{2}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{8 b}{3 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","-\frac{16 b^2 \sqrt{x}}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{2}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{8 b}{3 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(-16*b^2*Sqrt[x])/(3*(b*x - ArcTanh[Tanh[a + b*x]])^3*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (8*b)/(3*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]]) + 2/(3*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",3,2,17,0.1176,1,"{2171, 2167}"
256,1,148,0,0.0797879,"\int \frac{1}{x^{7/2} \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Int[1/(x^(7/2)*ArcTanh[Tanh[a + b*x]]^(3/2)),x]","-\frac{32 b^3 \sqrt{x}}{5 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{16 b^2}{5 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{4 b}{5 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{2}{5 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","-\frac{32 b^3 \sqrt{x}}{5 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{16 b^2}{5 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{4 b}{5 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{2}{5 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(-32*b^3*Sqrt[x])/(5*(b*x - ArcTanh[Tanh[a + b*x]])^4*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (16*b^2)/(5*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^3*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (4*b)/(5*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]]) + 2/(5*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",4,2,17,0.1176,1,"{2171, 2167}"
257,1,153,0,0.0959509,"\int \frac{x^{7/2}}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[x^(7/2)/ArcTanh[Tanh[a + b*x]]^(5/2),x]","-\frac{14 x^{5/2}}{3 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{35 x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{6 b^3}+\frac{35 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{4 b^4}+\frac{35 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{4 b^{9/2}}-\frac{2 x^{7/2}}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}","-\frac{14 x^{5/2}}{3 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{35 x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{6 b^3}+\frac{35 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{4 b^4}+\frac{35 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{4 b^{9/2}}-\frac{2 x^{7/2}}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(35*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]])^2)/(4*b^(9/2)) - (2*x^(7/2))/(3*b*ArcTanh[Tanh[a + b*x]]^(3/2)) - (14*x^(5/2))/(3*b^2*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (35*x^(3/2)*Sqrt[ArcTanh[Tanh[a + b*x]]])/(6*b^3) + (35*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])/(4*b^4)","A",5,3,17,0.1765,1,"{2168, 2169, 2165}"
258,1,111,0,0.0659394,"\int \frac{x^{5/2}}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[x^(5/2)/ArcTanh[Tanh[a + b*x]]^(5/2),x]","-\frac{10 x^{3/2}}{3 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{5 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^3}+\frac{5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^{7/2}}-\frac{2 x^{5/2}}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}","-\frac{10 x^{3/2}}{3 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{5 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^3}+\frac{5 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^{7/2}}-\frac{2 x^{5/2}}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(5*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]]*(b*x - ArcTanh[Tanh[a + b*x]]))/b^(7/2) - (2*x^(5/2))/(3*b*ArcTanh[Tanh[a + b*x]]^(3/2)) - (10*x^(3/2))/(3*b^2*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (5*Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]])/b^3","A",4,3,17,0.1765,1,"{2168, 2169, 2165}"
259,1,75,0,0.0419205,"\int \frac{x^{3/2}}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[x^(3/2)/ArcTanh[Tanh[a + b*x]]^(5/2),x]","-\frac{2 \sqrt{x}}{b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right)}{b^{5/2}}-\frac{2 x^{3/2}}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}","-\frac{2 \sqrt{x}}{b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right)}{b^{5/2}}-\frac{2 x^{3/2}}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(2*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[ArcTanh[Tanh[a + b*x]]]])/b^(5/2) - (2*x^(3/2))/(3*b*ArcTanh[Tanh[a + b*x]]^(3/2)) - (2*Sqrt[x])/(b^2*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",3,2,17,0.1176,1,"{2168, 2165}"
260,1,35,0,0.0121499,"\int \frac{\sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[Sqrt[x]/ArcTanh[Tanh[a + b*x]]^(5/2),x]","-\frac{2 x^{3/2}}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}","-\frac{2 x^{3/2}}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(-2*x^(3/2))/(3*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(3/2))","A",1,1,17,0.05882,1,"{2167}"
261,1,71,0,0.0315466,"\int \frac{1}{\sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[1/(Sqrt[x]*ArcTanh[Tanh[a + b*x]]^(5/2)),x]","\frac{4 \sqrt{x}}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{2 \sqrt{x}}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}","\frac{4 \sqrt{x}}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{2 \sqrt{x}}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(-2*Sqrt[x])/(3*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(3/2)) + (4*Sqrt[x])/(3*(b*x - ArcTanh[Tanh[a + b*x]])^2*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",2,2,17,0.1176,1,"{2171, 2167}"
262,1,106,0,0.0548497,"\int \frac{1}{x^{3/2} \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[1/(x^(3/2)*ArcTanh[Tanh[a + b*x]]^(5/2)),x]","\frac{16 b \sqrt{x}}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{8 b \sqrt{x}}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{2}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}","\frac{16 b \sqrt{x}}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{8 b \sqrt{x}}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{2}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(-8*b*Sqrt[x])/(3*(b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]]^(3/2)) + 2/(Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(3/2)) + (16*b*Sqrt[x])/(3*(b*x - ArcTanh[Tanh[a + b*x]])^3*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",3,2,17,0.1176,1,"{2171, 2167}"
263,1,146,0,0.0794707,"\int \frac{1}{x^{5/2} \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[1/(x^(5/2)*ArcTanh[Tanh[a + b*x]]^(5/2)),x]","\frac{32 b^2 \sqrt{x}}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{16 b^2 \sqrt{x}}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{2}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{4 b}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}","\frac{32 b^2 \sqrt{x}}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{16 b^2 \sqrt{x}}{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{2}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{4 b}{\sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(-16*b^2*Sqrt[x])/(3*(b*x - ArcTanh[Tanh[a + b*x]])^3*ArcTanh[Tanh[a + b*x]]^(3/2)) + (4*b)/(Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]]^(3/2)) + 2/(3*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(3/2)) + (32*b^2*Sqrt[x])/(3*(b*x - ArcTanh[Tanh[a + b*x]])^4*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",4,2,17,0.1176,1,"{2171, 2167}"
264,1,186,0,0.1044236,"\int \frac{1}{x^{7/2} \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Int[1/(x^(7/2)*ArcTanh[Tanh[a + b*x]]^(5/2)),x]","\frac{256 b^3 \sqrt{x}}{15 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^5 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{128 b^3 \sqrt{x}}{15 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{32 b^2}{5 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{16 b}{15 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{2}{5 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}","\frac{256 b^3 \sqrt{x}}{15 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^5 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{128 b^3 \sqrt{x}}{15 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^4 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{32 b^2}{5 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{16 b}{15 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{2}{5 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(-128*b^3*Sqrt[x])/(15*(b*x - ArcTanh[Tanh[a + b*x]])^4*ArcTanh[Tanh[a + b*x]]^(3/2)) + (32*b^2)/(5*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^3*ArcTanh[Tanh[a + b*x]]^(3/2)) + (16*b)/(15*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]]^(3/2)) + 2/(5*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(3/2)) + (256*b^3*Sqrt[x])/(15*(b*x - ArcTanh[Tanh[a + b*x]])^5*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",5,2,17,0.1176,1,"{2171, 2167}"
265,1,79,0,0.0432839,"\int x^m \tanh ^{-1}(\tanh (a+b x))^n \, dx","Int[x^m*ArcTanh[Tanh[a + b*x]]^n,x]","\frac{x^m \left(\frac{b x}{b x-\tanh ^{-1}(\tanh (a+b x))}\right)^{-m} \tanh ^{-1}(\tanh (a+b x))^{n+1} \, _2F_1\left(-m,n+1;n+2;-\frac{\tanh ^{-1}(\tanh (a+b x))}{b x-\tanh ^{-1}(\tanh (a+b x))}\right)}{b (n+1)}","\frac{x^m \left(\frac{b x}{b x-\tanh ^{-1}(\tanh (a+b x))}\right)^{-m} \tanh ^{-1}(\tanh (a+b x))^{n+1} \, _2F_1\left(-m,n+1;n+2;-\frac{\tanh ^{-1}(\tanh (a+b x))}{b x-\tanh ^{-1}(\tanh (a+b x))}\right)}{b (n+1)}",1,"(x^m*ArcTanh[Tanh[a + b*x]]^(1 + n)*Hypergeometric2F1[-m, 1 + n, 2 + n, -(ArcTanh[Tanh[a + b*x]]/(b*x - ArcTanh[Tanh[a + b*x]]))])/(b*(1 + n)*((b*x)/(b*x - ArcTanh[Tanh[a + b*x]]))^m)","A",1,1,13,0.07692,1,"{2173}"
266,1,165,0,0.1337383,"\int x^4 \tanh ^{-1}(\tanh (a+b x))^n \, dx","Int[x^4*ArcTanh[Tanh[a + b*x]]^n,x]","-\frac{4 x^3 \tanh ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}+\frac{12 x^2 \tanh ^{-1}(\tanh (a+b x))^{n+3}}{b^3 (n+1) (n+2) (n+3)}-\frac{24 x \tanh ^{-1}(\tanh (a+b x))^{n+4}}{b^4 (n+1) (n+2) (n+3) (n+4)}+\frac{24 \tanh ^{-1}(\tanh (a+b x))^{n+5}}{b^5 (n+1) (n+2) (n+3) (n+4) (n+5)}+\frac{x^4 \tanh ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}","-\frac{4 x^3 \tanh ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}+\frac{12 x^2 \tanh ^{-1}(\tanh (a+b x))^{n+3}}{b^3 (n+1) (n+2) (n+3)}-\frac{24 x \tanh ^{-1}(\tanh (a+b x))^{n+4}}{b^4 (n+1) (n+2) (n+3) (n+4)}+\frac{24 \tanh ^{-1}(\tanh (a+b x))^{n+5}}{b^5 (n+1) (n+2) (n+3) (n+4) (n+5)}+\frac{x^4 \tanh ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}",1,"(x^4*ArcTanh[Tanh[a + b*x]]^(1 + n))/(b*(1 + n)) - (4*x^3*ArcTanh[Tanh[a + b*x]]^(2 + n))/(b^2*(1 + n)*(2 + n)) + (12*x^2*ArcTanh[Tanh[a + b*x]]^(3 + n))/(b^3*(1 + n)*(2 + n)*(3 + n)) - (24*x*ArcTanh[Tanh[a + b*x]]^(4 + n))/(b^4*(1 + n)*(2 + n)*(3 + n)*(4 + n)) + (24*ArcTanh[Tanh[a + b*x]]^(5 + n))/(b^5*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n))","A",6,3,13,0.2308,1,"{2168, 2157, 30}"
267,1,121,0,0.0750075,"\int x^3 \tanh ^{-1}(\tanh (a+b x))^n \, dx","Int[x^3*ArcTanh[Tanh[a + b*x]]^n,x]","-\frac{3 x^2 \tanh ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}+\frac{6 x \tanh ^{-1}(\tanh (a+b x))^{n+3}}{b^3 (n+1) (n+2) (n+3)}-\frac{6 \tanh ^{-1}(\tanh (a+b x))^{n+4}}{b^4 (n+1) (n+2) (n+3) (n+4)}+\frac{x^3 \tanh ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}","-\frac{3 x^2 \tanh ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}+\frac{6 x \tanh ^{-1}(\tanh (a+b x))^{n+3}}{b^3 (n+1) (n+2) (n+3)}-\frac{6 \tanh ^{-1}(\tanh (a+b x))^{n+4}}{b^4 (n+1) (n+2) (n+3) (n+4)}+\frac{x^3 \tanh ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}",1,"(x^3*ArcTanh[Tanh[a + b*x]]^(1 + n))/(b*(1 + n)) - (3*x^2*ArcTanh[Tanh[a + b*x]]^(2 + n))/(b^2*(1 + n)*(2 + n)) + (6*x*ArcTanh[Tanh[a + b*x]]^(3 + n))/(b^3*(1 + n)*(2 + n)*(3 + n)) - (6*ArcTanh[Tanh[a + b*x]]^(4 + n))/(b^4*(1 + n)*(2 + n)*(3 + n)*(4 + n))","A",5,3,13,0.2308,1,"{2168, 2157, 30}"
