1,1,19,20,0.0043751,"\int \frac{\sinh ^4(x)}{a-a \cosh ^2(x)} \, dx","Integrate[Sinh[x]^4/(a - a*Cosh[x]^2),x]","-\frac{\frac{1}{4} \sinh (2 x)-\frac{x}{2}}{a}","\frac{x}{2 a}-\frac{\sinh (x) \cosh (x)}{2 a}",1,"-((-1/2*x + Sinh[2*x]/4)/a)","A",1
2,1,7,7,0.0028643,"\int \frac{\sinh ^3(x)}{a-a \cosh ^2(x)} \, dx","Integrate[Sinh[x]^3/(a - a*Cosh[x]^2),x]","-\frac{\cosh (x)}{a}","-\frac{\cosh (x)}{a}",1,"-(Cosh[x]/a)","A",1
3,1,6,6,0.0004381,"\int \frac{\sinh ^2(x)}{a-a \cosh ^2(x)} \, dx","Integrate[Sinh[x]^2/(a - a*Cosh[x]^2),x]","-\frac{x}{a}","-\frac{x}{a}",1,"-(x/a)","A",1
4,1,22,19,0.0040799,"\int \frac{\text{csch}^2(x)}{a-a \cosh ^2(x)} \, dx","Integrate[Csch[x]^2/(a - a*Cosh[x]^2),x]","-\frac{\frac{2 \coth (x)}{3}-\frac{1}{3} \coth (x) \text{csch}^2(x)}{a}","\frac{\coth ^3(x)}{3 a}-\frac{\coth (x)}{a}",1,"-(((2*Coth[x])/3 - (Coth[x]*Csch[x]^2)/3)/a)","A",1
5,1,32,29,0.0040637,"\int \frac{\text{csch}^4(x)}{a-a \cosh ^2(x)} \, dx","Integrate[Csch[x]^4/(a - a*Cosh[x]^2),x]","-\frac{-\frac{8 \coth (x)}{15}-\frac{1}{5} \coth (x) \text{csch}^4(x)+\frac{4}{15} \coth (x) \text{csch}^2(x)}{a}","\frac{\coth ^5(x)}{5 a}-\frac{2 \coth ^3(x)}{3 a}+\frac{\coth (x)}{a}",1,"-(((-8*Coth[x])/15 + (4*Coth[x]*Csch[x]^2)/15 - (Coth[x]*Csch[x]^4)/5)/a)","A",1
6,1,148,78,0.2458299,"\int \frac{\sinh ^7(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Sinh[x]^7/(a + b*Cosh[x]^2),x]","\frac{\left(8 a^2+22 a b+19 b^2\right) \cosh (x)}{8 b^3}-\frac{(a+b)^3 \tan ^{-1}\left(\frac{\sqrt{b}-i \sqrt{a+b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a}}\right)}{\sqrt{a} b^{7/2}}-\frac{(a+b)^3 \tan ^{-1}\left(\frac{\sqrt{b}+i \sqrt{a+b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a}}\right)}{\sqrt{a} b^{7/2}}-\frac{(4 a+9 b) \cosh (3 x)}{48 b^2}+\frac{\cosh (5 x)}{80 b}","\frac{\left(a^2+3 a b+3 b^2\right) \cosh (x)}{b^3}-\frac{(a+b)^3 \tan ^{-1}\left(\frac{\sqrt{b} \cosh (x)}{\sqrt{a}}\right)}{\sqrt{a} b^{7/2}}-\frac{(a+3 b) \cosh ^3(x)}{3 b^2}+\frac{\cosh ^5(x)}{5 b}",1,"-(((a + b)^3*ArcTan[(Sqrt[b] - I*Sqrt[a + b]*Tanh[x/2])/Sqrt[a]])/(Sqrt[a]*b^(7/2))) - ((a + b)^3*ArcTan[(Sqrt[b] + I*Sqrt[a + b]*Tanh[x/2])/Sqrt[a]])/(Sqrt[a]*b^(7/2)) + ((8*a^2 + 22*a*b + 19*b^2)*Cosh[x])/(8*b^3) - ((4*a + 9*b)*Cosh[3*x])/(48*b^2) + Cosh[5*x]/(80*b)","C",1
7,1,120,54,0.1874441,"\int \frac{\sinh ^5(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Sinh[x]^5/(a + b*Cosh[x]^2),x]","\frac{-3 \sqrt{b} (4 a+7 b) \cosh (x)+\frac{12 (a+b)^2 \tan ^{-1}\left(\frac{\sqrt{b}-i \sqrt{a+b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a}}\right)}{\sqrt{a}}+\frac{12 (a+b)^2 \tan ^{-1}\left(\frac{\sqrt{b}+i \sqrt{a+b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a}}\right)}{\sqrt{a}}+b^{3/2} \cosh (3 x)}{12 b^{5/2}}","\frac{(a+b)^2 \tan ^{-1}\left(\frac{\sqrt{b} \cosh (x)}{\sqrt{a}}\right)}{\sqrt{a} b^{5/2}}-\frac{(a+2 b) \cosh (x)}{b^2}+\frac{\cosh ^3(x)}{3 b}",1,"((12*(a + b)^2*ArcTan[(Sqrt[b] - I*Sqrt[a + b]*Tanh[x/2])/Sqrt[a]])/Sqrt[a] + (12*(a + b)^2*ArcTan[(Sqrt[b] + I*Sqrt[a + b]*Tanh[x/2])/Sqrt[a]])/Sqrt[a] - 3*Sqrt[b]*(4*a + 7*b)*Cosh[x] + b^(3/2)*Cosh[3*x])/(12*b^(5/2))","C",1
8,1,83,36,0.1882293,"\int \frac{\sinh ^3(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Sinh[x]^3/(a + b*Cosh[x]^2),x]","\frac{\cosh (x)}{b}-\frac{(a+b) \left(\tan ^{-1}\left(\frac{\sqrt{b}-i \sqrt{a+b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a}}\right)+\tan ^{-1}\left(\frac{\sqrt{b}+i \sqrt{a+b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a}}\right)\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] - I*Sqrt[a + b]*Tanh[x/2])/Sqrt[a]] + ArcTan[(Sqrt[b] + I*Sqrt[a + b]*Tanh[x/2])/Sqrt[a]]))/(Sqrt[a]*b^(3/2))) + Cosh[x]/b","C",1
9,1,25,25,0.0221388,"\int \frac{\sinh (x)}{a+b \cosh ^2(x)} \, dx","Integrate[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",1
10,1,99,42,0.1436809,"\int \frac{\text{csch}(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Csch[x]/(a + b*Cosh[x]^2),x]","\frac{-\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b}-i \sqrt{a+b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a}}\right)-\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b}+i \sqrt{a+b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a}}\right)+\sqrt{a} \log \left(\tanh \left(\frac{x}{2}\right)\right)}{\sqrt{a} (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] - I*Sqrt[a + b]*Tanh[x/2])/Sqrt[a]]) - Sqrt[b]*ArcTan[(Sqrt[b] + I*Sqrt[a + b]*Tanh[x/2])/Sqrt[a]] + Sqrt[a]*Log[Tanh[x/2]])/(Sqrt[a]*(a + b))","C",1
11,1,154,61,0.2907043,"\int \frac{\text{csch}^3(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Csch[x]^3/(a + b*Cosh[x]^2),x]","\frac{-4 a^{3/2} \log \left(\tanh \left(\frac{x}{2}\right)\right)+8 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b}-i \sqrt{a+b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a}}\right)+8 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b}+i \sqrt{a+b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a}}\right)-\sqrt{a} (a+b) \text{csch}^2\left(\frac{x}{2}\right)-\sqrt{a} (a+b) \text{sech}^2\left(\frac{x}{2}\right)-12 \sqrt{a} b \log \left(\tanh \left(\frac{x}{2}\right)\right)}{8 \sqrt{a} (a+b)^2}","\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,"(8*b^(3/2)*ArcTan[(Sqrt[b] - I*Sqrt[a + b]*Tanh[x/2])/Sqrt[a]] + 8*b^(3/2)*ArcTan[(Sqrt[b] + I*Sqrt[a + b]*Tanh[x/2])/Sqrt[a]] - Sqrt[a]*(a + b)*Csch[x/2]^2 - 4*a^(3/2)*Log[Tanh[x/2]] - 12*Sqrt[a]*b*Log[Tanh[x/2]] - Sqrt[a]*(a + b)*Sech[x/2]^2)/(8*Sqrt[a]*(a + b)^2)","C",1
