1,1,99,127,0.0798902,"\int x^5 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Integrate[x^5*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","\frac{15 d^3 \log \left(\sqrt{d+e x^2}+\sqrt{e} x\right)+\sqrt{e} x \sqrt{d+e x^2} \left(-15 d^2+10 d e x^2-8 e^2 x^4\right)+48 e^3 x^6 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{288 e^3}","\frac{5 d^3 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{96 e^3}-\frac{5 d^2 x \sqrt{d+e x^2}}{96 e^{5/2}}+\frac{5 d x^3 \sqrt{d+e x^2}}{144 e^{3/2}}+\frac{1}{6} x^6 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)-\frac{x^5 \sqrt{d+e x^2}}{36 \sqrt{e}}",1,"(Sqrt[e]*x*Sqrt[d + e*x^2]*(-15*d^2 + 10*d*e*x^2 - 8*e^2*x^4) + 48*e^3*x^6*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]] + 15*d^3*Log[Sqrt[e]*x + Sqrt[d + e*x^2]])/(288*e^3)","A",1
2,1,88,101,0.0514715,"\int x^3 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Integrate[x^3*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","\frac{-3 d^2 \log \left(\sqrt{d+e x^2}+\sqrt{e} x\right)+8 e^2 x^4 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)+\sqrt{e} x \left(3 d-2 e x^2\right) \sqrt{d+e x^2}}{32 e^2}","-\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{1}{4} x^4 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)-\frac{x^3 \sqrt{d+e x^2}}{16 \sqrt{e}}",1,"(Sqrt[e]*x*(3*d - 2*e*x^2)*Sqrt[d + e*x^2] + 8*e^2*x^4*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]] - 3*d^2*Log[Sqrt[e]*x + Sqrt[d + e*x^2]])/(32*e^2)","A",1
3,1,76,75,0.0330635,"\int x \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Integrate[x*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","-\frac{x \sqrt{d+e x^2}}{4 \sqrt{e}}+\frac{d \log \left(\sqrt{d+e x^2}+\sqrt{e} x\right)}{4 e}+\frac{1}{2} x^2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)","-\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,"-1/4*(x*Sqrt[d + e*x^2])/Sqrt[e] + (x^2*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/2 + (d*Log[Sqrt[e]*x + Sqrt[d + e*x^2]])/(4*e)","A",1
4,1,167,238,2.4776893,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x} \, dx","Integrate[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x,x]","\frac{\sqrt{e} \sqrt{\frac{e x^2}{d}+1} \left(-\text{Li}_2\left(e^{-2 \sinh ^{-1}\left(\sqrt{\frac{e}{d}} x\right)}\right)-2 \log (x) \log \left(\sqrt{\frac{e x^2}{d}+1}+x \sqrt{\frac{e}{d}}\right)+\sinh ^{-1}\left(x \sqrt{\frac{e}{d}}\right)^2+2 \sinh ^{-1}\left(x \sqrt{\frac{e}{d}}\right) \log \left(1-e^{-2 \sinh ^{-1}\left(x \sqrt{\frac{e}{d}}\right)}\right)\right)}{2 \sqrt{\frac{e}{d}} \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{Li}_2\left(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,"ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]*Log[x] + (Sqrt[e]*Sqrt[1 + (e*x^2)/d]*(ArcSinh[Sqrt[e/d]*x]^2 + 2*ArcSinh[Sqrt[e/d]*x]*Log[1 - E^(-2*ArcSinh[Sqrt[e/d]*x])] - 2*Log[x]*Log[Sqrt[e/d]*x + Sqrt[1 + (e*x^2)/d]] - PolyLog[2, E^(-2*ArcSinh[Sqrt[e/d]*x])]))/(2*Sqrt[e/d]*Sqrt[d + e*x^2])","A",0
5,1,50,53,0.0392706,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^3} \, dx","Integrate[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^3,x]","-\frac{\sqrt{e} x \sqrt{d+e x^2}+d \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{2 d 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,"-1/2*(Sqrt[e]*x*Sqrt[d + e*x^2] + d*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(d*x^2)","A",1
6,1,63,79,0.0457116,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^5} \, dx","Integrate[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^5,x]","\frac{\sqrt{e} x \sqrt{d+e x^2} \left(2 e x^2-d\right)-3 d^2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{12 d^2 x^4}","\frac{e^{3/2} \sqrt{d+e x^2}}{6 d^2 x}-\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{4 x^4}-\frac{\sqrt{e} \sqrt{d+e x^2}}{12 d x^3}",1,"(Sqrt[e]*x*Sqrt[d + e*x^2]*(-d + 2*e*x^2) - 3*d^2*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(12*d^2*x^4)","A",1
7,1,74,105,0.0536194,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^7} \, dx","Integrate[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^7,x]","\frac{\sqrt{e} x \sqrt{d+e x^2} \left(-3 d^2+4 d e x^2-8 e^2 x^4\right)-15 d^3 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{90 d^3 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{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{6 x^6}-\frac{\sqrt{e} \sqrt{d+e x^2}}{30 d x^5}",1,"(Sqrt[e]*x*Sqrt[d + e*x^2]*(-3*d^2 + 4*d*e*x^2 - 8*e^2*x^4) - 15*d^3*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(90*d^3*x^6)","A",1
8,1,85,131,0.0626528,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^9} \, dx","Integrate[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^9,x]","\frac{\sqrt{e} x \sqrt{d+e x^2} \left(-5 d^3+6 d^2 e x^2-8 d e^2 x^4+16 e^3 x^6\right)-35 d^4 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{280 d^4 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{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{8 x^8}-\frac{\sqrt{e} \sqrt{d+e x^2}}{56 d x^7}",1,"(Sqrt[e]*x*Sqrt[d + e*x^2]*(-5*d^3 + 6*d^2*e*x^2 - 8*d*e^2*x^4 + 16*e^3*x^6) - 35*d^4*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(280*d^4*x^8)","A",1
9,1,79,114,0.0606779,"\int x^6 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Integrate[x^6*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","\frac{\sqrt{d+e x^2} \left(16 d^3-8 d^2 e x^2+6 d e^2 x^4-5 e^3 x^6\right)}{245 e^{7/2}}+\frac{1}{7} x^7 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)","\frac{d^3 \sqrt{d+e x^2}}{7 e^{7/2}}-\frac{d^2 \left(d+e x^2\right)^{3/2}}{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,"(Sqrt[d + e*x^2]*(16*d^3 - 8*d^2*e*x^2 + 6*d*e^2*x^4 - 5*e^3*x^6))/(245*e^(7/2)) + (x^7*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/7","A",1
10,1,68,91,0.0642907,"\int x^4 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Integrate[x^4*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","\frac{1}{5} x^5 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)-\frac{\sqrt{d+e x^2} \left(8 d^2-4 d e x^2+3 e^2 x^4\right)}{75 e^{5/2}}","-\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,"-1/75*(Sqrt[d + e*x^2]*(8*d^2 - 4*d*e*x^2 + 3*e^2*x^4))/e^(5/2) + (x^5*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/5","A",1
11,1,56,68,0.0526568,"\int x^2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Integrate[x^2*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","\frac{1}{9} \left(\frac{\left(2 d-e x^2\right) \sqrt{d+e x^2}}{e^{3/2}}+3 x^3 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)\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,"(((2*d - e*x^2)*Sqrt[d + e*x^2])/e^(3/2) + 3*x^3*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/9","A",1
12,1,40,40,0.0135046,"\int \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Integrate[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",1
13,1,61,55,0.0489634,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^2} \, dx","Integrate[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^2,x]","\frac{\sqrt{e} \left(\log (x)-\log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)\right)}{\sqrt{d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{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}}",1,"-(ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x) + (Sqrt[e]*(Log[x] - Log[d + Sqrt[d]*Sqrt[d + e*x^2]]))/Sqrt[d]","A",1
14,1,92,85,0.1096184,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^4} \, dx","Integrate[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^4,x]","-\frac{\frac{\sqrt{e} x \left(\sqrt{d} \sqrt{d+e x^2}-e x^2 \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)+e x^2 \log (x)\right)}{d^{3/2}}+2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{6 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,"-1/6*(2*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]] + (Sqrt[e]*x*(Sqrt[d]*Sqrt[d + e*x^2] + e*x^2*Log[x] - e*x^2*Log[d + Sqrt[d]*Sqrt[d + e*x^2]]))/d^(3/2))/x^3","A",1
15,1,107,111,0.1643533,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^6} \, dx","Integrate[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^6,x]","\frac{\frac{\sqrt{e} x \left(-3 e^2 x^4 \log \left(\sqrt{d} \sqrt{d+e x^2}+d\right)+\sqrt{d} \sqrt{d+e x^2} \left(3 e x^2-2 d\right)+3 e^2 x^4 \log (x)\right)}{d^{5/2}}-8 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{40 x^5}","-\frac{3 e^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d}}\right)}{40 d^{5/2}}+\frac{3 e^{3/2} \sqrt{d+e x^2}}{40 d^2 x^2}-\frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{5 x^5}-\frac{\sqrt{e} \sqrt{d+e x^2}}{20 d x^4}",1,"(-8*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]] + (Sqrt[e]*x*(Sqrt[d]*Sqrt[d + e*x^2]*(-2*d + 3*e*x^2) + 3*e^2*x^4*Log[x] - 3*e^2*x^4*Log[d + Sqrt[d]*Sqrt[d + e*x^2]]))/d^(5/2))/(40*x^5)","A",1
16,1,161,196,0.6910236,"\int x^{9/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Integrate[x^(9/2)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","\frac{2}{847} \sqrt{x} \left(77 x^5 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)-\frac{2 \sqrt{d+e x^2} \left(15 d^2-9 d e x^2+7 e^2 x^4\right)}{e^{5/2}}\right)+\frac{60 d^{5/2} x \sqrt{\frac{i \sqrt{d}}{\sqrt{e}}} \sqrt{\frac{d}{e x^2}+1} F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{d}}{\sqrt{e}}}}{\sqrt{x}}\right)\right|-1\right)}{847 e^2 \sqrt{d+e x^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{60 d^2 \sqrt{x} \sqrt{d+e x^2}}{847 e^{5/2}}+\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,"(2*Sqrt[x]*((-2*Sqrt[d + e*x^2]*(15*d^2 - 9*d*e*x^2 + 7*e^2*x^4))/e^(5/2) + 77*x^5*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]))/847 + (60*d^(5/2)*Sqrt[(I*Sqrt[d])/Sqrt[e]]*Sqrt[1 + d/(e*x^2)]*x*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[d])/Sqrt[e]]/Sqrt[x]], -1])/(847*e^2*Sqrt[d + e*x^2])","C",1
17,1,147,168,0.5025513,"\int x^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Integrate[x^(5/2)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","\frac{2}{147} \sqrt{x} \left(\frac{2 \left(5 d-3 e x^2\right) \sqrt{d+e x^2}}{e^{3/2}}+21 x^3 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)\right)+\frac{20 \sqrt{d} x \left(\frac{i \sqrt{d}}{\sqrt{e}}\right)^{5/2} \sqrt{\frac{d}{e x^2}+1} F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{d}}{\sqrt{e}}}}{\sqrt{x}}\right)\right|-1\right)}{147 \sqrt{d+e x^2}}","-\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,"(2*Sqrt[x]*((2*(5*d - 3*e*x^2)*Sqrt[d + e*x^2])/e^(3/2) + 21*x^3*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]))/147 + (20*Sqrt[d]*((I*Sqrt[d])/Sqrt[e])^(5/2)*Sqrt[1 + d/(e*x^2)]*x*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[d])/Sqrt[e]]/Sqrt[x]], -1])/(147*Sqrt[d + e*x^2])","C",1
18,1,135,142,0.3065963,"\int \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Integrate[Sqrt[x]*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","\frac{2}{9} \sqrt{x} \left(3 x \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)-\frac{2 \sqrt{d+e x^2}}{\sqrt{e}}\right)+\frac{4 \sqrt{d} x \sqrt{\frac{i \sqrt{d}}{\sqrt{e}}} \sqrt{\frac{d}{e x^2}+1} F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{d}}{\sqrt{e}}}}{\sqrt{x}}\right)\right|-1\right)}{9 \sqrt{d+e x^2}}","\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,"(2*Sqrt[x]*((-2*Sqrt[d + e*x^2])/Sqrt[e] + 3*x*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]))/9 + (4*Sqrt[d]*Sqrt[(I*Sqrt[d])/Sqrt[e]]*Sqrt[1 + d/(e*x^2)]*x*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[d])/Sqrt[e]]/Sqrt[x]], -1])/(9*Sqrt[d + e*x^2])","C",1
19,1,111,113,0.1339349,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^{3/2}} \, dx","Integrate[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^(3/2),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{\sqrt{x}}+\frac{4 i \sqrt{e} x \sqrt{\frac{d}{e x^2}+1} F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{d}}{\sqrt{e}}}}{\sqrt{x}}\right)\right|-1\right)}{\sqrt{\frac{i \sqrt{d}}{\sqrt{e}}} \sqrt{d+e x^2}}","\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] + ((4*I)*Sqrt[e]*Sqrt[1 + d/(e*x^2)]*x*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[d])/Sqrt[e]]/Sqrt[x]], -1])/(Sqrt[(I*Sqrt[d])/Sqrt[e]]*Sqrt[d + e*x^2])","C",1
20,1,142,145,0.2425335,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^{7/2}} \, dx","Integrate[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^(7/2),x]","-\frac{2 \left(2 \sqrt{e} x \sqrt{d+e x^2}+3 d \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)\right)}{15 d x^{5/2}}-\frac{4 e^2 x \sqrt{\frac{i \sqrt{d}}{\sqrt{e}}} \sqrt{\frac{d}{e x^2}+1} F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{d}}{\sqrt{e}}}}{\sqrt{x}}\right)\right|-1\right)}{15 d^{3/2} \sqrt{d+e x^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,"(-2*(2*Sqrt[e]*x*Sqrt[d + e*x^2] + 3*d*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]))/(15*d*x^(5/2)) - (4*Sqrt[(I*Sqrt[d])/Sqrt[e]]*e^2*Sqrt[1 + d/(e*x^2)]*x*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[d])/Sqrt[e]]/Sqrt[x]], -1])/(15*d^(3/2)*Sqrt[d + e*x^2])","C",1
21,1,154,173,0.3397851,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^{11/2}} \, dx","Integrate[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^(11/2),x]","\frac{4 \sqrt{e} x \sqrt{d+e x^2} \left(5 e x^2-3 d\right)-42 d^2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{189 d^2 x^{9/2}}+\frac{20 e^3 x \sqrt{\frac{i \sqrt{d}}{\sqrt{e}}} \sqrt{\frac{d}{e x^2}+1} F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{d}}{\sqrt{e}}}}{\sqrt{x}}\right)\right|-1\right)}{189 d^{5/2} \sqrt{d+e x^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{20 e^{3/2} \sqrt{d+e x^2}}{189 d^2 x^{3/2}}-\frac{4 \sqrt{e} \sqrt{d+e x^2}}{63 d x^{7/2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{9 x^{9/2}}",1,"(4*Sqrt[e]*x*Sqrt[d + e*x^2]*(-3*d + 5*e*x^2) - 42*d^2*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(189*d^2*x^(9/2)) + (20*Sqrt[(I*Sqrt[d])/Sqrt[e]]*e^3*Sqrt[1 + d/(e*x^2)]*x*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[d])/Sqrt[e]]/Sqrt[x]], -1])/(189*d^(5/2)*Sqrt[d + e*x^2])","C",1
22,1,163,201,0.4728061,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^{15/2}} \, dx","Integrate[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^(15/2),x]","\frac{2 \left(-\frac{30 e^4 x^{15/2} \sqrt{\frac{i \sqrt{d}}{\sqrt{e}}} \sqrt{\frac{d}{e x^2}+1} F\left(\left.i \sinh ^{-1}\left(\frac{\sqrt{\frac{i \sqrt{d}}{\sqrt{e}}}}{\sqrt{x}}\right)\right|-1\right)}{d^{7/2} \sqrt{d+e x^2}}-\frac{2 \sqrt{e} x \sqrt{d+e x^2} \left(7 d^2-9 d e x^2+15 e^2 x^4\right)}{d^3}-77 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)\right)}{1001 x^{13/2}}","-\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{60 e^{5/2} \sqrt{d+e x^2}}{1001 d^3 x^{3/2}}+\frac{36 e^{3/2} \sqrt{d+e x^2}}{1001 d^2 x^{7/2}}-\frac{4 \sqrt{e} \sqrt{d+e x^2}}{143 d x^{11/2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{13 x^{13/2}}",1,"(2*((-2*Sqrt[e]*x*Sqrt[d + e*x^2]*(7*d^2 - 9*d*e*x^2 + 15*e^2*x^4))/d^3 - 77*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]] - (30*Sqrt[(I*Sqrt[d])/Sqrt[e]]*e^4*Sqrt[1 + d/(e*x^2)]*x^(15/2)*EllipticF[I*ArcSinh[Sqrt[(I*Sqrt[d])/Sqrt[e]]/Sqrt[x]], -1])/(d^(7/2)*Sqrt[d + e*x^2])))/(1001*x^(13/2))","C",1
23,1,124,297,0.1490206,"\int x^{7/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Integrate[x^(7/2)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","\frac{2 x^{3/2} \left(-14 d^2 \sqrt{\frac{e x^2}{d}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{e x^2}{d}\right)+14 d^2+45 e^{3/2} x^3 \sqrt{d+e x^2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)+4 d e x^2-10 e^2 x^4\right)}{405 e^{3/2} \sqrt{d+e x^2}}","-\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^2 \sqrt{x} \sqrt{d+e x^2}}{135 e^2 \left(\sqrt{d}+\sqrt{e} x\right)}+\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,"(2*x^(3/2)*(14*d^2 + 4*d*e*x^2 - 10*e^2*x^4 + 45*e^(3/2)*x^3*Sqrt[d + e*x^2]*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]] - 14*d^2*Sqrt[1 + (e*x^2)/d]*Hypergeometric2F1[1/2, 3/4, 7/4, -((e*x^2)/d)]))/(405*e^(3/2)*Sqrt[d + e*x^2])","C",1
24,1,109,269,0.1040444,"\int x^{3/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right) \, dx","Integrate[x^(3/2)*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]],x]","\frac{2 x^{3/2} \left(2 d \sqrt{\frac{e x^2}{d}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{e x^2}{d}\right)-2 \left(d+e x^2\right)+5 \sqrt{e} x \sqrt{d+e x^2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)\right)}{25 \sqrt{e} \sqrt{d+e x^2}}","\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{12 d \sqrt{x} \sqrt{d+e x^2}}{25 e \left(\sqrt{d}+\sqrt{e} x\right)}-\frac{4 x^{3/2} \sqrt{d+e x^2}}{25 \sqrt{e}}+\frac{2}{5} x^{5/2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)",1,"(2*x^(3/2)*(-2*(d + e*x^2) + 5*Sqrt[e]*x*Sqrt[d + e*x^2]*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]] + 2*d*Sqrt[1 + (e*x^2)/d]*Hypergeometric2F1[1/2, 3/4, 7/4, -((e*x^2)/d)]))/(25*Sqrt[e]*Sqrt[d + e*x^2])","C",1
25,1,85,232,0.1117841,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{\sqrt{x}} \, dx","Integrate[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/Sqrt[x],x]","2 \sqrt{x} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)-\frac{4 \sqrt{e} x^{3/2} \sqrt{\frac{e x^2}{d}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{e x^2}{d}\right)}{3 \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,"2*Sqrt[x]*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]] - (4*Sqrt[e]*x^(3/2)*Sqrt[1 + (e*x^2)/d]*Hypergeometric2F1[1/2, 3/4, 7/4, -((e*x^2)/d)])/(3*Sqrt[d + e*x^2])","C",1
26,1,118,272,0.1168423,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^{5/2}} \, dx","Integrate[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^(5/2),x]","\frac{4 e^{3/2} x^{3/2} \sqrt{\frac{e x^2}{d}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{e x^2}{d}\right)}{9 d \sqrt{d+e x^2}}-\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]) - (2*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]])/(3*x^(3/2)) + (4*e^(3/2)*x^(3/2)*Sqrt[1 + (e*x^2)/d]*Hypergeometric2F1[1/2, 3/4, 7/4, -((e*x^2)/d)])/(9*d*Sqrt[d + e*x^2])","C",1
27,1,131,302,0.1100395,"\int \frac{\tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)}{x^{9/2}} \, dx","Integrate[ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]]/x^(9/2),x]","\frac{4 \sqrt{e} x \left(-d^2+2 d e x^2+3 e^2 x^4\right)-10 d^2 \sqrt{d+e x^2} \tanh ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d+e x^2}}\right)-4 e^{5/2} x^5 \sqrt{\frac{e x^2}{d}+1} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-\frac{e x^2}{d}\right)}{35 d^2 x^{7/2} \sqrt{d+e x^2}}","-\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{12 e^{3/2} \sqrt{d+e x^2}}{35 d^2 \sqrt{x}}-\frac{12 e^2 \sqrt{x} \sqrt{d+e x^2}}{35 d^2 \left(\sqrt{d}+\sqrt{e} x\right)}-\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]*x*(-d^2 + 2*d*e*x^2 + 3*e^2*x^4) - 10*d^2*Sqrt[d + e*x^2]*ArcTanh[(Sqrt[e]*x)/Sqrt[d + e*x^2]] - 4*e^(5/2)*x^5*Sqrt[1 + (e*x^2)/d]*Hypergeometric2F1[1/2, 3/4, 7/4, -((e*x^2)/d)])/(35*d^2*x^(7/2)*Sqrt[d + e*x^2])","C",1
28,1,39,44,0.019273,"\int x^3 \tanh ^{-1}\left(a+b x^4\right) \, dx","Integrate[x^3*ArcTanh[a + b*x^4],x]","\frac{\log \left(1-\left(a+b x^4\right)^2\right)+2 \left(a+b x^4\right) \tanh ^{-1}\left(a+b x^4\right)}{8 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,"(2*(a + b*x^4)*ArcTanh[a + b*x^4] + Log[1 - (a + b*x^4)^2])/(8*b)","A",1
29,1,42,47,0.0392589,"\int x^{-1+n} \tanh ^{-1}\left(a+b x^n\right) \, dx","Integrate[x^(-1 + n)*ArcTanh[a + b*x^n],x]","\frac{\log \left(1-\left(a+b x^n\right)^2\right)+2 \left(a+b x^n\right) \tanh ^{-1}\left(a+b x^n\right)}{2 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,"(2*(a + b*x^n)*ArcTanh[a + b*x^n] + Log[1 - (a + b*x^n)^2])/(2*b*n)","A",1
30,0,0,43,0.0988105,"\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","Integrate[(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,"Integrate[(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2), x]","A",-1
31,1,482,409,0.1898444,"\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","Integrate[(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3/(1 - c^2*x^2),x]","-\frac{-6 b^2 \text{Li}_3\left(-\frac{\sqrt{1-c x}+\sqrt{c x+1}}{\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)+6 b^2 \text{Li}_3\left(\frac{\sqrt{1-c x}+\sqrt{c x+1}}{\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)+6 b \text{Li}_2\left(-\frac{\sqrt{1-c x}+\sqrt{c x+1}}{\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)^2-6 b \text{Li}_2\left(\frac{\sqrt{1-c x}+\sqrt{c x+1}}{\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+8 \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+3 b^3 \text{Li}_4\left(-\frac{\sqrt{1-c x}+\sqrt{c x+1}}{\sqrt{1-c x}-\sqrt{c x+1}}\right)-3 b^3 \text{Li}_4\left(\frac{\sqrt{1-c x}+\sqrt{c x+1}}{\sqrt{1-c x}-\sqrt{c x+1}}\right)}{4 c}","-\frac{3 b^2 \text{Li}_3\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{3 b^2 \text{Li}_3\left(\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{Li}_2\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}{2 c}-\frac{3 b \text{Li}_2\left(\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{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^3 \text{Li}_4\left(1-\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}\right)}{4 c}-\frac{3 b^3 \text{Li}_4\left(\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}-1\right)}{4 c}",1,"-1/4*(8*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3*ArcTanh[1 - 2/(1 - Sqrt[1 - c*x]/Sqrt[1 + c*x])] + 6*b*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*PolyLog[2, -((Sqrt[1 - c*x] + Sqrt[1 + c*x])/(Sqrt[1 - c*x] - Sqrt[1 + c*x]))] - 6*b*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*PolyLog[2, (Sqrt[1 - c*x] + Sqrt[1 + c*x])/(Sqrt[1 - c*x] - Sqrt[1 + c*x])] - 6*b^2*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[3, -((Sqrt[1 - c*x] + Sqrt[1 + c*x])/(Sqrt[1 - c*x] - Sqrt[1 + c*x]))] + 6*b^2*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[3, (Sqrt[1 - c*x] + Sqrt[1 + c*x])/(Sqrt[1 - c*x] - Sqrt[1 + c*x])] + 3*b^3*PolyLog[4, -((Sqrt[1 - c*x] + Sqrt[1 + c*x])/(Sqrt[1 - c*x] - Sqrt[1 + c*x]))] - 3*b^3*PolyLog[4, (Sqrt[1 - c*x] + Sqrt[1 + c*x])/(Sqrt[1 - c*x] - Sqrt[1 + c*x])])/c","A",1
32,1,324,268,0.1089629,"\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","Integrate[(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2/(1 - c^2*x^2),x]","-\frac{b \text{Li}_2\left(-\frac{\sqrt{1-c x}+\sqrt{c x+1}}{\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)-b \text{Li}_2\left(\frac{\sqrt{1-c x}+\sqrt{c x+1}}{\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 \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-\frac{1}{2} b^2 \text{Li}_3\left(-\frac{\sqrt{1-c x}+\sqrt{c x+1}}{\sqrt{1-c x}-\sqrt{c x+1}}\right)+\frac{1}{2} b^2 \text{Li}_3\left(\frac{\sqrt{1-c x}+\sqrt{c x+1}}{\sqrt{1-c x}-\sqrt{c x+1}}\right)}{c}","\frac{b \text{Li}_2\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)}{c}-\frac{b \text{Li}_2\left(\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{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^2 \text{Li}_3\left(1-\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}\right)}{2 c}+\frac{b^2 \text{Li}_3\left(\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}-1\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])] + b*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[2, -((Sqrt[1 - c*x] + Sqrt[1 + c*x])/(Sqrt[1 - c*x] - Sqrt[1 + c*x]))] - b*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[2, (Sqrt[1 - c*x] + Sqrt[1 + c*x])/(Sqrt[1 - c*x] - Sqrt[1 + c*x])] - (b^2*PolyLog[3, -((Sqrt[1 - c*x] + Sqrt[1 + c*x])/(Sqrt[1 - c*x] - Sqrt[1 + c*x]))])/2 + (b^2*PolyLog[3, (Sqrt[1 - c*x] + Sqrt[1 + c*x])/(Sqrt[1 - c*x] - Sqrt[1 + c*x])])/2)/c)","A",1
33,1,43,89,0.2953527,"\int \frac{a+b \tanh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)}{1-c^2 x^2} \, dx","Integrate[(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])/(1 - c^2*x^2),x]","\frac{a \tanh ^{-1}(c x)}{c}+\frac{b \left(\text{Li}_2\left(-e^{-\tanh ^{-1}(c x)}\right)-\text{Li}_2\left(e^{-\tanh ^{-1}(c x)}\right)\right)}{2 c}","-\frac{a \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}{c}+\frac{b \text{Li}_2\left(-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}{2 c}-\frac{b \text{Li}_2\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}{2 c}",1,"(a*ArcTanh[c*x])/c + (b*(PolyLog[2, -E^(-ArcTanh[c*x])] - PolyLog[2, E^(-ArcTanh[c*x])]))/(2*c)","A",0
34,0,0,43,0.0985847,"\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","Integrate[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,"Integrate[1/((1 - c^2*x^2)*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])), x]","A",-1
35,0,0,43,0.8376505,"\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","Integrate[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,"Integrate[1/((1 - c^2*x^2)*(a + b*ArcTanh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2), x]","A",-1
36,1,34,37,0.06474,"\int x^m \tanh ^{-1}(\tanh (a+b x)) \, dx","Integrate[x^m*ArcTanh[Tanh[a + b*x]],x]","x^m \left(\frac{x \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}{m+1}+\frac{b x^2}{m+2}\right)","\frac{x^{m+1} \tanh ^{-1}(\tanh (a+b x))}{m+1}-\frac{b x^{m+2}}{m^2+3 m+2}",1,"x^m*((b*x^2)/(2 + m) + (x*(-(b*x) + ArcTanh[Tanh[a + b*x]]))/(1 + m))","A",1
37,1,20,23,0.0179391,"\int x^2 \tanh ^{-1}(\tanh (a+b x)) \, dx","Integrate[x^2*ArcTanh[Tanh[a + b*x]],x]","-\frac{1}{12} x^3 \left(b x-4 \tanh ^{-1}(\tanh (a+b x))\right)","\frac{1}{3} x^3 \tanh ^{-1}(\tanh (a+b x))-\frac{b x^4}{12}",1,"-1/12*(x^3*(b*x - 4*ArcTanh[Tanh[a + b*x]]))","A",1
38,1,20,23,0.0160868,"\int x \tanh ^{-1}(\tanh (a+b x)) \, dx","Integrate[x*ArcTanh[Tanh[a + b*x]],x]","-\frac{1}{6} x^2 \left(b x-3 \tanh ^{-1}(\tanh (a+b x))\right)","\frac{1}{2} x^2 \tanh ^{-1}(\tanh (a+b x))-\frac{b x^3}{6}",1,"-1/6*(x^2*(b*x - 3*ArcTanh[Tanh[a + b*x]]))","A",1
39,1,18,16,0.0104886,"\int \tanh ^{-1}(\tanh (a+b x)) \, dx","Integrate[ArcTanh[Tanh[a + b*x]],x]","x \tanh ^{-1}(\tanh (a+b x))-\frac{b x^2}{2}","\frac{\tanh ^{-1}(\tanh (a+b x))^2}{2 b}",1,"-1/2*(b*x^2) + x*ArcTanh[Tanh[a + b*x]]","A",1
40,1,19,21,0.0150967,"\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]/x,x]","\log (x) \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)+b x","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",1
41,1,18,17,0.0214323,"\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^2} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]/x^2,x]","-\frac{\tanh ^{-1}(\tanh (a+b x))}{x}+b \log (x)+b","b \log (x)-\frac{\tanh ^{-1}(\tanh (a+b x))}{x}",1,"b - ArcTanh[Tanh[a + b*x]]/x + b*Log[x]","A",1
42,1,18,23,0.0147387,"\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^3} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]/x^3,x]","-\frac{\tanh ^{-1}(\tanh (a+b x))+b x}{2 x^2}","-\frac{\tanh ^{-1}(\tanh (a+b x))}{2 x^2}-\frac{b}{2 x}",1,"-1/2*(b*x + ArcTanh[Tanh[a + b*x]])/x^2","A",1
43,1,20,23,0.0159153,"\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^4} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]/x^4,x]","-\frac{2 \tanh ^{-1}(\tanh (a+b x))+b x}{6 x^3}","-\frac{\tanh ^{-1}(\tanh (a+b x))}{3 x^3}-\frac{b}{6 x^2}",1,"-1/6*(b*x + 2*ArcTanh[Tanh[a + b*x]])/x^3","A",1
44,1,62,71,0.1617591,"\int x^m \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Integrate[x^m*ArcTanh[Tanh[a + b*x]]^2,x]","\frac{x^{m+1} \left(\left(m^2+5 m+6\right) \tanh ^{-1}(\tanh (a+b x))^2-2 b (m+3) x \tanh ^{-1}(\tanh (a+b x))+2 b^2 x^2\right)}{(m+1) (m+2) (m+3)}","-\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,"(x^(1 + m)*(2*b^2*x^2 - 2*b*(3 + m)*x*ArcTanh[Tanh[a + b*x]] + (6 + 5*m + m^2)*ArcTanh[Tanh[a + b*x]]^2))/((1 + m)*(2 + m)*(3 + m))","A",1
45,1,37,42,0.0338551,"\int x^3 \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Integrate[x^3*ArcTanh[Tanh[a + b*x]]^2,x]","\frac{1}{60} x^4 \left(-6 b x \tanh ^{-1}(\tanh (a+b x))+15 \tanh ^{-1}(\tanh (a+b x))^2+b^2 x^2\right)","-\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,"(x^4*(b^2*x^2 - 6*b*x*ArcTanh[Tanh[a + b*x]] + 15*ArcTanh[Tanh[a + b*x]]^2))/60","A",1
46,1,37,42,0.0502232,"\int x^2 \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Integrate[x^2*ArcTanh[Tanh[a + b*x]]^2,x]","\frac{1}{30} x^3 \left(-5 b x \tanh ^{-1}(\tanh (a+b x))+10 \tanh ^{-1}(\tanh (a+b x))^2+b^2 x^2\right)","-\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,"(x^3*(b^2*x^2 - 5*b*x*ArcTanh[Tanh[a + b*x]] + 10*ArcTanh[Tanh[a + b*x]]^2))/30","A",1
47,1,74,34,0.0776672,"\int x \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Integrate[x*ArcTanh[Tanh[a + b*x]]^2,x]","\frac{(a+b x) \left(4 \left(2 a^2+a b x-b^2 x^2\right) \tanh ^{-1}(\tanh (a+b x))-\left((3 a-b x) (a+b x)^2\right)-6 (a-b x) \tanh ^{-1}(\tanh (a+b x))^2\right)}{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,"((a + b*x)*(-((3*a - b*x)*(a + b*x)^2) + 4*(2*a^2 + a*b*x - b^2*x^2)*ArcTanh[Tanh[a + b*x]] - 6*(a - b*x)*ArcTanh[Tanh[a + b*x]]^2))/(12*b^2)","B",1
48,1,16,16,0.0066761,"\int \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Integrate[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",1
49,1,53,49,0.0678524,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^2/x,x]","\frac{1}{2} (a+b x)^2-(a+b x) \left(-2 \tanh ^{-1}(\tanh (a+b x))+a+2 b x\right)+\log (b x) \left(\tanh ^{-1}(\tanh (a+b x))-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,"(a + b*x)^2/2 - (a + b*x)*(a + 2*b*x - 2*ArcTanh[Tanh[a + b*x]]) + (-(b*x) + ArcTanh[Tanh[a + b*x]])^2*Log[b*x]","A",1
50,1,37,39,0.0514901,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^2} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^2/x^2,x]","-\frac{\tanh ^{-1}(\tanh (a+b x))^2}{x}+2 b (\log (x)+1) \tanh ^{-1}(\tanh (a+b x))-2 b^2 x \log (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,"-(ArcTanh[Tanh[a + b*x]]^2/x) - 2*b^2*x*Log[x] + 2*b*ArcTanh[Tanh[a + b*x]]*(1 + Log[x])","A",1
51,1,42,36,0.035737,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^3} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^2/x^3,x]","-\frac{2 b x \tanh ^{-1}(\tanh (a+b x))+\tanh ^{-1}(\tanh (a+b x))^2-b^2 x^2 (2 \log (x)+3)}{2 x^2}","-\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,"-1/2*(2*b*x*ArcTanh[Tanh[a + b*x]] + ArcTanh[Tanh[a + b*x]]^2 - b^2*x^2*(3 + 2*Log[x]))/x^2","A",1
52,1,34,31,0.0413836,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^4} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^2/x^4,x]","-\frac{b x \tanh ^{-1}(\tanh (a+b x))+\tanh ^{-1}(\tanh (a+b x))^2+b^2 x^2}{3 x^3}","\frac{\tanh ^{-1}(\tanh (a+b x))^3}{3 x^3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"-1/3*(b^2*x^2 + b*x*ArcTanh[Tanh[a + b*x]] + ArcTanh[Tanh[a + b*x]]^2)/x^3","A",1
53,1,37,42,0.0302832,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^5} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^2/x^5,x]","-\frac{2 b x \tanh ^{-1}(\tanh (a+b x))+3 \tanh ^{-1}(\tanh (a+b x))^2+b^2 x^2}{12 x^4}","-\frac{\tanh ^{-1}(\tanh (a+b x))^2}{4 x^4}-\frac{b \tanh ^{-1}(\tanh (a+b x))}{6 x^3}-\frac{b^2}{12 x^2}",1,"-1/12*(b^2*x^2 + 2*b*x*ArcTanh[Tanh[a + b*x]] + 3*ArcTanh[Tanh[a + b*x]]^2)/x^4","A",1
54,1,97,110,0.2431273,"\int x^m \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Integrate[x^m*ArcTanh[Tanh[a + b*x]]^3,x]","\frac{x^{m+1} \left(6 b^2 (m+4) x^2 \tanh ^{-1}(\tanh (a+b x))-3 b \left(m^2+7 m+12\right) x \tanh ^{-1}(\tanh (a+b x))^2+\left(m^3+9 m^2+26 m+24\right) \tanh ^{-1}(\tanh (a+b x))^3-6 b^3 x^3\right)}{(m+1) (m+2) (m+3) (m+4)}","\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,"(x^(1 + m)*(-6*b^3*x^3 + 6*b^2*(4 + m)*x^2*ArcTanh[Tanh[a + b*x]] - 3*b*(12 + 7*m + m^2)*x*ArcTanh[Tanh[a + b*x]]^2 + (24 + 26*m + 9*m^2 + m^3)*ArcTanh[Tanh[a + b*x]]^3))/((1 + m)*(2 + m)*(3 + m)*(4 + m))","A",1
55,1,54,61,0.0286574,"\int x^3 \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Integrate[x^3*ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{1}{140} x^4 \left(-7 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+21 b x \tanh ^{-1}(\tanh (a+b x))^2-35 \tanh ^{-1}(\tanh (a+b x))^3+b^3 x^3\right)","\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,"-1/140*(x^4*(b^3*x^3 - 7*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 21*b*x*ArcTanh[Tanh[a + b*x]]^2 - 35*ArcTanh[Tanh[a + b*x]]^3))","A",1
56,1,54,53,0.032686,"\int x^2 \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Integrate[x^2*ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{1}{60} x^3 \left(-6 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+15 b x \tanh ^{-1}(\tanh (a+b x))^2-20 \tanh ^{-1}(\tanh (a+b x))^3+b^3 x^3\right)","\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,"-1/60*(x^3*(b^3*x^3 - 6*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 15*b*x*ArcTanh[Tanh[a + b*x]]^2 - 20*ArcTanh[Tanh[a + b*x]]^3))","A",1
57,1,99,34,0.0819152,"\int x \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Integrate[x*ArcTanh[Tanh[a + b*x]]^3,x]","\frac{(a+b x) \left(10 \left(2 a^2+a b x-b^2 x^2\right) \tanh ^{-1}(\tanh (a+b x))^2+(4 a-b x) (a+b x)^3-5 (3 a-b x) (a+b x)^2 \tanh ^{-1}(\tanh (a+b x))-10 (a-b x) \tanh ^{-1}(\tanh (a+b x))^3\right)}{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,"((a + b*x)*((4*a - b*x)*(a + b*x)^3 - 5*(3*a - b*x)*(a + b*x)^2*ArcTanh[Tanh[a + b*x]] + 10*(2*a^2 + a*b*x - b^2*x^2)*ArcTanh[Tanh[a + b*x]]^2 - 10*(a - b*x)*ArcTanh[Tanh[a + b*x]]^3))/(20*b^2)","B",1
