1,1,160,0,0.0921927,"\int \left(a+b \coth ^2(c+d x)\right)^5 \, dx","Int[(a + b*Coth[c + d*x]^2)^5,x]","-\frac{b^3 \left(10 a^2+5 a b+b^2\right) \coth ^5(c+d x)}{5 d}-\frac{b^2 \left(10 a^2 b+10 a^3+5 a b^2+b^3\right) \coth ^3(c+d x)}{3 d}-\frac{b \left(10 a^2 b^2+10 a^3 b+5 a^4+5 a b^3+b^4\right) \coth (c+d x)}{d}-\frac{b^4 (5 a+b) \coth ^7(c+d x)}{7 d}+x (a+b)^5-\frac{b^5 \coth ^9(c+d x)}{9 d}","-\frac{b^3 \left(10 a^2+5 a b+b^2\right) \coth ^5(c+d x)}{5 d}-\frac{b^2 \left(10 a^2 b+10 a^3+5 a b^2+b^3\right) \coth ^3(c+d x)}{3 d}-\frac{b \left(10 a^2 b^2+10 a^3 b+5 a^4+5 a b^3+b^4\right) \coth (c+d x)}{d}-\frac{b^4 (5 a+b) \coth ^7(c+d x)}{7 d}+x (a+b)^5-\frac{b^5 \coth ^9(c+d x)}{9 d}",1,"(a + b)^5*x - (b*(5*a^4 + 10*a^3*b + 10*a^2*b^2 + 5*a*b^3 + b^4)*Coth[c + d*x])/d - (b^2*(10*a^3 + 10*a^2*b + 5*a*b^2 + b^3)*Coth[c + d*x]^3)/(3*d) - (b^3*(10*a^2 + 5*a*b + b^2)*Coth[c + d*x]^5)/(5*d) - (b^4*(5*a + b)*Coth[c + d*x]^7)/(7*d) - (b^5*Coth[c + d*x]^9)/(9*d)","A",4,3,14,0.2143,1,"{3661, 390, 206}"
2,1,110,0,0.0677726,"\int \left(a+b \coth ^2(c+d x)\right)^4 \, dx","Int[(a + b*Coth[c + d*x]^2)^4,x]","-\frac{b^2 \left(6 a^2+4 a b+b^2\right) \coth ^3(c+d x)}{3 d}-\frac{b (2 a+b) \left(2 a^2+2 a b+b^2\right) \coth (c+d x)}{d}-\frac{b^3 (4 a+b) \coth ^5(c+d x)}{5 d}+x (a+b)^4-\frac{b^4 \coth ^7(c+d x)}{7 d}","-\frac{b^2 \left(6 a^2+4 a b+b^2\right) \coth ^3(c+d x)}{3 d}-\frac{b (2 a+b) \left(2 a^2+2 a b+b^2\right) \coth (c+d x)}{d}-\frac{b^3 (4 a+b) \coth ^5(c+d x)}{5 d}+x (a+b)^4-\frac{b^4 \coth ^7(c+d x)}{7 d}",1,"(a + b)^4*x - (b*(2*a + b)*(2*a^2 + 2*a*b + b^2)*Coth[c + d*x])/d - (b^2*(6*a^2 + 4*a*b + b^2)*Coth[c + d*x]^3)/(3*d) - (b^3*(4*a + b)*Coth[c + d*x]^5)/(5*d) - (b^4*Coth[c + d*x]^7)/(7*d)","A",4,3,14,0.2143,1,"{3661, 390, 206}"
3,1,74,0,0.0467793,"\int \left(a+b \coth ^2(c+d x)\right)^3 \, dx","Int[(a + b*Coth[c + d*x]^2)^3,x]","-\frac{b \left(3 a^2+3 a b+b^2\right) \coth (c+d x)}{d}-\frac{b^2 (3 a+b) \coth ^3(c+d x)}{3 d}+x (a+b)^3-\frac{b^3 \coth ^5(c+d x)}{5 d}","-\frac{b \left(3 a^2+3 a b+b^2\right) \coth (c+d x)}{d}-\frac{b^2 (3 a+b) \coth ^3(c+d x)}{3 d}+x (a+b)^3-\frac{b^3 \coth ^5(c+d x)}{5 d}",1,"(a + b)^3*x - (b*(3*a^2 + 3*a*b + b^2)*Coth[c + d*x])/d - (b^2*(3*a + b)*Coth[c + d*x]^3)/(3*d) - (b^3*Coth[c + d*x]^5)/(5*d)","A",4,3,14,0.2143,1,"{3661, 390, 206}"
4,1,43,0,0.0331715,"\int \left(a+b \coth ^2(c+d x)\right)^2 \, dx","Int[(a + b*Coth[c + d*x]^2)^2,x]","-\frac{b (2 a+b) \coth (c+d x)}{d}+x (a+b)^2-\frac{b^2 \coth ^3(c+d x)}{3 d}","-\frac{b (2 a+b) \coth (c+d x)}{d}+x (a+b)^2-\frac{b^2 \coth ^3(c+d x)}{3 d}",1,"(a + b)^2*x - (b*(2*a + b)*Coth[c + d*x])/d - (b^2*Coth[c + d*x]^3)/(3*d)","A",4,3,14,0.2143,1,"{3661, 390, 206}"
5,1,46,0,0.0774405,"\int \frac{1}{a+b \coth ^2(c+d x)} \, dx","Int[(a + b*Coth[c + d*x]^2)^(-1),x]","\frac{x}{a+b}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{b}}\right)}{\sqrt{a} d (a+b)}","\frac{x}{a+b}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{b}}\right)}{\sqrt{a} d (a+b)}",1,"x/(a + b) - (Sqrt[b]*ArcTan[(Sqrt[a]*Tanh[c + d*x])/Sqrt[b]])/(Sqrt[a]*(a + b)*d)","A",3,3,14,0.2143,1,"{3660, 3675, 205}"
6,1,89,0,0.1013906,"\int \frac{1}{\left(a+b \coth ^2(c+d x)\right)^2} \, dx","Int[(a + b*Coth[c + d*x]^2)^(-2),x]","-\frac{\sqrt{b} (3 a+b) \tan ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{b}}\right)}{2 a^{3/2} d (a+b)^2}+\frac{b \coth (c+d x)}{2 a d (a+b) \left(a+b \coth ^2(c+d x)\right)}+\frac{x}{(a+b)^2}","-\frac{\sqrt{b} (3 a+b) \tan ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{b}}\right)}{2 a^{3/2} d (a+b)^2}+\frac{b \coth (c+d x)}{2 a d (a+b) \left(a+b \coth ^2(c+d x)\right)}+\frac{x}{(a+b)^2}",1,"x/(a + b)^2 - (Sqrt[b]*(3*a + b)*ArcTan[(Sqrt[a]*Tanh[c + d*x])/Sqrt[b]])/(2*a^(3/2)*(a + b)^2*d) + (b*Coth[c + d*x])/(2*a*(a + b)*d*(a + b*Coth[c + d*x]^2))","A",5,5,14,0.3571,1,"{3661, 414, 522, 206, 205}"
