1,1,20,0,0.0460336,"\int \frac{\sinh ^4(x)}{a-a \cosh ^2(x)} \, dx","Int[Sinh[x]^4/(a - a*Cosh[x]^2),x]","\frac{x}{2 a}-\frac{\sinh (x) \cosh (x)}{2 a}","\frac{x}{2 a}-\frac{\sinh (x) \cosh (x)}{2 a}",1,"x/(2*a) - (Cosh[x]*Sinh[x])/(2*a)","A",3,3,16,0.1875,1,"{3175, 2635, 8}"
2,1,7,0,0.0439769,"\int \frac{\sinh ^3(x)}{a-a \cosh ^2(x)} \, dx","Int[Sinh[x]^3/(a - a*Cosh[x]^2),x]","-\frac{\cosh (x)}{a}","-\frac{\cosh (x)}{a}",1,"-(Cosh[x]/a)","A",2,2,16,0.1250,1,"{3175, 2638}"
3,1,6,0,0.039005,"\int \frac{\sinh ^2(x)}{a-a \cosh ^2(x)} \, dx","Int[Sinh[x]^2/(a - a*Cosh[x]^2),x]","-\frac{x}{a}","-\frac{x}{a}",1,"-(x/a)","A",2,2,16,0.1250,1,"{3175, 8}"
4,1,19,0,0.0478624,"\int \frac{\text{csch}^2(x)}{a-a \cosh ^2(x)} \, dx","Int[Csch[x]^2/(a - a*Cosh[x]^2),x]","\frac{\coth ^3(x)}{3 a}-\frac{\coth (x)}{a}","\frac{\coth ^3(x)}{3 a}-\frac{\coth (x)}{a}",1,"-(Coth[x]/a) + Coth[x]^3/(3*a)","A",3,2,16,0.1250,1,"{3175, 3767}"
5,1,29,0,0.0508984,"\int \frac{\text{csch}^4(x)}{a-a \cosh ^2(x)} \, dx","Int[Csch[x]^4/(a - a*Cosh[x]^2),x]","\frac{\coth ^5(x)}{5 a}-\frac{2 \coth ^3(x)}{3 a}+\frac{\coth (x)}{a}","\frac{\coth ^5(x)}{5 a}-\frac{2 \coth ^3(x)}{3 a}+\frac{\coth (x)}{a}",1,"Coth[x]/a - (2*Coth[x]^3)/(3*a) + Coth[x]^5/(5*a)","A",3,2,16,0.1250,1,"{3175, 3767}"
6,1,78,0,0.1053015,"\int \frac{\sinh ^7(x)}{a+b \cosh ^2(x)} \, dx","Int[Sinh[x]^7/(a + b*Cosh[x]^2),x]","\frac{\left(a^2+3 a b+3 b^2\right) \cosh (x)}{b^3}-\frac{(a+3 b) \cosh ^3(x)}{3 b^2}-\frac{(a+b)^3 \tan ^{-1}\left(\frac{\sqrt{b} \cosh (x)}{\sqrt{a}}\right)}{\sqrt{a} b^{7/2}}+\frac{\cosh ^5(x)}{5 b}","\frac{\left(a^2+3 a b+3 b^2\right) \cosh (x)}{b^3}-\frac{(a+3 b) \cosh ^3(x)}{3 b^2}-\frac{(a+b)^3 \tan ^{-1}\left(\frac{\sqrt{b} \cosh (x)}{\sqrt{a}}\right)}{\sqrt{a} b^{7/2}}+\frac{\cosh ^5(x)}{5 b}",1,"-(((a + b)^3*ArcTan[(Sqrt[b]*Cosh[x])/Sqrt[a]])/(Sqrt[a]*b^(7/2))) + ((a^2 + 3*a*b + 3*b^2)*Cosh[x])/b^3 - ((a + 3*b)*Cosh[x]^3)/(3*b^2) + Cosh[x]^5/(5*b)","A",4,3,15,0.2000,1,"{3190, 390, 205}"
7,1,54,0,0.0868472,"\int \frac{\sinh ^5(x)}{a+b \cosh ^2(x)} \, dx","Int[Sinh[x]^5/(a + b*Cosh[x]^2),x]","-\frac{(a+2 b) \cosh (x)}{b^2}+\frac{(a+b)^2 \tan ^{-1}\left(\frac{\sqrt{b} \cosh (x)}{\sqrt{a}}\right)}{\sqrt{a} b^{5/2}}+\frac{\cosh ^3(x)}{3 b}","-\frac{(a+2 b) \cosh (x)}{b^2}+\frac{(a+b)^2 \tan ^{-1}\left(\frac{\sqrt{b} \cosh (x)}{\sqrt{a}}\right)}{\sqrt{a} b^{5/2}}+\frac{\cosh ^3(x)}{3 b}",1,"((a + b)^2*ArcTan[(Sqrt[b]*Cosh[x])/Sqrt[a]])/(Sqrt[a]*b^(5/2)) - ((a + 2*b)*Cosh[x])/b^2 + Cosh[x]^3/(3*b)","A",4,3,15,0.2000,1,"{3190, 390, 205}"
8,1,36,0,0.0646584,"\int \frac{\sinh ^3(x)}{a+b \cosh ^2(x)} \, dx","Int[Sinh[x]^3/(a + b*Cosh[x]^2),x]","\frac{\cosh (x)}{b}-\frac{(a+b) \tan ^{-1}\left(\frac{\sqrt{b} \cosh (x)}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}","\frac{\cosh (x)}{b}-\frac{(a+b) \tan ^{-1}\left(\frac{\sqrt{b} \cosh (x)}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}",1,"-(((a + b)*ArcTan[(Sqrt[b]*Cosh[x])/Sqrt[a]])/(Sqrt[a]*b^(3/2))) + Cosh[x]/b","A",3,3,15,0.2000,1,"{3190, 388, 205}"
9,1,25,0,0.0357397,"\int \frac{\sinh (x)}{a+b \cosh ^2(x)} \, dx","Int[Sinh[x]/(a + b*Cosh[x]^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \cosh (x)}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \cosh (x)}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}",1,"ArcTan[(Sqrt[b]*Cosh[x])/Sqrt[a]]/(Sqrt[a]*Sqrt[b])","A",2,2,13,0.1538,1,"{3190, 205}"
10,1,42,0,0.0622791,"\int \frac{\text{csch}(x)}{a+b \cosh ^2(x)} \, dx","Int[Csch[x]/(a + b*Cosh[x]^2),x]","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \cosh (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)}-\frac{\tanh ^{-1}(\cosh (x))}{a+b}","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \cosh (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)}-\frac{\tanh ^{-1}(\cosh (x))}{a+b}",1,"-((Sqrt[b]*ArcTan[(Sqrt[b]*Cosh[x])/Sqrt[a]])/(Sqrt[a]*(a + b))) - ArcTanh[Cosh[x]]/(a + b)","A",4,4,13,0.3077,1,"{3190, 391, 206, 205}"
11,1,61,0,0.1043658,"\int \frac{\text{csch}^3(x)}{a+b \cosh ^2(x)} \, dx","Int[Csch[x]^3/(a + b*Cosh[x]^2),x]","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \cosh (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)^2}+\frac{(a+3 b) \tanh ^{-1}(\cosh (x))}{2 (a+b)^2}-\frac{\coth (x) \text{csch}(x)}{2 (a+b)}","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \cosh (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)^2}+\frac{(a+3 b) \tanh ^{-1}(\cosh (x))}{2 (a+b)^2}-\frac{\coth (x) \text{csch}(x)}{2 (a+b)}",1,"(b^(3/2)*ArcTan[(Sqrt[b]*Cosh[x])/Sqrt[a]])/(Sqrt[a]*(a + b)^2) + ((a + 3*b)*ArcTanh[Cosh[x]])/(2*(a + b)^2) - (Coth[x]*Csch[x])/(2*(a + b))","A",5,5,15,0.3333,1,"{3190, 414, 522, 206, 205}"
12,1,94,0,0.1720093,"\int \frac{\text{csch}^5(x)}{a+b \cosh ^2(x)} \, dx","Int[Csch[x]^5/(a + b*Cosh[x]^2),x]","-\frac{\left(3 a^2+10 a b+15 b^2\right) \tanh ^{-1}(\cosh (x))}{8 (a+b)^3}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \cosh (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)^3}-\frac{\coth (x) \text{csch}^3(x)}{4 (a+b)}+\frac{(3 a+7 b) \coth (x) \text{csch}(x)}{8 (a+b)^2}","-\frac{\left(3 a^2+10 a b+15 b^2\right) \tanh ^{-1}(\cosh (x))}{8 (a+b)^3}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \cosh (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)^3}-\frac{\coth (x) \text{csch}^3(x)}{4 (a+b)}+\frac{(3 a+7 b) \coth (x) \text{csch}(x)}{8 (a+b)^2}",1,"-((b^(5/2)*ArcTan[(Sqrt[b]*Cosh[x])/Sqrt[a]])/(Sqrt[a]*(a + b)^3)) - ((3*a^2 + 10*a*b + 15*b^2)*ArcTanh[Cosh[x]])/(8*(a + b)^3) + ((3*a + 7*b)*Coth[x]*Csch[x])/(8*(a + b)^2) - (Coth[x]*Csch[x]^3)/(4*(a + b))","A",6,6,15,0.4000,1,"{3190, 414, 527, 522, 206, 205}"
13,1,88,0,0.1680948,"\int \frac{\sinh ^6(x)}{a+b \cosh ^2(x)} \, dx","Int[Sinh[x]^6/(a + b*Cosh[x]^2),x]","\frac{x \left(8 a^2+20 a b+15 b^2\right)}{8 b^3}-\frac{(a+b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a} b^3}-\frac{(4 a+7 b) \sinh (x) \cosh (x)}{8 b^2}+\frac{\sinh ^3(x) \cosh (x)}{4 b}","\frac{x \left(8 a^2+20 a b+15 b^2\right)}{8 b^3}-\frac{(a+b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a} b^3}-\frac{(4 a+7 b) \sinh (x) \cosh (x)}{8 b^2}+\frac{\sinh ^3(x) \cosh (x)}{4 b}",1,"((8*a^2 + 20*a*b + 15*b^2)*x)/(8*b^3) - ((a + b)^(5/2)*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/(Sqrt[a]*b^3) - ((4*a + 7*b)*Cosh[x]*Sinh[x])/(8*b^2) + (Cosh[x]*Sinh[x]^3)/(4*b)","A",6,6,15,0.4000,1,"{3191, 414, 527, 522, 206, 208}"
14,1,59,0,0.1162427,"\int \frac{\sinh ^4(x)}{a+b \cosh ^2(x)} \, dx","Int[Sinh[x]^4/(a + b*Cosh[x]^2),x]","-\frac{x (2 a+3 b)}{2 b^2}+\frac{(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a} b^2}+\frac{\sinh (x) \cosh (x)}{2 b}","-\frac{x (2 a+3 b)}{2 b^2}+\frac{(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a} b^2}+\frac{\sinh (x) \cosh (x)}{2 b}",1,"-((2*a + 3*b)*x)/(2*b^2) + ((a + b)^(3/2)*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/(Sqrt[a]*b^2) + (Cosh[x]*Sinh[x])/(2*b)","A",5,5,15,0.3333,1,"{3191, 414, 522, 206, 208}"
15,1,39,0,0.0667251,"\int \frac{\sinh ^2(x)}{a+b \cosh ^2(x)} \, dx","Int[Sinh[x]^2/(a + b*Cosh[x]^2),x]","\frac{x}{b}-\frac{\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a} b}","\frac{x}{b}-\frac{\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a} b}",1,"x/b - (Sqrt[a + b]*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/(Sqrt[a]*b)","A",4,4,15,0.2667,1,"{3191, 391, 206, 208}"