58,1,16,16,0.0064671,"\int \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Integrate[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",1
59,1,104,77,0.0980376,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^3/x,x]","(a+b x) \left(a^2-3 a \left(-\tanh ^{-1}(\tanh (a+b x))+a+b x\right)+3 \left(-\tanh ^{-1}(\tanh (a+b x))+a+b x\right)^2\right)+\frac{1}{3} (a+b x)^3-\frac{1}{2} (a+b x)^2 \left(-3 \tanh ^{-1}(\tanh (a+b x))+2 a+3 b x\right)+\log (b x) \left(\tanh ^{-1}(\tanh (a+b x))-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,"(a + b*x)^3/3 + (a + b*x)*(a^2 - 3*a*(a + b*x - ArcTanh[Tanh[a + b*x]]) + 3*(a + b*x - ArcTanh[Tanh[a + b*x]])^2) - ((a + b*x)^2*(2*a + 3*b*x - 3*ArcTanh[Tanh[a + b*x]]))/2 + (-(b*x) + ArcTanh[Tanh[a + b*x]])^3*Log[b*x]","A",1
60,1,62,68,0.0524228,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^2} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^3/x^2,x]","-6 b^2 x \log (x) \tanh ^{-1}(\tanh (a+b x))-\frac{\tanh ^{-1}(\tanh (a+b x))^3}{x}+3 b (\log (x)+1) \tanh ^{-1}(\tanh (a+b x))^2+\frac{3}{2} b^3 x^2 (2 \log (x)-1)","-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,"-(ArcTanh[Tanh[a + b*x]]^3/x) - 6*b^2*x*ArcTanh[Tanh[a + b*x]]*Log[x] + 3*b*ArcTanh[Tanh[a + b*x]]^2*(1 + Log[x]) + (3*b^3*x^2*(-1 + 2*Log[x]))/2","A",1
61,1,66,60,0.0489541,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^3} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^3/x^3,x]","3 b^2 \log (x) \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)-\frac{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^3}{2 x^2}-\frac{3 b \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}{x}+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,"b^3*x - (3*b*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)/x - (-(b*x) + ArcTanh[Tanh[a + b*x]])^3/(2*x^2) + 3*b^2*(-(b*x) + ArcTanh[Tanh[a + b*x]])*Log[x]","A",1
62,1,60,55,0.0245623,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^4} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^3/x^4,x]","\frac{-6 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))-3 b x \tanh ^{-1}(\tanh (a+b x))^2-2 \tanh ^{-1}(\tanh (a+b x))^3+b^3 x^3 (6 \log (x)+11)}{6 x^3}","-\frac{b^2 \tanh ^{-1}(\tanh (a+b x))}{x}-\frac{\tanh ^{-1}(\tanh (a+b x))^3}{3 x^3}-\frac{b \tanh ^{-1}(\tanh (a+b x))^2}{2 x^2}+b^3 \log (x)",1,"(-6*b^2*x^2*ArcTanh[Tanh[a + b*x]] - 3*b*x*ArcTanh[Tanh[a + b*x]]^2 - 2*ArcTanh[Tanh[a + b*x]]^3 + b^3*x^3*(11 + 6*Log[x]))/(6*x^3)","A",1
63,1,50,31,0.0233085,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^5} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^3/x^5,x]","-\frac{b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+b x \tanh ^{-1}(\tanh (a+b x))^2+\tanh ^{-1}(\tanh (a+b x))^3+b^3 x^3}{4 x^4}","\frac{\tanh ^{-1}(\tanh (a+b x))^4}{4 x^4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"-1/4*(b^3*x^3 + b^2*x^2*ArcTanh[Tanh[a + b*x]] + b*x*ArcTanh[Tanh[a + b*x]]^2 + ArcTanh[Tanh[a + b*x]]^3)/x^4","A",1
64,1,54,64,0.0349988,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^6} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^3/x^6,x]","-\frac{2 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+3 b x \tanh ^{-1}(\tanh (a+b x))^2+4 \tanh ^{-1}(\tanh (a+b x))^3+b^3 x^3}{20 x^5}","\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,"-1/20*(b^3*x^3 + 2*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 3*b*x*ArcTanh[Tanh[a + b*x]]^2 + 4*ArcTanh[Tanh[a + b*x]]^3)/x^5","A",1
65,1,137,154,0.4139953,"\int x^m \tanh ^{-1}(\tanh (a+b x))^4 \, dx","Integrate[x^m*ArcTanh[Tanh[a + b*x]]^4,x]","\frac{x^{m+1} \left(-24 b^3 (m+5) x^3 \tanh ^{-1}(\tanh (a+b x))+12 b^2 \left(m^2+9 m+20\right) x^2 \tanh ^{-1}(\tanh (a+b x))^2-4 b \left(m^3+12 m^2+47 m+60\right) x \tanh ^{-1}(\tanh (a+b x))^3+\left(m^4+14 m^3+71 m^2+154 m+120\right) \tanh ^{-1}(\tanh (a+b x))^4+24 b^4 x^4\right)}{(m+1) (m+2) (m+3) (m+4) (m+5)}","-\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{12 b^2 x^{m+3} \tanh ^{-1}(\tanh (a+b x))^2}{m^3+6 m^2+11 m+6}-\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,"(x^(1 + m)*(24*b^4*x^4 - 24*b^3*(5 + m)*x^3*ArcTanh[Tanh[a + b*x]] + 12*b^2*(20 + 9*m + m^2)*x^2*ArcTanh[Tanh[a + b*x]]^2 - 4*b*(60 + 47*m + 12*m^2 + m^3)*x*ArcTanh[Tanh[a + b*x]]^3 + (120 + 154*m + 71*m^2 + 14*m^3 + m^4)*ArcTanh[Tanh[a + b*x]]^4))/((1 + m)*(2 + m)*(3 + m)*(4 + m)*(5 + m))","A",1
66,1,71,80,0.0677749,"\int x^6 \tanh ^{-1}(\tanh (a+b x))^4 \, dx","Integrate[x^6*ArcTanh[Tanh[a + b*x]]^4,x]","\frac{x^7 \left(-11 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+55 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2-165 b x \tanh ^{-1}(\tanh (a+b x))^3+330 \tanh ^{-1}(\tanh (a+b x))^4+b^4 x^4\right)}{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,"(x^7*(b^4*x^4 - 11*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 55*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 - 165*b*x*ArcTanh[Tanh[a + b*x]]^3 + 330*ArcTanh[Tanh[a + b*x]]^4))/2310","A",1
67,1,71,80,0.0340652,"\int x^5 \tanh ^{-1}(\tanh (a+b x))^4 \, dx","Integrate[x^5*ArcTanh[Tanh[a + b*x]]^4,x]","\frac{x^6 \left(-10 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+45 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2-120 b x \tanh ^{-1}(\tanh (a+b x))^3+210 \tanh ^{-1}(\tanh (a+b x))^4+b^4 x^4\right)}{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,"(x^6*(b^4*x^4 - 10*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 45*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 - 120*b*x*ArcTanh[Tanh[a + b*x]]^3 + 210*ArcTanh[Tanh[a + b*x]]^4))/1260","A",1
68,1,71,80,0.0354386,"\int x^4 \tanh ^{-1}(\tanh (a+b x))^4 \, dx","Integrate[x^4*ArcTanh[Tanh[a + b*x]]^4,x]","\frac{1}{630} x^5 \left(-9 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+36 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2-84 b x \tanh ^{-1}(\tanh (a+b x))^3+126 \tanh ^{-1}(\tanh (a+b x))^4+b^4 x^4\right)","-\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,"(x^5*(b^4*x^4 - 9*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 36*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 - 84*b*x*ArcTanh[Tanh[a + b*x]]^3 + 126*ArcTanh[Tanh[a + b*x]]^4))/630","A",1
69,1,71,72,0.0266578,"\int x^3 \tanh ^{-1}(\tanh (a+b x))^4 \, dx","Integrate[x^3*ArcTanh[Tanh[a + b*x]]^4,x]","\frac{1}{280} x^4 \left(-8 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+28 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2-56 b x \tanh ^{-1}(\tanh (a+b x))^3+70 \tanh ^{-1}(\tanh (a+b x))^4+b^4 x^4\right)","-\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^2 \tanh ^{-1}(\tanh (a+b x))^6}{10 b^2}+\frac{x^3 \tanh ^{-1}(\tanh (a+b x))^5}{5 b}",1,"(x^4*(b^4*x^4 - 8*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 28*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 - 56*b*x*ArcTanh[Tanh[a + b*x]]^3 + 70*ArcTanh[Tanh[a + b*x]]^4))/280","A",1
70,1,71,53,0.0594792,"\int x^2 \tanh ^{-1}(\tanh (a+b x))^4 \, dx","Integrate[x^2*ArcTanh[Tanh[a + b*x]]^4,x]","\frac{1}{105} x^3 \left(-7 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+21 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2-35 b x \tanh ^{-1}(\tanh (a+b x))^3+35 \tanh ^{-1}(\tanh (a+b x))^4+b^4 x^4\right)","\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^3*(b^4*x^4 - 7*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 21*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 - 35*b*x*ArcTanh[Tanh[a + b*x]]^3 + 35*ArcTanh[Tanh[a + b*x]]^4))/105","A",1
71,1,125,34,0.0967361,"\int x \tanh ^{-1}(\tanh (a+b x))^4 \, dx","Integrate[x*ArcTanh[Tanh[a + b*x]]^4,x]","-\frac{(a+b x) \left(-20 \left(2 a^2+a b x-b^2 x^2\right) \tanh ^{-1}(\tanh (a+b x))^3+(5 a-b x) (a+b x)^4-6 (4 a-b x) (a+b x)^3 \tanh ^{-1}(\tanh (a+b x))+15 (3 a-b x) (a+b x)^2 \tanh ^{-1}(\tanh (a+b x))^2+15 (a-b x) \tanh ^{-1}(\tanh (a+b x))^4\right)}{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,"-1/30*((a + b*x)*((5*a - b*x)*(a + b*x)^4 - 6*(4*a - b*x)*(a + b*x)^3*ArcTanh[Tanh[a + b*x]] + 15*(3*a - b*x)*(a + b*x)^2*ArcTanh[Tanh[a + b*x]]^2 - 20*(2*a^2 + a*b*x - b^2*x^2)*ArcTanh[Tanh[a + b*x]]^3 + 15*(a - b*x)*ArcTanh[Tanh[a + b*x]]^4))/b^2","B",1
72,1,16,16,0.0060223,"\int \tanh ^{-1}(\tanh (a+b x))^4 \, dx","Integrate[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",1
73,1,175,105,0.1711428,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^4/x,x]","\frac{1}{2} (a+b x)^2 \left(a^2-4 a \left(-\tanh ^{-1}(\tanh (a+b x))+a+b x\right)+6 \left(-\tanh ^{-1}(\tanh (a+b x))+a+b x\right)^2\right)+(a+b x) \left(a^3-4 a^2 \left(-\tanh ^{-1}(\tanh (a+b x))+a+b x\right)+6 a \left(-\tanh ^{-1}(\tanh (a+b x))+a+b x\right)^2-4 \left(-\tanh ^{-1}(\tanh (a+b x))+a+b x\right)^3\right)+\frac{1}{4} (a+b x)^4-\frac{1}{3} (a+b x)^3 \left(-4 \tanh ^{-1}(\tanh (a+b x))+3 a+4 b x\right)+\log (b x) \left(\tanh ^{-1}(\tanh (a+b x))-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,"(a + b*x)^4/4 + ((a + b*x)^2*(a^2 - 4*a*(a + b*x - ArcTanh[Tanh[a + b*x]]) + 6*(a + b*x - ArcTanh[Tanh[a + b*x]])^2))/2 + (a + b*x)*(a^3 - 4*a^2*(a + b*x - ArcTanh[Tanh[a + b*x]]) + 6*a*(a + b*x - ArcTanh[Tanh[a + b*x]])^2 - 4*(a + b*x - ArcTanh[Tanh[a + b*x]])^3) - ((a + b*x)^3*(3*a + 4*b*x - 4*ArcTanh[Tanh[a + b*x]]))/3 + (-(b*x) + ArcTanh[Tanh[a + b*x]])^4*Log[b*x]","A",1
74,1,85,95,0.0914127,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^2} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^4/x^2,x]","6 b^3 x^2 (2 \log (x)-1) \tanh ^{-1}(\tanh (a+b x))-12 b^2 x \log (x) \tanh ^{-1}(\tanh (a+b x))^2-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{x}+4 b (\log (x)+1) \tanh ^{-1}(\tanh (a+b x))^3+\frac{2}{3} b^4 x^3 (5-6 \log (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",1,"-(ArcTanh[Tanh[a + b*x]]^4/x) + (2*b^4*x^3*(5 - 6*Log[x]))/3 - 12*b^2*x*ArcTanh[Tanh[a + b*x]]^2*Log[x] + 4*b*ArcTanh[Tanh[a + b*x]]^3*(1 + Log[x]) + 6*b^3*x^2*ArcTanh[Tanh[a + b*x]]*(-1 + 2*Log[x])","A",1
75,1,81,87,0.0380053,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^3} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^4/x^3,x]","-6 b^3 x (2 \log (x)+1) \tanh ^{-1}(\tanh (a+b x))+3 b^2 (2 \log (x)+3) \tanh ^{-1}(\tanh (a+b x))^2-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{2 x^2}-\frac{2 b \tanh ^{-1}(\tanh (a+b x))^3}{x}+6 b^4 x^2 \log (x)","-6 b^3 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)+3 b^2 \tanh ^{-1}(\tanh (a+b x))^2+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,"(-2*b*ArcTanh[Tanh[a + b*x]]^3)/x - ArcTanh[Tanh[a + b*x]]^4/(2*x^2) + 6*b^4*x^2*Log[x] - 6*b^3*x*ArcTanh[Tanh[a + b*x]]*(1 + 2*Log[x]) + 3*b^2*ArcTanh[Tanh[a + b*x]]^2*(3 + 2*Log[x])","A",1
76,1,82,77,0.0539217,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^4} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^4/x^4,x]","-\frac{-2 b^3 x^3 (6 \log (x)+11) \tanh ^{-1}(\tanh (a+b x))+6 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2+2 b x \tanh ^{-1}(\tanh (a+b x))^3+\tanh ^{-1}(\tanh (a+b x))^4+2 b^4 x^4 (6 \log (x)+5)}{3 x^3}","-4 b^3 \log (x) \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)-\frac{2 b^2 \tanh ^{-1}(\tanh (a+b x))^2}{x}-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{3 x^3}-\frac{2 b \tanh ^{-1}(\tanh (a+b x))^3}{3 x^2}+4 b^4 x",1,"-1/3*(6*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 + 2*b*x*ArcTanh[Tanh[a + b*x]]^3 + ArcTanh[Tanh[a + b*x]]^4 + 2*b^4*x^4*(5 + 6*Log[x]) - 2*b^3*x^3*ArcTanh[Tanh[a + b*x]]*(11 + 6*Log[x]))/x^3","A",1
77,1,78,74,0.0327053,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^5} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^4/x^5,x]","-\frac{12 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+6 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2+4 b x \tanh ^{-1}(\tanh (a+b x))^3+3 \tanh ^{-1}(\tanh (a+b x))^4-b^4 x^4 (12 \log (x)+25)}{12 x^4}","-\frac{b^3 \tanh ^{-1}(\tanh (a+b x))}{x}-\frac{b^2 \tanh ^{-1}(\tanh (a+b x))^2}{2 x^2}-\frac{\tanh ^{-1}(\tanh (a+b x))^4}{4 x^4}-\frac{b \tanh ^{-1}(\tanh (a+b x))^3}{3 x^3}+b^4 \log (x)",1,"-1/12*(12*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 6*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 + 4*b*x*ArcTanh[Tanh[a + b*x]]^3 + 3*ArcTanh[Tanh[a + b*x]]^4 - b^4*x^4*(25 + 12*Log[x]))/x^4","A",1
78,1,66,31,0.0562448,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^6} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^4/x^6,x]","-\frac{b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2+b x \tanh ^{-1}(\tanh (a+b x))^3+\tanh ^{-1}(\tanh (a+b x))^4+b^4 x^4}{5 x^5}","\frac{\tanh ^{-1}(\tanh (a+b x))^5}{5 x^5 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}",1,"-1/5*(b^4*x^4 + b^3*x^3*ArcTanh[Tanh[a + b*x]] + b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 + b*x*ArcTanh[Tanh[a + b*x]]^3 + ArcTanh[Tanh[a + b*x]]^4)/x^5","B",1
79,1,71,64,0.0355188,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^7} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^4/x^7,x]","-\frac{2 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+3 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2+4 b x \tanh ^{-1}(\tanh (a+b x))^3+5 \tanh ^{-1}(\tanh (a+b x))^4+b^4 x^4}{30 x^6}","\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,"-1/30*(b^4*x^4 + 2*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 3*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 + 4*b*x*ArcTanh[Tanh[a + b*x]]^3 + 5*ArcTanh[Tanh[a + b*x]]^4)/x^6","A",1
80,1,71,98,0.0389015,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^8} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^4/x^8,x]","-\frac{3 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+6 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2+10 b x \tanh ^{-1}(\tanh (a+b x))^3+15 \tanh ^{-1}(\tanh (a+b x))^4+b^4 x^4}{105 x^7}","\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,"-1/105*(b^4*x^4 + 3*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 6*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 + 10*b*x*ArcTanh[Tanh[a + b*x]]^3 + 15*ArcTanh[Tanh[a + b*x]]^4)/x^7","A",1
81,1,71,80,0.0371976,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^9} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^4/x^9,x]","-\frac{4 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+10 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2+20 b x \tanh ^{-1}(\tanh (a+b x))^3+35 \tanh ^{-1}(\tanh (a+b x))^4+b^4 x^4}{280 x^8}","-\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{\tanh ^{-1}(\tanh (a+b x))^4}{8 x^8}-\frac{b \tanh ^{-1}(\tanh (a+b x))^3}{14 x^7}-\frac{b^4}{280 x^4}",1,"-1/280*(b^4*x^4 + 4*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 10*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 + 20*b*x*ArcTanh[Tanh[a + b*x]]^3 + 35*ArcTanh[Tanh[a + b*x]]^4)/x^8","A",1
82,1,71,80,0.0658612,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^{10}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^4/x^10,x]","-\frac{5 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+15 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2+35 b x \tanh ^{-1}(\tanh (a+b x))^3+70 \tanh ^{-1}(\tanh (a+b x))^4+b^4 x^4}{630 x^9}","-\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{\tanh ^{-1}(\tanh (a+b x))^4}{9 x^9}-\frac{b \tanh ^{-1}(\tanh (a+b x))^3}{18 x^8}-\frac{b^4}{630 x^5}",1,"-1/630*(b^4*x^4 + 5*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 15*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 + 35*b*x*ArcTanh[Tanh[a + b*x]]^3 + 70*ArcTanh[Tanh[a + b*x]]^4)/x^9","A",1
83,1,71,80,0.0364932,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^4}{x^{11}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^4/x^11,x]","-\frac{6 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+21 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2+56 b x \tanh ^{-1}(\tanh (a+b x))^3+126 \tanh ^{-1}(\tanh (a+b x))^4+b^4 x^4}{1260 x^{10}}","-\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{\tanh ^{-1}(\tanh (a+b x))^4}{10 x^{10}}-\frac{2 b \tanh ^{-1}(\tanh (a+b x))^3}{45 x^9}-\frac{b^4}{1260 x^6}",1,"-1/1260*(b^4*x^4 + 6*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 21*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 + 56*b*x*ArcTanh[Tanh[a + b*x]]^3 + 126*ArcTanh[Tanh[a + b*x]]^4)/x^10","A",1
84,1,177,34,0.1354185,"\int x \tanh ^{-1}(\tanh (a+b x))^6 \, dx","Integrate[x*ArcTanh[Tanh[a + b*x]]^6,x]","-\frac{(a+b x) \left(-56 \left(2 a^2+a b x-b^2 x^2\right) \tanh ^{-1}(\tanh (a+b x))^5+(7 a-b x) (a+b x)^6-8 (6 a-b x) (a+b x)^5 \tanh ^{-1}(\tanh (a+b x))+28 (5 a-b x) (a+b x)^4 \tanh ^{-1}(\tanh (a+b x))^2-56 (4 a-b x) (a+b x)^3 \tanh ^{-1}(\tanh (a+b x))^3+70 (3 a-b x) (a+b x)^2 \tanh ^{-1}(\tanh (a+b x))^4+28 (a-b x) \tanh ^{-1}(\tanh (a+b x))^6\right)}{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,"-1/56*((a + b*x)*((7*a - b*x)*(a + b*x)^6 - 8*(6*a - b*x)*(a + b*x)^5*ArcTanh[Tanh[a + b*x]] + 28*(5*a - b*x)*(a + b*x)^4*ArcTanh[Tanh[a + b*x]]^2 - 56*(4*a - b*x)*(a + b*x)^3*ArcTanh[Tanh[a + b*x]]^3 + 70*(3*a - b*x)*(a + b*x)^2*ArcTanh[Tanh[a + b*x]]^4 - 56*(2*a^2 + a*b*x - b^2*x^2)*ArcTanh[Tanh[a + b*x]]^5 + 28*(a - b*x)*ArcTanh[Tanh[a + b*x]]^6))/b^2","B",1
85,1,51,53,0.0918959,"\int \frac{x^m}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[x^m/ArcTanh[Tanh[a + b*x]],x]","\frac{x^{m+1} \, _2F_1\left(1,m+1;m+2;-\frac{b x}{\tanh ^{-1}(\tanh (a+b x))-b x}\right)}{(m+1) \left(\tanh ^{-1}(\tanh (a+b x))-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
86,1,79,81,0.046859,"\int \frac{x^3}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[x^3/ArcTanh[Tanh[a + b*x]],x]","-\frac{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^3 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^4}+\frac{x \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}{b^3}-\frac{x^2 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}{2 b^2}+\frac{x^3}{3 b}","\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 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{b^3}+\frac{x^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{2 b^2}+\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",1
87,1,55,56,0.0445183,"\int \frac{x^2}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[x^2/ArcTanh[Tanh[a + b*x]],x]","\frac{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}-\frac{x \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}{b^2}+\frac{x^2}{2 b}","\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 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^2}+\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",1
88,1,31,31,0.0262347,"\int \frac{x}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[x/ArcTanh[Tanh[a + b*x]],x]","\frac{x}{b}-\frac{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right) \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^2}","\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",1
89,1,12,12,0.0515152,"\int \frac{1}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[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",1
90,1,29,44,0.0290778,"\int \frac{1}{x \tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[1/(x*ArcTanh[Tanh[a + b*x]]),x]","\frac{\log \left(\tanh ^{-1}(\tanh (a+b x))\right)-\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] + Log[ArcTanh[Tanh[a + b*x]]])/(b*x - ArcTanh[Tanh[a + b*x]])","A",1
91,1,45,65,0.0336502,"\int \frac{1}{x^2 \tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[1/(x^2*ArcTanh[Tanh[a + b*x]]),x]","\frac{b x \left(\log \left(\tanh ^{-1}(\tanh (a+b x))\right)-\log (x)+1\right)-\tanh ^{-1}(\tanh (a+b x))}{x \left(\tanh ^{-1}(\tanh (a+b x))-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,"(-ArcTanh[Tanh[a + b*x]] + b*x*(1 - Log[x] + Log[ArcTanh[Tanh[a + b*x]]]))/(x*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)","A",1
92,1,66,92,0.036093,"\int \frac{1}{x^3 \tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[1/(x^3*ArcTanh[Tanh[a + b*x]]),x]","\frac{b^2 x^2 \left(2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)-2 \log (x)+3\right)-4 b x \tanh ^{-1}(\tanh (a+b x))+\tanh ^{-1}(\tanh (a+b x))^2}{2 x^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}","-\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,"(-4*b*x*ArcTanh[Tanh[a + b*x]] + ArcTanh[Tanh[a + b*x]]^2 + b^2*x^2*(3 - 2*Log[x] + 2*Log[ArcTanh[Tanh[a + b*x]]]))/(2*x^2*(b*x - ArcTanh[Tanh[a + b*x]])^3)","A",1
93,1,51,65,0.5503764,"\int \frac{x^m}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[x^m/ArcTanh[Tanh[a + b*x]]^2,x]","\frac{x^{m+1} \, _2F_1\left(2,m+1;m+2;-\frac{b x}{\tanh ^{-1}(\tanh (a+b x))-b x}\right)}{(m+1) \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}","-\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^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, -((b*x)/(-(b*x) + ArcTanh[Tanh[a + b*x]]))])/((1 + m)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)","A",1
94,1,106,98,0.0950771,"\int \frac{x^4}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[x^4/ArcTanh[Tanh[a + b*x]]^2,x]","-\frac{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4}{b^5 \tanh ^{-1}(\tanh (a+b x))}-\frac{4 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^3 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^5}+\frac{3 x \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}{b^4}-\frac{x^2 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}{b^3}+\frac{x^3}{3 b^2}","\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{4 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{b^4}+\frac{2 x^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}-\frac{x^4}{b \tanh ^{-1}(\tanh (a+b x))}+\frac{4 x^3}{3 b^2}",1,"x^3/(3*b^2) - (x^2*(-(b*x) + ArcTanh[Tanh[a + b*x]]))/b^3 + (3*x*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)/b^4 - (-(b*x) + ArcTanh[Tanh[a + b*x]])^4/(b^5*ArcTanh[Tanh[a + b*x]]) - (4*(-(b*x) + ArcTanh[Tanh[a + b*x]])^3*Log[ArcTanh[Tanh[a + b*x]]])/b^5","A",1
95,1,83,75,0.0563668,"\int \frac{x^3}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[x^3/ArcTanh[Tanh[a + b*x]]^2,x]","\frac{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^3}{b^4 \tanh ^{-1}(\tanh (a+b x))}+\frac{3 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^4}-\frac{2 x \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}{b^3}+\frac{x^2}{2 b^2}","\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{3 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}-\frac{x^3}{b \tanh ^{-1}(\tanh (a+b x))}+\frac{3 x^2}{2 b^2}",1,"x^2/(2*b^2) - (2*x*(-(b*x) + ArcTanh[Tanh[a + b*x]]))/b^3 + (-(b*x) + ArcTanh[Tanh[a + b*x]])^3/(b^4*ArcTanh[Tanh[a + b*x]]) + (3*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2*Log[ArcTanh[Tanh[a + b*x]]])/b^4","A",1
96,1,56,50,0.0735684,"\int \frac{x^2}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[x^2/ArcTanh[Tanh[a + b*x]]^2,x]","\frac{-\frac{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}{\tanh ^{-1}(\tanh (a+b x))}+2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \log \left(\tanh ^{-1}(\tanh (a+b x))\right)+b x}{b^3}","\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,"(b*x - (-(b*x) + ArcTanh[Tanh[a + b*x]])^2/ArcTanh[Tanh[a + b*x]] + 2*(b*x - ArcTanh[Tanh[a + b*x]])*Log[ArcTanh[Tanh[a + b*x]]])/b^3","A",1
97,1,27,28,0.0566144,"\int \frac{x}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[x/ArcTanh[Tanh[a + b*x]]^2,x]","\frac{-\frac{b x}{\tanh ^{-1}(\tanh (a+b x))}+\log \left(\tanh ^{-1}(\tanh (a+b x))\right)+1}{b^2}","\frac{\log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^2}-\frac{x}{b \tanh ^{-1}(\tanh (a+b x))}",1,"(1 - (b*x)/ArcTanh[Tanh[a + b*x]] + Log[ArcTanh[Tanh[a + b*x]]])/b^2","A",1
98,1,14,14,0.00666,"\int \frac{1}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[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",1
99,1,53,70,0.0778048,"\int \frac{1}{x \tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[1/(x*ArcTanh[Tanh[a + b*x]]^2),x]","\frac{\tanh ^{-1}(\tanh (a+b x)) \left(-\log \left(\tanh ^{-1}(\tanh (a+b x))\right)+\log (b x)+1\right)-b x}{\tanh ^{-1}(\tanh (a+b x)) \left(\tanh ^{-1}(\tanh (a+b x))-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,"(-(b*x) + ArcTanh[Tanh[a + b*x]]*(1 + Log[b*x] - Log[ArcTanh[Tanh[a + b*x]]]))/(ArcTanh[Tanh[a + b*x]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)","A",1
100,1,70,102,0.0685379,"\int \frac{1}{x^2 \tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[1/(x^2*ArcTanh[Tanh[a + b*x]]^2),x]","\frac{\tanh ^{-1}(\tanh (a+b x))^2+2 b x \tanh ^{-1}(\tanh (a+b x)) \left(\log (x)-\log \left(\tanh ^{-1}(\tanh (a+b x))\right)\right)-b^2 x^2}{x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b 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}",1,"(-(b^2*x^2) + ArcTanh[Tanh[a + b*x]]^2 + 2*b*x*ArcTanh[Tanh[a + b*x]]*(Log[x] - Log[ArcTanh[Tanh[a + b*x]]]))/(x*(b*x - ArcTanh[Tanh[a + b*x]])^3*ArcTanh[Tanh[a + b*x]])","A",1
101,1,92,143,0.052614,"\int \frac{1}{x^3 \tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[1/(x^3*ArcTanh[Tanh[a + b*x]]^2),x]","-\frac{-3 b^2 x^2 \tanh ^{-1}(\tanh (a+b x)) \left(-2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)+2 \log (x)-1\right)-6 b x \tanh ^{-1}(\tanh (a+b x))^2+\tanh ^{-1}(\tanh (a+b x))^3+2 b^3 x^3}{2 x^2 \tanh ^{-1}(\tanh (a+b x)) \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4}","-\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,"-1/2*(2*b^3*x^3 - 6*b*x*ArcTanh[Tanh[a + b*x]]^2 + ArcTanh[Tanh[a + b*x]]^3 - 3*b^2*x^2*ArcTanh[Tanh[a + b*x]]*(-1 + 2*Log[x] - 2*Log[ArcTanh[Tanh[a + b*x]]]))/(x^2*ArcTanh[Tanh[a + b*x]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4)","A",1
102,1,51,94,0.515732,"\int \frac{x^m}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[x^m/ArcTanh[Tanh[a + b*x]]^3,x]","\frac{x^{m+1} \, _2F_1\left(3,m+1;m+2;-\frac{b x}{\tanh ^{-1}(\tanh (a+b x))-b x}\right)}{(m+1) \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^3}","-\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^(1 + m)*Hypergeometric2F1[3, 1 + m, 2 + m, -((b*x)/(-(b*x) + ArcTanh[Tanh[a + b*x]]))])/((1 + m)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^3)","A",1
103,1,114,92,0.0464549,"\int \frac{x^4}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[x^4/ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4}{2 b^5 \tanh ^{-1}(\tanh (a+b x))^2}+\frac{4 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^3}{b^5 \tanh ^{-1}(\tanh (a+b x))}+\frac{6 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^5}-\frac{3 x \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}{b^4}+\frac{x^2}{2 b^3}","\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{6 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^4}-\frac{2 x^3}{b^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{x^4}{2 b \tanh ^{-1}(\tanh (a+b x))^2}+\frac{3 x^2}{b^3}",1,"x^2/(2*b^3) - (3*x*(-(b*x) + ArcTanh[Tanh[a + b*x]]))/b^4 + (4*(-(b*x) + ArcTanh[Tanh[a + b*x]])^3)/(b^5*ArcTanh[Tanh[a + b*x]]) - (-(b*x) + ArcTanh[Tanh[a + b*x]])^4/(2*b^5*ArcTanh[Tanh[a + b*x]]^2) + (6*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2*Log[ArcTanh[Tanh[a + b*x]]])/b^5","A",1
104,1,86,71,0.0469447,"\int \frac{x^3}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[x^3/ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{3 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))-b x \tanh ^{-1}(\tanh (a+b x))^2 \left(6 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)+11\right)+\tanh ^{-1}(\tanh (a+b x))^3 \left(6 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)+5\right)+b^3 x^3}{2 b^4 \tanh ^{-1}(\tanh (a+b x))^2}","\frac{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^4}-\frac{3 x^2}{2 b^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{x^3}{2 b \tanh ^{-1}(\tanh (a+b x))^2}+\frac{3 x}{b^3}",1,"-1/2*(b^3*x^3 + 3*b^2*x^2*ArcTanh[Tanh[a + b*x]] + ArcTanh[Tanh[a + b*x]]^3*(5 + 6*Log[ArcTanh[Tanh[a + b*x]]]) - b*x*ArcTanh[Tanh[a + b*x]]^2*(11 + 6*Log[ArcTanh[Tanh[a + b*x]]]))/(b^4*ArcTanh[Tanh[a + b*x]]^2)","A",1
105,1,49,47,0.0401252,"\int \frac{x^2}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[x^2/ArcTanh[Tanh[a + b*x]]^3,x]","\frac{-\frac{b^2 x^2}{\tanh ^{-1}(\tanh (a+b x))^2}-\frac{2 b x}{\tanh ^{-1}(\tanh (a+b x))}+2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)+3}{2 b^3}","\frac{\log \left(\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}-\frac{x}{b^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{x^2}{2 b \tanh ^{-1}(\tanh (a+b x))^2}",1,"(3 - (b^2*x^2)/ArcTanh[Tanh[a + b*x]]^2 - (2*b*x)/ArcTanh[Tanh[a + b*x]] + 2*Log[ArcTanh[Tanh[a + b*x]]])/(2*b^3)","A",1
106,1,27,34,0.0502532,"\int \frac{x}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[x/ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{\tanh ^{-1}(\tanh (a+b x))+b x}{2 b^2 \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,"-1/2*(b*x + ArcTanh[Tanh[a + b*x]])/(b^2*ArcTanh[Tanh[a + b*x]]^2)","A",1
107,1,16,16,0.0063702,"\int \frac{1}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[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*1/(b*ArcTanh[Tanh[a + b*x]]^2)","A",1
108,1,74,97,0.0994962,"\int \frac{1}{x \tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[1/(x*ArcTanh[Tanh[a + b*x]]^3),x]","\frac{-4 b x \tanh ^{-1}(\tanh (a+b x))+\tanh ^{-1}(\tanh (a+b x))^2 \left(-2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)+2 \log (b x)+3\right)+b^2 x^2}{2 \tanh ^{-1}(\tanh (a+b x))^2 \left(\tanh ^{-1}(\tanh (a+b x))-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,"(b^2*x^2 - 4*b*x*ArcTanh[Tanh[a + b*x]] + ArcTanh[Tanh[a + b*x]]^2*(3 + 2*Log[b*x] - 2*Log[ArcTanh[Tanh[a + b*x]]]))/(2*ArcTanh[Tanh[a + b*x]]^2*(-(b*x) + ArcTanh[Tanh[a + b*x]])^3)","A",1
109,1,93,131,0.0621377,"\int \frac{1}{x^2 \tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[1/(x^2*ArcTanh[Tanh[a + b*x]]^3),x]","-\frac{-6 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+2 \tanh ^{-1}(\tanh (a+b x))^3+3 b x \tanh ^{-1}(\tanh (a+b x))^2 \left(-2 \log \left(\tanh ^{-1}(\tanh (a+b x))\right)+2 \log (x)+1\right)+b^3 x^3}{2 x \tanh ^{-1}(\tanh (a+b x))^2 \left(\tanh ^{-1}(\tanh (a+b x))-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,"-1/2*(b^3*x^3 - 6*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 2*ArcTanh[Tanh[a + b*x]]^3 + 3*b*x*ArcTanh[Tanh[a + b*x]]^2*(1 + 2*Log[x] - 2*Log[ArcTanh[Tanh[a + b*x]]]))/(x*ArcTanh[Tanh[a + b*x]]^2*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4)","A",1
110,1,107,170,0.0500536,"\int \frac{1}{x^3 \tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[1/(x^3*ArcTanh[Tanh[a + b*x]]^3),x]","\frac{8 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))-12 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2 \left(\log (x)-\log \left(\tanh ^{-1}(\tanh (a+b x))\right)\right)-8 b x \tanh ^{-1}(\tanh (a+b x))^3+\tanh ^{-1}(\tanh (a+b x))^4-b^4 x^4}{2 x^2 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^5 \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,"(-(b^4*x^4) + 8*b^3*x^3*ArcTanh[Tanh[a + b*x]] - 8*b*x*ArcTanh[Tanh[a + b*x]]^3 + ArcTanh[Tanh[a + b*x]]^4 - 12*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2*(Log[x] - Log[ArcTanh[Tanh[a + b*x]]]))/(2*x^2*(b*x - ArcTanh[Tanh[a + b*x]])^5*ArcTanh[Tanh[a + b*x]]^2)","A",1
111,1,83,101,0.0335852,"\int x^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[x^4*Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2} \left(-1848 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+1584 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2-704 b x \tanh ^{-1}(\tanh (a+b x))^3+128 \tanh ^{-1}(\tanh (a+b x))^4+1155 b^4 x^4\right)}{3465 b^5}","\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{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{2 x^4 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b}",1,"(2*ArcTanh[Tanh[a + b*x]]^(3/2)*(1155*b^4*x^4 - 1848*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 1584*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 - 704*b*x*ArcTanh[Tanh[a + b*x]]^3 + 128*ArcTanh[Tanh[a + b*x]]^4))/(3465*b^5)","A",1
112,1,66,80,0.0348124,"\int x^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[x^3*Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2} \left(-126 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+72 b x \tanh ^{-1}(\tanh (a+b x))^2-16 \tanh ^{-1}(\tanh (a+b x))^3+105 b^3 x^3\right)}{315 b^4}","-\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{4 x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b^2}+\frac{2 x^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b}",1,"(2*ArcTanh[Tanh[a + b*x]]^(3/2)*(105*b^3*x^3 - 126*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 72*b*x*ArcTanh[Tanh[a + b*x]]^2 - 16*ArcTanh[Tanh[a + b*x]]^3))/(315*b^4)","A",1
113,1,49,59,0.0346815,"\int x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[x^2*Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2} \left(-28 b x \tanh ^{-1}(\tanh (a+b x))+8 \tanh ^{-1}(\tanh (a+b x))^2+35 b^2 x^2\right)}{105 b^3}","\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*ArcTanh[Tanh[a + b*x]]^(3/2)*(35*b^2*x^2 - 28*b*x*ArcTanh[Tanh[a + b*x]] + 8*ArcTanh[Tanh[a + b*x]]^2))/(105*b^3)","A",1