7,1,142,0,0.1599719,"\int \frac{1}{\left(a+b \coth ^2(c+d x)\right)^3} \, dx","Int[(a + b*Coth[c + d*x]^2)^(-3),x]","-\frac{\sqrt{b} \left(15 a^2+10 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{b}}\right)}{8 a^{5/2} d (a+b)^3}+\frac{b (7 a+3 b) \coth (c+d x)}{8 a^2 d (a+b)^2 \left(a+b \coth ^2(c+d x)\right)}+\frac{b \coth (c+d x)}{4 a d (a+b) \left(a+b \coth ^2(c+d x)\right)^2}+\frac{x}{(a+b)^3}","-\frac{\sqrt{b} \left(15 a^2+10 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{b}}\right)}{8 a^{5/2} d (a+b)^3}+\frac{b (7 a+3 b) \coth (c+d x)}{8 a^2 d (a+b)^2 \left(a+b \coth ^2(c+d x)\right)}+\frac{b \coth (c+d x)}{4 a d (a+b) \left(a+b \coth ^2(c+d x)\right)^2}+\frac{x}{(a+b)^3}",1,"x/(a + b)^3 - (Sqrt[b]*(15*a^2 + 10*a*b + 3*b^2)*ArcTan[(Sqrt[a]*Tanh[c + d*x])/Sqrt[b]])/(8*a^(5/2)*(a + b)^3*d) + (b*Coth[c + d*x])/(4*a*(a + b)*d*(a + b*Coth[c + d*x]^2)^2) + (b*(7*a + 3*b)*Coth[c + d*x])/(8*a^2*(a + b)^2*d*(a + b*Coth[c + d*x]^2))","A",6,6,14,0.4286,1,"{3661, 414, 527, 522, 206, 205}"
8,1,201,0,0.2785085,"\int \frac{1}{\left(a+b \coth ^2(c+d x)\right)^4} \, dx","Int[(a + b*Coth[c + d*x]^2)^(-4),x]","\frac{b \left(19 a^2+16 a b+5 b^2\right) \coth (c+d x)}{16 a^3 d (a+b)^3 \left(a+b \coth ^2(c+d x)\right)}-\frac{\sqrt{b} \left(35 a^2 b+35 a^3+21 a b^2+5 b^3\right) \tan ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{b}}\right)}{16 a^{7/2} d (a+b)^4}+\frac{b (11 a+5 b) \coth (c+d x)}{24 a^2 d (a+b)^2 \left(a+b \coth ^2(c+d x)\right)^2}+\frac{b \coth (c+d x)}{6 a d (a+b) \left(a+b \coth ^2(c+d x)\right)^3}+\frac{x}{(a+b)^4}","\frac{b \left(19 a^2+16 a b+5 b^2\right) \coth (c+d x)}{16 a^3 d (a+b)^3 \left(a+b \coth ^2(c+d x)\right)}-\frac{\sqrt{b} \left(35 a^2 b+35 a^3+21 a b^2+5 b^3\right) \tan ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{b}}\right)}{16 a^{7/2} d (a+b)^4}+\frac{b (11 a+5 b) \coth (c+d x)}{24 a^2 d (a+b)^2 \left(a+b \coth ^2(c+d x)\right)^2}+\frac{b \coth (c+d x)}{6 a d (a+b) \left(a+b \coth ^2(c+d x)\right)^3}+\frac{x}{(a+b)^4}",1,"x/(a + b)^4 - (Sqrt[b]*(35*a^3 + 35*a^2*b + 21*a*b^2 + 5*b^3)*ArcTan[(Sqrt[a]*Tanh[c + d*x])/Sqrt[b]])/(16*a^(7/2)*(a + b)^4*d) + (b*Coth[c + d*x])/(6*a*(a + b)*d*(a + b*Coth[c + d*x]^2)^3) + (b*(11*a + 5*b)*Coth[c + d*x])/(24*a^2*(a + b)^2*d*(a + b*Coth[c + d*x]^2)^2) + (b*(19*a^2 + 16*a*b + 5*b^2)*Coth[c + d*x])/(16*a^3*(a + b)^3*d*(a + b*Coth[c + d*x]^2))","A",7,6,14,0.4286,1,"{3661, 414, 527, 522, 206, 205}"
9,1,19,0,0.0514689,"\int \frac{1}{1-2 \coth ^2(x)} \, dx","Int[(1 - 2*Coth[x]^2)^(-1),x]","\sqrt{2} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)-x","\sqrt{2} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)-x",1,"-x + Sqrt[2]*ArcTanh[Tanh[x]/Sqrt[2]]","A",3,3,10,0.3000,1,"{3660, 3675, 206}"
10,1,3,0,0.0183658,"\int \sqrt{1-\coth ^2(x)} \, dx","Int[Sqrt[1 - Coth[x]^2],x]","\sin ^{-1}(\coth (x))","\sin ^{-1}(\coth (x))",1,"ArcSin[Coth[x]]","A",3,3,12,0.2500,1,"{3657, 4122, 216}"
11,1,14,0,0.0214563,"\int \sqrt{-1+\coth ^2(x)} \, dx","Int[Sqrt[-1 + Coth[x]^2],x]","-\tanh ^{-1}\left(\frac{\coth (x)}{\sqrt{\text{csch}^2(x)}}\right)","-\tanh ^{-1}\left(\frac{\coth (x)}{\sqrt{\text{csch}^2(x)}}\right)",1,"-ArcTanh[Coth[x]/Sqrt[Csch[x]^2]]","A",4,4,10,0.4000,1,"{3657, 4122, 217, 206}"
12,1,24,0,0.0216834,"\int \left(1-\coth ^2(x)\right)^{3/2} \, dx","Int[(1 - Coth[x]^2)^(3/2),x]","\frac{1}{2} \sin ^{-1}(\coth (x))+\frac{1}{2} \coth (x) \sqrt{-\text{csch}^2(x)}","\frac{1}{2} \sin ^{-1}(\coth (x))+\frac{1}{2} \coth (x) \sqrt{-\text{csch}^2(x)}",1,"ArcSin[Coth[x]]/2 + (Coth[x]*Sqrt[-Csch[x]^2])/2","A",4,4,12,0.3333,1,"{3657, 4122, 195, 216}"