12,1,219,94,0.6067862,"\int \frac{\text{csch}^5(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Csch[x]^5/(a + b*Cosh[x]^2),x]","\frac{2 \sqrt{a} \left(3 a^2+10 a b+7 b^2\right) \text{csch}^2\left(\frac{x}{2}\right)+2 \sqrt{a} \left(3 a^2+10 a b+7 b^2\right) \text{sech}^2\left(\frac{x}{2}\right)+8 \left(\sqrt{a} \left(3 a^2+10 a b+15 b^2\right) \log \left(\tanh \left(\frac{x}{2}\right)\right)-8 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b}-i \sqrt{a+b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a}}\right)-8 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b}+i \sqrt{a+b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a}}\right)\right)-\sqrt{a} (a+b)^2 \text{csch}^4\left(\frac{x}{2}\right)+\sqrt{a} (a+b)^2 \text{sech}^4\left(\frac{x}{2}\right)}{64 \sqrt{a} (a+b)^3}","-\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,"(2*Sqrt[a]*(3*a^2 + 10*a*b + 7*b^2)*Csch[x/2]^2 - Sqrt[a]*(a + b)^2*Csch[x/2]^4 + 8*(-8*b^(5/2)*ArcTan[(Sqrt[b] - I*Sqrt[a + b]*Tanh[x/2])/Sqrt[a]] - 8*b^(5/2)*ArcTan[(Sqrt[b] + I*Sqrt[a + b]*Tanh[x/2])/Sqrt[a]] + Sqrt[a]*(3*a^2 + 10*a*b + 15*b^2)*Log[Tanh[x/2]]) + 2*Sqrt[a]*(3*a^2 + 10*a*b + 7*b^2)*Sech[x/2]^2 + Sqrt[a]*(a + b)^2*Sech[x/2]^4)/(64*Sqrt[a]*(a + b)^3)","C",1
13,1,76,88,0.1728373,"\int \frac{\sinh ^6(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Sinh[x]^6/(a + b*Cosh[x]^2),x]","\frac{4 x \left(8 a^2+20 a b+15 b^2\right)-8 b (a+2 b) \sinh (2 x)-\frac{32 (a+b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a}}+b^2 \sinh (4 x)}{32 b^3}","\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,"(4*(8*a^2 + 20*a*b + 15*b^2)*x - (32*(a + b)^(5/2)*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/Sqrt[a] - 8*b*(a + 2*b)*Sinh[2*x] + b^2*Sinh[4*x])/(32*b^3)","A",1
14,1,52,59,0.0986705,"\int \frac{\sinh ^4(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Sinh[x]^4/(a + b*Cosh[x]^2),x]","\frac{\frac{4 (a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a}}-4 a x-6 b x+b \sinh (2 x)}{4 b^2}","-\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,"(-4*a*x - 6*b*x + (4*(a + b)^(3/2)*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/Sqrt[a] + b*Sinh[2*x])/(4*b^2)","A",1
15,1,36,39,0.0596925,"\int \frac{\sinh ^2(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Sinh[x]^2/(a + b*Cosh[x]^2),x]","\frac{x-\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 - (Sqrt[a + b]*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/Sqrt[a])/b","A",1
16,1,29,29,0.0674007,"\int \frac{1}{a+b \cosh ^2(x)} \, dx","Integrate[(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",1
17,1,59,59,0.2188592,"\int \frac{\text{csch}^4(x)}{a+b \cosh ^2(x)} \, dx","Integrate[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 (x) \left((a+b) \text{csch}^2(x)-2 a-5 b\right)}{3 (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)) - (Coth[x]*(-2*a - 5*b + (a + b)*Csch[x]^2))/(3*(a + b)^2)","A",1
18,1,92,89,0.3739605,"\int \frac{\text{csch}^6(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Csch[x]^6/(a + b*Cosh[x]^2),x]","-\frac{\coth (x) \left(-\left(4 a^2+13 a b+9 b^2\right) \text{csch}^2(x)+8 a^2+3 (a+b)^2 \text{csch}^4(x)+26 a b+33 b^2\right)}{15 (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{\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))) - (Coth[x]*(8*a^2 + 26*a*b + 33*b^2 - (4*a^2 + 13*a*b + 9*b^2)*Csch[x]^2 + 3*(a + b)^2*Csch[x]^4))/(15*(a + b)^3)","A",1
19,1,77,98,0.091762,"\int \frac{\sinh (x)}{4-3 \cosh ^3(x)} \, dx","Integrate[Sinh[x]/(4 - 3*Cosh[x]^3),x]","\frac{1}{72} \left(6^{2/3} \left(\log \left(6^{2/3} \cosh ^2(x)+2 \sqrt[3]{6} \cosh (x)+4\right)-2 \log \left(2-\sqrt[3]{6} \cosh (x)\right)\right)+6\ 2^{2/3} \sqrt[6]{3} \tan ^{-1}\left(\frac{\sqrt[3]{6} \cosh (x)+1}{\sqrt{3}}\right)\right)","\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,"(6*2^(2/3)*3^(1/6)*ArcTan[(1 + 6^(1/3)*Cosh[x])/Sqrt[3]] + 6^(2/3)*(-2*Log[2 - 6^(1/3)*Cosh[x]] + Log[4 + 2*6^(1/3)*Cosh[x] + 6^(2/3)*Cosh[x]^2]))/72","A",1
20,1,86,78,0.2900673,"\int \frac{\cosh ^7(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Cosh[x]^7/(a + b*Cosh[x]^2),x]","\frac{a^3 \tan ^{-1}\left(\frac{\sqrt{a+b} \text{csch}(x)}{\sqrt{b}}\right)}{b^{7/2} \sqrt{a+b}}+\frac{\left(8 a^2-6 a b+5 b^2\right) \sinh (x)}{8 b^3}-\frac{(4 a-5 b) \sinh (3 x)}{48 b^2}+\frac{\sinh (5 x)}{80 b}","-\frac{a^3 \tan ^{-1}\left(\frac{\sqrt{b} \sinh (x)}{\sqrt{a+b}}\right)}{b^{7/2} \sqrt{a+b}}+\frac{\left(a^2-a b+b^2\right) \sinh (x)}{b^3}-\frac{(a-2 b) \sinh ^3(x)}{3 b^2}+\frac{\sinh ^5(x)}{5 b}",1,"(a^3*ArcTan[(Sqrt[a + b]*Csch[x])/Sqrt[b]])/(b^(7/2)*Sqrt[a + b]) + ((8*a^2 - 6*a*b + 5*b^2)*Sinh[x])/(8*b^3) - ((4*a - 5*b)*Sinh[3*x])/(48*b^2) + Sinh[5*x]/(80*b)","A",1
21,1,76,88,0.2240398,"\int \frac{\cosh ^6(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Cosh[x]^6/(a + b*Cosh[x]^2),x]","\frac{-\frac{32 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a+b}}+4 x \left(8 a^2-4 a b+3 b^2\right)-8 b (a-b) \sinh (2 x)+b^2 \sinh (4 x)}{32 b^3}","-\frac{a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{b^3 \sqrt{a+b}}+\frac{x \left(8 a^2-4 a b+3 b^2\right)}{8 b^3}-\frac{(4 a-3 b) \sinh (x) \cosh (x)}{8 b^2}+\frac{\sinh (x) \cosh ^3(x)}{4 b}",1,"(4*(8*a^2 - 4*a*b + 3*b^2)*x - (32*a^(5/2)*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/Sqrt[a + b] - 8*(a - b)*b*Sinh[2*x] + b^2*Sinh[4*x])/(32*b^3)","A",1