268,1,82,0,0.0461799,"\int x^2 \tanh ^{-1}(\tanh (a+b x))^n \, dx","Int[x^2*ArcTanh[Tanh[a + b*x]]^n,x]","-\frac{2 x \tanh ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}+\frac{2 \tanh ^{-1}(\tanh (a+b x))^{n+3}}{b^3 (n+1) (n+2) (n+3)}+\frac{x^2 \tanh ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}","-\frac{2 x \tanh ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}+\frac{2 \tanh ^{-1}(\tanh (a+b x))^{n+3}}{b^3 (n+1) (n+2) (n+3)}+\frac{x^2 \tanh ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}",1,"(x^2*ArcTanh[Tanh[a + b*x]]^(1 + n))/(b*(1 + n)) - (2*x*ArcTanh[Tanh[a + b*x]]^(2 + n))/(b^2*(1 + n)*(2 + n)) + (2*ArcTanh[Tanh[a + b*x]]^(3 + n))/(b^3*(1 + n)*(2 + n)*(3 + n))","A",4,3,13,0.2308,1,"{2168, 2157, 30}"
269,1,48,0,0.0194814,"\int x \tanh ^{-1}(\tanh (a+b x))^n \, dx","Int[x*ArcTanh[Tanh[a + b*x]]^n,x]","\frac{x \tanh ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}-\frac{\tanh ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}","\frac{x \tanh ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}-\frac{\tanh ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}",1,"(x*ArcTanh[Tanh[a + b*x]]^(1 + n))/(b*(1 + n)) - ArcTanh[Tanh[a + b*x]]^(2 + n)/(b^2*(1 + n)*(2 + n))","A",3,3,11,0.2727,1,"{2168, 2157, 30}"
270,1,20,0,0.0067712,"\int \tanh ^{-1}(\tanh (a+b x))^n \, dx","Int[ArcTanh[Tanh[a + b*x]]^n,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}","\frac{\tanh ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}",1,"ArcTanh[Tanh[a + b*x]]^(1 + n)/(b*(1 + n))","A",2,2,9,0.2222,1,"{2157, 30}"
271,1,64,0,0.021127,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^n}{x} \, dx","Int[ArcTanh[Tanh[a + b*x]]^n/x,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^{n+1} \, _2F_1\left(1,n+1;n+2;-\frac{\tanh ^{-1}(\tanh (a+b x))}{b x-\tanh ^{-1}(\tanh (a+b x))}\right)}{(n+1) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}","\frac{\tanh ^{-1}(\tanh (a+b x))^{n+1} \, _2F_1\left(1,n+1;n+2;-\frac{\tanh ^{-1}(\tanh (a+b x))}{b x-\tanh ^{-1}(\tanh (a+b x))}\right)}{(n+1) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"(ArcTanh[Tanh[a + b*x]]^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, -(ArcTanh[Tanh[a + b*x]]/(b*x - ArcTanh[Tanh[a + b*x]]))])/((1 + n)*(b*x - ArcTanh[Tanh[a + b*x]]))","A",1,1,13,0.07692,1,"{2164}"
272,1,71,0,0.0415182,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^n}{x^2} \, dx","Int[ArcTanh[Tanh[a + b*x]]^n/x^2,x]","\frac{b \tanh ^{-1}(\tanh (a+b x))^n \, _2F_1\left(1,n;n+1;-\frac{\tanh ^{-1}(\tanh (a+b x))}{b x-\tanh ^{-1}(\tanh (a+b x))}\right)}{b x-\tanh ^{-1}(\tanh (a+b x))}-\frac{\tanh ^{-1}(\tanh (a+b x))^n}{x}","\frac{b \tanh ^{-1}(\tanh (a+b x))^n \, _2F_1\left(1,n;n+1;-\frac{\tanh ^{-1}(\tanh (a+b x))}{b x-\tanh ^{-1}(\tanh (a+b x))}\right)}{b x-\tanh ^{-1}(\tanh (a+b x))}-\frac{\tanh ^{-1}(\tanh (a+b x))^n}{x}",1,"-(ArcTanh[Tanh[a + b*x]]^n/x) + (b*ArcTanh[Tanh[a + b*x]]^n*Hypergeometric2F1[1, n, 1 + n, -(ArcTanh[Tanh[a + b*x]]/(b*x - ArcTanh[Tanh[a + b*x]]))])/(b*x - ArcTanh[Tanh[a + b*x]])","A",2,2,13,0.1538,1,"{2168, 2164}"
273,1,101,0,0.0668799,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^n}{x^3} \, dx","Int[ArcTanh[Tanh[a + b*x]]^n/x^3,x]","\frac{b^2 n \tanh ^{-1}(\tanh (a+b x))^{n-1} \, _2F_1\left(1,n-1;n;-\frac{\tanh ^{-1}(\tanh (a+b x))}{b x-\tanh ^{-1}(\tanh (a+b x))}\right)}{2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{\tanh ^{-1}(\tanh (a+b x))^n}{2 x^2}-\frac{b n \tanh ^{-1}(\tanh (a+b x))^{n-1}}{2 x}","\frac{b^2 n \tanh ^{-1}(\tanh (a+b x))^{n-1} \, _2F_1\left(1,n-1;n;-\frac{\tanh ^{-1}(\tanh (a+b x))}{b x-\tanh ^{-1}(\tanh (a+b x))}\right)}{2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}-\frac{\tanh ^{-1}(\tanh (a+b x))^n}{2 x^2}-\frac{b n \tanh ^{-1}(\tanh (a+b x))^{n-1}}{2 x}",1,"-(b*n*ArcTanh[Tanh[a + b*x]]^(-1 + n))/(2*x) - ArcTanh[Tanh[a + b*x]]^n/(2*x^2) + (b^2*n*ArcTanh[Tanh[a + b*x]]^(-1 + n)*Hypergeometric2F1[1, -1 + n, n, -(ArcTanh[Tanh[a + b*x]]/(b*x - ArcTanh[Tanh[a + b*x]]))])/(2*(b*x - ArcTanh[Tanh[a + b*x]]))","A",3,2,13,0.1538,1,"{2168, 2164}"
274,1,37,0,0.0181243,"\int x^m \coth ^{-1}(\tanh (a+b x)) \, dx","Int[x^m*ArcCoth[Tanh[a + b*x]],x]","\frac{x^{m+1} \coth ^{-1}(\tanh (a+b x))}{m+1}-\frac{b x^{m+2}}{m^2+3 m+2}","\frac{x^{m+1} \coth ^{-1}(\tanh (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)*ArcCoth[Tanh[a + b*x]])/(1 + m)","A",2,2,11,0.1818,1,"{2168, 30}"
275,1,23,0,0.0196044,"\int x^2 \tanh ^{-1}(\coth (a+b x)) \, dx","Int[x^2*ArcTanh[Coth[a + b*x]],x]","\frac{1}{3} x^3 \tanh ^{-1}(\coth (a+b x))-\frac{b x^4}{12}","\frac{1}{3} x^3 \tanh ^{-1}(\coth (a+b x))-\frac{b x^4}{12}",1,"-(b*x^4)/12 + (x^3*ArcTanh[Coth[a + b*x]])/3","A",2,2,11,0.1818,1,"{2168, 30}"
276,1,23,0,0.0070311,"\int x \tanh ^{-1}(\coth (a+b x)) \, dx","Int[x*ArcTanh[Coth[a + b*x]],x]","\frac{1}{2} x^2 \tanh ^{-1}(\coth (a+b x))-\frac{b x^3}{6}","\frac{1}{2} x^2 \tanh ^{-1}(\coth (a+b x))-\frac{b x^3}{6}",1,"-(b*x^3)/6 + (x^2*ArcTanh[Coth[a + b*x]])/2","A",2,2,9,0.2222,1,"{6241, 30}"
277,1,16,0,0.0031824,"\int \tanh ^{-1}(\coth (a+b x)) \, dx","Int[ArcTanh[Coth[a + b*x]],x]","\frac{\tanh ^{-1}(\coth (a+b x))^2}{2 b}","\frac{\tanh ^{-1}(\coth (a+b x))^2}{2 b}",1,"ArcTanh[Coth[a + b*x]]^2/(2*b)","A",2,2,7,0.2857,1,"{2157, 30}"
278,1,21,0,0.0303547,"\int \frac{\tanh ^{-1}(\coth (a+b x))}{x} \, dx","Int[ArcTanh[Coth[a + b*x]]/x,x]","b x-\log (x) \left(b x-\tanh ^{-1}(\coth (a+b x))\right)","b x-\log (x) \left(b x-\tanh ^{-1}(\coth (a+b x))\right)",1,"b*x - (b*x - ArcTanh[Coth[a + b*x]])*Log[x]","A",2,2,11,0.1818,1,"{2158, 29}"
279,1,17,0,0.0082163,"\int \frac{\tanh ^{-1}(\coth (a+b x))}{x^2} \, dx","Int[ArcTanh[Coth[a + b*x]]/x^2,x]","b \log (x)-\frac{\tanh ^{-1}(\coth (a+b x))}{x}","b \log (x)-\frac{\tanh ^{-1}(\coth (a+b x))}{x}",1,"-(ArcTanh[Coth[a + b*x]]/x) + b*Log[x]","A",2,2,11,0.1818,1,"{2168, 29}"
280,1,23,0,0.0089536,"\int \frac{\tanh ^{-1}(\coth (a+b x))}{x^3} \, dx","Int[ArcTanh[Coth[a + b*x]]/x^3,x]","-\frac{\tanh ^{-1}(\coth (a+b x))}{2 x^2}-\frac{b}{2 x}","-\frac{\tanh ^{-1}(\coth (a+b x))}{2 x^2}-\frac{b}{2 x}",1,"-b/(2*x) - ArcTanh[Coth[a + b*x]]/(2*x^2)","A",2,2,11,0.1818,1,"{2168, 30}"
281,1,27,0,0.0319938,"\int \tanh ^{-1}(\cosh (x)) \, dx","Int[ArcTanh[Cosh[x]],x]","-\text{PolyLog}\left(2,-e^x\right)+\text{PolyLog}\left(2,e^x\right)-2 x \tanh ^{-1}\left(e^x\right)+x \tanh ^{-1}(\cosh (x))","-\text{PolyLog}\left(2,-e^x\right)+\text{PolyLog}\left(2,e^x\right)-2 x \tanh ^{-1}\left(e^x\right)+x \tanh ^{-1}(\cosh (x))",1,"-2*x*ArcTanh[E^x] + x*ArcTanh[Cosh[x]] - PolyLog[2, -E^x] + PolyLog[2, E^x]","A",6,4,3,1.333,1,"{6271, 4182, 2279, 2391}"
282,1,51,0,0.0609738,"\int x \tanh ^{-1}(\cosh (x)) \, dx","Int[x*ArcTanh[Cosh[x]],x]","-x \text{PolyLog}\left(2,-e^x\right)+x \text{PolyLog}\left(2,e^x\right)+\text{PolyLog}\left(3,-e^x\right)-\text{PolyLog}\left(3,e^x\right)+x^2 \left(-\tanh ^{-1}\left(e^x\right)\right)+\frac{1}{2} x^2 \tanh ^{-1}(\cosh (x))","-x \text{PolyLog}\left(2,-e^x\right)+x \text{PolyLog}\left(2,e^x\right)+\text{PolyLog}\left(3,-e^x\right)-\text{PolyLog}\left(3,e^x\right)+x^2 \left(-\tanh ^{-1}\left(e^x\right)\right)+\frac{1}{2} x^2 \tanh ^{-1}(\cosh (x))",1,"-(x^2*ArcTanh[E^x]) + (x^2*ArcTanh[Cosh[x]])/2 - x*PolyLog[2, -E^x] + x*PolyLog[2, E^x] + PolyLog[3, -E^x] - PolyLog[3, E^x]","A",8,5,5,1.000,1,"{6273, 4182, 2531, 2282, 6589}"
283,1,77,0,0.0864298,"\int x^2 \tanh ^{-1}(\cosh (x)) \, dx","Int[x^2*ArcTanh[Cosh[x]],x]","-x^2 \text{PolyLog}\left(2,-e^x\right)+x^2 \text{PolyLog}\left(2,e^x\right)+2 x \text{PolyLog}\left(3,-e^x\right)-2 x \text{PolyLog}\left(3,e^x\right)-2 \text{PolyLog}\left(4,-e^x\right)+2 \text{PolyLog}\left(4,e^x\right)-\frac{2}{3} x^3 \tanh ^{-1}\left(e^x\right)+\frac{1}{3} x^3 \tanh ^{-1}(\cosh (x))","-x^2 \text{PolyLog}\left(2,-e^x\right)+x^2 \text{PolyLog}\left(2,e^x\right)+2 x \text{PolyLog}\left(3,-e^x\right)-2 x \text{PolyLog}\left(3,e^x\right)-2 \text{PolyLog}\left(4,-e^x\right)+2 \text{PolyLog}\left(4,e^x\right)-\frac{2}{3} x^3 \tanh ^{-1}\left(e^x\right)+\frac{1}{3} x^3 \tanh ^{-1}(\cosh (x))",1,"(-2*x^3*ArcTanh[E^x])/3 + (x^3*ArcTanh[Cosh[x]])/3 - x^2*PolyLog[2, -E^x] + x^2*PolyLog[2, E^x] + 2*x*PolyLog[3, -E^x] - 2*x*PolyLog[3, E^x] - 2*PolyLog[4, -E^x] + 2*PolyLog[4, E^x]","A",10,6,7,0.8571,1,"{6273, 4182, 2531, 6609, 2282, 6589}"
284,1,307,0,0.4687646,"\int x^2 \tanh ^{-1}(c+d \tanh (a+b x)) \, dx","Int[x^2*ArcTanh[c + d*Tanh[a + b*x]],x]","-\frac{x \text{PolyLog}\left(3,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b^2}+\frac{x \text{PolyLog}\left(3,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b^2}+\frac{\text{PolyLog}\left(4,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^3}-\frac{\text{PolyLog}\left(4,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^3}+\frac{x^2 \text{PolyLog}\left(2,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x^2 \text{PolyLog}\left(2,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{6} x^3 \log \left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}+1\right)-\frac{1}{6} x^3 \log \left(\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}+1\right)+\frac{1}{3} x^3 \tanh ^{-1}(d \tanh (a+b x)+c)","-\frac{x \text{PolyLog}\left(3,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b^2}+\frac{x \text{PolyLog}\left(3,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b^2}+\frac{\text{PolyLog}\left(4,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^3}-\frac{\text{PolyLog}\left(4,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^3}+\frac{x^2 \text{PolyLog}\left(2,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x^2 \text{PolyLog}\left(2,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{6} x^3 \log \left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}+1\right)-\frac{1}{6} x^3 \log \left(\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}+1\right)+\frac{1}{3} x^3 \tanh ^{-1}(d \tanh (a+b x)+c)",1,"(x^3*ArcTanh[c + d*Tanh[a + b*x]])/3 + (x^3*Log[1 + ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/6 - (x^3*Log[1 + ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/6 + (x^2*PolyLog[2, -(((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d))])/(4*b) - (x^2*PolyLog[2, -(((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d))])/(4*b) - (x*PolyLog[3, -(((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d))])/(4*b^2) + (x*PolyLog[3, -(((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d))])/(4*b^2) + PolyLog[4, -(((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d))]/(8*b^3) - PolyLog[4, -(((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d))]/(8*b^3)","A",11,6,15,0.4000,1,"{6243, 2190, 2531, 6609, 2282, 6589}"
285,1,231,0,0.3706687,"\int x \tanh ^{-1}(c+d \tanh (a+b x)) \, dx","Int[x*ArcTanh[c + d*Tanh[a + b*x]],x]","-\frac{\text{PolyLog}\left(3,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^2}+\frac{\text{PolyLog}\left(3,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^2}+\frac{x \text{PolyLog}\left(2,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x \text{PolyLog}\left(2,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{4} x^2 \log \left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}+1\right)-\frac{1}{4} x^2 \log \left(\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}+1\right)+\frac{1}{2} x^2 \tanh ^{-1}(d \tanh (a+b x)+c)","-\frac{\text{PolyLog}\left(3,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^2}+\frac{\text{PolyLog}\left(3,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^2}+\frac{x \text{PolyLog}\left(2,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x \text{PolyLog}\left(2,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{4} x^2 \log \left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}+1\right)-\frac{1}{4} x^2 \log \left(\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}+1\right)+\frac{1}{2} x^2 \tanh ^{-1}(d \tanh (a+b x)+c)",1,"(x^2*ArcTanh[c + d*Tanh[a + b*x]])/2 + (x^2*Log[1 + ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/4 - (x^2*Log[1 + ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/4 + (x*PolyLog[2, -(((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d))])/(4*b) - (x*PolyLog[2, -(((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d))])/(4*b) - PolyLog[3, -(((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d))]/(8*b^2) + PolyLog[3, -(((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d))]/(8*b^2)","A",9,5,13,0.3846,1,"{6243, 2190, 2531, 2282, 6589}"