13,1,31,0,0.0228202,"\int \left(-1+\coth ^2(x)\right)^{3/2} \, dx","Int[(-1 + Coth[x]^2)^(3/2),x]","\frac{1}{2} \tanh ^{-1}\left(\frac{\coth (x)}{\sqrt{\text{csch}^2(x)}}\right)-\frac{1}{2} \coth (x) \sqrt{\text{csch}^2(x)}","\frac{1}{2} \tanh ^{-1}\left(\frac{\coth (x)}{\sqrt{\text{csch}^2(x)}}\right)-\frac{1}{2} \coth (x) \sqrt{\text{csch}^2(x)}",1,"ArcTanh[Coth[x]/Sqrt[Csch[x]^2]]/2 - (Coth[x]*Sqrt[Csch[x]^2])/2","A",5,5,10,0.5000,1,"{3657, 4122, 195, 217, 206}"
14,1,13,0,0.0217987,"\int \frac{1}{\sqrt{1-\coth ^2(x)}} \, dx","Int[1/Sqrt[1 - Coth[x]^2],x]","\frac{\coth (x)}{\sqrt{-\text{csch}^2(x)}}","\frac{\coth (x)}{\sqrt{-\text{csch}^2(x)}}",1,"Coth[x]/Sqrt[-Csch[x]^2]","A",3,3,12,0.2500,1,"{3657, 4122, 191}"
15,1,11,0,0.020726,"\int \frac{1}{\sqrt{-1+\coth ^2(x)}} \, dx","Int[1/Sqrt[-1 + Coth[x]^2],x]","\frac{\coth (x)}{\sqrt{\text{csch}^2(x)}}","\frac{\coth (x)}{\sqrt{\text{csch}^2(x)}}",1,"Coth[x]/Sqrt[Csch[x]^2]","A",3,3,10,0.3000,1,"{3657, 4122, 191}"
16,1,63,0,0.1226897,"\int \coth ^3(x) \sqrt{a+b \coth ^2(x)} \, dx","Int[Coth[x]^3*Sqrt[a + b*Coth[x]^2],x]","-\frac{\left(a+b \coth ^2(x)\right)^{3/2}}{3 b}-\sqrt{a+b \coth ^2(x)}+\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)","-\frac{\left(a+b \coth ^2(x)\right)^{3/2}}{3 b}-\sqrt{a+b \coth ^2(x)}+\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)",1,"Sqrt[a + b]*ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a + b]] - Sqrt[a + b*Coth[x]^2] - (a + b*Coth[x]^2)^(3/2)/(3*b)","A",6,6,17,0.3529,1,"{3670, 446, 80, 50, 63, 208}"
17,1,85,0,0.1278817,"\int \coth ^2(x) \sqrt{a+b \coth ^2(x)} \, dx","Int[Coth[x]^2*Sqrt[a + b*Coth[x]^2],x]","-\frac{1}{2} \coth (x) \sqrt{a+b \coth ^2(x)}-\frac{(a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{2 \sqrt{b}}+\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)","-\frac{1}{2} \coth (x) \sqrt{a+b \coth ^2(x)}-\frac{(a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{2 \sqrt{b}}+\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)",1,"-((a + 2*b)*ArcTanh[(Sqrt[b]*Coth[x])/Sqrt[a + b*Coth[x]^2]])/(2*Sqrt[b]) + Sqrt[a + b]*ArcTanh[(Sqrt[a + b]*Coth[x])/Sqrt[a + b*Coth[x]^2]] - (Coth[x]*Sqrt[a + b*Coth[x]^2])/2","A",7,6,17,0.3529,1,"{3670, 478, 523, 217, 206, 377}"
18,1,44,0,0.0770213,"\int \coth (x) \sqrt{a+b \coth ^2(x)} \, dx","Int[Coth[x]*Sqrt[a + b*Coth[x]^2],x]","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)-\sqrt{a+b \coth ^2(x)}","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)-\sqrt{a+b \coth ^2(x)}",1,"Sqrt[a + b]*ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a + b]] - Sqrt[a + b*Coth[x]^2]","A",5,5,15,0.3333,1,"{3670, 444, 50, 63, 208}"
19,1,60,0,0.0453608,"\int \sqrt{a+b \coth ^2(x)} \, dx","Int[Sqrt[a + b*Coth[x]^2],x]","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)-\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)-\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)",1,"-(Sqrt[b]*ArcTanh[(Sqrt[b]*Coth[x])/Sqrt[a + b*Coth[x]^2]]) + Sqrt[a + b]*ArcTanh[(Sqrt[a + b]*Coth[x])/Sqrt[a + b*Coth[x]^2]]","A",6,5,12,0.4167,1,"{3661, 402, 217, 206, 377}"
20,1,56,0,0.1099635,"\int \sqrt{a+b \coth ^2(x)} \tanh (x) \, dx","Int[Sqrt[a + b*Coth[x]^2]*Tanh[x],x]","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)-\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a}}\right)","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)-\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a}}\right)",1,"-(Sqrt[a]*ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a]]) + Sqrt[a + b]*ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a + b]]","A",7,5,15,0.3333,1,"{3670, 446, 83, 63, 208}"
21,1,48,0,0.0889972,"\int \sqrt{a+b \coth ^2(x)} \tanh ^2(x) \, dx","Int[Sqrt[a + b*Coth[x]^2]*Tanh[x]^2,x]","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)-\tanh (x) \sqrt{a+b \coth ^2(x)}","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)-\tanh (x) \sqrt{a+b \coth ^2(x)}",1,"Sqrt[a + b]*ArcTanh[(Sqrt[a + b]*Coth[x])/Sqrt[a + b*Coth[x]^2]] - Sqrt[a + b*Coth[x]^2]*Tanh[x]","A",5,5,17,0.2941,1,"{3670, 475, 12, 377, 206}"