22,1,61,56,0.1709359,"\int \frac{\cosh ^5(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Cosh[x]^5/(a + b*Cosh[x]^2),x]","-\frac{a^2 \tan ^{-1}\left(\frac{\sqrt{a+b} \text{csch}(x)}{\sqrt{b}}\right)}{b^{5/2} \sqrt{a+b}}-\frac{(4 a-3 b) \sinh (x)}{4 b^2}+\frac{\sinh (3 x)}{12 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[a + b]*Csch[x])/Sqrt[b]])/(b^(5/2)*Sqrt[a + b])) - ((4*a - 3*b)*Sinh[x])/(4*b^2) + Sinh[3*x]/(12*b)","A",1
23,1,52,59,0.1325558,"\int \frac{\cosh ^4(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Cosh[x]^4/(a + b*Cosh[x]^2),x]","\frac{\frac{4 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a+b}}+2 x (b-2 a)+b \sinh (2 x)}{4 b^2}","\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*(-2*a + b)*x + (4*a^(3/2)*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/Sqrt[a + b] + b*Sinh[2*x])/(4*b^2)","A",1
24,1,38,38,0.0314778,"\int \frac{\cosh ^3(x)}{a+b \cosh ^2(x)} \, dx","Integrate[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",1
25,1,36,39,0.0844557,"\int \frac{\cosh ^2(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Cosh[x]^2/(a + b*Cosh[x]^2),x]","\frac{x-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{\sqrt{a+b}}}{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 - (Sqrt[a]*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/Sqrt[a + b])/b","A",1
26,1,29,29,0.0115174,"\int \frac{\cosh (x)}{a+b \cosh ^2(x)} \, dx","Integrate[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",1
27,1,29,29,0.0497604,"\int \frac{1}{a+b \cosh ^2(x)} \, dx","Integrate[(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",1
28,1,45,41,0.1003199,"\int \frac{\text{sech}(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Sech[x]/(a + b*Cosh[x]^2),x]","\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a+b} \text{csch}(x)}{\sqrt{b}}\right)}{a \sqrt{a+b}}+\frac{2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)}{a}","\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,"(Sqrt[b]*ArcTan[(Sqrt[a + b]*Csch[x])/Sqrt[b]])/(a*Sqrt[a + b]) + (2*ArcTan[Tanh[x/2]])/a","A",1
29,1,38,38,0.0869675,"\int \frac{\text{sech}^2(x)}{a+b \cosh ^2(x)} \, dx","Integrate[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",1
30,1,58,59,0.1749419,"\int \frac{\text{sech}^3(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Sech[x]^3/(a + b*Cosh[x]^2),x]","\frac{-\frac{2 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{a+b} \text{csch}(x)}{\sqrt{b}}\right)}{\sqrt{a+b}}+2 (a-2 b) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+a \tanh (x) \text{sech}(x)}{2 a^2}","\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,"((-2*b^(3/2)*ArcTan[(Sqrt[a + b]*Csch[x])/Sqrt[b]])/Sqrt[a + b] + 2*(a - 2*b)*ArcTan[Tanh[x/2]] + a*Sech[x]*Tanh[x])/(2*a^2)","A",1
31,1,55,55,0.1535965,"\int \frac{\text{sech}^4(x)}{a+b \cosh ^2(x)} \, dx","Integrate[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{\tanh (x) \left(a \text{sech}^2(x)+2 a-3 b\right)}{3 a^2}","\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]) + ((2*a - 3*b + a*Sech[x]^2)*Tanh[x])/(3*a^2)","A",1
32,1,86,90,0.309484,"\int \frac{\text{sech}^5(x)}{a+b \cosh ^2(x)} \, dx","Integrate[Sech[x]^5/(a + b*Cosh[x]^2),x]","\frac{2 \left(3 a^2-4 a b+8 b^2\right) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+2 a^2 \tanh (x) \text{sech}^3(x)+\frac{8 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{a+b} \text{csch}(x)}{\sqrt{b}}\right)}{\sqrt{a+b}}+a (3 a-4 b) \tanh (x) \text{sech}(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{\left(3 a^2-4 a b+8 b^2\right) \tan ^{-1}(\sinh (x))}{8 a^3}+\frac{\tanh (x) \text{sech}^3(x)}{4 a}",1,"((8*b^(5/2)*ArcTan[(Sqrt[a + b]*Csch[x])/Sqrt[b]])/Sqrt[a + b] + 2*(3*a^2 - 4*a*b + 8*b^2)*ArcTan[Tanh[x/2]] + a*(3*a - 4*b)*Sech[x]*Tanh[x] + 2*a^2*Sech[x]^3*Tanh[x])/(8*a^3)","A",1
33,1,68,65,0.2316806,"\int \frac{1}{\left(a+b \cosh ^2(x)\right)^2} \, dx","Integrate[(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 (2 x)}{2 a (a+b) (2 a+b \cosh (2 x)+b)}","\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*Sinh[2*x])/(2*a*(a + b)*(2*a + b + b*Cosh[2*x]))","A",1
34,1,106,107,0.6283657,"\int \frac{1}{\left(a+b \cosh ^2(x)\right)^3} \, dx","Integrate[(a + b*Cosh[x]^2)^(-3),x]","\frac{\frac{\left(8 a^2+8 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}-\frac{\sqrt{a} b \sinh (2 x) \left(16 a^2+3 b (2 a+b) \cosh (2 x)+16 a b+3 b^2\right)}{(a+b)^2 (2 a+b \cosh (2 x)+b)^2}}{8 a^{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{\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{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]])/(a + b)^(5/2) - (Sqrt[a]*b*(16*a^2 + 16*a*b + 3*b^2 + 3*b*(2*a + b)*Cosh[2*x])*Sinh[2*x])/((a + b)^2*(2*a + b + b*Cosh[2*x])^2))/(8*a^(5/2))","A",1
35,0,0,15,0.0233981,"\int \frac{1}{1+\cosh ^2(x)} \, dx","Integrate[(1 + Cosh[x]^2)^(-1),x]","\int \frac{1}{1+\cosh ^2(x)} \, dx","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{\sqrt{2}}",1,"Integrate[(1 + Cosh[x]^2)^(-1), x]","F",-1
36,1,35,35,0.1308544,"\int \frac{1}{\left(1+\cosh ^2(x)\right)^2} \, dx","Integrate[(1 + Cosh[x]^2)^(-2),x]","\frac{3 \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{4 \sqrt{2}}-\frac{\sinh (2 x)}{4 (\cosh (2 x)+3)}","\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]) - Sinh[2*x]/(4*(3 + Cosh[2*x]))","A",1