286,1,150,0,0.2218496,"\int \tanh ^{-1}(c+d \tanh (a+b x)) \, dx","Int[ArcTanh[c + d*Tanh[a + b*x]],x]","\frac{\text{PolyLog}\left(2,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{\text{PolyLog}\left(2,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{2} x \log \left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}+1\right)-\frac{1}{2} x \log \left(\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}+1\right)+x \tanh ^{-1}(d \tanh (a+b x)+c)","\frac{\text{PolyLog}\left(2,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{\text{PolyLog}\left(2,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{2} x \log \left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}+1\right)-\frac{1}{2} x \log \left(\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}+1\right)+x \tanh ^{-1}(d \tanh (a+b x)+c)",1,"x*ArcTanh[c + d*Tanh[a + b*x]] + (x*Log[1 + ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/2 - (x*Log[1 + ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/2 + PolyLog[2, -(((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d))]/(4*b) - PolyLog[2, -(((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d))]/(4*b)","A",7,4,11,0.3636,1,"{6235, 2190, 2279, 2391}"
287,0,0,0,0.1409791,"\int \frac{\tanh ^{-1}(c+d \tanh (a+b x))}{x} \, dx","Int[ArcTanh[c + d*Tanh[a + b*x]]/x,x]","\int \frac{\tanh ^{-1}(c+d \tanh (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tanh ^{-1}(d \tanh (a+b x)+c)}{x},x\right)",0,"Defer[Int][ArcTanh[c + d*Tanh[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
288,1,155,0,0.2959228,"\int x^3 \tanh ^{-1}(1+d+d \tanh (a+b x)) \, dx","Int[x^3*ArcTanh[1 + d + d*Tanh[a + b*x]],x]","\frac{3 x^2 \text{PolyLog}\left(3,-(d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 x \text{PolyLog}\left(4,-(d+1) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 \text{PolyLog}\left(5,-(d+1) e^{2 a+2 b x}\right)}{16 b^4}-\frac{x^3 \text{PolyLog}\left(2,-(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{8} x^4 \log \left((d+1) e^{2 a+2 b x}+1\right)+\frac{1}{4} x^4 \tanh ^{-1}(d \tanh (a+b x)+d+1)+\frac{b x^5}{20}","\frac{3 x^2 \text{PolyLog}\left(3,-(d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 x \text{PolyLog}\left(4,-(d+1) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 \text{PolyLog}\left(5,-(d+1) e^{2 a+2 b x}\right)}{16 b^4}-\frac{x^3 \text{PolyLog}\left(2,-(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{8} x^4 \log \left((d+1) e^{2 a+2 b x}+1\right)+\frac{1}{4} x^4 \tanh ^{-1}(d \tanh (a+b x)+d+1)+\frac{b x^5}{20}",1,"(b*x^5)/20 + (x^4*ArcTanh[1 + d + d*Tanh[a + b*x]])/4 - (x^4*Log[1 + (1 + d)*E^(2*a + 2*b*x)])/8 - (x^3*PolyLog[2, -((1 + d)*E^(2*a + 2*b*x))])/(4*b) + (3*x^2*PolyLog[3, -((1 + d)*E^(2*a + 2*b*x))])/(8*b^2) - (3*x*PolyLog[4, -((1 + d)*E^(2*a + 2*b*x))])/(8*b^3) + (3*PolyLog[5, -((1 + d)*E^(2*a + 2*b*x))])/(16*b^4)","A",8,7,16,0.4375,1,"{6239, 2184, 2190, 2531, 6609, 2282, 6589}"
289,1,128,0,0.2543884,"\int x^2 \tanh ^{-1}(1+d+d \tanh (a+b x)) \, dx","Int[x^2*ArcTanh[1 + d + d*Tanh[a + b*x]],x]","\frac{x \text{PolyLog}\left(3,-(d+1) e^{2 a+2 b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,-(d+1) e^{2 a+2 b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,-(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left((d+1) e^{2 a+2 b x}+1\right)+\frac{1}{3} x^3 \tanh ^{-1}(d \tanh (a+b x)+d+1)+\frac{b x^4}{12}","\frac{x \text{PolyLog}\left(3,-(d+1) e^{2 a+2 b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,-(d+1) e^{2 a+2 b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,-(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left((d+1) e^{2 a+2 b x}+1\right)+\frac{1}{3} x^3 \tanh ^{-1}(d \tanh (a+b x)+d+1)+\frac{b x^4}{12}",1,"(b*x^4)/12 + (x^3*ArcTanh[1 + d + d*Tanh[a + b*x]])/3 - (x^3*Log[1 + (1 + d)*E^(2*a + 2*b*x)])/6 - (x^2*PolyLog[2, -((1 + d)*E^(2*a + 2*b*x))])/(4*b) + (x*PolyLog[3, -((1 + d)*E^(2*a + 2*b*x))])/(4*b^2) - PolyLog[4, -((1 + d)*E^(2*a + 2*b*x))]/(8*b^3)","A",7,7,16,0.4375,1,"{6239, 2184, 2190, 2531, 6609, 2282, 6589}"
290,1,101,0,0.2235755,"\int x \tanh ^{-1}(1+d+d \tanh (a+b x)) \, dx","Int[x*ArcTanh[1 + d + d*Tanh[a + b*x]],x]","\frac{\text{PolyLog}\left(3,-(d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,-(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left((d+1) e^{2 a+2 b x}+1\right)+\frac{1}{2} x^2 \tanh ^{-1}(d \tanh (a+b x)+d+1)+\frac{b x^3}{6}","\frac{\text{PolyLog}\left(3,-(d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,-(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left((d+1) e^{2 a+2 b x}+1\right)+\frac{1}{2} x^2 \tanh ^{-1}(d \tanh (a+b x)+d+1)+\frac{b x^3}{6}",1,"(b*x^3)/6 + (x^2*ArcTanh[1 + d + d*Tanh[a + b*x]])/2 - (x^2*Log[1 + (1 + d)*E^(2*a + 2*b*x)])/4 - (x*PolyLog[2, -((1 + d)*E^(2*a + 2*b*x))])/(4*b) + PolyLog[3, -((1 + d)*E^(2*a + 2*b*x))]/(8*b^2)","A",6,6,14,0.4286,1,"{6239, 2184, 2190, 2531, 2282, 6589}"
291,1,69,0,0.1367165,"\int \tanh ^{-1}(1+d+d \tanh (a+b x)) \, dx","Int[ArcTanh[1 + d + d*Tanh[a + b*x]],x]","-\frac{\text{PolyLog}\left(2,-(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} x \log \left((d+1) e^{2 a+2 b x}+1\right)+x \tanh ^{-1}(d \tanh (a+b x)+d+1)+\frac{b x^2}{2}","-\frac{\text{PolyLog}\left(2,-(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} x \log \left((d+1) e^{2 a+2 b x}+1\right)+x \tanh ^{-1}(d \tanh (a+b x)+d+1)+\frac{b x^2}{2}",1,"(b*x^2)/2 + x*ArcTanh[1 + d + d*Tanh[a + b*x]] - (x*Log[1 + (1 + d)*E^(2*a + 2*b*x)])/2 - PolyLog[2, -((1 + d)*E^(2*a + 2*b*x))]/(4*b)","A",5,5,12,0.4167,1,"{6231, 2184, 2190, 2279, 2391}"
292,0,0,0,0.0790353,"\int \frac{\tanh ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx","Int[ArcTanh[1 + d + d*Tanh[a + b*x]]/x,x]","\int \frac{\tanh ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tanh ^{-1}(d \tanh (a+b x)+d+1)}{x},x\right)",0,"Defer[Int][ArcTanh[1 + d + d*Tanh[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
293,1,168,0,0.296893,"\int x^3 \tanh ^{-1}(1-d-d \tanh (a+b x)) \, dx","Int[x^3*ArcTanh[1 - d - d*Tanh[a + b*x]],x]","\frac{3 x^2 \text{PolyLog}\left(3,-(1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 x \text{PolyLog}\left(4,-(1-d) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 \text{PolyLog}\left(5,-(1-d) e^{2 a+2 b x}\right)}{16 b^4}-\frac{x^3 \text{PolyLog}\left(2,-(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{8} x^4 \log \left((1-d) e^{2 a+2 b x}+1\right)+\frac{1}{4} x^4 \tanh ^{-1}(d (-\tanh (a+b x))-d+1)+\frac{b x^5}{20}","\frac{3 x^2 \text{PolyLog}\left(3,-(1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 x \text{PolyLog}\left(4,-(1-d) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 \text{PolyLog}\left(5,-(1-d) e^{2 a+2 b x}\right)}{16 b^4}-\frac{x^3 \text{PolyLog}\left(2,-(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{8} x^4 \log \left((1-d) e^{2 a+2 b x}+1\right)+\frac{1}{4} x^4 \tanh ^{-1}(d (-\tanh (a+b x))-d+1)+\frac{b x^5}{20}",1,"(b*x^5)/20 + (x^4*ArcTanh[1 - d - d*Tanh[a + b*x]])/4 - (x^4*Log[1 + (1 - d)*E^(2*a + 2*b*x)])/8 - (x^3*PolyLog[2, -((1 - d)*E^(2*a + 2*b*x))])/(4*b) + (3*x^2*PolyLog[3, -((1 - d)*E^(2*a + 2*b*x))])/(8*b^2) - (3*x*PolyLog[4, -((1 - d)*E^(2*a + 2*b*x))])/(8*b^3) + (3*PolyLog[5, -((1 - d)*E^(2*a + 2*b*x))])/(16*b^4)","A",8,7,19,0.3684,1,"{6239, 2184, 2190, 2531, 6609, 2282, 6589}"
294,1,139,0,0.2584346,"\int x^2 \tanh ^{-1}(1-d-d \tanh (a+b x)) \, dx","Int[x^2*ArcTanh[1 - d - d*Tanh[a + b*x]],x]","\frac{x \text{PolyLog}\left(3,-(1-d) e^{2 a+2 b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,-(1-d) e^{2 a+2 b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,-(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left((1-d) e^{2 a+2 b x}+1\right)+\frac{1}{3} x^3 \tanh ^{-1}(d (-\tanh (a+b x))-d+1)+\frac{b x^4}{12}","\frac{x \text{PolyLog}\left(3,-(1-d) e^{2 a+2 b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,-(1-d) e^{2 a+2 b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,-(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left((1-d) e^{2 a+2 b x}+1\right)+\frac{1}{3} x^3 \tanh ^{-1}(d (-\tanh (a+b x))-d+1)+\frac{b x^4}{12}",1,"(b*x^4)/12 + (x^3*ArcTanh[1 - d - d*Tanh[a + b*x]])/3 - (x^3*Log[1 + (1 - d)*E^(2*a + 2*b*x)])/6 - (x^2*PolyLog[2, -((1 - d)*E^(2*a + 2*b*x))])/(4*b) + (x*PolyLog[3, -((1 - d)*E^(2*a + 2*b*x))])/(4*b^2) - PolyLog[4, -((1 - d)*E^(2*a + 2*b*x))]/(8*b^3)","A",7,7,19,0.3684,1,"{6239, 2184, 2190, 2531, 6609, 2282, 6589}"
295,1,110,0,0.2239666,"\int x \tanh ^{-1}(1-d-d \tanh (a+b x)) \, dx","Int[x*ArcTanh[1 - d - d*Tanh[a + b*x]],x]","\frac{\text{PolyLog}\left(3,-(1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,-(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left((1-d) e^{2 a+2 b x}+1\right)+\frac{1}{2} x^2 \tanh ^{-1}(d (-\tanh (a+b x))-d+1)+\frac{b x^3}{6}","\frac{\text{PolyLog}\left(3,-(1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,-(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left((1-d) e^{2 a+2 b x}+1\right)+\frac{1}{2} x^2 \tanh ^{-1}(d (-\tanh (a+b x))-d+1)+\frac{b x^3}{6}",1,"(b*x^3)/6 + (x^2*ArcTanh[1 - d - d*Tanh[a + b*x]])/2 - (x^2*Log[1 + (1 - d)*E^(2*a + 2*b*x)])/4 - (x*PolyLog[2, -((1 - d)*E^(2*a + 2*b*x))])/(4*b) + PolyLog[3, -((1 - d)*E^(2*a + 2*b*x))]/(8*b^2)","A",6,6,17,0.3529,1,"{6239, 2184, 2190, 2531, 2282, 6589}"
296,1,76,0,0.1383538,"\int \tanh ^{-1}(1-d-d \tanh (a+b x)) \, dx","Int[ArcTanh[1 - d - d*Tanh[a + b*x]],x]","-\frac{\text{PolyLog}\left(2,-(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} x \log \left((1-d) e^{2 a+2 b x}+1\right)+x \tanh ^{-1}(d (-\tanh (a+b x))-d+1)+\frac{b x^2}{2}","-\frac{\text{PolyLog}\left(2,-(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} x \log \left((1-d) e^{2 a+2 b x}+1\right)+x \tanh ^{-1}(d (-\tanh (a+b x))-d+1)+\frac{b x^2}{2}",1,"(b*x^2)/2 + x*ArcTanh[1 - d - d*Tanh[a + b*x]] - (x*Log[1 + (1 - d)*E^(2*a + 2*b*x)])/2 - PolyLog[2, -((1 - d)*E^(2*a + 2*b*x))]/(4*b)","A",5,5,15,0.3333,1,"{6231, 2184, 2190, 2279, 2391}"
297,0,0,0,0.0667474,"\int \frac{\tanh ^{-1}(1-d-d \tanh (a+b x))}{x} \, dx","Int[ArcTanh[1 - d - d*Tanh[a + b*x]]/x,x]","\int \frac{\tanh ^{-1}(1-d-d \tanh (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tanh ^{-1}(d (-\tanh (a+b x))-d+1)}{x},x\right)",0,"Defer[Int][ArcTanh[1 - d - d*Tanh[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