16,1,29,0,0.0218575,"\int \frac{1}{a+b \cosh ^2(x)} \, dx","Int[(a + b*Cosh[x]^2)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a} \sqrt{a+b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a} \sqrt{a+b}}",1,"ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]]/(Sqrt[a]*Sqrt[a + b])","A",2,2,10,0.2000,1,"{3181, 208}"
17,1,59,0,0.0857252,"\int \frac{\text{csch}^4(x)}{a+b \cosh ^2(x)} \, dx","Int[Csch[x]^4/(a + b*Cosh[x]^2),x]","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a} (a+b)^{5/2}}-\frac{\coth ^3(x)}{3 (a+b)}+\frac{(a+2 b) \coth (x)}{(a+b)^2}","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a} (a+b)^{5/2}}-\frac{\coth ^3(x)}{3 (a+b)}+\frac{(a+2 b) \coth (x)}{(a+b)^2}",1,"(b^2*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/(Sqrt[a]*(a + b)^(5/2)) + ((a + 2*b)*Coth[x])/(a + b)^2 - Coth[x]^3/(3*(a + b))","A",4,3,15,0.2000,1,"{3191, 390, 208}"
18,1,89,0,0.1080461,"\int \frac{\text{csch}^6(x)}{a+b \cosh ^2(x)} \, dx","Int[Csch[x]^6/(a + b*Cosh[x]^2),x]","-\frac{\left(a^2+3 a b+3 b^2\right) \coth (x)}{(a+b)^3}-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a} (a+b)^{7/2}}-\frac{\coth ^5(x)}{5 (a+b)}+\frac{(2 a+3 b) \coth ^3(x)}{3 (a+b)^2}","-\frac{\left(a^2+3 a b+3 b^2\right) \coth (x)}{(a+b)^3}-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a} (a+b)^{7/2}}-\frac{\coth ^5(x)}{5 (a+b)}+\frac{(2 a+3 b) \coth ^3(x)}{3 (a+b)^2}",1,"-((b^3*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/(Sqrt[a]*(a + b)^(7/2))) - ((a^2 + 3*a*b + 3*b^2)*Coth[x])/(a + b)^3 + ((2*a + 3*b)*Coth[x]^3)/(3*(a + b)^2) - Coth[x]^5/(5*(a + b))","A",4,3,15,0.2000,1,"{3191, 390, 208}"
19,1,98,0,0.1166888,"\int \frac{\sinh (x)}{4-3 \cosh ^3(x)} \, dx","Int[Sinh[x]/(4 - 3*Cosh[x]^3),x]","\frac{\log \left(3^{2/3} \cosh ^2(x)+2^{2/3} \sqrt[3]{3} \cosh (x)+2 \sqrt[3]{2}\right)}{12 \sqrt[3]{6}}-\frac{\log \left(2^{2/3}-\sqrt[3]{3} \cosh (x)\right)}{6 \sqrt[3]{6}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{6} \cosh (x)+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} 3^{5/6}}","\frac{\log \left(3^{2/3} \cosh ^2(x)+2^{2/3} \sqrt[3]{3} \cosh (x)+2 \sqrt[3]{2}\right)}{12 \sqrt[3]{6}}-\frac{\log \left(2^{2/3}-\sqrt[3]{3} \cosh (x)\right)}{6 \sqrt[3]{6}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{6} \cosh (x)+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} 3^{5/6}}",1,"ArcTan[(1 + 6^(1/3)*Cosh[x])/Sqrt[3]]/(2*2^(1/3)*3^(5/6)) - Log[2^(2/3) - 3^(1/3)*Cosh[x]]/(6*6^(1/3)) + Log[2*2^(1/3) + 2^(2/3)*3^(1/3)*Cosh[x] + 3^(2/3)*Cosh[x]^2]/(12*6^(1/3))","A",7,7,13,0.5385,1,"{3223, 200, 31, 634, 617, 204, 628}"
20,1,78,0,0.0902578,"\int \frac{\cosh ^7(x)}{a+b \cosh ^2(x)} \, dx","Int[Cosh[x]^7/(a + b*Cosh[x]^2),x]","\frac{\left(a^2-a b+b^2\right) \sinh (x)}{b^3}-\frac{a^3 \tan ^{-1}\left(\frac{\sqrt{b} \sinh (x)}{\sqrt{a+b}}\right)}{b^{7/2} \sqrt{a+b}}-\frac{(a-2 b) \sinh ^3(x)}{3 b^2}+\frac{\sinh ^5(x)}{5 b}","\frac{\left(a^2-a b+b^2\right) \sinh (x)}{b^3}-\frac{a^3 \tan ^{-1}\left(\frac{\sqrt{b} \sinh (x)}{\sqrt{a+b}}\right)}{b^{7/2} \sqrt{a+b}}-\frac{(a-2 b) \sinh ^3(x)}{3 b^2}+\frac{\sinh ^5(x)}{5 b}",1,"-((a^3*ArcTan[(Sqrt[b]*Sinh[x])/Sqrt[a + b]])/(b^(7/2)*Sqrt[a + b])) + ((a^2 - a*b + b^2)*Sinh[x])/b^3 - ((a - 2*b)*Sinh[x]^3)/(3*b^2) + Sinh[x]^5/(5*b)","A",4,3,15,0.2000,1,"{3186, 390, 205}"
21,1,88,0,0.2098981,"\int \frac{\cosh ^6(x)}{a+b \cosh ^2(x)} \, dx","Int[Cosh[x]^6/(a + b*Cosh[x]^2),x]","\frac{x \left(8 a^2-4 a b+3 b^2\right)}{8 b^3}-\frac{a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{b^3 \sqrt{a+b}}-\frac{(4 a-3 b) \sinh (x) \cosh (x)}{8 b^2}+\frac{\sinh (x) \cosh ^3(x)}{4 b}","\frac{x \left(8 a^2-4 a b+3 b^2\right)}{8 b^3}-\frac{a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{b^3 \sqrt{a+b}}-\frac{(4 a-3 b) \sinh (x) \cosh (x)}{8 b^2}+\frac{\sinh (x) \cosh ^3(x)}{4 b}",1,"((8*a^2 - 4*a*b + 3*b^2)*x)/(8*b^3) - (a^(5/2)*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/(b^3*Sqrt[a + b]) - ((4*a - 3*b)*Cosh[x]*Sinh[x])/(8*b^2) + (Cosh[x]^3*Sinh[x])/(4*b)","A",6,6,15,0.4000,1,"{3187, 470, 578, 522, 206, 208}"
22,1,56,0,0.0729572,"\int \frac{\cosh ^5(x)}{a+b \cosh ^2(x)} \, dx","Int[Cosh[x]^5/(a + b*Cosh[x]^2),x]","\frac{a^2 \tan ^{-1}\left(\frac{\sqrt{b} \sinh (x)}{\sqrt{a+b}}\right)}{b^{5/2} \sqrt{a+b}}-\frac{(a-b) \sinh (x)}{b^2}+\frac{\sinh ^3(x)}{3 b}","\frac{a^2 \tan ^{-1}\left(\frac{\sqrt{b} \sinh (x)}{\sqrt{a+b}}\right)}{b^{5/2} \sqrt{a+b}}-\frac{(a-b) \sinh (x)}{b^2}+\frac{\sinh ^3(x)}{3 b}",1,"(a^2*ArcTan[(Sqrt[b]*Sinh[x])/Sqrt[a + b]])/(b^(5/2)*Sqrt[a + b]) - ((a - b)*Sinh[x])/b^2 + Sinh[x]^3/(3*b)","A",4,3,15,0.2000,1,"{3186, 390, 205}"
23,1,59,0,0.1055522,"\int \frac{\cosh ^4(x)}{a+b \cosh ^2(x)} \, dx","Int[Cosh[x]^4/(a + b*Cosh[x]^2),x]","\frac{a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{b^2 \sqrt{a+b}}-\frac{x (2 a-b)}{2 b^2}+\frac{\sinh (x) \cosh (x)}{2 b}","\frac{a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{b^2 \sqrt{a+b}}-\frac{x (2 a-b)}{2 b^2}+\frac{\sinh (x) \cosh (x)}{2 b}",1,"-((2*a - b)*x)/(2*b^2) + (a^(3/2)*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/(b^2*Sqrt[a + b]) + (Cosh[x]*Sinh[x])/(2*b)","A",5,5,15,0.3333,1,"{3187, 470, 522, 206, 208}"
24,1,38,0,0.0592605,"\int \frac{\cosh ^3(x)}{a+b \cosh ^2(x)} \, dx","Int[Cosh[x]^3/(a + b*Cosh[x]^2),x]","\frac{\sinh (x)}{b}-\frac{a \tan ^{-1}\left(\frac{\sqrt{b} \sinh (x)}{\sqrt{a+b}}\right)}{b^{3/2} \sqrt{a+b}}","\frac{\sinh (x)}{b}-\frac{a \tan ^{-1}\left(\frac{\sqrt{b} \sinh (x)}{\sqrt{a+b}}\right)}{b^{3/2} \sqrt{a+b}}",1,"-((a*ArcTan[(Sqrt[b]*Sinh[x])/Sqrt[a + b]])/(b^(3/2)*Sqrt[a + b])) + Sinh[x]/b","A",3,3,15,0.2000,1,"{3186, 388, 205}"
25,1,39,0,0.0695004,"\int \frac{\cosh ^2(x)}{a+b \cosh ^2(x)} \, dx","Int[Cosh[x]^2/(a + b*Cosh[x]^2),x]","\frac{x}{b}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{b \sqrt{a+b}}","\frac{x}{b}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{b \sqrt{a+b}}",1,"x/b - (Sqrt[a]*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/(b*Sqrt[a + b])","A",3,3,15,0.2000,1,"{3171, 3181, 208}"
26,1,29,0,0.032059,"\int \frac{\cosh (x)}{a+b \cosh ^2(x)} \, dx","Int[Cosh[x]/(a + b*Cosh[x]^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sinh (x)}{\sqrt{a+b}}\right)}{\sqrt{b} \sqrt{a+b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sinh (x)}{\sqrt{a+b}}\right)}{\sqrt{b} \sqrt{a+b}}",1,"ArcTan[(Sqrt[b]*Sinh[x])/Sqrt[a + b]]/(Sqrt[b]*Sqrt[a + b])","A",2,2,13,0.1538,1,"{3186, 205}"
27,1,29,0,0.0223381,"\int \frac{1}{a+b \cosh ^2(x)} \, dx","Int[(a + b*Cosh[x]^2)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a} \sqrt{a+b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a} \sqrt{a+b}}",1,"ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]]/(Sqrt[a]*Sqrt[a + b])","A",2,2,10,0.2000,1,"{3181, 208}"