37,1,51,51,0.1786226,"\int \frac{1}{\left(1+\cosh ^2(x)\right)^3} \, dx","Integrate[(1 + Cosh[x]^2)^(-3),x]","\frac{19 \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{32 \sqrt{2}}-\frac{9 \sinh (2 x)}{32 (\cosh (2 x)+3)}-\frac{\sinh (2 x)}{4 (\cosh (2 x)+3)^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]) - Sinh[2*x]/(4*(3 + Cosh[2*x])^2) - (9*Sinh[2*x])/(32*(3 + Cosh[2*x]))","A",1
38,1,2,2,0.0033192,"\int \frac{1}{1-\cosh ^2(x)} \, dx","Integrate[(1 - Cosh[x]^2)^(-1),x]","\coth (x)","\coth (x)",1,"Coth[x]","A",1
39,1,17,11,0.0032106,"\int \frac{1}{\left(1-\cosh ^2(x)\right)^2} \, dx","Integrate[(1 - Cosh[x]^2)^(-2),x]","\frac{2 \coth (x)}{3}-\frac{1}{3} \coth (x) \text{csch}^2(x)","\coth (x)-\frac{\coth ^3(x)}{3}",1,"(2*Coth[x])/3 - (Coth[x]*Csch[x]^2)/3","A",1
40,1,27,19,0.0037392,"\int \frac{1}{\left(1-\cosh ^2(x)\right)^3} \, dx","Integrate[(1 - Cosh[x]^2)^(-3),x]","\frac{8 \coth (x)}{15}+\frac{1}{5} \coth (x) \text{csch}^4(x)-\frac{4}{15} \coth (x) \text{csch}^2(x)","\frac{\coth ^5(x)}{5}-\frac{2 \coth ^3(x)}{3}+\coth (x)",1,"(8*Coth[x])/15 - (4*Coth[x]*Csch[x]^2)/15 + (Coth[x]*Csch[x]^4)/5","A",1
41,1,53,49,0.0803005,"\int \sqrt{a+b \cosh ^2(x)} \, dx","Integrate[Sqrt[a + b*Cosh[x]^2],x]","-\frac{i \sqrt{2 a+b \cosh (2 x)+b} E\left(i x\left|\frac{b}{a+b}\right.\right)}{\sqrt{\frac{2 a+b \cosh (2 x)+b}{a+b}}}","-\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[2*a + b + b*Cosh[2*x]]*EllipticE[I*x, b/(a + b)])/Sqrt[(2*a + b + b*Cosh[2*x])/(a + b)]","A",1
42,1,18,17,0.022961,"\int \sqrt{1+\cosh ^2(x)} \, dx","Integrate[Sqrt[1 + Cosh[x]^2],x]","-i \sqrt{2} E\left(i x\left|\frac{1}{2}\right.\right)","-i E\left(\left.i x+\frac{\pi }{2}\right|-1\right)",1,"(-I)*Sqrt[2]*EllipticE[I*x, 1/2]","A",1
43,1,13,13,0.0049755,"\int \sqrt{1-\cosh ^2(x)} \, dx","Integrate[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",1
44,1,11,11,0.0066662,"\int \sqrt{-1+\cosh ^2(x)} \, dx","Integrate[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",1
45,1,40,39,0.042365,"\int \sqrt{-1-\cosh ^2(x)} \, dx","Integrate[Sqrt[-1 - Cosh[x]^2],x]","\frac{i \sqrt{2} \sqrt{\cosh (2 x)+3} E\left(i x\left|\frac{1}{2}\right.\right)}{\sqrt{-\cosh (2 x)-3}}","-\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[2]*Sqrt[3 + Cosh[2*x]]*EllipticE[I*x, 1/2])/Sqrt[-3 - Cosh[2*x]]","A",1
46,1,135,133,0.4752847,"\int \left(a+b \cosh ^2(x)\right)^{3/2} \, dx","Integrate[(a + b*Cosh[x]^2)^(3/2),x]","\frac{-8 i \left(2 a^2+3 a b+b^2\right) \sqrt{\frac{2 a+b \cosh (2 x)+b}{a+b}} E\left(i x\left|\frac{b}{a+b}\right.\right)+\sqrt{2} b \sinh (2 x) (2 a+b \cosh (2 x)+b)+4 i a (a+b) \sqrt{\frac{2 a+b \cosh (2 x)+b}{a+b}} F\left(i x\left|\frac{b}{a+b}\right.\right)}{12 \sqrt{2 a+b \cosh (2 x)+b}}","\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,"((-8*I)*(2*a^2 + 3*a*b + b^2)*Sqrt[(2*a + b + b*Cosh[2*x])/(a + b)]*EllipticE[I*x, b/(a + b)] + (4*I)*a*(a + b)*Sqrt[(2*a + b + b*Cosh[2*x])/(a + b)]*EllipticF[I*x, b/(a + b)] + Sqrt[2]*b*(2*a + b + b*Cosh[2*x])*Sinh[2*x])/(12*Sqrt[2*a + b + b*Cosh[2*x]])","A",1
47,1,51,55,0.051826,"\int \left(1+\cosh ^2(x)\right)^{3/2} \, dx","Integrate[(1 + Cosh[x]^2)^(3/2),x]","\frac{4 i F\left(i x\left|\frac{1}{2}\right.\right)-24 i E\left(i x\left|\frac{1}{2}\right.\right)+\sinh (2 x) \sqrt{\cosh (2 x)+3}}{6 \sqrt{2}}","\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,"((-24*I)*EllipticE[I*x, 1/2] + (4*I)*EllipticF[I*x, 1/2] + Sqrt[3 + Cosh[2*x]]*Sinh[2*x])/(6*Sqrt[2])","A",1
48,1,25,33,0.0311847,"\int \left(1-\cosh ^2(x)\right)^{3/2} \, dx","Integrate[(1 - Cosh[x]^2)^(3/2),x]","-\frac{1}{12} \sqrt{-\sinh ^2(x)} (\cosh (3 x)-9 \cosh (x)) \text{csch}(x)","\frac{1}{3} \left(-\sinh ^2(x)\right)^{3/2} \coth (x)+\frac{2}{3} \sqrt{-\sinh ^2(x)} \coth (x)",1,"-1/12*((-9*Cosh[x] + Cosh[3*x])*Csch[x]*Sqrt[-Sinh[x]^2])","A",1
49,1,23,29,0.0228054,"\int \left(-1+\cosh ^2(x)\right)^{3/2} \, dx","Integrate[(-1 + Cosh[x]^2)^(3/2),x]","\frac{1}{12} \sqrt{\sinh ^2(x)} (\cosh (3 x)-9 \cosh (x)) \text{csch}(x)","\frac{1}{3} \sinh ^2(x)^{3/2} \coth (x)-\frac{2}{3} \sqrt{\sinh ^2(x)} \coth (x)",1,"((-9*Cosh[x] + Cosh[3*x])*Csch[x]*Sqrt[Sinh[x]^2])/12","A",1
50,1,78,101,0.073713,"\int \left(-1-\cosh ^2(x)\right)^{3/2} \, dx","Integrate[(-1 - Cosh[x]^2)^(3/2),x]","\frac{6 \sinh (2 x)+\sinh (4 x)+8 i \sqrt{\cosh (2 x)+3} F\left(i x\left|\frac{1}{2}\right.\right)-48 i \sqrt{\cosh (2 x)+3} E\left(i x\left|\frac{1}{2}\right.\right)}{12 \sqrt{2} \sqrt{-\cosh (2 x)-3}}","-\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,"((-48*I)*Sqrt[3 + Cosh[2*x]]*EllipticE[I*x, 1/2] + (8*I)*Sqrt[3 + Cosh[2*x]]*EllipticF[I*x, 1/2] + 6*Sinh[2*x] + Sinh[4*x])/(12*Sqrt[2]*Sqrt[-3 - Cosh[2*x]])","A",1
51,1,53,49,0.0769687,"\int \frac{1}{\sqrt{a+b \cosh ^2(x)}} \, dx","Integrate[1/Sqrt[a + b*Cosh[x]^2],x]","-\frac{i \sqrt{\frac{2 a+b \cosh (2 x)+b}{a+b}} F\left(i x\left|\frac{b}{a+b}\right.\right)}{\sqrt{2 a+b \cosh (2 x)+b}}","-\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[(2*a + b + b*Cosh[2*x])/(a + b)]*EllipticF[I*x, b/(a + b)])/Sqrt[2*a + b + b*Cosh[2*x]]","A",1
52,1,18,17,0.0394679,"\int \frac{1}{\sqrt{1+\cosh ^2(x)}} \, dx","Integrate[1/Sqrt[1 + Cosh[x]^2],x]","-\frac{i F\left(i x\left|\frac{1}{2}\right.\right)}{\sqrt{2}}","-i F\left(\left.i x+\frac{\pi }{2}\right|-1\right)",1,"((-I)*EllipticF[I*x, 1/2])/Sqrt[2]","A",1
53,1,20,17,0.0087379,"\int \frac{1}{\sqrt{1-\cosh ^2(x)}} \, dx","Integrate[1/Sqrt[1 - Cosh[x]^2],x]","\frac{\sinh (x) \log \left(\tanh \left(\frac{x}{2}\right)\right)}{\sqrt{-\sinh ^2(x)}}","-\frac{\sinh (x) \tanh ^{-1}(\cosh (x))}{\sqrt{-\sinh ^2(x)}}",1,"(Log[Tanh[x/2]]*Sinh[x])/Sqrt[-Sinh[x]^2]","A",1
