1,1,11,11,0.0023268,"\int \text{sech}(a+b x) \, dx","Integrate[Sech[a + b*x],x]","\frac{\tan ^{-1}(\sinh (a+b x))}{b}","\frac{\tan ^{-1}(\sinh (a+b x))}{b}",1,"ArcTan[Sinh[a + b*x]]/b","A",1
2,1,10,10,0.0041364,"\int \text{sech}^2(a+b x) \, dx","Integrate[Sech[a + b*x]^2,x]","\frac{\tanh (a+b x)}{b}","\frac{\tanh (a+b x)}{b}",1,"Tanh[a + b*x]/b","A",1
3,1,34,34,0.0098604,"\int \text{sech}^3(a+b x) \, dx","Integrate[Sech[a + b*x]^3,x]","\frac{\tan ^{-1}(\sinh (a+b x))}{2 b}+\frac{\tanh (a+b x) \text{sech}(a+b x)}{2 b}","\frac{\tan ^{-1}(\sinh (a+b x))}{2 b}+\frac{\tanh (a+b x) \text{sech}(a+b x)}{2 b}",1,"ArcTan[Sinh[a + b*x]]/(2*b) + (Sech[a + b*x]*Tanh[a + b*x])/(2*b)","A",1
4,1,26,26,0.0062467,"\int \text{sech}^4(a+b x) \, dx","Integrate[Sech[a + b*x]^4,x]","\frac{\tanh (a+b x)}{b}-\frac{\tanh ^3(a+b x)}{3 b}","\frac{\tanh (a+b x)}{b}-\frac{\tanh ^3(a+b x)}{3 b}",1,"Tanh[a + b*x]/b - Tanh[a + b*x]^3/(3*b)","A",1
5,1,47,55,0.0423527,"\int \text{sech}^5(a+b x) \, dx","Integrate[Sech[a + b*x]^5,x]","\frac{3 \tan ^{-1}(\sinh (a+b x))+2 \tanh (a+b x) \text{sech}^3(a+b x)+3 \tanh (a+b x) \text{sech}(a+b x)}{8 b}","\frac{3 \tan ^{-1}(\sinh (a+b x))}{8 b}+\frac{\tanh (a+b x) \text{sech}^3(a+b x)}{4 b}+\frac{3 \tanh (a+b x) \text{sech}(a+b x)}{8 b}",1,"(3*ArcTan[Sinh[a + b*x]] + 3*Sech[a + b*x]*Tanh[a + b*x] + 2*Sech[a + b*x]^3*Tanh[a + b*x])/(8*b)","A",1
6,1,41,41,0.0108192,"\int \text{sech}^6(a+b x) \, dx","Integrate[Sech[a + b*x]^6,x]","\frac{\tanh ^5(a+b x)}{5 b}-\frac{2 \tanh ^3(a+b x)}{3 b}+\frac{\tanh (a+b x)}{b}","\frac{\tanh ^5(a+b x)}{5 b}-\frac{2 \tanh ^3(a+b x)}{3 b}+\frac{\tanh (a+b x)}{b}",1,"Tanh[a + b*x]/b - (2*Tanh[a + b*x]^3)/(3*b) + Tanh[a + b*x]^5/(5*b)","A",1
7,1,19,19,0.0038395,"\int \text{sech}^4(7 x) \, dx","Integrate[Sech[7*x]^4,x]","\frac{1}{7} \tanh (7 x)-\frac{1}{21} \tanh ^3(7 x)","\frac{1}{7} \tanh (7 x)-\frac{1}{21} \tanh ^3(7 x)",1,"Tanh[7*x]/7 - Tanh[7*x]^3/21","A",1
8,1,35,35,0.0044772,"\int \text{sech}^6(\pi  x) \, dx","Integrate[Sech[Pi*x]^6,x]","\frac{\tanh ^5(\pi  x)}{5 \pi }-\frac{2 \tanh ^3(\pi  x)}{3 \pi }+\frac{\tanh (\pi  x)}{\pi }","\frac{\tanh ^5(\pi  x)}{5 \pi }-\frac{2 \tanh ^3(\pi  x)}{3 \pi }+\frac{\tanh (\pi  x)}{\pi }",1,"Tanh[Pi*x]/Pi - (2*Tanh[Pi*x]^3)/(3*Pi) + Tanh[Pi*x]^5/(5*Pi)","A",1
