1,1,97,0,0.07041,"\int (b \coth (c+d x))^{7/2} \, dx","Int[(b*Coth[c + d*x])^(7/2),x]","-\frac{2 b^3 \sqrt{b \coth (c+d x)}}{d}+\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}+\frac{b^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{2 b (b \coth (c+d x))^{5/2}}{5 d}","-\frac{2 b^3 \sqrt{b \coth (c+d x)}}{d}+\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}+\frac{b^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{2 b (b \coth (c+d x))^{5/2}}{5 d}",1,"(b^(7/2)*ArcTan[Sqrt[b*Coth[c + d*x]]/Sqrt[b]])/d + (b^(7/2)*ArcTanh[Sqrt[b*Coth[c + d*x]]/Sqrt[b]])/d - (2*b^3*Sqrt[b*Coth[c + d*x]])/d - (2*b*(b*Coth[c + d*x])^(5/2))/(5*d)","A",7,6,12,0.5000,1,"{3473, 3476, 329, 212, 206, 203}"
2,1,78,0,0.0490394,"\int (b \coth (c+d x))^{5/2} \, dx","Int[(b*Coth[c + d*x])^(5/2),x]","-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}+\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{2 b (b \coth (c+d x))^{3/2}}{3 d}","-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}+\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{2 b (b \coth (c+d x))^{3/2}}{3 d}",1,"-((b^(5/2)*ArcTan[Sqrt[b*Coth[c + d*x]]/Sqrt[b]])/d) + (b^(5/2)*ArcTanh[Sqrt[b*Coth[c + d*x]]/Sqrt[b]])/d - (2*b*(b*Coth[c + d*x])^(3/2))/(3*d)","A",6,6,12,0.5000,1,"{3473, 3476, 329, 298, 203, 206}"
3,1,75,0,0.0500011,"\int (b \coth (c+d x))^{3/2} \, dx","Int[(b*Coth[c + d*x])^(3/2),x]","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}+\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{2 b \sqrt{b \coth (c+d x)}}{d}","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}+\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{2 b \sqrt{b \coth (c+d x)}}{d}",1,"(b^(3/2)*ArcTan[Sqrt[b*Coth[c + d*x]]/Sqrt[b]])/d + (b^(3/2)*ArcTanh[Sqrt[b*Coth[c + d*x]]/Sqrt[b]])/d - (2*b*Sqrt[b*Coth[c + d*x]])/d","A",6,6,12,0.5000,1,"{3473, 3476, 329, 212, 206, 203}"
4,1,58,0,0.0356433,"\int \sqrt{b \coth (c+d x)} \, dx","Int[Sqrt[b*Coth[c + d*x]],x]","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{d}",1,"-((Sqrt[b]*ArcTan[Sqrt[b*Coth[c + d*x]]/Sqrt[b]])/d) + (Sqrt[b]*ArcTanh[Sqrt[b*Coth[c + d*x]]/Sqrt[b]])/d","A",5,5,12,0.4167,1,"{3476, 329, 298, 203, 206}"
5,1,57,0,0.0308044,"\int \frac{1}{\sqrt{b \coth (c+d x)}} \, dx","Int[1/Sqrt[b*Coth[c + d*x]],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}","\frac{\tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{\sqrt{b} d}",1,"ArcTan[Sqrt[b*Coth[c + d*x]]/Sqrt[b]]/(Sqrt[b]*d) + ArcTanh[Sqrt[b*Coth[c + d*x]]/Sqrt[b]]/(Sqrt[b]*d)","A",5,5,12,0.4167,1,"{3476, 329, 212, 206, 203}"
6,1,78,0,0.0512037,"\int \frac{1}{(b \coth (c+d x))^{3/2}} \, dx","Int[(b*Coth[c + d*x])^(-3/2),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2}{b d \sqrt{b \coth (c+d x)}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2}{b d \sqrt{b \coth (c+d x)}}",1,"-(ArcTan[Sqrt[b*Coth[c + d*x]]/Sqrt[b]]/(b^(3/2)*d)) + ArcTanh[Sqrt[b*Coth[c + d*x]]/Sqrt[b]]/(b^(3/2)*d) - 2/(b*d*Sqrt[b*Coth[c + d*x]])","A",6,6,12,0.5000,1,"{3474, 3476, 329, 298, 203, 206}"
7,1,79,0,0.0495235,"\int \frac{1}{(b \coth (c+d x))^{5/2}} \, dx","Int[(b*Coth[c + d*x])^(-5/2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{5/2} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{5/2} d}-\frac{2}{3 b d (b \coth (c+d x))^{3/2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{5/2} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{5/2} d}-\frac{2}{3 b d (b \coth (c+d x))^{3/2}}",1,"ArcTan[Sqrt[b*Coth[c + d*x]]/Sqrt[b]]/(b^(5/2)*d) + ArcTanh[Sqrt[b*Coth[c + d*x]]/Sqrt[b]]/(b^(5/2)*d) - 2/(3*b*d*(b*Coth[c + d*x])^(3/2))","A",6,6,12,0.5000,1,"{3474, 3476, 329, 212, 206, 203}"
8,1,100,0,0.0705722,"\int \frac{1}{(b \coth (c+d x))^{7/2}} \, dx","Int[(b*Coth[c + d*x])^(-7/2),x]","-\frac{2}{b^3 d \sqrt{b \coth (c+d x)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{7/2} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{7/2} d}-\frac{2}{5 b d (b \coth (c+d x))^{5/2}}","-\frac{2}{b^3 d \sqrt{b \coth (c+d x)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{7/2} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b \coth (c+d x)}}{\sqrt{b}}\right)}{b^{7/2} d}-\frac{2}{5 b d (b \coth (c+d x))^{5/2}}",1,"-(ArcTan[Sqrt[b*Coth[c + d*x]]/Sqrt[b]]/(b^(7/2)*d)) + ArcTanh[Sqrt[b*Coth[c + d*x]]/Sqrt[b]]/(b^(7/2)*d) - 2/(5*b*d*(b*Coth[c + d*x])^(5/2)) - 2/(b^3*d*Sqrt[b*Coth[c + d*x]])","A",7,6,12,0.5000,1,"{3474, 3476, 329, 298, 203, 206}"
9,1,236,0,0.2819014,"\int (b \coth (c+d x))^{4/3} \, dx","Int[(b*Coth[c + d*x])^(4/3),x]","-\frac{b^{4/3} \log \left(b^{2/3}-\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 d}+\frac{b^{4/3} \log \left(b^{2/3}+\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 d}-\frac{\sqrt{3} b^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{2 d}+\frac{\sqrt{3} b^{4/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}+1}{\sqrt{3}}\right)}{2 d}+\frac{b^{4/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}\right)}{d}-\frac{3 b \sqrt[3]{b \coth (c+d x)}}{d}","-\frac{b^{4/3} \log \left(b^{2/3}-\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 d}+\frac{b^{4/3} \log \left(b^{2/3}+\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 d}-\frac{\sqrt{3} b^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{2 d}+\frac{\sqrt{3} b^{4/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}+1}{\sqrt{3}}\right)}{2 d}+\frac{b^{4/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}\right)}{d}-\frac{3 b \sqrt[3]{b \coth (c+d x)}}{d}",1,"-(Sqrt[3]*b^(4/3)*ArcTan[(1 - (2*(b*Coth[c + d*x])^(1/3))/b^(1/3))/Sqrt[3]])/(2*d) + (Sqrt[3]*b^(4/3)*ArcTan[(1 + (2*(b*Coth[c + d*x])^(1/3))/b^(1/3))/Sqrt[3]])/(2*d) + (b^(4/3)*ArcTanh[(b*Coth[c + d*x])^(1/3)/b^(1/3)])/d - (3*b*(b*Coth[c + d*x])^(1/3))/d - (b^(4/3)*Log[b^(2/3) - b^(1/3)*(b*Coth[c + d*x])^(1/3) + (b*Coth[c + d*x])^(2/3)])/(4*d) + (b^(4/3)*Log[b^(2/3) + b^(1/3)*(b*Coth[c + d*x])^(1/3) + (b*Coth[c + d*x])^(2/3)])/(4*d)","A",13,9,12,0.7500,1,"{3473, 3476, 329, 210, 634, 618, 204, 628, 206}"
10,1,218,0,0.2938666,"\int (b \coth (c+d x))^{2/3} \, dx","Int[(b*Coth[c + d*x])^(2/3),x]","-\frac{b^{2/3} \log \left(b^{2/3}-\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 d}+\frac{b^{2/3} \log \left(b^{2/3}+\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 d}+\frac{\sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{2 d}-\frac{\sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}+1}{\sqrt{3}}\right)}{2 d}+\frac{b^{2/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}\right)}{d}","-\frac{b^{2/3} \log \left(b^{2/3}-\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 d}+\frac{b^{2/3} \log \left(b^{2/3}+\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 d}+\frac{\sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{2 d}-\frac{\sqrt{3} b^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}+1}{\sqrt{3}}\right)}{2 d}+\frac{b^{2/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}\right)}{d}",1,"(Sqrt[3]*b^(2/3)*ArcTan[(1 - (2*(b*Coth[c + d*x])^(1/3))/b^(1/3))/Sqrt[3]])/(2*d) - (Sqrt[3]*b^(2/3)*ArcTan[(1 + (2*(b*Coth[c + d*x])^(1/3))/b^(1/3))/Sqrt[3]])/(2*d) + (b^(2/3)*ArcTanh[(b*Coth[c + d*x])^(1/3)/b^(1/3)])/d - (b^(2/3)*Log[b^(2/3) - b^(1/3)*(b*Coth[c + d*x])^(1/3) + (b*Coth[c + d*x])^(2/3)])/(4*d) + (b^(2/3)*Log[b^(2/3) + b^(1/3)*(b*Coth[c + d*x])^(1/3) + (b*Coth[c + d*x])^(2/3)])/(4*d)","A",12,8,12,0.6667,1,"{3476, 329, 296, 634, 618, 204, 628, 206}"
11,1,132,0,0.1091141,"\int \sqrt[3]{b \coth (c+d x)} \, dx","Int[(b*Coth[c + d*x])^(1/3),x]","-\frac{\sqrt[3]{b} \log \left(b^{2/3}-(b \coth (c+d x))^{2/3}\right)}{2 d}+\frac{\sqrt[3]{b} \log \left(b^{2/3} (b \coth (c+d x))^{2/3}+b^{4/3}+(b \coth (c+d x))^{4/3}\right)}{4 d}-\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{b^{2/3}+2 (b \coth (c+d x))^{2/3}}{\sqrt{3} b^{2/3}}\right)}{2 d}","-\frac{\sqrt[3]{b} \log \left(b^{2/3}-(b \coth (c+d x))^{2/3}\right)}{2 d}+\frac{\sqrt[3]{b} \log \left(b^{2/3} (b \coth (c+d x))^{2/3}+b^{4/3}+(b \coth (c+d x))^{4/3}\right)}{4 d}-\frac{\sqrt{3} \sqrt[3]{b} \tan ^{-1}\left(\frac{b^{2/3}+2 (b \coth (c+d x))^{2/3}}{\sqrt{3} b^{2/3}}\right)}{2 d}",1,"-(Sqrt[3]*b^(1/3)*ArcTan[(b^(2/3) + 2*(b*Coth[c + d*x])^(2/3))/(Sqrt[3]*b^(2/3))])/(2*d) - (b^(1/3)*Log[b^(2/3) - (b*Coth[c + d*x])^(2/3)])/(2*d) + (b^(1/3)*Log[b^(4/3) + b^(2/3)*(b*Coth[c + d*x])^(2/3) + (b*Coth[c + d*x])^(4/3)])/(4*d)","A",9,9,12,0.7500,1,"{3476, 329, 275, 292, 31, 634, 617, 204, 628}"
12,1,132,0,0.1039103,"\int \frac{1}{\sqrt[3]{b \coth (c+d x)}} \, dx","Int[(b*Coth[c + d*x])^(-1/3),x]","-\frac{\log \left(b^{2/3}-(b \coth (c+d x))^{2/3}\right)}{2 \sqrt[3]{b} d}+\frac{\log \left(b^{2/3} (b \coth (c+d x))^{2/3}+b^{4/3}+(b \coth (c+d x))^{4/3}\right)}{4 \sqrt[3]{b} d}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{b^{2/3}+2 (b \coth (c+d x))^{2/3}}{\sqrt{3} b^{2/3}}\right)}{2 \sqrt[3]{b} d}","-\frac{\log \left(b^{2/3}-(b \coth (c+d x))^{2/3}\right)}{2 \sqrt[3]{b} d}+\frac{\log \left(b^{2/3} (b \coth (c+d x))^{2/3}+b^{4/3}+(b \coth (c+d x))^{4/3}\right)}{4 \sqrt[3]{b} d}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{b^{2/3}+2 (b \coth (c+d x))^{2/3}}{\sqrt{3} b^{2/3}}\right)}{2 \sqrt[3]{b} d}",1,"(Sqrt[3]*ArcTan[(b^(2/3) + 2*(b*Coth[c + d*x])^(2/3))/(Sqrt[3]*b^(2/3))])/(2*b^(1/3)*d) - Log[b^(2/3) - (b*Coth[c + d*x])^(2/3)]/(2*b^(1/3)*d) + Log[b^(4/3) + b^(2/3)*(b*Coth[c + d*x])^(2/3) + (b*Coth[c + d*x])^(4/3)]/(4*b^(1/3)*d)","A",9,9,12,0.7500,1,"{3476, 329, 275, 200, 31, 634, 617, 204, 628}"
13,1,218,0,0.2353099,"\int \frac{1}{(b \coth (c+d x))^{2/3}} \, dx","Int[(b*Coth[c + d*x])^(-2/3),x]","-\frac{\log \left(b^{2/3}-\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 b^{2/3} d}+\frac{\log \left(b^{2/3}+\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 b^{2/3} d}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{2 b^{2/3} d}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}+1}{\sqrt{3}}\right)}{2 b^{2/3} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}\right)}{b^{2/3} d}","-\frac{\log \left(b^{2/3}-\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 b^{2/3} d}+\frac{\log \left(b^{2/3}+\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 b^{2/3} d}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{2 b^{2/3} d}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}+1}{\sqrt{3}}\right)}{2 b^{2/3} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}\right)}{b^{2/3} d}",1,"-(Sqrt[3]*ArcTan[(1 - (2*(b*Coth[c + d*x])^(1/3))/b^(1/3))/Sqrt[3]])/(2*b^(2/3)*d) + (Sqrt[3]*ArcTan[(1 + (2*(b*Coth[c + d*x])^(1/3))/b^(1/3))/Sqrt[3]])/(2*b^(2/3)*d) + ArcTanh[(b*Coth[c + d*x])^(1/3)/b^(1/3)]/(b^(2/3)*d) - Log[b^(2/3) - b^(1/3)*(b*Coth[c + d*x])^(1/3) + (b*Coth[c + d*x])^(2/3)]/(4*b^(2/3)*d) + Log[b^(2/3) + b^(1/3)*(b*Coth[c + d*x])^(1/3) + (b*Coth[c + d*x])^(2/3)]/(4*b^(2/3)*d)","A",12,8,12,0.6667,1,"{3476, 329, 210, 634, 618, 204, 628, 206}"
14,1,238,0,0.3157202,"\int \frac{1}{(b \coth (c+d x))^{4/3}} \, dx","Int[(b*Coth[c + d*x])^(-4/3),x]","-\frac{\log \left(b^{2/3}-\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 b^{4/3} d}+\frac{\log \left(b^{2/3}+\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 b^{4/3} d}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{2 b^{4/3} d}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}+1}{\sqrt{3}}\right)}{2 b^{4/3} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}\right)}{b^{4/3} d}-\frac{3}{b d \sqrt[3]{b \coth (c+d x)}}","-\frac{\log \left(b^{2/3}-\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 b^{4/3} d}+\frac{\log \left(b^{2/3}+\sqrt[3]{b} \sqrt[3]{b \coth (c+d x)}+(b \coth (c+d x))^{2/3}\right)}{4 b^{4/3} d}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}}{\sqrt{3}}\right)}{2 b^{4/3} d}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}+1}{\sqrt{3}}\right)}{2 b^{4/3} d}+\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{b \coth (c+d x)}}{\sqrt[3]{b}}\right)}{b^{4/3} d}-\frac{3}{b d \sqrt[3]{b \coth (c+d x)}}",1,"(Sqrt[3]*ArcTan[(1 - (2*(b*Coth[c + d*x])^(1/3))/b^(1/3))/Sqrt[3]])/(2*b^(4/3)*d) - (Sqrt[3]*ArcTan[(1 + (2*(b*Coth[c + d*x])^(1/3))/b^(1/3))/Sqrt[3]])/(2*b^(4/3)*d) + ArcTanh[(b*Coth[c + d*x])^(1/3)/b^(1/3)]/(b^(4/3)*d) - 3/(b*d*(b*Coth[c + d*x])^(1/3)) - Log[b^(2/3) - b^(1/3)*(b*Coth[c + d*x])^(1/3) + (b*Coth[c + d*x])^(2/3)]/(4*b^(4/3)*d) + Log[b^(2/3) + b^(1/3)*(b*Coth[c + d*x])^(1/3) + (b*Coth[c + d*x])^(2/3)]/(4*b^(4/3)*d)","A",13,9,12,0.7500,1,"{3474, 3476, 329, 296, 634, 618, 204, 628, 206}"
15,1,43,0,0.0223006,"\int \coth ^n(a+b x) \, dx","Int[Coth[a + b*x]^n,x]","\frac{\coth ^{n+1}(a+b x) \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\coth ^2(a+b x)\right)}{b (n+1)}","\frac{\coth ^{n+1}(a+b x) \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\coth ^2(a+b x)\right)}{b (n+1)}",1,"(Coth[a + b*x]^(1 + n)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, Coth[a + b*x]^2])/(b*(1 + n))","A",2,2,8,0.2500,1,"{3476, 364}"
16,1,48,0,0.0270079,"\int (b \coth (c+d x))^n \, dx","Int[(b*Coth[c + d*x])^n,x]","\frac{(b \coth (c+d x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\coth ^2(c+d x)\right)}{b d (n+1)}","\frac{(b \coth (c+d x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\coth ^2(c+d x)\right)}{b d (n+1)}",1,"((b*Coth[c + d*x])^(1 + n)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, Coth[c + d*x]^2])/(b*d*(1 + n))","A",2,2,10,0.2000,1,"{3476, 364}"
17,1,57,0,0.040331,"\int \left(b \coth ^2(c+d x)\right)^n \, dx","Int[(b*Coth[c + d*x]^2)^n,x]","\frac{\coth (c+d x) \left(b \coth ^2(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (2 n+1);\frac{1}{2} (2 n+3);\coth ^2(c+d x)\right)}{d (2 n+1)}","\frac{\coth (c+d x) \left(b \coth ^2(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (2 n+1);\frac{1}{2} (2 n+3);\coth ^2(c+d x)\right)}{d (2 n+1)}",1,"(Coth[c + d*x]*(b*Coth[c + d*x]^2)^n*Hypergeometric2F1[1, (1 + 2*n)/2, (3 + 2*n)/2, Coth[c + d*x]^2])/(d*(1 + 2*n))","A",3,3,12,0.2500,1,"{3658, 3476, 364}"
18,1,61,0,0.0368725,"\int \left(b \coth ^2(c+d x)\right)^{3/2} \, dx","Int[(b*Coth[c + d*x]^2)^(3/2),x]","\frac{b \tanh (c+d x) \sqrt{b \coth ^2(c+d x)} \log (\sinh (c+d x))}{d}-\frac{b \coth (c+d x) \sqrt{b \coth ^2(c+d x)}}{2 d}","\frac{b \tanh (c+d x) \sqrt{b \coth ^2(c+d x)} \log (\sinh (c+d x))}{d}-\frac{b \coth (c+d x) \sqrt{b \coth ^2(c+d x)}}{2 d}",1,"-(b*Coth[c + d*x]*Sqrt[b*Coth[c + d*x]^2])/(2*d) + (b*Sqrt[b*Coth[c + d*x]^2]*Log[Sinh[c + d*x]]*Tanh[c + d*x])/d","A",3,3,14,0.2143,1,"{3658, 3473, 3475}"
19,1,31,0,0.0196248,"\int \sqrt{b \coth ^2(c+d x)} \, dx","Int[Sqrt[b*Coth[c + d*x]^2],x]","\frac{\tanh (c+d x) \sqrt{b \coth ^2(c+d x)} \log (\sinh (c+d x))}{d}","\frac{\tanh (c+d x) \sqrt{b \coth ^2(c+d x)} \log (\sinh (c+d x))}{d}",1,"(Sqrt[b*Coth[c + d*x]^2]*Log[Sinh[c + d*x]]*Tanh[c + d*x])/d","A",2,2,14,0.1429,1,"{3658, 3475}"
20,1,31,0,0.0204262,"\int \frac{1}{\sqrt{b \coth ^2(c+d x)}} \, dx","Int[1/Sqrt[b*Coth[c + d*x]^2],x]","\frac{\coth (c+d x) \log (\cosh (c+d x))}{d \sqrt{b \coth ^2(c+d x)}}","\frac{\coth (c+d x) \log (\cosh (c+d x))}{d \sqrt{b \coth ^2(c+d x)}}",1,"(Coth[c + d*x]*Log[Cosh[c + d*x]])/(d*Sqrt[b*Coth[c + d*x]^2])","A",2,2,14,0.1429,1,"{3658, 3475}"
21,1,65,0,0.0356045,"\int \frac{1}{\left(b \coth ^2(c+d x)\right)^{3/2}} \, dx","Int[(b*Coth[c + d*x]^2)^(-3/2),x]","\frac{\coth (c+d x) \log (\cosh (c+d x))}{b d \sqrt{b \coth ^2(c+d x)}}-\frac{\tanh (c+d x)}{2 b d \sqrt{b \coth ^2(c+d x)}}","\frac{\coth (c+d x) \log (\cosh (c+d x))}{b d \sqrt{b \coth ^2(c+d x)}}-\frac{\tanh (c+d x)}{2 b d \sqrt{b \coth ^2(c+d x)}}",1,"(Coth[c + d*x]*Log[Cosh[c + d*x]])/(b*d*Sqrt[b*Coth[c + d*x]^2]) - Tanh[c + d*x]/(2*b*d*Sqrt[b*Coth[c + d*x]^2])","A",3,3,14,0.2143,1,"{3658, 3473, 3475}"
22,1,297,0,0.2844788,"\int \left(b \coth ^2(c+d x)\right)^{4/3} \, dx","Int[(b*Coth[c + d*x]^2)^(4/3),x]","-\frac{3 b \coth (c+d x) \sqrt[3]{b \coth ^2(c+d x)}}{5 d}-\frac{b \sqrt[3]{b \coth ^2(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{b \sqrt[3]{b \coth ^2(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{\sqrt{3} b \sqrt[3]{b \coth ^2(c+d x)} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{2}{3}}(c+d x)}-\frac{\sqrt{3} b \sqrt[3]{b \coth ^2(c+d x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{b \sqrt[3]{b \coth ^2(c+d x)} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{2}{3}}(c+d x)}","-\frac{3 b \coth (c+d x) \sqrt[3]{b \coth ^2(c+d x)}}{5 d}-\frac{b \sqrt[3]{b \coth ^2(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{b \sqrt[3]{b \coth ^2(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{\sqrt{3} b \sqrt[3]{b \coth ^2(c+d x)} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{2}{3}}(c+d x)}-\frac{\sqrt{3} b \sqrt[3]{b \coth ^2(c+d x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{b \sqrt[3]{b \coth ^2(c+d x)} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{2}{3}}(c+d x)}",1,"(Sqrt[3]*b*ArcTan[(1 - 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*(b*Coth[c + d*x]^2)^(1/3))/(2*d*Coth[c + d*x]^(2/3)) - (Sqrt[3]*b*ArcTan[(1 + 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*(b*Coth[c + d*x]^2)^(1/3))/(2*d*Coth[c + d*x]^(2/3)) + (b*ArcTanh[Coth[c + d*x]^(1/3)]*(b*Coth[c + d*x]^2)^(1/3))/(d*Coth[c + d*x]^(2/3)) - (3*b*Coth[c + d*x]*(b*Coth[c + d*x]^2)^(1/3))/(5*d) - (b*(b*Coth[c + d*x]^2)^(1/3)*Log[1 - Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*Coth[c + d*x]^(2/3)) + (b*(b*Coth[c + d*x]^2)^(1/3)*Log[1 + Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*Coth[c + d*x]^(2/3))","A",14,10,14,0.7143,1,"{3658, 3473, 3476, 329, 296, 634, 618, 204, 628, 206}"