54,1,18,15,0.0088852,"\int \frac{1}{\sqrt{-1+\cosh ^2(x)}} \, dx","Integrate[1/Sqrt[-1 + Cosh[x]^2],x]","\frac{\sinh (x) \log \left(\tanh \left(\frac{x}{2}\right)\right)}{\sqrt{\sinh ^2(x)}}","-\frac{\sinh (x) \tanh ^{-1}(\cosh (x))}{\sqrt{\sinh ^2(x)}}",1,"(Log[Tanh[x/2]]*Sinh[x])/Sqrt[Sinh[x]^2]","A",1
55,1,40,39,0.0492374,"\int \frac{1}{\sqrt{-1-\cosh ^2(x)}} \, dx","Integrate[1/Sqrt[-1 - Cosh[x]^2],x]","-\frac{i \sqrt{\cosh (2 x)+3} F\left(i x\left|\frac{1}{2}\right.\right)}{\sqrt{2} \sqrt{-\cosh (2 x)-3}}","-\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[3 + Cosh[2*x]]*EllipticF[I*x, 1/2])/(Sqrt[2]*Sqrt[-3 - Cosh[2*x]])","A",1
56,1,105,288,0.1286927,"\int \frac{1}{a+b \cosh ^3(x)} \, dx","Integrate[(a + b*Cosh[x]^3)^(-1),x]","\frac{2}{3} \text{RootSum}\left[\text{$\#$1}^6 b+3 \text{$\#$1}^4 b+8 \text{$\#$1}^3 a+3 \text{$\#$1}^2 b+b\&,\frac{\text{$\#$1} x+2 \text{$\#$1} \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)}{\text{$\#$1}^4 b+2 \text{$\#$1}^2 b+4 \text{$\#$1} a+b}\&\right]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-\sqrt[3]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}\right)}{3 a^{2/3} \sqrt{\sqrt[3]{a}-\sqrt[3]{b}} \sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}}}\right)}{3 a^{2/3} \sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}} \sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}}}\right)}{3 a^{2/3} \sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}} \sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}}}",1,"(2*RootSum[b + 3*b*#1^2 + 8*a*#1^3 + 3*b*#1^4 + b*#1^6 & , (x*#1 + 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1)/(b + 4*a*#1 + 2*b*#1^2 + b*#1^4) & ])/3","C",1
57,1,105,288,0.0928439,"\int \frac{1}{a-b \cosh ^3(x)} \, dx","Integrate[(a - b*Cosh[x]^3)^(-1),x]","-\frac{2}{3} \text{RootSum}\left[\text{$\#$1}^6 b+3 \text{$\#$1}^4 b-8 \text{$\#$1}^3 a+3 \text{$\#$1}^2 b+b\&,\frac{\text{$\#$1} x+2 \text{$\#$1} \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)}{\text{$\#$1}^4 b+2 \text{$\#$1}^2 b-4 \text{$\#$1} a+b}\&\right]","\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*RootSum[b + 3*b*#1^2 - 8*a*#1^3 + 3*b*#1^4 + b*#1^6 & , (x*#1 + 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1)/(b - 4*a*#1 + 2*b*#1^2 + b*#1^4) & ])/3","C",1
58,1,133,91,0.9948509,"\int \frac{1}{1+\cosh ^3(x)} \, dx","Integrate[(1 + Cosh[x]^3)^(-1),x]","\frac{1}{18} \left(6 \tanh \left(\frac{x}{2}\right)-\sqrt{6+2 i \sqrt{3}} \left(\sqrt{3}+3 i\right) \tan ^{-1}\left(\frac{\left(3+i \sqrt{3}\right) \tanh \left(\frac{x}{2}\right)}{\sqrt{6-2 i \sqrt{3}}}\right)-\sqrt{6-2 i \sqrt{3}} \left(\sqrt{3}-3 i\right) \tan ^{-1}\left(\frac{\left(3-i \sqrt{3}\right) \tanh \left(\frac{x}{2}\right)}{\sqrt{6+2 i \sqrt{3}}}\right)\right)","-\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,"(-(Sqrt[6 + (2*I)*Sqrt[3]]*(3*I + Sqrt[3])*ArcTan[((3 + I*Sqrt[3])*Tanh[x/2])/Sqrt[6 - (2*I)*Sqrt[3]]]) - Sqrt[6 - (2*I)*Sqrt[3]]*(-3*I + Sqrt[3])*ArcTan[((3 - I*Sqrt[3])*Tanh[x/2])/Sqrt[6 + (2*I)*Sqrt[3]]] + 6*Tanh[x/2])/18","C",1
59,1,147,95,0.6136373,"\int \frac{1}{1-\cosh ^3(x)} \, dx","Integrate[(1 - Cosh[x]^3)^(-1),x]","\frac{1}{3} \coth \left(\frac{x}{2}\right)+\frac{\left(\sqrt{3}+3 i\right) \tan ^{-1}\left(\frac{\left(1-i \sqrt{3}\right) \tanh \left(\frac{x}{2}\right)}{\sqrt{2 \left(3-i \sqrt{3}\right)}}\right)}{3 \sqrt{\frac{3}{2} \left(3-i \sqrt{3}\right)}}+\frac{\left(\sqrt{3}-3 i\right) \tan ^{-1}\left(\frac{\left(1+i \sqrt{3}\right) \tanh \left(\frac{x}{2}\right)}{\sqrt{2 \left(3+i \sqrt{3}\right)}}\right)}{3 \sqrt{\frac{3}{2} \left(3+i \sqrt{3}\right)}}","-\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,"((3*I + Sqrt[3])*ArcTan[((1 - I*Sqrt[3])*Tanh[x/2])/Sqrt[2*(3 - I*Sqrt[3])]])/(3*Sqrt[(3*(3 - I*Sqrt[3]))/2]) + ((-3*I + Sqrt[3])*ArcTan[((1 + I*Sqrt[3])*Tanh[x/2])/Sqrt[2*(3 + I*Sqrt[3])]])/(3*Sqrt[(3*(3 + I*Sqrt[3]))/2]) + Coth[x/2]/3","C",1
60,1,121,361,0.2402809,"\int \frac{1}{a+b \cosh ^4(x)} \, dx","Integrate[(a + b*Cosh[x]^4)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a+i \sqrt{a} \sqrt{b}}}\right)}{2 \sqrt{a} \sqrt{a+i \sqrt{a} \sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{-a+i \sqrt{a} \sqrt{b}}}\right)}{2 \sqrt{a} \sqrt{-a+i \sqrt{a} \sqrt{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,"-1/2*ArcTan[(Sqrt[a]*Tanh[x])/Sqrt[-a + I*Sqrt[a]*Sqrt[b]]]/(Sqrt[a]*Sqrt[-a + I*Sqrt[a]*Sqrt[b]]) + ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + I*Sqrt[a]*Sqrt[b]]]/(2*Sqrt[a]*Sqrt[a + I*Sqrt[a]*Sqrt[b]])","C",1
61,1,109,101,0.1992127,"\int \frac{1}{a-b \cosh ^4(x)} \, dx","Integrate[(a - b*Cosh[x]^4)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{\sqrt{a} \sqrt{b}+a}}\right)}{2 \sqrt{a} \sqrt{\sqrt{a} \sqrt{b}+a}}-\frac{\tan ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{\sqrt{a} \sqrt{b}-a}}\right)}{2 \sqrt{a} \sqrt{\sqrt{a} \sqrt{b}-a}}","\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,"-1/2*ArcTan[(Sqrt[a]*Tanh[x])/Sqrt[-a + Sqrt[a]*Sqrt[b]]]/(Sqrt[a]*Sqrt[-a + Sqrt[a]*Sqrt[b]]) + ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + Sqrt[a]*Sqrt[b]]]/(2*Sqrt[a]*Sqrt[a + Sqrt[a]*Sqrt[b]])","A",1
62,1,45,176,0.0758856,"\int \frac{1}{1+\cosh ^4(x)} \, dx","Integrate[(1 + Cosh[x]^4)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-i}}\right)}{2 \sqrt{1-i}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1+i}}\right)}{2 \sqrt{1+i}}","-\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,"ArcTanh[Tanh[x]/Sqrt[1 - I]]/(2*Sqrt[1 - I]) + ArcTanh[Tanh[x]/Sqrt[1 + I]]/(2*Sqrt[1 + I])","C",1
