1,1,51,0,0.0279481,"\int x^5 \coth ^{-1}(a x) \, dx","Int[x^5*ArcCoth[a*x],x]","\frac{x^3}{18 a^3}+\frac{x}{6 a^5}-\frac{\tanh ^{-1}(a x)}{6 a^6}+\frac{x^5}{30 a}+\frac{1}{6} x^6 \coth ^{-1}(a x)","\frac{x^3}{18 a^3}+\frac{x}{6 a^5}-\frac{\tanh ^{-1}(a x)}{6 a^6}+\frac{x^5}{30 a}+\frac{1}{6} x^6 \coth ^{-1}(a x)",1,"x/(6*a^5) + x^3/(18*a^3) + x^5/(30*a) + (x^6*ArcCoth[a*x])/6 - ArcTanh[a*x]/(6*a^6)","A",4,3,8,0.3750,1,"{5917, 302, 206}"
2,1,50,0,0.0371068,"\int x^4 \coth ^{-1}(a x) \, dx","Int[x^4*ArcCoth[a*x],x]","\frac{x^2}{10 a^3}+\frac{\log \left(1-a^2 x^2\right)}{10 a^5}+\frac{x^4}{20 a}+\frac{1}{5} x^5 \coth ^{-1}(a x)","\frac{x^2}{10 a^3}+\frac{\log \left(1-a^2 x^2\right)}{10 a^5}+\frac{x^4}{20 a}+\frac{1}{5} x^5 \coth ^{-1}(a x)",1,"x^2/(10*a^3) + x^4/(20*a) + (x^5*ArcCoth[a*x])/5 + Log[1 - a^2*x^2]/(10*a^5)","A",4,3,8,0.3750,1,"{5917, 266, 43}"
3,1,41,0,0.0237262,"\int x^3 \coth ^{-1}(a x) \, dx","Int[x^3*ArcCoth[a*x],x]","\frac{x}{4 a^3}-\frac{\tanh ^{-1}(a x)}{4 a^4}+\frac{x^3}{12 a}+\frac{1}{4} x^4 \coth ^{-1}(a x)","\frac{x}{4 a^3}-\frac{\tanh ^{-1}(a x)}{4 a^4}+\frac{x^3}{12 a}+\frac{1}{4} x^4 \coth ^{-1}(a x)",1,"x/(4*a^3) + x^3/(12*a) + (x^4*ArcCoth[a*x])/4 - ArcTanh[a*x]/(4*a^4)","A",4,3,8,0.3750,1,"{5917, 302, 206}"
4,1,40,0,0.0298628,"\int x^2 \coth ^{-1}(a x) \, dx","Int[x^2*ArcCoth[a*x],x]","\frac{\log \left(1-a^2 x^2\right)}{6 a^3}+\frac{x^2}{6 a}+\frac{1}{3} x^3 \coth ^{-1}(a x)","\frac{\log \left(1-a^2 x^2\right)}{6 a^3}+\frac{x^2}{6 a}+\frac{1}{3} x^3 \coth ^{-1}(a x)",1,"x^2/(6*a) + (x^3*ArcCoth[a*x])/3 + Log[1 - a^2*x^2]/(6*a^3)","A",4,3,8,0.3750,1,"{5917, 266, 43}"
5,1,31,0,0.0132059,"\int x \coth ^{-1}(a x) \, dx","Int[x*ArcCoth[a*x],x]","-\frac{\tanh ^{-1}(a x)}{2 a^2}+\frac{1}{2} x^2 \coth ^{-1}(a x)+\frac{x}{2 a}","-\frac{\tanh ^{-1}(a x)}{2 a^2}+\frac{1}{2} x^2 \coth ^{-1}(a x)+\frac{x}{2 a}",1,"x/(2*a) + (x^2*ArcCoth[a*x])/2 - ArcTanh[a*x]/(2*a^2)","A",3,3,6,0.5000,1,"{5917, 321, 206}"
6,1,25,0,0.0068101,"\int \coth ^{-1}(a x) \, dx","Int[ArcCoth[a*x],x]","\frac{\log \left(1-a^2 x^2\right)}{2 a}+x \coth ^{-1}(a x)","\frac{\log \left(1-a^2 x^2\right)}{2 a}+x \coth ^{-1}(a x)",1,"x*ArcCoth[a*x] + Log[1 - a^2*x^2]/(2*a)","A",2,2,4,0.5000,1,"{5911, 260}"
7,1,28,0,0.0097539,"\int \frac{\coth ^{-1}(a x)}{x} \, dx","Int[ArcCoth[a*x]/x,x]","\frac{1}{2} \text{PolyLog}\left(2,-\frac{1}{a x}\right)-\frac{1}{2} \text{PolyLog}\left(2,\frac{1}{a x}\right)","\frac{1}{2} \text{PolyLog}\left(2,-\frac{1}{a x}\right)-\frac{1}{2} \text{PolyLog}\left(2,\frac{1}{a x}\right)",1,"PolyLog[2, -(1/(a*x))]/2 - PolyLog[2, 1/(a*x)]/2","A",1,1,8,0.1250,1,"{5913}"
8,1,30,0,0.020794,"\int \frac{\coth ^{-1}(a x)}{x^2} \, dx","Int[ArcCoth[a*x]/x^2,x]","-\frac{1}{2} a \log \left(1-a^2 x^2\right)+a \log (x)-\frac{\coth ^{-1}(a x)}{x}","-\frac{1}{2} a \log \left(1-a^2 x^2\right)+a \log (x)-\frac{\coth ^{-1}(a x)}{x}",1,"-(ArcCoth[a*x]/x) + a*Log[x] - (a*Log[1 - a^2*x^2])/2","A",5,5,8,0.6250,1,"{5917, 266, 36, 29, 31}"
9,1,31,0,0.0163453,"\int \frac{\coth ^{-1}(a x)}{x^3} \, dx","Int[ArcCoth[a*x]/x^3,x]","\frac{1}{2} a^2 \tanh ^{-1}(a x)-\frac{\coth ^{-1}(a x)}{2 x^2}-\frac{a}{2 x}","\frac{1}{2} a^2 \tanh ^{-1}(a x)-\frac{\coth ^{-1}(a x)}{2 x^2}-\frac{a}{2 x}",1,"-a/(2*x) - ArcCoth[a*x]/(2*x^2) + (a^2*ArcTanh[a*x])/2","A",3,3,8,0.3750,1,"{5917, 325, 206}"
10,1,47,0,0.0302444,"\int \frac{\coth ^{-1}(a x)}{x^4} \, dx","Int[ArcCoth[a*x]/x^4,x]","-\frac{1}{6} a^3 \log \left(1-a^2 x^2\right)+\frac{1}{3} a^3 \log (x)-\frac{a}{6 x^2}-\frac{\coth ^{-1}(a x)}{3 x^3}","-\frac{1}{6} a^3 \log \left(1-a^2 x^2\right)+\frac{1}{3} a^3 \log (x)-\frac{a}{6 x^2}-\frac{\coth ^{-1}(a x)}{3 x^3}",1,"-a/(6*x^2) - ArcCoth[a*x]/(3*x^3) + (a^3*Log[x])/3 - (a^3*Log[1 - a^2*x^2])/6","A",4,3,8,0.3750,1,"{5917, 266, 44}"
11,1,41,0,0.0218977,"\int \frac{\coth ^{-1}(a x)}{x^5} \, dx","Int[ArcCoth[a*x]/x^5,x]","-\frac{a^3}{4 x}+\frac{1}{4} a^4 \tanh ^{-1}(a x)-\frac{a}{12 x^3}-\frac{\coth ^{-1}(a x)}{4 x^4}","-\frac{a^3}{4 x}+\frac{1}{4} a^4 \tanh ^{-1}(a x)-\frac{a}{12 x^3}-\frac{\coth ^{-1}(a x)}{4 x^4}",1,"-a/(12*x^3) - a^3/(4*x) - ArcCoth[a*x]/(4*x^4) + (a^4*ArcTanh[a*x])/4","A",4,3,8,0.3750,1,"{5917, 325, 206}"
12,1,105,0,0.2456909,"\int x^5 \coth ^{-1}(a x)^2 \, dx","Int[x^5*ArcCoth[a*x]^2,x]","\frac{x^4}{60 a^2}+\frac{4 x^2}{45 a^4}+\frac{23 \log \left(1-a^2 x^2\right)}{90 a^6}+\frac{x^3 \coth ^{-1}(a x)}{9 a^3}+\frac{x \coth ^{-1}(a x)}{3 a^5}-\frac{\coth ^{-1}(a x)^2}{6 a^6}+\frac{1}{6} x^6 \coth ^{-1}(a x)^2+\frac{x^5 \coth ^{-1}(a x)}{15 a}","\frac{x^4}{60 a^2}+\frac{4 x^2}{45 a^4}+\frac{23 \log \left(1-a^2 x^2\right)}{90 a^6}+\frac{x^3 \coth ^{-1}(a x)}{9 a^3}+\frac{x \coth ^{-1}(a x)}{3 a^5}-\frac{\coth ^{-1}(a x)^2}{6 a^6}+\frac{1}{6} x^6 \coth ^{-1}(a x)^2+\frac{x^5 \coth ^{-1}(a x)}{15 a}",1,"(4*x^2)/(45*a^4) + x^4/(60*a^2) + (x*ArcCoth[a*x])/(3*a^5) + (x^3*ArcCoth[a*x])/(9*a^3) + (x^5*ArcCoth[a*x])/(15*a) - ArcCoth[a*x]^2/(6*a^6) + (x^6*ArcCoth[a*x]^2)/6 + (23*Log[1 - a^2*x^2])/(90*a^6)","A",15,7,10,0.7000,1,"{5917, 5981, 266, 43, 5911, 260, 5949}"
13,1,127,0,0.2256594,"\int x^4 \coth ^{-1}(a x)^2 \, dx","Int[x^4*ArcCoth[a*x]^2,x]","-\frac{\text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{5 a^5}+\frac{x^3}{30 a^2}+\frac{x^2 \coth ^{-1}(a x)}{5 a^3}+\frac{3 x}{10 a^4}-\frac{3 \tanh ^{-1}(a x)}{10 a^5}+\frac{\coth ^{-1}(a x)^2}{5 a^5}-\frac{2 \log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)}{5 a^5}+\frac{1}{5} x^5 \coth ^{-1}(a x)^2+\frac{x^4 \coth ^{-1}(a x)}{10 a}","-\frac{\text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{5 a^5}+\frac{x^3}{30 a^2}+\frac{x^2 \coth ^{-1}(a x)}{5 a^3}+\frac{3 x}{10 a^4}-\frac{3 \tanh ^{-1}(a x)}{10 a^5}+\frac{\coth ^{-1}(a x)^2}{5 a^5}-\frac{2 \log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)}{5 a^5}+\frac{1}{5} x^5 \coth ^{-1}(a x)^2+\frac{x^4 \coth ^{-1}(a x)}{10 a}",1,"(3*x)/(10*a^4) + x^3/(30*a^2) + (x^2*ArcCoth[a*x])/(5*a^3) + (x^4*ArcCoth[a*x])/(10*a) + ArcCoth[a*x]^2/(5*a^5) + (x^5*ArcCoth[a*x]^2)/5 - (3*ArcTanh[a*x])/(10*a^5) - (2*ArcCoth[a*x]*Log[2/(1 - a*x)])/(5*a^5) - PolyLog[2, 1 - 2/(1 - a*x)]/(5*a^5)","A",14,9,10,0.9000,1,"{5917, 5981, 302, 206, 321, 5985, 5919, 2402, 2315}"
14,1,81,0,0.1629489,"\int x^3 \coth ^{-1}(a x)^2 \, dx","Int[x^3*ArcCoth[a*x]^2,x]","\frac{x^2}{12 a^2}+\frac{\log \left(1-a^2 x^2\right)}{3 a^4}+\frac{x \coth ^{-1}(a x)}{2 a^3}-\frac{\coth ^{-1}(a x)^2}{4 a^4}+\frac{1}{4} x^4 \coth ^{-1}(a x)^2+\frac{x^3 \coth ^{-1}(a x)}{6 a}","\frac{x^2}{12 a^2}+\frac{\log \left(1-a^2 x^2\right)}{3 a^4}+\frac{x \coth ^{-1}(a x)}{2 a^3}-\frac{\coth ^{-1}(a x)^2}{4 a^4}+\frac{1}{4} x^4 \coth ^{-1}(a x)^2+\frac{x^3 \coth ^{-1}(a x)}{6 a}",1,"x^2/(12*a^2) + (x*ArcCoth[a*x])/(2*a^3) + (x^3*ArcCoth[a*x])/(6*a) - ArcCoth[a*x]^2/(4*a^4) + (x^4*ArcCoth[a*x]^2)/4 + Log[1 - a^2*x^2]/(3*a^4)","A",10,7,10,0.7000,1,"{5917, 5981, 266, 43, 5911, 260, 5949}"
15,1,103,0,0.1532143,"\int x^2 \coth ^{-1}(a x)^2 \, dx","Int[x^2*ArcCoth[a*x]^2,x]","-\frac{\text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{3 a^3}+\frac{x}{3 a^2}-\frac{\tanh ^{-1}(a x)}{3 a^3}+\frac{\coth ^{-1}(a x)^2}{3 a^3}-\frac{2 \log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)}{3 a^3}+\frac{1}{3} x^3 \coth ^{-1}(a x)^2+\frac{x^2 \coth ^{-1}(a x)}{3 a}","-\frac{\text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{3 a^3}+\frac{x}{3 a^2}-\frac{\tanh ^{-1}(a x)}{3 a^3}+\frac{\coth ^{-1}(a x)^2}{3 a^3}-\frac{2 \log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)}{3 a^3}+\frac{1}{3} x^3 \coth ^{-1}(a x)^2+\frac{x^2 \coth ^{-1}(a x)}{3 a}",1,"x/(3*a^2) + (x^2*ArcCoth[a*x])/(3*a) + ArcCoth[a*x]^2/(3*a^3) + (x^3*ArcCoth[a*x]^2)/3 - ArcTanh[a*x]/(3*a^3) - (2*ArcCoth[a*x]*Log[2/(1 - a*x)])/(3*a^3) - PolyLog[2, 1 - 2/(1 - a*x)]/(3*a^3)","A",9,8,10,0.8000,1,"{5917, 5981, 321, 206, 5985, 5919, 2402, 2315}"
16,1,54,0,0.0783636,"\int x \coth ^{-1}(a x)^2 \, dx","Int[x*ArcCoth[a*x]^2,x]","\frac{\log \left(1-a^2 x^2\right)}{2 a^2}-\frac{\coth ^{-1}(a x)^2}{2 a^2}+\frac{1}{2} x^2 \coth ^{-1}(a x)^2+\frac{x \coth ^{-1}(a x)}{a}","\frac{\log \left(1-a^2 x^2\right)}{2 a^2}-\frac{\coth ^{-1}(a x)^2}{2 a^2}+\frac{1}{2} x^2 \coth ^{-1}(a x)^2+\frac{x \coth ^{-1}(a x)}{a}",1,"(x*ArcCoth[a*x])/a - ArcCoth[a*x]^2/(2*a^2) + (x^2*ArcCoth[a*x]^2)/2 + Log[1 - a^2*x^2]/(2*a^2)","A",5,5,8,0.6250,1,"{5917, 5981, 5911, 260, 5949}"
17,1,58,0,0.0777673,"\int \coth ^{-1}(a x)^2 \, dx","Int[ArcCoth[a*x]^2,x]","-\frac{\text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a}+x \coth ^{-1}(a x)^2+\frac{\coth ^{-1}(a x)^2}{a}-\frac{2 \log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)}{a}","-\frac{\text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a}+x \coth ^{-1}(a x)^2+\frac{\coth ^{-1}(a x)^2}{a}-\frac{2 \log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)}{a}",1,"ArcCoth[a*x]^2/a + x*ArcCoth[a*x]^2 - (2*ArcCoth[a*x]*Log[2/(1 - a*x)])/a - PolyLog[2, 1 - 2/(1 - a*x)]/a","A",5,5,6,0.8333,1,"{5911, 5985, 5919, 2402, 2315}"
18,1,97,0,0.2320094,"\int \frac{\coth ^{-1}(a x)^2}{x} \, dx","Int[ArcCoth[a*x]^2/x,x]","\frac{1}{2} \text{PolyLog}\left(3,1-\frac{2}{a x+1}\right)-\frac{1}{2} \text{PolyLog}\left(3,1-\frac{2 a x}{a x+1}\right)+\coth ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{a x+1}\right)-\coth ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2 a x}{a x+1}\right)+2 \coth ^{-1}\left(1-\frac{2}{1-a x}\right) \coth ^{-1}(a x)^2","\frac{1}{2} \text{PolyLog}\left(3,1-\frac{2}{a x+1}\right)-\frac{1}{2} \text{PolyLog}\left(3,1-\frac{2 a x}{a x+1}\right)+\coth ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{a x+1}\right)-\coth ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2 a x}{a x+1}\right)+2 \coth ^{-1}\left(1-\frac{2}{1-a x}\right) \coth ^{-1}(a x)^2",1,"2*ArcCoth[a*x]^2*ArcCoth[1 - 2/(1 - a*x)] + ArcCoth[a*x]*PolyLog[2, 1 - 2/(1 + a*x)] - ArcCoth[a*x]*PolyLog[2, 1 - (2*a*x)/(1 + a*x)] + PolyLog[3, 1 - 2/(1 + a*x)]/2 - PolyLog[3, 1 - (2*a*x)/(1 + a*x)]/2","A",6,5,10,0.5000,1,"{5915, 6053, 5949, 6057, 6610}"
19,1,55,0,0.1083289,"\int \frac{\coth ^{-1}(a x)^2}{x^2} \, dx","Int[ArcCoth[a*x]^2/x^2,x]","-a \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+a \coth ^{-1}(a x)^2-\frac{\coth ^{-1}(a x)^2}{x}+2 a \log \left(2-\frac{2}{a x+1}\right) \coth ^{-1}(a x)","-a \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+a \coth ^{-1}(a x)^2-\frac{\coth ^{-1}(a x)^2}{x}+2 a \log \left(2-\frac{2}{a x+1}\right) \coth ^{-1}(a x)",1,"a*ArcCoth[a*x]^2 - ArcCoth[a*x]^2/x + 2*a*ArcCoth[a*x]*Log[2 - 2/(1 + a*x)] - a*PolyLog[2, -1 + 2/(1 + a*x)]","A",4,4,10,0.4000,1,"{5917, 5989, 5933, 2447}"
20,1,61,0,0.0985716,"\int \frac{\coth ^{-1}(a x)^2}{x^3} \, dx","Int[ArcCoth[a*x]^2/x^3,x]","-\frac{1}{2} a^2 \log \left(1-a^2 x^2\right)+a^2 \log (x)+\frac{1}{2} a^2 \coth ^{-1}(a x)^2-\frac{\coth ^{-1}(a x)^2}{2 x^2}-\frac{a \coth ^{-1}(a x)}{x}","-\frac{1}{2} a^2 \log \left(1-a^2 x^2\right)+a^2 \log (x)+\frac{1}{2} a^2 \coth ^{-1}(a x)^2-\frac{\coth ^{-1}(a x)^2}{2 x^2}-\frac{a \coth ^{-1}(a x)}{x}",1,"-((a*ArcCoth[a*x])/x) + (a^2*ArcCoth[a*x]^2)/2 - ArcCoth[a*x]^2/(2*x^2) + a^2*Log[x] - (a^2*Log[1 - a^2*x^2])/2","A",8,7,10,0.7000,1,"{5917, 5983, 266, 36, 29, 31, 5949}"
21,1,103,0,0.1707835,"\int \frac{\coth ^{-1}(a x)^2}{x^4} \, dx","Int[ArcCoth[a*x]^2/x^4,x]","-\frac{1}{3} a^3 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{a^2}{3 x}+\frac{1}{3} a^3 \tanh ^{-1}(a x)+\frac{1}{3} a^3 \coth ^{-1}(a x)^2+\frac{2}{3} a^3 \log \left(2-\frac{2}{a x+1}\right) \coth ^{-1}(a x)-\frac{a \coth ^{-1}(a x)}{3 x^2}-\frac{\coth ^{-1}(a x)^2}{3 x^3}","-\frac{1}{3} a^3 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{a^2}{3 x}+\frac{1}{3} a^3 \tanh ^{-1}(a x)+\frac{1}{3} a^3 \coth ^{-1}(a x)^2+\frac{2}{3} a^3 \log \left(2-\frac{2}{a x+1}\right) \coth ^{-1}(a x)-\frac{a \coth ^{-1}(a x)}{3 x^2}-\frac{\coth ^{-1}(a x)^2}{3 x^3}",1,"-a^2/(3*x) - (a*ArcCoth[a*x])/(3*x^2) + (a^3*ArcCoth[a*x]^2)/3 - ArcCoth[a*x]^2/(3*x^3) + (a^3*ArcTanh[a*x])/3 + (2*a^3*ArcCoth[a*x]*Log[2 - 2/(1 + a*x)])/3 - (a^3*PolyLog[2, -1 + 2/(1 + a*x)])/3","A",8,7,10,0.7000,1,"{5917, 5983, 325, 206, 5989, 5933, 2447}"
22,1,90,0,0.1723403,"\int \frac{\coth ^{-1}(a x)^2}{x^5} \, dx","Int[ArcCoth[a*x]^2/x^5,x]","-\frac{a^2}{12 x^2}-\frac{1}{3} a^4 \log \left(1-a^2 x^2\right)+\frac{2}{3} a^4 \log (x)+\frac{1}{4} a^4 \coth ^{-1}(a x)^2-\frac{a^3 \coth ^{-1}(a x)}{2 x}-\frac{a \coth ^{-1}(a x)}{6 x^3}-\frac{\coth ^{-1}(a x)^2}{4 x^4}","-\frac{a^2}{12 x^2}-\frac{1}{3} a^4 \log \left(1-a^2 x^2\right)+\frac{2}{3} a^4 \log (x)+\frac{1}{4} a^4 \coth ^{-1}(a x)^2-\frac{a^3 \coth ^{-1}(a x)}{2 x}-\frac{a \coth ^{-1}(a x)}{6 x^3}-\frac{\coth ^{-1}(a x)^2}{4 x^4}",1,"-a^2/(12*x^2) - (a*ArcCoth[a*x])/(6*x^3) - (a^3*ArcCoth[a*x])/(2*x) + (a^4*ArcCoth[a*x]^2)/4 - ArcCoth[a*x]^2/(4*x^4) + (2*a^4*Log[x])/3 - (a^4*Log[1 - a^2*x^2])/3","A",13,8,10,0.8000,1,"{5917, 5983, 266, 44, 36, 29, 31, 5949}"
23,1,186,0,0.7171932,"\int x^5 \coth ^{-1}(a x)^3 \, dx","Int[x^5*ArcCoth[a*x]^3,x]","-\frac{23 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{30 a^6}+\frac{x^3}{60 a^3}+\frac{x^4 \coth ^{-1}(a x)}{20 a^2}+\frac{x^3 \coth ^{-1}(a x)^2}{6 a^3}+\frac{4 x^2 \coth ^{-1}(a x)}{15 a^4}+\frac{19 x}{60 a^5}-\frac{19 \tanh ^{-1}(a x)}{60 a^6}+\frac{x \coth ^{-1}(a x)^2}{2 a^5}-\frac{\coth ^{-1}(a x)^3}{6 a^6}+\frac{23 \coth ^{-1}(a x)^2}{30 a^6}-\frac{23 \log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)}{15 a^6}+\frac{1}{6} x^6 \coth ^{-1}(a x)^3+\frac{x^5 \coth ^{-1}(a x)^2}{10 a}","-\frac{23 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{30 a^6}+\frac{x^3}{60 a^3}+\frac{x^4 \coth ^{-1}(a x)}{20 a^2}+\frac{x^3 \coth ^{-1}(a x)^2}{6 a^3}+\frac{4 x^2 \coth ^{-1}(a x)}{15 a^4}+\frac{19 x}{60 a^5}-\frac{19 \tanh ^{-1}(a x)}{60 a^6}+\frac{x \coth ^{-1}(a x)^2}{2 a^5}-\frac{\coth ^{-1}(a x)^3}{6 a^6}+\frac{23 \coth ^{-1}(a x)^2}{30 a^6}-\frac{23 \log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)}{15 a^6}+\frac{1}{6} x^6 \coth ^{-1}(a x)^3+\frac{x^5 \coth ^{-1}(a x)^2}{10 a}",1,"(19*x)/(60*a^5) + x^3/(60*a^3) + (4*x^2*ArcCoth[a*x])/(15*a^4) + (x^4*ArcCoth[a*x])/(20*a^2) + (23*ArcCoth[a*x]^2)/(30*a^6) + (x*ArcCoth[a*x]^2)/(2*a^5) + (x^3*ArcCoth[a*x]^2)/(6*a^3) + (x^5*ArcCoth[a*x]^2)/(10*a) - ArcCoth[a*x]^3/(6*a^6) + (x^6*ArcCoth[a*x]^3)/6 - (19*ArcTanh[a*x])/(60*a^6) - (23*ArcCoth[a*x]*Log[2/(1 - a*x)])/(15*a^6) - (23*PolyLog[2, 1 - 2/(1 - a*x)])/(30*a^6)","A",33,11,10,1.100,1,"{5917, 5981, 302, 206, 321, 5985, 5919, 2402, 2315, 5911, 5949}"
24,1,196,0,0.5802819,"\int x^4 \coth ^{-1}(a x)^3 \, dx","Int[x^4*ArcCoth[a*x]^3,x]","\frac{3 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{10 a^5}-\frac{3 \coth ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{5 a^5}+\frac{x^2}{20 a^3}+\frac{\log \left(1-a^2 x^2\right)}{2 a^5}+\frac{x^3 \coth ^{-1}(a x)}{10 a^2}+\frac{3 x^2 \coth ^{-1}(a x)^2}{10 a^3}+\frac{9 x \coth ^{-1}(a x)}{10 a^4}+\frac{\coth ^{-1}(a x)^3}{5 a^5}-\frac{9 \coth ^{-1}(a x)^2}{20 a^5}-\frac{3 \log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)^2}{5 a^5}+\frac{1}{5} x^5 \coth ^{-1}(a x)^3+\frac{3 x^4 \coth ^{-1}(a x)^2}{20 a}","\frac{3 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{10 a^5}-\frac{3 \coth ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{5 a^5}+\frac{x^2}{20 a^3}+\frac{\log \left(1-a^2 x^2\right)}{2 a^5}+\frac{x^3 \coth ^{-1}(a x)}{10 a^2}+\frac{3 x^2 \coth ^{-1}(a x)^2}{10 a^3}+\frac{9 x \coth ^{-1}(a x)}{10 a^4}+\frac{\coth ^{-1}(a x)^3}{5 a^5}-\frac{9 \coth ^{-1}(a x)^2}{20 a^5}-\frac{3 \log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)^2}{5 a^5}+\frac{1}{5} x^5 \coth ^{-1}(a x)^3+\frac{3 x^4 \coth ^{-1}(a x)^2}{20 a}",1,"x^2/(20*a^3) + (9*x*ArcCoth[a*x])/(10*a^4) + (x^3*ArcCoth[a*x])/(10*a^2) - (9*ArcCoth[a*x]^2)/(20*a^5) + (3*x^2*ArcCoth[a*x]^2)/(10*a^3) + (3*x^4*ArcCoth[a*x]^2)/(20*a) + ArcCoth[a*x]^3/(5*a^5) + (x^5*ArcCoth[a*x]^3)/5 - (3*ArcCoth[a*x]^2*Log[2/(1 - a*x)])/(5*a^5) + Log[1 - a^2*x^2]/(2*a^5) - (3*ArcCoth[a*x]*PolyLog[2, 1 - 2/(1 - a*x)])/(5*a^5) + (3*PolyLog[3, 1 - 2/(1 - a*x)])/(10*a^5)","A",22,11,10,1.100,1,"{5917, 5981, 266, 43, 5911, 260, 5949, 5985, 5919, 6059, 6610}"
25,1,139,0,0.4166799,"\int x^3 \coth ^{-1}(a x)^3 \, dx","Int[x^3*ArcCoth[a*x]^3,x]","-\frac{\text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^4}+\frac{x^2 \coth ^{-1}(a x)}{4 a^2}+\frac{x}{4 a^3}-\frac{\tanh ^{-1}(a x)}{4 a^4}+\frac{3 x \coth ^{-1}(a x)^2}{4 a^3}-\frac{\coth ^{-1}(a x)^3}{4 a^4}+\frac{\coth ^{-1}(a x)^2}{a^4}-\frac{2 \log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)}{a^4}+\frac{1}{4} x^4 \coth ^{-1}(a x)^3+\frac{x^3 \coth ^{-1}(a x)^2}{4 a}","-\frac{\text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^4}+\frac{x^2 \coth ^{-1}(a x)}{4 a^2}+\frac{x}{4 a^3}-\frac{\tanh ^{-1}(a x)}{4 a^4}+\frac{3 x \coth ^{-1}(a x)^2}{4 a^3}-\frac{\coth ^{-1}(a x)^3}{4 a^4}+\frac{\coth ^{-1}(a x)^2}{a^4}-\frac{2 \log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)}{a^4}+\frac{1}{4} x^4 \coth ^{-1}(a x)^3+\frac{x^3 \coth ^{-1}(a x)^2}{4 a}",1,"x/(4*a^3) + (x^2*ArcCoth[a*x])/(4*a^2) + ArcCoth[a*x]^2/a^4 + (3*x*ArcCoth[a*x]^2)/(4*a^3) + (x^3*ArcCoth[a*x]^2)/(4*a) - ArcCoth[a*x]^3/(4*a^4) + (x^4*ArcCoth[a*x]^3)/4 - ArcTanh[a*x]/(4*a^4) - (2*ArcCoth[a*x]*Log[2/(1 - a*x)])/a^4 - PolyLog[2, 1 - 2/(1 - a*x)]/a^4","A",18,10,10,1.000,1,"{5917, 5981, 321, 206, 5985, 5919, 2402, 2315, 5911, 5949}"
26,1,149,0,0.3325223,"\int x^2 \coth ^{-1}(a x)^3 \, dx","Int[x^2*ArcCoth[a*x]^3,x]","\frac{\text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^3}-\frac{\coth ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^3}+\frac{\log \left(1-a^2 x^2\right)}{2 a^3}+\frac{\coth ^{-1}(a x)^3}{3 a^3}-\frac{\coth ^{-1}(a x)^2}{2 a^3}+\frac{x \coth ^{-1}(a x)}{a^2}-\frac{\log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)^2}{a^3}+\frac{1}{3} x^3 \coth ^{-1}(a x)^3+\frac{x^2 \coth ^{-1}(a x)^2}{2 a}","\frac{\text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a^3}-\frac{\coth ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a^3}+\frac{\log \left(1-a^2 x^2\right)}{2 a^3}+\frac{\coth ^{-1}(a x)^3}{3 a^3}-\frac{\coth ^{-1}(a x)^2}{2 a^3}+\frac{x \coth ^{-1}(a x)}{a^2}-\frac{\log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)^2}{a^3}+\frac{1}{3} x^3 \coth ^{-1}(a x)^3+\frac{x^2 \coth ^{-1}(a x)^2}{2 a}",1,"(x*ArcCoth[a*x])/a^2 - ArcCoth[a*x]^2/(2*a^3) + (x^2*ArcCoth[a*x]^2)/(2*a) + ArcCoth[a*x]^3/(3*a^3) + (x^3*ArcCoth[a*x]^3)/3 - (ArcCoth[a*x]^2*Log[2/(1 - a*x)])/a^3 + Log[1 - a^2*x^2]/(2*a^3) - (ArcCoth[a*x]*PolyLog[2, 1 - 2/(1 - a*x)])/a^3 + PolyLog[3, 1 - 2/(1 - a*x)]/(2*a^3)","A",11,9,10,0.9000,1,"{5917, 5981, 5911, 260, 5949, 5985, 5919, 6059, 6610}"
27,1,95,0,0.1833647,"\int x \coth ^{-1}(a x)^3 \, dx","Int[x*ArcCoth[a*x]^3,x]","-\frac{3 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^2}-\frac{\coth ^{-1}(a x)^3}{2 a^2}+\frac{3 \coth ^{-1}(a x)^2}{2 a^2}-\frac{3 \log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)}{a^2}+\frac{1}{2} x^2 \coth ^{-1}(a x)^3+\frac{3 x \coth ^{-1}(a x)^2}{2 a}","-\frac{3 \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{2 a^2}-\frac{\coth ^{-1}(a x)^3}{2 a^2}+\frac{3 \coth ^{-1}(a x)^2}{2 a^2}-\frac{3 \log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)}{a^2}+\frac{1}{2} x^2 \coth ^{-1}(a x)^3+\frac{3 x \coth ^{-1}(a x)^2}{2 a}",1,"(3*ArcCoth[a*x]^2)/(2*a^2) + (3*x*ArcCoth[a*x]^2)/(2*a) - ArcCoth[a*x]^3/(2*a^2) + (x^2*ArcCoth[a*x]^3)/2 - (3*ArcCoth[a*x]*Log[2/(1 - a*x)])/a^2 - (3*PolyLog[2, 1 - 2/(1 - a*x)])/(2*a^2)","A",8,8,8,1.000,1,"{5917, 5981, 5911, 5985, 5919, 2402, 2315, 5949}"
28,1,85,0,0.1654841,"\int \coth ^{-1}(a x)^3 \, dx","Int[ArcCoth[a*x]^3,x]","\frac{3 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a}-\frac{3 \coth ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a}+x \coth ^{-1}(a x)^3+\frac{\coth ^{-1}(a x)^3}{a}-\frac{3 \log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)^2}{a}","\frac{3 \text{PolyLog}\left(3,1-\frac{2}{1-a x}\right)}{2 a}-\frac{3 \coth ^{-1}(a x) \text{PolyLog}\left(2,1-\frac{2}{1-a x}\right)}{a}+x \coth ^{-1}(a x)^3+\frac{\coth ^{-1}(a x)^3}{a}-\frac{3 \log \left(\frac{2}{1-a x}\right) \coth ^{-1}(a x)^2}{a}",1,"ArcCoth[a*x]^3/a + x*ArcCoth[a*x]^3 - (3*ArcCoth[a*x]^2*Log[2/(1 - a*x)])/a - (3*ArcCoth[a*x]*PolyLog[2, 1 - 2/(1 - a*x)])/a + (3*PolyLog[3, 1 - 2/(1 - a*x)])/(2*a)","A",5,6,6,1.000,1,"{5911, 5985, 5919, 5949, 6059, 6610}"
29,1,150,0,0.3503854,"\int \frac{\coth ^{-1}(a x)^3}{x} \, dx","Int[ArcCoth[a*x]^3/x,x]","\frac{3}{4} \text{PolyLog}\left(4,1-\frac{2}{a x+1}\right)-\frac{3}{4} \text{PolyLog}\left(4,1-\frac{2 a x}{a x+1}\right)+\frac{3}{2} \coth ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{a x+1}\right)-\frac{3}{2} \coth ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2 a x}{a x+1}\right)+\frac{3}{2} \coth ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{a x+1}\right)-\frac{3}{2} \coth ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2 a x}{a x+1}\right)+2 \coth ^{-1}\left(1-\frac{2}{1-a x}\right) \coth ^{-1}(a x)^3","\frac{3}{4} \text{PolyLog}\left(4,1-\frac{2}{a x+1}\right)-\frac{3}{4} \text{PolyLog}\left(4,1-\frac{2 a x}{a x+1}\right)+\frac{3}{2} \coth ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2}{a x+1}\right)-\frac{3}{2} \coth ^{-1}(a x)^2 \text{PolyLog}\left(2,1-\frac{2 a x}{a x+1}\right)+\frac{3}{2} \coth ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2}{a x+1}\right)-\frac{3}{2} \coth ^{-1}(a x) \text{PolyLog}\left(3,1-\frac{2 a x}{a x+1}\right)+2 \coth ^{-1}\left(1-\frac{2}{1-a x}\right) \coth ^{-1}(a x)^3",1,"2*ArcCoth[a*x]^3*ArcCoth[1 - 2/(1 - a*x)] + (3*ArcCoth[a*x]^2*PolyLog[2, 1 - 2/(1 + a*x)])/2 - (3*ArcCoth[a*x]^2*PolyLog[2, 1 - (2*a*x)/(1 + a*x)])/2 + (3*ArcCoth[a*x]*PolyLog[3, 1 - 2/(1 + a*x)])/2 - (3*ArcCoth[a*x]*PolyLog[3, 1 - (2*a*x)/(1 + a*x)])/2 + (3*PolyLog[4, 1 - 2/(1 + a*x)])/4 - (3*PolyLog[4, 1 - (2*a*x)/(1 + a*x)])/4","A",8,6,10,0.6000,1,"{5915, 6053, 5949, 6057, 6061, 6610}"
30,1,79,0,0.1991219,"\int \frac{\coth ^{-1}(a x)^3}{x^2} \, dx","Int[ArcCoth[a*x]^3/x^2,x]","-\frac{3}{2} a \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-3 a \coth ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+a \coth ^{-1}(a x)^3-\frac{\coth ^{-1}(a x)^3}{x}+3 a \log \left(2-\frac{2}{a x+1}\right) \coth ^{-1}(a x)^2","-\frac{3}{2} a \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-3 a \coth ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+a \coth ^{-1}(a x)^3-\frac{\coth ^{-1}(a x)^3}{x}+3 a \log \left(2-\frac{2}{a x+1}\right) \coth ^{-1}(a x)^2",1,"a*ArcCoth[a*x]^3 - ArcCoth[a*x]^3/x + 3*a*ArcCoth[a*x]^2*Log[2 - 2/(1 + a*x)] - 3*a*ArcCoth[a*x]*PolyLog[2, -1 + 2/(1 + a*x)] - (3*a*PolyLog[3, -1 + 2/(1 + a*x)])/2","A",5,6,10,0.6000,1,"{5917, 5989, 5933, 5949, 6057, 6610}"
31,1,95,0,0.2192362,"\int \frac{\coth ^{-1}(a x)^3}{x^3} \, dx","Int[ArcCoth[a*x]^3/x^3,x]","-\frac{3}{2} a^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{1}{2} a^2 \coth ^{-1}(a x)^3+\frac{3}{2} a^2 \coth ^{-1}(a x)^2+3 a^2 \log \left(2-\frac{2}{a x+1}\right) \coth ^{-1}(a x)-\frac{\coth ^{-1}(a x)^3}{2 x^2}-\frac{3 a \coth ^{-1}(a x)^2}{2 x}","-\frac{3}{2} a^2 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)+\frac{1}{2} a^2 \coth ^{-1}(a x)^3+\frac{3}{2} a^2 \coth ^{-1}(a x)^2+3 a^2 \log \left(2-\frac{2}{a x+1}\right) \coth ^{-1}(a x)-\frac{\coth ^{-1}(a x)^3}{2 x^2}-\frac{3 a \coth ^{-1}(a x)^2}{2 x}",1,"(3*a^2*ArcCoth[a*x]^2)/2 - (3*a*ArcCoth[a*x]^2)/(2*x) + (a^2*ArcCoth[a*x]^3)/2 - ArcCoth[a*x]^3/(2*x^2) + 3*a^2*ArcCoth[a*x]*Log[2 - 2/(1 + a*x)] - (3*a^2*PolyLog[2, -1 + 2/(1 + a*x)])/2","A",7,6,10,0.6000,1,"{5917, 5983, 5989, 5933, 2447, 5949}"
32,1,154,0,0.3688265,"\int \frac{\coth ^{-1}(a x)^3}{x^4} \, dx","Int[ArcCoth[a*x]^3/x^4,x]","-\frac{1}{2} a^3 \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-a^3 \coth ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{1}{2} a^3 \log \left(1-a^2 x^2\right)+a^3 \log (x)+\frac{1}{3} a^3 \coth ^{-1}(a x)^3+\frac{1}{2} a^3 \coth ^{-1}(a x)^2-\frac{a^2 \coth ^{-1}(a x)}{x}+a^3 \log \left(2-\frac{2}{a x+1}\right) \coth ^{-1}(a x)^2-\frac{a \coth ^{-1}(a x)^2}{2 x^2}-\frac{\coth ^{-1}(a x)^3}{3 x^3}","-\frac{1}{2} a^3 \text{PolyLog}\left(3,\frac{2}{a x+1}-1\right)-a^3 \coth ^{-1}(a x) \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{1}{2} a^3 \log \left(1-a^2 x^2\right)+a^3 \log (x)+\frac{1}{3} a^3 \coth ^{-1}(a x)^3+\frac{1}{2} a^3 \coth ^{-1}(a x)^2-\frac{a^2 \coth ^{-1}(a x)}{x}+a^3 \log \left(2-\frac{2}{a x+1}\right) \coth ^{-1}(a x)^2-\frac{a \coth ^{-1}(a x)^2}{2 x^2}-\frac{\coth ^{-1}(a x)^3}{3 x^3}",1,"-((a^2*ArcCoth[a*x])/x) + (a^3*ArcCoth[a*x]^2)/2 - (a*ArcCoth[a*x]^2)/(2*x^2) + (a^3*ArcCoth[a*x]^3)/3 - ArcCoth[a*x]^3/(3*x^3) + a^3*Log[x] - (a^3*Log[1 - a^2*x^2])/2 + a^3*ArcCoth[a*x]^2*Log[2 - 2/(1 + a*x)] - a^3*ArcCoth[a*x]*PolyLog[2, -1 + 2/(1 + a*x)] - (a^3*PolyLog[3, -1 + 2/(1 + a*x)])/2","A",14,11,10,1.100,1,"{5917, 5983, 266, 36, 29, 31, 5949, 5989, 5933, 6057, 6610}"
33,1,141,0,0.4638852,"\int \frac{\coth ^{-1}(a x)^3}{x^5} \, dx","Int[ArcCoth[a*x]^3/x^5,x]","-a^4 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{a^2 \coth ^{-1}(a x)}{4 x^2}-\frac{a^3}{4 x}+\frac{1}{4} a^4 \tanh ^{-1}(a x)+\frac{1}{4} a^4 \coth ^{-1}(a x)^3+a^4 \coth ^{-1}(a x)^2-\frac{3 a^3 \coth ^{-1}(a x)^2}{4 x}+2 a^4 \log \left(2-\frac{2}{a x+1}\right) \coth ^{-1}(a x)-\frac{a \coth ^{-1}(a x)^2}{4 x^3}-\frac{\coth ^{-1}(a x)^3}{4 x^4}","-a^4 \text{PolyLog}\left(2,\frac{2}{a x+1}-1\right)-\frac{a^2 \coth ^{-1}(a x)}{4 x^2}-\frac{a^3}{4 x}+\frac{1}{4} a^4 \tanh ^{-1}(a x)+\frac{1}{4} a^4 \coth ^{-1}(a x)^3+a^4 \coth ^{-1}(a x)^2-\frac{3 a^3 \coth ^{-1}(a x)^2}{4 x}+2 a^4 \log \left(2-\frac{2}{a x+1}\right) \coth ^{-1}(a x)-\frac{a \coth ^{-1}(a x)^2}{4 x^3}-\frac{\coth ^{-1}(a x)^3}{4 x^4}",1,"-a^3/(4*x) - (a^2*ArcCoth[a*x])/(4*x^2) + a^4*ArcCoth[a*x]^2 - (a*ArcCoth[a*x]^2)/(4*x^3) - (3*a^3*ArcCoth[a*x]^2)/(4*x) + (a^4*ArcCoth[a*x]^3)/4 - ArcCoth[a*x]^3/(4*x^4) + (a^4*ArcTanh[a*x])/4 + 2*a^4*ArcCoth[a*x]*Log[2 - 2/(1 + a*x)] - a^4*PolyLog[2, -1 + 2/(1 + a*x)]","A",16,8,10,0.8000,1,"{5917, 5983, 325, 206, 5989, 5933, 2447, 5949}"
34,1,164,0,0.0337196,"\int \frac{\coth ^{-1}(c x)^2}{d+e x} \, dx","Int[ArcCoth[c*x]^2/(d + e*x),x]","-\frac{\text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e}-\frac{\coth ^{-1}(c x) \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e}+\frac{\text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 e}+\frac{\coth ^{-1}(c x) \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{e}+\frac{\coth ^{-1}(c x)^2 \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e}-\frac{\log \left(\frac{2}{c x+1}\right) \coth ^{-1}(c x)^2}{e}","-\frac{\text{PolyLog}\left(3,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{2 e}-\frac{\coth ^{-1}(c x) \text{PolyLog}\left(2,1-\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e}+\frac{\text{PolyLog}\left(3,1-\frac{2}{c x+1}\right)}{2 e}+\frac{\coth ^{-1}(c x) \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{e}+\frac{\coth ^{-1}(c x)^2 \log \left(\frac{2 c (d+e x)}{(c x+1) (c d+e)}\right)}{e}-\frac{\log \left(\frac{2}{c x+1}\right) \coth ^{-1}(c x)^2}{e}",1,"-((ArcCoth[c*x]^2*Log[2/(1 + c*x)])/e) + (ArcCoth[c*x]^2*Log[(2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/e + (ArcCoth[c*x]*PolyLog[2, 1 - 2/(1 + c*x)])/e - (ArcCoth[c*x]*PolyLog[2, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))])/e + PolyLog[3, 1 - 2/(1 + c*x)]/(2*e) - PolyLog[3, 1 - (2*c*(d + e*x))/((c*d + e)*(1 + c*x))]/(2*e)","A",1,1,14,0.07143,1,"{5923}"
35,1,245,0,0.1805385,"\int \left(c+d x^2\right)^4 \coth ^{-1}(a x) \, dx","Int[(c + d*x^2)^4*ArcCoth[a*x],x]","\frac{d^2 x^4 \left(378 a^4 c^2+180 a^2 c d+35 d^2\right)}{1260 a^5}+\frac{d x^2 \left(378 a^4 c^2 d+420 a^6 c^3+180 a^2 c d^2+35 d^3\right)}{630 a^7}+\frac{\left(378 a^4 c^2 d^2+420 a^6 c^3 d+315 a^8 c^4+180 a^2 c d^3+35 d^4\right) \log \left(1-a^2 x^2\right)}{630 a^9}+\frac{d^3 x^6 \left(36 a^2 c+7 d\right)}{378 a^3}+\frac{6}{5} c^2 d^2 x^5 \coth ^{-1}(a x)+\frac{4}{3} c^3 d x^3 \coth ^{-1}(a x)+c^4 x \coth ^{-1}(a x)+\frac{4}{7} c d^3 x^7 \coth ^{-1}(a x)+\frac{d^4 x^8}{72 a}+\frac{1}{9} d^4 x^9 \coth ^{-1}(a x)","\frac{d^2 x^4 \left(378 a^4 c^2+180 a^2 c d+35 d^2\right)}{1260 a^5}+\frac{d x^2 \left(378 a^4 c^2 d+420 a^6 c^3+180 a^2 c d^2+35 d^3\right)}{630 a^7}+\frac{\left(378 a^4 c^2 d^2+420 a^6 c^3 d+315 a^8 c^4+180 a^2 c d^3+35 d^4\right) \log \left(1-a^2 x^2\right)}{630 a^9}+\frac{d^3 x^6 \left(36 a^2 c+7 d\right)}{378 a^3}+\frac{6}{5} c^2 d^2 x^5 \coth ^{-1}(a x)+\frac{4}{3} c^3 d x^3 \coth ^{-1}(a x)+c^4 x \coth ^{-1}(a x)+\frac{4}{7} c d^3 x^7 \coth ^{-1}(a x)+\frac{d^4 x^8}{72 a}+\frac{1}{9} d^4 x^9 \coth ^{-1}(a x)",1,"(d*(420*a^6*c^3 + 378*a^4*c^2*d + 180*a^2*c*d^2 + 35*d^3)*x^2)/(630*a^7) + (d^2*(378*a^4*c^2 + 180*a^2*c*d + 35*d^2)*x^4)/(1260*a^5) + (d^3*(36*a^2*c + 7*d)*x^6)/(378*a^3) + (d^4*x^8)/(72*a) + c^4*x*ArcCoth[a*x] + (4*c^3*d*x^3*ArcCoth[a*x])/3 + (6*c^2*d^2*x^5*ArcCoth[a*x])/5 + (4*c*d^3*x^7*ArcCoth[a*x])/7 + (d^4*x^9*ArcCoth[a*x])/9 + ((315*a^8*c^4 + 420*a^6*c^3*d + 378*a^4*c^2*d^2 + 180*a^2*c*d^3 + 35*d^4)*Log[1 - a^2*x^2])/(630*a^9)","A",4,4,14,0.2857,1,"{194, 5977, 1810, 260}"
36,1,169,0,0.1268003,"\int \left(c+d x^2\right)^3 \coth ^{-1}(a x) \, dx","Int[(c + d*x^2)^3*ArcCoth[a*x],x]","\frac{d x^2 \left(35 a^4 c^2+21 a^2 c d+5 d^2\right)}{70 a^5}+\frac{\left(35 a^4 c^2 d+35 a^6 c^3+21 a^2 c d^2+5 d^3\right) \log \left(1-a^2 x^2\right)}{70 a^7}+\frac{d^2 x^4 \left(21 a^2 c+5 d\right)}{140 a^3}+c^2 d x^3 \coth ^{-1}(a x)+c^3 x \coth ^{-1}(a x)+\frac{3}{5} c d^2 x^5 \coth ^{-1}(a x)+\frac{d^3 x^6}{42 a}+\frac{1}{7} d^3 x^7 \coth ^{-1}(a x)","\frac{d x^2 \left(35 a^4 c^2+21 a^2 c d+5 d^2\right)}{70 a^5}+\frac{\left(35 a^4 c^2 d+35 a^6 c^3+21 a^2 c d^2+5 d^3\right) \log \left(1-a^2 x^2\right)}{70 a^7}+\frac{d^2 x^4 \left(21 a^2 c+5 d\right)}{140 a^3}+c^2 d x^3 \coth ^{-1}(a x)+c^3 x \coth ^{-1}(a x)+\frac{3}{5} c d^2 x^5 \coth ^{-1}(a x)+\frac{d^3 x^6}{42 a}+\frac{1}{7} d^3 x^7 \coth ^{-1}(a x)",1,"(d*(35*a^4*c^2 + 21*a^2*c*d + 5*d^2)*x^2)/(70*a^5) + (d^2*(21*a^2*c + 5*d)*x^4)/(140*a^3) + (d^3*x^6)/(42*a) + c^3*x*ArcCoth[a*x] + c^2*d*x^3*ArcCoth[a*x] + (3*c*d^2*x^5*ArcCoth[a*x])/5 + (d^3*x^7*ArcCoth[a*x])/7 + ((35*a^6*c^3 + 35*a^4*c^2*d + 21*a^2*c*d^2 + 5*d^3)*Log[1 - a^2*x^2])/(70*a^7)","A",4,4,14,0.2857,1,"{194, 5977, 1810, 260}"
37,1,110,0,0.1331642,"\int \left(c+d x^2\right)^2 \coth ^{-1}(a x) \, dx","Int[(c + d*x^2)^2*ArcCoth[a*x],x]","\frac{\left(15 a^4 c^2+10 a^2 c d+3 d^2\right) \log \left(1-a^2 x^2\right)}{30 a^5}+\frac{d x^2 \left(10 a^2 c+3 d\right)}{30 a^3}+c^2 x \coth ^{-1}(a x)+\frac{2}{3} c d x^3 \coth ^{-1}(a x)+\frac{d^2 x^4}{20 a}+\frac{1}{5} d^2 x^5 \coth ^{-1}(a x)","\frac{\left(15 a^4 c^2+10 a^2 c d+3 d^2\right) \log \left(1-a^2 x^2\right)}{30 a^5}+\frac{d x^2 \left(10 a^2 c+3 d\right)}{30 a^3}+c^2 x \coth ^{-1}(a x)+\frac{2}{3} c d x^3 \coth ^{-1}(a x)+\frac{d^2 x^4}{20 a}+\frac{1}{5} d^2 x^5 \coth ^{-1}(a x)",1,"(d*(10*a^2*c + 3*d)*x^2)/(30*a^3) + (d^2*x^4)/(20*a) + c^2*x*ArcCoth[a*x] + (2*c*d*x^3*ArcCoth[a*x])/3 + (d^2*x^5*ArcCoth[a*x])/5 + ((15*a^4*c^2 + 10*a^2*c*d + 3*d^2)*Log[1 - a^2*x^2])/(30*a^5)","A",5,5,14,0.3571,1,"{194, 5977, 1594, 1247, 698}"
38,1,57,0,0.0659503,"\int \left(c+d x^2\right) \coth ^{-1}(a x) \, dx","Int[(c + d*x^2)*ArcCoth[a*x],x]","\frac{\left(3 a^2 c+d\right) \log \left(1-a^2 x^2\right)}{6 a^3}+c x \coth ^{-1}(a x)+\frac{d x^2}{6 a}+\frac{1}{3} d x^3 \coth ^{-1}(a x)","\frac{\left(3 a^2 c+d\right) \log \left(1-a^2 x^2\right)}{6 a^3}+c x \coth ^{-1}(a x)+\frac{d x^2}{6 a}+\frac{1}{3} d x^3 \coth ^{-1}(a x)",1,"(d*x^2)/(6*a) + c*x*ArcCoth[a*x] + (d*x^3*ArcCoth[a*x])/3 + ((3*a^2*c + d)*Log[1 - a^2*x^2])/(6*a^3)","A",5,4,12,0.3333,1,"{5977, 1593, 444, 43}"
39,1,390,0,0.9466846,"\int \frac{\coth ^{-1}(a x)}{c+d x^2} \, dx","Int[ArcCoth[a*x]/(c + d*x^2),x]","-\frac{i \text{PolyLog}\left(2,1+\frac{2 \sqrt{c} \sqrt{d} (1-a x)}{\left(-\sqrt{d}+i a \sqrt{c}\right) \left(\sqrt{c}-i \sqrt{d} x\right)}\right)}{4 \sqrt{c} \sqrt{d}}+\frac{i \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \sqrt{d} (a x+1)}{\left(\sqrt{d}+i a \sqrt{c}\right) \left(\sqrt{c}-i \sqrt{d} x\right)}\right)}{4 \sqrt{c} \sqrt{d}}-\frac{\log \left(1-\frac{1}{a x}\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 \sqrt{c} \sqrt{d}}+\frac{\log \left(\frac{1}{a x}+1\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 \sqrt{c} \sqrt{d}}+\frac{\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{2 \sqrt{c} \sqrt{d} (1-a x)}{\left(-\sqrt{d}+i a \sqrt{c}\right) \left(\sqrt{c}-i \sqrt{d} x\right)}\right)}{2 \sqrt{c} \sqrt{d}}-\frac{\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \sqrt{d} (a x+1)}{\left(\sqrt{d}+i a \sqrt{c}\right) \left(\sqrt{c}-i \sqrt{d} x\right)}\right)}{2 \sqrt{c} \sqrt{d}}","-\frac{i \text{PolyLog}\left(2,1+\frac{2 \sqrt{c} \sqrt{d} (1-a x)}{\left(-\sqrt{d}+i a \sqrt{c}\right) \left(\sqrt{c}-i \sqrt{d} x\right)}\right)}{4 \sqrt{c} \sqrt{d}}+\frac{i \text{PolyLog}\left(2,1-\frac{2 \sqrt{c} \sqrt{d} (a x+1)}{\left(\sqrt{d}+i a \sqrt{c}\right) \left(\sqrt{c}-i \sqrt{d} x\right)}\right)}{4 \sqrt{c} \sqrt{d}}-\frac{\log \left(1-\frac{1}{a x}\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 \sqrt{c} \sqrt{d}}+\frac{\log \left(\frac{1}{a x}+1\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 \sqrt{c} \sqrt{d}}+\frac{\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{2 \sqrt{c} \sqrt{d} (1-a x)}{\left(-\sqrt{d}+i a \sqrt{c}\right) \left(\sqrt{c}-i \sqrt{d} x\right)}\right)}{2 \sqrt{c} \sqrt{d}}-\frac{\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{2 \sqrt{c} \sqrt{d} (a x+1)}{\left(\sqrt{d}+i a \sqrt{c}\right) \left(\sqrt{c}-i \sqrt{d} x\right)}\right)}{2 \sqrt{c} \sqrt{d}}",1,"-(ArcTan[(Sqrt[d]*x)/Sqrt[c]]*Log[1 - 1/(a*x)])/(2*Sqrt[c]*Sqrt[d]) + (ArcTan[(Sqrt[d]*x)/Sqrt[c]]*Log[1 + 1/(a*x)])/(2*Sqrt[c]*Sqrt[d]) + (ArcTan[(Sqrt[d]*x)/Sqrt[c]]*Log[(-2*Sqrt[c]*Sqrt[d]*(1 - a*x))/((I*a*Sqrt[c] - Sqrt[d])*(Sqrt[c] - I*Sqrt[d]*x))])/(2*Sqrt[c]*Sqrt[d]) - (ArcTan[(Sqrt[d]*x)/Sqrt[c]]*Log[(2*Sqrt[c]*Sqrt[d]*(1 + a*x))/((I*a*Sqrt[c] + Sqrt[d])*(Sqrt[c] - I*Sqrt[d]*x))])/(2*Sqrt[c]*Sqrt[d]) - ((I/4)*PolyLog[2, 1 + (2*Sqrt[c]*Sqrt[d]*(1 - a*x))/((I*a*Sqrt[c] - Sqrt[d])*(Sqrt[c] - I*Sqrt[d]*x))])/(Sqrt[c]*Sqrt[d]) + ((I/4)*PolyLog[2, 1 - (2*Sqrt[c]*Sqrt[d]*(1 + a*x))/((I*a*Sqrt[c] + Sqrt[d])*(Sqrt[c] - I*Sqrt[d]*x))])/(Sqrt[c]*Sqrt[d])","A",27,13,14,0.9286,1,"{5973, 205, 2470, 12, 260, 6688, 4876, 4848, 2391, 4856, 2402, 2315, 2447}"
40,1,590,0,0.8697027,"\int \frac{\coth ^{-1}(a x)}{\left(c+d x^2\right)^2} \, dx","Int[ArcCoth[a*x]/(c + d*x^2)^2,x]","\frac{i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}-i \sqrt{d} x\right)}{a \sqrt{c}-i \sqrt{d}}\right)}{8 c^{3/2} \sqrt{d}}-\frac{i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}-i \sqrt{d} x\right)}{a \sqrt{c}+i \sqrt{d}}\right)}{8 c^{3/2} \sqrt{d}}+\frac{i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}+i \sqrt{d} x\right)}{a \sqrt{c}-i \sqrt{d}}\right)}{8 c^{3/2} \sqrt{d}}-\frac{i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}+i \sqrt{d} x\right)}{a \sqrt{c}+i \sqrt{d}}\right)}{8 c^{3/2} \sqrt{d}}+\frac{a \log \left(1-a^2 x^2\right)}{4 c \left(a^2 c+d\right)}-\frac{a \log \left(c+d x^2\right)}{4 c \left(a^2 c+d\right)}+\frac{i \log \left(1-\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{\sqrt{d} (1-a x)}{\sqrt{d}+i a \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}-\frac{i \log \left(1-\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{\sqrt{d} (a x+1)}{-\sqrt{d}+i a \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}-\frac{i \log \left(1+\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{\sqrt{d} (1-a x)}{-\sqrt{d}+i a \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}+\frac{i \log \left(1+\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{\sqrt{d} (a x+1)}{\sqrt{d}+i a \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}+\frac{\coth ^{-1}(a x) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{3/2} \sqrt{d}}+\frac{x \coth ^{-1}(a x)}{2 c \left(c+d x^2\right)}","\frac{i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}-i \sqrt{d} x\right)}{a \sqrt{c}-i \sqrt{d}}\right)}{8 c^{3/2} \sqrt{d}}-\frac{i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}-i \sqrt{d} x\right)}{a \sqrt{c}+i \sqrt{d}}\right)}{8 c^{3/2} \sqrt{d}}+\frac{i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}+i \sqrt{d} x\right)}{a \sqrt{c}-i \sqrt{d}}\right)}{8 c^{3/2} \sqrt{d}}-\frac{i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}+i \sqrt{d} x\right)}{a \sqrt{c}+i \sqrt{d}}\right)}{8 c^{3/2} \sqrt{d}}+\frac{a \log \left(1-a^2 x^2\right)}{4 c \left(a^2 c+d\right)}-\frac{a \log \left(c+d x^2\right)}{4 c \left(a^2 c+d\right)}+\frac{i \log \left(1-\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{\sqrt{d} (1-a x)}{\sqrt{d}+i a \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}-\frac{i \log \left(1-\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{\sqrt{d} (a x+1)}{-\sqrt{d}+i a \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}-\frac{i \log \left(1+\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{\sqrt{d} (1-a x)}{-\sqrt{d}+i a \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}+\frac{i \log \left(1+\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{\sqrt{d} (a x+1)}{\sqrt{d}+i a \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}+\frac{\coth ^{-1}(a x) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{3/2} \sqrt{d}}+\frac{x \coth ^{-1}(a x)}{2 c \left(c+d x^2\right)}",1,"(x*ArcCoth[a*x])/(2*c*(c + d*x^2)) + (ArcCoth[a*x]*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(2*c^(3/2)*Sqrt[d]) + ((I/8)*Log[(Sqrt[d]*(1 - a*x))/(I*a*Sqrt[c] + Sqrt[d])]*Log[1 - (I*Sqrt[d]*x)/Sqrt[c]])/(c^(3/2)*Sqrt[d]) - ((I/8)*Log[-((Sqrt[d]*(1 + a*x))/(I*a*Sqrt[c] - Sqrt[d]))]*Log[1 - (I*Sqrt[d]*x)/Sqrt[c]])/(c^(3/2)*Sqrt[d]) - ((I/8)*Log[-((Sqrt[d]*(1 - a*x))/(I*a*Sqrt[c] - Sqrt[d]))]*Log[1 + (I*Sqrt[d]*x)/Sqrt[c]])/(c^(3/2)*Sqrt[d]) + ((I/8)*Log[(Sqrt[d]*(1 + a*x))/(I*a*Sqrt[c] + Sqrt[d])]*Log[1 + (I*Sqrt[d]*x)/Sqrt[c]])/(c^(3/2)*Sqrt[d]) + (a*Log[1 - a^2*x^2])/(4*c*(a^2*c + d)) - (a*Log[c + d*x^2])/(4*c*(a^2*c + d)) + ((I/8)*PolyLog[2, (a*(Sqrt[c] - I*Sqrt[d]*x))/(a*Sqrt[c] - I*Sqrt[d])])/(c^(3/2)*Sqrt[d]) - ((I/8)*PolyLog[2, (a*(Sqrt[c] - I*Sqrt[d]*x))/(a*Sqrt[c] + I*Sqrt[d])])/(c^(3/2)*Sqrt[d]) + ((I/8)*PolyLog[2, (a*(Sqrt[c] + I*Sqrt[d]*x))/(a*Sqrt[c] - I*Sqrt[d])])/(c^(3/2)*Sqrt[d]) - ((I/8)*PolyLog[2, (a*(Sqrt[c] + I*Sqrt[d]*x))/(a*Sqrt[c] + I*Sqrt[d])])/(c^(3/2)*Sqrt[d])","A",25,13,14,0.9286,1,"{199, 205, 5977, 6725, 517, 444, 36, 31, 4908, 2409, 2394, 2393, 2391}"