28,1,41,0,0.0535018,"\int \frac{\text{sech}(x)}{a+b \cosh ^2(x)} \, dx","Int[Sech[x]/(a + b*Cosh[x]^2),x]","\frac{\tan ^{-1}(\sinh (x))}{a}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sinh (x)}{\sqrt{a+b}}\right)}{a \sqrt{a+b}}","\frac{\tan ^{-1}(\sinh (x))}{a}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sinh (x)}{\sqrt{a+b}}\right)}{a \sqrt{a+b}}",1,"ArcTan[Sinh[x]]/a - (Sqrt[b]*ArcTan[(Sqrt[b]*Sinh[x])/Sqrt[a + b]])/(a*Sqrt[a + b])","A",4,4,13,0.3077,1,"{3186, 391, 203, 205}"
29,1,38,0,0.0789743,"\int \frac{\text{sech}^2(x)}{a+b \cosh ^2(x)} \, dx","Int[Sech[x]^2/(a + b*Cosh[x]^2),x]","\frac{\tanh (x)}{a}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{a^{3/2} \sqrt{a+b}}","\frac{\tanh (x)}{a}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{a^{3/2} \sqrt{a+b}}",1,"-((b*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/(a^(3/2)*Sqrt[a + b])) + Tanh[x]/a","A",3,3,15,0.2000,1,"{3187, 453, 208}"
30,1,59,0,0.090977,"\int \frac{\text{sech}^3(x)}{a+b \cosh ^2(x)} \, dx","Int[Sech[x]^3/(a + b*Cosh[x]^2),x]","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sinh (x)}{\sqrt{a+b}}\right)}{a^2 \sqrt{a+b}}+\frac{(a-2 b) \tan ^{-1}(\sinh (x))}{2 a^2}+\frac{\tanh (x) \text{sech}(x)}{2 a}","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sinh (x)}{\sqrt{a+b}}\right)}{a^2 \sqrt{a+b}}+\frac{(a-2 b) \tan ^{-1}(\sinh (x))}{2 a^2}+\frac{\tanh (x) \text{sech}(x)}{2 a}",1,"((a - 2*b)*ArcTan[Sinh[x]])/(2*a^2) + (b^(3/2)*ArcTan[(Sqrt[b]*Sinh[x])/Sqrt[a + b]])/(a^2*Sqrt[a + b]) + (Sech[x]*Tanh[x])/(2*a)","A",5,5,15,0.3333,1,"{3186, 414, 522, 203, 205}"
31,1,55,0,0.0991718,"\int \frac{\text{sech}^4(x)}{a+b \cosh ^2(x)} \, dx","Int[Sech[x]^4/(a + b*Cosh[x]^2),x]","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{a^{5/2} \sqrt{a+b}}+\frac{(a-b) \tanh (x)}{a^2}-\frac{\tanh ^3(x)}{3 a}","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{a^{5/2} \sqrt{a+b}}+\frac{(a-b) \tanh (x)}{a^2}-\frac{\tanh ^3(x)}{3 a}",1,"(b^2*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/(a^(5/2)*Sqrt[a + b]) + ((a - b)*Tanh[x])/a^2 - Tanh[x]^3/(3*a)","A",4,3,15,0.2000,1,"{3187, 461, 208}"
32,1,90,0,0.1382849,"\int \frac{\text{sech}^5(x)}{a+b \cosh ^2(x)} \, dx","Int[Sech[x]^5/(a + b*Cosh[x]^2),x]","\frac{\left(3 a^2-4 a b+8 b^2\right) \tan ^{-1}(\sinh (x))}{8 a^3}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sinh (x)}{\sqrt{a+b}}\right)}{a^3 \sqrt{a+b}}+\frac{(3 a-4 b) \tanh (x) \text{sech}(x)}{8 a^2}+\frac{\tanh (x) \text{sech}^3(x)}{4 a}","\frac{\left(3 a^2-4 a b+8 b^2\right) \tan ^{-1}(\sinh (x))}{8 a^3}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sinh (x)}{\sqrt{a+b}}\right)}{a^3 \sqrt{a+b}}+\frac{(3 a-4 b) \tanh (x) \text{sech}(x)}{8 a^2}+\frac{\tanh (x) \text{sech}^3(x)}{4 a}",1,"((3*a^2 - 4*a*b + 8*b^2)*ArcTan[Sinh[x]])/(8*a^3) - (b^(5/2)*ArcTan[(Sqrt[b]*Sinh[x])/Sqrt[a + b]])/(a^3*Sqrt[a + b]) + ((3*a - 4*b)*Sech[x]*Tanh[x])/(8*a^2) + (Sech[x]^3*Tanh[x])/(4*a)","A",6,6,15,0.4000,1,"{3186, 414, 527, 522, 203, 205}"
33,1,65,0,0.0574036,"\int \frac{1}{\left(a+b \cosh ^2(x)\right)^2} \, dx","Int[(a + b*Cosh[x]^2)^(-2),x]","\frac{(2 a+b) \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{2 a^{3/2} (a+b)^{3/2}}-\frac{b \sinh (x) \cosh (x)}{2 a (a+b) \left(a+b \cosh ^2(x)\right)}","\frac{(2 a+b) \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{2 a^{3/2} (a+b)^{3/2}}-\frac{b \sinh (x) \cosh (x)}{2 a (a+b) \left(a+b \cosh ^2(x)\right)}",1,"((2*a + b)*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/(2*a^(3/2)*(a + b)^(3/2)) - (b*Cosh[x]*Sinh[x])/(2*a*(a + b)*(a + b*Cosh[x]^2))","A",4,4,10,0.4000,1,"{3184, 12, 3181, 208}"
34,1,107,0,0.1227855,"\int \frac{1}{\left(a+b \cosh ^2(x)\right)^3} \, dx","Int[(a + b*Cosh[x]^2)^(-3),x]","\frac{\left(8 a^2+8 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{8 a^{5/2} (a+b)^{5/2}}-\frac{3 b (2 a+b) \sinh (x) \cosh (x)}{8 a^2 (a+b)^2 \left(a+b \cosh ^2(x)\right)}-\frac{b \sinh (x) \cosh (x)}{4 a (a+b) \left(a+b \cosh ^2(x)\right)^2}","\frac{\left(8 a^2+8 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{8 a^{5/2} (a+b)^{5/2}}-\frac{3 b (2 a+b) \sinh (x) \cosh (x)}{8 a^2 (a+b)^2 \left(a+b \cosh ^2(x)\right)}-\frac{b \sinh (x) \cosh (x)}{4 a (a+b) \left(a+b \cosh ^2(x)\right)^2}",1,"((8*a^2 + 8*a*b + 3*b^2)*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/(8*a^(5/2)*(a + b)^(5/2)) - (b*Cosh[x]*Sinh[x])/(4*a*(a + b)*(a + b*Cosh[x]^2)^2) - (3*b*(2*a + b)*Cosh[x]*Sinh[x])/(8*a^2*(a + b)^2*(a + b*Cosh[x]^2))","A",5,5,10,0.5000,1,"{3184, 3173, 12, 3181, 208}"
35,1,15,0,0.0117789,"\int \frac{1}{1+\cosh ^2(x)} \, dx","Int[(1 + Cosh[x]^2)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{\sqrt{2}}",1,"ArcTanh[Tanh[x]/Sqrt[2]]/Sqrt[2]","A",2,2,8,0.2500,1,"{3181, 206}"
36,1,35,0,0.0252306,"\int \frac{1}{\left(1+\cosh ^2(x)\right)^2} \, dx","Int[(1 + Cosh[x]^2)^(-2),x]","\frac{3 \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{4 \sqrt{2}}-\frac{\sinh (x) \cosh (x)}{4 \left(\cosh ^2(x)+1\right)}","\frac{3 \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{4 \sqrt{2}}-\frac{\sinh (x) \cosh (x)}{4 \left(\cosh ^2(x)+1\right)}",1,"(3*ArcTanh[Tanh[x]/Sqrt[2]])/(4*Sqrt[2]) - (Cosh[x]*Sinh[x])/(4*(1 + Cosh[x]^2))","A",4,4,8,0.5000,1,"{3184, 12, 3181, 206}"
37,1,51,0,0.0512598,"\int \frac{1}{\left(1+\cosh ^2(x)\right)^3} \, dx","Int[(1 + Cosh[x]^2)^(-3),x]","\frac{19 \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{32 \sqrt{2}}-\frac{9 \sinh (x) \cosh (x)}{32 \left(\cosh ^2(x)+1\right)}-\frac{\sinh (x) \cosh (x)}{8 \left(\cosh ^2(x)+1\right)^2}","\frac{19 \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{32 \sqrt{2}}-\frac{9 \sinh (x) \cosh (x)}{32 \left(\cosh ^2(x)+1\right)}-\frac{\sinh (x) \cosh (x)}{8 \left(\cosh ^2(x)+1\right)^2}",1,"(19*ArcTanh[Tanh[x]/Sqrt[2]])/(32*Sqrt[2]) - (Cosh[x]*Sinh[x])/(8*(1 + Cosh[x]^2)^2) - (9*Cosh[x]*Sinh[x])/(32*(1 + Cosh[x]^2))","A",5,5,8,0.6250,1,"{3184, 3173, 12, 3181, 206}"
38,1,2,0,0.0161028,"\int \frac{1}{1-\cosh ^2(x)} \, dx","Int[(1 - Cosh[x]^2)^(-1),x]","\coth (x)","\coth (x)",1,"Coth[x]","A",3,3,10,0.3000,1,"{3175, 3767, 8}"
39,1,11,0,0.0180271,"\int \frac{1}{\left(1-\cosh ^2(x)\right)^2} \, dx","Int[(1 - Cosh[x]^2)^(-2),x]","\coth (x)-\frac{\coth ^3(x)}{3}","\coth (x)-\frac{\coth ^3(x)}{3}",1,"Coth[x] - Coth[x]^3/3","A",3,2,10,0.2000,1,"{3175, 3767}"
40,1,19,0,0.0200164,"\int \frac{1}{\left(1-\cosh ^2(x)\right)^3} \, dx","Int[(1 - Cosh[x]^2)^(-3),x]","\frac{\coth ^5(x)}{5}-\frac{2 \coth ^3(x)}{3}+\coth (x)","\frac{\coth ^5(x)}{5}-\frac{2 \coth ^3(x)}{3}+\coth (x)",1,"Coth[x] - (2*Coth[x]^3)/3 + Coth[x]^5/5","A",3,2,10,0.2000,1,"{3175, 3767}"
41,1,49,0,0.0308935,"\int \sqrt{a+b \cosh ^2(x)} \, dx","Int[Sqrt[a + b*Cosh[x]^2],x]","-\frac{i \sqrt{a+b \cosh ^2(x)} E\left(i x+\frac{\pi }{2}|-\frac{b}{a}\right)}{\sqrt{\frac{b \cosh ^2(x)}{a}+1}}","-\frac{i \sqrt{a+b \cosh ^2(x)} E\left(i x+\frac{\pi }{2}|-\frac{b}{a}\right)}{\sqrt{\frac{b \cosh ^2(x)}{a}+1}}",1,"((-I)*Sqrt[a + b*Cosh[x]^2]*EllipticE[Pi/2 + I*x, -(b/a)])/Sqrt[1 + (b*Cosh[x]^2)/a]","A",2,2,12,0.1667,1,"{3178, 3177}"
42,1,17,0,0.0094512,"\int \sqrt{1+\cosh ^2(x)} \, dx","Int[Sqrt[1 + Cosh[x]^2],x]","-i E\left(\left.i x+\frac{\pi }{2}\right|-1\right)","-i E\left(\left.i x+\frac{\pi }{2}\right|-1\right)",1,"(-I)*EllipticE[Pi/2 + I*x, -1]","A",1,1,10,0.1000,1,"{3177}"
