1,1,62,0,0.0870773,"\int \frac{\sec ^{-1}\left(a x^5\right)}{x} \, dx","Int[ArcSec[a*x^5]/x,x]","\frac{1}{10} i \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}\left(a x^5\right)}\right)+\frac{1}{10} i \sec ^{-1}\left(a x^5\right)^2-\frac{1}{5} \sec ^{-1}\left(a x^5\right) \log \left(1+e^{2 i \sec ^{-1}\left(a x^5\right)}\right)","\frac{1}{10} i \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}\left(a x^5\right)}\right)+\frac{1}{10} i \sec ^{-1}\left(a x^5\right)^2-\frac{1}{5} \sec ^{-1}\left(a x^5\right) \log \left(1+e^{2 i \sec ^{-1}\left(a x^5\right)}\right)",1,"(I/10)*ArcSec[a*x^5]^2 - (ArcSec[a*x^5]*Log[1 + E^((2*I)*ArcSec[a*x^5])])/5 + (I/10)*PolyLog[2, -E^((2*I)*ArcSec[a*x^5])]","A",7,6,10,0.6000,1,"{5218, 4626, 3719, 2190, 2279, 2391}"
2,1,58,0,0.0197305,"\int x^3 \sec ^{-1}\left(\sqrt{x}\right) \, dx","Int[x^3*ArcSec[Sqrt[x]],x]","\frac{1}{4} x^4 \sec ^{-1}\left(\sqrt{x}\right)-\frac{1}{28} (x-1)^{7/2}-\frac{3}{20} (x-1)^{5/2}-\frac{1}{4} (x-1)^{3/2}-\frac{\sqrt{x-1}}{4}","\frac{1}{4} x^4 \sec ^{-1}\left(\sqrt{x}\right)-\frac{1}{28} (x-1)^{7/2}-\frac{3}{20} (x-1)^{5/2}-\frac{1}{4} (x-1)^{3/2}-\frac{\sqrt{x-1}}{4}",1,"-Sqrt[-1 + x]/4 - (-1 + x)^(3/2)/4 - (3*(-1 + x)^(5/2))/20 - (-1 + x)^(7/2)/28 + (x^4*ArcSec[Sqrt[x]])/4","A",4,3,10,0.3000,1,"{5270, 12, 43}"
3,1,47,0,0.017687,"\int x^2 \sec ^{-1}\left(\sqrt{x}\right) \, dx","Int[x^2*ArcSec[Sqrt[x]],x]","\frac{1}{3} x^3 \sec ^{-1}\left(\sqrt{x}\right)-\frac{1}{15} (x-1)^{5/2}-\frac{2}{9} (x-1)^{3/2}-\frac{\sqrt{x-1}}{3}","\frac{1}{3} x^3 \sec ^{-1}\left(\sqrt{x}\right)-\frac{1}{15} (x-1)^{5/2}-\frac{2}{9} (x-1)^{3/2}-\frac{\sqrt{x-1}}{3}",1,"-Sqrt[-1 + x]/3 - (2*(-1 + x)^(3/2))/9 - (-1 + x)^(5/2)/15 + (x^3*ArcSec[Sqrt[x]])/3","A",4,3,10,0.3000,1,"{5270, 12, 43}"
4,1,36,0,0.0113633,"\int x \sec ^{-1}\left(\sqrt{x}\right) \, dx","Int[x*ArcSec[Sqrt[x]],x]","\frac{1}{2} x^2 \sec ^{-1}\left(\sqrt{x}\right)-\frac{1}{6} (x-1)^{3/2}-\frac{\sqrt{x-1}}{2}","\frac{1}{2} x^2 \sec ^{-1}\left(\sqrt{x}\right)-\frac{1}{6} (x-1)^{3/2}-\frac{\sqrt{x-1}}{2}",1,"-Sqrt[-1 + x]/2 - (-1 + x)^(3/2)/6 + (x^2*ArcSec[Sqrt[x]])/2","A",4,3,8,0.3750,1,"{5270, 12, 43}"
5,1,18,0,0.0043606,"\int \sec ^{-1}\left(\sqrt{x}\right) \, dx","Int[ArcSec[Sqrt[x]],x]","x \sec ^{-1}\left(\sqrt{x}\right)-\sqrt{x-1}","x \sec ^{-1}\left(\sqrt{x}\right)-\sqrt{x-1}",1,"-Sqrt[-1 + x] + x*ArcSec[Sqrt[x]]","A",3,3,6,0.5000,1,"{5268, 12, 32}"
6,1,56,0,0.0788201,"\int \frac{\sec ^{-1}\left(\sqrt{x}\right)}{x} \, dx","Int[ArcSec[Sqrt[x]]/x,x]","i \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}\left(\sqrt{x}\right)}\right)+i \sec ^{-1}\left(\sqrt{x}\right)^2-2 \sec ^{-1}\left(\sqrt{x}\right) \log \left(1+e^{2 i \sec ^{-1}\left(\sqrt{x}\right)}\right)","i \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}\left(\sqrt{x}\right)}\right)+i \sec ^{-1}\left(\sqrt{x}\right)^2-2 \sec ^{-1}\left(\sqrt{x}\right) \log \left(1+e^{2 i \sec ^{-1}\left(\sqrt{x}\right)}\right)",1,"I*ArcSec[Sqrt[x]]^2 - 2*ArcSec[Sqrt[x]]*Log[1 + E^((2*I)*ArcSec[Sqrt[x]])] + I*PolyLog[2, -E^((2*I)*ArcSec[Sqrt[x]])]","A",7,6,10,0.6000,1,"{5218, 4626, 3719, 2190, 2279, 2391}"
7,1,38,0,0.0156021,"\int \frac{\sec ^{-1}\left(\sqrt{x}\right)}{x^2} \, dx","Int[ArcSec[Sqrt[x]]/x^2,x]","\frac{\sqrt{x-1}}{2 x}+\frac{1}{2} \tan ^{-1}\left(\sqrt{x-1}\right)-\frac{\sec ^{-1}\left(\sqrt{x}\right)}{x}","\frac{\sqrt{x-1}}{2 x}+\frac{1}{2} \tan ^{-1}\left(\sqrt{x-1}\right)-\frac{\sec ^{-1}\left(\sqrt{x}\right)}{x}",1,"Sqrt[-1 + x]/(2*x) - ArcSec[Sqrt[x]]/x + ArcTan[Sqrt[-1 + x]]/2","A",5,5,10,0.5000,1,"{5270, 12, 51, 63, 203}"
8,1,54,0,0.018859,"\int \frac{\sec ^{-1}\left(\sqrt{x}\right)}{x^3} \, dx","Int[ArcSec[Sqrt[x]]/x^3,x]","\frac{\sqrt{x-1}}{8 x^2}-\frac{\sec ^{-1}\left(\sqrt{x}\right)}{2 x^2}+\frac{3 \sqrt{x-1}}{16 x}+\frac{3}{16} \tan ^{-1}\left(\sqrt{x-1}\right)","\frac{\sqrt{x-1}}{8 x^2}-\frac{\sec ^{-1}\left(\sqrt{x}\right)}{2 x^2}+\frac{3 \sqrt{x-1}}{16 x}+\frac{3}{16} \tan ^{-1}\left(\sqrt{x-1}\right)",1,"Sqrt[-1 + x]/(8*x^2) + (3*Sqrt[-1 + x])/(16*x) - ArcSec[Sqrt[x]]/(2*x^2) + (3*ArcTan[Sqrt[-1 + x]])/16","A",6,5,10,0.5000,1,"{5270, 12, 51, 63, 203}"
9,1,68,0,0.0236281,"\int \frac{\sec ^{-1}\left(\sqrt{x}\right)}{x^4} \, dx","Int[ArcSec[Sqrt[x]]/x^4,x]","\frac{5 \sqrt{x-1}}{72 x^2}+\frac{\sqrt{x-1}}{18 x^3}-\frac{\sec ^{-1}\left(\sqrt{x}\right)}{3 x^3}+\frac{5 \sqrt{x-1}}{48 x}+\frac{5}{48} \tan ^{-1}\left(\sqrt{x-1}\right)","\frac{5 \sqrt{x-1}}{72 x^2}+\frac{\sqrt{x-1}}{18 x^3}-\frac{\sec ^{-1}\left(\sqrt{x}\right)}{3 x^3}+\frac{5 \sqrt{x-1}}{48 x}+\frac{5}{48} \tan ^{-1}\left(\sqrt{x-1}\right)",1,"Sqrt[-1 + x]/(18*x^3) + (5*Sqrt[-1 + x])/(72*x^2) + (5*Sqrt[-1 + x])/(48*x) - ArcSec[Sqrt[x]]/(3*x^3) + (5*ArcTan[Sqrt[-1 + x]])/48","A",7,5,10,0.5000,1,"{5270, 12, 51, 63, 203}"
10,1,56,0,0.0424593,"\int x^2 \sec ^{-1}\left(\frac{a}{x}\right) \, dx","Int[x^2*ArcSec[a/x],x]","\frac{1}{9} a^3 \left(1-\frac{x^2}{a^2}\right)^{3/2}-\frac{1}{3} a^3 \sqrt{1-\frac{x^2}{a^2}}+\frac{1}{3} x^3 \cos ^{-1}\left(\frac{x}{a}\right)","\frac{1}{9} a^3 \left(1-\frac{x^2}{a^2}\right)^{3/2}-\frac{1}{3} a^3 \sqrt{1-\frac{x^2}{a^2}}+\frac{1}{3} x^3 \cos ^{-1}\left(\frac{x}{a}\right)",1,"-(a^3*Sqrt[1 - x^2/a^2])/3 + (a^3*(1 - x^2/a^2)^(3/2))/9 + (x^3*ArcCos[x/a])/3","A",5,4,10,0.4000,1,"{5264, 4628, 266, 43}"
11,1,47,0,0.0201988,"\int x \sec ^{-1}\left(\frac{a}{x}\right) \, dx","Int[x*ArcSec[a/x],x]","-\frac{1}{4} a x \sqrt{1-\frac{x^2}{a^2}}+\frac{1}{4} a^2 \sin ^{-1}\left(\frac{x}{a}\right)+\frac{1}{2} x^2 \cos ^{-1}\left(\frac{x}{a}\right)","-\frac{1}{4} a x \sqrt{1-\frac{x^2}{a^2}}+\frac{1}{4} a^2 \sin ^{-1}\left(\frac{x}{a}\right)+\frac{1}{2} x^2 \cos ^{-1}\left(\frac{x}{a}\right)",1,"-(a*x*Sqrt[1 - x^2/a^2])/4 + (x^2*ArcCos[x/a])/2 + (a^2*ArcSin[x/a])/4","A",4,4,8,0.5000,1,"{5264, 4628, 321, 216}"
12,1,26,0,0.0092175,"\int \sec ^{-1}\left(\frac{a}{x}\right) \, dx","Int[ArcSec[a/x],x]","x \cos ^{-1}\left(\frac{x}{a}\right)-a \sqrt{1-\frac{x^2}{a^2}}","x \cos ^{-1}\left(\frac{x}{a}\right)-a \sqrt{1-\frac{x^2}{a^2}}",1,"-(a*Sqrt[1 - x^2/a^2]) + x*ArcCos[x/a]","A",3,3,6,0.5000,1,"{5264, 4620, 261}"