9,1,51,66,0.0784252,"\int \text{sech}^{\frac{5}{2}}(a+b x) \, dx","Integrate[Sech[a + b*x]^(5/2),x]","\frac{2 \text{sech}^{\frac{3}{2}}(a+b x) \left(\sinh (a+b x)-i \cosh ^{\frac{3}{2}}(a+b x) F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)\right)}{3 b}","\frac{2 \sinh (a+b x) \text{sech}^{\frac{3}{2}}(a+b x)}{3 b}-\frac{2 i \sqrt{\cosh (a+b x)} \sqrt{\text{sech}(a+b x)} F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{3 b}",1,"(2*Sech[a + b*x]^(3/2)*((-I)*Cosh[a + b*x]^(3/2)*EllipticF[(I/2)*(a + b*x), 2] + Sinh[a + b*x]))/(3*b)","A",1
10,1,49,62,0.0461119,"\int \text{sech}^{\frac{3}{2}}(a+b x) \, dx","Integrate[Sech[a + b*x]^(3/2),x]","\frac{2 \sqrt{\text{sech}(a+b x)} \left(\sinh (a+b x)+i \sqrt{\cosh (a+b x)} E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)\right)}{b}","\frac{2 \sinh (a+b x) \sqrt{\text{sech}(a+b x)}}{b}+\frac{2 i \sqrt{\cosh (a+b x)} \sqrt{\text{sech}(a+b x)} E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{b}",1,"(2*Sqrt[Sech[a + b*x]]*(I*Sqrt[Cosh[a + b*x]]*EllipticE[(I/2)*(a + b*x), 2] + Sinh[a + b*x]))/b","A",1
11,1,40,40,0.0294849,"\int \sqrt{\text{sech}(a+b x)} \, dx","Integrate[Sqrt[Sech[a + b*x]],x]","-\frac{2 i \sqrt{\cosh (a+b x)} \sqrt{\text{sech}(a+b x)} F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{b}","-\frac{2 i \sqrt{\cosh (a+b x)} \sqrt{\text{sech}(a+b x)} F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{b}",1,"((-2*I)*Sqrt[Cosh[a + b*x]]*EllipticF[(I/2)*(a + b*x), 2]*Sqrt[Sech[a + b*x]])/b","A",1
12,1,40,40,0.0371607,"\int \frac{1}{\sqrt{\text{sech}(a+b x)}} \, dx","Integrate[1/Sqrt[Sech[a + b*x]],x]","-\frac{2 i E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{b \sqrt{\cosh (a+b x)} \sqrt{\text{sech}(a+b x)}}","-\frac{2 i \sqrt{\cosh (a+b x)} \sqrt{\text{sech}(a+b x)} E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{b}",1,"((-2*I)*EllipticE[(I/2)*(a + b*x), 2])/(b*Sqrt[Cosh[a + b*x]]*Sqrt[Sech[a + b*x]])","A",1
13,1,53,66,0.0474643,"\int \frac{1}{\text{sech}^{\frac{3}{2}}(a+b x)} \, dx","Integrate[Sech[a + b*x]^(-3/2),x]","\frac{\sqrt{\text{sech}(a+b x)} \left(\sinh (2 (a+b x))-2 i \sqrt{\cosh (a+b x)} F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)\right)}{3 b}","\frac{2 \sinh (a+b x)}{3 b \sqrt{\text{sech}(a+b x)}}-\frac{2 i \sqrt{\cosh (a+b x)} \sqrt{\text{sech}(a+b x)} F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{3 b}",1,"(Sqrt[Sech[a + b*x]]*((-2*I)*Sqrt[Cosh[a + b*x]]*EllipticF[(I/2)*(a + b*x), 2] + Sinh[2*(a + b*x)]))/(3*b)","A",1