298,1,303,0,0.4566859,"\int x^2 \tanh ^{-1}(c+d \coth (a+b x)) \, dx","Int[x^2*ArcTanh[c + d*Coth[a + b*x]],x]","-\frac{x \text{PolyLog}\left(3,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b^2}+\frac{x \text{PolyLog}\left(3,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b^2}+\frac{\text{PolyLog}\left(4,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^3}-\frac{\text{PolyLog}\left(4,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^3}+\frac{x^2 \text{PolyLog}\left(2,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x^2 \text{PolyLog}\left(2,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{6} x^3 \log \left(1-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)-\frac{1}{6} x^3 \log \left(1-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d \coth (a+b x)+c)","-\frac{x \text{PolyLog}\left(3,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b^2}+\frac{x \text{PolyLog}\left(3,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b^2}+\frac{\text{PolyLog}\left(4,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^3}-\frac{\text{PolyLog}\left(4,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^3}+\frac{x^2 \text{PolyLog}\left(2,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x^2 \text{PolyLog}\left(2,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{6} x^3 \log \left(1-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)-\frac{1}{6} x^3 \log \left(1-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d \coth (a+b x)+c)",1,"(x^3*ArcTanh[c + d*Coth[a + b*x]])/3 + (x^3*Log[1 - ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/6 - (x^3*Log[1 - ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/6 + (x^2*PolyLog[2, ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/(4*b) - (x^2*PolyLog[2, ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/(4*b) - (x*PolyLog[3, ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/(4*b^2) + (x*PolyLog[3, ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/(4*b^2) + PolyLog[4, ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)]/(8*b^3) - PolyLog[4, ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)]/(8*b^3)","A",11,6,15,0.4000,1,"{6245, 2190, 2531, 6609, 2282, 6589}"
299,1,229,0,0.3716005,"\int x \tanh ^{-1}(c+d \coth (a+b x)) \, dx","Int[x*ArcTanh[c + d*Coth[a + b*x]],x]","-\frac{\text{PolyLog}\left(3,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^2}+\frac{\text{PolyLog}\left(3,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^2}+\frac{x \text{PolyLog}\left(2,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x \text{PolyLog}\left(2,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{4} x^2 \log \left(1-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)-\frac{1}{4} x^2 \log \left(1-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d \coth (a+b x)+c)","-\frac{\text{PolyLog}\left(3,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^2}+\frac{\text{PolyLog}\left(3,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^2}+\frac{x \text{PolyLog}\left(2,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x \text{PolyLog}\left(2,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{4} x^2 \log \left(1-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)-\frac{1}{4} x^2 \log \left(1-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d \coth (a+b x)+c)",1,"(x^2*ArcTanh[c + d*Coth[a + b*x]])/2 + (x^2*Log[1 - ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/4 - (x^2*Log[1 - ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/4 + (x*PolyLog[2, ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/(4*b) - (x*PolyLog[2, ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/(4*b) - PolyLog[3, ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)]/(8*b^2) + PolyLog[3, ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)]/(8*b^2)","A",9,5,13,0.3846,1,"{6245, 2190, 2531, 2282, 6589}"
300,1,150,0,0.2271156,"\int \tanh ^{-1}(c+d \coth (a+b x)) \, dx","Int[ArcTanh[c + d*Coth[a + b*x]],x]","\frac{\text{PolyLog}\left(2,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{\text{PolyLog}\left(2,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{2} x \log \left(1-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)-\frac{1}{2} x \log \left(1-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)+x \tanh ^{-1}(d \coth (a+b x)+c)","\frac{\text{PolyLog}\left(2,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{\text{PolyLog}\left(2,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{2} x \log \left(1-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)-\frac{1}{2} x \log \left(1-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)+x \tanh ^{-1}(d \coth (a+b x)+c)",1,"x*ArcTanh[c + d*Coth[a + b*x]] + (x*Log[1 - ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/2 - (x*Log[1 - ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/2 + PolyLog[2, ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)]/(4*b) - PolyLog[2, ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)]/(4*b)","A",7,4,11,0.3636,1,"{6237, 2190, 2279, 2391}"
301,0,0,0,0.1410199,"\int \frac{\tanh ^{-1}(c+d \coth (a+b x))}{x} \, dx","Int[ArcTanh[c + d*Coth[a + b*x]]/x,x]","\int \frac{\tanh ^{-1}(c+d \coth (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tanh ^{-1}(d \coth (a+b x)+c)}{x},x\right)",0,"Defer[Int][ArcTanh[c + d*Coth[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
302,1,152,0,0.3038118,"\int x^3 \tanh ^{-1}(1+d+d \coth (a+b x)) \, dx","Int[x^3*ArcTanh[1 + d + d*Coth[a + b*x]],x]","\frac{3 x^2 \text{PolyLog}\left(3,(d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 x \text{PolyLog}\left(4,(d+1) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 \text{PolyLog}\left(5,(d+1) e^{2 a+2 b x}\right)}{16 b^4}-\frac{x^3 \text{PolyLog}\left(2,(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{8} x^4 \log \left(1-(d+1) e^{2 a+2 b x}\right)+\frac{1}{4} x^4 \tanh ^{-1}(d \coth (a+b x)+d+1)+\frac{b x^5}{20}","\frac{3 x^2 \text{PolyLog}\left(3,(d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 x \text{PolyLog}\left(4,(d+1) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 \text{PolyLog}\left(5,(d+1) e^{2 a+2 b x}\right)}{16 b^4}-\frac{x^3 \text{PolyLog}\left(2,(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{8} x^4 \log \left(1-(d+1) e^{2 a+2 b x}\right)+\frac{1}{4} x^4 \tanh ^{-1}(d \coth (a+b x)+d+1)+\frac{b x^5}{20}",1,"(b*x^5)/20 + (x^4*ArcTanh[1 + d + d*Coth[a + b*x]])/4 - (x^4*Log[1 - (1 + d)*E^(2*a + 2*b*x)])/8 - (x^3*PolyLog[2, (1 + d)*E^(2*a + 2*b*x)])/(4*b) + (3*x^2*PolyLog[3, (1 + d)*E^(2*a + 2*b*x)])/(8*b^2) - (3*x*PolyLog[4, (1 + d)*E^(2*a + 2*b*x)])/(8*b^3) + (3*PolyLog[5, (1 + d)*E^(2*a + 2*b*x)])/(16*b^4)","A",8,7,16,0.4375,1,"{6241, 2184, 2190, 2531, 6609, 2282, 6589}"
303,1,126,0,0.258996,"\int x^2 \tanh ^{-1}(1+d+d \coth (a+b x)) \, dx","Int[x^2*ArcTanh[1 + d + d*Coth[a + b*x]],x]","\frac{x \text{PolyLog}\left(3,(d+1) e^{2 a+2 b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,(d+1) e^{2 a+2 b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1-(d+1) e^{2 a+2 b x}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d \coth (a+b x)+d+1)+\frac{b x^4}{12}","\frac{x \text{PolyLog}\left(3,(d+1) e^{2 a+2 b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,(d+1) e^{2 a+2 b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1-(d+1) e^{2 a+2 b x}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d \coth (a+b x)+d+1)+\frac{b x^4}{12}",1,"(b*x^4)/12 + (x^3*ArcTanh[1 + d + d*Coth[a + b*x]])/3 - (x^3*Log[1 - (1 + d)*E^(2*a + 2*b*x)])/6 - (x^2*PolyLog[2, (1 + d)*E^(2*a + 2*b*x)])/(4*b) + (x*PolyLog[3, (1 + d)*E^(2*a + 2*b*x)])/(4*b^2) - PolyLog[4, (1 + d)*E^(2*a + 2*b*x)]/(8*b^3)","A",7,7,16,0.4375,1,"{6241, 2184, 2190, 2531, 6609, 2282, 6589}"
304,1,100,0,0.229627,"\int x \tanh ^{-1}(1+d+d \coth (a+b x)) \, dx","Int[x*ArcTanh[1 + d + d*Coth[a + b*x]],x]","\frac{\text{PolyLog}\left(3,(d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1-(d+1) e^{2 a+2 b x}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d \coth (a+b x)+d+1)+\frac{b x^3}{6}","\frac{\text{PolyLog}\left(3,(d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1-(d+1) e^{2 a+2 b x}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d \coth (a+b x)+d+1)+\frac{b x^3}{6}",1,"(b*x^3)/6 + (x^2*ArcTanh[1 + d + d*Coth[a + b*x]])/2 - (x^2*Log[1 - (1 + d)*E^(2*a + 2*b*x)])/4 - (x*PolyLog[2, (1 + d)*E^(2*a + 2*b*x)])/(4*b) + PolyLog[3, (1 + d)*E^(2*a + 2*b*x)]/(8*b^2)","A",6,6,14,0.4286,1,"{6241, 2184, 2190, 2531, 2282, 6589}"
305,1,69,0,0.1420004,"\int \tanh ^{-1}(1+d+d \coth (a+b x)) \, dx","Int[ArcTanh[1 + d + d*Coth[a + b*x]],x]","-\frac{\text{PolyLog}\left(2,(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} x \log \left(1-(d+1) e^{2 a+2 b x}\right)+x \tanh ^{-1}(d \coth (a+b x)+d+1)+\frac{b x^2}{2}","-\frac{\text{PolyLog}\left(2,(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} x \log \left(1-(d+1) e^{2 a+2 b x}\right)+x \tanh ^{-1}(d \coth (a+b x)+d+1)+\frac{b x^2}{2}",1,"(b*x^2)/2 + x*ArcTanh[1 + d + d*Coth[a + b*x]] - (x*Log[1 - (1 + d)*E^(2*a + 2*b*x)])/2 - PolyLog[2, (1 + d)*E^(2*a + 2*b*x)]/(4*b)","A",5,5,12,0.4167,1,"{6233, 2184, 2190, 2279, 2391}"
306,0,0,0,0.0776305,"\int \frac{\tanh ^{-1}(1+d+d \coth (a+b x))}{x} \, dx","Int[ArcTanh[1 + d + d*Coth[a + b*x]]/x,x]","\int \frac{\tanh ^{-1}(1+d+d \coth (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tanh ^{-1}(d \coth (a+b x)+d+1)}{x},x\right)",0,"Defer[Int][ArcTanh[1 + d + d*Coth[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
307,1,165,0,0.2992629,"\int x^3 \tanh ^{-1}(1-d-d \coth (a+b x)) \, dx","Int[x^3*ArcTanh[1 - d - d*Coth[a + b*x]],x]","\frac{3 x^2 \text{PolyLog}\left(3,(1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 x \text{PolyLog}\left(4,(1-d) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 \text{PolyLog}\left(5,(1-d) e^{2 a+2 b x}\right)}{16 b^4}-\frac{x^3 \text{PolyLog}\left(2,(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{8} x^4 \log \left(1-(1-d) e^{2 a+2 b x}\right)+\frac{1}{4} x^4 \tanh ^{-1}(d (-\coth (a+b x))-d+1)+\frac{b x^5}{20}","\frac{3 x^2 \text{PolyLog}\left(3,(1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 x \text{PolyLog}\left(4,(1-d) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 \text{PolyLog}\left(5,(1-d) e^{2 a+2 b x}\right)}{16 b^4}-\frac{x^3 \text{PolyLog}\left(2,(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{8} x^4 \log \left(1-(1-d) e^{2 a+2 b x}\right)+\frac{1}{4} x^4 \tanh ^{-1}(d (-\coth (a+b x))-d+1)+\frac{b x^5}{20}",1,"(b*x^5)/20 + (x^4*ArcTanh[1 - d - d*Coth[a + b*x]])/4 - (x^4*Log[1 - (1 - d)*E^(2*a + 2*b*x)])/8 - (x^3*PolyLog[2, (1 - d)*E^(2*a + 2*b*x)])/(4*b) + (3*x^2*PolyLog[3, (1 - d)*E^(2*a + 2*b*x)])/(8*b^2) - (3*x*PolyLog[4, (1 - d)*E^(2*a + 2*b*x)])/(8*b^3) + (3*PolyLog[5, (1 - d)*E^(2*a + 2*b*x)])/(16*b^4)","A",8,7,19,0.3684,1,"{6241, 2184, 2190, 2531, 6609, 2282, 6589}"
308,1,137,0,0.2637038,"\int x^2 \tanh ^{-1}(1-d-d \coth (a+b x)) \, dx","Int[x^2*ArcTanh[1 - d - d*Coth[a + b*x]],x]","\frac{x \text{PolyLog}\left(3,(1-d) e^{2 a+2 b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,(1-d) e^{2 a+2 b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1-(1-d) e^{2 a+2 b x}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d (-\coth (a+b x))-d+1)+\frac{b x^4}{12}","\frac{x \text{PolyLog}\left(3,(1-d) e^{2 a+2 b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,(1-d) e^{2 a+2 b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1-(1-d) e^{2 a+2 b x}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d (-\coth (a+b x))-d+1)+\frac{b x^4}{12}",1,"(b*x^4)/12 + (x^3*ArcTanh[1 - d - d*Coth[a + b*x]])/3 - (x^3*Log[1 - (1 - d)*E^(2*a + 2*b*x)])/6 - (x^2*PolyLog[2, (1 - d)*E^(2*a + 2*b*x)])/(4*b) + (x*PolyLog[3, (1 - d)*E^(2*a + 2*b*x)])/(4*b^2) - PolyLog[4, (1 - d)*E^(2*a + 2*b*x)]/(8*b^3)","A",7,7,19,0.3684,1,"{6241, 2184, 2190, 2531, 6609, 2282, 6589}"
309,1,109,0,0.2312528,"\int x \tanh ^{-1}(1-d-d \coth (a+b x)) \, dx","Int[x*ArcTanh[1 - d - d*Coth[a + b*x]],x]","\frac{\text{PolyLog}\left(3,(1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1-(1-d) e^{2 a+2 b x}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d (-\coth (a+b x))-d+1)+\frac{b x^3}{6}","\frac{\text{PolyLog}\left(3,(1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1-(1-d) e^{2 a+2 b x}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d (-\coth (a+b x))-d+1)+\frac{b x^3}{6}",1,"(b*x^3)/6 + (x^2*ArcTanh[1 - d - d*Coth[a + b*x]])/2 - (x^2*Log[1 - (1 - d)*E^(2*a + 2*b*x)])/4 - (x*PolyLog[2, (1 - d)*E^(2*a + 2*b*x)])/(4*b) + PolyLog[3, (1 - d)*E^(2*a + 2*b*x)]/(8*b^2)","A",6,6,17,0.3529,1,"{6241, 2184, 2190, 2531, 2282, 6589}"