43,1,13,0,0.0218042,"\int \sqrt{1-\cosh ^2(x)} \, dx","Int[Sqrt[1 - Cosh[x]^2],x]","\sqrt{-\sinh ^2(x)} \coth (x)","\sqrt{-\sinh ^2(x)} \coth (x)",1,"Coth[x]*Sqrt[-Sinh[x]^2]","A",3,3,12,0.2500,1,"{3176, 3207, 2638}"
44,1,11,0,0.0175075,"\int \sqrt{-1+\cosh ^2(x)} \, dx","Int[Sqrt[-1 + Cosh[x]^2],x]","\sqrt{\sinh ^2(x)} \coth (x)","\sqrt{\sinh ^2(x)} \coth (x)",1,"Coth[x]*Sqrt[Sinh[x]^2]","A",3,3,10,0.3000,1,"{3176, 3207, 2638}"
45,1,39,0,0.0210998,"\int \sqrt{-1-\cosh ^2(x)} \, dx","Int[Sqrt[-1 - Cosh[x]^2],x]","-\frac{i \sqrt{-\cosh ^2(x)-1} E\left(\left.i x+\frac{\pi }{2}\right|-1\right)}{\sqrt{\cosh ^2(x)+1}}","-\frac{i \sqrt{-\cosh ^2(x)-1} E\left(\left.i x+\frac{\pi }{2}\right|-1\right)}{\sqrt{\cosh ^2(x)+1}}",1,"((-I)*Sqrt[-1 - Cosh[x]^2]*EllipticE[Pi/2 + I*x, -1])/Sqrt[1 + Cosh[x]^2]","A",2,2,12,0.1667,1,"{3178, 3177}"
46,1,133,0,0.1544027,"\int \left(a+b \cosh ^2(x)\right)^{3/2} \, dx","Int[(a + b*Cosh[x]^2)^(3/2),x]","\frac{1}{3} b \sinh (x) \cosh (x) \sqrt{a+b \cosh ^2(x)}+\frac{i a (a+b) \sqrt{\frac{b \cosh ^2(x)}{a}+1} F\left(i x+\frac{\pi }{2}|-\frac{b}{a}\right)}{3 \sqrt{a+b \cosh ^2(x)}}-\frac{2 i (2 a+b) \sqrt{a+b \cosh ^2(x)} E\left(i x+\frac{\pi }{2}|-\frac{b}{a}\right)}{3 \sqrt{\frac{b \cosh ^2(x)}{a}+1}}","\frac{1}{3} b \sinh (x) \cosh (x) \sqrt{a+b \cosh ^2(x)}+\frac{i a (a+b) \sqrt{\frac{b \cosh ^2(x)}{a}+1} F\left(i x+\frac{\pi }{2}|-\frac{b}{a}\right)}{3 \sqrt{a+b \cosh ^2(x)}}-\frac{2 i (2 a+b) \sqrt{a+b \cosh ^2(x)} E\left(i x+\frac{\pi }{2}|-\frac{b}{a}\right)}{3 \sqrt{\frac{b \cosh ^2(x)}{a}+1}}",1,"(((-2*I)/3)*(2*a + b)*Sqrt[a + b*Cosh[x]^2]*EllipticE[Pi/2 + I*x, -(b/a)])/Sqrt[1 + (b*Cosh[x]^2)/a] + ((I/3)*a*(a + b)*Sqrt[1 + (b*Cosh[x]^2)/a]*EllipticF[Pi/2 + I*x, -(b/a)])/Sqrt[a + b*Cosh[x]^2] + (b*Cosh[x]*Sqrt[a + b*Cosh[x]^2]*Sinh[x])/3","A",6,6,12,0.5000,1,"{3180, 3172, 3178, 3177, 3183, 3182}"
47,1,55,0,0.0612031,"\int \left(1+\cosh ^2(x)\right)^{3/2} \, dx","Int[(1 + Cosh[x]^2)^(3/2),x]","\frac{2}{3} i F\left(\left.i x+\frac{\pi }{2}\right|-1\right)-2 i E\left(\left.i x+\frac{\pi }{2}\right|-1\right)+\frac{1}{3} \sinh (x) \cosh (x) \sqrt{\cosh ^2(x)+1}","\frac{2}{3} i F\left(\left.i x+\frac{\pi }{2}\right|-1\right)-2 i E\left(\left.i x+\frac{\pi }{2}\right|-1\right)+\frac{1}{3} \sinh (x) \cosh (x) \sqrt{\cosh ^2(x)+1}",1,"(-2*I)*EllipticE[Pi/2 + I*x, -1] + ((2*I)/3)*EllipticF[Pi/2 + I*x, -1] + (Cosh[x]*Sqrt[1 + Cosh[x]^2]*Sinh[x])/3","A",4,4,10,0.4000,1,"{3180, 3172, 3177, 3182}"
48,1,33,0,0.028454,"\int \left(1-\cosh ^2(x)\right)^{3/2} \, dx","Int[(1 - Cosh[x]^2)^(3/2),x]","\frac{1}{3} \left(-\sinh ^2(x)\right)^{3/2} \coth (x)+\frac{2}{3} \sqrt{-\sinh ^2(x)} \coth (x)","\frac{1}{3} \left(-\sinh ^2(x)\right)^{3/2} \coth (x)+\frac{2}{3} \sqrt{-\sinh ^2(x)} \coth (x)",1,"(2*Coth[x]*Sqrt[-Sinh[x]^2])/3 + (Coth[x]*(-Sinh[x]^2)^(3/2))/3","A",4,4,12,0.3333,1,"{3176, 3203, 3207, 2638}"
49,1,29,0,0.0255441,"\int \left(-1+\cosh ^2(x)\right)^{3/2} \, dx","Int[(-1 + Cosh[x]^2)^(3/2),x]","\frac{1}{3} \sinh ^2(x)^{3/2} \coth (x)-\frac{2}{3} \sqrt{\sinh ^2(x)} \coth (x)","\frac{1}{3} \sinh ^2(x)^{3/2} \coth (x)-\frac{2}{3} \sqrt{\sinh ^2(x)} \coth (x)",1,"(-2*Coth[x]*Sqrt[Sinh[x]^2])/3 + (Coth[x]*(Sinh[x]^2)^(3/2))/3","A",4,4,10,0.4000,1,"{3176, 3203, 3207, 2638}"
50,1,101,0,0.0923304,"\int \left(-1-\cosh ^2(x)\right)^{3/2} \, dx","Int[(-1 - Cosh[x]^2)^(3/2),x]","-\frac{1}{3} \sinh (x) \cosh (x) \sqrt{-\cosh ^2(x)-1}+\frac{2 i \sqrt{\cosh ^2(x)+1} F\left(\left.i x+\frac{\pi }{2}\right|-1\right)}{3 \sqrt{-\cosh ^2(x)-1}}+\frac{2 i \sqrt{-\cosh ^2(x)-1} E\left(\left.i x+\frac{\pi }{2}\right|-1\right)}{\sqrt{\cosh ^2(x)+1}}","-\frac{1}{3} \sinh (x) \cosh (x) \sqrt{-\cosh ^2(x)-1}+\frac{2 i \sqrt{\cosh ^2(x)+1} F\left(\left.i x+\frac{\pi }{2}\right|-1\right)}{3 \sqrt{-\cosh ^2(x)-1}}+\frac{2 i \sqrt{-\cosh ^2(x)-1} E\left(\left.i x+\frac{\pi }{2}\right|-1\right)}{\sqrt{\cosh ^2(x)+1}}",1,"((2*I)*Sqrt[-1 - Cosh[x]^2]*EllipticE[Pi/2 + I*x, -1])/Sqrt[1 + Cosh[x]^2] + (((2*I)/3)*Sqrt[1 + Cosh[x]^2]*EllipticF[Pi/2 + I*x, -1])/Sqrt[-1 - Cosh[x]^2] - (Cosh[x]*Sqrt[-1 - Cosh[x]^2]*Sinh[x])/3","A",6,6,12,0.5000,1,"{3180, 3172, 3178, 3177, 3183, 3182}"
51,1,49,0,0.0297244,"\int \frac{1}{\sqrt{a+b \cosh ^2(x)}} \, dx","Int[1/Sqrt[a + b*Cosh[x]^2],x]","-\frac{i \sqrt{\frac{b \cosh ^2(x)}{a}+1} F\left(i x+\frac{\pi }{2}|-\frac{b}{a}\right)}{\sqrt{a+b \cosh ^2(x)}}","-\frac{i \sqrt{\frac{b \cosh ^2(x)}{a}+1} F\left(i x+\frac{\pi }{2}|-\frac{b}{a}\right)}{\sqrt{a+b \cosh ^2(x)}}",1,"((-I)*Sqrt[1 + (b*Cosh[x]^2)/a]*EllipticF[Pi/2 + I*x, -(b/a)])/Sqrt[a + b*Cosh[x]^2]","A",2,2,12,0.1667,1,"{3183, 3182}"
52,1,17,0,0.0090285,"\int \frac{1}{\sqrt{1+\cosh ^2(x)}} \, dx","Int[1/Sqrt[1 + Cosh[x]^2],x]","-i F\left(\left.i x+\frac{\pi }{2}\right|-1\right)","-i F\left(\left.i x+\frac{\pi }{2}\right|-1\right)",1,"(-I)*EllipticF[Pi/2 + I*x, -1]","A",1,1,10,0.1000,1,"{3182}"
53,1,17,0,0.0218475,"\int \frac{1}{\sqrt{1-\cosh ^2(x)}} \, dx","Int[1/Sqrt[1 - Cosh[x]^2],x]","-\frac{\sinh (x) \tanh ^{-1}(\cosh (x))}{\sqrt{-\sinh ^2(x)}}","-\frac{\sinh (x) \tanh ^{-1}(\cosh (x))}{\sqrt{-\sinh ^2(x)}}",1,"-((ArcTanh[Cosh[x]]*Sinh[x])/Sqrt[-Sinh[x]^2])","A",3,3,12,0.2500,1,"{3176, 3207, 3770}"
54,1,15,0,0.0188273,"\int \frac{1}{\sqrt{-1+\cosh ^2(x)}} \, dx","Int[1/Sqrt[-1 + Cosh[x]^2],x]","-\frac{\sinh (x) \tanh ^{-1}(\cosh (x))}{\sqrt{\sinh ^2(x)}}","-\frac{\sinh (x) \tanh ^{-1}(\cosh (x))}{\sqrt{\sinh ^2(x)}}",1,"-((ArcTanh[Cosh[x]]*Sinh[x])/Sqrt[Sinh[x]^2])","A",3,3,10,0.3000,1,"{3176, 3207, 3770}"
55,1,39,0,0.0202647,"\int \frac{1}{\sqrt{-1-\cosh ^2(x)}} \, dx","Int[1/Sqrt[-1 - Cosh[x]^2],x]","-\frac{i \sqrt{\cosh ^2(x)+1} F\left(\left.i x+\frac{\pi }{2}\right|-1\right)}{\sqrt{-\cosh ^2(x)-1}}","-\frac{i \sqrt{\cosh ^2(x)+1} F\left(\left.i x+\frac{\pi }{2}\right|-1\right)}{\sqrt{-\cosh ^2(x)-1}}",1,"((-I)*Sqrt[1 + Cosh[x]^2]*EllipticF[Pi/2 + I*x, -1])/Sqrt[-1 - Cosh[x]^2]","A",2,2,12,0.1667,1,"{3183, 3182}"
56,1,288,0,0.4783949,"\int \frac{1}{a+b \cosh ^3(x)} \, dx","Int[(a + b*Cosh[x]^3)^(-1),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-\sqrt[3]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}\right)}{3 a^{2/3} \sqrt{\sqrt[3]{a}-\sqrt[3]{b}} \sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}}}\right)}{3 a^{2/3} \sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}} \sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}}}\right)}{3 a^{2/3} \sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}} \sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-\sqrt[3]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}\right)}{3 a^{2/3} \sqrt{\sqrt[3]{a}-\sqrt[3]{b}} \sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}}}\right)}{3 a^{2/3} \sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}} \sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}}}\right)}{3 a^{2/3} \sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}} \sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}}}",1,"(2*ArcTanh[(Sqrt[a^(1/3) - b^(1/3)]*Tanh[x/2])/Sqrt[a^(1/3) + b^(1/3)]])/(3*a^(2/3)*Sqrt[a^(1/3) - b^(1/3)]*Sqrt[a^(1/3) + b^(1/3)]) + (2*ArcTanh[(Sqrt[a^(1/3) + (-1)^(1/3)*b^(1/3)]*Tanh[x/2])/Sqrt[a^(1/3) - (-1)^(1/3)*b^(1/3)]])/(3*a^(2/3)*Sqrt[a^(1/3) - (-1)^(1/3)*b^(1/3)]*Sqrt[a^(1/3) + (-1)^(1/3)*b^(1/3)]) + (2*ArcTanh[(Sqrt[a^(1/3) - (-1)^(2/3)*b^(1/3)]*Tanh[x/2])/Sqrt[a^(1/3) + (-1)^(2/3)*b^(1/3)]])/(3*a^(2/3)*Sqrt[a^(1/3) - (-1)^(2/3)*b^(1/3)]*Sqrt[a^(1/3) + (-1)^(2/3)*b^(1/3)])","A",8,3,10,0.3000,1,"{3213, 2659, 208}"