14,1,59,66,0.0707366,"\int \frac{1}{\text{sech}^{\frac{5}{2}}(a+b x)} \, dx","Integrate[Sech[a + b*x]^(-5/2),x]","\frac{\sqrt{\text{sech}(a+b x)} \left(\sinh (a+b x)+\sinh (3 (a+b x))-12 i \sqrt{\cosh (a+b x)} E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)\right)}{10 b}","\frac{2 \sinh (a+b x)}{5 b \text{sech}^{\frac{3}{2}}(a+b x)}-\frac{6 i \sqrt{\cosh (a+b x)} \sqrt{\text{sech}(a+b x)} E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{5 b}",1,"(Sqrt[Sech[a + b*x]]*((-12*I)*Sqrt[Cosh[a + b*x]]*EllipticE[(I/2)*(a + b*x), 2] + Sinh[a + b*x] + Sinh[3*(a + b*x)]))/(10*b)","A",1
15,1,68,102,0.2025357,"\int (b \text{sech}(c+d x))^{7/2} \, dx","Integrate[(b*Sech[c + d*x])^(7/2),x]","\frac{b^2 (b \text{sech}(c+d x))^{3/2} \left(3 \sinh (2 (c+d x))+2 \tanh (c+d x)+6 i \cosh ^{\frac{3}{2}}(c+d x) E\left(\left.\frac{1}{2} i (c+d x)\right|2\right)\right)}{5 d}","\frac{6 i b^4 E\left(\left.\frac{1}{2} i (c+d x)\right|2\right)}{5 d \sqrt{\cosh (c+d x)} \sqrt{b \text{sech}(c+d x)}}+\frac{6 b^3 \sinh (c+d x) \sqrt{b \text{sech}(c+d x)}}{5 d}+\frac{2 b \sinh (c+d x) (b \text{sech}(c+d x))^{5/2}}{5 d}",1,"(b^2*(b*Sech[c + d*x])^(3/2)*((6*I)*Cosh[c + d*x]^(3/2)*EllipticE[(I/2)*(c + d*x), 2] + 3*Sinh[2*(c + d*x)] + 2*Tanh[c + d*x]))/(5*d)","A",1
16,1,56,74,0.0734218,"\int (b \text{sech}(c+d x))^{5/2} \, dx","Integrate[(b*Sech[c + d*x])^(5/2),x]","\frac{2 b^2 \sqrt{b \text{sech}(c+d x)} \left(\tanh (c+d x)-i \sqrt{\cosh (c+d x)} F\left(\left.\frac{1}{2} i (c+d x)\right|2\right)\right)}{3 d}","\frac{2 b \sinh (c+d x) (b \text{sech}(c+d x))^{3/2}}{3 d}-\frac{2 i b^2 \sqrt{\cosh (c+d x)} F\left(\left.\frac{1}{2} i (c+d x)\right|2\right) \sqrt{b \text{sech}(c+d x)}}{3 d}",1,"(2*b^2*Sqrt[b*Sech[c + d*x]]*((-I)*Sqrt[Cosh[c + d*x]]*EllipticF[(I/2)*(c + d*x), 2] + Tanh[c + d*x]))/(3*d)","A",1
17,1,52,70,0.0397752,"\int (b \text{sech}(c+d x))^{3/2} \, dx","Integrate[(b*Sech[c + d*x])^(3/2),x]","\frac{2 b \sqrt{b \text{sech}(c+d x)} \left(\sinh (c+d x)+i \sqrt{\cosh (c+d x)} E\left(\left.\frac{1}{2} i (c+d x)\right|2\right)\right)}{d}","\frac{2 b \sinh (c+d x) \sqrt{b \text{sech}(c+d x)}}{d}+\frac{2 i b^2 E\left(\left.\frac{1}{2} i (c+d x)\right|2\right)}{d \sqrt{\cosh (c+d x)} \sqrt{b \text{sech}(c+d x)}}",1,"(2*b*Sqrt[b*Sech[c + d*x]]*(I*Sqrt[Cosh[c + d*x]]*EllipticE[(I/2)*(c + d*x), 2] + Sinh[c + d*x]))/d","A",1