23,1,289,0,0.180361,"\int \left(b \coth ^2(c+d x)\right)^{2/3} \, dx","Int[(b*Coth[c + d*x]^2)^(2/3),x]","-\frac{\left(b \coth ^2(c+d x)\right)^{2/3} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\left(b \coth ^2(c+d x)\right)^{2/3} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}-\frac{\sqrt{3} \left(b \coth ^2(c+d x)\right)^{2/3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\sqrt{3} \left(b \coth ^2(c+d x)\right)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\left(b \coth ^2(c+d x)\right)^{2/3} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{4}{3}}(c+d x)}-\frac{3 \tanh (c+d x) \left(b \coth ^2(c+d x)\right)^{2/3}}{d}","-\frac{\left(b \coth ^2(c+d x)\right)^{2/3} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\left(b \coth ^2(c+d x)\right)^{2/3} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}-\frac{\sqrt{3} \left(b \coth ^2(c+d x)\right)^{2/3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\sqrt{3} \left(b \coth ^2(c+d x)\right)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\left(b \coth ^2(c+d x)\right)^{2/3} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{4}{3}}(c+d x)}-\frac{3 \tanh (c+d x) \left(b \coth ^2(c+d x)\right)^{2/3}}{d}",1,"-(Sqrt[3]*ArcTan[(1 - 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*(b*Coth[c + d*x]^2)^(2/3))/(2*d*Coth[c + d*x]^(4/3)) + (Sqrt[3]*ArcTan[(1 + 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*(b*Coth[c + d*x]^2)^(2/3))/(2*d*Coth[c + d*x]^(4/3)) + (ArcTanh[Coth[c + d*x]^(1/3)]*(b*Coth[c + d*x]^2)^(2/3))/(d*Coth[c + d*x]^(4/3)) - ((b*Coth[c + d*x]^2)^(2/3)*Log[1 - Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*Coth[c + d*x]^(4/3)) + ((b*Coth[c + d*x]^2)^(2/3)*Log[1 + Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*Coth[c + d*x]^(4/3)) - (3*(b*Coth[c + d*x]^2)^(2/3)*Tanh[c + d*x])/d","A",14,10,14,0.7143,1,"{3658, 3473, 3476, 329, 210, 634, 618, 204, 628, 206}"
24,1,264,0,0.2116625,"\int \sqrt[3]{b \coth ^2(c+d x)} \, dx","Int[(b*Coth[c + d*x]^2)^(1/3),x]","-\frac{\sqrt[3]{b \coth ^2(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{\sqrt[3]{b \coth ^2(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{\sqrt{3} \sqrt[3]{b \coth ^2(c+d x)} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{2}{3}}(c+d x)}-\frac{\sqrt{3} \sqrt[3]{b \coth ^2(c+d x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{\sqrt[3]{b \coth ^2(c+d x)} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{2}{3}}(c+d x)}","-\frac{\sqrt[3]{b \coth ^2(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{\sqrt[3]{b \coth ^2(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{\sqrt{3} \sqrt[3]{b \coth ^2(c+d x)} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{2}{3}}(c+d x)}-\frac{\sqrt{3} \sqrt[3]{b \coth ^2(c+d x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{2}{3}}(c+d x)}+\frac{\sqrt[3]{b \coth ^2(c+d x)} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{2}{3}}(c+d x)}",1,"(Sqrt[3]*ArcTan[(1 - 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*(b*Coth[c + d*x]^2)^(1/3))/(2*d*Coth[c + d*x]^(2/3)) - (Sqrt[3]*ArcTan[(1 + 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*(b*Coth[c + d*x]^2)^(1/3))/(2*d*Coth[c + d*x]^(2/3)) + (ArcTanh[Coth[c + d*x]^(1/3)]*(b*Coth[c + d*x]^2)^(1/3))/(d*Coth[c + d*x]^(2/3)) - ((b*Coth[c + d*x]^2)^(1/3)*Log[1 - Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*Coth[c + d*x]^(2/3)) + ((b*Coth[c + d*x]^2)^(1/3)*Log[1 + Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*Coth[c + d*x]^(2/3))","A",13,9,14,0.6429,1,"{3658, 3476, 329, 296, 634, 618, 204, 628, 206}"
25,1,264,0,0.1691391,"\int \frac{1}{\sqrt[3]{b \coth ^2(c+d x)}} \, dx","Int[(b*Coth[c + d*x]^2)^(-1/3),x]","-\frac{\coth ^{\frac{2}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\coth ^{\frac{2}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \sqrt[3]{b \coth ^2(c+d x)}}-\frac{\sqrt{3} \coth ^{\frac{2}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\sqrt{3} \coth ^{\frac{2}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\coth ^{\frac{2}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \sqrt[3]{b \coth ^2(c+d x)}}","-\frac{\coth ^{\frac{2}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\coth ^{\frac{2}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \sqrt[3]{b \coth ^2(c+d x)}}-\frac{\sqrt{3} \coth ^{\frac{2}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\sqrt{3} \coth ^{\frac{2}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\coth ^{\frac{2}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \sqrt[3]{b \coth ^2(c+d x)}}",1,"-(Sqrt[3]*ArcTan[(1 - 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*Coth[c + d*x]^(2/3))/(2*d*(b*Coth[c + d*x]^2)^(1/3)) + (Sqrt[3]*ArcTan[(1 + 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*Coth[c + d*x]^(2/3))/(2*d*(b*Coth[c + d*x]^2)^(1/3)) + (ArcTanh[Coth[c + d*x]^(1/3)]*Coth[c + d*x]^(2/3))/(d*(b*Coth[c + d*x]^2)^(1/3)) - (Coth[c + d*x]^(2/3)*Log[1 - Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*(b*Coth[c + d*x]^2)^(1/3)) + (Coth[c + d*x]^(2/3)*Log[1 + Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*(b*Coth[c + d*x]^2)^(1/3))","A",13,9,14,0.6429,1,"{3658, 3476, 329, 210, 634, 618, 204, 628, 206}"
26,1,289,0,0.2219711,"\int \frac{1}{\left(b \coth ^2(c+d x)\right)^{2/3}} \, dx","Int[(b*Coth[c + d*x]^2)^(-2/3),x]","-\frac{3 \coth (c+d x)}{d \left(b \coth ^2(c+d x)\right)^{2/3}}-\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \left(b \coth ^2(c+d x)\right)^{2/3}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \left(b \coth ^2(c+d x)\right)^{2/3}}+\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \left(b \coth ^2(c+d x)\right)^{2/3}}-\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \left(b \coth ^2(c+d x)\right)^{2/3}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \left(b \coth ^2(c+d x)\right)^{2/3}}","-\frac{3 \coth (c+d x)}{d \left(b \coth ^2(c+d x)\right)^{2/3}}-\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \left(b \coth ^2(c+d x)\right)^{2/3}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \left(b \coth ^2(c+d x)\right)^{2/3}}+\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \left(b \coth ^2(c+d x)\right)^{2/3}}-\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \left(b \coth ^2(c+d x)\right)^{2/3}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \left(b \coth ^2(c+d x)\right)^{2/3}}",1,"(-3*Coth[c + d*x])/(d*(b*Coth[c + d*x]^2)^(2/3)) + (Sqrt[3]*ArcTan[(1 - 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*Coth[c + d*x]^(4/3))/(2*d*(b*Coth[c + d*x]^2)^(2/3)) - (Sqrt[3]*ArcTan[(1 + 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*Coth[c + d*x]^(4/3))/(2*d*(b*Coth[c + d*x]^2)^(2/3)) + (ArcTanh[Coth[c + d*x]^(1/3)]*Coth[c + d*x]^(4/3))/(d*(b*Coth[c + d*x]^2)^(2/3)) - (Coth[c + d*x]^(4/3)*Log[1 - Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*(b*Coth[c + d*x]^2)^(2/3)) + (Coth[c + d*x]^(4/3)*Log[1 + Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*(b*Coth[c + d*x]^2)^(2/3))","A",14,10,14,0.7143,1,"{3658, 3474, 3476, 329, 296, 634, 618, 204, 628, 206}"
27,1,309,0,0.1822343,"\int \frac{1}{\left(b \coth ^2(c+d x)\right)^{4/3}} \, dx","Int[(b*Coth[c + d*x]^2)^(-4/3),x]","-\frac{\coth ^{\frac{2}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 b d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\coth ^{\frac{2}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 b d \sqrt[3]{b \coth ^2(c+d x)}}-\frac{\sqrt{3} \coth ^{\frac{2}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 b d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\sqrt{3} \coth ^{\frac{2}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 b d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\coth ^{\frac{2}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{b d \sqrt[3]{b \coth ^2(c+d x)}}-\frac{3 \tanh (c+d x)}{5 b d \sqrt[3]{b \coth ^2(c+d x)}}","-\frac{\coth ^{\frac{2}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 b d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\coth ^{\frac{2}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 b d \sqrt[3]{b \coth ^2(c+d x)}}-\frac{\sqrt{3} \coth ^{\frac{2}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 b d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\sqrt{3} \coth ^{\frac{2}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 b d \sqrt[3]{b \coth ^2(c+d x)}}+\frac{\coth ^{\frac{2}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{b d \sqrt[3]{b \coth ^2(c+d x)}}-\frac{3 \tanh (c+d x)}{5 b d \sqrt[3]{b \coth ^2(c+d x)}}",1,"-(Sqrt[3]*ArcTan[(1 - 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*Coth[c + d*x]^(2/3))/(2*b*d*(b*Coth[c + d*x]^2)^(1/3)) + (Sqrt[3]*ArcTan[(1 + 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*Coth[c + d*x]^(2/3))/(2*b*d*(b*Coth[c + d*x]^2)^(1/3)) + (ArcTanh[Coth[c + d*x]^(1/3)]*Coth[c + d*x]^(2/3))/(b*d*(b*Coth[c + d*x]^2)^(1/3)) - (Coth[c + d*x]^(2/3)*Log[1 - Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*b*d*(b*Coth[c + d*x]^2)^(1/3)) + (Coth[c + d*x]^(2/3)*Log[1 + Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*b*d*(b*Coth[c + d*x]^2)^(1/3)) - (3*Tanh[c + d*x])/(5*b*d*(b*Coth[c + d*x]^2)^(1/3))","A",14,10,14,0.7143,1,"{3658, 3474, 3476, 329, 210, 634, 618, 204, 628, 206}"
28,1,55,0,0.0394953,"\int \left(b \coth ^3(c+d x)\right)^n \, dx","Int[(b*Coth[c + d*x]^3)^n,x]","\frac{\coth (c+d x) \left(b \coth ^3(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (3 n+1);\frac{3 (n+1)}{2};\coth ^2(c+d x)\right)}{d (3 n+1)}","\frac{\coth (c+d x) \left(b \coth ^3(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (3 n+1);\frac{3 (n+1)}{2};\coth ^2(c+d x)\right)}{d (3 n+1)}",1,"(Coth[c + d*x]*(b*Coth[c + d*x]^3)^n*Hypergeometric2F1[1, (1 + 3*n)/2, (3*(1 + n))/2, Coth[c + d*x]^2])/(d*(1 + 3*n))","A",3,3,12,0.2500,1,"{3658, 3476, 364}"
29,1,134,0,0.0602026,"\int \left(b \coth ^3(c+d x)\right)^{3/2} \, dx","Int[(b*Coth[c + d*x]^3)^(3/2),x]","-\frac{2 b \coth ^2(c+d x) \sqrt{b \coth ^3(c+d x)}}{7 d}-\frac{2 b \sqrt{b \coth ^3(c+d x)}}{3 d}-\frac{b \sqrt{b \coth ^3(c+d x)} \tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \coth ^{\frac{3}{2}}(c+d x)}+\frac{b \sqrt{b \coth ^3(c+d x)} \tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \coth ^{\frac{3}{2}}(c+d x)}","-\frac{2 b \coth ^2(c+d x) \sqrt{b \coth ^3(c+d x)}}{7 d}-\frac{2 b \sqrt{b \coth ^3(c+d x)}}{3 d}-\frac{b \sqrt{b \coth ^3(c+d x)} \tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \coth ^{\frac{3}{2}}(c+d x)}+\frac{b \sqrt{b \coth ^3(c+d x)} \tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \coth ^{\frac{3}{2}}(c+d x)}",1,"(-2*b*Sqrt[b*Coth[c + d*x]^3])/(3*d) - (b*ArcTan[Sqrt[Coth[c + d*x]]]*Sqrt[b*Coth[c + d*x]^3])/(d*Coth[c + d*x]^(3/2)) + (b*ArcTanh[Sqrt[Coth[c + d*x]]]*Sqrt[b*Coth[c + d*x]^3])/(d*Coth[c + d*x]^(3/2)) - (2*b*Coth[c + d*x]^2*Sqrt[b*Coth[c + d*x]^3])/(7*d)","A",8,7,14,0.5000,1,"{3658, 3473, 3476, 329, 298, 203, 206}"
30,1,104,0,0.0474185,"\int \sqrt{b \coth ^3(c+d x)} \, dx","Int[Sqrt[b*Coth[c + d*x]^3],x]","\frac{\sqrt{b \coth ^3(c+d x)} \tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \coth ^{\frac{3}{2}}(c+d x)}+\frac{\sqrt{b \coth ^3(c+d x)} \tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \coth ^{\frac{3}{2}}(c+d x)}-\frac{2 \tanh (c+d x) \sqrt{b \coth ^3(c+d x)}}{d}","\frac{\sqrt{b \coth ^3(c+d x)} \tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \coth ^{\frac{3}{2}}(c+d x)}+\frac{\sqrt{b \coth ^3(c+d x)} \tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \coth ^{\frac{3}{2}}(c+d x)}-\frac{2 \tanh (c+d x) \sqrt{b \coth ^3(c+d x)}}{d}",1,"(ArcTan[Sqrt[Coth[c + d*x]]]*Sqrt[b*Coth[c + d*x]^3])/(d*Coth[c + d*x]^(3/2)) + (ArcTanh[Sqrt[Coth[c + d*x]]]*Sqrt[b*Coth[c + d*x]^3])/(d*Coth[c + d*x]^(3/2)) - (2*Sqrt[b*Coth[c + d*x]^3]*Tanh[c + d*x])/d","A",7,7,14,0.5000,1,"{3658, 3473, 3476, 329, 212, 206, 203}"
31,1,105,0,0.0480527,"\int \frac{1}{\sqrt{b \coth ^3(c+d x)}} \, dx","Int[1/Sqrt[b*Coth[c + d*x]^3],x]","-\frac{2 \coth (c+d x)}{d \sqrt{b \coth ^3(c+d x)}}-\frac{\coth ^{\frac{3}{2}}(c+d x) \tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \sqrt{b \coth ^3(c+d x)}}+\frac{\coth ^{\frac{3}{2}}(c+d x) \tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \sqrt{b \coth ^3(c+d x)}}","-\frac{2 \coth (c+d x)}{d \sqrt{b \coth ^3(c+d x)}}-\frac{\coth ^{\frac{3}{2}}(c+d x) \tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \sqrt{b \coth ^3(c+d x)}}+\frac{\coth ^{\frac{3}{2}}(c+d x) \tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{d \sqrt{b \coth ^3(c+d x)}}",1,"(-2*Coth[c + d*x])/(d*Sqrt[b*Coth[c + d*x]^3]) - (ArcTan[Sqrt[Coth[c + d*x]]]*Coth[c + d*x]^(3/2))/(d*Sqrt[b*Coth[c + d*x]^3]) + (ArcTanh[Sqrt[Coth[c + d*x]]]*Coth[c + d*x]^(3/2))/(d*Sqrt[b*Coth[c + d*x]^3])","A",7,7,14,0.5000,1,"{3658, 3474, 3476, 329, 298, 203, 206}"
32,1,141,0,0.0608829,"\int \frac{1}{\left(b \coth ^3(c+d x)\right)^{3/2}} \, dx","Int[(b*Coth[c + d*x]^3)^(-3/2),x]","-\frac{2}{3 b d \sqrt{b \coth ^3(c+d x)}}+\frac{\coth ^{\frac{3}{2}}(c+d x) \tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{b d \sqrt{b \coth ^3(c+d x)}}-\frac{2 \tanh ^2(c+d x)}{7 b d \sqrt{b \coth ^3(c+d x)}}+\frac{\coth ^{\frac{3}{2}}(c+d x) \tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{b d \sqrt{b \coth ^3(c+d x)}}","-\frac{2}{3 b d \sqrt{b \coth ^3(c+d x)}}+\frac{\coth ^{\frac{3}{2}}(c+d x) \tan ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{b d \sqrt{b \coth ^3(c+d x)}}-\frac{2 \tanh ^2(c+d x)}{7 b d \sqrt{b \coth ^3(c+d x)}}+\frac{\coth ^{\frac{3}{2}}(c+d x) \tanh ^{-1}\left(\sqrt{\coth (c+d x)}\right)}{b d \sqrt{b \coth ^3(c+d x)}}",1,"-2/(3*b*d*Sqrt[b*Coth[c + d*x]^3]) + (ArcTan[Sqrt[Coth[c + d*x]]]*Coth[c + d*x]^(3/2))/(b*d*Sqrt[b*Coth[c + d*x]^3]) + (ArcTanh[Sqrt[Coth[c + d*x]]]*Coth[c + d*x]^(3/2))/(b*d*Sqrt[b*Coth[c + d*x]^3]) - (2*Tanh[c + d*x]^2)/(7*b*d*Sqrt[b*Coth[c + d*x]^3])","A",8,7,14,0.5000,1,"{3658, 3474, 3476, 329, 212, 206, 203}"
33,1,74,0,0.0335459,"\int \left(b \coth ^3(c+d x)\right)^{4/3} \, dx","Int[(b*Coth[c + d*x]^3)^(4/3),x]","-\frac{b \coth ^2(c+d x) \sqrt[3]{b \coth ^3(c+d x)}}{3 d}-\frac{b \sqrt[3]{b \coth ^3(c+d x)}}{d}+b x \tanh (c+d x) \sqrt[3]{b \coth ^3(c+d x)}","-\frac{b \coth ^2(c+d x) \sqrt[3]{b \coth ^3(c+d x)}}{3 d}-\frac{b \sqrt[3]{b \coth ^3(c+d x)}}{d}+b x \tanh (c+d x) \sqrt[3]{b \coth ^3(c+d x)}",1,"-((b*(b*Coth[c + d*x]^3)^(1/3))/d) - (b*Coth[c + d*x]^2*(b*Coth[c + d*x]^3)^(1/3))/(3*d) + b*x*(b*Coth[c + d*x]^3)^(1/3)*Tanh[c + d*x]","A",4,3,14,0.2143,1,"{3658, 3473, 8}"
34,1,50,0,0.0244887,"\int \left(b \coth ^3(c+d x)\right)^{2/3} \, dx","Int[(b*Coth[c + d*x]^3)^(2/3),x]","x \tanh ^2(c+d x) \left(b \coth ^3(c+d x)\right)^{2/3}-\frac{\tanh (c+d x) \left(b \coth ^3(c+d x)\right)^{2/3}}{d}","x \tanh ^2(c+d x) \left(b \coth ^3(c+d x)\right)^{2/3}-\frac{\tanh (c+d x) \left(b \coth ^3(c+d x)\right)^{2/3}}{d}",1,"-(((b*Coth[c + d*x]^3)^(2/3)*Tanh[c + d*x])/d) + x*(b*Coth[c + d*x]^3)^(2/3)*Tanh[c + d*x]^2","A",3,3,14,0.2143,1,"{3658, 3473, 8}"
35,1,31,0,0.0202028,"\int \sqrt[3]{b \coth ^3(c+d x)} \, dx","Int[(b*Coth[c + d*x]^3)^(1/3),x]","\frac{\tanh (c+d x) \sqrt[3]{b \coth ^3(c+d x)} \log (\sinh (c+d x))}{d}","\frac{\tanh (c+d x) \sqrt[3]{b \coth ^3(c+d x)} \log (\sinh (c+d x))}{d}",1,"((b*Coth[c + d*x]^3)^(1/3)*Log[Sinh[c + d*x]]*Tanh[c + d*x])/d","A",2,2,14,0.1429,1,"{3658, 3475}"
36,1,31,0,0.0202842,"\int \frac{1}{\sqrt[3]{b \coth ^3(c+d x)}} \, dx","Int[(b*Coth[c + d*x]^3)^(-1/3),x]","\frac{\coth (c+d x) \log (\cosh (c+d x))}{d \sqrt[3]{b \coth ^3(c+d x)}}","\frac{\coth (c+d x) \log (\cosh (c+d x))}{d \sqrt[3]{b \coth ^3(c+d x)}}",1,"(Coth[c + d*x]*Log[Cosh[c + d*x]])/(d*(b*Coth[c + d*x]^3)^(1/3))","A",2,2,14,0.1429,1,"{3658, 3475}"
37,1,50,0,0.0242453,"\int \frac{1}{\left(b \coth ^3(c+d x)\right)^{2/3}} \, dx","Int[(b*Coth[c + d*x]^3)^(-2/3),x]","\frac{x \coth ^2(c+d x)}{\left(b \coth ^3(c+d x)\right)^{2/3}}-\frac{\coth (c+d x)}{d \left(b \coth ^3(c+d x)\right)^{2/3}}","\frac{x \coth ^2(c+d x)}{\left(b \coth ^3(c+d x)\right)^{2/3}}-\frac{\coth (c+d x)}{d \left(b \coth ^3(c+d x)\right)^{2/3}}",1,"-(Coth[c + d*x]/(d*(b*Coth[c + d*x]^3)^(2/3))) + (x*Coth[c + d*x]^2)/(b*Coth[c + d*x]^3)^(2/3)","A",3,3,14,0.2143,1,"{3658, 3473, 8}"
38,1,80,0,0.0353556,"\int \frac{1}{\left(b \coth ^3(c+d x)\right)^{4/3}} \, dx","Int[(b*Coth[c + d*x]^3)^(-4/3),x]","\frac{x \coth (c+d x)}{b \sqrt[3]{b \coth ^3(c+d x)}}-\frac{1}{b d \sqrt[3]{b \coth ^3(c+d x)}}-\frac{\tanh ^2(c+d x)}{3 b d \sqrt[3]{b \coth ^3(c+d x)}}","\frac{x \coth (c+d x)}{b \sqrt[3]{b \coth ^3(c+d x)}}-\frac{1}{b d \sqrt[3]{b \coth ^3(c+d x)}}-\frac{\tanh ^2(c+d x)}{3 b d \sqrt[3]{b \coth ^3(c+d x)}}",1,"-(1/(b*d*(b*Coth[c + d*x]^3)^(1/3))) + (x*Coth[c + d*x])/(b*(b*Coth[c + d*x]^3)^(1/3)) - Tanh[c + d*x]^2/(3*b*d*(b*Coth[c + d*x]^3)^(1/3))","A",4,3,14,0.2143,1,"{3658, 3473, 8}"
39,1,57,0,0.0388827,"\int \left(b \coth ^4(c+d x)\right)^n \, dx","Int[(b*Coth[c + d*x]^4)^n,x]","\frac{\coth (c+d x) \left(b \coth ^4(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (4 n+1);\frac{1}{2} (4 n+3);\coth ^2(c+d x)\right)}{d (4 n+1)}","\frac{\coth (c+d x) \left(b \coth ^4(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (4 n+1);\frac{1}{2} (4 n+3);\coth ^2(c+d x)\right)}{d (4 n+1)}",1,"(Coth[c + d*x]*(b*Coth[c + d*x]^4)^n*Hypergeometric2F1[1, (1 + 4*n)/2, (3 + 4*n)/2, Coth[c + d*x]^2])/(d*(1 + 4*n))","A",3,3,12,0.2500,1,"{3658, 3476, 364}"
40,1,110,0,0.0452879,"\int \left(b \coth ^4(c+d x)\right)^{3/2} \, dx","Int[(b*Coth[c + d*x]^4)^(3/2),x]","-\frac{b \coth ^3(c+d x) \sqrt{b \coth ^4(c+d x)}}{5 d}-\frac{b \coth (c+d x) \sqrt{b \coth ^4(c+d x)}}{3 d}+b x \tanh ^2(c+d x) \sqrt{b \coth ^4(c+d x)}-\frac{b \tanh (c+d x) \sqrt{b \coth ^4(c+d x)}}{d}","-\frac{b \coth ^3(c+d x) \sqrt{b \coth ^4(c+d x)}}{5 d}-\frac{b \coth (c+d x) \sqrt{b \coth ^4(c+d x)}}{3 d}+b x \tanh ^2(c+d x) \sqrt{b \coth ^4(c+d x)}-\frac{b \tanh (c+d x) \sqrt{b \coth ^4(c+d x)}}{d}",1,"-(b*Coth[c + d*x]*Sqrt[b*Coth[c + d*x]^4])/(3*d) - (b*Coth[c + d*x]^3*Sqrt[b*Coth[c + d*x]^4])/(5*d) - (b*Sqrt[b*Coth[c + d*x]^4]*Tanh[c + d*x])/d + b*x*Sqrt[b*Coth[c + d*x]^4]*Tanh[c + d*x]^2","A",5,3,14,0.2143,1,"{3658, 3473, 8}"
41,1,50,0,0.0228098,"\int \sqrt{b \coth ^4(c+d x)} \, dx","Int[Sqrt[b*Coth[c + d*x]^4],x]","x \tanh ^2(c+d x) \sqrt{b \coth ^4(c+d x)}-\frac{\tanh (c+d x) \sqrt{b \coth ^4(c+d x)}}{d}","x \tanh ^2(c+d x) \sqrt{b \coth ^4(c+d x)}-\frac{\tanh (c+d x) \sqrt{b \coth ^4(c+d x)}}{d}",1,"-((Sqrt[b*Coth[c + d*x]^4]*Tanh[c + d*x])/d) + x*Sqrt[b*Coth[c + d*x]^4]*Tanh[c + d*x]^2","A",3,3,14,0.2143,1,"{3658, 3473, 8}"