57,1,288,0,0.2331808,"\int \frac{1}{a-b \cosh ^3(x)} \, dx","Int[(a - b*Cosh[x]^3)^(-1),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}+\sqrt[3]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[3]{a}-\sqrt[3]{b}}}\right)}{3 a^{2/3} \sqrt{\sqrt[3]{a}-\sqrt[3]{b}} \sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}\right)}{3 a^{2/3} \sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}} \sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}}}\right)}{3 a^{2/3} \sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}} \sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}+\sqrt[3]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[3]{a}-\sqrt[3]{b}}}\right)}{3 a^{2/3} \sqrt{\sqrt[3]{a}-\sqrt[3]{b}} \sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}\right)}{3 a^{2/3} \sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}} \sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}}}\right)}{3 a^{2/3} \sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}} \sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}}}",1,"(2*ArcTanh[(Sqrt[a^(1/3) + b^(1/3)]*Tanh[x/2])/Sqrt[a^(1/3) - b^(1/3)]])/(3*a^(2/3)*Sqrt[a^(1/3) - b^(1/3)]*Sqrt[a^(1/3) + b^(1/3)]) + (2*ArcTanh[(Sqrt[a^(1/3) - (-1)^(1/3)*b^(1/3)]*Tanh[x/2])/Sqrt[a^(1/3) + (-1)^(1/3)*b^(1/3)]])/(3*a^(2/3)*Sqrt[a^(1/3) - (-1)^(1/3)*b^(1/3)]*Sqrt[a^(1/3) + (-1)^(1/3)*b^(1/3)]) + (2*ArcTanh[(Sqrt[a^(1/3) + (-1)^(2/3)*b^(1/3)]*Tanh[x/2])/Sqrt[a^(1/3) - (-1)^(2/3)*b^(1/3)]])/(3*a^(2/3)*Sqrt[a^(1/3) - (-1)^(2/3)*b^(1/3)]*Sqrt[a^(1/3) + (-1)^(2/3)*b^(1/3)])","A",8,3,11,0.2727,1,"{3213, 2659, 208}"
58,1,91,0,0.1300559,"\int \frac{1}{1+\cosh ^3(x)} \, dx","Int[(1 + Cosh[x]^3)^(-1),x]","-\frac{2 \sqrt[4]{-\frac{1}{3}} \tanh ^{-1}\left((-1)^{3/4} \sqrt[4]{3} \tanh \left(\frac{x}{2}\right)\right)}{3 \left(1+(-1)^{2/3}\right)}-\frac{2 \sqrt[4]{-\frac{1}{3}} \tan ^{-1}\left((-1)^{3/4} \sqrt[4]{3} \tanh \left(\frac{x}{2}\right)\right)}{3 \left(1-\sqrt[3]{-1}\right)}+\frac{\sinh (x)}{3 (\cosh (x)+1)}","-\frac{2 \sqrt[4]{-\frac{1}{3}} \tanh ^{-1}\left((-1)^{3/4} \sqrt[4]{3} \tanh \left(\frac{x}{2}\right)\right)}{3 \left(1+(-1)^{2/3}\right)}-\frac{2 \sqrt[4]{-\frac{1}{3}} \tan ^{-1}\left((-1)^{3/4} \sqrt[4]{3} \tanh \left(\frac{x}{2}\right)\right)}{3 \left(1-\sqrt[3]{-1}\right)}+\frac{\sinh (x)}{3 (\cosh (x)+1)}",1,"(-2*(-1/3)^(1/4)*ArcTan[(-1)^(3/4)*3^(1/4)*Tanh[x/2]])/(3*(1 - (-1)^(1/3))) - (2*(-1/3)^(1/4)*ArcTanh[(-1)^(3/4)*3^(1/4)*Tanh[x/2]])/(3*(1 + (-1)^(2/3))) + Sinh[x]/(3*(1 + Cosh[x]))","A",7,5,8,0.6250,1,"{3213, 2648, 2659, 205, 208}"
59,1,95,0,0.1209995,"\int \frac{1}{1-\cosh ^3(x)} \, dx","Int[(1 - Cosh[x]^3)^(-1),x]","-\frac{2 \sqrt[4]{-1} \tanh ^{-1}\left(\frac{(-1)^{3/4} \tanh \left(\frac{x}{2}\right)}{\sqrt[4]{3}}\right)}{3^{3/4} \left(1+\sqrt[3]{-1}\right)}-\frac{2 \sqrt[4]{-1} \tan ^{-1}\left(\frac{(-1)^{3/4} \tanh \left(\frac{x}{2}\right)}{\sqrt[4]{3}}\right)}{3^{3/4} \left(1-(-1)^{2/3}\right)}-\frac{\sinh (x)}{3 (1-\cosh (x))}","-\frac{2 \sqrt[4]{-1} \tanh ^{-1}\left(\frac{(-1)^{3/4} \tanh \left(\frac{x}{2}\right)}{\sqrt[4]{3}}\right)}{3^{3/4} \left(1+\sqrt[3]{-1}\right)}-\frac{2 \sqrt[4]{-1} \tan ^{-1}\left(\frac{(-1)^{3/4} \tanh \left(\frac{x}{2}\right)}{\sqrt[4]{3}}\right)}{3^{3/4} \left(1-(-1)^{2/3}\right)}-\frac{\sinh (x)}{3 (1-\cosh (x))}",1,"(-2*(-1)^(1/4)*ArcTan[((-1)^(3/4)*Tanh[x/2])/3^(1/4)])/(3^(3/4)*(1 - (-1)^(2/3))) - (2*(-1)^(1/4)*ArcTanh[((-1)^(3/4)*Tanh[x/2])/3^(1/4)])/(3^(3/4)*(1 + (-1)^(1/3))) - Sinh[x]/(3*(1 - Cosh[x]))","A",7,5,10,0.5000,1,"{3213, 2648, 2659, 208, 205}"
60,1,485,0,1.0371572,"\int \frac{1}{a+b \cosh ^4(x)} \, dx","Int[(a + b*Cosh[x]^4)^(-1),x]","-\frac{\left(\sqrt{a+b}+\sqrt{a}\right) \log \left((a+b)^{3/4} \coth ^2(x)-\sqrt{2} \sqrt[4]{a} \sqrt{\sqrt{a} \sqrt{a+b}+a+b} \coth (x)+\sqrt{a} \sqrt[4]{a+b}\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{a+b} \sqrt{\sqrt{a} \sqrt{a+b}+a+b}}+\frac{\left(\sqrt{a+b}+\sqrt{a}\right) \log \left((a+b)^{3/4} \coth ^2(x)+\sqrt{2} \sqrt[4]{a} \sqrt{\sqrt{a} \sqrt{a+b}+a+b} \coth (x)+\sqrt{a} \sqrt[4]{a+b}\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{a+b} \sqrt{\sqrt{a} \sqrt{a+b}+a+b}}+\frac{\left(\sqrt{a}-\sqrt{a+b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{\sqrt{a} \sqrt{a+b}+a+b}-\sqrt{2} (a+b)^{3/4} \coth (x)}{\sqrt[4]{a} \sqrt{-\sqrt{a} \sqrt{a+b}+a+b}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{a+b} \sqrt{-\sqrt{a} \sqrt{a+b}+a+b}}-\frac{\left(\sqrt{a}-\sqrt{a+b}\right) \tan ^{-1}\left(\frac{\sqrt{2} (a+b)^{3/4} \coth (x)+\sqrt[4]{a} \sqrt{\sqrt{a} \sqrt{a+b}+a+b}}{\sqrt[4]{a} \sqrt{-\sqrt{a} \sqrt{a+b}+a+b}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{a+b} \sqrt{-\sqrt{a} \sqrt{a+b}+a+b}}","\frac{\sqrt{\sqrt{a}-\sqrt{a+b}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a+b}+\sqrt{a}}-\sqrt{2} \sqrt[4]{a} \tanh (x)}{\sqrt{\sqrt{a}-\sqrt{a+b}}}\right)}{2 \sqrt{2} a^{3/4} \sqrt{a+b}}-\frac{\sqrt{\sqrt{a}-\sqrt{a+b}} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a+b}+\sqrt{a}}+\sqrt{2} \sqrt[4]{a} \tanh (x)}{\sqrt{\sqrt{a}-\sqrt{a+b}}}\right)}{2 \sqrt{2} a^{3/4} \sqrt{a+b}}-\frac{\sqrt{\sqrt{a+b}+\sqrt{a}} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt{\sqrt{a+b}+\sqrt{a}} \tanh (x)+\sqrt{a+b}+\sqrt{a} \tanh ^2(x)\right)}{4 \sqrt{2} a^{3/4} \sqrt{a+b}}+\frac{\sqrt{\sqrt{a+b}+\sqrt{a}} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt{\sqrt{a+b}+\sqrt{a}} \tanh (x)+\sqrt{a+b}+\sqrt{a} \tanh ^2(x)\right)}{4 \sqrt{2} a^{3/4} \sqrt{a+b}}",1,"((Sqrt[a] - Sqrt[a + b])*ArcTan[(a^(1/4)*Sqrt[a + b + Sqrt[a]*Sqrt[a + b]] - Sqrt[2]*(a + b)^(3/4)*Coth[x])/(a^(1/4)*Sqrt[a + b - Sqrt[a]*Sqrt[a + b]])])/(2*Sqrt[2]*a^(3/4)*(a + b)^(1/4)*Sqrt[a + b - Sqrt[a]*Sqrt[a + b]]) - ((Sqrt[a] - Sqrt[a + b])*ArcTan[(a^(1/4)*Sqrt[a + b + Sqrt[a]*Sqrt[a + b]] + Sqrt[2]*(a + b)^(3/4)*Coth[x])/(a^(1/4)*Sqrt[a + b - Sqrt[a]*Sqrt[a + b]])])/(2*Sqrt[2]*a^(3/4)*(a + b)^(1/4)*Sqrt[a + b - Sqrt[a]*Sqrt[a + b]]) - ((Sqrt[a] + Sqrt[a + b])*Log[Sqrt[a]*(a + b)^(1/4) - Sqrt[2]*a^(1/4)*Sqrt[a + b + Sqrt[a]*Sqrt[a + b]]*Coth[x] + (a + b)^(3/4)*Coth[x]^2])/(4*Sqrt[2]*a^(3/4)*(a + b)^(1/4)*Sqrt[a + b + Sqrt[a]*Sqrt[a + b]]) + ((Sqrt[a] + Sqrt[a + b])*Log[Sqrt[a]*(a + b)^(1/4) + Sqrt[2]*a^(1/4)*Sqrt[a + b + Sqrt[a]*Sqrt[a + b]]*Coth[x] + (a + b)^(3/4)*Coth[x]^2])/(4*Sqrt[2]*a^(3/4)*(a + b)^(1/4)*Sqrt[a + b + Sqrt[a]*Sqrt[a + b]])","A",10,6,10,0.6000,1,"{3209, 1169, 634, 618, 204, 628}"
61,1,101,0,0.1254796,"\int \frac{1}{a-b \cosh ^4(x)} \, dx","Int[(a - b*Cosh[x]^4)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} \tanh (x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 a^{3/4} \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} \tanh (x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 a^{3/4} \sqrt{\sqrt{a}+\sqrt{b}}}","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} \tanh (x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 a^{3/4} \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{a} \tanh (x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 a^{3/4} \sqrt{\sqrt{a}+\sqrt{b}}}",1,"ArcTanh[(a^(1/4)*Tanh[x])/Sqrt[Sqrt[a] - Sqrt[b]]]/(2*a^(3/4)*Sqrt[Sqrt[a] - Sqrt[b]]) + ArcTanh[(a^(1/4)*Tanh[x])/Sqrt[Sqrt[a] + Sqrt[b]]]/(2*a^(3/4)*Sqrt[Sqrt[a] + Sqrt[b]])","A",4,3,11,0.2727,1,"{3209, 1166, 208}"