63,1,24,25,0.1065459,"\int \frac{1}{1-\cosh ^4(x)} \, dx","Integrate[(1 - Cosh[x]^4)^(-1),x]","\frac{1}{4} \left(\sqrt{2} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)+2 \coth (x)\right)","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)}{2 \sqrt{2}}+\frac{\coth (x)}{2}",1,"(Sqrt[2]*ArcTanh[Tanh[x]/Sqrt[2]] + 2*Coth[x])/4","A",1
64,1,139,494,0.2867332,"\int \frac{1}{a+b \cosh ^5(x)} \, dx","Integrate[(a + b*Cosh[x]^5)^(-1),x]","\frac{8}{5} \text{RootSum}\left[\text{$\#$1}^{10} b+5 \text{$\#$1}^8 b+10 \text{$\#$1}^6 b+32 \text{$\#$1}^5 a+10 \text{$\#$1}^4 b+5 \text{$\#$1}^2 b+b\&,\frac{\text{$\#$1}^3 x+2 \text{$\#$1}^3 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)}{\text{$\#$1}^8 b+4 \text{$\#$1}^6 b+6 \text{$\#$1}^4 b+16 \text{$\#$1}^3 a+4 \text{$\#$1}^2 b+b}\&\right]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-\sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+\sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}}}",1,"(8*RootSum[b + 5*b*#1^2 + 10*b*#1^4 + 32*a*#1^5 + 10*b*#1^6 + 5*b*#1^8 + b*#1^10 & , (x*#1^3 + 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^3)/(b + 4*b*#1^2 + 16*a*#1^3 + 6*b*#1^4 + 4*b*#1^6 + b*#1^8) & ])/5","C",1
65,1,132,171,0.2175535,"\int \frac{1}{a+b \cosh ^6(x)} \, dx","Integrate[(a + b*Cosh[x]^6)^(-1),x]","\frac{16}{3} \text{RootSum}\left[\text{$\#$1}^6 b+6 \text{$\#$1}^5 b+15 \text{$\#$1}^4 b+64 \text{$\#$1}^3 a+20 \text{$\#$1}^3 b+15 \text{$\#$1}^2 b+6 \text{$\#$1} b+b\&,\frac{\text{$\#$1}^2 x+\text{$\#$1}^2 \log (-\text{$\#$1} \sinh (x)+\text{$\#$1} \cosh (x)-\sinh (x)-\cosh (x))}{\text{$\#$1}^5 b+5 \text{$\#$1}^4 b+10 \text{$\#$1}^3 b+32 \text{$\#$1}^2 a+10 \text{$\#$1}^2 b+5 \text{$\#$1} b+b}\&\right]","\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}}}",1,"(16*RootSum[b + 6*b*#1 + 15*b*#1^2 + 64*a*#1^3 + 20*b*#1^3 + 15*b*#1^4 + 6*b*#1^5 + b*#1^6 & , (x*#1^2 + Log[-Cosh[x] - Sinh[x] + Cosh[x]*#1 - Sinh[x]*#1]*#1^2)/(b + 5*b*#1 + 32*a*#1^2 + 10*b*#1^2 + 10*b*#1^3 + 5*b*#1^4 + b*#1^5) & ])/3","C",1
66,1,158,245,0.2822016,"\int \frac{1}{a+b \cosh ^8(x)} \, dx","Integrate[(a + b*Cosh[x]^8)^(-1),x]","16 \text{RootSum}\left[\text{$\#$1}^8 b+8 \text{$\#$1}^7 b+28 \text{$\#$1}^6 b+56 \text{$\#$1}^5 b+256 \text{$\#$1}^4 a+70 \text{$\#$1}^4 b+56 \text{$\#$1}^3 b+28 \text{$\#$1}^2 b+8 \text{$\#$1} b+b\&,\frac{\text{$\#$1}^3 x+\text{$\#$1}^3 \log (-\text{$\#$1} \sinh (x)+\text{$\#$1} \cosh (x)-\sinh (x)-\cosh (x))}{\text{$\#$1}^7 b+7 \text{$\#$1}^6 b+21 \text{$\#$1}^5 b+35 \text{$\#$1}^4 b+128 \text{$\#$1}^3 a+35 \text{$\#$1}^3 b+21 \text{$\#$1}^2 b+7 \text{$\#$1} b+b}\&\right]","-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{-a} \tanh (x)}{\sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{-a} \tanh (x)}{\sqrt{\sqrt[4]{-a}-i \sqrt[4]{b}}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}-i \sqrt[4]{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{-a} \tanh (x)}{\sqrt{\sqrt[4]{-a}+i \sqrt[4]{b}}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}+i \sqrt[4]{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{-a} \tanh (x)}{\sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}",1,"16*RootSum[b + 8*b*#1 + 28*b*#1^2 + 56*b*#1^3 + 256*a*#1^4 + 70*b*#1^4 + 56*b*#1^5 + 28*b*#1^6 + 8*b*#1^7 + b*#1^8 & , (x*#1^3 + Log[-Cosh[x] - Sinh[x] + Cosh[x]*#1 - Sinh[x]*#1]*#1^3)/(b + 7*b*#1 + 21*b*#1^2 + 128*a*#1^3 + 35*b*#1^3 + 35*b*#1^4 + 21*b*#1^5 + 7*b*#1^6 + b*#1^7) & ]","C",1
67,1,139,494,0.2693435,"\int \frac{1}{a-b \cosh ^5(x)} \, dx","Integrate[(a - b*Cosh[x]^5)^(-1),x]","-\frac{8}{5} \text{RootSum}\left[\text{$\#$1}^{10} b+5 \text{$\#$1}^8 b+10 \text{$\#$1}^6 b-32 \text{$\#$1}^5 a+10 \text{$\#$1}^4 b+5 \text{$\#$1}^2 b+b\&,\frac{\text{$\#$1}^3 x+2 \text{$\#$1}^3 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)}{\text{$\#$1}^8 b+4 \text{$\#$1}^6 b+6 \text{$\#$1}^4 b-16 \text{$\#$1}^3 a+4 \text{$\#$1}^2 b+b}\&\right]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+\sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-\sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}} \tanh \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}}}",1,"(-8*RootSum[b + 5*b*#1^2 + 10*b*#1^4 - 32*a*#1^5 + 10*b*#1^6 + 5*b*#1^8 + b*#1^10 & , (x*#1^3 + 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^3)/(b + 4*b*#1^2 - 16*a*#1^3 + 6*b*#1^4 + 4*b*#1^6 + b*#1^8) & ])/5","C",1
68,1,132,175,0.173783,"\int \frac{1}{a-b \cosh ^6(x)} \, dx","Integrate[(a - b*Cosh[x]^6)^(-1),x]","-\frac{16}{3} \text{RootSum}\left[\text{$\#$1}^6 b+6 \text{$\#$1}^5 b+15 \text{$\#$1}^4 b-64 \text{$\#$1}^3 a+20 \text{$\#$1}^3 b+15 \text{$\#$1}^2 b+6 \text{$\#$1} b+b\&,\frac{\text{$\#$1}^2 x+\text{$\#$1}^2 \log (-\text{$\#$1} \sinh (x)+\text{$\#$1} \cosh (x)-\sinh (x)-\cosh (x))}{\text{$\#$1}^5 b+5 \text{$\#$1}^4 b+10 \text{$\#$1}^3 b-32 \text{$\#$1}^2 a+10 \text{$\#$1}^2 b+5 \text{$\#$1} b+b}\&\right]","\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}-\sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-\sqrt[3]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{a} \tanh (x)}{\sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}}}",1,"(-16*RootSum[b + 6*b*#1 + 15*b*#1^2 - 64*a*#1^3 + 20*b*#1^3 + 15*b*#1^4 + 6*b*#1^5 + b*#1^6 & , (x*#1^2 + Log[-Cosh[x] - Sinh[x] + Cosh[x]*#1 - Sinh[x]*#1]*#1^2)/(b + 5*b*#1 - 32*a*#1^2 + 10*b*#1^2 + 10*b*#1^3 + 5*b*#1^4 + b*#1^5) & ])/3","C",1