42,1,50,0,0.0226638,"\int \frac{1}{\sqrt{b \coth ^4(c+d x)}} \, dx","Int[1/Sqrt[b*Coth[c + d*x]^4],x]","\frac{x \coth ^2(c+d x)}{\sqrt{b \coth ^4(c+d x)}}-\frac{\coth (c+d x)}{d \sqrt{b \coth ^4(c+d x)}}","\frac{x \coth ^2(c+d x)}{\sqrt{b \coth ^4(c+d x)}}-\frac{\coth (c+d x)}{d \sqrt{b \coth ^4(c+d x)}}",1,"-(Coth[c + d*x]/(d*Sqrt[b*Coth[c + d*x]^4])) + (x*Coth[c + d*x]^2)/Sqrt[b*Coth[c + d*x]^4]","A",3,3,14,0.2143,1,"{3658, 3473, 8}"
43,1,118,0,0.0459973,"\int \frac{1}{\left(b \coth ^4(c+d x)\right)^{3/2}} \, dx","Int[(b*Coth[c + d*x]^4)^(-3/2),x]","\frac{x \coth ^2(c+d x)}{b \sqrt{b \coth ^4(c+d x)}}-\frac{\coth (c+d x)}{b d \sqrt{b \coth ^4(c+d x)}}-\frac{\tanh ^3(c+d x)}{5 b d \sqrt{b \coth ^4(c+d x)}}-\frac{\tanh (c+d x)}{3 b d \sqrt{b \coth ^4(c+d x)}}","\frac{x \coth ^2(c+d x)}{b \sqrt{b \coth ^4(c+d x)}}-\frac{\coth (c+d x)}{b d \sqrt{b \coth ^4(c+d x)}}-\frac{\tanh ^3(c+d x)}{5 b d \sqrt{b \coth ^4(c+d x)}}-\frac{\tanh (c+d x)}{3 b d \sqrt{b \coth ^4(c+d x)}}",1,"-(Coth[c + d*x]/(b*d*Sqrt[b*Coth[c + d*x]^4])) + (x*Coth[c + d*x]^2)/(b*Sqrt[b*Coth[c + d*x]^4]) - Tanh[c + d*x]/(3*b*d*Sqrt[b*Coth[c + d*x]^4]) - Tanh[c + d*x]^3/(5*b*d*Sqrt[b*Coth[c + d*x]^4])","A",5,3,14,0.2143,1,"{3658, 3473, 8}"
44,1,353,0,0.1960077,"\int \left(b \coth ^4(c+d x)\right)^{4/3} \, dx","Int[(b*Coth[c + d*x]^4)^(4/3),x]","-\frac{3 b \coth ^3(c+d x) \sqrt[3]{b \coth ^4(c+d x)}}{13 d}-\frac{3 b \coth (c+d x) \sqrt[3]{b \coth ^4(c+d x)}}{7 d}-\frac{b \sqrt[3]{b \coth ^4(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{b \sqrt[3]{b \coth ^4(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}-\frac{\sqrt{3} b \sqrt[3]{b \coth ^4(c+d x)} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\sqrt{3} b \sqrt[3]{b \coth ^4(c+d x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{b \sqrt[3]{b \coth ^4(c+d x)} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{4}{3}}(c+d x)}-\frac{3 b \tanh (c+d x) \sqrt[3]{b \coth ^4(c+d x)}}{d}","-\frac{3 b \coth ^3(c+d x) \sqrt[3]{b \coth ^4(c+d x)}}{13 d}-\frac{3 b \coth (c+d x) \sqrt[3]{b \coth ^4(c+d x)}}{7 d}-\frac{b \sqrt[3]{b \coth ^4(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{b \sqrt[3]{b \coth ^4(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}-\frac{\sqrt{3} b \sqrt[3]{b \coth ^4(c+d x)} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\sqrt{3} b \sqrt[3]{b \coth ^4(c+d x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{b \sqrt[3]{b \coth ^4(c+d x)} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{4}{3}}(c+d x)}-\frac{3 b \tanh (c+d x) \sqrt[3]{b \coth ^4(c+d x)}}{d}",1,"-(Sqrt[3]*b*ArcTan[(1 - 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*(b*Coth[c + d*x]^4)^(1/3))/(2*d*Coth[c + d*x]^(4/3)) + (Sqrt[3]*b*ArcTan[(1 + 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*(b*Coth[c + d*x]^4)^(1/3))/(2*d*Coth[c + d*x]^(4/3)) + (b*ArcTanh[Coth[c + d*x]^(1/3)]*(b*Coth[c + d*x]^4)^(1/3))/(d*Coth[c + d*x]^(4/3)) - (3*b*Coth[c + d*x]*(b*Coth[c + d*x]^4)^(1/3))/(7*d) - (3*b*Coth[c + d*x]^3*(b*Coth[c + d*x]^4)^(1/3))/(13*d) - (b*(b*Coth[c + d*x]^4)^(1/3)*Log[1 - Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*Coth[c + d*x]^(4/3)) + (b*(b*Coth[c + d*x]^4)^(1/3)*Log[1 + Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*Coth[c + d*x]^(4/3)) - (3*b*(b*Coth[c + d*x]^4)^(1/3)*Tanh[c + d*x])/d","A",16,10,14,0.7143,1,"{3658, 3473, 3476, 329, 210, 634, 618, 204, 628, 206}"
45,1,291,0,0.2150866,"\int \left(b \coth ^4(c+d x)\right)^{2/3} \, dx","Int[(b*Coth[c + d*x]^4)^(2/3),x]","-\frac{\left(b \coth ^4(c+d x)\right)^{2/3} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{8}{3}}(c+d x)}+\frac{\left(b \coth ^4(c+d x)\right)^{2/3} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{8}{3}}(c+d x)}+\frac{\sqrt{3} \left(b \coth ^4(c+d x)\right)^{2/3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{8}{3}}(c+d x)}-\frac{\sqrt{3} \left(b \coth ^4(c+d x)\right)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{8}{3}}(c+d x)}+\frac{\left(b \coth ^4(c+d x)\right)^{2/3} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{8}{3}}(c+d x)}-\frac{3 \tanh (c+d x) \left(b \coth ^4(c+d x)\right)^{2/3}}{5 d}","-\frac{\left(b \coth ^4(c+d x)\right)^{2/3} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{8}{3}}(c+d x)}+\frac{\left(b \coth ^4(c+d x)\right)^{2/3} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{8}{3}}(c+d x)}+\frac{\sqrt{3} \left(b \coth ^4(c+d x)\right)^{2/3} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{8}{3}}(c+d x)}-\frac{\sqrt{3} \left(b \coth ^4(c+d x)\right)^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{8}{3}}(c+d x)}+\frac{\left(b \coth ^4(c+d x)\right)^{2/3} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{8}{3}}(c+d x)}-\frac{3 \tanh (c+d x) \left(b \coth ^4(c+d x)\right)^{2/3}}{5 d}",1,"(Sqrt[3]*ArcTan[(1 - 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*(b*Coth[c + d*x]^4)^(2/3))/(2*d*Coth[c + d*x]^(8/3)) - (Sqrt[3]*ArcTan[(1 + 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*(b*Coth[c + d*x]^4)^(2/3))/(2*d*Coth[c + d*x]^(8/3)) + (ArcTanh[Coth[c + d*x]^(1/3)]*(b*Coth[c + d*x]^4)^(2/3))/(d*Coth[c + d*x]^(8/3)) - ((b*Coth[c + d*x]^4)^(2/3)*Log[1 - Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*Coth[c + d*x]^(8/3)) + ((b*Coth[c + d*x]^4)^(2/3)*Log[1 + Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*Coth[c + d*x]^(8/3)) - (3*(b*Coth[c + d*x]^4)^(2/3)*Tanh[c + d*x])/(5*d)","A",14,10,14,0.7143,1,"{3658, 3473, 3476, 329, 296, 634, 618, 204, 628, 206}"
46,1,289,0,0.1757379,"\int \sqrt[3]{b \coth ^4(c+d x)} \, dx","Int[(b*Coth[c + d*x]^4)^(1/3),x]","-\frac{\sqrt[3]{b \coth ^4(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\sqrt[3]{b \coth ^4(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}-\frac{\sqrt{3} \sqrt[3]{b \coth ^4(c+d x)} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\sqrt{3} \sqrt[3]{b \coth ^4(c+d x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\sqrt[3]{b \coth ^4(c+d x)} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{4}{3}}(c+d x)}-\frac{3 \tanh (c+d x) \sqrt[3]{b \coth ^4(c+d x)}}{d}","-\frac{\sqrt[3]{b \coth ^4(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\sqrt[3]{b \coth ^4(c+d x)} \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \coth ^{\frac{4}{3}}(c+d x)}-\frac{\sqrt{3} \sqrt[3]{b \coth ^4(c+d x)} \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\sqrt{3} \sqrt[3]{b \coth ^4(c+d x)} \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \coth ^{\frac{4}{3}}(c+d x)}+\frac{\sqrt[3]{b \coth ^4(c+d x)} \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \coth ^{\frac{4}{3}}(c+d x)}-\frac{3 \tanh (c+d x) \sqrt[3]{b \coth ^4(c+d x)}}{d}",1,"-(Sqrt[3]*ArcTan[(1 - 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*(b*Coth[c + d*x]^4)^(1/3))/(2*d*Coth[c + d*x]^(4/3)) + (Sqrt[3]*ArcTan[(1 + 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*(b*Coth[c + d*x]^4)^(1/3))/(2*d*Coth[c + d*x]^(4/3)) + (ArcTanh[Coth[c + d*x]^(1/3)]*(b*Coth[c + d*x]^4)^(1/3))/(d*Coth[c + d*x]^(4/3)) - ((b*Coth[c + d*x]^4)^(1/3)*Log[1 - Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*Coth[c + d*x]^(4/3)) + ((b*Coth[c + d*x]^4)^(1/3)*Log[1 + Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*Coth[c + d*x]^(4/3)) - (3*(b*Coth[c + d*x]^4)^(1/3)*Tanh[c + d*x])/d","A",14,10,14,0.7143,1,"{3658, 3473, 3476, 329, 210, 634, 618, 204, 628, 206}"
47,1,289,0,0.2178837,"\int \frac{1}{\sqrt[3]{b \coth ^4(c+d x)}} \, dx","Int[(b*Coth[c + d*x]^4)^(-1/3),x]","-\frac{3 \coth (c+d x)}{d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \sqrt[3]{b \coth ^4(c+d x)}}","-\frac{3 \coth (c+d x)}{d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \sqrt[3]{b \coth ^4(c+d x)}}",1,"(-3*Coth[c + d*x])/(d*(b*Coth[c + d*x]^4)^(1/3)) + (Sqrt[3]*ArcTan[(1 - 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*Coth[c + d*x]^(4/3))/(2*d*(b*Coth[c + d*x]^4)^(1/3)) - (Sqrt[3]*ArcTan[(1 + 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*Coth[c + d*x]^(4/3))/(2*d*(b*Coth[c + d*x]^4)^(1/3)) + (ArcTanh[Coth[c + d*x]^(1/3)]*Coth[c + d*x]^(4/3))/(d*(b*Coth[c + d*x]^4)^(1/3)) - (Coth[c + d*x]^(4/3)*Log[1 - Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*(b*Coth[c + d*x]^4)^(1/3)) + (Coth[c + d*x]^(4/3)*Log[1 + Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*(b*Coth[c + d*x]^4)^(1/3))","A",14,10,14,0.7143,1,"{3658, 3474, 3476, 329, 296, 634, 618, 204, 628, 206}"
48,1,291,0,0.1849448,"\int \frac{1}{\left(b \coth ^4(c+d x)\right)^{2/3}} \, dx","Int[(b*Coth[c + d*x]^4)^(-2/3),x]","-\frac{3 \coth (c+d x)}{5 d \left(b \coth ^4(c+d x)\right)^{2/3}}-\frac{\coth ^{\frac{8}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \left(b \coth ^4(c+d x)\right)^{2/3}}+\frac{\coth ^{\frac{8}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \left(b \coth ^4(c+d x)\right)^{2/3}}-\frac{\sqrt{3} \coth ^{\frac{8}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \left(b \coth ^4(c+d x)\right)^{2/3}}+\frac{\sqrt{3} \coth ^{\frac{8}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \left(b \coth ^4(c+d x)\right)^{2/3}}+\frac{\coth ^{\frac{8}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \left(b \coth ^4(c+d x)\right)^{2/3}}","-\frac{3 \coth (c+d x)}{5 d \left(b \coth ^4(c+d x)\right)^{2/3}}-\frac{\coth ^{\frac{8}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \left(b \coth ^4(c+d x)\right)^{2/3}}+\frac{\coth ^{\frac{8}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 d \left(b \coth ^4(c+d x)\right)^{2/3}}-\frac{\sqrt{3} \coth ^{\frac{8}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 d \left(b \coth ^4(c+d x)\right)^{2/3}}+\frac{\sqrt{3} \coth ^{\frac{8}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 d \left(b \coth ^4(c+d x)\right)^{2/3}}+\frac{\coth ^{\frac{8}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{d \left(b \coth ^4(c+d x)\right)^{2/3}}",1,"(-3*Coth[c + d*x])/(5*d*(b*Coth[c + d*x]^4)^(2/3)) - (Sqrt[3]*ArcTan[(1 - 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*Coth[c + d*x]^(8/3))/(2*d*(b*Coth[c + d*x]^4)^(2/3)) + (Sqrt[3]*ArcTan[(1 + 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*Coth[c + d*x]^(8/3))/(2*d*(b*Coth[c + d*x]^4)^(2/3)) + (ArcTanh[Coth[c + d*x]^(1/3)]*Coth[c + d*x]^(8/3))/(d*(b*Coth[c + d*x]^4)^(2/3)) - (Coth[c + d*x]^(8/3)*Log[1 - Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*(b*Coth[c + d*x]^4)^(2/3)) + (Coth[c + d*x]^(8/3)*Log[1 + Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*d*(b*Coth[c + d*x]^4)^(2/3))","A",14,10,14,0.7143,1,"{3658, 3474, 3476, 329, 210, 634, 618, 204, 628, 206}"
49,1,369,0,0.2446831,"\int \frac{1}{\left(b \coth ^4(c+d x)\right)^{4/3}} \, dx","Int[(b*Coth[c + d*x]^4)^(-4/3),x]","-\frac{3 \coth (c+d x)}{b d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 b d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 b d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 b d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 b d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{3 \tanh ^3(c+d x)}{13 b d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{b d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{3 \tanh (c+d x)}{7 b d \sqrt[3]{b \coth ^4(c+d x)}}","-\frac{3 \coth (c+d x)}{b d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)-\sqrt[3]{\coth (c+d x)}+1\right)}{4 b d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \log \left(\coth ^{\frac{2}{3}}(c+d x)+\sqrt[3]{\coth (c+d x)}+1\right)}{4 b d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{1-2 \sqrt[3]{\coth (c+d x)}}{\sqrt{3}}\right)}{2 b d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{\sqrt{3} \coth ^{\frac{4}{3}}(c+d x) \tan ^{-1}\left(\frac{2 \sqrt[3]{\coth (c+d x)}+1}{\sqrt{3}}\right)}{2 b d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{3 \tanh ^3(c+d x)}{13 b d \sqrt[3]{b \coth ^4(c+d x)}}+\frac{\coth ^{\frac{4}{3}}(c+d x) \tanh ^{-1}\left(\sqrt[3]{\coth (c+d x)}\right)}{b d \sqrt[3]{b \coth ^4(c+d x)}}-\frac{3 \tanh (c+d x)}{7 b d \sqrt[3]{b \coth ^4(c+d x)}}",1,"(-3*Coth[c + d*x])/(b*d*(b*Coth[c + d*x]^4)^(1/3)) + (Sqrt[3]*ArcTan[(1 - 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*Coth[c + d*x]^(4/3))/(2*b*d*(b*Coth[c + d*x]^4)^(1/3)) - (Sqrt[3]*ArcTan[(1 + 2*Coth[c + d*x]^(1/3))/Sqrt[3]]*Coth[c + d*x]^(4/3))/(2*b*d*(b*Coth[c + d*x]^4)^(1/3)) + (ArcTanh[Coth[c + d*x]^(1/3)]*Coth[c + d*x]^(4/3))/(b*d*(b*Coth[c + d*x]^4)^(1/3)) - (Coth[c + d*x]^(4/3)*Log[1 - Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*b*d*(b*Coth[c + d*x]^4)^(1/3)) + (Coth[c + d*x]^(4/3)*Log[1 + Coth[c + d*x]^(1/3) + Coth[c + d*x]^(2/3)])/(4*b*d*(b*Coth[c + d*x]^4)^(1/3)) - (3*Tanh[c + d*x])/(7*b*d*(b*Coth[c + d*x]^4)^(1/3)) - (3*Tanh[c + d*x]^3)/(13*b*d*(b*Coth[c + d*x]^4)^(1/3))","A",16,10,14,0.7143,1,"{3658, 3474, 3476, 329, 296, 634, 618, 204, 628, 206}"
50,1,57,0,0.0423468,"\int \left(b \coth ^m(c+d x)\right)^n \, dx","Int[(b*Coth[c + d*x]^m)^n,x]","\frac{\coth (c+d x) \left(b \coth ^m(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (m n+1);\frac{1}{2} (m n+3);\coth ^2(c+d x)\right)}{d (m n+1)}","\frac{\coth (c+d x) \left(b \coth ^m(c+d x)\right)^n \, _2F_1\left(1,\frac{1}{2} (m n+1);\frac{1}{2} (m n+3);\coth ^2(c+d x)\right)}{d (m n+1)}",1,"(Coth[c + d*x]*(b*Coth[c + d*x]^m)^n*Hypergeometric2F1[1, (1 + m*n)/2, (3 + m*n)/2, Coth[c + d*x]^2])/(d*(1 + m*n))","A",3,3,12,0.2500,1,"{3659, 3476, 364}"
51,1,63,0,0.0454474,"\int \left(b \coth ^m(c+d x)\right)^{3/2} \, dx","Int[(b*Coth[c + d*x]^m)^(3/2),x]","\frac{2 b \coth ^{m+1}(c+d x) \sqrt{b \coth ^m(c+d x)} \, _2F_1\left(1,\frac{1}{4} (3 m+2);\frac{3 (m+2)}{4};\coth ^2(c+d x)\right)}{d (3 m+2)}","\frac{2 b \coth ^{m+1}(c+d x) \sqrt{b \coth ^m(c+d x)} \, _2F_1\left(1,\frac{1}{4} (3 m+2);\frac{3 (m+2)}{4};\coth ^2(c+d x)\right)}{d (3 m+2)}",1,"(2*b*Coth[c + d*x]^(1 + m)*Sqrt[b*Coth[c + d*x]^m]*Hypergeometric2F1[1, (2 + 3*m)/4, (3*(2 + m))/4, Coth[c + d*x]^2])/(d*(2 + 3*m))","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
52,1,54,0,0.0407944,"\int \sqrt{b \coth ^m(c+d x)} \, dx","Int[Sqrt[b*Coth[c + d*x]^m],x]","\frac{2 \coth (c+d x) \sqrt{b \coth ^m(c+d x)} \, _2F_1\left(1,\frac{m+2}{4};\frac{m+6}{4};\coth ^2(c+d x)\right)}{d (m+2)}","\frac{2 \coth (c+d x) \sqrt{b \coth ^m(c+d x)} \, _2F_1\left(1,\frac{m+2}{4};\frac{m+6}{4};\coth ^2(c+d x)\right)}{d (m+2)}",1,"(2*Coth[c + d*x]*Sqrt[b*Coth[c + d*x]^m]*Hypergeometric2F1[1, (2 + m)/4, (6 + m)/4, Coth[c + d*x]^2])/(d*(2 + m))","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
53,1,60,0,0.047278,"\int \frac{1}{\sqrt{b \coth ^m(c+d x)}} \, dx","Int[1/Sqrt[b*Coth[c + d*x]^m],x]","\frac{2 \coth (c+d x) \, _2F_1\left(1,\frac{2-m}{4};\frac{6-m}{4};\coth ^2(c+d x)\right)}{d (2-m) \sqrt{b \coth ^m(c+d x)}}","\frac{2 \coth (c+d x) \, _2F_1\left(1,\frac{2-m}{4};\frac{6-m}{4};\coth ^2(c+d x)\right)}{d (2-m) \sqrt{b \coth ^m(c+d x)}}",1,"(2*Coth[c + d*x]*Hypergeometric2F1[1, (2 - m)/4, (6 - m)/4, Coth[c + d*x]^2])/(d*(2 - m)*Sqrt[b*Coth[c + d*x]^m])","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
54,1,69,0,0.0481878,"\int \frac{1}{\left(b \coth ^m(c+d x)\right)^{3/2}} \, dx","Int[(b*Coth[c + d*x]^m)^(-3/2),x]","\frac{2 \coth ^{1-m}(c+d x) \, _2F_1\left(1,\frac{1}{4} (2-3 m);\frac{3 (2-m)}{4};\coth ^2(c+d x)\right)}{b d (2-3 m) \sqrt{b \coth ^m(c+d x)}}","\frac{2 \coth ^{1-m}(c+d x) \, _2F_1\left(1,\frac{1}{4} (2-3 m);\frac{3 (2-m)}{4};\coth ^2(c+d x)\right)}{b d (2-3 m) \sqrt{b \coth ^m(c+d x)}}",1,"(2*Coth[c + d*x]^(1 - m)*Hypergeometric2F1[1, (2 - 3*m)/4, (3*(2 - m))/4, Coth[c + d*x]^2])/(b*d*(2 - 3*m)*Sqrt[b*Coth[c + d*x]^m])","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
55,1,65,0,0.0453596,"\int \left(b \coth ^m(c+d x)\right)^{4/3} \, dx","Int[(b*Coth[c + d*x]^m)^(4/3),x]","\frac{3 b \coth ^{m+1}(c+d x) \sqrt[3]{b \coth ^m(c+d x)} \, _2F_1\left(1,\frac{1}{6} (4 m+3);\frac{1}{6} (4 m+9);\coth ^2(c+d x)\right)}{d (4 m+3)}","\frac{3 b \coth ^{m+1}(c+d x) \sqrt[3]{b \coth ^m(c+d x)} \, _2F_1\left(1,\frac{1}{6} (4 m+3);\frac{1}{6} (4 m+9);\coth ^2(c+d x)\right)}{d (4 m+3)}",1,"(3*b*Coth[c + d*x]^(1 + m)*(b*Coth[c + d*x]^m)^(1/3)*Hypergeometric2F1[1, (3 + 4*m)/6, (9 + 4*m)/6, Coth[c + d*x]^2])/(d*(3 + 4*m))","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
56,1,60,0,0.0430382,"\int \left(b \coth ^m(c+d x)\right)^{2/3} \, dx","Int[(b*Coth[c + d*x]^m)^(2/3),x]","\frac{3 \coth (c+d x) \left(b \coth ^m(c+d x)\right)^{2/3} \, _2F_1\left(1,\frac{1}{6} (2 m+3);\frac{1}{6} (2 m+9);\coth ^2(c+d x)\right)}{d (2 m+3)}","\frac{3 \coth (c+d x) \left(b \coth ^m(c+d x)\right)^{2/3} \, _2F_1\left(1,\frac{1}{6} (2 m+3);\frac{1}{6} (2 m+9);\coth ^2(c+d x)\right)}{d (2 m+3)}",1,"(3*Coth[c + d*x]*(b*Coth[c + d*x]^m)^(2/3)*Hypergeometric2F1[1, (3 + 2*m)/6, (9 + 2*m)/6, Coth[c + d*x]^2])/(d*(3 + 2*m))","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
57,1,54,0,0.0437366,"\int \sqrt[3]{b \coth ^m(c+d x)} \, dx","Int[(b*Coth[c + d*x]^m)^(1/3),x]","\frac{3 \coth (c+d x) \sqrt[3]{b \coth ^m(c+d x)} \, _2F_1\left(1,\frac{m+3}{6};\frac{m+9}{6};\coth ^2(c+d x)\right)}{d (m+3)}","\frac{3 \coth (c+d x) \sqrt[3]{b \coth ^m(c+d x)} \, _2F_1\left(1,\frac{m+3}{6};\frac{m+9}{6};\coth ^2(c+d x)\right)}{d (m+3)}",1,"(3*Coth[c + d*x]*(b*Coth[c + d*x]^m)^(1/3)*Hypergeometric2F1[1, (3 + m)/6, (9 + m)/6, Coth[c + d*x]^2])/(d*(3 + m))","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
58,1,60,0,0.0426262,"\int \frac{1}{\sqrt[3]{b \coth ^m(c+d x)}} \, dx","Int[(b*Coth[c + d*x]^m)^(-1/3),x]","\frac{3 \coth (c+d x) \, _2F_1\left(1,\frac{3-m}{6};\frac{9-m}{6};\coth ^2(c+d x)\right)}{d (3-m) \sqrt[3]{b \coth ^m(c+d x)}}","\frac{3 \coth (c+d x) \, _2F_1\left(1,\frac{3-m}{6};\frac{9-m}{6};\coth ^2(c+d x)\right)}{d (3-m) \sqrt[3]{b \coth ^m(c+d x)}}",1,"(3*Coth[c + d*x]*Hypergeometric2F1[1, (3 - m)/6, (9 - m)/6, Coth[c + d*x]^2])/(d*(3 - m)*(b*Coth[c + d*x]^m)^(1/3))","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