62,1,176,0,0.1551041,"\int \frac{1}{1+\cosh ^4(x)} \, dx","Int[(1 + Cosh[x]^4)^(-1),x]","-\frac{1}{8} \sqrt{1+\sqrt{2}} \log \left(2 \coth ^2(x)-2 \sqrt{1+\sqrt{2}} \coth (x)+\sqrt{2}\right)+\frac{1}{8} \sqrt{1+\sqrt{2}} \log \left(\sqrt{2} \coth ^2(x)+\sqrt{2 \left(1+\sqrt{2}\right)} \coth (x)+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{1+\sqrt{2}}-2 \coth (x)}{\sqrt{\sqrt{2}-1}}\right)}{4 \sqrt{1+\sqrt{2}}}+\frac{\tan ^{-1}\left(\frac{2 \coth (x)+\sqrt{1+\sqrt{2}}}{\sqrt{\sqrt{2}-1}}\right)}{4 \sqrt{1+\sqrt{2}}}","-\frac{1}{8} \sqrt{1+\sqrt{2}} \log \left(2 \coth ^2(x)-2 \sqrt{1+\sqrt{2}} \coth (x)+\sqrt{2}\right)+\frac{1}{8} \sqrt{1+\sqrt{2}} \log \left(\sqrt{2} \coth ^2(x)+\sqrt{2 \left(1+\sqrt{2}\right)} \coth (x)+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{1+\sqrt{2}}-2 \coth (x)}{\sqrt{\sqrt{2}-1}}\right)}{4 \sqrt{1+\sqrt{2}}}+\frac{\tan ^{-1}\left(\frac{2 \coth (x)+\sqrt{1+\sqrt{2}}}{\sqrt{\sqrt{2}-1}}\right)}{4 \sqrt{1+\sqrt{2}}}",1,"-ArcTan[(Sqrt[1 + Sqrt[2]] - 2*Coth[x])/Sqrt[-1 + Sqrt[2]]]/(4*Sqrt[1 + Sqrt[2]]) + ArcTan[(Sqrt[1 + Sqrt[2]] + 2*Coth[x])/Sqrt[-1 + Sqrt[2]]]/(4*Sqrt[1 + Sqrt[2]]) - (Sqrt[1 + Sqrt[2]]*Log[Sqrt[2] - 2*Sqrt[1 + Sqrt[2]]*Coth[x] + 2*Coth[x]^2])/8 + (Sqrt[1 + Sqrt[2]]*Log[1 + Sqrt[2*(1 + Sqrt[2])]*Coth[x] + Sqrt[2]*Coth[x]^2])/8","A",10,6,8,0.7500,1,"{3209, 1169, 634, 618, 204, 628}"
63,1,25,0,0.0169727,"\int \frac{1}{1-\cosh ^4(x)} \, dx","Int[(1 - Cosh[x]^4)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{2 \sqrt{2}}+\frac{\coth (x)}{2}","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{2 \sqrt{2}}+\frac{\coth (x)}{2}",1,"ArcTanh[Tanh[x]/Sqrt[2]]/(2*Sqrt[2]) + Coth[x]/2","A",3,3,10,0.3000,1,"{3209, 388, 206}"
64,1,494,0,0.9035624,"\int \frac{1}{a+b \cosh ^5(x)} \, dx","Int[(a + b*Cosh[x]^5)^(-1),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-\sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+\sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-\sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+\sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}}}",1,"(2*ArcTanh[(Sqrt[a^(1/5) - b^(1/5)]*Tanh[x/2])/Sqrt[a^(1/5) + b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - b^(1/5)]*Sqrt[a^(1/5) + b^(1/5)]) + (2*ArcTanh[(Sqrt[a^(1/5) + (-1)^(1/5)*b^(1/5)]*Tanh[x/2])/Sqrt[a^(1/5) - (-1)^(1/5)*b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - (-1)^(1/5)*b^(1/5)]*Sqrt[a^(1/5) + (-1)^(1/5)*b^(1/5)]) + (2*ArcTanh[(Sqrt[a^(1/5) - (-1)^(2/5)*b^(1/5)]*Tanh[x/2])/Sqrt[a^(1/5) + (-1)^(2/5)*b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - (-1)^(2/5)*b^(1/5)]*Sqrt[a^(1/5) + (-1)^(2/5)*b^(1/5)]) + (2*ArcTanh[(Sqrt[a^(1/5) + (-1)^(3/5)*b^(1/5)]*Tanh[x/2])/Sqrt[a^(1/5) - (-1)^(3/5)*b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - (-1)^(3/5)*b^(1/5)]*Sqrt[a^(1/5) + (-1)^(3/5)*b^(1/5)]) + (2*ArcTanh[(Sqrt[a^(1/5) - (-1)^(4/5)*b^(1/5)]*Tanh[x/2])/Sqrt[a^(1/5) + (-1)^(4/5)*b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - (-1)^(4/5)*b^(1/5)]*Sqrt[a^(1/5) + (-1)^(4/5)*b^(1/5)])","A",12,3,10,0.3000,1,"{3213, 2659, 208}"
65,1,171,0,0.2259108,"\int \frac{1}{a+b \cosh ^6(x)} \, dx","Int[(a + b*Cosh[x]^6)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}}}","\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}}}",1,"ArcTanh[(a^(1/6)*Tanh[x])/Sqrt[a^(1/3) + b^(1/3)]]/(3*a^(5/6)*Sqrt[a^(1/3) + b^(1/3)]) + ArcTanh[(a^(1/6)*Tanh[x])/Sqrt[a^(1/3) - (-1)^(1/3)*b^(1/3)]]/(3*a^(5/6)*Sqrt[a^(1/3) - (-1)^(1/3)*b^(1/3)]) + ArcTanh[(a^(1/6)*Tanh[x])/Sqrt[a^(1/3) + (-1)^(2/3)*b^(1/3)]]/(3*a^(5/6)*Sqrt[a^(1/3) + (-1)^(2/3)*b^(1/3)])","A",7,3,10,0.3000,1,"{3211, 3181, 206}"
66,1,245,0,0.4869651,"\int \frac{1}{a+b \cosh ^8(x)} \, dx","Int[(a + b*Cosh[x]^8)^(-1),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{-a} \tanh (x)}{\sqrt{\sqrt[4]{-a}-i \sqrt[4]{b}}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}-i \sqrt[4]{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{-a} \tanh (x)}{\sqrt{\sqrt[4]{-a}+i \sqrt[4]{b}}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}+i \sqrt[4]{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{-a} \tanh (x)}{\sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}-\frac{\tanh ^{-1}\left(\frac{(-a)^{5/8} \tanh (x)}{\sqrt{a \sqrt[4]{b}+(-a)^{5/4}}}\right)}{4 (-a)^{3/8} \sqrt{a \sqrt[4]{b}+(-a)^{5/4}}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{-a} \tanh (x)}{\sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{-a} \tanh (x)}{\sqrt{\sqrt[4]{-a}-i \sqrt[4]{b}}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}-i \sqrt[4]{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{-a} \tanh (x)}{\sqrt{\sqrt[4]{-a}+i \sqrt[4]{b}}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}+i \sqrt[4]{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{-a} \tanh (x)}{\sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}",1,"-ArcTanh[((-a)^(1/8)*Tanh[x])/Sqrt[(-a)^(1/4) - I*b^(1/4)]]/(4*(-a)^(7/8)*Sqrt[(-a)^(1/4) - I*b^(1/4)]) - ArcTanh[((-a)^(1/8)*Tanh[x])/Sqrt[(-a)^(1/4) + I*b^(1/4)]]/(4*(-a)^(7/8)*Sqrt[(-a)^(1/4) + I*b^(1/4)]) - ArcTanh[((-a)^(1/8)*Tanh[x])/Sqrt[(-a)^(1/4) + b^(1/4)]]/(4*(-a)^(7/8)*Sqrt[(-a)^(1/4) + b^(1/4)]) - ArcTanh[((-a)^(5/8)*Tanh[x])/Sqrt[(-a)^(5/4) + a*b^(1/4)]]/(4*(-a)^(3/8)*Sqrt[(-a)^(5/4) + a*b^(1/4)])","A",9,3,10,0.3000,1,"{3211, 3181, 206}"
67,1,494,0,0.6254873,"\int \frac{1}{a-b \cosh ^5(x)} \, dx","Int[(a - b*Cosh[x]^5)^(-1),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+\sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-\sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+\sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-\sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}}}",1,"(2*ArcTanh[(Sqrt[a^(1/5) + b^(1/5)]*Tanh[x/2])/Sqrt[a^(1/5) - b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - b^(1/5)]*Sqrt[a^(1/5) + b^(1/5)]) + (2*ArcTanh[(Sqrt[a^(1/5) - (-1)^(1/5)*b^(1/5)]*Tanh[x/2])/Sqrt[a^(1/5) + (-1)^(1/5)*b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - (-1)^(1/5)*b^(1/5)]*Sqrt[a^(1/5) + (-1)^(1/5)*b^(1/5)]) + (2*ArcTanh[(Sqrt[a^(1/5) + (-1)^(2/5)*b^(1/5)]*Tanh[x/2])/Sqrt[a^(1/5) - (-1)^(2/5)*b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - (-1)^(2/5)*b^(1/5)]*Sqrt[a^(1/5) + (-1)^(2/5)*b^(1/5)]) + (2*ArcTanh[(Sqrt[a^(1/5) - (-1)^(3/5)*b^(1/5)]*Tanh[x/2])/Sqrt[a^(1/5) + (-1)^(3/5)*b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - (-1)^(3/5)*b^(1/5)]*Sqrt[a^(1/5) + (-1)^(3/5)*b^(1/5)]) + (2*ArcTanh[(Sqrt[a^(1/5) + (-1)^(4/5)*b^(1/5)]*Tanh[x/2])/Sqrt[a^(1/5) - (-1)^(4/5)*b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - (-1)^(4/5)*b^(1/5)]*Sqrt[a^(1/5) + (-1)^(4/5)*b^(1/5)])","A",12,3,11,0.2727,1,"{3213, 2659, 208}"