310,1,76,0,0.1373862,"\int \tanh ^{-1}(1-d-d \coth (a+b x)) \, dx","Int[ArcTanh[1 - d - d*Coth[a + b*x]],x]","-\frac{\text{PolyLog}\left(2,(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} x \log \left(1-(1-d) e^{2 a+2 b x}\right)+x \tanh ^{-1}(d (-\coth (a+b x))-d+1)+\frac{b x^2}{2}","-\frac{\text{PolyLog}\left(2,(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} x \log \left(1-(1-d) e^{2 a+2 b x}\right)+x \tanh ^{-1}(d (-\coth (a+b x))-d+1)+\frac{b x^2}{2}",1,"(b*x^2)/2 + x*ArcTanh[1 - d - d*Coth[a + b*x]] - (x*Log[1 - (1 - d)*E^(2*a + 2*b*x)])/2 - PolyLog[2, (1 - d)*E^(2*a + 2*b*x)]/(4*b)","A",5,5,15,0.3333,1,"{6233, 2184, 2190, 2279, 2391}"
311,0,0,0,0.0888822,"\int \frac{\tanh ^{-1}(1-d-d \coth (a+b x))}{x} \, dx","Int[ArcTanh[1 - d - d*Coth[a + b*x]]/x,x]","\int \frac{\tanh ^{-1}(1-d-d \coth (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tanh ^{-1}(d (-\coth (a+b x))-d+1)}{x},x\right)",0,"Defer[Int][ArcTanh[1 - d - d*Coth[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
312,1,302,0,0.2315031,"\int (e+f x)^3 \tanh ^{-1}(\tan (a+b x)) \, dx","Int[(e + f*x)^3*ArcTanh[Tan[a + b*x]],x]","\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,i e^{2 i (a+b x)}\right)}{8 b^3}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f^3 \text{PolyLog}\left(5,-i e^{2 i (a+b x)}\right)}{16 b^4}+\frac{3 f^3 \text{PolyLog}\left(5,i e^{2 i (a+b x)}\right)}{16 b^4}-\frac{i (e+f x)^3 \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^4 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{4 f}+\frac{(e+f x)^4 \tanh ^{-1}(\tan (a+b x))}{4 f}","\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,i e^{2 i (a+b x)}\right)}{8 b^3}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f^3 \text{PolyLog}\left(5,-i e^{2 i (a+b x)}\right)}{16 b^4}+\frac{3 f^3 \text{PolyLog}\left(5,i e^{2 i (a+b x)}\right)}{16 b^4}-\frac{i (e+f x)^3 \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^4 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{4 f}+\frac{(e+f x)^4 \tanh ^{-1}(\tan (a+b x))}{4 f}",1,"((I/4)*(e + f*x)^4*ArcTan[E^((2*I)*(a + b*x))])/f + ((e + f*x)^4*ArcTanh[Tan[a + b*x]])/(4*f) - ((I/4)*(e + f*x)^3*PolyLog[2, (-I)*E^((2*I)*(a + b*x))])/b + ((I/4)*(e + f*x)^3*PolyLog[2, I*E^((2*I)*(a + b*x))])/b + (3*f*(e + f*x)^2*PolyLog[3, (-I)*E^((2*I)*(a + b*x))])/(8*b^2) - (3*f*(e + f*x)^2*PolyLog[3, I*E^((2*I)*(a + b*x))])/(8*b^2) + (((3*I)/8)*f^2*(e + f*x)*PolyLog[4, (-I)*E^((2*I)*(a + b*x))])/b^3 - (((3*I)/8)*f^2*(e + f*x)*PolyLog[4, I*E^((2*I)*(a + b*x))])/b^3 - (3*f^3*PolyLog[5, (-I)*E^((2*I)*(a + b*x))])/(16*b^4) + (3*f^3*PolyLog[5, I*E^((2*I)*(a + b*x))])/(16*b^4)","A",12,6,15,0.4000,1,"{6251, 4181, 2531, 6609, 2282, 6589}"
313,1,234,0,0.1652407,"\int (e+f x)^2 \tanh ^{-1}(\tan (a+b x)) \, dx","Int[(e + f*x)^2*ArcTanh[Tan[a + b*x]],x]","\frac{f (e+f x) \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{4 b^2}-\frac{f (e+f x) \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{4 b^2}+\frac{i f^2 \text{PolyLog}\left(4,-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i f^2 \text{PolyLog}\left(4,i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i (e+f x)^2 \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{3 f}+\frac{(e+f x)^3 \tanh ^{-1}(\tan (a+b x))}{3 f}","\frac{f (e+f x) \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{4 b^2}-\frac{f (e+f x) \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{4 b^2}+\frac{i f^2 \text{PolyLog}\left(4,-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i f^2 \text{PolyLog}\left(4,i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i (e+f x)^2 \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{3 f}+\frac{(e+f x)^3 \tanh ^{-1}(\tan (a+b x))}{3 f}",1,"((I/3)*(e + f*x)^3*ArcTan[E^((2*I)*(a + b*x))])/f + ((e + f*x)^3*ArcTanh[Tan[a + b*x]])/(3*f) - ((I/4)*(e + f*x)^2*PolyLog[2, (-I)*E^((2*I)*(a + b*x))])/b + ((I/4)*(e + f*x)^2*PolyLog[2, I*E^((2*I)*(a + b*x))])/b + (f*(e + f*x)*PolyLog[3, (-I)*E^((2*I)*(a + b*x))])/(4*b^2) - (f*(e + f*x)*PolyLog[3, I*E^((2*I)*(a + b*x))])/(4*b^2) + ((I/8)*f^2*PolyLog[4, (-I)*E^((2*I)*(a + b*x))])/b^3 - ((I/8)*f^2*PolyLog[4, I*E^((2*I)*(a + b*x))])/b^3","A",10,6,15,0.4000,1,"{6251, 4181, 2531, 6609, 2282, 6589}"
314,1,162,0,0.1080987,"\int (e+f x) \tanh ^{-1}(\tan (a+b x)) \, dx","Int[(e + f*x)*ArcTanh[Tan[a + b*x]],x]","\frac{f \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{f \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{i (e+f x) \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x) \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{2 f}+\frac{(e+f x)^2 \tanh ^{-1}(\tan (a+b x))}{2 f}","\frac{f \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{f \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{i (e+f x) \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x) \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{2 f}+\frac{(e+f x)^2 \tanh ^{-1}(\tan (a+b x))}{2 f}",1,"((I/2)*(e + f*x)^2*ArcTan[E^((2*I)*(a + b*x))])/f + ((e + f*x)^2*ArcTanh[Tan[a + b*x]])/(2*f) - ((I/4)*(e + f*x)*PolyLog[2, (-I)*E^((2*I)*(a + b*x))])/b + ((I/4)*(e + f*x)*PolyLog[2, I*E^((2*I)*(a + b*x))])/b + (f*PolyLog[3, (-I)*E^((2*I)*(a + b*x))])/(8*b^2) - (f*PolyLog[3, I*E^((2*I)*(a + b*x))])/(8*b^2)","A",8,5,13,0.3846,1,"{6251, 4181, 2531, 2282, 6589}"
315,1,79,0,0.04757,"\int \tanh ^{-1}(\tan (a+b x)) \, dx","Int[ArcTanh[Tan[a + b*x]],x]","-\frac{i \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+i x \tan ^{-1}\left(e^{2 i (a+b x)}\right)+x \tanh ^{-1}(\tan (a+b x))","-\frac{i \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+i x \tan ^{-1}\left(e^{2 i (a+b x)}\right)+x \tanh ^{-1}(\tan (a+b x))",1,"I*x*ArcTan[E^((2*I)*(a + b*x))] + x*ArcTanh[Tan[a + b*x]] - ((I/4)*PolyLog[2, (-I)*E^((2*I)*(a + b*x))])/b + ((I/4)*PolyLog[2, I*E^((2*I)*(a + b*x))])/b","A",6,4,7,0.5714,1,"{6247, 4181, 2279, 2391}"
316,0,0,0,0.0400403,"\int \frac{\tanh ^{-1}(\tan (a+b x))}{e+f x} \, dx","Int[ArcTanh[Tan[a + b*x]]/(e + f*x),x]","\int \frac{\tanh ^{-1}(\tan (a+b x))}{e+f x} \, dx","\text{Int}\left(\frac{\tanh ^{-1}(\tan (a+b x))}{e+f x},x\right)",0,"Defer[Int][ArcTanh[Tan[a + b*x]]/(e + f*x), x]","A",0,0,0,0,-1,"{}"
317,1,395,0,0.4986102,"\int x^2 \tanh ^{-1}(c+d \tan (a+b x)) \, dx","Int[x^2*ArcTanh[c + d*Tan[a + b*x]],x]","\frac{x \text{PolyLog}\left(3,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b^2}-\frac{x \text{PolyLog}\left(3,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b^2}+\frac{i \text{PolyLog}\left(4,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{8 b^3}-\frac{i \text{PolyLog}\left(4,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{8 b^3}-\frac{i x^2 \text{PolyLog}\left(2,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b}+\frac{i x^2 \text{PolyLog}\left(2,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b}+\frac{1}{6} x^3 \log \left(1+\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)-\frac{1}{6} x^3 \log \left(1+\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d \tan (a+b x)+c)","\frac{x \text{PolyLog}\left(3,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b^2}-\frac{x \text{PolyLog}\left(3,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b^2}+\frac{i \text{PolyLog}\left(4,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{8 b^3}-\frac{i \text{PolyLog}\left(4,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{8 b^3}-\frac{i x^2 \text{PolyLog}\left(2,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b}+\frac{i x^2 \text{PolyLog}\left(2,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b}+\frac{1}{6} x^3 \log \left(1+\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)-\frac{1}{6} x^3 \log \left(1+\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d \tan (a+b x)+c)",1,"(x^3*ArcTanh[c + d*Tan[a + b*x]])/3 + (x^3*Log[1 + ((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d)])/6 - (x^3*Log[1 + ((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d)])/6 - ((I/4)*x^2*PolyLog[2, -(((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d))])/b + ((I/4)*x^2*PolyLog[2, -(((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d))])/b + (x*PolyLog[3, -(((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d))])/(4*b^2) - (x*PolyLog[3, -(((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d))])/(4*b^2) + ((I/8)*PolyLog[4, -(((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d))])/b^3 - ((I/8)*PolyLog[4, -(((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d))])/b^3","A",11,6,15,0.4000,1,"{6267, 2190, 2531, 6609, 2282, 6589}"
318,1,295,0,0.4033136,"\int x \tanh ^{-1}(c+d \tan (a+b x)) \, dx","Int[x*ArcTanh[c + d*Tan[a + b*x]],x]","\frac{\text{PolyLog}\left(3,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{8 b^2}-\frac{\text{PolyLog}\left(3,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{8 b^2}-\frac{i x \text{PolyLog}\left(2,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b}+\frac{i x \text{PolyLog}\left(2,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b}+\frac{1}{4} x^2 \log \left(1+\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)-\frac{1}{4} x^2 \log \left(1+\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d \tan (a+b x)+c)","\frac{\text{PolyLog}\left(3,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{8 b^2}-\frac{\text{PolyLog}\left(3,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{8 b^2}-\frac{i x \text{PolyLog}\left(2,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b}+\frac{i x \text{PolyLog}\left(2,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b}+\frac{1}{4} x^2 \log \left(1+\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)-\frac{1}{4} x^2 \log \left(1+\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d \tan (a+b x)+c)",1,"(x^2*ArcTanh[c + d*Tan[a + b*x]])/2 + (x^2*Log[1 + ((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d)])/4 - (x^2*Log[1 + ((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d)])/4 - ((I/4)*x*PolyLog[2, -(((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d))])/b + ((I/4)*x*PolyLog[2, -(((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d))])/b + PolyLog[3, -(((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d))]/(8*b^2) - PolyLog[3, -(((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d))]/(8*b^2)","A",9,5,13,0.3846,1,"{6267, 2190, 2531, 2282, 6589}"
319,1,194,0,0.2392752,"\int \tanh ^{-1}(c+d \tan (a+b x)) \, dx","Int[ArcTanh[c + d*Tan[a + b*x]],x]","-\frac{i \text{PolyLog}\left(2,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b}+\frac{1}{2} x \log \left(1+\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)-\frac{1}{2} x \log \left(1+\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)+x \tanh ^{-1}(d \tan (a+b x)+c)","-\frac{i \text{PolyLog}\left(2,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b}+\frac{1}{2} x \log \left(1+\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)-\frac{1}{2} x \log \left(1+\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)+x \tanh ^{-1}(d \tan (a+b x)+c)",1,"x*ArcTanh[c + d*Tan[a + b*x]] + (x*Log[1 + ((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d)])/2 - (x*Log[1 + ((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d)])/2 - ((I/4)*PolyLog[2, -(((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d))])/b + ((I/4)*PolyLog[2, -(((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d))])/b","A",7,4,11,0.3636,1,"{6259, 2190, 2279, 2391}"
320,0,0,0,0.1502907,"\int \frac{\tanh ^{-1}(c+d \tan (a+b x))}{x} \, dx","Int[ArcTanh[c + d*Tan[a + b*x]]/x,x]","\int \frac{\tanh ^{-1}(c+d \tan (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tanh ^{-1}(d \tan (a+b x)+c)}{x},x\right)",0,"Defer[Int][ArcTanh[c + d*Tan[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