22,1,82,0,0.1485132,"\int \coth ^3(x) \left(a+b \coth ^2(x)\right)^{3/2} \, dx","Int[Coth[x]^3*(a + b*Coth[x]^2)^(3/2),x]","-\frac{\left(a+b \coth ^2(x)\right)^{5/2}}{5 b}-\frac{1}{3} \left(a+b \coth ^2(x)\right)^{3/2}-(a+b) \sqrt{a+b \coth ^2(x)}+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)","-\frac{\left(a+b \coth ^2(x)\right)^{5/2}}{5 b}-\frac{1}{3} \left(a+b \coth ^2(x)\right)^{3/2}-(a+b) \sqrt{a+b \coth ^2(x)}+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)",1,"(a + b)^(3/2)*ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a + b]] - (a + b)*Sqrt[a + b*Coth[x]^2] - (a + b*Coth[x]^2)^(3/2)/3 - (a + b*Coth[x]^2)^(5/2)/(5*b)","A",7,6,17,0.3529,1,"{3670, 446, 80, 50, 63, 208}"
23,1,123,0,0.2440353,"\int \coth ^2(x) \left(a+b \coth ^2(x)\right)^{3/2} \, dx","Int[Coth[x]^2*(a + b*Coth[x]^2)^(3/2),x]","-\frac{\left(3 a^2+12 a b+8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{8 \sqrt{b}}-\frac{1}{4} b \coth ^3(x) \sqrt{a+b \coth ^2(x)}-\frac{1}{8} (5 a+4 b) \coth (x) \sqrt{a+b \coth ^2(x)}+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)","-\frac{\left(3 a^2+12 a b+8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{8 \sqrt{b}}-\frac{1}{4} b \coth ^3(x) \sqrt{a+b \coth ^2(x)}-\frac{1}{8} (5 a+4 b) \coth (x) \sqrt{a+b \coth ^2(x)}+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)",1,"-((3*a^2 + 12*a*b + 8*b^2)*ArcTanh[(Sqrt[b]*Coth[x])/Sqrt[a + b*Coth[x]^2]])/(8*Sqrt[b]) + (a + b)^(3/2)*ArcTanh[(Sqrt[a + b]*Coth[x])/Sqrt[a + b*Coth[x]^2]] - ((5*a + 4*b)*Coth[x]*Sqrt[a + b*Coth[x]^2])/8 - (b*Coth[x]^3*Sqrt[a + b*Coth[x]^2])/4","A",8,7,17,0.4118,1,"{3670, 477, 582, 523, 217, 206, 377}"
24,1,63,0,0.1021835,"\int \coth (x) \left(a+b \coth ^2(x)\right)^{3/2} \, dx","Int[Coth[x]*(a + b*Coth[x]^2)^(3/2),x]","-(a+b) \sqrt{a+b \coth ^2(x)}-\frac{1}{3} \left(a+b \coth ^2(x)\right)^{3/2}+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)","-(a+b) \sqrt{a+b \coth ^2(x)}-\frac{1}{3} \left(a+b \coth ^2(x)\right)^{3/2}+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)",1,"(a + b)^(3/2)*ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a + b]] - (a + b)*Sqrt[a + b*Coth[x]^2] - (a + b*Coth[x]^2)^(3/2)/3","A",6,5,15,0.3333,1,"{3670, 444, 50, 63, 208}"
25,1,88,0,0.0894205,"\int \left(a+b \coth ^2(x)\right)^{3/2} \, dx","Int[(a + b*Coth[x]^2)^(3/2),x]","-\frac{1}{2} b \coth (x) \sqrt{a+b \coth ^2(x)}+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)-\frac{1}{2} \sqrt{b} (3 a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)","-\frac{1}{2} b \coth (x) \sqrt{a+b \coth ^2(x)}+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)-\frac{1}{2} \sqrt{b} (3 a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)",1,"-(Sqrt[b]*(3*a + 2*b)*ArcTanh[(Sqrt[b]*Coth[x])/Sqrt[a + b*Coth[x]^2]])/2 + (a + b)^(3/2)*ArcTanh[(Sqrt[a + b]*Coth[x])/Sqrt[a + b*Coth[x]^2]] - (b*Coth[x]*Sqrt[a + b*Coth[x]^2])/2","A",7,6,12,0.5000,1,"{3661, 416, 523, 217, 206, 377}"
26,1,71,0,0.1391046,"\int \left(a+b \coth ^2(x)\right)^{3/2} \tanh (x) \, dx","Int[(a + b*Coth[x]^2)^(3/2)*Tanh[x],x]","a^{3/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a}}\right)\right)-b \sqrt{a+b \coth ^2(x)}+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)","a^{3/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a}}\right)\right)-b \sqrt{a+b \coth ^2(x)}+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)",1,"-(a^(3/2)*ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a]]) + (a + b)^(3/2)*ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a + b]] - b*Sqrt[a + b*Coth[x]^2]","A",8,6,15,0.4000,1,"{3670, 446, 84, 156, 63, 208}"