114,1,32,38,0.0621748,"\int x \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[x*Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{2 \left(5 b x-2 \tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}{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*(5*b*x - 2*ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(3/2))/(15*b^2)","A",1
115,1,18,18,0.0065386,"\int \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[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",1
116,1,61,63,0.0834683,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x} \, dx","Integrate[Sqrt[ArcTanh[Tanh[a + b*x]]]/x,x]","2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}-2 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))-b 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)",1,"2*Sqrt[ArcTanh[Tanh[a + b*x]]] - 2*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]*Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]","A",1
117,1,65,66,0.0483602,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^2} \, dx","Integrate[Sqrt[ArcTanh[Tanh[a + b*x]]]/x^2,x]","-\frac{b \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-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,"-(Sqrt[ArcTanh[Tanh[a + b*x]]]/x) - (b*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]","A",1
118,1,89,125,0.1019638,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^3} \, dx","Integrate[Sqrt[ArcTanh[Tanh[a + b*x]]]/x^3,x]","\frac{1}{4} \left(\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{3/2}}+\frac{\left(\frac{b x}{b x-\tanh ^{-1}(\tanh (a+b x))}-2\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^2}\right)","\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,"(((-2 + (b*x)/(b*x - ArcTanh[Tanh[a + b*x]]))*Sqrt[ArcTanh[Tanh[a + b*x]]])/x^2 + (b^2*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(-(b*x) + ArcTanh[Tanh[a + b*x]])^(3/2))/4","A",1
119,1,115,179,0.1037157,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^4} \, dx","Integrate[Sqrt[ArcTanh[Tanh[a + b*x]]]/x^4,x]","\frac{1}{24} \left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(14 b x \tanh ^{-1}(\tanh (a+b x))-8 \tanh ^{-1}(\tanh (a+b x))^2-3 b^2 x^2\right)}{x^3 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}-\frac{3 b^3 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{5/2}}\right)","\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^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^2}{24 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}-\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{3 x^3}-\frac{b}{12 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"((-3*b^3*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(-(b*x) + ArcTanh[Tanh[a + b*x]])^(5/2) + (Sqrt[ArcTanh[Tanh[a + b*x]]]*(-3*b^2*x^2 + 14*b*x*ArcTanh[Tanh[a + b*x]] - 8*ArcTanh[Tanh[a + b*x]]^2))/(x^3*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2))/24","A",1
120,1,83,101,0.0394167,"\int x^4 \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx","Integrate[x^4*ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2} \left(-3432 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+2288 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2-832 b x \tanh ^{-1}(\tanh (a+b x))^3+128 \tanh ^{-1}(\tanh (a+b x))^4+3003 b^4 x^4\right)}{15015 b^5}","\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{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{2 x^4 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b}",1,"(2*ArcTanh[Tanh[a + b*x]]^(5/2)*(3003*b^4*x^4 - 3432*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 2288*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 - 832*b*x*ArcTanh[Tanh[a + b*x]]^3 + 128*ArcTanh[Tanh[a + b*x]]^4))/(15015*b^5)","A",1
121,1,66,80,0.0367467,"\int x^3 \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx","Integrate[x^3*ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2} \left(-198 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+88 b x \tanh ^{-1}(\tanh (a+b x))^2-16 \tanh ^{-1}(\tanh (a+b x))^3+231 b^3 x^3\right)}{1155 b^4}","-\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{12 x^2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^2}+\frac{2 x^3 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b}",1,"(2*ArcTanh[Tanh[a + b*x]]^(5/2)*(231*b^3*x^3 - 198*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 88*b*x*ArcTanh[Tanh[a + b*x]]^2 - 16*ArcTanh[Tanh[a + b*x]]^3))/(1155*b^4)","A",1
122,1,49,59,0.0367344,"\int x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx","Integrate[x^2*ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2} \left(-36 b x \tanh ^{-1}(\tanh (a+b x))+8 \tanh ^{-1}(\tanh (a+b x))^2+63 b^2 x^2\right)}{315 b^3}","\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*ArcTanh[Tanh[a + b*x]]^(5/2)*(63*b^2*x^2 - 36*b*x*ArcTanh[Tanh[a + b*x]] + 8*ArcTanh[Tanh[a + b*x]]^2))/(315*b^3)","A",1
123,1,32,38,0.076261,"\int x \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx","Integrate[x*ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{2 \left(7 b x-2 \tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{5/2}}{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*(7*b*x - 2*ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(5/2))/(35*b^2)","A",1
124,1,18,18,0.0063477,"\int \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx","Integrate[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",1
125,1,80,91,0.0893704,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(3/2)/x,x]","-\frac{2}{3} \left(-4 \tanh ^{-1}(\tanh (a+b x))^{3/2}+3 b x \sqrt{\tanh ^{-1}(\tanh (a+b x))}+3 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right) \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{3/2}\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*(3*b*x*Sqrt[ArcTanh[Tanh[a + b*x]]] - 4*ArcTanh[Tanh[a + b*x]]^(3/2) + 3*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^(3/2)))/3","A",1
126,1,79,81,0.0488441,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^2} \, dx","Integrate[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 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))-b 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)",1,"3*b*Sqrt[ArcTanh[Tanh[a + b*x]]] - ArcTanh[Tanh[a + b*x]]^(3/2)/x - 3*b*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]*Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]","A",1
127,1,88,92,0.0662401,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^3} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(3/2)/x^3,x]","\frac{1}{4} \left(-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}-\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^2}-\frac{3 b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x}\right)","\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*Sqrt[ArcTanh[Tanh[a + b*x]]])/x - (2*ArcTanh[Tanh[a + b*x]]^(3/2))/x^2 - (3*b^2*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]])/4","A",1
128,1,117,146,0.0983347,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^4} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(3/2)/x^4,x]","\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{8 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{3/2}}+\sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(-\frac{b^2}{8 x \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}-\frac{\tanh ^{-1}(\tanh (a+b x))-b x}{3 x^3}-\frac{7 b}{12 x^2}\right)","\frac{b^3}{8 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \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^2}{8 x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 x^3}-\frac{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{4 x^2}",1,"(b^3*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(8*(-(b*x) + ArcTanh[Tanh[a + b*x]])^(3/2)) + Sqrt[ArcTanh[Tanh[a + b*x]]]*((-7*b)/(12*x^2) - b^2/(8*x*(-(b*x) + ArcTanh[Tanh[a + b*x]])) - (-(b*x) + ArcTanh[Tanh[a + b*x]])/(3*x^3))","A",1
129,1,83,101,0.0403833,"\int x^4 \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx","Integrate[x^4*ArcTanh[Tanh[a + b*x]]^(5/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{7/2} \left(-5720 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+3120 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2-960 b x \tanh ^{-1}(\tanh (a+b x))^3+128 \tanh ^{-1}(\tanh (a+b x))^4+6435 b^4 x^4\right)}{45045 b^5}","\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{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{2 x^4 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{7 b}",1,"(2*ArcTanh[Tanh[a + b*x]]^(7/2)*(6435*b^4*x^4 - 5720*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 3120*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 - 960*b*x*ArcTanh[Tanh[a + b*x]]^3 + 128*ArcTanh[Tanh[a + b*x]]^4))/(45045*b^5)","A",1
130,1,66,80,0.038381,"\int x^3 \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx","Integrate[x^3*ArcTanh[Tanh[a + b*x]]^(5/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{7/2} \left(-286 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+104 b x \tanh ^{-1}(\tanh (a+b x))^2-16 \tanh ^{-1}(\tanh (a+b x))^3+429 b^3 x^3\right)}{3003 b^4}","-\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{4 x^2 \tanh ^{-1}(\tanh (a+b x))^{9/2}}{21 b^2}+\frac{2 x^3 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{7 b}",1,"(2*ArcTanh[Tanh[a + b*x]]^(7/2)*(429*b^3*x^3 - 286*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 104*b*x*ArcTanh[Tanh[a + b*x]]^2 - 16*ArcTanh[Tanh[a + b*x]]^3))/(3003*b^4)","A",1
131,1,49,59,0.0383024,"\int x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx","Integrate[x^2*ArcTanh[Tanh[a + b*x]]^(5/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{7/2} \left(-44 b x \tanh ^{-1}(\tanh (a+b x))+8 \tanh ^{-1}(\tanh (a+b x))^2+99 b^2 x^2\right)}{693 b^3}","\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*ArcTanh[Tanh[a + b*x]]^(7/2)*(99*b^2*x^2 - 44*b*x*ArcTanh[Tanh[a + b*x]] + 8*ArcTanh[Tanh[a + b*x]]^2))/(693*b^3)","A",1
132,1,32,38,0.0798761,"\int x \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx","Integrate[x*ArcTanh[Tanh[a + b*x]]^(5/2),x]","\frac{2 \left(9 b x-2 \tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{7/2}}{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*(9*b*x - 2*ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(7/2))/(63*b^2)","A",1
133,1,18,18,0.0072379,"\int \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx","Integrate[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",1
134,1,99,121,0.095589,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(5/2)/x,x]","\frac{2}{15} \left(15 b^2 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}+23 \tanh ^{-1}(\tanh (a+b x))^{5/2}-35 b x \tanh ^{-1}(\tanh (a+b x))^{3/2}-15 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right) \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{5/2}\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*(15*b^2*x^2*Sqrt[ArcTanh[Tanh[a + b*x]]] - 35*b*x*ArcTanh[Tanh[a + b*x]]^(3/2) + 23*ArcTanh[Tanh[a + b*x]]^(5/2) - 15*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^(5/2)))/15","A",1
135,1,106,110,0.0682832,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^2} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(5/2)/x^2,x]","\sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(\frac{14}{3} b \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)-\frac{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}{x}+\frac{2 b^2 x}{3}\right)-5 b \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right) \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{3/2}","-\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*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^(3/2) + Sqrt[ArcTanh[Tanh[a + b*x]]]*((2*b^2*x)/3 + (14*b*(-(b*x) + ArcTanh[Tanh[a + b*x]]))/3 - (-(b*x) + ArcTanh[Tanh[a + b*x]])^2/x)","A",1
136,1,108,110,0.0466411,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^3} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(5/2)/x^3,x]","-\frac{-15 b^2 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}+15 b^2 x^2 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}+2 \tanh ^{-1}(\tanh (a+b x))^{5/2}+5 b x \tanh ^{-1}(\tanh (a+b x))^{3/2}}{4 x^2}","\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,"-1/4*(-15*b^2*x^2*Sqrt[ArcTanh[Tanh[a + b*x]]] + 5*b*x*ArcTanh[Tanh[a + b*x]]^(3/2) + 2*ArcTanh[Tanh[a + b*x]]^(5/2) + 15*b^2*x^2*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]*Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]])/x^2","A",1
137,1,107,113,0.0831822,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^4} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(5/2)/x^4,x]","\frac{1}{24} \left(-\frac{15 b^3 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}-\frac{15 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x}-\frac{8 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^3}-\frac{10 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^2}\right)","\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^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{8 x}-\frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{3 x^3}-\frac{5 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{12 x^2}",1,"((-15*b^2*Sqrt[ArcTanh[Tanh[a + b*x]]])/x - (10*b*ArcTanh[Tanh[a + b*x]]^(3/2))/x^2 - (8*ArcTanh[Tanh[a + b*x]]^(5/2))/x^3 - (15*b^3*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]])/24","A",1
138,1,134,167,0.1228424,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^5} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(5/2)/x^5,x]","\frac{5 b^4 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{64 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{3/2}}-\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(10 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+8 b x \tanh ^{-1}(\tanh (a+b x))^2-48 \tanh ^{-1}(\tanh (a+b x))^3+15 b^3 x^3\right)}{192 x^4 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}","\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^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^3}{64 x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{5 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{32 x^2}-\frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{4 x^4}-\frac{5 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{24 x^3}",1,"(5*b^4*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(64*(-(b*x) + ArcTanh[Tanh[a + b*x]])^(3/2)) - (Sqrt[ArcTanh[Tanh[a + b*x]]]*(15*b^3*x^3 + 10*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 8*b*x*ArcTanh[Tanh[a + b*x]]^2 - 48*ArcTanh[Tanh[a + b*x]]^3))/(192*x^4*(b*x - ArcTanh[Tanh[a + b*x]]))","A",1
139,1,150,221,0.1327544,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^6} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(5/2)/x^6,x]","\frac{1}{640} \left(-\frac{15 b^5 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{5/2}}-\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(10 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+8 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2-176 b x \tanh ^{-1}(\tanh (a+b x))^3+128 \tanh ^{-1}(\tanh (a+b x))^4+15 b^4 x^4\right)}{x^5 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}\right)","\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{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^4}{128 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}-\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{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 x^5}-\frac{b \tanh ^{-1}(\tanh (a+b x))^{3/2}}{8 x^4}",1,"((-15*b^5*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(-(b*x) + ArcTanh[Tanh[a + b*x]])^(5/2) - (Sqrt[ArcTanh[Tanh[a + b*x]]]*(15*b^4*x^4 + 10*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 8*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 - 176*b*x*ArcTanh[Tanh[a + b*x]]^3 + 128*ArcTanh[Tanh[a + b*x]]^4))/(x^5*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2))/640","A",1
140,1,83,99,0.0465299,"\int \frac{x^4}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[x^4/Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(-840 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+1008 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2-576 b x \tanh ^{-1}(\tanh (a+b x))^3+128 \tanh ^{-1}(\tanh (a+b x))^4+315 b^4 x^4\right)}{315 b^5}","\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{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{2 x^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b}",1,"(2*Sqrt[ArcTanh[Tanh[a + b*x]]]*(315*b^4*x^4 - 840*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 1008*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 - 576*b*x*ArcTanh[Tanh[a + b*x]]^3 + 128*ArcTanh[Tanh[a + b*x]]^4))/(315*b^5)","A",1
141,1,66,76,0.040885,"\int \frac{x^3}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[x^3/Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(-70 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+56 b x \tanh ^{-1}(\tanh (a+b x))^2-16 \tanh ^{-1}(\tanh (a+b x))^3+35 b^3 x^3\right)}{35 b^4}","-\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{4 x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{b^2}+\frac{2 x^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b}",1,"(2*Sqrt[ArcTanh[Tanh[a + b*x]]]*(35*b^3*x^3 - 70*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 56*b*x*ArcTanh[Tanh[a + b*x]]^2 - 16*ArcTanh[Tanh[a + b*x]]^3))/(35*b^4)","A",1
142,1,49,57,0.0425237,"\int \frac{x^2}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[x^2/Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(-20 b x \tanh ^{-1}(\tanh (a+b x))+8 \tanh ^{-1}(\tanh (a+b x))^2+15 b^2 x^2\right)}{15 b^3}","\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*Sqrt[ArcTanh[Tanh[a + b*x]]]*(15*b^2*x^2 - 20*b*x*ArcTanh[Tanh[a + b*x]] + 8*ArcTanh[Tanh[a + b*x]]^2))/(15*b^3)","A",1
143,1,32,36,0.0628884,"\int \frac{x}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[x/Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{2 \left(3 b x-2 \tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{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*(3*b*x - 2*ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])/(3*b^2)","A",1
144,1,16,16,0.0071019,"\int \frac{1}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[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",1
145,1,47,49,0.0600369,"\int \frac{1}{x \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[1/(x*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-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*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]","A",1
146,1,78,94,0.083068,"\int \frac{1}{x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[1/(x^2*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","\frac{b \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{3/2}}-\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}","\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*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(-(b*x) + ArcTanh[Tanh[a + b*x]])^(3/2) - Sqrt[ArcTanh[Tanh[a + b*x]]]/(x*(-(b*x) + ArcTanh[Tanh[a + b*x]]))","A",1
147,1,98,158,0.0973334,"\int \frac{1}{x^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[1/(x^3*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","\frac{1}{4} \left(\frac{\left(5 b x-2 \tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^2 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}-\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{5/2}}\right)","\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*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(-(b*x) + ArcTanh[Tanh[a + b*x]])^(5/2) + ((5*b*x - 2*ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])/(x^2*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2))/4","A",1
148,1,117,212,0.1308535,"\int \frac{1}{x^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[1/(x^4*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","\frac{5 b^3 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{8 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{7/2}}+\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(-26 b x \tanh ^{-1}(\tanh (a+b x))+8 \tanh ^{-1}(\tanh (a+b x))^2+33 b^2 x^2\right)}{24 x^3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}","\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{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^2}{8 x \tanh ^{-1}(\tanh (a+b x))^{5/2}}-\frac{1}{3 x^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}+\frac{b}{12 x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(5*b^3*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(8*(-(b*x) + ArcTanh[Tanh[a + b*x]])^(7/2)) + (Sqrt[ArcTanh[Tanh[a + b*x]]]*(33*b^2*x^2 - 26*b*x*ArcTanh[Tanh[a + b*x]] + 8*ArcTanh[Tanh[a + b*x]]^2))/(24*x^3*(b*x - ArcTanh[Tanh[a + b*x]])^3)","A",1
149,1,83,95,0.0531426,"\int \frac{x^4}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[x^4/ArcTanh[Tanh[a + b*x]]^(3/2),x]","-\frac{2 \left(-280 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+560 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2-448 b x \tanh ^{-1}(\tanh (a+b x))^3+128 \tanh ^{-1}(\tanh (a+b x))^4+35 b^4 x^4\right)}{35 b^5 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","-\frac{256 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{35 b^5}+\frac{128 x \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b^4}-\frac{32 x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{b^3}+\frac{16 x^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^2}-\frac{2 x^4}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(-2*(35*b^4*x^4 - 280*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 560*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 - 448*b*x*ArcTanh[Tanh[a + b*x]]^3 + 128*ArcTanh[Tanh[a + b*x]]^4))/(35*b^5*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",1
150,1,66,74,0.047454,"\int \frac{x^3}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[x^3/ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{2 \left(30 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))-40 b x \tanh ^{-1}(\tanh (a+b x))^2+16 \tanh ^{-1}(\tanh (a+b x))^3-5 b^3 x^3\right)}{5 b^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","\frac{32 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{5 b^4}-\frac{16 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}{b^3}+\frac{12 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^2}-\frac{2 x^3}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(2*(-5*b^3*x^3 + 30*b^2*x^2*ArcTanh[Tanh[a + b*x]] - 40*b*x*ArcTanh[Tanh[a + b*x]]^2 + 16*ArcTanh[Tanh[a + b*x]]^3))/(5*b^4*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",1
151,1,49,55,0.0634032,"\int \frac{x^2}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[x^2/ArcTanh[Tanh[a + b*x]]^(3/2),x]","-\frac{2 \left(-12 b x \tanh ^{-1}(\tanh (a+b x))+8 \tanh ^{-1}(\tanh (a+b x))^2+3 b^2 x^2\right)}{3 b^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","-\frac{16 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b^3}+\frac{8 x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^2}-\frac{2 x^2}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(-2*(3*b^2*x^2 - 12*b*x*ArcTanh[Tanh[a + b*x]] + 8*ArcTanh[Tanh[a + b*x]]^2))/(3*b^3*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",1
152,1,29,34,0.081603,"\int \frac{x}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[x/ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{4 \tanh ^{-1}(\tanh (a+b x))-2 b x}{b^2 \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*b*x + 4*ArcTanh[Tanh[a + b*x]])/(b^2*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",1
153,1,16,16,0.0145047,"\int \frac{1}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[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",1
154,1,75,78,0.1192744,"\int \frac{1}{x \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[1/(x*ArcTanh[Tanh[a + b*x]]^(3/2)),x]","\frac{2}{\sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-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*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(-(b*x) + ArcTanh[Tanh[a + b*x]])^(3/2) + 2/(Sqrt[ArcTanh[Tanh[a + b*x]]]*(-(b*x) + ArcTanh[Tanh[a + b*x]]))","A",1
155,1,91,124,0.1041724,"\int \frac{1}{x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[1/(x^2*ArcTanh[Tanh[a + b*x]]^(3/2)),x]","\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{5/2}}-\frac{\tanh ^{-1}(\tanh (a+b x))+2 b x}{x \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^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*ArcTanh[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]])/(x*Sqrt[ArcTanh[Tanh[a + b*x]]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)","A",1
156,1,115,191,0.1293006,"\int \frac{1}{x^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[1/(x^3*ArcTanh[Tanh[a + b*x]]^(3/2)),x]","\frac{1}{4} \left(\frac{9 b x \tanh ^{-1}(\tanh (a+b x))-2 \tanh ^{-1}(\tanh (a+b x))^2+8 b^2 x^2}{x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^3}-\frac{15 b^2 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{7/2}}\right)","-\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*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(-(b*x) + ArcTanh[Tanh[a + b*x]])^(7/2) + (8*b^2*x^2 + 9*b*x*ArcTanh[Tanh[a + b*x]] - 2*ArcTanh[Tanh[a + b*x]]^2)/(x^2*Sqrt[ArcTanh[Tanh[a + b*x]]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^3))/4","A",1
157,1,133,245,0.1472583,"\int \frac{1}{x^4 \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[1/(x^4*ArcTanh[Tanh[a + b*x]]^(3/2)),x]","\frac{35 b^3 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{8 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{9/2}}-\frac{87 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))-38 b x \tanh ^{-1}(\tanh (a+b x))^2+8 \tanh ^{-1}(\tanh (a+b x))^3+48 b^3 x^3}{24 x^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4}","-\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{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{5 b^2}{8 x \tanh ^{-1}(\tanh (a+b x))^{7/2}}-\frac{1}{3 x^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{b}{4 x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}",1,"(35*b^3*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(8*(-(b*x) + ArcTanh[Tanh[a + b*x]])^(9/2)) - (48*b^3*x^3 + 87*b^2*x^2*ArcTanh[Tanh[a + b*x]] - 38*b*x*ArcTanh[Tanh[a + b*x]]^2 + 8*ArcTanh[Tanh[a + b*x]]^3)/(24*x^3*Sqrt[ArcTanh[Tanh[a + b*x]]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4)","A",1
158,1,83,99,0.0561539,"\int \frac{x^4}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[x^4/ArcTanh[Tanh[a + b*x]]^(5/2),x]","-\frac{2 \left(40 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))-240 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2+320 b x \tanh ^{-1}(\tanh (a+b x))^3-128 \tanh ^{-1}(\tanh (a+b x))^4+5 b^4 x^4\right)}{15 b^5 \tanh ^{-1}(\tanh (a+b x))^{3/2}}","\frac{256 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{15 b^5}-\frac{128 x \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b^4}+\frac{32 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^3}-\frac{16 x^3}{3 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{2 x^4}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(-2*(5*b^4*x^4 + 40*b^3*x^3*ArcTanh[Tanh[a + b*x]] - 240*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 + 320*b*x*ArcTanh[Tanh[a + b*x]]^3 - 128*ArcTanh[Tanh[a + b*x]]^4))/(15*b^5*ArcTanh[Tanh[a + b*x]]^(3/2))","A",1
159,1,65,76,0.0410782,"\int \frac{x^3}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[x^3/ArcTanh[Tanh[a + b*x]]^(5/2),x]","-\frac{2 \left(6 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))-24 b x \tanh ^{-1}(\tanh (a+b x))^2+16 \tanh ^{-1}(\tanh (a+b x))^3+b^3 x^3\right)}{3 b^4 \tanh ^{-1}(\tanh (a+b x))^{3/2}}","-\frac{32 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{3 b^4}+\frac{16 x \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^3}-\frac{4 x^2}{b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{2 x^3}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(-2*(b^3*x^3 + 6*b^2*x^2*ArcTanh[Tanh[a + b*x]] - 24*b*x*ArcTanh[Tanh[a + b*x]]^2 + 16*ArcTanh[Tanh[a + b*x]]^3))/(3*b^4*ArcTanh[Tanh[a + b*x]]^(3/2))","A",1
160,1,48,59,0.0517388,"\int \frac{x^2}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[x^2/ArcTanh[Tanh[a + b*x]]^(5/2),x]","-\frac{2 \left(4 b x \tanh ^{-1}(\tanh (a+b x))-8 \tanh ^{-1}(\tanh (a+b x))^2+b^2 x^2\right)}{3 b^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}","\frac{16 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{3 b^3}-\frac{8 x}{3 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{2 x^2}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(-2*(b^2*x^2 + 4*b*x*ArcTanh[Tanh[a + b*x]] - 8*ArcTanh[Tanh[a + b*x]]^2))/(3*b^3*ArcTanh[Tanh[a + b*x]]^(3/2))","A",1
161,1,31,38,0.0630719,"\int \frac{x}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[x/ArcTanh[Tanh[a + b*x]]^(5/2),x]","-\frac{2 \left(2 \tanh ^{-1}(\tanh (a+b x))+b x\right)}{3 b^2 \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*(b*x + 2*ArcTanh[Tanh[a + b*x]]))/(3*b^2*ArcTanh[Tanh[a + b*x]]^(3/2))","A",1
162,1,18,18,0.007766,"\int \frac{1}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[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",1
163,1,91,108,0.167042,"\int \frac{1}{x \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[1/(x*ArcTanh[Tanh[a + b*x]]^(5/2)),x]","\frac{2 \left(4 \tanh ^{-1}(\tanh (a+b x))-b x\right)}{3 \tanh ^{-1}(\tanh (a+b x))^{3/2} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-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*ArcTanh[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) + 4*ArcTanh[Tanh[a + b*x]]))/(3*ArcTanh[Tanh[a + b*x]]^(3/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)","A",1
164,1,113,155,0.1478564,"\int \frac{1}{x^2 \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[1/(x^2*ArcTanh[Tanh[a + b*x]]^(5/2)),x]","\frac{14 b x \tanh ^{-1}(\tanh (a+b x))+3 \tanh ^{-1}(\tanh (a+b x))^2-2 b^2 x^2}{3 x \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}+\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-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*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(-(b*x) + ArcTanh[Tanh[a + b*x]])^(7/2) + (-2*b^2*x^2 + 14*b*x*ArcTanh[Tanh[a + b*x]] + 3*ArcTanh[Tanh[a + b*x]]^2)/(3*x*(b*x - ArcTanh[Tanh[a + b*x]])^3*ArcTanh[Tanh[a + b*x]]^(3/2))","A",1
165,1,133,224,0.1267702,"\int \frac{1}{x^3 \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[1/(x^3*ArcTanh[Tanh[a + b*x]]^(5/2)),x]","\frac{80 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+39 b x \tanh ^{-1}(\tanh (a+b x))^2-6 \tanh ^{-1}(\tanh (a+b x))^3-8 b^3 x^3}{12 x^2 \tanh ^{-1}(\tanh (a+b x))^{3/2} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4}-\frac{35 b^2 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{4 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{9/2}}","\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*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(4*(-(b*x) + ArcTanh[Tanh[a + b*x]])^(9/2)) + (-8*b^3*x^3 + 80*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 39*b*x*ArcTanh[Tanh[a + b*x]]^2 - 6*ArcTanh[Tanh[a + b*x]]^3)/(12*x^2*ArcTanh[Tanh[a + b*x]]^(3/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4)","A",1
166,1,150,278,0.2213542,"\int \frac{1}{x^4 \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[1/(x^4*ArcTanh[Tanh[a + b*x]]^(5/2)),x]","\frac{1}{24} \left(\frac{315 b^3 \tanh ^{-1}\left(\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{11/2}}+\frac{208 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+165 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2-50 b x \tanh ^{-1}(\tanh (a+b x))^3+8 \tanh ^{-1}(\tanh (a+b x))^4-16 b^4 x^4}{x^3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^5 \tanh ^{-1}(\tanh (a+b x))^{3/2}}\right)","\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{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{35 b^2}{24 x \tanh ^{-1}(\tanh (a+b x))^{9/2}}-\frac{1}{3 x^3 \tanh ^{-1}(\tanh (a+b x))^{5/2}}+\frac{5 b}{12 x^2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}",1,"((315*b^3*ArcTanh[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(-(b*x) + ArcTanh[Tanh[a + b*x]])^(11/2) + (-16*b^4*x^4 + 208*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 165*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 - 50*b*x*ArcTanh[Tanh[a + b*x]]^3 + 8*ArcTanh[Tanh[a + b*x]]^4)/(x^3*(b*x - ArcTanh[Tanh[a + b*x]])^5*ArcTanh[Tanh[a + b*x]]^(3/2)))/24","A",1
167,1,23,27,0.0505105,"\int x^{7/2} \tanh ^{-1}(\tanh (a+b x)) \, dx","Integrate[x^(7/2)*ArcTanh[Tanh[a + b*x]],x]","\frac{2}{99} x^{9/2} \left(11 \tanh ^{-1}(\tanh (a+b x))-2 b x\right)","\frac{2}{9} x^{9/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{99} b x^{11/2}",1,"(2*x^(9/2)*(-2*b*x + 11*ArcTanh[Tanh[a + b*x]]))/99","A",1
168,1,23,27,0.0296681,"\int x^{5/2} \tanh ^{-1}(\tanh (a+b x)) \, dx","Integrate[x^(5/2)*ArcTanh[Tanh[a + b*x]],x]","\frac{2}{63} x^{7/2} \left(9 \tanh ^{-1}(\tanh (a+b x))-2 b x\right)","\frac{2}{7} x^{7/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{63} b x^{9/2}",1,"(2*x^(7/2)*(-2*b*x + 9*ArcTanh[Tanh[a + b*x]]))/63","A",1