321,1,170,0,0.2916128,"\int x^2 \tanh ^{-1}(1-i d+d \tan (a+b x)) \, dx","Int[x^2*ArcTanh[1 - I*d + d*Tan[a + b*x]],x]","-\frac{x \text{PolyLog}\left(3,-(1-i d) e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,-(1-i d) e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,-(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1+(1-i d) e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d \tan (a+b x)-i d+1)+\frac{1}{12} i b x^4","-\frac{x \text{PolyLog}\left(3,-(1-i d) e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,-(1-i d) e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,-(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1+(1-i d) e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d \tan (a+b x)-i d+1)+\frac{1}{12} i b x^4",1,"(I/12)*b*x^4 + (x^3*ArcTanh[1 - I*d + d*Tan[a + b*x]])/3 - (x^3*Log[1 + (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/6 + ((I/4)*x^2*PolyLog[2, -((1 - I*d)*E^((2*I)*a + (2*I)*b*x))])/b - (x*PolyLog[3, -((1 - I*d)*E^((2*I)*a + (2*I)*b*x))])/(4*b^2) - ((I/8)*PolyLog[4, -((1 - I*d)*E^((2*I)*a + (2*I)*b*x))])/b^3","A",7,7,20,0.3500,1,"{6263, 2184, 2190, 2531, 6609, 2282, 6589}"
322,1,133,0,0.2463914,"\int x \tanh ^{-1}(1-i d+d \tan (a+b x)) \, dx","Int[x*ArcTanh[1 - I*d + d*Tan[a + b*x]],x]","-\frac{\text{PolyLog}\left(3,-(1-i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,-(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1+(1-i d) e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d \tan (a+b x)-i d+1)+\frac{1}{6} i b x^3","-\frac{\text{PolyLog}\left(3,-(1-i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,-(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1+(1-i d) e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d \tan (a+b x)-i d+1)+\frac{1}{6} i b x^3",1,"(I/6)*b*x^3 + (x^2*ArcTanh[1 - I*d + d*Tan[a + b*x]])/2 - (x^2*Log[1 + (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/4 + ((I/4)*x*PolyLog[2, -((1 - I*d)*E^((2*I)*a + (2*I)*b*x))])/b - PolyLog[3, -((1 - I*d)*E^((2*I)*a + (2*I)*b*x))]/(8*b^2)","A",6,6,18,0.3333,1,"{6263, 2184, 2190, 2531, 2282, 6589}"
323,1,93,0,0.1514188,"\int \tanh ^{-1}(1-i d+d \tan (a+b x)) \, dx","Int[ArcTanh[1 - I*d + d*Tan[a + b*x]],x]","\frac{i \text{PolyLog}\left(2,-(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} x \log \left(1+(1-i d) e^{2 i a+2 i b x}\right)+x \tanh ^{-1}(d \tan (a+b x)-i d+1)+\frac{1}{2} i b x^2","\frac{i \text{PolyLog}\left(2,-(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} x \log \left(1+(1-i d) e^{2 i a+2 i b x}\right)+x \tanh ^{-1}(d \tan (a+b x)-i d+1)+\frac{1}{2} i b x^2",1,"(I/2)*b*x^2 + x*ArcTanh[1 - I*d + d*Tan[a + b*x]] - (x*Log[1 + (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/2 + ((I/4)*PolyLog[2, -((1 - I*d)*E^((2*I)*a + (2*I)*b*x))])/b","A",5,5,16,0.3125,1,"{6255, 2184, 2190, 2279, 2391}"
324,0,0,0,0.0964059,"\int \frac{\tanh ^{-1}(1-i d+d \tan (a+b x))}{x} \, dx","Int[ArcTanh[1 - I*d + d*Tan[a + b*x]]/x,x]","\int \frac{\tanh ^{-1}(1-i d+d \tan (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tanh ^{-1}(d \tan (a+b x)-i d+1)}{x},x\right)",0,"Defer[Int][ArcTanh[1 - I*d + d*Tan[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
325,1,171,0,0.2891154,"\int x^2 \tanh ^{-1}(1+i d-d \tan (a+b x)) \, dx","Int[x^2*ArcTanh[1 + I*d - d*Tan[a + b*x]],x]","-\frac{x \text{PolyLog}\left(3,-(1+i d) e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,-(1+i d) e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,-(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1+(1+i d) e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d (-\tan (a+b x))+i d+1)+\frac{1}{12} i b x^4","-\frac{x \text{PolyLog}\left(3,-(1+i d) e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,-(1+i d) e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,-(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1+(1+i d) e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d (-\tan (a+b x))+i d+1)+\frac{1}{12} i b x^4",1,"(I/12)*b*x^4 + (x^3*ArcTanh[1 + I*d - d*Tan[a + b*x]])/3 - (x^3*Log[1 + (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/6 + ((I/4)*x^2*PolyLog[2, -((1 + I*d)*E^((2*I)*a + (2*I)*b*x))])/b - (x*PolyLog[3, -((1 + I*d)*E^((2*I)*a + (2*I)*b*x))])/(4*b^2) - ((I/8)*PolyLog[4, -((1 + I*d)*E^((2*I)*a + (2*I)*b*x))])/b^3","A",7,7,21,0.3333,1,"{6263, 2184, 2190, 2531, 6609, 2282, 6589}"
326,1,134,0,0.2442794,"\int x \tanh ^{-1}(1+i d-d \tan (a+b x)) \, dx","Int[x*ArcTanh[1 + I*d - d*Tan[a + b*x]],x]","-\frac{\text{PolyLog}\left(3,-(1+i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,-(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1+(1+i d) e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d (-\tan (a+b x))+i d+1)+\frac{1}{6} i b x^3","-\frac{\text{PolyLog}\left(3,-(1+i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,-(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1+(1+i d) e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d (-\tan (a+b x))+i d+1)+\frac{1}{6} i b x^3",1,"(I/6)*b*x^3 + (x^2*ArcTanh[1 + I*d - d*Tan[a + b*x]])/2 - (x^2*Log[1 + (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/4 + ((I/4)*x*PolyLog[2, -((1 + I*d)*E^((2*I)*a + (2*I)*b*x))])/b - PolyLog[3, -((1 + I*d)*E^((2*I)*a + (2*I)*b*x))]/(8*b^2)","A",6,6,19,0.3158,1,"{6263, 2184, 2190, 2531, 2282, 6589}"
327,1,94,0,0.1478651,"\int \tanh ^{-1}(1+i d-d \tan (a+b x)) \, dx","Int[ArcTanh[1 + I*d - d*Tan[a + b*x]],x]","\frac{i \text{PolyLog}\left(2,-(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} x \log \left(1+(1+i d) e^{2 i a+2 i b x}\right)+x \tanh ^{-1}(d (-\tan (a+b x))+i d+1)+\frac{1}{2} i b x^2","\frac{i \text{PolyLog}\left(2,-(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} x \log \left(1+(1+i d) e^{2 i a+2 i b x}\right)+x \tanh ^{-1}(d (-\tan (a+b x))+i d+1)+\frac{1}{2} i b x^2",1,"(I/2)*b*x^2 + x*ArcTanh[1 + I*d - d*Tan[a + b*x]] - (x*Log[1 + (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/2 + ((I/4)*PolyLog[2, -((1 + I*d)*E^((2*I)*a + (2*I)*b*x))])/b","A",5,5,17,0.2941,1,"{6255, 2184, 2190, 2279, 2391}"
328,0,0,0,0.0912821,"\int \frac{\tanh ^{-1}(1+i d-d \tan (a+b x))}{x} \, dx","Int[ArcTanh[1 + I*d - d*Tan[a + b*x]]/x,x]","\int \frac{\tanh ^{-1}(1+i d-d \tan (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tanh ^{-1}(d (-\tan (a+b x))+i d+1)}{x},x\right)",0,"Defer[Int][ArcTanh[1 + I*d - d*Tan[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
329,1,302,0,0.2330017,"\int (e+f x)^3 \tanh ^{-1}(\cot (a+b x)) \, dx","Int[(e + f*x)^3*ArcTanh[Cot[a + b*x]],x]","\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,i e^{2 i (a+b x)}\right)}{8 b^3}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f^3 \text{PolyLog}\left(5,-i e^{2 i (a+b x)}\right)}{16 b^4}+\frac{3 f^3 \text{PolyLog}\left(5,i e^{2 i (a+b x)}\right)}{16 b^4}-\frac{i (e+f x)^3 \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^4 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{4 f}+\frac{(e+f x)^4 \tanh ^{-1}(\cot (a+b x))}{4 f}","\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,i e^{2 i (a+b x)}\right)}{8 b^3}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f^3 \text{PolyLog}\left(5,-i e^{2 i (a+b x)}\right)}{16 b^4}+\frac{3 f^3 \text{PolyLog}\left(5,i e^{2 i (a+b x)}\right)}{16 b^4}-\frac{i (e+f x)^3 \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^4 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{4 f}+\frac{(e+f x)^4 \tanh ^{-1}(\cot (a+b x))}{4 f}",1,"((I/4)*(e + f*x)^4*ArcTan[E^((2*I)*(a + b*x))])/f + ((e + f*x)^4*ArcTanh[Cot[a + b*x]])/(4*f) - ((I/4)*(e + f*x)^3*PolyLog[2, (-I)*E^((2*I)*(a + b*x))])/b + ((I/4)*(e + f*x)^3*PolyLog[2, I*E^((2*I)*(a + b*x))])/b + (3*f*(e + f*x)^2*PolyLog[3, (-I)*E^((2*I)*(a + b*x))])/(8*b^2) - (3*f*(e + f*x)^2*PolyLog[3, I*E^((2*I)*(a + b*x))])/(8*b^2) + (((3*I)/8)*f^2*(e + f*x)*PolyLog[4, (-I)*E^((2*I)*(a + b*x))])/b^3 - (((3*I)/8)*f^2*(e + f*x)*PolyLog[4, I*E^((2*I)*(a + b*x))])/b^3 - (3*f^3*PolyLog[5, (-I)*E^((2*I)*(a + b*x))])/(16*b^4) + (3*f^3*PolyLog[5, I*E^((2*I)*(a + b*x))])/(16*b^4)","A",12,6,15,0.4000,1,"{6253, 4181, 2531, 6609, 2282, 6589}"
330,1,234,0,0.1697511,"\int (e+f x)^2 \tanh ^{-1}(\cot (a+b x)) \, dx","Int[(e + f*x)^2*ArcTanh[Cot[a + b*x]],x]","\frac{f (e+f x) \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{4 b^2}-\frac{f (e+f x) \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{4 b^2}+\frac{i f^2 \text{PolyLog}\left(4,-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i f^2 \text{PolyLog}\left(4,i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i (e+f x)^2 \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{3 f}+\frac{(e+f x)^3 \tanh ^{-1}(\cot (a+b x))}{3 f}","\frac{f (e+f x) \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{4 b^2}-\frac{f (e+f x) \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{4 b^2}+\frac{i f^2 \text{PolyLog}\left(4,-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i f^2 \text{PolyLog}\left(4,i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i (e+f x)^2 \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{3 f}+\frac{(e+f x)^3 \tanh ^{-1}(\cot (a+b x))}{3 f}",1,"((I/3)*(e + f*x)^3*ArcTan[E^((2*I)*(a + b*x))])/f + ((e + f*x)^3*ArcTanh[Cot[a + b*x]])/(3*f) - ((I/4)*(e + f*x)^2*PolyLog[2, (-I)*E^((2*I)*(a + b*x))])/b + ((I/4)*(e + f*x)^2*PolyLog[2, I*E^((2*I)*(a + b*x))])/b + (f*(e + f*x)*PolyLog[3, (-I)*E^((2*I)*(a + b*x))])/(4*b^2) - (f*(e + f*x)*PolyLog[3, I*E^((2*I)*(a + b*x))])/(4*b^2) + ((I/8)*f^2*PolyLog[4, (-I)*E^((2*I)*(a + b*x))])/b^3 - ((I/8)*f^2*PolyLog[4, I*E^((2*I)*(a + b*x))])/b^3","A",10,6,15,0.4000,1,"{6253, 4181, 2531, 6609, 2282, 6589}"
331,1,162,0,0.1093965,"\int (e+f x) \tanh ^{-1}(\cot (a+b x)) \, dx","Int[(e + f*x)*ArcTanh[Cot[a + b*x]],x]","\frac{f \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{f \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{i (e+f x) \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x) \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{2 f}+\frac{(e+f x)^2 \tanh ^{-1}(\cot (a+b x))}{2 f}","\frac{f \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{f \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{i (e+f x) \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x) \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{2 f}+\frac{(e+f x)^2 \tanh ^{-1}(\cot (a+b x))}{2 f}",1,"((I/2)*(e + f*x)^2*ArcTan[E^((2*I)*(a + b*x))])/f + ((e + f*x)^2*ArcTanh[Cot[a + b*x]])/(2*f) - ((I/4)*(e + f*x)*PolyLog[2, (-I)*E^((2*I)*(a + b*x))])/b + ((I/4)*(e + f*x)*PolyLog[2, I*E^((2*I)*(a + b*x))])/b + (f*PolyLog[3, (-I)*E^((2*I)*(a + b*x))])/(8*b^2) - (f*PolyLog[3, I*E^((2*I)*(a + b*x))])/(8*b^2)","A",8,5,13,0.3846,1,"{6253, 4181, 2531, 2282, 6589}"
332,1,79,0,0.0462235,"\int \tanh ^{-1}(\cot (a+b x)) \, dx","Int[ArcTanh[Cot[a + b*x]],x]","-\frac{i \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+i x \tan ^{-1}\left(e^{2 i (a+b x)}\right)+x \tanh ^{-1}(\cot (a+b x))","-\frac{i \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+i x \tan ^{-1}\left(e^{2 i (a+b x)}\right)+x \tanh ^{-1}(\cot (a+b x))",1,"I*x*ArcTan[E^((2*I)*(a + b*x))] + x*ArcTanh[Cot[a + b*x]] - ((I/4)*PolyLog[2, (-I)*E^((2*I)*(a + b*x))])/b + ((I/4)*PolyLog[2, I*E^((2*I)*(a + b*x))])/b","A",6,4,7,0.5714,1,"{6249, 4181, 2279, 2391}"
333,0,0,0,0.0418305,"\int \frac{\tanh ^{-1}(\cot (a+b x))}{e+f x} \, dx","Int[ArcTanh[Cot[a + b*x]]/(e + f*x),x]","\int \frac{\tanh ^{-1}(\cot (a+b x))}{e+f x} \, dx","\text{Int}\left(\frac{\tanh ^{-1}(\cot (a+b x))}{e+f x},x\right)",0,"Defer[Int][ArcTanh[Cot[a + b*x]]/(e + f*x), x]","A",0,0,0,0,-1,"{}"