59,1,60,0,0.0445252,"\int \frac{1}{\left(b \coth ^m(c+d x)\right)^{2/3}} \, dx","Int[(b*Coth[c + d*x]^m)^(-2/3),x]","\frac{3 \coth (c+d x) \, _2F_1\left(1,\frac{1}{6} (3-2 m);\frac{1}{6} (9-2 m);\coth ^2(c+d x)\right)}{d (3-2 m) \left(b \coth ^m(c+d x)\right)^{2/3}}","\frac{3 \coth (c+d x) \, _2F_1\left(1,\frac{1}{6} (3-2 m);\frac{1}{6} (9-2 m);\coth ^2(c+d x)\right)}{d (3-2 m) \left(b \coth ^m(c+d x)\right)^{2/3}}",1,"(3*Coth[c + d*x]*Hypergeometric2F1[1, (3 - 2*m)/6, (9 - 2*m)/6, Coth[c + d*x]^2])/(d*(3 - 2*m)*(b*Coth[c + d*x]^m)^(2/3))","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
60,1,69,0,0.0472706,"\int \frac{1}{\left(b \coth ^m(c+d x)\right)^{4/3}} \, dx","Int[(b*Coth[c + d*x]^m)^(-4/3),x]","\frac{3 \coth ^{1-m}(c+d x) \, _2F_1\left(1,\frac{1}{6} (3-4 m);\frac{1}{6} (9-4 m);\coth ^2(c+d x)\right)}{b d (3-4 m) \sqrt[3]{b \coth ^m(c+d x)}}","\frac{3 \coth ^{1-m}(c+d x) \, _2F_1\left(1,\frac{1}{6} (3-4 m);\frac{1}{6} (9-4 m);\coth ^2(c+d x)\right)}{b d (3-4 m) \sqrt[3]{b \coth ^m(c+d x)}}",1,"(3*Coth[c + d*x]^(1 - m)*Hypergeometric2F1[1, (3 - 4*m)/6, (9 - 4*m)/6, Coth[c + d*x]^2])/(b*d*(3 - 4*m)*(b*Coth[c + d*x]^m)^(1/3))","A",3,3,14,0.2143,1,"{3659, 3476, 364}"
61,1,41,0,0.0394656,"\int (1+\coth (x))^5 \, dx","Int[(1 + Coth[x])^5,x]","16 x-\frac{1}{4} (\coth (x)+1)^4-\frac{2}{3} (\coth (x)+1)^3-2 (\coth (x)+1)^2-8 \coth (x)+16 \log (\sinh (x))","16 x-\frac{1}{4} (\coth (x)+1)^4-\frac{2}{3} (\coth (x)+1)^3-2 (\coth (x)+1)^2-8 \coth (x)+16 \log (\sinh (x))",1,"16*x - 8*Coth[x] - 2*(1 + Coth[x])^2 - (2*(1 + Coth[x])^3)/3 - (1 + Coth[x])^4/4 + 16*Log[Sinh[x]]","A",5,3,6,0.5000,1,"{3478, 3477, 3475}"
62,1,31,0,0.0309066,"\int (1+\coth (x))^4 \, dx","Int[(1 + Coth[x])^4,x]","8 x-\frac{1}{3} (\coth (x)+1)^3-(\coth (x)+1)^2-4 \coth (x)+8 \log (\sinh (x))","8 x-\frac{1}{3} (\coth (x)+1)^3-(\coth (x)+1)^2-4 \coth (x)+8 \log (\sinh (x))",1,"8*x - 4*Coth[x] - (1 + Coth[x])^2 - (1 + Coth[x])^3/3 + 8*Log[Sinh[x]]","A",4,3,6,0.5000,1,"{3478, 3477, 3475}"
63,1,23,0,0.0214076,"\int (1+\coth (x))^3 \, dx","Int[(1 + Coth[x])^3,x]","4 x-\frac{1}{2} (\coth (x)+1)^2-2 \coth (x)+4 \log (\sinh (x))","4 x-\frac{1}{2} (\coth (x)+1)^2-2 \coth (x)+4 \log (\sinh (x))",1,"4*x - 2*Coth[x] - (1 + Coth[x])^2/2 + 4*Log[Sinh[x]]","A",3,3,6,0.5000,1,"{3478, 3477, 3475}"
64,1,13,0,0.0133208,"\int (1+\coth (x))^2 \, dx","Int[(1 + Coth[x])^2,x]","2 x-\coth (x)+2 \log (\sinh (x))","2 x-\coth (x)+2 \log (\sinh (x))",1,"2*x - Coth[x] + 2*Log[Sinh[x]]","A",2,2,6,0.3333,1,"{3477, 3475}"
65,1,16,0,0.0086758,"\int \frac{1}{1+\coth (x)} \, dx","Int[(1 + Coth[x])^(-1),x]","\frac{x}{2}-\frac{1}{2 (\coth (x)+1)}","\frac{x}{2}-\frac{1}{2 (\coth (x)+1)}",1,"x/2 - 1/(2*(1 + Coth[x]))","A",2,2,6,0.3333,1,"{3479, 8}"
66,1,26,0,0.0169901,"\int \frac{1}{(1+\coth (x))^2} \, dx","Int[(1 + Coth[x])^(-2),x]","\frac{x}{4}-\frac{1}{4 (\coth (x)+1)}-\frac{1}{4 (\coth (x)+1)^2}","\frac{x}{4}-\frac{1}{4 (\coth (x)+1)}-\frac{1}{4 (\coth (x)+1)^2}",1,"x/4 - 1/(4*(1 + Coth[x])^2) - 1/(4*(1 + Coth[x]))","A",3,2,6,0.3333,1,"{3479, 8}"
67,1,36,0,0.0274045,"\int \frac{1}{(1+\coth (x))^3} \, dx","Int[(1 + Coth[x])^(-3),x]","\frac{x}{8}-\frac{1}{8 (\coth (x)+1)}-\frac{1}{8 (\coth (x)+1)^2}-\frac{1}{6 (\coth (x)+1)^3}","\frac{x}{8}-\frac{1}{8 (\coth (x)+1)}-\frac{1}{8 (\coth (x)+1)^2}-\frac{1}{6 (\coth (x)+1)^3}",1,"x/8 - 1/(6*(1 + Coth[x])^3) - 1/(8*(1 + Coth[x])^2) - 1/(8*(1 + Coth[x]))","A",4,2,6,0.3333,1,"{3479, 8}"
68,1,46,0,0.0359077,"\int \frac{1}{(1+\coth (x))^4} \, dx","Int[(1 + Coth[x])^(-4),x]","\frac{x}{16}-\frac{1}{16 (\coth (x)+1)}-\frac{1}{16 (\coth (x)+1)^2}-\frac{1}{12 (\coth (x)+1)^3}-\frac{1}{8 (\coth (x)+1)^4}","\frac{x}{16}-\frac{1}{16 (\coth (x)+1)}-\frac{1}{16 (\coth (x)+1)^2}-\frac{1}{12 (\coth (x)+1)^3}-\frac{1}{8 (\coth (x)+1)^4}",1,"x/16 - 1/(8*(1 + Coth[x])^4) - 1/(12*(1 + Coth[x])^3) - 1/(16*(1 + Coth[x])^2) - 1/(16*(1 + Coth[x]))","A",5,2,6,0.3333,1,"{3479, 8}"
69,1,56,0,0.0462366,"\int \frac{1}{(1+\coth (x))^5} \, dx","Int[(1 + Coth[x])^(-5),x]","\frac{x}{32}-\frac{1}{32 (\coth (x)+1)}-\frac{1}{32 (\coth (x)+1)^2}-\frac{1}{24 (\coth (x)+1)^3}-\frac{1}{16 (\coth (x)+1)^4}-\frac{1}{10 (\coth (x)+1)^5}","\frac{x}{32}-\frac{1}{32 (\coth (x)+1)}-\frac{1}{32 (\coth (x)+1)^2}-\frac{1}{24 (\coth (x)+1)^3}-\frac{1}{16 (\coth (x)+1)^4}-\frac{1}{10 (\coth (x)+1)^5}",1,"x/32 - 1/(10*(1 + Coth[x])^5) - 1/(16*(1 + Coth[x])^4) - 1/(24*(1 + Coth[x])^3) - 1/(32*(1 + Coth[x])^2) - 1/(32*(1 + Coth[x]))","A",6,2,6,0.3333,1,"{3479, 8}"
70,1,57,0,0.0419785,"\int (1+\coth (x))^{7/2} \, dx","Int[(1 + Coth[x])^(7/2),x]","-\frac{2}{5} (\coth (x)+1)^{5/2}-\frac{4}{3} (\coth (x)+1)^{3/2}-8 \sqrt{\coth (x)+1}+8 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)","-\frac{2}{5} (\coth (x)+1)^{5/2}-\frac{4}{3} (\coth (x)+1)^{3/2}-8 \sqrt{\coth (x)+1}+8 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)",1,"8*Sqrt[2]*ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]] - 8*Sqrt[1 + Coth[x]] - (4*(1 + Coth[x])^(3/2))/3 - (2*(1 + Coth[x])^(5/2))/5","A",5,3,8,0.3750,1,"{3478, 3480, 206}"
71,1,45,0,0.031965,"\int (1+\coth (x))^{5/2} \, dx","Int[(1 + Coth[x])^(5/2),x]","-\frac{2}{3} (\coth (x)+1)^{3/2}-4 \sqrt{\coth (x)+1}+4 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)","-\frac{2}{3} (\coth (x)+1)^{3/2}-4 \sqrt{\coth (x)+1}+4 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)",1,"4*Sqrt[2]*ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]] - 4*Sqrt[1 + Coth[x]] - (2*(1 + Coth[x])^(3/2))/3","A",4,3,8,0.3750,1,"{3478, 3480, 206}"
72,1,33,0,0.0219855,"\int (1+\coth (x))^{3/2} \, dx","Int[(1 + Coth[x])^(3/2),x]","2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)-2 \sqrt{\coth (x)+1}","2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)-2 \sqrt{\coth (x)+1}",1,"2*Sqrt[2]*ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]] - 2*Sqrt[1 + Coth[x]]","A",3,3,8,0.3750,1,"{3478, 3480, 206}"
73,1,21,0,0.0120375,"\int \sqrt{1+\coth (x)} \, dx","Int[Sqrt[1 + Coth[x]],x]","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)",1,"Sqrt[2]*ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]]","A",2,2,8,0.2500,1,"{3480, 206}"
74,1,32,0,0.0228691,"\int \frac{1}{\sqrt{1+\coth (x)}} \, dx","Int[1/Sqrt[1 + Coth[x]],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{1}{\sqrt{\coth (x)+1}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{1}{\sqrt{\coth (x)+1}}",1,"ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]]/Sqrt[2] - 1/Sqrt[1 + Coth[x]]","A",3,3,8,0.3750,1,"{3479, 3480, 206}"
75,1,49,0,0.0307411,"\int \frac{1}{(1+\coth (x))^{3/2}} \, dx","Int[(1 + Coth[x])^(-3/2),x]","-\frac{1}{2 \sqrt{\coth (x)+1}}-\frac{1}{3 (\coth (x)+1)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{2 \sqrt{2}}","-\frac{1}{2 \sqrt{\coth (x)+1}}-\frac{1}{3 (\coth (x)+1)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{2 \sqrt{2}}",1,"ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]]/(2*Sqrt[2]) - 1/(3*(1 + Coth[x])^(3/2)) - 1/(2*Sqrt[1 + Coth[x]])","A",4,3,8,0.3750,1,"{3479, 3480, 206}"
76,1,61,0,0.0419238,"\int \frac{1}{(1+\coth (x))^{5/2}} \, dx","Int[(1 + Coth[x])^(-5/2),x]","-\frac{1}{4 \sqrt{\coth (x)+1}}-\frac{1}{6 (\coth (x)+1)^{3/2}}-\frac{1}{5 (\coth (x)+1)^{5/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{4 \sqrt{2}}","-\frac{1}{4 \sqrt{\coth (x)+1}}-\frac{1}{6 (\coth (x)+1)^{3/2}}-\frac{1}{5 (\coth (x)+1)^{5/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{4 \sqrt{2}}",1,"ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]]/(4*Sqrt[2]) - 1/(5*(1 + Coth[x])^(5/2)) - 1/(6*(1 + Coth[x])^(3/2)) - 1/(4*Sqrt[1 + Coth[x]])","A",5,3,8,0.3750,1,"{3479, 3480, 206}"
77,1,142,0,0.2087678,"\int (a+b \coth (c+d x))^5 \, dx","Int[(a + b*Coth[c + d*x])^5,x]","-\frac{b \left(3 a^2+b^2\right) (a+b \coth (c+d x))^2}{2 d}-\frac{4 a b^2 \left(a^2+b^2\right) \coth (c+d x)}{d}+\frac{b \left(10 a^2 b^2+5 a^4+b^4\right) \log (\sinh (c+d x))}{d}+a x \left(10 a^2 b^2+a^4+5 b^4\right)-\frac{b (a+b \coth (c+d x))^4}{4 d}-\frac{2 a b (a+b \coth (c+d x))^3}{3 d}","-\frac{b \left(3 a^2+b^2\right) (a+b \coth (c+d x))^2}{2 d}-\frac{4 a b^2 \left(a^2+b^2\right) \coth (c+d x)}{d}+\frac{b \left(10 a^2 b^2+5 a^4+b^4\right) \log (\sinh (c+d x))}{d}+a x \left(10 a^2 b^2+a^4+5 b^4\right)-\frac{b (a+b \coth (c+d x))^4}{4 d}-\frac{2 a b (a+b \coth (c+d x))^3}{3 d}",1,"a*(a^4 + 10*a^2*b^2 + 5*b^4)*x - (4*a*b^2*(a^2 + b^2)*Coth[c + d*x])/d - (b*(3*a^2 + b^2)*(a + b*Coth[c + d*x])^2)/(2*d) - (2*a*b*(a + b*Coth[c + d*x])^3)/(3*d) - (b*(a + b*Coth[c + d*x])^4)/(4*d) + (b*(5*a^4 + 10*a^2*b^2 + b^4)*Log[Sinh[c + d*x]])/d","A",5,4,12,0.3333,1,"{3482, 3528, 3525, 3475}"
78,1,101,0,0.1225388,"\int (a+b \coth (c+d x))^4 \, dx","Int[(a + b*Coth[c + d*x])^4,x]","-\frac{b^2 \left(3 a^2+b^2\right) \coth (c+d x)}{d}+\frac{4 a b \left(a^2+b^2\right) \log (\sinh (c+d x))}{d}+x \left(6 a^2 b^2+a^4+b^4\right)-\frac{b (a+b \coth (c+d x))^3}{3 d}-\frac{a b (a+b \coth (c+d x))^2}{d}","-\frac{b^2 \left(3 a^2+b^2\right) \coth (c+d x)}{d}+\frac{4 a b \left(a^2+b^2\right) \log (\sinh (c+d x))}{d}+x \left(6 a^2 b^2+a^4+b^4\right)-\frac{b (a+b \coth (c+d x))^3}{3 d}-\frac{a b (a+b \coth (c+d x))^2}{d}",1,"(a^4 + 6*a^2*b^2 + b^4)*x - (b^2*(3*a^2 + b^2)*Coth[c + d*x])/d - (a*b*(a + b*Coth[c + d*x])^2)/d - (b*(a + b*Coth[c + d*x])^3)/(3*d) + (4*a*b*(a^2 + b^2)*Log[Sinh[c + d*x]])/d","A",4,4,12,0.3333,1,"{3482, 3528, 3525, 3475}"
79,1,69,0,0.0638579,"\int (a+b \coth (c+d x))^3 \, dx","Int[(a + b*Coth[c + d*x])^3,x]","\frac{b \left(3 a^2+b^2\right) \log (\sinh (c+d x))}{d}+a x \left(a^2+3 b^2\right)-\frac{2 a b^2 \coth (c+d x)}{d}-\frac{b (a+b \coth (c+d x))^2}{2 d}","\frac{b \left(3 a^2+b^2\right) \log (\sinh (c+d x))}{d}+a x \left(a^2+3 b^2\right)-\frac{2 a b^2 \coth (c+d x)}{d}-\frac{b (a+b \coth (c+d x))^2}{2 d}",1,"a*(a^2 + 3*b^2)*x - (2*a*b^2*Coth[c + d*x])/d - (b*(a + b*Coth[c + d*x])^2)/(2*d) + (b*(3*a^2 + b^2)*Log[Sinh[c + d*x]])/d","A",3,3,12,0.2500,1,"{3482, 3525, 3475}"
80,1,38,0,0.024292,"\int (a+b \coth (c+d x))^2 \, dx","Int[(a + b*Coth[c + d*x])^2,x]","x \left(a^2+b^2\right)+\frac{2 a b \log (\sinh (c+d x))}{d}-\frac{b^2 \coth (c+d x)}{d}","x \left(a^2+b^2\right)+\frac{2 a b \log (\sinh (c+d x))}{d}-\frac{b^2 \coth (c+d x)}{d}",1,"(a^2 + b^2)*x - (b^2*Coth[c + d*x])/d + (2*a*b*Log[Sinh[c + d*x]])/d","A",2,2,12,0.1667,1,"{3477, 3475}"
81,1,50,0,0.0539133,"\int \frac{1}{a+b \coth (c+d x)} \, dx","Int[(a + b*Coth[c + d*x])^(-1),x]","\frac{a x}{a^2-b^2}-\frac{b \log (a \sinh (c+d x)+b \cosh (c+d x))}{d \left(a^2-b^2\right)}","\frac{a x}{a^2-b^2}-\frac{b \log (a \sinh (c+d x)+b \cosh (c+d x))}{d \left(a^2-b^2\right)}",1,"(a*x)/(a^2 - b^2) - (b*Log[b*Cosh[c + d*x] + a*Sinh[c + d*x]])/((a^2 - b^2)*d)","A",2,2,12,0.1667,1,"{3484, 3530}"
82,1,85,0,0.0946267,"\int \frac{1}{(a+b \coth (c+d x))^2} \, dx","Int[(a + b*Coth[c + d*x])^(-2),x]","\frac{b}{d \left(a^2-b^2\right) (a+b \coth (c+d x))}-\frac{2 a b \log (a \sinh (c+d x)+b \cosh (c+d x))}{d \left(a^2-b^2\right)^2}+\frac{x \left(a^2+b^2\right)}{\left(a^2-b^2\right)^2}","\frac{b}{d \left(a^2-b^2\right) (a+b \coth (c+d x))}-\frac{2 a b \log (a \sinh (c+d x)+b \cosh (c+d x))}{d \left(a^2-b^2\right)^2}+\frac{x \left(a^2+b^2\right)}{\left(a^2-b^2\right)^2}",1,"((a^2 + b^2)*x)/(a^2 - b^2)^2 + b/((a^2 - b^2)*d*(a + b*Coth[c + d*x])) - (2*a*b*Log[b*Cosh[c + d*x] + a*Sinh[c + d*x]])/((a^2 - b^2)^2*d)","A",3,3,12,0.2500,1,"{3483, 3531, 3530}"
83,1,129,0,0.1797175,"\int \frac{1}{(a+b \coth (c+d x))^3} \, dx","Int[(a + b*Coth[c + d*x])^(-3),x]","\frac{2 a b}{d \left(a^2-b^2\right)^2 (a+b \coth (c+d x))}+\frac{b}{2 d \left(a^2-b^2\right) (a+b \coth (c+d x))^2}-\frac{b \left(3 a^2+b^2\right) \log (a \sinh (c+d x)+b \cosh (c+d x))}{d \left(a^2-b^2\right)^3}+\frac{a x \left(a^2+3 b^2\right)}{\left(a^2-b^2\right)^3}","\frac{2 a b}{d \left(a^2-b^2\right)^2 (a+b \coth (c+d x))}+\frac{b}{2 d \left(a^2-b^2\right) (a+b \coth (c+d x))^2}-\frac{b \left(3 a^2+b^2\right) \log (a \sinh (c+d x)+b \cosh (c+d x))}{d \left(a^2-b^2\right)^3}+\frac{a x \left(a^2+3 b^2\right)}{\left(a^2-b^2\right)^3}",1,"(a*(a^2 + 3*b^2)*x)/(a^2 - b^2)^3 + b/(2*(a^2 - b^2)*d*(a + b*Coth[c + d*x])^2) + (2*a*b)/((a^2 - b^2)^2*d*(a + b*Coth[c + d*x])) - (b*(3*a^2 + b^2)*Log[b*Cosh[c + d*x] + a*Sinh[c + d*x]])/((a^2 - b^2)^3*d)","A",4,4,12,0.3333,1,"{3483, 3529, 3531, 3530}"
84,1,169,0,0.2642591,"\int \frac{1}{(a+b \coth (c+d x))^4} \, dx","Int[(a + b*Coth[c + d*x])^(-4),x]","\frac{b \left(3 a^2+b^2\right)}{d \left(a^2-b^2\right)^3 (a+b \coth (c+d x))}+\frac{a b}{d \left(a^2-b^2\right)^2 (a+b \coth (c+d x))^2}+\frac{b}{3 d \left(a^2-b^2\right) (a+b \coth (c+d x))^3}-\frac{4 a b \left(a^2+b^2\right) \log (a \sinh (c+d x)+b \cosh (c+d x))}{d \left(a^2-b^2\right)^4}+\frac{x \left(6 a^2 b^2+a^4+b^4\right)}{\left(a^2-b^2\right)^4}","\frac{b \left(3 a^2+b^2\right)}{d \left(a^2-b^2\right)^3 (a+b \coth (c+d x))}+\frac{a b}{d \left(a^2-b^2\right)^2 (a+b \coth (c+d x))^2}+\frac{b}{3 d \left(a^2-b^2\right) (a+b \coth (c+d x))^3}-\frac{4 a b \left(a^2+b^2\right) \log (a \sinh (c+d x)+b \cosh (c+d x))}{d \left(a^2-b^2\right)^4}+\frac{x \left(6 a^2 b^2+a^4+b^4\right)}{\left(a^2-b^2\right)^4}",1,"((a^4 + 6*a^2*b^2 + b^4)*x)/(a^2 - b^2)^4 + b/(3*(a^2 - b^2)*d*(a + b*Coth[c + d*x])^3) + (a*b)/((a^2 - b^2)^2*d*(a + b*Coth[c + d*x])^2) + (b*(3*a^2 + b^2))/((a^2 - b^2)^3*d*(a + b*Coth[c + d*x])) - (4*a*b*(a^2 + b^2)*Log[b*Cosh[c + d*x] + a*Sinh[c + d*x]])/((a^2 - b^2)^4*d)","A",5,4,12,0.3333,1,"{3483, 3529, 3531, 3530}"
85,1,31,0,0.0438151,"\int \frac{1}{4+6 \coth (c+d x)} \, dx","Int[(4 + 6*Coth[c + d*x])^(-1),x]","\frac{3 \log (2 \sinh (c+d x)+3 \cosh (c+d x))}{10 d}-\frac{x}{5}","\frac{3 \log (2 \sinh (c+d x)+3 \cosh (c+d x))}{10 d}-\frac{x}{5}",1,"-x/5 + (3*Log[3*Cosh[c + d*x] + 2*Sinh[c + d*x]])/(10*d)","A",2,2,12,0.1667,1,"{3484, 3530}"
86,1,31,0,0.0424359,"\int \frac{1}{4-6 \coth (c+d x)} \, dx","Int[(4 - 6*Coth[c + d*x])^(-1),x]","-\frac{3 \log (3 \cosh (c+d x)-2 \sinh (c+d x))}{10 d}-\frac{x}{5}","-\frac{3 \log (3 \cosh (c+d x)-2 \sinh (c+d x))}{10 d}-\frac{x}{5}",1,"-x/5 - (3*Log[3*Cosh[c + d*x] - 2*Sinh[c + d*x]])/(10*d)","A",2,2,12,0.1667,1,"{3484, 3530}"
87,1,74,0,0.0700508,"\int \sqrt{a+b \coth (c+d x)} \, dx","Int[Sqrt[a + b*Coth[c + d*x]],x]","\frac{\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth (c+d x)}}{\sqrt{a+b}}\right)}{d}-\frac{\sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth (c+d x)}}{\sqrt{a-b}}\right)}{d}","\frac{\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth (c+d x)}}{\sqrt{a+b}}\right)}{d}-\frac{\sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth (c+d x)}}{\sqrt{a-b}}\right)}{d}",1,"-((Sqrt[a - b]*ArcTanh[Sqrt[a + b*Coth[c + d*x]]/Sqrt[a - b]])/d) + (Sqrt[a + b]*ArcTanh[Sqrt[a + b*Coth[c + d*x]]/Sqrt[a + b]])/d","A",5,4,14,0.2857,1,"{3485, 700, 1130, 207}"
88,1,74,0,0.0678776,"\int \frac{1}{\sqrt{a+b \coth (c+d x)}} \, dx","Int[1/Sqrt[a + b*Coth[c + d*x]],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth (c+d x)}}{\sqrt{a+b}}\right)}{d \sqrt{a+b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth (c+d x)}}{\sqrt{a-b}}\right)}{d \sqrt{a-b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth (c+d x)}}{\sqrt{a+b}}\right)}{d \sqrt{a+b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth (c+d x)}}{\sqrt{a-b}}\right)}{d \sqrt{a-b}}",1,"-(ArcTanh[Sqrt[a + b*Coth[c + d*x]]/Sqrt[a - b]]/(Sqrt[a - b]*d)) + ArcTanh[Sqrt[a + b*Coth[c + d*x]]/Sqrt[a + b]]/(Sqrt[a + b]*d)","A",5,4,14,0.2857,1,"{3485, 708, 1093, 207}"
89,1,60,0,0.062674,"\int \frac{\sinh ^4(x)}{1+\coth (x)} \, dx","Int[Sinh[x]^4/(1 + Coth[x]),x]","\frac{5 x}{16}+\frac{1}{8 (1-\coth (x))}-\frac{3}{16 (\coth (x)+1)}+\frac{1}{32 (1-\coth (x))^2}-\frac{3}{32 (\coth (x)+1)^2}-\frac{1}{24 (\coth (x)+1)^3}","\frac{5 x}{16}+\frac{1}{8 (1-\coth (x))}-\frac{3}{16 (\coth (x)+1)}+\frac{1}{32 (1-\coth (x))^2}-\frac{3}{32 (\coth (x)+1)^2}-\frac{1}{24 (\coth (x)+1)^3}",1,"(5*x)/16 + 1/(32*(1 - Coth[x])^2) + 1/(8*(1 - Coth[x])) - 1/(24*(1 + Coth[x])^3) - 3/(32*(1 + Coth[x])^2) - 3/(16*(1 + Coth[x]))","A",4,3,11,0.2727,1,"{3487, 44, 207}"
90,1,29,0,0.0474609,"\int \frac{\sinh ^3(x)}{1+\coth (x)} \, dx","Int[Sinh[x]^3/(1 + Coth[x]),x]","\frac{4 \cosh ^3(x)}{15}-\frac{4 \cosh (x)}{5}-\frac{\sinh ^3(x)}{5 (\coth (x)+1)}","\frac{4 \cosh ^3(x)}{15}-\frac{4 \cosh (x)}{5}-\frac{\sinh ^3(x)}{5 (\coth (x)+1)}",1,"(-4*Cosh[x])/5 + (4*Cosh[x]^3)/15 - Sinh[x]^3/(5*(1 + Coth[x]))","A",3,2,11,0.1818,1,"{3502, 2633}"
91,1,38,0,0.0522239,"\int \frac{\sinh ^2(x)}{1+\coth (x)} \, dx","Int[Sinh[x]^2/(1 + Coth[x]),x]","-\frac{3 x}{8}-\frac{1}{8 (1-\coth (x))}+\frac{1}{4 (\coth (x)+1)}+\frac{1}{8 (\coth (x)+1)^2}","-\frac{3 x}{8}-\frac{1}{8 (1-\coth (x))}+\frac{1}{4 (\coth (x)+1)}+\frac{1}{8 (\coth (x)+1)^2}",1,"(-3*x)/8 - 1/(8*(1 - Coth[x])) + 1/(8*(1 + Coth[x])^2) + 1/(4*(1 + Coth[x]))","A",4,3,11,0.2727,1,"{3487, 44, 207}"
92,1,19,0,0.0355857,"\int \frac{\sinh (x)}{1+\coth (x)} \, dx","Int[Sinh[x]/(1 + Coth[x]),x]","\frac{2 \cosh (x)}{3}-\frac{\sinh (x)}{3 (\coth (x)+1)}","\frac{2 \cosh (x)}{3}-\frac{\sinh (x)}{3 (\coth (x)+1)}",1,"(2*Cosh[x])/3 - Sinh[x]/(3*(1 + Coth[x]))","A",2,2,9,0.2222,1,"{3502, 2638}"
93,1,10,0,0.0221637,"\int \frac{\text{csch}(x)}{1+\coth (x)} \, dx","Int[Csch[x]/(1 + Coth[x]),x]","-\frac{\text{csch}(x)}{\coth (x)+1}","-\frac{\text{csch}(x)}{\coth (x)+1}",1,"-(Csch[x]/(1 + Coth[x]))","A",1,1,9,0.1111,1,"{3488}"
94,1,7,0,0.0357077,"\int \frac{\text{csch}^2(x)}{1+\coth (x)} \, dx","Int[Csch[x]^2/(1 + Coth[x]),x]","-\log (\coth (x)+1)","-\log (\coth (x)+1)",1,"-Log[1 + Coth[x]]","A",2,2,11,0.1818,1,"{3487, 31}"
95,1,8,0,0.0400128,"\int \frac{\text{csch}^3(x)}{1+\coth (x)} \, dx","Int[Csch[x]^3/(1 + Coth[x]),x]","\tanh ^{-1}(\cosh (x))-\text{csch}(x)","\tanh ^{-1}(\cosh (x))-\text{csch}(x)",1,"ArcTanh[Cosh[x]] - Csch[x]","A",2,2,11,0.1818,1,"{3501, 3770}"
96,1,11,0,0.0343565,"\int \frac{\text{csch}^4(x)}{1+\coth (x)} \, dx","Int[Csch[x]^4/(1 + Coth[x]),x]","\coth (x)-\frac{\coth ^2(x)}{2}","\coth (x)-\frac{\coth ^2(x)}{2}",1,"Coth[x] - Coth[x]^2/2","A",2,1,11,0.09091,1,"{3487}"