41,1,657,0,0.9509089,"\int \frac{\coth ^{-1}(a x)}{\left(c+d x^2\right)^3} \, dx","Int[ArcCoth[a*x]/(c + d*x^2)^3,x]","\frac{3 i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}-i \sqrt{d} x\right)}{a \sqrt{c}-i \sqrt{d}}\right)}{32 c^{5/2} \sqrt{d}}-\frac{3 i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}-i \sqrt{d} x\right)}{a \sqrt{c}+i \sqrt{d}}\right)}{32 c^{5/2} \sqrt{d}}+\frac{3 i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}+i \sqrt{d} x\right)}{a \sqrt{c}-i \sqrt{d}}\right)}{32 c^{5/2} \sqrt{d}}-\frac{3 i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}+i \sqrt{d} x\right)}{a \sqrt{c}+i \sqrt{d}}\right)}{32 c^{5/2} \sqrt{d}}+\frac{a \left(5 a^2 c+3 d\right) \log \left(1-a^2 x^2\right)}{16 c^2 \left(a^2 c+d\right)^2}-\frac{a \left(5 a^2 c+3 d\right) \log \left(c+d x^2\right)}{16 c^2 \left(a^2 c+d\right)^2}+\frac{a}{8 c \left(a^2 c+d\right) \left(c+d x^2\right)}+\frac{3 x \coth ^{-1}(a x)}{8 c^2 \left(c+d x^2\right)}+\frac{3 i \log \left(1-\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{\sqrt{d} (1-a x)}{\sqrt{d}+i a \sqrt{c}}\right)}{32 c^{5/2} \sqrt{d}}-\frac{3 i \log \left(1-\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{\sqrt{d} (a x+1)}{-\sqrt{d}+i a \sqrt{c}}\right)}{32 c^{5/2} \sqrt{d}}-\frac{3 i \log \left(1+\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{\sqrt{d} (1-a x)}{-\sqrt{d}+i a \sqrt{c}}\right)}{32 c^{5/2} \sqrt{d}}+\frac{3 i \log \left(1+\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{\sqrt{d} (a x+1)}{\sqrt{d}+i a \sqrt{c}}\right)}{32 c^{5/2} \sqrt{d}}+\frac{3 \coth ^{-1}(a x) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{5/2} \sqrt{d}}+\frac{x \coth ^{-1}(a x)}{4 c \left(c+d x^2\right)^2}","\frac{3 i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}-i \sqrt{d} x\right)}{a \sqrt{c}-i \sqrt{d}}\right)}{32 c^{5/2} \sqrt{d}}-\frac{3 i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}-i \sqrt{d} x\right)}{a \sqrt{c}+i \sqrt{d}}\right)}{32 c^{5/2} \sqrt{d}}+\frac{3 i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}+i \sqrt{d} x\right)}{a \sqrt{c}-i \sqrt{d}}\right)}{32 c^{5/2} \sqrt{d}}-\frac{3 i \text{PolyLog}\left(2,\frac{a \left(\sqrt{c}+i \sqrt{d} x\right)}{a \sqrt{c}+i \sqrt{d}}\right)}{32 c^{5/2} \sqrt{d}}+\frac{a \left(5 a^2 c+3 d\right) \log \left(1-a^2 x^2\right)}{16 c^2 \left(a^2 c+d\right)^2}-\frac{a \left(5 a^2 c+3 d\right) \log \left(c+d x^2\right)}{16 c^2 \left(a^2 c+d\right)^2}+\frac{a}{8 c \left(a^2 c+d\right) \left(c+d x^2\right)}+\frac{3 x \coth ^{-1}(a x)}{8 c^2 \left(c+d x^2\right)}+\frac{3 i \log \left(1-\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{\sqrt{d} (1-a x)}{\sqrt{d}+i a \sqrt{c}}\right)}{32 c^{5/2} \sqrt{d}}-\frac{3 i \log \left(1-\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{\sqrt{d} (a x+1)}{-\sqrt{d}+i a \sqrt{c}}\right)}{32 c^{5/2} \sqrt{d}}-\frac{3 i \log \left(1+\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(-\frac{\sqrt{d} (1-a x)}{-\sqrt{d}+i a \sqrt{c}}\right)}{32 c^{5/2} \sqrt{d}}+\frac{3 i \log \left(1+\frac{i \sqrt{d} x}{\sqrt{c}}\right) \log \left(\frac{\sqrt{d} (a x+1)}{\sqrt{d}+i a \sqrt{c}}\right)}{32 c^{5/2} \sqrt{d}}+\frac{3 \coth ^{-1}(a x) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{5/2} \sqrt{d}}+\frac{x \coth ^{-1}(a x)}{4 c \left(c+d x^2\right)^2}",1,"a/(8*c*(a^2*c + d)*(c + d*x^2)) + (x*ArcCoth[a*x])/(4*c*(c + d*x^2)^2) + (3*x*ArcCoth[a*x])/(8*c^2*(c + d*x^2)) + (3*ArcCoth[a*x]*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(8*c^(5/2)*Sqrt[d]) + (((3*I)/32)*Log[(Sqrt[d]*(1 - a*x))/(I*a*Sqrt[c] + Sqrt[d])]*Log[1 - (I*Sqrt[d]*x)/Sqrt[c]])/(c^(5/2)*Sqrt[d]) - (((3*I)/32)*Log[-((Sqrt[d]*(1 + a*x))/(I*a*Sqrt[c] - Sqrt[d]))]*Log[1 - (I*Sqrt[d]*x)/Sqrt[c]])/(c^(5/2)*Sqrt[d]) - (((3*I)/32)*Log[-((Sqrt[d]*(1 - a*x))/(I*a*Sqrt[c] - Sqrt[d]))]*Log[1 + (I*Sqrt[d]*x)/Sqrt[c]])/(c^(5/2)*Sqrt[d]) + (((3*I)/32)*Log[(Sqrt[d]*(1 + a*x))/(I*a*Sqrt[c] + Sqrt[d])]*Log[1 + (I*Sqrt[d]*x)/Sqrt[c]])/(c^(5/2)*Sqrt[d]) + (a*(5*a^2*c + 3*d)*Log[1 - a^2*x^2])/(16*c^2*(a^2*c + d)^2) - (a*(5*a^2*c + 3*d)*Log[c + d*x^2])/(16*c^2*(a^2*c + d)^2) + (((3*I)/32)*PolyLog[2, (a*(Sqrt[c] - I*Sqrt[d]*x))/(a*Sqrt[c] - I*Sqrt[d])])/(c^(5/2)*Sqrt[d]) - (((3*I)/32)*PolyLog[2, (a*(Sqrt[c] - I*Sqrt[d]*x))/(a*Sqrt[c] + I*Sqrt[d])])/(c^(5/2)*Sqrt[d]) + (((3*I)/32)*PolyLog[2, (a*(Sqrt[c] + I*Sqrt[d]*x))/(a*Sqrt[c] - I*Sqrt[d])])/(c^(5/2)*Sqrt[d]) - (((3*I)/32)*PolyLog[2, (a*(Sqrt[c] + I*Sqrt[d]*x))/(a*Sqrt[c] + I*Sqrt[d])])/(c^(5/2)*Sqrt[d])","A",23,11,14,0.7857,1,"{199, 205, 5977, 6725, 571, 77, 4908, 2409, 2394, 2393, 2391}"
42,0,0,0,0.0208016,"\int \sqrt{c+d x^2} \coth ^{-1}(a x) \, dx","Int[Sqrt[c + d*x^2]*ArcCoth[a*x],x]","\int \sqrt{c+d x^2} \coth ^{-1}(a x) \, dx","\text{Int}\left(\coth ^{-1}(a x) \sqrt{c+d x^2},x\right)",0,"Defer[Int][Sqrt[c + d*x^2]*ArcCoth[a*x], x]","A",0,0,0,0,-1,"{}"
43,0,0,0,0.0234482,"\int \frac{\coth ^{-1}(a x)}{\sqrt{c+d x^2}} \, dx","Int[ArcCoth[a*x]/Sqrt[c + d*x^2],x]","\int \frac{\coth ^{-1}(a x)}{\sqrt{c+d x^2}} \, dx","\text{Int}\left(\frac{\coth ^{-1}(a x)}{\sqrt{c+d x^2}},x\right)",0,"Defer[Int][ArcCoth[a*x]/Sqrt[c + d*x^2], x]","A",0,0,0,0,-1,"{}"
44,1,62,0,0.1129506,"\int \frac{\coth ^{-1}(a x)}{\left(c+d x^2\right)^{3/2}} \, dx","Int[ArcCoth[a*x]/(c + d*x^2)^(3/2),x]","\frac{x \coth ^{-1}(a x)}{c \sqrt{c+d x^2}}-\frac{\tanh ^{-1}\left(\frac{a \sqrt{c+d x^2}}{\sqrt{a^2 c+d}}\right)}{c \sqrt{a^2 c+d}}","\frac{x \coth ^{-1}(a x)}{c \sqrt{c+d x^2}}-\frac{\tanh ^{-1}\left(\frac{a \sqrt{c+d x^2}}{\sqrt{a^2 c+d}}\right)}{c \sqrt{a^2 c+d}}",1,"(x*ArcCoth[a*x])/(c*Sqrt[c + d*x^2]) - ArcTanh[(a*Sqrt[c + d*x^2])/Sqrt[a^2*c + d]]/(c*Sqrt[a^2*c + d])","A",5,6,16,0.3750,1,"{191, 5977, 12, 444, 63, 208}"
45,1,128,0,0.3398282,"\int \frac{\coth ^{-1}(a x)}{\left(c+d x^2\right)^{5/2}} \, dx","Int[ArcCoth[a*x]/(c + d*x^2)^(5/2),x]","-\frac{\left(3 a^2 c+2 d\right) \tanh ^{-1}\left(\frac{a \sqrt{c+d x^2}}{\sqrt{a^2 c+d}}\right)}{3 c^2 \left(a^2 c+d\right)^{3/2}}+\frac{a}{3 c \left(a^2 c+d\right) \sqrt{c+d x^2}}+\frac{2 x \coth ^{-1}(a x)}{3 c^2 \sqrt{c+d x^2}}+\frac{x \coth ^{-1}(a x)}{3 c \left(c+d x^2\right)^{3/2}}","-\frac{\left(3 a^2 c+2 d\right) \tanh ^{-1}\left(\frac{a \sqrt{c+d x^2}}{\sqrt{a^2 c+d}}\right)}{3 c^2 \left(a^2 c+d\right)^{3/2}}+\frac{a}{3 c \left(a^2 c+d\right) \sqrt{c+d x^2}}+\frac{2 x \coth ^{-1}(a x)}{3 c^2 \sqrt{c+d x^2}}+\frac{x \coth ^{-1}(a x)}{3 c \left(c+d x^2\right)^{3/2}}",1,"a/(3*c*(a^2*c + d)*Sqrt[c + d*x^2]) + (x*ArcCoth[a*x])/(3*c*(c + d*x^2)^(3/2)) + (2*x*ArcCoth[a*x])/(3*c^2*Sqrt[c + d*x^2]) - ((3*a^2*c + 2*d)*ArcTanh[(a*Sqrt[c + d*x^2])/Sqrt[a^2*c + d]])/(3*c^2*(a^2*c + d)^(3/2))","A",7,9,16,0.5625,1,"{192, 191, 5977, 6688, 12, 571, 78, 63, 208}"
46,1,200,0,1.0474758,"\int \frac{\coth ^{-1}(a x)}{\left(c+d x^2\right)^{7/2}} \, dx","Int[ArcCoth[a*x]/(c + d*x^2)^(7/2),x]","-\frac{\left(15 a^4 c^2+20 a^2 c d+8 d^2\right) \tanh ^{-1}\left(\frac{a \sqrt{c+d x^2}}{\sqrt{a^2 c+d}}\right)}{15 c^3 \left(a^2 c+d\right)^{5/2}}+\frac{a \left(7 a^2 c+4 d\right)}{15 c^2 \left(a^2 c+d\right)^2 \sqrt{c+d x^2}}+\frac{a}{15 c \left(a^2 c+d\right) \left(c+d x^2\right)^{3/2}}+\frac{8 x \coth ^{-1}(a x)}{15 c^3 \sqrt{c+d x^2}}+\frac{4 x \coth ^{-1}(a x)}{15 c^2 \left(c+d x^2\right)^{3/2}}+\frac{x \coth ^{-1}(a x)}{5 c \left(c+d x^2\right)^{5/2}}","-\frac{\left(15 a^4 c^2+20 a^2 c d+8 d^2\right) \tanh ^{-1}\left(\frac{a \sqrt{c+d x^2}}{\sqrt{a^2 c+d}}\right)}{15 c^3 \left(a^2 c+d\right)^{5/2}}+\frac{a \left(7 a^2 c+4 d\right)}{15 c^2 \left(a^2 c+d\right)^2 \sqrt{c+d x^2}}+\frac{a}{15 c \left(a^2 c+d\right) \left(c+d x^2\right)^{3/2}}+\frac{8 x \coth ^{-1}(a x)}{15 c^3 \sqrt{c+d x^2}}+\frac{4 x \coth ^{-1}(a x)}{15 c^2 \left(c+d x^2\right)^{3/2}}+\frac{x \coth ^{-1}(a x)}{5 c \left(c+d x^2\right)^{5/2}}",1,"a/(15*c*(a^2*c + d)*(c + d*x^2)^(3/2)) + (a*(7*a^2*c + 4*d))/(15*c^2*(a^2*c + d)^2*Sqrt[c + d*x^2]) + (x*ArcCoth[a*x])/(5*c*(c + d*x^2)^(5/2)) + (4*x*ArcCoth[a*x])/(15*c^2*(c + d*x^2)^(3/2)) + (8*x*ArcCoth[a*x])/(15*c^3*Sqrt[c + d*x^2]) - ((15*a^4*c^2 + 20*a^2*c*d + 8*d^2)*ArcTanh[(a*Sqrt[c + d*x^2])/Sqrt[a^2*c + d]])/(15*c^3*(a^2*c + d)^(5/2))","A",8,9,16,0.5625,1,"{192, 191, 5977, 6688, 12, 6715, 897, 1261, 208}"
47,1,283,0,1.3432295,"\int \frac{\coth ^{-1}(a x)}{\left(c+d x^2\right)^{9/2}} \, dx","Int[ArcCoth[a*x]/(c + d*x^2)^(9/2),x]","\frac{a \left(19 a^4 c^2+22 a^2 c d+8 d^2\right)}{35 c^3 \left(a^2 c+d\right)^3 \sqrt{c+d x^2}}-\frac{\left(70 a^4 c^2 d+35 a^6 c^3+56 a^2 c d^2+16 d^3\right) \tanh ^{-1}\left(\frac{a \sqrt{c+d x^2}}{\sqrt{a^2 c+d}}\right)}{35 c^4 \left(a^2 c+d\right)^{7/2}}+\frac{a \left(11 a^2 c+6 d\right)}{105 c^2 \left(a^2 c+d\right)^2 \left(c+d x^2\right)^{3/2}}+\frac{a}{35 c \left(a^2 c+d\right) \left(c+d x^2\right)^{5/2}}+\frac{16 x \coth ^{-1}(a x)}{35 c^4 \sqrt{c+d x^2}}+\frac{8 x \coth ^{-1}(a x)}{35 c^3 \left(c+d x^2\right)^{3/2}}+\frac{6 x \coth ^{-1}(a x)}{35 c^2 \left(c+d x^2\right)^{5/2}}+\frac{x \coth ^{-1}(a x)}{7 c \left(c+d x^2\right)^{7/2}}","\frac{a \left(19 a^4 c^2+22 a^2 c d+8 d^2\right)}{35 c^3 \left(a^2 c+d\right)^3 \sqrt{c+d x^2}}-\frac{\left(70 a^4 c^2 d+35 a^6 c^3+56 a^2 c d^2+16 d^3\right) \tanh ^{-1}\left(\frac{a \sqrt{c+d x^2}}{\sqrt{a^2 c+d}}\right)}{35 c^4 \left(a^2 c+d\right)^{7/2}}+\frac{a \left(11 a^2 c+6 d\right)}{105 c^2 \left(a^2 c+d\right)^2 \left(c+d x^2\right)^{3/2}}+\frac{a}{35 c \left(a^2 c+d\right) \left(c+d x^2\right)^{5/2}}+\frac{16 x \coth ^{-1}(a x)}{35 c^4 \sqrt{c+d x^2}}+\frac{8 x \coth ^{-1}(a x)}{35 c^3 \left(c+d x^2\right)^{3/2}}+\frac{6 x \coth ^{-1}(a x)}{35 c^2 \left(c+d x^2\right)^{5/2}}+\frac{x \coth ^{-1}(a x)}{7 c \left(c+d x^2\right)^{7/2}}",1,"a/(35*c*(a^2*c + d)*(c + d*x^2)^(5/2)) + (a*(11*a^2*c + 6*d))/(105*c^2*(a^2*c + d)^2*(c + d*x^2)^(3/2)) + (a*(19*a^4*c^2 + 22*a^2*c*d + 8*d^2))/(35*c^3*(a^2*c + d)^3*Sqrt[c + d*x^2]) + (x*ArcCoth[a*x])/(7*c*(c + d*x^2)^(7/2)) + (6*x*ArcCoth[a*x])/(35*c^2*(c + d*x^2)^(5/2)) + (8*x*ArcCoth[a*x])/(35*c^3*(c + d*x^2)^(3/2)) + (16*x*ArcCoth[a*x])/(35*c^4*Sqrt[c + d*x^2]) - ((35*a^6*c^3 + 70*a^4*c^2*d + 56*a^2*c*d^2 + 16*d^3)*ArcTanh[(a*Sqrt[c + d*x^2])/Sqrt[a^2*c + d]])/(35*c^4*(a^2*c + d)^(7/2))","A",8,9,16,0.5625,1,"{192, 191, 5977, 6688, 12, 6715, 1619, 63, 208}"
48,1,186,0,0.0831836,"\int \sqrt{a-a x^2} \coth ^{-1}(x) \, dx","Int[Sqrt[a - a*x^2]*ArcCoth[x],x]","-\frac{i a \sqrt{1-x^2} \text{PolyLog}\left(2,-\frac{i \sqrt{1-x}}{\sqrt{x+1}}\right)}{2 \sqrt{a-a x^2}}+\frac{i a \sqrt{1-x^2} \text{PolyLog}\left(2,\frac{i \sqrt{1-x}}{\sqrt{x+1}}\right)}{2 \sqrt{a-a x^2}}+\frac{1}{2} \sqrt{a-a x^2}+\frac{1}{2} x \sqrt{a-a x^2} \coth ^{-1}(x)-\frac{a \sqrt{1-x^2} \tan ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{x+1}}\right) \coth ^{-1}(x)}{\sqrt{a-a x^2}}","-\frac{i a \sqrt{1-x^2} \text{PolyLog}\left(2,-\frac{i \sqrt{1-x}}{\sqrt{x+1}}\right)}{2 \sqrt{a-a x^2}}+\frac{i a \sqrt{1-x^2} \text{PolyLog}\left(2,\frac{i \sqrt{1-x}}{\sqrt{x+1}}\right)}{2 \sqrt{a-a x^2}}+\frac{1}{2} \sqrt{a-a x^2}+\frac{1}{2} x \sqrt{a-a x^2} \coth ^{-1}(x)-\frac{a \sqrt{1-x^2} \tan ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{x+1}}\right) \coth ^{-1}(x)}{\sqrt{a-a x^2}}",1,"Sqrt[a - a*x^2]/2 + (x*Sqrt[a - a*x^2]*ArcCoth[x])/2 - (a*Sqrt[1 - x^2]*ArcCoth[x]*ArcTan[Sqrt[1 - x]/Sqrt[1 + x]])/Sqrt[a - a*x^2] - ((I/2)*a*Sqrt[1 - x^2]*PolyLog[2, ((-I)*Sqrt[1 - x])/Sqrt[1 + x]])/Sqrt[a - a*x^2] + ((I/2)*a*Sqrt[1 - x^2]*PolyLog[2, (I*Sqrt[1 - x])/Sqrt[1 + x]])/Sqrt[a - a*x^2]","A",3,3,15,0.2000,1,"{5943, 5955, 5951}"
49,1,144,0,0.0495992,"\int \frac{\coth ^{-1}(x)}{\sqrt{a-a x^2}} \, dx","Int[ArcCoth[x]/Sqrt[a - a*x^2],x]","-\frac{i \sqrt{1-x^2} \text{PolyLog}\left(2,-\frac{i \sqrt{1-x}}{\sqrt{x+1}}\right)}{\sqrt{a-a x^2}}+\frac{i \sqrt{1-x^2} \text{PolyLog}\left(2,\frac{i \sqrt{1-x}}{\sqrt{x+1}}\right)}{\sqrt{a-a x^2}}-\frac{2 \sqrt{1-x^2} \tan ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{x+1}}\right) \coth ^{-1}(x)}{\sqrt{a-a x^2}}","-\frac{i \sqrt{1-x^2} \text{PolyLog}\left(2,-\frac{i \sqrt{1-x}}{\sqrt{x+1}}\right)}{\sqrt{a-a x^2}}+\frac{i \sqrt{1-x^2} \text{PolyLog}\left(2,\frac{i \sqrt{1-x}}{\sqrt{x+1}}\right)}{\sqrt{a-a x^2}}-\frac{2 \sqrt{1-x^2} \tan ^{-1}\left(\frac{\sqrt{1-x}}{\sqrt{x+1}}\right) \coth ^{-1}(x)}{\sqrt{a-a x^2}}",1,"(-2*Sqrt[1 - x^2]*ArcCoth[x]*ArcTan[Sqrt[1 - x]/Sqrt[1 + x]])/Sqrt[a - a*x^2] - (I*Sqrt[1 - x^2]*PolyLog[2, ((-I)*Sqrt[1 - x])/Sqrt[1 + x]])/Sqrt[a - a*x^2] + (I*Sqrt[1 - x^2]*PolyLog[2, (I*Sqrt[1 - x])/Sqrt[1 + x]])/Sqrt[a - a*x^2]","A",2,2,15,0.1333,1,"{5955, 5951}"
50,1,37,0,0.0254153,"\int \frac{\coth ^{-1}(x)}{\left(a-a x^2\right)^{3/2}} \, dx","Int[ArcCoth[x]/(a - a*x^2)^(3/2),x]","\frac{x \coth ^{-1}(x)}{a \sqrt{a-a x^2}}-\frac{1}{a \sqrt{a-a x^2}}","\frac{x \coth ^{-1}(x)}{a \sqrt{a-a x^2}}-\frac{1}{a \sqrt{a-a x^2}}",1,"-(1/(a*Sqrt[a - a*x^2])) + (x*ArcCoth[x])/(a*Sqrt[a - a*x^2])","A",1,1,15,0.06667,1,"{5959}"
51,1,83,0,0.0534298,"\int \frac{\coth ^{-1}(x)}{\left(a-a x^2\right)^{5/2}} \, dx","Int[ArcCoth[x]/(a - a*x^2)^(5/2),x]","-\frac{2}{3 a^2 \sqrt{a-a x^2}}+\frac{2 x \coth ^{-1}(x)}{3 a^2 \sqrt{a-a x^2}}-\frac{1}{9 a \left(a-a x^2\right)^{3/2}}+\frac{x \coth ^{-1}(x)}{3 a \left(a-a x^2\right)^{3/2}}","-\frac{2}{3 a^2 \sqrt{a-a x^2}}+\frac{2 x \coth ^{-1}(x)}{3 a^2 \sqrt{a-a x^2}}-\frac{1}{9 a \left(a-a x^2\right)^{3/2}}+\frac{x \coth ^{-1}(x)}{3 a \left(a-a x^2\right)^{3/2}}",1,"-1/(9*a*(a - a*x^2)^(3/2)) - 2/(3*a^2*Sqrt[a - a*x^2]) + (x*ArcCoth[x])/(3*a*(a - a*x^2)^(3/2)) + (2*x*ArcCoth[x])/(3*a^2*Sqrt[a - a*x^2])","A",2,2,15,0.1333,1,"{5961, 5959}"
52,1,124,0,0.0820825,"\int \frac{\coth ^{-1}(x)}{\left(a-a x^2\right)^{7/2}} \, dx","Int[ArcCoth[x]/(a - a*x^2)^(7/2),x]","-\frac{8}{15 a^3 \sqrt{a-a x^2}}-\frac{4}{45 a^2 \left(a-a x^2\right)^{3/2}}+\frac{8 x \coth ^{-1}(x)}{15 a^3 \sqrt{a-a x^2}}+\frac{4 x \coth ^{-1}(x)}{15 a^2 \left(a-a x^2\right)^{3/2}}-\frac{1}{25 a \left(a-a x^2\right)^{5/2}}+\frac{x \coth ^{-1}(x)}{5 a \left(a-a x^2\right)^{5/2}}","-\frac{8}{15 a^3 \sqrt{a-a x^2}}-\frac{4}{45 a^2 \left(a-a x^2\right)^{3/2}}+\frac{8 x \coth ^{-1}(x)}{15 a^3 \sqrt{a-a x^2}}+\frac{4 x \coth ^{-1}(x)}{15 a^2 \left(a-a x^2\right)^{3/2}}-\frac{1}{25 a \left(a-a x^2\right)^{5/2}}+\frac{x \coth ^{-1}(x)}{5 a \left(a-a x^2\right)^{5/2}}",1,"-1/(25*a*(a - a*x^2)^(5/2)) - 4/(45*a^2*(a - a*x^2)^(3/2)) - 8/(15*a^3*Sqrt[a - a*x^2]) + (x*ArcCoth[x])/(5*a*(a - a*x^2)^(5/2)) + (4*x*ArcCoth[x])/(15*a^2*(a - a*x^2)^(3/2)) + (8*x*ArcCoth[x])/(15*a^3*Sqrt[a - a*x^2])","A",3,2,15,0.1333,1,"{5961, 5959}"
53,1,3,0,0.0233692,"\int \frac{1}{\left(1-x^2\right) \coth ^{-1}(x)} \, dx","Int[1/((1 - x^2)*ArcCoth[x]),x]","\log \left(\coth ^{-1}(x)\right)","\log \left(\coth ^{-1}(x)\right)",1,"Log[ArcCoth[x]]","A",1,1,14,0.07143,1,"{5947}"
54,1,12,0,0.0263976,"\int \frac{\coth ^{-1}(x)^n}{1-x^2} \, dx","Int[ArcCoth[x]^n/(1 - x^2),x]","\frac{\coth ^{-1}(x)^{n+1}}{n+1}","\frac{\coth ^{-1}(x)^{n+1}}{n+1}",1,"ArcCoth[x]^(1 + n)/(1 + n)","A",1,1,14,0.07143,1,"{5949}"
55,1,62,0,0.0506488,"\int \frac{\coth ^{-1}(x)^2}{\left(1-x^2\right)^2} \, dx","Int[ArcCoth[x]^2/(1 - x^2)^2,x]","\frac{x}{4 \left(1-x^2\right)}+\frac{x \coth ^{-1}(x)^2}{2 \left(1-x^2\right)}-\frac{\coth ^{-1}(x)}{2 \left(1-x^2\right)}+\frac{1}{4} \tanh ^{-1}(x)+\frac{1}{6} \coth ^{-1}(x)^3","\frac{x}{4 \left(1-x^2\right)}+\frac{x \coth ^{-1}(x)^2}{2 \left(1-x^2\right)}-\frac{\coth ^{-1}(x)}{2 \left(1-x^2\right)}+\frac{1}{4} \tanh ^{-1}(x)+\frac{1}{6} \coth ^{-1}(x)^3",1,"x/(4*(1 - x^2)) - ArcCoth[x]/(2*(1 - x^2)) + (x*ArcCoth[x]^2)/(2*(1 - x^2)) + ArcCoth[x]^3/6 + ArcTanh[x]/4","A",4,4,14,0.2857,1,"{5957, 5995, 199, 206}"
56,1,37,0,0.0592361,"\int \frac{x \coth ^{-1}(x)}{1-x^2} \, dx","Int[(x*ArcCoth[x])/(1 - x^2),x]","\frac{1}{2} \text{PolyLog}\left(2,\frac{x+1}{x-1}\right)-\frac{1}{2} \coth ^{-1}(x)^2+\log \left(\frac{2}{1-x}\right) \coth ^{-1}(x)","\frac{1}{2} \text{PolyLog}\left(2,\frac{x+1}{x-1}\right)-\frac{1}{2} \coth ^{-1}(x)^2+\log \left(\frac{2}{1-x}\right) \coth ^{-1}(x)",1,"-ArcCoth[x]^2/2 + ArcCoth[x]*Log[2/(1 - x)] + PolyLog[2, (1 + x)/(-1 + x)]/2","A",4,4,13,0.3077,1,"{5985, 5919, 2402, 2315}"
57,1,8,0,0.0138965,"\int \frac{\coth ^{-1}(x)}{1-x^2} \, dx","Int[ArcCoth[x]/(1 - x^2),x]","\frac{1}{2} \coth ^{-1}(x)^2","\frac{1}{2} \coth ^{-1}(x)^2",1,"ArcCoth[x]^2/2","A",1,1,12,0.08333,1,"{5949}"
58,1,36,0,0.0307194,"\int \frac{x \coth ^{-1}(x)}{\left(1-x^2\right)^2} \, dx","Int[(x*ArcCoth[x])/(1 - x^2)^2,x]","-\frac{x}{4 \left(1-x^2\right)}+\frac{\coth ^{-1}(x)}{2 \left(1-x^2\right)}-\frac{1}{4} \tanh ^{-1}(x)","-\frac{x}{4 \left(1-x^2\right)}+\frac{\coth ^{-1}(x)}{2 \left(1-x^2\right)}-\frac{1}{4} \tanh ^{-1}(x)",1,"-x/(4*(1 - x^2)) + ArcCoth[x]/(2*(1 - x^2)) - ArcTanh[x]/4","A",3,3,13,0.2308,1,"{5995, 199, 206}"
59,1,38,0,0.0174931,"\int \frac{\coth ^{-1}(x)}{\left(1-x^2\right)^2} \, dx","Int[ArcCoth[x]/(1 - x^2)^2,x]","-\frac{1}{4 \left(1-x^2\right)}+\frac{x \coth ^{-1}(x)}{2 \left(1-x^2\right)}+\frac{1}{4} \coth ^{-1}(x)^2","-\frac{1}{4 \left(1-x^2\right)}+\frac{x \coth ^{-1}(x)}{2 \left(1-x^2\right)}+\frac{1}{4} \coth ^{-1}(x)^2",1,"-1/(4*(1 - x^2)) + (x*ArcCoth[x])/(2*(1 - x^2)) + ArcCoth[x]^2/4","A",2,2,12,0.1667,1,"{5957, 261}"
60,1,50,0,0.0341809,"\int \frac{x \coth ^{-1}(x)}{\left(1-x^2\right)^3} \, dx","Int[(x*ArcCoth[x])/(1 - x^2)^3,x]","-\frac{3 x}{32 \left(1-x^2\right)}-\frac{x}{16 \left(1-x^2\right)^2}+\frac{\coth ^{-1}(x)}{4 \left(1-x^2\right)^2}-\frac{3}{32} \tanh ^{-1}(x)","-\frac{3 x}{32 \left(1-x^2\right)}-\frac{x}{16 \left(1-x^2\right)^2}+\frac{\coth ^{-1}(x)}{4 \left(1-x^2\right)^2}-\frac{3}{32} \tanh ^{-1}(x)",1,"-x/(16*(1 - x^2)^2) - (3*x)/(32*(1 - x^2)) + ArcCoth[x]/(4*(1 - x^2)^2) - (3*ArcTanh[x])/32","A",4,3,13,0.2308,1,"{5995, 199, 206}"
61,1,67,0,0.0352498,"\int \frac{\coth ^{-1}(x)}{\left(1-x^2\right)^3} \, dx","Int[ArcCoth[x]/(1 - x^2)^3,x]","-\frac{3}{16 \left(1-x^2\right)}-\frac{1}{16 \left(1-x^2\right)^2}+\frac{3 x \coth ^{-1}(x)}{8 \left(1-x^2\right)}+\frac{x \coth ^{-1}(x)}{4 \left(1-x^2\right)^2}+\frac{3}{16} \coth ^{-1}(x)^2","-\frac{3}{16 \left(1-x^2\right)}-\frac{1}{16 \left(1-x^2\right)^2}+\frac{3 x \coth ^{-1}(x)}{8 \left(1-x^2\right)}+\frac{x \coth ^{-1}(x)}{4 \left(1-x^2\right)^2}+\frac{3}{16} \coth ^{-1}(x)^2",1,"-1/(16*(1 - x^2)^2) - 3/(16*(1 - x^2)) + (x*ArcCoth[x])/(4*(1 - x^2)^2) + (3*x*ArcCoth[x])/(8*(1 - x^2)) + (3*ArcCoth[x]^2)/16","A",3,3,12,0.2500,1,"{5961, 5957, 261}"
62,1,101,0,0.1263329,"\int x^3 \coth ^{-1}(a+b x) \, dx","Int[x^3*ArcCoth[a + b*x],x]","\frac{\left(6 a^2+1\right) x}{4 b^3}+\frac{(a+b x)^3}{12 b^4}-\frac{a (a+b x)^2}{2 b^4}+\frac{(1-a)^4 \log (-a-b x+1)}{8 b^4}-\frac{(a+1)^4 \log (a+b x+1)}{8 b^4}+\frac{1}{4} x^4 \coth ^{-1}(a+b x)","\frac{\left(6 a^2+1\right) x}{4 b^3}+\frac{(a+b x)^3}{12 b^4}-\frac{a (a+b x)^2}{2 b^4}+\frac{(1-a)^4 \log (-a-b x+1)}{8 b^4}-\frac{(a+1)^4 \log (a+b x+1)}{8 b^4}+\frac{1}{4} x^4 \coth ^{-1}(a+b x)",1,"((1 + 6*a^2)*x)/(4*b^3) - (a*(a + b*x)^2)/(2*b^4) + (a + b*x)^3/(12*b^4) + (x^4*ArcCoth[a + b*x])/4 + ((1 - a)^4*Log[1 - a - b*x])/(8*b^4) - ((1 + a)^4*Log[1 + a + b*x])/(8*b^4)","A",7,5,10,0.5000,1,"{6112, 5927, 702, 633, 31}"
63,1,78,0,0.1018365,"\int x^2 \coth ^{-1}(a+b x) \, dx","Int[x^2*ArcCoth[a + b*x],x]","\frac{(a+b x)^2}{6 b^3}-\frac{a x}{b^2}+\frac{(1-a)^3 \log (-a-b x+1)}{6 b^3}+\frac{(a+1)^3 \log (a+b x+1)}{6 b^3}+\frac{1}{3} x^3 \coth ^{-1}(a+b x)","\frac{(a+b x)^2}{6 b^3}-\frac{a x}{b^2}+\frac{(1-a)^3 \log (-a-b x+1)}{6 b^3}+\frac{(a+1)^3 \log (a+b x+1)}{6 b^3}+\frac{1}{3} x^3 \coth ^{-1}(a+b x)",1,"-((a*x)/b^2) + (a + b*x)^2/(6*b^3) + (x^3*ArcCoth[a + b*x])/3 + ((1 - a)^3*Log[1 - a - b*x])/(6*b^3) + ((1 + a)^3*Log[1 + a + b*x])/(6*b^3)","A",7,5,10,0.5000,1,"{6112, 5927, 702, 633, 31}"
64,1,65,0,0.0716315,"\int x \coth ^{-1}(a+b x) \, dx","Int[x*ArcCoth[a + b*x],x]","\frac{(1-a)^2 \log (-a-b x+1)}{4 b^2}-\frac{(a+1)^2 \log (a+b x+1)}{4 b^2}+\frac{1}{2} x^2 \coth ^{-1}(a+b x)+\frac{x}{2 b}","\frac{(1-a)^2 \log (-a-b x+1)}{4 b^2}-\frac{(a+1)^2 \log (a+b x+1)}{4 b^2}+\frac{1}{2} x^2 \coth ^{-1}(a+b x)+\frac{x}{2 b}",1,"x/(2*b) + (x^2*ArcCoth[a + b*x])/2 + ((1 - a)^2*Log[1 - a - b*x])/(4*b^2) - ((1 + a)^2*Log[1 + a + b*x])/(4*b^2)","A",7,5,8,0.6250,1,"{6112, 5927, 702, 633, 31}"
65,1,35,0,0.0159401,"\int \coth ^{-1}(a+b x) \, dx","Int[ArcCoth[a + b*x],x]","\frac{\log \left(1-(a+b x)^2\right)}{2 b}+\frac{(a+b x) \coth ^{-1}(a+b x)}{b}","\frac{\log \left(1-(a+b x)^2\right)}{2 b}+\frac{(a+b x) \coth ^{-1}(a+b x)}{b}",1,"((a + b*x)*ArcCoth[a + b*x])/b + Log[1 - (a + b*x)^2]/(2*b)","A",3,3,6,0.5000,1,"{6104, 5911, 260}"
66,1,92,0,0.0973951,"\int \frac{\coth ^{-1}(a+b x)}{x} \, dx","Int[ArcCoth[a + b*x]/x,x]","\frac{1}{2} \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)-\frac{1}{2} \text{PolyLog}\left(2,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)+\log \left(\frac{2}{a+b x+1}\right) \left(-\coth ^{-1}(a+b x)\right)+\log \left(\frac{2 b x}{(1-a) (a+b x+1)}\right) \coth ^{-1}(a+b x)","\frac{1}{2} \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)-\frac{1}{2} \text{PolyLog}\left(2,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)+\log \left(\frac{2}{a+b x+1}\right) \left(-\coth ^{-1}(a+b x)\right)+\log \left(\frac{2 b x}{(1-a) (a+b x+1)}\right) \coth ^{-1}(a+b x)",1,"-(ArcCoth[a + b*x]*Log[2/(1 + a + b*x)]) + ArcCoth[a + b*x]*Log[(2*b*x)/((1 - a)*(1 + a + b*x))] + PolyLog[2, 1 - 2/(1 + a + b*x)]/2 - PolyLog[2, 1 - (2*b*x)/((1 - a)*(1 + a + b*x))]/2","A",5,5,10,0.5000,1,"{6112, 5921, 2402, 2315, 2447}"
67,1,64,0,0.0510754,"\int \frac{\coth ^{-1}(a+b x)}{x^2} \, dx","Int[ArcCoth[a + b*x]/x^2,x]","\frac{b \log (x)}{1-a^2}-\frac{b \log (-a-b x+1)}{2 (1-a)}-\frac{b \log (a+b x+1)}{2 (a+1)}-\frac{\coth ^{-1}(a+b x)}{x}","\frac{b \log (x)}{1-a^2}-\frac{b \log (-a-b x+1)}{2 (1-a)}-\frac{b \log (a+b x+1)}{2 (a+1)}-\frac{\coth ^{-1}(a+b x)}{x}",1,"-(ArcCoth[a + b*x]/x) + (b*Log[x])/(1 - a^2) - (b*Log[1 - a - b*x])/(2*(1 - a)) - (b*Log[1 + a + b*x])/(2*(1 + a))","A",7,5,10,0.5000,1,"{6110, 371, 706, 31, 633}"
68,1,90,0,0.0997384,"\int \frac{\coth ^{-1}(a+b x)}{x^3} \, dx","Int[ArcCoth[a + b*x]/x^3,x]","\frac{a b^2 \log (x)}{\left(1-a^2\right)^2}-\frac{b}{2 \left(1-a^2\right) x}-\frac{b^2 \log (-a-b x+1)}{4 (1-a)^2}+\frac{b^2 \log (a+b x+1)}{4 (a+1)^2}-\frac{\coth ^{-1}(a+b x)}{2 x^2}","\frac{a b^2 \log (x)}{\left(1-a^2\right)^2}-\frac{b}{2 \left(1-a^2\right) x}-\frac{b^2 \log (-a-b x+1)}{4 (1-a)^2}+\frac{b^2 \log (a+b x+1)}{4 (a+1)^2}-\frac{\coth ^{-1}(a+b x)}{2 x^2}",1,"-b/(2*(1 - a^2)*x) - ArcCoth[a + b*x]/(2*x^2) + (a*b^2*Log[x])/(1 - a^2)^2 - (b^2*Log[1 - a - b*x])/(4*(1 - a)^2) + (b^2*Log[1 + a + b*x])/(4*(1 + a)^2)","A",5,4,10,0.4000,1,"{6110, 371, 710, 801}"
69,1,263,0,0.3487789,"\int x^3 \coth ^{-1}(a+b x)^2 \, dx","Int[x^3*ArcCoth[a + b*x]^2,x]","\frac{a \left(a^2+1\right) \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{b^4}+\frac{\left(6 a^2+1\right) \log \left(1-(a+b x)^2\right)}{4 b^4}-\frac{a \left(a^2+1\right) \coth ^{-1}(a+b x)^2}{b^4}-\frac{\left(a^4+6 a^2+1\right) \coth ^{-1}(a+b x)^2}{4 b^4}+\frac{\left(6 a^2+1\right) (a+b x) \coth ^{-1}(a+b x)}{2 b^4}+\frac{2 a \left(a^2+1\right) \log \left(\frac{2}{-a-b x+1}\right) \coth ^{-1}(a+b x)}{b^4}-\frac{a x}{b^3}+\frac{(a+b x)^2}{12 b^4}+\frac{\log \left(1-(a+b x)^2\right)}{12 b^4}+\frac{a \tanh ^{-1}(a+b x)}{b^4}+\frac{(a+b x)^3 \coth ^{-1}(a+b x)}{6 b^4}-\frac{a (a+b x)^2 \coth ^{-1}(a+b x)}{b^4}+\frac{1}{4} x^4 \coth ^{-1}(a+b x)^2","\frac{a \left(a^2+1\right) \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{b^4}+\frac{\left(6 a^2+1\right) \log \left(1-(a+b x)^2\right)}{4 b^4}-\frac{a \left(a^2+1\right) \coth ^{-1}(a+b x)^2}{b^4}-\frac{\left(a^4+6 a^2+1\right) \coth ^{-1}(a+b x)^2}{4 b^4}+\frac{\left(6 a^2+1\right) (a+b x) \coth ^{-1}(a+b x)}{2 b^4}+\frac{2 a \left(a^2+1\right) \log \left(\frac{2}{-a-b x+1}\right) \coth ^{-1}(a+b x)}{b^4}-\frac{a x}{b^3}+\frac{(a+b x)^2}{12 b^4}+\frac{\log \left(1-(a+b x)^2\right)}{12 b^4}+\frac{a \tanh ^{-1}(a+b x)}{b^4}+\frac{(a+b x)^3 \coth ^{-1}(a+b x)}{6 b^4}-\frac{a (a+b x)^2 \coth ^{-1}(a+b x)}{b^4}+\frac{1}{4} x^4 \coth ^{-1}(a+b x)^2",1,"-((a*x)/b^3) + (a + b*x)^2/(12*b^4) + ((1 + 6*a^2)*(a + b*x)*ArcCoth[a + b*x])/(2*b^4) - (a*(a + b*x)^2*ArcCoth[a + b*x])/b^4 + ((a + b*x)^3*ArcCoth[a + b*x])/(6*b^4) - (a*(1 + a^2)*ArcCoth[a + b*x]^2)/b^4 - ((1 + 6*a^2 + a^4)*ArcCoth[a + b*x]^2)/(4*b^4) + (x^4*ArcCoth[a + b*x]^2)/4 + (a*ArcTanh[a + b*x])/b^4 + (2*a*(1 + a^2)*ArcCoth[a + b*x]*Log[2/(1 - a - b*x)])/b^4 + Log[1 - (a + b*x)^2]/(12*b^4) + ((1 + 6*a^2)*Log[1 - (a + b*x)^2])/(4*b^4) + (a*(1 + a^2)*PolyLog[2, -((1 + a + b*x)/(1 - a - b*x))])/b^4","A",19,15,12,1.250,1,"{6112, 5929, 5911, 260, 5917, 321, 206, 266, 43, 6049, 5949, 5985, 5919, 2402, 2315}"
70,1,204,0,0.2782722,"\int x^2 \coth ^{-1}(a+b x)^2 \, dx","Int[x^2*ArcCoth[a + b*x]^2,x]","-\frac{\left(3 a^2+1\right) \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{3 b^3}+\frac{a \left(a^2+3\right) \coth ^{-1}(a+b x)^2}{3 b^3}+\frac{\left(3 a^2+1\right) \coth ^{-1}(a+b x)^2}{3 b^3}-\frac{2 \left(3 a^2+1\right) \log \left(\frac{2}{-a-b x+1}\right) \coth ^{-1}(a+b x)}{3 b^3}-\frac{a \log \left(1-(a+b x)^2\right)}{b^3}-\frac{\tanh ^{-1}(a+b x)}{3 b^3}+\frac{(a+b x)^2 \coth ^{-1}(a+b x)}{3 b^3}-\frac{2 a (a+b x) \coth ^{-1}(a+b x)}{b^3}+\frac{1}{3} x^3 \coth ^{-1}(a+b x)^2+\frac{x}{3 b^2}","-\frac{\left(3 a^2+1\right) \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{3 b^3}+\frac{a \left(a^2+3\right) \coth ^{-1}(a+b x)^2}{3 b^3}+\frac{\left(3 a^2+1\right) \coth ^{-1}(a+b x)^2}{3 b^3}-\frac{2 \left(3 a^2+1\right) \log \left(\frac{2}{-a-b x+1}\right) \coth ^{-1}(a+b x)}{3 b^3}-\frac{a \log \left(1-(a+b x)^2\right)}{b^3}-\frac{\tanh ^{-1}(a+b x)}{3 b^3}+\frac{(a+b x)^2 \coth ^{-1}(a+b x)}{3 b^3}-\frac{2 a (a+b x) \coth ^{-1}(a+b x)}{b^3}+\frac{1}{3} x^3 \coth ^{-1}(a+b x)^2+\frac{x}{3 b^2}",1,"x/(3*b^2) - (2*a*(a + b*x)*ArcCoth[a + b*x])/b^3 + ((a + b*x)^2*ArcCoth[a + b*x])/(3*b^3) + (a*(3 + a^2)*ArcCoth[a + b*x]^2)/(3*b^3) + ((1 + 3*a^2)*ArcCoth[a + b*x]^2)/(3*b^3) + (x^3*ArcCoth[a + b*x]^2)/3 - ArcTanh[a + b*x]/(3*b^3) - (2*(1 + 3*a^2)*ArcCoth[a + b*x]*Log[2/(1 - a - b*x)])/(3*b^3) - (a*Log[1 - (a + b*x)^2])/b^3 - ((1 + 3*a^2)*PolyLog[2, -((1 + a + b*x)/(1 - a - b*x))])/(3*b^3)","A",15,13,12,1.083,1,"{6112, 5929, 5911, 260, 5917, 321, 206, 6049, 5949, 5985, 5919, 2402, 2315}"
71,1,136,0,0.2090946,"\int x \coth ^{-1}(a+b x)^2 \, dx","Int[x*ArcCoth[a + b*x]^2,x]","\frac{a \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{b^2}-\frac{\left(a^2+1\right) \coth ^{-1}(a+b x)^2}{2 b^2}+\frac{\log \left(1-(a+b x)^2\right)}{2 b^2}-\frac{a \coth ^{-1}(a+b x)^2}{b^2}+\frac{(a+b x) \coth ^{-1}(a+b x)}{b^2}+\frac{2 a \log \left(\frac{2}{-a-b x+1}\right) \coth ^{-1}(a+b x)}{b^2}+\frac{1}{2} x^2 \coth ^{-1}(a+b x)^2","\frac{a \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{b^2}-\frac{\left(a^2+1\right) \coth ^{-1}(a+b x)^2}{2 b^2}+\frac{\log \left(1-(a+b x)^2\right)}{2 b^2}-\frac{a \coth ^{-1}(a+b x)^2}{b^2}+\frac{(a+b x) \coth ^{-1}(a+b x)}{b^2}+\frac{2 a \log \left(\frac{2}{-a-b x+1}\right) \coth ^{-1}(a+b x)}{b^2}+\frac{1}{2} x^2 \coth ^{-1}(a+b x)^2",1,"((a + b*x)*ArcCoth[a + b*x])/b^2 - (a*ArcCoth[a + b*x]^2)/b^2 - ((1 + a^2)*ArcCoth[a + b*x]^2)/(2*b^2) + (x^2*ArcCoth[a + b*x]^2)/2 + (2*a*ArcCoth[a + b*x]*Log[2/(1 - a - b*x)])/b^2 + Log[1 - (a + b*x)^2]/(2*b^2) + (a*PolyLog[2, -((1 + a + b*x)/(1 - a - b*x))])/b^2","A",12,10,10,1.000,1,"{6112, 5929, 5911, 260, 6049, 5949, 5985, 5919, 2402, 2315}"
72,1,81,0,0.0902758,"\int \coth ^{-1}(a+b x)^2 \, dx","Int[ArcCoth[a + b*x]^2,x]","-\frac{\text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{b}+\frac{(a+b x) \coth ^{-1}(a+b x)^2}{b}+\frac{\coth ^{-1}(a+b x)^2}{b}-\frac{2 \log \left(\frac{2}{-a-b x+1}\right) \coth ^{-1}(a+b x)}{b}","-\frac{\text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{b}+\frac{(a+b x) \coth ^{-1}(a+b x)^2}{b}+\frac{\coth ^{-1}(a+b x)^2}{b}-\frac{2 \log \left(\frac{2}{-a-b x+1}\right) \coth ^{-1}(a+b x)}{b}",1,"ArcCoth[a + b*x]^2/b + ((a + b*x)*ArcCoth[a + b*x]^2)/b - (2*ArcCoth[a + b*x]*Log[2/(1 - a - b*x)])/b - PolyLog[2, -((1 + a + b*x)/(1 - a - b*x))]/b","A",6,6,8,0.7500,1,"{6104, 5911, 5985, 5919, 2402, 2315}"
73,1,148,0,0.0913941,"\int \frac{\coth ^{-1}(a+b x)^2}{x} \, dx","Int[ArcCoth[a + b*x]^2/x,x]","\frac{1}{2} \text{PolyLog}\left(3,1-\frac{2}{a+b x+1}\right)-\frac{1}{2} \text{PolyLog}\left(3,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)+\coth ^{-1}(a+b x) \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)-\coth ^{-1}(a+b x) \text{PolyLog}\left(2,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)-\log \left(\frac{2}{a+b x+1}\right) \coth ^{-1}(a+b x)^2+\log \left(\frac{2 b x}{(1-a) (a+b x+1)}\right) \coth ^{-1}(a+b x)^2","\frac{1}{2} \text{PolyLog}\left(3,1-\frac{2}{a+b x+1}\right)-\frac{1}{2} \text{PolyLog}\left(3,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)+\coth ^{-1}(a+b x) \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)-\coth ^{-1}(a+b x) \text{PolyLog}\left(2,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)-\log \left(\frac{2}{a+b x+1}\right) \coth ^{-1}(a+b x)^2+\log \left(\frac{2 b x}{(1-a) (a+b x+1)}\right) \coth ^{-1}(a+b x)^2",1,"-(ArcCoth[a + b*x]^2*Log[2/(1 + a + b*x)]) + ArcCoth[a + b*x]^2*Log[(2*b*x)/((1 - a)*(1 + a + b*x))] + ArcCoth[a + b*x]*PolyLog[2, 1 - 2/(1 + a + b*x)] - ArcCoth[a + b*x]*PolyLog[2, 1 - (2*b*x)/((1 - a)*(1 + a + b*x))] + PolyLog[3, 1 - 2/(1 + a + b*x)]/2 - PolyLog[3, 1 - (2*b*x)/((1 - a)*(1 + a + b*x))]/2","A",2,2,12,0.1667,1,"{6112, 5923}"
74,1,251,0,0.7192777,"\int \frac{\coth ^{-1}(a+b x)^2}{x^2} \, dx","Int[ArcCoth[a + b*x]^2/x^2,x]","\frac{b \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{1-a^2}-\frac{b \text{PolyLog}\left(2,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)}{1-a^2}+\frac{b \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{2 (1-a)}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{2 (a+1)}-\frac{2 b \log \left(\frac{2}{a+b x+1}\right) \coth ^{-1}(a+b x)}{1-a^2}+\frac{2 b \log \left(\frac{2 b x}{(1-a) (a+b x+1)}\right) \coth ^{-1}(a+b x)}{1-a^2}-\frac{\coth ^{-1}(a+b x)^2}{x}+\frac{b \log \left(\frac{2}{-a-b x+1}\right) \coth ^{-1}(a+b x)}{1-a}+\frac{b \log \left(\frac{2}{a+b x+1}\right) \coth ^{-1}(a+b x)}{a+1}","\frac{b \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{1-a^2}-\frac{b \text{PolyLog}\left(2,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)}{1-a^2}+\frac{b \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{2 (1-a)}-\frac{b \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{2 (a+1)}-\frac{2 b \log \left(\frac{2}{a+b x+1}\right) \coth ^{-1}(a+b x)}{1-a^2}+\frac{2 b \log \left(\frac{2 b x}{(1-a) (a+b x+1)}\right) \coth ^{-1}(a+b x)}{1-a^2}-\frac{\coth ^{-1}(a+b x)^2}{x}+\frac{b \log \left(\frac{2}{-a-b x+1}\right) \coth ^{-1}(a+b x)}{1-a}+\frac{b \log \left(\frac{2}{a+b x+1}\right) \coth ^{-1}(a+b x)}{a+1}",1,"-(ArcCoth[a + b*x]^2/x) + (b*ArcCoth[a + b*x]*Log[2/(1 - a - b*x)])/(1 - a) + (b*ArcCoth[a + b*x]*Log[2/(1 + a + b*x)])/(1 + a) - (2*b*ArcCoth[a + b*x]*Log[2/(1 + a + b*x)])/(1 - a^2) + (2*b*ArcCoth[a + b*x]*Log[(2*b*x)/((1 - a)*(1 + a + b*x))])/(1 - a^2) + (b*PolyLog[2, -((1 + a + b*x)/(1 - a - b*x))])/(2*(1 - a)) - (b*PolyLog[2, 1 - 2/(1 + a + b*x)])/(2*(1 + a)) + (b*PolyLog[2, 1 - 2/(1 + a + b*x)])/(1 - a^2) - (b*PolyLog[2, 1 - (2*b*x)/((1 - a)*(1 + a + b*x))])/(1 - a^2)","A",17,15,12,1.250,1,"{6110, 371, 706, 31, 633, 6741, 6122, 6688, 12, 6725, 5921, 2402, 2315, 2447, 5919}"
75,1,370,0,0.8299862,"\int \frac{\coth ^{-1}(a+b x)^2}{x^3} \, dx","Int[ArcCoth[a + b*x]^2/x^3,x]","\frac{a b^2 \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{\left(1-a^2\right)^2}-\frac{a b^2 \text{PolyLog}\left(2,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)}{\left(1-a^2\right)^2}+\frac{b^2 \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{4 (1-a)^2}+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{4 (a+1)^2}+\frac{b^2 \log (x)}{\left(1-a^2\right)^2}-\frac{2 a b^2 \log \left(\frac{2}{a+b x+1}\right) \coth ^{-1}(a+b x)}{\left(1-a^2\right)^2}+\frac{2 a b^2 \log \left(\frac{2 b x}{(1-a) (a+b x+1)}\right) \coth ^{-1}(a+b x)}{\left(1-a^2\right)^2}-\frac{b \coth ^{-1}(a+b x)}{\left(1-a^2\right) x}-\frac{b^2 \log (-a-b x+1)}{2 (1-a)^2 (a+1)}-\frac{b^2 \log (a+b x+1)}{2 (1-a) (a+1)^2}+\frac{b^2 \log \left(\frac{2}{-a-b x+1}\right) \coth ^{-1}(a+b x)}{2 (1-a)^2}-\frac{b^2 \log \left(\frac{2}{a+b x+1}\right) \coth ^{-1}(a+b x)}{2 (a+1)^2}-\frac{\coth ^{-1}(a+b x)^2}{2 x^2}","\frac{a b^2 \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{\left(1-a^2\right)^2}-\frac{a b^2 \text{PolyLog}\left(2,1-\frac{2 b x}{(1-a) (a+b x+1)}\right)}{\left(1-a^2\right)^2}+\frac{b^2 \text{PolyLog}\left(2,-\frac{a+b x+1}{-a-b x+1}\right)}{4 (1-a)^2}+\frac{b^2 \text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{4 (a+1)^2}+\frac{b^2 \log (x)}{\left(1-a^2\right)^2}-\frac{2 a b^2 \log \left(\frac{2}{a+b x+1}\right) \coth ^{-1}(a+b x)}{\left(1-a^2\right)^2}+\frac{2 a b^2 \log \left(\frac{2 b x}{(1-a) (a+b x+1)}\right) \coth ^{-1}(a+b x)}{\left(1-a^2\right)^2}-\frac{b \coth ^{-1}(a+b x)}{\left(1-a^2\right) x}-\frac{b^2 \log (-a-b x+1)}{2 (1-a)^2 (a+1)}-\frac{b^2 \log (a+b x+1)}{2 (1-a) (a+1)^2}+\frac{b^2 \log \left(\frac{2}{-a-b x+1}\right) \coth ^{-1}(a+b x)}{2 (1-a)^2}-\frac{b^2 \log \left(\frac{2}{a+b x+1}\right) \coth ^{-1}(a+b x)}{2 (a+1)^2}-\frac{\coth ^{-1}(a+b x)^2}{2 x^2}",1,"-((b*ArcCoth[a + b*x])/((1 - a^2)*x)) - ArcCoth[a + b*x]^2/(2*x^2) + (b^2*Log[x])/(1 - a^2)^2 + (b^2*ArcCoth[a + b*x]*Log[2/(1 - a - b*x)])/(2*(1 - a)^2) - (b^2*Log[1 - a - b*x])/(2*(1 - a)^2*(1 + a)) - (b^2*ArcCoth[a + b*x]*Log[2/(1 + a + b*x)])/(2*(1 + a)^2) - (2*a*b^2*ArcCoth[a + b*x]*Log[2/(1 + a + b*x)])/(1 - a^2)^2 + (2*a*b^2*ArcCoth[a + b*x]*Log[(2*b*x)/((1 - a)*(1 + a + b*x))])/(1 - a^2)^2 - (b^2*Log[1 + a + b*x])/(2*(1 - a)*(1 + a)^2) + (b^2*PolyLog[2, -((1 + a + b*x)/(1 - a - b*x))])/(4*(1 - a)^2) + (b^2*PolyLog[2, 1 - 2/(1 + a + b*x)])/(4*(1 + a)^2) + (a*b^2*PolyLog[2, 1 - 2/(1 + a + b*x)])/(1 - a^2)^2 - (a*b^2*PolyLog[2, 1 - (2*b*x)/((1 - a)*(1 + a + b*x))])/(1 - a^2)^2","A",21,16,12,1.333,1,"{6110, 371, 710, 801, 6741, 6122, 6725, 5927, 706, 31, 633, 5921, 2402, 2315, 2447, 5919}"
76,1,597,0,1.0994743,"\int \frac{\coth ^{-1}(a+b x)}{c+d x^2} \, dx","Int[ArcCoth[a + b*x]/(c + d*x^2),x]","-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} (-a-b x+1)}{b \sqrt{-c}-(1-a) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} (-a-b x+1)}{(1-a) \sqrt{d}+b \sqrt{-c}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} (a+b x+1)}{b \sqrt{-c}-(a+1) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} (a+b x+1)}{(a+1) \sqrt{d}+b \sqrt{-c}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\log (a+b x-1) \log \left(\frac{b \left(\sqrt{-c}-\sqrt{d} x\right)}{b \sqrt{-c}-(1-a) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\log (a+b x+1) \log \left(\frac{b \left(\sqrt{-c}-\sqrt{d} x\right)}{(a+1) \sqrt{d}+b \sqrt{-c}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\log (a+b x-1) \log \left(\frac{b \left(\sqrt{-c}+\sqrt{d} x\right)}{(1-a) \sqrt{d}+b \sqrt{-c}}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\log (a+b x+1) \log \left(\frac{b \left(\sqrt{-c}+\sqrt{d} x\right)}{b \sqrt{-c}-(a+1) \sqrt{d}}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\left(\log (a+b x-1)-\log \left(-\frac{-a-b x+1}{a+b x}\right)-\log (a+b x)\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 \sqrt{c} \sqrt{d}}+\frac{\left(\log (a+b x)-\log (a+b x+1)+\log \left(\frac{a+b x+1}{a+b x}\right)\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 \sqrt{c} \sqrt{d}}","\frac{\text{PolyLog}\left(2,-\frac{(-a-b x+1) \left(a^2 d+b^2 c\right)}{(a+b x) \left(-(1-a) a d+b^2 c-b \sqrt{-c} \sqrt{d}\right)}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\text{PolyLog}\left(2,-\frac{(-a-b x+1) \left(a^2 d+b^2 c\right)}{(a+b x) \left(-(1-a) a d+b^2 c+b \sqrt{-c} \sqrt{d}\right)}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\text{PolyLog}\left(2,\frac{(a+b x+1) \left(a^2 d+b^2 c\right)}{(a+b x) \left(a (a+1) d+b^2 c-b \sqrt{-c} \sqrt{d}\right)}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\text{PolyLog}\left(2,\frac{(a+b x+1) \left(a^2 d+b^2 c\right)}{(a+b x) \left(a (a+1) d+b^2 c+b \sqrt{-c} \sqrt{d}\right)}\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\log \left(-\frac{-a-b x+1}{a+b x}\right) \log \left(\frac{(-a-b x+1) \left(a^2 d+b^2 c\right)}{(a+b x) \left(-(1-a) a d+b^2 c-b \sqrt{-c} \sqrt{d}\right)}+1\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\log \left(-\frac{-a-b x+1}{a+b x}\right) \log \left(\frac{(-a-b x+1) \left(a^2 d+b^2 c\right)}{(a+b x) \left(-(1-a) a d+b^2 c+b \sqrt{-c} \sqrt{d}\right)}+1\right)}{4 \sqrt{-c} \sqrt{d}}+\frac{\log \left(\frac{a+b x+1}{a+b x}\right) \log \left(1-\frac{(a+b x+1) \left(a^2 d+b^2 c\right)}{(a+b x) \left(a (a+1) d+b^2 c-b \sqrt{-c} \sqrt{d}\right)}\right)}{4 \sqrt{-c} \sqrt{d}}-\frac{\log \left(\frac{a+b x+1}{a+b x}\right) \log \left(1-\frac{(a+b x+1) \left(a^2 d+b^2 c\right)}{(a+b x) \left(a (a+1) d+b^2 c+b \sqrt{-c} \sqrt{d}\right)}\right)}{4 \sqrt{-c} \sqrt{d}}",1,"(ArcTan[(Sqrt[d]*x)/Sqrt[c]]*(Log[-1 + a + b*x] - Log[-((1 - a - b*x)/(a + b*x))] - Log[a + b*x]))/(2*Sqrt[c]*Sqrt[d]) + (ArcTan[(Sqrt[d]*x)/Sqrt[c]]*(Log[a + b*x] - Log[1 + a + b*x] + Log[(1 + a + b*x)/(a + b*x)]))/(2*Sqrt[c]*Sqrt[d]) - (Log[-1 + a + b*x]*Log[(b*(Sqrt[-c] - Sqrt[d]*x))/(b*Sqrt[-c] - (1 - a)*Sqrt[d])])/(4*Sqrt[-c]*Sqrt[d]) + (Log[1 + a + b*x]*Log[(b*(Sqrt[-c] - Sqrt[d]*x))/(b*Sqrt[-c] + (1 + a)*Sqrt[d])])/(4*Sqrt[-c]*Sqrt[d]) + (Log[-1 + a + b*x]*Log[(b*(Sqrt[-c] + Sqrt[d]*x))/(b*Sqrt[-c] + (1 - a)*Sqrt[d])])/(4*Sqrt[-c]*Sqrt[d]) - (Log[1 + a + b*x]*Log[(b*(Sqrt[-c] + Sqrt[d]*x))/(b*Sqrt[-c] - (1 + a)*Sqrt[d])])/(4*Sqrt[-c]*Sqrt[d]) - PolyLog[2, -((Sqrt[d]*(1 - a - b*x))/(b*Sqrt[-c] - (1 - a)*Sqrt[d]))]/(4*Sqrt[-c]*Sqrt[d]) + PolyLog[2, (Sqrt[d]*(1 - a - b*x))/(b*Sqrt[-c] + (1 - a)*Sqrt[d])]/(4*Sqrt[-c]*Sqrt[d]) - PolyLog[2, -((Sqrt[d]*(1 + a + b*x))/(b*Sqrt[-c] - (1 + a)*Sqrt[d]))]/(4*Sqrt[-c]*Sqrt[d]) + PolyLog[2, (Sqrt[d]*(1 + a + b*x))/(b*Sqrt[-c] + (1 + a)*Sqrt[d])]/(4*Sqrt[-c]*Sqrt[d])","A",37,7,16,0.4375,0,"{6116, 2513, 2409, 2394, 2393, 2391, 205}"
77,1,120,0,0.1265008,"\int \frac{\coth ^{-1}(a+b x)}{c+d x} \, dx","Int[ArcCoth[a + b*x]/(c + d*x),x]","-\frac{\text{PolyLog}\left(2,1-\frac{2 b (c+d x)}{(a+b x+1) (-a d+b c+d)}\right)}{2 d}+\frac{\text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{2 d}+\frac{\coth ^{-1}(a+b x) \log \left(\frac{2 b (c+d x)}{(a+b x+1) (-a d+b c+d)}\right)}{d}-\frac{\log \left(\frac{2}{a+b x+1}\right) \coth ^{-1}(a+b x)}{d}","-\frac{\text{PolyLog}\left(2,1-\frac{2 b (c+d x)}{(a+b x+1) (-a d+b c+d)}\right)}{2 d}+\frac{\text{PolyLog}\left(2,1-\frac{2}{a+b x+1}\right)}{2 d}+\frac{\coth ^{-1}(a+b x) \log \left(\frac{2 b (c+d x)}{(a+b x+1) (-a d+b c+d)}\right)}{d}-\frac{\log \left(\frac{2}{a+b x+1}\right) \coth ^{-1}(a+b x)}{d}",1,"-((ArcCoth[a + b*x]*Log[2/(1 + a + b*x)])/d) + (ArcCoth[a + b*x]*Log[(2*b*(c + d*x))/((b*c + d - a*d)*(1 + a + b*x))])/d + PolyLog[2, 1 - 2/(1 + a + b*x)]/(2*d) - PolyLog[2, 1 - (2*b*(c + d*x))/((b*c + d - a*d)*(1 + a + b*x))]/(2*d)","A",5,5,14,0.3571,1,"{6112, 5921, 2402, 2315, 2447}"