69,1,158,213,0.2177909,"\int \frac{1}{a-b \cosh ^8(x)} \, dx","Integrate[(a - b*Cosh[x]^8)^(-1),x]","-16 \text{RootSum}\left[\text{$\#$1}^8 b+8 \text{$\#$1}^7 b+28 \text{$\#$1}^6 b+56 \text{$\#$1}^5 b-256 \text{$\#$1}^4 a+70 \text{$\#$1}^4 b+56 \text{$\#$1}^3 b+28 \text{$\#$1}^2 b+8 \text{$\#$1} b+b\&,\frac{\text{$\#$1}^3 x+\text{$\#$1}^3 \log (-\text{$\#$1} \sinh (x)+\text{$\#$1} \cosh (x)-\sinh (x)-\cosh (x))}{\text{$\#$1}^7 b+7 \text{$\#$1}^6 b+21 \text{$\#$1}^5 b+35 \text{$\#$1}^4 b-128 \text{$\#$1}^3 a+35 \text{$\#$1}^3 b+21 \text{$\#$1}^2 b+7 \text{$\#$1} b+b}\&\right]","\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{a} \tanh (x)}{\sqrt{\sqrt[4]{a}-\sqrt[4]{b}}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}-\sqrt[4]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{a} \tanh (x)}{\sqrt{\sqrt[4]{a}-i \sqrt[4]{b}}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}-i \sqrt[4]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{a} \tanh (x)}{\sqrt{\sqrt[4]{a}+i \sqrt[4]{b}}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}+i \sqrt[4]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[8]{a} \tanh (x)}{\sqrt{\sqrt[4]{a}+\sqrt[4]{b}}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}+\sqrt[4]{b}}}",1,"-16*RootSum[b + 8*b*#1 + 28*b*#1^2 + 56*b*#1^3 - 256*a*#1^4 + 70*b*#1^4 + 56*b*#1^5 + 28*b*#1^6 + 8*b*#1^7 + b*#1^8 & , (x*#1^3 + Log[-Cosh[x] - Sinh[x] + Cosh[x]*#1 - Sinh[x]*#1]*#1^3)/(b + 7*b*#1 + 21*b*#1^2 - 128*a*#1^3 + 35*b*#1^3 + 35*b*#1^4 + 21*b*#1^5 + 7*b*#1^6 + b*#1^7) & ]","C",1
70,1,445,223,0.1035086,"\int \frac{1}{1+\cosh ^5(x)} \, dx","Integrate[(1 + Cosh[x]^5)^(-1),x]","\frac{1}{5} \tanh \left(\frac{x}{2}\right)-\frac{1}{10} \text{RootSum}\left[\text{$\#$1}^8-2 \text{$\#$1}^7+8 \text{$\#$1}^6-14 \text{$\#$1}^5+30 \text{$\#$1}^4-14 \text{$\#$1}^3+8 \text{$\#$1}^2-2 \text{$\#$1}+1\&,\frac{\text{$\#$1}^6 x+2 \text{$\#$1}^6 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)-4 \text{$\#$1}^5 x-8 \text{$\#$1}^5 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)+15 \text{$\#$1}^4 x+30 \text{$\#$1}^4 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)-40 \text{$\#$1}^3 x-80 \text{$\#$1}^3 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)+15 \text{$\#$1}^2 x+30 \text{$\#$1}^2 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)-4 \text{$\#$1} x-8 \text{$\#$1} \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)+2 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)+x}{4 \text{$\#$1}^7-7 \text{$\#$1}^6+24 \text{$\#$1}^5-35 \text{$\#$1}^4+60 \text{$\#$1}^3-21 \text{$\#$1}^2+8 \text{$\#$1}-1}\&\right]","\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,"-1/10*RootSum[1 - 2*#1 + 8*#1^2 - 14*#1^3 + 30*#1^4 - 14*#1^5 + 8*#1^6 - 2*#1^7 + #1^8 & , (x + 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1] - 4*x*#1 - 8*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1 + 15*x*#1^2 + 30*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^2 - 40*x*#1^3 - 80*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^3 + 15*x*#1^4 + 30*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^4 - 4*x*#1^5 - 8*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^5 + x*#1^6 + 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^6)/(-1 + 8*#1 - 21*#1^2 + 60*#1^3 - 35*#1^4 + 24*#1^5 - 7*#1^6 + 4*#1^7) & ] + Tanh[x/2]/5","C",1
71,1,68,83,0.4643387,"\int \frac{1}{1+\cosh ^6(x)} \, dx","Integrate[(1 + Cosh[x]^6)^(-1),x]","\frac{1}{6} \left(\sqrt{2} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)+i \sqrt{3} \left(\tan ^{-1}\left(\frac{1-2 i \tanh (x)}{\sqrt{3}}\right)-\tan ^{-1}\left(\frac{1+2 i \tanh (x)}{\sqrt{3}}\right)\right)+\tan ^{-1}(\text{csch}(x) \text{sech}(x))\right)","\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,"(ArcTan[Csch[x]*Sech[x]] + I*Sqrt[3]*(ArcTan[(1 - (2*I)*Tanh[x])/Sqrt[3]] - ArcTan[(1 + (2*I)*Tanh[x])/Sqrt[3]]) + Sqrt[2]*ArcTanh[Tanh[x]/Sqrt[2]])/6","C",1
72,1,127,129,0.1378216,"\int \frac{1}{1+\cosh ^8(x)} \, dx","Integrate[(1 + Cosh[x]^8)^(-1),x]","16 \text{RootSum}\left[\text{$\#$1}^8+8 \text{$\#$1}^7+28 \text{$\#$1}^6+56 \text{$\#$1}^5+326 \text{$\#$1}^4+56 \text{$\#$1}^3+28 \text{$\#$1}^2+8 \text{$\#$1}+1\&,\frac{\text{$\#$1}^3 x+\text{$\#$1}^3 \log (-\text{$\#$1} \sinh (x)+\text{$\#$1} \cosh (x)-\sinh (x)-\cosh (x))}{\text{$\#$1}^7+7 \text{$\#$1}^6+21 \text{$\#$1}^5+35 \text{$\#$1}^4+163 \text{$\#$1}^3+21 \text{$\#$1}^2+7 \text{$\#$1}+1}\&\right]","\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-\sqrt[4]{-1}}}\right)}{4 \sqrt{1-\sqrt[4]{-1}}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1+\sqrt[4]{-1}}}\right)}{4 \sqrt{1+\sqrt[4]{-1}}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-(-1)^{3/4}}}\right)}{4 \sqrt{1-(-1)^{3/4}}}+\frac{\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1+(-1)^{3/4}}}\right)}{4 \sqrt{1+(-1)^{3/4}}}",1,"16*RootSum[1 + 8*#1 + 28*#1^2 + 56*#1^3 + 326*#1^4 + 56*#1^5 + 28*#1^6 + 8*#1^7 + #1^8 & , (x*#1^3 + Log[-Cosh[x] - Sinh[x] + Cosh[x]*#1 - Sinh[x]*#1]*#1^3)/(1 + 7*#1 + 21*#1^2 + 163*#1^3 + 35*#1^4 + 21*#1^5 + 7*#1^6 + #1^7) & ]","C",1