97,1,155,0,0.2399744,"\int \frac{\sinh ^4(x)}{a+b \coth (x)} \, dx","Int[Sinh[x]^4/(a + b*Coth[x]),x]","-\frac{b^5 \log (a+b \coth (x))}{\left(a^2-b^2\right)^3}-\frac{\left(3 a^2+9 a b+8 b^2\right) \log (1-\coth (x))}{16 (a+b)^3}+\frac{\left(3 a^2-9 a b+8 b^2\right) \log (\coth (x)+1)}{16 (a-b)^3}-\frac{\sinh ^4(x) (b-a \coth (x))}{4 \left(a^2-b^2\right)}-\frac{\sinh ^2(x) \left(4 b^3-a b^2 \left(7-\frac{3 a^2}{b^2}\right) \coth (x)\right)}{8 \left(a^2-b^2\right)^2}","-\frac{b^5 \log (a+b \coth (x))}{\left(a^2-b^2\right)^3}-\frac{\left(3 a^2+9 a b+8 b^2\right) \log (1-\coth (x))}{16 (a+b)^3}+\frac{\left(3 a^2-9 a b+8 b^2\right) \log (\coth (x)+1)}{16 (a-b)^3}-\frac{\sinh ^4(x) (b-a \coth (x))}{4 \left(a^2-b^2\right)}-\frac{\sinh ^2(x) \left(4 b^3-a b^2 \left(7-\frac{3 a^2}{b^2}\right) \coth (x)\right)}{8 \left(a^2-b^2\right)^2}",1,"-((3*a^2 + 9*a*b + 8*b^2)*Log[1 - Coth[x]])/(16*(a + b)^3) + ((3*a^2 - 9*a*b + 8*b^2)*Log[1 + Coth[x]])/(16*(a - b)^3) - (b^5*Log[a + b*Coth[x]])/(a^2 - b^2)^3 - ((4*b^3 - a*(7 - (3*a^2)/b^2)*b^2*Coth[x])*Sinh[x]^2)/(8*(a^2 - b^2)^2) - ((b - a*Coth[x])*Sinh[x]^4)/(4*(a^2 - b^2))","A",5,4,13,0.3077,1,"{3506, 741, 823, 801}"
98,1,134,0,0.2373687,"\int \frac{\sinh ^3(x)}{a+b \coth (x)} \, dx","Int[Sinh[x]^3/(a + b*Coth[x]),x]","-\frac{b \sinh ^3(x)}{3 \left(a^2-b^2\right)}-\frac{b^3 \sinh (x)}{\left(a^2-b^2\right)^2}+\frac{a \cosh ^3(x)}{3 \left(a^2-b^2\right)}+\frac{a b^2 \cosh (x)}{\left(a^2-b^2\right)^2}-\frac{a \cosh (x)}{a^2-b^2}-\frac{b^4 \tanh ^{-1}\left(\frac{\sinh (x) (a \coth (x)+b)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}","-\frac{b \sinh ^3(x)}{3 \left(a^2-b^2\right)}-\frac{b^3 \sinh (x)}{\left(a^2-b^2\right)^2}+\frac{a \cosh ^3(x)}{3 \left(a^2-b^2\right)}+\frac{a b^2 \cosh (x)}{\left(a^2-b^2\right)^2}-\frac{a \cosh (x)}{a^2-b^2}-\frac{b^4 \tanh ^{-1}\left(\frac{\sinh (x) (a \coth (x)+b)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}",1,"-((b^4*ArcTanh[((b + a*Coth[x])*Sinh[x])/Sqrt[a^2 - b^2]])/(a^2 - b^2)^(5/2)) + (a*b^2*Cosh[x])/(a^2 - b^2)^2 - (a*Cosh[x])/(a^2 - b^2) + (a*Cosh[x]^3)/(3*(a^2 - b^2)) - (b^3*Sinh[x])/(a^2 - b^2)^2 - (b*Sinh[x]^3)/(3*(a^2 - b^2))","A",9,6,13,0.4615,1,"{3511, 3486, 2633, 2638, 3509, 206}"
99,1,92,0,0.1415635,"\int \frac{\sinh ^2(x)}{a+b \coth (x)} \, dx","Int[Sinh[x]^2/(a + b*Coth[x]),x]","-\frac{b^3 \log (a+b \coth (x))}{\left(a^2-b^2\right)^2}-\frac{\sinh ^2(x) (b-a \coth (x))}{2 \left(a^2-b^2\right)}+\frac{(a+2 b) \log (1-\coth (x))}{4 (a+b)^2}-\frac{(a-2 b) \log (\coth (x)+1)}{4 (a-b)^2}","-\frac{b^3 \log (a+b \coth (x))}{\left(a^2-b^2\right)^2}-\frac{\sinh ^2(x) (b-a \coth (x))}{2 \left(a^2-b^2\right)}+\frac{(a+2 b) \log (1-\coth (x))}{4 (a+b)^2}-\frac{(a-2 b) \log (\coth (x)+1)}{4 (a-b)^2}",1,"((a + 2*b)*Log[1 - Coth[x]])/(4*(a + b)^2) - ((a - 2*b)*Log[1 + Coth[x]])/(4*(a - b)^2) - (b^3*Log[a + b*Coth[x]])/(a^2 - b^2)^2 - ((b - a*Coth[x])*Sinh[x]^2)/(2*(a^2 - b^2))","A",4,3,13,0.2308,1,"{3506, 741, 801}"
100,1,73,0,0.1067473,"\int \frac{\sinh (x)}{a+b \coth (x)} \, dx","Int[Sinh[x]/(a + b*Coth[x]),x]","-\frac{b \sinh (x)}{a^2-b^2}+\frac{a \cosh (x)}{a^2-b^2}-\frac{b^2 \tanh ^{-1}\left(\frac{\sinh (x) (a \coth (x)+b)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2}}","-\frac{b \sinh (x)}{a^2-b^2}+\frac{a \cosh (x)}{a^2-b^2}-\frac{b^2 \tanh ^{-1}\left(\frac{\sinh (x) (a \coth (x)+b)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2}}",1,"-((b^2*ArcTanh[((b + a*Coth[x])*Sinh[x])/Sqrt[a^2 - b^2]])/(a^2 - b^2)^(3/2)) + (a*Cosh[x])/(a^2 - b^2) - (b*Sinh[x])/(a^2 - b^2)","A",5,5,11,0.4545,1,"{3511, 3486, 2638, 3509, 206}"
101,1,38,0,0.035892,"\int \frac{\text{csch}(x)}{a+b \coth (x)} \, dx","Int[Csch[x]/(a + b*Coth[x]),x]","-\frac{\tanh ^{-1}\left(\frac{\sinh (x) (a \coth (x)+b)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}","-\frac{\tanh ^{-1}\left(\frac{\sinh (x) (a \coth (x)+b)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}",1,"-(ArcTanh[((b + a*Coth[x])*Sinh[x])/Sqrt[a^2 - b^2]]/Sqrt[a^2 - b^2])","A",2,2,11,0.1818,1,"{3509, 206}"
102,1,12,0,0.0438356,"\int \frac{\text{csch}^2(x)}{a+b \coth (x)} \, dx","Int[Csch[x]^2/(a + b*Coth[x]),x]","-\frac{\log (a+b \coth (x))}{b}","-\frac{\log (a+b \coth (x))}{b}",1,"-(Log[a + b*Coth[x]]/b)","A",2,2,13,0.1538,1,"{3506, 31}"
103,1,57,0,0.1091731,"\int \frac{\text{csch}^3(x)}{a+b \coth (x)} \, dx","Int[Csch[x]^3/(a + b*Coth[x]),x]","-\frac{\sqrt{a^2-b^2} \tanh ^{-1}\left(\frac{\sinh (x) (a \coth (x)+b)}{\sqrt{a^2-b^2}}\right)}{b^2}+\frac{a \tanh ^{-1}(\cosh (x))}{b^2}-\frac{\text{csch}(x)}{b}","-\frac{\sqrt{a^2-b^2} \tanh ^{-1}\left(\frac{\sinh (x) (a \coth (x)+b)}{\sqrt{a^2-b^2}}\right)}{b^2}+\frac{a \tanh ^{-1}(\cosh (x))}{b^2}-\frac{\text{csch}(x)}{b}",1,"(a*ArcTanh[Cosh[x]])/b^2 - (Sqrt[a^2 - b^2]*ArcTanh[((b + a*Coth[x])*Sinh[x])/Sqrt[a^2 - b^2]])/b^2 - Csch[x]/b","A",5,5,13,0.3846,1,"{3510, 3486, 3770, 3509, 206}"
104,1,40,0,0.0674236,"\int \frac{\text{csch}^4(x)}{a+b \coth (x)} \, dx","Int[Csch[x]^4/(a + b*Coth[x]),x]","-\frac{\left(a^2-b^2\right) \log (a+b \coth (x))}{b^3}+\frac{a \coth (x)}{b^2}-\frac{\coth ^2(x)}{2 b}","-\frac{\left(a^2-b^2\right) \log (a+b \coth (x))}{b^3}+\frac{a \coth (x)}{b^2}-\frac{\coth ^2(x)}{2 b}",1,"(a*Coth[x])/b^2 - Coth[x]^2/(2*b) - ((a^2 - b^2)*Log[a + b*Coth[x]])/b^3","A",3,2,13,0.1538,1,"{3506, 697}"
105,1,60,0,0.0669269,"\int \frac{\cosh ^4(x)}{1+\coth (x)} \, dx","Int[Cosh[x]^4/(1 + Coth[x]),x]","\frac{x}{16}-\frac{1}{8 (1-\coth (x))}-\frac{3}{16 (\coth (x)+1)}+\frac{1}{32 (1-\coth (x))^2}+\frac{5}{32 (\coth (x)+1)^2}-\frac{1}{24 (\coth (x)+1)^3}","\frac{x}{16}-\frac{1}{8 (1-\coth (x))}-\frac{3}{16 (\coth (x)+1)}+\frac{1}{32 (1-\coth (x))^2}+\frac{5}{32 (\coth (x)+1)^2}-\frac{1}{24 (\coth (x)+1)^3}",1,"x/16 + 1/(32*(1 - Coth[x])^2) - 1/(8*(1 - Coth[x])) - 1/(24*(1 + Coth[x])^3) + 5/(32*(1 + Coth[x])^2) - 3/(16*(1 + Coth[x]))","A",5,4,11,0.3636,1,"{3516, 848, 88, 207}"
106,1,25,0,0.1768298,"\int \frac{\cosh ^3(x)}{1+\coth (x)} \, dx","Int[Cosh[x]^3/(1 + Coth[x]),x]","-\frac{\sinh ^5(x)}{5}-\frac{\sinh ^3(x)}{3}+\frac{\cosh ^5(x)}{5}","-\frac{\sinh ^5(x)}{5}-\frac{\sinh ^3(x)}{3}+\frac{\cosh ^5(x)}{5}",1,"Cosh[x]^5/5 - Sinh[x]^3/3 - Sinh[x]^5/5","A",9,7,11,0.6364,1,"{3518, 3108, 3107, 2565, 30, 2564, 14}"
107,1,38,0,0.0592763,"\int \frac{\cosh ^2(x)}{1+\coth (x)} \, dx","Int[Cosh[x]^2/(1 + Coth[x]),x]","\frac{x}{8}-\frac{1}{8 (1-\coth (x))}-\frac{1}{4 (\coth (x)+1)}+\frac{1}{8 (\coth (x)+1)^2}","\frac{x}{8}-\frac{1}{8 (1-\coth (x))}-\frac{1}{4 (\coth (x)+1)}+\frac{1}{8 (\coth (x)+1)^2}",1,"x/8 - 1/(8*(1 - Coth[x])) + 1/(8*(1 + Coth[x])^2) - 1/(4*(1 + Coth[x]))","A",5,4,11,0.3636,1,"{3516, 848, 88, 207}"
108,1,17,0,0.1134006,"\int \frac{\cosh (x)}{1+\coth (x)} \, dx","Int[Cosh[x]/(1 + Coth[x]),x]","\frac{\cosh ^3(x)}{3}-\frac{\sinh ^3(x)}{3}","\frac{\cosh ^3(x)}{3}-\frac{\sinh ^3(x)}{3}",1,"Cosh[x]^3/3 - Sinh[x]^3/3","A",8,6,9,0.6667,1,"{3518, 3108, 3107, 2565, 30, 2564}"
109,1,10,0,0.114155,"\int \frac{\text{sech}(x)}{1+\coth (x)} \, dx","Int[Sech[x]/(1 + Coth[x]),x]","-\sinh (x)+\cosh (x)+\tan ^{-1}(\sinh (x))","-\sinh (x)+\cosh (x)+\tan ^{-1}(\sinh (x))",1,"ArcTan[Sinh[x]] + Cosh[x] - Sinh[x]","A",8,7,9,0.7778,1,"{3518, 3108, 3107, 2638, 2592, 321, 203}"
110,1,15,0,0.0411416,"\int \frac{\text{sech}^2(x)}{1+\coth (x)} \, dx","Int[Sech[x]^2/(1 + Coth[x]),x]","\tanh (x)-\log (\tanh (x))-\log (\coth (x)+1)","\tanh (x)-\log (\tanh (x))-\log (\coth (x)+1)",1,"-Log[1 + Coth[x]] - Log[Tanh[x]] + Tanh[x]","A",3,2,11,0.1818,1,"{3516, 44}"
111,1,20,0,0.1673091,"\int \frac{\text{sech}^3(x)}{1+\coth (x)} \, dx","Int[Sech[x]^3/(1 + Coth[x]),x]","-\text{sech}(x)-\frac{1}{2} \tan ^{-1}(\sinh (x))+\frac{1}{2} \tanh (x) \text{sech}(x)","-\text{sech}(x)-\frac{1}{2} \tan ^{-1}(\sinh (x))+\frac{1}{2} \tanh (x) \text{sech}(x)",1,"-ArcTan[Sinh[x]]/2 - Sech[x] + (Sech[x]*Tanh[x])/2","A",8,7,11,0.6364,1,"{3518, 3108, 3107, 2606, 8, 2611, 3770}"
112,1,17,0,0.0454175,"\int \frac{\text{sech}^4(x)}{1+\coth (x)} \, dx","Int[Sech[x]^4/(1 + Coth[x]),x]","\frac{\tanh ^2(x)}{2}-\frac{\tanh ^3(x)}{3}","\frac{\tanh ^2(x)}{2}-\frac{\tanh ^3(x)}{3}",1,"Tanh[x]^2/2 - Tanh[x]^3/3","A",4,3,11,0.2727,1,"{3516, 848, 43}"
113,1,21,0,0.045848,"\int \sqrt{1+\coth (x)} \text{sech}^2(x) \, dx","Int[Sqrt[1 + Coth[x]]*Sech[x]^2,x]","\tanh ^{-1}\left(\sqrt{\coth (x)+1}\right)+\tanh (x) \sqrt{\coth (x)+1}","\tanh ^{-1}\left(\sqrt{\coth (x)+1}\right)+\tanh (x) \sqrt{\coth (x)+1}",1,"ArcTanh[Sqrt[1 + Coth[x]]] + Sqrt[1 + Coth[x]]*Tanh[x]","A",4,4,13,0.3077,1,"{3516, 47, 63, 207}"
114,1,147,0,0.339408,"\int \frac{\cosh ^4(x)}{a+b \coth (x)} \, dx","Int[Cosh[x]^4/(a + b*Coth[x]),x]","-\frac{a^4 b \log (a+b \coth (x))}{\left(a^2-b^2\right)^3}-\frac{\sinh ^4(x) (b-a \coth (x))}{4 \left(a^2-b^2\right)}-\frac{\sinh ^2(x) \left(4 b \left(2 a^2-b^2\right)-a \left(5 a^2-b^2\right) \coth (x)\right)}{8 \left(a^2-b^2\right)^2}-\frac{a (3 a+b) \log (1-\coth (x))}{16 (a+b)^3}+\frac{a (3 a-b) \log (\coth (x)+1)}{16 (a-b)^3}","-\frac{a^4 b \log (a+b \coth (x))}{\left(a^2-b^2\right)^3}-\frac{\sinh ^4(x) (b-a \coth (x))}{4 \left(a^2-b^2\right)}-\frac{\sinh ^2(x) \left(4 b \left(2 a^2-b^2\right)-a \left(5 a^2-b^2\right) \coth (x)\right)}{8 \left(a^2-b^2\right)^2}-\frac{a (3 a+b) \log (1-\coth (x))}{16 (a+b)^3}+\frac{a (3 a-b) \log (\coth (x)+1)}{16 (a-b)^3}",1,"-(a*(3*a + b)*Log[1 - Coth[x]])/(16*(a + b)^3) + (a*(3*a - b)*Log[1 + Coth[x]])/(16*(a - b)^3) - (a^4*b*Log[a + b*Coth[x]])/(a^2 - b^2)^3 - ((4*b*(2*a^2 - b^2) - a*(5*a^2 - b^2)*Coth[x])*Sinh[x]^2)/(8*(a^2 - b^2)^2) - ((b - a*Coth[x])*Sinh[x]^4)/(4*(a^2 - b^2))","A",5,3,13,0.2308,1,"{3516, 1647, 801}"
115,1,135,0,0.2508809,"\int \frac{\cosh ^3(x)}{a+b \coth (x)} \, dx","Int[Cosh[x]^3/(a + b*Coth[x]),x]","\frac{a \sinh ^3(x)}{3 \left(a^2-b^2\right)}+\frac{a \sinh (x)}{a^2-b^2}+\frac{a b^2 \sinh (x)}{\left(a^2-b^2\right)^2}-\frac{b \cosh ^3(x)}{3 \left(a^2-b^2\right)}-\frac{a^2 b \cosh (x)}{\left(a^2-b^2\right)^2}+\frac{a^3 b \tanh ^{-1}\left(\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}","\frac{a \sinh ^3(x)}{3 \left(a^2-b^2\right)}+\frac{a \sinh (x)}{a^2-b^2}+\frac{a b^2 \sinh (x)}{\left(a^2-b^2\right)^2}-\frac{b \cosh ^3(x)}{3 \left(a^2-b^2\right)}-\frac{a^2 b \cosh (x)}{\left(a^2-b^2\right)^2}+\frac{a^3 b \tanh ^{-1}\left(\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}",1,"(a^3*b*ArcTanh[(a*Cosh[x] + b*Sinh[x])/Sqrt[a^2 - b^2]])/(a^2 - b^2)^(5/2) - (a^2*b*Cosh[x])/(a^2 - b^2)^2 - (b*Cosh[x]^3)/(3*(a^2 - b^2)) + (a*b^2*Sinh[x])/(a^2 - b^2)^2 + (a*Sinh[x])/(a^2 - b^2) + (a*Sinh[x]^3)/(3*(a^2 - b^2))","A",10,9,13,0.6923,1,"{3518, 3109, 2633, 2565, 30, 3100, 2637, 3074, 206}"
116,1,85,0,0.1637907,"\int \frac{\cosh ^2(x)}{a+b \coth (x)} \, dx","Int[Cosh[x]^2/(a + b*Coth[x]),x]","-\frac{a^2 b \log (a+b \coth (x))}{\left(a^2-b^2\right)^2}-\frac{\sinh ^2(x) (b-a \coth (x))}{2 \left(a^2-b^2\right)}-\frac{a \log (1-\coth (x))}{4 (a+b)^2}+\frac{a \log (\coth (x)+1)}{4 (a-b)^2}","-\frac{a^2 b \log (a+b \coth (x))}{\left(a^2-b^2\right)^2}-\frac{\sinh ^2(x) (b-a \coth (x))}{2 \left(a^2-b^2\right)}-\frac{a \log (1-\coth (x))}{4 (a+b)^2}+\frac{a \log (\coth (x)+1)}{4 (a-b)^2}",1,"-(a*Log[1 - Coth[x]])/(4*(a + b)^2) + (a*Log[1 + Coth[x]])/(4*(a - b)^2) - (a^2*b*Log[a + b*Coth[x]])/(a^2 - b^2)^2 - ((b - a*Coth[x])*Sinh[x]^2)/(2*(a^2 - b^2))","A",4,3,13,0.2308,1,"{3516, 1647, 801}"
117,1,72,0,0.1124248,"\int \frac{\cosh (x)}{a+b \coth (x)} \, dx","Int[Cosh[x]/(a + b*Coth[x]),x]","\frac{a \sinh (x)}{a^2-b^2}-\frac{b \cosh (x)}{a^2-b^2}+\frac{a b \tanh ^{-1}\left(\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2}}","\frac{a \sinh (x)}{a^2-b^2}-\frac{b \cosh (x)}{a^2-b^2}+\frac{a b \tanh ^{-1}\left(\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2}}",1,"(a*b*ArcTanh[(a*Cosh[x] + b*Sinh[x])/Sqrt[a^2 - b^2]])/(a^2 - b^2)^(3/2) - (b*Cosh[x])/(a^2 - b^2) + (a*Sinh[x])/(a^2 - b^2)","A",6,6,11,0.5455,1,"{3518, 3109, 2637, 2638, 3074, 206}"
118,1,50,0,0.1384115,"\int \frac{\text{sech}(x)}{a+b \coth (x)} \, dx","Int[Sech[x]/(a + b*Coth[x]),x]","\frac{b \tanh ^{-1}\left(\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}\right)}{a \sqrt{a^2-b^2}}+\frac{\tan ^{-1}(\sinh (x))}{a}","\frac{b \tanh ^{-1}\left(\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}\right)}{a \sqrt{a^2-b^2}}+\frac{\tan ^{-1}(\sinh (x))}{a}",1,"ArcTan[Sinh[x]]/a + (b*ArcTanh[(a*Cosh[x] + b*Sinh[x])/Sqrt[a^2 - b^2]])/(a*Sqrt[a^2 - b^2])","A",6,5,11,0.4545,1,"{3518, 3110, 3770, 3074, 206}"
119,1,29,0,0.0554407,"\int \frac{\text{sech}^2(x)}{a+b \coth (x)} \, dx","Int[Sech[x]^2/(a + b*Coth[x]),x]","-\frac{b \log (\tanh (x))}{a^2}-\frac{b \log (a+b \coth (x))}{a^2}+\frac{\tanh (x)}{a}","-\frac{b \log (\tanh (x))}{a^2}-\frac{b \log (a+b \coth (x))}{a^2}+\frac{\tanh (x)}{a}",1,"-((b*Log[a + b*Coth[x]])/a^2) - (b*Log[Tanh[x]])/a^2 + Tanh[x]/a","A",3,2,13,0.1538,1,"{3516, 44}"
120,1,83,0,0.2370531,"\int \frac{\text{sech}^3(x)}{a+b \coth (x)} \, dx","Int[Sech[x]^3/(a + b*Coth[x]),x]","-\frac{b^2 \tan ^{-1}(\sinh (x))}{a^3}+\frac{b \sqrt{a^2-b^2} \tanh ^{-1}\left(\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}\right)}{a^3}-\frac{b \text{sech}(x)}{a^2}+\frac{\tan ^{-1}(\sinh (x))}{2 a}+\frac{\tanh (x) \text{sech}(x)}{2 a}","-\frac{b^2 \tan ^{-1}(\sinh (x))}{a^3}+\frac{b \sqrt{a^2-b^2} \tanh ^{-1}\left(\frac{a \cosh (x)+b \sinh (x)}{\sqrt{a^2-b^2}}\right)}{a^3}-\frac{b \text{sech}(x)}{a^2}+\frac{\tan ^{-1}(\sinh (x))}{2 a}+\frac{\tanh (x) \text{sech}(x)}{2 a}",1,"ArcTan[Sinh[x]]/(2*a) - (b^2*ArcTan[Sinh[x]])/a^3 + (b*Sqrt[a^2 - b^2]*ArcTanh[(a*Cosh[x] + b*Sinh[x])/Sqrt[a^2 - b^2]])/a^3 - (b*Sech[x])/a^2 + (Sech[x]*Tanh[x])/(2*a)","A",9,7,13,0.5385,1,"{3518, 3110, 3768, 3770, 3104, 3074, 206}"
121,1,79,0,0.099762,"\int \frac{\text{sech}^4(x)}{a+b \coth (x)} \, dx","Int[Sech[x]^4/(a + b*Coth[x]),x]","\frac{\left(a^2-b^2\right) \tanh (x)}{a^3}-\frac{b \left(a^2-b^2\right) \log (\tanh (x))}{a^4}-\frac{b \left(a^2-b^2\right) \log (a+b \coth (x))}{a^4}+\frac{b \tanh ^2(x)}{2 a^2}-\frac{\tanh ^3(x)}{3 a}","\frac{\left(a^2-b^2\right) \tanh (x)}{a^3}-\frac{b \left(a^2-b^2\right) \log (\tanh (x))}{a^4}-\frac{b \left(a^2-b^2\right) \log (a+b \coth (x))}{a^4}+\frac{b \tanh ^2(x)}{2 a^2}-\frac{\tanh ^3(x)}{3 a}",1,"-((b*(a^2 - b^2)*Log[a + b*Coth[x]])/a^4) - (b*(a^2 - b^2)*Log[Tanh[x]])/a^4 + ((a^2 - b^2)*Tanh[x])/a^3 + (b*Tanh[x]^2)/(2*a^2) - Tanh[x]^3/(3*a)","A",3,2,13,0.1538,1,"{3516, 894}"
122,1,31,0,0.1033162,"\int \frac{\text{sech}(x)}{i+2 \coth (x)} \, dx","Int[Sech[x]/(I + 2*Coth[x]),x]","-i \tan ^{-1}(\sinh (x))-\frac{2 \tanh ^{-1}\left(\frac{\cosh (x)-2 i \sinh (x)}{\sqrt{5}}\right)}{\sqrt{5}}","-i \tan ^{-1}(\sinh (x))-\frac{2 \tanh ^{-1}\left(\frac{\cosh (x)-2 i \sinh (x)}{\sqrt{5}}\right)}{\sqrt{5}}",1,"(-I)*ArcTan[Sinh[x]] - (2*ArcTanh[(Cosh[x] - (2*I)*Sinh[x])/Sqrt[5]])/Sqrt[5]","A",6,5,13,0.3846,1,"{3518, 3110, 3770, 3074, 206}"
123,1,43,0,0.1146137,"\int \frac{\tanh ^4(x)}{1+\coth (x)} \, dx","Int[Tanh[x]^4/(1 + Coth[x]),x]","\frac{5 x}{2}-\frac{5 \tanh ^3(x)}{6}+\tanh ^2(x)-\frac{5 \tanh (x)}{2}-2 \log (\cosh (x))+\frac{\tanh ^3(x)}{2 (\coth (x)+1)}","\frac{5 x}{2}-\frac{5 \tanh ^3(x)}{6}+\tanh ^2(x)-\frac{5 \tanh (x)}{2}-2 \log (\cosh (x))+\frac{\tanh ^3(x)}{2 (\coth (x)+1)}",1,"(5*x)/2 - 2*Log[Cosh[x]] - (5*Tanh[x])/2 + Tanh[x]^2 - (5*Tanh[x]^3)/6 + Tanh[x]^3/(2*(1 + Coth[x]))","A",6,4,11,0.3636,1,"{3552, 3529, 3531, 3475}"
124,1,37,0,0.0991369,"\int \frac{\tanh ^3(x)}{1+\coth (x)} \, dx","Int[Tanh[x]^3/(1 + Coth[x]),x]","-\frac{3 x}{2}-\tanh ^2(x)+\frac{3 \tanh (x)}{2}+2 \log (\cosh (x))+\frac{\tanh ^2(x)}{2 (\coth (x)+1)}","-\frac{3 x}{2}-\tanh ^2(x)+\frac{3 \tanh (x)}{2}+2 \log (\cosh (x))+\frac{\tanh ^2(x)}{2 (\coth (x)+1)}",1,"(-3*x)/2 + 2*Log[Cosh[x]] + (3*Tanh[x])/2 - Tanh[x]^2 + Tanh[x]^2/(2*(1 + Coth[x]))","A",5,4,11,0.3636,1,"{3552, 3529, 3531, 3475}"
125,1,29,0,0.0742931,"\int \frac{\tanh ^2(x)}{1+\coth (x)} \, dx","Int[Tanh[x]^2/(1 + Coth[x]),x]","\frac{3 x}{2}-\frac{3 \tanh (x)}{2}-\log (\cosh (x))+\frac{\tanh (x)}{2 (\coth (x)+1)}","\frac{3 x}{2}-\frac{3 \tanh (x)}{2}-\log (\cosh (x))+\frac{\tanh (x)}{2 (\coth (x)+1)}",1,"(3*x)/2 - Log[Cosh[x]] - (3*Tanh[x])/2 + Tanh[x]/(2*(1 + Coth[x]))","A",4,4,11,0.3636,1,"{3552, 3529, 3531, 3475}"
126,1,19,0,0.0417203,"\int \frac{\tanh (x)}{1+\coth (x)} \, dx","Int[Tanh[x]/(1 + Coth[x]),x]","-\frac{x}{2}+\frac{1}{2 (\coth (x)+1)}+\log (\cosh (x))","-\frac{x}{2}+\frac{1}{2 (\coth (x)+1)}+\log (\cosh (x))",1,"-x/2 + 1/(2*(1 + Coth[x])) + Log[Cosh[x]]","A",4,4,9,0.4444,1,"{3551, 3479, 8, 3475}"
127,1,16,0,0.0083708,"\int \frac{1}{1+\coth (x)} \, dx","Int[(1 + Coth[x])^(-1),x]","\frac{x}{2}-\frac{1}{2 (\coth (x)+1)}","\frac{x}{2}-\frac{1}{2 (\coth (x)+1)}",1,"x/2 - 1/(2*(1 + Coth[x]))","A",2,2,6,0.3333,1,"{3479, 8}"
128,1,16,0,0.0215589,"\int \frac{\coth (x)}{1+\coth (x)} \, dx","Int[Coth[x]/(1 + Coth[x]),x]","\frac{x}{2}+\frac{1}{2 (\coth (x)+1)}","\frac{x}{2}+\frac{1}{2 (\coth (x)+1)}",1,"x/2 + 1/(2*(1 + Coth[x]))","A",2,2,9,0.2222,1,"{3526, 8}"
129,1,19,0,0.0382739,"\int \frac{\coth ^2(x)}{1+\coth (x)} \, dx","Int[Coth[x]^2/(1 + Coth[x]),x]","-\frac{x}{2}-\frac{1}{2 (\coth (x)+1)}+\log (\sinh (x))","-\frac{x}{2}-\frac{1}{2 (\coth (x)+1)}+\log (\sinh (x))",1,"-x/2 - 1/(2*(1 + Coth[x])) + Log[Sinh[x]]","A",3,2,11,0.1818,1,"{3540, 3475}"
130,1,31,0,0.0553428,"\int \frac{\coth ^3(x)}{1+\coth (x)} \, dx","Int[Coth[x]^3/(1 + Coth[x]),x]","\frac{3 x}{2}+\frac{\coth ^2(x)}{2 (\coth (x)+1)}-\frac{3 \coth (x)}{2}-\log (\sinh (x))","\frac{3 x}{2}+\frac{\coth ^2(x)}{2 (\coth (x)+1)}-\frac{3 \coth (x)}{2}-\log (\sinh (x))",1,"(3*x)/2 - (3*Coth[x])/2 + Coth[x]^2/(2*(1 + Coth[x])) - Log[Sinh[x]]","A",3,3,11,0.2727,1,"{3550, 3525, 3475}"
131,1,37,0,0.0677348,"\int \frac{\coth ^4(x)}{1+\coth (x)} \, dx","Int[Coth[x]^4/(1 + Coth[x]),x]","-\frac{3 x}{2}+\frac{\coth ^3(x)}{2 (\coth (x)+1)}-\coth ^2(x)+\frac{3 \coth (x)}{2}+2 \log (\sinh (x))","-\frac{3 x}{2}+\frac{\coth ^3(x)}{2 (\coth (x)+1)}-\coth ^2(x)+\frac{3 \coth (x)}{2}+2 \log (\sinh (x))",1,"(-3*x)/2 + (3*Coth[x])/2 - Coth[x]^2 + Coth[x]^3/(2*(1 + Coth[x])) + 2*Log[Sinh[x]]","A",4,4,11,0.3636,1,"{3550, 3528, 3525, 3475}"
132,1,45,0,0.051792,"\int \coth (x) (1+\coth (x))^{3/2} \, dx","Int[Coth[x]*(1 + Coth[x])^(3/2),x]","-\frac{2}{3} (\coth (x)+1)^{3/2}-2 \sqrt{\coth (x)+1}+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)","-\frac{2}{3} (\coth (x)+1)^{3/2}-2 \sqrt{\coth (x)+1}+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)",1,"2*Sqrt[2]*ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]] - 2*Sqrt[1 + Coth[x]] - (2*(1 + Coth[x])^(3/2))/3","A",4,4,11,0.3636,1,"{3527, 3478, 3480, 206}"