169,1,23,27,0.0297115,"\int x^{3/2} \tanh ^{-1}(\tanh (a+b x)) \, dx","Integrate[x^(3/2)*ArcTanh[Tanh[a + b*x]],x]","\frac{2}{35} x^{5/2} \left(7 \tanh ^{-1}(\tanh (a+b x))-2 b x\right)","\frac{2}{5} x^{5/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{35} b x^{7/2}",1,"(2*x^(5/2)*(-2*b*x + 7*ArcTanh[Tanh[a + b*x]]))/35","A",1
170,1,23,27,0.0285946,"\int \sqrt{x} \tanh ^{-1}(\tanh (a+b x)) \, dx","Integrate[Sqrt[x]*ArcTanh[Tanh[a + b*x]],x]","\frac{2}{15} x^{3/2} \left(5 \tanh ^{-1}(\tanh (a+b x))-2 b x\right)","\frac{2}{3} x^{3/2} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{15} b x^{5/2}",1,"(2*x^(3/2)*(-2*b*x + 5*ArcTanh[Tanh[a + b*x]]))/15","A",1
171,1,23,25,0.0203231,"\int \frac{\tanh ^{-1}(\tanh (a+b x))}{\sqrt{x}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]/Sqrt[x],x]","\frac{2}{3} \sqrt{x} \left(3 \tanh ^{-1}(\tanh (a+b x))-2 b x\right)","2 \sqrt{x} \tanh ^{-1}(\tanh (a+b x))-\frac{4}{3} b x^{3/2}",1,"(2*Sqrt[x]*(-2*b*x + 3*ArcTanh[Tanh[a + b*x]]))/3","A",1
172,1,20,23,0.0273535,"\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^{3/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]/x^(3/2),x]","\frac{4 b x-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*x - 2*ArcTanh[Tanh[a + b*x]])/Sqrt[x]","A",1
173,1,21,27,0.0212976,"\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^{5/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]/x^(5/2),x]","-\frac{2 \left(\tanh ^{-1}(\tanh (a+b x))+2 b x\right)}{3 x^{3/2}}","-\frac{2 \tanh ^{-1}(\tanh (a+b x))}{3 x^{3/2}}-\frac{4 b}{3 \sqrt{x}}",1,"(-2*(2*b*x + ArcTanh[Tanh[a + b*x]]))/(3*x^(3/2))","A",1
174,1,23,27,0.0214022,"\int \frac{\tanh ^{-1}(\tanh (a+b x))}{x^{7/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]/x^(7/2),x]","-\frac{2 \left(3 \tanh ^{-1}(\tanh (a+b x))+2 b x\right)}{15 x^{5/2}}","-\frac{2 \tanh ^{-1}(\tanh (a+b x))}{5 x^{5/2}}-\frac{4 b}{15 x^{3/2}}",1,"(-2*(2*b*x + 3*ArcTanh[Tanh[a + b*x]]))/(15*x^(5/2))","A",1
175,1,40,48,0.0574613,"\int x^{7/2} \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Integrate[x^(7/2)*ArcTanh[Tanh[a + b*x]]^2,x]","\frac{2 x^{9/2} \left(-52 b x \tanh ^{-1}(\tanh (a+b x))+143 \tanh ^{-1}(\tanh (a+b x))^2+8 b^2 x^2\right)}{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,"(2*x^(9/2)*(8*b^2*x^2 - 52*b*x*ArcTanh[Tanh[a + b*x]] + 143*ArcTanh[Tanh[a + b*x]]^2))/1287","A",1
176,1,40,48,0.0494499,"\int x^{5/2} \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Integrate[x^(5/2)*ArcTanh[Tanh[a + b*x]]^2,x]","\frac{2}{693} x^{7/2} \left(-44 b x \tanh ^{-1}(\tanh (a+b x))+99 \tanh ^{-1}(\tanh (a+b x))^2+8 b^2 x^2\right)","-\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,"(2*x^(7/2)*(8*b^2*x^2 - 44*b*x*ArcTanh[Tanh[a + b*x]] + 99*ArcTanh[Tanh[a + b*x]]^2))/693","A",1
177,1,40,48,0.0437928,"\int x^{3/2} \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Integrate[x^(3/2)*ArcTanh[Tanh[a + b*x]]^2,x]","\frac{2}{315} x^{5/2} \left(-36 b x \tanh ^{-1}(\tanh (a+b x))+63 \tanh ^{-1}(\tanh (a+b x))^2+8 b^2 x^2\right)","-\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,"(2*x^(5/2)*(8*b^2*x^2 - 36*b*x*ArcTanh[Tanh[a + b*x]] + 63*ArcTanh[Tanh[a + b*x]]^2))/315","A",1
178,1,40,48,0.0548315,"\int \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^2 \, dx","Integrate[Sqrt[x]*ArcTanh[Tanh[a + b*x]]^2,x]","\frac{2}{105} x^{3/2} \left(-28 b x \tanh ^{-1}(\tanh (a+b x))+35 \tanh ^{-1}(\tanh (a+b x))^2+8 b^2 x^2\right)","-\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,"(2*x^(3/2)*(8*b^2*x^2 - 28*b*x*ArcTanh[Tanh[a + b*x]] + 35*ArcTanh[Tanh[a + b*x]]^2))/105","A",1
179,1,40,46,0.0318761,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{\sqrt{x}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^2/Sqrt[x],x]","\frac{2}{15} \sqrt{x} \left(-20 b x \tanh ^{-1}(\tanh (a+b x))+15 \tanh ^{-1}(\tanh (a+b x))^2+8 b^2 x^2\right)","-\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,"(2*Sqrt[x]*(8*b^2*x^2 - 20*b*x*ArcTanh[Tanh[a + b*x]] + 15*ArcTanh[Tanh[a + b*x]]^2))/15","A",1
180,1,40,44,0.0494225,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^{3/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^2/x^(3/2),x]","-\frac{2 \left(-12 b x \tanh ^{-1}(\tanh (a+b x))+3 \tanh ^{-1}(\tanh (a+b x))^2+8 b^2 x^2\right)}{3 \sqrt{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}",1,"(-2*(8*b^2*x^2 - 12*b*x*ArcTanh[Tanh[a + b*x]] + 3*ArcTanh[Tanh[a + b*x]]^2))/(3*Sqrt[x])","A",1
181,1,40,48,0.0532405,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^{5/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^2/x^(5/2),x]","\frac{2 \left(-4 b x \tanh ^{-1}(\tanh (a+b x))-\tanh ^{-1}(\tanh (a+b x))^2+8 b^2 x^2\right)}{3 x^{3/2}}","-\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,"(2*(8*b^2*x^2 - 4*b*x*ArcTanh[Tanh[a + b*x]] - ArcTanh[Tanh[a + b*x]]^2))/(3*x^(3/2))","A",1
182,1,40,48,0.048152,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^2}{x^{7/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^2/x^(7/2),x]","-\frac{2 \left(4 b x \tanh ^{-1}(\tanh (a+b x))+3 \tanh ^{-1}(\tanh (a+b x))^2+8 b^2 x^2\right)}{15 x^{5/2}}","-\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,"(-2*(8*b^2*x^2 + 4*b*x*ArcTanh[Tanh[a + b*x]] + 3*ArcTanh[Tanh[a + b*x]]^2))/(15*x^(5/2))","A",1
183,1,57,69,0.0314077,"\int x^{7/2} \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Integrate[x^(7/2)*ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{2 x^{9/2} \left(-120 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+390 b x \tanh ^{-1}(\tanh (a+b x))^2-715 \tanh ^{-1}(\tanh (a+b x))^3+16 b^3 x^3\right)}{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,"(-2*x^(9/2)*(16*b^3*x^3 - 120*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 390*b*x*ArcTanh[Tanh[a + b*x]]^2 - 715*ArcTanh[Tanh[a + b*x]]^3))/6435","A",1
184,1,57,69,0.0538893,"\int x^{5/2} \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Integrate[x^(5/2)*ArcTanh[Tanh[a + b*x]]^3,x]","\frac{2 x^{7/2} \left(104 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))-286 b x \tanh ^{-1}(\tanh (a+b x))^2+429 \tanh ^{-1}(\tanh (a+b x))^3-16 b^3 x^3\right)}{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,"(2*x^(7/2)*(-16*b^3*x^3 + 104*b^2*x^2*ArcTanh[Tanh[a + b*x]] - 286*b*x*ArcTanh[Tanh[a + b*x]]^2 + 429*ArcTanh[Tanh[a + b*x]]^3))/3003","A",1
185,1,57,69,0.032678,"\int x^{3/2} \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Integrate[x^(3/2)*ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{2 x^{5/2} \left(-88 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+198 b x \tanh ^{-1}(\tanh (a+b x))^2-231 \tanh ^{-1}(\tanh (a+b x))^3+16 b^3 x^3\right)}{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,"(-2*x^(5/2)*(16*b^3*x^3 - 88*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 198*b*x*ArcTanh[Tanh[a + b*x]]^2 - 231*ArcTanh[Tanh[a + b*x]]^3))/1155","A",1
186,1,57,69,0.028917,"\int \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^3 \, dx","Integrate[Sqrt[x]*ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{2}{315} x^{3/2} \left(-72 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+126 b x \tanh ^{-1}(\tanh (a+b x))^2-105 \tanh ^{-1}(\tanh (a+b x))^3+16 b^3 x^3\right)","\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,"(-2*x^(3/2)*(16*b^3*x^3 - 72*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 126*b*x*ArcTanh[Tanh[a + b*x]]^2 - 105*ArcTanh[Tanh[a + b*x]]^3))/315","A",1
187,1,57,65,0.0306509,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{\sqrt{x}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^3/Sqrt[x],x]","\frac{2}{35} \sqrt{x} \left(56 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))-70 b x \tanh ^{-1}(\tanh (a+b x))^2+35 \tanh ^{-1}(\tanh (a+b x))^3-16 b^3 x^3\right)","\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,"(2*Sqrt[x]*(-16*b^3*x^3 + 56*b^2*x^2*ArcTanh[Tanh[a + b*x]] - 70*b*x*ArcTanh[Tanh[a + b*x]]^2 + 35*ArcTanh[Tanh[a + b*x]]^3))/35","A",1
188,1,57,63,0.0343283,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^{3/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^3/x^(3/2),x]","\frac{2 \left(-40 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+30 b x \tanh ^{-1}(\tanh (a+b x))^2-5 \tanh ^{-1}(\tanh (a+b x))^3+16 b^3 x^3\right)}{5 \sqrt{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}",1,"(2*(16*b^3*x^3 - 40*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 30*b*x*ArcTanh[Tanh[a + b*x]]^2 - 5*ArcTanh[Tanh[a + b*x]]^3))/(5*Sqrt[x])","A",1
189,1,55,65,0.0321285,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^{5/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^3/x^(5/2),x]","-\frac{2 \left(-24 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+6 b x \tanh ^{-1}(\tanh (a+b x))^2+\tanh ^{-1}(\tanh (a+b x))^3+16 b^3 x^3\right)}{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,"(-2*(16*b^3*x^3 - 24*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 6*b*x*ArcTanh[Tanh[a + b*x]]^2 + ArcTanh[Tanh[a + b*x]]^3))/(3*x^(3/2))","A",1
190,1,57,69,0.0341013,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^3}{x^{7/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^3/x^(7/2),x]","\frac{2 \left(-8 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))-2 b x \tanh ^{-1}(\tanh (a+b x))^2-\tanh ^{-1}(\tanh (a+b x))^3+16 b^3 x^3\right)}{5 x^{5/2}}","-\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,"(2*(16*b^3*x^3 - 8*b^2*x^2*ArcTanh[Tanh[a + b*x]] - 2*b*x*ArcTanh[Tanh[a + b*x]]^2 - ArcTanh[Tanh[a + b*x]]^3))/(5*x^(5/2))","A",1
191,1,129,143,0.0691834,"\int \frac{x^{7/2}}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[x^(7/2)/ArcTanh[Tanh[a + b*x]],x]","\frac{2 \left(-406 b^{5/2} x^{5/2} \tanh ^{-1}(\tanh (a+b x))+350 b^{3/2} x^{3/2} \tanh ^{-1}(\tanh (a+b x))^2-105 \sqrt{b} \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^3+105 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)+176 b^{7/2} x^{7/2}\right)}{105 b^{9/2}}","-\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)^{7/2}}{b^{9/2}}+\frac{2 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}{b^4}+\frac{2 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{3 b^3}+\frac{2 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{5 b^2}+\frac{2 x^{7/2}}{7 b}",1,"(2*(176*b^(7/2)*x^(7/2) - 406*b^(5/2)*x^(5/2)*ArcTanh[Tanh[a + b*x]] + 350*b^(3/2)*x^(3/2)*ArcTanh[Tanh[a + b*x]]^2 - 105*Sqrt[b]*Sqrt[x]*ArcTanh[Tanh[a + b*x]]^3 + 105*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^(7/2)))/(105*b^(9/2))","A",1
192,1,108,116,0.129445,"\int \frac{x^{5/2}}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[x^(5/2)/ArcTanh[Tanh[a + b*x]],x]","\frac{2 \left(-35 b^{3/2} x^{3/2} \tanh ^{-1}(\tanh (a+b x))+15 \sqrt{b} \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^2-15 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)+23 b^{5/2} x^{5/2}\right)}{15 b^{7/2}}","-\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)^{5/2}}{b^{7/2}}+\frac{2 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{b^3}+\frac{2 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{3 b^2}+\frac{2 x^{5/2}}{5 b}",1,"(2*(23*b^(5/2)*x^(5/2) - 35*b^(3/2)*x^(3/2)*ArcTanh[Tanh[a + b*x]] + 15*Sqrt[b]*Sqrt[x]*ArcTanh[Tanh[a + b*x]]^2 - 15*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^(5/2)))/(15*b^(7/2))","A",1
193,1,86,89,0.093862,"\int \frac{x^{3/2}}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[x^(3/2)/ArcTanh[Tanh[a + b*x]],x]","\frac{2 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{b^{5/2}}-\frac{2 \sqrt{x} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}{b^2}+\frac{2 x^{3/2}}{3 b}","-\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 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^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*ArcTan[(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",1
194,1,62,64,0.0463003,"\int \frac{\sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[Sqrt[x]/ArcTanh[Tanh[a + b*x]],x]","\frac{2 \sqrt{x}}{b}-\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))-b x} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{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*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]*Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]])/b^(3/2)","A",1
195,1,51,53,0.0301374,"\int \frac{1}{\sqrt{x} \tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[1/(Sqrt[x]*ArcTanh[Tanh[a + b*x]]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))-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*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(Sqrt[b]*Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]])","A",1
196,1,73,76,0.0655992,"\int \frac{1}{x^{3/2} \tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[1/(x^(3/2)*ArcTanh[Tanh[a + b*x]]),x]","-\frac{2}{\sqrt{x} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}-\frac{2 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-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]*ArcTan[(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",1
197,1,89,101,0.1956288,"\int \frac{1}{x^{5/2} \tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[1/(x^(5/2)*ArcTanh[Tanh[a + b*x]]),x]","\frac{2 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{5/2}}+\frac{2 \left(4 b x-\tanh ^{-1}(\tanh (a+b x))\right)}{3 x^{3/2} \left(\tanh ^{-1}(\tanh (a+b x))-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)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(-(b*x) + ArcTanh[Tanh[a + b*x]])^(5/2) + (2*(4*b*x - ArcTanh[Tanh[a + b*x]]))/(3*x^(3/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)","A",1
198,1,107,128,0.1610311,"\int \frac{1}{x^{7/2} \tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[1/(x^(7/2)*ArcTanh[Tanh[a + b*x]]),x]","\frac{2 \left(-11 b x \tanh ^{-1}(\tanh (a+b x))+3 \tanh ^{-1}(\tanh (a+b x))^2+23 b^2 x^2\right)}{15 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}-\frac{2 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{7/2}}","-\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)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(-(b*x) + ArcTanh[Tanh[a + b*x]])^(7/2) + (2*(23*b^2*x^2 - 11*b*x*ArcTanh[Tanh[a + b*x]] + 3*ArcTanh[Tanh[a + b*x]]^2))/(15*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3)","A",1
199,1,144,135,0.2051181,"\int \frac{x^{7/2}}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[x^(7/2)/ArcTanh[Tanh[a + b*x]]^2,x]","-\frac{7 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{b^{9/2}}+\frac{\sqrt{x} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^3}{b^4 \tanh ^{-1}(\tanh (a+b x))}+\frac{6 \sqrt{x} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}{b^4}-\frac{4 x^{3/2} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}{3 b^3}+\frac{2 x^{5/2}}{5 b^2}","-\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{7 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^2}{b^4}+\frac{7 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{3 b^3}-\frac{x^{7/2}}{b \tanh ^{-1}(\tanh (a+b x))}+\frac{7 x^{5/2}}{5 b^2}",1,"(2*x^(5/2))/(5*b^2) - (4*x^(3/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]]))/(3*b^3) + (6*Sqrt[x]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)/b^4 - (7*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^(5/2))/b^(9/2) + (Sqrt[x]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^3)/(b^4*ArcTanh[Tanh[a + b*x]])","A",1
200,1,119,108,0.1560216,"\int \frac{x^{5/2}}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[x^(5/2)/ArcTanh[Tanh[a + b*x]]^2,x]","\frac{5 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{b^{7/2}}-\frac{\sqrt{x} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}{b^3 \tanh ^{-1}(\tanh (a+b x))}-\frac{4 \sqrt{x} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}{b^3}+\frac{2 x^{3/2}}{3 b^2}","-\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{5 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{b^3}-\frac{x^{5/2}}{b \tanh ^{-1}(\tanh (a+b x))}+\frac{5 x^{3/2}}{3 b^2}",1,"(2*x^(3/2))/(3*b^2) - (4*Sqrt[x]*(-(b*x) + ArcTanh[Tanh[a + b*x]]))/b^3 + (5*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^(3/2))/b^(7/2) - (Sqrt[x]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)/(b^3*ArcTanh[Tanh[a + b*x]])","A",1
201,1,81,83,0.0873164,"\int \frac{x^{3/2}}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[x^(3/2)/ArcTanh[Tanh[a + b*x]]^2,x]","-\frac{3 \sqrt{\tanh ^{-1}(\tanh (a+b x))-b x} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{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 - x^(3/2)/(b*ArcTanh[Tanh[a + b*x]]) - (3*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]*Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]])/b^(5/2)","A",1
202,1,70,73,0.0612545,"\int \frac{\sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[Sqrt[x]/ArcTanh[Tanh[a + b*x]]^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{b^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))-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,"-(Sqrt[x]/(b*ArcTanh[Tanh[a + b*x]])) + ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]/(b^(3/2)*Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]])","A",1
203,1,80,97,0.0637122,"\int \frac{1}{\sqrt{x} \tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[1/(Sqrt[x]*ArcTanh[Tanh[a + b*x]]^2),x]","\frac{\sqrt{x}}{\tanh ^{-1}(\tanh (a+b x)) \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\sqrt{b} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{3/2}}","\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,"ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]/(Sqrt[b]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^(3/2)) + Sqrt[x]/(ArcTanh[Tanh[a + b*x]]*(-(b*x) + ArcTanh[Tanh[a + b*x]]))","A",1
204,1,104,120,0.1202723,"\int \frac{1}{x^{3/2} \tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[1/(x^(3/2)*ArcTanh[Tanh[a + b*x]]^2),x]","-\frac{b \sqrt{x}}{\tanh ^{-1}(\tanh (a+b x)) \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}-\frac{2}{\sqrt{x} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{5/2}}","-\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]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(-(b*x) + ArcTanh[Tanh[a + b*x]])^(5/2) - 2/(Sqrt[x]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2) - (b*Sqrt[x])/(ArcTanh[Tanh[a + b*x]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)","A",1
205,1,120,145,0.2205846,"\int \frac{1}{x^{5/2} \tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[1/(x^(5/2)*ArcTanh[Tanh[a + b*x]]^2),x]","\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{7/2}}+\frac{b^2 \sqrt{x}}{\tanh ^{-1}(\tanh (a+b x)) \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^3}+\frac{2 \left(\tanh ^{-1}(\tanh (a+b x))-7 b x\right)}{3 x^{3/2} \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,"(2*(-7*b*x + ArcTanh[Tanh[a + b*x]]))/(3*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3) + (5*b^(3/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(-(b*x) + ArcTanh[Tanh[a + b*x]])^(7/2) + (b^2*Sqrt[x])/(ArcTanh[Tanh[a + b*x]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^3)","A",1
206,1,139,172,0.275218,"\int \frac{1}{x^{7/2} \tanh ^{-1}(\tanh (a+b x))^2} \, dx","Integrate[1/(x^(7/2)*ArcTanh[Tanh[a + b*x]]^2),x]","-\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{9/2}}-\frac{b^3 \sqrt{x}}{\tanh ^{-1}(\tanh (a+b x)) \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4}-\frac{2 \left(-16 b x \tanh ^{-1}(\tanh (a+b x))+3 \tanh ^{-1}(\tanh (a+b x))^2+58 b^2 x^2\right)}{15 x^{5/2} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4}","\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)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(-(b*x) + ArcTanh[Tanh[a + b*x]])^(9/2) - (b^3*Sqrt[x])/(ArcTanh[Tanh[a + b*x]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4) - (2*(58*b^2*x^2 - 16*b*x*ArcTanh[Tanh[a + b*x]] + 3*ArcTanh[Tanh[a + b*x]]^2))/(15*x^(5/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4)","A",1
207,1,147,135,0.1126935,"\int \frac{x^{7/2}}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[x^(7/2)/ArcTanh[Tanh[a + b*x]]^3,x]","-\frac{21 b^{5/2} x^{5/2} \tanh ^{-1}(\tanh (a+b x))-140 b^{3/2} x^{3/2} \tanh ^{-1}(\tanh (a+b x))^2+105 \sqrt{b} \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^3-105 \tanh ^{-1}(\tanh (a+b x))^2 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)+6 b^{7/2} x^{7/2}}{12 b^{9/2} \tanh ^{-1}(\tanh (a+b x))^2}","-\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{35 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)}{4 b^4}-\frac{7 x^{5/2}}{4 b^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{x^{7/2}}{2 b \tanh ^{-1}(\tanh (a+b x))^2}+\frac{35 x^{3/2}}{12 b^3}",1,"-1/12*(6*b^(7/2)*x^(7/2) + 21*b^(5/2)*x^(5/2)*ArcTanh[Tanh[a + b*x]] - 140*b^(3/2)*x^(3/2)*ArcTanh[Tanh[a + b*x]]^2 + 105*Sqrt[b]*Sqrt[x]*ArcTanh[Tanh[a + b*x]]^3 - 105*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]*ArcTanh[Tanh[a + b*x]]^2*(-(b*x) + ArcTanh[Tanh[a + b*x]])^(3/2))/(b^(9/2)*ArcTanh[Tanh[a + b*x]]^2)","A",1
208,1,104,110,0.1032957,"\int \frac{x^{5/2}}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[x^(5/2)/ArcTanh[Tanh[a + b*x]]^3,x]","\frac{1}{4} \left(-\frac{15 \sqrt{\tanh ^{-1}(\tanh (a+b x))-b x} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{b^{7/2}}-\frac{5 x^{3/2}}{b^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{2 x^{5/2}}{b \tanh ^{-1}(\tanh (a+b x))^2}+\frac{15 \sqrt{x}}{b^3}\right)","-\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{5 x^{3/2}}{4 b^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{x^{5/2}}{2 b \tanh ^{-1}(\tanh (a+b x))^2}+\frac{15 \sqrt{x}}{4 b^3}",1,"((15*Sqrt[x])/b^3 - (2*x^(5/2))/(b*ArcTanh[Tanh[a + b*x]]^2) - (5*x^(3/2))/(b^2*ArcTanh[Tanh[a + b*x]]) - (15*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]*Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]])/b^(7/2))/4","A",1
209,1,96,98,0.0811712,"\int \frac{x^{3/2}}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[x^(3/2)/ArcTanh[Tanh[a + b*x]]^3,x]","\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{4 b^{5/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}-\frac{3 \sqrt{x}}{4 b^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{x^{3/2}}{2 b \tanh ^{-1}(\tanh (a+b x))^2}","-\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{3 \sqrt{x}}{4 b^2 \tanh ^{-1}(\tanh (a+b x))}-\frac{x^{3/2}}{2 b \tanh ^{-1}(\tanh (a+b x))^2}",1,"-1/2*x^(3/2)/(b*ArcTanh[Tanh[a + b*x]]^2) - (3*Sqrt[x])/(4*b^2*ArcTanh[Tanh[a + b*x]]) + (3*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(4*b^(5/2)*Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]])","A",1
210,1,107,125,0.1514823,"\int \frac{\sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[Sqrt[x]/ArcTanh[Tanh[a + b*x]]^3,x]","\frac{1}{4} \left(\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{b^{3/2} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{3/2}}+\frac{\sqrt{x}}{b \tanh ^{-1}(\tanh (a+b x))^2-b^2 x \tanh ^{-1}(\tanh (a+b x))}-\frac{2 \sqrt{x}}{b \tanh ^{-1}(\tanh (a+b x))^2}\right)","\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,"((-2*Sqrt[x])/(b*ArcTanh[Tanh[a + b*x]]^2) + ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]]/(b^(3/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^(3/2)) + Sqrt[x]/(-(b^2*x*ArcTanh[Tanh[a + b*x]]) + b*ArcTanh[Tanh[a + b*x]]^2))/4","A",1
211,1,118,152,0.088616,"\int \frac{1}{\sqrt{x} \tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[1/(Sqrt[x]*ArcTanh[Tanh[a + b*x]]^3),x]","\frac{\sqrt{x}}{2 \tanh ^{-1}(\tanh (a+b x))^2 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}+\frac{3 \sqrt{x}}{4 \tanh ^{-1}(\tanh (a+b x)) \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{4 \sqrt{b} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{5/2}}","\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*ArcTan[(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*Sqrt[x])/(4*ArcTanh[Tanh[a + b*x]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2) + Sqrt[x]/(2*ArcTanh[Tanh[a + b*x]]^2*(-(b*x) + ArcTanh[Tanh[a + b*x]]))","A",1
212,1,141,176,0.1779818,"\int \frac{1}{x^{3/2} \tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[1/(x^(3/2)*ArcTanh[Tanh[a + b*x]]^3),x]","-\frac{b \sqrt{x}}{2 \tanh ^{-1}(\tanh (a+b x))^2 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}-\frac{7 b \sqrt{x}}{4 \tanh ^{-1}(\tanh (a+b x)) \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^3}-\frac{2}{\sqrt{x} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^3}-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{4 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{7/2}}","\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]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(4*(-(b*x) + ArcTanh[Tanh[a + b*x]])^(7/2)) - 2/(Sqrt[x]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^3) - (7*b*Sqrt[x])/(4*ArcTanh[Tanh[a + b*x]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^3) - (b*Sqrt[x])/(2*ArcTanh[Tanh[a + b*x]]^2*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)","A",1
213,1,156,201,0.2777128,"\int \frac{1}{x^{5/2} \tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[1/(x^(5/2)*ArcTanh[Tanh[a + b*x]]^3),x]","\frac{1}{12} \left(\frac{105 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{9/2}}+\frac{6 b^2 \sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))^2 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^3}+\frac{33 b^2 \sqrt{x}}{\tanh ^{-1}(\tanh (a+b x)) \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4}+\frac{80 b x-8 \tanh ^{-1}(\tanh (a+b x))}{x^{3/2} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4}\right)","-\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{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}{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,"((105*b^(3/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(-(b*x) + ArcTanh[Tanh[a + b*x]])^(9/2) + (80*b*x - 8*ArcTanh[Tanh[a + b*x]])/(x^(3/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4) + (33*b^2*Sqrt[x])/(ArcTanh[Tanh[a + b*x]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4) + (6*b^2*Sqrt[x])/(ArcTanh[Tanh[a + b*x]]^2*(-(b*x) + ArcTanh[Tanh[a + b*x]])^3))/12","A",1
214,1,174,228,0.3548431,"\int \frac{1}{x^{7/2} \tanh ^{-1}(\tanh (a+b x))^3} \, dx","Integrate[1/(x^(7/2)*ArcTanh[Tanh[a + b*x]]^3),x]","\frac{1}{20} \left(-\frac{315 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))-b x}}\right)}{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^{11/2}}+\frac{75 b^3 \sqrt{x}}{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^5 \tanh ^{-1}(\tanh (a+b x))}-\frac{10 b^3 \sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))^2 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4}+\frac{8 \left(-7 b x \tanh ^{-1}(\tanh (a+b x))+\tanh ^{-1}(\tanh (a+b x))^2+36 b^2 x^2\right)}{x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^5}\right)","-\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{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^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,"((75*b^3*Sqrt[x])/((b*x - ArcTanh[Tanh[a + b*x]])^5*ArcTanh[Tanh[a + b*x]]) - (315*b^(5/2)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[-(b*x) + ArcTanh[Tanh[a + b*x]]]])/(-(b*x) + ArcTanh[Tanh[a + b*x]])^(11/2) - (10*b^3*Sqrt[x])/(ArcTanh[Tanh[a + b*x]]^2*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4) + (8*(36*b^2*x^2 - 7*b*x*ArcTanh[Tanh[a + b*x]] + ArcTanh[Tanh[a + b*x]]^2))/(x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])^5))/20","A",1
215,1,104,142,0.0926171,"\int x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[x^(3/2)*Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^3 \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)}{8 b^{5/2}}+\frac{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(8 b x \tanh ^{-1}(\tanh (a+b x))-3 \tanh ^{-1}(\tanh (a+b x))^2+3 b^2 x^2\right)}{24 b^2}","-\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,"(Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]]*(3*b^2*x^2 + 8*b*x*ArcTanh[Tanh[a + b*x]] - 3*ArcTanh[Tanh[a + b*x]]^2))/(24*b^2) + ((-(b*x) + ArcTanh[Tanh[a + b*x]])^3*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/(8*b^(5/2))","A",1
216,1,84,104,0.068858,"\int \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \, dx","Integrate[Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(\tanh ^{-1}(\tanh (a+b x))+b x\right)}{4 b}-\frac{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2 \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)}{4 b^{3/2}}","-\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,"(Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]]*(b*x + ArcTanh[Tanh[a + b*x]]))/(4*b) - ((-(b*x) + ArcTanh[Tanh[a + b*x]])^2*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/(4*b^(3/2))","A",1
217,1,62,61,0.0404574,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{x}} \, dx","Integrate[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[x],x]","\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+\frac{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right) \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{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,"Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]] + ((-(b*x) + ArcTanh[Tanh[a + b*x]])*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/Sqrt[b]","A",1
218,1,52,49,0.0421691,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^{3/2}} \, dx","Integrate[Sqrt[ArcTanh[Tanh[a + b*x]]]/x^(3/2),x]","2 \sqrt{b} \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{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[ArcTanh[Tanh[a + b*x]]])/Sqrt[x] + 2*Sqrt[b]*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]]","A",1
219,1,34,35,0.0361825,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^{5/2}} \, dx","Integrate[Sqrt[ArcTanh[Tanh[a + b*x]]]/x^(5/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{3/2} \left(3 b x-3 \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))/(x^(3/2)*(3*b*x - 3*ArcTanh[Tanh[a + b*x]]))","A",1
220,1,48,72,0.0397878,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^{7/2}} \, dx","Integrate[Sqrt[ArcTanh[Tanh[a + b*x]]]/x^(7/2),x]","\frac{2 \left(5 b x-3 \tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{3/2}}{15 x^{5/2} \left(\tanh ^{-1}(\tanh (a+b x))-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,"(2*(5*b*x - 3*ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(3/2))/(15*x^(5/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)","A",1
221,1,66,110,0.0640721,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^{9/2}} \, dx","Integrate[Sqrt[ArcTanh[Tanh[a + b*x]]]/x^(9/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2} \left(-42 b x \tanh ^{-1}(\tanh (a+b x))+15 \tanh ^{-1}(\tanh (a+b x))^2+35 b^2 x^2\right)}{105 x^{7/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}","\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,"(2*ArcTanh[Tanh[a + b*x]]^(3/2)*(35*b^2*x^2 - 42*b*x*ArcTanh[Tanh[a + b*x]] + 15*ArcTanh[Tanh[a + b*x]]^2))/(105*x^(7/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3)","A",1
222,1,82,148,0.0696578,"\int \frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}{x^{11/2}} \, dx","Integrate[Sqrt[ArcTanh[Tanh[a + b*x]]]/x^(11/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{3/2} \left(-189 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+135 b x \tanh ^{-1}(\tanh (a+b x))^2-35 \tanh ^{-1}(\tanh (a+b x))^3+105 b^3 x^3\right)}{315 x^{9/2} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4}","\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,"(2*ArcTanh[Tanh[a + b*x]]^(3/2)*(105*b^3*x^3 - 189*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 135*b*x*ArcTanh[Tanh[a + b*x]]^2 - 35*ArcTanh[Tanh[a + b*x]]^3))/(315*x^(9/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4)","A",1
223,1,122,177,0.0955828,"\int x^{3/2} \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx","Integrate[x^(3/2)*ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{\sqrt{b} \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(11 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+11 b x \tanh ^{-1}(\tanh (a+b x))^2-3 \tanh ^{-1}(\tanh (a+b x))^3-3 b^3 x^3\right)+3 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4 \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)}{64 b^{5/2}}","\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,"(Sqrt[b]*Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]]*(-3*b^3*x^3 + 11*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 11*b*x*ArcTanh[Tanh[a + b*x]]^2 - 3*ArcTanh[Tanh[a + b*x]]^3) + 3*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/(64*b^(5/2))","A",1
224,1,105,139,0.0758962,"\int \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{3/2} \, dx","Integrate[Sqrt[x]*ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{\left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)}{8 b^{3/2}}+\frac{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(8 b x \tanh ^{-1}(\tanh (a+b x))+3 \tanh ^{-1}(\tanh (a+b x))^2-3 b^2 x^2\right)}{24 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,"(Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]]*(-3*b^2*x^2 + 8*b*x*ArcTanh[Tanh[a + b*x]] + 3*ArcTanh[Tanh[a + b*x]]^2))/(24*b) + ((b*x - ArcTanh[Tanh[a + b*x]])^3*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/(8*b^(3/2))","A",1