13,1,59,0,0.0598754,"\int \frac{\sec ^{-1}\left(\frac{a}{x}\right)}{x} \, dx","Int[ArcSec[a/x]/x,x]","-\frac{1}{2} i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(\frac{x}{a}\right)}\right)-\frac{1}{2} i \cos ^{-1}\left(\frac{x}{a}\right)^2+\cos ^{-1}\left(\frac{x}{a}\right) \log \left(1+e^{2 i \cos ^{-1}\left(\frac{x}{a}\right)}\right)","-\frac{1}{2} i \text{PolyLog}\left(2,-e^{2 i \cos ^{-1}\left(\frac{x}{a}\right)}\right)-\frac{1}{2} i \cos ^{-1}\left(\frac{x}{a}\right)^2+\cos ^{-1}\left(\frac{x}{a}\right) \log \left(1+e^{2 i \cos ^{-1}\left(\frac{x}{a}\right)}\right)",1,"(-I/2)*ArcCos[x/a]^2 + ArcCos[x/a]*Log[1 + E^((2*I)*ArcCos[x/a])] - (I/2)*PolyLog[2, -E^((2*I)*ArcCos[x/a])]","A",6,6,10,0.6000,1,"{5264, 4626, 3719, 2190, 2279, 2391}"
14,1,31,0,0.0296163,"\int \frac{\sec ^{-1}\left(\frac{a}{x}\right)}{x^2} \, dx","Int[ArcSec[a/x]/x^2,x]","\frac{\tanh ^{-1}\left(\sqrt{1-\frac{x^2}{a^2}}\right)}{a}-\frac{\cos ^{-1}\left(\frac{x}{a}\right)}{x}","\frac{\tanh ^{-1}\left(\sqrt{1-\frac{x^2}{a^2}}\right)}{a}-\frac{\cos ^{-1}\left(\frac{x}{a}\right)}{x}",1,"-(ArcCos[x/a]/x) + ArcTanh[Sqrt[1 - x^2/a^2]]/a","A",5,5,10,0.5000,1,"{5264, 4628, 266, 63, 208}"
15,1,38,0,0.0213249,"\int \frac{\sec ^{-1}\left(\frac{a}{x}\right)}{x^3} \, dx","Int[ArcSec[a/x]/x^3,x]","\frac{\sqrt{1-\frac{x^2}{a^2}}}{2 a x}-\frac{\cos ^{-1}\left(\frac{x}{a}\right)}{2 x^2}","\frac{\sqrt{1-\frac{x^2}{a^2}}}{2 a x}-\frac{\cos ^{-1}\left(\frac{x}{a}\right)}{2 x^2}",1,"Sqrt[1 - x^2/a^2]/(2*a*x) - ArcCos[x/a]/(2*x^2)","A",3,3,10,0.3000,1,"{5264, 4628, 264}"
16,1,60,0,0.04213,"\int \frac{\sec ^{-1}\left(\frac{a}{x}\right)}{x^4} \, dx","Int[ArcSec[a/x]/x^4,x]","\frac{\sqrt{1-\frac{x^2}{a^2}}}{6 a x^2}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{x^2}{a^2}}\right)}{6 a^3}-\frac{\cos ^{-1}\left(\frac{x}{a}\right)}{3 x^3}","\frac{\sqrt{1-\frac{x^2}{a^2}}}{6 a x^2}+\frac{\tanh ^{-1}\left(\sqrt{1-\frac{x^2}{a^2}}\right)}{6 a^3}-\frac{\cos ^{-1}\left(\frac{x}{a}\right)}{3 x^3}",1,"Sqrt[1 - x^2/a^2]/(6*a*x^2) - ArcCos[x/a]/(3*x^3) + ArcTanh[Sqrt[1 - x^2/a^2]]/(6*a^3)","A",6,6,10,0.6000,1,"{5264, 4628, 266, 51, 63, 208}"
17,1,69,0,0.0925888,"\int \frac{\sec ^{-1}\left(a x^n\right)}{x} \, dx","Int[ArcSec[a*x^n]/x,x]","\frac{i \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}\left(a x^n\right)}\right)}{2 n}+\frac{i \sec ^{-1}\left(a x^n\right)^2}{2 n}-\frac{\sec ^{-1}\left(a x^n\right) \log \left(1+e^{2 i \sec ^{-1}\left(a x^n\right)}\right)}{n}","\frac{i \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}\left(a x^n\right)}\right)}{2 n}+\frac{i \sec ^{-1}\left(a x^n\right)^2}{2 n}-\frac{\sec ^{-1}\left(a x^n\right) \log \left(1+e^{2 i \sec ^{-1}\left(a x^n\right)}\right)}{n}",1,"((I/2)*ArcSec[a*x^n]^2)/n - (ArcSec[a*x^n]*Log[1 + E^((2*I)*ArcSec[a*x^n])])/n + ((I/2)*PolyLog[2, -E^((2*I)*ArcSec[a*x^n])])/n","A",7,6,10,0.6000,1,"{5218, 4626, 3719, 2190, 2279, 2391}"
18,1,197,0,0.2316453,"\int x^4 \sec ^{-1}(a+b x) \, dx","Int[x^4*ArcSec[a + b*x],x]","\frac{\left(53 a^2+20\right) a (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{30 b^5}-\frac{\left(58 a^2+9\right) (a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}}}{120 b^5}+\frac{a^5 \sec ^{-1}(a+b x)}{5 b^5}-\frac{\left(40 a^4+40 a^2+3\right) \tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{40 b^5}+\frac{11 a x^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{60 b^3}-\frac{x^3 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{20 b^2}+\frac{1}{5} x^5 \sec ^{-1}(a+b x)","\frac{\left(53 a^2+20\right) a (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{30 b^5}-\frac{\left(58 a^2+9\right) (a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}}}{120 b^5}+\frac{a^5 \sec ^{-1}(a+b x)}{5 b^5}-\frac{\left(40 a^4+40 a^2+3\right) \tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{40 b^5}+\frac{11 a x^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{60 b^3}-\frac{x^3 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{20 b^2}+\frac{1}{5} x^5 \sec ^{-1}(a+b x)",1,"(a*(20 + 53*a^2)*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(30*b^5) + (11*a*x^2*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(60*b^3) - (x^3*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(20*b^2) - ((9 + 58*a^2)*(a + b*x)^2*Sqrt[1 - (a + b*x)^(-2)])/(120*b^5) + (a^5*ArcSec[a + b*x])/(5*b^5) + (x^5*ArcSec[a + b*x])/5 - ((3 + 40*a^2 + 40*a^4)*ArcTanh[Sqrt[1 - (a + b*x)^(-2)]])/(40*b^5)","A",9,8,10,0.8000,1,"{5258, 4426, 3782, 4056, 4048, 3770, 3767, 8}"
19,1,155,0,0.1390381,"\int x^3 \sec ^{-1}(a+b x) \, dx","Int[x^3*ArcSec[a + b*x],x]","-\frac{\left(17 a^2+2\right) (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{12 b^4}-\frac{a^4 \sec ^{-1}(a+b x)}{4 b^4}+\frac{\left(2 a^2+1\right) a \tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{2 b^4}-\frac{x^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{12 b^2}+\frac{a (a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}}}{3 b^4}+\frac{1}{4} x^4 \sec ^{-1}(a+b x)","-\frac{\left(17 a^2+2\right) (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{12 b^4}-\frac{a^4 \sec ^{-1}(a+b x)}{4 b^4}+\frac{\left(2 a^2+1\right) a \tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{2 b^4}-\frac{x^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{12 b^2}+\frac{a (a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}}}{3 b^4}+\frac{1}{4} x^4 \sec ^{-1}(a+b x)",1,"-((2 + 17*a^2)*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(12*b^4) - (x^2*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(12*b^2) + (a*(a + b*x)^2*Sqrt[1 - (a + b*x)^(-2)])/(3*b^4) - (a^4*ArcSec[a + b*x])/(4*b^4) + (x^4*ArcSec[a + b*x])/4 + (a*(1 + 2*a^2)*ArcTanh[Sqrt[1 - (a + b*x)^(-2)]])/(2*b^4)","A",8,7,10,0.7000,1,"{5258, 4426, 3782, 4048, 3770, 3767, 8}"
20,1,116,0,0.089765,"\int x^2 \sec ^{-1}(a+b x) \, dx","Int[x^2*ArcSec[a + b*x],x]","\frac{a^3 \sec ^{-1}(a+b x)}{3 b^3}-\frac{\left(6 a^2+1\right) \tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{6 b^3}+\frac{5 a (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{6 b^3}-\frac{x (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{6 b^2}+\frac{1}{3} x^3 \sec ^{-1}(a+b x)","\frac{a^3 \sec ^{-1}(a+b x)}{3 b^3}-\frac{\left(6 a^2+1\right) \tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{6 b^3}+\frac{5 a (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{6 b^3}-\frac{x (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{6 b^2}+\frac{1}{3} x^3 \sec ^{-1}(a+b x)",1,"(5*a*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(6*b^3) - (x*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(6*b^2) + (a^3*ArcSec[a + b*x])/(3*b^3) + (x^3*ArcSec[a + b*x])/3 - ((1 + 6*a^2)*ArcTanh[Sqrt[1 - (a + b*x)^(-2)]])/(6*b^3)","A",7,6,10,0.6000,1,"{5258, 4426, 3782, 3770, 3767, 8}"