27,1,77,0,0.1275319,"\int \left(a+b \coth ^2(x)\right)^{3/2} \tanh ^2(x) \, dx","Int[(a + b*Coth[x]^2)^(3/2)*Tanh[x]^2,x]","b^{3/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)\right)+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)-a \tanh (x) \sqrt{a+b \coth ^2(x)}","b^{3/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)\right)+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)-a \tanh (x) \sqrt{a+b \coth ^2(x)}",1,"-(b^(3/2)*ArcTanh[(Sqrt[b]*Coth[x])/Sqrt[a + b*Coth[x]^2]]) + (a + b)^(3/2)*ArcTanh[(Sqrt[a + b]*Coth[x])/Sqrt[a + b*Coth[x]^2]] - a*Sqrt[a + b*Coth[x]^2]*Tanh[x]","A",7,6,17,0.3529,1,"{3670, 474, 523, 217, 206, 377}"
28,1,31,0,0.0261764,"\int \sqrt{1+\coth ^2(x)} \, dx","Int[Sqrt[1 + Coth[x]^2],x]","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \coth (x)}{\sqrt{\coth ^2(x)+1}}\right)-\sinh ^{-1}(\coth (x))","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \coth (x)}{\sqrt{\coth ^2(x)+1}}\right)-\sinh ^{-1}(\coth (x))",1,"-ArcSinh[Coth[x]] + Sqrt[2]*ArcTanh[(Sqrt[2]*Coth[x])/Sqrt[1 + Coth[x]^2]]","A",5,5,10,0.5000,1,"{3661, 402, 215, 377, 206}"
29,1,45,0,0.0336847,"\int \sqrt{-1-\coth ^2(x)} \, dx","Int[Sqrt[-1 - Coth[x]^2],x]","\tan ^{-1}\left(\frac{\coth (x)}{\sqrt{-\coth ^2(x)-1}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \coth (x)}{\sqrt{-\coth ^2(x)-1}}\right)","\tan ^{-1}\left(\frac{\coth (x)}{\sqrt{-\coth ^2(x)-1}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \coth (x)}{\sqrt{-\coth ^2(x)-1}}\right)",1,"ArcTan[Coth[x]/Sqrt[-1 - Coth[x]^2]] - Sqrt[2]*ArcTan[(Sqrt[2]*Coth[x])/Sqrt[-1 - Coth[x]^2]]","A",6,5,12,0.4167,1,"{3661, 402, 217, 203, 377}"
30,1,50,0,0.0392872,"\int \left(1+\coth ^2(x)\right)^{3/2} \, dx","Int[(1 + Coth[x]^2)^(3/2),x]","-\frac{1}{2} \coth (x) \sqrt{\coth ^2(x)+1}+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \coth (x)}{\sqrt{\coth ^2(x)+1}}\right)-\frac{5}{2} \sinh ^{-1}(\coth (x))","-\frac{1}{2} \coth (x) \sqrt{\coth ^2(x)+1}+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \coth (x)}{\sqrt{\coth ^2(x)+1}}\right)-\frac{5}{2} \sinh ^{-1}(\coth (x))",1,"(-5*ArcSinh[Coth[x]])/2 + 2*Sqrt[2]*ArcTanh[(Sqrt[2]*Coth[x])/Sqrt[1 + Coth[x]^2]] - (Coth[x]*Sqrt[1 + Coth[x]^2])/2","A",6,6,10,0.6000,1,"{3661, 416, 523, 215, 377, 206}"
31,1,67,0,0.0478565,"\int \left(-1-\coth ^2(x)\right)^{3/2} \, dx","Int[(-1 - Coth[x]^2)^(3/2),x]","\frac{1}{2} \coth (x) \sqrt{-\coth ^2(x)-1}-\frac{5}{2} \tan ^{-1}\left(\frac{\coth (x)}{\sqrt{-\coth ^2(x)-1}}\right)+2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \coth (x)}{\sqrt{-\coth ^2(x)-1}}\right)","\frac{1}{2} \coth (x) \sqrt{-\coth ^2(x)-1}-\frac{5}{2} \tan ^{-1}\left(\frac{\coth (x)}{\sqrt{-\coth ^2(x)-1}}\right)+2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \coth (x)}{\sqrt{-\coth ^2(x)-1}}\right)",1,"(-5*ArcTan[Coth[x]/Sqrt[-1 - Coth[x]^2]])/2 + 2*Sqrt[2]*ArcTan[(Sqrt[2]*Coth[x])/Sqrt[-1 - Coth[x]^2]] + (Coth[x]*Sqrt[-1 - Coth[x]^2])/2","A",7,6,12,0.5000,1,"{3661, 416, 523, 217, 203, 377}"
32,1,47,0,0.1096948,"\int \frac{\coth ^3(x)}{\sqrt{a+b \coth ^2(x)}} \, dx","Int[Coth[x]^3/Sqrt[a + b*Coth[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}-\frac{\sqrt{a+b \coth ^2(x)}}{b}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}-\frac{\sqrt{a+b \coth ^2(x)}}{b}",1,"ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a + b]]/Sqrt[a + b] - Sqrt[a + b*Coth[x]^2]/b","A",5,5,17,0.2941,1,"{3670, 446, 80, 63, 208}"
33,1,60,0,0.0950472,"\int \frac{\coth ^2(x)}{\sqrt{a+b \coth ^2(x)}} \, dx","Int[Coth[x]^2/Sqrt[a + b*Coth[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{\sqrt{a+b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{\sqrt{b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{\sqrt{a+b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{\sqrt{b}}",1,"-(ArcTanh[(Sqrt[b]*Coth[x])/Sqrt[a + b*Coth[x]^2]]/Sqrt[b]) + ArcTanh[(Sqrt[a + b]*Coth[x])/Sqrt[a + b*Coth[x]^2]]/Sqrt[a + b]","A",6,5,17,0.2941,1,"{3670, 483, 217, 206, 377}"