225,1,83,101,0.0629705,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{\sqrt{x}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(3/2)/Sqrt[x],x]","\frac{1}{4} \left(\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(5 \tanh ^{-1}(\tanh (a+b x))-3 b x\right)+\frac{3 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2 \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)}{\sqrt{b}}\right)","\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,"(Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]]*(-3*b*x + 5*ArcTanh[Tanh[a + b*x]]) + (3*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/Sqrt[b])/4","A",1
226,1,77,81,0.0586109,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{3/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(3/2)/x^(3/2),x]","\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(3 b x-2 \tanh ^{-1}(\tanh (a+b x))\right)}{\sqrt{x}}+3 \sqrt{b} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right) \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{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*b*x - 2*ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]])/Sqrt[x] + 3*Sqrt[b]*(-(b*x) + ArcTanh[Tanh[a + b*x]])*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]]","A",1
227,1,74,70,0.0491293,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{5/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(3/2)/x^(5/2),x]","-\frac{2 \left(-3 b^{3/2} x^{3/2} \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)+3 b x \sqrt{\tanh ^{-1}(\tanh (a+b x))}+\tanh ^{-1}(\tanh (a+b x))^{3/2}\right)}{3 x^{3/2}}","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*(3*b*x*Sqrt[ArcTanh[Tanh[a + b*x]]] + ArcTanh[Tanh[a + b*x]]^(3/2) - 3*b^(3/2)*x^(3/2)*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]]))/(3*x^(3/2))","A",1
228,1,34,35,0.0440794,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{7/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(3/2)/x^(7/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{5/2} \left(5 b x-5 \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))/(x^(5/2)*(5*b*x - 5*ArcTanh[Tanh[a + b*x]]))","A",1
229,1,48,72,0.0491438,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{9/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(3/2)/x^(9/2),x]","\frac{2 \left(7 b x-5 \tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{5/2}}{35 x^{7/2} \left(\tanh ^{-1}(\tanh (a+b x))-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,"(2*(7*b*x - 5*ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(5/2))/(35*x^(7/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)","A",1
230,1,66,110,0.054041,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{11/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(3/2)/x^(11/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2} \left(-90 b x \tanh ^{-1}(\tanh (a+b x))+35 \tanh ^{-1}(\tanh (a+b x))^2+63 b^2 x^2\right)}{315 x^{9/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}","\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,"(2*ArcTanh[Tanh[a + b*x]]^(5/2)*(63*b^2*x^2 - 90*b*x*ArcTanh[Tanh[a + b*x]] + 35*ArcTanh[Tanh[a + b*x]]^2))/(315*x^(9/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3)","A",1
231,1,82,148,0.0771971,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{3/2}}{x^{13/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(3/2)/x^(13/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{5/2} \left(-495 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+385 b x \tanh ^{-1}(\tanh (a+b x))^2-105 \tanh ^{-1}(\tanh (a+b x))^3+231 b^3 x^3\right)}{1155 x^{11/2} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4}","\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,"(2*ArcTanh[Tanh[a + b*x]]^(5/2)*(231*b^3*x^3 - 495*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 385*b*x*ArcTanh[Tanh[a + b*x]]^2 - 105*ArcTanh[Tanh[a + b*x]]^3))/(1155*x^(11/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4)","A",1
232,1,121,174,0.0864198,"\int \sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{5/2} \, dx","Integrate[Sqrt[x]*ArcTanh[Tanh[a + b*x]]^(5/2),x]","\frac{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(-55 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+73 b x \tanh ^{-1}(\tanh (a+b x))^2+15 \tanh ^{-1}(\tanh (a+b x))^3+15 b^3 x^3\right)}{192 b}-\frac{5 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4 \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)}{64 b^{3/2}}","-\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)^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,"(Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]]*(15*b^3*x^3 - 55*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 73*b*x*ArcTanh[Tanh[a + b*x]]^2 + 15*ArcTanh[Tanh[a + b*x]]^3))/(192*b) - (5*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/(64*b^(3/2))","A",1
233,1,101,136,0.0630642,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{\sqrt{x}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(5/2)/Sqrt[x],x]","\frac{1}{24} \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(-40 b x \tanh ^{-1}(\tanh (a+b x))+33 \tanh ^{-1}(\tanh (a+b x))^2+15 b^2 x^2\right)+\frac{5 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^3 \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)}{8 \sqrt{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)^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,"(Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]]*(15*b^2*x^2 - 40*b*x*ArcTanh[Tanh[a + b*x]] + 33*ArcTanh[Tanh[a + b*x]]^2))/24 + (5*(-(b*x) + ArcTanh[Tanh[a + b*x]])^3*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/(8*Sqrt[b])","A",1
234,1,101,121,0.0766583,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{3/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(5/2)/x^(3/2),x]","\frac{15}{4} \sqrt{b} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2 \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)-\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(-25 b x \tanh ^{-1}(\tanh (a+b x))+8 \tanh ^{-1}(\tanh (a+b x))^2+15 b^2 x^2\right)}{4 \sqrt{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",1,"-1/4*(Sqrt[ArcTanh[Tanh[a + b*x]]]*(15*b^2*x^2 - 25*b*x*ArcTanh[Tanh[a + b*x]] + 8*ArcTanh[Tanh[a + b*x]]^2))/Sqrt[x] + (15*Sqrt[b]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/4","A",1
235,1,97,106,0.0750323,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{5/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(5/2)/x^(5/2),x]","5 b^{3/2} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right) \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)+\frac{\sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(-10 b x \tanh ^{-1}(\tanh (a+b x))-2 \tanh ^{-1}(\tanh (a+b x))^2+15 b^2 x^2\right)}{3 x^{3/2}}","-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)+5 b^2 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}-\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,"(Sqrt[ArcTanh[Tanh[a + b*x]]]*(15*b^2*x^2 - 10*b*x*ArcTanh[Tanh[a + b*x]] - 2*ArcTanh[Tanh[a + b*x]]^2))/(3*x^(3/2)) + 5*b^(3/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]]","A",1
236,1,95,93,0.057136,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{7/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(5/2)/x^(7/2),x]","-\frac{2 \left(-15 b^{5/2} x^{5/2} \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)+15 b^2 x^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}+5 b x \tanh ^{-1}(\tanh (a+b x))^{3/2}+3 \tanh ^{-1}(\tanh (a+b x))^{5/2}\right)}{15 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*(15*b^2*x^2*Sqrt[ArcTanh[Tanh[a + b*x]]] + 5*b*x*ArcTanh[Tanh[a + b*x]]^(3/2) + 3*ArcTanh[Tanh[a + b*x]]^(5/2) - 15*b^(5/2)*x^(5/2)*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]]))/(15*x^(5/2))","A",1
237,1,34,35,0.049111,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{9/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(5/2)/x^(9/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{7/2}}{x^{7/2} \left(7 b x-7 \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))/(x^(7/2)*(7*b*x - 7*ArcTanh[Tanh[a + b*x]]))","A",1
238,1,48,72,0.0563297,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{11/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(5/2)/x^(11/2),x]","\frac{2 \left(9 b x-7 \tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{7/2}}{63 x^{9/2} \left(\tanh ^{-1}(\tanh (a+b x))-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,"(2*(9*b*x - 7*ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(7/2))/(63*x^(9/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)","A",1
239,1,66,110,0.0558456,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{13/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(5/2)/x^(13/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{7/2} \left(-154 b x \tanh ^{-1}(\tanh (a+b x))+63 \tanh ^{-1}(\tanh (a+b x))^2+99 b^2 x^2\right)}{693 x^{11/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}","\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,"(2*ArcTanh[Tanh[a + b*x]]^(7/2)*(99*b^2*x^2 - 154*b*x*ArcTanh[Tanh[a + b*x]] + 63*ArcTanh[Tanh[a + b*x]]^2))/(693*x^(11/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3)","A",1
240,1,82,148,0.088171,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^{5/2}}{x^{15/2}} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^(5/2)/x^(15/2),x]","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{7/2} \left(-1001 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+819 b x \tanh ^{-1}(\tanh (a+b x))^2-231 \tanh ^{-1}(\tanh (a+b x))^3+429 b^3 x^3\right)}{3003 x^{13/2} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4}","\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{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{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,"(2*ArcTanh[Tanh[a + b*x]]^(7/2)*(429*b^3*x^3 - 1001*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 819*b*x*ArcTanh[Tanh[a + b*x]]^2 - 231*ArcTanh[Tanh[a + b*x]]^3))/(3003*x^(13/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4)","A",1
241,1,105,145,0.1015901,"\int \frac{x^{5/2}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[x^(5/2)/Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{5 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)}{8 b^{7/2}}+\frac{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(-40 b x \tanh ^{-1}(\tanh (a+b x))+15 \tanh ^{-1}(\tanh (a+b x))^2+33 b^2 x^2\right)}{24 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)^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{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{x^{5/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{3 b}",1,"(Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]]*(33*b^2*x^2 - 40*b*x*ArcTanh[Tanh[a + b*x]] + 15*ArcTanh[Tanh[a + b*x]]^2))/(24*b^3) + (5*(b*x - ArcTanh[Tanh[a + b*x]])^3*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/(8*b^(7/2))","A",1
242,1,88,107,0.0791775,"\int \frac{x^{3/2}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[x^(3/2)/Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{\sqrt{b} \sqrt{x} \left(5 b x-3 \tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}+3 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2 \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)}{4 b^{5/2}}","\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 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,"(Sqrt[b]*Sqrt[x]*(5*b*x - 3*ArcTanh[Tanh[a + b*x]])*Sqrt[ArcTanh[Tanh[a + b*x]]] + 3*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/(4*b^(5/2))","A",1
243,1,66,63,0.0623174,"\int \frac{\sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[Sqrt[x]/Sqrt[ArcTanh[Tanh[a + b*x]]],x]","\frac{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b}-\frac{\left(\tanh ^{-1}(\tanh (a+b x))-b x\right) \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)}{b^{3/2}}","\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,"(Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]])/b - ((-(b*x) + ArcTanh[Tanh[a + b*x]])*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/b^(3/2)","A",1
244,1,33,30,0.0325024,"\int \frac{1}{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[1/(Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","\frac{2 \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{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*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/Sqrt[b]","A",1
245,1,32,33,0.0432516,"\int \frac{1}{x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[1/(x^(3/2)*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","-\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{\sqrt{x} \left(\tanh ^{-1}(\tanh (a+b x))-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
246,1,46,72,0.0455314,"\int \frac{1}{x^{5/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[1/(x^(5/2)*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","-\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(\tanh ^{-1}(\tanh (a+b x))-3 b x\right)}{3 x^{3/2} \left(\tanh ^{-1}(\tanh (a+b x))-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,"(-2*Sqrt[ArcTanh[Tanh[a + b*x]]]*(-3*b*x + ArcTanh[Tanh[a + b*x]]))/(3*x^(3/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)","A",1
247,1,66,110,0.0574034,"\int \frac{1}{x^{7/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[1/(x^(7/2)*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(-10 b x \tanh ^{-1}(\tanh (a+b x))+3 \tanh ^{-1}(\tanh (a+b x))^2+15 b^2 x^2\right)}{15 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3}","\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,"(2*Sqrt[ArcTanh[Tanh[a + b*x]]]*(15*b^2*x^2 - 10*b*x*ArcTanh[Tanh[a + b*x]] + 3*ArcTanh[Tanh[a + b*x]]^2))/(15*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3)","A",1
248,1,82,148,0.0609799,"\int \frac{1}{x^{9/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}} \, dx","Integrate[1/(x^(9/2)*Sqrt[ArcTanh[Tanh[a + b*x]]]),x]","\frac{2 \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(-35 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))+21 b x \tanh ^{-1}(\tanh (a+b x))^2-5 \tanh ^{-1}(\tanh (a+b x))^3+35 b^3 x^3\right)}{35 x^{7/2} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4}","\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{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{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,"(2*Sqrt[ArcTanh[Tanh[a + b*x]]]*(35*b^3*x^3 - 35*b^2*x^2*ArcTanh[Tanh[a + b*x]] + 21*b*x*ArcTanh[Tanh[a + b*x]]^2 - 5*ArcTanh[Tanh[a + b*x]]^3))/(35*x^(7/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4)","A",1
249,1,122,166,0.1135247,"\int \frac{x^{7/2}}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[x^(7/2)/ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{35 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)}{8 b^{9/2}}+\frac{\sqrt{x} \left(231 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))-280 b x \tanh ^{-1}(\tanh (a+b x))^2+105 \tanh ^{-1}(\tanh (a+b x))^3-48 b^3 x^3\right)}{24 b^4 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","\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{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 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{12 b^3}+\frac{7 x^{5/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{3 b^2}-\frac{2 x^{7/2}}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(Sqrt[x]*(-48*b^3*x^3 + 231*b^2*x^2*ArcTanh[Tanh[a + b*x]] - 280*b*x*ArcTanh[Tanh[a + b*x]]^2 + 105*ArcTanh[Tanh[a + b*x]]^3))/(24*b^4*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (35*(b*x - ArcTanh[Tanh[a + b*x]])^3*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/(8*b^(9/2))","A",1
250,1,104,128,0.0990652,"\int \frac{x^{5/2}}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[x^(5/2)/ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{15 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2 \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)}{4 b^{7/2}}-\frac{\sqrt{x} \left(-25 b x \tanh ^{-1}(\tanh (a+b x))+15 \tanh ^{-1}(\tanh (a+b x))^2+8 b^2 x^2\right)}{4 b^3 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}","\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{15 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{4 b^3}+\frac{5 x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{2 b^2}-\frac{2 x^{5/2}}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"-1/4*(Sqrt[x]*(8*b^2*x^2 - 25*b*x*ArcTanh[Tanh[a + b*x]] + 15*ArcTanh[Tanh[a + b*x]]^2))/(b^3*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (15*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/(4*b^(7/2))","A",1
251,1,81,86,0.0863042,"\int \frac{x^{3/2}}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[x^(3/2)/ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{3 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)}{b^{5/2}}+\frac{\sqrt{x} \left(3 \tanh ^{-1}(\tanh (a+b x))-2 b x\right)}{b^2 \sqrt{\tanh ^{-1}(\tanh (a+b 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)}{b^{5/2}}+\frac{3 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^2}-\frac{2 x^{3/2}}{b \sqrt{\tanh ^{-1}(\tanh (a+b x))}}",1,"(Sqrt[x]*(-2*b*x + 3*ArcTanh[Tanh[a + b*x]]))/(b^2*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (3*(b*x - ArcTanh[Tanh[a + b*x]])*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/b^(5/2)","A",1
252,1,55,52,0.05388,"\int \frac{\sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[Sqrt[x]/ArcTanh[Tanh[a + b*x]]^(3/2),x]","\frac{2 \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{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*Sqrt[x])/(b*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (2*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/b^(3/2)","A",1
253,1,32,33,0.0332115,"\int \frac{1}{\sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[1/(Sqrt[x]*ArcTanh[Tanh[a + b*x]]^(3/2)),x]","\frac{2 \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}","-\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])/(Sqrt[ArcTanh[Tanh[a + b*x]]]*(-(b*x) + ArcTanh[Tanh[a + b*x]]))","A",1
254,1,43,68,0.0517003,"\int \frac{1}{x^{3/2} \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[1/(x^(3/2)*ArcTanh[Tanh[a + b*x]]^(3/2)),x]","-\frac{2 \left(\tanh ^{-1}(\tanh (a+b x))+b x\right)}{\sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2}","\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,"(-2*(b*x + ArcTanh[Tanh[a + b*x]]))/(Sqrt[x]*Sqrt[ArcTanh[Tanh[a + b*x]]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)","A",1
255,1,64,110,0.0597512,"\int \frac{1}{x^{5/2} \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[1/(x^(5/2)*ArcTanh[Tanh[a + b*x]]^(3/2)),x]","\frac{2 \left(-6 b x \tanh ^{-1}(\tanh (a+b x))+\tanh ^{-1}(\tanh (a+b x))^2-3 b^2 x^2\right)}{3 x^{3/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \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,"(2*(-3*b^2*x^2 - 6*b*x*ArcTanh[Tanh[a + b*x]] + ArcTanh[Tanh[a + b*x]]^2))/(3*x^(3/2)*(b*x - ArcTanh[Tanh[a + b*x]])^3*Sqrt[ArcTanh[Tanh[a + b*x]]])","A",1
256,1,80,148,0.0698833,"\int \frac{1}{x^{7/2} \tanh ^{-1}(\tanh (a+b x))^{3/2}} \, dx","Integrate[1/(x^(7/2)*ArcTanh[Tanh[a + b*x]]^(3/2)),x]","-\frac{2 \left(15 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))-5 b x \tanh ^{-1}(\tanh (a+b x))^2+\tanh ^{-1}(\tanh (a+b x))^3+5 b^3 x^3\right)}{5 x^{5/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4}","-\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,"(-2*(5*b^3*x^3 + 15*b^2*x^2*ArcTanh[Tanh[a + b*x]] - 5*b*x*ArcTanh[Tanh[a + b*x]]^2 + ArcTanh[Tanh[a + b*x]]^3))/(5*x^(5/2)*Sqrt[ArcTanh[Tanh[a + b*x]]]*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4)","A",1
257,1,121,153,0.109384,"\int \frac{x^{7/2}}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[x^(7/2)/ArcTanh[Tanh[a + b*x]]^(5/2),x]","\frac{35 \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^2 \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)}{4 b^{9/2}}-\frac{\sqrt{x} \left(56 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))-175 b x \tanh ^{-1}(\tanh (a+b x))^2+105 \tanh ^{-1}(\tanh (a+b x))^3+8 b^3 x^3\right)}{12 b^4 \tanh ^{-1}(\tanh (a+b x))^{3/2}}","\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{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 x^{3/2} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{6 b^3}-\frac{14 x^{5/2}}{3 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{2 x^{7/2}}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"-1/12*(Sqrt[x]*(8*b^3*x^3 + 56*b^2*x^2*ArcTanh[Tanh[a + b*x]] - 175*b*x*ArcTanh[Tanh[a + b*x]]^2 + 105*ArcTanh[Tanh[a + b*x]]^3))/(b^4*ArcTanh[Tanh[a + b*x]]^(3/2)) + (35*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/(4*b^(9/2))","A",1
258,1,101,111,0.0943727,"\int \frac{x^{5/2}}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[x^(5/2)/ArcTanh[Tanh[a + b*x]]^(5/2),x]","\frac{5 \left(b x-\tanh ^{-1}(\tanh (a+b x))\right) \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)}{b^{7/2}}-\frac{\sqrt{x} \left(10 b x \tanh ^{-1}(\tanh (a+b x))-15 \tanh ^{-1}(\tanh (a+b x))^2+2 b^2 x^2\right)}{3 b^3 \tanh ^{-1}(\tanh (a+b x))^{3/2}}","\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)}{b^{7/2}}+\frac{5 \sqrt{x} \sqrt{\tanh ^{-1}(\tanh (a+b x))}}{b^3}-\frac{10 x^{3/2}}{3 b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{2 x^{5/2}}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"-1/3*(Sqrt[x]*(2*b^2*x^2 + 10*b*x*ArcTanh[Tanh[a + b*x]] - 15*ArcTanh[Tanh[a + b*x]]^2))/(b^3*ArcTanh[Tanh[a + b*x]]^(3/2)) + (5*(b*x - ArcTanh[Tanh[a + b*x]])*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/b^(7/2)","A",1
259,1,78,75,0.069709,"\int \frac{x^{3/2}}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[x^(3/2)/ArcTanh[Tanh[a + b*x]]^(5/2),x]","\frac{2 \log \left(\sqrt{b} \sqrt{\tanh ^{-1}(\tanh (a+b x))}+b \sqrt{x}\right)}{b^{5/2}}-\frac{2 \sqrt{x}}{b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{2 x^{3/2}}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{\tanh ^{-1}(\tanh (a+b x))}}\right)}{b^{5/2}}-\frac{2 \sqrt{x}}{b^2 \sqrt{\tanh ^{-1}(\tanh (a+b x))}}-\frac{2 x^{3/2}}{3 b \tanh ^{-1}(\tanh (a+b x))^{3/2}}",1,"(-2*x^(3/2))/(3*b*ArcTanh[Tanh[a + b*x]]^(3/2)) - (2*Sqrt[x])/(b^2*Sqrt[ArcTanh[Tanh[a + b*x]]]) + (2*Log[b*Sqrt[x] + Sqrt[b]*Sqrt[ArcTanh[Tanh[a + b*x]]]])/b^(5/2)","A",1
260,1,34,35,0.0484293,"\int \frac{\sqrt{x}}{\tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[Sqrt[x]/ArcTanh[Tanh[a + b*x]]^(5/2),x]","\frac{2 x^{3/2}}{3 \tanh ^{-1}(\tanh (a+b x))^{3/2} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)}","-\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*ArcTanh[Tanh[a + b*x]]^(3/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]]))","A",1
261,1,47,71,0.0419382,"\int \frac{1}{\sqrt{x} \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[1/(Sqrt[x]*ArcTanh[Tanh[a + b*x]]^(5/2)),x]","-\frac{2 \sqrt{x} \left(b x-3 \tanh ^{-1}(\tanh (a+b x))\right)}{3 \tanh ^{-1}(\tanh (a+b x))^{3/2} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^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]*(b*x - 3*ArcTanh[Tanh[a + b*x]]))/(3*ArcTanh[Tanh[a + b*x]]^(3/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^2)","A",1
262,1,66,106,0.0603655,"\int \frac{1}{x^{3/2} \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[1/(x^(3/2)*ArcTanh[Tanh[a + b*x]]^(5/2)),x]","\frac{2 \left(6 b x \tanh ^{-1}(\tanh (a+b x))+3 \tanh ^{-1}(\tanh (a+b x))^2-b^2 x^2\right)}{3 \sqrt{x} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^3 \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,"(2*(-(b^2*x^2) + 6*b*x*ArcTanh[Tanh[a + b*x]] + 3*ArcTanh[Tanh[a + b*x]]^2))/(3*Sqrt[x]*(b*x - ArcTanh[Tanh[a + b*x]])^3*ArcTanh[Tanh[a + b*x]]^(3/2))","A",1
263,1,79,146,0.071494,"\int \frac{1}{x^{5/2} \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[1/(x^(5/2)*ArcTanh[Tanh[a + b*x]]^(5/2)),x]","-\frac{2 \left(-9 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))-9 b x \tanh ^{-1}(\tanh (a+b x))^2+\tanh ^{-1}(\tanh (a+b x))^3+b^3 x^3\right)}{3 x^{3/2} \tanh ^{-1}(\tanh (a+b x))^{3/2} \left(\tanh ^{-1}(\tanh (a+b x))-b x\right)^4}","\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,"(-2*(b^3*x^3 - 9*b^2*x^2*ArcTanh[Tanh[a + b*x]] - 9*b*x*ArcTanh[Tanh[a + b*x]]^2 + ArcTanh[Tanh[a + b*x]]^3))/(3*x^(3/2)*ArcTanh[Tanh[a + b*x]]^(3/2)*(-(b*x) + ArcTanh[Tanh[a + b*x]])^4)","A",1
264,1,100,186,0.0790057,"\int \frac{1}{x^{7/2} \tanh ^{-1}(\tanh (a+b x))^{5/2}} \, dx","Integrate[1/(x^(7/2)*ArcTanh[Tanh[a + b*x]]^(5/2)),x]","\frac{2 \left(60 b^3 x^3 \tanh ^{-1}(\tanh (a+b x))+90 b^2 x^2 \tanh ^{-1}(\tanh (a+b x))^2-20 b x \tanh ^{-1}(\tanh (a+b x))^3+3 \tanh ^{-1}(\tanh (a+b x))^4-5 b^4 x^4\right)}{15 x^{5/2} \left(b x-\tanh ^{-1}(\tanh (a+b x))\right)^5 \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,"(2*(-5*b^4*x^4 + 60*b^3*x^3*ArcTanh[Tanh[a + b*x]] + 90*b^2*x^2*ArcTanh[Tanh[a + b*x]]^2 - 20*b*x*ArcTanh[Tanh[a + b*x]]^3 + 3*ArcTanh[Tanh[a + b*x]]^4))/(15*x^(5/2)*(b*x - ArcTanh[Tanh[a + b*x]])^5*ArcTanh[Tanh[a + b*x]]^(3/2))","A",1
265,1,71,79,0.1401566,"\int x^m \tanh ^{-1}(\tanh (a+b x))^n \, dx","Integrate[x^m*ArcTanh[Tanh[a + b*x]]^n,x]","\frac{x^{m+1} \tanh ^{-1}(\tanh (a+b x))^n \left(\frac{b x}{\tanh ^{-1}(\tanh (a+b x))-b x}+1\right)^{-n} \, _2F_1\left(m+1,-n;m+2;-\frac{b x}{\tanh ^{-1}(\tanh (a+b x))-b x}\right)}{m+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^(1 + m)*ArcTanh[Tanh[a + b*x]]^n*Hypergeometric2F1[1 + m, -n, 2 + m, -((b*x)/(-(b*x) + ArcTanh[Tanh[a + b*x]]))])/((1 + m)*(1 + (b*x)/(-(b*x) + ArcTanh[Tanh[a + b*x]]))^n)","A",1
266,1,146,165,0.1121135,"\int x^4 \tanh ^{-1}(\tanh (a+b x))^n \, dx","Integrate[x^4*ArcTanh[Tanh[a + b*x]]^n,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^{n+1} \left(-4 b^3 \left(n^3+12 n^2+47 n+60\right) x^3 \tanh ^{-1}(\tanh (a+b x))+12 b^2 \left(n^2+9 n+20\right) x^2 \tanh ^{-1}(\tanh (a+b x))^2-24 b (n+5) x \tanh ^{-1}(\tanh (a+b x))^3+24 \tanh ^{-1}(\tanh (a+b x))^4+b^4 \left(n^4+14 n^3+71 n^2+154 n+120\right) x^4\right)}{b^5 (n+1) (n+2) (n+3) (n+4) (n+5)}","\frac{24 \tanh ^{-1}(\tanh (a+b x))^{n+5}}{b^5 (n+1) (n+2) (n+3) (n+4) (n+5)}-\frac{24 x \tanh ^{-1}(\tanh (a+b x))^{n+4}}{b^4 (n+1) (n+2) (n+3) (n+4)}+\frac{12 x^2 \tanh ^{-1}(\tanh (a+b x))^{n+3}}{b^3 (n+1) (n+2) (n+3)}-\frac{4 x^3 \tanh ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}+\frac{x^4 \tanh ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}",1,"(ArcTanh[Tanh[a + b*x]]^(1 + n)*(b^4*(120 + 154*n + 71*n^2 + 14*n^3 + n^4)*x^4 - 4*b^3*(60 + 47*n + 12*n^2 + n^3)*x^3*ArcTanh[Tanh[a + b*x]] + 12*b^2*(20 + 9*n + n^2)*x^2*ArcTanh[Tanh[a + b*x]]^2 - 24*b*(5 + n)*x*ArcTanh[Tanh[a + b*x]]^3 + 24*ArcTanh[Tanh[a + b*x]]^4))/(b^5*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n))","A",1
267,1,106,121,0.0972938,"\int x^3 \tanh ^{-1}(\tanh (a+b x))^n \, dx","Integrate[x^3*ArcTanh[Tanh[a + b*x]]^n,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^{n+1} \left(-3 b^2 \left(n^2+7 n+12\right) x^2 \tanh ^{-1}(\tanh (a+b x))+6 b (n+4) x \tanh ^{-1}(\tanh (a+b x))^2-6 \tanh ^{-1}(\tanh (a+b x))^3+b^3 \left(n^3+9 n^2+26 n+24\right) x^3\right)}{b^4 (n+1) (n+2) (n+3) (n+4)}","-\frac{6 \tanh ^{-1}(\tanh (a+b x))^{n+4}}{b^4 (n+1) (n+2) (n+3) (n+4)}+\frac{6 x \tanh ^{-1}(\tanh (a+b x))^{n+3}}{b^3 (n+1) (n+2) (n+3)}-\frac{3 x^2 \tanh ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}+\frac{x^3 \tanh ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}",1,"(ArcTanh[Tanh[a + b*x]]^(1 + n)*(b^3*(24 + 26*n + 9*n^2 + n^3)*x^3 - 3*b^2*(12 + 7*n + n^2)*x^2*ArcTanh[Tanh[a + b*x]] + 6*b*(4 + n)*x*ArcTanh[Tanh[a + b*x]]^2 - 6*ArcTanh[Tanh[a + b*x]]^3))/(b^4*(1 + n)*(2 + n)*(3 + n)*(4 + n))","A",1
268,1,71,82,0.0724199,"\int x^2 \tanh ^{-1}(\tanh (a+b x))^n \, dx","Integrate[x^2*ArcTanh[Tanh[a + b*x]]^n,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^{n+1} \left(-2 b (n+3) x \tanh ^{-1}(\tanh (a+b x))+2 \tanh ^{-1}(\tanh (a+b x))^2+b^2 \left(n^2+5 n+6\right) x^2\right)}{b^3 (n+1) (n+2) (n+3)}","\frac{2 \tanh ^{-1}(\tanh (a+b x))^{n+3}}{b^3 (n+1) (n+2) (n+3)}-\frac{2 x \tanh ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}+\frac{x^2 \tanh ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}",1,"(ArcTanh[Tanh[a + b*x]]^(1 + n)*(b^2*(6 + 5*n + n^2)*x^2 - 2*b*(3 + n)*x*ArcTanh[Tanh[a + b*x]] + 2*ArcTanh[Tanh[a + b*x]]^2))/(b^3*(1 + n)*(2 + n)*(3 + n))","A",1
269,1,41,48,0.0459887,"\int x \tanh ^{-1}(\tanh (a+b x))^n \, dx","Integrate[x*ArcTanh[Tanh[a + b*x]]^n,x]","\frac{\left(b (n+2) x-\tanh ^{-1}(\tanh (a+b x))\right) \tanh ^{-1}(\tanh (a+b x))^{n+1}}{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,"((b*(2 + n)*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^(1 + n))/(b^2*(1 + n)*(2 + n))","A",1
270,1,20,20,0.0160868,"\int \tanh ^{-1}(\tanh (a+b x))^n \, dx","Integrate[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",1
271,1,60,64,0.0923591,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^n}{x} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^n/x,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^n \left(\frac{\tanh ^{-1}(\tanh (a+b x))}{b x}\right)^{-n} \, _2F_1\left(-n,-n;1-n;1-\frac{\tanh ^{-1}(\tanh (a+b x))}{b x}\right)}{n}","\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]]^n*Hypergeometric2F1[-n, -n, 1 - n, 1 - ArcTanh[Tanh[a + b*x]]/(b*x)])/(n*(ArcTanh[Tanh[a + b*x]]/(b*x))^n)","A",1
272,1,67,71,0.0517699,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^n}{x^2} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^n/x^2,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^n \left(\frac{\tanh ^{-1}(\tanh (a+b x))}{b x}\right)^{-n} \, _2F_1\left(1-n,-n;2-n;1-\frac{\tanh ^{-1}(\tanh (a+b x))}{b x}\right)}{(n-1) 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*Hypergeometric2F1[1 - n, -n, 2 - n, 1 - ArcTanh[Tanh[a + b*x]]/(b*x)])/((-1 + n)*x*(ArcTanh[Tanh[a + b*x]]/(b*x))^n)","A",1
273,1,67,101,0.058268,"\int \frac{\tanh ^{-1}(\tanh (a+b x))^n}{x^3} \, dx","Integrate[ArcTanh[Tanh[a + b*x]]^n/x^3,x]","\frac{\tanh ^{-1}(\tanh (a+b x))^n \left(\frac{\tanh ^{-1}(\tanh (a+b x))}{b x}\right)^{-n} \, _2F_1\left(2-n,-n;3-n;1-\frac{\tanh ^{-1}(\tanh (a+b x))}{b x}\right)}{(n-2) x^2}","\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,"(ArcTanh[Tanh[a + b*x]]^n*Hypergeometric2F1[2 - n, -n, 3 - n, 1 - ArcTanh[Tanh[a + b*x]]/(b*x)])/((-2 + n)*x^2*(ArcTanh[Tanh[a + b*x]]/(b*x))^n)","A",1
274,1,34,37,0.0701726,"\int x^m \coth ^{-1}(\tanh (a+b x)) \, dx","Integrate[x^m*ArcCoth[Tanh[a + b*x]],x]","x^m \left(\frac{x \left(\coth ^{-1}(\tanh (a+b x))-b x\right)}{m+1}+\frac{b x^2}{m+2}\right)","\frac{x^{m+1} \coth ^{-1}(\tanh (a+b x))}{m+1}-\frac{b x^{m+2}}{m^2+3 m+2}",1,"x^m*((b*x^2)/(2 + m) + (x*(-(b*x) + ArcCoth[Tanh[a + b*x]]))/(1 + m))","A",1
275,1,20,23,0.0463482,"\int x^2 \tanh ^{-1}(\coth (a+b x)) \, dx","Integrate[x^2*ArcTanh[Coth[a + b*x]],x]","-\frac{1}{12} x^3 \left(b x-4 \tanh ^{-1}(\coth (a+b x))\right)","\frac{1}{3} x^3 \tanh ^{-1}(\coth (a+b x))-\frac{b x^4}{12}",1,"-1/12*(x^3*(b*x - 4*ArcTanh[Coth[a + b*x]]))","A",1
276,1,20,23,0.0162998,"\int x \tanh ^{-1}(\coth (a+b x)) \, dx","Integrate[x*ArcTanh[Coth[a + b*x]],x]","-\frac{1}{6} x^2 \left(b x-3 \tanh ^{-1}(\coth (a+b x))\right)","\frac{1}{2} x^2 \tanh ^{-1}(\coth (a+b x))-\frac{b x^3}{6}",1,"-1/6*(x^2*(b*x - 3*ArcTanh[Coth[a + b*x]]))","A",1
277,1,18,16,0.0082555,"\int \tanh ^{-1}(\coth (a+b x)) \, dx","Integrate[ArcTanh[Coth[a + b*x]],x]","x \tanh ^{-1}(\coth (a+b x))-\frac{b x^2}{2}","\frac{\tanh ^{-1}(\coth (a+b x))^2}{2 b}",1,"-1/2*(b*x^2) + x*ArcTanh[Coth[a + b*x]]","A",1
278,1,19,21,0.0174249,"\int \frac{\tanh ^{-1}(\coth (a+b x))}{x} \, dx","Integrate[ArcTanh[Coth[a + b*x]]/x,x]","\log (x) \left(\tanh ^{-1}(\coth (a+b x))-b x\right)+b x","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",1
279,1,18,17,0.0200423,"\int \frac{\tanh ^{-1}(\coth (a+b x))}{x^2} \, dx","Integrate[ArcTanh[Coth[a + b*x]]/x^2,x]","-\frac{\tanh ^{-1}(\coth (a+b x))}{x}+b \log (x)+b","b \log (x)-\frac{\tanh ^{-1}(\coth (a+b x))}{x}",1,"b - ArcTanh[Coth[a + b*x]]/x + b*Log[x]","A",1
280,1,18,23,0.0164768,"\int \frac{\tanh ^{-1}(\coth (a+b x))}{x^3} \, dx","Integrate[ArcTanh[Coth[a + b*x]]/x^3,x]","-\frac{\tanh ^{-1}(\coth (a+b x))+b x}{2 x^2}","-\frac{\tanh ^{-1}(\coth (a+b x))}{2 x^2}-\frac{b}{2 x}",1,"-1/2*(b*x + ArcTanh[Coth[a + b*x]])/x^2","A",1
281,1,47,27,0.0241629,"\int \tanh ^{-1}(\cosh (x)) \, dx","Integrate[ArcTanh[Cosh[x]],x]","\text{Li}_2\left(-e^{-x}\right)-\text{Li}_2\left(e^{-x}\right)+x \left(\log \left(1-e^{-x}\right)-\log \left(e^{-x}+1\right)\right)+x \tanh ^{-1}(\cosh (x))","-\text{Li}_2\left(-e^x\right)+\text{Li}_2\left(e^x\right)-2 x \tanh ^{-1}\left(e^x\right)+x \tanh ^{-1}(\cosh (x))",1,"x*ArcTanh[Cosh[x]] + x*(Log[1 - E^(-x)] - Log[1 + E^(-x)]) + PolyLog[2, -E^(-x)] - PolyLog[2, E^(-x)]","A",1
282,1,81,51,0.0163932,"\int x \tanh ^{-1}(\cosh (x)) \, dx","Integrate[x*ArcTanh[Cosh[x]],x]","\frac{1}{2} \left(2 x \text{Li}_2\left(-e^{-x}\right)-2 x \text{Li}_2\left(e^{-x}\right)+2 \text{Li}_3\left(-e^{-x}\right)-2 \text{Li}_3\left(e^{-x}\right)+x^2 \log \left(1-e^{-x}\right)-x^2 \log \left(e^{-x}+1\right)+x^2 \tanh ^{-1}(\cosh (x))\right)","-x \text{Li}_2\left(-e^x\right)+x \text{Li}_2\left(e^x\right)+\text{Li}_3\left(-e^x\right)-\text{Li}_3\left(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[Cosh[x]] + x^2*Log[1 - E^(-x)] - x^2*Log[1 + E^(-x)] + 2*x*PolyLog[2, -E^(-x)] - 2*x*PolyLog[2, E^(-x)] + 2*PolyLog[3, -E^(-x)] - 2*PolyLog[3, E^(-x)])/2","A",1