133,1,32,0,0.0381682,"\int \coth (x) \sqrt{1+\coth (x)} \, dx","Int[Coth[x]*Sqrt[1 + Coth[x]],x]","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)-2 \sqrt{\coth (x)+1}","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)-2 \sqrt{\coth (x)+1}",1,"Sqrt[2]*ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]] - 2*Sqrt[1 + Coth[x]]","A",3,3,11,0.2727,1,"{3527, 3480, 206}"
134,1,30,0,0.0386308,"\int \frac{\coth (x)}{\sqrt{1+\coth (x)}} \, dx","Int[Coth[x]/Sqrt[1 + Coth[x]],x]","\frac{1}{\sqrt{\coth (x)+1}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{\sqrt{2}}","\frac{1}{\sqrt{\coth (x)+1}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{\sqrt{2}}",1,"ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]]/Sqrt[2] + 1/Sqrt[1 + Coth[x]]","A",3,3,11,0.2727,1,"{3526, 3480, 206}"
135,1,49,0,0.0508973,"\int \frac{\coth (x)}{(1+\coth (x))^{3/2}} \, dx","Int[Coth[x]/(1 + Coth[x])^(3/2),x]","-\frac{1}{2 \sqrt{\coth (x)+1}}+\frac{1}{3 (\coth (x)+1)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{2 \sqrt{2}}","-\frac{1}{2 \sqrt{\coth (x)+1}}+\frac{1}{3 (\coth (x)+1)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{2 \sqrt{2}}",1,"ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]]/(2*Sqrt[2]) + 1/(3*(1 + Coth[x])^(3/2)) - 1/(2*Sqrt[1 + Coth[x]])","A",4,4,11,0.3636,1,"{3526, 3479, 3480, 206}"
136,1,45,0,0.0628274,"\int \coth ^2(x) (1+\coth (x))^{3/2} \, dx","Int[Coth[x]^2*(1 + Coth[x])^(3/2),x]","-\frac{2}{5} (\coth (x)+1)^{5/2}-2 \sqrt{\coth (x)+1}+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)","-\frac{2}{5} (\coth (x)+1)^{5/2}-2 \sqrt{\coth (x)+1}+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)",1,"2*Sqrt[2]*ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]] - 2*Sqrt[1 + Coth[x]] - (2*(1 + Coth[x])^(5/2))/5","A",4,4,13,0.3077,1,"{3543, 3478, 3480, 206}"
137,1,34,0,0.0478325,"\int \coth ^2(x) \sqrt{1+\coth (x)} \, dx","Int[Coth[x]^2*Sqrt[1 + Coth[x]],x]","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)-\frac{2}{3} (\coth (x)+1)^{3/2}","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)-\frac{2}{3} (\coth (x)+1)^{3/2}",1,"Sqrt[2]*ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]] - (2*(1 + Coth[x])^(3/2))/3","A",3,3,13,0.2308,1,"{3543, 3480, 206}"
138,1,42,0,0.058539,"\int \frac{\coth ^2(x)}{\sqrt{1+\coth (x)}} \, dx","Int[Coth[x]^2/Sqrt[1 + Coth[x]],x]","-2 \sqrt{\coth (x)+1}-\frac{1}{\sqrt{\coth (x)+1}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{\sqrt{2}}","-2 \sqrt{\coth (x)+1}-\frac{1}{\sqrt{\coth (x)+1}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{\sqrt{2}}",1,"ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]]/Sqrt[2] - 1/Sqrt[1 + Coth[x]] - 2*Sqrt[1 + Coth[x]]","A",4,4,13,0.3077,1,"{3543, 3479, 3480, 206}"
139,1,49,0,0.0821066,"\int \frac{\coth ^2(x)}{(1+\coth (x))^{3/2}} \, dx","Int[Coth[x]^2/(1 + Coth[x])^(3/2),x]","\frac{3}{2 \sqrt{\coth (x)+1}}-\frac{1}{3 (\coth (x)+1)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{2 \sqrt{2}}","\frac{3}{2 \sqrt{\coth (x)+1}}-\frac{1}{3 (\coth (x)+1)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\coth (x)+1}}{\sqrt{2}}\right)}{2 \sqrt{2}}",1,"ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]]/(2*Sqrt[2]) - 1/(3*(1 + Coth[x])^(3/2)) + 3/(2*Sqrt[1 + Coth[x]])","A",4,4,13,0.3077,1,"{3540, 3526, 3480, 206}"
140,1,97,0,0.5251958,"\int \frac{\tanh ^4(x)}{a+b \coth (x)} \, dx","Int[Tanh[x]^4/(a + b*Coth[x]),x]","\frac{a x}{a^2-b^2}-\frac{\left(a^2+b^2\right) \tanh (x)}{a^3}-\frac{b \left(a^2+b^2\right) \log (\cosh (x))}{a^4}-\frac{b^5 \log (a \sinh (x)+b \cosh (x))}{a^4 \left(a^2-b^2\right)}+\frac{b \tanh ^2(x)}{2 a^2}-\frac{\tanh ^3(x)}{3 a}","\frac{a x}{a^2-b^2}-\frac{\left(a^2+b^2\right) \tanh (x)}{a^3}-\frac{b \left(a^2+b^2\right) \log (\cosh (x))}{a^4}-\frac{b^5 \log (a \sinh (x)+b \cosh (x))}{a^4 \left(a^2-b^2\right)}+\frac{b \tanh ^2(x)}{2 a^2}-\frac{\tanh ^3(x)}{3 a}",1,"(a*x)/(a^2 - b^2) - (b*(a^2 + b^2)*Log[Cosh[x]])/a^4 - (b^5*Log[b*Cosh[x] + a*Sinh[x]])/(a^4*(a^2 - b^2)) - ((a^2 + b^2)*Tanh[x])/a^3 + (b*Tanh[x]^2)/(2*a^2) - Tanh[x]^3/(3*a)","A",6,6,13,0.4615,1,"{3569, 3649, 3650, 3651, 3530, 3475}"
141,1,76,0,0.3257548,"\int \frac{\tanh ^3(x)}{a+b \coth (x)} \, dx","Int[Tanh[x]^3/(a + b*Coth[x]),x]","-\frac{b x}{a^2-b^2}+\frac{\left(a^2+b^2\right) \log (\cosh (x))}{a^3}+\frac{b^4 \log (a \sinh (x)+b \cosh (x))}{a^3 \left(a^2-b^2\right)}+\frac{b \tanh (x)}{a^2}-\frac{\tanh ^2(x)}{2 a}","-\frac{b x}{a^2-b^2}+\frac{\left(a^2+b^2\right) \log (\cosh (x))}{a^3}+\frac{b^4 \log (a \sinh (x)+b \cosh (x))}{a^3 \left(a^2-b^2\right)}+\frac{b \tanh (x)}{a^2}-\frac{\tanh ^2(x)}{2 a}",1,"-((b*x)/(a^2 - b^2)) + ((a^2 + b^2)*Log[Cosh[x]])/a^3 + (b^4*Log[b*Cosh[x] + a*Sinh[x]])/(a^3*(a^2 - b^2)) + (b*Tanh[x])/a^2 - Tanh[x]^2/(2*a)","A",5,5,13,0.3846,1,"{3569, 3649, 3652, 3530, 3475}"
142,1,60,0,0.1930887,"\int \frac{\tanh ^2(x)}{a+b \coth (x)} \, dx","Int[Tanh[x]^2/(a + b*Coth[x]),x]","\frac{a x}{a^2-b^2}-\frac{b^3 \log (a \sinh (x)+b \cosh (x))}{a^2 \left(a^2-b^2\right)}-\frac{b \log (\cosh (x))}{a^2}-\frac{\tanh (x)}{a}","\frac{a x}{a^2-b^2}-\frac{b^3 \log (a \sinh (x)+b \cosh (x))}{a^2 \left(a^2-b^2\right)}-\frac{b \log (\cosh (x))}{a^2}-\frac{\tanh (x)}{a}",1,"(a*x)/(a^2 - b^2) - (b*Log[Cosh[x]])/a^2 - (b^3*Log[b*Cosh[x] + a*Sinh[x]])/(a^2*(a^2 - b^2)) - Tanh[x]/a","A",4,4,13,0.3077,1,"{3569, 3651, 3530, 3475}"
143,1,51,0,0.0824597,"\int \frac{\tanh (x)}{a+b \coth (x)} \, dx","Int[Tanh[x]/(a + b*Coth[x]),x]","-\frac{b x}{a^2-b^2}+\frac{b^2 \log (a \sinh (x)+b \cosh (x))}{a \left(a^2-b^2\right)}+\frac{\log (\cosh (x))}{a}","-\frac{b x}{a^2-b^2}+\frac{b^2 \log (a \sinh (x)+b \cosh (x))}{a \left(a^2-b^2\right)}+\frac{\log (\cosh (x))}{a}",1,"-((b*x)/(a^2 - b^2)) + Log[Cosh[x]]/a + (b^2*Log[b*Cosh[x] + a*Sinh[x]])/(a*(a^2 - b^2))","A",3,3,11,0.2727,1,"{3571, 3530, 3475}"
144,1,39,0,0.0458942,"\int \frac{1}{a+b \coth (x)} \, dx","Int[(a + b*Coth[x])^(-1),x]","\frac{a x}{a^2-b^2}-\frac{b \log (a \sinh (x)+b \cosh (x))}{a^2-b^2}","\frac{a x}{a^2-b^2}-\frac{b \log (a \sinh (x)+b \cosh (x))}{a^2-b^2}",1,"(a*x)/(a^2 - b^2) - (b*Log[b*Cosh[x] + a*Sinh[x]])/(a^2 - b^2)","A",2,2,8,0.2500,1,"{3484, 3530}"
145,1,39,0,0.0584835,"\int \frac{\coth (x)}{a+b \coth (x)} \, dx","Int[Coth[x]/(a + b*Coth[x]),x]","\frac{a \log (a \sinh (x)+b \cosh (x))}{a^2-b^2}-\frac{b x}{a^2-b^2}","\frac{a \log (a \sinh (x)+b \cosh (x))}{a^2-b^2}-\frac{b x}{a^2-b^2}",1,"-((b*x)/(a^2 - b^2)) + (a*Log[b*Cosh[x] + a*Sinh[x]])/(a^2 - b^2)","A",2,2,11,0.1818,1,"{3531, 3530}"
146,1,63,0,0.0920795,"\int \frac{\coth ^2(x)}{a+b \coth (x)} \, dx","Int[Coth[x]^2/(a + b*Coth[x]),x]","\frac{a^3 x}{b^2 \left(a^2-b^2\right)}-\frac{a^2 \log (a \sinh (x)+b \cosh (x))}{b \left(a^2-b^2\right)}-\frac{a x}{b^2}+\frac{\log (\sinh (x))}{b}","\frac{a^3 x}{b^2 \left(a^2-b^2\right)}-\frac{a^2 \log (a \sinh (x)+b \cosh (x))}{b \left(a^2-b^2\right)}-\frac{a x}{b^2}+\frac{\log (\sinh (x))}{b}",1,"-((a*x)/b^2) + (a^3*x)/(b^2*(a^2 - b^2)) + Log[Sinh[x]]/b - (a^2*Log[b*Cosh[x] + a*Sinh[x]])/(b*(a^2 - b^2))","A",4,4,13,0.3077,1,"{3541, 3475, 3484, 3530}"
147,1,64,0,0.1299627,"\int \frac{\coth ^3(x)}{a+b \coth (x)} \, dx","Int[Coth[x]^3/(a + b*Coth[x]),x]","-\frac{b x}{a^2-b^2}+\frac{a \log (\sinh (x))}{a^2-b^2}+\frac{a^3 \log (a+b \coth (x))}{b^2 \left(a^2-b^2\right)}-\frac{\coth (x)}{b}","-\frac{b x}{a^2-b^2}+\frac{a \log (\sinh (x))}{a^2-b^2}+\frac{a^3 \log (a+b \coth (x))}{b^2 \left(a^2-b^2\right)}-\frac{\coth (x)}{b}",1,"-((b*x)/(a^2 - b^2)) - Coth[x]/b + (a^3*Log[a + b*Coth[x]])/(b^2*(a^2 - b^2)) + (a*Log[Sinh[x]])/(a^2 - b^2)","A",5,5,13,0.3846,1,"{3566, 3626, 3617, 31, 3475}"
148,1,76,0,0.2212553,"\int \frac{\coth ^4(x)}{a+b \coth (x)} \, dx","Int[Coth[x]^4/(a + b*Coth[x]),x]","\frac{a x}{a^2-b^2}-\frac{b \log (\sinh (x))}{a^2-b^2}-\frac{a^4 \log (a+b \coth (x))}{b^3 \left(a^2-b^2\right)}+\frac{a \coth (x)}{b^2}-\frac{\coth ^2(x)}{2 b}","\frac{a x}{a^2-b^2}-\frac{b \log (\sinh (x))}{a^2-b^2}-\frac{a^4 \log (a+b \coth (x))}{b^3 \left(a^2-b^2\right)}+\frac{a \coth (x)}{b^2}-\frac{\coth ^2(x)}{2 b}",1,"(a*x)/(a^2 - b^2) + (a*Coth[x])/b^2 - Coth[x]^2/(2*b) - (a^4*Log[a + b*Coth[x]])/(b^3*(a^2 - b^2)) - (b*Log[Sinh[x]])/(a^2 - b^2)","A",6,6,13,0.4615,1,"{3566, 3647, 3627, 3617, 31, 3475}"
149,1,94,0,0.3918477,"\int \frac{\coth ^5(x)}{a+b \coth (x)} \, dx","Int[Coth[x]^5/(a + b*Coth[x]),x]","-\frac{b x}{a^2-b^2}-\frac{\left(a^2+b^2\right) \coth (x)}{b^3}+\frac{a \log (\sinh (x))}{a^2-b^2}+\frac{a^5 \log (a+b \coth (x))}{b^4 \left(a^2-b^2\right)}+\frac{a \coth ^2(x)}{2 b^2}-\frac{\coth ^3(x)}{3 b}","-\frac{b x}{a^2-b^2}-\frac{\left(a^2+b^2\right) \coth (x)}{b^3}+\frac{a \log (\sinh (x))}{a^2-b^2}+\frac{a^5 \log (a+b \coth (x))}{b^4 \left(a^2-b^2\right)}+\frac{a \coth ^2(x)}{2 b^2}-\frac{\coth ^3(x)}{3 b}",1,"-((b*x)/(a^2 - b^2)) - ((a^2 + b^2)*Coth[x])/b^3 + (a*Coth[x]^2)/(2*b^2) - Coth[x]^3/(3*b) + (a^5*Log[a + b*Coth[x]])/(b^4*(a^2 - b^2)) + (a*Log[Sinh[x]])/(a^2 - b^2)","A",7,7,13,0.5385,1,"{3566, 3647, 3648, 3626, 3617, 31, 3475}"
150,1,54,0,0.0850082,"\int \frac{x \text{csch}^2(x)}{(a+b \coth (x))^2} \, dx","Int[(x*Csch[x]^2)/(a + b*Coth[x])^2,x]","-\frac{a x}{b \left(a^2-b^2\right)}+\frac{\log (a \sinh (x)+b \cosh (x))}{a^2-b^2}+\frac{x}{b (a+b \coth (x))}","-\frac{a x}{b \left(a^2-b^2\right)}+\frac{\log (a \sinh (x)+b \cosh (x))}{a^2-b^2}+\frac{x}{b (a+b \coth (x))}",1,"-((a*x)/(b*(a^2 - b^2))) + x/(b*(a + b*Coth[x])) + Log[b*Cosh[x] + a*Sinh[x]]/(a^2 - b^2)","A",3,3,14,0.2143,1,"{5467, 3484, 3530}"
151,0,0,0,0.0285749,"\int x^3 \coth (a+2 \log (x)) \, dx","Int[x^3*Coth[a + 2*Log[x]],x]","\int x^3 \coth (a+2 \log (x)) \, dx","\frac{1}{2} e^{-2 a} \log \left(1-e^{2 a} x^4\right)+\frac{x^4}{4}",1,"Defer[Int][x^3*Coth[a + 2*Log[x]], x]","F",0,0,0,0,-1,"{}"
152,0,0,0,0.0213207,"\int x^2 \coth (a+2 \log (x)) \, dx","Int[x^2*Coth[a + 2*Log[x]],x]","\int x^2 \coth (a+2 \log (x)) \, dx","e^{-3 a/2} \tan ^{-1}\left(e^{a/2} x\right)-e^{-3 a/2} \tanh ^{-1}\left(e^{a/2} x\right)+\frac{x^3}{3}",1,"Defer[Int][x^2*Coth[a + 2*Log[x]], x]","F",0,0,0,0,-1,"{}"
153,0,0,0,0.0156127,"\int x \coth (a+2 \log (x)) \, dx","Int[x*Coth[a + 2*Log[x]],x]","\int x \coth (a+2 \log (x)) \, dx","\frac{x^2}{2}-e^{-a} \tanh ^{-1}\left(e^a x^2\right)",1,"Defer[Int][x*Coth[a + 2*Log[x]], x]","F",0,0,0,0,-1,"{}"
154,0,0,0,0.0071696,"\int \coth (a+2 \log (x)) \, dx","Int[Coth[a + 2*Log[x]],x]","\int \coth (a+2 \log (x)) \, dx","-e^{-a/2} \tan ^{-1}\left(e^{a/2} x\right)-e^{-a/2} \tanh ^{-1}\left(e^{a/2} x\right)+x",1,"Defer[Int][Coth[a + 2*Log[x]], x]","F",0,0,0,0,-1,"{}"
155,1,12,0,0.0137687,"\int \frac{\coth (a+2 \log (x))}{x} \, dx","Int[Coth[a + 2*Log[x]]/x,x]","\frac{1}{2} \log (\sinh (a+2 \log (x)))","\frac{1}{2} \log (\sinh (a+2 \log (x)))",1,"Log[Sinh[a + 2*Log[x]]]/2","A",2,1,11,0.09091,1,"{3475}"
156,0,0,0,0.0222044,"\int \frac{\coth (a+2 \log (x))}{x^2} \, dx","Int[Coth[a + 2*Log[x]]/x^2,x]","\int \frac{\coth (a+2 \log (x))}{x^2} \, dx","e^{a/2} \tan ^{-1}\left(e^{a/2} x\right)-e^{a/2} \tanh ^{-1}\left(e^{a/2} x\right)+\frac{1}{x}",1,"Defer[Int][Coth[a + 2*Log[x]]/x^2, x]","F",0,0,0,0,-1,"{}"
157,0,0,0,0.0213417,"\int \frac{\coth (a+2 \log (x))}{x^3} \, dx","Int[Coth[a + 2*Log[x]]/x^3,x]","\int \frac{\coth (a+2 \log (x))}{x^3} \, dx","\frac{1}{2 x^2}-e^a \tanh ^{-1}\left(e^a x^2\right)",1,"Defer[Int][Coth[a + 2*Log[x]]/x^3, x]","F",0,0,0,0,-1,"{}"
158,0,0,0,0.0662787,"\int x^3 \coth ^2(a+2 \log (x)) \, dx","Int[x^3*Coth[a + 2*Log[x]]^2,x]","\int x^3 \coth ^2(a+2 \log (x)) \, dx","\frac{e^{-2 a}}{1-e^{2 a} x^4}+e^{-2 a} \log \left(1-e^{2 a} x^4\right)+\frac{x^4}{4}",1,"Defer[Int][x^3*Coth[a + 2*Log[x]]^2, x]","F",0,0,0,0,-1,"{}"
159,0,0,0,0.0477565,"\int x^2 \coth ^2(a+2 \log (x)) \, dx","Int[x^2*Coth[a + 2*Log[x]]^2,x]","\int x^2 \coth ^2(a+2 \log (x)) \, dx","\frac{x^3}{1-e^{2 a} x^4}+\frac{3}{2} e^{-3 a/2} \tan ^{-1}\left(e^{a/2} x\right)-\frac{3}{2} e^{-3 a/2} \tanh ^{-1}\left(e^{a/2} x\right)+\frac{x^3}{3}",1,"Defer[Int][x^2*Coth[a + 2*Log[x]]^2, x]","F",0,0,0,0,-1,"{}"
160,0,0,0,0.0298197,"\int x \coth ^2(a+2 \log (x)) \, dx","Int[x*Coth[a + 2*Log[x]]^2,x]","\int x \coth ^2(a+2 \log (x)) \, dx","\frac{x^2}{1-e^{2 a} x^4}-e^{-a} \tanh ^{-1}\left(e^a x^2\right)+\frac{x^2}{2}",1,"Defer[Int][x*Coth[a + 2*Log[x]]^2, x]","F",0,0,0,0,-1,"{}"
161,0,0,0,0.0098684,"\int \coth ^2(a+2 \log (x)) \, dx","Int[Coth[a + 2*Log[x]]^2,x]","\int \coth ^2(a+2 \log (x)) \, dx","\frac{x}{1-e^{2 a} x^4}-\frac{1}{2} e^{-a/2} \tan ^{-1}\left(e^{a/2} x\right)-\frac{1}{2} e^{-a/2} \tanh ^{-1}\left(e^{a/2} x\right)+x",1,"Defer[Int][Coth[a + 2*Log[x]]^2, x]","F",0,0,0,0,-1,"{}"
162,1,14,0,0.0239965,"\int \frac{\coth ^2(a+2 \log (x))}{x} \, dx","Int[Coth[a + 2*Log[x]]^2/x,x]","\log (x)-\frac{1}{2} \coth (a+2 \log (x))","\log (x)-\frac{1}{2} \coth (a+2 \log (x))",1,"-Coth[a + 2*Log[x]]/2 + Log[x]","A",3,2,13,0.1538,1,"{3473, 8}"
163,0,0,0,0.0448182,"\int \frac{\coth ^2(a+2 \log (x))}{x^2} \, dx","Int[Coth[a + 2*Log[x]]^2/x^2,x]","\int \frac{\coth ^2(a+2 \log (x))}{x^2} \, dx","\frac{2 e^{2 a} x^3}{1-e^{2 a} x^4}-\frac{1}{x \left(1-e^{2 a} x^4\right)}-\frac{1}{2} e^{a/2} \tan ^{-1}\left(e^{a/2} x\right)+\frac{1}{2} e^{a/2} \tanh ^{-1}\left(e^{a/2} x\right)",1,"Defer[Int][Coth[a + 2*Log[x]]^2/x^2, x]","F",0,0,0,0,-1,"{}"
164,0,0,0,0.0460271,"\int \frac{\coth ^2(a+2 \log (x))}{x^3} \, dx","Int[Coth[a + 2*Log[x]]^2/x^3,x]","\int \frac{\coth ^2(a+2 \log (x))}{x^3} \, dx","\frac{3 e^{2 a} x^2}{2 \left(1-e^{2 a} x^4\right)}-\frac{1}{2 x^2 \left(1-e^{2 a} x^4\right)}+e^a \tanh ^{-1}\left(e^a x^2\right)",1,"Defer[Int][Coth[a + 2*Log[x]]^2/x^3, x]","F",0,0,0,0,-1,"{}"
165,0,0,0,0.0387854,"\int (e x)^m \coth (a+2 \log (x)) \, dx","Int[(e*x)^m*Coth[a + 2*Log[x]],x]","\int (e x)^m \coth (a+2 \log (x)) \, dx","\frac{(e x)^{m+1}}{e (m+1)}-\frac{2 (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};e^{2 a} x^4\right)}{e (m+1)}",1,"Defer[Int][(e*x)^m*Coth[a + 2*Log[x]], x]","F",0,0,0,0,-1,"{}"
166,0,0,0,0.0679443,"\int (e x)^m \coth ^2(a+2 \log (x)) \, dx","Int[(e*x)^m*Coth[a + 2*Log[x]]^2,x]","\int (e x)^m \coth ^2(a+2 \log (x)) \, dx","-\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};e^{2 a} x^4\right)}{e}+\frac{(e x)^{m+1}}{e \left(1-e^{2 a} x^4\right)}+\frac{(e x)^{m+1}}{e (m+1)}",1,"Defer[Int][(e*x)^m*Coth[a + 2*Log[x]]^2, x]","F",0,0,0,0,-1,"{}"
167,0,0,0,0.0728497,"\int (e x)^m \coth ^3(a+2 \log (x)) \, dx","Int[(e*x)^m*Coth[a + 2*Log[x]]^3,x]","\int (e x)^m \coth ^3(a+2 \log (x)) \, dx","-\frac{\left(m^2+2 m+9\right) (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{4};\frac{m+5}{4};e^{2 a} x^4\right)}{4 e (m+1)}-\frac{\left(e^{2 a} x^4+1\right)^2 (e x)^{m+1}}{4 e \left(1-e^{2 a} x^4\right)^2}-\frac{e^{-2 a} \left(e^{2 a} (3-m)-e^{4 a} (m+5) x^4\right) (e x)^{m+1}}{8 e \left(1-e^{2 a} x^4\right)}+\frac{(m+3) (m+5) (e x)^{m+1}}{8 e (m+1)}",1,"Defer[Int][(e*x)^m*Coth[a + 2*Log[x]]^3, x]","F",0,0,0,0,-1,"{}"
168,0,0,0,0.0221232,"\int \coth ^p(a+b \log (x)) \, dx","Int[Coth[a + b*Log[x]]^p,x]","\int \coth ^p(a+b \log (x)) \, dx","x \left(-e^{2 a} x^{2 b}-1\right)^p \left(e^{2 a} x^{2 b}+1\right)^{-p} F_1\left(\frac{1}{2 b};p,-p;\frac{1}{2} \left(2+\frac{1}{b}\right);e^{2 a} x^{2 b},-e^{2 a} x^{2 b}\right)",1,"Defer[Int][Coth[a + b*Log[x]]^p, x]","F",0,0,0,0,-1,"{}"
169,0,0,0,0.1158306,"\int (e x)^m \coth ^p(a+b \log (x)) \, dx","Int[(e*x)^m*Coth[a + b*Log[x]]^p,x]","\int (e x)^m \coth ^p(a+b \log (x)) \, dx","\frac{(e x)^{m+1} \left(-e^{2 a} x^{2 b}-1\right)^p \left(e^{2 a} x^{2 b}+1\right)^{-p} F_1\left(\frac{m+1}{2 b};p,-p;\frac{m+1}{2 b}+1;e^{2 a} x^{2 b},-e^{2 a} x^{2 b}\right)}{e (m+1)}",1,"Defer[Int][(e*x)^m*Coth[a + b*Log[x]]^p, x]","F",0,0,0,0,-1,"{}"
170,0,0,0,0.046479,"\int \coth ^p\left(a+\frac{\log (x)}{2}\right) \, dx","Int[Coth[a + Log[x]/2]^p,x]","\int \coth ^p\left(a+\frac{\log (x)}{2}\right) \, dx","-\frac{e^{-2 a} 2^{-p} \left(-e^{2 a} x-1\right)^{p+1} \, _2F_1\left(p,p+1;p+2;\frac{1}{2} \left(e^{2 a} x+1\right)\right)}{p+1}",1,"Defer[Int][Coth[(2*a + Log[x])/2]^p, x]","F",0,0,0,0,-1,"{}"
171,0,0,0,0.0508788,"\int \coth ^p\left(a+\frac{\log (x)}{4}\right) \, dx","Int[Coth[a + Log[x]/4]^p,x]","\int \coth ^p\left(a+\frac{\log (x)}{4}\right) \, dx","e^{-4 a} \left(-e^{2 a} \sqrt{x}-1\right)^{p+1} \left(1-e^{2 a} \sqrt{x}\right)^{1-p}-\frac{e^{-4 a} 2^{1-p} p \left(-e^{2 a} \sqrt{x}-1\right)^{p+1} \, _2F_1\left(p,p+1;p+2;\frac{1}{2} \left(e^{2 a} \sqrt{x}+1\right)\right)}{p+1}",1,"Defer[Int][Coth[(4*a + Log[x])/4]^p, x]","F",0,0,0,0,-1,"{}"
172,0,0,0,0.0499177,"\int \coth ^p\left(a+\frac{\log (x)}{6}\right) \, dx","Int[Coth[a + Log[x]/6]^p,x]","\int \coth ^p\left(a+\frac{\log (x)}{6}\right) \, dx","-\frac{e^{-6 a} 2^{-p} \left(2 p^2+1\right) \left(-e^{2 a} \sqrt[3]{x}-1\right)^{p+1} \, _2F_1\left(p,p+1;p+2;\frac{1}{2} \left(e^{2 a} \sqrt[3]{x}+1\right)\right)}{p+1}+e^{-6 a} p \left(-e^{2 a} \sqrt[3]{x}-1\right)^{p+1} \left(1-e^{2 a} \sqrt[3]{x}\right)^{1-p}+e^{-4 a} \sqrt[3]{x} \left(-e^{2 a} \sqrt[3]{x}-1\right)^{p+1} \left(1-e^{2 a} \sqrt[3]{x}\right)^{1-p}",1,"Defer[Int][Coth[(6*a + Log[x])/6]^p, x]","F",0,0,0,0,-1,"{}"
173,0,0,0,0.0507109,"\int \coth ^p\left(a+\frac{\log (x)}{8}\right) \, dx","Int[Coth[a + Log[x]/8]^p,x]","\int \coth ^p\left(a+\frac{\log (x)}{8}\right) \, dx","-\frac{e^{-8 a} 2^{2-p} p \left(p^2+2\right) \left(-e^{2 a} \sqrt[4]{x}-1\right)^{p+1} \, _2F_1\left(p,p+1;p+2;\frac{1}{2} \left(e^{2 a} \sqrt[4]{x}+1\right)\right)}{3 (p+1)}+\frac{1}{3} e^{-12 a} \left(-e^{2 a} \sqrt[4]{x}-1\right)^{p+1} \left(e^{4 a} \left(2 p^2+3\right)+2 e^{6 a} p \sqrt[4]{x}\right) \left(1-e^{2 a} \sqrt[4]{x}\right)^{1-p}+e^{-4 a} \sqrt{x} \left(-e^{2 a} \sqrt[4]{x}-1\right)^{p+1} \left(1-e^{2 a} \sqrt[4]{x}\right)^{1-p}",1,"Defer[Int][Coth[(8*a + Log[x])/8]^p, x]","F",0,0,0,0,-1,"{}"