78,1,360,0,0.4999285,"\int \frac{\coth ^{-1}(a+b x)}{c+\frac{d}{x}} \, dx","Int[ArcCoth[a + b*x]/(c + d/x),x]","\frac{d \text{PolyLog}\left(2,\frac{c (-a-b x+1)}{-a c+b d+c}\right)}{2 c^2}-\frac{d \text{PolyLog}\left(2,\frac{c (a+b x+1)}{a c-b d+c}\right)}{2 c^2}+\frac{d \log (a+b x-1) \log \left(\frac{b (c x+d)}{-a c+b d+c}\right)}{2 c^2}-\frac{d \left(\log (a+b x-1)-\log \left(-\frac{-a-b x+1}{a+b x}\right)-\log (a+b x)\right) \log (c x+d)}{2 c^2}-\frac{d \left(\log (a+b x)-\log (a+b x+1)+\log \left(\frac{a+b x+1}{a+b x}\right)\right) \log (c x+d)}{2 c^2}-\frac{d \log (a+b x+1) \log \left(-\frac{b (c x+d)}{a c-b d+c}\right)}{2 c^2}+\frac{(-a-b x+1) \log (a+b x-1)}{2 b c}+\frac{x \left(\log (a+b x-1)-\log \left(-\frac{-a-b x+1}{a+b x}\right)-\log (a+b x)\right)}{2 c}+\frac{(a+b x+1) \log (a+b x+1)}{2 b c}+\frac{x \left(\log (a+b x)-\log (a+b x+1)+\log \left(\frac{a+b x+1}{a+b x}\right)\right)}{2 c}","\frac{d \text{PolyLog}\left(2,-\frac{b (c x+d)}{a c-b d+c}\right)}{2 c^2}-\frac{d \text{PolyLog}\left(2,\frac{b (c x+d)}{-a c+b d+c}\right)}{2 c^2}+\frac{d \log \left(-\frac{-a-b x+1}{a+b x}\right) \log (c x+d)}{2 c^2}-\frac{d \log (c x+d) \log \left(\frac{c (-a-b x+1)}{-a c+b d+c}\right)}{2 c^2}+\frac{d \log (c x+d) \log \left(\frac{c (a+b x+1)}{a c-b d+c}\right)}{2 c^2}-\frac{d \log \left(\frac{a+b x+1}{a+b x}\right) \log (c x+d)}{2 c^2}+\frac{(-a-b x+1) \log \left(-\frac{-a-b x+1}{a+b x}\right)}{2 b c}+\frac{\log (a+b x)}{2 b c}+\frac{\log (a+b x+1)}{2 b c}+\frac{(a+b x) \log \left(\frac{a+b x+1}{a+b x}\right)}{2 b c}",1,"((1 - a - b*x)*Log[-1 + a + b*x])/(2*b*c) + (x*(Log[-1 + a + b*x] - Log[-((1 - a - b*x)/(a + b*x))] - Log[a + b*x]))/(2*c) + ((1 + a + b*x)*Log[1 + a + b*x])/(2*b*c) + (x*(Log[a + b*x] - Log[1 + a + b*x] + Log[(1 + a + b*x)/(a + b*x)]))/(2*c) - (d*(Log[-1 + a + b*x] - Log[-((1 - a - b*x)/(a + b*x))] - Log[a + b*x])*Log[d + c*x])/(2*c^2) - (d*(Log[a + b*x] - Log[1 + a + b*x] + Log[(1 + a + b*x)/(a + b*x)])*Log[d + c*x])/(2*c^2) - (d*Log[1 + a + b*x]*Log[-((b*(d + c*x))/(c + a*c - b*d))])/(2*c^2) + (d*Log[-1 + a + b*x]*Log[(b*(d + c*x))/(c - a*c + b*d)])/(2*c^2) + (d*PolyLog[2, (c*(1 - a - b*x))/(c - a*c + b*d)])/(2*c^2) - (d*PolyLog[2, (c*(1 + a + b*x))/(c + a*c - b*d)])/(2*c^2)","A",37,10,16,0.6250,0,"{6116, 2513, 2409, 2389, 2295, 2394, 2393, 2391, 193, 43}"
79,1,738,0,1.5303222,"\int \frac{\coth ^{-1}(a+b x)}{c+\frac{d}{x^2}} \, dx","Int[ArcCoth[a + b*x]/(c + d/x^2),x]","\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (-a-b x+1)}{(1-a) \sqrt{-c}-b \sqrt{d}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (-a-b x+1)}{(1-a) \sqrt{-c}+b \sqrt{d}}\right)}{4 (-c)^{3/2}}+\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (a+b x+1)}{(a+1) \sqrt{-c}-b \sqrt{d}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (a+b x+1)}{(a+1) \sqrt{-c}+b \sqrt{d}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \left(\log (a+b x-1)-\log \left(-\frac{-a-b x+1}{a+b x}\right)-\log (a+b x)\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)}{2 c^{3/2}}-\frac{\sqrt{d} \left(\log (a+b x)-\log (a+b x+1)+\log \left(\frac{a+b x+1}{a+b x}\right)\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)}{2 c^{3/2}}+\frac{\sqrt{d} \log (a+b x-1) \log \left(-\frac{b \left(\sqrt{d}-\sqrt{-c} x\right)}{(1-a) \sqrt{-c}-b \sqrt{d}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \log (a+b x-1) \log \left(\frac{b \left(\sqrt{-c} x+\sqrt{d}\right)}{(1-a) \sqrt{-c}+b \sqrt{d}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \log (a+b x+1) \log \left(\frac{b \left(\sqrt{d}-\sqrt{-c} x\right)}{(a+1) \sqrt{-c}+b \sqrt{d}}\right)}{4 (-c)^{3/2}}+\frac{\sqrt{d} \log (a+b x+1) \log \left(-\frac{b \left(\sqrt{-c} x+\sqrt{d}\right)}{(a+1) \sqrt{-c}-b \sqrt{d}}\right)}{4 (-c)^{3/2}}+\frac{(-a-b x+1) \log (a+b x-1)}{2 b c}+\frac{x \left(\log (a+b x-1)-\log \left(-\frac{-a-b x+1}{a+b x}\right)-\log (a+b x)\right)}{2 c}+\frac{(a+b x+1) \log (a+b x+1)}{2 b c}+\frac{x \left(\log (a+b x)-\log (a+b x+1)+\log \left(\frac{a+b x+1}{a+b x}\right)\right)}{2 c}","\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (-a-b x+1)}{(1-a) \sqrt{-c}-b \sqrt{d}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (-a-b x+1)}{(1-a) \sqrt{-c}+b \sqrt{d}}\right)}{4 (-c)^{3/2}}+\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (a+b x+1)}{(a+1) \sqrt{-c}-b \sqrt{d}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \text{PolyLog}\left(2,\frac{\sqrt{-c} (a+b x+1)}{(a+1) \sqrt{-c}+b \sqrt{d}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \left(\log (a+b x-1)-\log \left(-\frac{-a-b x+1}{a+b x}\right)-\log (a+b x)\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)}{2 c^{3/2}}-\frac{\sqrt{d} \left(\log (a+b x)-\log (a+b x+1)+\log \left(\frac{a+b x+1}{a+b x}\right)\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d}}\right)}{2 c^{3/2}}+\frac{\sqrt{d} \log (a+b x-1) \log \left(-\frac{b \left(\sqrt{d}-\sqrt{-c} x\right)}{(1-a) \sqrt{-c}-b \sqrt{d}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \log (a+b x-1) \log \left(\frac{b \left(\sqrt{-c} x+\sqrt{d}\right)}{(1-a) \sqrt{-c}+b \sqrt{d}}\right)}{4 (-c)^{3/2}}-\frac{\sqrt{d} \log (a+b x+1) \log \left(\frac{b \left(\sqrt{d}-\sqrt{-c} x\right)}{(a+1) \sqrt{-c}+b \sqrt{d}}\right)}{4 (-c)^{3/2}}+\frac{\sqrt{d} \log (a+b x+1) \log \left(-\frac{b \left(\sqrt{-c} x+\sqrt{d}\right)}{(a+1) \sqrt{-c}-b \sqrt{d}}\right)}{4 (-c)^{3/2}}+\frac{(-a-b x+1) \log (a+b x-1)}{2 b c}+\frac{x \left(\log (a+b x-1)-\log \left(-\frac{-a-b x+1}{a+b x}\right)-\log (a+b x)\right)}{2 c}+\frac{(a+b x+1) \log (a+b x+1)}{2 b c}+\frac{x \left(\log (a+b x)-\log (a+b x+1)+\log \left(\frac{a+b x+1}{a+b x}\right)\right)}{2 c}",1,"((1 - a - b*x)*Log[-1 + a + b*x])/(2*b*c) + (x*(Log[-1 + a + b*x] - Log[-((1 - a - b*x)/(a + b*x))] - Log[a + b*x]))/(2*c) - (Sqrt[d]*ArcTan[(Sqrt[c]*x)/Sqrt[d]]*(Log[-1 + a + b*x] - Log[-((1 - a - b*x)/(a + b*x))] - Log[a + b*x]))/(2*c^(3/2)) + ((1 + a + b*x)*Log[1 + a + b*x])/(2*b*c) + (x*(Log[a + b*x] - Log[1 + a + b*x] + Log[(1 + a + b*x)/(a + b*x)]))/(2*c) - (Sqrt[d]*ArcTan[(Sqrt[c]*x)/Sqrt[d]]*(Log[a + b*x] - Log[1 + a + b*x] + Log[(1 + a + b*x)/(a + b*x)]))/(2*c^(3/2)) + (Sqrt[d]*Log[-1 + a + b*x]*Log[-((b*(Sqrt[d] - Sqrt[-c]*x))/((1 - a)*Sqrt[-c] - b*Sqrt[d]))])/(4*(-c)^(3/2)) - (Sqrt[d]*Log[1 + a + b*x]*Log[(b*(Sqrt[d] - Sqrt[-c]*x))/((1 + a)*Sqrt[-c] + b*Sqrt[d])])/(4*(-c)^(3/2)) + (Sqrt[d]*Log[1 + a + b*x]*Log[-((b*(Sqrt[d] + Sqrt[-c]*x))/((1 + a)*Sqrt[-c] - b*Sqrt[d]))])/(4*(-c)^(3/2)) - (Sqrt[d]*Log[-1 + a + b*x]*Log[(b*(Sqrt[d] + Sqrt[-c]*x))/((1 - a)*Sqrt[-c] + b*Sqrt[d])])/(4*(-c)^(3/2)) + (Sqrt[d]*PolyLog[2, (Sqrt[-c]*(1 - a - b*x))/((1 - a)*Sqrt[-c] - b*Sqrt[d])])/(4*(-c)^(3/2)) - (Sqrt[d]*PolyLog[2, (Sqrt[-c]*(1 - a - b*x))/((1 - a)*Sqrt[-c] + b*Sqrt[d])])/(4*(-c)^(3/2)) + (Sqrt[d]*PolyLog[2, (Sqrt[-c]*(1 + a + b*x))/((1 + a)*Sqrt[-c] - b*Sqrt[d])])/(4*(-c)^(3/2)) - (Sqrt[d]*PolyLog[2, (Sqrt[-c]*(1 + a + b*x))/((1 + a)*Sqrt[-c] + b*Sqrt[d])])/(4*(-c)^(3/2))","A",57,11,16,0.6875,1,"{6116, 2513, 2409, 2389, 2295, 2394, 2393, 2391, 193, 321, 205}"
80,1,619,0,2.1989607,"\int \frac{\coth ^{-1}(a+b x)}{c+d \sqrt{x}} \, dx","Int[ArcCoth[a + b*x]/(c + d*Sqrt[x]),x]","\frac{c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{b} c-\sqrt{-a-1} d}\right)}{d^2}+\frac{c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{-a-1} d+\sqrt{b} c}\right)}{d^2}-\frac{c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{b} c-\sqrt{1-a} d}\right)}{d^2}-\frac{c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{1-a} d+\sqrt{b} c}\right)}{d^2}+\frac{c \log \left(c+d \sqrt{x}\right) \log \left(\frac{d \left(\sqrt{-a-1}-\sqrt{b} \sqrt{x}\right)}{\sqrt{-a-1} d+\sqrt{b} c}\right)}{d^2}-\frac{c \log \left(c+d \sqrt{x}\right) \log \left(\frac{d \left(\sqrt{1-a}-\sqrt{b} \sqrt{x}\right)}{\sqrt{1-a} d+\sqrt{b} c}\right)}{d^2}+\frac{c \log \left(c+d \sqrt{x}\right) \log \left(-\frac{d \left(\sqrt{-a-1}+\sqrt{b} \sqrt{x}\right)}{\sqrt{b} c-\sqrt{-a-1} d}\right)}{d^2}-\frac{c \log \left(c+d \sqrt{x}\right) \log \left(-\frac{d \left(\sqrt{1-a}+\sqrt{b} \sqrt{x}\right)}{\sqrt{b} c-\sqrt{1-a} d}\right)}{d^2}+\frac{c \log \left(-\frac{-a-b x+1}{a+b x}\right) \log \left(c+d \sqrt{x}\right)}{d^2}-\frac{c \log \left(\frac{a+b x+1}{a+b x}\right) \log \left(c+d \sqrt{x}\right)}{d^2}-\frac{\sqrt{x} \log \left(-\frac{-a-b x+1}{a+b x}\right)}{d}+\frac{\sqrt{x} \log \left(\frac{a+b x+1}{a+b x}\right)}{d}+\frac{2 \sqrt{a+1} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+1}}\right)}{\sqrt{b} d}-\frac{2 \sqrt{1-a} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{1-a}}\right)}{\sqrt{b} d}","\frac{c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{b} c-\sqrt{-a-1} d}\right)}{d^2}+\frac{c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{-a-1} d+\sqrt{b} c}\right)}{d^2}-\frac{c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{b} c-\sqrt{1-a} d}\right)}{d^2}-\frac{c \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c+d \sqrt{x}\right)}{\sqrt{1-a} d+\sqrt{b} c}\right)}{d^2}+\frac{c \log \left(c+d \sqrt{x}\right) \log \left(\frac{d \left(\sqrt{-a-1}-\sqrt{b} \sqrt{x}\right)}{\sqrt{-a-1} d+\sqrt{b} c}\right)}{d^2}-\frac{c \log \left(c+d \sqrt{x}\right) \log \left(\frac{d \left(\sqrt{1-a}-\sqrt{b} \sqrt{x}\right)}{\sqrt{1-a} d+\sqrt{b} c}\right)}{d^2}+\frac{c \log \left(c+d \sqrt{x}\right) \log \left(-\frac{d \left(\sqrt{-a-1}+\sqrt{b} \sqrt{x}\right)}{\sqrt{b} c-\sqrt{-a-1} d}\right)}{d^2}-\frac{c \log \left(c+d \sqrt{x}\right) \log \left(-\frac{d \left(\sqrt{1-a}+\sqrt{b} \sqrt{x}\right)}{\sqrt{b} c-\sqrt{1-a} d}\right)}{d^2}+\frac{c \log \left(-\frac{-a-b x+1}{a+b x}\right) \log \left(c+d \sqrt{x}\right)}{d^2}-\frac{c \log \left(\frac{a+b x+1}{a+b x}\right) \log \left(c+d \sqrt{x}\right)}{d^2}-\frac{\sqrt{x} \log \left(-\frac{-a-b x+1}{a+b x}\right)}{d}+\frac{\sqrt{x} \log \left(\frac{a+b x+1}{a+b x}\right)}{d}+\frac{2 \sqrt{a+1} \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+1}}\right)}{\sqrt{b} d}-\frac{2 \sqrt{1-a} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{1-a}}\right)}{\sqrt{b} d}",1,"(2*Sqrt[1 + a]*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[1 + a]])/(Sqrt[b]*d) - (2*Sqrt[1 - a]*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[1 - a]])/(Sqrt[b]*d) + (c*Log[(d*(Sqrt[-1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[b]*c + Sqrt[-1 - a]*d)]*Log[c + d*Sqrt[x]])/d^2 - (c*Log[(d*(Sqrt[1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[b]*c + Sqrt[1 - a]*d)]*Log[c + d*Sqrt[x]])/d^2 + (c*Log[-((d*(Sqrt[-1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[b]*c - Sqrt[-1 - a]*d))]*Log[c + d*Sqrt[x]])/d^2 - (c*Log[-((d*(Sqrt[1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[b]*c - Sqrt[1 - a]*d))]*Log[c + d*Sqrt[x]])/d^2 - (Sqrt[x]*Log[-((1 - a - b*x)/(a + b*x))])/d + (c*Log[c + d*Sqrt[x]]*Log[-((1 - a - b*x)/(a + b*x))])/d^2 + (Sqrt[x]*Log[(1 + a + b*x)/(a + b*x)])/d - (c*Log[c + d*Sqrt[x]]*Log[(1 + a + b*x)/(a + b*x)])/d^2 + (c*PolyLog[2, (Sqrt[b]*(c + d*Sqrt[x]))/(Sqrt[b]*c - Sqrt[-1 - a]*d)])/d^2 + (c*PolyLog[2, (Sqrt[b]*(c + d*Sqrt[x]))/(Sqrt[b]*c + Sqrt[-1 - a]*d)])/d^2 - (c*PolyLog[2, (Sqrt[b]*(c + d*Sqrt[x]))/(Sqrt[b]*c - Sqrt[1 - a]*d)])/d^2 - (c*PolyLog[2, (Sqrt[b]*(c + d*Sqrt[x]))/(Sqrt[b]*c + Sqrt[1 - a]*d)])/d^2","A",55,16,18,0.8889,1,"{6116, 190, 43, 2528, 2523, 12, 481, 205, 2524, 2418, 260, 2416, 2394, 2393, 2391, 208}"
81,1,738,0,2.3714943,"\int \frac{\coth ^{-1}(a+b x)}{c+\frac{d}{\sqrt{x}}} \, dx","Int[ArcCoth[a + b*x]/(c + d/Sqrt[x]),x]","-\frac{d^2 \text{PolyLog}\left(2,-\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{-a-1} c-\sqrt{b} d}\right)}{c^3}+\frac{d^2 \text{PolyLog}\left(2,-\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{1-a} c-\sqrt{b} d}\right)}{c^3}-\frac{d^2 \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{-a-1} c+\sqrt{b} d}\right)}{c^3}+\frac{d^2 \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{1-a} c+\sqrt{b} d}\right)}{c^3}-\frac{d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{-a-1}-\sqrt{b} \sqrt{x}\right)}{\sqrt{-a-1} c+\sqrt{b} d}\right)}{c^3}+\frac{d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{1-a}-\sqrt{b} \sqrt{x}\right)}{\sqrt{1-a} c+\sqrt{b} d}\right)}{c^3}-\frac{d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{-a-1}+\sqrt{b} \sqrt{x}\right)}{\sqrt{-a-1} c-\sqrt{b} d}\right)}{c^3}+\frac{d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{1-a}+\sqrt{b} \sqrt{x}\right)}{\sqrt{1-a} c-\sqrt{b} d}\right)}{c^3}-\frac{d^2 \log \left(-\frac{-a-b x+1}{a+b x}\right) \log \left(c \sqrt{x}+d\right)}{c^3}+\frac{d^2 \log \left(\frac{a+b x+1}{a+b x}\right) \log \left(c \sqrt{x}+d\right)}{c^3}+\frac{d \sqrt{x} \log \left(-\frac{-a-b x+1}{a+b x}\right)}{c^2}-\frac{d \sqrt{x} \log \left(\frac{a+b x+1}{a+b x}\right)}{c^2}-\frac{2 \sqrt{a+1} d \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+1}}\right)}{\sqrt{b} c^2}+\frac{2 \sqrt{1-a} d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{1-a}}\right)}{\sqrt{b} c^2}+\frac{(1-a) \log (-a-b x+1)}{2 b c}-\frac{x \log \left(-\frac{-a-b x+1}{a+b x}\right)}{2 c}+\frac{(a+1) \log (a+b x+1)}{2 b c}+\frac{x \log \left(\frac{a+b x+1}{a+b x}\right)}{2 c}","-\frac{d^2 \text{PolyLog}\left(2,-\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{-a-1} c-\sqrt{b} d}\right)}{c^3}+\frac{d^2 \text{PolyLog}\left(2,-\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{1-a} c-\sqrt{b} d}\right)}{c^3}-\frac{d^2 \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{-a-1} c+\sqrt{b} d}\right)}{c^3}+\frac{d^2 \text{PolyLog}\left(2,\frac{\sqrt{b} \left(c \sqrt{x}+d\right)}{\sqrt{1-a} c+\sqrt{b} d}\right)}{c^3}-\frac{d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{-a-1}-\sqrt{b} \sqrt{x}\right)}{\sqrt{-a-1} c+\sqrt{b} d}\right)}{c^3}+\frac{d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{1-a}-\sqrt{b} \sqrt{x}\right)}{\sqrt{1-a} c+\sqrt{b} d}\right)}{c^3}-\frac{d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{-a-1}+\sqrt{b} \sqrt{x}\right)}{\sqrt{-a-1} c-\sqrt{b} d}\right)}{c^3}+\frac{d^2 \log \left(c \sqrt{x}+d\right) \log \left(\frac{c \left(\sqrt{1-a}+\sqrt{b} \sqrt{x}\right)}{\sqrt{1-a} c-\sqrt{b} d}\right)}{c^3}-\frac{d^2 \log \left(-\frac{-a-b x+1}{a+b x}\right) \log \left(c \sqrt{x}+d\right)}{c^3}+\frac{d^2 \log \left(\frac{a+b x+1}{a+b x}\right) \log \left(c \sqrt{x}+d\right)}{c^3}+\frac{d \sqrt{x} \log \left(-\frac{-a-b x+1}{a+b x}\right)}{c^2}-\frac{d \sqrt{x} \log \left(\frac{a+b x+1}{a+b x}\right)}{c^2}-\frac{2 \sqrt{a+1} d \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a+1}}\right)}{\sqrt{b} c^2}+\frac{2 \sqrt{1-a} d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{1-a}}\right)}{\sqrt{b} c^2}+\frac{(1-a) \log (-a-b x+1)}{2 b c}-\frac{x \log \left(-\frac{-a-b x+1}{a+b x}\right)}{2 c}+\frac{(a+1) \log (a+b x+1)}{2 b c}+\frac{x \log \left(\frac{a+b x+1}{a+b x}\right)}{2 c}",1,"(-2*Sqrt[1 + a]*d*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[1 + a]])/(Sqrt[b]*c^2) + (2*Sqrt[1 - a]*d*ArcTanh[(Sqrt[b]*Sqrt[x])/Sqrt[1 - a]])/(Sqrt[b]*c^2) - (d^2*Log[(c*(Sqrt[-1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[-1 - a]*c + Sqrt[b]*d)]*Log[d + c*Sqrt[x]])/c^3 + (d^2*Log[(c*(Sqrt[1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[1 - a]*c + Sqrt[b]*d)]*Log[d + c*Sqrt[x]])/c^3 - (d^2*Log[(c*(Sqrt[-1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[-1 - a]*c - Sqrt[b]*d)]*Log[d + c*Sqrt[x]])/c^3 + (d^2*Log[(c*(Sqrt[1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[1 - a]*c - Sqrt[b]*d)]*Log[d + c*Sqrt[x]])/c^3 + ((1 - a)*Log[1 - a - b*x])/(2*b*c) + (d*Sqrt[x]*Log[-((1 - a - b*x)/(a + b*x))])/c^2 - (x*Log[-((1 - a - b*x)/(a + b*x))])/(2*c) - (d^2*Log[d + c*Sqrt[x]]*Log[-((1 - a - b*x)/(a + b*x))])/c^3 + ((1 + a)*Log[1 + a + b*x])/(2*b*c) - (d*Sqrt[x]*Log[(1 + a + b*x)/(a + b*x)])/c^2 + (x*Log[(1 + a + b*x)/(a + b*x)])/(2*c) + (d^2*Log[d + c*Sqrt[x]]*Log[(1 + a + b*x)/(a + b*x)])/c^3 - (d^2*PolyLog[2, -((Sqrt[b]*(d + c*Sqrt[x]))/(Sqrt[-1 - a]*c - Sqrt[b]*d))])/c^3 + (d^2*PolyLog[2, -((Sqrt[b]*(d + c*Sqrt[x]))/(Sqrt[1 - a]*c - Sqrt[b]*d))])/c^3 - (d^2*PolyLog[2, (Sqrt[b]*(d + c*Sqrt[x]))/(Sqrt[-1 - a]*c + Sqrt[b]*d)])/c^3 + (d^2*PolyLog[2, (Sqrt[b]*(d + c*Sqrt[x]))/(Sqrt[1 - a]*c + Sqrt[b]*d)])/c^3","A",65,19,18,1.056,1,"{6116, 190, 44, 2528, 2523, 12, 481, 205, 2525, 446, 72, 2524, 2418, 260, 2416, 2394, 2393, 2391, 208}"
82,1,335,0,0.7485767,"\int \frac{\coth ^{-1}(d+e x)}{a+b x+c x^2} \, dx","Int[ArcCoth[d + e*x]/(a + b*x + c*x^2),x]","-\frac{\text{PolyLog}\left(2,\frac{2 \left(-e \left(b-\sqrt{b^2-4 a c}\right)-2 c (d+e x)+2 c d\right)}{(d+e x+1) \left(-e \sqrt{b^2-4 a c}+b e-2 c d+2 c\right)}+1\right)}{2 \sqrt{b^2-4 a c}}+\frac{\text{PolyLog}\left(2,\frac{2 \left(-e \left(\sqrt{b^2-4 a c}+b\right)-2 c (d+e x)+2 c d\right)}{(d+e x+1) \left(e \left(\sqrt{b^2-4 a c}+b\right)+2 c (1-d)\right)}+1\right)}{2 \sqrt{b^2-4 a c}}+\frac{\coth ^{-1}(d+e x) \log \left(\frac{2 e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{(d+e x+1) \left(e \left(b-\sqrt{b^2-4 a c}\right)+2 c (1-d)\right)}\right)}{\sqrt{b^2-4 a c}}-\frac{\coth ^{-1}(d+e x) \log \left(\frac{2 e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{(d+e x+1) \left(e \left(\sqrt{b^2-4 a c}+b\right)+2 c (1-d)\right)}\right)}{\sqrt{b^2-4 a c}}","-\frac{\text{PolyLog}\left(2,\frac{2 \left(-e \left(b-\sqrt{b^2-4 a c}\right)-2 c (d+e x)+2 c d\right)}{(d+e x+1) \left(-e \sqrt{b^2-4 a c}+b e-2 c d+2 c\right)}+1\right)}{2 \sqrt{b^2-4 a c}}+\frac{\text{PolyLog}\left(2,\frac{2 \left(-e \left(\sqrt{b^2-4 a c}+b\right)-2 c (d+e x)+2 c d\right)}{(d+e x+1) \left(e \left(\sqrt{b^2-4 a c}+b\right)+2 c (1-d)\right)}+1\right)}{2 \sqrt{b^2-4 a c}}+\frac{\coth ^{-1}(d+e x) \log \left(\frac{2 e \left(-\sqrt{b^2-4 a c}+b+2 c x\right)}{(d+e x+1) \left(e \left(b-\sqrt{b^2-4 a c}\right)+2 c (1-d)\right)}\right)}{\sqrt{b^2-4 a c}}-\frac{\coth ^{-1}(d+e x) \log \left(\frac{2 e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{(d+e x+1) \left(e \left(\sqrt{b^2-4 a c}+b\right)+2 c (1-d)\right)}\right)}{\sqrt{b^2-4 a c}}",1,"(ArcCoth[d + e*x]*Log[(2*e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/((2*c*(1 - d) + (b - Sqrt[b^2 - 4*a*c])*e)*(1 + d + e*x))])/Sqrt[b^2 - 4*a*c] - (ArcCoth[d + e*x]*Log[(2*e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((2*c*(1 - d) + (b + Sqrt[b^2 - 4*a*c])*e)*(1 + d + e*x))])/Sqrt[b^2 - 4*a*c] - PolyLog[2, 1 + (2*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e - 2*c*(d + e*x)))/((2*c - 2*c*d + b*e - Sqrt[b^2 - 4*a*c]*e)*(1 + d + e*x))]/(2*Sqrt[b^2 - 4*a*c]) + PolyLog[2, 1 + (2*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e - 2*c*(d + e*x)))/((2*c*(1 - d) + (b + Sqrt[b^2 - 4*a*c])*e)*(1 + d + e*x))]/(2*Sqrt[b^2 - 4*a*c])","A",12,8,19,0.4211,1,"{618, 206, 6728, 6112, 5921, 2402, 2315, 2447}"
83,1,51,0,0.0147834,"\int x^2 \coth ^{-1}\left(\sqrt{x}\right) \, dx","Int[x^2*ArcCoth[Sqrt[x]],x]","\frac{x^{5/2}}{15}+\frac{x^{3/2}}{9}+\frac{1}{3} x^3 \coth ^{-1}\left(\sqrt{x}\right)+\frac{\sqrt{x}}{3}-\frac{1}{3} \tanh ^{-1}\left(\sqrt{x}\right)","\frac{x^{5/2}}{15}+\frac{x^{3/2}}{9}+\frac{1}{3} x^3 \coth ^{-1}\left(\sqrt{x}\right)+\frac{\sqrt{x}}{3}-\frac{1}{3} \tanh ^{-1}\left(\sqrt{x}\right)",1,"Sqrt[x]/3 + x^(3/2)/9 + x^(5/2)/15 + (x^3*ArcCoth[Sqrt[x]])/3 - ArcTanh[Sqrt[x]]/3","A",6,4,10,0.4000,1,"{6098, 50, 63, 206}"
84,1,42,0,0.0107724,"\int x \coth ^{-1}\left(\sqrt{x}\right) \, dx","Int[x*ArcCoth[Sqrt[x]],x]","\frac{x^{3/2}}{6}+\frac{1}{2} x^2 \coth ^{-1}\left(\sqrt{x}\right)+\frac{\sqrt{x}}{2}-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x}\right)","\frac{x^{3/2}}{6}+\frac{1}{2} x^2 \coth ^{-1}\left(\sqrt{x}\right)+\frac{\sqrt{x}}{2}-\frac{1}{2} \tanh ^{-1}\left(\sqrt{x}\right)",1,"Sqrt[x]/2 + x^(3/2)/6 + (x^2*ArcCoth[Sqrt[x]])/2 - ArcTanh[Sqrt[x]]/2","A",5,4,8,0.5000,1,"{6098, 50, 63, 206}"
85,1,22,0,0.006253,"\int \coth ^{-1}\left(\sqrt{x}\right) \, dx","Int[ArcCoth[Sqrt[x]],x]","\sqrt{x}-\tanh ^{-1}\left(\sqrt{x}\right)+x \coth ^{-1}\left(\sqrt{x}\right)","\sqrt{x}-\tanh ^{-1}\left(\sqrt{x}\right)+x \coth ^{-1}\left(\sqrt{x}\right)",1,"Sqrt[x] + x*ArcCoth[Sqrt[x]] - ArcTanh[Sqrt[x]]","A",4,4,6,0.6667,1,"{6092, 50, 63, 206}"
86,1,19,0,0.0197034,"\int \frac{\coth ^{-1}\left(\sqrt{x}\right)}{x} \, dx","Int[ArcCoth[Sqrt[x]]/x,x]","\text{PolyLog}\left(2,-\frac{1}{\sqrt{x}}\right)-\text{PolyLog}\left(2,\frac{1}{\sqrt{x}}\right)","\text{PolyLog}\left(2,-\frac{1}{\sqrt{x}}\right)-\text{PolyLog}\left(2,\frac{1}{\sqrt{x}}\right)",1,"PolyLog[2, -(1/Sqrt[x])] - PolyLog[2, 1/Sqrt[x]]","A",2,2,10,0.2000,1,"{6096, 5913}"
87,1,25,0,0.013518,"\int \frac{\coth ^{-1}\left(\sqrt{x}\right)}{x^2} \, dx","Int[ArcCoth[Sqrt[x]]/x^2,x]","-\frac{1}{\sqrt{x}}+\tanh ^{-1}\left(\sqrt{x}\right)-\frac{\coth ^{-1}\left(\sqrt{x}\right)}{x}","-\frac{1}{\sqrt{x}}+\tanh ^{-1}\left(\sqrt{x}\right)-\frac{\coth ^{-1}\left(\sqrt{x}\right)}{x}",1,"-(1/Sqrt[x]) - ArcCoth[Sqrt[x]]/x + ArcTanh[Sqrt[x]]","A",4,4,10,0.4000,1,"{6098, 51, 63, 206}"
88,1,42,0,0.0147932,"\int \frac{\coth ^{-1}\left(\sqrt{x}\right)}{x^3} \, dx","Int[ArcCoth[Sqrt[x]]/x^3,x]","-\frac{1}{6 x^{3/2}}-\frac{\coth ^{-1}\left(\sqrt{x}\right)}{2 x^2}-\frac{1}{2 \sqrt{x}}+\frac{1}{2} \tanh ^{-1}\left(\sqrt{x}\right)","-\frac{1}{6 x^{3/2}}-\frac{\coth ^{-1}\left(\sqrt{x}\right)}{2 x^2}-\frac{1}{2 \sqrt{x}}+\frac{1}{2} \tanh ^{-1}\left(\sqrt{x}\right)",1,"-1/(6*x^(3/2)) - 1/(2*Sqrt[x]) - ArcCoth[Sqrt[x]]/(2*x^2) + ArcTanh[Sqrt[x]]/2","A",5,4,10,0.4000,1,"{6098, 51, 63, 206}"
89,1,38,0,0.0177347,"\int x^{3/2} \coth ^{-1}\left(\sqrt{x}\right) \, dx","Int[x^(3/2)*ArcCoth[Sqrt[x]],x]","\frac{x^2}{10}+\frac{2}{5} x^{5/2} \coth ^{-1}\left(\sqrt{x}\right)+\frac{x}{5}+\frac{1}{5} \log (1-x)","\frac{x^2}{10}+\frac{2}{5} x^{5/2} \coth ^{-1}\left(\sqrt{x}\right)+\frac{x}{5}+\frac{1}{5} \log (1-x)",1,"x/5 + x^2/10 + (2*x^(5/2)*ArcCoth[Sqrt[x]])/5 + Log[1 - x]/5","A",3,2,12,0.1667,1,"{6098, 43}"
90,1,31,0,0.0135038,"\int \sqrt{x} \coth ^{-1}\left(\sqrt{x}\right) \, dx","Int[Sqrt[x]*ArcCoth[Sqrt[x]],x]","\frac{2}{3} x^{3/2} \coth ^{-1}\left(\sqrt{x}\right)+\frac{x}{3}+\frac{1}{3} \log (1-x)","\frac{2}{3} x^{3/2} \coth ^{-1}\left(\sqrt{x}\right)+\frac{x}{3}+\frac{1}{3} \log (1-x)",1,"x/3 + (2*x^(3/2)*ArcCoth[Sqrt[x]])/3 + Log[1 - x]/3","A",3,2,12,0.1667,1,"{6098, 43}"
91,1,20,0,0.0092563,"\int \frac{\coth ^{-1}\left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Int[ArcCoth[Sqrt[x]]/Sqrt[x],x]","\log (1-x)+2 \sqrt{x} \coth ^{-1}\left(\sqrt{x}\right)","\log (1-x)+2 \sqrt{x} \coth ^{-1}\left(\sqrt{x}\right)",1,"2*Sqrt[x]*ArcCoth[Sqrt[x]] + Log[1 - x]","A",2,2,12,0.1667,1,"{6098, 31}"
92,1,24,0,0.0104366,"\int \frac{\coth ^{-1}\left(\sqrt{x}\right)}{x^{3/2}} \, dx","Int[ArcCoth[Sqrt[x]]/x^(3/2),x]","-\log (1-x)+\log (x)-\frac{2 \coth ^{-1}\left(\sqrt{x}\right)}{\sqrt{x}}","-\log (1-x)+\log (x)-\frac{2 \coth ^{-1}\left(\sqrt{x}\right)}{\sqrt{x}}",1,"(-2*ArcCoth[Sqrt[x]])/Sqrt[x] - Log[1 - x] + Log[x]","A",4,4,12,0.3333,1,"{6098, 36, 31, 29}"
93,1,28,0,0.0217677,"\int \frac{\coth ^{-1}\left(a x^5\right)}{x} \, dx","Int[ArcCoth[a*x^5]/x,x]","\frac{1}{10} \text{PolyLog}\left(2,-\frac{1}{a x^5}\right)-\frac{1}{10} \text{PolyLog}\left(2,\frac{1}{a x^5}\right)","\frac{1}{10} \text{PolyLog}\left(2,-\frac{1}{a x^5}\right)-\frac{1}{10} \text{PolyLog}\left(2,\frac{1}{a x^5}\right)",1,"PolyLog[2, -(1/(a*x^5))]/10 - PolyLog[2, 1/(a*x^5)]/10","A",2,2,10,0.2000,1,"{6096, 5913}"
94,1,19,0,0.0060927,"\int \coth ^{-1}\left(\frac{1}{x}\right) \, dx","Int[ArcCoth[x^(-1)],x]","\frac{1}{2} \log \left(1-x^2\right)+x \coth ^{-1}\left(\frac{1}{x}\right)","\frac{1}{2} \log \left(1-x^2\right)+x \coth ^{-1}\left(\frac{1}{x}\right)",1,"x*ArcCoth[x^(-1)] + Log[1 - x^2]/2","A",3,3,4,0.7500,1,"{6092, 263, 260}"
95,1,38,0,0.023247,"\int \frac{\coth ^{-1}\left(a x^n\right)}{x} \, dx","Int[ArcCoth[a*x^n]/x,x]","\frac{\text{PolyLog}\left(2,-\frac{x^{-n}}{a}\right)}{2 n}-\frac{\text{PolyLog}\left(2,\frac{x^{-n}}{a}\right)}{2 n}","\frac{\text{PolyLog}\left(2,-\frac{x^{-n}}{a}\right)}{2 n}-\frac{\text{PolyLog}\left(2,\frac{x^{-n}}{a}\right)}{2 n}",1,"PolyLog[2, -(1/(a*x^n))]/(2*n) - PolyLog[2, 1/(a*x^n)]/(2*n)","A",2,2,10,0.2000,1,"{6096, 5913}"
96,1,39,0,0.0224787,"\int (a+b x) \coth ^{-1}(a+b x) \, dx","Int[(a + b*x)*ArcCoth[a + b*x],x]","-\frac{\tanh ^{-1}(a+b x)}{2 b}+\frac{(a+b x)^2 \coth ^{-1}(a+b x)}{2 b}+\frac{x}{2}","-\frac{\tanh ^{-1}(a+b x)}{2 b}+\frac{(a+b x)^2 \coth ^{-1}(a+b x)}{2 b}+\frac{x}{2}",1,"x/2 + ((a + b*x)^2*ArcCoth[a + b*x])/(2*b) - ArcTanh[a + b*x]/(2*b)","A",4,4,12,0.3333,1,"{6108, 5917, 321, 206}"
97,1,54,0,0.0479171,"\int (a+b x)^2 \coth ^{-1}(a+b x) \, dx","Int[(a + b*x)^2*ArcCoth[a + b*x],x]","\frac{(a+b x)^2}{6 b}+\frac{\log \left(1-(a+b x)^2\right)}{6 b}+\frac{(a+b x)^3 \coth ^{-1}(a+b x)}{3 b}","\frac{(a+b x)^2}{6 b}+\frac{\log \left(1-(a+b x)^2\right)}{6 b}+\frac{(a+b x)^3 \coth ^{-1}(a+b x)}{3 b}",1,"(a + b*x)^2/(6*b) + ((a + b*x)^3*ArcCoth[a + b*x])/(3*b) + Log[1 - (a + b*x)^2]/(6*b)","A",5,4,14,0.2857,1,"{6108, 5917, 266, 43}"
98,1,35,0,0.0254893,"\int \frac{\coth ^{-1}(a+b x)}{a+b x} \, dx","Int[ArcCoth[a + b*x]/(a + b*x),x]","\frac{\text{PolyLog}\left(2,-\frac{1}{a+b x}\right)}{2 b}-\frac{\text{PolyLog}\left(2,\frac{1}{a+b x}\right)}{2 b}","\frac{\text{PolyLog}\left(2,-\frac{1}{a+b x}\right)}{2 b}-\frac{\text{PolyLog}\left(2,\frac{1}{a+b x}\right)}{2 b}",1,"PolyLog[2, -(a + b*x)^(-1)]/(2*b) - PolyLog[2, (a + b*x)^(-1)]/(2*b)","A",2,2,14,0.1429,1,"{6108, 5913}"
99,1,48,0,0.0451322,"\int \frac{\coth ^{-1}(a+b x)}{(a+b x)^2} \, dx","Int[ArcCoth[a + b*x]/(a + b*x)^2,x]","\frac{\log (a+b x)}{b}-\frac{\log \left(1-(a+b x)^2\right)}{2 b}-\frac{\coth ^{-1}(a+b x)}{b (a+b x)}","\frac{\log (a+b x)}{b}-\frac{\log \left(1-(a+b x)^2\right)}{2 b}-\frac{\coth ^{-1}(a+b x)}{b (a+b x)}",1,"-(ArcCoth[a + b*x]/(b*(a + b*x))) + Log[a + b*x]/b - Log[1 - (a + b*x)^2]/(2*b)","A",6,6,14,0.4286,1,"{6108, 5917, 266, 36, 31, 29}"
100,1,25,0,0.0227001,"\int \frac{\coth ^{-1}(1+x)}{2+2 x} \, dx","Int[ArcCoth[1 + x]/(2 + 2*x),x]","\frac{1}{4} \text{PolyLog}\left(2,-\frac{1}{x+1}\right)-\frac{1}{4} \text{PolyLog}\left(2,\frac{1}{x+1}\right)","\frac{1}{4} \text{PolyLog}\left(2,-\frac{1}{x+1}\right)-\frac{1}{4} \text{PolyLog}\left(2,\frac{1}{x+1}\right)",1,"PolyLog[2, -(1 + x)^(-1)]/4 - PolyLog[2, (1 + x)^(-1)]/4","A",3,3,12,0.2500,1,"{6108, 12, 5913}"
101,1,35,0,0.0301393,"\int \frac{\coth ^{-1}(a+b x)}{\frac{a d}{b}+d x} \, dx","Int[ArcCoth[a + b*x]/((a*d)/b + d*x),x]","\frac{\text{PolyLog}\left(2,-\frac{1}{a+b x}\right)}{2 d}-\frac{\text{PolyLog}\left(2,\frac{1}{a+b x}\right)}{2 d}","\frac{\text{PolyLog}\left(2,-\frac{1}{a+b x}\right)}{2 d}-\frac{\text{PolyLog}\left(2,\frac{1}{a+b x}\right)}{2 d}",1,"PolyLog[2, -(a + b*x)^(-1)]/(2*d) - PolyLog[2, (a + b*x)^(-1)]/(2*d)","A",3,3,19,0.1579,1,"{6108, 12, 5913}"
102,1,168,0,0.3419812,"\int (e+f x)^3 \left(a+b \coth ^{-1}(c+d x)\right) \, dx","Int[(e + f*x)^3*(a + b*ArcCoth[c + d*x]),x]","\frac{(e+f x)^4 \left(a+b \coth ^{-1}(c+d x)\right)}{4 f}+\frac{b f x \left(\left(6 c^2+1\right) f^2-12 c d e f+6 d^2 e^2\right)}{4 d^3}+\frac{b f^2 (c+d x)^2 (d e-c f)}{2 d^4}-\frac{b (-c f+d e-f)^4 \log (c+d x+1)}{8 d^4 f}+\frac{b (-c f+d e+f)^4 \log (-c-d x+1)}{8 d^4 f}+\frac{b f^3 (c+d x)^3}{12 d^4}","\frac{(e+f x)^4 \left(a+b \coth ^{-1}(c+d x)\right)}{4 f}+\frac{b f x \left(\left(6 c^2+1\right) f^2-12 c d e f+6 d^2 e^2\right)}{4 d^3}+\frac{b f^2 (c+d x)^2 (d e-c f)}{2 d^4}-\frac{b (-c f+d e-f)^4 \log (c+d x+1)}{8 d^4 f}+\frac{b (-c f+d e+f)^4 \log (-c-d x+1)}{8 d^4 f}+\frac{b f^3 (c+d x)^3}{12 d^4}",1,"(b*f*(6*d^2*e^2 - 12*c*d*e*f + (1 + 6*c^2)*f^2)*x)/(4*d^3) + (b*f^2*(d*e - c*f)*(c + d*x)^2)/(2*d^4) + (b*f^3*(c + d*x)^3)/(12*d^4) + ((e + f*x)^4*(a + b*ArcCoth[c + d*x]))/(4*f) + (b*(d*e + f - c*f)^4*Log[1 - c - d*x])/(8*d^4*f) - (b*(d*e - f - c*f)^4*Log[1 + c + d*x])/(8*d^4*f)","A",7,5,18,0.2778,1,"{6112, 5927, 702, 633, 31}"
103,1,120,0,0.2039793,"\int (e+f x)^2 \left(a+b \coth ^{-1}(c+d x)\right) \, dx","Int[(e + f*x)^2*(a + b*ArcCoth[c + d*x]),x]","\frac{(e+f x)^3 \left(a+b \coth ^{-1}(c+d x)\right)}{3 f}+\frac{b f x (d e-c f)}{d^2}+\frac{b (-c f+d e+f)^3 \log (-c-d x+1)}{6 d^3 f}-\frac{b (d e-(c+1) f)^3 \log (c+d x+1)}{6 d^3 f}+\frac{b f^2 (c+d x)^2}{6 d^3}","\frac{(e+f x)^3 \left(a+b \coth ^{-1}(c+d x)\right)}{3 f}+\frac{b f x (d e-c f)}{d^2}+\frac{b (-c f+d e+f)^3 \log (-c-d x+1)}{6 d^3 f}-\frac{b (d e-(c+1) f)^3 \log (c+d x+1)}{6 d^3 f}+\frac{b f^2 (c+d x)^2}{6 d^3}",1,"(b*f*(d*e - c*f)*x)/d^2 + (b*f^2*(c + d*x)^2)/(6*d^3) + ((e + f*x)^3*(a + b*ArcCoth[c + d*x]))/(3*f) + (b*(d*e + f - c*f)^3*Log[1 - c - d*x])/(6*d^3*f) - (b*(d*e - (1 + c)*f)^3*Log[1 + c + d*x])/(6*d^3*f)","A",7,5,18,0.2778,1,"{6112, 5927, 702, 633, 31}"
104,1,97,0,0.1711946,"\int (e+f x) \left(a+b \coth ^{-1}(c+d x)\right) \, dx","Int[(e + f*x)*(a + b*ArcCoth[c + d*x]),x]","\frac{(e+f x)^2 \left(a+b \coth ^{-1}(c+d x)\right)}{2 f}+\frac{b (-c f+d e+f)^2 \log (-c-d x+1)}{4 d^2 f}-\frac{b (d e-(c+1) f)^2 \log (c+d x+1)}{4 d^2 f}+\frac{b f x}{2 d}","\frac{(e+f x)^2 \left(a+b \coth ^{-1}(c+d x)\right)}{2 f}+\frac{b (-c f+d e+f)^2 \log (-c-d x+1)}{4 d^2 f}-\frac{b (d e-(c+1) f)^2 \log (c+d x+1)}{4 d^2 f}+\frac{b f x}{2 d}",1,"(b*f*x)/(2*d) + ((e + f*x)^2*(a + b*ArcCoth[c + d*x]))/(2*f) + (b*(d*e + f - c*f)^2*Log[1 - c - d*x])/(4*d^2*f) - (b*(d*e - (1 + c)*f)^2*Log[1 + c + d*x])/(4*d^2*f)","A",7,5,16,0.3125,1,"{6112, 5927, 702, 633, 31}"
105,1,40,0,0.0245296,"\int \left(a+b \coth ^{-1}(c+d x)\right) \, dx","Int[a + b*ArcCoth[c + d*x],x]","a x+\frac{b \log \left(1-(c+d x)^2\right)}{2 d}+\frac{b (c+d x) \coth ^{-1}(c+d x)}{d}","a x+\frac{b \log \left(1-(c+d x)^2\right)}{2 d}+\frac{b (c+d x) \coth ^{-1}(c+d x)}{d}",1,"a*x + (b*(c + d*x)*ArcCoth[c + d*x])/d + (b*Log[1 - (c + d*x)^2])/(2*d)","A",4,3,10,0.3000,1,"{6104, 5911, 260}"
106,1,130,0,0.1423103,"\int \frac{a+b \coth ^{-1}(c+d x)}{e+f x} \, dx","Int[(a + b*ArcCoth[c + d*x])/(e + f*x),x]","-\frac{b \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{2 f}+\frac{b \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right)}{2 f}+\frac{\left(a+b \coth ^{-1}(c+d x)\right) \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{f}-\frac{\log \left(\frac{2}{c+d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{f}","-\frac{b \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{2 f}+\frac{b \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right)}{2 f}+\frac{\left(a+b \coth ^{-1}(c+d x)\right) \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{f}-\frac{\log \left(\frac{2}{c+d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{f}",1,"-(((a + b*ArcCoth[c + d*x])*Log[2/(1 + c + d*x)])/f) + ((a + b*ArcCoth[c + d*x])*Log[(2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/f + (b*PolyLog[2, 1 - 2/(1 + c + d*x)])/(2*f) - (b*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/(2*f)","A",5,5,18,0.2778,1,"{6112, 5921, 2402, 2315, 2447}"
107,1,115,0,0.1687239,"\int \frac{a+b \coth ^{-1}(c+d x)}{(e+f x)^2} \, dx","Int[(a + b*ArcCoth[c + d*x])/(e + f*x)^2,x]","-\frac{a+b \coth ^{-1}(c+d x)}{f (e+f x)}-\frac{b d \log (-c-d x+1)}{2 f (-c f+d e+f)}+\frac{b d \log (c+d x+1)}{2 f (-c f+d e-f)}-\frac{b d \log (e+f x)}{(-c f+d e+f) (d e-(c+1) f)}","-\frac{a+b \coth ^{-1}(c+d x)}{f (e+f x)}-\frac{b d \log (-c-d x+1)}{2 f (-c f+d e+f)}+\frac{b d \log (c+d x+1)}{2 f (-c f+d e-f)}-\frac{b d \log (e+f x)}{(-c f+d e+f) (d e-(c+1) f)}",1,"-((a + b*ArcCoth[c + d*x])/(f*(e + f*x))) - (b*d*Log[1 - c - d*x])/(2*f*(d*e + f - c*f)) + (b*d*Log[1 + c + d*x])/(2*f*(d*e - f - c*f)) - (b*d*Log[e + f*x])/((d*e + f - c*f)*(d*e - (1 + c)*f))","A",7,5,18,0.2778,1,"{6110, 1982, 705, 31, 632}"
108,1,167,0,0.234421,"\int \frac{a+b \coth ^{-1}(c+d x)}{(e+f x)^3} \, dx","Int[(a + b*ArcCoth[c + d*x])/(e + f*x)^3,x]","-\frac{a+b \coth ^{-1}(c+d x)}{2 f (e+f x)^2}-\frac{b d^2 \log (-c-d x+1)}{4 f (-c f+d e+f)^2}+\frac{b d^2 \log (c+d x+1)}{4 f (-c f+d e-f)^2}-\frac{b d^2 (d e-c f) \log (e+f x)}{(-c f+d e+f)^2 (d e-(c+1) f)^2}+\frac{b d}{2 (e+f x) (-c f+d e+f) (d e-(c+1) f)}","-\frac{a+b \coth ^{-1}(c+d x)}{2 f (e+f x)^2}-\frac{b d^2 \log (-c-d x+1)}{4 f (-c f+d e+f)^2}+\frac{b d^2 \log (c+d x+1)}{4 f (-c f+d e-f)^2}-\frac{b d^2 (d e-c f) \log (e+f x)}{(-c f+d e+f)^2 (d e-(c+1) f)^2}+\frac{b d}{2 (e+f x) (-c f+d e+f) (d e-(c+1) f)}",1,"(b*d)/(2*(d*e + f - c*f)*(d*e - (1 + c)*f)*(e + f*x)) - (a + b*ArcCoth[c + d*x])/(2*f*(e + f*x)^2) - (b*d^2*Log[1 - c - d*x])/(4*f*(d*e + f - c*f)^2) + (b*d^2*Log[1 + c + d*x])/(4*f*(d*e - f - c*f)^2) - (b*d^2*(d*e - c*f)*Log[e + f*x])/((d*e + f - c*f)^2*(d*e - (1 + c)*f)^2)","A",5,4,18,0.2222,1,"{6110, 1982, 709, 800}"
109,1,374,0,0.6365357,"\int (e+f x)^2 \left(a+b \coth ^{-1}(c+d x)\right)^2 \, dx","Int[(e + f*x)^2*(a + b*ArcCoth[c + d*x])^2,x]","-\frac{b^2 \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{3 d^3}-\frac{(d e-c f) \left(\left(c^2+3\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \coth ^{-1}(c+d x)\right)^2}{3 d^3 f}+\frac{\left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \left(a+b \coth ^{-1}(c+d x)\right)^2}{3 d^3}-\frac{2 b \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{3 d^3}+\frac{2 a b f x (d e-c f)}{d^2}+\frac{b f^2 (c+d x)^2 \left(a+b \coth ^{-1}(c+d x)\right)}{3 d^3}+\frac{(e+f x)^3 \left(a+b \coth ^{-1}(c+d x)\right)^2}{3 f}+\frac{b^2 f (d e-c f) \log \left(1-(c+d x)^2\right)}{d^3}+\frac{2 b^2 f (c+d x) (d e-c f) \coth ^{-1}(c+d x)}{d^3}-\frac{b^2 f^2 \tanh ^{-1}(c+d x)}{3 d^3}+\frac{b^2 f^2 x}{3 d^2}","-\frac{b^2 \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{3 d^3}-\frac{(d e-c f) \left(\left(c^2+3\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \coth ^{-1}(c+d x)\right)^2}{3 d^3 f}+\frac{\left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \left(a+b \coth ^{-1}(c+d x)\right)^2}{3 d^3}-\frac{2 b \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{3 d^3}+\frac{2 a b f x (d e-c f)}{d^2}+\frac{b f^2 (c+d x)^2 \left(a+b \coth ^{-1}(c+d x)\right)}{3 d^3}+\frac{(e+f x)^3 \left(a+b \coth ^{-1}(c+d x)\right)^2}{3 f}+\frac{b^2 f (d e-c f) \log \left(1-(c+d x)^2\right)}{d^3}+\frac{2 b^2 f (c+d x) (d e-c f) \coth ^{-1}(c+d x)}{d^3}-\frac{b^2 f^2 \tanh ^{-1}(c+d x)}{3 d^3}+\frac{b^2 f^2 x}{3 d^2}",1,"(b^2*f^2*x)/(3*d^2) + (2*a*b*f*(d*e - c*f)*x)/d^2 + (2*b^2*f*(d*e - c*f)*(c + d*x)*ArcCoth[c + d*x])/d^3 + (b*f^2*(c + d*x)^2*(a + b*ArcCoth[c + d*x]))/(3*d^3) - ((d*e - c*f)*(d^2*e^2 - 2*c*d*e*f + (3 + c^2)*f^2)*(a + b*ArcCoth[c + d*x])^2)/(3*d^3*f) + ((3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*(a + b*ArcCoth[c + d*x])^2)/(3*d^3) + ((e + f*x)^3*(a + b*ArcCoth[c + d*x])^2)/(3*f) - (b^2*f^2*ArcTanh[c + d*x])/(3*d^3) - (2*b*(3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*(a + b*ArcCoth[c + d*x])*Log[2/(1 - c - d*x)])/(3*d^3) + (b^2*f*(d*e - c*f)*Log[1 - (c + d*x)^2])/d^3 - (b^2*(3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/(3*d^3)","A",16,13,20,0.6500,1,"{6112, 5929, 5911, 260, 5917, 321, 206, 6049, 5949, 5985, 5919, 2402, 2315}"
110,1,220,0,0.4426636,"\int (e+f x) \left(a+b \coth ^{-1}(c+d x)\right)^2 \, dx","Int[(e + f*x)*(a + b*ArcCoth[c + d*x])^2,x]","-\frac{b^2 (d e-c f) \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{d^2}+\frac{\left(-\frac{\left(c^2+1\right) f}{d}+2 c e-\frac{d e^2}{f}\right) \left(a+b \coth ^{-1}(c+d x)\right)^2}{2 d}+\frac{(d e-c f) \left(a+b \coth ^{-1}(c+d x)\right)^2}{d^2}-\frac{2 b (d e-c f) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{d^2}+\frac{(e+f x)^2 \left(a+b \coth ^{-1}(c+d x)\right)^2}{2 f}+\frac{a b f x}{d}+\frac{b^2 f \log \left(1-(c+d x)^2\right)}{2 d^2}+\frac{b^2 f (c+d x) \coth ^{-1}(c+d x)}{d^2}","-\frac{b^2 (d e-c f) \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{d^2}-\frac{\left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \coth ^{-1}(c+d x)\right)^2}{2 d^2 f}+\frac{(d e-c f) \left(a+b \coth ^{-1}(c+d x)\right)^2}{d^2}-\frac{2 b (d e-c f) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{d^2}+\frac{(e+f x)^2 \left(a+b \coth ^{-1}(c+d x)\right)^2}{2 f}+\frac{a b f x}{d}+\frac{b^2 f \log \left(1-(c+d x)^2\right)}{2 d^2}+\frac{b^2 f (c+d x) \coth ^{-1}(c+d x)}{d^2}",1,"(a*b*f*x)/d + (b^2*f*(c + d*x)*ArcCoth[c + d*x])/d^2 + ((d*e - c*f)*(a + b*ArcCoth[c + d*x])^2)/d^2 + ((2*c*e - (d*e^2)/f - ((1 + c^2)*f)/d)*(a + b*ArcCoth[c + d*x])^2)/(2*d) + ((e + f*x)^2*(a + b*ArcCoth[c + d*x])^2)/(2*f) - (2*b*(d*e - c*f)*(a + b*ArcCoth[c + d*x])*Log[2/(1 - c - d*x)])/d^2 + (b^2*f*Log[1 - (c + d*x)^2])/(2*d^2) - (b^2*(d*e - c*f)*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/d^2","A",13,10,18,0.5556,1,"{6112, 5929, 5911, 260, 6049, 5949, 5985, 5919, 2402, 2315}"
111,1,97,0,0.1162096,"\int \left(a+b \coth ^{-1}(c+d x)\right)^2 \, dx","Int[(a + b*ArcCoth[c + d*x])^2,x]","-\frac{b^2 \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{d}+\frac{(c+d x) \left(a+b \coth ^{-1}(c+d x)\right)^2}{d}+\frac{\left(a+b \coth ^{-1}(c+d x)\right)^2}{d}-\frac{2 b \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{d}","-\frac{b^2 \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{d}+\frac{(c+d x) \left(a+b \coth ^{-1}(c+d x)\right)^2}{d}+\frac{\left(a+b \coth ^{-1}(c+d x)\right)^2}{d}-\frac{2 b \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{d}",1,"(a + b*ArcCoth[c + d*x])^2/d + ((c + d*x)*(a + b*ArcCoth[c + d*x])^2)/d - (2*b*(a + b*ArcCoth[c + d*x])*Log[2/(1 - c - d*x)])/d - (b^2*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/d","A",6,6,12,0.5000,1,"{6104, 5911, 5985, 5919, 2402, 2315}"
112,1,214,0,0.1533473,"\int \frac{\left(a+b \coth ^{-1}(c+d x)\right)^2}{e+f x} \, dx","Int[(a + b*ArcCoth[c + d*x])^2/(e + f*x),x]","-\frac{b \left(a+b \coth ^{-1}(c+d x)\right) \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{f}+\frac{b \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{f}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{2 f}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c+d x+1}\right)}{2 f}+\frac{\left(a+b \coth ^{-1}(c+d x)\right)^2 \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{f}-\frac{\log \left(\frac{2}{c+d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)^2}{f}","-\frac{b \left(a+b \coth ^{-1}(c+d x)\right) \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{f}+\frac{b \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{f}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{2 f}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{c+d x+1}\right)}{2 f}+\frac{\left(a+b \coth ^{-1}(c+d x)\right)^2 \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{f}-\frac{\log \left(\frac{2}{c+d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)^2}{f}",1,"-(((a + b*ArcCoth[c + d*x])^2*Log[2/(1 + c + d*x)])/f) + ((a + b*ArcCoth[c + d*x])^2*Log[(2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/f + (b*(a + b*ArcCoth[c + d*x])*PolyLog[2, 1 - 2/(1 + c + d*x)])/f - (b*(a + b*ArcCoth[c + d*x])*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/f + (b^2*PolyLog[3, 1 - 2/(1 + c + d*x)])/(2*f) - (b^2*PolyLog[3, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/(2*f)","A",2,2,20,0.1000,1,"{6112, 5923}"