34,1,29,0,0.0647116,"\int \frac{\coth (x)}{\sqrt{a+b \coth ^2(x)}} \, dx","Int[Coth[x]/Sqrt[a + b*Coth[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}",1,"ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a + b]]/Sqrt[a + b]","A",4,4,15,0.2667,1,"{3670, 444, 63, 208}"
35,1,31,0,0.0267725,"\int \frac{1}{\sqrt{a+b \coth ^2(x)}} \, dx","Int[1/Sqrt[a + b*Coth[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{\sqrt{a+b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{\sqrt{a+b}}",1,"ArcTanh[(Sqrt[a + b]*Coth[x])/Sqrt[a + b*Coth[x]^2]]/Sqrt[a + b]","A",3,3,12,0.2500,1,"{3661, 377, 206}"
36,1,56,0,0.1092993,"\int \frac{\tanh (x)}{\sqrt{a+b \coth ^2(x)}} \, dx","Int[Tanh[x]/Sqrt[a + b*Coth[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"-(ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a]]/Sqrt[a]) + ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a + b]]/Sqrt[a + b]","A",7,5,15,0.3333,1,"{3670, 446, 86, 63, 208}"
37,1,51,0,0.0960036,"\int \frac{\tanh ^2(x)}{\sqrt{a+b \coth ^2(x)}} \, dx","Int[Tanh[x]^2/Sqrt[a + b*Coth[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{\sqrt{a+b}}-\frac{\tanh (x) \sqrt{a+b \coth ^2(x)}}{a}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{\sqrt{a+b}}-\frac{\tanh (x) \sqrt{a+b \coth ^2(x)}}{a}",1,"ArcTanh[(Sqrt[a + b]*Coth[x])/Sqrt[a + b*Coth[x]^2]]/Sqrt[a + b] - (Sqrt[a + b*Coth[x]^2]*Tanh[x])/a","A",5,5,17,0.2941,1,"{3670, 480, 12, 377, 206}"
38,1,52,0,0.1235851,"\int \frac{\coth ^3(x)}{\left(a+b \coth ^2(x)\right)^{3/2}} \, dx","Int[Coth[x]^3/(a + b*Coth[x]^2)^(3/2),x]","\frac{a}{b (a+b) \sqrt{a+b \coth ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{3/2}}","\frac{a}{b (a+b) \sqrt{a+b \coth ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{3/2}}",1,"ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a + b]]/(a + b)^(3/2) + a/(b*(a + b)*Sqrt[a + b*Coth[x]^2])","A",5,5,17,0.2941,1,"{3670, 446, 78, 63, 208}"
39,1,53,0,0.0998092,"\int \frac{\coth ^2(x)}{\left(a+b \coth ^2(x)\right)^{3/2}} \, dx","Int[Coth[x]^2/(a + b*Coth[x]^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{(a+b)^{3/2}}-\frac{\coth (x)}{(a+b) \sqrt{a+b \coth ^2(x)}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{(a+b)^{3/2}}-\frac{\coth (x)}{(a+b) \sqrt{a+b \coth ^2(x)}}",1,"ArcTanh[(Sqrt[a + b]*Coth[x])/Sqrt[a + b*Coth[x]^2]]/(a + b)^(3/2) - Coth[x]/((a + b)*Sqrt[a + b*Coth[x]^2])","A",4,4,17,0.2353,1,"{3670, 471, 377, 206}"
40,1,49,0,0.0868578,"\int \frac{\coth (x)}{\left(a+b \coth ^2(x)\right)^{3/2}} \, dx","Int[Coth[x]/(a + b*Coth[x]^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{3/2}}-\frac{1}{(a+b) \sqrt{a+b \coth ^2(x)}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{3/2}}-\frac{1}{(a+b) \sqrt{a+b \coth ^2(x)}}",1,"ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a + b]]/(a + b)^(3/2) - 1/((a + b)*Sqrt[a + b*Coth[x]^2])","A",5,5,15,0.3333,1,"{3670, 444, 51, 63, 208}"
41,1,78,0,0.1457571,"\int \frac{\tanh (x)}{\left(a+b \coth ^2(x)\right)^{3/2}} \, dx","Int[Tanh[x]/(a + b*Coth[x]^2)^(3/2),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a}}\right)}{a^{3/2}}+\frac{b}{a (a+b) \sqrt{a+b \coth ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{3/2}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a}}\right)}{a^{3/2}}+\frac{b}{a (a+b) \sqrt{a+b \coth ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{3/2}}",1,"-(ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a]]/a^(3/2)) + ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a + b]]/(a + b)^(3/2) + b/(a*(a + b)*Sqrt[a + b*Coth[x]^2])","A",8,6,15,0.4000,1,"{3670, 446, 85, 156, 63, 208}"