73,1,445,205,0.0961406,"\int \frac{1}{1-\cosh ^5(x)} \, dx","Integrate[(1 - Cosh[x]^5)^(-1),x]","\frac{1}{10} \text{RootSum}\left[\text{$\#$1}^8+2 \text{$\#$1}^7+8 \text{$\#$1}^6+14 \text{$\#$1}^5+30 \text{$\#$1}^4+14 \text{$\#$1}^3+8 \text{$\#$1}^2+2 \text{$\#$1}+1\&,\frac{\text{$\#$1}^6 x+2 \text{$\#$1}^6 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)+4 \text{$\#$1}^5 x+8 \text{$\#$1}^5 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)+15 \text{$\#$1}^4 x+30 \text{$\#$1}^4 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)+40 \text{$\#$1}^3 x+80 \text{$\#$1}^3 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)+15 \text{$\#$1}^2 x+30 \text{$\#$1}^2 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)+4 \text{$\#$1} x+8 \text{$\#$1} \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)+2 \log \left(-\text{$\#$1} \sinh \left(\frac{x}{2}\right)+\text{$\#$1} \cosh \left(\frac{x}{2}\right)-\sinh \left(\frac{x}{2}\right)-\cosh \left(\frac{x}{2}\right)\right)+x}{4 \text{$\#$1}^7+7 \text{$\#$1}^6+24 \text{$\#$1}^5+35 \text{$\#$1}^4+60 \text{$\#$1}^3+21 \text{$\#$1}^2+8 \text{$\#$1}+1}\&\right]+\frac{1}{5} \coth \left(\frac{x}{2}\right)","\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,"Coth[x/2]/5 + RootSum[1 + 2*#1 + 8*#1^2 + 14*#1^3 + 30*#1^4 + 14*#1^5 + 8*#1^6 + 2*#1^7 + #1^8 & , (x + 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1] + 4*x*#1 + 8*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1 + 15*x*#1^2 + 30*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^2 + 40*x*#1^3 + 80*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^3 + 15*x*#1^4 + 30*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^4 + 4*x*#1^5 + 8*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^5 + x*#1^6 + 2*Log[-Cosh[x/2] - Sinh[x/2] + Cosh[x/2]*#1 - Sinh[x/2]*#1]*#1^6)/(1 + 8*#1 + 21*#1^2 + 60*#1^3 + 35*#1^4 + 24*#1^5 + 7*#1^6 + 4*#1^7) & ]/10","C",1
74,1,111,71,0.2341803,"\int \frac{1}{1-\cosh ^6(x)} \, dx","Integrate[(1 - Cosh[x]^6)^(-1),x]","-\frac{\sinh (x) (8 \cosh (2 x)+\cosh (4 x)+15) \left(-6 \cosh (x)+\sqrt[4]{-3} \sinh (x) \left(\left(\sqrt{3}+3 i\right) \tan ^{-1}\left(\frac{(-1)^{3/4} \left(\sqrt{3}-i\right) \tanh (x)}{2 \sqrt[4]{3}}\right)+\left(3+i \sqrt{3}\right) \tan ^{-1}\left(\frac{1}{2} \sqrt[4]{-\frac{1}{3}} \left(\sqrt{3}+i\right) \tanh (x)\right)\right)\right)}{144 \left(\cosh ^6(x)-1\right)}","\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,"-1/144*((15 + 8*Cosh[2*x] + Cosh[4*x])*Sinh[x]*(-6*Cosh[x] + (-3)^(1/4)*((3*I + Sqrt[3])*ArcTan[((-1)^(3/4)*(-I + Sqrt[3])*Tanh[x])/(2*3^(1/4))] + (3 + I*Sqrt[3])*ArcTan[((-1/3)^(1/4)*(I + Sqrt[3])*Tanh[x])/2])*Sinh[x]))/(-1 + Cosh[x]^6)","C",1
75,1,64,69,0.4551973,"\int \frac{1}{1-\cosh ^8(x)} \, dx","Integrate[(1 - Cosh[x]^8)^(-1),x]","\frac{1}{8} \left(\frac{2 \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-i}}\right)}{\sqrt{1-i}}+\frac{2 \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1+i}}\right)}{\sqrt{1+i}}+\sqrt{2} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{2}}\right)+2 \coth (x)\right)","\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,"((2*ArcTanh[Tanh[x]/Sqrt[1 - I]])/Sqrt[1 - I] + (2*ArcTanh[Tanh[x]/Sqrt[1 + I]])/Sqrt[1 + I] + Sqrt[2]*ArcTanh[Tanh[x]/Sqrt[2]] + 2*Coth[x])/8","A",1
76,1,15,15,0.0085618,"\int \frac{\tanh (x)}{1+\cosh ^2(x)} \, dx","Integrate[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",1
77,1,39,39,0.0257893,"\int \sqrt{a+b \cosh ^2(x)} \tanh (x) \, dx","Integrate[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",1
78,1,26,26,0.0165816,"\int \frac{\tanh (x)}{\sqrt{a+b \cosh ^2(x)}} \, dx","Integrate[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",1
79,1,13,13,0.0108151,"\int \frac{\tanh (x)}{\sqrt{1+\cosh ^2(x)}} \, dx","Integrate[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",1
80,1,21,13,0.0120647,"\int \frac{\tanh (x)}{\sqrt{1-\cosh ^2(x)}} \, dx","Integrate[Tanh[x]/Sqrt[1 - Cosh[x]^2],x]","\frac{2 \sinh (x) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)}{\sqrt{-\sinh ^2(x)}}","-\tanh ^{-1}\left(\sqrt{-\sinh ^2(x)}\right)",1,"(2*ArcTan[Tanh[x/2]]*Sinh[x])/Sqrt[-Sinh[x]^2]","A",1
81,1,145,153,1.4191844,"\int \frac{\tanh ^3(x)}{a+b \cosh ^3(x)} \, dx","Integrate[Tanh[x]^3/(a + b*Cosh[x]^3),x]","\frac{-2 \text{RootSum}\left[\text{$\#$1}^6 b+3 \text{$\#$1}^4 b+8 \text{$\#$1}^3 a+3 \text{$\#$1}^2 b+b\&,\frac{-3 \text{$\#$1}^4 b x+3 \text{$\#$1}^4 b \log \left(e^x-\text{$\#$1}\right)-4 \text{$\#$1}^3 a x+4 \text{$\#$1}^3 a \log \left(e^x-\text{$\#$1}\right)+b \log \left(e^x-\text{$\#$1}\right)-b x}{\text{$\#$1}^4 b+4 \text{$\#$1}^3 a+2 \text{$\#$1}^2 b+b}\&\right]-6 x+3 \text{sech}^2(x)+6 \log (\cosh (x))}{6 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,"(-6*x + 6*Log[Cosh[x]] - 2*RootSum[b + 3*b*#1^2 + 8*a*#1^3 + 3*b*#1^4 + b*#1^6 & , (-(b*x) + b*Log[E^x - #1] - 4*a*x*#1^3 + 4*a*Log[E^x - #1]*#1^3 - 3*b*x*#1^4 + 3*b*Log[E^x - #1]*#1^4)/(b + 2*b*#1^2 + 4*a*#1^3 + b*#1^4) & ] + 3*Sech[x]^2)/(6*a)","C",1
82,1,28,28,0.0214892,"\int \frac{\tanh (x)}{\sqrt{a+b \cosh ^3(x)}} \, dx","Integrate[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",1
83,1,45,45,0.0215548,"\int \sqrt{a+b \cosh ^3(x)} \tanh (x) \, dx","Integrate[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",1
84,1,29,29,0.0231851,"\int \frac{\tanh (x)}{\sqrt{a+b \cosh ^n(x)}} \, dx","Integrate[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",1
85,1,45,47,0.0220193,"\int \sqrt{a+b \cosh ^n(x)} \tanh (x) \, dx","Integrate[Sqrt[a + b*Cosh[x]^n]*Tanh[x],x]","\frac{2 \sqrt{a+b \cosh ^n(x)}-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]] + 2*Sqrt[a + b*Cosh[x]^n])/n","A",1