21,1,78,0,0.0530349,"\int x \sec ^{-1}(a+b x) \, dx","Int[x*ArcSec[a + b*x],x]","-\frac{a^2 \sec ^{-1}(a+b x)}{2 b^2}-\frac{(a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{2 b^2}+\frac{a \tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{b^2}+\frac{1}{2} x^2 \sec ^{-1}(a+b x)","-\frac{a^2 \sec ^{-1}(a+b x)}{2 b^2}-\frac{(a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{2 b^2}+\frac{a \tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{b^2}+\frac{1}{2} x^2 \sec ^{-1}(a+b x)",1,"-((a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(2*b^2) - (a^2*ArcSec[a + b*x])/(2*b^2) + (x^2*ArcSec[a + b*x])/2 + (a*ArcTanh[Sqrt[1 - (a + b*x)^(-2)]])/b^2","A",6,6,8,0.7500,1,"{5258, 4426, 3773, 3770, 3767, 8}"
22,1,37,0,0.0230683,"\int \sec ^{-1}(a+b x) \, dx","Int[ArcSec[a + b*x],x]","\frac{(a+b x) \sec ^{-1}(a+b x)}{b}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{b}","\frac{(a+b x) \sec ^{-1}(a+b x)}{b}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{b}",1,"((a + b*x)*ArcSec[a + b*x])/b - ArcTanh[Sqrt[1 - (a + b*x)^(-2)]]/b","A",5,5,6,0.8333,1,"{5250, 372, 266, 63, 206}"
23,1,200,0,0.3091195,"\int \frac{\sec ^{-1}(a+b x)}{x} \, dx","Int[ArcSec[a + b*x]/x,x]","-i \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-i \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+\frac{1}{2} i \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(a+b x)}\right)+\sec ^{-1}(a+b x) \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\sec ^{-1}(a+b x) \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\sec ^{-1}(a+b x) \log \left(1+e^{2 i \sec ^{-1}(a+b x)}\right)","-i \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-i \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+\frac{1}{2} i \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(a+b x)}\right)+\sec ^{-1}(a+b x) \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\sec ^{-1}(a+b x) \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\sec ^{-1}(a+b x) \log \left(1+e^{2 i \sec ^{-1}(a+b x)}\right)",1,"ArcSec[a + b*x]*Log[1 - (a*E^(I*ArcSec[a + b*x]))/(1 - Sqrt[1 - a^2])] + ArcSec[a + b*x]*Log[1 - (a*E^(I*ArcSec[a + b*x]))/(1 + Sqrt[1 - a^2])] - ArcSec[a + b*x]*Log[1 + E^((2*I)*ArcSec[a + b*x])] - I*PolyLog[2, (a*E^(I*ArcSec[a + b*x]))/(1 - Sqrt[1 - a^2])] - I*PolyLog[2, (a*E^(I*ArcSec[a + b*x]))/(1 + Sqrt[1 - a^2])] + (I/2)*PolyLog[2, -E^((2*I)*ArcSec[a + b*x])]","A",14,8,10,0.8000,1,"{5258, 4551, 4530, 3719, 2190, 2279, 2391, 4520}"
24,1,70,0,0.0974052,"\int \frac{\sec ^{-1}(a+b x)}{x^2} \, dx","Int[ArcSec[a + b*x]/x^2,x]","\frac{2 b \tan ^{-1}\left(\frac{\sqrt{a+1} \tan \left(\frac{1}{2} \sec ^{-1}(a+b x)\right)}{\sqrt{1-a}}\right)}{a \sqrt{1-a^2}}-\frac{b \sec ^{-1}(a+b x)}{a}-\frac{\sec ^{-1}(a+b x)}{x}","\frac{2 b \tan ^{-1}\left(\frac{\sqrt{a+1} \tan \left(\frac{1}{2} \sec ^{-1}(a+b x)\right)}{\sqrt{1-a}}\right)}{a \sqrt{1-a^2}}-\frac{b \sec ^{-1}(a+b x)}{a}-\frac{\sec ^{-1}(a+b x)}{x}",1,"-((b*ArcSec[a + b*x])/a) - ArcSec[a + b*x]/x + (2*b*ArcTan[(Sqrt[1 + a]*Tan[ArcSec[a + b*x]/2])/Sqrt[1 - a]])/(a*Sqrt[1 - a^2])","A",5,5,10,0.5000,1,"{5258, 4426, 3783, 2659, 205}"
25,1,125,0,0.1924703,"\int \frac{\sec ^{-1}(a+b x)}{x^3} \, dx","Int[ArcSec[a + b*x]/x^3,x]","\frac{b^2 \sec ^{-1}(a+b x)}{2 a^2}-\frac{\left(1-2 a^2\right) b^2 \tan ^{-1}\left(\frac{\sqrt{a+1} \tan \left(\frac{1}{2} \sec ^{-1}(a+b x)\right)}{\sqrt{1-a}}\right)}{a^2 \left(1-a^2\right)^{3/2}}+\frac{b (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{2 a \left(1-a^2\right) x}-\frac{\sec ^{-1}(a+b x)}{2 x^2}","\frac{b^2 \sec ^{-1}(a+b x)}{2 a^2}-\frac{\left(1-2 a^2\right) b^2 \tan ^{-1}\left(\frac{\sqrt{a+1} \tan \left(\frac{1}{2} \sec ^{-1}(a+b x)\right)}{\sqrt{1-a}}\right)}{a^2 \left(1-a^2\right)^{3/2}}+\frac{b (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{2 a \left(1-a^2\right) x}-\frac{\sec ^{-1}(a+b x)}{2 x^2}",1,"(b*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(2*a*(1 - a^2)*x) + (b^2*ArcSec[a + b*x])/(2*a^2) - ArcSec[a + b*x]/(2*x^2) - ((1 - 2*a^2)*b^2*ArcTan[(Sqrt[1 + a]*Tan[ArcSec[a + b*x]/2])/Sqrt[1 - a]])/(a^2*(1 - a^2)^(3/2))","A",7,7,10,0.7000,1,"{5258, 4426, 3785, 3919, 3831, 2659, 205}"
26,1,181,0,0.2877615,"\int \frac{\sec ^{-1}(a+b x)}{x^4} \, dx","Int[ArcSec[a + b*x]/x^4,x]","-\frac{\left(2-5 a^2\right) b^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{6 a^2 \left(1-a^2\right)^2 x}-\frac{b^3 \sec ^{-1}(a+b x)}{3 a^3}+\frac{\left(6 a^4-5 a^2+2\right) b^3 \tan ^{-1}\left(\frac{\sqrt{a+1} \tan \left(\frac{1}{2} \sec ^{-1}(a+b x)\right)}{\sqrt{1-a}}\right)}{3 a^3 \left(1-a^2\right)^{5/2}}+\frac{b (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{6 a \left(1-a^2\right) x^2}-\frac{\sec ^{-1}(a+b x)}{3 x^3}","-\frac{\left(2-5 a^2\right) b^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{6 a^2 \left(1-a^2\right)^2 x}-\frac{b^3 \sec ^{-1}(a+b x)}{3 a^3}+\frac{\left(6 a^4-5 a^2+2\right) b^3 \tan ^{-1}\left(\frac{\sqrt{a+1} \tan \left(\frac{1}{2} \sec ^{-1}(a+b x)\right)}{\sqrt{1-a}}\right)}{3 a^3 \left(1-a^2\right)^{5/2}}+\frac{b (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}}}{6 a \left(1-a^2\right) x^2}-\frac{\sec ^{-1}(a+b x)}{3 x^3}",1,"(b*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(6*a*(1 - a^2)*x^2) - ((2 - 5*a^2)*b^2*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)])/(6*a^2*(1 - a^2)^2*x) - (b^3*ArcSec[a + b*x])/(3*a^3) - ArcSec[a + b*x]/(3*x^3) + ((2 - 5*a^2 + 6*a^4)*b^3*ArcTan[(Sqrt[1 + a]*Tan[ArcSec[a + b*x]/2])/Sqrt[1 - a]])/(3*a^3*(1 - a^2)^(5/2))","A",8,8,10,0.8000,1,"{5258, 4426, 3785, 4060, 3919, 3831, 2659, 205}"