283,1,109,77,0.0356185,"\int x^2 \tanh ^{-1}(\cosh (x)) \, dx","Integrate[x^2*ArcTanh[Cosh[x]],x]","\frac{1}{24} \left(24 x^2 \text{Li}_2\left(-e^{-x}\right)+24 x^2 \text{Li}_2\left(e^x\right)+48 x \text{Li}_3\left(-e^{-x}\right)-48 x \text{Li}_3\left(e^x\right)+48 \text{Li}_4\left(-e^{-x}\right)+48 \text{Li}_4\left(e^x\right)-2 x^4-8 x^3 \log \left(e^{-x}+1\right)+8 x^3 \log \left(1-e^x\right)+8 x^3 \tanh ^{-1}(\cosh (x))+\pi ^4\right)","-x^2 \text{Li}_2\left(-e^x\right)+x^2 \text{Li}_2\left(e^x\right)+2 x \text{Li}_3\left(-e^x\right)-2 x \text{Li}_3\left(e^x\right)-2 \text{Li}_4\left(-e^x\right)+2 \text{Li}_4\left(e^x\right)-\frac{2}{3} x^3 \tanh ^{-1}\left(e^x\right)+\frac{1}{3} x^3 \tanh ^{-1}(\cosh (x))",1,"(Pi^4 - 2*x^4 + 8*x^3*ArcTanh[Cosh[x]] - 8*x^3*Log[1 + E^(-x)] + 8*x^3*Log[1 - E^x] + 24*x^2*PolyLog[2, -E^(-x)] + 24*x^2*PolyLog[2, E^x] + 48*x*PolyLog[3, -E^(-x)] - 48*x*PolyLog[3, E^x] + 48*PolyLog[4, -E^(-x)] + 48*PolyLog[4, E^x])/24","A",1
284,1,345,307,12.6948614,"\int x^2 \tanh ^{-1}(c+d \tanh (a+b x)) \, dx","Integrate[x^2*ArcTanh[c + d*Tanh[a + b*x]],x]","\frac{4 b^3 x^3 \log \left(\frac{(c-d-1) (\cosh (2 (a+b x))-\sinh (2 (a+b x)))}{c+d-1}+1\right)-4 b^3 x^3 \log \left(\frac{(c-d+1) (\cosh (2 (a+b x))-\sinh (2 (a+b x)))}{c+d+1}+1\right)-6 b^2 x^2 \text{Li}_2\left(\frac{(c-d-1) (\sinh (2 (a+b x))-\cosh (2 (a+b x)))}{c+d-1}\right)+6 b^2 x^2 \text{Li}_2\left(\frac{(c-d+1) (\sinh (2 (a+b x))-\cosh (2 (a+b x)))}{c+d+1}\right)-6 b x \text{Li}_3\left(\frac{(c-d-1) (\sinh (2 (a+b x))-\cosh (2 (a+b x)))}{c+d-1}\right)+6 b x \text{Li}_3\left(\frac{(c-d+1) (\sinh (2 (a+b x))-\cosh (2 (a+b x)))}{c+d+1}\right)-3 \text{Li}_4\left(\frac{(c-d-1) (\sinh (2 (a+b x))-\cosh (2 (a+b x)))}{c+d-1}\right)+3 \text{Li}_4\left(\frac{(c-d+1) (\sinh (2 (a+b x))-\cosh (2 (a+b x)))}{c+d+1}\right)}{24 b^3}+\frac{1}{3} x^3 \tanh ^{-1}(d \tanh (a+b x)+c)","\frac{\text{Li}_4\left(-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^3}-\frac{\text{Li}_4\left(-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^3}-\frac{x \text{Li}_3\left(-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b^2}+\frac{x \text{Li}_3\left(-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b^2}+\frac{x^2 \text{Li}_2\left(-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x^2 \text{Li}_2\left(-\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 + (4*b^3*x^3*Log[1 + ((-1 + c - d)*(Cosh[2*(a + b*x)] - Sinh[2*(a + b*x)]))/(-1 + c + d)] - 4*b^3*x^3*Log[1 + ((1 + c - d)*(Cosh[2*(a + b*x)] - Sinh[2*(a + b*x)]))/(1 + c + d)] - 6*b^2*x^2*PolyLog[2, ((-1 + c - d)*(-Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)]))/(-1 + c + d)] + 6*b^2*x^2*PolyLog[2, ((1 + c - d)*(-Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)]))/(1 + c + d)] - 6*b*x*PolyLog[3, ((-1 + c - d)*(-Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)]))/(-1 + c + d)] + 6*b*x*PolyLog[3, ((1 + c - d)*(-Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)]))/(1 + c + d)] - 3*PolyLog[4, ((-1 + c - d)*(-Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)]))/(-1 + c + d)] + 3*PolyLog[4, ((1 + c - d)*(-Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)]))/(1 + c + d)])/(24*b^3)","A",1
285,1,259,231,10.3781674,"\int x \tanh ^{-1}(c+d \tanh (a+b x)) \, dx","Integrate[x*ArcTanh[c + d*Tanh[a + b*x]],x]","\frac{2 b^2 x^2 \log \left(\frac{(c-d-1) (\cosh (2 (a+b x))-\sinh (2 (a+b x)))}{c+d-1}+1\right)-2 b^2 x^2 \log \left(\frac{(c-d+1) (\cosh (2 (a+b x))-\sinh (2 (a+b x)))}{c+d+1}+1\right)-2 b x \text{Li}_2\left(\frac{(c-d-1) (\sinh (2 (a+b x))-\cosh (2 (a+b x)))}{c+d-1}\right)+2 b x \text{Li}_2\left(\frac{(c-d+1) (\sinh (2 (a+b x))-\cosh (2 (a+b x)))}{c+d+1}\right)-\text{Li}_3\left(\frac{(c-d-1) (\sinh (2 (a+b x))-\cosh (2 (a+b x)))}{c+d-1}\right)+\text{Li}_3\left(\frac{(c-d+1) (\sinh (2 (a+b x))-\cosh (2 (a+b x)))}{c+d+1}\right)}{8 b^2}+\frac{1}{2} x^2 \tanh ^{-1}(d \tanh (a+b x)+c)","-\frac{\text{Li}_3\left(-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^2}+\frac{\text{Li}_3\left(-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^2}+\frac{x \text{Li}_2\left(-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x \text{Li}_2\left(-\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 + (2*b^2*x^2*Log[1 + ((-1 + c - d)*(Cosh[2*(a + b*x)] - Sinh[2*(a + b*x)]))/(-1 + c + d)] - 2*b^2*x^2*Log[1 + ((1 + c - d)*(Cosh[2*(a + b*x)] - Sinh[2*(a + b*x)]))/(1 + c + d)] - 2*b*x*PolyLog[2, ((-1 + c - d)*(-Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)]))/(-1 + c + d)] + 2*b*x*PolyLog[2, ((1 + c - d)*(-Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)]))/(1 + c + d)] - PolyLog[3, ((-1 + c - d)*(-Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)]))/(-1 + c + d)] + PolyLog[3, ((1 + c - d)*(-Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)]))/(1 + c + d)])/(8*b^2)","A",1
286,1,131,150,6.8076788,"\int \tanh ^{-1}(c+d \tanh (a+b x)) \, dx","Integrate[ArcTanh[c + d*Tanh[a + b*x]],x]","\frac{\text{Li}_2\left(-\frac{(c+d-1) e^{2 (a+b x)}}{c-d-1}\right)-\text{Li}_2\left(-\frac{(c+d+1) e^{2 (a+b x)}}{c-d+1}\right)+2 b x \left(\log \left(\frac{(c+d-1) e^{2 (a+b x)}}{c-d-1}+1\right)-\log \left(\frac{(c+d+1) e^{2 (a+b x)}}{c-d+1}+1\right)\right)}{4 b}+x \tanh ^{-1}(d \tanh (a+b x)+c)","\frac{\text{Li}_2\left(-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{\text{Li}_2\left(-\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]] + (2*b*x*(Log[1 + ((-1 + c + d)*E^(2*(a + b*x)))/(-1 + c - d)] - Log[1 + ((1 + c + d)*E^(2*(a + b*x)))/(1 + c - d)]) + PolyLog[2, -(((-1 + c + d)*E^(2*(a + b*x)))/(-1 + c - d))] - PolyLog[2, -(((1 + c + d)*E^(2*(a + b*x)))/(1 + c - d))])/(4*b)","A",1
287,0,0,18,14.6845978,"\int \frac{\tanh ^{-1}(c+d \tanh (a+b x))}{x} \, dx","Integrate[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,"Integrate[ArcTanh[c + d*Tanh[a + b*x]]/x, x]","A",-1
288,1,144,155,4.6706601,"\int x^3 \tanh ^{-1}(1+d+d \tanh (a+b x)) \, dx","Integrate[x^3*ArcTanh[1 + d + d*Tanh[a + b*x]],x]","\frac{1}{16} \left(\frac{3 \text{Li}_5\left(-\frac{e^{-2 (a+b x)}}{d+1}\right)}{b^4}+\frac{6 x \text{Li}_4\left(-\frac{e^{-2 (a+b x)}}{d+1}\right)}{b^3}+\frac{6 x^2 \text{Li}_3\left(-\frac{e^{-2 (a+b x)}}{d+1}\right)}{b^2}+\frac{4 x^3 \text{Li}_2\left(-\frac{e^{-2 (a+b x)}}{d+1}\right)}{b}-2 x^4 \log \left(\frac{e^{-2 (a+b x)}}{d+1}+1\right)+4 x^4 \tanh ^{-1}(d \tanh (a+b x)+d+1)\right)","\frac{3 \text{Li}_5\left(-\left((d+1) e^{2 a+2 b x}\right)\right)}{16 b^4}-\frac{3 x \text{Li}_4\left(-\left((d+1) e^{2 a+2 b x}\right)\right)}{8 b^3}+\frac{3 x^2 \text{Li}_3\left(-\left((d+1) e^{2 a+2 b x}\right)\right)}{8 b^2}-\frac{x^3 \text{Li}_2\left(-\left((d+1) e^{2 a+2 b x}\right)\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,"(4*x^4*ArcTanh[1 + d + d*Tanh[a + b*x]] - 2*x^4*Log[1 + 1/((1 + d)*E^(2*(a + b*x)))] + (4*x^3*PolyLog[2, -(1/((1 + d)*E^(2*(a + b*x))))])/b + (6*x^2*PolyLog[3, -(1/((1 + d)*E^(2*(a + b*x))))])/b^2 + (6*x*PolyLog[4, -(1/((1 + d)*E^(2*(a + b*x))))])/b^3 + (3*PolyLog[5, -(1/((1 + d)*E^(2*(a + b*x))))])/b^4)/16","A",1
289,1,118,128,5.2847523,"\int x^2 \tanh ^{-1}(1+d+d \tanh (a+b x)) \, dx","Integrate[x^2*ArcTanh[1 + d + d*Tanh[a + b*x]],x]","\frac{1}{24} \left(\frac{3 \text{Li}_4\left(-\frac{e^{-2 (a+b x)}}{d+1}\right)}{b^3}+\frac{6 x \text{Li}_3\left(-\frac{e^{-2 (a+b x)}}{d+1}\right)}{b^2}+\frac{6 x^2 \text{Li}_2\left(-\frac{e^{-2 (a+b x)}}{d+1}\right)}{b}-4 x^3 \log \left(\frac{e^{-2 (a+b x)}}{d+1}+1\right)+8 x^3 \tanh ^{-1}(d \tanh (a+b x)+d+1)\right)","-\frac{\text{Li}_4\left(-\left((d+1) e^{2 a+2 b x}\right)\right)}{8 b^3}+\frac{x \text{Li}_3\left(-\left((d+1) e^{2 a+2 b x}\right)\right)}{4 b^2}-\frac{x^2 \text{Li}_2\left(-\left((d+1) e^{2 a+2 b x}\right)\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,"(8*x^3*ArcTanh[1 + d + d*Tanh[a + b*x]] - 4*x^3*Log[1 + 1/((1 + d)*E^(2*(a + b*x)))] + (6*x^2*PolyLog[2, -(1/((1 + d)*E^(2*(a + b*x))))])/b + (6*x*PolyLog[3, -(1/((1 + d)*E^(2*(a + b*x))))])/b^2 + (3*PolyLog[4, -(1/((1 + d)*E^(2*(a + b*x))))])/b^3)/24","A",1
290,1,91,101,5.2730142,"\int x \tanh ^{-1}(1+d+d \tanh (a+b x)) \, dx","Integrate[x*ArcTanh[1 + d + d*Tanh[a + b*x]],x]","\frac{2 b^2 x^2 \left(2 \tanh ^{-1}(d \tanh (a+b x)+d+1)-\log \left(\frac{e^{-2 (a+b x)}}{d+1}+1\right)\right)+2 b x \text{Li}_2\left(-\frac{e^{-2 (a+b x)}}{d+1}\right)+\text{Li}_3\left(-\frac{e^{-2 (a+b x)}}{d+1}\right)}{8 b^2}","\frac{\text{Li}_3\left(-\left((d+1) e^{2 a+2 b x}\right)\right)}{8 b^2}-\frac{x \text{Li}_2\left(-\left((d+1) e^{2 a+2 b x}\right)\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,"(2*b^2*x^2*(2*ArcTanh[1 + d + d*Tanh[a + b*x]] - Log[1 + 1/((1 + d)*E^(2*(a + b*x)))]) + 2*b*x*PolyLog[2, -(1/((1 + d)*E^(2*(a + b*x))))] + PolyLog[3, -(1/((1 + d)*E^(2*(a + b*x))))])/(8*b^2)","A",1
291,1,201,69,4.7623901,"\int \tanh ^{-1}(1+d+d \tanh (a+b x)) \, dx","Integrate[ArcTanh[1 + d + d*Tanh[a + b*x]],x]","\frac{-2 \text{Li}_2\left(-\sqrt{-d-1} e^{a+b x}\right)-2 \text{Li}_2\left(\sqrt{-d-1} e^{a+b x}\right)-2 \log \left(e^{a+b x}\right) \log \left(1-\sqrt{-d-1} e^{a+b x}\right)-2 \log \left(e^{a+b x}\right) \log \left(\sqrt{-d-1} e^{a+b x}+1\right)+2 \log \left(e^{a+b x}\right) \log \left((d+1) e^{a+b x}+e^{-a-b x}\right)-2 b x \log (d \sinh (a+b x)+(d+2) \cosh (a+b x))+\log ^2\left(e^{a+b x}\right)+b^2 x^2}{4 b}+x \tanh ^{-1}(d \tanh (a+b x)+d+1)","-\frac{\text{Li}_2\left(-\left((d+1) e^{2 a+2 b x}\right)\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,"x*ArcTanh[1 + d + d*Tanh[a + b*x]] + (b^2*x^2 + Log[E^(a + b*x)]^2 - 2*Log[E^(a + b*x)]*Log[1 - Sqrt[-1 - d]*E^(a + b*x)] - 2*Log[E^(a + b*x)]*Log[1 + Sqrt[-1 - d]*E^(a + b*x)] + 2*Log[E^(a + b*x)]*Log[E^(-a - b*x) + (1 + d)*E^(a + b*x)] - 2*b*x*Log[(2 + d)*Cosh[a + b*x] + d*Sinh[a + b*x]] - 2*PolyLog[2, -(Sqrt[-1 - d]*E^(a + b*x))] - 2*PolyLog[2, Sqrt[-1 - d]*E^(a + b*x)])/(4*b)","B",0
292,0,0,19,4.7592494,"\int \frac{\tanh ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx","Integrate[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,"Integrate[ArcTanh[1 + d + d*Tanh[a + b*x]]/x, x]","A",-1
293,1,144,168,4.740604,"\int x^3 \tanh ^{-1}(1-d-d \tanh (a+b x)) \, dx","Integrate[x^3*ArcTanh[1 - d - d*Tanh[a + b*x]],x]","\frac{1}{16} \left(\frac{3 \text{Li}_5\left(\frac{e^{-2 (a+b x)}}{d-1}\right)}{b^4}+\frac{6 x \text{Li}_4\left(\frac{e^{-2 (a+b x)}}{d-1}\right)}{b^3}+\frac{6 x^2 \text{Li}_3\left(\frac{e^{-2 (a+b x)}}{d-1}\right)}{b^2}+\frac{4 x^3 \text{Li}_2\left(\frac{e^{-2 (a+b x)}}{d-1}\right)}{b}-2 x^4 \log \left(1-\frac{e^{-2 (a+b x)}}{d-1}\right)+4 x^4 \tanh ^{-1}(d (-\tanh (a+b x))-d+1)\right)","\frac{3 \text{Li}_5\left(-\left((1-d) e^{2 a+2 b x}\right)\right)}{16 b^4}-\frac{3 x \text{Li}_4\left(-\left((1-d) e^{2 a+2 b x}\right)\right)}{8 b^3}+\frac{3 x^2 \text{Li}_3\left(-\left((1-d) e^{2 a+2 b x}\right)\right)}{8 b^2}-\frac{x^3 \text{Li}_2\left(-\left((1-d) e^{2 a+2 b x}\right)\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,"(4*x^4*ArcTanh[1 - d - d*Tanh[a + b*x]] - 2*x^4*Log[1 - 1/((-1 + d)*E^(2*(a + b*x)))] + (4*x^3*PolyLog[2, 1/((-1 + d)*E^(2*(a + b*x)))])/b + (6*x^2*PolyLog[3, 1/((-1 + d)*E^(2*(a + b*x)))])/b^2 + (6*x*PolyLog[4, 1/((-1 + d)*E^(2*(a + b*x)))])/b^3 + (3*PolyLog[5, 1/((-1 + d)*E^(2*(a + b*x)))])/b^4)/16","A",1
294,1,119,139,5.5439877,"\int x^2 \tanh ^{-1}(1-d-d \tanh (a+b x)) \, dx","Integrate[x^2*ArcTanh[1 - d - d*Tanh[a + b*x]],x]","\frac{1}{24} \left(\frac{3 \text{Li}_4\left(\frac{e^{-2 (a+b x)}}{d-1}\right)}{b^3}+\frac{6 x \text{Li}_3\left(\frac{e^{-2 (a+b x)}}{d-1}\right)}{b^2}+\frac{6 x^2 \text{Li}_2\left(\frac{e^{-2 (a+b x)}}{d-1}\right)}{b}-4 x^3 \log \left(1-\frac{e^{-2 (a+b x)}}{d-1}\right)+8 x^3 \tanh ^{-1}(d (-\tanh (a+b x))-d+1)\right)","-\frac{\text{Li}_4\left(-\left((1-d) e^{2 a+2 b x}\right)\right)}{8 b^3}+\frac{x \text{Li}_3\left(-\left((1-d) e^{2 a+2 b x}\right)\right)}{4 b^2}-\frac{x^2 \text{Li}_2\left(-\left((1-d) e^{2 a+2 b x}\right)\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,"(8*x^3*ArcTanh[1 - d - d*Tanh[a + b*x]] - 4*x^3*Log[1 - 1/((-1 + d)*E^(2*(a + b*x)))] + (6*x^2*PolyLog[2, 1/((-1 + d)*E^(2*(a + b*x)))])/b + (6*x*PolyLog[3, 1/((-1 + d)*E^(2*(a + b*x)))])/b^2 + (3*PolyLog[4, 1/((-1 + d)*E^(2*(a + b*x)))])/b^3)/24","A",1
295,1,93,110,5.3724506,"\int x \tanh ^{-1}(1-d-d \tanh (a+b x)) \, dx","Integrate[x*ArcTanh[1 - d - d*Tanh[a + b*x]],x]","\frac{2 b^2 x^2 \left(2 \tanh ^{-1}(d (-\tanh (a+b x))-d+1)-\log \left(1-\frac{e^{-2 (a+b x)}}{d-1}\right)\right)+2 b x \text{Li}_2\left(\frac{e^{-2 (a+b x)}}{d-1}\right)+\text{Li}_3\left(\frac{e^{-2 (a+b x)}}{d-1}\right)}{8 b^2}","\frac{\text{Li}_3\left(-\left((1-d) e^{2 a+2 b x}\right)\right)}{8 b^2}-\frac{x \text{Li}_2\left(-\left((1-d) e^{2 a+2 b x}\right)\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,"(2*b^2*x^2*(2*ArcTanh[1 - d - d*Tanh[a + b*x]] - Log[1 - 1/((-1 + d)*E^(2*(a + b*x)))]) + 2*b*x*PolyLog[2, 1/((-1 + d)*E^(2*(a + b*x)))] + PolyLog[3, 1/((-1 + d)*E^(2*(a + b*x)))])/(8*b^2)","A",1
296,1,200,76,4.6958615,"\int \tanh ^{-1}(1-d-d \tanh (a+b x)) \, dx","Integrate[ArcTanh[1 - d - d*Tanh[a + b*x]],x]","\frac{-2 \text{Li}_2\left(-\sqrt{d-1} e^{a+b x}\right)-2 \text{Li}_2\left(\sqrt{d-1} e^{a+b x}\right)-2 \log \left(e^{a+b x}\right) \log \left(1-\sqrt{d-1} e^{a+b x}\right)-2 \log \left(e^{a+b x}\right) \log \left(\sqrt{d-1} e^{a+b x}+1\right)+2 \log \left(e^{a+b x}\right) \log \left(e^{-a-b x} \left((d-1) e^{2 (a+b x)}-1\right)\right)-2 b x \log (d \sinh (a+b x)+(d-2) \cosh (a+b x))+\log ^2\left(e^{a+b x}\right)+b^2 x^2}{4 b}+x \tanh ^{-1}(d (-\tanh (a+b x))-d+1)","-\frac{\text{Li}_2\left(-\left((1-d) e^{2 a+2 b x}\right)\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,"x*ArcTanh[1 - d - d*Tanh[a + b*x]] + (b^2*x^2 + Log[E^(a + b*x)]^2 - 2*Log[E^(a + b*x)]*Log[1 - Sqrt[-1 + d]*E^(a + b*x)] - 2*Log[E^(a + b*x)]*Log[1 + Sqrt[-1 + d]*E^(a + b*x)] + 2*Log[E^(a + b*x)]*Log[E^(-a - b*x)*(-1 + (-1 + d)*E^(2*(a + b*x)))] - 2*b*x*Log[(-2 + d)*Cosh[a + b*x] + d*Sinh[a + b*x]] - 2*PolyLog[2, -(Sqrt[-1 + d]*E^(a + b*x))] - 2*PolyLog[2, Sqrt[-1 + d]*E^(a + b*x)])/(4*b)","B",0
297,0,0,22,5.8873578,"\int \frac{\tanh ^{-1}(1-d-d \tanh (a+b x))}{x} \, dx","Integrate[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,"Integrate[ArcTanh[1 - d - d*Tanh[a + b*x]]/x, x]","A",-1
298,1,353,303,11.274264,"\int x^2 \tanh ^{-1}(c+d \coth (a+b x)) \, dx","Integrate[x^2*ArcTanh[c + d*Coth[a + b*x]],x]","\frac{4 b^3 x^3 \log \left(\frac{2 (\cosh (a+b x)-\sinh (a+b x)) ((c-1) \sinh (a+b x)+d \cosh (a+b x))}{c+d-1}\right)-4 b^3 x^3 \log \left(\frac{(c-d+1) (\sinh (2 (a+b x))-\cosh (2 (a+b x)))}{c+d+1}+1\right)-6 b^2 x^2 \text{Li}_2\left(\frac{(c-d-1) (\cosh (2 (a+b x))-\sinh (2 (a+b x)))}{c+d-1}\right)+6 b^2 x^2 \text{Li}_2\left(\frac{(c-d+1) (\cosh (2 (a+b x))-\sinh (2 (a+b x)))}{c+d+1}\right)-6 b x \text{Li}_3\left(\frac{(c-d-1) (\cosh (2 (a+b x))-\sinh (2 (a+b x)))}{c+d-1}\right)+6 b x \text{Li}_3\left(\frac{(c-d+1) (\cosh (2 (a+b x))-\sinh (2 (a+b x)))}{c+d+1}\right)-3 \text{Li}_4\left(\frac{(c-d-1) (\cosh (2 (a+b x))-\sinh (2 (a+b x)))}{c+d-1}\right)+3 \text{Li}_4\left(\frac{(c-d+1) (\cosh (2 (a+b x))-\sinh (2 (a+b x)))}{c+d+1}\right)}{24 b^3}+\frac{1}{3} x^3 \tanh ^{-1}(d \coth (a+b x)+c)","\frac{\text{Li}_4\left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^3}-\frac{\text{Li}_4\left(\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^3}-\frac{x \text{Li}_3\left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b^2}+\frac{x \text{Li}_3\left(\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b^2}+\frac{x^2 \text{Li}_2\left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x^2 \text{Li}_2\left(\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 + (4*b^3*x^3*Log[(2*(Cosh[a + b*x] - Sinh[a + b*x])*(d*Cosh[a + b*x] + (-1 + c)*Sinh[a + b*x]))/(-1 + c + d)] - 4*b^3*x^3*Log[1 + ((1 + c - d)*(-Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)]))/(1 + c + d)] - 6*b^2*x^2*PolyLog[2, ((-1 + c - d)*(Cosh[2*(a + b*x)] - Sinh[2*(a + b*x)]))/(-1 + c + d)] + 6*b^2*x^2*PolyLog[2, ((1 + c - d)*(Cosh[2*(a + b*x)] - Sinh[2*(a + b*x)]))/(1 + c + d)] - 6*b*x*PolyLog[3, ((-1 + c - d)*(Cosh[2*(a + b*x)] - Sinh[2*(a + b*x)]))/(-1 + c + d)] + 6*b*x*PolyLog[3, ((1 + c - d)*(Cosh[2*(a + b*x)] - Sinh[2*(a + b*x)]))/(1 + c + d)] - 3*PolyLog[4, ((-1 + c - d)*(Cosh[2*(a + b*x)] - Sinh[2*(a + b*x)]))/(-1 + c + d)] + 3*PolyLog[4, ((1 + c - d)*(Cosh[2*(a + b*x)] - Sinh[2*(a + b*x)]))/(1 + c + d)])/(24*b^3)","A",0
299,1,267,229,9.5405908,"\int x \tanh ^{-1}(c+d \coth (a+b x)) \, dx","Integrate[x*ArcTanh[c + d*Coth[a + b*x]],x]","\frac{2 b^2 x^2 \log \left(\frac{2 (\cosh (a+b x)-\sinh (a+b x)) ((c-1) \sinh (a+b x)+d \cosh (a+b x))}{c+d-1}\right)-2 b^2 x^2 \log \left(\frac{(c-d+1) (\sinh (2 (a+b x))-\cosh (2 (a+b x)))}{c+d+1}+1\right)-2 b x \text{Li}_2\left(\frac{(c-d-1) (\cosh (2 (a+b x))-\sinh (2 (a+b x)))}{c+d-1}\right)+2 b x \text{Li}_2\left(\frac{(c-d+1) (\cosh (2 (a+b x))-\sinh (2 (a+b x)))}{c+d+1}\right)-\text{Li}_3\left(\frac{(c-d-1) (\cosh (2 (a+b x))-\sinh (2 (a+b x)))}{c+d-1}\right)+\text{Li}_3\left(\frac{(c-d+1) (\cosh (2 (a+b x))-\sinh (2 (a+b x)))}{c+d+1}\right)}{8 b^2}+\frac{1}{2} x^2 \tanh ^{-1}(d \coth (a+b x)+c)","-\frac{\text{Li}_3\left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^2}+\frac{\text{Li}_3\left(\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^2}+\frac{x \text{Li}_2\left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x \text{Li}_2\left(\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 + (2*b^2*x^2*Log[(2*(Cosh[a + b*x] - Sinh[a + b*x])*(d*Cosh[a + b*x] + (-1 + c)*Sinh[a + b*x]))/(-1 + c + d)] - 2*b^2*x^2*Log[1 + ((1 + c - d)*(-Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)]))/(1 + c + d)] - 2*b*x*PolyLog[2, ((-1 + c - d)*(Cosh[2*(a + b*x)] - Sinh[2*(a + b*x)]))/(-1 + c + d)] + 2*b*x*PolyLog[2, ((1 + c - d)*(Cosh[2*(a + b*x)] - Sinh[2*(a + b*x)]))/(1 + c + d)] - PolyLog[3, ((-1 + c - d)*(Cosh[2*(a + b*x)] - Sinh[2*(a + b*x)]))/(-1 + c + d)] + PolyLog[3, ((1 + c - d)*(Cosh[2*(a + b*x)] - Sinh[2*(a + b*x)]))/(1 + c + d)])/(8*b^2)","A",0
300,1,131,150,5.4167127,"\int \tanh ^{-1}(c+d \coth (a+b x)) \, dx","Integrate[ArcTanh[c + d*Coth[a + b*x]],x]","x \tanh ^{-1}(d \coth (a+b x)+c)-\frac{-\text{Li}_2\left(\frac{(c+d-1) e^{2 (a+b x)}}{c-d-1}\right)+\text{Li}_2\left(\frac{(c+d+1) e^{2 (a+b x)}}{c-d+1}\right)-2 b x \left(\log \left(1-\frac{(c+d-1) e^{2 (a+b x)}}{c-d-1}\right)-\log \left(1-\frac{(c+d+1) e^{2 (a+b x)}}{c-d+1}\right)\right)}{4 b}","\frac{\text{Li}_2\left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{\text{Li}_2\left(\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]] - (-2*b*x*(Log[1 - ((-1 + c + d)*E^(2*(a + b*x)))/(-1 + c - d)] - Log[1 - ((1 + c + d)*E^(2*(a + b*x)))/(1 + c - d)]) - PolyLog[2, ((-1 + c + d)*E^(2*(a + b*x)))/(-1 + c - d)] + PolyLog[2, ((1 + c + d)*E^(2*(a + b*x)))/(1 + c - d)])/(4*b)","A",1
301,0,0,18,14.6205155,"\int \frac{\tanh ^{-1}(c+d \coth (a+b x))}{x} \, dx","Integrate[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,"Integrate[ArcTanh[c + d*Coth[a + b*x]]/x, x]","A",-1
302,1,141,152,4.6505656,"\int x^3 \tanh ^{-1}(1+d+d \coth (a+b x)) \, dx","Integrate[x^3*ArcTanh[1 + d + d*Coth[a + b*x]],x]","\frac{1}{16} \left(\frac{3 \text{Li}_5\left(\frac{e^{-2 (a+b x)}}{d+1}\right)}{b^4}+\frac{6 x \text{Li}_4\left(\frac{e^{-2 (a+b x)}}{d+1}\right)}{b^3}+\frac{6 x^2 \text{Li}_3\left(\frac{e^{-2 (a+b x)}}{d+1}\right)}{b^2}+\frac{4 x^3 \text{Li}_2\left(\frac{e^{-2 (a+b x)}}{d+1}\right)}{b}-2 x^4 \log \left(1-\frac{e^{-2 (a+b x)}}{d+1}\right)+4 x^4 \tanh ^{-1}(d \coth (a+b x)+d+1)\right)","\frac{3 \text{Li}_5\left((d+1) e^{2 a+2 b x}\right)}{16 b^4}-\frac{3 x \text{Li}_4\left((d+1) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 x^2 \text{Li}_3\left((d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x^3 \text{Li}_2\left((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,"(4*x^4*ArcTanh[1 + d + d*Coth[a + b*x]] - 2*x^4*Log[1 - 1/((1 + d)*E^(2*(a + b*x)))] + (4*x^3*PolyLog[2, 1/((1 + d)*E^(2*(a + b*x)))])/b + (6*x^2*PolyLog[3, 1/((1 + d)*E^(2*(a + b*x)))])/b^2 + (6*x*PolyLog[4, 1/((1 + d)*E^(2*(a + b*x)))])/b^3 + (3*PolyLog[5, 1/((1 + d)*E^(2*(a + b*x)))])/b^4)/16","A",1
303,1,116,126,5.4208543,"\int x^2 \tanh ^{-1}(1+d+d \coth (a+b x)) \, dx","Integrate[x^2*ArcTanh[1 + d + d*Coth[a + b*x]],x]","\frac{1}{24} \left(\frac{3 \text{Li}_4\left(\frac{e^{-2 (a+b x)}}{d+1}\right)}{b^3}+\frac{6 x \text{Li}_3\left(\frac{e^{-2 (a+b x)}}{d+1}\right)}{b^2}+\frac{6 x^2 \text{Li}_2\left(\frac{e^{-2 (a+b x)}}{d+1}\right)}{b}-4 x^3 \log \left(1-\frac{e^{-2 (a+b x)}}{d+1}\right)+8 x^3 \tanh ^{-1}(d \coth (a+b x)+d+1)\right)","-\frac{\text{Li}_4\left((d+1) e^{2 a+2 b x}\right)}{8 b^3}+\frac{x \text{Li}_3\left((d+1) e^{2 a+2 b x}\right)}{4 b^2}-\frac{x^2 \text{Li}_2\left((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,"(8*x^3*ArcTanh[1 + d + d*Coth[a + b*x]] - 4*x^3*Log[1 - 1/((1 + d)*E^(2*(a + b*x)))] + (6*x^2*PolyLog[2, 1/((1 + d)*E^(2*(a + b*x)))])/b + (6*x*PolyLog[3, 1/((1 + d)*E^(2*(a + b*x)))])/b^2 + (3*PolyLog[4, 1/((1 + d)*E^(2*(a + b*x)))])/b^3)/24","A",1
304,1,90,100,5.2248848,"\int x \tanh ^{-1}(1+d+d \coth (a+b x)) \, dx","Integrate[x*ArcTanh[1 + d + d*Coth[a + b*x]],x]","\frac{2 b^2 x^2 \left(2 \tanh ^{-1}(d \coth (a+b x)+d+1)-\log \left(1-\frac{e^{-2 (a+b x)}}{d+1}\right)\right)+2 b x \text{Li}_2\left(\frac{e^{-2 (a+b x)}}{d+1}\right)+\text{Li}_3\left(\frac{e^{-2 (a+b x)}}{d+1}\right)}{8 b^2}","\frac{\text{Li}_3\left((d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{Li}_2\left((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,"(2*b^2*x^2*(2*ArcTanh[1 + d + d*Coth[a + b*x]] - Log[1 - 1/((1 + d)*E^(2*(a + b*x)))]) + 2*b*x*PolyLog[2, 1/((1 + d)*E^(2*(a + b*x)))] + PolyLog[3, 1/((1 + d)*E^(2*(a + b*x)))])/(8*b^2)","A",1
305,1,197,69,3.8837061,"\int \tanh ^{-1}(1+d+d \coth (a+b x)) \, dx","Integrate[ArcTanh[1 + d + d*Coth[a + b*x]],x]","\frac{-2 \text{Li}_2\left(-\sqrt{d+1} e^{a+b x}\right)-2 \text{Li}_2\left(\sqrt{d+1} e^{a+b x}\right)-2 \log \left(e^{a+b x}\right) \log \left(1-\sqrt{d+1} e^{a+b x}\right)-2 \log \left(e^{a+b x}\right) \log \left(\sqrt{d+1} e^{a+b x}+1\right)+2 \log \left(e^{a+b x}\right) \log \left(e^{-a-b x} \left((d+1) e^{2 (a+b x)}-1\right)\right)-2 b x \log ((d+2) \sinh (a+b x)+d \cosh (a+b x))+\log ^2\left(e^{a+b x}\right)+b^2 x^2}{4 b}+x \tanh ^{-1}(d \coth (a+b x)+d+1)","-\frac{\text{Li}_2\left((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,"x*ArcTanh[1 + d + d*Coth[a + b*x]] + (b^2*x^2 + Log[E^(a + b*x)]^2 - 2*Log[E^(a + b*x)]*Log[1 - Sqrt[1 + d]*E^(a + b*x)] - 2*Log[E^(a + b*x)]*Log[1 + Sqrt[1 + d]*E^(a + b*x)] + 2*Log[E^(a + b*x)]*Log[E^(-a - b*x)*(-1 + (1 + d)*E^(2*(a + b*x)))] - 2*b*x*Log[d*Cosh[a + b*x] + (2 + d)*Sinh[a + b*x]] - 2*PolyLog[2, -(Sqrt[1 + d]*E^(a + b*x))] - 2*PolyLog[2, Sqrt[1 + d]*E^(a + b*x)])/(4*b)","B",0
306,0,0,19,4.6809408,"\int \frac{\tanh ^{-1}(1+d+d \coth (a+b x))}{x} \, dx","Integrate[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,"Integrate[ArcTanh[1 + d + d*Coth[a + b*x]]/x, x]","A",-1
307,1,147,165,4.6685865,"\int x^3 \tanh ^{-1}(1-d-d \coth (a+b x)) \, dx","Integrate[x^3*ArcTanh[1 - d - d*Coth[a + b*x]],x]","\frac{1}{16} \left(\frac{3 \text{Li}_5\left(-\frac{e^{-2 (a+b x)}}{d-1}\right)}{b^4}+\frac{6 x \text{Li}_4\left(-\frac{e^{-2 (a+b x)}}{d-1}\right)}{b^3}+\frac{6 x^2 \text{Li}_3\left(-\frac{e^{-2 (a+b x)}}{d-1}\right)}{b^2}+\frac{4 x^3 \text{Li}_2\left(-\frac{e^{-2 (a+b x)}}{d-1}\right)}{b}-2 x^4 \log \left(\frac{e^{-2 (a+b x)}}{d-1}+1\right)+4 x^4 \tanh ^{-1}(d (-\coth (a+b x))-d+1)\right)","\frac{3 \text{Li}_5\left((1-d) e^{2 a+2 b x}\right)}{16 b^4}-\frac{3 x \text{Li}_4\left((1-d) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 x^2 \text{Li}_3\left((1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x^3 \text{Li}_2\left((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,"(4*x^4*ArcTanh[1 - d - d*Coth[a + b*x]] - 2*x^4*Log[1 + 1/((-1 + d)*E^(2*(a + b*x)))] + (4*x^3*PolyLog[2, -(1/((-1 + d)*E^(2*(a + b*x))))])/b + (6*x^2*PolyLog[3, -(1/((-1 + d)*E^(2*(a + b*x))))])/b^2 + (6*x*PolyLog[4, -(1/((-1 + d)*E^(2*(a + b*x))))])/b^3 + (3*PolyLog[5, -(1/((-1 + d)*E^(2*(a + b*x))))])/b^4)/16","A",1
308,1,121,137,5.3536719,"\int x^2 \tanh ^{-1}(1-d-d \coth (a+b x)) \, dx","Integrate[x^2*ArcTanh[1 - d - d*Coth[a + b*x]],x]","\frac{1}{24} \left(\frac{3 \text{Li}_4\left(-\frac{e^{-2 (a+b x)}}{d-1}\right)}{b^3}+\frac{6 x \text{Li}_3\left(-\frac{e^{-2 (a+b x)}}{d-1}\right)}{b^2}+\frac{6 x^2 \text{Li}_2\left(-\frac{e^{-2 (a+b x)}}{d-1}\right)}{b}-4 x^3 \log \left(\frac{e^{-2 (a+b x)}}{d-1}+1\right)+8 x^3 \tanh ^{-1}(d (-\coth (a+b x))-d+1)\right)","-\frac{\text{Li}_4\left((1-d) e^{2 a+2 b x}\right)}{8 b^3}+\frac{x \text{Li}_3\left((1-d) e^{2 a+2 b x}\right)}{4 b^2}-\frac{x^2 \text{Li}_2\left((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,"(8*x^3*ArcTanh[1 - d - d*Coth[a + b*x]] - 4*x^3*Log[1 + 1/((-1 + d)*E^(2*(a + b*x)))] + (6*x^2*PolyLog[2, -(1/((-1 + d)*E^(2*(a + b*x))))])/b + (6*x*PolyLog[3, -(1/((-1 + d)*E^(2*(a + b*x))))])/b^2 + (3*PolyLog[4, -(1/((-1 + d)*E^(2*(a + b*x))))])/b^3)/24","A",1
309,1,94,109,5.3783913,"\int x \tanh ^{-1}(1-d-d \coth (a+b x)) \, dx","Integrate[x*ArcTanh[1 - d - d*Coth[a + b*x]],x]","\frac{2 b^2 x^2 \left(2 \tanh ^{-1}(d (-\coth (a+b x))-d+1)-\log \left(\frac{e^{-2 (a+b x)}}{d-1}+1\right)\right)+2 b x \text{Li}_2\left(-\frac{e^{-2 (a+b x)}}{d-1}\right)+\text{Li}_3\left(-\frac{e^{-2 (a+b x)}}{d-1}\right)}{8 b^2}","\frac{\text{Li}_3\left((1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{Li}_2\left((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,"(2*b^2*x^2*(2*ArcTanh[1 - d - d*Coth[a + b*x]] - Log[1 + 1/((-1 + d)*E^(2*(a + b*x)))]) + 2*b*x*PolyLog[2, -(1/((-1 + d)*E^(2*(a + b*x))))] + PolyLog[3, -(1/((-1 + d)*E^(2*(a + b*x))))])/(8*b^2)","A",1
310,1,208,76,4.3971209,"\int \tanh ^{-1}(1-d-d \coth (a+b x)) \, dx","Integrate[ArcTanh[1 - d - d*Coth[a + b*x]],x]","\frac{-2 \text{Li}_2\left(-\sqrt{1-d} e^{a+b x}\right)-2 \text{Li}_2\left(\sqrt{1-d} e^{a+b x}\right)-2 \log \left(e^{a+b x}\right) \log \left(1-\sqrt{1-d} e^{a+b x}\right)-2 \log \left(e^{a+b x}\right) \log \left(\sqrt{1-d} e^{a+b x}+1\right)+2 \log \left(e^{a+b x}\right) \log \left(e^{-a-b x} \left((d-1) e^{2 (a+b x)}+1\right)\right)-2 b x \log ((d-2) \sinh (a+b x)+d \cosh (a+b x))+\log ^2\left(e^{a+b x}\right)+b^2 x^2}{4 b}+x \tanh ^{-1}(d (-\coth (a+b x))-d+1)","-\frac{\text{Li}_2\left((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,"x*ArcTanh[1 - d - d*Coth[a + b*x]] + (b^2*x^2 + Log[E^(a + b*x)]^2 - 2*Log[E^(a + b*x)]*Log[1 - Sqrt[1 - d]*E^(a + b*x)] - 2*Log[E^(a + b*x)]*Log[1 + Sqrt[1 - d]*E^(a + b*x)] + 2*Log[E^(a + b*x)]*Log[E^(-a - b*x)*(1 + (-1 + d)*E^(2*(a + b*x)))] - 2*b*x*Log[d*Cosh[a + b*x] + (-2 + d)*Sinh[a + b*x]] - 2*PolyLog[2, -(Sqrt[1 - d]*E^(a + b*x))] - 2*PolyLog[2, Sqrt[1 - d]*E^(a + b*x)])/(4*b)","B",0
311,0,0,22,4.7533636,"\int \frac{\tanh ^{-1}(1-d-d \coth (a+b x))}{x} \, dx","Integrate[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,"Integrate[ArcTanh[1 - d - d*Coth[a + b*x]]/x, x]","A",-1
312,1,654,302,1.3165041,"\int (e+f x)^3 \tanh ^{-1}(\tan (a+b x)) \, dx","Integrate[(e + f*x)^3*ArcTanh[Tan[a + b*x]],x]","\frac{1}{4} x \left(4 e^3+6 e^2 f x+4 e f^2 x^2+f^3 x^3\right) \tanh ^{-1}(\tan (a+b x))+\frac{-8 b^4 e^3 x \log \left(1-i e^{2 i (a+b x)}\right)+8 b^4 e^3 x \log \left(1+i e^{2 i (a+b x)}\right)-12 b^4 e^2 f x^2 \log \left(1-i e^{2 i (a+b x)}\right)+12 b^4 e^2 f x^2 \log \left(1+i e^{2 i (a+b x)}\right)-8 b^4 e f^2 x^3 \log \left(1-i e^{2 i (a+b x)}\right)+8 b^4 e f^2 x^3 \log \left(1+i e^{2 i (a+b x)}\right)-2 b^4 f^3 x^4 \log \left(1-i e^{2 i (a+b x)}\right)+2 b^4 f^3 x^4 \log \left(1+i e^{2 i (a+b x)}\right)-4 i b^3 (e+f x)^3 \text{Li}_2\left(-i e^{2 i (a+b x)}\right)+4 i b^3 (e+f x)^3 \text{Li}_2\left(i e^{2 i (a+b x)}\right)+6 b^2 e^2 f \text{Li}_3\left(-i e^{2 i (a+b x)}\right)-6 b^2 e^2 f \text{Li}_3\left(i e^{2 i (a+b x)}\right)+12 b^2 e f^2 x \text{Li}_3\left(-i e^{2 i (a+b x)}\right)-12 b^2 e f^2 x \text{Li}_3\left(i e^{2 i (a+b x)}\right)+6 b^2 f^3 x^2 \text{Li}_3\left(-i e^{2 i (a+b x)}\right)-6 b^2 f^3 x^2 \text{Li}_3\left(i e^{2 i (a+b x)}\right)+6 i b e f^2 \text{Li}_4\left(-i e^{2 i (a+b x)}\right)-6 i b e f^2 \text{Li}_4\left(i e^{2 i (a+b x)}\right)+6 i b f^3 x \text{Li}_4\left(-i e^{2 i (a+b x)}\right)-6 i b f^3 x \text{Li}_4\left(i e^{2 i (a+b x)}\right)-3 f^3 \text{Li}_5\left(-i e^{2 i (a+b x)}\right)+3 f^3 \text{Li}_5\left(i e^{2 i (a+b x)}\right)}{16 b^4}","-\frac{3 f^3 \text{Li}_5\left(-i e^{2 i (a+b x)}\right)}{16 b^4}+\frac{3 f^3 \text{Li}_5\left(i e^{2 i (a+b x)}\right)}{16 b^4}+\frac{3 i f^2 (e+f x) \text{Li}_4\left(-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{3 i f^2 (e+f x) \text{Li}_4\left(i e^{2 i (a+b x)}\right)}{8 b^3}+\frac{3 f (e+f x)^2 \text{Li}_3\left(-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f (e+f x)^2 \text{Li}_3\left(i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{i (e+f x)^3 \text{Li}_2\left(-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \text{Li}_2\left(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,"(x*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3)*ArcTanh[Tan[a + b*x]])/4 + (-8*b^4*e^3*x*Log[1 - I*E^((2*I)*(a + b*x))] - 12*b^4*e^2*f*x^2*Log[1 - I*E^((2*I)*(a + b*x))] - 8*b^4*e*f^2*x^3*Log[1 - I*E^((2*I)*(a + b*x))] - 2*b^4*f^3*x^4*Log[1 - I*E^((2*I)*(a + b*x))] + 8*b^4*e^3*x*Log[1 + I*E^((2*I)*(a + b*x))] + 12*b^4*e^2*f*x^2*Log[1 + I*E^((2*I)*(a + b*x))] + 8*b^4*e*f^2*x^3*Log[1 + I*E^((2*I)*(a + b*x))] + 2*b^4*f^3*x^4*Log[1 + I*E^((2*I)*(a + b*x))] - (4*I)*b^3*(e + f*x)^3*PolyLog[2, (-I)*E^((2*I)*(a + b*x))] + (4*I)*b^3*(e + f*x)^3*PolyLog[2, I*E^((2*I)*(a + b*x))] + 6*b^2*e^2*f*PolyLog[3, (-I)*E^((2*I)*(a + b*x))] + 12*b^2*e*f^2*x*PolyLog[3, (-I)*E^((2*I)*(a + b*x))] + 6*b^2*f^3*x^2*PolyLog[3, (-I)*E^((2*I)*(a + b*x))] - 6*b^2*e^2*f*PolyLog[3, I*E^((2*I)*(a + b*x))] - 12*b^2*e*f^2*x*PolyLog[3, I*E^((2*I)*(a + b*x))] - 6*b^2*f^3*x^2*PolyLog[3, I*E^((2*I)*(a + b*x))] + (6*I)*b*e*f^2*PolyLog[4, (-I)*E^((2*I)*(a + b*x))] + (6*I)*b*f^3*x*PolyLog[4, (-I)*E^((2*I)*(a + b*x))] - (6*I)*b*e*f^2*PolyLog[4, I*E^((2*I)*(a + b*x))] - (6*I)*b*f^3*x*PolyLog[4, I*E^((2*I)*(a + b*x))] - 3*f^3*PolyLog[5, (-I)*E^((2*I)*(a + b*x))] + 3*f^3*PolyLog[5, I*E^((2*I)*(a + b*x))])/(16*b^4)","B",1
313,1,409,234,0.7101843,"\int (e+f x)^2 \tanh ^{-1}(\tan (a+b x)) \, dx","Integrate[(e + f*x)^2*ArcTanh[Tan[a + b*x]],x]","\frac{1}{3} x \left(3 e^2+3 e f x+f^2 x^2\right) \tanh ^{-1}(\tan (a+b x))+\frac{-12 b^3 e^2 x \log \left(1-i e^{2 i (a+b x)}\right)+12 b^3 e^2 x \log \left(1+i e^{2 i (a+b x)}\right)-12 b^3 e f x^2 \log \left(1-i e^{2 i (a+b x)}\right)+12 b^3 e f x^2 \log \left(1+i e^{2 i (a+b x)}\right)-4 b^3 f^2 x^3 \log \left(1-i e^{2 i (a+b x)}\right)+4 b^3 f^2 x^3 \log \left(1+i e^{2 i (a+b x)}\right)-6 i b^2 (e+f x)^2 \text{Li}_2\left(-i e^{2 i (a+b x)}\right)+6 i b^2 (e+f x)^2 \text{Li}_2\left(i e^{2 i (a+b x)}\right)+6 b e f \text{Li}_3\left(-i e^{2 i (a+b x)}\right)-6 b e f \text{Li}_3\left(i e^{2 i (a+b x)}\right)+6 b f^2 x \text{Li}_3\left(-i e^{2 i (a+b x)}\right)-6 b f^2 x \text{Li}_3\left(i e^{2 i (a+b x)}\right)+3 i f^2 \text{Li}_4\left(-i e^{2 i (a+b x)}\right)-3 i f^2 \text{Li}_4\left(i e^{2 i (a+b x)}\right)}{24 b^3}","\frac{i f^2 \text{Li}_4\left(-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i f^2 \text{Li}_4\left(i e^{2 i (a+b x)}\right)}{8 b^3}+\frac{f (e+f x) \text{Li}_3\left(-i e^{2 i (a+b x)}\right)}{4 b^2}-\frac{f (e+f x) \text{Li}_3\left(i e^{2 i (a+b x)}\right)}{4 b^2}-\frac{i (e+f x)^2 \text{Li}_2\left(-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \text{Li}_2\left(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,"(x*(3*e^2 + 3*e*f*x + f^2*x^2)*ArcTanh[Tan[a + b*x]])/3 + (-12*b^3*e^2*x*Log[1 - I*E^((2*I)*(a + b*x))] - 12*b^3*e*f*x^2*Log[1 - I*E^((2*I)*(a + b*x))] - 4*b^3*f^2*x^3*Log[1 - I*E^((2*I)*(a + b*x))] + 12*b^3*e^2*x*Log[1 + I*E^((2*I)*(a + b*x))] + 12*b^3*e*f*x^2*Log[1 + I*E^((2*I)*(a + b*x))] + 4*b^3*f^2*x^3*Log[1 + I*E^((2*I)*(a + b*x))] - (6*I)*b^2*(e + f*x)^2*PolyLog[2, (-I)*E^((2*I)*(a + b*x))] + (6*I)*b^2*(e + f*x)^2*PolyLog[2, I*E^((2*I)*(a + b*x))] + 6*b*e*f*PolyLog[3, (-I)*E^((2*I)*(a + b*x))] + 6*b*f^2*x*PolyLog[3, (-I)*E^((2*I)*(a + b*x))] - 6*b*e*f*PolyLog[3, I*E^((2*I)*(a + b*x))] - 6*b*f^2*x*PolyLog[3, I*E^((2*I)*(a + b*x))] + (3*I)*f^2*PolyLog[4, (-I)*E^((2*I)*(a + b*x))] - (3*I)*f^2*PolyLog[4, I*E^((2*I)*(a + b*x))])/(24*b^3)","A",1