113,1,485,0,1.7430128,"\int \frac{\left(a+b \coth ^{-1}(c+d x)\right)^2}{(e+f x)^2} \, dx","Int[(a + b*ArcCoth[c + d*x])^2/(e + f*x)^2,x]","\frac{b^2 d \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{2 f (-c f+d e+f)}+\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right)}{2 f (-c f+d e-f)}-\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right)}{(-c f+d e+f) (d e-(c+1) f)}+\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{(-c f+d e+f) (d e-(c+1) f)}-\frac{a b d \log (-c-d x+1)}{f (-c f+d e+f)}+\frac{a b d \log (c+d x+1)}{f (-c f+d e-f)}-\frac{2 a b d \log (e+f x)}{(-c f+d e+f) (d e-(c+1) f)}-\frac{\left(a+b \coth ^{-1}(c+d x)\right)^2}{f (e+f x)}+\frac{b^2 d \log \left(\frac{2}{-c-d x+1}\right) \coth ^{-1}(c+d x)}{f (-c f+d e+f)}-\frac{b^2 d \log \left(\frac{2}{c+d x+1}\right) \coth ^{-1}(c+d x)}{f (-c f+d e-f)}+\frac{2 b^2 d \log \left(\frac{2}{c+d x+1}\right) \coth ^{-1}(c+d x)}{(-c f+d e+f) (d e-(c+1) f)}-\frac{2 b^2 d \coth ^{-1}(c+d x) \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{(-c f+d e+f) (d e-(c+1) f)}","\frac{b^2 d \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{2 f (-c f+d e+f)}+\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right)}{2 f (-c f+d e-f)}-\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right)}{(-c f+d e+f) (d e-(c+1) f)}+\frac{b^2 d \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{(-c f+d e+f) (d e-(c+1) f)}+\frac{2 a b d \log (e+f x)}{f^2-(d e-c f)^2}-\frac{a b d \log (-c-d x+1)}{f (-c f+d e+f)}+\frac{a b d \log (c+d x+1)}{f (-c f+d e-f)}-\frac{\left(a+b \coth ^{-1}(c+d x)\right)^2}{f (e+f x)}+\frac{b^2 d \log \left(\frac{2}{-c-d x+1}\right) \coth ^{-1}(c+d x)}{f (-c f+d e+f)}-\frac{b^2 d \log \left(\frac{2}{c+d x+1}\right) \coth ^{-1}(c+d x)}{f (-c f+d e-f)}+\frac{2 b^2 d \log \left(\frac{2}{c+d x+1}\right) \coth ^{-1}(c+d x)}{(-c f+d e+f) (d e-(c+1) f)}-\frac{2 b^2 d \coth ^{-1}(c+d x) \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{(-c f+d e+f) (d e-(c+1) f)}",1,"-((a + b*ArcCoth[c + d*x])^2/(f*(e + f*x))) + (b^2*d*ArcCoth[c + d*x]*Log[2/(1 - c - d*x)])/(f*(d*e + f - c*f)) - (a*b*d*Log[1 - c - d*x])/(f*(d*e + f - c*f)) - (b^2*d*ArcCoth[c + d*x]*Log[2/(1 + c + d*x)])/(f*(d*e - f - c*f)) + (2*b^2*d*ArcCoth[c + d*x]*Log[2/(1 + c + d*x)])/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (a*b*d*Log[1 + c + d*x])/(f*(d*e - f - c*f)) - (2*a*b*d*Log[e + f*x])/((d*e + f - c*f)*(d*e - (1 + c)*f)) - (2*b^2*d*ArcCoth[c + d*x]*Log[(2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (b^2*d*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/(2*f*(d*e + f - c*f)) + (b^2*d*PolyLog[2, 1 - 2/(1 + c + d*x)])/(2*f*(d*e - f - c*f)) - (b^2*d*PolyLog[2, 1 - 2/(1 + c + d*x)])/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (b^2*d*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/((d*e + f - c*f)*(d*e - (1 + c)*f))","A",21,19,20,0.9500,1,"{6110, 1982, 705, 31, 632, 6741, 6122, 706, 633, 6688, 12, 6725, 72, 6742, 5919, 2402, 2315, 5921, 2447}"
114,1,546,0,1.0428345,"\int (e+f x)^2 \left(a+b \coth ^{-1}(c+d x)\right)^3 \, dx","Int[(e + f*x)^2*(a + b*ArcCoth[c + d*x])^3,x]","-\frac{b^2 \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{d^3}+\frac{b^3 \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right)}{2 d^3}-\frac{3 b^3 f (d e-c f) \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{d^3}-\frac{6 b^2 f (d e-c f) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{d^3}+\frac{a b^2 f^2 x}{d^2}-\frac{(d e-c f) \left(\left(c^2+3\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \coth ^{-1}(c+d x)\right)^3}{3 d^3 f}+\frac{\left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \left(a+b \coth ^{-1}(c+d x)\right)^3}{3 d^3}-\frac{b \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)^2}{d^3}+\frac{3 b f (d e-c f) \left(a+b \coth ^{-1}(c+d x)\right)^2}{d^3}+\frac{3 b f (c+d x) (d e-c f) \left(a+b \coth ^{-1}(c+d x)\right)^2}{d^3}-\frac{b f^2 \left(a+b \coth ^{-1}(c+d x)\right)^2}{2 d^3}+\frac{b f^2 (c+d x)^2 \left(a+b \coth ^{-1}(c+d x)\right)^2}{2 d^3}+\frac{(e+f x)^3 \left(a+b \coth ^{-1}(c+d x)\right)^3}{3 f}+\frac{b^3 f^2 \log \left(1-(c+d x)^2\right)}{2 d^3}+\frac{b^3 f^2 (c+d x) \coth ^{-1}(c+d x)}{d^3}","-\frac{b^2 \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{d^3}+\frac{b^3 \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right)}{2 d^3}-\frac{3 b^3 f (d e-c f) \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{d^3}-\frac{6 b^2 f (d e-c f) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{d^3}+\frac{a b^2 f^2 x}{d^2}-\frac{(d e-c f) \left(\left(c^2+3\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \coth ^{-1}(c+d x)\right)^3}{3 d^3 f}+\frac{\left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \left(a+b \coth ^{-1}(c+d x)\right)^3}{3 d^3}-\frac{b \left(\left(3 c^2+1\right) f^2-6 c d e f+3 d^2 e^2\right) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)^2}{d^3}+\frac{3 b f (d e-c f) \left(a+b \coth ^{-1}(c+d x)\right)^2}{d^3}+\frac{3 b f (c+d x) (d e-c f) \left(a+b \coth ^{-1}(c+d x)\right)^2}{d^3}-\frac{b f^2 \left(a+b \coth ^{-1}(c+d x)\right)^2}{2 d^3}+\frac{b f^2 (c+d x)^2 \left(a+b \coth ^{-1}(c+d x)\right)^2}{2 d^3}+\frac{(e+f x)^3 \left(a+b \coth ^{-1}(c+d x)\right)^3}{3 f}+\frac{b^3 f^2 \log \left(1-(c+d x)^2\right)}{2 d^3}+\frac{b^3 f^2 (c+d x) \coth ^{-1}(c+d x)}{d^3}",1,"(a*b^2*f^2*x)/d^2 + (b^3*f^2*(c + d*x)*ArcCoth[c + d*x])/d^3 - (b*f^2*(a + b*ArcCoth[c + d*x])^2)/(2*d^3) + (3*b*f*(d*e - c*f)*(a + b*ArcCoth[c + d*x])^2)/d^3 + (3*b*f*(d*e - c*f)*(c + d*x)*(a + b*ArcCoth[c + d*x])^2)/d^3 + (b*f^2*(c + d*x)^2*(a + b*ArcCoth[c + d*x])^2)/(2*d^3) - ((d*e - c*f)*(d^2*e^2 - 2*c*d*e*f + (3 + c^2)*f^2)*(a + b*ArcCoth[c + d*x])^3)/(3*d^3*f) + ((3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*(a + b*ArcCoth[c + d*x])^3)/(3*d^3) + ((e + f*x)^3*(a + b*ArcCoth[c + d*x])^3)/(3*f) - (6*b^2*f*(d*e - c*f)*(a + b*ArcCoth[c + d*x])*Log[2/(1 - c - d*x)])/d^3 - (b*(3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*(a + b*ArcCoth[c + d*x])^2*Log[2/(1 - c - d*x)])/d^3 + (b^3*f^2*Log[1 - (c + d*x)^2])/(2*d^3) - (3*b^3*f*(d*e - c*f)*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/d^3 - (b^2*(3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*(a + b*ArcCoth[c + d*x])*PolyLog[2, 1 - 2/(1 - c - d*x)])/d^3 + (b^3*(3*d^2*e^2 - 6*c*d*e*f + (1 + 3*c^2)*f^2)*PolyLog[3, 1 - 2/(1 - c - d*x)])/(2*d^3)","A",21,14,20,0.7000,1,"{6112, 5929, 5911, 5985, 5919, 2402, 2315, 5917, 5981, 260, 5949, 6049, 6059, 6610}"
115,1,325,0,0.7207918,"\int (e+f x) \left(a+b \coth ^{-1}(c+d x)\right)^3 \, dx","Int[(e + f*x)*(a + b*ArcCoth[c + d*x])^3,x]","-\frac{3 b^2 (d e-c f) \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{d^2}+\frac{3 b^3 (d e-c f) \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right)}{2 d^2}-\frac{3 b^3 f \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{2 d^2}-\frac{3 b^2 f \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{d^2}+\frac{\left(-\frac{\left(c^2+1\right) f}{d}+2 c e-\frac{d e^2}{f}\right) \left(a+b \coth ^{-1}(c+d x)\right)^3}{2 d}+\frac{(d e-c f) \left(a+b \coth ^{-1}(c+d x)\right)^3}{d^2}-\frac{3 b (d e-c f) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)^2}{d^2}+\frac{3 b f \left(a+b \coth ^{-1}(c+d x)\right)^2}{2 d^2}+\frac{3 b f (c+d x) \left(a+b \coth ^{-1}(c+d x)\right)^2}{2 d^2}+\frac{(e+f x)^2 \left(a+b \coth ^{-1}(c+d x)\right)^3}{2 f}","-\frac{3 b^2 (d e-c f) \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{d^2}+\frac{3 b^3 (d e-c f) \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right)}{2 d^2}-\frac{3 b^3 f \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right)}{2 d^2}-\frac{3 b^2 f \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{d^2}-\frac{\left(\left(c^2+1\right) f^2-2 c d e f+d^2 e^2\right) \left(a+b \coth ^{-1}(c+d x)\right)^3}{2 d^2 f}+\frac{(d e-c f) \left(a+b \coth ^{-1}(c+d x)\right)^3}{d^2}-\frac{3 b (d e-c f) \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)^2}{d^2}+\frac{3 b f \left(a+b \coth ^{-1}(c+d x)\right)^2}{2 d^2}+\frac{3 b f (c+d x) \left(a+b \coth ^{-1}(c+d x)\right)^2}{2 d^2}+\frac{(e+f x)^2 \left(a+b \coth ^{-1}(c+d x)\right)^3}{2 f}",1,"(3*b*f*(a + b*ArcCoth[c + d*x])^2)/(2*d^2) + (3*b*f*(c + d*x)*(a + b*ArcCoth[c + d*x])^2)/(2*d^2) + ((d*e - c*f)*(a + b*ArcCoth[c + d*x])^3)/d^2 + ((2*c*e - (d*e^2)/f - ((1 + c^2)*f)/d)*(a + b*ArcCoth[c + d*x])^3)/(2*d) + ((e + f*x)^2*(a + b*ArcCoth[c + d*x])^3)/(2*f) - (3*b^2*f*(a + b*ArcCoth[c + d*x])*Log[2/(1 - c - d*x)])/d^2 - (3*b*(d*e - c*f)*(a + b*ArcCoth[c + d*x])^2*Log[2/(1 - c - d*x)])/d^2 - (3*b^3*f*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/(2*d^2) - (3*b^2*(d*e - c*f)*(a + b*ArcCoth[c + d*x])*PolyLog[2, 1 - 2/(1 - c - d*x)])/d^2 + (3*b^3*(d*e - c*f)*PolyLog[3, 1 - 2/(1 - c - d*x)])/(2*d^2)","A",15,11,18,0.6111,1,"{6112, 5929, 5911, 5985, 5919, 2402, 2315, 6049, 5949, 6059, 6610}"
116,1,132,0,0.2273343,"\int \left(a+b \coth ^{-1}(c+d x)\right)^3 \, dx","Int[(a + b*ArcCoth[c + d*x])^3,x]","-\frac{3 b^2 \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{d}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right)}{2 d}+\frac{(c+d x) \left(a+b \coth ^{-1}(c+d x)\right)^3}{d}+\frac{\left(a+b \coth ^{-1}(c+d x)\right)^3}{d}-\frac{3 b \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)^2}{d}","-\frac{3 b^2 \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{d}+\frac{3 b^3 \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right)}{2 d}+\frac{(c+d x) \left(a+b \coth ^{-1}(c+d x)\right)^3}{d}+\frac{\left(a+b \coth ^{-1}(c+d x)\right)^3}{d}-\frac{3 b \log \left(\frac{2}{-c-d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)^2}{d}",1,"(a + b*ArcCoth[c + d*x])^3/d + ((c + d*x)*(a + b*ArcCoth[c + d*x])^3)/d - (3*b*(a + b*ArcCoth[c + d*x])^2*Log[2/(1 - c - d*x)])/d - (3*b^2*(a + b*ArcCoth[c + d*x])*PolyLog[2, 1 - 2/(1 - c - d*x)])/d + (3*b^3*PolyLog[3, 1 - 2/(1 - c - d*x)])/(2*d)","A",6,7,12,0.5833,1,"{6104, 5911, 5985, 5919, 5949, 6059, 6610}"
117,1,308,0,0.1871354,"\int \frac{\left(a+b \coth ^{-1}(c+d x)\right)^3}{e+f x} \, dx","Int[(a + b*ArcCoth[c + d*x])^3/(e + f*x),x]","-\frac{3 b^2 \left(a+b \coth ^{-1}(c+d x)\right) \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{2 f}+\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{c+d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{2 f}-\frac{3 b \left(a+b \coth ^{-1}(c+d x)\right)^2 \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{2 f}+\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)^2}{2 f}-\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{4 f}+\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2}{c+d x+1}\right)}{4 f}+\frac{\left(a+b \coth ^{-1}(c+d x)\right)^3 \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{f}-\frac{\log \left(\frac{2}{c+d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)^3}{f}","-\frac{3 b^2 \left(a+b \coth ^{-1}(c+d x)\right) \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{2 f}+\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{c+d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)}{2 f}-\frac{3 b \left(a+b \coth ^{-1}(c+d x)\right)^2 \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{2 f}+\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)^2}{2 f}-\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{4 f}+\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2}{c+d x+1}\right)}{4 f}+\frac{\left(a+b \coth ^{-1}(c+d x)\right)^3 \log \left(\frac{2 d (e+f x)}{(c+d x+1) (-c f+d e+f)}\right)}{f}-\frac{\log \left(\frac{2}{c+d x+1}\right) \left(a+b \coth ^{-1}(c+d x)\right)^3}{f}",1,"-(((a + b*ArcCoth[c + d*x])^3*Log[2/(1 + c + d*x)])/f) + ((a + b*ArcCoth[c + d*x])^3*Log[(2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/f + (3*b*(a + b*ArcCoth[c + d*x])^2*PolyLog[2, 1 - 2/(1 + c + d*x)])/(2*f) - (3*b*(a + b*ArcCoth[c + d*x])^2*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/(2*f) + (3*b^2*(a + b*ArcCoth[c + d*x])*PolyLog[3, 1 - 2/(1 + c + d*x)])/(2*f) - (3*b^2*(a + b*ArcCoth[c + d*x])*PolyLog[3, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/(2*f) + (3*b^3*PolyLog[4, 1 - 2/(1 + c + d*x)])/(4*f) - (3*b^3*PolyLog[4, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/(4*f)","A",2,2,20,0.1000,1,"{6112, 5925}"
118,1,1094,0,2.7821364,"\int \frac{\left(a+b \coth ^{-1}(c+d x)\right)^3}{(e+f x)^2} \, dx","Int[(a + b*ArcCoth[c + d*x])^3/(e + f*x)^2,x]","\frac{3 d \coth ^{-1}(c+d x)^2 \log \left(\frac{2}{-c-d x+1}\right) b^3}{2 f (d e-c f+f)}-\frac{3 d \coth ^{-1}(c+d x)^2 \log \left(\frac{2}{c+d x+1}\right) b^3}{2 f (d e-c f-f)}+\frac{3 d \coth ^{-1}(c+d x)^2 \log \left(\frac{2}{c+d x+1}\right) b^3}{(d e-c f+f) (d e-(c+1) f)}-\frac{3 d \coth ^{-1}(c+d x)^2 \log \left(\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^3}{(d e-c f+f) (d e-(c+1) f)}+\frac{3 d \coth ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) b^3}{2 f (d e-c f+f)}+\frac{3 d \coth ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) b^3}{2 f (d e-c f-f)}-\frac{3 d \coth ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) b^3}{(d e-c f+f) (d e-(c+1) f)}+\frac{3 d \coth ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^3}{(d e-c f+f) (d e-(c+1) f)}-\frac{3 d \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right) b^3}{4 f (d e-c f+f)}+\frac{3 d \text{PolyLog}\left(3,1-\frac{2}{c+d x+1}\right) b^3}{4 f (d e-c f-f)}-\frac{3 d \text{PolyLog}\left(3,1-\frac{2}{c+d x+1}\right) b^3}{2 (d e-c f+f) (d e-(c+1) f)}+\frac{3 d \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^3}{2 (d e-c f+f) (d e-(c+1) f)}+\frac{3 a d \coth ^{-1}(c+d x) \log \left(\frac{2}{-c-d x+1}\right) b^2}{f (d e-c f+f)}-\frac{3 a d \coth ^{-1}(c+d x) \log \left(\frac{2}{c+d x+1}\right) b^2}{f (d e-c f-f)}+\frac{6 a d \coth ^{-1}(c+d x) \log \left(\frac{2}{c+d x+1}\right) b^2}{(d e-c f+f) (d e-(c+1) f)}-\frac{6 a d \coth ^{-1}(c+d x) \log \left(\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^2}{(d e-c f+f) (d e-(c+1) f)}+\frac{3 a d \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right) b^2}{2 f (d e-c f+f)}+\frac{3 a d \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) b^2}{2 f (d e-c f-f)}-\frac{3 a d \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) b^2}{(d e-c f+f) (d e-(c+1) f)}+\frac{3 a d \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^2}{(d e-c f+f) (d e-(c+1) f)}-\frac{3 a^2 d \log (-c-d x+1) b}{2 f (d e-c f+f)}+\frac{3 a^2 d \log (c+d x+1) b}{2 f (d e-c f-f)}-\frac{3 a^2 d \log (e+f x) b}{(d e-c f+f) (d e-(c+1) f)}-\frac{\left(a+b \coth ^{-1}(c+d x)\right)^3}{f (e+f x)}","\frac{3 d \coth ^{-1}(c+d x)^2 \log \left(\frac{2}{-c-d x+1}\right) b^3}{2 f (d e-c f+f)}-\frac{3 d \coth ^{-1}(c+d x)^2 \log \left(\frac{2}{c+d x+1}\right) b^3}{2 f (d e-c f-f)}+\frac{3 d \coth ^{-1}(c+d x)^2 \log \left(\frac{2}{c+d x+1}\right) b^3}{(d e-c f+f) (d e-(c+1) f)}-\frac{3 d \coth ^{-1}(c+d x)^2 \log \left(\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^3}{(d e-c f+f) (d e-(c+1) f)}+\frac{3 d \coth ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2}{-c-d x+1}\right) b^3}{2 f (d e-c f+f)}+\frac{3 d \coth ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) b^3}{2 f (d e-c f-f)}-\frac{3 d \coth ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) b^3}{(d e-c f+f) (d e-(c+1) f)}+\frac{3 d \coth ^{-1}(c+d x) \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^3}{(d e-c f+f) (d e-(c+1) f)}-\frac{3 d \text{PolyLog}\left(3,1-\frac{2}{-c-d x+1}\right) b^3}{4 f (d e-c f+f)}+\frac{3 d \text{PolyLog}\left(3,1-\frac{2}{c+d x+1}\right) b^3}{4 f (d e-c f-f)}-\frac{3 d \text{PolyLog}\left(3,1-\frac{2}{c+d x+1}\right) b^3}{2 (d e-c f+f) (d e-(c+1) f)}+\frac{3 d \text{PolyLog}\left(3,1-\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^3}{2 (d e-c f+f) (d e-(c+1) f)}+\frac{3 a d \coth ^{-1}(c+d x) \log \left(\frac{2}{-c-d x+1}\right) b^2}{f (d e-c f+f)}-\frac{3 a d \coth ^{-1}(c+d x) \log \left(\frac{2}{c+d x+1}\right) b^2}{f (d e-c f-f)}+\frac{6 a d \coth ^{-1}(c+d x) \log \left(\frac{2}{c+d x+1}\right) b^2}{(d e-c f+f) (d e-(c+1) f)}-\frac{6 a d \coth ^{-1}(c+d x) \log \left(\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^2}{(d e-c f+f) (d e-(c+1) f)}+\frac{3 a d \text{PolyLog}\left(2,-\frac{c+d x+1}{-c-d x+1}\right) b^2}{2 f (d e-c f+f)}+\frac{3 a d \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) b^2}{2 f (d e-c f-f)}-\frac{3 a d \text{PolyLog}\left(2,1-\frac{2}{c+d x+1}\right) b^2}{(d e-c f+f) (d e-(c+1) f)}+\frac{3 a d \text{PolyLog}\left(2,1-\frac{2 d (e+f x)}{(d e-c f+f) (c+d x+1)}\right) b^2}{(d e-c f+f) (d e-(c+1) f)}-\frac{3 a^2 d \log (-c-d x+1) b}{2 f (d e-c f+f)}+\frac{3 a^2 d \log (c+d x+1) b}{2 f (d e-c f-f)}+\frac{3 a^2 d \log (e+f x) b}{f^2-(d e-c f)^2}-\frac{\left(a+b \coth ^{-1}(c+d x)\right)^3}{f (e+f x)}",1,"-((a + b*ArcCoth[c + d*x])^3/(f*(e + f*x))) + (3*a*b^2*d*ArcCoth[c + d*x]*Log[2/(1 - c - d*x)])/(f*(d*e + f - c*f)) + (3*b^3*d*ArcCoth[c + d*x]^2*Log[2/(1 - c - d*x)])/(2*f*(d*e + f - c*f)) - (3*a^2*b*d*Log[1 - c - d*x])/(2*f*(d*e + f - c*f)) - (3*a*b^2*d*ArcCoth[c + d*x]*Log[2/(1 + c + d*x)])/(f*(d*e - f - c*f)) + (6*a*b^2*d*ArcCoth[c + d*x]*Log[2/(1 + c + d*x)])/((d*e + f - c*f)*(d*e - (1 + c)*f)) - (3*b^3*d*ArcCoth[c + d*x]^2*Log[2/(1 + c + d*x)])/(2*f*(d*e - f - c*f)) + (3*b^3*d*ArcCoth[c + d*x]^2*Log[2/(1 + c + d*x)])/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*a^2*b*d*Log[1 + c + d*x])/(2*f*(d*e - f - c*f)) - (3*a^2*b*d*Log[e + f*x])/((d*e + f - c*f)*(d*e - (1 + c)*f)) - (6*a*b^2*d*ArcCoth[c + d*x]*Log[(2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/((d*e + f - c*f)*(d*e - (1 + c)*f)) - (3*b^3*d*ArcCoth[c + d*x]^2*Log[(2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*a*b^2*d*PolyLog[2, -((1 + c + d*x)/(1 - c - d*x))])/(2*f*(d*e + f - c*f)) + (3*b^3*d*ArcCoth[c + d*x]*PolyLog[2, 1 - 2/(1 - c - d*x)])/(2*f*(d*e + f - c*f)) + (3*a*b^2*d*PolyLog[2, 1 - 2/(1 + c + d*x)])/(2*f*(d*e - f - c*f)) - (3*a*b^2*d*PolyLog[2, 1 - 2/(1 + c + d*x)])/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*b^3*d*ArcCoth[c + d*x]*PolyLog[2, 1 - 2/(1 + c + d*x)])/(2*f*(d*e - f - c*f)) - (3*b^3*d*ArcCoth[c + d*x]*PolyLog[2, 1 - 2/(1 + c + d*x)])/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*a*b^2*d*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/((d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*b^3*d*ArcCoth[c + d*x]*PolyLog[2, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/((d*e + f - c*f)*(d*e - (1 + c)*f)) - (3*b^3*d*PolyLog[3, 1 - 2/(1 - c - d*x)])/(4*f*(d*e + f - c*f)) + (3*b^3*d*PolyLog[3, 1 - 2/(1 + c + d*x)])/(4*f*(d*e - f - c*f)) - (3*b^3*d*PolyLog[3, 1 - 2/(1 + c + d*x)])/(2*(d*e + f - c*f)*(d*e - (1 + c)*f)) + (3*b^3*d*PolyLog[3, 1 - (2*d*(e + f*x))/((d*e + f - c*f)*(1 + c + d*x))])/(2*(d*e + f - c*f)*(d*e - (1 + c)*f))","A",30,18,20,0.9000,1,"{6110, 6741, 6122, 6688, 12, 6725, 72, 6742, 5919, 2402, 2315, 5921, 2447, 5949, 6059, 6610, 6057, 5923}"
119,1,162,0,0.2460041,"\int (e+f x)^m \left(a+b \coth ^{-1}(c+d x)\right) \, dx","Int[(e + f*x)^m*(a + b*ArcCoth[c + d*x]),x]","\frac{(e+f x)^{m+1} \left(a+b \coth ^{-1}(c+d x)\right)}{f (m+1)}+\frac{b d (e+f x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{d (e+f x)}{d e-c f-f}\right)}{2 f (m+1) (m+2) (d e-(c+1) f)}-\frac{b d (e+f x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{d (e+f x)}{d e-c f+f}\right)}{2 f (m+1) (m+2) (-c f+d e+f)}","\frac{(e+f x)^{m+1} \left(a+b \coth ^{-1}(c+d x)\right)}{f (m+1)}+\frac{b d (e+f x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{d (e+f x)}{d e-c f-f}\right)}{2 f (m+1) (m+2) (d e-(c+1) f)}-\frac{b d (e+f x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{d (e+f x)}{d e-c f+f}\right)}{2 f (m+1) (m+2) (-c f+d e+f)}",1,"((e + f*x)^(1 + m)*(a + b*ArcCoth[c + d*x]))/(f*(1 + m)) + (b*d*(e + f*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (d*(e + f*x))/(d*e - f - c*f)])/(2*f*(d*e - (1 + c)*f)*(1 + m)*(2 + m)) - (b*d*(e + f*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (d*(e + f*x))/(d*e + f - c*f)])/(2*f*(d*e + f - c*f)*(1 + m)*(2 + m))","A",6,4,18,0.2222,1,"{6112, 5927, 712, 68}"
120,0,0,0,0.0665056,"\int (e+f x)^m \left(a+b \coth ^{-1}(c+d x)\right)^2 \, dx","Int[(e + f*x)^m*(a + b*ArcCoth[c + d*x])^2,x]","\int (e+f x)^m \left(a+b \coth ^{-1}(c+d x)\right)^2 \, dx","\text{Int}\left((e+f x)^m \left(a+b \coth ^{-1}(c+d x)\right)^2,x\right)",0,"Defer[Subst][Defer[Int][((d*e - c*f)/d + (f*x)/d)^m*(a + b*ArcCoth[x])^2, x], x, c + d*x]/d","A",0,0,0,0,-1,"{}"
121,0,0,0,0.0654614,"\int (e+f x)^m \left(a+b \coth ^{-1}(c+d x)\right)^3 \, dx","Int[(e + f*x)^m*(a + b*ArcCoth[c + d*x])^3,x]","\int (e+f x)^m \left(a+b \coth ^{-1}(c+d x)\right)^3 \, dx","\text{Int}\left((e+f x)^m \left(a+b \coth ^{-1}(c+d x)\right)^3,x\right)",0,"Defer[Subst][Defer[Int][((d*e - c*f)/d + (f*x)/d)^m*(a + b*ArcCoth[x])^3, x], x, c + d*x]/d","A",0,0,0,0,-1,"{}"
122,0,0,0,0.047806,"\int \frac{\left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^n}{1-c^2 x^2} \, dx","Int[(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2),x]","\int \frac{\left(a+b \coth ^{-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 \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^n}{1-c^2 x^2},x\right)",0,"Defer[Int][(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2), x]","A",0,0,0,0,-1,"{}"
123,1,460,0,0.5982339,"\int \frac{\left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^3}{1-c^2 x^2} \, dx","Int[(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3/(1 - c^2*x^2),x]","-\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1}\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}+\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2 \sqrt{1-c x}}{\sqrt{c x+1} \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1\right)}\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}-\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1}\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}+\frac{3 b \text{PolyLog}\left(2,1-\frac{2 \sqrt{1-c x}}{\sqrt{c x+1} \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1\right)}\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}-\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2}{\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1}\right)}{4 c}+\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2 \sqrt{1-c x}}{\sqrt{c x+1} \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1\right)}\right)}{4 c}-\frac{2 \coth ^{-1}\left(1-\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{c}","-\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2}{\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1}\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}+\frac{3 b^2 \text{PolyLog}\left(3,1-\frac{2 \sqrt{1-c x}}{\sqrt{c x+1} \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1\right)}\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}-\frac{3 b \text{PolyLog}\left(2,1-\frac{2}{\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1}\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}+\frac{3 b \text{PolyLog}\left(2,1-\frac{2 \sqrt{1-c x}}{\sqrt{c x+1} \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1\right)}\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}-\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2}{\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1}\right)}{4 c}+\frac{3 b^3 \text{PolyLog}\left(4,1-\frac{2 \sqrt{1-c x}}{\sqrt{c x+1} \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1\right)}\right)}{4 c}-\frac{2 \coth ^{-1}\left(1-\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{c}",1,"(-2*(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3*ArcCoth[1 - 2/(1 - Sqrt[1 - c*x]/Sqrt[1 + c*x])])/c - (3*b*(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*PolyLog[2, 1 - 2/(1 + Sqrt[1 - c*x]/Sqrt[1 + c*x])])/(2*c) + (3*b*(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*PolyLog[2, 1 - (2*Sqrt[1 - c*x])/(Sqrt[1 + c*x]*(1 + Sqrt[1 - c*x]/Sqrt[1 + c*x]))])/(2*c) - (3*b^2*(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[3, 1 - 2/(1 + Sqrt[1 - c*x]/Sqrt[1 + c*x])])/(2*c) + (3*b^2*(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[3, 1 - (2*Sqrt[1 - c*x])/(Sqrt[1 + c*x]*(1 + Sqrt[1 - c*x]/Sqrt[1 + c*x]))])/(2*c) - (3*b^3*PolyLog[4, 1 - 2/(1 + Sqrt[1 - c*x]/Sqrt[1 + c*x])])/(4*c) + (3*b^3*PolyLog[4, 1 - (2*Sqrt[1 - c*x])/(Sqrt[1 + c*x]*(1 + Sqrt[1 - c*x]/Sqrt[1 + c*x]))])/(4*c)","A",9,7,40,0.1750,1,"{6681, 5915, 6053, 5949, 6057, 6061, 6610}"
124,1,302,0,0.3463654,"\int \frac{\left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2}{1-c^2 x^2} \, dx","Int[(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2/(1 - c^2*x^2),x]","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1}\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}+\frac{b \text{PolyLog}\left(2,1-\frac{2 \sqrt{1-c x}}{\sqrt{c x+1} \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1\right)}\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1}\right)}{2 c}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2 \sqrt{1-c x}}{\sqrt{c x+1} \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1\right)}\right)}{2 c}-\frac{2 \coth ^{-1}\left(1-\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{c}","-\frac{b \text{PolyLog}\left(2,1-\frac{2}{\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1}\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}+\frac{b \text{PolyLog}\left(2,1-\frac{2 \sqrt{1-c x}}{\sqrt{c x+1} \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1\right)}\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}-\frac{b^2 \text{PolyLog}\left(3,1-\frac{2}{\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1}\right)}{2 c}+\frac{b^2 \text{PolyLog}\left(3,1-\frac{2 \sqrt{1-c x}}{\sqrt{c x+1} \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}+1\right)}\right)}{2 c}-\frac{2 \coth ^{-1}\left(1-\frac{2}{1-\frac{\sqrt{1-c x}}{\sqrt{c x+1}}}\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{c}",1,"(-2*(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*ArcCoth[1 - 2/(1 - Sqrt[1 - c*x]/Sqrt[1 + c*x])])/c - (b*(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[2, 1 - 2/(1 + Sqrt[1 - c*x]/Sqrt[1 + c*x])])/c + (b*(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[2, 1 - (2*Sqrt[1 - c*x])/(Sqrt[1 + c*x]*(1 + Sqrt[1 - c*x]/Sqrt[1 + c*x]))])/c - (b^2*PolyLog[3, 1 - 2/(1 + Sqrt[1 - c*x]/Sqrt[1 + c*x])])/(2*c) + (b^2*PolyLog[3, 1 - (2*Sqrt[1 - c*x])/(Sqrt[1 + c*x]*(1 + Sqrt[1 - c*x]/Sqrt[1 + c*x]))])/(2*c)","A",7,6,40,0.1500,1,"{6681, 5915, 6053, 5949, 6057, 6610}"
125,1,89,0,0.0586061,"\int \frac{a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)}{1-c^2 x^2} \, dx","Int[(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])/(1 - c^2*x^2),x]","-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{c x+1}}{\sqrt{1-c x}}\right)}{2 c}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{c x+1}}{\sqrt{1-c x}}\right)}{2 c}-\frac{a \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}{c}","-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{c x+1}}{\sqrt{1-c x}}\right)}{2 c}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{c x+1}}{\sqrt{1-c x}}\right)}{2 c}-\frac{a \log \left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}{c}",1,"-((a*Log[Sqrt[1 - c*x]/Sqrt[1 + c*x]])/c) - (b*PolyLog[2, -(Sqrt[1 + c*x]/Sqrt[1 - c*x])])/(2*c) + (b*PolyLog[2, Sqrt[1 + c*x]/Sqrt[1 - c*x]])/(2*c)","A",2,3,38,0.07895,1,"{206, 6681, 5913}"
126,0,0,0,0.0447068,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)} \, dx","Int[1/((1 - c^2*x^2)*(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])),x]","\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \coth ^{-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 \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)},x\right)",0,"Defer[Int][1/((1 - c^2*x^2)*(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])), x]","A",0,0,0,0,-1,"{}"
127,0,0,0,0.0426659,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2} \, dx","Int[1/((1 - c^2*x^2)*(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2),x]","\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \coth ^{-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 \coth ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2},x\right)",0,"Defer[Int][1/((1 - c^2*x^2)*(a + b*ArcCoth[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2), x]","A",0,0,0,0,-1,"{}"
128,1,37,0,0.027411,"\int x^m \coth ^{-1}(\tanh (a+b x)) \, dx","Int[x^m*ArcCoth[Tanh[a + b*x]],x]","\frac{x^{m+1} \coth ^{-1}(\tanh (a+b x))}{m+1}-\frac{b x^{m+2}}{m^2+3 m+2}","\frac{x^{m+1} \coth ^{-1}(\tanh (a+b x))}{m+1}-\frac{b x^{m+2}}{m^2+3 m+2}",1,"-((b*x^(2 + m))/(2 + 3*m + m^2)) + (x^(1 + m)*ArcCoth[Tanh[a + b*x]])/(1 + m)","A",2,2,11,0.1818,1,"{2168, 30}"
129,1,23,0,0.0090215,"\int x^2 \coth ^{-1}(\tanh (a+b x)) \, dx","Int[x^2*ArcCoth[Tanh[a + b*x]],x]","\frac{1}{3} x^3 \coth ^{-1}(\tanh (a+b x))-\frac{b x^4}{12}","\frac{1}{3} x^3 \coth ^{-1}(\tanh (a+b x))-\frac{b x^4}{12}",1,"-(b*x^4)/12 + (x^3*ArcCoth[Tanh[a + b*x]])/3","A",2,2,11,0.1818,1,"{2168, 30}"
130,1,23,0,0.0074933,"\int x \coth ^{-1}(\tanh (a+b x)) \, dx","Int[x*ArcCoth[Tanh[a + b*x]],x]","\frac{1}{2} x^2 \coth ^{-1}(\tanh (a+b x))-\frac{b x^3}{6}","\frac{1}{2} x^2 \coth ^{-1}(\tanh (a+b x))-\frac{b x^3}{6}",1,"-(b*x^3)/6 + (x^2*ArcCoth[Tanh[a + b*x]])/2","A",2,2,9,0.2222,1,"{6240, 30}"
131,1,16,0,0.003068,"\int \coth ^{-1}(\tanh (a+b x)) \, dx","Int[ArcCoth[Tanh[a + b*x]],x]","\frac{\coth ^{-1}(\tanh (a+b x))^2}{2 b}","\frac{\coth ^{-1}(\tanh (a+b x))^2}{2 b}",1,"ArcCoth[Tanh[a + b*x]]^2/(2*b)","A",2,2,7,0.2857,1,"{2157, 30}"
132,1,21,0,0.0439774,"\int \frac{\coth ^{-1}(\tanh (a+b x))}{x} \, dx","Int[ArcCoth[Tanh[a + b*x]]/x,x]","b x-\log (x) \left(b x-\coth ^{-1}(\tanh (a+b x))\right)","b x-\log (x) \left(b x-\coth ^{-1}(\tanh (a+b x))\right)",1,"b*x - (b*x - ArcCoth[Tanh[a + b*x]])*Log[x]","A",2,2,11,0.1818,1,"{2158, 29}"
133,1,17,0,0.0092769,"\int \frac{\coth ^{-1}(\tanh (a+b x))}{x^2} \, dx","Int[ArcCoth[Tanh[a + b*x]]/x^2,x]","b \log (x)-\frac{\coth ^{-1}(\tanh (a+b x))}{x}","b \log (x)-\frac{\coth ^{-1}(\tanh (a+b x))}{x}",1,"-(ArcCoth[Tanh[a + b*x]]/x) + b*Log[x]","A",2,2,11,0.1818,1,"{2168, 29}"
134,1,23,0,0.0095948,"\int \frac{\coth ^{-1}(\tanh (a+b x))}{x^3} \, dx","Int[ArcCoth[Tanh[a + b*x]]/x^3,x]","-\frac{\coth ^{-1}(\tanh (a+b x))}{2 x^2}-\frac{b}{2 x}","-\frac{\coth ^{-1}(\tanh (a+b x))}{2 x^2}-\frac{b}{2 x}",1,"-b/(2*x) - ArcCoth[Tanh[a + b*x]]/(2*x^2)","A",2,2,11,0.1818,1,"{2168, 30}"
135,1,23,0,0.0088794,"\int \frac{\coth ^{-1}(\tanh (a+b x))}{x^4} \, dx","Int[ArcCoth[Tanh[a + b*x]]/x^4,x]","-\frac{\coth ^{-1}(\tanh (a+b x))}{3 x^3}-\frac{b}{6 x^2}","-\frac{\coth ^{-1}(\tanh (a+b x))}{3 x^3}-\frac{b}{6 x^2}",1,"-b/(6*x^2) - ArcCoth[Tanh[a + b*x]]/(3*x^3)","A",2,2,11,0.1818,1,"{2168, 30}"
136,1,71,0,0.0352614,"\int x^m \coth ^{-1}(\tanh (a+b x))^2 \, dx","Int[x^m*ArcCoth[Tanh[a + b*x]]^2,x]","-\frac{2 b x^{m+2} \coth ^{-1}(\tanh (a+b x))}{m^2+3 m+2}+\frac{x^{m+1} \coth ^{-1}(\tanh (a+b x))^2}{m+1}+\frac{2 b^2 x^{m+3}}{m^3+6 m^2+11 m+6}","-\frac{2 b x^{m+2} \coth ^{-1}(\tanh (a+b x))}{m^2+3 m+2}+\frac{x^{m+1} \coth ^{-1}(\tanh (a+b x))^2}{m+1}+\frac{2 b^2 x^{m+3}}{m^3+6 m^2+11 m+6}",1,"(2*b^2*x^(3 + m))/(6 + 11*m + 6*m^2 + m^3) - (2*b*x^(2 + m)*ArcCoth[Tanh[a + b*x]])/(2 + 3*m + m^2) + (x^(1 + m)*ArcCoth[Tanh[a + b*x]]^2)/(1 + m)","A",3,2,13,0.1538,1,"{2168, 30}"
137,1,42,0,0.0260149,"\int x^3 \coth ^{-1}(\tanh (a+b x))^2 \, dx","Int[x^3*ArcCoth[Tanh[a + b*x]]^2,x]","-\frac{1}{10} b x^5 \coth ^{-1}(\tanh (a+b x))+\frac{1}{4} x^4 \coth ^{-1}(\tanh (a+b x))^2+\frac{b^2 x^6}{60}","-\frac{1}{10} b x^5 \coth ^{-1}(\tanh (a+b x))+\frac{1}{4} x^4 \coth ^{-1}(\tanh (a+b x))^2+\frac{b^2 x^6}{60}",1,"(b^2*x^6)/60 - (b*x^5*ArcCoth[Tanh[a + b*x]])/10 + (x^4*ArcCoth[Tanh[a + b*x]]^2)/4","A",3,2,13,0.1538,1,"{2168, 30}"
138,1,42,0,0.02533,"\int x^2 \coth ^{-1}(\tanh (a+b x))^2 \, dx","Int[x^2*ArcCoth[Tanh[a + b*x]]^2,x]","-\frac{1}{6} b x^4 \coth ^{-1}(\tanh (a+b x))+\frac{1}{3} x^3 \coth ^{-1}(\tanh (a+b x))^2+\frac{b^2 x^5}{30}","-\frac{1}{6} b x^4 \coth ^{-1}(\tanh (a+b x))+\frac{1}{3} x^3 \coth ^{-1}(\tanh (a+b x))^2+\frac{b^2 x^5}{30}",1,"(b^2*x^5)/30 - (b*x^4*ArcCoth[Tanh[a + b*x]])/6 + (x^3*ArcCoth[Tanh[a + b*x]]^2)/3","A",3,2,13,0.1538,1,"{2168, 30}"
139,1,34,0,0.0253549,"\int x \coth ^{-1}(\tanh (a+b x))^2 \, dx","Int[x*ArcCoth[Tanh[a + b*x]]^2,x]","\frac{x \coth ^{-1}(\tanh (a+b x))^3}{3 b}-\frac{\coth ^{-1}(\tanh (a+b x))^4}{12 b^2}","\frac{x \coth ^{-1}(\tanh (a+b x))^3}{3 b}-\frac{\coth ^{-1}(\tanh (a+b x))^4}{12 b^2}",1,"(x*ArcCoth[Tanh[a + b*x]]^3)/(3*b) - ArcCoth[Tanh[a + b*x]]^4/(12*b^2)","A",3,3,11,0.2727,1,"{2168, 2157, 30}"
140,1,16,0,0.0053532,"\int \coth ^{-1}(\tanh (a+b x))^2 \, dx","Int[ArcCoth[Tanh[a + b*x]]^2,x]","\frac{\coth ^{-1}(\tanh (a+b x))^3}{3 b}","\frac{\coth ^{-1}(\tanh (a+b x))^3}{3 b}",1,"ArcCoth[Tanh[a + b*x]]^3/(3*b)","A",2,2,9,0.2222,1,"{2157, 30}"
141,1,49,0,0.0259427,"\int \frac{\coth ^{-1}(\tanh (a+b x))^2}{x} \, dx","Int[ArcCoth[Tanh[a + b*x]]^2/x,x]","-b x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)+\frac{1}{2} \coth ^{-1}(\tanh (a+b x))^2+\log (x) \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2","-b x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)+\frac{1}{2} \coth ^{-1}(\tanh (a+b x))^2+\log (x) \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2",1,"-(b*x*(b*x - ArcCoth[Tanh[a + b*x]])) + ArcCoth[Tanh[a + b*x]]^2/2 + (b*x - ArcCoth[Tanh[a + b*x]])^2*Log[x]","A",3,3,13,0.2308,1,"{2159, 2158, 29}"
142,1,39,0,0.0258467,"\int \frac{\coth ^{-1}(\tanh (a+b x))^2}{x^2} \, dx","Int[ArcCoth[Tanh[a + b*x]]^2/x^2,x]","-\frac{\coth ^{-1}(\tanh (a+b x))^2}{x}-2 b \log (x) \left(b x-\coth ^{-1}(\tanh (a+b x))\right)+2 b^2 x","-\frac{\coth ^{-1}(\tanh (a+b x))^2}{x}-2 b \log (x) \left(b x-\coth ^{-1}(\tanh (a+b x))\right)+2 b^2 x",1,"2*b^2*x - ArcCoth[Tanh[a + b*x]]^2/x - 2*b*(b*x - ArcCoth[Tanh[a + b*x]])*Log[x]","A",3,3,13,0.2308,1,"{2168, 2158, 29}"
143,1,36,0,0.0228216,"\int \frac{\coth ^{-1}(\tanh (a+b x))^2}{x^3} \, dx","Int[ArcCoth[Tanh[a + b*x]]^2/x^3,x]","-\frac{\coth ^{-1}(\tanh (a+b x))^2}{2 x^2}-\frac{b \coth ^{-1}(\tanh (a+b x))}{x}+b^2 \log (x)","-\frac{\coth ^{-1}(\tanh (a+b x))^2}{2 x^2}-\frac{b \coth ^{-1}(\tanh (a+b x))}{x}+b^2 \log (x)",1,"-((b*ArcCoth[Tanh[a + b*x]])/x) - ArcCoth[Tanh[a + b*x]]^2/(2*x^2) + b^2*Log[x]","A",3,2,13,0.1538,1,"{2168, 29}"
144,1,31,0,0.0135441,"\int \frac{\coth ^{-1}(\tanh (a+b x))^2}{x^4} \, dx","Int[ArcCoth[Tanh[a + b*x]]^2/x^4,x]","\frac{\coth ^{-1}(\tanh (a+b x))^3}{3 x^3 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}","\frac{\coth ^{-1}(\tanh (a+b x))^3}{3 x^3 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}",1,"ArcCoth[Tanh[a + b*x]]^3/(3*x^3*(b*x - ArcCoth[Tanh[a + b*x]]))","A",1,1,13,0.07692,1,"{2167}"
145,1,64,0,0.0351377,"\int \frac{\coth ^{-1}(\tanh (a+b x))^2}{x^5} \, dx","Int[ArcCoth[Tanh[a + b*x]]^2/x^5,x]","\frac{\coth ^{-1}(\tanh (a+b x))^3}{4 x^4 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}+\frac{b \coth ^{-1}(\tanh (a+b x))^3}{12 x^3 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}","\frac{\coth ^{-1}(\tanh (a+b x))^3}{4 x^4 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}+\frac{b \coth ^{-1}(\tanh (a+b x))^3}{12 x^3 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}",1,"(b*ArcCoth[Tanh[a + b*x]]^3)/(12*x^3*(b*x - ArcCoth[Tanh[a + b*x]])^2) + ArcCoth[Tanh[a + b*x]]^3/(4*x^4*(b*x - ArcCoth[Tanh[a + b*x]]))","A",2,2,13,0.1538,1,"{2171, 2167}"
146,1,110,0,0.0593837,"\int x^m \coth ^{-1}(\tanh (a+b x))^3 \, dx","Int[x^m*ArcCoth[Tanh[a + b*x]]^3,x]","\frac{6 b^2 x^{m+3} \coth ^{-1}(\tanh (a+b x))}{m^3+6 m^2+11 m+6}-\frac{3 b x^{m+2} \coth ^{-1}(\tanh (a+b x))^2}{m^2+3 m+2}+\frac{x^{m+1} \coth ^{-1}(\tanh (a+b x))^3}{m+1}-\frac{6 b^3 x^{m+4}}{(m+1) \left(m^3+9 m^2+26 m+24\right)}","\frac{6 b^2 x^{m+3} \coth ^{-1}(\tanh (a+b x))}{m^3+6 m^2+11 m+6}-\frac{3 b x^{m+2} \coth ^{-1}(\tanh (a+b x))^2}{m^2+3 m+2}+\frac{x^{m+1} \coth ^{-1}(\tanh (a+b x))^3}{m+1}-\frac{6 b^3 x^{m+4}}{(m+1) \left(m^3+9 m^2+26 m+24\right)}",1,"(-6*b^3*x^(4 + m))/((1 + m)*(24 + 26*m + 9*m^2 + m^3)) + (6*b^2*x^(3 + m)*ArcCoth[Tanh[a + b*x]])/(6 + 11*m + 6*m^2 + m^3) - (3*b*x^(2 + m)*ArcCoth[Tanh[a + b*x]]^2)/(2 + 3*m + m^2) + (x^(1 + m)*ArcCoth[Tanh[a + b*x]]^3)/(1 + m)","A",4,2,13,0.1538,1,"{2168, 30}"
147,1,61,0,0.0411641,"\int x^4 \coth ^{-1}(\tanh (a+b x))^3 \, dx","Int[x^4*ArcCoth[Tanh[a + b*x]]^3,x]","\frac{1}{35} b^2 x^7 \coth ^{-1}(\tanh (a+b x))-\frac{1}{10} b x^6 \coth ^{-1}(\tanh (a+b x))^2+\frac{1}{5} x^5 \coth ^{-1}(\tanh (a+b x))^3-\frac{1}{280} b^3 x^8","\frac{1}{35} b^2 x^7 \coth ^{-1}(\tanh (a+b x))-\frac{1}{10} b x^6 \coth ^{-1}(\tanh (a+b x))^2+\frac{1}{5} x^5 \coth ^{-1}(\tanh (a+b x))^3-\frac{1}{280} b^3 x^8",1,"-(b^3*x^8)/280 + (b^2*x^7*ArcCoth[Tanh[a + b*x]])/35 - (b*x^6*ArcCoth[Tanh[a + b*x]]^2)/10 + (x^5*ArcCoth[Tanh[a + b*x]]^3)/5","A",4,2,13,0.1538,1,"{2168, 30}"
148,1,61,0,0.0407912,"\int x^3 \coth ^{-1}(\tanh (a+b x))^3 \, dx","Int[x^3*ArcCoth[Tanh[a + b*x]]^3,x]","\frac{1}{20} b^2 x^6 \coth ^{-1}(\tanh (a+b x))-\frac{3}{20} b x^5 \coth ^{-1}(\tanh (a+b x))^2+\frac{1}{4} x^4 \coth ^{-1}(\tanh (a+b x))^3-\frac{1}{140} b^3 x^7","\frac{1}{20} b^2 x^6 \coth ^{-1}(\tanh (a+b x))-\frac{3}{20} b x^5 \coth ^{-1}(\tanh (a+b x))^2+\frac{1}{4} x^4 \coth ^{-1}(\tanh (a+b x))^3-\frac{1}{140} b^3 x^7",1,"-(b^3*x^7)/140 + (b^2*x^6*ArcCoth[Tanh[a + b*x]])/20 - (3*b*x^5*ArcCoth[Tanh[a + b*x]]^2)/20 + (x^4*ArcCoth[Tanh[a + b*x]]^3)/4","A",4,2,13,0.1538,1,"{2168, 30}"
149,1,53,0,0.0312969,"\int x^2 \coth ^{-1}(\tanh (a+b x))^3 \, dx","Int[x^2*ArcCoth[Tanh[a + b*x]]^3,x]","\frac{\coth ^{-1}(\tanh (a+b x))^6}{60 b^3}-\frac{x \coth ^{-1}(\tanh (a+b x))^5}{10 b^2}+\frac{x^2 \coth ^{-1}(\tanh (a+b x))^4}{4 b}","\frac{\coth ^{-1}(\tanh (a+b x))^6}{60 b^3}-\frac{x \coth ^{-1}(\tanh (a+b x))^5}{10 b^2}+\frac{x^2 \coth ^{-1}(\tanh (a+b x))^4}{4 b}",1,"(x^2*ArcCoth[Tanh[a + b*x]]^4)/(4*b) - (x*ArcCoth[Tanh[a + b*x]]^5)/(10*b^2) + ArcCoth[Tanh[a + b*x]]^6/(60*b^3)","A",4,3,13,0.2308,1,"{2168, 2157, 30}"