18,1,42,42,0.0213748,"\int \sqrt{b \text{sech}(c+d x)} \, dx","Integrate[Sqrt[b*Sech[c + d*x]],x]","-\frac{2 i \sqrt{\cosh (c+d x)} F\left(\left.\frac{1}{2} i (c+d x)\right|2\right) \sqrt{b \text{sech}(c+d x)}}{d}","-\frac{2 i \sqrt{\cosh (c+d x)} F\left(\left.\frac{1}{2} i (c+d x)\right|2\right) \sqrt{b \text{sech}(c+d x)}}{d}",1,"((-2*I)*Sqrt[Cosh[c + d*x]]*EllipticF[(I/2)*(c + d*x), 2]*Sqrt[b*Sech[c + d*x]])/d","A",1
19,1,42,42,0.0292913,"\int \frac{1}{\sqrt{b \text{sech}(c+d x)}} \, dx","Integrate[1/Sqrt[b*Sech[c + d*x]],x]","-\frac{2 i E\left(\left.\frac{1}{2} i (c+d x)\right|2\right)}{d \sqrt{\cosh (c+d x)} \sqrt{b \text{sech}(c+d x)}}","-\frac{2 i E\left(\left.\frac{1}{2} i (c+d x)\right|2\right)}{d \sqrt{\cosh (c+d x)} \sqrt{b \text{sech}(c+d x)}}",1,"((-2*I)*EllipticE[(I/2)*(c + d*x), 2])/(d*Sqrt[Cosh[c + d*x]]*Sqrt[b*Sech[c + d*x]])","A",1
20,1,63,76,0.068138,"\int \frac{1}{(b \text{sech}(c+d x))^{3/2}} \, dx","Integrate[(b*Sech[c + d*x])^(-3/2),x]","\frac{\text{sech}^2(c+d x) \left(\sinh (2 (c+d x))-2 i \sqrt{\cosh (c+d x)} F\left(\left.\frac{1}{2} i (c+d x)\right|2\right)\right)}{3 d (b \text{sech}(c+d x))^{3/2}}","\frac{2 \sinh (c+d x)}{3 b d \sqrt{b \text{sech}(c+d x)}}-\frac{2 i \sqrt{\cosh (c+d x)} F\left(\left.\frac{1}{2} i (c+d x)\right|2\right) \sqrt{b \text{sech}(c+d x)}}{3 b^2 d}",1,"(Sech[c + d*x]^2*((-2*I)*Sqrt[Cosh[c + d*x]]*EllipticF[(I/2)*(c + d*x), 2] + Sinh[2*(c + d*x)]))/(3*d*(b*Sech[c + d*x])^(3/2))","A",1
21,1,64,76,0.085294,"\int \frac{1}{(b \text{sech}(c+d x))^{5/2}} \, dx","Integrate[(b*Sech[c + d*x])^(-5/2),x]","\frac{\sqrt{b \text{sech}(c+d x)} \left(\sinh (c+d x)+\sinh (3 (c+d x))-12 i \sqrt{\cosh (c+d x)} E\left(\left.\frac{1}{2} i (c+d x)\right|2\right)\right)}{10 b^3 d}","\frac{2 \sinh (c+d x)}{5 b d (b \text{sech}(c+d x))^{3/2}}-\frac{6 i E\left(\left.\frac{1}{2} i (c+d x)\right|2\right)}{5 b^2 d \sqrt{\cosh (c+d x)} \sqrt{b \text{sech}(c+d x)}}",1,"(Sqrt[b*Sech[c + d*x]]*((-12*I)*Sqrt[Cosh[c + d*x]]*EllipticE[(I/2)*(c + d*x), 2] + Sinh[c + d*x] + Sinh[3*(c + d*x)]))/(10*b^3*d)","A",1
22,1,70,104,0.1315233,"\int \frac{1}{(b \text{sech}(c+d x))^{7/2}} \, dx","Integrate[(b*Sech[c + d*x])^(-7/2),x]","\frac{\sqrt{b \text{sech}(c+d x)} \left(26 \sinh (2 (c+d x))+3 \sinh (4 (c+d x))-40 i \sqrt{\cosh (c+d x)} F\left(\left.\frac{1}{2} i (c+d x)\right|2\right)\right)}{84 b^4 d}","-\frac{10 i \sqrt{\cosh (c+d x)} F\left(\left.\frac{1}{2} i (c+d x)\right|2\right) \sqrt{b \text{sech}(c+d x)}}{21 b^4 d}+\frac{10 \sinh (c+d x)}{21 b^3 d \sqrt{b \text{sech}(c+d x)}}+\frac{2 \sinh (c+d x)}{7 b d (b \text{sech}(c+d x))^{5/2}}",1,"(Sqrt[b*Sech[c + d*x]]*((-40*I)*Sqrt[Cosh[c + d*x]]*EllipticF[(I/2)*(c + d*x), 2] + 26*Sinh[2*(c + d*x)] + 3*Sinh[4*(c + d*x)]))/(84*b^4*d)","A",1