314,1,263,162,0.3089107,"\int (e+f x) \tanh ^{-1}(\tan (a+b x)) \, dx","Integrate[(e + f*x)*ArcTanh[Tan[a + b*x]],x]","-b e \left(\frac{i \text{Li}_2\left(-i e^{i (2 a+2 b x)}\right)}{4 b^2}-\frac{i \text{Li}_2\left(i e^{i (2 a+2 b x)}\right)}{4 b^2}-\frac{i x \tan ^{-1}\left(e^{2 i a+2 i b x}\right)}{b}\right)+\frac{f \left(4 i b^2 x^2 \tan ^{-1}(\cos (2 (a+b x))+i \sin (2 (a+b x)))+2 i b x \text{Li}_2(i \cos (2 (a+b x))-\sin (2 (a+b x)))-2 i b x \text{Li}_2(\sin (2 (a+b x))-i \cos (2 (a+b x)))-\text{Li}_3(i \cos (2 (a+b x))-\sin (2 (a+b x)))+\text{Li}_3(\sin (2 (a+b x))-i \cos (2 (a+b x)))\right)}{8 b^2}+e x \tanh ^{-1}(\tan (a+b x))+\frac{1}{2} f x^2 \tanh ^{-1}(\tan (a+b x))","\frac{f \text{Li}_3\left(-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{f \text{Li}_3\left(i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{i (e+f x) \text{Li}_2\left(-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x) \text{Li}_2\left(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,"e*x*ArcTanh[Tan[a + b*x]] + (f*x^2*ArcTanh[Tan[a + b*x]])/2 - b*e*(((-I)*x*ArcTan[E^((2*I)*a + (2*I)*b*x)])/b + ((I/4)*PolyLog[2, (-I)*E^(I*(2*a + 2*b*x))])/b^2 - ((I/4)*PolyLog[2, I*E^(I*(2*a + 2*b*x))])/b^2) + (f*((4*I)*b^2*x^2*ArcTan[Cos[2*(a + b*x)] + I*Sin[2*(a + b*x)]] + (2*I)*b*x*PolyLog[2, I*Cos[2*(a + b*x)] - Sin[2*(a + b*x)]] - (2*I)*b*x*PolyLog[2, (-I)*Cos[2*(a + b*x)] + Sin[2*(a + b*x)]] - PolyLog[3, I*Cos[2*(a + b*x)] - Sin[2*(a + b*x)]] + PolyLog[3, (-I)*Cos[2*(a + b*x)] + Sin[2*(a + b*x)]]))/(8*b^2)","A",0
315,1,74,79,0.0271697,"\int \tanh ^{-1}(\tan (a+b x)) \, dx","Integrate[ArcTanh[Tan[a + b*x]],x]","\frac{i \left(-\text{Li}_2\left(-i e^{2 i (a+b x)}\right)+\text{Li}_2\left(i e^{2 i (a+b x)}\right)+4 b x \left(\tan ^{-1}\left(e^{2 i (a+b x)}\right)-i \tanh ^{-1}(\tan (a+b x))\right)\right)}{4 b}","-\frac{i \text{Li}_2\left(-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i \text{Li}_2\left(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/4)*(4*b*x*(ArcTan[E^((2*I)*(a + b*x))] - I*ArcTanh[Tan[a + b*x]]) - PolyLog[2, (-I)*E^((2*I)*(a + b*x))] + PolyLog[2, I*E^((2*I)*(a + b*x))]))/b","A",1
316,0,0,18,5.0660279,"\int \frac{\tanh ^{-1}(\tan (a+b x))}{e+f x} \, dx","Integrate[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,"Integrate[ArcTanh[Tan[a + b*x]]/(e + f*x), x]","A",-1
317,1,346,395,0.9348868,"\int x^2 \tanh ^{-1}(c+d \tan (a+b x)) \, dx","Integrate[x^2*ArcTanh[c + d*Tan[a + b*x]],x]","\frac{1}{3} x^3 \tanh ^{-1}(d \tan (a+b x)+c)+\frac{4 b^3 x^3 \log \left(1+\frac{(c-i d-1) e^{2 i (a+b x)}}{c+i d-1}\right)-4 b^3 x^3 \log \left(1+\frac{(c-i d+1) e^{2 i (a+b x)}}{c+i d+1}\right)-6 i b^2 x^2 \text{Li}_2\left(\frac{(-c+i d+1) e^{2 i (a+b x)}}{c+i d-1}\right)+6 i b^2 x^2 \text{Li}_2\left(-\frac{(c-i d+1) e^{2 i (a+b x)}}{c+i d+1}\right)+6 b x \text{Li}_3\left(\frac{(-c+i d+1) e^{2 i (a+b x)}}{c+i d-1}\right)-6 b x \text{Li}_3\left(-\frac{(c-i d+1) e^{2 i (a+b x)}}{c+i d+1}\right)+3 i \text{Li}_4\left(\frac{(-c+i d+1) e^{2 i (a+b x)}}{c+i d-1}\right)-3 i \text{Li}_4\left(-\frac{(c-i d+1) e^{2 i (a+b x)}}{c+i d+1}\right)}{24 b^3}","\frac{i \text{Li}_4\left(-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{8 b^3}-\frac{i \text{Li}_4\left(-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{8 b^3}+\frac{x \text{Li}_3\left(-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b^2}-\frac{x \text{Li}_3\left(-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b^2}-\frac{i x^2 \text{Li}_2\left(-\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{Li}_2\left(-\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 + (4*b^3*x^3*Log[1 + ((-1 + c - I*d)*E^((2*I)*(a + b*x)))/(-1 + c + I*d)] - 4*b^3*x^3*Log[1 + ((1 + c - I*d)*E^((2*I)*(a + b*x)))/(1 + c + I*d)] - (6*I)*b^2*x^2*PolyLog[2, ((1 - c + I*d)*E^((2*I)*(a + b*x)))/(-1 + c + I*d)] + (6*I)*b^2*x^2*PolyLog[2, -(((1 + c - I*d)*E^((2*I)*(a + b*x)))/(1 + c + I*d))] + 6*b*x*PolyLog[3, ((1 - c + I*d)*E^((2*I)*(a + b*x)))/(-1 + c + I*d)] - 6*b*x*PolyLog[3, -(((1 + c - I*d)*E^((2*I)*(a + b*x)))/(1 + c + I*d))] + (3*I)*PolyLog[4, ((1 - c + I*d)*E^((2*I)*(a + b*x)))/(-1 + c + I*d)] - (3*I)*PolyLog[4, -(((1 + c - I*d)*E^((2*I)*(a + b*x)))/(1 + c + I*d))])/(24*b^3)","A",1
318,1,257,295,0.6024717,"\int x \tanh ^{-1}(c+d \tan (a+b x)) \, dx","Integrate[x*ArcTanh[c + d*Tan[a + b*x]],x]","\frac{1}{2} x^2 \tanh ^{-1}(d \tan (a+b x)+c)+\frac{2 b^2 x^2 \log \left(1+\frac{(c-i d-1) e^{2 i (a+b x)}}{c+i d-1}\right)-2 b^2 x^2 \log \left(1+\frac{(c-i d+1) e^{2 i (a+b x)}}{c+i d+1}\right)-2 i b x \text{Li}_2\left(\frac{(-c+i d+1) e^{2 i (a+b x)}}{c+i d-1}\right)+2 i b x \text{Li}_2\left(-\frac{(c-i d+1) e^{2 i (a+b x)}}{c+i d+1}\right)+\text{Li}_3\left(\frac{(-c+i d+1) e^{2 i (a+b x)}}{c+i d-1}\right)-\text{Li}_3\left(-\frac{(c-i d+1) e^{2 i (a+b x)}}{c+i d+1}\right)}{8 b^2}","\frac{\text{Li}_3\left(-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{8 b^2}-\frac{\text{Li}_3\left(-\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{Li}_2\left(-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b}+\frac{i x \text{Li}_2\left(-\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 + (2*b^2*x^2*Log[1 + ((-1 + c - I*d)*E^((2*I)*(a + b*x)))/(-1 + c + I*d)] - 2*b^2*x^2*Log[1 + ((1 + c - I*d)*E^((2*I)*(a + b*x)))/(1 + c + I*d)] - (2*I)*b*x*PolyLog[2, ((1 - c + I*d)*E^((2*I)*(a + b*x)))/(-1 + c + I*d)] + (2*I)*b*x*PolyLog[2, -(((1 + c - I*d)*E^((2*I)*(a + b*x)))/(1 + c + I*d))] + PolyLog[3, ((1 - c + I*d)*E^((2*I)*(a + b*x)))/(-1 + c + I*d)] - PolyLog[3, -(((1 + c - I*d)*E^((2*I)*(a + b*x)))/(1 + c + I*d))])/(8*b^2)","A",1
319,1,4654,194,32.9784377,"\int \tanh ^{-1}(c+d \tan (a+b x)) \, dx","Integrate[ArcTanh[c + d*Tan[a + b*x]],x]","\text{Result too large to show}","-\frac{i \text{Li}_2\left(-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b}+\frac{i \text{Li}_2\left(-\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]] + (d*(-(a*Log[-(Sec[(a + b*x)/2]^2*((-1 + c)*Cos[a + b*x] + d*Sin[a + b*x]))]) + a*Log[Sec[(a + b*x)/2]^2*(Cos[a + b*x] + c*Cos[a + b*x] + d*Sin[a + b*x])] + (a + b*x)*Log[(-d + Sqrt[1 - 2*c + c^2 + d^2])/(-1 + c) + Tan[(a + b*x)/2]] + I*Log[((-1 + c)*(1 + I*Tan[(a + b*x)/2]))/(-1 + c + I*d - I*Sqrt[1 - 2*c + c^2 + d^2])]*Log[(-d + Sqrt[1 - 2*c + c^2 + d^2])/(-1 + c) + Tan[(a + b*x)/2]] - I*Log[-(((-1 + c)*(I + Tan[(a + b*x)/2]))/(I - I*c - d + Sqrt[1 - 2*c + c^2 + d^2]))]*Log[(-d + Sqrt[1 - 2*c + c^2 + d^2])/(-1 + c) + Tan[(a + b*x)/2]] + (a + b*x)*Log[(d + Sqrt[1 - 2*c + c^2 + d^2])/(1 - c) + Tan[(a + b*x)/2]] + I*Log[((-1 + c)*(-I + Tan[(a + b*x)/2]))/(I - I*c + d + Sqrt[1 - 2*c + c^2 + d^2])]*Log[(d + Sqrt[1 - 2*c + c^2 + d^2])/(1 - c) + Tan[(a + b*x)/2]] - I*Log[((-1 + c)*(I + Tan[(a + b*x)/2]))/(-I + I*c + d + Sqrt[1 - 2*c + c^2 + d^2])]*Log[(d + Sqrt[1 - 2*c + c^2 + d^2])/(1 - c) + Tan[(a + b*x)/2]] - (a + b*x)*Log[-((d + Sqrt[1 + 2*c + c^2 + d^2])/(1 + c)) + Tan[(a + b*x)/2]] - I*Log[((1 + c)*(-I + Tan[(a + b*x)/2]))/(-I - I*c + d + Sqrt[1 + 2*c + c^2 + d^2])]*Log[-((d + Sqrt[1 + 2*c + c^2 + d^2])/(1 + c)) + Tan[(a + b*x)/2]] + I*Log[((1 + c)*(I + Tan[(a + b*x)/2]))/(I + I*c + d + Sqrt[1 + 2*c + c^2 + d^2])]*Log[-((d + Sqrt[1 + 2*c + c^2 + d^2])/(1 + c)) + Tan[(a + b*x)/2]] - (a + b*x)*Log[(-d + Sqrt[1 + 2*c + c^2 + d^2] + (1 + c)*Tan[(a + b*x)/2])/(1 + c)] + I*Log[((1 + c)*(1 - I*Tan[(a + b*x)/2]))/(1 + c - I*d + I*Sqrt[1 + 2*c + c^2 + d^2])]*Log[(-d + Sqrt[1 + 2*c + c^2 + d^2] + (1 + c)*Tan[(a + b*x)/2])/(1 + c)] - I*Log[((1 + c)*(1 + I*Tan[(a + b*x)/2]))/(1 + c + I*d - I*Sqrt[1 + 2*c + c^2 + d^2])]*Log[(-d + Sqrt[1 + 2*c + c^2 + d^2] + (1 + c)*Tan[(a + b*x)/2])/(1 + c)] + I*PolyLog[2, (d + Sqrt[1 - 2*c + c^2 + d^2] - (-1 + c)*Tan[(a + b*x)/2])/(I - I*c + d + Sqrt[1 - 2*c + c^2 + d^2])] - I*PolyLog[2, (d + Sqrt[1 - 2*c + c^2 + d^2] - (-1 + c)*Tan[(a + b*x)/2])/(-I + I*c + d + Sqrt[1 - 2*c + c^2 + d^2])] - I*PolyLog[2, (-d + Sqrt[1 - 2*c + c^2 + d^2] + (-1 + c)*Tan[(a + b*x)/2])/(I - I*c - d + Sqrt[1 - 2*c + c^2 + d^2])] + I*PolyLog[2, (-d + Sqrt[1 - 2*c + c^2 + d^2] + (-1 + c)*Tan[(a + b*x)/2])/(-I + I*c - d + Sqrt[1 - 2*c + c^2 + d^2])] - I*PolyLog[2, (d + Sqrt[1 + 2*c + c^2 + d^2] - (1 + c)*Tan[(a + b*x)/2])/(-I - I*c + d + Sqrt[1 + 2*c + c^2 + d^2])] + I*PolyLog[2, (d + Sqrt[1 + 2*c + c^2 + d^2] - (1 + c)*Tan[(a + b*x)/2])/(I + I*c + d + Sqrt[1 + 2*c + c^2 + d^2])] + I*PolyLog[2, (-d + Sqrt[1 + 2*c + c^2 + d^2] + (1 + c)*Tan[(a + b*x)/2])/(-I - I*c - d + Sqrt[1 + 2*c + c^2 + d^2])] - I*PolyLog[2, (-d + Sqrt[1 + 2*c + c^2 + d^2] + (1 + c)*Tan[(a + b*x)/2])/(I + I*c - d + Sqrt[1 + 2*c + c^2 + d^2])])*((-2*a)/(b*(-1 + c^2 + d^2 - Cos[2*(a + b*x)] + c^2*Cos[2*(a + b*x)] - d^2*Cos[2*(a + b*x)] + 2*c*d*Sin[2*(a + b*x)])) + (2*(a + b*x))/(b*(-1 + c^2 + d^2 - Cos[2*(a + b*x)] + c^2*Cos[2*(a + b*x)] - d^2*Cos[2*(a + b*x)] + 2*c*d*Sin[2*(a + b*x)]))))/(Log[(-d + Sqrt[1 - 2*c + c^2 + d^2])/(-1 + c) + Tan[(a + b*x)/2]] + Log[(d + Sqrt[1 - 2*c + c^2 + d^2])/(1 - c) + Tan[(a + b*x)/2]] - Log[-((d + Sqrt[1 + 2*c + c^2 + d^2])/(1 + c)) + Tan[(a + b*x)/2]] - Log[(-d + Sqrt[1 + 2*c + c^2 + d^2] + (1 + c)*Tan[(a + b*x)/2])/(1 + c)] + (Log[(-d + Sqrt[1 + 2*c + c^2 + d^2] + (1 + c)*Tan[(a + b*x)/2])/(1 + c)]*Sec[(a + b*x)/2]^2)/(2*(1 - I*Tan[(a + b*x)/2])) - (Log[(-d + Sqrt[1 - 2*c + c^2 + d^2])/(-1 + c) + Tan[(a + b*x)/2]]*Sec[(a + b*x)/2]^2)/(2*(1 + I*Tan[(a + b*x)/2])) + (Log[(-d + Sqrt[1 + 2*c + c^2 + d^2] + (1 + c)*Tan[(a + b*x)/2])/(1 + c)]*Sec[(a + b*x)/2]^2)/(2*(1 + I*Tan[(a + b*x)/2])) + ((I/2)*Log[(d + Sqrt[1 - 2*c + c^2 + d^2])/(1 - c) + Tan[(a + b*x)/2]]*Sec[(a + b*x)/2]^2)/(-I + Tan[(a + b*x)/2]) - ((I/2)*Log[-((d + Sqrt[1 + 2*c + c^2 + d^2])/(1 + c)) + Tan[(a + b*x)/2]]*Sec[(a + b*x)/2]^2)/(-I + Tan[(a + b*x)/2]) - ((I/2)*Log[(-d + Sqrt[1 - 2*c + c^2 + d^2])/(-1 + c) + Tan[(a + b*x)/2]]*Sec[(a + b*x)/2]^2)/(I + Tan[(a + b*x)/2]) - ((I/2)*Log[(d + Sqrt[1 - 2*c + c^2 + d^2])/(1 - c) + Tan[(a + b*x)/2]]*Sec[(a + b*x)/2]^2)/(I + Tan[(a + b*x)/2]) + ((I/2)*Log[-((d + Sqrt[1 + 2*c + c^2 + d^2])/(1 + c)) + Tan[(a + b*x)/2]]*Sec[(a + b*x)/2]^2)/(I + Tan[(a + b*x)/2]) + ((a + b*x)*Sec[(a + b*x)/2]^2)/(2*((-d + Sqrt[1 - 2*c + c^2 + d^2])/(-1 + c) + Tan[(a + b*x)/2])) + ((I/2)*Log[((-1 + c)*(1 + I*Tan[(a + b*x)/2]))/(-1 + c + I*d - I*Sqrt[1 - 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/((-d + Sqrt[1 - 2*c + c^2 + d^2])/(-1 + c) + Tan[(a + b*x)/2]) - ((I/2)*Log[-(((-1 + c)*(I + Tan[(a + b*x)/2]))/(I - I*c - d + Sqrt[1 - 2*c + c^2 + d^2]))]*Sec[(a + b*x)/2]^2)/((-d + Sqrt[1 - 2*c + c^2 + d^2])/(-1 + c) + Tan[(a + b*x)/2]) + ((a + b*x)*Sec[(a + b*x)/2]^2)/(2*((d + Sqrt[1 - 2*c + c^2 + d^2])/(1 - c) + Tan[(a + b*x)/2])) + ((I/2)*Log[((-1 + c)*(-I + Tan[(a + b*x)/2]))/(I - I*c + d + Sqrt[1 - 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/((d + Sqrt[1 - 2*c + c^2 + d^2])/(1 - c) + Tan[(a + b*x)/2]) - ((I/2)*Log[((-1 + c)*(I + Tan[(a + b*x)/2]))/(-I + I*c + d + Sqrt[1 - 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/((d + Sqrt[1 - 2*c + c^2 + d^2])/(1 - c) + Tan[(a + b*x)/2]) - ((a + b*x)*Sec[(a + b*x)/2]^2)/(2*(-((d + Sqrt[1 + 2*c + c^2 + d^2])/(1 + c)) + Tan[(a + b*x)/2])) - ((I/2)*Log[((1 + c)*(-I + Tan[(a + b*x)/2]))/(-I - I*c + d + Sqrt[1 + 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(-((d + Sqrt[1 + 2*c + c^2 + d^2])/(1 + c)) + Tan[(a + b*x)/2]) + ((I/2)*Log[((1 + c)*(I + Tan[(a + b*x)/2]))/(I + I*c + d + Sqrt[1 + 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(-((d + Sqrt[1 + 2*c + c^2 + d^2])/(1 + c)) + Tan[(a + b*x)/2]) + ((I/2)*(-1 + c)*Log[1 - (d + Sqrt[1 - 2*c + c^2 + d^2] - (-1 + c)*Tan[(a + b*x)/2])/(I - I*c + d + Sqrt[1 - 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(d + Sqrt[1 - 2*c + c^2 + d^2] - (-1 + c)*Tan[(a + b*x)/2]) - ((I/2)*(-1 + c)*Log[1 - (d + Sqrt[1 - 2*c + c^2 + d^2] - (-1 + c)*Tan[(a + b*x)/2])/(-I + I*c + d + Sqrt[1 - 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(d + Sqrt[1 - 2*c + c^2 + d^2] - (-1 + c)*Tan[(a + b*x)/2]) + ((I/2)*(-1 + c)*Log[1 - (-d + Sqrt[1 - 2*c + c^2 + d^2] + (-1 + c)*Tan[(a + b*x)/2])/(I - I*c - d + Sqrt[1 - 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(-d + Sqrt[1 - 2*c + c^2 + d^2] + (-1 + c)*Tan[(a + b*x)/2]) - ((I/2)*(-1 + c)*Log[1 - (-d + Sqrt[1 - 2*c + c^2 + d^2] + (-1 + c)*Tan[(a + b*x)/2])/(-I + I*c - d + Sqrt[1 - 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(-d + Sqrt[1 - 2*c + c^2 + d^2] + (-1 + c)*Tan[(a + b*x)/2]) - ((I/2)*(1 + c)*Log[1 - (d + Sqrt[1 + 2*c + c^2 + d^2] - (1 + c)*Tan[(a + b*x)/2])/(-I - I*c + d + Sqrt[1 + 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(d + Sqrt[1 + 2*c + c^2 + d^2] - (1 + c)*Tan[(a + b*x)/2]) + ((I/2)*(1 + c)*Log[1 - (d + Sqrt[1 + 2*c + c^2 + d^2] - (1 + c)*Tan[(a + b*x)/2])/(I + I*c + d + Sqrt[1 + 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(d + Sqrt[1 + 2*c + c^2 + d^2] - (1 + c)*Tan[(a + b*x)/2]) - ((1 + c)*(a + b*x)*Sec[(a + b*x)/2]^2)/(2*(-d + Sqrt[1 + 2*c + c^2 + d^2] + (1 + c)*Tan[(a + b*x)/2])) + ((I/2)*(1 + c)*Log[((1 + c)*(1 - I*Tan[(a + b*x)/2]))/(1 + c - I*d + I*Sqrt[1 + 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(-d + Sqrt[1 + 2*c + c^2 + d^2] + (1 + c)*Tan[(a + b*x)/2]) - ((I/2)*(1 + c)*Log[((1 + c)*(1 + I*Tan[(a + b*x)/2]))/(1 + c + I*d - I*Sqrt[1 + 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(-d + Sqrt[1 + 2*c + c^2 + d^2] + (1 + c)*Tan[(a + b*x)/2]) - ((I/2)*(1 + c)*Log[1 - (-d + Sqrt[1 + 2*c + c^2 + d^2] + (1 + c)*Tan[(a + b*x)/2])/(-I - I*c - d + Sqrt[1 + 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(-d + Sqrt[1 + 2*c + c^2 + d^2] + (1 + c)*Tan[(a + b*x)/2]) + ((I/2)*(1 + c)*Log[1 - (-d + Sqrt[1 + 2*c + c^2 + d^2] + (1 + c)*Tan[(a + b*x)/2])/(I + I*c - d + Sqrt[1 + 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(-d + Sqrt[1 + 2*c + c^2 + d^2] + (1 + c)*Tan[(a + b*x)/2]) + (a*Cos[(a + b*x)/2]^2*(-(Sec[(a + b*x)/2]^2*(d*Cos[a + b*x] - (-1 + c)*Sin[a + b*x])) - Sec[(a + b*x)/2]^2*((-1 + c)*Cos[a + b*x] + d*Sin[a + b*x])*Tan[(a + b*x)/2]))/((-1 + c)*Cos[a + b*x] + d*Sin[a + b*x]) + (a*Cos[(a + b*x)/2]^2*(Sec[(a + b*x)/2]^2*(d*Cos[a + b*x] - Sin[a + b*x] - c*Sin[a + b*x]) + Sec[(a + b*x)/2]^2*(Cos[a + b*x] + c*Cos[a + b*x] + d*Sin[a + b*x])*Tan[(a + b*x)/2]))/(Cos[a + b*x] + c*Cos[a + b*x] + d*Sin[a + b*x]))","B",0
320,0,0,18,4.8022313,"\int \frac{\tanh ^{-1}(c+d \tan (a+b x))}{x} \, dx","Integrate[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,"Integrate[ArcTanh[c + d*Tan[a + b*x]]/x, x]","A",-1
321,1,155,170,0.4423807,"\int x^2 \tanh ^{-1}(1-i d+d \tan (a+b x)) \, dx","Integrate[x^2*ArcTanh[1 - I*d + d*Tan[a + b*x]],x]","\frac{1}{3} x^3 \tanh ^{-1}(d \tan (a+b x)-i d+1)-\frac{4 b^3 x^3 \log \left(1+\frac{i e^{-2 i (a+b x)}}{d+i}\right)+6 i b^2 x^2 \text{Li}_2\left(-\frac{i e^{-2 i (a+b x)}}{d+i}\right)+6 b x \text{Li}_3\left(-\frac{i e^{-2 i (a+b x)}}{d+i}\right)-3 i \text{Li}_4\left(-\frac{i e^{-2 i (a+b x)}}{d+i}\right)}{24 b^3}","-\frac{i \text{Li}_4\left(-\left((1-i d) e^{2 i a+2 i b x}\right)\right)}{8 b^3}-\frac{x \text{Li}_3\left(-\left((1-i d) e^{2 i a+2 i b x}\right)\right)}{4 b^2}+\frac{i x^2 \text{Li}_2\left(-\left((1-i d) e^{2 i a+2 i b x}\right)\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,"(x^3*ArcTanh[1 - I*d + d*Tan[a + b*x]])/3 - (4*b^3*x^3*Log[1 + I/((I + d)*E^((2*I)*(a + b*x)))] + (6*I)*b^2*x^2*PolyLog[2, (-I)/((I + d)*E^((2*I)*(a + b*x)))] + 6*b*x*PolyLog[3, (-I)/((I + d)*E^((2*I)*(a + b*x)))] - (3*I)*PolyLog[4, (-I)/((I + d)*E^((2*I)*(a + b*x)))])/(24*b^3)","A",1
322,1,119,133,0.3148201,"\int x \tanh ^{-1}(1-i d+d \tan (a+b x)) \, dx","Integrate[x*ArcTanh[1 - I*d + d*Tan[a + b*x]],x]","\frac{1}{2} x^2 \tanh ^{-1}(d \tan (a+b x)-i d+1)-\frac{2 b^2 x^2 \log \left(1+\frac{i e^{-2 i (a+b x)}}{d+i}\right)+2 i b x \text{Li}_2\left(-\frac{i e^{-2 i (a+b x)}}{d+i}\right)+\text{Li}_3\left(-\frac{i e^{-2 i (a+b x)}}{d+i}\right)}{8 b^2}","-\frac{\text{Li}_3\left(-\left((1-i d) e^{2 i a+2 i b x}\right)\right)}{8 b^2}+\frac{i x \text{Li}_2\left(-\left((1-i d) e^{2 i a+2 i b x}\right)\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,"(x^2*ArcTanh[1 - I*d + d*Tan[a + b*x]])/2 - (2*b^2*x^2*Log[1 + I/((I + d)*E^((2*I)*(a + b*x)))] + (2*I)*b*x*PolyLog[2, (-I)/((I + d)*E^((2*I)*(a + b*x)))] + PolyLog[3, (-I)/((I + d)*E^((2*I)*(a + b*x)))])/(8*b^2)","A",1
323,1,766,93,14.366798,"\int \tanh ^{-1}(1-i d+d \tan (a+b x)) \, dx","Integrate[ArcTanh[1 - I*d + d*Tan[a + b*x]],x]","\frac{x \sec ^2(a+b x) (\cos (b x)+i \sin (b x)) (\sin (b x)+i \cos (b x)) (d \sin (a+b x)+(2-i d) \cos (a+b x)) \left(\text{Li}_2\left(-\frac{1}{2} (\cos (a)+i \sin (a)) (d \cos (a)+i (d+2 i) \sin (a)) (\tan (b x)-i)\right)-\text{Li}_2\left(\frac{\sec (b x) (d \cos (a)+i (d+2 i) \sin (a)) (\cos (a+b x)-i \sin (a+b x))}{2 (d+i)}\right)-\log (1-i \tan (b x)) \log \left(\frac{(\cos (a)-i \sin (a)) \sec (b x) (i d \sin (a+b x)+(d+2 i) \cos (a+b x))}{2 (d+i)}\right)+\log (1+i \tan (b x)) \log \left(\frac{\sec (b x) (d \sin (a+b x)+(2-i d) \cos (a+b x))}{2 \cos (a)-2 i \sin (a)}\right)-\text{Li}_2(i \sin (2 b x)-\cos (2 b x))+2 i b x \log (2 \cos (b x) (\cos (b x)-i \sin (b x)))\right)}{(\tan (a+b x)-i) (d \tan (a+b x)-i d+2) (i d \sin (a+b x)+(d+2 i) \cos (a+b x)) \left(\frac{\sec ^2(b x) \log \left(\frac{\sec (b x) (d \sin (a+b x)+(2-i d) \cos (a+b x))}{2 \cos (a)-2 i \sin (a)}\right)}{\tan (b x)-i}-\frac{\sec ^2(b x) \log \left(1+\frac{1}{2} (\cos (a)+i \sin (a)) (\tan (b x)-i) (d \cos (a)+i (d+2 i) \sin (a))\right)}{\tan (b x)-i}-\frac{\sec ^2(b x) \log \left(\frac{(\cos (a)-i \sin (a)) \sec (b x) (i d \sin (a+b x)+(d+2 i) \cos (a+b x))}{2 (d+i)}\right)}{\tan (b x)+i}+\frac{i \sec (b x) (d \cos (a)+i (d+2 i) \sin (a)) \log (1+i \tan (b x))}{i d \sin (a+b x)+(d+2 i) \cos (a+b x)}+\frac{\sec (b x) ((d+2 i) \sin (a)-i d \cos (a)) \log (1-i \tan (b x))}{i d \sin (a+b x)+(d+2 i) \cos (a+b x)}+(\tan (b x)-i) \log \left(\frac{(\cos (a)-i \sin (a)) \sec (b x) (i d \sin (a+b x)+(d+2 i) \cos (a+b x))}{2 (d+i)}\right)+2 b x (1-i \tan (b x))\right)}+x \tanh ^{-1}(d \tan (a+b x)-i d+1)","\frac{i \text{Li}_2\left(-\left((1-i d) e^{2 i a+2 i b x}\right)\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,"x*ArcTanh[1 - I*d + d*Tan[a + b*x]] + (x*((2*I)*b*x*Log[2*Cos[b*x]*(Cos[b*x] - I*Sin[b*x])] - Log[(Sec[b*x]*(Cos[a] - I*Sin[a])*((2*I + d)*Cos[a + b*x] + I*d*Sin[a + b*x]))/(2*(I + d))]*Log[1 - I*Tan[b*x]] + Log[(Sec[b*x]*((2 - I*d)*Cos[a + b*x] + d*Sin[a + b*x]))/(2*Cos[a] - (2*I)*Sin[a])]*Log[1 + I*Tan[b*x]] - PolyLog[2, -Cos[2*b*x] + I*Sin[2*b*x]] - PolyLog[2, (Sec[b*x]*(d*Cos[a] + I*(2*I + d)*Sin[a])*(Cos[a + b*x] - I*Sin[a + b*x]))/(2*(I + d))] + PolyLog[2, -1/2*((Cos[a] + I*Sin[a])*(d*Cos[a] + I*(2*I + d)*Sin[a])*(-I + Tan[b*x]))])*Sec[a + b*x]^2*(Cos[b*x] + I*Sin[b*x])*(I*Cos[b*x] + Sin[b*x])*((2 - I*d)*Cos[a + b*x] + d*Sin[a + b*x]))/(((2*I + d)*Cos[a + b*x] + I*d*Sin[a + b*x])*((I*Log[1 + I*Tan[b*x]]*Sec[b*x]*(d*Cos[a] + I*(2*I + d)*Sin[a]))/((2*I + d)*Cos[a + b*x] + I*d*Sin[a + b*x]) + (Log[1 - I*Tan[b*x]]*Sec[b*x]*((-I)*d*Cos[a] + (2*I + d)*Sin[a]))/((2*I + d)*Cos[a + b*x] + I*d*Sin[a + b*x]) + 2*b*x*(1 - I*Tan[b*x]) + (Log[(Sec[b*x]*((2 - I*d)*Cos[a + b*x] + d*Sin[a + b*x]))/(2*Cos[a] - (2*I)*Sin[a])]*Sec[b*x]^2)/(-I + Tan[b*x]) - (Log[1 + ((Cos[a] + I*Sin[a])*(d*Cos[a] + I*(2*I + d)*Sin[a])*(-I + Tan[b*x]))/2]*Sec[b*x]^2)/(-I + Tan[b*x]) + Log[(Sec[b*x]*(Cos[a] - I*Sin[a])*((2*I + d)*Cos[a + b*x] + I*d*Sin[a + b*x]))/(2*(I + d))]*(-I + Tan[b*x]) - (Log[(Sec[b*x]*(Cos[a] - I*Sin[a])*((2*I + d)*Cos[a + b*x] + I*d*Sin[a + b*x]))/(2*(I + d))]*Sec[b*x]^2)/(I + Tan[b*x]))*(-I + Tan[a + b*x])*(2 - I*d + d*Tan[a + b*x]))","B",0
324,0,0,23,1.0761834,"\int \frac{\tanh ^{-1}(1-i d+d \tan (a+b x))}{x} \, dx","Integrate[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,"Integrate[ArcTanh[1 - I*d + d*Tan[a + b*x]]/x, x]","A",-1
325,1,156,171,0.4114152,"\int x^2 \tanh ^{-1}(1+i d-d \tan (a+b x)) \, dx","Integrate[x^2*ArcTanh[1 + I*d - d*Tan[a + b*x]],x]","\frac{1}{3} x^3 \tanh ^{-1}(d (-\tan (a+b x))+i d+1)-\frac{4 b^3 x^3 \log \left(1-\frac{i e^{-2 i (a+b x)}}{d-i}\right)+6 i b^2 x^2 \text{Li}_2\left(\frac{i e^{-2 i (a+b x)}}{d-i}\right)+6 b x \text{Li}_3\left(\frac{i e^{-2 i (a+b x)}}{d-i}\right)-3 i \text{Li}_4\left(\frac{i e^{-2 i (a+b x)}}{d-i}\right)}{24 b^3}","-\frac{i \text{Li}_4\left(-\left((i d+1) e^{2 i a+2 i b x}\right)\right)}{8 b^3}-\frac{x \text{Li}_3\left(-\left((i d+1) e^{2 i a+2 i b x}\right)\right)}{4 b^2}+\frac{i x^2 \text{Li}_2\left(-\left((i d+1) e^{2 i a+2 i b x}\right)\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,"(x^3*ArcTanh[1 + I*d - d*Tan[a + b*x]])/3 - (4*b^3*x^3*Log[1 - I/((-I + d)*E^((2*I)*(a + b*x)))] + (6*I)*b^2*x^2*PolyLog[2, I/((-I + d)*E^((2*I)*(a + b*x)))] + 6*b*x*PolyLog[3, I/((-I + d)*E^((2*I)*(a + b*x)))] - (3*I)*PolyLog[4, I/((-I + d)*E^((2*I)*(a + b*x)))])/(24*b^3)","A",1
326,1,120,134,0.3154802,"\int x \tanh ^{-1}(1+i d-d \tan (a+b x)) \, dx","Integrate[x*ArcTanh[1 + I*d - d*Tan[a + b*x]],x]","\frac{1}{2} x^2 \tanh ^{-1}(d (-\tan (a+b x))+i d+1)-\frac{2 b^2 x^2 \log \left(1-\frac{i e^{-2 i (a+b x)}}{d-i}\right)+2 i b x \text{Li}_2\left(\frac{i e^{-2 i (a+b x)}}{d-i}\right)+\text{Li}_3\left(\frac{i e^{-2 i (a+b x)}}{d-i}\right)}{8 b^2}","-\frac{\text{Li}_3\left(-\left((i d+1) e^{2 i a+2 i b x}\right)\right)}{8 b^2}+\frac{i x \text{Li}_2\left(-\left((i d+1) e^{2 i a+2 i b x}\right)\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,"(x^2*ArcTanh[1 + I*d - d*Tan[a + b*x]])/2 - (2*b^2*x^2*Log[1 - I/((-I + d)*E^((2*I)*(a + b*x)))] + (2*I)*b*x*PolyLog[2, I/((-I + d)*E^((2*I)*(a + b*x)))] + PolyLog[3, I/((-I + d)*E^((2*I)*(a + b*x)))])/(8*b^2)","A",1
327,1,723,94,15.5350479,"\int \tanh ^{-1}(1+i d-d \tan (a+b x)) \, dx","Integrate[ArcTanh[1 + I*d - d*Tan[a + b*x]],x]","x \tanh ^{-1}(d (-\tan (a+b x))+i d+1)-\frac{x \sec (a+b x) (\cos (b x)+i \sin (b x)) (\sin (b x)+i \cos (b x)) \left(-\text{Li}_2\left(\frac{1}{2} (\cos (a)+i \sin (a)) (d \cos (a)+(i d+2) \sin (a)) (\tan (b x)-i)\right)+\text{Li}_2\left(\frac{\sec (b x) (d \cos (a)+(i d+2) \sin (a)) (\cos (a+b x)-i \sin (a+b x))}{2 (d-i)}\right)+\log (1-i \tan (b x)) \log \left(\frac{(\cos (a)-i \sin (a)) \sec (b x) (i d \sin (a+b x)+(d-2 i) \cos (a+b x))}{2 (d-i)}\right)-\log (1+i \tan (b x)) \log \left(\frac{\sec (b x) (-d \sin (a+b x)+(2+i d) \cos (a+b x))}{2 \cos (a)-2 i \sin (a)}\right)+\text{Li}_2(i \sin (2 b x)-\cos (2 b x))-2 i b x \log (2 \cos (b x) (\cos (b x)-i \sin (b x)))\right)}{(\tan (a+b x)-i) (i d \sin (a+b x)+(d-2 i) \cos (a+b x)) \left(-\frac{\sec ^2(b x) \log \left(\frac{\sec (b x) (-d \sin (a+b x)+(2+i d) \cos (a+b x))}{2 \cos (a)-2 i \sin (a)}\right)}{\tan (b x)-i}+\frac{\sec ^2(b x) \log \left(1-\frac{1}{2} (\cos (a)+i \sin (a)) (\tan (b x)-i) (d \cos (a)+(2+i d) \sin (a))\right)}{\tan (b x)-i}+\frac{\sec ^2(b x) \log \left(\frac{(\cos (a)-i \sin (a)) \sec (b x) (i d \sin (a+b x)+(d-2 i) \cos (a+b x))}{2 (d-i)}\right)}{\tan (b x)+i}+\frac{i \sec (b x) (d \cos (a)+(2+i d) \sin (a)) \log (1-i \tan (b x))}{i d \sin (a+b x)+(d-2 i) \cos (a+b x)}+\frac{\sec (b x) ((d-2 i) \sin (a)-i d \cos (a)) \log (1+i \tan (b x))}{i d \sin (a+b x)+(d-2 i) \cos (a+b x)}-(\tan (b x)-i) \log \left(1-\frac{\sec (b x) (d \cos (a)+(2+i d) \sin (a)) (\cos (a+b x)-i \sin (a+b x))}{2 (d-i)}\right)+2 i b x (\tan (b x)+i)\right)}","\frac{i \text{Li}_2\left(-\left((i d+1) e^{2 i a+2 i b x}\right)\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,"x*ArcTanh[1 + I*d - d*Tan[a + b*x]] - (x*((-2*I)*b*x*Log[2*Cos[b*x]*(Cos[b*x] - I*Sin[b*x])] + Log[(Sec[b*x]*(Cos[a] - I*Sin[a])*((-2*I + d)*Cos[a + b*x] + I*d*Sin[a + b*x]))/(2*(-I + d))]*Log[1 - I*Tan[b*x]] - Log[(Sec[b*x]*((2 + I*d)*Cos[a + b*x] - d*Sin[a + b*x]))/(2*Cos[a] - (2*I)*Sin[a])]*Log[1 + I*Tan[b*x]] + PolyLog[2, -Cos[2*b*x] + I*Sin[2*b*x]] + PolyLog[2, (Sec[b*x]*(d*Cos[a] + (2 + I*d)*Sin[a])*(Cos[a + b*x] - I*Sin[a + b*x]))/(2*(-I + d))] - PolyLog[2, ((Cos[a] + I*Sin[a])*(d*Cos[a] + (2 + I*d)*Sin[a])*(-I + Tan[b*x]))/2])*Sec[a + b*x]*(Cos[b*x] + I*Sin[b*x])*(I*Cos[b*x] + Sin[b*x]))/(((-2*I + d)*Cos[a + b*x] + I*d*Sin[a + b*x])*((I*Log[1 - I*Tan[b*x]]*Sec[b*x]*(d*Cos[a] + (2 + I*d)*Sin[a]))/((-2*I + d)*Cos[a + b*x] + I*d*Sin[a + b*x]) + (Log[1 + I*Tan[b*x]]*Sec[b*x]*((-I)*d*Cos[a] + (-2*I + d)*Sin[a]))/((-2*I + d)*Cos[a + b*x] + I*d*Sin[a + b*x]) - (Log[(Sec[b*x]*((2 + I*d)*Cos[a + b*x] - d*Sin[a + b*x]))/(2*Cos[a] - (2*I)*Sin[a])]*Sec[b*x]^2)/(-I + Tan[b*x]) + (Log[1 - ((Cos[a] + I*Sin[a])*(d*Cos[a] + (2 + I*d)*Sin[a])*(-I + Tan[b*x]))/2]*Sec[b*x]^2)/(-I + Tan[b*x]) - Log[1 - (Sec[b*x]*(d*Cos[a] + (2 + I*d)*Sin[a])*(Cos[a + b*x] - I*Sin[a + b*x]))/(2*(-I + d))]*(-I + Tan[b*x]) + (Log[(Sec[b*x]*(Cos[a] - I*Sin[a])*((-2*I + d)*Cos[a + b*x] + I*d*Sin[a + b*x]))/(2*(-I + d))]*Sec[b*x]^2)/(I + Tan[b*x]) + (2*I)*b*x*(I + Tan[b*x]))*(-I + Tan[a + b*x]))","B",0
328,0,0,24,1.0613726,"\int \frac{\tanh ^{-1}(1+i d-d \tan (a+b x))}{x} \, dx","Integrate[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,"Integrate[ArcTanh[1 + I*d - d*Tan[a + b*x]]/x, x]","A",-1
329,1,654,302,0.3038904,"\int (e+f x)^3 \tanh ^{-1}(\cot (a+b x)) \, dx","Integrate[(e + f*x)^3*ArcTanh[Cot[a + b*x]],x]","\frac{1}{4} x \left(4 e^3+6 e^2 f x+4 e f^2 x^2+f^3 x^3\right) \tanh ^{-1}(\cot (a+b x))+\frac{-8 b^4 e^3 x \log \left(1-i e^{2 i (a+b x)}\right)+8 b^4 e^3 x \log \left(1+i e^{2 i (a+b x)}\right)-12 b^4 e^2 f x^2 \log \left(1-i e^{2 i (a+b x)}\right)+12 b^4 e^2 f x^2 \log \left(1+i e^{2 i (a+b x)}\right)-8 b^4 e f^2 x^3 \log \left(1-i e^{2 i (a+b x)}\right)+8 b^4 e f^2 x^3 \log \left(1+i e^{2 i (a+b x)}\right)-2 b^4 f^3 x^4 \log \left(1-i e^{2 i (a+b x)}\right)+2 b^4 f^3 x^4 \log \left(1+i e^{2 i (a+b x)}\right)-4 i b^3 (e+f x)^3 \text{Li}_2\left(-i e^{2 i (a+b x)}\right)+4 i b^3 (e+f x)^3 \text{Li}_2\left(i e^{2 i (a+b x)}\right)+6 b^2 e^2 f \text{Li}_3\left(-i e^{2 i (a+b x)}\right)-6 b^2 e^2 f \text{Li}_3\left(i e^{2 i (a+b x)}\right)+12 b^2 e f^2 x \text{Li}_3\left(-i e^{2 i (a+b x)}\right)-12 b^2 e f^2 x \text{Li}_3\left(i e^{2 i (a+b x)}\right)+6 b^2 f^3 x^2 \text{Li}_3\left(-i e^{2 i (a+b x)}\right)-6 b^2 f^3 x^2 \text{Li}_3\left(i e^{2 i (a+b x)}\right)+6 i b e f^2 \text{Li}_4\left(-i e^{2 i (a+b x)}\right)-6 i b e f^2 \text{Li}_4\left(i e^{2 i (a+b x)}\right)+6 i b f^3 x \text{Li}_4\left(-i e^{2 i (a+b x)}\right)-6 i b f^3 x \text{Li}_4\left(i e^{2 i (a+b x)}\right)-3 f^3 \text{Li}_5\left(-i e^{2 i (a+b x)}\right)+3 f^3 \text{Li}_5\left(i e^{2 i (a+b x)}\right)}{16 b^4}","-\frac{3 f^3 \text{Li}_5\left(-i e^{2 i (a+b x)}\right)}{16 b^4}+\frac{3 f^3 \text{Li}_5\left(i e^{2 i (a+b x)}\right)}{16 b^4}+\frac{3 i f^2 (e+f x) \text{Li}_4\left(-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{3 i f^2 (e+f x) \text{Li}_4\left(i e^{2 i (a+b x)}\right)}{8 b^3}+\frac{3 f (e+f x)^2 \text{Li}_3\left(-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f (e+f x)^2 \text{Li}_3\left(i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{i (e+f x)^3 \text{Li}_2\left(-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \text{Li}_2\left(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,"(x*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3)*ArcTanh[Cot[a + b*x]])/4 + (-8*b^4*e^3*x*Log[1 - I*E^((2*I)*(a + b*x))] - 12*b^4*e^2*f*x^2*Log[1 - I*E^((2*I)*(a + b*x))] - 8*b^4*e*f^2*x^3*Log[1 - I*E^((2*I)*(a + b*x))] - 2*b^4*f^3*x^4*Log[1 - I*E^((2*I)*(a + b*x))] + 8*b^4*e^3*x*Log[1 + I*E^((2*I)*(a + b*x))] + 12*b^4*e^2*f*x^2*Log[1 + I*E^((2*I)*(a + b*x))] + 8*b^4*e*f^2*x^3*Log[1 + I*E^((2*I)*(a + b*x))] + 2*b^4*f^3*x^4*Log[1 + I*E^((2*I)*(a + b*x))] - (4*I)*b^3*(e + f*x)^3*PolyLog[2, (-I)*E^((2*I)*(a + b*x))] + (4*I)*b^3*(e + f*x)^3*PolyLog[2, I*E^((2*I)*(a + b*x))] + 6*b^2*e^2*f*PolyLog[3, (-I)*E^((2*I)*(a + b*x))] + 12*b^2*e*f^2*x*PolyLog[3, (-I)*E^((2*I)*(a + b*x))] + 6*b^2*f^3*x^2*PolyLog[3, (-I)*E^((2*I)*(a + b*x))] - 6*b^2*e^2*f*PolyLog[3, I*E^((2*I)*(a + b*x))] - 12*b^2*e*f^2*x*PolyLog[3, I*E^((2*I)*(a + b*x))] - 6*b^2*f^3*x^2*PolyLog[3, I*E^((2*I)*(a + b*x))] + (6*I)*b*e*f^2*PolyLog[4, (-I)*E^((2*I)*(a + b*x))] + (6*I)*b*f^3*x*PolyLog[4, (-I)*E^((2*I)*(a + b*x))] - (6*I)*b*e*f^2*PolyLog[4, I*E^((2*I)*(a + b*x))] - (6*I)*b*f^3*x*PolyLog[4, I*E^((2*I)*(a + b*x))] - 3*f^3*PolyLog[5, (-I)*E^((2*I)*(a + b*x))] + 3*f^3*PolyLog[5, I*E^((2*I)*(a + b*x))])/(16*b^4)","B",1
330,1,409,234,0.1824807,"\int (e+f x)^2 \tanh ^{-1}(\cot (a+b x)) \, dx","Integrate[(e + f*x)^2*ArcTanh[Cot[a + b*x]],x]","\frac{1}{3} x \left(3 e^2+3 e f x+f^2 x^2\right) \tanh ^{-1}(\cot (a+b x))+\frac{-12 b^3 e^2 x \log \left(1-i e^{2 i (a+b x)}\right)+12 b^3 e^2 x \log \left(1+i e^{2 i (a+b x)}\right)-12 b^3 e f x^2 \log \left(1-i e^{2 i (a+b x)}\right)+12 b^3 e f x^2 \log \left(1+i e^{2 i (a+b x)}\right)-4 b^3 f^2 x^3 \log \left(1-i e^{2 i (a+b x)}\right)+4 b^3 f^2 x^3 \log \left(1+i e^{2 i (a+b x)}\right)-6 i b^2 (e+f x)^2 \text{Li}_2\left(-i e^{2 i (a+b x)}\right)+6 i b^2 (e+f x)^2 \text{Li}_2\left(i e^{2 i (a+b x)}\right)+6 b e f \text{Li}_3\left(-i e^{2 i (a+b x)}\right)-6 b e f \text{Li}_3\left(i e^{2 i (a+b x)}\right)+6 b f^2 x \text{Li}_3\left(-i e^{2 i (a+b x)}\right)-6 b f^2 x \text{Li}_3\left(i e^{2 i (a+b x)}\right)+3 i f^2 \text{Li}_4\left(-i e^{2 i (a+b x)}\right)-3 i f^2 \text{Li}_4\left(i e^{2 i (a+b x)}\right)}{24 b^3}","\frac{i f^2 \text{Li}_4\left(-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i f^2 \text{Li}_4\left(i e^{2 i (a+b x)}\right)}{8 b^3}+\frac{f (e+f x) \text{Li}_3\left(-i e^{2 i (a+b x)}\right)}{4 b^2}-\frac{f (e+f x) \text{Li}_3\left(i e^{2 i (a+b x)}\right)}{4 b^2}-\frac{i (e+f x)^2 \text{Li}_2\left(-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \text{Li}_2\left(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,"(x*(3*e^2 + 3*e*f*x + f^2*x^2)*ArcTanh[Cot[a + b*x]])/3 + (-12*b^3*e^2*x*Log[1 - I*E^((2*I)*(a + b*x))] - 12*b^3*e*f*x^2*Log[1 - I*E^((2*I)*(a + b*x))] - 4*b^3*f^2*x^3*Log[1 - I*E^((2*I)*(a + b*x))] + 12*b^3*e^2*x*Log[1 + I*E^((2*I)*(a + b*x))] + 12*b^3*e*f*x^2*Log[1 + I*E^((2*I)*(a + b*x))] + 4*b^3*f^2*x^3*Log[1 + I*E^((2*I)*(a + b*x))] - (6*I)*b^2*(e + f*x)^2*PolyLog[2, (-I)*E^((2*I)*(a + b*x))] + (6*I)*b^2*(e + f*x)^2*PolyLog[2, I*E^((2*I)*(a + b*x))] + 6*b*e*f*PolyLog[3, (-I)*E^((2*I)*(a + b*x))] + 6*b*f^2*x*PolyLog[3, (-I)*E^((2*I)*(a + b*x))] - 6*b*e*f*PolyLog[3, I*E^((2*I)*(a + b*x))] - 6*b*f^2*x*PolyLog[3, I*E^((2*I)*(a + b*x))] + (3*I)*f^2*PolyLog[4, (-I)*E^((2*I)*(a + b*x))] - (3*I)*f^2*PolyLog[4, I*E^((2*I)*(a + b*x))])/(24*b^3)","A",1
331,1,263,162,0.1281108,"\int (e+f x) \tanh ^{-1}(\cot (a+b x)) \, dx","Integrate[(e + f*x)*ArcTanh[Cot[a + b*x]],x]","-b e \left(\frac{i \text{Li}_2\left(-i e^{i (2 a+2 b x)}\right)}{4 b^2}-\frac{i \text{Li}_2\left(i e^{i (2 a+2 b x)}\right)}{4 b^2}-\frac{i x \tan ^{-1}\left(e^{2 i a+2 i b x}\right)}{b}\right)+\frac{f \left(4 i b^2 x^2 \tan ^{-1}(\cos (2 (a+b x))+i \sin (2 (a+b x)))+2 i b x \text{Li}_2(i \cos (2 (a+b x))-\sin (2 (a+b x)))-2 i b x \text{Li}_2(\sin (2 (a+b x))-i \cos (2 (a+b x)))-\text{Li}_3(i \cos (2 (a+b x))-\sin (2 (a+b x)))+\text{Li}_3(\sin (2 (a+b x))-i \cos (2 (a+b x)))\right)}{8 b^2}+e x \tanh ^{-1}(\cot (a+b x))+\frac{1}{2} f x^2 \tanh ^{-1}(\cot (a+b x))","\frac{f \text{Li}_3\left(-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{f \text{Li}_3\left(i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{i (e+f x) \text{Li}_2\left(-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x) \text{Li}_2\left(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,"e*x*ArcTanh[Cot[a + b*x]] + (f*x^2*ArcTanh[Cot[a + b*x]])/2 - b*e*(((-I)*x*ArcTan[E^((2*I)*a + (2*I)*b*x)])/b + ((I/4)*PolyLog[2, (-I)*E^(I*(2*a + 2*b*x))])/b^2 - ((I/4)*PolyLog[2, I*E^(I*(2*a + 2*b*x))])/b^2) + (f*((4*I)*b^2*x^2*ArcTan[Cos[2*(a + b*x)] + I*Sin[2*(a + b*x)]] + (2*I)*b*x*PolyLog[2, I*Cos[2*(a + b*x)] - Sin[2*(a + b*x)]] - (2*I)*b*x*PolyLog[2, (-I)*Cos[2*(a + b*x)] + Sin[2*(a + b*x)]] - PolyLog[3, I*Cos[2*(a + b*x)] - Sin[2*(a + b*x)]] + PolyLog[3, (-I)*Cos[2*(a + b*x)] + Sin[2*(a + b*x)]]))/(8*b^2)","A",0
332,1,74,79,0.0368115,"\int \tanh ^{-1}(\cot (a+b x)) \, dx","Integrate[ArcTanh[Cot[a + b*x]],x]","\frac{i \left(-\text{Li}_2\left(-i e^{2 i (a+b x)}\right)+\text{Li}_2\left(i e^{2 i (a+b x)}\right)+4 b x \left(\tan ^{-1}\left(e^{2 i (a+b x)}\right)-i \tanh ^{-1}(\cot (a+b x))\right)\right)}{4 b}","-\frac{i \text{Li}_2\left(-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i \text{Li}_2\left(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/4)*(4*b*x*(ArcTan[E^((2*I)*(a + b*x))] - I*ArcTanh[Cot[a + b*x]]) - PolyLog[2, (-I)*E^((2*I)*(a + b*x))] + PolyLog[2, I*E^((2*I)*(a + b*x))]))/b","A",1
333,0,0,18,5.0672687,"\int \frac{\tanh ^{-1}(\cot (a+b x))}{e+f x} \, dx","Integrate[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,"Integrate[ArcTanh[Cot[a + b*x]]/(e + f*x), x]","A",-1
334,1,339,391,0.9721876,"\int x^2 \tanh ^{-1}(c+d \cot (a+b x)) \, dx","Integrate[x^2*ArcTanh[c + d*Cot[a + b*x]],x]","\frac{1}{3} x^3 \tanh ^{-1}(d \cot (a+b x)+c)+\frac{4 b^3 x^3 \log \left(1-\frac{(c+i d-1) e^{2 i (a+b x)}}{c-i d-1}\right)-4 b^3 x^3 \log \left(1-\frac{(c+i d+1) e^{2 i (a+b x)}}{c-i d+1}\right)-6 i b^2 x^2 \text{Li}_2\left(\frac{(c+i d-1) e^{2 i (a+b x)}}{c-i d-1}\right)+6 i b^2 x^2 \text{Li}_2\left(\frac{(c+i d+1) e^{2 i (a+b x)}}{c-i d+1}\right)+6 b x \text{Li}_3\left(\frac{(c+i d-1) e^{2 i (a+b x)}}{c-i d-1}\right)-6 b x \text{Li}_3\left(\frac{(c+i d+1) e^{2 i (a+b x)}}{c-i d+1}\right)+3 i \text{Li}_4\left(\frac{(c+i d-1) e^{2 i (a+b x)}}{c-i d-1}\right)-3 i \text{Li}_4\left(\frac{(c+i d+1) e^{2 i (a+b x)}}{c-i d+1}\right)}{24 b^3}","\frac{i \text{Li}_4\left(\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{8 b^3}-\frac{i \text{Li}_4\left(\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{8 b^3}+\frac{x \text{Li}_3\left(\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b^2}-\frac{x \text{Li}_3\left(\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b^2}-\frac{i x^2 \text{Li}_2\left(\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{Li}_2\left(\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 + (4*b^3*x^3*Log[1 - ((-1 + c + I*d)*E^((2*I)*(a + b*x)))/(-1 + c - I*d)] - 4*b^3*x^3*Log[1 - ((1 + c + I*d)*E^((2*I)*(a + b*x)))/(1 + c - I*d)] - (6*I)*b^2*x^2*PolyLog[2, ((-1 + c + I*d)*E^((2*I)*(a + b*x)))/(-1 + c - I*d)] + (6*I)*b^2*x^2*PolyLog[2, ((1 + c + I*d)*E^((2*I)*(a + b*x)))/(1 + c - I*d)] + 6*b*x*PolyLog[3, ((-1 + c + I*d)*E^((2*I)*(a + b*x)))/(-1 + c - I*d)] - 6*b*x*PolyLog[3, ((1 + c + I*d)*E^((2*I)*(a + b*x)))/(1 + c - I*d)] + (3*I)*PolyLog[4, ((-1 + c + I*d)*E^((2*I)*(a + b*x)))/(-1 + c - I*d)] - (3*I)*PolyLog[4, ((1 + c + I*d)*E^((2*I)*(a + b*x)))/(1 + c - I*d)])/(24*b^3)","A",1