150,1,34,0,0.0149233,"\int x \coth ^{-1}(\tanh (a+b x))^3 \, dx","Int[x*ArcCoth[Tanh[a + b*x]]^3,x]","\frac{x \coth ^{-1}(\tanh (a+b x))^4}{4 b}-\frac{\coth ^{-1}(\tanh (a+b x))^5}{20 b^2}","\frac{x \coth ^{-1}(\tanh (a+b x))^4}{4 b}-\frac{\coth ^{-1}(\tanh (a+b x))^5}{20 b^2}",1,"(x*ArcCoth[Tanh[a + b*x]]^4)/(4*b) - ArcCoth[Tanh[a + b*x]]^5/(20*b^2)","A",3,3,11,0.2727,1,"{2168, 2157, 30}"
151,1,16,0,0.0051923,"\int \coth ^{-1}(\tanh (a+b x))^3 \, dx","Int[ArcCoth[Tanh[a + b*x]]^3,x]","\frac{\coth ^{-1}(\tanh (a+b x))^4}{4 b}","\frac{\coth ^{-1}(\tanh (a+b x))^4}{4 b}",1,"ArcCoth[Tanh[a + b*x]]^4/(4*b)","A",2,2,9,0.2222,1,"{2157, 30}"
152,1,77,0,0.0962767,"\int \frac{\coth ^{-1}(\tanh (a+b x))^3}{x} \, dx","Int[ArcCoth[Tanh[a + b*x]]^3/x,x]","b x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2-\frac{1}{2} \coth ^{-1}(\tanh (a+b x))^2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)+\frac{1}{3} \coth ^{-1}(\tanh (a+b x))^3-\log (x) \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3","b x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2-\frac{1}{2} \coth ^{-1}(\tanh (a+b x))^2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)+\frac{1}{3} \coth ^{-1}(\tanh (a+b x))^3-\log (x) \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3",1,"b*x*(b*x - ArcCoth[Tanh[a + b*x]])^2 - ((b*x - ArcCoth[Tanh[a + b*x]])*ArcCoth[Tanh[a + b*x]]^2)/2 + ArcCoth[Tanh[a + b*x]]^3/3 - (b*x - ArcCoth[Tanh[a + b*x]])^3*Log[x]","A",4,3,13,0.2308,1,"{2159, 2158, 29}"
153,1,68,0,0.0435156,"\int \frac{\coth ^{-1}(\tanh (a+b x))^3}{x^2} \, dx","Int[ArcCoth[Tanh[a + b*x]]^3/x^2,x]","-3 b^2 x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)-\frac{\coth ^{-1}(\tanh (a+b x))^3}{x}+\frac{3}{2} b \coth ^{-1}(\tanh (a+b x))^2+3 b \log (x) \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2","-3 b^2 x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)-\frac{\coth ^{-1}(\tanh (a+b x))^3}{x}+\frac{3}{2} b \coth ^{-1}(\tanh (a+b x))^2+3 b \log (x) \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2",1,"-3*b^2*x*(b*x - ArcCoth[Tanh[a + b*x]]) + (3*b*ArcCoth[Tanh[a + b*x]]^2)/2 - ArcCoth[Tanh[a + b*x]]^3/x + 3*b*(b*x - ArcCoth[Tanh[a + b*x]])^2*Log[x]","A",4,4,13,0.3077,1,"{2168, 2159, 2158, 29}"
154,1,60,0,0.0411344,"\int \frac{\coth ^{-1}(\tanh (a+b x))^3}{x^3} \, dx","Int[ArcCoth[Tanh[a + b*x]]^3/x^3,x]","-3 b^2 \log (x) \left(b x-\coth ^{-1}(\tanh (a+b x))\right)-\frac{\coth ^{-1}(\tanh (a+b x))^3}{2 x^2}-\frac{3 b \coth ^{-1}(\tanh (a+b x))^2}{2 x}+3 b^3 x","-3 b^2 \log (x) \left(b x-\coth ^{-1}(\tanh (a+b x))\right)-\frac{\coth ^{-1}(\tanh (a+b x))^3}{2 x^2}-\frac{3 b \coth ^{-1}(\tanh (a+b x))^2}{2 x}+3 b^3 x",1,"3*b^3*x - (3*b*ArcCoth[Tanh[a + b*x]]^2)/(2*x) - ArcCoth[Tanh[a + b*x]]^3/(2*x^2) - 3*b^2*(b*x - ArcCoth[Tanh[a + b*x]])*Log[x]","A",4,3,13,0.2308,1,"{2168, 2158, 29}"
155,1,55,0,0.0381152,"\int \frac{\coth ^{-1}(\tanh (a+b x))^3}{x^4} \, dx","Int[ArcCoth[Tanh[a + b*x]]^3/x^4,x]","-\frac{b^2 \coth ^{-1}(\tanh (a+b x))}{x}-\frac{b \coth ^{-1}(\tanh (a+b x))^2}{2 x^2}-\frac{\coth ^{-1}(\tanh (a+b x))^3}{3 x^3}+b^3 \log (x)","-\frac{b^2 \coth ^{-1}(\tanh (a+b x))}{x}-\frac{b \coth ^{-1}(\tanh (a+b x))^2}{2 x^2}-\frac{\coth ^{-1}(\tanh (a+b x))^3}{3 x^3}+b^3 \log (x)",1,"-((b^2*ArcCoth[Tanh[a + b*x]])/x) - (b*ArcCoth[Tanh[a + b*x]]^2)/(2*x^2) - ArcCoth[Tanh[a + b*x]]^3/(3*x^3) + b^3*Log[x]","A",4,2,13,0.1538,1,"{2168, 29}"
156,1,31,0,0.0137358,"\int \frac{\coth ^{-1}(\tanh (a+b x))^3}{x^5} \, dx","Int[ArcCoth[Tanh[a + b*x]]^3/x^5,x]","\frac{\coth ^{-1}(\tanh (a+b x))^4}{4 x^4 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}","\frac{\coth ^{-1}(\tanh (a+b x))^4}{4 x^4 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}",1,"ArcCoth[Tanh[a + b*x]]^4/(4*x^4*(b*x - ArcCoth[Tanh[a + b*x]]))","A",1,1,13,0.07692,1,"{2167}"
157,1,64,0,0.0335485,"\int \frac{\coth ^{-1}(\tanh (a+b x))^3}{x^6} \, dx","Int[ArcCoth[Tanh[a + b*x]]^3/x^6,x]","\frac{\coth ^{-1}(\tanh (a+b x))^4}{5 x^5 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}+\frac{b \coth ^{-1}(\tanh (a+b x))^4}{20 x^4 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}","\frac{\coth ^{-1}(\tanh (a+b x))^4}{5 x^5 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}+\frac{b \coth ^{-1}(\tanh (a+b x))^4}{20 x^4 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}",1,"(b*ArcCoth[Tanh[a + b*x]]^4)/(20*x^4*(b*x - ArcCoth[Tanh[a + b*x]])^2) + ArcCoth[Tanh[a + b*x]]^4/(5*x^5*(b*x - ArcCoth[Tanh[a + b*x]]))","A",2,2,13,0.1538,1,"{2171, 2167}"
158,1,53,0,0.0284971,"\int \frac{x^m}{\coth ^{-1}(\tanh (a+b x))} \, dx","Int[x^m/ArcCoth[Tanh[a + b*x]],x]","-\frac{x^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{b x}{b x-\coth ^{-1}(\tanh (a+b x))}\right)}{(m+1) \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}","-\frac{x^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{b x}{b x-\coth ^{-1}(\tanh (a+b x))}\right)}{(m+1) \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}",1,"-((x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (b*x)/(b*x - ArcCoth[Tanh[a + b*x]])])/((1 + m)*(b*x - ArcCoth[Tanh[a + b*x]])))","A",1,1,13,0.07692,1,"{2164}"
159,1,81,0,0.0588508,"\int \frac{x^3}{\coth ^{-1}(\tanh (a+b x))} \, dx","Int[x^3/ArcCoth[Tanh[a + b*x]],x]","\frac{x^2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}{2 b^2}+\frac{x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}{b^3}+\frac{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3 \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^4}+\frac{x^3}{3 b}","\frac{x^2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}{2 b^2}+\frac{x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}{b^3}+\frac{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3 \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^4}+\frac{x^3}{3 b}",1,"x^3/(3*b) + (x^2*(b*x - ArcCoth[Tanh[a + b*x]]))/(2*b^2) + (x*(b*x - ArcCoth[Tanh[a + b*x]])^2)/b^3 + ((b*x - ArcCoth[Tanh[a + b*x]])^3*Log[ArcCoth[Tanh[a + b*x]]])/b^4","A",5,4,13,0.3077,1,"{2159, 2158, 2157, 29}"
160,1,56,0,0.0346625,"\int \frac{x^2}{\coth ^{-1}(\tanh (a+b x))} \, dx","Int[x^2/ArcCoth[Tanh[a + b*x]],x]","\frac{x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}{b^2}+\frac{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2 \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^3}+\frac{x^2}{2 b}","\frac{x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}{b^2}+\frac{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2 \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^3}+\frac{x^2}{2 b}",1,"x^2/(2*b) + (x*(b*x - ArcCoth[Tanh[a + b*x]]))/b^2 + ((b*x - ArcCoth[Tanh[a + b*x]])^2*Log[ArcCoth[Tanh[a + b*x]]])/b^3","A",4,4,13,0.3077,1,"{2159, 2158, 2157, 29}"
161,1,31,0,0.0150948,"\int \frac{x}{\coth ^{-1}(\tanh (a+b x))} \, dx","Int[x/ArcCoth[Tanh[a + b*x]],x]","\frac{\left(b x-\coth ^{-1}(\tanh (a+b x))\right) \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^2}+\frac{x}{b}","\frac{\left(b x-\coth ^{-1}(\tanh (a+b x))\right) \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^2}+\frac{x}{b}",1,"x/b + ((b*x - ArcCoth[Tanh[a + b*x]])*Log[ArcCoth[Tanh[a + b*x]]])/b^2","A",3,3,11,0.2727,1,"{2158, 2157, 29}"
162,1,12,0,0.0040205,"\int \frac{1}{\coth ^{-1}(\tanh (a+b x))} \, dx","Int[ArcCoth[Tanh[a + b*x]]^(-1),x]","\frac{\log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b}","\frac{\log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b}",1,"Log[ArcCoth[Tanh[a + b*x]]]/b","A",2,2,9,0.2222,1,"{2157, 29}"
163,1,44,0,0.0284736,"\int \frac{1}{x \coth ^{-1}(\tanh (a+b x))} \, dx","Int[1/(x*ArcCoth[Tanh[a + b*x]]),x]","\frac{\log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b x-\coth ^{-1}(\tanh (a+b x))}-\frac{\log (x)}{b x-\coth ^{-1}(\tanh (a+b x))}","\frac{\log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b x-\coth ^{-1}(\tanh (a+b x))}-\frac{\log (x)}{b x-\coth ^{-1}(\tanh (a+b x))}",1,"-(Log[x]/(b*x - ArcCoth[Tanh[a + b*x]])) + Log[ArcCoth[Tanh[a + b*x]]]/(b*x - ArcCoth[Tanh[a + b*x]])","A",4,3,13,0.2308,1,"{2160, 2157, 29}"
164,1,65,0,0.0378546,"\int \frac{1}{x^2 \coth ^{-1}(\tanh (a+b x))} \, dx","Int[1/(x^2*ArcCoth[Tanh[a + b*x]]),x]","\frac{1}{x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}-\frac{b \log (x)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}+\frac{b \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}","\frac{1}{x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}-\frac{b \log (x)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}+\frac{b \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}",1,"1/(x*(b*x - ArcCoth[Tanh[a + b*x]])) - (b*Log[x])/(b*x - ArcCoth[Tanh[a + b*x]])^2 + (b*Log[ArcCoth[Tanh[a + b*x]]])/(b*x - ArcCoth[Tanh[a + b*x]])^2","A",5,4,13,0.3077,1,"{2163, 2160, 2157, 29}"
165,1,92,0,0.0628528,"\int \frac{1}{x^3 \coth ^{-1}(\tanh (a+b x))} \, dx","Int[1/(x^3*ArcCoth[Tanh[a + b*x]]),x]","-\frac{b^2 \log (x)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3}+\frac{b^2 \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3}+\frac{1}{2 x^2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}+\frac{b}{x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}","-\frac{b^2 \log (x)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3}+\frac{b^2 \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3}+\frac{1}{2 x^2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}+\frac{b}{x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}",1,"b/(x*(b*x - ArcCoth[Tanh[a + b*x]])^2) + 1/(2*x^2*(b*x - ArcCoth[Tanh[a + b*x]])) - (b^2*Log[x])/(b*x - ArcCoth[Tanh[a + b*x]])^3 + (b^2*Log[ArcCoth[Tanh[a + b*x]]])/(b*x - ArcCoth[Tanh[a + b*x]])^3","A",6,4,13,0.3077,1,"{2163, 2160, 2157, 29}"
166,1,65,0,0.0390504,"\int \frac{x^m}{\coth ^{-1}(\tanh (a+b x))^2} \, dx","Int[x^m/ArcCoth[Tanh[a + b*x]]^2,x]","-\frac{x^m \, _2F_1\left(1,m;m+1;\frac{b x}{b x-\coth ^{-1}(\tanh (a+b x))}\right)}{b \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}-\frac{x^m}{b \coth ^{-1}(\tanh (a+b x))}","-\frac{x^m \, _2F_1\left(1,m;m+1;\frac{b x}{b x-\coth ^{-1}(\tanh (a+b x))}\right)}{b \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}-\frac{x^m}{b \coth ^{-1}(\tanh (a+b x))}",1,"-(x^m/(b*ArcCoth[Tanh[a + b*x]])) - (x^m*Hypergeometric2F1[1, m, 1 + m, (b*x)/(b*x - ArcCoth[Tanh[a + b*x]])])/(b*(b*x - ArcCoth[Tanh[a + b*x]]))","A",2,2,13,0.1538,1,"{2168, 2164}"
167,1,98,0,0.0808205,"\int \frac{x^4}{\coth ^{-1}(\tanh (a+b x))^2} \, dx","Int[x^4/ArcCoth[Tanh[a + b*x]]^2,x]","\frac{2 x^2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}{b^3}+\frac{4 x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}{b^4}+\frac{4 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3 \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^5}-\frac{x^4}{b \coth ^{-1}(\tanh (a+b x))}+\frac{4 x^3}{3 b^2}","\frac{2 x^2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}{b^3}+\frac{4 x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}{b^4}+\frac{4 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3 \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^5}-\frac{x^4}{b \coth ^{-1}(\tanh (a+b x))}+\frac{4 x^3}{3 b^2}",1,"(4*x^3)/(3*b^2) + (2*x^2*(b*x - ArcCoth[Tanh[a + b*x]]))/b^3 + (4*x*(b*x - ArcCoth[Tanh[a + b*x]])^2)/b^4 - x^4/(b*ArcCoth[Tanh[a + b*x]]) + (4*(b*x - ArcCoth[Tanh[a + b*x]])^3*Log[ArcCoth[Tanh[a + b*x]]])/b^5","A",6,5,13,0.3846,1,"{2168, 2159, 2158, 2157, 29}"
168,1,75,0,0.0537226,"\int \frac{x^3}{\coth ^{-1}(\tanh (a+b x))^2} \, dx","Int[x^3/ArcCoth[Tanh[a + b*x]]^2,x]","\frac{3 x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}{b^3}+\frac{3 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2 \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^4}-\frac{x^3}{b \coth ^{-1}(\tanh (a+b x))}+\frac{3 x^2}{2 b^2}","\frac{3 x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}{b^3}+\frac{3 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2 \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^4}-\frac{x^3}{b \coth ^{-1}(\tanh (a+b x))}+\frac{3 x^2}{2 b^2}",1,"(3*x^2)/(2*b^2) + (3*x*(b*x - ArcCoth[Tanh[a + b*x]]))/b^3 - x^3/(b*ArcCoth[Tanh[a + b*x]]) + (3*(b*x - ArcCoth[Tanh[a + b*x]])^2*Log[ArcCoth[Tanh[a + b*x]]])/b^4","A",5,5,13,0.3846,1,"{2168, 2159, 2158, 2157, 29}"
169,1,50,0,0.031317,"\int \frac{x^2}{\coth ^{-1}(\tanh (a+b x))^2} \, dx","Int[x^2/ArcCoth[Tanh[a + b*x]]^2,x]","\frac{2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right) \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^3}-\frac{x^2}{b \coth ^{-1}(\tanh (a+b x))}+\frac{2 x}{b^2}","\frac{2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right) \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^3}-\frac{x^2}{b \coth ^{-1}(\tanh (a+b x))}+\frac{2 x}{b^2}",1,"(2*x)/b^2 - x^2/(b*ArcCoth[Tanh[a + b*x]]) + (2*(b*x - ArcCoth[Tanh[a + b*x]])*Log[ArcCoth[Tanh[a + b*x]]])/b^3","A",4,4,13,0.3077,1,"{2168, 2158, 2157, 29}"
170,1,28,0,0.013374,"\int \frac{x}{\coth ^{-1}(\tanh (a+b x))^2} \, dx","Int[x/ArcCoth[Tanh[a + b*x]]^2,x]","\frac{\log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^2}-\frac{x}{b \coth ^{-1}(\tanh (a+b x))}","\frac{\log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^2}-\frac{x}{b \coth ^{-1}(\tanh (a+b x))}",1,"-(x/(b*ArcCoth[Tanh[a + b*x]])) + Log[ArcCoth[Tanh[a + b*x]]]/b^2","A",3,3,11,0.2727,1,"{2168, 2157, 29}"
171,1,14,0,0.0048201,"\int \frac{1}{\coth ^{-1}(\tanh (a+b x))^2} \, dx","Int[ArcCoth[Tanh[a + b*x]]^(-2),x]","-\frac{1}{b \coth ^{-1}(\tanh (a+b x))}","-\frac{1}{b \coth ^{-1}(\tanh (a+b x))}",1,"-(1/(b*ArcCoth[Tanh[a + b*x]]))","A",2,2,9,0.2222,1,"{2157, 30}"
172,1,70,0,0.0479788,"\int \frac{1}{x \coth ^{-1}(\tanh (a+b x))^2} \, dx","Int[1/(x*ArcCoth[Tanh[a + b*x]]^2),x]","-\frac{1}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right) \coth ^{-1}(\tanh (a+b x))}+\frac{\log (x)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}-\frac{\log \left(\coth ^{-1}(\tanh (a+b x))\right)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}","-\frac{1}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right) \coth ^{-1}(\tanh (a+b x))}+\frac{\log (x)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}-\frac{\log \left(\coth ^{-1}(\tanh (a+b x))\right)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2}",1,"-(1/((b*x - ArcCoth[Tanh[a + b*x]])*ArcCoth[Tanh[a + b*x]])) + Log[x]/(b*x - ArcCoth[Tanh[a + b*x]])^2 - Log[ArcCoth[Tanh[a + b*x]]]/(b*x - ArcCoth[Tanh[a + b*x]])^2","A",5,4,13,0.3077,1,"{2163, 2160, 2157, 29}"
173,1,102,0,0.0626622,"\int \frac{1}{x^2 \coth ^{-1}(\tanh (a+b x))^2} \, dx","Int[1/(x^2*ArcCoth[Tanh[a + b*x]]^2),x]","-\frac{2 b}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2 \coth ^{-1}(\tanh (a+b x))}+\frac{1}{x \left(b x-\coth ^{-1}(\tanh (a+b x))\right) \coth ^{-1}(\tanh (a+b x))}+\frac{2 b \log (x)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3}-\frac{2 b \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3}","-\frac{2 b}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2 \coth ^{-1}(\tanh (a+b x))}+\frac{1}{x \left(b x-\coth ^{-1}(\tanh (a+b x))\right) \coth ^{-1}(\tanh (a+b x))}+\frac{2 b \log (x)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3}-\frac{2 b \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3}",1,"(-2*b)/((b*x - ArcCoth[Tanh[a + b*x]])^2*ArcCoth[Tanh[a + b*x]]) + 1/(x*(b*x - ArcCoth[Tanh[a + b*x]])*ArcCoth[Tanh[a + b*x]]) + (2*b*Log[x])/(b*x - ArcCoth[Tanh[a + b*x]])^3 - (2*b*Log[ArcCoth[Tanh[a + b*x]]])/(b*x - ArcCoth[Tanh[a + b*x]])^3","A",6,5,13,0.3846,1,"{2171, 2163, 2160, 2157, 29}"
174,1,143,0,0.0896868,"\int \frac{1}{x^3 \coth ^{-1}(\tanh (a+b x))^2} \, dx","Int[1/(x^3*ArcCoth[Tanh[a + b*x]]^2),x]","-\frac{3 b^2}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3 \coth ^{-1}(\tanh (a+b x))}+\frac{3 b^2 \log (x)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^4}-\frac{3 b^2 \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^4}+\frac{1}{2 x^2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right) \coth ^{-1}(\tanh (a+b x))}+\frac{3 b}{2 x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2 \coth ^{-1}(\tanh (a+b x))}","-\frac{3 b^2}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3 \coth ^{-1}(\tanh (a+b x))}+\frac{3 b^2 \log (x)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^4}-\frac{3 b^2 \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^4}+\frac{1}{2 x^2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right) \coth ^{-1}(\tanh (a+b x))}+\frac{3 b}{2 x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2 \coth ^{-1}(\tanh (a+b x))}",1,"(-3*b^2)/((b*x - ArcCoth[Tanh[a + b*x]])^3*ArcCoth[Tanh[a + b*x]]) + (3*b)/(2*x*(b*x - ArcCoth[Tanh[a + b*x]])^2*ArcCoth[Tanh[a + b*x]]) + 1/(2*x^2*(b*x - ArcCoth[Tanh[a + b*x]])*ArcCoth[Tanh[a + b*x]]) + (3*b^2*Log[x])/(b*x - ArcCoth[Tanh[a + b*x]])^4 - (3*b^2*Log[ArcCoth[Tanh[a + b*x]]])/(b*x - ArcCoth[Tanh[a + b*x]])^4","A",7,5,13,0.3846,1,"{2171, 2163, 2160, 2157, 29}"
175,1,94,0,0.0599338,"\int \frac{x^m}{\coth ^{-1}(\tanh (a+b x))^3} \, dx","Int[x^m/ArcCoth[Tanh[a + b*x]]^3,x]","-\frac{m x^{m-1} \, _2F_1\left(1,m-1;m;\frac{b x}{b x-\coth ^{-1}(\tanh (a+b x))}\right)}{2 b^2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}-\frac{m x^{m-1}}{2 b^2 \coth ^{-1}(\tanh (a+b x))}-\frac{x^m}{2 b \coth ^{-1}(\tanh (a+b x))^2}","-\frac{m x^{m-1} \, _2F_1\left(1,m-1;m;\frac{b x}{b x-\coth ^{-1}(\tanh (a+b x))}\right)}{2 b^2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}-\frac{m x^{m-1}}{2 b^2 \coth ^{-1}(\tanh (a+b x))}-\frac{x^m}{2 b \coth ^{-1}(\tanh (a+b x))^2}",1,"-x^m/(2*b*ArcCoth[Tanh[a + b*x]]^2) - (m*x^(-1 + m))/(2*b^2*ArcCoth[Tanh[a + b*x]]) - (m*x^(-1 + m)*Hypergeometric2F1[1, -1 + m, m, (b*x)/(b*x - ArcCoth[Tanh[a + b*x]])])/(2*b^2*(b*x - ArcCoth[Tanh[a + b*x]]))","A",3,2,13,0.1538,1,"{2168, 2164}"
176,1,92,0,0.0712986,"\int \frac{x^4}{\coth ^{-1}(\tanh (a+b x))^3} \, dx","Int[x^4/ArcCoth[Tanh[a + b*x]]^3,x]","-\frac{2 x^3}{b^2 \coth ^{-1}(\tanh (a+b x))}+\frac{6 x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}{b^4}+\frac{6 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2 \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^5}-\frac{x^4}{2 b \coth ^{-1}(\tanh (a+b x))^2}+\frac{3 x^2}{b^3}","-\frac{2 x^3}{b^2 \coth ^{-1}(\tanh (a+b x))}+\frac{6 x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}{b^4}+\frac{6 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2 \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^5}-\frac{x^4}{2 b \coth ^{-1}(\tanh (a+b x))^2}+\frac{3 x^2}{b^3}",1,"(3*x^2)/b^3 + (6*x*(b*x - ArcCoth[Tanh[a + b*x]]))/b^4 - x^4/(2*b*ArcCoth[Tanh[a + b*x]]^2) - (2*x^3)/(b^2*ArcCoth[Tanh[a + b*x]]) + (6*(b*x - ArcCoth[Tanh[a + b*x]])^2*Log[ArcCoth[Tanh[a + b*x]]])/b^5","A",6,5,13,0.3846,1,"{2168, 2159, 2158, 2157, 29}"
177,1,71,0,0.0491256,"\int \frac{x^3}{\coth ^{-1}(\tanh (a+b x))^3} \, dx","Int[x^3/ArcCoth[Tanh[a + b*x]]^3,x]","-\frac{3 x^2}{2 b^2 \coth ^{-1}(\tanh (a+b x))}+\frac{3 \left(b x-\coth ^{-1}(\tanh (a+b x))\right) \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^4}-\frac{x^3}{2 b \coth ^{-1}(\tanh (a+b x))^2}+\frac{3 x}{b^3}","-\frac{3 x^2}{2 b^2 \coth ^{-1}(\tanh (a+b x))}+\frac{3 \left(b x-\coth ^{-1}(\tanh (a+b x))\right) \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^4}-\frac{x^3}{2 b \coth ^{-1}(\tanh (a+b x))^2}+\frac{3 x}{b^3}",1,"(3*x)/b^3 - x^3/(2*b*ArcCoth[Tanh[a + b*x]]^2) - (3*x^2)/(2*b^2*ArcCoth[Tanh[a + b*x]]) + (3*(b*x - ArcCoth[Tanh[a + b*x]])*Log[ArcCoth[Tanh[a + b*x]]])/b^4","A",5,4,13,0.3077,1,"{2168, 2158, 2157, 29}"
178,1,47,0,0.0286383,"\int \frac{x^2}{\coth ^{-1}(\tanh (a+b x))^3} \, dx","Int[x^2/ArcCoth[Tanh[a + b*x]]^3,x]","-\frac{x}{b^2 \coth ^{-1}(\tanh (a+b x))}+\frac{\log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^3}-\frac{x^2}{2 b \coth ^{-1}(\tanh (a+b x))^2}","-\frac{x}{b^2 \coth ^{-1}(\tanh (a+b x))}+\frac{\log \left(\coth ^{-1}(\tanh (a+b x))\right)}{b^3}-\frac{x^2}{2 b \coth ^{-1}(\tanh (a+b x))^2}",1,"-x^2/(2*b*ArcCoth[Tanh[a + b*x]]^2) - x/(b^2*ArcCoth[Tanh[a + b*x]]) + Log[ArcCoth[Tanh[a + b*x]]]/b^3","A",4,3,13,0.2308,1,"{2168, 2157, 29}"
179,1,34,0,0.0141126,"\int \frac{x}{\coth ^{-1}(\tanh (a+b x))^3} \, dx","Int[x/ArcCoth[Tanh[a + b*x]]^3,x]","-\frac{1}{2 b^2 \coth ^{-1}(\tanh (a+b x))}-\frac{x}{2 b \coth ^{-1}(\tanh (a+b x))^2}","-\frac{1}{2 b^2 \coth ^{-1}(\tanh (a+b x))}-\frac{x}{2 b \coth ^{-1}(\tanh (a+b x))^2}",1,"-x/(2*b*ArcCoth[Tanh[a + b*x]]^2) - 1/(2*b^2*ArcCoth[Tanh[a + b*x]])","A",3,3,11,0.2727,1,"{2168, 2157, 30}"
180,1,16,0,0.0053586,"\int \frac{1}{\coth ^{-1}(\tanh (a+b x))^3} \, dx","Int[ArcCoth[Tanh[a + b*x]]^(-3),x]","-\frac{1}{2 b \coth ^{-1}(\tanh (a+b x))^2}","-\frac{1}{2 b \coth ^{-1}(\tanh (a+b x))^2}",1,"-1/(2*b*ArcCoth[Tanh[a + b*x]]^2)","A",2,2,9,0.2222,1,"{2157, 30}"
181,1,97,0,0.0658827,"\int \frac{1}{x \coth ^{-1}(\tanh (a+b x))^3} \, dx","Int[1/(x*ArcCoth[Tanh[a + b*x]]^3),x]","\frac{1}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2 \coth ^{-1}(\tanh (a+b x))}-\frac{1}{2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right) \coth ^{-1}(\tanh (a+b x))^2}-\frac{\log (x)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3}+\frac{\log \left(\coth ^{-1}(\tanh (a+b x))\right)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3}","\frac{1}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2 \coth ^{-1}(\tanh (a+b x))}-\frac{1}{2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right) \coth ^{-1}(\tanh (a+b x))^2}-\frac{\log (x)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3}+\frac{\log \left(\coth ^{-1}(\tanh (a+b x))\right)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3}",1,"-1/(2*(b*x - ArcCoth[Tanh[a + b*x]])*ArcCoth[Tanh[a + b*x]]^2) + 1/((b*x - ArcCoth[Tanh[a + b*x]])^2*ArcCoth[Tanh[a + b*x]]) - Log[x]/(b*x - ArcCoth[Tanh[a + b*x]])^3 + Log[ArcCoth[Tanh[a + b*x]]]/(b*x - ArcCoth[Tanh[a + b*x]])^3","A",6,4,13,0.3077,1,"{2163, 2160, 2157, 29}"
182,1,131,0,0.0874151,"\int \frac{1}{x^2 \coth ^{-1}(\tanh (a+b x))^3} \, dx","Int[1/(x^2*ArcCoth[Tanh[a + b*x]]^3),x]","\frac{3 b}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3 \coth ^{-1}(\tanh (a+b x))}-\frac{3 b}{2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2 \coth ^{-1}(\tanh (a+b x))^2}+\frac{1}{x \left(b x-\coth ^{-1}(\tanh (a+b x))\right) \coth ^{-1}(\tanh (a+b x))^2}-\frac{3 b \log (x)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^4}+\frac{3 b \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^4}","\frac{3 b}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3 \coth ^{-1}(\tanh (a+b x))}-\frac{3 b}{2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2 \coth ^{-1}(\tanh (a+b x))^2}+\frac{1}{x \left(b x-\coth ^{-1}(\tanh (a+b x))\right) \coth ^{-1}(\tanh (a+b x))^2}-\frac{3 b \log (x)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^4}+\frac{3 b \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^4}",1,"(-3*b)/(2*(b*x - ArcCoth[Tanh[a + b*x]])^2*ArcCoth[Tanh[a + b*x]]^2) + 1/(x*(b*x - ArcCoth[Tanh[a + b*x]])*ArcCoth[Tanh[a + b*x]]^2) + (3*b)/((b*x - ArcCoth[Tanh[a + b*x]])^3*ArcCoth[Tanh[a + b*x]]) - (3*b*Log[x])/(b*x - ArcCoth[Tanh[a + b*x]])^4 + (3*b*Log[ArcCoth[Tanh[a + b*x]]])/(b*x - ArcCoth[Tanh[a + b*x]])^4","A",7,5,13,0.3846,1,"{2171, 2163, 2160, 2157, 29}"
183,1,170,0,0.1267655,"\int \frac{1}{x^3 \coth ^{-1}(\tanh (a+b x))^3} \, dx","Int[1/(x^3*ArcCoth[Tanh[a + b*x]]^3),x]","\frac{6 b^2}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^4 \coth ^{-1}(\tanh (a+b x))}-\frac{3 b^2}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3 \coth ^{-1}(\tanh (a+b x))^2}-\frac{6 b^2 \log (x)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^5}+\frac{6 b^2 \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^5}+\frac{1}{2 x^2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right) \coth ^{-1}(\tanh (a+b x))^2}+\frac{2 b}{x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2 \coth ^{-1}(\tanh (a+b x))^2}","\frac{6 b^2}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^4 \coth ^{-1}(\tanh (a+b x))}-\frac{3 b^2}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^3 \coth ^{-1}(\tanh (a+b x))^2}-\frac{6 b^2 \log (x)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^5}+\frac{6 b^2 \log \left(\coth ^{-1}(\tanh (a+b x))\right)}{\left(b x-\coth ^{-1}(\tanh (a+b x))\right)^5}+\frac{1}{2 x^2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right) \coth ^{-1}(\tanh (a+b x))^2}+\frac{2 b}{x \left(b x-\coth ^{-1}(\tanh (a+b x))\right)^2 \coth ^{-1}(\tanh (a+b x))^2}",1,"(-3*b^2)/((b*x - ArcCoth[Tanh[a + b*x]])^3*ArcCoth[Tanh[a + b*x]]^2) + (2*b)/(x*(b*x - ArcCoth[Tanh[a + b*x]])^2*ArcCoth[Tanh[a + b*x]]^2) + 1/(2*x^2*(b*x - ArcCoth[Tanh[a + b*x]])*ArcCoth[Tanh[a + b*x]]^2) + (6*b^2)/((b*x - ArcCoth[Tanh[a + b*x]])^4*ArcCoth[Tanh[a + b*x]]) - (6*b^2*Log[x])/(b*x - ArcCoth[Tanh[a + b*x]])^5 + (6*b^2*Log[ArcCoth[Tanh[a + b*x]]])/(b*x - ArcCoth[Tanh[a + b*x]])^5","A",8,5,13,0.3846,1,"{2171, 2163, 2160, 2157, 29}"
184,1,79,0,0.0494153,"\int x^m \coth ^{-1}(\tanh (a+b x))^n \, dx","Int[x^m*ArcCoth[Tanh[a + b*x]]^n,x]","\frac{x^m \left(\frac{b x}{b x-\coth ^{-1}(\tanh (a+b x))}\right)^{-m} \coth ^{-1}(\tanh (a+b x))^{n+1} \, _2F_1\left(-m,n+1;n+2;-\frac{\coth ^{-1}(\tanh (a+b x))}{b x-\coth ^{-1}(\tanh (a+b x))}\right)}{b (n+1)}","\frac{x^m \left(\frac{b x}{b x-\coth ^{-1}(\tanh (a+b x))}\right)^{-m} \coth ^{-1}(\tanh (a+b x))^{n+1} \, _2F_1\left(-m,n+1;n+2;-\frac{\coth ^{-1}(\tanh (a+b x))}{b x-\coth ^{-1}(\tanh (a+b x))}\right)}{b (n+1)}",1,"(x^m*ArcCoth[Tanh[a + b*x]]^(1 + n)*Hypergeometric2F1[-m, 1 + n, 2 + n, -(ArcCoth[Tanh[a + b*x]]/(b*x - ArcCoth[Tanh[a + b*x]]))])/(b*(1 + n)*((b*x)/(b*x - ArcCoth[Tanh[a + b*x]]))^m)","A",1,1,13,0.07692,1,"{2173}"
185,1,165,0,0.1330381,"\int x^4 \coth ^{-1}(\tanh (a+b x))^n \, dx","Int[x^4*ArcCoth[Tanh[a + b*x]]^n,x]","-\frac{4 x^3 \coth ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}+\frac{12 x^2 \coth ^{-1}(\tanh (a+b x))^{n+3}}{b^3 (n+1) (n+2) (n+3)}-\frac{24 x \coth ^{-1}(\tanh (a+b x))^{n+4}}{b^4 (n+1) (n+2) (n+3) (n+4)}+\frac{24 \coth ^{-1}(\tanh (a+b x))^{n+5}}{b^5 (n+1) (n+2) (n+3) (n+4) (n+5)}+\frac{x^4 \coth ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}","-\frac{4 x^3 \coth ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}+\frac{12 x^2 \coth ^{-1}(\tanh (a+b x))^{n+3}}{b^3 (n+1) (n+2) (n+3)}-\frac{24 x \coth ^{-1}(\tanh (a+b x))^{n+4}}{b^4 (n+1) (n+2) (n+3) (n+4)}+\frac{24 \coth ^{-1}(\tanh (a+b x))^{n+5}}{b^5 (n+1) (n+2) (n+3) (n+4) (n+5)}+\frac{x^4 \coth ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}",1,"(x^4*ArcCoth[Tanh[a + b*x]]^(1 + n))/(b*(1 + n)) - (4*x^3*ArcCoth[Tanh[a + b*x]]^(2 + n))/(b^2*(1 + n)*(2 + n)) + (12*x^2*ArcCoth[Tanh[a + b*x]]^(3 + n))/(b^3*(1 + n)*(2 + n)*(3 + n)) - (24*x*ArcCoth[Tanh[a + b*x]]^(4 + n))/(b^4*(1 + n)*(2 + n)*(3 + n)*(4 + n)) + (24*ArcCoth[Tanh[a + b*x]]^(5 + n))/(b^5*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n))","A",6,3,13,0.2308,1,"{2168, 2157, 30}"
186,1,121,0,0.0796348,"\int x^3 \coth ^{-1}(\tanh (a+b x))^n \, dx","Int[x^3*ArcCoth[Tanh[a + b*x]]^n,x]","-\frac{3 x^2 \coth ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}+\frac{6 x \coth ^{-1}(\tanh (a+b x))^{n+3}}{b^3 (n+1) (n+2) (n+3)}-\frac{6 \coth ^{-1}(\tanh (a+b x))^{n+4}}{b^4 (n+1) (n+2) (n+3) (n+4)}+\frac{x^3 \coth ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}","-\frac{3 x^2 \coth ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}+\frac{6 x \coth ^{-1}(\tanh (a+b x))^{n+3}}{b^3 (n+1) (n+2) (n+3)}-\frac{6 \coth ^{-1}(\tanh (a+b x))^{n+4}}{b^4 (n+1) (n+2) (n+3) (n+4)}+\frac{x^3 \coth ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}",1,"(x^3*ArcCoth[Tanh[a + b*x]]^(1 + n))/(b*(1 + n)) - (3*x^2*ArcCoth[Tanh[a + b*x]]^(2 + n))/(b^2*(1 + n)*(2 + n)) + (6*x*ArcCoth[Tanh[a + b*x]]^(3 + n))/(b^3*(1 + n)*(2 + n)*(3 + n)) - (6*ArcCoth[Tanh[a + b*x]]^(4 + n))/(b^4*(1 + n)*(2 + n)*(3 + n)*(4 + n))","A",5,3,13,0.2308,1,"{2168, 2157, 30}"
187,1,82,0,0.0461923,"\int x^2 \coth ^{-1}(\tanh (a+b x))^n \, dx","Int[x^2*ArcCoth[Tanh[a + b*x]]^n,x]","-\frac{2 x \coth ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}+\frac{2 \coth ^{-1}(\tanh (a+b x))^{n+3}}{b^3 (n+1) (n+2) (n+3)}+\frac{x^2 \coth ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}","-\frac{2 x \coth ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}+\frac{2 \coth ^{-1}(\tanh (a+b x))^{n+3}}{b^3 (n+1) (n+2) (n+3)}+\frac{x^2 \coth ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}",1,"(x^2*ArcCoth[Tanh[a + b*x]]^(1 + n))/(b*(1 + n)) - (2*x*ArcCoth[Tanh[a + b*x]]^(2 + n))/(b^2*(1 + n)*(2 + n)) + (2*ArcCoth[Tanh[a + b*x]]^(3 + n))/(b^3*(1 + n)*(2 + n)*(3 + n))","A",4,3,13,0.2308,1,"{2168, 2157, 30}"
188,1,48,0,0.0200901,"\int x \coth ^{-1}(\tanh (a+b x))^n \, dx","Int[x*ArcCoth[Tanh[a + b*x]]^n,x]","\frac{x \coth ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}-\frac{\coth ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}","\frac{x \coth ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}-\frac{\coth ^{-1}(\tanh (a+b x))^{n+2}}{b^2 (n+1) (n+2)}",1,"(x*ArcCoth[Tanh[a + b*x]]^(1 + n))/(b*(1 + n)) - ArcCoth[Tanh[a + b*x]]^(2 + n)/(b^2*(1 + n)*(2 + n))","A",3,3,11,0.2727,1,"{2168, 2157, 30}"
189,1,20,0,0.0065514,"\int \coth ^{-1}(\tanh (a+b x))^n \, dx","Int[ArcCoth[Tanh[a + b*x]]^n,x]","\frac{\coth ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}","\frac{\coth ^{-1}(\tanh (a+b x))^{n+1}}{b (n+1)}",1,"ArcCoth[Tanh[a + b*x]]^(1 + n)/(b*(1 + n))","A",2,2,9,0.2222,1,"{2157, 30}"
190,1,64,0,0.0208313,"\int \frac{\coth ^{-1}(\tanh (a+b x))^n}{x} \, dx","Int[ArcCoth[Tanh[a + b*x]]^n/x,x]","\frac{\coth ^{-1}(\tanh (a+b x))^{n+1} \, _2F_1\left(1,n+1;n+2;-\frac{\coth ^{-1}(\tanh (a+b x))}{b x-\coth ^{-1}(\tanh (a+b x))}\right)}{(n+1) \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}","\frac{\coth ^{-1}(\tanh (a+b x))^{n+1} \, _2F_1\left(1,n+1;n+2;-\frac{\coth ^{-1}(\tanh (a+b x))}{b x-\coth ^{-1}(\tanh (a+b x))}\right)}{(n+1) \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}",1,"(ArcCoth[Tanh[a + b*x]]^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, -(ArcCoth[Tanh[a + b*x]]/(b*x - ArcCoth[Tanh[a + b*x]]))])/((1 + n)*(b*x - ArcCoth[Tanh[a + b*x]]))","A",1,1,13,0.07692,1,"{2164}"
191,1,71,0,0.0412581,"\int \frac{\coth ^{-1}(\tanh (a+b x))^n}{x^2} \, dx","Int[ArcCoth[Tanh[a + b*x]]^n/x^2,x]","\frac{b \coth ^{-1}(\tanh (a+b x))^n \, _2F_1\left(1,n;n+1;-\frac{\coth ^{-1}(\tanh (a+b x))}{b x-\coth ^{-1}(\tanh (a+b x))}\right)}{b x-\coth ^{-1}(\tanh (a+b x))}-\frac{\coth ^{-1}(\tanh (a+b x))^n}{x}","\frac{b \coth ^{-1}(\tanh (a+b x))^n \, _2F_1\left(1,n;n+1;-\frac{\coth ^{-1}(\tanh (a+b x))}{b x-\coth ^{-1}(\tanh (a+b x))}\right)}{b x-\coth ^{-1}(\tanh (a+b x))}-\frac{\coth ^{-1}(\tanh (a+b x))^n}{x}",1,"-(ArcCoth[Tanh[a + b*x]]^n/x) + (b*ArcCoth[Tanh[a + b*x]]^n*Hypergeometric2F1[1, n, 1 + n, -(ArcCoth[Tanh[a + b*x]]/(b*x - ArcCoth[Tanh[a + b*x]]))])/(b*x - ArcCoth[Tanh[a + b*x]])","A",2,2,13,0.1538,1,"{2168, 2164}"
192,1,101,0,0.0692208,"\int \frac{\coth ^{-1}(\tanh (a+b x))^n}{x^3} \, dx","Int[ArcCoth[Tanh[a + b*x]]^n/x^3,x]","\frac{b^2 n \coth ^{-1}(\tanh (a+b x))^{n-1} \, _2F_1\left(1,n-1;n;-\frac{\coth ^{-1}(\tanh (a+b x))}{b x-\coth ^{-1}(\tanh (a+b x))}\right)}{2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}-\frac{\coth ^{-1}(\tanh (a+b x))^n}{2 x^2}-\frac{b n \coth ^{-1}(\tanh (a+b x))^{n-1}}{2 x}","\frac{b^2 n \coth ^{-1}(\tanh (a+b x))^{n-1} \, _2F_1\left(1,n-1;n;-\frac{\coth ^{-1}(\tanh (a+b x))}{b x-\coth ^{-1}(\tanh (a+b x))}\right)}{2 \left(b x-\coth ^{-1}(\tanh (a+b x))\right)}-\frac{\coth ^{-1}(\tanh (a+b x))^n}{2 x^2}-\frac{b n \coth ^{-1}(\tanh (a+b x))^{n-1}}{2 x}",1,"-(b*n*ArcCoth[Tanh[a + b*x]]^(-1 + n))/(2*x) - ArcCoth[Tanh[a + b*x]]^n/(2*x^2) + (b^2*n*ArcCoth[Tanh[a + b*x]]^(-1 + n)*Hypergeometric2F1[1, -1 + n, n, -(ArcCoth[Tanh[a + b*x]]/(b*x - ArcCoth[Tanh[a + b*x]]))])/(2*(b*x - ArcCoth[Tanh[a + b*x]]))","A",3,2,13,0.1538,1,"{2168, 2164}"
193,1,37,0,0.0100579,"\int x^m \coth ^{-1}(\tanh (a+b x)) \, dx","Int[x^m*ArcCoth[Tanh[a + b*x]],x]","\frac{x^{m+1} \coth ^{-1}(\tanh (a+b x))}{m+1}-\frac{b x^{m+2}}{m^2+3 m+2}","\frac{x^{m+1} \coth ^{-1}(\tanh (a+b x))}{m+1}-\frac{b x^{m+2}}{m^2+3 m+2}",1,"-((b*x^(2 + m))/(2 + 3*m + m^2)) + (x^(1 + m)*ArcCoth[Tanh[a + b*x]])/(1 + m)","A",2,2,11,0.1818,1,"{2168, 30}"
194,1,23,0,0.014254,"\int x^2 \coth ^{-1}(\coth (a+b x)) \, dx","Int[x^2*ArcCoth[Coth[a + b*x]],x]","\frac{1}{3} x^3 \coth ^{-1}(\coth (a+b x))-\frac{b x^4}{12}","\frac{1}{3} x^3 \coth ^{-1}(\coth (a+b x))-\frac{b x^4}{12}",1,"-(b*x^4)/12 + (x^3*ArcCoth[Coth[a + b*x]])/3","A",2,2,11,0.1818,1,"{2168, 30}"
195,1,23,0,0.0077072,"\int x \coth ^{-1}(\coth (a+b x)) \, dx","Int[x*ArcCoth[Coth[a + b*x]],x]","\frac{1}{2} x^2 \coth ^{-1}(\coth (a+b x))-\frac{b x^3}{6}","\frac{1}{2} x^2 \coth ^{-1}(\coth (a+b x))-\frac{b x^3}{6}",1,"-(b*x^3)/6 + (x^2*ArcCoth[Coth[a + b*x]])/2","A",2,2,9,0.2222,1,"{6242, 30}"
196,1,16,0,0.0031558,"\int \coth ^{-1}(\coth (a+b x)) \, dx","Int[ArcCoth[Coth[a + b*x]],x]","\frac{\coth ^{-1}(\coth (a+b x))^2}{2 b}","\frac{\coth ^{-1}(\coth (a+b x))^2}{2 b}",1,"ArcCoth[Coth[a + b*x]]^2/(2*b)","A",2,2,7,0.2857,1,"{2157, 30}"
197,1,21,0,0.0309233,"\int \frac{\coth ^{-1}(\coth (a+b x))}{x} \, dx","Int[ArcCoth[Coth[a + b*x]]/x,x]","b x-\log (x) \left(b x-\coth ^{-1}(\coth (a+b x))\right)","b x-\log (x) \left(b x-\coth ^{-1}(\coth (a+b x))\right)",1,"b*x - (b*x - ArcCoth[Coth[a + b*x]])*Log[x]","A",2,2,11,0.1818,1,"{2158, 29}"
198,1,17,0,0.008717,"\int \frac{\coth ^{-1}(\coth (a+b x))}{x^2} \, dx","Int[ArcCoth[Coth[a + b*x]]/x^2,x]","b \log (x)-\frac{\coth ^{-1}(\coth (a+b x))}{x}","b \log (x)-\frac{\coth ^{-1}(\coth (a+b x))}{x}",1,"-(ArcCoth[Coth[a + b*x]]/x) + b*Log[x]","A",2,2,11,0.1818,1,"{2168, 29}"
199,1,23,0,0.009241,"\int \frac{\coth ^{-1}(\coth (a+b x))}{x^3} \, dx","Int[ArcCoth[Coth[a + b*x]]/x^3,x]","-\frac{\coth ^{-1}(\coth (a+b x))}{2 x^2}-\frac{b}{2 x}","-\frac{\coth ^{-1}(\coth (a+b x))}{2 x^2}-\frac{b}{2 x}",1,"-b/(2*x) - ArcCoth[Coth[a + b*x]]/(2*x^2)","A",2,2,11,0.1818,1,"{2168, 30}"
200,1,27,0,0.0342236,"\int \coth ^{-1}(\cosh (x)) \, dx","Int[ArcCoth[Cosh[x]],x]","-\text{PolyLog}\left(2,-e^x\right)+\text{PolyLog}\left(2,e^x\right)-2 x \tanh ^{-1}\left(e^x\right)+x \coth ^{-1}(\cosh (x))","-\text{PolyLog}\left(2,-e^x\right)+\text{PolyLog}\left(2,e^x\right)-2 x \tanh ^{-1}\left(e^x\right)+x \coth ^{-1}(\cosh (x))",1,"x*ArcCoth[Cosh[x]] - 2*x*ArcTanh[E^x] - PolyLog[2, -E^x] + PolyLog[2, E^x]","A",6,4,3,1.333,1,"{6272, 4182, 2279, 2391}"
201,1,51,0,0.0664171,"\int x \coth ^{-1}(\cosh (x)) \, dx","Int[x*ArcCoth[Cosh[x]],x]","-x \text{PolyLog}\left(2,-e^x\right)+x \text{PolyLog}\left(2,e^x\right)+\text{PolyLog}\left(3,-e^x\right)-\text{PolyLog}\left(3,e^x\right)-x^2 \tanh ^{-1}\left(e^x\right)+\frac{1}{2} x^2 \coth ^{-1}(\cosh (x))","-x \text{PolyLog}\left(2,-e^x\right)+x \text{PolyLog}\left(2,e^x\right)+\text{PolyLog}\left(3,-e^x\right)-\text{PolyLog}\left(3,e^x\right)-x^2 \tanh ^{-1}\left(e^x\right)+\frac{1}{2} x^2 \coth ^{-1}(\cosh (x))",1,"(x^2*ArcCoth[Cosh[x]])/2 - x^2*ArcTanh[E^x] - x*PolyLog[2, -E^x] + x*PolyLog[2, E^x] + PolyLog[3, -E^x] - PolyLog[3, E^x]","A",8,5,5,1.000,1,"{6274, 4182, 2531, 2282, 6589}"
202,1,77,0,0.0900436,"\int x^2 \coth ^{-1}(\cosh (x)) \, dx","Int[x^2*ArcCoth[Cosh[x]],x]","-x^2 \text{PolyLog}\left(2,-e^x\right)+x^2 \text{PolyLog}\left(2,e^x\right)+2 x \text{PolyLog}\left(3,-e^x\right)-2 x \text{PolyLog}\left(3,e^x\right)-2 \text{PolyLog}\left(4,-e^x\right)+2 \text{PolyLog}\left(4,e^x\right)-\frac{2}{3} x^3 \tanh ^{-1}\left(e^x\right)+\frac{1}{3} x^3 \coth ^{-1}(\cosh (x))","-x^2 \text{PolyLog}\left(2,-e^x\right)+x^2 \text{PolyLog}\left(2,e^x\right)+2 x \text{PolyLog}\left(3,-e^x\right)-2 x \text{PolyLog}\left(3,e^x\right)-2 \text{PolyLog}\left(4,-e^x\right)+2 \text{PolyLog}\left(4,e^x\right)-\frac{2}{3} x^3 \tanh ^{-1}\left(e^x\right)+\frac{1}{3} x^3 \coth ^{-1}(\cosh (x))",1,"(x^3*ArcCoth[Cosh[x]])/3 - (2*x^3*ArcTanh[E^x])/3 - x^2*PolyLog[2, -E^x] + x^2*PolyLog[2, E^x] + 2*x*PolyLog[3, -E^x] - 2*x*PolyLog[3, E^x] - 2*PolyLog[4, -E^x] + 2*PolyLog[4, E^x]","A",10,6,7,0.8571,1,"{6274, 4182, 2531, 6609, 2282, 6589}"
203,1,307,0,0.4648913,"\int x^2 \coth ^{-1}(c+d \tanh (a+b x)) \, dx","Int[x^2*ArcCoth[c + d*Tanh[a + b*x]],x]","-\frac{x \text{PolyLog}\left(3,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b^2}+\frac{x \text{PolyLog}\left(3,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b^2}+\frac{\text{PolyLog}\left(4,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^3}-\frac{\text{PolyLog}\left(4,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^3}+\frac{x^2 \text{PolyLog}\left(2,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x^2 \text{PolyLog}\left(2,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{6} x^3 \log \left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}+1\right)-\frac{1}{6} x^3 \log \left(\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}+1\right)+\frac{1}{3} x^3 \coth ^{-1}(d \tanh (a+b x)+c)","-\frac{x \text{PolyLog}\left(3,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b^2}+\frac{x \text{PolyLog}\left(3,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b^2}+\frac{\text{PolyLog}\left(4,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^3}-\frac{\text{PolyLog}\left(4,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^3}+\frac{x^2 \text{PolyLog}\left(2,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x^2 \text{PolyLog}\left(2,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{6} x^3 \log \left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}+1\right)-\frac{1}{6} x^3 \log \left(\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}+1\right)+\frac{1}{3} x^3 \coth ^{-1}(d \tanh (a+b x)+c)",1,"(x^3*ArcCoth[c + d*Tanh[a + b*x]])/3 + (x^3*Log[1 + ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/6 - (x^3*Log[1 + ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/6 + (x^2*PolyLog[2, -(((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d))])/(4*b) - (x^2*PolyLog[2, -(((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d))])/(4*b) - (x*PolyLog[3, -(((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d))])/(4*b^2) + (x*PolyLog[3, -(((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d))])/(4*b^2) + PolyLog[4, -(((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d))]/(8*b^3) - PolyLog[4, -(((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d))]/(8*b^3)","A",11,6,15,0.4000,1,"{6244, 2190, 2531, 6609, 2282, 6589}"