68,1,175,0,0.2305587,"\int \frac{1}{a-b \cosh ^6(x)} \, dx","Int[(a - b*Cosh[x]^6)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}-\sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-\sqrt[3]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}}}","\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}-\sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-\sqrt[3]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}}}",1,"ArcTanh[(a^(1/6)*Tanh[x])/Sqrt[a^(1/3) - b^(1/3)]]/(3*a^(5/6)*Sqrt[a^(1/3) - b^(1/3)]) + ArcTanh[(a^(1/6)*Tanh[x])/Sqrt[a^(1/3) + (-1)^(1/3)*b^(1/3)]]/(3*a^(5/6)*Sqrt[a^(1/3) + (-1)^(1/3)*b^(1/3)]) + ArcTanh[(a^(1/6)*Tanh[x])/Sqrt[a^(1/3) - (-1)^(2/3)*b^(1/3)]]/(3*a^(5/6)*Sqrt[a^(1/3) - (-1)^(2/3)*b^(1/3)])","A",7,3,11,0.2727,1,"{3211, 3181, 206}"
69,1,213,0,0.234569,"\int \frac{1}{a-b \cosh ^8(x)} \, dx","Int[(a - b*Cosh[x]^8)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{a} \tanh (x)}{\sqrt{\sqrt[4]{a}-\sqrt[4]{b}}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}-\sqrt[4]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{a} \tanh (x)}{\sqrt{\sqrt[4]{a}-i \sqrt[4]{b}}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}-i \sqrt[4]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{a} \tanh (x)}{\sqrt{\sqrt[4]{a}+i \sqrt[4]{b}}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}+i \sqrt[4]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{a} \tanh (x)}{\sqrt{\sqrt[4]{a}+\sqrt[4]{b}}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}+\sqrt[4]{b}}}","\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{a} \tanh (x)}{\sqrt{\sqrt[4]{a}-\sqrt[4]{b}}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}-\sqrt[4]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{a} \tanh (x)}{\sqrt{\sqrt[4]{a}-i \sqrt[4]{b}}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}-i \sqrt[4]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{a} \tanh (x)}{\sqrt{\sqrt[4]{a}+i \sqrt[4]{b}}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}+i \sqrt[4]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{a} \tanh (x)}{\sqrt{\sqrt[4]{a}+\sqrt[4]{b}}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}+\sqrt[4]{b}}}",1,"ArcTanh[(a^(1/8)*Tanh[x])/Sqrt[a^(1/4) - b^(1/4)]]/(4*a^(7/8)*Sqrt[a^(1/4) - b^(1/4)]) + ArcTanh[(a^(1/8)*Tanh[x])/Sqrt[a^(1/4) - I*b^(1/4)]]/(4*a^(7/8)*Sqrt[a^(1/4) - I*b^(1/4)]) + ArcTanh[(a^(1/8)*Tanh[x])/Sqrt[a^(1/4) + I*b^(1/4)]]/(4*a^(7/8)*Sqrt[a^(1/4) + I*b^(1/4)]) + ArcTanh[(a^(1/8)*Tanh[x])/Sqrt[a^(1/4) + b^(1/4)]]/(4*a^(7/8)*Sqrt[a^(1/4) + b^(1/4)])","A",9,3,11,0.2727,1,"{3211, 3181, 206}"
70,1,223,0,0.5619429,"\int \frac{1}{1+\cosh ^5(x)} \, dx","Int[(1 + Cosh[x]^5)^(-1),x]","\frac{2 \tanh ^{-1}\left(\sqrt{\frac{1-(-1)^{2/5}}{1+(-1)^{2/5}}} \tanh \left(\frac{x}{2}\right)\right)}{5 \sqrt{1-(-1)^{4/5}}}+\frac{2 \tanh ^{-1}\left(\sqrt{\frac{1-(-1)^{4/5}}{1+(-1)^{4/5}}} \tanh \left(\frac{x}{2}\right)\right)}{5 \sqrt{1+(-1)^{3/5}}}-\frac{2 \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right)}{\sqrt{-\frac{1-\sqrt[5]{-1}}{1+\sqrt[5]{-1}}}}\right)}{5 \sqrt{(-1)^{2/5}-1}}-\frac{2 \sqrt{-\frac{1+(-1)^{3/5}}{1-(-1)^{3/5}}} \tan ^{-1}\left(\sqrt{-\frac{1+(-1)^{3/5}}{1-(-1)^{3/5}}} \tanh \left(\frac{x}{2}\right)\right)}{5 \left(1+(-1)^{3/5}\right)}+\frac{\sinh (x)}{5 (\cosh (x)+1)}","\frac{2 \tanh ^{-1}\left(\sqrt{\frac{1-(-1)^{2/5}}{1+(-1)^{2/5}}} \tanh \left(\frac{x}{2}\right)\right)}{5 \sqrt{1-(-1)^{4/5}}}+\frac{2 \tanh ^{-1}\left(\sqrt{\frac{1-(-1)^{4/5}}{1+(-1)^{4/5}}} \tanh \left(\frac{x}{2}\right)\right)}{5 \sqrt{1+(-1)^{3/5}}}-\frac{2 \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right)}{\sqrt{-\frac{1-\sqrt[5]{-1}}{1+\sqrt[5]{-1}}}}\right)}{5 \sqrt{(-1)^{2/5}-1}}-\frac{2 \sqrt{-\frac{1+(-1)^{3/5}}{1-(-1)^{3/5}}} \tan ^{-1}\left(\sqrt{-\frac{1+(-1)^{3/5}}{1-(-1)^{3/5}}} \tanh \left(\frac{x}{2}\right)\right)}{5 \left(1+(-1)^{3/5}\right)}+\frac{\sinh (x)}{5 (\cosh (x)+1)}",1,"(-2*ArcTan[Tanh[x/2]/Sqrt[-((1 - (-1)^(1/5))/(1 + (-1)^(1/5)))]])/(5*Sqrt[-1 + (-1)^(2/5)]) - (2*Sqrt[-((1 + (-1)^(3/5))/(1 - (-1)^(3/5)))]*ArcTan[Sqrt[-((1 + (-1)^(3/5))/(1 - (-1)^(3/5)))]*Tanh[x/2]])/(5*(1 + (-1)^(3/5))) + (2*ArcTanh[Sqrt[(1 - (-1)^(2/5))/(1 + (-1)^(2/5))]*Tanh[x/2]])/(5*Sqrt[1 - (-1)^(4/5)]) + (2*ArcTanh[Sqrt[(1 - (-1)^(4/5))/(1 + (-1)^(4/5))]*Tanh[x/2]])/(5*Sqrt[1 + (-1)^(3/5)]) + Sinh[x]/(5*(1 + Cosh[x]))","A",11,5,8,0.6250,1,"{3213, 2648, 2659, 205, 208}"
71,1,83,0,0.1045962,"\int \frac{1}{1+\cosh ^6(x)} \, dx","Int[(1 + Cosh[x]^6)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{3 \sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-\sqrt[3]{-1}}}\right)}{3 \sqrt{1-\sqrt[3]{-1}}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1+(-1)^{2/3}}}\right)}{3 \sqrt{1+(-1)^{2/3}}}","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{3 \sqrt{2}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-\sqrt[3]{-1}}}\right)}{3 \sqrt{1-\sqrt[3]{-1}}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1+(-1)^{2/3}}}\right)}{3 \sqrt{1+(-1)^{2/3}}}",1,"ArcTanh[Tanh[x]/Sqrt[2]]/(3*Sqrt[2]) + ArcTanh[Tanh[x]/Sqrt[1 - (-1)^(1/3)]]/(3*Sqrt[1 - (-1)^(1/3)]) + ArcTanh[Tanh[x]/Sqrt[1 + (-1)^(2/3)]]/(3*Sqrt[1 + (-1)^(2/3)])","A",7,3,8,0.3750,1,"{3211, 3181, 206}"
72,1,129,0,0.18512,"\int \frac{1}{1+\cosh ^8(x)} \, dx","Int[(1 + Cosh[x]^8)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-\sqrt[4]{-1}}}\right)}{4 \sqrt{1-\sqrt[4]{-1}}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1+\sqrt[4]{-1}}}\right)}{4 \sqrt{1+\sqrt[4]{-1}}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-(-1)^{3/4}}}\right)}{4 \sqrt{1-(-1)^{3/4}}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1+(-1)^{3/4}}}\right)}{4 \sqrt{1+(-1)^{3/4}}}","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-\sqrt[4]{-1}}}\right)}{4 \sqrt{1-\sqrt[4]{-1}}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1+\sqrt[4]{-1}}}\right)}{4 \sqrt{1+\sqrt[4]{-1}}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-(-1)^{3/4}}}\right)}{4 \sqrt{1-(-1)^{3/4}}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1+(-1)^{3/4}}}\right)}{4 \sqrt{1+(-1)^{3/4}}}",1,"ArcTanh[Tanh[x]/Sqrt[1 - (-1)^(1/4)]]/(4*Sqrt[1 - (-1)^(1/4)]) + ArcTanh[Tanh[x]/Sqrt[1 + (-1)^(1/4)]]/(4*Sqrt[1 + (-1)^(1/4)]) + ArcTanh[Tanh[x]/Sqrt[1 - (-1)^(3/4)]]/(4*Sqrt[1 - (-1)^(3/4)]) + ArcTanh[Tanh[x]/Sqrt[1 + (-1)^(3/4)]]/(4*Sqrt[1 + (-1)^(3/4)])","A",9,3,8,0.3750,1,"{3211, 3181, 206}"
73,1,205,0,0.462816,"\int \frac{1}{1-\cosh ^5(x)} \, dx","Int[(1 - Cosh[x]^5)^(-1),x]","\frac{2 \tanh ^{-1}\left(\sqrt{\frac{1-\sqrt[5]{-1}}{1+\sqrt[5]{-1}}} \tanh \left(\frac{x}{2}\right)\right)}{5 \sqrt{1-(-1)^{2/5}}}+\frac{2 \tanh ^{-1}\left(\sqrt{\frac{1-(-1)^{3/5}}{1+(-1)^{3/5}}} \tanh \left(\frac{x}{2}\right)\right)}{5 \sqrt{1+\sqrt[5]{-1}}}-\frac{2 \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right)}{\sqrt{-\frac{1-(-1)^{2/5}}{1+(-1)^{2/5}}}}\right)}{5 \sqrt{(-1)^{4/5}-1}}+\frac{2 \tan ^{-1}\left(\sqrt{-\frac{1+(-1)^{4/5}}{1-(-1)^{4/5}}} \tanh \left(\frac{x}{2}\right)\right)}{5 \sqrt{-1-(-1)^{3/5}}}-\frac{\sinh (x)}{5 (1-\cosh (x))}","\frac{2 \tanh ^{-1}\left(\sqrt{\frac{1-\sqrt[5]{-1}}{1+\sqrt[5]{-1}}} \tanh \left(\frac{x}{2}\right)\right)}{5 \sqrt{1-(-1)^{2/5}}}+\frac{2 \tanh ^{-1}\left(\sqrt{\frac{1-(-1)^{3/5}}{1+(-1)^{3/5}}} \tanh \left(\frac{x}{2}\right)\right)}{5 \sqrt{1+\sqrt[5]{-1}}}-\frac{2 \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right)}{\sqrt{-\frac{1-(-1)^{2/5}}{1+(-1)^{2/5}}}}\right)}{5 \sqrt{(-1)^{4/5}-1}}+\frac{2 \tan ^{-1}\left(\sqrt{-\frac{1+(-1)^{4/5}}{1-(-1)^{4/5}}} \tanh \left(\frac{x}{2}\right)\right)}{5 \sqrt{-1-(-1)^{3/5}}}-\frac{\sinh (x)}{5 (1-\cosh (x))}",1,"(-2*ArcTan[Tanh[x/2]/Sqrt[-((1 - (-1)^(2/5))/(1 + (-1)^(2/5)))]])/(5*Sqrt[-1 + (-1)^(4/5)]) + (2*ArcTan[Sqrt[-((1 + (-1)^(4/5))/(1 - (-1)^(4/5)))]*Tanh[x/2]])/(5*Sqrt[-1 - (-1)^(3/5)]) + (2*ArcTanh[Sqrt[(1 - (-1)^(1/5))/(1 + (-1)^(1/5))]*Tanh[x/2]])/(5*Sqrt[1 - (-1)^(2/5)]) + (2*ArcTanh[Sqrt[(1 - (-1)^(3/5))/(1 + (-1)^(3/5))]*Tanh[x/2]])/(5*Sqrt[1 + (-1)^(1/5)]) - Sinh[x]/(5*(1 - Cosh[x]))","A",11,5,10,0.5000,1,"{3213, 2648, 2659, 208, 205}"