335,1,253,293,0.5668574,"\int x \tanh ^{-1}(c+d \cot (a+b x)) \, dx","Integrate[x*ArcTanh[c + d*Cot[a + b*x]],x]","\frac{1}{2} x^2 \tanh ^{-1}(d \cot (a+b x)+c)+\frac{2 b^2 x^2 \log \left(1-\frac{(c+i d-1) e^{2 i (a+b x)}}{c-i d-1}\right)-2 b^2 x^2 \log \left(1-\frac{(c+i d+1) e^{2 i (a+b x)}}{c-i d+1}\right)-2 i b x \text{Li}_2\left(\frac{(c+i d-1) e^{2 i (a+b x)}}{c-i d-1}\right)+2 i b x \text{Li}_2\left(\frac{(c+i d+1) e^{2 i (a+b x)}}{c-i d+1}\right)+\text{Li}_3\left(\frac{(c+i d-1) e^{2 i (a+b x)}}{c-i d-1}\right)-\text{Li}_3\left(\frac{(c+i d+1) e^{2 i (a+b x)}}{c-i d+1}\right)}{8 b^2}","\frac{\text{Li}_3\left(\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{8 b^2}-\frac{\text{Li}_3\left(\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{Li}_2\left(\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b}+\frac{i x \text{Li}_2\left(\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 + (2*b^2*x^2*Log[1 - ((-1 + c + I*d)*E^((2*I)*(a + b*x)))/(-1 + c - I*d)] - 2*b^2*x^2*Log[1 - ((1 + c + I*d)*E^((2*I)*(a + b*x)))/(1 + c - I*d)] - (2*I)*b*x*PolyLog[2, ((-1 + c + I*d)*E^((2*I)*(a + b*x)))/(-1 + c - I*d)] + (2*I)*b*x*PolyLog[2, ((1 + c + I*d)*E^((2*I)*(a + b*x)))/(1 + c - I*d)] + PolyLog[3, ((-1 + c + I*d)*E^((2*I)*(a + b*x)))/(-1 + c - I*d)] - PolyLog[3, ((1 + c + I*d)*E^((2*I)*(a + b*x)))/(1 + c - I*d)])/(8*b^2)","A",1
336,1,4463,194,31.7077051,"\int \tanh ^{-1}(c+d \cot (a+b x)) \, dx","Integrate[ArcTanh[c + d*Cot[a + b*x]],x]","\text{Result too large to show}","-\frac{i \text{Li}_2\left(\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b}+\frac{i \text{Li}_2\left(\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]] - (d*(a*Log[-(Sec[(a + b*x)/2]^2*(d*Cos[a + b*x] + (-1 + c)*Sin[a + b*x]))] - a*Log[-(Sec[(a + b*x)/2]^2*(d*Cos[a + b*x] + Sin[a + b*x] + c*Sin[a + b*x]))] - (a + b*x)*Log[-((-1 + c + Sqrt[1 - 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2]] - I*Log[(d*(-I + Tan[(a + b*x)/2]))/(-1 + c - I*d + Sqrt[1 - 2*c + c^2 + d^2])]*Log[-((-1 + c + Sqrt[1 - 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2]] + I*Log[(d*(I + Tan[(a + b*x)/2]))/(-1 + c + I*d + Sqrt[1 - 2*c + c^2 + d^2])]*Log[-((-1 + c + Sqrt[1 - 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2]] + (a + b*x)*Log[-((1 + c + Sqrt[1 + 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2]] + I*Log[(d*(-I + Tan[(a + b*x)/2]))/(1 + c - I*d + Sqrt[1 + 2*c + c^2 + d^2])]*Log[-((1 + c + Sqrt[1 + 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2]] - I*Log[(d*(I + Tan[(a + b*x)/2]))/(1 + c + I*d + Sqrt[1 + 2*c + c^2 + d^2])]*Log[-((1 + c + Sqrt[1 + 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2]] - (a + b*x)*Log[(1 - c + Sqrt[1 - 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/d] - I*Log[-((d*(-I + Tan[(a + b*x)/2]))/(1 - c + I*d + Sqrt[1 - 2*c + c^2 + d^2]))]*Log[(1 - c + Sqrt[1 - 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/d] + I*Log[-((d*(I + Tan[(a + b*x)/2]))/(1 - c - I*d + Sqrt[1 - 2*c + c^2 + d^2]))]*Log[(1 - c + Sqrt[1 - 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/d] + (a + b*x)*Log[(-1 - c + Sqrt[1 + 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/d] + I*Log[-((d*(-I + Tan[(a + b*x)/2]))/(-1 - c + I*d + Sqrt[1 + 2*c + c^2 + d^2]))]*Log[(-1 - c + Sqrt[1 + 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/d] - I*Log[-((d*(I + Tan[(a + b*x)/2]))/(-1 - c - I*d + Sqrt[1 + 2*c + c^2 + d^2]))]*Log[(-1 - c + Sqrt[1 + 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/d] - I*PolyLog[2, (-1 + c + Sqrt[1 - 2*c + c^2 + d^2] - d*Tan[(a + b*x)/2])/(-1 + c - I*d + Sqrt[1 - 2*c + c^2 + d^2])] + I*PolyLog[2, (-1 + c + Sqrt[1 - 2*c + c^2 + d^2] - d*Tan[(a + b*x)/2])/(-1 + c + I*d + Sqrt[1 - 2*c + c^2 + d^2])] - I*PolyLog[2, (1 + c - Sqrt[1 + 2*c + c^2 + d^2] - d*Tan[(a + b*x)/2])/(1 + c + I*d - Sqrt[1 + 2*c + c^2 + d^2])] + I*PolyLog[2, (1 + c + Sqrt[1 + 2*c + c^2 + d^2] - d*Tan[(a + b*x)/2])/(1 + c - I*d + Sqrt[1 + 2*c + c^2 + d^2])] - I*PolyLog[2, (1 + c + Sqrt[1 + 2*c + c^2 + d^2] - d*Tan[(a + b*x)/2])/(1 + c + I*d + Sqrt[1 + 2*c + c^2 + d^2])] + I*PolyLog[2, (1 - c + Sqrt[1 - 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/(1 - c - I*d + Sqrt[1 - 2*c + c^2 + d^2])] - I*PolyLog[2, (1 - c + Sqrt[1 - 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/(1 - c + I*d + Sqrt[1 - 2*c + c^2 + d^2])] + I*PolyLog[2, (-1 - c + Sqrt[1 + 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/(-1 - c + I*d + Sqrt[1 + 2*c + c^2 + d^2])])*((2*a)/(b*(1 - c^2 - d^2 - Cos[2*(a + b*x)] + c^2*Cos[2*(a + b*x)] - d^2*Cos[2*(a + b*x)] - 2*c*d*Sin[2*(a + b*x)])) - (2*(a + b*x))/(b*(1 - c^2 - d^2 - Cos[2*(a + b*x)] + c^2*Cos[2*(a + b*x)] - d^2*Cos[2*(a + b*x)] - 2*c*d*Sin[2*(a + b*x)]))))/(-Log[-((-1 + c + Sqrt[1 - 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2]] + Log[-((1 + c + Sqrt[1 + 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2]] - Log[(1 - c + Sqrt[1 - 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/d] + Log[(-1 - c + Sqrt[1 + 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/d] - ((I/2)*Log[-((-1 + c + Sqrt[1 - 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2]]*Sec[(a + b*x)/2]^2)/(-I + Tan[(a + b*x)/2]) + ((I/2)*Log[-((1 + c + Sqrt[1 + 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2]]*Sec[(a + b*x)/2]^2)/(-I + Tan[(a + b*x)/2]) - ((I/2)*Log[(1 - c + Sqrt[1 - 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/d]*Sec[(a + b*x)/2]^2)/(-I + Tan[(a + b*x)/2]) + ((I/2)*Log[(-1 - c + Sqrt[1 + 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/d]*Sec[(a + b*x)/2]^2)/(-I + Tan[(a + b*x)/2]) + ((I/2)*Log[-((-1 + c + Sqrt[1 - 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2]]*Sec[(a + b*x)/2]^2)/(I + Tan[(a + b*x)/2]) - ((I/2)*Log[-((1 + c + Sqrt[1 + 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2]]*Sec[(a + b*x)/2]^2)/(I + Tan[(a + b*x)/2]) + ((I/2)*Log[(1 - c + Sqrt[1 - 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/d]*Sec[(a + b*x)/2]^2)/(I + Tan[(a + b*x)/2]) - ((I/2)*Log[(-1 - c + Sqrt[1 + 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/d]*Sec[(a + b*x)/2]^2)/(I + Tan[(a + b*x)/2]) - ((a + b*x)*Sec[(a + b*x)/2]^2)/(2*(-((-1 + c + Sqrt[1 - 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2])) - ((I/2)*Log[(d*(-I + Tan[(a + b*x)/2]))/(-1 + c - I*d + Sqrt[1 - 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(-((-1 + c + Sqrt[1 - 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2]) + ((I/2)*Log[(d*(I + Tan[(a + b*x)/2]))/(-1 + c + I*d + Sqrt[1 - 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(-((-1 + c + Sqrt[1 - 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2]) + ((a + b*x)*Sec[(a + b*x)/2]^2)/(2*(-((1 + c + Sqrt[1 + 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2])) + ((I/2)*Log[(d*(-I + Tan[(a + b*x)/2]))/(1 + c - I*d + Sqrt[1 + 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(-((1 + c + Sqrt[1 + 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2]) - ((I/2)*Log[(d*(I + Tan[(a + b*x)/2]))/(1 + c + I*d + Sqrt[1 + 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(-((1 + c + Sqrt[1 + 2*c + c^2 + d^2])/d) + Tan[(a + b*x)/2]) - ((I/2)*d*Log[1 - (-1 + c + Sqrt[1 - 2*c + c^2 + d^2] - d*Tan[(a + b*x)/2])/(-1 + c - I*d + Sqrt[1 - 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(-1 + c + Sqrt[1 - 2*c + c^2 + d^2] - d*Tan[(a + b*x)/2]) + ((I/2)*d*Log[1 - (-1 + c + Sqrt[1 - 2*c + c^2 + d^2] - d*Tan[(a + b*x)/2])/(-1 + c + I*d + Sqrt[1 - 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(-1 + c + Sqrt[1 - 2*c + c^2 + d^2] - d*Tan[(a + b*x)/2]) - ((I/2)*d*Log[1 - (1 + c - Sqrt[1 + 2*c + c^2 + d^2] - d*Tan[(a + b*x)/2])/(1 + c + I*d - Sqrt[1 + 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(1 + c - Sqrt[1 + 2*c + c^2 + d^2] - d*Tan[(a + b*x)/2]) + ((I/2)*d*Log[1 - (1 + c + Sqrt[1 + 2*c + c^2 + d^2] - d*Tan[(a + b*x)/2])/(1 + c - I*d + Sqrt[1 + 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(1 + c + Sqrt[1 + 2*c + c^2 + d^2] - d*Tan[(a + b*x)/2]) - ((I/2)*d*Log[1 - (1 + c + Sqrt[1 + 2*c + c^2 + d^2] - d*Tan[(a + b*x)/2])/(1 + c + I*d + Sqrt[1 + 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(1 + c + Sqrt[1 + 2*c + c^2 + d^2] - d*Tan[(a + b*x)/2]) - (d*(a + b*x)*Sec[(a + b*x)/2]^2)/(2*(1 - c + Sqrt[1 - 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])) - ((I/2)*d*Log[-((d*(-I + Tan[(a + b*x)/2]))/(1 - c + I*d + Sqrt[1 - 2*c + c^2 + d^2]))]*Sec[(a + b*x)/2]^2)/(1 - c + Sqrt[1 - 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2]) + ((I/2)*d*Log[-((d*(I + Tan[(a + b*x)/2]))/(1 - c - I*d + Sqrt[1 - 2*c + c^2 + d^2]))]*Sec[(a + b*x)/2]^2)/(1 - c + Sqrt[1 - 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2]) - ((I/2)*d*Log[1 - (1 - c + Sqrt[1 - 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/(1 - c - I*d + Sqrt[1 - 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(1 - c + Sqrt[1 - 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2]) + ((I/2)*d*Log[1 - (1 - c + Sqrt[1 - 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/(1 - c + I*d + Sqrt[1 - 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(1 - c + Sqrt[1 - 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2]) + (d*(a + b*x)*Sec[(a + b*x)/2]^2)/(2*(-1 - c + Sqrt[1 + 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])) + ((I/2)*d*Log[-((d*(-I + Tan[(a + b*x)/2]))/(-1 - c + I*d + Sqrt[1 + 2*c + c^2 + d^2]))]*Sec[(a + b*x)/2]^2)/(-1 - c + Sqrt[1 + 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2]) - ((I/2)*d*Log[-((d*(I + Tan[(a + b*x)/2]))/(-1 - c - I*d + Sqrt[1 + 2*c + c^2 + d^2]))]*Sec[(a + b*x)/2]^2)/(-1 - c + Sqrt[1 + 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2]) - ((I/2)*d*Log[1 - (-1 - c + Sqrt[1 + 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2])/(-1 - c + I*d + Sqrt[1 + 2*c + c^2 + d^2])]*Sec[(a + b*x)/2]^2)/(-1 - c + Sqrt[1 + 2*c + c^2 + d^2] + d*Tan[(a + b*x)/2]) - (a*Cos[(a + b*x)/2]^2*(-(Sec[(a + b*x)/2]^2*((-1 + c)*Cos[a + b*x] - d*Sin[a + b*x])) - Sec[(a + b*x)/2]^2*(d*Cos[a + b*x] + (-1 + c)*Sin[a + b*x])*Tan[(a + b*x)/2]))/(d*Cos[a + b*x] + (-1 + c)*Sin[a + b*x]) + (a*Cos[(a + b*x)/2]^2*(-(Sec[(a + b*x)/2]^2*(Cos[a + b*x] + c*Cos[a + b*x] - d*Sin[a + b*x])) - Sec[(a + b*x)/2]^2*(d*Cos[a + b*x] + Sin[a + b*x] + c*Sin[a + b*x])*Tan[(a + b*x)/2]))/(d*Cos[a + b*x] + Sin[a + b*x] + c*Sin[a + b*x]))","B",0
337,0,0,18,5.2575258,"\int \frac{\tanh ^{-1}(c+d \cot (a+b x))}{x} \, dx","Integrate[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,"Integrate[ArcTanh[c + d*Cot[a + b*x]]/x, x]","A",-1
338,1,155,168,0.4574267,"\int x^2 \tanh ^{-1}(1+i d+d \cot (a+b x)) \, dx","Integrate[x^2*ArcTanh[1 + I*d + d*Cot[a + b*x]],x]","\frac{1}{3} x^3 \tanh ^{-1}(d \cot (a+b x)+i d+1)-\frac{4 b^3 x^3 \log \left(1+\frac{i e^{-2 i (a+b x)}}{d-i}\right)+6 i b^2 x^2 \text{Li}_2\left(-\frac{i e^{-2 i (a+b x)}}{d-i}\right)+6 b x \text{Li}_3\left(-\frac{i e^{-2 i (a+b x)}}{d-i}\right)-3 i \text{Li}_4\left(-\frac{i e^{-2 i (a+b x)}}{d-i}\right)}{24 b^3}","-\frac{i \text{Li}_4\left((i d+1) e^{2 i a+2 i b x}\right)}{8 b^3}-\frac{x \text{Li}_3\left((i d+1) e^{2 i a+2 i b x}\right)}{4 b^2}+\frac{i x^2 \text{Li}_2\left((i d+1) 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,"(x^3*ArcTanh[1 + I*d + d*Cot[a + b*x]])/3 - (4*b^3*x^3*Log[1 + I/((-I + d)*E^((2*I)*(a + b*x)))] + (6*I)*b^2*x^2*PolyLog[2, (-I)/((-I + d)*E^((2*I)*(a + b*x)))] + 6*b*x*PolyLog[3, (-I)/((-I + d)*E^((2*I)*(a + b*x)))] - (3*I)*PolyLog[4, (-I)/((-I + d)*E^((2*I)*(a + b*x)))])/(24*b^3)","A",1
339,1,119,132,0.3157328,"\int x \tanh ^{-1}(1+i d+d \cot (a+b x)) \, dx","Integrate[x*ArcTanh[1 + I*d + d*Cot[a + b*x]],x]","\frac{1}{2} x^2 \tanh ^{-1}(d \cot (a+b x)+i d+1)-\frac{2 b^2 x^2 \log \left(1+\frac{i e^{-2 i (a+b x)}}{d-i}\right)+2 i b x \text{Li}_2\left(-\frac{i e^{-2 i (a+b x)}}{d-i}\right)+\text{Li}_3\left(-\frac{i e^{-2 i (a+b x)}}{d-i}\right)}{8 b^2}","-\frac{\text{Li}_3\left((i d+1) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{Li}_2\left((i d+1) 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,"(x^2*ArcTanh[1 + I*d + d*Cot[a + b*x]])/2 - (2*b^2*x^2*Log[1 + I/((-I + d)*E^((2*I)*(a + b*x)))] + (2*I)*b*x*PolyLog[2, (-I)/((-I + d)*E^((2*I)*(a + b*x)))] + PolyLog[3, (-I)/((-I + d)*E^((2*I)*(a + b*x)))])/(8*b^2)","A",1
340,1,709,93,39.2538786,"\int \tanh ^{-1}(1+i d+d \cot (a+b x)) \, dx","Integrate[ArcTanh[1 + I*d + d*Cot[a + b*x]],x]","\frac{x \csc ^2(a+b x) (\cos (b x)-i \sin (b x)) (\cos (b x)+i \sin (b x)) \left(i \text{Li}_2\left(\frac{(\cos (a)-i \sin (a)) ((-i d-2) \cos (a)+d \sin (a)) (\tan (b x)+i)}{2 (d-i)}\right)-i \text{Li}_2\left(\frac{1}{2} \sec (b x) ((i d+2) \cos (a)-d \sin (a)) (\cos (a+b x)+i \sin (a+b x))\right)+i \log (1-i \tan (b x)) \log \left(\frac{(\cos (a)-i \sin (a)) \sec (b x) (d \cos (a+b x)+(2+i d) \sin (a+b x))}{2 (d-i)}\right)-i \log (1+i \tan (b x)) \log \left(\frac{1}{2} (\sin (a)-i \cos (a)) \sec (b x) (d \cos (a+b x)+(2+i d) \sin (a+b x))\right)+i \text{Li}_2(i \sin (2 b x)-\cos (2 b x))+2 b x \log (2 \cos (b x) (\cos (b x)-i \sin (b x)))\right)}{(\cot (a+b x)+i) (d \cot (a+b x)+i d+2) \left(\frac{(d-2 i) \cos (a+b x) (\log (1-i \tan (b x))-\log (1+i \tan (b x)))}{d \cos (a+b x)+(2+i d) \sin (a+b x)}+\frac{d \sin (a+b x) (\log (1-i \tan (b x))-\log (1+i \tan (b x)))}{(d-2 i) \sin (a+b x)-i d \cos (a+b x)}+\log \left(1+\frac{1}{2} \sec (b x) (d \sin (a)+(-2-i d) \cos (a)) (\cos (a+b x)+i \sin (a+b x))\right)-\log \left(\frac{1}{2} (\sin (a)-i \cos (a)) \sec (b x) (d \cos (a+b x)+(2+i d) \sin (a+b x))\right)-i \tan (b x) \log \left(1+\frac{1}{2} \sec (b x) (d \sin (a)+(-2-i d) \cos (a)) (\cos (a+b x)+i \sin (a+b x))\right)+i \tan (b x) \log \left(\frac{1}{2} (\sin (a)-i \cos (a)) \sec (b x) (d \cos (a+b x)+(2+i d) \sin (a+b x))\right)+2 i b x+2 b x \tan (b x)-i \tan (b x) \log (1-i \tan (b x))+i \tan (b x) \log (1+i \tan (b x))\right)}+x \tanh ^{-1}(d \cot (a+b x)+i d+1)","\frac{i \text{Li}_2\left((i d+1) 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,"x*ArcTanh[1 + I*d + d*Cot[a + b*x]] + (x*Csc[a + b*x]^2*(2*b*x*Log[2*Cos[b*x]*(Cos[b*x] - I*Sin[b*x])] + I*Log[(Sec[b*x]*(Cos[a] - I*Sin[a])*(d*Cos[a + b*x] + (2 + I*d)*Sin[a + b*x]))/(2*(-I + d))]*Log[1 - I*Tan[b*x]] - I*Log[(Sec[b*x]*((-I)*Cos[a] + Sin[a])*(d*Cos[a + b*x] + (2 + I*d)*Sin[a + b*x]))/2]*Log[1 + I*Tan[b*x]] + I*PolyLog[2, -Cos[2*b*x] + I*Sin[2*b*x]] - I*PolyLog[2, (Sec[b*x]*((2 + I*d)*Cos[a] - d*Sin[a])*(Cos[a + b*x] + I*Sin[a + b*x]))/2] + I*PolyLog[2, ((Cos[a] - I*Sin[a])*((-2 - I*d)*Cos[a] + d*Sin[a])*(I + Tan[b*x]))/(2*(-I + d))])*(Cos[b*x] - I*Sin[b*x])*(Cos[b*x] + I*Sin[b*x]))/((I + Cot[a + b*x])*(2 + I*d + d*Cot[a + b*x])*((2*I)*b*x + Log[1 + (Sec[b*x]*((-2 - I*d)*Cos[a] + d*Sin[a])*(Cos[a + b*x] + I*Sin[a + b*x]))/2] - Log[(Sec[b*x]*((-I)*Cos[a] + Sin[a])*(d*Cos[a + b*x] + (2 + I*d)*Sin[a + b*x]))/2] + ((-2*I + d)*Cos[a + b*x]*(Log[1 - I*Tan[b*x]] - Log[1 + I*Tan[b*x]]))/(d*Cos[a + b*x] + (2 + I*d)*Sin[a + b*x]) + (d*(Log[1 - I*Tan[b*x]] - Log[1 + I*Tan[b*x]])*Sin[a + b*x])/((-I)*d*Cos[a + b*x] + (-2*I + d)*Sin[a + b*x]) + 2*b*x*Tan[b*x] - I*Log[1 + (Sec[b*x]*((-2 - I*d)*Cos[a] + d*Sin[a])*(Cos[a + b*x] + I*Sin[a + b*x]))/2]*Tan[b*x] + I*Log[(Sec[b*x]*((-I)*Cos[a] + Sin[a])*(d*Cos[a + b*x] + (2 + I*d)*Sin[a + b*x]))/2]*Tan[b*x] - I*Log[1 - I*Tan[b*x]]*Tan[b*x] + I*Log[1 + I*Tan[b*x]]*Tan[b*x]))","B",0
341,0,0,23,1.0656471,"\int \frac{\tanh ^{-1}(1+i d+d \cot (a+b x))}{x} \, dx","Integrate[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,"Integrate[ArcTanh[1 + I*d + d*Cot[a + b*x]]/x, x]","A",-1
342,1,155,169,0.4347907,"\int x^2 \tanh ^{-1}(1-i d-d \cot (a+b x)) \, dx","Integrate[x^2*ArcTanh[1 - I*d - d*Cot[a + b*x]],x]","\frac{1}{3} x^3 \tanh ^{-1}(d (-\cot (a+b x))-i d+1)-\frac{4 b^3 x^3 \log \left(1+\frac{e^{-2 i (a+b x)}}{-1+i d}\right)+6 i b^2 x^2 \text{Li}_2\left(\frac{i e^{-2 i (a+b x)}}{d+i}\right)+6 b x \text{Li}_3\left(\frac{i e^{-2 i (a+b x)}}{d+i}\right)-3 i \text{Li}_4\left(\frac{i e^{-2 i (a+b x)}}{d+i}\right)}{24 b^3}","-\frac{i \text{Li}_4\left((1-i d) e^{2 i a+2 i b x}\right)}{8 b^3}-\frac{x \text{Li}_3\left((1-i d) e^{2 i a+2 i b x}\right)}{4 b^2}+\frac{i x^2 \text{Li}_2\left((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,"(x^3*ArcTanh[1 - I*d - d*Cot[a + b*x]])/3 - (4*b^3*x^3*Log[1 + 1/((-1 + I*d)*E^((2*I)*(a + b*x)))] + (6*I)*b^2*x^2*PolyLog[2, I/((I + d)*E^((2*I)*(a + b*x)))] + 6*b*x*PolyLog[3, I/((I + d)*E^((2*I)*(a + b*x)))] - (3*I)*PolyLog[4, I/((I + d)*E^((2*I)*(a + b*x)))])/(24*b^3)","A",1
343,1,119,133,0.3073252,"\int x \tanh ^{-1}(1-i d-d \cot (a+b x)) \, dx","Integrate[x*ArcTanh[1 - I*d - d*Cot[a + b*x]],x]","\frac{1}{2} x^2 \tanh ^{-1}(d (-\cot (a+b x))-i d+1)-\frac{2 b^2 x^2 \log \left(1+\frac{e^{-2 i (a+b x)}}{-1+i d}\right)+2 i b x \text{Li}_2\left(\frac{i e^{-2 i (a+b x)}}{d+i}\right)+\text{Li}_3\left(\frac{i e^{-2 i (a+b x)}}{d+i}\right)}{8 b^2}","-\frac{\text{Li}_3\left((1-i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{Li}_2\left((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,"(x^2*ArcTanh[1 - I*d - d*Cot[a + b*x]])/2 - (2*b^2*x^2*Log[1 + 1/((-1 + I*d)*E^((2*I)*(a + b*x)))] + (2*I)*b*x*PolyLog[2, I/((I + d)*E^((2*I)*(a + b*x)))] + PolyLog[3, I/((I + d)*E^((2*I)*(a + b*x)))])/(8*b^2)","A",1
344,1,605,94,30.0100188,"\int \tanh ^{-1}(1-i d-d \cot (a+b x)) \, dx","Integrate[ArcTanh[1 - I*d - d*Cot[a + b*x]],x]","\frac{x \csc ^2(a+b x) (\cos (b x)-i \sin (b x)) (\cos (b x)+i \sin (b x)) \left(i \text{Li}_2\left(\frac{(\cos (a)-i \sin (a)) ((2-i d) \cos (a)+d \sin (a)) (\tan (b x)+i)}{2 (d+i)}\right)-i \text{Li}_2\left(\frac{1}{2} \sec (b x) ((2-i d) \cos (a)+d \sin (a)) (\cos (a+b x)+i \sin (a+b x))\right)+i \log (1-i \tan (b x)) \log \left(\frac{(\cos (a)-i \sin (a)) \sec (b x) (d \cos (a+b x)+i (d+2 i) \sin (a+b x))}{2 (d+i)}\right)-i \log (1+i \tan (b x)) \log \left(\frac{i \sec (b x) (d \cos (a+b x)+i (d+2 i) \sin (a+b x))}{2 \cos (a)-2 i \sin (a)}\right)+i \text{Li}_2(i \sin (2 b x)-\cos (2 b x))+2 b x \log (2 \cos (b x) (\cos (b x)-i \sin (b x)))\right)}{(\cot (a+b x)+i) (d \cot (a+b x)+i d-2) \left(\frac{\sec ^2(b x) \log \left(\frac{i \sec (b x) (d \cos (a+b x)+i (d+2 i) \sin (a+b x))}{2 \cos (a)-2 i \sin (a)}\right)}{1+i \tan (b x)}-\frac{\sec (b x) (i d \sin (a)+(d+2 i) \cos (a)) \log (1-i \tan (b x))}{d \cos (a+b x)+i (d+2 i) \sin (a+b x)}+\frac{\sec (b x) (i d \sin (a)+(d+2 i) \cos (a)) \log (1+i \tan (b x))}{d \cos (a+b x)+i (d+2 i) \sin (a+b x)}+i (\tan (b x)+i) \log \left(1-\frac{1}{2} \sec (b x) (d \sin (a)+(2-i d) \cos (a)) (\cos (a+b x)+i \sin (a+b x))\right)-2 b x (\tan (b x)+i)\right)}+x \tanh ^{-1}(d (-\cot (a+b x))-i d+1)","\frac{i \text{Li}_2\left((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,"x*ArcTanh[1 - I*d - d*Cot[a + b*x]] + (x*Csc[a + b*x]^2*(2*b*x*Log[2*Cos[b*x]*(Cos[b*x] - I*Sin[b*x])] + I*Log[(Sec[b*x]*(Cos[a] - I*Sin[a])*(d*Cos[a + b*x] + I*(2*I + d)*Sin[a + b*x]))/(2*(I + d))]*Log[1 - I*Tan[b*x]] - I*Log[(I*Sec[b*x]*(d*Cos[a + b*x] + I*(2*I + d)*Sin[a + b*x]))/(2*Cos[a] - (2*I)*Sin[a])]*Log[1 + I*Tan[b*x]] + I*PolyLog[2, -Cos[2*b*x] + I*Sin[2*b*x]] - I*PolyLog[2, (Sec[b*x]*((2 - I*d)*Cos[a] + d*Sin[a])*(Cos[a + b*x] + I*Sin[a + b*x]))/2] + I*PolyLog[2, ((Cos[a] - I*Sin[a])*((2 - I*d)*Cos[a] + d*Sin[a])*(I + Tan[b*x]))/(2*(I + d))])*(Cos[b*x] - I*Sin[b*x])*(Cos[b*x] + I*Sin[b*x]))/((I + Cot[a + b*x])*(-2 + I*d + d*Cot[a + b*x])*(-((Log[1 - I*Tan[b*x]]*Sec[b*x]*((2*I + d)*Cos[a] + I*d*Sin[a]))/(d*Cos[a + b*x] + I*(2*I + d)*Sin[a + b*x])) + (Log[1 + I*Tan[b*x]]*Sec[b*x]*((2*I + d)*Cos[a] + I*d*Sin[a]))/(d*Cos[a + b*x] + I*(2*I + d)*Sin[a + b*x]) + (Log[(I*Sec[b*x]*(d*Cos[a + b*x] + I*(2*I + d)*Sin[a + b*x]))/(2*Cos[a] - (2*I)*Sin[a])]*Sec[b*x]^2)/(1 + I*Tan[b*x]) - 2*b*x*(I + Tan[b*x]) + I*Log[1 - (Sec[b*x]*((2 - I*d)*Cos[a] + d*Sin[a])*(Cos[a + b*x] + I*Sin[a + b*x]))/2]*(I + Tan[b*x])))","B",0
345,0,0,24,1.0933057,"\int \frac{\tanh ^{-1}(1-i d-d \cot (a+b x))}{x} \, dx","Integrate[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,"Integrate[ArcTanh[1 - I*d - d*Cot[a + b*x]]/x, x]","A",-1
346,1,51,21,0.0340583,"\int \tanh ^{-1}\left(e^x\right) \, dx","Integrate[ArcTanh[E^x],x]","-\frac{\text{Li}_2\left(-e^x\right)}{2}+\frac{\text{Li}_2\left(e^x\right)}{2}+\frac{1}{2} x \log \left(1-e^x\right)-\frac{1}{2} x \log \left(e^x+1\right)+x \tanh ^{-1}\left(e^x\right)","\frac{\text{Li}_2\left(e^x\right)}{2}-\frac{\text{Li}_2\left(-e^x\right)}{2}",1,"x*ArcTanh[E^x] + (x*Log[1 - E^x])/2 - (x*Log[1 + E^x])/2 - PolyLog[2, -E^x]/2 + PolyLog[2, E^x]/2","B",1
347,1,71,43,0.027432,"\int x \tanh ^{-1}\left(e^x\right) \, dx","Integrate[x*ArcTanh[E^x],x]","\frac{1}{4} \left(-2 x \text{Li}_2\left(-e^x\right)+2 x \text{Li}_2\left(e^x\right)+2 \text{Li}_3\left(-e^x\right)-2 \text{Li}_3\left(e^x\right)+x^2 \log \left(1-e^x\right)-x^2 \log \left(e^x+1\right)+2 x^2 \tanh ^{-1}\left(e^x\right)\right)","-\frac{1}{2} x \text{Li}_2\left(-e^x\right)+\frac{x \text{Li}_2\left(e^x\right)}{2}+\frac{\text{Li}_3\left(-e^x\right)}{2}-\frac{\text{Li}_3\left(e^x\right)}{2}",1,"(2*x^2*ArcTanh[E^x] + x^2*Log[1 - E^x] - x^2*Log[1 + E^x] - 2*x*PolyLog[2, -E^x] + 2*x*PolyLog[2, E^x] + 2*PolyLog[3, -E^x] - 2*PolyLog[3, E^x])/4","A",1
348,1,93,58,0.026729,"\int x^2 \tanh ^{-1}\left(e^x\right) \, dx","Integrate[x^2*ArcTanh[E^x],x]","\frac{1}{6} \left(-3 x^2 \text{Li}_2\left(-e^x\right)+3 x^2 \text{Li}_2\left(e^x\right)+6 x \text{Li}_3\left(-e^x\right)-6 x \text{Li}_3\left(e^x\right)-6 \text{Li}_4\left(-e^x\right)+6 \text{Li}_4\left(e^x\right)+x^3 \log \left(1-e^x\right)-x^3 \log \left(e^x+1\right)+2 x^3 \tanh ^{-1}\left(e^x\right)\right)","-\frac{1}{2} x^2 \text{Li}_2\left(-e^x\right)+\frac{1}{2} x^2 \text{Li}_2\left(e^x\right)+x \text{Li}_3\left(-e^x\right)-x \text{Li}_3\left(e^x\right)-\text{Li}_4\left(-e^x\right)+\text{Li}_4\left(e^x\right)",1,"(2*x^3*ArcTanh[E^x] + x^3*Log[1 - E^x] - x^3*Log[1 + E^x] - 3*x^2*PolyLog[2, -E^x] + 3*x^2*PolyLog[2, E^x] + 6*x*PolyLog[3, -E^x] - 6*x*PolyLog[3, E^x] - 6*PolyLog[4, -E^x] + 6*PolyLog[4, E^x])/6","A",1
349,1,68,35,0.0802109,"\int \tanh ^{-1}\left(e^{a+b x}\right) \, dx","Integrate[ArcTanh[E^(a + b*x)],x]","\frac{-\text{Li}_2\left(-e^{a+b x}\right)+\text{Li}_2\left(e^{a+b x}\right)+b x \left(\log \left(1-e^{a+b x}\right)-\log \left(e^{a+b x}+1\right)+2 \tanh ^{-1}\left(e^{a+b x}\right)\right)}{2 b}","\frac{\text{Li}_2\left(e^{a+b x}\right)}{2 b}-\frac{\text{Li}_2\left(-e^{a+b x}\right)}{2 b}",1,"(b*x*(2*ArcTanh[E^(a + b*x)] + Log[1 - E^(a + b*x)] - Log[1 + E^(a + b*x)]) - PolyLog[2, -E^(a + b*x)] + PolyLog[2, E^(a + b*x)])/(2*b)","A",1
350,1,113,71,0.0511212,"\int x \tanh ^{-1}\left(e^{a+b x}\right) \, dx","Integrate[x*ArcTanh[E^(a + b*x)],x]","\frac{b^2 x^2 \log \left(1-e^{a+b x}\right)-b^2 x^2 \log \left(e^{a+b x}+1\right)+2 b^2 x^2 \tanh ^{-1}\left(e^{a+b x}\right)-2 b x \text{Li}_2\left(-e^{a+b x}\right)+2 b x \text{Li}_2\left(e^{a+b x}\right)+2 \text{Li}_3\left(-e^{a+b x}\right)-2 \text{Li}_3\left(e^{a+b x}\right)}{4 b^2}","\frac{\text{Li}_3\left(-e^{a+b x}\right)}{2 b^2}-\frac{\text{Li}_3\left(e^{a+b x}\right)}{2 b^2}-\frac{x \text{Li}_2\left(-e^{a+b x}\right)}{2 b}+\frac{x \text{Li}_2\left(e^{a+b x}\right)}{2 b}",1,"(2*b^2*x^2*ArcTanh[E^(a + b*x)] + b^2*x^2*Log[1 - E^(a + b*x)] - b^2*x^2*Log[1 + E^(a + b*x)] - 2*b*x*PolyLog[2, -E^(a + b*x)] + 2*b*x*PolyLog[2, E^(a + b*x)] + 2*PolyLog[3, -E^(a + b*x)] - 2*PolyLog[3, E^(a + b*x)])/(4*b^2)","A",1
351,1,149,101,0.0467314,"\int x^2 \tanh ^{-1}\left(e^{a+b x}\right) \, dx","Integrate[x^2*ArcTanh[E^(a + b*x)],x]","\frac{b^3 x^3 \log \left(1-e^{a+b x}\right)-b^3 x^3 \log \left(e^{a+b x}+1\right)+2 b^3 x^3 \tanh ^{-1}\left(e^{a+b x}\right)-3 b^2 x^2 \text{Li}_2\left(-e^{a+b x}\right)+3 b^2 x^2 \text{Li}_2\left(e^{a+b x}\right)+6 b x \text{Li}_3\left(-e^{a+b x}\right)-6 b x \text{Li}_3\left(e^{a+b x}\right)-6 \text{Li}_4\left(-e^{a+b x}\right)+6 \text{Li}_4\left(e^{a+b x}\right)}{6 b^3}","-\frac{\text{Li}_4\left(-e^{a+b x}\right)}{b^3}+\frac{\text{Li}_4\left(e^{a+b x}\right)}{b^3}+\frac{x \text{Li}_3\left(-e^{a+b x}\right)}{b^2}-\frac{x \text{Li}_3\left(e^{a+b x}\right)}{b^2}-\frac{x^2 \text{Li}_2\left(-e^{a+b x}\right)}{2 b}+\frac{x^2 \text{Li}_2\left(e^{a+b x}\right)}{2 b}",1,"(2*b^3*x^3*ArcTanh[E^(a + b*x)] + b^3*x^3*Log[1 - E^(a + b*x)] - b^3*x^3*Log[1 + E^(a + b*x)] - 3*b^2*x^2*PolyLog[2, -E^(a + b*x)] + 3*b^2*x^2*PolyLog[2, E^(a + b*x)] + 6*b*x*PolyLog[3, -E^(a + b*x)] - 6*b*x*PolyLog[3, E^(a + b*x)] - 6*PolyLog[4, -E^(a + b*x)] + 6*PolyLog[4, E^(a + b*x)])/(6*b^3)","A",1
352,1,108,168,0.0778946,"\int \tanh ^{-1}\left(a+b f^{c+d x}\right) \, dx","Integrate[ArcTanh[a + b*f^(c + d*x)],x]","\frac{\text{Li}_2\left(-\frac{b f^{c+d x}}{a-1}\right)-\text{Li}_2\left(-\frac{b f^{c+d x}}{a+1}\right)+d x \log (f) \left(\log \left(\frac{a+b f^{c+d x}-1}{a-1}\right)-\log \left(\frac{a+b f^{c+d x}+1}{a+1}\right)+2 \tanh ^{-1}\left(a+b f^{c+d x}\right)\right)}{2 d \log (f)}","\frac{\text{Li}_2\left(1-\frac{2}{b f^{c+d x}+a+1}\right)}{2 d \log (f)}-\frac{\text{Li}_2\left(1-\frac{2 b f^{c+d x}}{(1-a) \left(b f^{c+d x}+a+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,"(d*x*Log[f]*(2*ArcTanh[a + b*f^(c + d*x)] + Log[(-1 + a + b*f^(c + d*x))/(-1 + a)] - Log[(1 + a + b*f^(c + d*x))/(1 + a)]) + PolyLog[2, -((b*f^(c + d*x))/(-1 + a))] - PolyLog[2, -((b*f^(c + d*x))/(1 + a))])/(2*d*Log[f])","A",1
353,1,177,211,0.1204692,"\int x \tanh ^{-1}\left(a+b f^{c+d x}\right) \, dx","Integrate[x*ArcTanh[a + b*f^(c + d*x)],x]","\frac{d^2 x^2 \log ^2(f) \log \left(\frac{b f^{c+d x}}{a-1}+1\right)-d^2 x^2 \log ^2(f) \log \left(\frac{b f^{c+d x}}{a+1}+1\right)+2 d^2 x^2 \log ^2(f) \tanh ^{-1}\left(a+b f^{c+d x}\right)-2 \text{Li}_3\left(-\frac{b f^{c+d x}}{a-1}\right)+2 \text{Li}_3\left(-\frac{b f^{c+d x}}{a+1}\right)+2 d x \log (f) \text{Li}_2\left(-\frac{b f^{c+d x}}{a-1}\right)-2 d x \log (f) \text{Li}_2\left(-\frac{b f^{c+d x}}{a+1}\right)}{4 d^2 \log ^2(f)}","-\frac{\text{Li}_3\left(\frac{b f^{c+d x}}{1-a}\right)}{2 d^2 \log ^2(f)}+\frac{\text{Li}_3\left(-\frac{b f^{c+d x}}{a+1}\right)}{2 d^2 \log ^2(f)}+\frac{x \text{Li}_2\left(\frac{b f^{c+d x}}{1-a}\right)}{2 d \log (f)}-\frac{x \text{Li}_2\left(-\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,"(2*d^2*x^2*ArcTanh[a + b*f^(c + d*x)]*Log[f]^2 + d^2*x^2*Log[f]^2*Log[1 + (b*f^(c + d*x))/(-1 + a)] - d^2*x^2*Log[f]^2*Log[1 + (b*f^(c + d*x))/(1 + a)] + 2*d*x*Log[f]*PolyLog[2, -((b*f^(c + d*x))/(-1 + a))] - 2*d*x*Log[f]*PolyLog[2, -((b*f^(c + d*x))/(1 + a))] - 2*PolyLog[3, -((b*f^(c + d*x))/(-1 + a))] + 2*PolyLog[3, -((b*f^(c + d*x))/(1 + a))])/(4*d^2*Log[f]^2)","A",1
354,1,235,264,0.0854638,"\int x^2 \tanh ^{-1}\left(a+b f^{c+d x}\right) \, dx","Integrate[x^2*ArcTanh[a + b*f^(c + d*x)],x]","\frac{d^3 x^3 \log ^3(f) \log \left(\frac{b f^{c+d x}}{a-1}+1\right)-d^3 x^3 \log ^3(f) \log \left(\frac{b f^{c+d x}}{a+1}+1\right)+2 d^3 x^3 \log ^3(f) \tanh ^{-1}\left(a+b f^{c+d x}\right)+3 d^2 x^2 \log ^2(f) \text{Li}_2\left(-\frac{b f^{c+d x}}{a-1}\right)-3 d^2 x^2 \log ^2(f) \text{Li}_2\left(-\frac{b f^{c+d x}}{a+1}\right)+6 \text{Li}_4\left(-\frac{b f^{c+d x}}{a-1}\right)-6 \text{Li}_4\left(-\frac{b f^{c+d x}}{a+1}\right)-6 d x \log (f) \text{Li}_3\left(-\frac{b f^{c+d x}}{a-1}\right)+6 d x \log (f) \text{Li}_3\left(-\frac{b f^{c+d x}}{a+1}\right)}{6 d^3 \log ^3(f)}","\frac{\text{Li}_4\left(\frac{b f^{c+d x}}{1-a}\right)}{d^3 \log ^3(f)}-\frac{\text{Li}_4\left(-\frac{b f^{c+d x}}{a+1}\right)}{d^3 \log ^3(f)}-\frac{x \text{Li}_3\left(\frac{b f^{c+d x}}{1-a}\right)}{d^2 \log ^2(f)}+\frac{x \text{Li}_3\left(-\frac{b f^{c+d x}}{a+1}\right)}{d^2 \log ^2(f)}+\frac{x^2 \text{Li}_2\left(\frac{b f^{c+d x}}{1-a}\right)}{2 d \log (f)}-\frac{x^2 \text{Li}_2\left(-\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,"(2*d^3*x^3*ArcTanh[a + b*f^(c + d*x)]*Log[f]^3 + d^3*x^3*Log[f]^3*Log[1 + (b*f^(c + d*x))/(-1 + a)] - d^3*x^3*Log[f]^3*Log[1 + (b*f^(c + d*x))/(1 + a)] + 3*d^2*x^2*Log[f]^2*PolyLog[2, -((b*f^(c + d*x))/(-1 + a))] - 3*d^2*x^2*Log[f]^2*PolyLog[2, -((b*f^(c + d*x))/(1 + a))] - 6*d*x*Log[f]*PolyLog[3, -((b*f^(c + d*x))/(-1 + a))] + 6*d*x*Log[f]*PolyLog[3, -((b*f^(c + d*x))/(1 + a))] + 6*PolyLog[4, -((b*f^(c + d*x))/(-1 + a))] - 6*PolyLog[4, -((b*f^(c + d*x))/(1 + a))])/(6*d^3*Log[f]^3)","A",1
355,1,153,107,0.1735096,"\int e^{c (a+b x)} \tanh ^{-1}(\sinh (a c+b c x)) \, dx","Integrate[E^(c*(a + b*x))*ArcTanh[Sinh[a*c + b*c*x]],x]","\frac{\log \left(-2 e^{c (a+b x)}-e^{2 c (a+b x)}+1\right)+\log \left(2 e^{c (a+b x)}-e^{2 c (a+b x)}+1\right)-2 e^{c (a+b x)} \tanh ^{-1}\left(\frac{1}{2} e^{-c (a+b x)}-\frac{1}{2} e^{c (a+b x)}\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{e^{c (a+b x)}-1}{\sqrt{2}}\right)+2 \sqrt{2} \tanh ^{-1}\left(\frac{e^{c (a+b x)}+1}{\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{\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,"(-2*E^(c*(a + b*x))*ArcTanh[1/(2*E^(c*(a + b*x))) - E^(c*(a + b*x))/2] - 2*Sqrt[2]*ArcTanh[(-1 + E^(c*(a + b*x)))/Sqrt[2]] + 2*Sqrt[2]*ArcTanh[(1 + E^(c*(a + b*x)))/Sqrt[2]] + Log[1 - 2*E^(c*(a + b*x)) - E^(2*c*(a + b*x))] + Log[1 + 2*E^(c*(a + b*x)) - E^(2*c*(a + b*x))])/(2*b*c)","A",0
356,1,60,49,0.0881924,"\int e^{c (a+b x)} \tanh ^{-1}(\cosh (a c+b c x)) \, dx","Integrate[E^(c*(a + b*x))*ArcTanh[Cosh[a*c + b*c*x]],x]","\frac{\log \left(1-e^{2 c (a+b x)}\right)+e^{c (a+b x)} \tanh ^{-1}\left(\frac{1}{2} e^{-c (a+b x)} \left(e^{2 c (a+b x)}+1\right)\right)}{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^(c*(a + b*x))*ArcTanh[(1 + E^(2*c*(a + b*x)))/(2*E^(c*(a + b*x)))] + Log[1 - E^(2*c*(a + b*x))])/(b*c)","A",0
357,1,46,45,0.0883056,"\int e^{c (a+b x)} \tanh ^{-1}(\tanh (a c+b c x)) \, dx","Integrate[E^(c*(a + b*x))*ArcTanh[Tanh[a*c + b*c*x]],x]","\frac{e^{c (a+b x)} \left(\tanh ^{-1}\left(\frac{e^{2 c (a+b x)}-1}{e^{2 c (a+b x)}+1}\right)-1\right)}{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^(c*(a + b*x))*(-1 + ArcTanh[(-1 + E^(2*c*(a + b*x)))/(1 + E^(2*c*(a + b*x)))]))/(b*c)","A",0
358,1,46,45,0.0895114,"\int e^{c (a+b x)} \tanh ^{-1}(\coth (a c+b c x)) \, dx","Integrate[E^(c*(a + b*x))*ArcTanh[Coth[a*c + b*c*x]],x]","\frac{e^{c (a+b x)} \left(\tanh ^{-1}\left(\frac{e^{2 c (a+b x)}+1}{e^{2 c (a+b x)}-1}\right)-1\right)}{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^(c*(a + b*x))*(-1 + ArcTanh[(1 + E^(2*c*(a + b*x)))/(-1 + E^(2*c*(a + b*x)))]))/(b*c)","A",0
359,1,59,49,0.0842416,"\int e^{c (a+b x)} \tanh ^{-1}(\text{sech}(a c+b c x)) \, dx","Integrate[E^(c*(a + b*x))*ArcTanh[Sech[a*c + b*c*x]],x]","\frac{\log \left(1-e^{2 c (a+b x)}\right)+e^{c (a+b x)} \tanh ^{-1}\left(\frac{2 e^{c (a+b x)}}{e^{2 c (a+b x)}+1}\right)}{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^(c*(a + b*x))*ArcTanh[(2*E^(c*(a + b*x)))/(1 + E^(2*c*(a + b*x)))] + Log[1 - E^(2*c*(a + b*x))])/(b*c)","A",0
360,1,150,107,0.1711057,"\int e^{c (a+b x)} \tanh ^{-1}(\text{csch}(a c+b c x)) \, dx","Integrate[E^(c*(a + b*x))*ArcTanh[Csch[a*c + b*c*x]],x]","\frac{\log \left(-2 e^{c (a+b x)}-e^{2 c (a+b x)}+1\right)+\log \left(2 e^{c (a+b x)}-e^{2 c (a+b x)}+1\right)-2 \sqrt{2} \tanh ^{-1}\left(\frac{e^{c (a+b x)}-1}{\sqrt{2}}\right)+2 \sqrt{2} \tanh ^{-1}\left(\frac{e^{c (a+b x)}+1}{\sqrt{2}}\right)+2 e^{c (a+b x)} \tanh ^{-1}\left(\frac{2 e^{c (a+b x)}}{e^{2 c (a+b x)}-1}\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{\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,"(-2*Sqrt[2]*ArcTanh[(-1 + E^(c*(a + b*x)))/Sqrt[2]] + 2*Sqrt[2]*ArcTanh[(1 + E^(c*(a + b*x)))/Sqrt[2]] + 2*E^(c*(a + b*x))*ArcTanh[(2*E^(c*(a + b*x)))/(-1 + E^(2*c*(a + b*x)))] + Log[1 - 2*E^(c*(a + b*x)) - E^(2*c*(a + b*x))] + Log[1 + 2*E^(c*(a + b*x)) - E^(2*c*(a + b*x))])/(2*b*c)","A",0
361,1,114,136,0.2863817,"\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","Integrate[((a + b*ArcTanh[c*x^n])*(d + e*Log[f*x^m]))/x,x]","\frac{b c x^n \left(d+e \log \left(f x^m\right)\right) \, _3F_2\left(\frac{1}{2},\frac{1}{2},1;\frac{3}{2},\frac{3}{2};c^2 x^{2 n}\right)}{n}-\frac{b c e m x^n \, _4F_3\left(\frac{1}{2},\frac{1}{2},\frac{1}{2},1;\frac{3}{2},\frac{3}{2},\frac{3}{2};c^2 x^{2 n}\right)}{n^2}+\frac{1}{2} a \log (x) \left(2 d+2 e \log \left(f x^m\right)-e m \log (x)\right)","a d \log (x)+\frac{a e \log ^2\left(f x^m\right)}{2 m}-\frac{b d \text{Li}_2\left(-c x^n\right)}{2 n}+\frac{b d \text{Li}_2\left(c x^n\right)}{2 n}-\frac{b e \text{Li}_2\left(-c x^n\right) \log \left(f x^m\right)}{2 n}+\frac{b e \text{Li}_2\left(c x^n\right) \log \left(f x^m\right)}{2 n}+\frac{b e m \text{Li}_3\left(-c x^n\right)}{2 n^2}-\frac{b e m \text{Li}_3\left(c x^n\right)}{2 n^2}",1,"-((b*c*e*m*x^n*HypergeometricPFQ[{1/2, 1/2, 1/2, 1}, {3/2, 3/2, 3/2}, c^2*x^(2*n)])/n^2) + (b*c*x^n*HypergeometricPFQ[{1/2, 1/2, 1}, {3/2, 3/2}, c^2*x^(2*n)]*(d + e*Log[f*x^m]))/n + (a*Log[x]*(2*d - e*m*Log[x] + 2*e*Log[f*x^m]))/2","C",1