23,1,60,75,0.0609133,"\int (b \text{sech}(c+d x))^n \, dx","Integrate[(b*Sech[c + d*x])^n,x]","-\frac{\sqrt{\tanh ^2(c+d x)} \coth (c+d x) (b \text{sech}(c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n}{2};\frac{n+2}{2};\text{sech}^2(c+d x)\right)}{d n}","-\frac{b \sinh (c+d x) (b \text{sech}(c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\cosh ^2(c+d x)\right)}{d (1-n) \sqrt{-\sinh ^2(c+d x)}}",1,"-((Coth[c + d*x]*Hypergeometric2F1[1/2, n/2, (2 + n)/2, Sech[c + d*x]^2]*(b*Sech[c + d*x])^n*Sqrt[Tanh[c + d*x]^2])/(d*n))","A",1
24,1,81,90,0.1056718,"\int \text{sech}^2(a+b x)^{7/2} \, dx","Integrate[(Sech[a + b*x]^2)^(7/2),x]","\frac{\cosh (a+b x) \sqrt{\text{sech}^2(a+b x)} \left(15 \tan ^{-1}(\sinh (a+b x))+8 \tanh (a+b x) \text{sech}^5(a+b x)+10 \tanh (a+b x) \text{sech}^3(a+b x)+15 \tanh (a+b x) \text{sech}(a+b x)\right)}{48 b}","\frac{5 \sin ^{-1}(\tanh (a+b x))}{16 b}+\frac{\tanh (a+b x) \text{sech}^2(a+b x)^{5/2}}{6 b}+\frac{5 \tanh (a+b x) \text{sech}^2(a+b x)^{3/2}}{24 b}+\frac{5 \tanh (a+b x) \sqrt{\text{sech}^2(a+b x)}}{16 b}",1,"(Cosh[a + b*x]*Sqrt[Sech[a + b*x]^2]*(15*ArcTan[Sinh[a + b*x]] + 15*Sech[a + b*x]*Tanh[a + b*x] + 10*Sech[a + b*x]^3*Tanh[a + b*x] + 8*Sech[a + b*x]^5*Tanh[a + b*x]))/(48*b)","A",1
25,1,55,65,0.1226461,"\int \text{sech}^2(a+b x)^{5/2} \, dx","Integrate[(Sech[a + b*x]^2)^(5/2),x]","\frac{\text{sech}^2(a+b x)^{3/2} \left(3 \sinh (2 (a+b x))+4 \tanh (a+b x)+6 \cosh ^3(a+b x) \tan ^{-1}(\sinh (a+b x))\right)}{16 b}","\frac{3 \sin ^{-1}(\tanh (a+b x))}{8 b}+\frac{\tanh (a+b x) \text{sech}^2(a+b x)^{3/2}}{4 b}+\frac{3 \tanh (a+b x) \sqrt{\text{sech}^2(a+b x)}}{8 b}",1,"((Sech[a + b*x]^2)^(3/2)*(6*ArcTan[Sinh[a + b*x]]*Cosh[a + b*x]^3 + 3*Sinh[2*(a + b*x)] + 4*Tanh[a + b*x]))/(16*b)","A",1
26,1,46,40,0.042407,"\int \text{sech}^2(a+b x)^{3/2} \, dx","Integrate[(Sech[a + b*x]^2)^(3/2),x]","\frac{\text{sech}(a+b x) \left(\tan ^{-1}(\sinh (a+b x))+\tanh (a+b x) \text{sech}(a+b x)\right)}{2 b \sqrt{\text{sech}^2(a+b x)}}","\frac{\sin ^{-1}(\tanh (a+b x))}{2 b}+\frac{\tanh (a+b x) \sqrt{\text{sech}^2(a+b x)}}{2 b}",1,"(Sech[a + b*x]*(ArcTan[Sinh[a + b*x]] + Sech[a + b*x]*Tanh[a + b*x]))/(2*b*Sqrt[Sech[a + b*x]^2])","A",1