334,1,391,0,0.4863389,"\int x^2 \tanh ^{-1}(c+d \cot (a+b x)) \, dx","Int[x^2*ArcTanh[c + d*Cot[a + b*x]],x]","\frac{x \text{PolyLog}\left(3,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b^2}-\frac{x \text{PolyLog}\left(3,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b^2}+\frac{i \text{PolyLog}\left(4,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{8 b^3}-\frac{i \text{PolyLog}\left(4,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{8 b^3}-\frac{i x^2 \text{PolyLog}\left(2,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b}+\frac{i x^2 \text{PolyLog}\left(2,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b}+\frac{1}{6} x^3 \log \left(1-\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)-\frac{1}{6} x^3 \log \left(1-\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d \cot (a+b x)+c)","\frac{x \text{PolyLog}\left(3,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b^2}-\frac{x \text{PolyLog}\left(3,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b^2}+\frac{i \text{PolyLog}\left(4,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{8 b^3}-\frac{i \text{PolyLog}\left(4,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{8 b^3}-\frac{i x^2 \text{PolyLog}\left(2,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b}+\frac{i x^2 \text{PolyLog}\left(2,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b}+\frac{1}{6} x^3 \log \left(1-\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)-\frac{1}{6} x^3 \log \left(1-\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d \cot (a+b x)+c)",1,"(x^3*ArcTanh[c + d*Cot[a + b*x]])/3 + (x^3*Log[1 - ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)])/6 - (x^3*Log[1 - ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)])/6 - ((I/4)*x^2*PolyLog[2, ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)])/b + ((I/4)*x^2*PolyLog[2, ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)])/b + (x*PolyLog[3, ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)])/(4*b^2) - (x*PolyLog[3, ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)])/(4*b^2) + ((I/8)*PolyLog[4, ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)])/b^3 - ((I/8)*PolyLog[4, ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)])/b^3","A",11,6,15,0.4000,1,"{6269, 2190, 2531, 6609, 2282, 6589}"
335,1,293,0,0.4004961,"\int x \tanh ^{-1}(c+d \cot (a+b x)) \, dx","Int[x*ArcTanh[c + d*Cot[a + b*x]],x]","\frac{\text{PolyLog}\left(3,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{8 b^2}-\frac{\text{PolyLog}\left(3,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{8 b^2}-\frac{i x \text{PolyLog}\left(2,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b}+\frac{i x \text{PolyLog}\left(2,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b}+\frac{1}{4} x^2 \log \left(1-\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)-\frac{1}{4} x^2 \log \left(1-\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d \cot (a+b x)+c)","\frac{\text{PolyLog}\left(3,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{8 b^2}-\frac{\text{PolyLog}\left(3,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{8 b^2}-\frac{i x \text{PolyLog}\left(2,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b}+\frac{i x \text{PolyLog}\left(2,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b}+\frac{1}{4} x^2 \log \left(1-\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)-\frac{1}{4} x^2 \log \left(1-\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d \cot (a+b x)+c)",1,"(x^2*ArcTanh[c + d*Cot[a + b*x]])/2 + (x^2*Log[1 - ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)])/4 - (x^2*Log[1 - ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)])/4 - ((I/4)*x*PolyLog[2, ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)])/b + ((I/4)*x*PolyLog[2, ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)])/b + PolyLog[3, ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)]/(8*b^2) - PolyLog[3, ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)]/(8*b^2)","A",9,5,13,0.3846,1,"{6269, 2190, 2531, 2282, 6589}"
336,1,194,0,0.2413355,"\int \tanh ^{-1}(c+d \cot (a+b x)) \, dx","Int[ArcTanh[c + d*Cot[a + b*x]],x]","-\frac{i \text{PolyLog}\left(2,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b}+\frac{1}{2} x \log \left(1-\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)-\frac{1}{2} x \log \left(1-\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)+x \tanh ^{-1}(d \cot (a+b x)+c)","-\frac{i \text{PolyLog}\left(2,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b}+\frac{1}{2} x \log \left(1-\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)-\frac{1}{2} x \log \left(1-\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)+x \tanh ^{-1}(d \cot (a+b x)+c)",1,"x*ArcTanh[c + d*Cot[a + b*x]] + (x*Log[1 - ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)])/2 - (x*Log[1 - ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)])/2 - ((I/4)*PolyLog[2, ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)])/b + ((I/4)*PolyLog[2, ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)])/b","A",7,4,11,0.3636,1,"{6261, 2190, 2279, 2391}"
337,0,0,0,0.1420221,"\int \frac{\tanh ^{-1}(c+d \cot (a+b x))}{x} \, dx","Int[ArcTanh[c + d*Cot[a + b*x]]/x,x]","\int \frac{\tanh ^{-1}(c+d \cot (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tanh ^{-1}(d \cot (a+b x)+c)}{x},x\right)",0,"Defer[Int][ArcTanh[c + d*Cot[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
338,1,168,0,0.2962571,"\int x^2 \tanh ^{-1}(1+i d+d \cot (a+b x)) \, dx","Int[x^2*ArcTanh[1 + I*d + d*Cot[a + b*x]],x]","-\frac{x \text{PolyLog}\left(3,(1+i d) e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,(1+i d) e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1-(1+i d) e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d \cot (a+b x)+i d+1)+\frac{1}{12} i b x^4","-\frac{x \text{PolyLog}\left(3,(1+i d) e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,(1+i d) e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1-(1+i d) e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d \cot (a+b x)+i d+1)+\frac{1}{12} i b x^4",1,"(I/12)*b*x^4 + (x^3*ArcTanh[1 + I*d + d*Cot[a + b*x]])/3 - (x^3*Log[1 - (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/6 + ((I/4)*x^2*PolyLog[2, (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/b - (x*PolyLog[3, (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/(4*b^2) - ((I/8)*PolyLog[4, (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/b^3","A",7,7,20,0.3500,1,"{6265, 2184, 2190, 2531, 6609, 2282, 6589}"
339,1,132,0,0.2460784,"\int x \tanh ^{-1}(1+i d+d \cot (a+b x)) \, dx","Int[x*ArcTanh[1 + I*d + d*Cot[a + b*x]],x]","-\frac{\text{PolyLog}\left(3,(1+i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1-(1+i d) e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d \cot (a+b x)+i d+1)+\frac{1}{6} i b x^3","-\frac{\text{PolyLog}\left(3,(1+i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1-(1+i d) e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d \cot (a+b x)+i d+1)+\frac{1}{6} i b x^3",1,"(I/6)*b*x^3 + (x^2*ArcTanh[1 + I*d + d*Cot[a + b*x]])/2 - (x^2*Log[1 - (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/4 + ((I/4)*x*PolyLog[2, (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/b - PolyLog[3, (1 + I*d)*E^((2*I)*a + (2*I)*b*x)]/(8*b^2)","A",6,6,18,0.3333,1,"{6265, 2184, 2190, 2531, 2282, 6589}"
340,1,93,0,0.1492874,"\int \tanh ^{-1}(1+i d+d \cot (a+b x)) \, dx","Int[ArcTanh[1 + I*d + d*Cot[a + b*x]],x]","\frac{i \text{PolyLog}\left(2,(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} x \log \left(1-(1+i d) e^{2 i a+2 i b x}\right)+x \tanh ^{-1}(d \cot (a+b x)+i d+1)+\frac{1}{2} i b x^2","\frac{i \text{PolyLog}\left(2,(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} x \log \left(1-(1+i d) e^{2 i a+2 i b x}\right)+x \tanh ^{-1}(d \cot (a+b x)+i d+1)+\frac{1}{2} i b x^2",1,"(I/2)*b*x^2 + x*ArcTanh[1 + I*d + d*Cot[a + b*x]] - (x*Log[1 - (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/2 + ((I/4)*PolyLog[2, (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/b","A",5,5,16,0.3125,1,"{6257, 2184, 2190, 2279, 2391}"
341,0,0,0,0.0858041,"\int \frac{\tanh ^{-1}(1+i d+d \cot (a+b x))}{x} \, dx","Int[ArcTanh[1 + I*d + d*Cot[a + b*x]]/x,x]","\int \frac{\tanh ^{-1}(1+i d+d \cot (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tanh ^{-1}(d \cot (a+b x)+i d+1)}{x},x\right)",0,"Defer[Int][ArcTanh[1 + I*d + d*Cot[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
342,1,169,0,0.2954914,"\int x^2 \tanh ^{-1}(1-i d-d \cot (a+b x)) \, dx","Int[x^2*ArcTanh[1 - I*d - d*Cot[a + b*x]],x]","-\frac{x \text{PolyLog}\left(3,(1-i d) e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,(1-i d) e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1-(1-i d) e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d (-\cot (a+b x))-i d+1)+\frac{1}{12} i b x^4","-\frac{x \text{PolyLog}\left(3,(1-i d) e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,(1-i d) e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1-(1-i d) e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \tanh ^{-1}(d (-\cot (a+b x))-i d+1)+\frac{1}{12} i b x^4",1,"(I/12)*b*x^4 + (x^3*ArcTanh[1 - I*d - d*Cot[a + b*x]])/3 - (x^3*Log[1 - (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/6 + ((I/4)*x^2*PolyLog[2, (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/b - (x*PolyLog[3, (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/(4*b^2) - ((I/8)*PolyLog[4, (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/b^3","A",7,7,21,0.3333,1,"{6265, 2184, 2190, 2531, 6609, 2282, 6589}"
343,1,133,0,0.2499081,"\int x \tanh ^{-1}(1-i d-d \cot (a+b x)) \, dx","Int[x*ArcTanh[1 - I*d - d*Cot[a + b*x]],x]","-\frac{\text{PolyLog}\left(3,(1-i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1-(1-i d) e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d (-\cot (a+b x))-i d+1)+\frac{1}{6} i b x^3","-\frac{\text{PolyLog}\left(3,(1-i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1-(1-i d) e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \tanh ^{-1}(d (-\cot (a+b x))-i d+1)+\frac{1}{6} i b x^3",1,"(I/6)*b*x^3 + (x^2*ArcTanh[1 - I*d - d*Cot[a + b*x]])/2 - (x^2*Log[1 - (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/4 + ((I/4)*x*PolyLog[2, (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/b - PolyLog[3, (1 - I*d)*E^((2*I)*a + (2*I)*b*x)]/(8*b^2)","A",6,6,19,0.3158,1,"{6265, 2184, 2190, 2531, 2282, 6589}"
344,1,94,0,0.1491995,"\int \tanh ^{-1}(1-i d-d \cot (a+b x)) \, dx","Int[ArcTanh[1 - I*d - d*Cot[a + b*x]],x]","\frac{i \text{PolyLog}\left(2,(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} x \log \left(1-(1-i d) e^{2 i a+2 i b x}\right)+x \tanh ^{-1}(d (-\cot (a+b x))-i d+1)+\frac{1}{2} i b x^2","\frac{i \text{PolyLog}\left(2,(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} x \log \left(1-(1-i d) e^{2 i a+2 i b x}\right)+x \tanh ^{-1}(d (-\cot (a+b x))-i d+1)+\frac{1}{2} i b x^2",1,"(I/2)*b*x^2 + x*ArcTanh[1 - I*d - d*Cot[a + b*x]] - (x*Log[1 - (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/2 + ((I/4)*PolyLog[2, (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/b","A",5,5,17,0.2941,1,"{6257, 2184, 2190, 2279, 2391}"
345,0,0,0,0.0960844,"\int \frac{\tanh ^{-1}(1-i d-d \cot (a+b x))}{x} \, dx","Int[ArcTanh[1 - I*d - d*Cot[a + b*x]]/x,x]","\int \frac{\tanh ^{-1}(1-i d-d \cot (a+b x))}{x} \, dx","\text{Int}\left(\frac{\tanh ^{-1}(d (-\cot (a+b x))-i d+1)}{x},x\right)",0,"Defer[Int][ArcTanh[1 - I*d - d*Cot[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
346,1,21,0,0.0115109,"\int \tanh ^{-1}\left(e^x\right) \, dx","Int[ArcTanh[E^x],x]","\frac{1}{2} \text{PolyLog}\left(2,e^x\right)-\frac{1}{2} \text{PolyLog}\left(2,-e^x\right)","\frac{1}{2} \text{PolyLog}\left(2,e^x\right)-\frac{1}{2} \text{PolyLog}\left(2,-e^x\right)",1,"-PolyLog[2, -E^x]/2 + PolyLog[2, E^x]/2","A",2,2,4,0.5000,1,"{2282, 5912}"
347,1,43,0,0.0429293,"\int x \tanh ^{-1}\left(e^x\right) \, dx","Int[x*ArcTanh[E^x],x]","-\frac{1}{2} x \text{PolyLog}\left(2,-e^x\right)+\frac{1}{2} x \text{PolyLog}\left(2,e^x\right)+\frac{1}{2} \text{PolyLog}\left(3,-e^x\right)-\frac{1}{2} \text{PolyLog}\left(3,e^x\right)","-\frac{1}{2} x \text{PolyLog}\left(2,-e^x\right)+\frac{1}{2} x \text{PolyLog}\left(2,e^x\right)+\frac{1}{2} \text{PolyLog}\left(3,-e^x\right)-\frac{1}{2} \text{PolyLog}\left(3,e^x\right)",1,"-(x*PolyLog[2, -E^x])/2 + (x*PolyLog[2, E^x])/2 + PolyLog[3, -E^x]/2 - PolyLog[3, E^x]/2","A",7,4,6,0.6667,1,"{6213, 2531, 2282, 6589}"