174,0,0,0,0.0153368,"\int \coth ^p(a+\log (x)) \, dx","Int[Coth[a + Log[x]]^p,x]","\int \coth ^p(a+\log (x)) \, dx","x \left(-e^{2 a} x^2-1\right)^p \left(e^{2 a} x^2+1\right)^{-p} F_1\left(\frac{1}{2};p,-p;\frac{3}{2};e^{2 a} x^2,-e^{2 a} x^2\right)",1,"Defer[Int][Coth[a + Log[x]]^p, x]","F",0,0,0,0,-1,"{}"
175,0,0,0,0.0105149,"\int \coth ^p(a+2 \log (x)) \, dx","Int[Coth[a + 2*Log[x]]^p,x]","\int \coth ^p(a+2 \log (x)) \, dx","x \left(-e^{2 a} x^4-1\right)^p \left(e^{2 a} x^4+1\right)^{-p} F_1\left(\frac{1}{4};p,-p;\frac{5}{4};e^{2 a} x^4,-e^{2 a} x^4\right)",1,"Defer[Int][Coth[a + 2*Log[x]]^p, x]","F",0,0,0,0,-1,"{}"
176,0,0,0,0.0179362,"\int \coth ^p(a+3 \log (x)) \, dx","Int[Coth[a + 3*Log[x]]^p,x]","\int \coth ^p(a+3 \log (x)) \, dx","x \left(-e^{2 a} x^6-1\right)^p \left(e^{2 a} x^6+1\right)^{-p} F_1\left(\frac{1}{6};p,-p;\frac{7}{6};e^{2 a} x^6,-e^{2 a} x^6\right)",1,"Defer[Int][Coth[a + 3*Log[x]]^p, x]","F",0,0,0,0,-1,"{}"
177,0,0,0,0.0390568,"\int x^3 \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x^3*Coth[d*(a + b*Log[c*x^n])],x]","\int x^3 \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","\frac{x^4}{4}-\frac{1}{2} x^4 \, _2F_1\left(1,\frac{2}{b d n};1+\frac{2}{b d n};e^{2 a d} \left(c x^n\right)^{2 b d}\right)",1,"Defer[Int][x^3*Coth[d*(a + b*Log[c*x^n])], x]","F",0,0,0,0,-1,"{}"
178,0,0,0,0.0299628,"\int x^2 \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x^2*Coth[d*(a + b*Log[c*x^n])],x]","\int x^2 \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","\frac{x^3}{3}-\frac{2}{3} x^3 \, _2F_1\left(1,\frac{3}{2 b d n};1+\frac{3}{2 b d n};e^{2 a d} \left(c x^n\right)^{2 b d}\right)",1,"Defer[Int][x^2*Coth[d*(a + b*Log[c*x^n])], x]","F",0,0,0,0,-1,"{}"
179,0,0,0,0.0239149,"\int x \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x*Coth[d*(a + b*Log[c*x^n])],x]","\int x \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","\frac{x^2}{2}-x^2 \, _2F_1\left(1,\frac{1}{b d n};1+\frac{1}{b d n};e^{2 a d} \left(c x^n\right)^{2 b d}\right)",1,"Defer[Int][x*Coth[d*(a + b*Log[c*x^n])], x]","F",0,0,0,0,-1,"{}"
180,0,0,0,0.0114539,"\int \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[Coth[d*(a + b*Log[c*x^n])],x]","\int \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","x-2 x \, _2F_1\left(1,\frac{1}{2 b d n};1+\frac{1}{2 b d n};e^{2 a d} \left(c x^n\right)^{2 b d}\right)",1,"Defer[Int][Coth[d*(a + b*Log[c*x^n])], x]","F",0,0,0,0,-1,"{}"
181,1,25,0,0.0206705,"\int \frac{\coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Int[Coth[d*(a + b*Log[c*x^n])]/x,x]","\frac{\log \left(\sinh \left(a d+b d \log \left(c x^n\right)\right)\right)}{b d n}","\frac{\log \left(\sinh \left(a d+b d \log \left(c x^n\right)\right)\right)}{b d n}",1,"Log[Sinh[a*d + b*d*Log[c*x^n]]]/(b*d*n)","A",2,1,17,0.05882,1,"{3475}"
182,0,0,0,0.0313433,"\int \frac{\coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Int[Coth[d*(a + b*Log[c*x^n])]/x^2,x]","\int \frac{\coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","\frac{2 \, _2F_1\left(1,-\frac{1}{2 b d n};1-\frac{1}{2 b d n};e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{x}-\frac{1}{x}",1,"Defer[Int][Coth[d*(a + b*Log[c*x^n])]/x^2, x]","F",0,0,0,0,-1,"{}"
183,0,0,0,0.0296067,"\int \frac{\coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Int[Coth[d*(a + b*Log[c*x^n])]/x^3,x]","\int \frac{\coth \left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","\frac{\, _2F_1\left(1,-\frac{1}{b d n};1-\frac{1}{b d n};e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{x^2}-\frac{1}{2 x^2}",1,"Defer[Int][Coth[d*(a + b*Log[c*x^n])]/x^3, x]","F",0,0,0,0,-1,"{}"
184,0,0,0,0.0864764,"\int x^3 \coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x^3*Coth[d*(a + b*Log[c*x^n])]^2,x]","\int x^3 \coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{2 x^4 \, _2F_1\left(1,\frac{2}{b d n};1+\frac{2}{b d n};e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d n}+\frac{x^4 \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}{b d n \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}+\frac{1}{4} x^4 \left(\frac{4}{b d n}+1\right)",1,"Defer[Int][x^3*Coth[d*(a + b*Log[c*x^n])]^2, x]","F",0,0,0,0,-1,"{}"
185,0,0,0,0.0584018,"\int x^2 \coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x^2*Coth[d*(a + b*Log[c*x^n])]^2,x]","\int x^2 \coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{2 x^3 \, _2F_1\left(1,\frac{3}{2 b d n};1+\frac{3}{2 b d n};e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d n}+\frac{x^3 \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}{b d n \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}+\frac{1}{3} x^3 \left(\frac{3}{b d n}+1\right)",1,"Defer[Int][x^2*Coth[d*(a + b*Log[c*x^n])]^2, x]","F",0,0,0,0,-1,"{}"
186,0,0,0,0.0427788,"\int x \coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x*Coth[d*(a + b*Log[c*x^n])]^2,x]","\int x \coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{2 x^2 \, _2F_1\left(1,\frac{1}{b d n};1+\frac{1}{b d n};e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d n}+\frac{x^2 \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}{b d n \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}+\frac{1}{2} x^2 \left(\frac{2}{b d n}+1\right)",1,"Defer[Int][x*Coth[d*(a + b*Log[c*x^n])]^2, x]","F",0,0,0,0,-1,"{}"
187,0,0,0,0.0139827,"\int \coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[Coth[d*(a + b*Log[c*x^n])]^2,x]","\int \coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{2 x \, _2F_1\left(1,\frac{1}{2 b d n};1+\frac{1}{2 b d n};e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d n}+\frac{x \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}{b d n \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}+x \left(\frac{1}{b d n}+1\right)",1,"Defer[Int][Coth[d*(a + b*Log[c*x^n])]^2, x]","F",0,0,0,0,-1,"{}"
188,1,28,0,0.0291035,"\int \frac{\coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Int[Coth[d*(a + b*Log[c*x^n])]^2/x,x]","\log (x)-\frac{\coth \left(a d+b d \log \left(c x^n\right)\right)}{b d n}","\log (x)-\frac{\coth \left(a d+b d \log \left(c x^n\right)\right)}{b d n}",1,"-(Coth[a*d + b*d*Log[c*x^n]]/(b*d*n)) + Log[x]","A",3,2,19,0.1053,1,"{3473, 8}"
189,0,0,0,0.0506045,"\int \frac{\coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Int[Coth[d*(a + b*Log[c*x^n])]^2/x^2,x]","\int \frac{\coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","-\frac{2 \, _2F_1\left(1,-\frac{1}{2 b d n};1-\frac{1}{2 b d n};e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d n x}+\frac{e^{2 a d} \left(c x^n\right)^{2 b d}+1}{b d n x \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}-\frac{1-\frac{1}{b d n}}{x}",1,"Defer[Int][Coth[d*(a + b*Log[c*x^n])]^2/x^2, x]","F",0,0,0,0,-1,"{}"
190,0,0,0,0.0530002,"\int \frac{\coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Int[Coth[d*(a + b*Log[c*x^n])]^2/x^3,x]","\int \frac{\coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","-\frac{2 \, _2F_1\left(1,-\frac{1}{b d n};1-\frac{1}{b d n};e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d n x^2}+\frac{e^{2 a d} \left(c x^n\right)^{2 b d}+1}{b d n x^2 \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}+\frac{2-b d n}{2 b d n x^2}",1,"Defer[Int][Coth[d*(a + b*Log[c*x^n])]^2/x^3, x]","F",0,0,0,0,-1,"{}"
191,1,43,0,0.0402723,"\int \frac{\coth ^3\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Coth[a + b*Log[c*x^n]]^3/x,x]","\frac{\log \left(\sinh \left(a+b \log \left(c x^n\right)\right)\right)}{b n}-\frac{\coth ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}","\frac{\log \left(\sinh \left(a+b \log \left(c x^n\right)\right)\right)}{b n}-\frac{\coth ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}",1,"-Coth[a + b*Log[c*x^n]]^2/(2*b*n) + Log[Sinh[a + b*Log[c*x^n]]]/(b*n)","A",3,2,17,0.1176,1,"{3473, 3475}"
192,1,45,0,0.0374456,"\int \frac{\coth ^4\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Coth[a + b*Log[c*x^n]]^4/x,x]","-\frac{\coth ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{\coth \left(a+b \log \left(c x^n\right)\right)}{b n}+\log (x)","-\frac{\coth ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{\coth \left(a+b \log \left(c x^n\right)\right)}{b n}+\log (x)",1,"-(Coth[a + b*Log[c*x^n]]/(b*n)) - Coth[a + b*Log[c*x^n]]^3/(3*b*n) + Log[x]","A",4,2,17,0.1176,1,"{3473, 8}"
193,1,66,0,0.0573933,"\int \frac{\coth ^5\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Coth[a + b*Log[c*x^n]]^5/x,x]","\frac{\log \left(\sinh \left(a+b \log \left(c x^n\right)\right)\right)}{b n}-\frac{\coth ^4\left(a+b \log \left(c x^n\right)\right)}{4 b n}-\frac{\coth ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}","\frac{\log \left(\sinh \left(a+b \log \left(c x^n\right)\right)\right)}{b n}-\frac{\coth ^4\left(a+b \log \left(c x^n\right)\right)}{4 b n}-\frac{\coth ^2\left(a+b \log \left(c x^n\right)\right)}{2 b n}",1,"-Coth[a + b*Log[c*x^n]]^2/(2*b*n) - Coth[a + b*Log[c*x^n]]^4/(4*b*n) + Log[Sinh[a + b*Log[c*x^n]]]/(b*n)","A",4,2,17,0.1176,1,"{3473, 3475}"
194,0,0,0,0.0464916,"\int (e x)^m \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Coth[d*(a + b*Log[c*x^n])],x]","\int (e x)^m \coth \left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","\frac{(e x)^{m+1}}{e (m+1)}-\frac{2 (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2 b d n};\frac{m+1}{2 b d n}+1;e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{e (m+1)}",1,"Defer[Int][(e*x)^m*Coth[d*(a + b*Log[c*x^n])], x]","F",0,0,0,0,-1,"{}"
195,0,0,0,0.0769521,"\int (e x)^m \coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Coth[d*(a + b*Log[c*x^n])]^2,x]","\int (e x)^m \coth ^2\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{2 (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2 b d n};\frac{m+1}{2 b d n}+1;e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b d e n}+\frac{(e x)^{m+1} \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)}{b d e n \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}+\frac{(e x)^{m+1} (b d n+m+1)}{b d e (m+1) n}",1,"Defer[Int][(e*x)^m*Coth[d*(a + b*Log[c*x^n])]^2, x]","F",0,0,0,0,-1,"{}"
196,0,0,0,0.0694341,"\int (e x)^m \coth ^3\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Coth[d*(a + b*Log[c*x^n])]^3,x]","\int (e x)^m \coth ^3\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","-\frac{(e x)^{m+1} \left(2 b^2 d^2 n^2+m^2+2 m+1\right) \, _2F_1\left(1,\frac{m+1}{2 b d n};\frac{m+1}{2 b d n}+1;e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{b^2 d^2 e (m+1) n^2}+\frac{e^{-2 a d} (e x)^{m+1} \left(\frac{e^{4 a d} (2 b d n+m+1) \left(c x^n\right)^{2 b d}}{n}+\frac{e^{2 a d} (-2 b d n+m+1)}{n}\right)}{2 b^2 d^2 e n \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}-\frac{(e x)^{m+1} \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)^2}{2 b d e n \left(1-e^{2 a d} \left(c x^n\right)^{2 b d}\right)^2}+\frac{(e x)^{m+1} (b d n+m+1) (2 b d n+m+1)}{2 b^2 d^2 e (m+1) n^2}",1,"Defer[Int][(e*x)^m*Coth[d*(a + b*Log[c*x^n])]^3, x]","F",0,0,0,0,-1,"{}"
197,0,0,0,0.0150993,"\int \coth ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[Coth[d*(a + b*Log[c*x^n])]^p,x]","\int \coth ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","x \left(-e^{2 a d} \left(c x^n\right)^{2 b d}-1\right)^p \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)^{-p} F_1\left(\frac{1}{2 b d n};p,-p;1+\frac{1}{2 b d n};e^{2 a d} \left(c x^n\right)^{2 b d},-e^{2 a d} \left(c x^n\right)^{2 b d}\right)",1,"Defer[Int][Coth[d*(a + b*Log[c*x^n])]^p, x]","F",0,0,0,0,-1,"{}"
198,0,0,0,0.0973732,"\int (e x)^m \coth ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*Coth[d*(a + b*Log[c*x^n])]^p,x]","\int (e x)^m \coth ^p\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","\frac{(e x)^{m+1} \left(-e^{2 a d} \left(c x^n\right)^{2 b d}-1\right)^p \left(e^{2 a d} \left(c x^n\right)^{2 b d}+1\right)^{-p} F_1\left(\frac{m+1}{2 b d n};p,-p;\frac{m+1}{2 b d n}+1;e^{2 a d} \left(c x^n\right)^{2 b d},-e^{2 a d} \left(c x^n\right)^{2 b d}\right)}{e (m+1)}",1,"Defer[Int][(e*x)^m*Coth[d*(a + b*Log[c*x^n])]^p, x]","F",0,0,0,0,-1,"{}"
199,1,73,0,0.0514403,"\int \frac{\coth ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Coth[a + b*Log[c*x^n]]^(5/2)/x,x]","-\frac{2 \coth ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}","-\frac{2 \coth ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"-(ArcTan[Sqrt[Coth[a + b*Log[c*x^n]]]]/(b*n)) + ArcTanh[Sqrt[Coth[a + b*Log[c*x^n]]]]/(b*n) - (2*Coth[a + b*Log[c*x^n]]^(3/2))/(3*b*n)","A",7,6,19,0.3158,1,"{3473, 3476, 329, 298, 203, 206}"
200,1,70,0,0.0502198,"\int \frac{\coth ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Coth[a + b*Log[c*x^n]]^(3/2)/x,x]","-\frac{2 \sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}}{b n}+\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}","-\frac{2 \sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}}{b n}+\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"ArcTan[Sqrt[Coth[a + b*Log[c*x^n]]]]/(b*n) + ArcTanh[Sqrt[Coth[a + b*Log[c*x^n]]]]/(b*n) - (2*Sqrt[Coth[a + b*Log[c*x^n]]])/(b*n)","A",7,6,19,0.3158,1,"{3473, 3476, 329, 212, 206, 203}"
201,1,48,0,0.0390491,"\int \frac{\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}}{x} \, dx","Int[Sqrt[Coth[a + b*Log[c*x^n]]]/x,x]","\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}-\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}","\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}-\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"-(ArcTan[Sqrt[Coth[a + b*Log[c*x^n]]]]/(b*n)) + ArcTanh[Sqrt[Coth[a + b*Log[c*x^n]]]]/(b*n)","A",6,5,19,0.2632,1,"{3476, 329, 298, 203, 206}"
202,1,47,0,0.0398971,"\int \frac{1}{x \sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}} \, dx","Int[1/(x*Sqrt[Coth[a + b*Log[c*x^n]]]),x]","\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}","\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"ArcTan[Sqrt[Coth[a + b*Log[c*x^n]]]]/(b*n) + ArcTanh[Sqrt[Coth[a + b*Log[c*x^n]]]]/(b*n)","A",6,5,19,0.2632,1,"{3476, 329, 212, 206, 203}"
203,1,71,0,0.0517306,"\int \frac{1}{x \coth ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Coth[a + b*Log[c*x^n]]^(3/2)),x]","-\frac{2}{b n \sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}}-\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}","-\frac{2}{b n \sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}}-\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"-(ArcTan[Sqrt[Coth[a + b*Log[c*x^n]]]]/(b*n)) + ArcTanh[Sqrt[Coth[a + b*Log[c*x^n]]]]/(b*n) - 2/(b*n*Sqrt[Coth[a + b*Log[c*x^n]]])","A",7,6,19,0.3158,1,"{3474, 3476, 329, 298, 203, 206}"
204,1,72,0,0.0510296,"\int \frac{1}{x \coth ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Coth[a + b*Log[c*x^n]]^(5/2)),x]","-\frac{2}{3 b n \coth ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}+\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}","-\frac{2}{3 b n \coth ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}+\frac{\tan ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}+\frac{\tanh ^{-1}\left(\sqrt{\coth \left(a+b \log \left(c x^n\right)\right)}\right)}{b n}",1,"ArcTan[Sqrt[Coth[a + b*Log[c*x^n]]]]/(b*n) + ArcTanh[Sqrt[Coth[a + b*Log[c*x^n]]]]/(b*n) - 2/(3*b*n*Coth[a + b*Log[c*x^n]]^(3/2))","A",7,6,19,0.3158,1,"{3474, 3476, 329, 212, 206, 203}"
205,1,135,0,0.3530854,"\int \frac{\coth ^5(x)}{\sqrt{a+b \coth ^2(x)+c \coth ^4(x)}} \, dx","Int[Coth[x]^5/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4],x]","\frac{(b-2 c) \tanh ^{-1}\left(\frac{b+2 c \coth ^2(x)}{2 \sqrt{c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{4 c^{3/2}}-\frac{\sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}{2 c}+\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a+b+c}}","\frac{(b-2 c) \tanh ^{-1}\left(\frac{b+2 c \coth ^2(x)}{2 \sqrt{c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{4 c^{3/2}}-\frac{\sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}{2 c}+\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a+b+c}}",1,"((b - 2*c)*ArcTanh[(b + 2*c*Coth[x]^2)/(2*Sqrt[c]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4])])/(4*c^(3/2)) + ArcTanh[(2*a + b + (b + 2*c)*Coth[x]^2)/(2*Sqrt[a + b + c]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4])]/(2*Sqrt[a + b + c]) - Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4]/(2*c)","A",8,7,23,0.3043,1,"{3701, 1251, 1653, 843, 621, 206, 724}"
206,1,105,0,0.2165744,"\int \frac{\coth ^3(x)}{\sqrt{a+b \coth ^2(x)+c \coth ^4(x)}} \, dx","Int[Coth[x]^3/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4],x]","\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a+b+c}}-\frac{\tanh ^{-1}\left(\frac{b+2 c \coth ^2(x)}{2 \sqrt{c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{c}}","\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a+b+c}}-\frac{\tanh ^{-1}\left(\frac{b+2 c \coth ^2(x)}{2 \sqrt{c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{c}}",1,"-ArcTanh[(b + 2*c*Coth[x]^2)/(2*Sqrt[c]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4])]/(2*Sqrt[c]) + ArcTanh[(2*a + b + (b + 2*c)*Coth[x]^2)/(2*Sqrt[a + b + c]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4])]/(2*Sqrt[a + b + c])","A",7,6,23,0.2609,1,"{3701, 1251, 843, 621, 206, 724}"
207,1,58,0,0.1173391,"\int \frac{\coth (x)}{\sqrt{a+b \coth ^2(x)+c \coth ^4(x)}} \, dx","Int[Coth[x]/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4],x]","\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a+b+c}}","\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a+b+c}}",1,"ArcTanh[(2*a + b + (b + 2*c)*Coth[x]^2)/(2*Sqrt[a + b + c]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4])]/(2*Sqrt[a + b + c])","A",4,4,21,0.1905,1,"{3701, 1247, 724, 206}"
208,1,106,0,0.2395813,"\int \frac{\tanh (x)}{\sqrt{a+b \coth ^2(x)+c \coth ^4(x)}} \, dx","Int[Tanh[x]/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4],x]","\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a+b+c}}-\frac{\tanh ^{-1}\left(\frac{2 a+b \coth ^2(x)}{2 \sqrt{a} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a}}","\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a+b+c}}-\frac{\tanh ^{-1}\left(\frac{2 a+b \coth ^2(x)}{2 \sqrt{a} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a}}",1,"-ArcTanh[(2*a + b*Coth[x]^2)/(2*Sqrt[a]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4])]/(2*Sqrt[a]) + ArcTanh[(2*a + b + (b + 2*c)*Coth[x]^2)/(2*Sqrt[a + b + c]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4])]/(2*Sqrt[a + b + c])","A",8,5,21,0.2381,1,"{3701, 1251, 960, 724, 206}"