204,1,231,0,0.3794663,"\int x \coth ^{-1}(c+d \tanh (a+b x)) \, dx","Int[x*ArcCoth[c + d*Tanh[a + b*x]],x]","-\frac{\text{PolyLog}\left(3,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^2}+\frac{\text{PolyLog}\left(3,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^2}+\frac{x \text{PolyLog}\left(2,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x \text{PolyLog}\left(2,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{4} x^2 \log \left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}+1\right)-\frac{1}{4} x^2 \log \left(\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}+1\right)+\frac{1}{2} x^2 \coth ^{-1}(d \tanh (a+b x)+c)","-\frac{\text{PolyLog}\left(3,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^2}+\frac{\text{PolyLog}\left(3,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^2}+\frac{x \text{PolyLog}\left(2,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x \text{PolyLog}\left(2,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{4} x^2 \log \left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}+1\right)-\frac{1}{4} x^2 \log \left(\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}+1\right)+\frac{1}{2} x^2 \coth ^{-1}(d \tanh (a+b x)+c)",1,"(x^2*ArcCoth[c + d*Tanh[a + b*x]])/2 + (x^2*Log[1 + ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/4 - (x^2*Log[1 + ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/4 + (x*PolyLog[2, -(((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d))])/(4*b) - (x*PolyLog[2, -(((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d))])/(4*b) - PolyLog[3, -(((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d))]/(8*b^2) + PolyLog[3, -(((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d))]/(8*b^2)","A",9,5,13,0.3846,1,"{6244, 2190, 2531, 2282, 6589}"
205,1,150,0,0.2319659,"\int \coth ^{-1}(c+d \tanh (a+b x)) \, dx","Int[ArcCoth[c + d*Tanh[a + b*x]],x]","\frac{\text{PolyLog}\left(2,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{\text{PolyLog}\left(2,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{2} x \log \left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}+1\right)-\frac{1}{2} x \log \left(\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}+1\right)+x \coth ^{-1}(d \tanh (a+b x)+c)","\frac{\text{PolyLog}\left(2,-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{\text{PolyLog}\left(2,-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{2} x \log \left(\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}+1\right)-\frac{1}{2} x \log \left(\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}+1\right)+x \coth ^{-1}(d \tanh (a+b x)+c)",1,"x*ArcCoth[c + d*Tanh[a + b*x]] + (x*Log[1 + ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/2 - (x*Log[1 + ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/2 + PolyLog[2, -(((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d))]/(4*b) - PolyLog[2, -(((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d))]/(4*b)","A",7,4,11,0.3636,1,"{6236, 2190, 2279, 2391}"
206,0,0,0,0.0662613,"\int \frac{\coth ^{-1}(c+d \tanh (a+b x))}{x} \, dx","Int[ArcCoth[c + d*Tanh[a + b*x]]/x,x]","\int \frac{\coth ^{-1}(c+d \tanh (a+b x))}{x} \, dx","\text{Int}\left(\frac{\coth ^{-1}(d \tanh (a+b x)+c)}{x},x\right)",0,"Defer[Int][ArcCoth[c + d*Tanh[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
207,1,155,0,0.30719,"\int x^3 \coth ^{-1}(1+d+d \tanh (a+b x)) \, dx","Int[x^3*ArcCoth[1 + d + d*Tanh[a + b*x]],x]","\frac{3 x^2 \text{PolyLog}\left(3,-(d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 x \text{PolyLog}\left(4,-(d+1) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 \text{PolyLog}\left(5,-(d+1) e^{2 a+2 b x}\right)}{16 b^4}-\frac{x^3 \text{PolyLog}\left(2,-(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{8} x^4 \log \left((d+1) e^{2 a+2 b x}+1\right)+\frac{1}{4} x^4 \coth ^{-1}(d \tanh (a+b x)+d+1)+\frac{b x^5}{20}","\frac{3 x^2 \text{PolyLog}\left(3,-(d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 x \text{PolyLog}\left(4,-(d+1) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 \text{PolyLog}\left(5,-(d+1) e^{2 a+2 b x}\right)}{16 b^4}-\frac{x^3 \text{PolyLog}\left(2,-(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{8} x^4 \log \left((d+1) e^{2 a+2 b x}+1\right)+\frac{1}{4} x^4 \coth ^{-1}(d \tanh (a+b x)+d+1)+\frac{b x^5}{20}",1,"(b*x^5)/20 + (x^4*ArcCoth[1 + d + d*Tanh[a + b*x]])/4 - (x^4*Log[1 + (1 + d)*E^(2*a + 2*b*x)])/8 - (x^3*PolyLog[2, -((1 + d)*E^(2*a + 2*b*x))])/(4*b) + (3*x^2*PolyLog[3, -((1 + d)*E^(2*a + 2*b*x))])/(8*b^2) - (3*x*PolyLog[4, -((1 + d)*E^(2*a + 2*b*x))])/(8*b^3) + (3*PolyLog[5, -((1 + d)*E^(2*a + 2*b*x))])/(16*b^4)","A",8,7,16,0.4375,1,"{6240, 2184, 2190, 2531, 6609, 2282, 6589}"
208,1,128,0,0.2690031,"\int x^2 \coth ^{-1}(1+d+d \tanh (a+b x)) \, dx","Int[x^2*ArcCoth[1 + d + d*Tanh[a + b*x]],x]","\frac{x \text{PolyLog}\left(3,-(d+1) e^{2 a+2 b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,-(d+1) e^{2 a+2 b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,-(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left((d+1) e^{2 a+2 b x}+1\right)+\frac{1}{3} x^3 \coth ^{-1}(d \tanh (a+b x)+d+1)+\frac{b x^4}{12}","\frac{x \text{PolyLog}\left(3,-(d+1) e^{2 a+2 b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,-(d+1) e^{2 a+2 b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,-(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left((d+1) e^{2 a+2 b x}+1\right)+\frac{1}{3} x^3 \coth ^{-1}(d \tanh (a+b x)+d+1)+\frac{b x^4}{12}",1,"(b*x^4)/12 + (x^3*ArcCoth[1 + d + d*Tanh[a + b*x]])/3 - (x^3*Log[1 + (1 + d)*E^(2*a + 2*b*x)])/6 - (x^2*PolyLog[2, -((1 + d)*E^(2*a + 2*b*x))])/(4*b) + (x*PolyLog[3, -((1 + d)*E^(2*a + 2*b*x))])/(4*b^2) - PolyLog[4, -((1 + d)*E^(2*a + 2*b*x))]/(8*b^3)","A",7,7,16,0.4375,1,"{6240, 2184, 2190, 2531, 6609, 2282, 6589}"
209,1,101,0,0.2309032,"\int x \coth ^{-1}(1+d+d \tanh (a+b x)) \, dx","Int[x*ArcCoth[1 + d + d*Tanh[a + b*x]],x]","\frac{\text{PolyLog}\left(3,-(d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,-(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left((d+1) e^{2 a+2 b x}+1\right)+\frac{1}{2} x^2 \coth ^{-1}(d \tanh (a+b x)+d+1)+\frac{b x^3}{6}","\frac{\text{PolyLog}\left(3,-(d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,-(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left((d+1) e^{2 a+2 b x}+1\right)+\frac{1}{2} x^2 \coth ^{-1}(d \tanh (a+b x)+d+1)+\frac{b x^3}{6}",1,"(b*x^3)/6 + (x^2*ArcCoth[1 + d + d*Tanh[a + b*x]])/2 - (x^2*Log[1 + (1 + d)*E^(2*a + 2*b*x)])/4 - (x*PolyLog[2, -((1 + d)*E^(2*a + 2*b*x))])/(4*b) + PolyLog[3, -((1 + d)*E^(2*a + 2*b*x))]/(8*b^2)","A",6,6,14,0.4286,1,"{6240, 2184, 2190, 2531, 2282, 6589}"
210,1,69,0,0.1400058,"\int \coth ^{-1}(1+d+d \tanh (a+b x)) \, dx","Int[ArcCoth[1 + d + d*Tanh[a + b*x]],x]","-\frac{\text{PolyLog}\left(2,-(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} x \log \left((d+1) e^{2 a+2 b x}+1\right)+x \coth ^{-1}(d \tanh (a+b x)+d+1)+\frac{b x^2}{2}","-\frac{\text{PolyLog}\left(2,-(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} x \log \left((d+1) e^{2 a+2 b x}+1\right)+x \coth ^{-1}(d \tanh (a+b x)+d+1)+\frac{b x^2}{2}",1,"(b*x^2)/2 + x*ArcCoth[1 + d + d*Tanh[a + b*x]] - (x*Log[1 + (1 + d)*E^(2*a + 2*b*x)])/2 - PolyLog[2, -((1 + d)*E^(2*a + 2*b*x))]/(4*b)","A",5,5,12,0.4167,1,"{6232, 2184, 2190, 2279, 2391}"
211,0,0,0,0.0772992,"\int \frac{\coth ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx","Int[ArcCoth[1 + d + d*Tanh[a + b*x]]/x,x]","\int \frac{\coth ^{-1}(1+d+d \tanh (a+b x))}{x} \, dx","\text{Int}\left(\frac{\coth ^{-1}(d \tanh (a+b x)+d+1)}{x},x\right)",0,"Defer[Int][ArcCoth[1 + d + d*Tanh[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
212,1,168,0,0.3032795,"\int x^3 \coth ^{-1}(1-d-d \tanh (a+b x)) \, dx","Int[x^3*ArcCoth[1 - d - d*Tanh[a + b*x]],x]","\frac{3 x^2 \text{PolyLog}\left(3,-(1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 x \text{PolyLog}\left(4,-(1-d) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 \text{PolyLog}\left(5,-(1-d) e^{2 a+2 b x}\right)}{16 b^4}-\frac{x^3 \text{PolyLog}\left(2,-(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{8} x^4 \log \left((1-d) e^{2 a+2 b x}+1\right)+\frac{1}{4} x^4 \coth ^{-1}(d (-\tanh (a+b x))-d+1)+\frac{b x^5}{20}","\frac{3 x^2 \text{PolyLog}\left(3,-(1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 x \text{PolyLog}\left(4,-(1-d) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 \text{PolyLog}\left(5,-(1-d) e^{2 a+2 b x}\right)}{16 b^4}-\frac{x^3 \text{PolyLog}\left(2,-(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{8} x^4 \log \left((1-d) e^{2 a+2 b x}+1\right)+\frac{1}{4} x^4 \coth ^{-1}(d (-\tanh (a+b x))-d+1)+\frac{b x^5}{20}",1,"(b*x^5)/20 + (x^4*ArcCoth[1 - d - d*Tanh[a + b*x]])/4 - (x^4*Log[1 + (1 - d)*E^(2*a + 2*b*x)])/8 - (x^3*PolyLog[2, -((1 - d)*E^(2*a + 2*b*x))])/(4*b) + (3*x^2*PolyLog[3, -((1 - d)*E^(2*a + 2*b*x))])/(8*b^2) - (3*x*PolyLog[4, -((1 - d)*E^(2*a + 2*b*x))])/(8*b^3) + (3*PolyLog[5, -((1 - d)*E^(2*a + 2*b*x))])/(16*b^4)","A",8,7,19,0.3684,1,"{6240, 2184, 2190, 2531, 6609, 2282, 6589}"
213,1,139,0,0.2684577,"\int x^2 \coth ^{-1}(1-d-d \tanh (a+b x)) \, dx","Int[x^2*ArcCoth[1 - d - d*Tanh[a + b*x]],x]","\frac{x \text{PolyLog}\left(3,-(1-d) e^{2 a+2 b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,-(1-d) e^{2 a+2 b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,-(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left((1-d) e^{2 a+2 b x}+1\right)+\frac{1}{3} x^3 \coth ^{-1}(d (-\tanh (a+b x))-d+1)+\frac{b x^4}{12}","\frac{x \text{PolyLog}\left(3,-(1-d) e^{2 a+2 b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,-(1-d) e^{2 a+2 b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,-(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left((1-d) e^{2 a+2 b x}+1\right)+\frac{1}{3} x^3 \coth ^{-1}(d (-\tanh (a+b x))-d+1)+\frac{b x^4}{12}",1,"(b*x^4)/12 + (x^3*ArcCoth[1 - d - d*Tanh[a + b*x]])/3 - (x^3*Log[1 + (1 - d)*E^(2*a + 2*b*x)])/6 - (x^2*PolyLog[2, -((1 - d)*E^(2*a + 2*b*x))])/(4*b) + (x*PolyLog[3, -((1 - d)*E^(2*a + 2*b*x))])/(4*b^2) - PolyLog[4, -((1 - d)*E^(2*a + 2*b*x))]/(8*b^3)","A",7,7,19,0.3684,1,"{6240, 2184, 2190, 2531, 6609, 2282, 6589}"
214,1,110,0,0.2381741,"\int x \coth ^{-1}(1-d-d \tanh (a+b x)) \, dx","Int[x*ArcCoth[1 - d - d*Tanh[a + b*x]],x]","\frac{\text{PolyLog}\left(3,-(1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,-(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left((1-d) e^{2 a+2 b x}+1\right)+\frac{1}{2} x^2 \coth ^{-1}(d (-\tanh (a+b x))-d+1)+\frac{b x^3}{6}","\frac{\text{PolyLog}\left(3,-(1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,-(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left((1-d) e^{2 a+2 b x}+1\right)+\frac{1}{2} x^2 \coth ^{-1}(d (-\tanh (a+b x))-d+1)+\frac{b x^3}{6}",1,"(b*x^3)/6 + (x^2*ArcCoth[1 - d - d*Tanh[a + b*x]])/2 - (x^2*Log[1 + (1 - d)*E^(2*a + 2*b*x)])/4 - (x*PolyLog[2, -((1 - d)*E^(2*a + 2*b*x))])/(4*b) + PolyLog[3, -((1 - d)*E^(2*a + 2*b*x))]/(8*b^2)","A",6,6,17,0.3529,1,"{6240, 2184, 2190, 2531, 2282, 6589}"
215,1,76,0,0.1495272,"\int \coth ^{-1}(1-d-d \tanh (a+b x)) \, dx","Int[ArcCoth[1 - d - d*Tanh[a + b*x]],x]","-\frac{\text{PolyLog}\left(2,-(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} x \log \left((1-d) e^{2 a+2 b x}+1\right)+x \coth ^{-1}(d (-\tanh (a+b x))-d+1)+\frac{b x^2}{2}","-\frac{\text{PolyLog}\left(2,-(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} x \log \left((1-d) e^{2 a+2 b x}+1\right)+x \coth ^{-1}(d (-\tanh (a+b x))-d+1)+\frac{b x^2}{2}",1,"(b*x^2)/2 + x*ArcCoth[1 - d - d*Tanh[a + b*x]] - (x*Log[1 + (1 - d)*E^(2*a + 2*b*x)])/2 - PolyLog[2, -((1 - d)*E^(2*a + 2*b*x))]/(4*b)","A",5,5,15,0.3333,1,"{6232, 2184, 2190, 2279, 2391}"
216,0,0,0,0.0645733,"\int \frac{\coth ^{-1}(1-d-d \tanh (a+b x))}{x} \, dx","Int[ArcCoth[1 - d - d*Tanh[a + b*x]]/x,x]","\int \frac{\coth ^{-1}(1-d-d \tanh (a+b x))}{x} \, dx","\text{Int}\left(\frac{\coth ^{-1}(d (-\tanh (a+b x))-d+1)}{x},x\right)",0,"Defer[Int][ArcCoth[1 - d - d*Tanh[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
217,1,303,0,0.4654451,"\int x^2 \coth ^{-1}(c+d \coth (a+b x)) \, dx","Int[x^2*ArcCoth[c + d*Coth[a + b*x]],x]","-\frac{x \text{PolyLog}\left(3,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b^2}+\frac{x \text{PolyLog}\left(3,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b^2}+\frac{\text{PolyLog}\left(4,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^3}-\frac{\text{PolyLog}\left(4,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^3}+\frac{x^2 \text{PolyLog}\left(2,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x^2 \text{PolyLog}\left(2,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{6} x^3 \log \left(1-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)-\frac{1}{6} x^3 \log \left(1-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)+\frac{1}{3} x^3 \coth ^{-1}(d \coth (a+b x)+c)","-\frac{x \text{PolyLog}\left(3,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b^2}+\frac{x \text{PolyLog}\left(3,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b^2}+\frac{\text{PolyLog}\left(4,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^3}-\frac{\text{PolyLog}\left(4,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^3}+\frac{x^2 \text{PolyLog}\left(2,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x^2 \text{PolyLog}\left(2,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{6} x^3 \log \left(1-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)-\frac{1}{6} x^3 \log \left(1-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)+\frac{1}{3} x^3 \coth ^{-1}(d \coth (a+b x)+c)",1,"(x^3*ArcCoth[c + d*Coth[a + b*x]])/3 + (x^3*Log[1 - ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/6 - (x^3*Log[1 - ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/6 + (x^2*PolyLog[2, ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/(4*b) - (x^2*PolyLog[2, ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/(4*b) - (x*PolyLog[3, ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/(4*b^2) + (x*PolyLog[3, ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/(4*b^2) + PolyLog[4, ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)]/(8*b^3) - PolyLog[4, ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)]/(8*b^3)","A",11,6,15,0.4000,1,"{6246, 2190, 2531, 6609, 2282, 6589}"
218,1,229,0,0.3822992,"\int x \coth ^{-1}(c+d \coth (a+b x)) \, dx","Int[x*ArcCoth[c + d*Coth[a + b*x]],x]","-\frac{\text{PolyLog}\left(3,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^2}+\frac{\text{PolyLog}\left(3,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^2}+\frac{x \text{PolyLog}\left(2,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x \text{PolyLog}\left(2,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{4} x^2 \log \left(1-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)-\frac{1}{4} x^2 \log \left(1-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)+\frac{1}{2} x^2 \coth ^{-1}(d \coth (a+b x)+c)","-\frac{\text{PolyLog}\left(3,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{8 b^2}+\frac{\text{PolyLog}\left(3,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{8 b^2}+\frac{x \text{PolyLog}\left(2,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{x \text{PolyLog}\left(2,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{4} x^2 \log \left(1-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)-\frac{1}{4} x^2 \log \left(1-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)+\frac{1}{2} x^2 \coth ^{-1}(d \coth (a+b x)+c)",1,"(x^2*ArcCoth[c + d*Coth[a + b*x]])/2 + (x^2*Log[1 - ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/4 - (x^2*Log[1 - ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/4 + (x*PolyLog[2, ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/(4*b) - (x*PolyLog[2, ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/(4*b) - PolyLog[3, ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)]/(8*b^2) + PolyLog[3, ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)]/(8*b^2)","A",9,5,13,0.3846,1,"{6246, 2190, 2531, 2282, 6589}"
219,1,150,0,0.234753,"\int \coth ^{-1}(c+d \coth (a+b x)) \, dx","Int[ArcCoth[c + d*Coth[a + b*x]],x]","\frac{\text{PolyLog}\left(2,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{\text{PolyLog}\left(2,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{2} x \log \left(1-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)-\frac{1}{2} x \log \left(1-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)+x \coth ^{-1}(d \coth (a+b x)+c)","\frac{\text{PolyLog}\left(2,\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)}{4 b}-\frac{\text{PolyLog}\left(2,\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)}{4 b}+\frac{1}{2} x \log \left(1-\frac{(-c-d+1) e^{2 a+2 b x}}{-c+d+1}\right)-\frac{1}{2} x \log \left(1-\frac{(c+d+1) e^{2 a+2 b x}}{c-d+1}\right)+x \coth ^{-1}(d \coth (a+b x)+c)",1,"x*ArcCoth[c + d*Coth[a + b*x]] + (x*Log[1 - ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)])/2 - (x*Log[1 - ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)])/2 + PolyLog[2, ((1 - c - d)*E^(2*a + 2*b*x))/(1 - c + d)]/(4*b) - PolyLog[2, ((1 + c + d)*E^(2*a + 2*b*x))/(1 + c - d)]/(4*b)","A",7,4,11,0.3636,1,"{6238, 2190, 2279, 2391}"
220,0,0,0,0.147025,"\int \frac{\coth ^{-1}(c+d \coth (a+b x))}{x} \, dx","Int[ArcCoth[c + d*Coth[a + b*x]]/x,x]","\int \frac{\coth ^{-1}(c+d \coth (a+b x))}{x} \, dx","\text{Int}\left(\frac{\coth ^{-1}(d \coth (a+b x)+c)}{x},x\right)",0,"Defer[Int][ArcCoth[c + d*Coth[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
221,1,152,0,0.3075102,"\int x^3 \coth ^{-1}(1+d+d \coth (a+b x)) \, dx","Int[x^3*ArcCoth[1 + d + d*Coth[a + b*x]],x]","\frac{3 x^2 \text{PolyLog}\left(3,(d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 x \text{PolyLog}\left(4,(d+1) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 \text{PolyLog}\left(5,(d+1) e^{2 a+2 b x}\right)}{16 b^4}-\frac{x^3 \text{PolyLog}\left(2,(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{8} x^4 \log \left(1-(d+1) e^{2 a+2 b x}\right)+\frac{1}{4} x^4 \coth ^{-1}(d \coth (a+b x)+d+1)+\frac{b x^5}{20}","\frac{3 x^2 \text{PolyLog}\left(3,(d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 x \text{PolyLog}\left(4,(d+1) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 \text{PolyLog}\left(5,(d+1) e^{2 a+2 b x}\right)}{16 b^4}-\frac{x^3 \text{PolyLog}\left(2,(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{8} x^4 \log \left(1-(d+1) e^{2 a+2 b x}\right)+\frac{1}{4} x^4 \coth ^{-1}(d \coth (a+b x)+d+1)+\frac{b x^5}{20}",1,"(b*x^5)/20 + (x^4*ArcCoth[1 + d + d*Coth[a + b*x]])/4 - (x^4*Log[1 - (1 + d)*E^(2*a + 2*b*x)])/8 - (x^3*PolyLog[2, (1 + d)*E^(2*a + 2*b*x)])/(4*b) + (3*x^2*PolyLog[3, (1 + d)*E^(2*a + 2*b*x)])/(8*b^2) - (3*x*PolyLog[4, (1 + d)*E^(2*a + 2*b*x)])/(8*b^3) + (3*PolyLog[5, (1 + d)*E^(2*a + 2*b*x)])/(16*b^4)","A",8,7,16,0.4375,1,"{6242, 2184, 2190, 2531, 6609, 2282, 6589}"
222,1,126,0,0.2690903,"\int x^2 \coth ^{-1}(1+d+d \coth (a+b x)) \, dx","Int[x^2*ArcCoth[1 + d + d*Coth[a + b*x]],x]","\frac{x \text{PolyLog}\left(3,(d+1) e^{2 a+2 b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,(d+1) e^{2 a+2 b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1-(d+1) e^{2 a+2 b x}\right)+\frac{1}{3} x^3 \coth ^{-1}(d \coth (a+b x)+d+1)+\frac{b x^4}{12}","\frac{x \text{PolyLog}\left(3,(d+1) e^{2 a+2 b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,(d+1) e^{2 a+2 b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1-(d+1) e^{2 a+2 b x}\right)+\frac{1}{3} x^3 \coth ^{-1}(d \coth (a+b x)+d+1)+\frac{b x^4}{12}",1,"(b*x^4)/12 + (x^3*ArcCoth[1 + d + d*Coth[a + b*x]])/3 - (x^3*Log[1 - (1 + d)*E^(2*a + 2*b*x)])/6 - (x^2*PolyLog[2, (1 + d)*E^(2*a + 2*b*x)])/(4*b) + (x*PolyLog[3, (1 + d)*E^(2*a + 2*b*x)])/(4*b^2) - PolyLog[4, (1 + d)*E^(2*a + 2*b*x)]/(8*b^3)","A",7,7,16,0.4375,1,"{6242, 2184, 2190, 2531, 6609, 2282, 6589}"
223,1,100,0,0.2403904,"\int x \coth ^{-1}(1+d+d \coth (a+b x)) \, dx","Int[x*ArcCoth[1 + d + d*Coth[a + b*x]],x]","\frac{\text{PolyLog}\left(3,(d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1-(d+1) e^{2 a+2 b x}\right)+\frac{1}{2} x^2 \coth ^{-1}(d \coth (a+b x)+d+1)+\frac{b x^3}{6}","\frac{\text{PolyLog}\left(3,(d+1) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1-(d+1) e^{2 a+2 b x}\right)+\frac{1}{2} x^2 \coth ^{-1}(d \coth (a+b x)+d+1)+\frac{b x^3}{6}",1,"(b*x^3)/6 + (x^2*ArcCoth[1 + d + d*Coth[a + b*x]])/2 - (x^2*Log[1 - (1 + d)*E^(2*a + 2*b*x)])/4 - (x*PolyLog[2, (1 + d)*E^(2*a + 2*b*x)])/(4*b) + PolyLog[3, (1 + d)*E^(2*a + 2*b*x)]/(8*b^2)","A",6,6,14,0.4286,1,"{6242, 2184, 2190, 2531, 2282, 6589}"
224,1,69,0,0.1447762,"\int \coth ^{-1}(1+d+d \coth (a+b x)) \, dx","Int[ArcCoth[1 + d + d*Coth[a + b*x]],x]","-\frac{\text{PolyLog}\left(2,(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} x \log \left(1-(d+1) e^{2 a+2 b x}\right)+x \coth ^{-1}(d \coth (a+b x)+d+1)+\frac{b x^2}{2}","-\frac{\text{PolyLog}\left(2,(d+1) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} x \log \left(1-(d+1) e^{2 a+2 b x}\right)+x \coth ^{-1}(d \coth (a+b x)+d+1)+\frac{b x^2}{2}",1,"(b*x^2)/2 + x*ArcCoth[1 + d + d*Coth[a + b*x]] - (x*Log[1 - (1 + d)*E^(2*a + 2*b*x)])/2 - PolyLog[2, (1 + d)*E^(2*a + 2*b*x)]/(4*b)","A",5,5,12,0.4167,1,"{6234, 2184, 2190, 2279, 2391}"
225,0,0,0,0.0609226,"\int \frac{\coth ^{-1}(1+d+d \coth (a+b x))}{x} \, dx","Int[ArcCoth[1 + d + d*Coth[a + b*x]]/x,x]","\int \frac{\coth ^{-1}(1+d+d \coth (a+b x))}{x} \, dx","\text{Int}\left(\frac{\coth ^{-1}(d \coth (a+b x)+d+1)}{x},x\right)",0,"Defer[Int][ArcCoth[1 + d + d*Coth[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
226,1,165,0,0.3097015,"\int x^3 \coth ^{-1}(1-d-d \coth (a+b x)) \, dx","Int[x^3*ArcCoth[1 - d - d*Coth[a + b*x]],x]","\frac{3 x^2 \text{PolyLog}\left(3,(1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 x \text{PolyLog}\left(4,(1-d) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 \text{PolyLog}\left(5,(1-d) e^{2 a+2 b x}\right)}{16 b^4}-\frac{x^3 \text{PolyLog}\left(2,(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{8} x^4 \log \left(1-(1-d) e^{2 a+2 b x}\right)+\frac{1}{4} x^4 \coth ^{-1}(d (-\coth (a+b x))-d+1)+\frac{b x^5}{20}","\frac{3 x^2 \text{PolyLog}\left(3,(1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{3 x \text{PolyLog}\left(4,(1-d) e^{2 a+2 b x}\right)}{8 b^3}+\frac{3 \text{PolyLog}\left(5,(1-d) e^{2 a+2 b x}\right)}{16 b^4}-\frac{x^3 \text{PolyLog}\left(2,(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{8} x^4 \log \left(1-(1-d) e^{2 a+2 b x}\right)+\frac{1}{4} x^4 \coth ^{-1}(d (-\coth (a+b x))-d+1)+\frac{b x^5}{20}",1,"(b*x^5)/20 + (x^4*ArcCoth[1 - d - d*Coth[a + b*x]])/4 - (x^4*Log[1 - (1 - d)*E^(2*a + 2*b*x)])/8 - (x^3*PolyLog[2, (1 - d)*E^(2*a + 2*b*x)])/(4*b) + (3*x^2*PolyLog[3, (1 - d)*E^(2*a + 2*b*x)])/(8*b^2) - (3*x*PolyLog[4, (1 - d)*E^(2*a + 2*b*x)])/(8*b^3) + (3*PolyLog[5, (1 - d)*E^(2*a + 2*b*x)])/(16*b^4)","A",8,7,19,0.3684,1,"{6242, 2184, 2190, 2531, 6609, 2282, 6589}"
227,1,137,0,0.2701007,"\int x^2 \coth ^{-1}(1-d-d \coth (a+b x)) \, dx","Int[x^2*ArcCoth[1 - d - d*Coth[a + b*x]],x]","\frac{x \text{PolyLog}\left(3,(1-d) e^{2 a+2 b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,(1-d) e^{2 a+2 b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1-(1-d) e^{2 a+2 b x}\right)+\frac{1}{3} x^3 \coth ^{-1}(d (-\coth (a+b x))-d+1)+\frac{b x^4}{12}","\frac{x \text{PolyLog}\left(3,(1-d) e^{2 a+2 b x}\right)}{4 b^2}-\frac{\text{PolyLog}\left(4,(1-d) e^{2 a+2 b x}\right)}{8 b^3}-\frac{x^2 \text{PolyLog}\left(2,(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1-(1-d) e^{2 a+2 b x}\right)+\frac{1}{3} x^3 \coth ^{-1}(d (-\coth (a+b x))-d+1)+\frac{b x^4}{12}",1,"(b*x^4)/12 + (x^3*ArcCoth[1 - d - d*Coth[a + b*x]])/3 - (x^3*Log[1 - (1 - d)*E^(2*a + 2*b*x)])/6 - (x^2*PolyLog[2, (1 - d)*E^(2*a + 2*b*x)])/(4*b) + (x*PolyLog[3, (1 - d)*E^(2*a + 2*b*x)])/(4*b^2) - PolyLog[4, (1 - d)*E^(2*a + 2*b*x)]/(8*b^3)","A",7,7,19,0.3684,1,"{6242, 2184, 2190, 2531, 6609, 2282, 6589}"
228,1,109,0,0.2377283,"\int x \coth ^{-1}(1-d-d \coth (a+b x)) \, dx","Int[x*ArcCoth[1 - d - d*Coth[a + b*x]],x]","\frac{\text{PolyLog}\left(3,(1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1-(1-d) e^{2 a+2 b x}\right)+\frac{1}{2} x^2 \coth ^{-1}(d (-\coth (a+b x))-d+1)+\frac{b x^3}{6}","\frac{\text{PolyLog}\left(3,(1-d) e^{2 a+2 b x}\right)}{8 b^2}-\frac{x \text{PolyLog}\left(2,(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1-(1-d) e^{2 a+2 b x}\right)+\frac{1}{2} x^2 \coth ^{-1}(d (-\coth (a+b x))-d+1)+\frac{b x^3}{6}",1,"(b*x^3)/6 + (x^2*ArcCoth[1 - d - d*Coth[a + b*x]])/2 - (x^2*Log[1 - (1 - d)*E^(2*a + 2*b*x)])/4 - (x*PolyLog[2, (1 - d)*E^(2*a + 2*b*x)])/(4*b) + PolyLog[3, (1 - d)*E^(2*a + 2*b*x)]/(8*b^2)","A",6,6,17,0.3529,1,"{6242, 2184, 2190, 2531, 2282, 6589}"
229,1,76,0,0.144469,"\int \coth ^{-1}(1-d-d \coth (a+b x)) \, dx","Int[ArcCoth[1 - d - d*Coth[a + b*x]],x]","-\frac{\text{PolyLog}\left(2,(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} x \log \left(1-(1-d) e^{2 a+2 b x}\right)+x \coth ^{-1}(d (-\coth (a+b x))-d+1)+\frac{b x^2}{2}","-\frac{\text{PolyLog}\left(2,(1-d) e^{2 a+2 b x}\right)}{4 b}-\frac{1}{2} x \log \left(1-(1-d) e^{2 a+2 b x}\right)+x \coth ^{-1}(d (-\coth (a+b x))-d+1)+\frac{b x^2}{2}",1,"(b*x^2)/2 + x*ArcCoth[1 - d - d*Coth[a + b*x]] - (x*Log[1 - (1 - d)*E^(2*a + 2*b*x)])/2 - PolyLog[2, (1 - d)*E^(2*a + 2*b*x)]/(4*b)","A",5,5,15,0.3333,1,"{6234, 2184, 2190, 2279, 2391}"
230,0,0,0,0.0834828,"\int \frac{\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx","Int[ArcCoth[1 - d - d*Coth[a + b*x]]/x,x]","\int \frac{\coth ^{-1}(1-d-d \coth (a+b x))}{x} \, dx","\text{Int}\left(\frac{\coth ^{-1}(d (-\coth (a+b x))-d+1)}{x},x\right)",0,"Defer[Int][ArcCoth[1 - d - d*Coth[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
231,1,302,0,0.2424803,"\int (e+f x)^3 \coth ^{-1}(\tan (a+b x)) \, dx","Int[(e + f*x)^3*ArcCoth[Tan[a + b*x]],x]","\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,i e^{2 i (a+b x)}\right)}{8 b^3}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f^3 \text{PolyLog}\left(5,-i e^{2 i (a+b x)}\right)}{16 b^4}+\frac{3 f^3 \text{PolyLog}\left(5,i e^{2 i (a+b x)}\right)}{16 b^4}-\frac{i (e+f x)^3 \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^4 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{4 f}+\frac{(e+f x)^4 \coth ^{-1}(\tan (a+b x))}{4 f}","\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,i e^{2 i (a+b x)}\right)}{8 b^3}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f^3 \text{PolyLog}\left(5,-i e^{2 i (a+b x)}\right)}{16 b^4}+\frac{3 f^3 \text{PolyLog}\left(5,i e^{2 i (a+b x)}\right)}{16 b^4}-\frac{i (e+f x)^3 \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^4 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{4 f}+\frac{(e+f x)^4 \coth ^{-1}(\tan (a+b x))}{4 f}",1,"((e + f*x)^4*ArcCoth[Tan[a + b*x]])/(4*f) + ((I/4)*(e + f*x)^4*ArcTan[E^((2*I)*(a + b*x))])/f - ((I/4)*(e + f*x)^3*PolyLog[2, (-I)*E^((2*I)*(a + b*x))])/b + ((I/4)*(e + f*x)^3*PolyLog[2, I*E^((2*I)*(a + b*x))])/b + (3*f*(e + f*x)^2*PolyLog[3, (-I)*E^((2*I)*(a + b*x))])/(8*b^2) - (3*f*(e + f*x)^2*PolyLog[3, I*E^((2*I)*(a + b*x))])/(8*b^2) + (((3*I)/8)*f^2*(e + f*x)*PolyLog[4, (-I)*E^((2*I)*(a + b*x))])/b^3 - (((3*I)/8)*f^2*(e + f*x)*PolyLog[4, I*E^((2*I)*(a + b*x))])/b^3 - (3*f^3*PolyLog[5, (-I)*E^((2*I)*(a + b*x))])/(16*b^4) + (3*f^3*PolyLog[5, I*E^((2*I)*(a + b*x))])/(16*b^4)","A",12,6,15,0.4000,1,"{6252, 4181, 2531, 6609, 2282, 6589}"
232,1,234,0,0.1716698,"\int (e+f x)^2 \coth ^{-1}(\tan (a+b x)) \, dx","Int[(e + f*x)^2*ArcCoth[Tan[a + b*x]],x]","\frac{f (e+f x) \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{4 b^2}-\frac{f (e+f x) \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{4 b^2}+\frac{i f^2 \text{PolyLog}\left(4,-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i f^2 \text{PolyLog}\left(4,i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i (e+f x)^2 \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{3 f}+\frac{(e+f x)^3 \coth ^{-1}(\tan (a+b x))}{3 f}","\frac{f (e+f x) \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{4 b^2}-\frac{f (e+f x) \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{4 b^2}+\frac{i f^2 \text{PolyLog}\left(4,-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i f^2 \text{PolyLog}\left(4,i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i (e+f x)^2 \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{3 f}+\frac{(e+f x)^3 \coth ^{-1}(\tan (a+b x))}{3 f}",1,"((e + f*x)^3*ArcCoth[Tan[a + b*x]])/(3*f) + ((I/3)*(e + f*x)^3*ArcTan[E^((2*I)*(a + b*x))])/f - ((I/4)*(e + f*x)^2*PolyLog[2, (-I)*E^((2*I)*(a + b*x))])/b + ((I/4)*(e + f*x)^2*PolyLog[2, I*E^((2*I)*(a + b*x))])/b + (f*(e + f*x)*PolyLog[3, (-I)*E^((2*I)*(a + b*x))])/(4*b^2) - (f*(e + f*x)*PolyLog[3, I*E^((2*I)*(a + b*x))])/(4*b^2) + ((I/8)*f^2*PolyLog[4, (-I)*E^((2*I)*(a + b*x))])/b^3 - ((I/8)*f^2*PolyLog[4, I*E^((2*I)*(a + b*x))])/b^3","A",10,6,15,0.4000,1,"{6252, 4181, 2531, 6609, 2282, 6589}"
233,1,162,0,0.1114016,"\int (e+f x) \coth ^{-1}(\tan (a+b x)) \, dx","Int[(e + f*x)*ArcCoth[Tan[a + b*x]],x]","\frac{f \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{f \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{i (e+f x) \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x) \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{2 f}+\frac{(e+f x)^2 \coth ^{-1}(\tan (a+b x))}{2 f}","\frac{f \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{f \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{i (e+f x) \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x) \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{2 f}+\frac{(e+f x)^2 \coth ^{-1}(\tan (a+b x))}{2 f}",1,"((e + f*x)^2*ArcCoth[Tan[a + b*x]])/(2*f) + ((I/2)*(e + f*x)^2*ArcTan[E^((2*I)*(a + b*x))])/f - ((I/4)*(e + f*x)*PolyLog[2, (-I)*E^((2*I)*(a + b*x))])/b + ((I/4)*(e + f*x)*PolyLog[2, I*E^((2*I)*(a + b*x))])/b + (f*PolyLog[3, (-I)*E^((2*I)*(a + b*x))])/(8*b^2) - (f*PolyLog[3, I*E^((2*I)*(a + b*x))])/(8*b^2)","A",8,5,13,0.3846,1,"{6252, 4181, 2531, 2282, 6589}"
234,1,79,0,0.047899,"\int \coth ^{-1}(\tan (a+b x)) \, dx","Int[ArcCoth[Tan[a + b*x]],x]","-\frac{i \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+i x \tan ^{-1}\left(e^{2 i (a+b x)}\right)+x \coth ^{-1}(\tan (a+b x))","-\frac{i \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+i x \tan ^{-1}\left(e^{2 i (a+b x)}\right)+x \coth ^{-1}(\tan (a+b x))",1,"x*ArcCoth[Tan[a + b*x]] + I*x*ArcTan[E^((2*I)*(a + b*x))] - ((I/4)*PolyLog[2, (-I)*E^((2*I)*(a + b*x))])/b + ((I/4)*PolyLog[2, I*E^((2*I)*(a + b*x))])/b","A",6,4,7,0.5714,1,"{6248, 4181, 2279, 2391}"
235,0,0,0,0.0410895,"\int \frac{\coth ^{-1}(\tan (a+b x))}{e+f x} \, dx","Int[ArcCoth[Tan[a + b*x]]/(e + f*x),x]","\int \frac{\coth ^{-1}(\tan (a+b x))}{e+f x} \, dx","\text{Int}\left(\frac{\coth ^{-1}(\tan (a+b x))}{e+f x},x\right)",0,"Defer[Int][ArcCoth[Tan[a + b*x]]/(e + f*x), x]","A",0,0,0,0,-1,"{}"
236,1,395,0,0.5000787,"\int x^2 \coth ^{-1}(c+d \tan (a+b x)) \, dx","Int[x^2*ArcCoth[c + d*Tan[a + b*x]],x]","\frac{x \text{PolyLog}\left(3,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b^2}-\frac{x \text{PolyLog}\left(3,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b^2}+\frac{i \text{PolyLog}\left(4,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{8 b^3}-\frac{i \text{PolyLog}\left(4,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{8 b^3}-\frac{i x^2 \text{PolyLog}\left(2,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b}+\frac{i x^2 \text{PolyLog}\left(2,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b}+\frac{1}{6} x^3 \log \left(1+\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)-\frac{1}{6} x^3 \log \left(1+\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)+\frac{1}{3} x^3 \coth ^{-1}(d \tan (a+b x)+c)","\frac{x \text{PolyLog}\left(3,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b^2}-\frac{x \text{PolyLog}\left(3,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b^2}+\frac{i \text{PolyLog}\left(4,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{8 b^3}-\frac{i \text{PolyLog}\left(4,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{8 b^3}-\frac{i x^2 \text{PolyLog}\left(2,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b}+\frac{i x^2 \text{PolyLog}\left(2,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b}+\frac{1}{6} x^3 \log \left(1+\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)-\frac{1}{6} x^3 \log \left(1+\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)+\frac{1}{3} x^3 \coth ^{-1}(d \tan (a+b x)+c)",1,"(x^3*ArcCoth[c + d*Tan[a + b*x]])/3 + (x^3*Log[1 + ((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d)])/6 - (x^3*Log[1 + ((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d)])/6 - ((I/4)*x^2*PolyLog[2, -(((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d))])/b + ((I/4)*x^2*PolyLog[2, -(((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d))])/b + (x*PolyLog[3, -(((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d))])/(4*b^2) - (x*PolyLog[3, -(((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d))])/(4*b^2) + ((I/8)*PolyLog[4, -(((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d))])/b^3 - ((I/8)*PolyLog[4, -(((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d))])/b^3","A",11,6,15,0.4000,1,"{6268, 2190, 2531, 6609, 2282, 6589}"
237,1,295,0,0.3969988,"\int x \coth ^{-1}(c+d \tan (a+b x)) \, dx","Int[x*ArcCoth[c + d*Tan[a + b*x]],x]","\frac{\text{PolyLog}\left(3,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{8 b^2}-\frac{\text{PolyLog}\left(3,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{8 b^2}-\frac{i x \text{PolyLog}\left(2,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b}+\frac{i x \text{PolyLog}\left(2,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b}+\frac{1}{4} x^2 \log \left(1+\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)-\frac{1}{4} x^2 \log \left(1+\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)+\frac{1}{2} x^2 \coth ^{-1}(d \tan (a+b x)+c)","\frac{\text{PolyLog}\left(3,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{8 b^2}-\frac{\text{PolyLog}\left(3,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{8 b^2}-\frac{i x \text{PolyLog}\left(2,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b}+\frac{i x \text{PolyLog}\left(2,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b}+\frac{1}{4} x^2 \log \left(1+\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)-\frac{1}{4} x^2 \log \left(1+\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)+\frac{1}{2} x^2 \coth ^{-1}(d \tan (a+b x)+c)",1,"(x^2*ArcCoth[c + d*Tan[a + b*x]])/2 + (x^2*Log[1 + ((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d)])/4 - (x^2*Log[1 + ((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d)])/4 - ((I/4)*x*PolyLog[2, -(((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d))])/b + ((I/4)*x*PolyLog[2, -(((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d))])/b + PolyLog[3, -(((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d))]/(8*b^2) - PolyLog[3, -(((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d))]/(8*b^2)","A",9,5,13,0.3846,1,"{6268, 2190, 2531, 2282, 6589}"
238,1,194,0,0.250733,"\int \coth ^{-1}(c+d \tan (a+b x)) \, dx","Int[ArcCoth[c + d*Tan[a + b*x]],x]","-\frac{i \text{PolyLog}\left(2,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b}+\frac{1}{2} x \log \left(1+\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)-\frac{1}{2} x \log \left(1+\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)+x \coth ^{-1}(d \tan (a+b x)+c)","-\frac{i \text{PolyLog}\left(2,-\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,-\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)}{4 b}+\frac{1}{2} x \log \left(1+\frac{(-c+i d+1) e^{2 i a+2 i b x}}{-c-i d+1}\right)-\frac{1}{2} x \log \left(1+\frac{(c-i d+1) e^{2 i a+2 i b x}}{c+i d+1}\right)+x \coth ^{-1}(d \tan (a+b x)+c)",1,"x*ArcCoth[c + d*Tan[a + b*x]] + (x*Log[1 + ((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d)])/2 - (x*Log[1 + ((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d)])/2 - ((I/4)*PolyLog[2, -(((1 - c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c - I*d))])/b + ((I/4)*PolyLog[2, -(((1 + c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c + I*d))])/b","A",7,4,11,0.3636,1,"{6260, 2190, 2279, 2391}"
239,0,0,0,0.1456209,"\int \frac{\coth ^{-1}(c+d \tan (a+b x))}{x} \, dx","Int[ArcCoth[c + d*Tan[a + b*x]]/x,x]","\int \frac{\coth ^{-1}(c+d \tan (a+b x))}{x} \, dx","\text{Int}\left(\frac{\coth ^{-1}(d \tan (a+b x)+c)}{x},x\right)",0,"Defer[Int][ArcCoth[c + d*Tan[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
240,1,170,0,0.3043447,"\int x^2 \coth ^{-1}(1-i d+d \tan (a+b x)) \, dx","Int[x^2*ArcCoth[1 - I*d + d*Tan[a + b*x]],x]","-\frac{x \text{PolyLog}\left(3,-(1-i d) e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,-(1-i d) e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,-(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1+(1-i d) e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \coth ^{-1}(d \tan (a+b x)-i d+1)+\frac{1}{12} i b x^4","-\frac{x \text{PolyLog}\left(3,-(1-i d) e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,-(1-i d) e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,-(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1+(1-i d) e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \coth ^{-1}(d \tan (a+b x)-i d+1)+\frac{1}{12} i b x^4",1,"(I/12)*b*x^4 + (x^3*ArcCoth[1 - I*d + d*Tan[a + b*x]])/3 - (x^3*Log[1 + (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/6 + ((I/4)*x^2*PolyLog[2, -((1 - I*d)*E^((2*I)*a + (2*I)*b*x))])/b - (x*PolyLog[3, -((1 - I*d)*E^((2*I)*a + (2*I)*b*x))])/(4*b^2) - ((I/8)*PolyLog[4, -((1 - I*d)*E^((2*I)*a + (2*I)*b*x))])/b^3","A",7,7,20,0.3500,1,"{6264, 2184, 2190, 2531, 6609, 2282, 6589}"
241,1,133,0,0.2534737,"\int x \coth ^{-1}(1-i d+d \tan (a+b x)) \, dx","Int[x*ArcCoth[1 - I*d + d*Tan[a + b*x]],x]","-\frac{\text{PolyLog}\left(3,-(1-i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,-(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1+(1-i d) e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \coth ^{-1}(d \tan (a+b x)-i d+1)+\frac{1}{6} i b x^3","-\frac{\text{PolyLog}\left(3,-(1-i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,-(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1+(1-i d) e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \coth ^{-1}(d \tan (a+b x)-i d+1)+\frac{1}{6} i b x^3",1,"(I/6)*b*x^3 + (x^2*ArcCoth[1 - I*d + d*Tan[a + b*x]])/2 - (x^2*Log[1 + (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/4 + ((I/4)*x*PolyLog[2, -((1 - I*d)*E^((2*I)*a + (2*I)*b*x))])/b - PolyLog[3, -((1 - I*d)*E^((2*I)*a + (2*I)*b*x))]/(8*b^2)","A",6,6,18,0.3333,1,"{6264, 2184, 2190, 2531, 2282, 6589}"