27,1,381,0,0.3019532,"\int x^3 \sec ^{-1}(a+b x)^2 \, dx","Int[x^3*ArcSec[a + b*x]^2,x]","\frac{2 i a^3 \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^4}-\frac{2 i a^3 \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b^4}+\frac{i a \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^4}-\frac{i a \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b^4}+\frac{3 a^2 \log (a+b x)}{b^4}-\frac{a^4 \sec ^{-1}(a+b x)^2}{4 b^4}-\frac{3 a^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)}{b^4}-\frac{4 i a^3 \sec ^{-1}(a+b x) \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b^4}-\frac{a x}{b^3}+\frac{(a+b x)^2}{12 b^4}+\frac{\log (a+b x)}{3 b^4}+\frac{a (a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)}{b^4}-\frac{(a+b x)^3 \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)}{6 b^4}-\frac{(a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)}{3 b^4}-\frac{2 i a \sec ^{-1}(a+b x) \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b^4}+\frac{1}{4} x^4 \sec ^{-1}(a+b x)^2","\frac{2 i a^3 \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^4}-\frac{2 i a^3 \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b^4}+\frac{i a \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^4}-\frac{i a \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b^4}+\frac{3 a^2 \log (a+b x)}{b^4}-\frac{a^4 \sec ^{-1}(a+b x)^2}{4 b^4}-\frac{3 a^2 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)}{b^4}-\frac{4 i a^3 \sec ^{-1}(a+b x) \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b^4}-\frac{a x}{b^3}+\frac{(a+b x)^2}{12 b^4}+\frac{\log (a+b x)}{3 b^4}+\frac{a (a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)}{b^4}-\frac{(a+b x)^3 \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)}{6 b^4}-\frac{(a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)}{3 b^4}-\frac{2 i a \sec ^{-1}(a+b x) \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b^4}+\frac{1}{4} x^4 \sec ^{-1}(a+b x)^2",1,"-((a*x)/b^3) + (a + b*x)^2/(12*b^4) - ((a + b*x)*Sqrt[1 - (a + b*x)^(-2)]*ArcSec[a + b*x])/(3*b^4) - (3*a^2*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)]*ArcSec[a + b*x])/b^4 + (a*(a + b*x)^2*Sqrt[1 - (a + b*x)^(-2)]*ArcSec[a + b*x])/b^4 - ((a + b*x)^3*Sqrt[1 - (a + b*x)^(-2)]*ArcSec[a + b*x])/(6*b^4) - (a^4*ArcSec[a + b*x]^2)/(4*b^4) + (x^4*ArcSec[a + b*x]^2)/4 - ((2*I)*a*ArcSec[a + b*x]*ArcTan[E^(I*ArcSec[a + b*x])])/b^4 - ((4*I)*a^3*ArcSec[a + b*x]*ArcTan[E^(I*ArcSec[a + b*x])])/b^4 + Log[a + b*x]/(3*b^4) + (3*a^2*Log[a + b*x])/b^4 + (I*a*PolyLog[2, (-I)*E^(I*ArcSec[a + b*x])])/b^4 + ((2*I)*a^3*PolyLog[2, (-I)*E^(I*ArcSec[a + b*x])])/b^4 - (I*a*PolyLog[2, I*E^(I*ArcSec[a + b*x])])/b^4 - ((2*I)*a^3*PolyLog[2, I*E^(I*ArcSec[a + b*x])])/b^4","A",20,9,12,0.7500,1,"{5258, 4426, 4190, 4181, 2279, 2391, 4184, 3475, 4185}"
28,1,288,0,0.23176,"\int x^2 \sec ^{-1}(a+b x)^2 \, dx","Int[x^2*ArcSec[a + b*x]^2,x]","-\frac{2 i a^2 \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}+\frac{2 i a^2 \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}-\frac{i \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{3 b^3}+\frac{i \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{3 b^3}+\frac{a^3 \sec ^{-1}(a+b x)^2}{3 b^3}+\frac{4 i a^2 \sec ^{-1}(a+b x) \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b^3}-\frac{2 a \log (a+b x)}{b^3}+\frac{2 a (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)}{b^3}-\frac{(a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)}{3 b^3}+\frac{2 i \sec ^{-1}(a+b x) \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{3 b^3}+\frac{1}{3} x^3 \sec ^{-1}(a+b x)^2+\frac{x}{3 b^2}","-\frac{2 i a^2 \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}+\frac{2 i a^2 \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}-\frac{i \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{3 b^3}+\frac{i \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{3 b^3}+\frac{a^3 \sec ^{-1}(a+b x)^2}{3 b^3}+\frac{4 i a^2 \sec ^{-1}(a+b x) \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b^3}-\frac{2 a \log (a+b x)}{b^3}+\frac{2 a (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)}{b^3}-\frac{(a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)}{3 b^3}+\frac{2 i \sec ^{-1}(a+b x) \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{3 b^3}+\frac{1}{3} x^3 \sec ^{-1}(a+b x)^2+\frac{x}{3 b^2}",1,"x/(3*b^2) + (2*a*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)]*ArcSec[a + b*x])/b^3 - ((a + b*x)^2*Sqrt[1 - (a + b*x)^(-2)]*ArcSec[a + b*x])/(3*b^3) + (a^3*ArcSec[a + b*x]^2)/(3*b^3) + (x^3*ArcSec[a + b*x]^2)/3 + (((2*I)/3)*ArcSec[a + b*x]*ArcTan[E^(I*ArcSec[a + b*x])])/b^3 + ((4*I)*a^2*ArcSec[a + b*x]*ArcTan[E^(I*ArcSec[a + b*x])])/b^3 - (2*a*Log[a + b*x])/b^3 - ((I/3)*PolyLog[2, (-I)*E^(I*ArcSec[a + b*x])])/b^3 - ((2*I)*a^2*PolyLog[2, (-I)*E^(I*ArcSec[a + b*x])])/b^3 + ((I/3)*PolyLog[2, I*E^(I*ArcSec[a + b*x])])/b^3 + ((2*I)*a^2*PolyLog[2, I*E^(I*ArcSec[a + b*x])])/b^3","A",17,9,12,0.7500,1,"{5258, 4426, 4190, 4181, 2279, 2391, 4184, 3475, 4185}"
29,1,154,0,0.1313702,"\int x \sec ^{-1}(a+b x)^2 \, dx","Int[x*ArcSec[a + b*x]^2,x]","\frac{2 i a \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^2}-\frac{2 i a \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b^2}-\frac{a^2 \sec ^{-1}(a+b x)^2}{2 b^2}+\frac{\log (a+b x)}{b^2}-\frac{(a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)}{b^2}-\frac{4 i a \sec ^{-1}(a+b x) \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b^2}+\frac{1}{2} x^2 \sec ^{-1}(a+b x)^2","\frac{2 i a \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^2}-\frac{2 i a \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b^2}-\frac{a^2 \sec ^{-1}(a+b x)^2}{2 b^2}+\frac{\log (a+b x)}{b^2}-\frac{(a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)}{b^2}-\frac{4 i a \sec ^{-1}(a+b x) \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b^2}+\frac{1}{2} x^2 \sec ^{-1}(a+b x)^2",1,"-(((a + b*x)*Sqrt[1 - (a + b*x)^(-2)]*ArcSec[a + b*x])/b^2) - (a^2*ArcSec[a + b*x]^2)/(2*b^2) + (x^2*ArcSec[a + b*x]^2)/2 - ((4*I)*a*ArcSec[a + b*x]*ArcTan[E^(I*ArcSec[a + b*x])])/b^2 + Log[a + b*x]/b^2 + ((2*I)*a*PolyLog[2, (-I)*E^(I*ArcSec[a + b*x])])/b^2 - ((2*I)*a*PolyLog[2, I*E^(I*ArcSec[a + b*x])])/b^2","A",11,8,10,0.8000,1,"{5258, 4426, 4190, 4181, 2279, 2391, 4184, 3475}"
30,1,94,0,0.0627073,"\int \sec ^{-1}(a+b x)^2 \, dx","Int[ArcSec[a + b*x]^2,x]","-\frac{2 i \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b}+\frac{2 i \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b}+\frac{(a+b x) \sec ^{-1}(a+b x)^2}{b}+\frac{4 i \sec ^{-1}(a+b x) \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b}","-\frac{2 i \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b}+\frac{2 i \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b}+\frac{(a+b x) \sec ^{-1}(a+b x)^2}{b}+\frac{4 i \sec ^{-1}(a+b x) \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b}",1,"((a + b*x)*ArcSec[a + b*x]^2)/b + ((4*I)*ArcSec[a + b*x]*ArcTan[E^(I*ArcSec[a + b*x])])/b - ((2*I)*PolyLog[2, (-I)*E^(I*ArcSec[a + b*x])])/b + ((2*I)*PolyLog[2, I*E^(I*ArcSec[a + b*x])])/b","A",8,6,8,0.7500,1,"{5252, 5216, 3757, 4181, 2279, 2391}"