42,1,85,0,0.1553088,"\int \frac{\tanh ^2(x)}{\left(a+b \coth ^2(x)\right)^{3/2}} \, dx","Int[Tanh[x]^2/(a + b*Coth[x]^2)^(3/2),x]","-\frac{(a+2 b) \tanh (x) \sqrt{a+b \coth ^2(x)}}{a^2 (a+b)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{(a+b)^{3/2}}+\frac{b \tanh (x)}{a (a+b) \sqrt{a+b \coth ^2(x)}}","-\frac{(a+2 b) \tanh (x) \sqrt{a+b \coth ^2(x)}}{a^2 (a+b)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{(a+b)^{3/2}}+\frac{b \tanh (x)}{a (a+b) \sqrt{a+b \coth ^2(x)}}",1,"ArcTanh[(Sqrt[a + b]*Coth[x])/Sqrt[a + b*Coth[x]^2]]/(a + b)^(3/2) + (b*Tanh[x])/(a*(a + b)*Sqrt[a + b*Coth[x]^2]) - ((a + 2*b)*Sqrt[a + b*Coth[x]^2]*Tanh[x])/(a^2*(a + b))","A",6,6,17,0.3529,1,"{3670, 472, 583, 12, 377, 206}"
43,1,74,0,0.146045,"\int \frac{\coth ^3(x)}{\left(a+b \coth ^2(x)\right)^{5/2}} \, dx","Int[Coth[x]^3/(a + b*Coth[x]^2)^(5/2),x]","\frac{a}{3 b (a+b) \left(a+b \coth ^2(x)\right)^{3/2}}-\frac{1}{(a+b)^2 \sqrt{a+b \coth ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}","\frac{a}{3 b (a+b) \left(a+b \coth ^2(x)\right)^{3/2}}-\frac{1}{(a+b)^2 \sqrt{a+b \coth ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}",1,"ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a + b]]/(a + b)^(5/2) + a/(3*b*(a + b)*(a + b*Coth[x]^2)^(3/2)) - 1/((a + b)^2*Sqrt[a + b*Coth[x]^2])","A",6,6,17,0.3529,1,"{3670, 446, 78, 51, 63, 208}"
44,1,88,0,0.1277735,"\int \frac{\coth ^2(x)}{\left(a+b \coth ^2(x)\right)^{5/2}} \, dx","Int[Coth[x]^2/(a + b*Coth[x]^2)^(5/2),x]","-\frac{(2 a-b) \coth (x)}{3 a (a+b)^2 \sqrt{a+b \coth ^2(x)}}-\frac{\coth (x)}{3 (a+b) \left(a+b \coth ^2(x)\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{(a+b)^{5/2}}","-\frac{(2 a-b) \coth (x)}{3 a (a+b)^2 \sqrt{a+b \coth ^2(x)}}-\frac{\coth (x)}{3 (a+b) \left(a+b \coth ^2(x)\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{(a+b)^{5/2}}",1,"ArcTanh[(Sqrt[a + b]*Coth[x])/Sqrt[a + b*Coth[x]^2]]/(a + b)^(5/2) - Coth[x]/(3*(a + b)*(a + b*Coth[x]^2)^(3/2)) - ((2*a - b)*Coth[x])/(3*a*(a + b)^2*Sqrt[a + b*Coth[x]^2])","A",6,6,17,0.3529,1,"{3670, 471, 527, 12, 377, 206}"
45,1,70,0,0.1020006,"\int \frac{\coth (x)}{\left(a+b \coth ^2(x)\right)^{5/2}} \, dx","Int[Coth[x]/(a + b*Coth[x]^2)^(5/2),x]","-\frac{1}{(a+b)^2 \sqrt{a+b \coth ^2(x)}}-\frac{1}{3 (a+b) \left(a+b \coth ^2(x)\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}","-\frac{1}{(a+b)^2 \sqrt{a+b \coth ^2(x)}}-\frac{1}{3 (a+b) \left(a+b \coth ^2(x)\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}",1,"ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a + b]]/(a + b)^(5/2) - 1/(3*(a + b)*(a + b*Coth[x]^2)^(3/2)) - 1/((a + b)^2*Sqrt[a + b*Coth[x]^2])","A",6,5,15,0.3333,1,"{3670, 444, 51, 63, 208}"
46,1,108,0,0.2047914,"\int \frac{\tanh (x)}{\left(a+b \coth ^2(x)\right)^{5/2}} \, dx","Int[Tanh[x]/(a + b*Coth[x]^2)^(5/2),x]","\frac{b (2 a+b)}{a^2 (a+b)^2 \sqrt{a+b \coth ^2(x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{b}{3 a (a+b) \left(a+b \coth ^2(x)\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}","\frac{b (2 a+b)}{a^2 (a+b)^2 \sqrt{a+b \coth ^2(x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{b}{3 a (a+b) \left(a+b \coth ^2(x)\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \coth ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}",1,"-(ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a]]/a^(5/2)) + ArcTanh[Sqrt[a + b*Coth[x]^2]/Sqrt[a + b]]/(a + b)^(5/2) + b/(3*a*(a + b)*(a + b*Coth[x]^2)^(3/2)) + (b*(2*a + b))/(a^2*(a + b)^2*Sqrt[a + b*Coth[x]^2])","A",9,7,15,0.4667,1,"{3670, 446, 85, 152, 156, 63, 208}"