242,1,93,0,0.154592,"\int \coth ^{-1}(1-i d+d \tan (a+b x)) \, dx","Int[ArcCoth[1 - I*d + d*Tan[a + b*x]],x]","\frac{i \text{PolyLog}\left(2,-(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} x \log \left(1+(1-i d) e^{2 i a+2 i b x}\right)+x \coth ^{-1}(d \tan (a+b x)-i d+1)+\frac{1}{2} i b x^2","\frac{i \text{PolyLog}\left(2,-(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} x \log \left(1+(1-i d) e^{2 i a+2 i b x}\right)+x \coth ^{-1}(d \tan (a+b x)-i d+1)+\frac{1}{2} i b x^2",1,"(I/2)*b*x^2 + x*ArcCoth[1 - I*d + d*Tan[a + b*x]] - (x*Log[1 + (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/2 + ((I/4)*PolyLog[2, -((1 - I*d)*E^((2*I)*a + (2*I)*b*x))])/b","A",5,5,16,0.3125,1,"{6256, 2184, 2190, 2279, 2391}"
243,0,0,0,0.0885803,"\int \frac{\coth ^{-1}(1-i d+d \tan (a+b x))}{x} \, dx","Int[ArcCoth[1 - I*d + d*Tan[a + b*x]]/x,x]","\int \frac{\coth ^{-1}(1-i d+d \tan (a+b x))}{x} \, dx","\text{Int}\left(\frac{\coth ^{-1}(d \tan (a+b x)-i d+1)}{x},x\right)",0,"Defer[Int][ArcCoth[1 - I*d + d*Tan[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
244,1,171,0,0.297572,"\int x^2 \coth ^{-1}(1+i d-d \tan (a+b x)) \, dx","Int[x^2*ArcCoth[1 + I*d - d*Tan[a + b*x]],x]","-\frac{x \text{PolyLog}\left(3,-(1+i d) e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,-(1+i d) e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,-(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1+(1+i d) e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \coth ^{-1}(d (-\tan (a+b x))+i d+1)+\frac{1}{12} i b x^4","-\frac{x \text{PolyLog}\left(3,-(1+i d) e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,-(1+i d) e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,-(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1+(1+i d) e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \coth ^{-1}(d (-\tan (a+b x))+i d+1)+\frac{1}{12} i b x^4",1,"(I/12)*b*x^4 + (x^3*ArcCoth[1 + I*d - d*Tan[a + b*x]])/3 - (x^3*Log[1 + (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/6 + ((I/4)*x^2*PolyLog[2, -((1 + I*d)*E^((2*I)*a + (2*I)*b*x))])/b - (x*PolyLog[3, -((1 + I*d)*E^((2*I)*a + (2*I)*b*x))])/(4*b^2) - ((I/8)*PolyLog[4, -((1 + I*d)*E^((2*I)*a + (2*I)*b*x))])/b^3","A",7,7,21,0.3333,1,"{6264, 2184, 2190, 2531, 6609, 2282, 6589}"
245,1,134,0,0.2453796,"\int x \coth ^{-1}(1+i d-d \tan (a+b x)) \, dx","Int[x*ArcCoth[1 + I*d - d*Tan[a + b*x]],x]","-\frac{\text{PolyLog}\left(3,-(1+i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,-(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1+(1+i d) e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \coth ^{-1}(d (-\tan (a+b x))+i d+1)+\frac{1}{6} i b x^3","-\frac{\text{PolyLog}\left(3,-(1+i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,-(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1+(1+i d) e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \coth ^{-1}(d (-\tan (a+b x))+i d+1)+\frac{1}{6} i b x^3",1,"(I/6)*b*x^3 + (x^2*ArcCoth[1 + I*d - d*Tan[a + b*x]])/2 - (x^2*Log[1 + (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/4 + ((I/4)*x*PolyLog[2, -((1 + I*d)*E^((2*I)*a + (2*I)*b*x))])/b - PolyLog[3, -((1 + I*d)*E^((2*I)*a + (2*I)*b*x))]/(8*b^2)","A",6,6,19,0.3158,1,"{6264, 2184, 2190, 2531, 2282, 6589}"
246,1,94,0,0.1564407,"\int \coth ^{-1}(1+i d-d \tan (a+b x)) \, dx","Int[ArcCoth[1 + I*d - d*Tan[a + b*x]],x]","\frac{i \text{PolyLog}\left(2,-(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} x \log \left(1+(1+i d) e^{2 i a+2 i b x}\right)+x \coth ^{-1}(d (-\tan (a+b x))+i d+1)+\frac{1}{2} i b x^2","\frac{i \text{PolyLog}\left(2,-(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} x \log \left(1+(1+i d) e^{2 i a+2 i b x}\right)+x \coth ^{-1}(d (-\tan (a+b x))+i d+1)+\frac{1}{2} i b x^2",1,"(I/2)*b*x^2 + x*ArcCoth[1 + I*d - d*Tan[a + b*x]] - (x*Log[1 + (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/2 + ((I/4)*PolyLog[2, -((1 + I*d)*E^((2*I)*a + (2*I)*b*x))])/b","A",5,5,17,0.2941,1,"{6256, 2184, 2190, 2279, 2391}"
247,0,0,0,0.0846946,"\int \frac{\coth ^{-1}(1+i d-d \tan (a+b x))}{x} \, dx","Int[ArcCoth[1 + I*d - d*Tan[a + b*x]]/x,x]","\int \frac{\coth ^{-1}(1+i d-d \tan (a+b x))}{x} \, dx","\text{Int}\left(\frac{\coth ^{-1}(d (-\tan (a+b x))+i d+1)}{x},x\right)",0,"Defer[Int][ArcCoth[1 + I*d - d*Tan[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
248,1,302,0,0.2350766,"\int (e+f x)^3 \coth ^{-1}(\cot (a+b x)) \, dx","Int[(e + f*x)^3*ArcCoth[Cot[a + b*x]],x]","\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,i e^{2 i (a+b x)}\right)}{8 b^3}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f^3 \text{PolyLog}\left(5,-i e^{2 i (a+b x)}\right)}{16 b^4}+\frac{3 f^3 \text{PolyLog}\left(5,i e^{2 i (a+b x)}\right)}{16 b^4}-\frac{i (e+f x)^3 \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^4 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{4 f}+\frac{(e+f x)^4 \coth ^{-1}(\cot (a+b x))}{4 f}","\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(4,i e^{2 i (a+b x)}\right)}{8 b^3}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{3 f^3 \text{PolyLog}\left(5,-i e^{2 i (a+b x)}\right)}{16 b^4}+\frac{3 f^3 \text{PolyLog}\left(5,i e^{2 i (a+b x)}\right)}{16 b^4}-\frac{i (e+f x)^3 \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^4 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{4 f}+\frac{(e+f x)^4 \coth ^{-1}(\cot (a+b x))}{4 f}",1,"((e + f*x)^4*ArcCoth[Cot[a + b*x]])/(4*f) + ((I/4)*(e + f*x)^4*ArcTan[E^((2*I)*(a + b*x))])/f - ((I/4)*(e + f*x)^3*PolyLog[2, (-I)*E^((2*I)*(a + b*x))])/b + ((I/4)*(e + f*x)^3*PolyLog[2, I*E^((2*I)*(a + b*x))])/b + (3*f*(e + f*x)^2*PolyLog[3, (-I)*E^((2*I)*(a + b*x))])/(8*b^2) - (3*f*(e + f*x)^2*PolyLog[3, I*E^((2*I)*(a + b*x))])/(8*b^2) + (((3*I)/8)*f^2*(e + f*x)*PolyLog[4, (-I)*E^((2*I)*(a + b*x))])/b^3 - (((3*I)/8)*f^2*(e + f*x)*PolyLog[4, I*E^((2*I)*(a + b*x))])/b^3 - (3*f^3*PolyLog[5, (-I)*E^((2*I)*(a + b*x))])/(16*b^4) + (3*f^3*PolyLog[5, I*E^((2*I)*(a + b*x))])/(16*b^4)","A",12,6,15,0.4000,1,"{6254, 4181, 2531, 6609, 2282, 6589}"
249,1,234,0,0.1709114,"\int (e+f x)^2 \coth ^{-1}(\cot (a+b x)) \, dx","Int[(e + f*x)^2*ArcCoth[Cot[a + b*x]],x]","\frac{f (e+f x) \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{4 b^2}-\frac{f (e+f x) \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{4 b^2}+\frac{i f^2 \text{PolyLog}\left(4,-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i f^2 \text{PolyLog}\left(4,i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i (e+f x)^2 \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{3 f}+\frac{(e+f x)^3 \coth ^{-1}(\cot (a+b x))}{3 f}","\frac{f (e+f x) \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{4 b^2}-\frac{f (e+f x) \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{4 b^2}+\frac{i f^2 \text{PolyLog}\left(4,-i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i f^2 \text{PolyLog}\left(4,i e^{2 i (a+b x)}\right)}{8 b^3}-\frac{i (e+f x)^2 \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^3 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{3 f}+\frac{(e+f x)^3 \coth ^{-1}(\cot (a+b x))}{3 f}",1,"((e + f*x)^3*ArcCoth[Cot[a + b*x]])/(3*f) + ((I/3)*(e + f*x)^3*ArcTan[E^((2*I)*(a + b*x))])/f - ((I/4)*(e + f*x)^2*PolyLog[2, (-I)*E^((2*I)*(a + b*x))])/b + ((I/4)*(e + f*x)^2*PolyLog[2, I*E^((2*I)*(a + b*x))])/b + (f*(e + f*x)*PolyLog[3, (-I)*E^((2*I)*(a + b*x))])/(4*b^2) - (f*(e + f*x)*PolyLog[3, I*E^((2*I)*(a + b*x))])/(4*b^2) + ((I/8)*f^2*PolyLog[4, (-I)*E^((2*I)*(a + b*x))])/b^3 - ((I/8)*f^2*PolyLog[4, I*E^((2*I)*(a + b*x))])/b^3","A",10,6,15,0.4000,1,"{6254, 4181, 2531, 6609, 2282, 6589}"
250,1,162,0,0.1101492,"\int (e+f x) \coth ^{-1}(\cot (a+b x)) \, dx","Int[(e + f*x)*ArcCoth[Cot[a + b*x]],x]","\frac{f \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{f \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{i (e+f x) \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x) \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{2 f}+\frac{(e+f x)^2 \coth ^{-1}(\cot (a+b x))}{2 f}","\frac{f \text{PolyLog}\left(3,-i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{f \text{PolyLog}\left(3,i e^{2 i (a+b x)}\right)}{8 b^2}-\frac{i (e+f x) \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x) \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+\frac{i (e+f x)^2 \tan ^{-1}\left(e^{2 i (a+b x)}\right)}{2 f}+\frac{(e+f x)^2 \coth ^{-1}(\cot (a+b x))}{2 f}",1,"((e + f*x)^2*ArcCoth[Cot[a + b*x]])/(2*f) + ((I/2)*(e + f*x)^2*ArcTan[E^((2*I)*(a + b*x))])/f - ((I/4)*(e + f*x)*PolyLog[2, (-I)*E^((2*I)*(a + b*x))])/b + ((I/4)*(e + f*x)*PolyLog[2, I*E^((2*I)*(a + b*x))])/b + (f*PolyLog[3, (-I)*E^((2*I)*(a + b*x))])/(8*b^2) - (f*PolyLog[3, I*E^((2*I)*(a + b*x))])/(8*b^2)","A",8,5,13,0.3846,1,"{6254, 4181, 2531, 2282, 6589}"
251,1,79,0,0.048343,"\int \coth ^{-1}(\cot (a+b x)) \, dx","Int[ArcCoth[Cot[a + b*x]],x]","-\frac{i \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+i x \tan ^{-1}\left(e^{2 i (a+b x)}\right)+x \coth ^{-1}(\cot (a+b x))","-\frac{i \text{PolyLog}\left(2,-i e^{2 i (a+b x)}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,i e^{2 i (a+b x)}\right)}{4 b}+i x \tan ^{-1}\left(e^{2 i (a+b x)}\right)+x \coth ^{-1}(\cot (a+b x))",1,"x*ArcCoth[Cot[a + b*x]] + I*x*ArcTan[E^((2*I)*(a + b*x))] - ((I/4)*PolyLog[2, (-I)*E^((2*I)*(a + b*x))])/b + ((I/4)*PolyLog[2, I*E^((2*I)*(a + b*x))])/b","A",6,4,7,0.5714,1,"{6250, 4181, 2279, 2391}"
252,0,0,0,0.0417984,"\int \frac{\coth ^{-1}(\cot (a+b x))}{e+f x} \, dx","Int[ArcCoth[Cot[a + b*x]]/(e + f*x),x]","\int \frac{\coth ^{-1}(\cot (a+b x))}{e+f x} \, dx","\text{Int}\left(\frac{\coth ^{-1}(\cot (a+b x))}{e+f x},x\right)",0,"Defer[Int][ArcCoth[Cot[a + b*x]]/(e + f*x), x]","A",0,0,0,0,-1,"{}"
253,1,391,0,0.503235,"\int x^2 \coth ^{-1}(c+d \cot (a+b x)) \, dx","Int[x^2*ArcCoth[c + d*Cot[a + b*x]],x]","\frac{x \text{PolyLog}\left(3,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b^2}-\frac{x \text{PolyLog}\left(3,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b^2}+\frac{i \text{PolyLog}\left(4,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{8 b^3}-\frac{i \text{PolyLog}\left(4,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{8 b^3}-\frac{i x^2 \text{PolyLog}\left(2,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b}+\frac{i x^2 \text{PolyLog}\left(2,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b}+\frac{1}{6} x^3 \log \left(1-\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)-\frac{1}{6} x^3 \log \left(1-\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)+\frac{1}{3} x^3 \coth ^{-1}(d \cot (a+b x)+c)","\frac{x \text{PolyLog}\left(3,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b^2}-\frac{x \text{PolyLog}\left(3,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b^2}+\frac{i \text{PolyLog}\left(4,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{8 b^3}-\frac{i \text{PolyLog}\left(4,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{8 b^3}-\frac{i x^2 \text{PolyLog}\left(2,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b}+\frac{i x^2 \text{PolyLog}\left(2,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b}+\frac{1}{6} x^3 \log \left(1-\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)-\frac{1}{6} x^3 \log \left(1-\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)+\frac{1}{3} x^3 \coth ^{-1}(d \cot (a+b x)+c)",1,"(x^3*ArcCoth[c + d*Cot[a + b*x]])/3 + (x^3*Log[1 - ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)])/6 - (x^3*Log[1 - ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)])/6 - ((I/4)*x^2*PolyLog[2, ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)])/b + ((I/4)*x^2*PolyLog[2, ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)])/b + (x*PolyLog[3, ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)])/(4*b^2) - (x*PolyLog[3, ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)])/(4*b^2) + ((I/8)*PolyLog[4, ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)])/b^3 - ((I/8)*PolyLog[4, ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)])/b^3","A",11,6,15,0.4000,1,"{6270, 2190, 2531, 6609, 2282, 6589}"
254,1,293,0,0.4034702,"\int x \coth ^{-1}(c+d \cot (a+b x)) \, dx","Int[x*ArcCoth[c + d*Cot[a + b*x]],x]","\frac{\text{PolyLog}\left(3,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{8 b^2}-\frac{\text{PolyLog}\left(3,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{8 b^2}-\frac{i x \text{PolyLog}\left(2,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b}+\frac{i x \text{PolyLog}\left(2,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b}+\frac{1}{4} x^2 \log \left(1-\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)-\frac{1}{4} x^2 \log \left(1-\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)+\frac{1}{2} x^2 \coth ^{-1}(d \cot (a+b x)+c)","\frac{\text{PolyLog}\left(3,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{8 b^2}-\frac{\text{PolyLog}\left(3,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{8 b^2}-\frac{i x \text{PolyLog}\left(2,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b}+\frac{i x \text{PolyLog}\left(2,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b}+\frac{1}{4} x^2 \log \left(1-\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)-\frac{1}{4} x^2 \log \left(1-\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)+\frac{1}{2} x^2 \coth ^{-1}(d \cot (a+b x)+c)",1,"(x^2*ArcCoth[c + d*Cot[a + b*x]])/2 + (x^2*Log[1 - ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)])/4 - (x^2*Log[1 - ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)])/4 - ((I/4)*x*PolyLog[2, ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)])/b + ((I/4)*x*PolyLog[2, ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)])/b + PolyLog[3, ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)]/(8*b^2) - PolyLog[3, ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)]/(8*b^2)","A",9,5,13,0.3846,1,"{6270, 2190, 2531, 2282, 6589}"
255,1,194,0,0.249007,"\int \coth ^{-1}(c+d \cot (a+b x)) \, dx","Int[ArcCoth[c + d*Cot[a + b*x]],x]","-\frac{i \text{PolyLog}\left(2,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b}+\frac{1}{2} x \log \left(1-\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)-\frac{1}{2} x \log \left(1-\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)+x \coth ^{-1}(d \cot (a+b x)+c)","-\frac{i \text{PolyLog}\left(2,\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)}{4 b}+\frac{i \text{PolyLog}\left(2,\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)}{4 b}+\frac{1}{2} x \log \left(1-\frac{(-c-i d+1) e^{2 i a+2 i b x}}{-c+i d+1}\right)-\frac{1}{2} x \log \left(1-\frac{(c+i d+1) e^{2 i a+2 i b x}}{c-i d+1}\right)+x \coth ^{-1}(d \cot (a+b x)+c)",1,"x*ArcCoth[c + d*Cot[a + b*x]] + (x*Log[1 - ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)])/2 - (x*Log[1 - ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)])/2 - ((I/4)*PolyLog[2, ((1 - c - I*d)*E^((2*I)*a + (2*I)*b*x))/(1 - c + I*d)])/b + ((I/4)*PolyLog[2, ((1 + c + I*d)*E^((2*I)*a + (2*I)*b*x))/(1 + c - I*d)])/b","A",7,4,11,0.3636,1,"{6262, 2190, 2279, 2391}"
256,0,0,0,0.0933881,"\int \frac{\coth ^{-1}(c+d \cot (a+b x))}{x} \, dx","Int[ArcCoth[c + d*Cot[a + b*x]]/x,x]","\int \frac{\coth ^{-1}(c+d \cot (a+b x))}{x} \, dx","\text{Int}\left(\frac{\coth ^{-1}(d \cot (a+b x)+c)}{x},x\right)",0,"Defer[Int][ArcCoth[c + d*Cot[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
257,1,168,0,0.305705,"\int x^2 \coth ^{-1}(1+i d+d \cot (a+b x)) \, dx","Int[x^2*ArcCoth[1 + I*d + d*Cot[a + b*x]],x]","-\frac{x \text{PolyLog}\left(3,(1+i d) e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,(1+i d) e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1-(1+i d) e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \coth ^{-1}(d \cot (a+b x)+i d+1)+\frac{1}{12} i b x^4","-\frac{x \text{PolyLog}\left(3,(1+i d) e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,(1+i d) e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1-(1+i d) e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \coth ^{-1}(d \cot (a+b x)+i d+1)+\frac{1}{12} i b x^4",1,"(I/12)*b*x^4 + (x^3*ArcCoth[1 + I*d + d*Cot[a + b*x]])/3 - (x^3*Log[1 - (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/6 + ((I/4)*x^2*PolyLog[2, (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/b - (x*PolyLog[3, (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/(4*b^2) - ((I/8)*PolyLog[4, (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/b^3","A",7,7,20,0.3500,1,"{6266, 2184, 2190, 2531, 6609, 2282, 6589}"
258,1,132,0,0.2565048,"\int x \coth ^{-1}(1+i d+d \cot (a+b x)) \, dx","Int[x*ArcCoth[1 + I*d + d*Cot[a + b*x]],x]","-\frac{\text{PolyLog}\left(3,(1+i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1-(1+i d) e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \coth ^{-1}(d \cot (a+b x)+i d+1)+\frac{1}{6} i b x^3","-\frac{\text{PolyLog}\left(3,(1+i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1-(1+i d) e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \coth ^{-1}(d \cot (a+b x)+i d+1)+\frac{1}{6} i b x^3",1,"(I/6)*b*x^3 + (x^2*ArcCoth[1 + I*d + d*Cot[a + b*x]])/2 - (x^2*Log[1 - (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/4 + ((I/4)*x*PolyLog[2, (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/b - PolyLog[3, (1 + I*d)*E^((2*I)*a + (2*I)*b*x)]/(8*b^2)","A",6,6,18,0.3333,1,"{6266, 2184, 2190, 2531, 2282, 6589}"
259,1,93,0,0.1587148,"\int \coth ^{-1}(1+i d+d \cot (a+b x)) \, dx","Int[ArcCoth[1 + I*d + d*Cot[a + b*x]],x]","\frac{i \text{PolyLog}\left(2,(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} x \log \left(1-(1+i d) e^{2 i a+2 i b x}\right)+x \coth ^{-1}(d \cot (a+b x)+i d+1)+\frac{1}{2} i b x^2","\frac{i \text{PolyLog}\left(2,(1+i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} x \log \left(1-(1+i d) e^{2 i a+2 i b x}\right)+x \coth ^{-1}(d \cot (a+b x)+i d+1)+\frac{1}{2} i b x^2",1,"(I/2)*b*x^2 + x*ArcCoth[1 + I*d + d*Cot[a + b*x]] - (x*Log[1 - (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/2 + ((I/4)*PolyLog[2, (1 + I*d)*E^((2*I)*a + (2*I)*b*x)])/b","A",5,5,16,0.3125,1,"{6258, 2184, 2190, 2279, 2391}"
260,0,0,0,0.0877378,"\int \frac{\coth ^{-1}(1+i d+d \cot (a+b x))}{x} \, dx","Int[ArcCoth[1 + I*d + d*Cot[a + b*x]]/x,x]","\int \frac{\coth ^{-1}(1+i d+d \cot (a+b x))}{x} \, dx","\text{Int}\left(\frac{\coth ^{-1}(d \cot (a+b x)+i d+1)}{x},x\right)",0,"Defer[Int][ArcCoth[1 + I*d + d*Cot[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
261,1,169,0,0.2947714,"\int x^2 \coth ^{-1}(1-i d-d \cot (a+b x)) \, dx","Int[x^2*ArcCoth[1 - I*d - d*Cot[a + b*x]],x]","-\frac{x \text{PolyLog}\left(3,(1-i d) e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,(1-i d) e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1-(1-i d) e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \coth ^{-1}(d (-\cot (a+b x))-i d+1)+\frac{1}{12} i b x^4","-\frac{x \text{PolyLog}\left(3,(1-i d) e^{2 i a+2 i b x}\right)}{4 b^2}-\frac{i \text{PolyLog}\left(4,(1-i d) e^{2 i a+2 i b x}\right)}{8 b^3}+\frac{i x^2 \text{PolyLog}\left(2,(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{6} x^3 \log \left(1-(1-i d) e^{2 i a+2 i b x}\right)+\frac{1}{3} x^3 \coth ^{-1}(d (-\cot (a+b x))-i d+1)+\frac{1}{12} i b x^4",1,"(I/12)*b*x^4 + (x^3*ArcCoth[1 - I*d - d*Cot[a + b*x]])/3 - (x^3*Log[1 - (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/6 + ((I/4)*x^2*PolyLog[2, (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/b - (x*PolyLog[3, (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/(4*b^2) - ((I/8)*PolyLog[4, (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/b^3","A",7,7,21,0.3333,1,"{6266, 2184, 2190, 2531, 6609, 2282, 6589}"
262,1,133,0,0.2475888,"\int x \coth ^{-1}(1-i d-d \cot (a+b x)) \, dx","Int[x*ArcCoth[1 - I*d - d*Cot[a + b*x]],x]","-\frac{\text{PolyLog}\left(3,(1-i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1-(1-i d) e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \coth ^{-1}(d (-\cot (a+b x))-i d+1)+\frac{1}{6} i b x^3","-\frac{\text{PolyLog}\left(3,(1-i d) e^{2 i a+2 i b x}\right)}{8 b^2}+\frac{i x \text{PolyLog}\left(2,(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{4} x^2 \log \left(1-(1-i d) e^{2 i a+2 i b x}\right)+\frac{1}{2} x^2 \coth ^{-1}(d (-\cot (a+b x))-i d+1)+\frac{1}{6} i b x^3",1,"(I/6)*b*x^3 + (x^2*ArcCoth[1 - I*d - d*Cot[a + b*x]])/2 - (x^2*Log[1 - (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/4 + ((I/4)*x*PolyLog[2, (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/b - PolyLog[3, (1 - I*d)*E^((2*I)*a + (2*I)*b*x)]/(8*b^2)","A",6,6,19,0.3158,1,"{6266, 2184, 2190, 2531, 2282, 6589}"
263,1,94,0,0.1502081,"\int \coth ^{-1}(1-i d-d \cot (a+b x)) \, dx","Int[ArcCoth[1 - I*d - d*Cot[a + b*x]],x]","\frac{i \text{PolyLog}\left(2,(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} x \log \left(1-(1-i d) e^{2 i a+2 i b x}\right)+x \coth ^{-1}(d (-\cot (a+b x))-i d+1)+\frac{1}{2} i b x^2","\frac{i \text{PolyLog}\left(2,(1-i d) e^{2 i a+2 i b x}\right)}{4 b}-\frac{1}{2} x \log \left(1-(1-i d) e^{2 i a+2 i b x}\right)+x \coth ^{-1}(d (-\cot (a+b x))-i d+1)+\frac{1}{2} i b x^2",1,"(I/2)*b*x^2 + x*ArcCoth[1 - I*d - d*Cot[a + b*x]] - (x*Log[1 - (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/2 + ((I/4)*PolyLog[2, (1 - I*d)*E^((2*I)*a + (2*I)*b*x)])/b","A",5,5,17,0.2941,1,"{6258, 2184, 2190, 2279, 2391}"
264,0,0,0,0.0800919,"\int \frac{\coth ^{-1}(1-i d-d \cot (a+b x))}{x} \, dx","Int[ArcCoth[1 - I*d - d*Cot[a + b*x]]/x,x]","\int \frac{\coth ^{-1}(1-i d-d \cot (a+b x))}{x} \, dx","\text{Int}\left(\frac{\coth ^{-1}(d (-\cot (a+b x))-i d+1)}{x},x\right)",0,"Defer[Int][ArcCoth[1 - I*d - d*Cot[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
265,1,160,0,0.573596,"\int \frac{\left(a+b \coth ^{-1}\left(c x^n\right)\right) \left(d+e \log \left(f x^m\right)\right)}{x} \, dx","Int[((a + b*ArcCoth[c*x^n])*(d + e*Log[f*x^m]))/x,x]","\frac{b d \text{PolyLog}\left(2,-\frac{x^{-n}}{c}\right)}{2 n}-\frac{b d \text{PolyLog}\left(2,\frac{x^{-n}}{c}\right)}{2 n}+\frac{b e \log \left(f x^m\right) \text{PolyLog}\left(2,-\frac{x^{-n}}{c}\right)}{2 n}-\frac{b e \log \left(f x^m\right) \text{PolyLog}\left(2,\frac{x^{-n}}{c}\right)}{2 n}+\frac{b e m \text{PolyLog}\left(3,-\frac{x^{-n}}{c}\right)}{2 n^2}-\frac{b e m \text{PolyLog}\left(3,\frac{x^{-n}}{c}\right)}{2 n^2}+a d \log (x)+\frac{a e \log ^2\left(f x^m\right)}{2 m}","\frac{b d \text{PolyLog}\left(2,-\frac{x^{-n}}{c}\right)}{2 n}-\frac{b d \text{PolyLog}\left(2,\frac{x^{-n}}{c}\right)}{2 n}+\frac{b e \log \left(f x^m\right) \text{PolyLog}\left(2,-\frac{x^{-n}}{c}\right)}{2 n}-\frac{b e \log \left(f x^m\right) \text{PolyLog}\left(2,\frac{x^{-n}}{c}\right)}{2 n}+\frac{b e m \text{PolyLog}\left(3,-\frac{x^{-n}}{c}\right)}{2 n^2}-\frac{b e m \text{PolyLog}\left(3,\frac{x^{-n}}{c}\right)}{2 n^2}+a d \log (x)+\frac{a e \log ^2\left(f x^m\right)}{2 m}",1,"a*d*Log[x] + (a*e*Log[f*x^m]^2)/(2*m) + (b*d*PolyLog[2, -(1/(c*x^n))])/(2*n) + (b*e*Log[f*x^m]*PolyLog[2, -(1/(c*x^n))])/(2*n) - (b*d*PolyLog[2, 1/(c*x^n)])/(2*n) - (b*e*Log[f*x^m]*PolyLog[2, 1/(c*x^n)])/(2*n) + (b*e*m*PolyLog[3, -(1/(c*x^n))])/(2*n^2) - (b*e*m*PolyLog[3, 1/(c*x^n)])/(2*n^2)","A",11,8,24,0.3333,1,"{2301, 6742, 6096, 5913, 6072, 6070, 2374, 6589}"
266,1,297,0,0.3855117,"\int x^5 \left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right) \, dx","Int[x^5*(a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]),x]","\frac{1}{6} x^6 \left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{e x^4 \left(a+b \coth ^{-1}(c x)\right)}{12 c^2}-\frac{e x^2 \left(a+b \coth ^{-1}(c x)\right)}{6 c^4}-\frac{e \log \left(1-c^2 x^2\right) \left(a+b \coth ^{-1}(c x)\right)}{6 c^6}-\frac{1}{18} e x^6 \left(a+b \coth ^{-1}(c x)\right)+\frac{b x^3 (3 d-e)}{54 c^3}+\frac{b x (3 d-e)}{18 c^5}-\frac{b (3 d-e) \tanh ^{-1}(c x)}{18 c^6}-\frac{47 b e x^3}{540 c^3}+\frac{b e x^5 \log \left(1-c^2 x^2\right)}{30 c}+\frac{b e x^3 \log \left(1-c^2 x^2\right)}{18 c^3}+\frac{b e x \log \left(1-c^2 x^2\right)}{6 c^5}-\frac{137 b e x}{180 c^5}+\frac{137 b e \tanh ^{-1}(c x)}{180 c^6}+\frac{b x^5 (3 d-e)}{90 c}-\frac{b e x^5}{75 c}","\frac{1}{6} x^6 \left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{e x^4 \left(a+b \coth ^{-1}(c x)\right)}{12 c^2}-\frac{e x^2 \left(a+b \coth ^{-1}(c x)\right)}{6 c^4}-\frac{e \log \left(1-c^2 x^2\right) \left(a+b \coth ^{-1}(c x)\right)}{6 c^6}-\frac{1}{18} e x^6 \left(a+b \coth ^{-1}(c x)\right)+\frac{b x^3 (3 d-e)}{54 c^3}+\frac{b x (3 d-e)}{18 c^5}-\frac{b (3 d-e) \tanh ^{-1}(c x)}{18 c^6}-\frac{47 b e x^3}{540 c^3}+\frac{b e x^5 \log \left(1-c^2 x^2\right)}{30 c}+\frac{b e x^3 \log \left(1-c^2 x^2\right)}{18 c^3}+\frac{b e x \log \left(1-c^2 x^2\right)}{6 c^5}-\frac{137 b e x}{180 c^5}+\frac{137 b e \tanh ^{-1}(c x)}{180 c^6}+\frac{b x^5 (3 d-e)}{90 c}-\frac{b e x^5}{75 c}",1,"(b*(3*d - e)*x)/(18*c^5) - (137*b*e*x)/(180*c^5) + (b*(3*d - e)*x^3)/(54*c^3) - (47*b*e*x^3)/(540*c^3) + (b*(3*d - e)*x^5)/(90*c) - (b*e*x^5)/(75*c) - (e*x^2*(a + b*ArcCoth[c*x]))/(6*c^4) - (e*x^4*(a + b*ArcCoth[c*x]))/(12*c^2) - (e*x^6*(a + b*ArcCoth[c*x]))/18 - (b*(3*d - e)*ArcTanh[c*x])/(18*c^6) + (137*b*e*ArcTanh[c*x])/(180*c^6) + (b*e*x*Log[1 - c^2*x^2])/(6*c^5) + (b*e*x^3*Log[1 - c^2*x^2])/(18*c^3) + (b*e*x^5*Log[1 - c^2*x^2])/(30*c) - (e*(a + b*ArcCoth[c*x])*Log[1 - c^2*x^2])/(6*c^6) + (x^6*(a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]))/6","A",23,11,27,0.4074,1,"{2454, 2395, 43, 6084, 321, 207, 302, 2528, 2448, 206, 2455}"
267,1,225,0,0.2562424,"\int x^3 \left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right) \, dx","Int[x^3*(a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]),x]","\frac{1}{4} x^4 \left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{e x^2 \left(a+b \coth ^{-1}(c x)\right)}{4 c^2}-\frac{e \log \left(1-c^2 x^2\right) \left(a+b \coth ^{-1}(c x)\right)}{4 c^4}-\frac{1}{8} e x^4 \left(a+b \coth ^{-1}(c x)\right)+\frac{b x (2 d-3 e)}{8 c^3}-\frac{b (2 d-3 e) \tanh ^{-1}(c x)}{8 c^4}+\frac{b e x^3 \log \left(1-c^2 x^2\right)}{12 c}+\frac{b e x \log \left(1-c^2 x^2\right)}{4 c^3}-\frac{2 b e x}{3 c^3}+\frac{2 b e \tanh ^{-1}(c x)}{3 c^4}+\frac{b x^3 (2 d-e)}{24 c}-\frac{b e x^3}{18 c}","\frac{1}{4} x^4 \left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{e x^2 \left(a+b \coth ^{-1}(c x)\right)}{4 c^2}-\frac{e \log \left(1-c^2 x^2\right) \left(a+b \coth ^{-1}(c x)\right)}{4 c^4}-\frac{1}{8} e x^4 \left(a+b \coth ^{-1}(c x)\right)+\frac{b x (2 d-3 e)}{8 c^3}-\frac{b (2 d-3 e) \tanh ^{-1}(c x)}{8 c^4}+\frac{b e x^3 \log \left(1-c^2 x^2\right)}{12 c}+\frac{b e x \log \left(1-c^2 x^2\right)}{4 c^3}-\frac{2 b e x}{3 c^3}+\frac{2 b e \tanh ^{-1}(c x)}{3 c^4}+\frac{b x^3 (2 d-e)}{24 c}-\frac{b e x^3}{18 c}",1,"(b*(2*d - 3*e)*x)/(8*c^3) - (2*b*e*x)/(3*c^3) + (b*(2*d - e)*x^3)/(24*c) - (b*e*x^3)/(18*c) - (e*x^2*(a + b*ArcCoth[c*x]))/(4*c^2) - (e*x^4*(a + b*ArcCoth[c*x]))/8 - (b*(2*d - 3*e)*ArcTanh[c*x])/(8*c^4) + (2*b*e*ArcTanh[c*x])/(3*c^4) + (b*e*x*Log[1 - c^2*x^2])/(4*c^3) + (b*e*x^3*Log[1 - c^2*x^2])/(12*c) - (e*(a + b*ArcCoth[c*x])*Log[1 - c^2*x^2])/(4*c^4) + (x^4*(a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]))/4","A",14,11,27,0.4074,1,"{2454, 2395, 43, 6084, 459, 321, 206, 2471, 2448, 2455, 302}"
268,1,140,0,0.1186284,"\int x \left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right) \, dx","Int[x*(a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]),x]","-\frac{e \left(1-c^2 x^2\right) \log \left(1-c^2 x^2\right) \left(a+b \coth ^{-1}(c x)\right)}{2 c^2}+\frac{1}{2} d x^2 \left(a+b \coth ^{-1}(c x)\right)-\frac{1}{2} e x^2 \left(a+b \coth ^{-1}(c x)\right)-\frac{b (d-e) \tanh ^{-1}(c x)}{2 c^2}+\frac{b e x \log \left(1-c^2 x^2\right)}{2 c}+\frac{b e \tanh ^{-1}(c x)}{c^2}+\frac{b x (d-e)}{2 c}-\frac{b e x}{c}","-\frac{e \left(1-c^2 x^2\right) \log \left(1-c^2 x^2\right) \left(a+b \coth ^{-1}(c x)\right)}{2 c^2}+\frac{1}{2} d x^2 \left(a+b \coth ^{-1}(c x)\right)-\frac{1}{2} e x^2 \left(a+b \coth ^{-1}(c x)\right)-\frac{b (d-e) \tanh ^{-1}(c x)}{2 c^2}+\frac{b e x \log \left(1-c^2 x^2\right)}{2 c}+\frac{b e \tanh ^{-1}(c x)}{c^2}+\frac{b x (d-e)}{2 c}-\frac{b e x}{c}",1,"(b*(d - e)*x)/(2*c) - (b*e*x)/c + (d*x^2*(a + b*ArcCoth[c*x]))/2 - (e*x^2*(a + b*ArcCoth[c*x]))/2 - (b*(d - e)*ArcTanh[c*x])/(2*c^2) + (b*e*ArcTanh[c*x])/c^2 + (b*e*x*Log[1 - c^2*x^2])/(2*c) - (e*(1 - c^2*x^2)*(a + b*ArcCoth[c*x])*Log[1 - c^2*x^2])/(2*c^2)","A",7,8,25,0.3200,1,"{2454, 2389, 2295, 6084, 321, 207, 2448, 206}"
269,1,381,0,0.4394954,"\int \frac{\left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right)}{x} \, dx","Int[((a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]))/x,x]","-\frac{1}{2} a e \text{PolyLog}\left(2,c^2 x^2\right)+\frac{1}{2} b e \log \left(-c^2 x^2\right) \text{PolyLog}\left(2,-\frac{1}{c x}\right)-\frac{1}{2} b e \left(\log \left(-c^2 x^2\right)-\log \left(1-c^2 x^2\right)+\log \left(1-\frac{1}{c x}\right)+\log \left(\frac{1}{c x}+1\right)\right) \text{PolyLog}\left(2,-\frac{1}{c x}\right)-\frac{1}{2} b e \log \left(-c^2 x^2\right) \text{PolyLog}\left(2,\frac{1}{c x}\right)+\frac{1}{2} b e \left(\log \left(-c^2 x^2\right)-\log \left(1-c^2 x^2\right)+\log \left(1-\frac{1}{c x}\right)+\log \left(\frac{1}{c x}+1\right)\right) \text{PolyLog}\left(2,\frac{1}{c x}\right)+\frac{1}{2} b d \text{PolyLog}\left(2,-\frac{1}{c x}\right)-\frac{1}{2} b d \text{PolyLog}\left(2,\frac{1}{c x}\right)+b e \text{PolyLog}\left(3,\frac{c+\frac{1}{x}}{c}\right)-b e \text{PolyLog}\left(3,1-\frac{1}{c x}\right)+b e \text{PolyLog}\left(3,-\frac{1}{c x}\right)-b e \text{PolyLog}\left(3,\frac{1}{c x}\right)+b e \log \left(1-\frac{1}{c x}\right) \text{PolyLog}\left(2,1-\frac{1}{c x}\right)-b e \log \left(\frac{c+\frac{1}{x}}{c}\right) \text{PolyLog}\left(2,\frac{c+\frac{1}{x}}{c}\right)+a d \log (x)+\frac{1}{2} b e \log \left(\frac{1}{c x}\right) \log ^2\left(1-\frac{1}{c x}\right)-\frac{1}{2} b e \log ^2\left(\frac{1}{c x}+1\right) \log \left(-\frac{1}{c x}\right)","-\frac{1}{2} a e \text{PolyLog}\left(2,c^2 x^2\right)+\frac{1}{2} b e \log \left(-c^2 x^2\right) \text{PolyLog}\left(2,-\frac{1}{c x}\right)-\frac{1}{2} b e \left(\log \left(-c^2 x^2\right)-\log \left(1-c^2 x^2\right)+\log \left(1-\frac{1}{c x}\right)+\log \left(\frac{1}{c x}+1\right)\right) \text{PolyLog}\left(2,-\frac{1}{c x}\right)-\frac{1}{2} b e \log \left(-c^2 x^2\right) \text{PolyLog}\left(2,\frac{1}{c x}\right)+\frac{1}{2} b e \left(\log \left(-c^2 x^2\right)-\log \left(1-c^2 x^2\right)+\log \left(1-\frac{1}{c x}\right)+\log \left(\frac{1}{c x}+1\right)\right) \text{PolyLog}\left(2,\frac{1}{c x}\right)+\frac{1}{2} b d \text{PolyLog}\left(2,-\frac{1}{c x}\right)-\frac{1}{2} b d \text{PolyLog}\left(2,\frac{1}{c x}\right)+b e \text{PolyLog}\left(3,\frac{c+\frac{1}{x}}{c}\right)-b e \text{PolyLog}\left(3,1-\frac{1}{c x}\right)+b e \text{PolyLog}\left(3,-\frac{1}{c x}\right)-b e \text{PolyLog}\left(3,\frac{1}{c x}\right)+b e \log \left(1-\frac{1}{c x}\right) \text{PolyLog}\left(2,1-\frac{1}{c x}\right)-b e \log \left(\frac{c+\frac{1}{x}}{c}\right) \text{PolyLog}\left(2,\frac{c+\frac{1}{x}}{c}\right)+a d \log (x)+\frac{1}{2} b e \log \left(\frac{1}{c x}\right) \log ^2\left(1-\frac{1}{c x}\right)-\frac{1}{2} b e \log ^2\left(\frac{1}{c x}+1\right) \log \left(-\frac{1}{c x}\right)",1,"-(b*e*Log[1 + 1/(c*x)]^2*Log[-(1/(c*x))])/2 + (b*e*Log[1 - 1/(c*x)]^2*Log[1/(c*x)])/2 + a*d*Log[x] - b*e*Log[(c + x^(-1))/c]*PolyLog[2, (c + x^(-1))/c] + b*e*Log[1 - 1/(c*x)]*PolyLog[2, 1 - 1/(c*x)] + (b*d*PolyLog[2, -(1/(c*x))])/2 + (b*e*Log[-(c^2*x^2)]*PolyLog[2, -(1/(c*x))])/2 - (b*e*(Log[1 - 1/(c*x)] + Log[1 + 1/(c*x)] + Log[-(c^2*x^2)] - Log[1 - c^2*x^2])*PolyLog[2, -(1/(c*x))])/2 - (b*d*PolyLog[2, 1/(c*x)])/2 - (b*e*Log[-(c^2*x^2)]*PolyLog[2, 1/(c*x)])/2 + (b*e*(Log[1 - 1/(c*x)] + Log[1 + 1/(c*x)] + Log[-(c^2*x^2)] - Log[1 - c^2*x^2])*PolyLog[2, 1/(c*x)])/2 - (a*e*PolyLog[2, c^2*x^2])/2 + b*e*PolyLog[3, (c + x^(-1))/c] - b*e*PolyLog[3, 1 - 1/(c*x)] + b*e*PolyLog[3, -(1/(c*x))] - b*e*PolyLog[3, 1/(c*x)]","A",21,11,27,0.4074,1,"{6080, 5913, 6078, 2391, 6076, 2454, 2396, 2433, 2374, 6589, 6070}"
270,1,247,0,0.4875506,"\int \frac{\left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right)}{x^3} \, dx","Int[((a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]))/x^3,x]","\frac{1}{2} b c^2 e \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)+\frac{1}{2} b c^2 e \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)-\frac{\left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{2 x^2}+\frac{1}{2} c^2 e (a+b) \log (1-c x)+\frac{1}{2} c^2 e (a-b) \log (c x+1)-a c^2 e \log (x)-\frac{b c \left(e \log \left(1-c^2 x^2\right)+d\right)}{2 x}+\frac{1}{2} b c^2 \tanh ^{-1}(c x) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{1}{2} b c^2 e \tanh ^{-1}(c x)^2-\frac{1}{2} b c^2 e \coth ^{-1}(c x)^2+b c^2 e \log \left(\frac{2}{1-c x}\right) \tanh ^{-1}(c x)-b c^2 e \log \left(2-\frac{2}{c x+1}\right) \coth ^{-1}(c x)","\frac{1}{2} b c^2 e \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)+\frac{1}{2} b c^2 e \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)-\frac{\left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{2 x^2}+\frac{1}{2} c^2 e (a+b) \log (1-c x)+\frac{1}{2} c^2 e (a-b) \log (c x+1)-a c^2 e \log (x)-\frac{b c \left(e \log \left(1-c^2 x^2\right)+d\right)}{2 x}+\frac{1}{2} b c^2 \tanh ^{-1}(c x) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{1}{2} b c^2 e \tanh ^{-1}(c x)^2-\frac{1}{2} b c^2 e \coth ^{-1}(c x)^2+b c^2 e \log \left(\frac{2}{1-c x}\right) \tanh ^{-1}(c x)-b c^2 e \log \left(2-\frac{2}{c x+1}\right) \coth ^{-1}(c x)",1,"-(b*c^2*e*ArcCoth[c*x]^2)/2 - (b*c^2*e*ArcTanh[c*x]^2)/2 - a*c^2*e*Log[x] + b*c^2*e*ArcTanh[c*x]*Log[2/(1 - c*x)] + ((a + b)*c^2*e*Log[1 - c*x])/2 + ((a - b)*c^2*e*Log[1 + c*x])/2 - (b*c*(d + e*Log[1 - c^2*x^2]))/(2*x) - ((a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]))/(2*x^2) + (b*c^2*ArcTanh[c*x]*(d + e*Log[1 - c^2*x^2]))/2 - b*c^2*e*ArcCoth[c*x]*Log[2 - 2/(1 + c*x)] + (b*c^2*e*PolyLog[2, 1 - 2/(1 - c*x)])/2 + (b*c^2*e*PolyLog[2, -1 + 2/(1 + c*x)])/2","A",13,13,27,0.4815,1,"{5917, 325, 206, 6086, 6725, 801, 5989, 5933, 2447, 5984, 5918, 2402, 2315}"
271,1,339,0,0.7172315,"\int \frac{\left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right)}{x^5} \, dx","Int[((a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]))/x^5,x]","\frac{1}{4} b c^4 e \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)+\frac{1}{4} b c^4 e \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)-\frac{\left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{4 x^4}+\frac{1}{12} c^4 e (3 a+4 b) \log (1-c x)+\frac{1}{12} c^4 e (3 a-4 b) \log (c x+1)+\frac{a c^2 e}{4 x^2}-\frac{1}{2} a c^4 e \log (x)-\frac{b c^3 \left(e \log \left(1-c^2 x^2\right)+d\right)}{4 x}-\frac{b c \left(e \log \left(1-c^2 x^2\right)+d\right)}{12 x^3}+\frac{1}{4} b c^4 \tanh ^{-1}(c x) \left(e \log \left(1-c^2 x^2\right)+d\right)+\frac{b c^2 e \coth ^{-1}(c x)}{4 x^2}+\frac{5 b c^3 e}{12 x}-\frac{1}{4} b c^4 e \tanh ^{-1}(c x)^2-\frac{1}{4} b c^4 e \tanh ^{-1}(c x)-\frac{1}{4} b c^4 e \coth ^{-1}(c x)^2+\frac{1}{2} b c^4 e \log \left(\frac{2}{1-c x}\right) \tanh ^{-1}(c x)-\frac{1}{2} b c^4 e \log \left(2-\frac{2}{c x+1}\right) \coth ^{-1}(c x)","\frac{1}{4} b c^4 e \text{PolyLog}\left(2,1-\frac{2}{1-c x}\right)+\frac{1}{4} b c^4 e \text{PolyLog}\left(2,\frac{2}{c x+1}-1\right)-\frac{\left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{4 x^4}+\frac{1}{12} c^4 e (3 a+4 b) \log (1-c x)+\frac{1}{12} c^4 e (3 a-4 b) \log (c x+1)+\frac{a c^2 e}{4 x^2}-\frac{1}{2} a c^4 e \log (x)-\frac{b c^3 \left(e \log \left(1-c^2 x^2\right)+d\right)}{4 x}-\frac{b c \left(e \log \left(1-c^2 x^2\right)+d\right)}{12 x^3}+\frac{1}{4} b c^4 \tanh ^{-1}(c x) \left(e \log \left(1-c^2 x^2\right)+d\right)+\frac{b c^2 e \coth ^{-1}(c x)}{4 x^2}+\frac{5 b c^3 e}{12 x}-\frac{1}{4} b c^4 e \tanh ^{-1}(c x)^2-\frac{1}{4} b c^4 e \tanh ^{-1}(c x)-\frac{1}{4} b c^4 e \coth ^{-1}(c x)^2+\frac{1}{2} b c^4 e \log \left(\frac{2}{1-c x}\right) \tanh ^{-1}(c x)-\frac{1}{2} b c^4 e \log \left(2-\frac{2}{c x+1}\right) \coth ^{-1}(c x)",1,"(a*c^2*e)/(4*x^2) + (5*b*c^3*e)/(12*x) + (b*c^2*e*ArcCoth[c*x])/(4*x^2) - (b*c^4*e*ArcCoth[c*x]^2)/4 - (b*c^4*e*ArcTanh[c*x])/4 - (b*c^4*e*ArcTanh[c*x]^2)/4 - (a*c^4*e*Log[x])/2 + (b*c^4*e*ArcTanh[c*x]*Log[2/(1 - c*x)])/2 + ((3*a + 4*b)*c^4*e*Log[1 - c*x])/12 + ((3*a - 4*b)*c^4*e*Log[1 + c*x])/12 - (b*c*(d + e*Log[1 - c^2*x^2]))/(12*x^3) - (b*c^3*(d + e*Log[1 - c^2*x^2]))/(4*x) - ((a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]))/(4*x^4) + (b*c^4*ArcTanh[c*x]*(d + e*Log[1 - c^2*x^2]))/4 - (b*c^4*e*ArcCoth[c*x]*Log[2 - 2/(1 + c*x)])/2 + (b*c^4*e*PolyLog[2, 1 - 2/(1 - c*x)])/4 + (b*c^4*e*PolyLog[2, -1 + 2/(1 + c*x)])/4","A",17,14,27,0.5185,1,"{5917, 325, 206, 6086, 6725, 1802, 5983, 5989, 5933, 2447, 5984, 5918, 2402, 2315}"
272,1,315,0,0.7490209,"\int x^4 \left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right) \, dx","Int[x^4*(a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]),x]","\frac{1}{5} x^5 \left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{e (4 a+3 b) \log (1-c x)}{20 c^5}+\frac{e (4 a-3 b) \log (c x+1)}{20 c^5}-\frac{2 a e x^3}{15 c^2}-\frac{2 a e x}{5 c^4}-\frac{2}{25} a e x^5+\frac{b x^4 \left(e \log \left(1-c^2 x^2\right)+d\right)}{20 c}+\frac{b x^2 \left(e \log \left(1-c^2 x^2\right)+d\right)}{10 c^3}+\frac{b \log \left(1-c^2 x^2\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{10 c^5}-\frac{77 b e x^2}{300 c^3}-\frac{b e \log ^2\left(1-c^2 x^2\right)}{20 c^5}-\frac{23 b e \log \left(1-c^2 x^2\right)}{75 c^5}-\frac{2 b e x^3 \coth ^{-1}(c x)}{15 c^2}-\frac{2 b e x \coth ^{-1}(c x)}{5 c^4}+\frac{b e \coth ^{-1}(c x)^2}{5 c^5}-\frac{9 b e x^4}{200 c}-\frac{2}{25} b e x^5 \coth ^{-1}(c x)","\frac{1}{5} x^5 \left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{e (4 a+3 b) \log (1-c x)}{20 c^5}+\frac{e (4 a-3 b) \log (c x+1)}{20 c^5}-\frac{2 a e x^3}{15 c^2}-\frac{2 a e x}{5 c^4}-\frac{2}{25} a e x^5+\frac{b x^4 \left(e \log \left(1-c^2 x^2\right)+d\right)}{20 c}+\frac{b x^2 \left(e \log \left(1-c^2 x^2\right)+d\right)}{10 c^3}+\frac{b \log \left(1-c^2 x^2\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{10 c^5}-\frac{77 b e x^2}{300 c^3}-\frac{b e \log ^2\left(1-c^2 x^2\right)}{20 c^5}-\frac{23 b e \log \left(1-c^2 x^2\right)}{75 c^5}-\frac{2 b e x^3 \coth ^{-1}(c x)}{15 c^2}-\frac{2 b e x \coth ^{-1}(c x)}{5 c^4}+\frac{b e \coth ^{-1}(c x)^2}{5 c^5}-\frac{9 b e x^4}{200 c}-\frac{2}{25} b e x^5 \coth ^{-1}(c x)",1,"(-2*a*e*x)/(5*c^4) - (77*b*e*x^2)/(300*c^3) - (2*a*e*x^3)/(15*c^2) - (9*b*e*x^4)/(200*c) - (2*a*e*x^5)/25 - (2*b*e*x*ArcCoth[c*x])/(5*c^4) - (2*b*e*x^3*ArcCoth[c*x])/(15*c^2) - (2*b*e*x^5*ArcCoth[c*x])/25 + (b*e*ArcCoth[c*x]^2)/(5*c^5) - ((4*a + 3*b)*e*Log[1 - c*x])/(20*c^5) + ((4*a - 3*b)*e*Log[1 + c*x])/(20*c^5) - (23*b*e*Log[1 - c^2*x^2])/(75*c^5) - (b*e*Log[1 - c^2*x^2]^2)/(20*c^5) + (b*x^2*(d + e*Log[1 - c^2*x^2]))/(10*c^3) + (b*x^4*(d + e*Log[1 - c^2*x^2]))/(20*c) + (x^5*(a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]))/5 + (b*Log[1 - c^2*x^2]*(d + e*Log[1 - c^2*x^2]))/(10*c^5)","A",26,15,27,0.5556,1,"{5917, 266, 43, 6086, 6725, 1802, 633, 31, 5981, 5911, 260, 5949, 2475, 2390, 2301}"