209,1,183,0,0.3323678,"\int \frac{\tanh ^3(x)}{\sqrt{a+b \coth ^2(x)+c \coth ^4(x)}} \, dx","Int[Tanh[x]^3/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4],x]","\frac{b \tanh ^{-1}\left(\frac{2 a+b \coth ^2(x)}{2 \sqrt{a} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{4 a^{3/2}}-\frac{\tanh ^2(x) \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}{2 a}-\frac{\tanh ^{-1}\left(\frac{2 a+b \coth ^2(x)}{2 \sqrt{a} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a}}+\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a+b+c}}","\frac{b \tanh ^{-1}\left(\frac{2 a+b \coth ^2(x)}{2 \sqrt{a} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{4 a^{3/2}}-\frac{\tanh ^2(x) \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}{2 a}-\frac{\tanh ^{-1}\left(\frac{2 a+b \coth ^2(x)}{2 \sqrt{a} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a}}+\frac{\tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{2 \sqrt{a+b+c}}",1,"-ArcTanh[(2*a + b*Coth[x]^2)/(2*Sqrt[a]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4])]/(2*Sqrt[a]) + (b*ArcTanh[(2*a + b*Coth[x]^2)/(2*Sqrt[a]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4])])/(4*a^(3/2)) + ArcTanh[(2*a + b + (b + 2*c)*Coth[x]^2)/(2*Sqrt[a + b + c]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4])]/(2*Sqrt[a + b + c]) - (Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4]*Tanh[x]^2)/(2*a)","A",11,6,23,0.2609,1,"{3701, 1251, 960, 730, 724, 206}"
210,1,132,0,0.2307967,"\int \coth (x) \sqrt{a+b \coth ^2(x)+c \coth ^4(x)} \, dx","Int[Coth[x]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4],x]","-\frac{1}{2} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}-\frac{(b+2 c) \tanh ^{-1}\left(\frac{b+2 c \coth ^2(x)}{2 \sqrt{c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{4 \sqrt{c}}+\frac{1}{2} \sqrt{a+b+c} \tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)","-\frac{1}{2} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}-\frac{(b+2 c) \tanh ^{-1}\left(\frac{b+2 c \coth ^2(x)}{2 \sqrt{c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)}{4 \sqrt{c}}+\frac{1}{2} \sqrt{a+b+c} \tanh ^{-1}\left(\frac{2 a+(b+2 c) \coth ^2(x)+b}{2 \sqrt{a+b+c} \sqrt{a+b \coth ^2(x)+c \coth ^4(x)}}\right)",1,"-((b + 2*c)*ArcTanh[(b + 2*c*Coth[x]^2)/(2*Sqrt[c]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4])])/(4*Sqrt[c]) + (Sqrt[a + b + c]*ArcTanh[(2*a + b + (b + 2*c)*Coth[x]^2)/(2*Sqrt[a + b + c]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4])])/2 - Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4]/2","A",8,7,21,0.3333,1,"{3701, 1247, 734, 843, 621, 206, 724}"
211,1,319,0,0.912047,"\int e^{c (a+b x)} \coth ^2(a c+b c x)^{5/2} \, dx","Int[E^(c*(a + b*x))*(Coth[a*c + b*c*x]^2)^(5/2),x]","-\frac{15 \tanh ^{-1}\left(e^{c (a+b x)}\right) \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{4 b c}+\frac{e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c}+\frac{25 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{4 b c \left(1-e^{2 c (a+b x)}\right)}-\frac{55 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{6 b c \left(1-e^{2 c (a+b x)}\right)^2}+\frac{26 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{3 b c \left(1-e^{2 c (a+b x)}\right)^3}-\frac{4 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c \left(1-e^{2 c (a+b x)}\right)^4}","-\frac{15 \tanh ^{-1}\left(e^{c (a+b x)}\right) \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{4 b c}+\frac{e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c}+\frac{25 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{4 b c \left(1-e^{2 c (a+b x)}\right)}-\frac{55 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{6 b c \left(1-e^{2 c (a+b x)}\right)^2}+\frac{26 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{3 b c \left(1-e^{2 c (a+b x)}\right)^3}-\frac{4 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c \left(1-e^{2 c (a+b x)}\right)^4}",1,"(E^(c*(a + b*x))*Sqrt[Coth[a*c + b*c*x]^2]*Tanh[a*c + b*c*x])/(b*c) - (4*E^(c*(a + b*x))*Sqrt[Coth[a*c + b*c*x]^2]*Tanh[a*c + b*c*x])/(b*c*(1 - E^(2*c*(a + b*x)))^4) + (26*E^(c*(a + b*x))*Sqrt[Coth[a*c + b*c*x]^2]*Tanh[a*c + b*c*x])/(3*b*c*(1 - E^(2*c*(a + b*x)))^3) - (55*E^(c*(a + b*x))*Sqrt[Coth[a*c + b*c*x]^2]*Tanh[a*c + b*c*x])/(6*b*c*(1 - E^(2*c*(a + b*x)))^2) + (25*E^(c*(a + b*x))*Sqrt[Coth[a*c + b*c*x]^2]*Tanh[a*c + b*c*x])/(4*b*c*(1 - E^(2*c*(a + b*x)))) - (15*ArcTanh[E^(c*(a + b*x))]*Sqrt[Coth[a*c + b*c*x]^2]*Tanh[a*c + b*c*x])/(4*b*c)","A",9,7,25,0.2800,1,"{6720, 2282, 390, 1814, 1157, 385, 207}"
212,1,197,0,0.2836002,"\int e^{c (a+b x)} \coth ^2(a c+b c x)^{3/2} \, dx","Int[E^(c*(a + b*x))*(Coth[a*c + b*c*x]^2)^(3/2),x]","-\frac{3 \tanh ^{-1}\left(e^{c (a+b x)}\right) \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c}+\frac{e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c}+\frac{3 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c \left(1-e^{2 c (a+b x)}\right)}-\frac{2 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c \left(1-e^{2 c (a+b x)}\right)^2}","-\frac{3 \tanh ^{-1}\left(e^{c (a+b x)}\right) \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c}+\frac{e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c}+\frac{3 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c \left(1-e^{2 c (a+b x)}\right)}-\frac{2 e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c \left(1-e^{2 c (a+b x)}\right)^2}",1,"(E^(c*(a + b*x))*Sqrt[Coth[a*c + b*c*x]^2]*Tanh[a*c + b*c*x])/(b*c) - (2*E^(c*(a + b*x))*Sqrt[Coth[a*c + b*c*x]^2]*Tanh[a*c + b*c*x])/(b*c*(1 - E^(2*c*(a + b*x)))^2) + (3*E^(c*(a + b*x))*Sqrt[Coth[a*c + b*c*x]^2]*Tanh[a*c + b*c*x])/(b*c*(1 - E^(2*c*(a + b*x)))) - (3*ArcTanh[E^(c*(a + b*x))]*Sqrt[Coth[a*c + b*c*x]^2]*Tanh[a*c + b*c*x])/(b*c)","A",8,7,25,0.2800,1,"{6720, 2282, 390, 1158, 12, 288, 207}"
213,1,83,0,0.1436208,"\int e^{c (a+b x)} \sqrt{\coth ^2(a c+b c x)} \, dx","Int[E^(c*(a + b*x))*Sqrt[Coth[a*c + b*c*x]^2],x]","\frac{e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c}-\frac{2 \tanh ^{-1}\left(e^{c (a+b x)}\right) \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c}","\frac{e^{c (a+b x)} \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c}-\frac{2 \tanh ^{-1}\left(e^{c (a+b x)}\right) \tanh (a c+b c x) \sqrt{\coth ^2(a c+b c x)}}{b c}",1,"(E^(c*(a + b*x))*Sqrt[Coth[a*c + b*c*x]^2]*Tanh[a*c + b*c*x])/(b*c) - (2*ArcTanh[E^(c*(a + b*x))]*Sqrt[Coth[a*c + b*c*x]^2]*Tanh[a*c + b*c*x])/(b*c)","A",4,4,25,0.1600,1,"{6720, 2282, 388, 206}"
214,1,83,0,0.1941863,"\int \frac{e^{c (a+b x)}}{\sqrt{\coth ^2(a c+b c x)}} \, dx","Int[E^(c*(a + b*x))/Sqrt[Coth[a*c + b*c*x]^2],x]","\frac{e^{c (a+b x)} \coth (a c+b c x)}{b c \sqrt{\coth ^2(a c+b c x)}}-\frac{2 \tan ^{-1}\left(e^{c (a+b x)}\right) \coth (a c+b c x)}{b c \sqrt{\coth ^2(a c+b c x)}}","\frac{e^{c (a+b x)} \coth (a c+b c x)}{b c \sqrt{\coth ^2(a c+b c x)}}-\frac{2 \tan ^{-1}\left(e^{c (a+b x)}\right) \coth (a c+b c x)}{b c \sqrt{\coth ^2(a c+b c x)}}",1,"(E^(c*(a + b*x))*Coth[a*c + b*c*x])/(b*c*Sqrt[Coth[a*c + b*c*x]^2]) - (2*ArcTan[E^(c*(a + b*x))]*Coth[a*c + b*c*x])/(b*c*Sqrt[Coth[a*c + b*c*x]^2])","A",4,4,25,0.1600,1,"{6720, 2282, 388, 203}"
215,1,193,0,0.8638197,"\int \frac{e^{c (a+b x)}}{\coth ^2(a c+b c x)^{3/2}} \, dx","Int[E^(c*(a + b*x))/(Coth[a*c + b*c*x]^2)^(3/2),x]","\frac{e^{c (a+b x)} \coth (a c+b c x)}{b c \sqrt{\coth ^2(a c+b c x)}}+\frac{3 e^{c (a+b x)} \coth (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right) \sqrt{\coth ^2(a c+b c x)}}-\frac{2 e^{c (a+b x)} \coth (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)^2 \sqrt{\coth ^2(a c+b c x)}}-\frac{3 \tan ^{-1}\left(e^{c (a+b x)}\right) \coth (a c+b c x)}{b c \sqrt{\coth ^2(a c+b c x)}}","\frac{e^{c (a+b x)} \coth (a c+b c x)}{b c \sqrt{\coth ^2(a c+b c x)}}+\frac{3 e^{c (a+b x)} \coth (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right) \sqrt{\coth ^2(a c+b c x)}}-\frac{2 e^{c (a+b x)} \coth (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)^2 \sqrt{\coth ^2(a c+b c x)}}-\frac{3 \tan ^{-1}\left(e^{c (a+b x)}\right) \coth (a c+b c x)}{b c \sqrt{\coth ^2(a c+b c x)}}",1,"(E^(c*(a + b*x))*Coth[a*c + b*c*x])/(b*c*Sqrt[Coth[a*c + b*c*x]^2]) - (2*E^(c*(a + b*x))*Coth[a*c + b*c*x])/(b*c*(1 + E^(2*c*(a + b*x)))^2*Sqrt[Coth[a*c + b*c*x]^2]) + (3*E^(c*(a + b*x))*Coth[a*c + b*c*x])/(b*c*(1 + E^(2*c*(a + b*x)))*Sqrt[Coth[a*c + b*c*x]^2]) - (3*ArcTan[E^(c*(a + b*x))]*Coth[a*c + b*c*x])/(b*c*Sqrt[Coth[a*c + b*c*x]^2])","A",8,7,25,0.2800,1,"{6720, 2282, 390, 1158, 12, 288, 203}"
216,1,311,0,1.7427376,"\int \frac{e^{c (a+b x)}}{\coth ^2(a c+b c x)^{5/2}} \, dx","Int[E^(c*(a + b*x))/(Coth[a*c + b*c*x]^2)^(5/2),x]","\frac{e^{c (a+b x)} \coth (a c+b c x)}{b c \sqrt{\coth ^2(a c+b c x)}}+\frac{25 e^{c (a+b x)} \coth (a c+b c x)}{4 b c \left(e^{2 c (a+b x)}+1\right) \sqrt{\coth ^2(a c+b c x)}}-\frac{55 e^{c (a+b x)} \coth (a c+b c x)}{6 b c \left(e^{2 c (a+b x)}+1\right)^2 \sqrt{\coth ^2(a c+b c x)}}+\frac{26 e^{c (a+b x)} \coth (a c+b c x)}{3 b c \left(e^{2 c (a+b x)}+1\right)^3 \sqrt{\coth ^2(a c+b c x)}}-\frac{4 e^{c (a+b x)} \coth (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)^4 \sqrt{\coth ^2(a c+b c x)}}-\frac{15 \tan ^{-1}\left(e^{c (a+b x)}\right) \coth (a c+b c x)}{4 b c \sqrt{\coth ^2(a c+b c x)}}","\frac{e^{c (a+b x)} \coth (a c+b c x)}{b c \sqrt{\coth ^2(a c+b c x)}}+\frac{25 e^{c (a+b x)} \coth (a c+b c x)}{4 b c \left(e^{2 c (a+b x)}+1\right) \sqrt{\coth ^2(a c+b c x)}}-\frac{55 e^{c (a+b x)} \coth (a c+b c x)}{6 b c \left(e^{2 c (a+b x)}+1\right)^2 \sqrt{\coth ^2(a c+b c x)}}+\frac{26 e^{c (a+b x)} \coth (a c+b c x)}{3 b c \left(e^{2 c (a+b x)}+1\right)^3 \sqrt{\coth ^2(a c+b c x)}}-\frac{4 e^{c (a+b x)} \coth (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)^4 \sqrt{\coth ^2(a c+b c x)}}-\frac{15 \tan ^{-1}\left(e^{c (a+b x)}\right) \coth (a c+b c x)}{4 b c \sqrt{\coth ^2(a c+b c x)}}",1,"(E^(c*(a + b*x))*Coth[a*c + b*c*x])/(b*c*Sqrt[Coth[a*c + b*c*x]^2]) - (4*E^(c*(a + b*x))*Coth[a*c + b*c*x])/(b*c*(1 + E^(2*c*(a + b*x)))^4*Sqrt[Coth[a*c + b*c*x]^2]) + (26*E^(c*(a + b*x))*Coth[a*c + b*c*x])/(3*b*c*(1 + E^(2*c*(a + b*x)))^3*Sqrt[Coth[a*c + b*c*x]^2]) - (55*E^(c*(a + b*x))*Coth[a*c + b*c*x])/(6*b*c*(1 + E^(2*c*(a + b*x)))^2*Sqrt[Coth[a*c + b*c*x]^2]) + (25*E^(c*(a + b*x))*Coth[a*c + b*c*x])/(4*b*c*(1 + E^(2*c*(a + b*x)))*Sqrt[Coth[a*c + b*c*x]^2]) - (15*ArcTan[E^(c*(a + b*x))]*Coth[a*c + b*c*x])/(4*b*c*Sqrt[Coth[a*c + b*c*x]^2])","A",9,7,25,0.2800,1,"{6720, 2282, 390, 1814, 1157, 385, 203}"
217,1,157,0,0.3746716,"\int \sin ^3(\coth (a+b x)) \, dx","Int[Sin[Coth[a + b*x]]^3,x]","\frac{\sin (3) \text{CosIntegral}(3-3 \coth (a+b x))}{8 b}+\frac{\sin (3) \text{CosIntegral}(3 \coth (a+b x)+3)}{8 b}-\frac{3 \sin (1) \text{CosIntegral}(1-\coth (a+b x))}{8 b}-\frac{3 \sin (1) \text{CosIntegral}(\coth (a+b x)+1)}{8 b}-\frac{\cos (3) \text{Si}(3-3 \coth (a+b x))}{8 b}+\frac{3 \cos (1) \text{Si}(1-\coth (a+b x))}{8 b}+\frac{3 \cos (1) \text{Si}(\coth (a+b x)+1)}{8 b}-\frac{\cos (3) \text{Si}(3 \coth (a+b x)+3)}{8 b}","\frac{\sin (3) \text{CosIntegral}(3-3 \coth (a+b x))}{8 b}+\frac{\sin (3) \text{CosIntegral}(3 \coth (a+b x)+3)}{8 b}-\frac{3 \sin (1) \text{CosIntegral}(1-\coth (a+b x))}{8 b}-\frac{3 \sin (1) \text{CosIntegral}(\coth (a+b x)+1)}{8 b}-\frac{\cos (3) \text{Si}(3-3 \coth (a+b x))}{8 b}+\frac{3 \cos (1) \text{Si}(1-\coth (a+b x))}{8 b}+\frac{3 \cos (1) \text{Si}(\coth (a+b x)+1)}{8 b}-\frac{\cos (3) \text{Si}(3 \coth (a+b x)+3)}{8 b}",1,"(-3*CosIntegral[1 - Coth[a + b*x]]*Sin[1])/(8*b) - (3*CosIntegral[1 + Coth[a + b*x]]*Sin[1])/(8*b) + (CosIntegral[3 - 3*Coth[a + b*x]]*Sin[3])/(8*b) + (CosIntegral[3 + 3*Coth[a + b*x]]*Sin[3])/(8*b) - (Cos[3]*SinIntegral[3 - 3*Coth[a + b*x]])/(8*b) + (3*Cos[1]*SinIntegral[1 - Coth[a + b*x]])/(8*b) + (3*Cos[1]*SinIntegral[1 + Coth[a + b*x]])/(8*b) - (Cos[3]*SinIntegral[3 + 3*Coth[a + b*x]])/(8*b)","A",19,5,9,0.5556,1,"{6725, 3312, 3303, 3299, 3302}"
218,1,115,0,0.2620452,"\int \sin ^2(\coth (a+b x)) \, dx","Int[Sin[Coth[a + b*x]]^2,x]","\frac{\cos (2) \text{CosIntegral}(2-2 \coth (a+b x))}{4 b}-\frac{\cos (2) \text{CosIntegral}(2 \coth (a+b x)+2)}{4 b}+\frac{\sin (2) \text{Si}(2-2 \coth (a+b x))}{4 b}-\frac{\sin (2) \text{Si}(2 \coth (a+b x)+2)}{4 b}-\frac{\log (1-\coth (a+b x))}{4 b}+\frac{\log (\coth (a+b x)+1)}{4 b}","\frac{\cos (2) \text{CosIntegral}(2-2 \coth (a+b x))}{4 b}-\frac{\cos (2) \text{CosIntegral}(2 \coth (a+b x)+2)}{4 b}+\frac{\sin (2) \text{Si}(2-2 \coth (a+b x))}{4 b}-\frac{\sin (2) \text{Si}(2 \coth (a+b x)+2)}{4 b}-\frac{\log (1-\coth (a+b x))}{4 b}+\frac{\log (\coth (a+b x)+1)}{4 b}",1,"(Cos[2]*CosIntegral[2 - 2*Coth[a + b*x]])/(4*b) - (Cos[2]*CosIntegral[2 + 2*Coth[a + b*x]])/(4*b) - Log[1 - Coth[a + b*x]]/(4*b) + Log[1 + Coth[a + b*x]]/(4*b) + (Sin[2]*SinIntegral[2 - 2*Coth[a + b*x]])/(4*b) - (Sin[2]*SinIntegral[2 + 2*Coth[a + b*x]])/(4*b)","A",13,5,9,0.5556,1,"{6725, 3312, 3303, 3299, 3302}"
219,1,77,0,0.1441866,"\int \sin (\coth (a+b x)) \, dx","Int[Sin[Coth[a + b*x]],x]","-\frac{\sin (1) \text{CosIntegral}(1-\coth (a+b x))}{2 b}-\frac{\sin (1) \text{CosIntegral}(\coth (a+b x)+1)}{2 b}+\frac{\cos (1) \text{Si}(1-\coth (a+b x))}{2 b}+\frac{\cos (1) \text{Si}(\coth (a+b x)+1)}{2 b}","-\frac{\sin (1) \text{CosIntegral}(1-\coth (a+b x))}{2 b}-\frac{\sin (1) \text{CosIntegral}(\coth (a+b x)+1)}{2 b}+\frac{\cos (1) \text{Si}(1-\coth (a+b x))}{2 b}+\frac{\cos (1) \text{Si}(\coth (a+b x)+1)}{2 b}",1,"-(CosIntegral[1 - Coth[a + b*x]]*Sin[1])/(2*b) - (CosIntegral[1 + Coth[a + b*x]]*Sin[1])/(2*b) + (Cos[1]*SinIntegral[1 - Coth[a + b*x]])/(2*b) + (Cos[1]*SinIntegral[1 + Coth[a + b*x]])/(2*b)","A",9,4,7,0.5714,1,"{3333, 3303, 3299, 3302}"
220,0,0,0,0.0772917,"\int \csc (\coth (a+b x)) \, dx","Int[Csc[Coth[a + b*x]],x]","\int \csc (\coth (a+b x)) \, dx","\frac{1}{2} \text{Int}\left(\frac{\text{csch}^2(a+b x) \csc (\coth (a+b x))}{\coth (a+b x)-1},x\right)-\frac{1}{2} \text{Int}\left(\frac{\text{csch}^2(a+b x) \csc (\coth (a+b x))}{\coth (a+b x)+1},x\right)",0,"-Defer[Subst][Defer[Int][Csc[x]/(-1 + x), x], x, Coth[a + b*x]]/(2*b) + Defer[Subst][Defer[Int][Csc[x]/(1 + x), x], x, Coth[a + b*x]]/(2*b)","A",0,0,0,0,-1,"{}"
221,1,157,0,0.3734507,"\int \cos ^3(\coth (a+b x)) \, dx","Int[Cos[Coth[a + b*x]]^3,x]","-\frac{\cos (3) \text{CosIntegral}(3-3 \coth (a+b x))}{8 b}-\frac{3 \cos (1) \text{CosIntegral}(1-\coth (a+b x))}{8 b}+\frac{3 \cos (1) \text{CosIntegral}(\coth (a+b x)+1)}{8 b}+\frac{\cos (3) \text{CosIntegral}(3 \coth (a+b x)+3)}{8 b}-\frac{\sin (3) \text{Si}(3-3 \coth (a+b x))}{8 b}-\frac{3 \sin (1) \text{Si}(1-\coth (a+b x))}{8 b}+\frac{3 \sin (1) \text{Si}(\coth (a+b x)+1)}{8 b}+\frac{\sin (3) \text{Si}(3 \coth (a+b x)+3)}{8 b}","-\frac{\cos (3) \text{CosIntegral}(3-3 \coth (a+b x))}{8 b}-\frac{3 \cos (1) \text{CosIntegral}(1-\coth (a+b x))}{8 b}+\frac{3 \cos (1) \text{CosIntegral}(\coth (a+b x)+1)}{8 b}+\frac{\cos (3) \text{CosIntegral}(3 \coth (a+b x)+3)}{8 b}-\frac{\sin (3) \text{Si}(3-3 \coth (a+b x))}{8 b}-\frac{3 \sin (1) \text{Si}(1-\coth (a+b x))}{8 b}+\frac{3 \sin (1) \text{Si}(\coth (a+b x)+1)}{8 b}+\frac{\sin (3) \text{Si}(3 \coth (a+b x)+3)}{8 b}",1,"-(Cos[3]*CosIntegral[3 - 3*Coth[a + b*x]])/(8*b) - (3*Cos[1]*CosIntegral[1 - Coth[a + b*x]])/(8*b) + (3*Cos[1]*CosIntegral[1 + Coth[a + b*x]])/(8*b) + (Cos[3]*CosIntegral[3 + 3*Coth[a + b*x]])/(8*b) - (Sin[3]*SinIntegral[3 - 3*Coth[a + b*x]])/(8*b) - (3*Sin[1]*SinIntegral[1 - Coth[a + b*x]])/(8*b) + (3*Sin[1]*SinIntegral[1 + Coth[a + b*x]])/(8*b) + (Sin[3]*SinIntegral[3 + 3*Coth[a + b*x]])/(8*b)","A",19,5,9,0.5556,1,"{6725, 3312, 3303, 3299, 3302}"
222,1,115,0,0.2512062,"\int \cos ^2(\coth (a+b x)) \, dx","Int[Cos[Coth[a + b*x]]^2,x]","-\frac{\cos (2) \text{CosIntegral}(2-2 \coth (a+b x))}{4 b}+\frac{\cos (2) \text{CosIntegral}(2 \coth (a+b x)+2)}{4 b}-\frac{\sin (2) \text{Si}(2-2 \coth (a+b x))}{4 b}+\frac{\sin (2) \text{Si}(2 \coth (a+b x)+2)}{4 b}-\frac{\log (1-\coth (a+b x))}{4 b}+\frac{\log (\coth (a+b x)+1)}{4 b}","-\frac{\cos (2) \text{CosIntegral}(2-2 \coth (a+b x))}{4 b}+\frac{\cos (2) \text{CosIntegral}(2 \coth (a+b x)+2)}{4 b}-\frac{\sin (2) \text{Si}(2-2 \coth (a+b x))}{4 b}+\frac{\sin (2) \text{Si}(2 \coth (a+b x)+2)}{4 b}-\frac{\log (1-\coth (a+b x))}{4 b}+\frac{\log (\coth (a+b x)+1)}{4 b}",1,"-(Cos[2]*CosIntegral[2 - 2*Coth[a + b*x]])/(4*b) + (Cos[2]*CosIntegral[2 + 2*Coth[a + b*x]])/(4*b) - Log[1 - Coth[a + b*x]]/(4*b) + Log[1 + Coth[a + b*x]]/(4*b) - (Sin[2]*SinIntegral[2 - 2*Coth[a + b*x]])/(4*b) + (Sin[2]*SinIntegral[2 + 2*Coth[a + b*x]])/(4*b)","A",13,5,9,0.5556,1,"{6725, 3312, 3303, 3299, 3302}"
223,1,77,0,0.1400221,"\int \cos (\coth (a+b x)) \, dx","Int[Cos[Coth[a + b*x]],x]","-\frac{\cos (1) \text{CosIntegral}(1-\coth (a+b x))}{2 b}+\frac{\cos (1) \text{CosIntegral}(\coth (a+b x)+1)}{2 b}-\frac{\sin (1) \text{Si}(1-\coth (a+b x))}{2 b}+\frac{\sin (1) \text{Si}(\coth (a+b x)+1)}{2 b}","-\frac{\cos (1) \text{CosIntegral}(1-\coth (a+b x))}{2 b}+\frac{\cos (1) \text{CosIntegral}(\coth (a+b x)+1)}{2 b}-\frac{\sin (1) \text{Si}(1-\coth (a+b x))}{2 b}+\frac{\sin (1) \text{Si}(\coth (a+b x)+1)}{2 b}",1,"-(Cos[1]*CosIntegral[1 - Coth[a + b*x]])/(2*b) + (Cos[1]*CosIntegral[1 + Coth[a + b*x]])/(2*b) - (Sin[1]*SinIntegral[1 - Coth[a + b*x]])/(2*b) + (Sin[1]*SinIntegral[1 + Coth[a + b*x]])/(2*b)","A",9,4,7,0.5714,1,"{3334, 3303, 3299, 3302}"
224,0,0,0,0.0770718,"\int \sec (\coth (a+b x)) \, dx","Int[Sec[Coth[a + b*x]],x]","\int \sec (\coth (a+b x)) \, dx","\frac{1}{2} \text{Int}\left(\frac{\text{csch}^2(a+b x) \sec (\coth (a+b x))}{\coth (a+b x)-1},x\right)-\frac{1}{2} \text{Int}\left(\frac{\text{csch}^2(a+b x) \sec (\coth (a+b x))}{\coth (a+b x)+1},x\right)",0,"-Defer[Subst][Defer[Int][Sec[x]/(-1 + x), x], x, Coth[a + b*x]]/(2*b) + Defer[Subst][Defer[Int][Sec[x]/(1 + x), x], x, Coth[a + b*x]]/(2*b)","A",0,0,0,0,-1,"{}"