31,1,310,0,0.4852166,"\int \frac{\sec ^{-1}(a+b x)^2}{x} \, dx","Int[ArcSec[a + b*x]^2/x,x]","-2 i \sec ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-2 i \sec ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+2 \text{PolyLog}\left(3,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+2 \text{PolyLog}\left(3,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+i \sec ^{-1}(a+b x) \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(a+b x)}\right)-\frac{1}{2} \text{PolyLog}\left(3,-e^{2 i \sec ^{-1}(a+b x)}\right)+\sec ^{-1}(a+b x)^2 \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\sec ^{-1}(a+b x)^2 \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\sec ^{-1}(a+b x)^2 \log \left(1+e^{2 i \sec ^{-1}(a+b x)}\right)","-2 i \sec ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-2 i \sec ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+2 \text{PolyLog}\left(3,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+2 \text{PolyLog}\left(3,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+i \sec ^{-1}(a+b x) \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(a+b x)}\right)-\frac{1}{2} \text{PolyLog}\left(3,-e^{2 i \sec ^{-1}(a+b x)}\right)+\sec ^{-1}(a+b x)^2 \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\sec ^{-1}(a+b x)^2 \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\sec ^{-1}(a+b x)^2 \log \left(1+e^{2 i \sec ^{-1}(a+b x)}\right)",1,"ArcSec[a + b*x]^2*Log[1 - (a*E^(I*ArcSec[a + b*x]))/(1 - Sqrt[1 - a^2])] + ArcSec[a + b*x]^2*Log[1 - (a*E^(I*ArcSec[a + b*x]))/(1 + Sqrt[1 - a^2])] - ArcSec[a + b*x]^2*Log[1 + E^((2*I)*ArcSec[a + b*x])] - (2*I)*ArcSec[a + b*x]*PolyLog[2, (a*E^(I*ArcSec[a + b*x]))/(1 - Sqrt[1 - a^2])] - (2*I)*ArcSec[a + b*x]*PolyLog[2, (a*E^(I*ArcSec[a + b*x]))/(1 + Sqrt[1 - a^2])] + I*ArcSec[a + b*x]*PolyLog[2, -E^((2*I)*ArcSec[a + b*x])] + 2*PolyLog[3, (a*E^(I*ArcSec[a + b*x]))/(1 - Sqrt[1 - a^2])] + 2*PolyLog[3, (a*E^(I*ArcSec[a + b*x]))/(1 + Sqrt[1 - a^2])] - PolyLog[3, -E^((2*I)*ArcSec[a + b*x])]/2","A",17,9,12,0.7500,1,"{5258, 4551, 4530, 3719, 2190, 2531, 2282, 6589, 4520}"
32,1,244,0,0.3948656,"\int \frac{\sec ^{-1}(a+b x)^2}{x^2} \, dx","Int[ArcSec[a + b*x]^2/x^2,x]","-\frac{2 b \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{2 b \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{2 i b \sec ^{-1}(a+b x) \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{2 i b \sec ^{-1}(a+b x) \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{b \sec ^{-1}(a+b x)^2}{a}-\frac{\sec ^{-1}(a+b x)^2}{x}","-\frac{2 b \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{2 b \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{2 i b \sec ^{-1}(a+b x) \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{2 i b \sec ^{-1}(a+b x) \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{b \sec ^{-1}(a+b x)^2}{a}-\frac{\sec ^{-1}(a+b x)^2}{x}",1,"-((b*ArcSec[a + b*x]^2)/a) - ArcSec[a + b*x]^2/x - ((2*I)*b*ArcSec[a + b*x]*Log[1 - (a*E^(I*ArcSec[a + b*x]))/(1 - Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) + ((2*I)*b*ArcSec[a + b*x]*Log[1 - (a*E^(I*ArcSec[a + b*x]))/(1 + Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) - (2*b*PolyLog[2, (a*E^(I*ArcSec[a + b*x]))/(1 - Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) + (2*b*PolyLog[2, (a*E^(I*ArcSec[a + b*x]))/(1 + Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2])","A",12,8,12,0.6667,1,"{5258, 4426, 4191, 3321, 2264, 2190, 2279, 2391}"
33,1,494,0,0.3968089,"\int x^2 \sec ^{-1}(a+b x)^3 \, dx","Int[x^2*ArcSec[a + b*x]^3,x]","-\frac{6 i a^2 \sec ^{-1}(a+b x) \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}+\frac{6 i a^2 \sec ^{-1}(a+b x) \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}+\frac{6 a^2 \text{PolyLog}\left(3,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}-\frac{6 a^2 \text{PolyLog}\left(3,i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}-\frac{i \sec ^{-1}(a+b x) \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}+\frac{i \sec ^{-1}(a+b x) \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}-\frac{3 i a \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(a+b x)}\right)}{b^3}+\frac{\text{PolyLog}\left(3,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}-\frac{\text{PolyLog}\left(3,i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}+\frac{a^3 \sec ^{-1}(a+b x)^3}{3 b^3}+\frac{6 i a^2 \sec ^{-1}(a+b x)^2 \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b^3}-\frac{(a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)^2}{2 b^3}+\frac{3 a (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)^2}{b^3}-\frac{3 i a \sec ^{-1}(a+b x)^2}{b^3}+\frac{(a+b x) \sec ^{-1}(a+b x)}{b^3}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{b^3}+\frac{6 a \sec ^{-1}(a+b x) \log \left(1+e^{2 i \sec ^{-1}(a+b x)}\right)}{b^3}+\frac{i \sec ^{-1}(a+b x)^2 \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b^3}+\frac{1}{3} x^3 \sec ^{-1}(a+b x)^3","-\frac{6 i a^2 \sec ^{-1}(a+b x) \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}+\frac{6 i a^2 \sec ^{-1}(a+b x) \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}+\frac{6 a^2 \text{PolyLog}\left(3,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}-\frac{6 a^2 \text{PolyLog}\left(3,i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}-\frac{i \sec ^{-1}(a+b x) \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}+\frac{i \sec ^{-1}(a+b x) \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}-\frac{3 i a \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(a+b x)}\right)}{b^3}+\frac{\text{PolyLog}\left(3,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}-\frac{\text{PolyLog}\left(3,i e^{i \sec ^{-1}(a+b x)}\right)}{b^3}+\frac{a^3 \sec ^{-1}(a+b x)^3}{3 b^3}+\frac{6 i a^2 \sec ^{-1}(a+b x)^2 \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b^3}-\frac{(a+b x)^2 \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)^2}{2 b^3}+\frac{3 a (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)^2}{b^3}-\frac{3 i a \sec ^{-1}(a+b x)^2}{b^3}+\frac{(a+b x) \sec ^{-1}(a+b x)}{b^3}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{(a+b x)^2}}\right)}{b^3}+\frac{6 a \sec ^{-1}(a+b x) \log \left(1+e^{2 i \sec ^{-1}(a+b x)}\right)}{b^3}+\frac{i \sec ^{-1}(a+b x)^2 \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b^3}+\frac{1}{3} x^3 \sec ^{-1}(a+b x)^3",1,"((a + b*x)*ArcSec[a + b*x])/b^3 - ((3*I)*a*ArcSec[a + b*x]^2)/b^3 + (3*a*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)]*ArcSec[a + b*x]^2)/b^3 - ((a + b*x)^2*Sqrt[1 - (a + b*x)^(-2)]*ArcSec[a + b*x]^2)/(2*b^3) + (a^3*ArcSec[a + b*x]^3)/(3*b^3) + (x^3*ArcSec[a + b*x]^3)/3 + (I*ArcSec[a + b*x]^2*ArcTan[E^(I*ArcSec[a + b*x])])/b^3 + ((6*I)*a^2*ArcSec[a + b*x]^2*ArcTan[E^(I*ArcSec[a + b*x])])/b^3 - ArcTanh[Sqrt[1 - (a + b*x)^(-2)]]/b^3 + (6*a*ArcSec[a + b*x]*Log[1 + E^((2*I)*ArcSec[a + b*x])])/b^3 - (I*ArcSec[a + b*x]*PolyLog[2, (-I)*E^(I*ArcSec[a + b*x])])/b^3 - ((6*I)*a^2*ArcSec[a + b*x]*PolyLog[2, (-I)*E^(I*ArcSec[a + b*x])])/b^3 + (I*ArcSec[a + b*x]*PolyLog[2, I*E^(I*ArcSec[a + b*x])])/b^3 + ((6*I)*a^2*ArcSec[a + b*x]*PolyLog[2, I*E^(I*ArcSec[a + b*x])])/b^3 - ((3*I)*a*PolyLog[2, -E^((2*I)*ArcSec[a + b*x])])/b^3 + PolyLog[3, (-I)*E^(I*ArcSec[a + b*x])]/b^3 + (6*a^2*PolyLog[3, (-I)*E^(I*ArcSec[a + b*x])])/b^3 - PolyLog[3, I*E^(I*ArcSec[a + b*x])]/b^3 - (6*a^2*PolyLog[3, I*E^(I*ArcSec[a + b*x])])/b^3","A",25,14,12,1.167,1,"{5258, 4426, 4190, 4181, 2531, 2282, 6589, 4184, 3719, 2190, 2279, 2391, 4186, 3770}"
34,1,278,0,0.2592437,"\int x \sec ^{-1}(a+b x)^3 \, dx","Int[x*ArcSec[a + b*x]^3,x]","\frac{6 i a \sec ^{-1}(a+b x) \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^2}-\frac{6 i a \sec ^{-1}(a+b x) \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b^2}+\frac{3 i \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(a+b x)}\right)}{2 b^2}-\frac{6 a \text{PolyLog}\left(3,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^2}+\frac{6 a \text{PolyLog}\left(3,i e^{i \sec ^{-1}(a+b x)}\right)}{b^2}-\frac{a^2 \sec ^{-1}(a+b x)^3}{2 b^2}-\frac{3 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)^2}{2 b^2}+\frac{3 i \sec ^{-1}(a+b x)^2}{2 b^2}-\frac{3 \sec ^{-1}(a+b x) \log \left(1+e^{2 i \sec ^{-1}(a+b x)}\right)}{b^2}-\frac{6 i a \sec ^{-1}(a+b x)^2 \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b^2}+\frac{1}{2} x^2 \sec ^{-1}(a+b x)^3","\frac{6 i a \sec ^{-1}(a+b x) \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^2}-\frac{6 i a \sec ^{-1}(a+b x) \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b^2}+\frac{3 i \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(a+b x)}\right)}{2 b^2}-\frac{6 a \text{PolyLog}\left(3,-i e^{i \sec ^{-1}(a+b x)}\right)}{b^2}+\frac{6 a \text{PolyLog}\left(3,i e^{i \sec ^{-1}(a+b x)}\right)}{b^2}-\frac{a^2 \sec ^{-1}(a+b x)^3}{2 b^2}-\frac{3 (a+b x) \sqrt{1-\frac{1}{(a+b x)^2}} \sec ^{-1}(a+b x)^2}{2 b^2}+\frac{3 i \sec ^{-1}(a+b x)^2}{2 b^2}-\frac{3 \sec ^{-1}(a+b x) \log \left(1+e^{2 i \sec ^{-1}(a+b x)}\right)}{b^2}-\frac{6 i a \sec ^{-1}(a+b x)^2 \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b^2}+\frac{1}{2} x^2 \sec ^{-1}(a+b x)^3",1,"(((3*I)/2)*ArcSec[a + b*x]^2)/b^2 - (3*(a + b*x)*Sqrt[1 - (a + b*x)^(-2)]*ArcSec[a + b*x]^2)/(2*b^2) - (a^2*ArcSec[a + b*x]^3)/(2*b^2) + (x^2*ArcSec[a + b*x]^3)/2 - ((6*I)*a*ArcSec[a + b*x]^2*ArcTan[E^(I*ArcSec[a + b*x])])/b^2 - (3*ArcSec[a + b*x]*Log[1 + E^((2*I)*ArcSec[a + b*x])])/b^2 + ((6*I)*a*ArcSec[a + b*x]*PolyLog[2, (-I)*E^(I*ArcSec[a + b*x])])/b^2 - ((6*I)*a*ArcSec[a + b*x]*PolyLog[2, I*E^(I*ArcSec[a + b*x])])/b^2 + (((3*I)/2)*PolyLog[2, -E^((2*I)*ArcSec[a + b*x])])/b^2 - (6*a*PolyLog[3, (-I)*E^(I*ArcSec[a + b*x])])/b^2 + (6*a*PolyLog[3, I*E^(I*ArcSec[a + b*x])])/b^2","A",16,12,10,1.200,1,"{5258, 4426, 4190, 4181, 2531, 2282, 6589, 4184, 3719, 2190, 2279, 2391}"
35,1,154,0,0.1038376,"\int \sec ^{-1}(a+b x)^3 \, dx","Int[ArcSec[a + b*x]^3,x]","-\frac{6 i \sec ^{-1}(a+b x) \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b}+\frac{6 i \sec ^{-1}(a+b x) \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b}+\frac{6 \text{PolyLog}\left(3,-i e^{i \sec ^{-1}(a+b x)}\right)}{b}-\frac{6 \text{PolyLog}\left(3,i e^{i \sec ^{-1}(a+b x)}\right)}{b}+\frac{(a+b x) \sec ^{-1}(a+b x)^3}{b}+\frac{6 i \sec ^{-1}(a+b x)^2 \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b}","-\frac{6 i \sec ^{-1}(a+b x) \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(a+b x)}\right)}{b}+\frac{6 i \sec ^{-1}(a+b x) \text{PolyLog}\left(2,i e^{i \sec ^{-1}(a+b x)}\right)}{b}+\frac{6 \text{PolyLog}\left(3,-i e^{i \sec ^{-1}(a+b x)}\right)}{b}-\frac{6 \text{PolyLog}\left(3,i e^{i \sec ^{-1}(a+b x)}\right)}{b}+\frac{(a+b x) \sec ^{-1}(a+b x)^3}{b}+\frac{6 i \sec ^{-1}(a+b x)^2 \tan ^{-1}\left(e^{i \sec ^{-1}(a+b x)}\right)}{b}",1,"((a + b*x)*ArcSec[a + b*x]^3)/b + ((6*I)*ArcSec[a + b*x]^2*ArcTan[E^(I*ArcSec[a + b*x])])/b - ((6*I)*ArcSec[a + b*x]*PolyLog[2, (-I)*E^(I*ArcSec[a + b*x])])/b + ((6*I)*ArcSec[a + b*x]*PolyLog[2, I*E^(I*ArcSec[a + b*x])])/b + (6*PolyLog[3, (-I)*E^(I*ArcSec[a + b*x])])/b - (6*PolyLog[3, I*E^(I*ArcSec[a + b*x])])/b","A",10,7,8,0.8750,1,"{5252, 5216, 3757, 4181, 2531, 2282, 6589}"
36,1,430,0,0.5330901,"\int \frac{\sec ^{-1}(a+b x)^3}{x} \, dx","Int[ArcSec[a + b*x]^3/x,x]","-3 i \sec ^{-1}(a+b x)^2 \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-3 i \sec ^{-1}(a+b x)^2 \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+6 \sec ^{-1}(a+b x) \text{PolyLog}\left(3,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+6 \sec ^{-1}(a+b x) \text{PolyLog}\left(3,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+6 i \text{PolyLog}\left(4,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+6 i \text{PolyLog}\left(4,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+\frac{3}{2} i \sec ^{-1}(a+b x)^2 \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(a+b x)}\right)-\frac{3}{2} \sec ^{-1}(a+b x) \text{PolyLog}\left(3,-e^{2 i \sec ^{-1}(a+b x)}\right)-\frac{3}{4} i \text{PolyLog}\left(4,-e^{2 i \sec ^{-1}(a+b x)}\right)+\sec ^{-1}(a+b x)^3 \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\sec ^{-1}(a+b x)^3 \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\sec ^{-1}(a+b x)^3 \log \left(1+e^{2 i \sec ^{-1}(a+b x)}\right)","-3 i \sec ^{-1}(a+b x)^2 \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)-3 i \sec ^{-1}(a+b x)^2 \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+6 \sec ^{-1}(a+b x) \text{PolyLog}\left(3,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+6 \sec ^{-1}(a+b x) \text{PolyLog}\left(3,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+6 i \text{PolyLog}\left(4,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+6 i \text{PolyLog}\left(4,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)+\frac{3}{2} i \sec ^{-1}(a+b x)^2 \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(a+b x)}\right)-\frac{3}{2} \sec ^{-1}(a+b x) \text{PolyLog}\left(3,-e^{2 i \sec ^{-1}(a+b x)}\right)-\frac{3}{4} i \text{PolyLog}\left(4,-e^{2 i \sec ^{-1}(a+b x)}\right)+\sec ^{-1}(a+b x)^3 \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)+\sec ^{-1}(a+b x)^3 \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)-\sec ^{-1}(a+b x)^3 \log \left(1+e^{2 i \sec ^{-1}(a+b x)}\right)",1,"ArcSec[a + b*x]^3*Log[1 - (a*E^(I*ArcSec[a + b*x]))/(1 - Sqrt[1 - a^2])] + ArcSec[a + b*x]^3*Log[1 - (a*E^(I*ArcSec[a + b*x]))/(1 + Sqrt[1 - a^2])] - ArcSec[a + b*x]^3*Log[1 + E^((2*I)*ArcSec[a + b*x])] - (3*I)*ArcSec[a + b*x]^2*PolyLog[2, (a*E^(I*ArcSec[a + b*x]))/(1 - Sqrt[1 - a^2])] - (3*I)*ArcSec[a + b*x]^2*PolyLog[2, (a*E^(I*ArcSec[a + b*x]))/(1 + Sqrt[1 - a^2])] + ((3*I)/2)*ArcSec[a + b*x]^2*PolyLog[2, -E^((2*I)*ArcSec[a + b*x])] + 6*ArcSec[a + b*x]*PolyLog[3, (a*E^(I*ArcSec[a + b*x]))/(1 - Sqrt[1 - a^2])] + 6*ArcSec[a + b*x]*PolyLog[3, (a*E^(I*ArcSec[a + b*x]))/(1 + Sqrt[1 - a^2])] - (3*ArcSec[a + b*x]*PolyLog[3, -E^((2*I)*ArcSec[a + b*x])])/2 + (6*I)*PolyLog[4, (a*E^(I*ArcSec[a + b*x]))/(1 - Sqrt[1 - a^2])] + (6*I)*PolyLog[4, (a*E^(I*ArcSec[a + b*x]))/(1 + Sqrt[1 - a^2])] - ((3*I)/4)*PolyLog[4, -E^((2*I)*ArcSec[a + b*x])]","A",20,10,12,0.8333,1,"{5258, 4551, 4530, 3719, 2190, 2531, 6609, 2282, 6589, 4520}"
37,1,362,0,0.5947696,"\int \frac{\sec ^{-1}(a+b x)^3}{x^2} \, dx","Int[ArcSec[a + b*x]^3/x^2,x]","-\frac{6 b \sec ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{6 b \sec ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{6 i b \text{PolyLog}\left(3,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{6 i b \text{PolyLog}\left(3,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{3 i b \sec ^{-1}(a+b x)^2 \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{3 i b \sec ^{-1}(a+b x)^2 \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{b \sec ^{-1}(a+b x)^3}{a}-\frac{\sec ^{-1}(a+b x)^3}{x}","-\frac{6 b \sec ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{6 b \sec ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{6 i b \text{PolyLog}\left(3,\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{6 i b \text{PolyLog}\left(3,\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{3 i b \sec ^{-1}(a+b x)^2 \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{1-\sqrt{1-a^2}}\right)}{a \sqrt{1-a^2}}+\frac{3 i b \sec ^{-1}(a+b x)^2 \log \left(1-\frac{a e^{i \sec ^{-1}(a+b x)}}{\sqrt{1-a^2}+1}\right)}{a \sqrt{1-a^2}}-\frac{b \sec ^{-1}(a+b x)^3}{a}-\frac{\sec ^{-1}(a+b x)^3}{x}",1,"-((b*ArcSec[a + b*x]^3)/a) - ArcSec[a + b*x]^3/x - ((3*I)*b*ArcSec[a + b*x]^2*Log[1 - (a*E^(I*ArcSec[a + b*x]))/(1 - Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) + ((3*I)*b*ArcSec[a + b*x]^2*Log[1 - (a*E^(I*ArcSec[a + b*x]))/(1 + Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) - (6*b*ArcSec[a + b*x]*PolyLog[2, (a*E^(I*ArcSec[a + b*x]))/(1 - Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) + (6*b*ArcSec[a + b*x]*PolyLog[2, (a*E^(I*ArcSec[a + b*x]))/(1 + Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) - ((6*I)*b*PolyLog[3, (a*E^(I*ArcSec[a + b*x]))/(1 - Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2]) + ((6*I)*b*PolyLog[3, (a*E^(I*ArcSec[a + b*x]))/(1 + Sqrt[1 - a^2])])/(a*Sqrt[1 - a^2])","A",14,9,12,0.7500,1,"{5258, 4426, 4191, 3321, 2264, 2190, 2531, 2282, 6589}"
38,1,58,0,0.0729258,"\int x \left(a+b \sec ^{-1}\left(c+d x^2\right)\right) \, dx","Int[x*(a + b*ArcSec[c + d*x^2]),x]","\frac{a x^2}{2}+\frac{b \left(c+d x^2\right) \sec ^{-1}\left(c+d x^2\right)}{2 d}-\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{\left(c+d x^2\right)^2}}\right)}{2 d}","\frac{a x^2}{2}+\frac{b \left(c+d x^2\right) \sec ^{-1}\left(c+d x^2\right)}{2 d}-\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{\left(c+d x^2\right)^2}}\right)}{2 d}",1,"(a*x^2)/2 + (b*(c + d*x^2)*ArcSec[c + d*x^2])/(2*d) - (b*ArcTanh[Sqrt[1 - (c + d*x^2)^(-2)]])/(2*d)","A",7,6,14,0.4286,1,"{6715, 5250, 372, 266, 63, 206}"
39,1,58,0,0.0761917,"\int x^2 \left(a+b \sec ^{-1}\left(c+d x^3\right)\right) \, dx","Int[x^2*(a + b*ArcSec[c + d*x^3]),x]","\frac{a x^3}{3}+\frac{b \left(c+d x^3\right) \sec ^{-1}\left(c+d x^3\right)}{3 d}-\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{\left(c+d x^3\right)^2}}\right)}{3 d}","\frac{a x^3}{3}+\frac{b \left(c+d x^3\right) \sec ^{-1}\left(c+d x^3\right)}{3 d}-\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{\left(c+d x^3\right)^2}}\right)}{3 d}",1,"(a*x^3)/3 + (b*(c + d*x^3)*ArcSec[c + d*x^3])/(3*d) - (b*ArcTanh[Sqrt[1 - (c + d*x^3)^(-2)]])/(3*d)","A",7,6,16,0.3750,1,"{6715, 5250, 372, 266, 63, 206}"
40,1,58,0,0.0776517,"\int x^3 \left(a+b \sec ^{-1}\left(c+d x^4\right)\right) \, dx","Int[x^3*(a + b*ArcSec[c + d*x^4]),x]","\frac{a x^4}{4}+\frac{b \left(c+d x^4\right) \sec ^{-1}\left(c+d x^4\right)}{4 d}-\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{\left(c+d x^4\right)^2}}\right)}{4 d}","\frac{a x^4}{4}+\frac{b \left(c+d x^4\right) \sec ^{-1}\left(c+d x^4\right)}{4 d}-\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{\left(c+d x^4\right)^2}}\right)}{4 d}",1,"(a*x^4)/4 + (b*(c + d*x^4)*ArcSec[c + d*x^4])/(4*d) - (b*ArcTanh[Sqrt[1 - (c + d*x^4)^(-2)]])/(4*d)","A",7,6,16,0.3750,1,"{6715, 5250, 372, 266, 63, 206}"
41,1,49,0,0.0716714,"\int x^{-1+n} \sec ^{-1}\left(a+b x^n\right) \, dx","Int[x^(-1 + n)*ArcSec[a + b*x^n],x]","\frac{\left(a+b x^n\right) \sec ^{-1}\left(a+b x^n\right)}{b n}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{\left(a+b x^n\right)^2}}\right)}{b n}","\frac{\left(a+b x^n\right) \sec ^{-1}\left(a+b x^n\right)}{b n}-\frac{\tanh ^{-1}\left(\sqrt{1-\frac{1}{\left(a+b x^n\right)^2}}\right)}{b n}",1,"((a + b*x^n)*ArcSec[a + b*x^n])/(b*n) - ArcTanh[Sqrt[1 - (a + b*x^n)^(-2)]]/(b*n)","A",6,6,14,0.4286,1,"{6715, 5250, 372, 266, 63, 206}"