348,1,58,0,0.0670158,"\int x^2 \tanh ^{-1}\left(e^x\right) \, dx","Int[x^2*ArcTanh[E^x],x]","-\frac{1}{2} x^2 \text{PolyLog}\left(2,-e^x\right)+\frac{1}{2} x^2 \text{PolyLog}\left(2,e^x\right)+x \text{PolyLog}\left(3,-e^x\right)-x \text{PolyLog}\left(3,e^x\right)-\text{PolyLog}\left(4,-e^x\right)+\text{PolyLog}\left(4,e^x\right)","-\frac{1}{2} x^2 \text{PolyLog}\left(2,-e^x\right)+\frac{1}{2} x^2 \text{PolyLog}\left(2,e^x\right)+x \text{PolyLog}\left(3,-e^x\right)-x \text{PolyLog}\left(3,e^x\right)-\text{PolyLog}\left(4,-e^x\right)+\text{PolyLog}\left(4,e^x\right)",1,"-(x^2*PolyLog[2, -E^x])/2 + (x^2*PolyLog[2, E^x])/2 + x*PolyLog[3, -E^x] - x*PolyLog[3, E^x] - PolyLog[4, -E^x] + PolyLog[4, E^x]","A",9,5,8,0.6250,1,"{6213, 2531, 6609, 2282, 6589}"
349,1,35,0,0.0139707,"\int \tanh ^{-1}\left(e^{a+b x}\right) \, dx","Int[ArcTanh[E^(a + b*x)],x]","\frac{\text{PolyLog}\left(2,e^{a+b x}\right)}{2 b}-\frac{\text{PolyLog}\left(2,-e^{a+b x}\right)}{2 b}","\frac{\text{PolyLog}\left(2,e^{a+b x}\right)}{2 b}-\frac{\text{PolyLog}\left(2,-e^{a+b x}\right)}{2 b}",1,"-PolyLog[2, -E^(a + b*x)]/(2*b) + PolyLog[2, E^(a + b*x)]/(2*b)","A",2,2,8,0.2500,1,"{2282, 5912}"
350,1,71,0,0.057715,"\int x \tanh ^{-1}\left(e^{a+b x}\right) \, dx","Int[x*ArcTanh[E^(a + b*x)],x]","\frac{\text{PolyLog}\left(3,-e^{a+b x}\right)}{2 b^2}-\frac{\text{PolyLog}\left(3,e^{a+b x}\right)}{2 b^2}-\frac{x \text{PolyLog}\left(2,-e^{a+b x}\right)}{2 b}+\frac{x \text{PolyLog}\left(2,e^{a+b x}\right)}{2 b}","\frac{\text{PolyLog}\left(3,-e^{a+b x}\right)}{2 b^2}-\frac{\text{PolyLog}\left(3,e^{a+b x}\right)}{2 b^2}-\frac{x \text{PolyLog}\left(2,-e^{a+b x}\right)}{2 b}+\frac{x \text{PolyLog}\left(2,e^{a+b x}\right)}{2 b}",1,"-(x*PolyLog[2, -E^(a + b*x)])/(2*b) + (x*PolyLog[2, E^(a + b*x)])/(2*b) + PolyLog[3, -E^(a + b*x)]/(2*b^2) - PolyLog[3, E^(a + b*x)]/(2*b^2)","A",7,4,10,0.4000,1,"{6213, 2531, 2282, 6589}"
351,1,101,0,0.092033,"\int x^2 \tanh ^{-1}\left(e^{a+b x}\right) \, dx","Int[x^2*ArcTanh[E^(a + b*x)],x]","\frac{x \text{PolyLog}\left(3,-e^{a+b x}\right)}{b^2}-\frac{x \text{PolyLog}\left(3,e^{a+b x}\right)}{b^2}-\frac{\text{PolyLog}\left(4,-e^{a+b x}\right)}{b^3}+\frac{\text{PolyLog}\left(4,e^{a+b x}\right)}{b^3}-\frac{x^2 \text{PolyLog}\left(2,-e^{a+b x}\right)}{2 b}+\frac{x^2 \text{PolyLog}\left(2,e^{a+b x}\right)}{2 b}","\frac{x \text{PolyLog}\left(3,-e^{a+b x}\right)}{b^2}-\frac{x \text{PolyLog}\left(3,e^{a+b x}\right)}{b^2}-\frac{\text{PolyLog}\left(4,-e^{a+b x}\right)}{b^3}+\frac{\text{PolyLog}\left(4,e^{a+b x}\right)}{b^3}-\frac{x^2 \text{PolyLog}\left(2,-e^{a+b x}\right)}{2 b}+\frac{x^2 \text{PolyLog}\left(2,e^{a+b x}\right)}{2 b}",1,"-(x^2*PolyLog[2, -E^(a + b*x)])/(2*b) + (x^2*PolyLog[2, E^(a + b*x)])/(2*b) + (x*PolyLog[3, -E^(a + b*x)])/b^2 - (x*PolyLog[3, E^(a + b*x)])/b^2 - PolyLog[4, -E^(a + b*x)]/b^3 + PolyLog[4, E^(a + b*x)]/b^3","A",9,5,12,0.4167,1,"{6213, 2531, 6609, 2282, 6589}"
352,1,168,0,0.1298248,"\int \tanh ^{-1}\left(a+b f^{c+d x}\right) \, dx","Int[ArcTanh[a + b*f^(c + d*x)],x]","\frac{\text{PolyLog}\left(2,1-\frac{2}{a+b f^{c+d x}+1}\right)}{2 d \log (f)}-\frac{\text{PolyLog}\left(2,1-\frac{2 b f^{c+d x}}{(1-a) \left(a+b f^{c+d x}+1\right)}\right)}{2 d \log (f)}-\frac{\log \left(\frac{2}{a+b f^{c+d x}+1}\right) \tanh ^{-1}\left(a+b f^{c+d x}\right)}{d \log (f)}+\frac{\log \left(\frac{2 b f^{c+d x}}{(1-a) \left(a+b f^{c+d x}+1\right)}\right) \tanh ^{-1}\left(a+b f^{c+d x}\right)}{d \log (f)}","\frac{\text{PolyLog}\left(2,1-\frac{2}{a+b f^{c+d x}+1}\right)}{2 d \log (f)}-\frac{\text{PolyLog}\left(2,1-\frac{2 b f^{c+d x}}{(1-a) \left(a+b f^{c+d x}+1\right)}\right)}{2 d \log (f)}-\frac{\log \left(\frac{2}{a+b f^{c+d x}+1}\right) \tanh ^{-1}\left(a+b f^{c+d x}\right)}{d \log (f)}+\frac{\log \left(\frac{2 b f^{c+d x}}{(1-a) \left(a+b f^{c+d x}+1\right)}\right) \tanh ^{-1}\left(a+b f^{c+d x}\right)}{d \log (f)}",1,"-((ArcTanh[a + b*f^(c + d*x)]*Log[2/(1 + a + b*f^(c + d*x))])/(d*Log[f])) + (ArcTanh[a + b*f^(c + d*x)]*Log[(2*b*f^(c + d*x))/((1 - a)*(1 + a + b*f^(c + d*x)))])/(d*Log[f]) + PolyLog[2, 1 - 2/(1 + a + b*f^(c + d*x))]/(2*d*Log[f]) - PolyLog[2, 1 - (2*b*f^(c + d*x))/((1 - a)*(1 + a + b*f^(c + d*x)))]/(2*d*Log[f])","A",6,6,12,0.5000,1,"{2282, 6111, 5920, 2402, 2315, 2447}"
353,1,211,0,0.150448,"\int x \tanh ^{-1}\left(a+b f^{c+d x}\right) \, dx","Int[x*ArcTanh[a + b*f^(c + d*x)],x]","-\frac{\text{PolyLog}\left(3,\frac{b f^{c+d x}}{1-a}\right)}{2 d^2 \log ^2(f)}+\frac{\text{PolyLog}\left(3,-\frac{b f^{c+d x}}{a+1}\right)}{2 d^2 \log ^2(f)}+\frac{x \text{PolyLog}\left(2,\frac{b f^{c+d x}}{1-a}\right)}{2 d \log (f)}-\frac{x \text{PolyLog}\left(2,-\frac{b f^{c+d x}}{a+1}\right)}{2 d \log (f)}-\frac{1}{4} x^2 \log \left(-a-b f^{c+d x}+1\right)+\frac{1}{4} x^2 \log \left(a+b f^{c+d x}+1\right)+\frac{1}{4} x^2 \log \left(1-\frac{b f^{c+d x}}{1-a}\right)-\frac{1}{4} x^2 \log \left(\frac{b f^{c+d x}}{a+1}+1\right)","-\frac{\text{PolyLog}\left(3,\frac{b f^{c+d x}}{1-a}\right)}{2 d^2 \log ^2(f)}+\frac{\text{PolyLog}\left(3,-\frac{b f^{c+d x}}{a+1}\right)}{2 d^2 \log ^2(f)}+\frac{x \text{PolyLog}\left(2,\frac{b f^{c+d x}}{1-a}\right)}{2 d \log (f)}-\frac{x \text{PolyLog}\left(2,-\frac{b f^{c+d x}}{a+1}\right)}{2 d \log (f)}-\frac{1}{4} x^2 \log \left(-a-b f^{c+d x}+1\right)+\frac{1}{4} x^2 \log \left(a+b f^{c+d x}+1\right)+\frac{1}{4} x^2 \log \left(1-\frac{b f^{c+d x}}{1-a}\right)-\frac{1}{4} x^2 \log \left(\frac{b f^{c+d x}}{a+1}+1\right)",1,"-(x^2*Log[1 - a - b*f^(c + d*x)])/4 + (x^2*Log[1 + a + b*f^(c + d*x)])/4 + (x^2*Log[1 - (b*f^(c + d*x))/(1 - a)])/4 - (x^2*Log[1 + (b*f^(c + d*x))/(1 + a)])/4 + (x*PolyLog[2, (b*f^(c + d*x))/(1 - a)])/(2*d*Log[f]) - (x*PolyLog[2, -((b*f^(c + d*x))/(1 + a))])/(2*d*Log[f]) - PolyLog[3, (b*f^(c + d*x))/(1 - a)]/(2*d^2*Log[f]^2) + PolyLog[3, -((b*f^(c + d*x))/(1 + a))]/(2*d^2*Log[f]^2)","A",9,5,14,0.3571,1,"{6213, 2532, 2531, 2282, 6589}"
354,1,264,0,0.1966333,"\int x^2 \tanh ^{-1}\left(a+b f^{c+d x}\right) \, dx","Int[x^2*ArcTanh[a + b*f^(c + d*x)],x]","-\frac{x \text{PolyLog}\left(3,\frac{b f^{c+d x}}{1-a}\right)}{d^2 \log ^2(f)}+\frac{x \text{PolyLog}\left(3,-\frac{b f^{c+d x}}{a+1}\right)}{d^2 \log ^2(f)}+\frac{\text{PolyLog}\left(4,\frac{b f^{c+d x}}{1-a}\right)}{d^3 \log ^3(f)}-\frac{\text{PolyLog}\left(4,-\frac{b f^{c+d x}}{a+1}\right)}{d^3 \log ^3(f)}+\frac{x^2 \text{PolyLog}\left(2,\frac{b f^{c+d x}}{1-a}\right)}{2 d \log (f)}-\frac{x^2 \text{PolyLog}\left(2,-\frac{b f^{c+d x}}{a+1}\right)}{2 d \log (f)}-\frac{1}{6} x^3 \log \left(-a-b f^{c+d x}+1\right)+\frac{1}{6} x^3 \log \left(a+b f^{c+d x}+1\right)+\frac{1}{6} x^3 \log \left(1-\frac{b f^{c+d x}}{1-a}\right)-\frac{1}{6} x^3 \log \left(\frac{b f^{c+d x}}{a+1}+1\right)","-\frac{x \text{PolyLog}\left(3,\frac{b f^{c+d x}}{1-a}\right)}{d^2 \log ^2(f)}+\frac{x \text{PolyLog}\left(3,-\frac{b f^{c+d x}}{a+1}\right)}{d^2 \log ^2(f)}+\frac{\text{PolyLog}\left(4,\frac{b f^{c+d x}}{1-a}\right)}{d^3 \log ^3(f)}-\frac{\text{PolyLog}\left(4,-\frac{b f^{c+d x}}{a+1}\right)}{d^3 \log ^3(f)}+\frac{x^2 \text{PolyLog}\left(2,\frac{b f^{c+d x}}{1-a}\right)}{2 d \log (f)}-\frac{x^2 \text{PolyLog}\left(2,-\frac{b f^{c+d x}}{a+1}\right)}{2 d \log (f)}-\frac{1}{6} x^3 \log \left(-a-b f^{c+d x}+1\right)+\frac{1}{6} x^3 \log \left(a+b f^{c+d x}+1\right)+\frac{1}{6} x^3 \log \left(1-\frac{b f^{c+d x}}{1-a}\right)-\frac{1}{6} x^3 \log \left(\frac{b f^{c+d x}}{a+1}+1\right)",1,"-(x^3*Log[1 - a - b*f^(c + d*x)])/6 + (x^3*Log[1 + a + b*f^(c + d*x)])/6 + (x^3*Log[1 - (b*f^(c + d*x))/(1 - a)])/6 - (x^3*Log[1 + (b*f^(c + d*x))/(1 + a)])/6 + (x^2*PolyLog[2, (b*f^(c + d*x))/(1 - a)])/(2*d*Log[f]) - (x^2*PolyLog[2, -((b*f^(c + d*x))/(1 + a))])/(2*d*Log[f]) - (x*PolyLog[3, (b*f^(c + d*x))/(1 - a)])/(d^2*Log[f]^2) + (x*PolyLog[3, -((b*f^(c + d*x))/(1 + a))])/(d^2*Log[f]^2) + PolyLog[4, (b*f^(c + d*x))/(1 - a)]/(d^3*Log[f]^3) - PolyLog[4, -((b*f^(c + d*x))/(1 + a))]/(d^3*Log[f]^3)","A",11,6,16,0.3750,1,"{6213, 2532, 2531, 6609, 2282, 6589}"
355,1,107,0,0.1708766,"\int e^{c (a+b x)} \tanh ^{-1}(\sinh (a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcTanh[Sinh[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} \tanh ^{-1}(\sinh (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} \tanh ^{-1}(\sinh (c (a+b x)))}{b c}",1,"(E^(a*c + b*c*x)*ArcTanh[Sinh[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, 6275, 2282, 12, 1247, 632, 31}"
356,1,49,0,0.0746668,"\int e^{c (a+b x)} \tanh ^{-1}(\cosh (a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcTanh[Cosh[a*c + b*c*x]],x]","\frac{\log \left(1-e^{2 c (a+b x)}\right)}{b c}+\frac{e^{a c+b c x} \tanh ^{-1}(\cosh (c (a+b x)))}{b c}","\frac{\log \left(1-e^{2 c (a+b x)}\right)}{b c}+\frac{e^{a c+b c x} \tanh ^{-1}(\cosh (c (a+b x)))}{b c}",1,"(E^(a*c + b*c*x)*ArcTanh[Cosh[c*(a + b*x)]])/(b*c) + Log[1 - E^(2*c*(a + b*x))]/(b*c)","A",5,5,20,0.2500,1,"{2194, 6275, 2282, 12, 260}"
357,1,45,0,0.0543779,"\int e^{c (a+b x)} \tanh ^{-1}(\tanh (a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcTanh[Tanh[a*c + b*c*x]],x]","\frac{e^{a c+b c x} \tanh ^{-1}(\tanh (c (a+b x)))}{b c}-\frac{e^{a c+b c x}}{b c}","\frac{e^{a c+b c x} \tanh ^{-1}(\tanh (c (a+b x)))}{b c}-\frac{e^{a c+b c x}}{b c}",1,"-(E^(a*c + b*c*x)/(b*c)) + (E^(a*c + b*c*x)*ArcTanh[Tanh[c*(a + b*x)]])/(b*c)","A",3,2,20,0.1000,1,"{2194, 6275}"
358,1,45,0,0.0543121,"\int e^{c (a+b x)} \tanh ^{-1}(\coth (a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcTanh[Coth[a*c + b*c*x]],x]","\frac{e^{a c+b c x} \tanh ^{-1}(\coth (c (a+b x)))}{b c}-\frac{e^{a c+b c x}}{b c}","\frac{e^{a c+b c x} \tanh ^{-1}(\coth (c (a+b x)))}{b c}-\frac{e^{a c+b c x}}{b c}",1,"-(E^(a*c + b*c*x)/(b*c)) + (E^(a*c + b*c*x)*ArcTanh[Coth[c*(a + b*x)]])/(b*c)","A",3,2,20,0.1000,1,"{2194, 6275}"
359,1,49,0,0.0678644,"\int e^{c (a+b x)} \tanh ^{-1}(\text{sech}(a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcTanh[Sech[a*c + b*c*x]],x]","\frac{\log \left(1-e^{2 c (a+b x)}\right)}{b c}+\frac{e^{a c+b c x} \tanh ^{-1}(\text{sech}(c (a+b x)))}{b c}","\frac{\log \left(1-e^{2 c (a+b x)}\right)}{b c}+\frac{e^{a c+b c x} \tanh ^{-1}(\text{sech}(c (a+b x)))}{b c}",1,"(E^(a*c + b*c*x)*ArcTanh[Sech[c*(a + b*x)]])/(b*c) + Log[1 - E^(2*c*(a + b*x))]/(b*c)","A",5,5,20,0.2500,1,"{2194, 6275, 2282, 12, 260}"
360,1,107,0,0.1700982,"\int e^{c (a+b x)} \tanh ^{-1}(\text{csch}(a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcTanh[Csch[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} \tanh ^{-1}(\text{csch}(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} \tanh ^{-1}(\text{csch}(c (a+b x)))}{b c}",1,"(E^(a*c + b*c*x)*ArcTanh[Csch[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, 6275, 2282, 12, 1247, 632, 31}"
361,1,136,0,0.5376215,"\int \frac{\left(a+b \tanh ^{-1}\left(c x^n\right)\right) \left(d+e \log \left(f x^m\right)\right)}{x} \, dx","Int[((a + b*ArcTanh[c*x^n])*(d + e*Log[f*x^m]))/x,x]","-\frac{b d \text{PolyLog}\left(2,-c x^n\right)}{2 n}+\frac{b d \text{PolyLog}\left(2,c x^n\right)}{2 n}-\frac{b e \log \left(f x^m\right) \text{PolyLog}\left(2,-c x^n\right)}{2 n}+\frac{b e \log \left(f x^m\right) \text{PolyLog}\left(2,c x^n\right)}{2 n}+\frac{b e m \text{PolyLog}\left(3,-c x^n\right)}{2 n^2}-\frac{b e m \text{PolyLog}\left(3,c x^n\right)}{2 n^2}+a d \log (x)+\frac{a e \log ^2\left(f x^m\right)}{2 m}","-\frac{b d \text{PolyLog}\left(2,-c x^n\right)}{2 n}+\frac{b d \text{PolyLog}\left(2,c x^n\right)}{2 n}-\frac{b e \log \left(f x^m\right) \text{PolyLog}\left(2,-c x^n\right)}{2 n}+\frac{b e \log \left(f x^m\right) \text{PolyLog}\left(2,c x^n\right)}{2 n}+\frac{b e m \text{PolyLog}\left(3,-c x^n\right)}{2 n^2}-\frac{b e m \text{PolyLog}\left(3,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) - (b*d*PolyLog[2, -(c*x^n)])/(2*n) - (b*e*Log[f*x^m]*PolyLog[2, -(c*x^n)])/(2*n) + (b*d*PolyLog[2, c*x^n])/(2*n) + (b*e*Log[f*x^m]*PolyLog[2, c*x^n])/(2*n) + (b*e*m*PolyLog[3, -(c*x^n)])/(2*n^2) - (b*e*m*PolyLog[3, c*x^n])/(2*n^2)","A",11,8,24,0.3333,1,"{2301, 6742, 6095, 5912, 6071, 6069, 2374, 6589}"