27,1,29,11,0.0171514,"\int \sqrt{\text{sech}^2(a+b x)} \, dx","Integrate[Sqrt[Sech[a + b*x]^2],x]","\frac{\cosh (a+b x) \sqrt{\text{sech}^2(a+b x)} \tan ^{-1}(\sinh (a+b x))}{b}","\frac{\sin ^{-1}(\tanh (a+b x))}{b}",1,"(ArcTan[Sinh[a + b*x]]*Cosh[a + b*x]*Sqrt[Sech[a + b*x]^2])/b","B",1
28,1,22,22,0.0258652,"\int \frac{1}{\sqrt{\text{sech}^2(a+b x)}} \, dx","Integrate[1/Sqrt[Sech[a + b*x]^2],x]","\frac{\tanh (a+b x)}{b \sqrt{\text{sech}^2(a+b x)}}","\frac{\tanh (a+b x)}{b \sqrt{\text{sech}^2(a+b x)}}",1,"Tanh[a + b*x]/(b*Sqrt[Sech[a + b*x]^2])","A",1
29,1,44,51,0.070545,"\int \frac{1}{\text{sech}^2(a+b x)^{3/2}} \, dx","Integrate[(Sech[a + b*x]^2)^(-3/2),x]","\frac{\tanh ^3(a+b x)+3 \tanh (a+b x) \text{sech}^2(a+b x)}{3 b \text{sech}^2(a+b x)^{3/2}}","\frac{2 \tanh (a+b x)}{3 b \sqrt{\text{sech}^2(a+b x)}}+\frac{\tanh (a+b x)}{3 b \text{sech}^2(a+b x)^{3/2}}",1,"(3*Sech[a + b*x]^2*Tanh[a + b*x] + Tanh[a + b*x]^3)/(3*b*(Sech[a + b*x]^2)^(3/2))","A",1
30,1,47,76,0.0836952,"\int \frac{1}{\text{sech}^2(a+b x)^{5/2}} \, dx","Integrate[(Sech[a + b*x]^2)^(-5/2),x]","\frac{\left(3 \sinh ^4(a+b x)+10 \sinh ^2(a+b x)+15\right) \tanh (a+b x)}{15 b \sqrt{\text{sech}^2(a+b x)}}","\frac{8 \tanh (a+b x)}{15 b \sqrt{\text{sech}^2(a+b x)}}+\frac{4 \tanh (a+b x)}{15 b \text{sech}^2(a+b x)^{3/2}}+\frac{\tanh (a+b x)}{5 b \text{sech}^2(a+b x)^{5/2}}",1,"((15 + 10*Sinh[a + b*x]^2 + 3*Sinh[a + b*x]^4)*Tanh[a + b*x])/(15*b*Sqrt[Sech[a + b*x]^2])","A",1
31,1,57,101,0.1392064,"\int \frac{1}{\text{sech}^2(a+b x)^{7/2}} \, dx","Integrate[(Sech[a + b*x]^2)^(-7/2),x]","\frac{\left(5 \sinh ^6(a+b x)+21 \sinh ^4(a+b x)+35 \sinh ^2(a+b x)+35\right) \tanh (a+b x)}{35 b \sqrt{\text{sech}^2(a+b x)}}","\frac{16 \tanh (a+b x)}{35 b \sqrt{\text{sech}^2(a+b x)}}+\frac{8 \tanh (a+b x)}{35 b \text{sech}^2(a+b x)^{3/2}}+\frac{6 \tanh (a+b x)}{35 b \text{sech}^2(a+b x)^{5/2}}+\frac{\tanh (a+b x)}{7 b \text{sech}^2(a+b x)^{7/2}}",1,"((35 + 35*Sinh[a + b*x]^2 + 21*Sinh[a + b*x]^4 + 5*Sinh[a + b*x]^6)*Tanh[a + b*x])/(35*b*Sqrt[Sech[a + b*x]^2])","A",1
32,1,42,65,0.0359722,"\int \left(a \text{sech}^2(x)\right)^{5/2} \, dx","Integrate[(a*Sech[x]^2)^(5/2),x]","\frac{1}{8} \cosh (x) \left(a \text{sech}^2(x)\right)^{5/2} \left(2 \sinh (x)+3 \sinh (x) \cosh ^2(x)+6 \cosh ^4(x) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)\right)","\frac{3}{8} a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a \text{sech}^2(x)}}\right)+\frac{3}{8} a^2 \tanh (x) \sqrt{a \text{sech}^2(x)}+\frac{1}{4} a \tanh (x) \left(a \text{sech}^2(x)\right)^{3/2}",1,"(Cosh[x]*(a*Sech[x]^2)^(5/2)*(6*ArcTan[Tanh[x/2]]*Cosh[x]^4 + 2*Sinh[x] + 3*Cosh[x]^2*Sinh[x]))/8","A",1