42,1,85,0,0.081309,"\int \sec ^{-1}\left(c e^{a+b x}\right) \, dx","Int[ArcSec[c*E^(a + b*x)],x]","\frac{i \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}\left(c e^{a+b x}\right)}\right)}{2 b}+\frac{i \sec ^{-1}\left(c e^{a+b x}\right)^2}{2 b}-\frac{\sec ^{-1}\left(c e^{a+b x}\right) \log \left(1+e^{2 i \sec ^{-1}\left(c e^{a+b x}\right)}\right)}{b}","\frac{i \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}\left(c e^{a+b x}\right)}\right)}{2 b}+\frac{i \sec ^{-1}\left(c e^{a+b x}\right)^2}{2 b}-\frac{\sec ^{-1}\left(c e^{a+b x}\right) \log \left(1+e^{2 i \sec ^{-1}\left(c e^{a+b x}\right)}\right)}{b}",1,"((I/2)*ArcSec[c*E^(a + b*x)]^2)/b - (ArcSec[c*E^(a + b*x)]*Log[1 + E^((2*I)*ArcSec[c*E^(a + b*x)])])/b + ((I/2)*PolyLog[2, -E^((2*I)*ArcSec[c*E^(a + b*x)])])/b","A",7,7,10,0.7000,1,"{2282, 5218, 4626, 3719, 2190, 2279, 2391}"
43,1,99,0,0.1173912,"\int e^{\sec ^{-1}(a x)} x^2 \, dx","Int[E^ArcSec[a*x]*x^2,x]","\frac{\left(\frac{24}{5}+\frac{8 i}{5}\right) e^{(1+3 i) \sec ^{-1}(a x)} \, _2F_1\left(\frac{3}{2}-\frac{i}{2},4;\frac{5}{2}-\frac{i}{2};-e^{2 i \sec ^{-1}(a x)}\right)}{a^3}-\frac{\left(\frac{12}{5}+\frac{4 i}{5}\right) e^{(1+3 i) \sec ^{-1}(a x)} \, _2F_1\left(\frac{3}{2}-\frac{i}{2},3;\frac{5}{2}-\frac{i}{2};-e^{2 i \sec ^{-1}(a x)}\right)}{a^3}","\frac{\left(\frac{24}{5}+\frac{8 i}{5}\right) e^{(1+3 i) \sec ^{-1}(a x)} \, _2F_1\left(\frac{3}{2}-\frac{i}{2},4;\frac{5}{2}-\frac{i}{2};-e^{2 i \sec ^{-1}(a x)}\right)}{a^3}-\frac{\left(\frac{12}{5}+\frac{4 i}{5}\right) e^{(1+3 i) \sec ^{-1}(a x)} \, _2F_1\left(\frac{3}{2}-\frac{i}{2},3;\frac{5}{2}-\frac{i}{2};-e^{2 i \sec ^{-1}(a x)}\right)}{a^3}",1,"((-12/5 - (4*I)/5)*E^((1 + 3*I)*ArcSec[a*x])*Hypergeometric2F1[3/2 - I/2, 3, 5/2 - I/2, -E^((2*I)*ArcSec[a*x])])/a^3 + ((24/5 + (8*I)/5)*E^((1 + 3*I)*ArcSec[a*x])*Hypergeometric2F1[3/2 - I/2, 4, 5/2 - I/2, -E^((2*I)*ArcSec[a*x])])/a^3","A",6,4,10,0.4000,1,"{5266, 12, 4471, 2251}"
44,1,91,0,0.1066669,"\int e^{\sec ^{-1}(a x)} x \, dx","Int[E^ArcSec[a*x]*x,x]","\frac{\left(\frac{16}{5}+\frac{8 i}{5}\right) e^{(1+2 i) \sec ^{-1}(a x)} \, _2F_1\left(1-\frac{i}{2},3;2-\frac{i}{2};-e^{2 i \sec ^{-1}(a x)}\right)}{a^2}-\frac{\left(\frac{8}{5}+\frac{4 i}{5}\right) e^{(1+2 i) \sec ^{-1}(a x)} \, _2F_1\left(1-\frac{i}{2},2;2-\frac{i}{2};-e^{2 i \sec ^{-1}(a x)}\right)}{a^2}","\frac{\left(\frac{16}{5}+\frac{8 i}{5}\right) e^{(1+2 i) \sec ^{-1}(a x)} \, _2F_1\left(1-\frac{i}{2},3;2-\frac{i}{2};-e^{2 i \sec ^{-1}(a x)}\right)}{a^2}-\frac{\left(\frac{8}{5}+\frac{4 i}{5}\right) e^{(1+2 i) \sec ^{-1}(a x)} \, _2F_1\left(1-\frac{i}{2},2;2-\frac{i}{2};-e^{2 i \sec ^{-1}(a x)}\right)}{a^2}",1,"((-8/5 - (4*I)/5)*E^((1 + 2*I)*ArcSec[a*x])*Hypergeometric2F1[1 - I/2, 2, 2 - I/2, -E^((2*I)*ArcSec[a*x])])/a^2 + ((16/5 + (8*I)/5)*E^((1 + 2*I)*ArcSec[a*x])*Hypergeometric2F1[1 - I/2, 3, 2 - I/2, -E^((2*I)*ArcSec[a*x])])/a^2","A",6,4,8,0.5000,1,"{5266, 12, 4471, 2251}"
45,1,91,0,0.0922147,"\int e^{\sec ^{-1}(a x)} \, dx","Int[E^ArcSec[a*x],x]","\frac{(2+2 i) e^{(1+i) \sec ^{-1}(a x)} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},2;\frac{3}{2}-\frac{i}{2};-e^{2 i \sec ^{-1}(a x)}\right)}{a}-\frac{(1+i) e^{(1+i) \sec ^{-1}(a x)} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},1;\frac{3}{2}-\frac{i}{2};-e^{2 i \sec ^{-1}(a x)}\right)}{a}","\frac{(2+2 i) e^{(1+i) \sec ^{-1}(a x)} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},2;\frac{3}{2}-\frac{i}{2};-e^{2 i \sec ^{-1}(a x)}\right)}{a}-\frac{(1+i) e^{(1+i) \sec ^{-1}(a x)} \, _2F_1\left(\frac{1}{2}-\frac{i}{2},1;\frac{3}{2}-\frac{i}{2};-e^{2 i \sec ^{-1}(a x)}\right)}{a}",1,"((-1 - I)*E^((1 + I)*ArcSec[a*x])*Hypergeometric2F1[1/2 - I/2, 1, 3/2 - I/2, -E^((2*I)*ArcSec[a*x])])/a + ((2 + 2*I)*E^((1 + I)*ArcSec[a*x])*Hypergeometric2F1[1/2 - I/2, 2, 3/2 - I/2, -E^((2*I)*ArcSec[a*x])])/a","A",5,3,6,0.5000,1,"{5266, 4471, 2251}"
46,1,45,0,0.0578664,"\int \frac{e^{\sec ^{-1}(a x)}}{x} \, dx","Int[E^ArcSec[a*x]/x,x]","2 i e^{\sec ^{-1}(a x)} \, _2F_1\left(-\frac{i}{2},1;1-\frac{i}{2};-e^{2 i \sec ^{-1}(a x)}\right)-i e^{\sec ^{-1}(a x)}","2 i e^{\sec ^{-1}(a x)} \, _2F_1\left(-\frac{i}{2},1;1-\frac{i}{2};-e^{2 i \sec ^{-1}(a x)}\right)-i e^{\sec ^{-1}(a x)}",1,"(-I)*E^ArcSec[a*x] + (2*I)*E^ArcSec[a*x]*Hypergeometric2F1[-I/2, 1, 1 - I/2, -E^((2*I)*ArcSec[a*x])]","A",6,5,10,0.5000,1,"{5266, 12, 4442, 2194, 2251}"
47,1,39,0,0.0298828,"\int \frac{e^{\sec ^{-1}(a x)}}{x^2} \, dx","Int[E^ArcSec[a*x]/x^2,x]","\frac{1}{2} a \sqrt{1-\frac{1}{a^2 x^2}} e^{\sec ^{-1}(a x)}-\frac{e^{\sec ^{-1}(a x)}}{2 x}","\frac{1}{2} a \sqrt{1-\frac{1}{a^2 x^2}} e^{\sec ^{-1}(a x)}-\frac{e^{\sec ^{-1}(a x)}}{2 x}",1,"(a*E^ArcSec[a*x]*Sqrt[1 - 1/(a^2*x^2)])/2 - E^ArcSec[a*x]/(2*x)","A",3,3,10,0.3000,1,"{5266, 12, 4432}"
48,1,41,0,0.0416936,"\int \frac{e^{\sec ^{-1}(a x)}}{x^3} \, dx","Int[E^ArcSec[a*x]/x^3,x]","\frac{1}{10} a^2 e^{\sec ^{-1}(a x)} \sin \left(2 \sec ^{-1}(a x)\right)-\frac{1}{5} a^2 e^{\sec ^{-1}(a x)} \cos \left(2 \sec ^{-1}(a x)\right)","\frac{1}{10} a^2 e^{\sec ^{-1}(a x)} \sin \left(2 \sec ^{-1}(a x)\right)-\frac{1}{5} a^2 e^{\sec ^{-1}(a x)} \cos \left(2 \sec ^{-1}(a x)\right)",1,"-(a^2*E^ArcSec[a*x]*Cos[2*ArcSec[a*x]])/5 + (a^2*E^ArcSec[a*x]*Sin[2*ArcSec[a*x]])/10","A",5,4,10,0.4000,1,"{5266, 12, 4469, 4432}"
49,1,84,0,0.065074,"\int \frac{e^{\sec ^{-1}(a x)}}{x^4} \, dx","Int[E^ArcSec[a*x]/x^4,x]","\frac{1}{8} a^3 \sqrt{1-\frac{1}{a^2 x^2}} e^{\sec ^{-1}(a x)}-\frac{a^2 e^{\sec ^{-1}(a x)}}{8 x}-\frac{3}{40} a^3 e^{\sec ^{-1}(a x)} \cos \left(3 \sec ^{-1}(a x)\right)+\frac{1}{40} a^3 e^{\sec ^{-1}(a x)} \sin \left(3 \sec ^{-1}(a x)\right)","\frac{1}{8} a^3 \sqrt{1-\frac{1}{a^2 x^2}} e^{\sec ^{-1}(a x)}-\frac{a^2 e^{\sec ^{-1}(a x)}}{8 x}-\frac{3}{40} a^3 e^{\sec ^{-1}(a x)} \cos \left(3 \sec ^{-1}(a x)\right)+\frac{1}{40} a^3 e^{\sec ^{-1}(a x)} \sin \left(3 \sec ^{-1}(a x)\right)",1,"(a^3*E^ArcSec[a*x]*Sqrt[1 - 1/(a^2*x^2)])/8 - (a^2*E^ArcSec[a*x])/(8*x) - (3*a^3*E^ArcSec[a*x]*Cos[3*ArcSec[a*x]])/40 + (a^3*E^ArcSec[a*x]*Sin[3*ArcSec[a*x]])/40","A",6,4,10,0.4000,1,"{5266, 12, 4469, 4432}"
50,1,69,0,0.0913614,"\int \frac{\sec ^{-1}(a+b x)}{\frac{a d}{b}+d x} \, dx","Int[ArcSec[a + b*x]/((a*d)/b + d*x),x]","\frac{i \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(a+b x)}\right)}{2 d}+\frac{i \sec ^{-1}(a+b x)^2}{2 d}-\frac{\sec ^{-1}(a+b x) \log \left(1+e^{2 i \sec ^{-1}(a+b x)}\right)}{d}","\frac{i \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(a+b x)}\right)}{2 d}+\frac{i \sec ^{-1}(a+b x)^2}{2 d}-\frac{\sec ^{-1}(a+b x) \log \left(1+e^{2 i \sec ^{-1}(a+b x)}\right)}{d}",1,"((I/2)*ArcSec[a + b*x]^2)/d - (ArcSec[a + b*x]*Log[1 + E^((2*I)*ArcSec[a + b*x])])/d + ((I/2)*PolyLog[2, -E^((2*I)*ArcSec[a + b*x])])/d","A",8,8,19,0.4211,1,"{5256, 12, 5218, 4626, 3719, 2190, 2279, 2391}"