273,1,247,0,0.6209574,"\int x^2 \left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right) \, dx","Int[x^2*(a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]),x]","\frac{1}{3} x^3 \left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{e (2 a+b) \log (1-c x)}{6 c^3}+\frac{e (2 a-b) \log (c x+1)}{6 c^3}-\frac{2 a e x}{3 c^2}-\frac{2}{9} a e x^3+\frac{b x^2 \left(e \log \left(1-c^2 x^2\right)+d\right)}{6 c}+\frac{b \log \left(1-c^2 x^2\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{6 c^3}-\frac{b e \log ^2\left(1-c^2 x^2\right)}{12 c^3}-\frac{4 b e \log \left(1-c^2 x^2\right)}{9 c^3}-\frac{2 b e x \coth ^{-1}(c x)}{3 c^2}+\frac{b e \coth ^{-1}(c x)^2}{3 c^3}-\frac{5 b e x^2}{18 c}-\frac{2}{9} b e x^3 \coth ^{-1}(c x)","\frac{1}{3} x^3 \left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{e (2 a+b) \log (1-c x)}{6 c^3}+\frac{e (2 a-b) \log (c x+1)}{6 c^3}-\frac{2 a e x}{3 c^2}-\frac{2}{9} a e x^3+\frac{b x^2 \left(e \log \left(1-c^2 x^2\right)+d\right)}{6 c}+\frac{b \log \left(1-c^2 x^2\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{6 c^3}-\frac{b e \log ^2\left(1-c^2 x^2\right)}{12 c^3}-\frac{4 b e \log \left(1-c^2 x^2\right)}{9 c^3}-\frac{2 b e x \coth ^{-1}(c x)}{3 c^2}+\frac{b e \coth ^{-1}(c x)^2}{3 c^3}-\frac{5 b e x^2}{18 c}-\frac{2}{9} b e x^3 \coth ^{-1}(c x)",1,"(-2*a*e*x)/(3*c^2) - (5*b*e*x^2)/(18*c) - (2*a*e*x^3)/9 - (2*b*e*x*ArcCoth[c*x])/(3*c^2) - (2*b*e*x^3*ArcCoth[c*x])/9 + (b*e*ArcCoth[c*x]^2)/(3*c^3) - ((2*a + b)*e*Log[1 - c*x])/(6*c^3) + ((2*a - b)*e*Log[1 + c*x])/(6*c^3) - (4*b*e*Log[1 - c^2*x^2])/(9*c^3) - (b*e*Log[1 - c^2*x^2]^2)/(12*c^3) + (b*x^2*(d + e*Log[1 - c^2*x^2]))/(6*c) + (x^3*(a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]))/3 + (b*Log[1 - c^2*x^2]*(d + e*Log[1 - c^2*x^2]))/(6*c^3)","A",21,15,27,0.5556,1,"{5917, 266, 43, 6086, 6725, 801, 633, 31, 5981, 5911, 260, 5949, 2475, 2390, 2301}"
274,1,104,0,0.1982261,"\int \left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right) \, dx","Int[(a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]),x]","x \left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)+\frac{e \left(a+b \coth ^{-1}(c x)\right)^2}{b c}-2 a e x+\frac{b \left(e \log \left(1-c^2 x^2\right)+d\right)^2}{4 c e}-\frac{b e \log \left(1-c^2 x^2\right)}{c}-2 b e x \coth ^{-1}(c x)","x \left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)+\frac{e \left(a+b \coth ^{-1}(c x)\right)^2}{b c}-2 a e x+\frac{b \left(e \log \left(1-c^2 x^2\right)+d\right)^2}{4 c e}-\frac{b e \log \left(1-c^2 x^2\right)}{c}-2 b e x \coth ^{-1}(c x)",1,"-2*a*e*x - 2*b*e*x*ArcCoth[c*x] + (e*(a + b*ArcCoth[c*x])^2)/(b*c) - (b*e*Log[1 - c^2*x^2])/c + x*(a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]) + (b*(d + e*Log[1 - c^2*x^2])^2)/(4*c*e)","A",9,8,24,0.3333,1,"{6074, 2475, 2390, 2301, 5981, 5911, 260, 5949}"
275,1,94,0,0.2690755,"\int \frac{\left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right)}{x^2} \, dx","Int[((a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]))/x^2,x]","-\frac{1}{2} b c e \text{PolyLog}\left(2,c^2 x^2\right)-\frac{\left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{x}-\frac{c e \left(a+b \coth ^{-1}(c x)\right)^2}{b}-\frac{b c \left(e \log \left(1-c^2 x^2\right)+d\right)^2}{4 e}+b c d \log (x)","-\frac{1}{2} b c e \text{PolyLog}\left(2,\frac{1}{1-c^2 x^2}\right)-\frac{\left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{x}-\frac{c e \left(a+b \coth ^{-1}(c x)\right)^2}{b}+\frac{1}{2} b c \log \left(1-\frac{1}{1-c^2 x^2}\right) \left(e \log \left(1-c^2 x^2\right)+d\right)",1,"-((c*e*(a + b*ArcCoth[c*x])^2)/b) + b*c*d*Log[x] - ((a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]))/x - (b*c*(d + e*Log[1 - c^2*x^2])^2)/(4*e) - (b*c*e*PolyLog[2, c^2*x^2])/2","A",8,8,27,0.2963,1,"{6082, 2475, 2411, 2344, 2301, 2316, 2315, 5949}"
276,1,191,0,0.4633909,"\int \frac{\left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right)}{x^4} \, dx","Int[((a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]))/x^4,x]","-\frac{1}{6} b c^3 e \text{PolyLog}\left(2,c^2 x^2\right)-\frac{\left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{3 x^3}-\frac{c^3 e \left(a+b \coth ^{-1}(c x)\right)^2}{3 b}+\frac{2 c^2 e \left(a+b \coth ^{-1}(c x)\right)}{3 x}-\frac{b c^3 \left(e \log \left(1-c^2 x^2\right)+d\right)^2}{12 e}-\frac{b c \left(1-c^2 x^2\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{6 x^2}+\frac{1}{3} b c^3 d \log (x)+\frac{1}{3} b c^3 e \log \left(1-c^2 x^2\right)-b c^3 e \log (x)","-\frac{1}{6} b c^3 e \text{PolyLog}\left(2,\frac{1}{1-c^2 x^2}\right)-\frac{\left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{3 x^3}-\frac{c^3 e \left(a+b \coth ^{-1}(c x)\right)^2}{3 b}+\frac{2 c^2 e \left(a+b \coth ^{-1}(c x)\right)}{3 x}+\frac{1}{6} b c^3 \log \left(1-\frac{1}{1-c^2 x^2}\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{b c \left(1-c^2 x^2\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{6 x^2}+\frac{1}{3} b c^3 e \log \left(1-c^2 x^2\right)-b c^3 e \log (x)",1,"(2*c^2*e*(a + b*ArcCoth[c*x]))/(3*x) - (c^3*e*(a + b*ArcCoth[c*x])^2)/(3*b) + (b*c^3*d*Log[x])/3 - b*c^3*e*Log[x] + (b*c^3*e*Log[1 - c^2*x^2])/3 - (b*c*(1 - c^2*x^2)*(d + e*Log[1 - c^2*x^2]))/(6*x^2) - ((a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]))/(3*x^3) - (b*c^3*(d + e*Log[1 - c^2*x^2])^2)/(12*e) - (b*c^3*e*PolyLog[2, c^2*x^2])/6","A",17,16,27,0.5926,1,"{6082, 2475, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 5983, 5917, 266, 36, 29, 5949}"
277,1,250,0,0.6700723,"\int \frac{\left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(1-c^2 x^2\right)\right)}{x^6} \, dx","Int[((a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]))/x^6,x]","-\frac{1}{10} b c^5 e \text{PolyLog}\left(2,c^2 x^2\right)-\frac{\left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{5 x^5}+\frac{2 c^2 e \left(a+b \coth ^{-1}(c x)\right)}{15 x^3}-\frac{c^5 e \left(a+b \coth ^{-1}(c x)\right)^2}{5 b}+\frac{2 c^4 e \left(a+b \coth ^{-1}(c x)\right)}{5 x}-\frac{b c^5 \left(e \log \left(1-c^2 x^2\right)+d\right)^2}{20 e}-\frac{b c^3 \left(1-c^2 x^2\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{10 x^2}-\frac{b c \left(e \log \left(1-c^2 x^2\right)+d\right)}{20 x^4}+\frac{1}{5} b c^5 d \log (x)+\frac{7 b c^3 e}{60 x^2}+\frac{19}{60} b c^5 e \log \left(1-c^2 x^2\right)-\frac{5}{6} b c^5 e \log (x)","-\frac{1}{10} b c^5 e \text{PolyLog}\left(2,\frac{1}{1-c^2 x^2}\right)-\frac{\left(a+b \coth ^{-1}(c x)\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{5 x^5}+\frac{2 c^2 e \left(a+b \coth ^{-1}(c x)\right)}{15 x^3}-\frac{c^5 e \left(a+b \coth ^{-1}(c x)\right)^2}{5 b}+\frac{2 c^4 e \left(a+b \coth ^{-1}(c x)\right)}{5 x}+\frac{1}{10} b c^5 \log \left(1-\frac{1}{1-c^2 x^2}\right) \left(e \log \left(1-c^2 x^2\right)+d\right)-\frac{b c^3 \left(1-c^2 x^2\right) \left(e \log \left(1-c^2 x^2\right)+d\right)}{10 x^2}-\frac{b c \left(e \log \left(1-c^2 x^2\right)+d\right)}{20 x^4}+\frac{7 b c^3 e}{60 x^2}+\frac{19}{60} b c^5 e \log \left(1-c^2 x^2\right)-\frac{5}{6} b c^5 e \log (x)",1,"(7*b*c^3*e)/(60*x^2) + (2*c^2*e*(a + b*ArcCoth[c*x]))/(15*x^3) + (2*c^4*e*(a + b*ArcCoth[c*x]))/(5*x) - (c^5*e*(a + b*ArcCoth[c*x])^2)/(5*b) + (b*c^5*d*Log[x])/5 - (5*b*c^5*e*Log[x])/6 + (19*b*c^5*e*Log[1 - c^2*x^2])/60 - (b*c*(d + e*Log[1 - c^2*x^2]))/(20*x^4) - (b*c^3*(1 - c^2*x^2)*(d + e*Log[1 - c^2*x^2]))/(10*x^2) - ((a + b*ArcCoth[c*x])*(d + e*Log[1 - c^2*x^2]))/(5*x^5) - (b*c^5*(d + e*Log[1 - c^2*x^2])^2)/(20*e) - (b*c^5*e*PolyLog[2, c^2*x^2])/10","A",26,18,27,0.6667,1,"{6082, 2475, 2411, 2347, 2344, 2301, 2316, 2315, 2314, 31, 2319, 44, 5983, 5917, 266, 36, 29, 5949}"
278,1,512,0,0.7672299,"\int x \left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right) \, dx","Int[x*(a + b*ArcCoth[c*x])*(d + e*Log[f + g*x^2]),x]","\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^2 g}-\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)}{4 c^2 g}-\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)}{4 c^2 g}+\frac{1}{2} d x^2 \left(a+b \coth ^{-1}(c x)\right)+\frac{e \left(f+g x^2\right) \log \left(f+g x^2\right) \left(a+b \coth ^{-1}(c x)\right)}{2 g}-\frac{1}{2} e x^2 \left(a+b \coth ^{-1}(c x)\right)-\frac{b (d-e) \tanh ^{-1}(c x)}{2 c^2}-\frac{b e \left(c^2 f+g\right) \tanh ^{-1}(c x) \log \left(f+g x^2\right)}{2 c^2 g}-\frac{b e \left(c^2 f+g\right) \log \left(\frac{2}{c x+1}\right) \tanh ^{-1}(c x)}{c^2 g}+\frac{b e \left(c^2 f+g\right) \tanh ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)}{2 c^2 g}+\frac{b e \left(c^2 f+g\right) \tanh ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)}{2 c^2 g}+\frac{b x (d-e)}{2 c}+\frac{b e x \log \left(f+g x^2\right)}{2 c}+\frac{b e \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{c \sqrt{g}}-\frac{b e x}{c}","\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 c^2 g}-\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)}{4 c^2 g}-\frac{b e \left(c^2 f+g\right) \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)}{4 c^2 g}+\frac{1}{2} d x^2 \left(a+b \coth ^{-1}(c x)\right)+\frac{e \left(f+g x^2\right) \log \left(f+g x^2\right) \left(a+b \coth ^{-1}(c x)\right)}{2 g}-\frac{1}{2} e x^2 \left(a+b \coth ^{-1}(c x)\right)-\frac{b (d-e) \tanh ^{-1}(c x)}{2 c^2}-\frac{b e \left(c^2 f+g\right) \tanh ^{-1}(c x) \log \left(f+g x^2\right)}{2 c^2 g}-\frac{b e \left(c^2 f+g\right) \log \left(\frac{2}{c x+1}\right) \tanh ^{-1}(c x)}{c^2 g}+\frac{b e \left(c^2 f+g\right) \tanh ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)}{2 c^2 g}+\frac{b e \left(c^2 f+g\right) \tanh ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)}{2 c^2 g}+\frac{b x (d-e)}{2 c}+\frac{b e x \log \left(f+g x^2\right)}{2 c}+\frac{b e \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{c \sqrt{g}}-\frac{b e x}{c}",1,"(b*(d - e)*x)/(2*c) - (b*e*x)/c + (d*x^2*(a + b*ArcCoth[c*x]))/2 - (e*x^2*(a + b*ArcCoth[c*x]))/2 + (b*e*Sqrt[f]*ArcTan[(Sqrt[g]*x)/Sqrt[f]])/(c*Sqrt[g]) - (b*(d - e)*ArcTanh[c*x])/(2*c^2) - (b*e*(c^2*f + g)*ArcTanh[c*x]*Log[2/(1 + c*x)])/(c^2*g) + (b*e*(c^2*f + g)*ArcTanh[c*x]*Log[(2*c*(Sqrt[-f] - Sqrt[g]*x))/((c*Sqrt[-f] - Sqrt[g])*(1 + c*x))])/(2*c^2*g) + (b*e*(c^2*f + g)*ArcTanh[c*x]*Log[(2*c*(Sqrt[-f] + Sqrt[g]*x))/((c*Sqrt[-f] + Sqrt[g])*(1 + c*x))])/(2*c^2*g) + (b*e*x*Log[f + g*x^2])/(2*c) + (e*(f + g*x^2)*(a + b*ArcCoth[c*x])*Log[f + g*x^2])/(2*g) - (b*e*(c^2*f + g)*ArcTanh[c*x]*Log[f + g*x^2])/(2*c^2*g) + (b*e*(c^2*f + g)*PolyLog[2, 1 - 2/(1 + c*x)])/(2*c^2*g) - (b*e*(c^2*f + g)*PolyLog[2, 1 - (2*c*(Sqrt[-f] - Sqrt[g]*x))/((c*Sqrt[-f] - Sqrt[g])*(1 + c*x))])/(4*c^2*g) - (b*e*(c^2*f + g)*PolyLog[2, 1 - (2*c*(Sqrt[-f] + Sqrt[g]*x))/((c*Sqrt[-f] + Sqrt[g])*(1 + c*x))])/(4*c^2*g)","A",22,17,22,0.7727,1,"{2454, 2389, 2295, 6084, 321, 207, 517, 2528, 2448, 205, 2470, 12, 5992, 5920, 2402, 2315, 2447}"
279,1,546,0,1.3874086,"\int \left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right) \, dx","Int[(a + b*ArcCoth[c*x])*(d + e*Log[f + g*x^2]),x]","\frac{b e \text{PolyLog}\left(2,\frac{c^2 \left(f+g x^2\right)}{c^2 f+g}\right)}{2 c}-\frac{i b e \sqrt{f} \text{PolyLog}\left(2,1+\frac{2 \sqrt{f} \sqrt{g} (1-c x)}{\left(-\sqrt{g}+i c \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 \sqrt{g}}+\frac{i b e \sqrt{f} \text{PolyLog}\left(2,1-\frac{2 \sqrt{f} \sqrt{g} (c x+1)}{\left(\sqrt{g}+i c \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 \sqrt{g}}+x \left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)+\frac{2 a e \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{g}}-2 a e x+\frac{b \log \left(\frac{g \left(1-c^2 x^2\right)}{c^2 f+g}\right) \left(d+e \log \left(f+g x^2\right)\right)}{2 c}-\frac{b e \log \left(1-c^2 x^2\right)}{c}-\frac{b e \sqrt{f} \log \left(1-\frac{1}{c x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{g}}+\frac{b e \sqrt{f} \log \left(\frac{1}{c x}+1\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{g}}+\frac{b e \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} (1-c x)}{\left(-\sqrt{g}+i c \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{\sqrt{g}}-\frac{b e \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} (c x+1)}{\left(\sqrt{g}+i c \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{\sqrt{g}}-2 b e x \coth ^{-1}(c x)","\frac{b e \text{PolyLog}\left(2,\frac{c^2 \left(f+g x^2\right)}{c^2 f+g}\right)}{2 c}-\frac{i b e \sqrt{f} \text{PolyLog}\left(2,1+\frac{2 \sqrt{f} \sqrt{g} (1-c x)}{\left(-\sqrt{g}+i c \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 \sqrt{g}}+\frac{i b e \sqrt{f} \text{PolyLog}\left(2,1-\frac{2 \sqrt{f} \sqrt{g} (c x+1)}{\left(\sqrt{g}+i c \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 \sqrt{g}}+x \left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)+\frac{2 a e \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{g}}-2 a e x+\frac{b \log \left(\frac{g \left(1-c^2 x^2\right)}{c^2 f+g}\right) \left(d+e \log \left(f+g x^2\right)\right)}{2 c}-\frac{b e \log \left(1-c^2 x^2\right)}{c}-\frac{b e \sqrt{f} \log \left(1-\frac{1}{c x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{g}}+\frac{b e \sqrt{f} \log \left(\frac{1}{c x}+1\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{g}}+\frac{b e \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} (1-c x)}{\left(-\sqrt{g}+i c \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{\sqrt{g}}-\frac{b e \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} (c x+1)}{\left(\sqrt{g}+i c \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{\sqrt{g}}-2 b e x \coth ^{-1}(c x)",1,"-2*a*e*x - 2*b*e*x*ArcCoth[c*x] + (2*a*e*Sqrt[f]*ArcTan[(Sqrt[g]*x)/Sqrt[f]])/Sqrt[g] - (b*e*Sqrt[f]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[1 - 1/(c*x)])/Sqrt[g] + (b*e*Sqrt[f]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[1 + 1/(c*x)])/Sqrt[g] + (b*e*Sqrt[f]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(-2*Sqrt[f]*Sqrt[g]*(1 - c*x))/((I*c*Sqrt[f] - Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/Sqrt[g] - (b*e*Sqrt[f]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(1 + c*x))/((I*c*Sqrt[f] + Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/Sqrt[g] - (b*e*Log[1 - c^2*x^2])/c + x*(a + b*ArcCoth[c*x])*(d + e*Log[f + g*x^2]) + (b*Log[(g*(1 - c^2*x^2))/(c^2*f + g)]*(d + e*Log[f + g*x^2]))/(2*c) + (b*e*PolyLog[2, (c^2*(f + g*x^2))/(c^2*f + g)])/(2*c) - ((I/2)*b*e*Sqrt[f]*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*(1 - c*x))/((I*c*Sqrt[f] - Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/Sqrt[g] + ((I/2)*b*e*Sqrt[f]*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(1 + c*x))/((I*c*Sqrt[f] + Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/Sqrt[g]","A",38,20,21,0.9524,1,"{6074, 2475, 2394, 2393, 2391, 5981, 5911, 260, 5975, 205, 5973, 2470, 12, 6688, 4876, 4848, 4856, 2402, 2315, 2447}"
280,0,0,0,0.2515188,"\int \frac{\left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)}{x} \, dx","Int[((a + b*ArcCoth[c*x])*(d + e*Log[f + g*x^2]))/x,x]","\int \frac{\left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)}{x} \, dx","\frac{1}{2} a e \text{PolyLog}\left(2,\frac{g x^2}{f}+1\right)+\frac{1}{2} b d \text{PolyLog}\left(2,-\frac{1}{c x}\right)-\frac{1}{2} b d \text{PolyLog}\left(2,\frac{1}{c x}\right)+b e \text{Int}\left(\frac{\coth ^{-1}(c x) \log \left(f+g x^2\right)}{x},x\right)+a d \log (x)+\frac{1}{2} a e \log \left(-\frac{g x^2}{f}\right) \log \left(f+g x^2\right)",0,"a*d*Log[x] + (a*e*Log[-((g*x^2)/f)]*Log[f + g*x^2])/2 + (b*d*PolyLog[2, -(1/(c*x))])/2 - (b*d*PolyLog[2, 1/(c*x)])/2 + (a*e*PolyLog[2, 1 + (g*x^2)/f])/2 + b*e*Defer[Int][(ArcCoth[c*x]*Log[f + g*x^2])/x, x]","A",0,0,0,0,-1,"{}"
281,1,560,0,1.2614438,"\int \frac{\left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)}{x^2} \, dx","Int[((a + b*ArcCoth[c*x])*(d + e*Log[f + g*x^2]))/x^2,x]","-\frac{1}{2} b c e \text{PolyLog}\left(2,\frac{c^2 \left(f+g x^2\right)}{c^2 f+g}\right)+\frac{1}{2} b c e \text{PolyLog}\left(2,\frac{g x^2}{f}+1\right)-\frac{i b e \sqrt{g} \text{PolyLog}\left(2,1+\frac{2 \sqrt{f} \sqrt{g} (1-c x)}{\left(-\sqrt{g}+i c \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 \sqrt{f}}+\frac{i b e \sqrt{g} \text{PolyLog}\left(2,1-\frac{2 \sqrt{f} \sqrt{g} (c x+1)}{\left(\sqrt{g}+i c \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 \sqrt{f}}-\frac{\left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)}{x}+\frac{2 a e \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f}}-\frac{1}{2} b c \log \left(\frac{g \left(1-c^2 x^2\right)}{c^2 f+g}\right) \left(d+e \log \left(f+g x^2\right)\right)+\frac{1}{2} b c \log \left(-\frac{g x^2}{f}\right) \left(d+e \log \left(f+g x^2\right)\right)-\frac{b e \sqrt{g} \log \left(1-\frac{1}{c x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f}}+\frac{b e \sqrt{g} \log \left(\frac{1}{c x}+1\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f}}+\frac{b e \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} (1-c x)}{\left(-\sqrt{g}+i c \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{\sqrt{f}}-\frac{b e \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} (c x+1)}{\left(\sqrt{g}+i c \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{\sqrt{f}}","-\frac{1}{2} b c e \text{PolyLog}\left(2,\frac{c^2 \left(f+g x^2\right)}{c^2 f+g}\right)+\frac{1}{2} b c e \text{PolyLog}\left(2,\frac{g x^2}{f}+1\right)-\frac{i b e \sqrt{g} \text{PolyLog}\left(2,1+\frac{2 \sqrt{f} \sqrt{g} (1-c x)}{\left(-\sqrt{g}+i c \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 \sqrt{f}}+\frac{i b e \sqrt{g} \text{PolyLog}\left(2,1-\frac{2 \sqrt{f} \sqrt{g} (c x+1)}{\left(\sqrt{g}+i c \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 \sqrt{f}}-\frac{\left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)}{x}+\frac{2 a e \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f}}-\frac{1}{2} b c \log \left(\frac{g \left(1-c^2 x^2\right)}{c^2 f+g}\right) \left(d+e \log \left(f+g x^2\right)\right)+\frac{1}{2} b c \log \left(-\frac{g x^2}{f}\right) \left(d+e \log \left(f+g x^2\right)\right)-\frac{b e \sqrt{g} \log \left(1-\frac{1}{c x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f}}+\frac{b e \sqrt{g} \log \left(\frac{1}{c x}+1\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f}}+\frac{b e \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} (1-c x)}{\left(-\sqrt{g}+i c \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{\sqrt{f}}-\frac{b e \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} (c x+1)}{\left(\sqrt{g}+i c \sqrt{f}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{\sqrt{f}}",1,"(2*a*e*Sqrt[g]*ArcTan[(Sqrt[g]*x)/Sqrt[f]])/Sqrt[f] - (b*e*Sqrt[g]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[1 - 1/(c*x)])/Sqrt[f] + (b*e*Sqrt[g]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[1 + 1/(c*x)])/Sqrt[f] + (b*e*Sqrt[g]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(-2*Sqrt[f]*Sqrt[g]*(1 - c*x))/((I*c*Sqrt[f] - Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/Sqrt[f] - (b*e*Sqrt[g]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(1 + c*x))/((I*c*Sqrt[f] + Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/Sqrt[f] - ((a + b*ArcCoth[c*x])*(d + e*Log[f + g*x^2]))/x + (b*c*Log[-((g*x^2)/f)]*(d + e*Log[f + g*x^2]))/2 - (b*c*Log[(g*(1 - c^2*x^2))/(c^2*f + g)]*(d + e*Log[f + g*x^2]))/2 - (b*c*e*PolyLog[2, (c^2*(f + g*x^2))/(c^2*f + g)])/2 + (b*c*e*PolyLog[2, 1 + (g*x^2)/f])/2 - ((I/2)*b*e*Sqrt[g]*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*(1 - c*x))/((I*c*Sqrt[f] - Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/Sqrt[f] + ((I/2)*b*e*Sqrt[g]*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(1 + c*x))/((I*c*Sqrt[f] + Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/Sqrt[f]","A",38,22,24,0.9167,1,"{6082, 2475, 36, 29, 31, 2416, 2394, 2315, 2393, 2391, 5975, 205, 5973, 2470, 12, 260, 6688, 4876, 4848, 4856, 2402, 2447}"
282,1,712,0,1.1131396,"\int \frac{\left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)}{x^3} \, dx","Int[((a + b*ArcCoth[c*x])*(d + e*Log[f + g*x^2]))/x^3,x]","\frac{1}{4} b c^2 e \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)+\frac{1}{4} b c^2 e \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)-\frac{1}{2} b c^2 e \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)+\frac{b e g \text{PolyLog}\left(2,-\frac{1}{c x}\right)}{2 f}-\frac{b e g \text{PolyLog}\left(2,\frac{1}{c x}\right)}{2 f}-\frac{b e g \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 f}+\frac{b e g \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)}{4 f}+\frac{b e g \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)}{4 f}-\frac{\left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)}{2 x^2}-\frac{a e g \log \left(f+g x^2\right)}{2 f}+\frac{a e g \log (x)}{f}+\frac{1}{2} b c^2 \tanh ^{-1}(c x) \left(d+e \log \left(f+g x^2\right)\right)-\frac{1}{2} b c^2 e \tanh ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)-\frac{1}{2} b c^2 e \tanh ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)+b c^2 e \log \left(\frac{2}{c x+1}\right) \tanh ^{-1}(c x)-\frac{b c \left(d+e \log \left(f+g x^2\right)\right)}{2 x}+\frac{b c e \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f}}+\frac{b e g \log \left(\frac{2}{c x+1}\right) \coth ^{-1}(c x)}{f}-\frac{b e g \coth ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)}{2 f}-\frac{b e g \coth ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)}{2 f}","\frac{1}{4} b c^2 e \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)+\frac{1}{4} b c^2 e \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)-\frac{1}{2} b c^2 e \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)+\frac{b e g \text{PolyLog}\left(2,-\frac{1}{c x}\right)}{2 f}-\frac{b e g \text{PolyLog}\left(2,\frac{1}{c x}\right)}{2 f}-\frac{b e g \text{PolyLog}\left(2,1-\frac{2}{c x+1}\right)}{2 f}+\frac{b e g \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)}{4 f}+\frac{b e g \text{PolyLog}\left(2,1-\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)}{4 f}-\frac{\left(a+b \coth ^{-1}(c x)\right) \left(d+e \log \left(f+g x^2\right)\right)}{2 x^2}-\frac{a e g \log \left(f+g x^2\right)}{2 f}+\frac{a e g \log (x)}{f}+\frac{1}{2} b c^2 \tanh ^{-1}(c x) \left(d+e \log \left(f+g x^2\right)\right)-\frac{1}{2} b c^2 e \tanh ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)-\frac{1}{2} b c^2 e \tanh ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)+b c^2 e \log \left(\frac{2}{c x+1}\right) \tanh ^{-1}(c x)-\frac{b c \left(d+e \log \left(f+g x^2\right)\right)}{2 x}+\frac{b c e \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f}}+\frac{b e g \log \left(\frac{2}{c x+1}\right) \coth ^{-1}(c x)}{f}-\frac{b e g \coth ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}-\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}-\sqrt{g}\right)}\right)}{2 f}-\frac{b e g \coth ^{-1}(c x) \log \left(\frac{2 c \left(\sqrt{-f}+\sqrt{g} x\right)}{(c x+1) \left(c \sqrt{-f}+\sqrt{g}\right)}\right)}{2 f}",1,"(b*c*e*Sqrt[g]*ArcTan[(Sqrt[g]*x)/Sqrt[f]])/Sqrt[f] + (a*e*g*Log[x])/f + (b*e*g*ArcCoth[c*x]*Log[2/(1 + c*x)])/f + b*c^2*e*ArcTanh[c*x]*Log[2/(1 + c*x)] - (b*e*g*ArcCoth[c*x]*Log[(2*c*(Sqrt[-f] - Sqrt[g]*x))/((c*Sqrt[-f] - Sqrt[g])*(1 + c*x))])/(2*f) - (b*c^2*e*ArcTanh[c*x]*Log[(2*c*(Sqrt[-f] - Sqrt[g]*x))/((c*Sqrt[-f] - Sqrt[g])*(1 + c*x))])/2 - (b*e*g*ArcCoth[c*x]*Log[(2*c*(Sqrt[-f] + Sqrt[g]*x))/((c*Sqrt[-f] + Sqrt[g])*(1 + c*x))])/(2*f) - (b*c^2*e*ArcTanh[c*x]*Log[(2*c*(Sqrt[-f] + Sqrt[g]*x))/((c*Sqrt[-f] + Sqrt[g])*(1 + c*x))])/2 - (a*e*g*Log[f + g*x^2])/(2*f) - (b*c*(d + e*Log[f + g*x^2]))/(2*x) - ((a + b*ArcCoth[c*x])*(d + e*Log[f + g*x^2]))/(2*x^2) + (b*c^2*ArcTanh[c*x]*(d + e*Log[f + g*x^2]))/2 + (b*e*g*PolyLog[2, -(1/(c*x))])/(2*f) - (b*e*g*PolyLog[2, 1/(c*x)])/(2*f) - (b*c^2*e*PolyLog[2, 1 - 2/(1 + c*x)])/2 - (b*e*g*PolyLog[2, 1 - 2/(1 + c*x)])/(2*f) + (b*c^2*e*PolyLog[2, 1 - (2*c*(Sqrt[-f] - Sqrt[g]*x))/((c*Sqrt[-f] - Sqrt[g])*(1 + c*x))])/4 + (b*e*g*PolyLog[2, 1 - (2*c*(Sqrt[-f] - Sqrt[g]*x))/((c*Sqrt[-f] - Sqrt[g])*(1 + c*x))])/(4*f) + (b*c^2*e*PolyLog[2, 1 - (2*c*(Sqrt[-f] + Sqrt[g]*x))/((c*Sqrt[-f] + Sqrt[g])*(1 + c*x))])/4 + (b*e*g*PolyLog[2, 1 - (2*c*(Sqrt[-f] + Sqrt[g]*x))/((c*Sqrt[-f] + Sqrt[g])*(1 + c*x))])/(4*f)","A",32,17,24,0.7083,1,"{5917, 325, 206, 6086, 6725, 801, 635, 205, 260, 5993, 5913, 5921, 2402, 2315, 2447, 5992, 5920}"
283,1,25,0,0.0121473,"\int \coth ^{-1}\left(e^x\right) \, dx","Int[ArcCoth[E^x],x]","\frac{1}{2} \text{PolyLog}\left(2,-e^{-x}\right)-\frac{1}{2} \text{PolyLog}\left(2,e^{-x}\right)","\frac{1}{2} \text{PolyLog}\left(2,-e^{-x}\right)-\frac{1}{2} \text{PolyLog}\left(2,e^{-x}\right)",1,"PolyLog[2, -E^(-x)]/2 - PolyLog[2, E^(-x)]/2","A",2,2,4,0.5000,1,"{2282, 5913}"
284,1,51,0,0.0474447,"\int x \coth ^{-1}\left(e^x\right) \, dx","Int[x*ArcCoth[E^x],x]","\frac{1}{2} x \text{PolyLog}\left(2,-e^{-x}\right)-\frac{1}{2} x \text{PolyLog}\left(2,e^{-x}\right)+\frac{1}{2} \text{PolyLog}\left(3,-e^{-x}\right)-\frac{1}{2} \text{PolyLog}\left(3,e^{-x}\right)","\frac{1}{2} x \text{PolyLog}\left(2,-e^{-x}\right)-\frac{1}{2} x \text{PolyLog}\left(2,e^{-x}\right)+\frac{1}{2} \text{PolyLog}\left(3,-e^{-x}\right)-\frac{1}{2} \text{PolyLog}\left(3,e^{-x}\right)",1,"(x*PolyLog[2, -E^(-x)])/2 - (x*PolyLog[2, E^(-x)])/2 + PolyLog[3, -E^(-x)]/2 - PolyLog[3, E^(-x)]/2","A",7,4,6,0.6667,1,"{6214, 2531, 2282, 6589}"
285,1,70,0,0.0730378,"\int x^2 \coth ^{-1}\left(e^x\right) \, dx","Int[x^2*ArcCoth[E^x],x]","\frac{1}{2} x^2 \text{PolyLog}\left(2,-e^{-x}\right)-\frac{1}{2} x^2 \text{PolyLog}\left(2,e^{-x}\right)+x \text{PolyLog}\left(3,-e^{-x}\right)-x \text{PolyLog}\left(3,e^{-x}\right)+\text{PolyLog}\left(4,-e^{-x}\right)-\text{PolyLog}\left(4,e^{-x}\right)","\frac{1}{2} x^2 \text{PolyLog}\left(2,-e^{-x}\right)-\frac{1}{2} x^2 \text{PolyLog}\left(2,e^{-x}\right)+x \text{PolyLog}\left(3,-e^{-x}\right)-x \text{PolyLog}\left(3,e^{-x}\right)+\text{PolyLog}\left(4,-e^{-x}\right)-\text{PolyLog}\left(4,e^{-x}\right)",1,"(x^2*PolyLog[2, -E^(-x)])/2 - (x^2*PolyLog[2, E^(-x)])/2 + x*PolyLog[3, -E^(-x)] - x*PolyLog[3, E^(-x)] + PolyLog[4, -E^(-x)] - PolyLog[4, E^(-x)]","A",9,5,8,0.6250,1,"{6214, 2531, 6609, 2282, 6589}"
286,1,41,0,0.0164433,"\int \coth ^{-1}\left(e^{a+b x}\right) \, dx","Int[ArcCoth[E^(a + b*x)],x]","\frac{\text{PolyLog}\left(2,-e^{-a-b x}\right)}{2 b}-\frac{\text{PolyLog}\left(2,e^{-a-b x}\right)}{2 b}","\frac{\text{PolyLog}\left(2,-e^{-a-b x}\right)}{2 b}-\frac{\text{PolyLog}\left(2,e^{-a-b x}\right)}{2 b}",1,"PolyLog[2, -E^(-a - b*x)]/(2*b) - PolyLog[2, E^(-a - b*x)]/(2*b)","A",2,2,8,0.2500,1,"{2282, 5913}"
287,1,83,0,0.0642786,"\int x \coth ^{-1}\left(e^{a+b x}\right) \, dx","Int[x*ArcCoth[E^(a + b*x)],x]","\frac{\text{PolyLog}\left(3,-e^{-a-b x}\right)}{2 b^2}-\frac{\text{PolyLog}\left(3,e^{-a-b x}\right)}{2 b^2}+\frac{x \text{PolyLog}\left(2,-e^{-a-b x}\right)}{2 b}-\frac{x \text{PolyLog}\left(2,e^{-a-b x}\right)}{2 b}","\frac{\text{PolyLog}\left(3,-e^{-a-b x}\right)}{2 b^2}-\frac{\text{PolyLog}\left(3,e^{-a-b x}\right)}{2 b^2}+\frac{x \text{PolyLog}\left(2,-e^{-a-b x}\right)}{2 b}-\frac{x \text{PolyLog}\left(2,e^{-a-b x}\right)}{2 b}",1,"(x*PolyLog[2, -E^(-a - b*x)])/(2*b) - (x*PolyLog[2, E^(-a - b*x)])/(2*b) + PolyLog[3, -E^(-a - b*x)]/(2*b^2) - PolyLog[3, E^(-a - b*x)]/(2*b^2)","A",7,4,10,0.4000,1,"{6214, 2531, 2282, 6589}"
288,1,119,0,0.0994868,"\int x^2 \coth ^{-1}\left(e^{a+b x}\right) \, dx","Int[x^2*ArcCoth[E^(a + b*x)],x]","\frac{x \text{PolyLog}\left(3,-e^{-a-b x}\right)}{b^2}-\frac{x \text{PolyLog}\left(3,e^{-a-b x}\right)}{b^2}+\frac{\text{PolyLog}\left(4,-e^{-a-b x}\right)}{b^3}-\frac{\text{PolyLog}\left(4,e^{-a-b x}\right)}{b^3}+\frac{x^2 \text{PolyLog}\left(2,-e^{-a-b x}\right)}{2 b}-\frac{x^2 \text{PolyLog}\left(2,e^{-a-b x}\right)}{2 b}","\frac{x \text{PolyLog}\left(3,-e^{-a-b x}\right)}{b^2}-\frac{x \text{PolyLog}\left(3,e^{-a-b x}\right)}{b^2}+\frac{\text{PolyLog}\left(4,-e^{-a-b x}\right)}{b^3}-\frac{\text{PolyLog}\left(4,e^{-a-b x}\right)}{b^3}+\frac{x^2 \text{PolyLog}\left(2,-e^{-a-b x}\right)}{2 b}-\frac{x^2 \text{PolyLog}\left(2,e^{-a-b x}\right)}{2 b}",1,"(x^2*PolyLog[2, -E^(-a - b*x)])/(2*b) - (x^2*PolyLog[2, E^(-a - b*x)])/(2*b) + (x*PolyLog[3, -E^(-a - b*x)])/b^2 - (x*PolyLog[3, E^(-a - b*x)])/b^2 + PolyLog[4, -E^(-a - b*x)]/b^3 - PolyLog[4, E^(-a - b*x)]/b^3","A",9,5,12,0.4167,1,"{6214, 2531, 6609, 2282, 6589}"
289,1,168,0,0.1320839,"\int \coth ^{-1}\left(a+b f^{c+d x}\right) \, dx","Int[ArcCoth[a + b*f^(c + d*x)],x]","\frac{\text{PolyLog}\left(2,1-\frac{2}{a+b f^{c+d x}+1}\right)}{2 d \log (f)}-\frac{\text{PolyLog}\left(2,1-\frac{2 b f^{c+d x}}{(1-a) \left(a+b f^{c+d x}+1\right)}\right)}{2 d \log (f)}-\frac{\log \left(\frac{2}{a+b f^{c+d x}+1}\right) \coth ^{-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) \coth ^{-1}\left(a+b f^{c+d x}\right)}{d \log (f)}","\frac{\text{PolyLog}\left(2,1-\frac{2}{a+b f^{c+d x}+1}\right)}{2 d \log (f)}-\frac{\text{PolyLog}\left(2,1-\frac{2 b f^{c+d x}}{(1-a) \left(a+b f^{c+d x}+1\right)}\right)}{2 d \log (f)}-\frac{\log \left(\frac{2}{a+b f^{c+d x}+1}\right) \coth ^{-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) \coth ^{-1}\left(a+b f^{c+d x}\right)}{d \log (f)}",1,"-((ArcCoth[a + b*f^(c + d*x)]*Log[2/(1 + a + b*f^(c + d*x))])/(d*Log[f])) + (ArcCoth[a + b*f^(c + d*x)]*Log[(2*b*f^(c + d*x))/((1 - a)*(1 + a + b*f^(c + d*x)))])/(d*Log[f]) + PolyLog[2, 1 - 2/(1 + a + b*f^(c + d*x))]/(2*d*Log[f]) - PolyLog[2, 1 - (2*b*f^(c + d*x))/((1 - a)*(1 + a + b*f^(c + d*x)))]/(2*d*Log[f])","A",6,6,12,0.5000,1,"{2282, 6112, 5921, 2402, 2315, 2447}"
290,1,216,0,2.7142053,"\int x \coth ^{-1}\left(a+b f^{c+d x}\right) \, dx","Int[x*ArcCoth[a + b*f^(c + d*x)],x]","-\frac{\text{PolyLog}\left(3,\frac{b f^{c+d x}}{1-a}\right)}{2 d^2 \log ^2(f)}+\frac{\text{PolyLog}\left(3,-\frac{b f^{c+d x}}{a+1}\right)}{2 d^2 \log ^2(f)}+\frac{x \text{PolyLog}\left(2,\frac{b f^{c+d x}}{1-a}\right)}{2 d \log (f)}-\frac{x \text{PolyLog}\left(2,-\frac{b f^{c+d x}}{a+1}\right)}{2 d \log (f)}+\frac{1}{4} x^2 \log \left(1-\frac{b f^{c+d x}}{1-a}\right)-\frac{1}{4} x^2 \log \left(\frac{b f^{c+d x}}{a+1}+1\right)-\frac{1}{4} x^2 \log \left(1-\frac{1}{a+b f^{c+d x}}\right)+\frac{1}{4} x^2 \log \left(\frac{1}{a+b f^{c+d x}}+1\right)","-\frac{\text{PolyLog}\left(3,\frac{b f^{c+d x}}{1-a}\right)}{2 d^2 \log ^2(f)}+\frac{\text{PolyLog}\left(3,-\frac{b f^{c+d x}}{a+1}\right)}{2 d^2 \log ^2(f)}+\frac{x \text{PolyLog}\left(2,\frac{b f^{c+d x}}{1-a}\right)}{2 d \log (f)}-\frac{x \text{PolyLog}\left(2,-\frac{b f^{c+d x}}{a+1}\right)}{2 d \log (f)}+\frac{1}{4} x^2 \log \left(1-\frac{b f^{c+d x}}{1-a}\right)-\frac{1}{4} x^2 \log \left(\frac{b f^{c+d x}}{a+1}+1\right)-\frac{1}{4} x^2 \log \left(1-\frac{1}{a+b f^{c+d x}}\right)+\frac{1}{4} x^2 \log \left(\frac{1}{a+b f^{c+d x}}+1\right)",1,"(x^2*Log[1 - (b*f^(c + d*x))/(1 - a)])/4 - (x^2*Log[1 + (b*f^(c + d*x))/(1 + a)])/4 - (x^2*Log[1 - (a + b*f^(c + d*x))^(-1)])/4 + (x^2*Log[1 + (a + b*f^(c + d*x))^(-1)])/4 + (x*PolyLog[2, (b*f^(c + d*x))/(1 - a)])/(2*d*Log[f]) - (x*PolyLog[2, -((b*f^(c + d*x))/(1 + a))])/(2*d*Log[f]) - PolyLog[3, (b*f^(c + d*x))/(1 - a)]/(2*d^2*Log[f]^2) + PolyLog[3, -((b*f^(c + d*x))/(1 + a))]/(2*d^2*Log[f]^2)","A",25,8,14,0.5714,1,"{6214, 2551, 12, 6742, 2190, 2531, 2282, 6589}"
291,1,269,0,2.5856488,"\int x^2 \coth ^{-1}\left(a+b f^{c+d x}\right) \, dx","Int[x^2*ArcCoth[a + b*f^(c + d*x)],x]","-\frac{x \text{PolyLog}\left(3,\frac{b f^{c+d x}}{1-a}\right)}{d^2 \log ^2(f)}+\frac{x \text{PolyLog}\left(3,-\frac{b f^{c+d x}}{a+1}\right)}{d^2 \log ^2(f)}+\frac{\text{PolyLog}\left(4,\frac{b f^{c+d x}}{1-a}\right)}{d^3 \log ^3(f)}-\frac{\text{PolyLog}\left(4,-\frac{b f^{c+d x}}{a+1}\right)}{d^3 \log ^3(f)}+\frac{x^2 \text{PolyLog}\left(2,\frac{b f^{c+d x}}{1-a}\right)}{2 d \log (f)}-\frac{x^2 \text{PolyLog}\left(2,-\frac{b f^{c+d x}}{a+1}\right)}{2 d \log (f)}+\frac{1}{6} x^3 \log \left(1-\frac{b f^{c+d x}}{1-a}\right)-\frac{1}{6} x^3 \log \left(\frac{b f^{c+d x}}{a+1}+1\right)-\frac{1}{6} x^3 \log \left(1-\frac{1}{a+b f^{c+d x}}\right)+\frac{1}{6} x^3 \log \left(\frac{1}{a+b f^{c+d x}}+1\right)","-\frac{x \text{PolyLog}\left(3,\frac{b f^{c+d x}}{1-a}\right)}{d^2 \log ^2(f)}+\frac{x \text{PolyLog}\left(3,-\frac{b f^{c+d x}}{a+1}\right)}{d^2 \log ^2(f)}+\frac{\text{PolyLog}\left(4,\frac{b f^{c+d x}}{1-a}\right)}{d^3 \log ^3(f)}-\frac{\text{PolyLog}\left(4,-\frac{b f^{c+d x}}{a+1}\right)}{d^3 \log ^3(f)}+\frac{x^2 \text{PolyLog}\left(2,\frac{b f^{c+d x}}{1-a}\right)}{2 d \log (f)}-\frac{x^2 \text{PolyLog}\left(2,-\frac{b f^{c+d x}}{a+1}\right)}{2 d \log (f)}+\frac{1}{6} x^3 \log \left(1-\frac{b f^{c+d x}}{1-a}\right)-\frac{1}{6} x^3 \log \left(\frac{b f^{c+d x}}{a+1}+1\right)-\frac{1}{6} x^3 \log \left(1-\frac{1}{a+b f^{c+d x}}\right)+\frac{1}{6} x^3 \log \left(\frac{1}{a+b f^{c+d x}}+1\right)",1,"(x^3*Log[1 - (b*f^(c + d*x))/(1 - a)])/6 - (x^3*Log[1 + (b*f^(c + d*x))/(1 + a)])/6 - (x^3*Log[1 - (a + b*f^(c + d*x))^(-1)])/6 + (x^3*Log[1 + (a + b*f^(c + d*x))^(-1)])/6 + (x^2*PolyLog[2, (b*f^(c + d*x))/(1 - a)])/(2*d*Log[f]) - (x^2*PolyLog[2, -((b*f^(c + d*x))/(1 + a))])/(2*d*Log[f]) - (x*PolyLog[3, (b*f^(c + d*x))/(1 - a)])/(d^2*Log[f]^2) + (x*PolyLog[3, -((b*f^(c + d*x))/(1 + a))])/(d^2*Log[f]^2) + PolyLog[4, (b*f^(c + d*x))/(1 - a)]/(d^3*Log[f]^3) - PolyLog[4, -((b*f^(c + d*x))/(1 + a))]/(d^3*Log[f]^3)","A",29,9,16,0.5625,1,"{6214, 2551, 12, 6742, 2190, 2531, 6609, 2282, 6589}"
292,1,17,0,0.0443519,"\int \frac{1}{\left(a-a x^2\right) \left(b-2 b \coth ^{-1}(x)\right)} \, dx","Int[1/((a - a*x^2)*(b - 2*b*ArcCoth[x])),x]","-\frac{\log \left(1-2 \coth ^{-1}(x)\right)}{2 a b}","-\frac{\log \left(1-2 \coth ^{-1}(x)\right)}{2 a b}",1,"-Log[1 - 2*ArcCoth[x]]/(2*a*b)","A",1,1,20,0.05000,1,"{5947}"
293,1,44,0,0.0523872,"\int x^3 \coth ^{-1}\left(a+b x^4\right) \, dx","Int[x^3*ArcCoth[a + b*x^4],x]","\frac{\log \left(1-\left(a+b x^4\right)^2\right)}{8 b}+\frac{\left(a+b x^4\right) \coth ^{-1}\left(a+b x^4\right)}{4 b}","\frac{\log \left(1-\left(a+b x^4\right)^2\right)}{8 b}+\frac{\left(a+b x^4\right) \coth ^{-1}\left(a+b x^4\right)}{4 b}",1,"((a + b*x^4)*ArcCoth[a + b*x^4])/(4*b) + Log[1 - (a + b*x^4)^2]/(8*b)","A",4,4,12,0.3333,1,"{6715, 6104, 5911, 260}"
294,1,47,0,0.0552597,"\int x^{-1+n} \coth ^{-1}\left(a+b x^n\right) \, dx","Int[x^(-1 + n)*ArcCoth[a + b*x^n],x]","\frac{\log \left(1-\left(a+b x^n\right)^2\right)}{2 b n}+\frac{\left(a+b x^n\right) \coth ^{-1}\left(a+b x^n\right)}{b n}","\frac{\log \left(1-\left(a+b x^n\right)^2\right)}{2 b n}+\frac{\left(a+b x^n\right) \coth ^{-1}\left(a+b x^n\right)}{b n}",1,"((a + b*x^n)*ArcCoth[a + b*x^n])/(b*n) + Log[1 - (a + b*x^n)^2]/(2*b*n)","A",4,4,14,0.2857,1,"{6715, 6104, 5911, 260}"
295,1,107,0,0.1546001,"\int e^{c (a+b x)} \coth ^{-1}(\sinh (a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcCoth[Sinh[a*c + b*c*x]],x]","\frac{\left(1-\sqrt{2}\right) \log \left(-e^{2 c (a+b x)}+3-2 \sqrt{2}\right)}{2 b c}+\frac{\left(1+\sqrt{2}\right) \log \left(-e^{2 c (a+b x)}+3+2 \sqrt{2}\right)}{2 b c}+\frac{e^{a c+b c x} \coth ^{-1}(\sinh (c (a+b x)))}{b c}","\frac{\left(1-\sqrt{2}\right) \log \left(-e^{2 c (a+b x)}+3-2 \sqrt{2}\right)}{2 b c}+\frac{\left(1+\sqrt{2}\right) \log \left(-e^{2 c (a+b x)}+3+2 \sqrt{2}\right)}{2 b c}+\frac{e^{a c+b c x} \coth ^{-1}(\sinh (c (a+b x)))}{b c}",1,"(E^(a*c + b*c*x)*ArcCoth[Sinh[c*(a + b*x)]])/(b*c) + ((1 - Sqrt[2])*Log[3 - 2*Sqrt[2] - E^(2*c*(a + b*x))])/(2*b*c) + ((1 + Sqrt[2])*Log[3 + 2*Sqrt[2] - E^(2*c*(a + b*x))])/(2*b*c)","A",8,7,20,0.3500,1,"{2194, 6276, 2282, 12, 1247, 632, 31}"
296,1,49,0,0.0793503,"\int e^{c (a+b x)} \coth ^{-1}(\cosh (a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcCoth[Cosh[a*c + b*c*x]],x]","\frac{\log \left(1-e^{2 c (a+b x)}\right)}{b c}+\frac{e^{a c+b c x} \coth ^{-1}(\cosh (c (a+b x)))}{b c}","\frac{\log \left(1-e^{2 c (a+b x)}\right)}{b c}+\frac{e^{a c+b c x} \coth ^{-1}(\cosh (c (a+b x)))}{b c}",1,"(E^(a*c + b*c*x)*ArcCoth[Cosh[c*(a + b*x)]])/(b*c) + Log[1 - E^(2*c*(a + b*x))]/(b*c)","A",5,5,20,0.2500,1,"{2194, 6276, 2282, 12, 260}"
297,1,45,0,0.0596168,"\int e^{c (a+b x)} \coth ^{-1}(\tanh (a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcCoth[Tanh[a*c + b*c*x]],x]","\frac{e^{a c+b c x} \coth ^{-1}(\tanh (c (a+b x)))}{b c}-\frac{e^{a c+b c x}}{b c}","\frac{e^{a c+b c x} \coth ^{-1}(\tanh (c (a+b x)))}{b c}-\frac{e^{a c+b c x}}{b c}",1,"-(E^(a*c + b*c*x)/(b*c)) + (E^(a*c + b*c*x)*ArcCoth[Tanh[c*(a + b*x)]])/(b*c)","A",3,2,20,0.1000,1,"{2194, 6276}"
298,1,45,0,0.0586381,"\int e^{c (a+b x)} \coth ^{-1}(\coth (a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcCoth[Coth[a*c + b*c*x]],x]","\frac{e^{a c+b c x} \coth ^{-1}(\coth (c (a+b x)))}{b c}-\frac{e^{a c+b c x}}{b c}","\frac{e^{a c+b c x} \coth ^{-1}(\coth (c (a+b x)))}{b c}-\frac{e^{a c+b c x}}{b c}",1,"-(E^(a*c + b*c*x)/(b*c)) + (E^(a*c + b*c*x)*ArcCoth[Coth[c*(a + b*x)]])/(b*c)","A",3,2,20,0.1000,1,"{2194, 6276}"
299,1,49,0,0.0706529,"\int e^{c (a+b x)} \coth ^{-1}(\text{sech}(a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcCoth[Sech[a*c + b*c*x]],x]","\frac{\log \left(1-e^{2 c (a+b x)}\right)}{b c}+\frac{e^{a c+b c x} \coth ^{-1}(\text{sech}(c (a+b x)))}{b c}","\frac{\log \left(1-e^{2 c (a+b x)}\right)}{b c}+\frac{e^{a c+b c x} \coth ^{-1}(\text{sech}(c (a+b x)))}{b c}",1,"(E^(a*c + b*c*x)*ArcCoth[Sech[c*(a + b*x)]])/(b*c) + Log[1 - E^(2*c*(a + b*x))]/(b*c)","A",5,5,20,0.2500,1,"{2194, 6276, 2282, 12, 260}"
300,1,107,0,0.1475994,"\int e^{c (a+b x)} \coth ^{-1}(\text{csch}(a c+b c x)) \, dx","Int[E^(c*(a + b*x))*ArcCoth[Csch[a*c + b*c*x]],x]","\frac{\left(1-\sqrt{2}\right) \log \left(-e^{2 c (a+b x)}+3-2 \sqrt{2}\right)}{2 b c}+\frac{\left(1+\sqrt{2}\right) \log \left(-e^{2 c (a+b x)}+3+2 \sqrt{2}\right)}{2 b c}+\frac{e^{a c+b c x} \coth ^{-1}(\text{csch}(c (a+b x)))}{b c}","\frac{\left(1-\sqrt{2}\right) \log \left(-e^{2 c (a+b x)}+3-2 \sqrt{2}\right)}{2 b c}+\frac{\left(1+\sqrt{2}\right) \log \left(-e^{2 c (a+b x)}+3+2 \sqrt{2}\right)}{2 b c}+\frac{e^{a c+b c x} \coth ^{-1}(\text{csch}(c (a+b x)))}{b c}",1,"(E^(a*c + b*c*x)*ArcCoth[Csch[c*(a + b*x)]])/(b*c) + ((1 - Sqrt[2])*Log[3 - 2*Sqrt[2] - E^(2*c*(a + b*x))])/(2*b*c) + ((1 + Sqrt[2])*Log[3 + 2*Sqrt[2] - E^(2*c*(a + b*x))])/(2*b*c)","A",8,7,20,0.3500,1,"{2194, 6276, 2282, 12, 1247, 632, 31}"