33,1,29,46,0.0200872,"\int \left(a \text{sech}^2(x)\right)^{3/2} \, dx","Integrate[(a*Sech[x]^2)^(3/2),x]","\frac{1}{2} a \sqrt{a \text{sech}^2(x)} \left(\tanh (x)+2 \cosh (x) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)\right)","\frac{1}{2} a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a \text{sech}^2(x)}}\right)+\frac{1}{2} a \tanh (x) \sqrt{a \text{sech}^2(x)}",1,"(a*Sqrt[a*Sech[x]^2]*(2*ArcTan[Tanh[x/2]]*Cosh[x] + Tanh[x]))/2","A",1
34,1,21,25,0.0064404,"\int \sqrt{a \text{sech}^2(x)} \, dx","Integrate[Sqrt[a*Sech[x]^2],x]","2 \cosh (x) \sqrt{a \text{sech}^2(x)} \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)","\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a \text{sech}^2(x)}}\right)",1,"2*ArcTan[Tanh[x/2]]*Cosh[x]*Sqrt[a*Sech[x]^2]","A",1
35,1,13,13,0.006274,"\int \frac{1}{\sqrt{a \text{sech}^2(x)}} \, dx","Integrate[1/Sqrt[a*Sech[x]^2],x]","\frac{\tanh (x)}{\sqrt{a \text{sech}^2(x)}}","\frac{\tanh (x)}{\sqrt{a \text{sech}^2(x)}}",1,"Tanh[x]/Sqrt[a*Sech[x]^2]","A",1
36,1,27,36,0.021577,"\int \frac{1}{\left(a \text{sech}^2(x)\right)^{3/2}} \, dx","Integrate[(a*Sech[x]^2)^(-3/2),x]","\frac{(9 \sinh (x)+\sinh (3 x)) \text{sech}^3(x)}{12 \left(a \text{sech}^2(x)\right)^{3/2}}","\frac{2 \tanh (x)}{3 a \sqrt{a \text{sech}^2(x)}}+\frac{\tanh (x)}{3 \left(a \text{sech}^2(x)\right)^{3/2}}",1,"(Sech[x]^3*(9*Sinh[x] + Sinh[3*x]))/(12*(a*Sech[x]^2)^(3/2))","A",1
37,1,36,55,0.0393279,"\int \frac{1}{\left(a \text{sech}^2(x)\right)^{5/2}} \, dx","Integrate[(a*Sech[x]^2)^(-5/2),x]","\frac{(150 \sinh (x)+25 \sinh (3 x)+3 \sinh (5 x)) \cosh (x) \sqrt{a \text{sech}^2(x)}}{240 a^3}","\frac{8 \tanh (x)}{15 a^2 \sqrt{a \text{sech}^2(x)}}+\frac{4 \tanh (x)}{15 a \left(a \text{sech}^2(x)\right)^{3/2}}+\frac{\tanh (x)}{5 \left(a \text{sech}^2(x)\right)^{5/2}}",1,"(Cosh[x]*Sqrt[a*Sech[x]^2]*(150*Sinh[x] + 25*Sinh[3*x] + 3*Sinh[5*x]))/(240*a^3)","A",1