74,1,71,0,0.1224648,"\int \frac{1}{1-\cosh ^6(x)} \, dx","Int[(1 - Cosh[x]^6)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1+\sqrt[3]{-1}}}\right)}{3 \sqrt{1+\sqrt[3]{-1}}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-(-1)^{2/3}}}\right)}{3 \sqrt{1-(-1)^{2/3}}}+\frac{\coth (x)}{3}","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1+\sqrt[3]{-1}}}\right)}{3 \sqrt{1+\sqrt[3]{-1}}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-(-1)^{2/3}}}\right)}{3 \sqrt{1-(-1)^{2/3}}}+\frac{\coth (x)}{3}",1,"ArcTanh[Tanh[x]/Sqrt[1 + (-1)^(1/3)]]/(3*Sqrt[1 + (-1)^(1/3)]) + ArcTanh[Tanh[x]/Sqrt[1 - (-1)^(2/3)]]/(3*Sqrt[1 - (-1)^(2/3)]) + Coth[x]/3","A",8,6,10,0.6000,1,"{3211, 3181, 206, 3175, 3767, 8}"
75,1,69,0,0.0774158,"\int \frac{1}{1-\cosh ^8(x)} \, dx","Int[(1 - Cosh[x]^8)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-i}}\right)}{4 \sqrt{1-i}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1+i}}\right)}{4 \sqrt{1+i}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{4 \sqrt{2}}+\frac{\coth (x)}{4}","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-i}}\right)}{4 \sqrt{1-i}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1+i}}\right)}{4 \sqrt{1+i}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{4 \sqrt{2}}+\frac{\coth (x)}{4}",1,"ArcTanh[Tanh[x]/Sqrt[1 - I]]/(4*Sqrt[1 - I]) + ArcTanh[Tanh[x]/Sqrt[1 + I]]/(4*Sqrt[1 + I]) + ArcTanh[Tanh[x]/Sqrt[2]]/(4*Sqrt[2]) + Coth[x]/4","A",10,6,10,0.6000,1,"{3211, 3181, 206, 3175, 3767, 8}"
76,1,15,0,0.0326715,"\int \frac{\tanh (x)}{1+\cosh ^2(x)} \, dx","Int[Tanh[x]/(1 + Cosh[x]^2),x]","\log (\cosh (x))-\frac{1}{2} \log \left(\cosh ^2(x)+1\right)","\log (\cosh (x))-\frac{1}{2} \log \left(\cosh ^2(x)+1\right)",1,"Log[Cosh[x]] - Log[1 + Cosh[x]^2]/2","A",4,4,11,0.3636,1,"{3194, 36, 29, 31}"
77,1,39,0,0.0687702,"\int \sqrt{a+b \cosh ^2(x)} \tanh (x) \, dx","Int[Sqrt[a + b*Cosh[x]^2]*Tanh[x],x]","\sqrt{a+b \cosh ^2(x)}-\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \cosh ^2(x)}}{\sqrt{a}}\right)","\sqrt{a+b \cosh ^2(x)}-\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \cosh ^2(x)}}{\sqrt{a}}\right)",1,"-(Sqrt[a]*ArcTanh[Sqrt[a + b*Cosh[x]^2]/Sqrt[a]]) + Sqrt[a + b*Cosh[x]^2]","A",4,4,15,0.2667,1,"{3194, 50, 63, 208}"
78,1,26,0,0.063703,"\int \frac{\tanh (x)}{\sqrt{a+b \cosh ^2(x)}} \, dx","Int[Tanh[x]/Sqrt[a + b*Cosh[x]^2],x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \cosh ^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \cosh ^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"-(ArcTanh[Sqrt[a + b*Cosh[x]^2]/Sqrt[a]]/Sqrt[a])","A",3,3,15,0.2000,1,"{3194, 63, 208}"
79,1,13,0,0.0408253,"\int \frac{\tanh (x)}{\sqrt{1+\cosh ^2(x)}} \, dx","Int[Tanh[x]/Sqrt[1 + Cosh[x]^2],x]","-\tanh ^{-1}\left(\sqrt{\cosh ^2(x)+1}\right)","-\tanh ^{-1}\left(\sqrt{\cosh ^2(x)+1}\right)",1,"-ArcTanh[Sqrt[1 + Cosh[x]^2]]","A",3,3,13,0.2308,1,"{3194, 63, 207}"
80,1,13,0,0.0607551,"\int \frac{\tanh (x)}{\sqrt{1-\cosh ^2(x)}} \, dx","Int[Tanh[x]/Sqrt[1 - Cosh[x]^2],x]","-\tanh ^{-1}\left(\sqrt{-\sinh ^2(x)}\right)","-\tanh ^{-1}\left(\sqrt{-\sinh ^2(x)}\right)",1,"-ArcTanh[Sqrt[-Sinh[x]^2]]","A",4,4,15,0.2667,1,"{3176, 3205, 63, 206}"
81,1,153,0,0.2347478,"\int \frac{\tanh ^3(x)}{a+b \cosh ^3(x)} \, dx","Int[Tanh[x]^3/(a + b*Cosh[x]^3),x]","-\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \cosh (x)+b^{2/3} \cosh ^2(x)\right)}{6 a^{5/3}}+\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \cosh (x)\right)}{3 a^{5/3}}-\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \cosh (x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3}}-\frac{\log \left(a+b \cosh ^3(x)\right)}{3 a}+\frac{\text{sech}^2(x)}{2 a}+\frac{\log (\cosh (x))}{a}","-\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \cosh (x)+b^{2/3} \cosh ^2(x)\right)}{6 a^{5/3}}+\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \cosh (x)\right)}{3 a^{5/3}}-\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \cosh (x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3}}-\frac{\log \left(a+b \cosh ^3(x)\right)}{3 a}+\frac{\text{sech}^2(x)}{2 a}+\frac{\log (\cosh (x))}{a}",1,"-((b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*Cosh[x])/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3))) + Log[Cosh[x]]/a + (b^(2/3)*Log[a^(1/3) + b^(1/3)*Cosh[x]])/(3*a^(5/3)) - (b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*Cosh[x] + b^(2/3)*Cosh[x]^2])/(6*a^(5/3)) - Log[a + b*Cosh[x]^3]/(3*a) + Sech[x]^2/(2*a)","A",11,10,15,0.6667,1,"{3230, 1834, 1871, 200, 31, 634, 617, 204, 628, 260}"
82,1,28,0,0.0747128,"\int \frac{\tanh (x)}{\sqrt{a+b \cosh ^3(x)}} \, dx","Int[Tanh[x]/Sqrt[a + b*Cosh[x]^3],x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \cosh ^3(x)}}{\sqrt{a}}\right)}{3 \sqrt{a}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \cosh ^3(x)}}{\sqrt{a}}\right)}{3 \sqrt{a}}",1,"(-2*ArcTanh[Sqrt[a + b*Cosh[x]^3]/Sqrt[a]])/(3*Sqrt[a])","A",4,4,15,0.2667,1,"{3230, 266, 63, 208}"
83,1,45,0,0.0818281,"\int \sqrt{a+b \cosh ^3(x)} \tanh (x) \, dx","Int[Sqrt[a + b*Cosh[x]^3]*Tanh[x],x]","\frac{2}{3} \sqrt{a+b \cosh ^3(x)}-\frac{2}{3} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \cosh ^3(x)}}{\sqrt{a}}\right)","\frac{2}{3} \sqrt{a+b \cosh ^3(x)}-\frac{2}{3} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \cosh ^3(x)}}{\sqrt{a}}\right)",1,"(-2*Sqrt[a]*ArcTanh[Sqrt[a + b*Cosh[x]^3]/Sqrt[a]])/3 + (2*Sqrt[a + b*Cosh[x]^3])/3","A",5,5,15,0.3333,1,"{3230, 266, 50, 63, 208}"
84,1,29,0,0.0867427,"\int \frac{\tanh (x)}{\sqrt{a+b \cosh ^n(x)}} \, dx","Int[Tanh[x]/Sqrt[a + b*Cosh[x]^n],x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \cosh ^n(x)}}{\sqrt{a}}\right)}{\sqrt{a} n}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \cosh ^n(x)}}{\sqrt{a}}\right)}{\sqrt{a} n}",1,"(-2*ArcTanh[Sqrt[a + b*Cosh[x]^n]/Sqrt[a]])/(Sqrt[a]*n)","A",4,4,15,0.2667,1,"{3230, 266, 63, 208}"
85,1,47,0,0.089022,"\int \sqrt{a+b \cosh ^n(x)} \tanh (x) \, dx","Int[Sqrt[a + b*Cosh[x]^n]*Tanh[x],x]","\frac{2 \sqrt{a+b \cosh ^n(x)}}{n}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \cosh ^n(x)}}{\sqrt{a}}\right)}{n}","\frac{2 \sqrt{a+b \cosh ^n(x)}}{n}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \cosh ^n(x)}}{\sqrt{a}}\right)}{n}",1,"(-2*Sqrt[a]*ArcTanh[Sqrt[a + b*Cosh[x]^n]/Sqrt[a]])/n + (2*Sqrt[a + b*Cosh[x]^n])/n","A",5,5,15,0.3333,1,"{3230, 266, 50, 63, 208}"