47,1,131,0,0.235652,"\int \frac{\tanh ^2(x)}{\left(a+b \coth ^2(x)\right)^{5/2}} \, dx","Int[Tanh[x]^2/(a + b*Coth[x]^2)^(5/2),x]","-\frac{(3 a+2 b) (a+4 b) \tanh (x) \sqrt{a+b \coth ^2(x)}}{3 a^3 (a+b)^2}+\frac{b (7 a+4 b) \tanh (x)}{3 a^2 (a+b)^2 \sqrt{a+b \coth ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{(a+b)^{5/2}}+\frac{b \tanh (x)}{3 a (a+b) \left(a+b \coth ^2(x)\right)^{3/2}}","-\frac{(3 a+2 b) (a+4 b) \tanh (x) \sqrt{a+b \coth ^2(x)}}{3 a^3 (a+b)^2}+\frac{b (7 a+4 b) \tanh (x)}{3 a^2 (a+b)^2 \sqrt{a+b \coth ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \coth (x)}{\sqrt{a+b \coth ^2(x)}}\right)}{(a+b)^{5/2}}+\frac{b \tanh (x)}{3 a (a+b) \left(a+b \coth ^2(x)\right)^{3/2}}",1,"ArcTanh[(Sqrt[a + b]*Coth[x])/Sqrt[a + b*Coth[x]^2]]/(a + b)^(5/2) + (b*Tanh[x])/(3*a*(a + b)*(a + b*Coth[x]^2)^(3/2)) + (b*(7*a + 4*b)*Tanh[x])/(3*a^2*(a + b)^2*Sqrt[a + b*Coth[x]^2]) - ((3*a + 2*b)*(a + 4*b)*Sqrt[a + b*Coth[x]^2]*Tanh[x])/(3*a^3*(a + b)^2)","A",7,7,17,0.4118,1,"{3670, 472, 579, 583, 12, 377, 206}"
48,1,25,0,0.0193541,"\int \frac{1}{\sqrt{1+\coth ^2(x)}} \, dx","Int[1/Sqrt[1 + Coth[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \coth (x)}{\sqrt{\coth ^2(x)+1}}\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \coth (x)}{\sqrt{\coth ^2(x)+1}}\right)}{\sqrt{2}}",1,"ArcTanh[(Sqrt[2]*Coth[x])/Sqrt[1 + Coth[x]^2]]/Sqrt[2]","A",3,3,10,0.3000,1,"{3661, 377, 206}"
49,1,27,0,0.0204859,"\int \frac{1}{\sqrt{-1-\coth ^2(x)}} \, dx","Int[1/Sqrt[-1 - Coth[x]^2],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \coth (x)}{\sqrt{-\coth ^2(x)-1}}\right)}{\sqrt{2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \coth (x)}{\sqrt{-\coth ^2(x)-1}}\right)}{\sqrt{2}}",1,"ArcTan[(Sqrt[2]*Coth[x])/Sqrt[-1 - Coth[x]^2]]/Sqrt[2]","A",3,3,12,0.2500,1,"{3661, 377, 203}"
50,1,38,0,0.0667445,"\int \frac{1}{1+\coth ^3(x)} \, dx","Int[(1 + Coth[x]^3)^(-1),x]","\frac{x}{2}-\frac{1}{6 (\coth (x)+1)}-\frac{2 \tan ^{-1}\left(\frac{1-2 \coth (x)}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{x}{2}-\frac{1}{6 (\coth (x)+1)}-\frac{2 \tan ^{-1}\left(\frac{1-2 \coth (x)}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"x/2 - (2*ArcTan[(1 - 2*Coth[x])/Sqrt[3]])/(3*Sqrt[3]) - 1/(6*(1 + Coth[x]))","A",6,5,8,0.6250,1,"{3661, 2074, 207, 618, 204}"
51,1,89,0,0.1411368,"\int \coth (x) \sqrt{a+b \coth ^4(x)} \, dx","Int[Coth[x]*Sqrt[a + b*Coth[x]^4],x]","-\frac{1}{2} \sqrt{a+b \coth ^4(x)}-\frac{1}{2} \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \coth ^2(x)}{\sqrt{a+b \coth ^4(x)}}\right)+\frac{1}{2} \sqrt{a+b} \tanh ^{-1}\left(\frac{a+b \coth ^2(x)}{\sqrt{a+b} \sqrt{a+b \coth ^4(x)}}\right)","-\frac{1}{2} \sqrt{a+b \coth ^4(x)}-\frac{1}{2} \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \coth ^2(x)}{\sqrt{a+b \coth ^4(x)}}\right)+\frac{1}{2} \sqrt{a+b} \tanh ^{-1}\left(\frac{a+b \coth ^2(x)}{\sqrt{a+b} \sqrt{a+b \coth ^4(x)}}\right)",1,"-(Sqrt[b]*ArcTanh[(Sqrt[b]*Coth[x]^2)/Sqrt[a + b*Coth[x]^4]])/2 + (Sqrt[a + b]*ArcTanh[(a + b*Coth[x]^2)/(Sqrt[a + b]*Sqrt[a + b*Coth[x]^4])])/2 - Sqrt[a + b*Coth[x]^4]/2","A",8,7,15,0.4667,1,"{3670, 1248, 735, 844, 217, 206, 725}"
52,1,40,0,0.0764436,"\int \frac{\coth (x)}{\sqrt{a+b \coth ^4(x)}} \, dx","Int[Coth[x]/Sqrt[a + b*Coth[x]^4],x]","\frac{\tanh ^{-1}\left(\frac{a+b \coth ^2(x)}{\sqrt{a+b} \sqrt{a+b \coth ^4(x)}}\right)}{2 \sqrt{a+b}}","\frac{\tanh ^{-1}\left(\frac{a+b \coth ^2(x)}{\sqrt{a+b} \sqrt{a+b \coth ^4(x)}}\right)}{2 \sqrt{a+b}}",1,"ArcTanh[(a + b*Coth[x]^2)/(Sqrt[a + b]*Sqrt[a + b*Coth[x]^4])]/(2*Sqrt[a + b])","A",4,4,15,0.2667,1,"{3670, 1248, 725, 206}"
53,1,74,0,0.12001,"\int \frac{\coth (x)}{\left(a+b \coth ^4(x)\right)^{3/2}} \, dx","Int[Coth[x]/(a + b*Coth[x]^4)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{a+b \coth ^2(x)}{\sqrt{a+b} \sqrt{a+b \coth ^4(x)}}\right)}{2 (a+b)^{3/2}}-\frac{a-b \coth ^2(x)}{2 a (a+b) \sqrt{a+b \coth ^4(x)}}","\frac{\tanh ^{-1}\left(\frac{a+b \coth ^2(x)}{\sqrt{a+b} \sqrt{a+b \coth ^4(x)}}\right)}{2 (a+b)^{3/2}}-\frac{a-b \coth ^2(x)}{2 a (a+b) \sqrt{a+b \coth ^4(x)}}",1,"ArcTanh[(a + b*Coth[x]^2)/(Sqrt[a + b]*Sqrt[a + b*Coth[x]^4])]/(2*(a + b)^(3/2)) - (a - b*Coth[x]^2)/(2*a*(a + b)*Sqrt[a + b*Coth[x]^4])","A",6,6,15,0.4000,1,"{3670, 1248, 741, 12, 725, 206}"