38,1,42,74,0.0521412,"\int \frac{1}{\left(a \text{sech}^2(x)\right)^{7/2}} \, dx","Integrate[(a*Sech[x]^2)^(-7/2),x]","\frac{(1225 \sinh (x)+245 \sinh (3 x)+49 \sinh (5 x)+5 \sinh (7 x)) \cosh (x) \sqrt{a \text{sech}^2(x)}}{2240 a^4}","\frac{16 \tanh (x)}{35 a^3 \sqrt{a \text{sech}^2(x)}}+\frac{8 \tanh (x)}{35 a^2 \left(a \text{sech}^2(x)\right)^{3/2}}+\frac{6 \tanh (x)}{35 a \left(a \text{sech}^2(x)\right)^{5/2}}+\frac{\tanh (x)}{7 \left(a \text{sech}^2(x)\right)^{7/2}}",1,"(Cosh[x]*Sqrt[a*Sech[x]^2]*(1225*Sinh[x] + 245*Sinh[3*x] + 49*Sinh[5*x] + 5*Sinh[7*x]))/(2240*a^4)","A",1
39,1,63,121,0.1025963,"\int \left(a \text{sech}^3(x)\right)^{5/2} \, dx","Integrate[(a*Sech[x]^3)^(5/2),x]","\frac{2}{585} a \text{sech}(x) \left(a \text{sech}^3(x)\right)^{3/2} \left(45 \tanh (x)+231 i \cosh ^{\frac{11}{2}}(x) E\left(\left.\frac{i x}{2}\right|2\right)+231 \sinh (x) \cosh ^5(x)+77 \sinh (x) \cosh ^3(x)+55 \sinh (x) \cosh (x)\right)","\frac{154}{585} a^2 \tanh (x) \sqrt{a \text{sech}^3(x)}+\frac{2}{13} a^2 \tanh (x) \text{sech}^4(x) \sqrt{a \text{sech}^3(x)}+\frac{22}{117} a^2 \tanh (x) \text{sech}^2(x) \sqrt{a \text{sech}^3(x)}+\frac{154}{195} i a^2 \cosh ^{\frac{3}{2}}(x) E\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \text{sech}^3(x)}+\frac{154}{195} a^2 \sinh (x) \cosh (x) \sqrt{a \text{sech}^3(x)}",1,"(2*a*Sech[x]*(a*Sech[x]^3)^(3/2)*((231*I)*Cosh[x]^(11/2)*EllipticE[(I/2)*x, 2] + 55*Cosh[x]*Sinh[x] + 77*Cosh[x]^3*Sinh[x] + 231*Cosh[x]^5*Sinh[x] + 45*Tanh[x]))/585","A",1
40,1,47,69,0.0387294,"\int \left(a \text{sech}^3(x)\right)^{3/2} \, dx","Integrate[(a*Sech[x]^3)^(3/2),x]","\frac{2}{21} a \text{sech}(x) \sqrt{a \text{sech}^3(x)} \left(3 \tanh (x)-5 i \cosh ^{\frac{5}{2}}(x) F\left(\left.\frac{i x}{2}\right|2\right)+5 \sinh (x) \cosh (x)\right)","\frac{10}{21} a \sinh (x) \sqrt{a \text{sech}^3(x)}+\frac{2}{7} a \tanh (x) \text{sech}(x) \sqrt{a \text{sech}^3(x)}-\frac{10}{21} i a \cosh ^{\frac{3}{2}}(x) F\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \text{sech}^3(x)}",1,"(2*a*Sech[x]*Sqrt[a*Sech[x]^3]*((-5*I)*Cosh[x]^(5/2)*EllipticF[(I/2)*x, 2] + 5*Cosh[x]*Sinh[x] + 3*Tanh[x]))/21","A",1
41,1,36,46,0.0191202,"\int \sqrt{a \text{sech}^3(x)} \, dx","Integrate[Sqrt[a*Sech[x]^3],x]","2 \cosh (x) \sqrt{a \text{sech}^3(x)} \left(\sinh (x)+i \sqrt{\cosh (x)} E\left(\left.\frac{i x}{2}\right|2\right)\right)","2 \sinh (x) \cosh (x) \sqrt{a \text{sech}^3(x)}+2 i \cosh ^{\frac{3}{2}}(x) E\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \text{sech}^3(x)}",1,"2*Cosh[x]*Sqrt[a*Sech[x]^3]*(I*Sqrt[Cosh[x]]*EllipticE[(I/2)*x, 2] + Sinh[x])","A",1
42,1,38,48,0.0419597,"\int \frac{1}{\sqrt{a \text{sech}^3(x)}} \, dx","Integrate[1/Sqrt[a*Sech[x]^3],x]","\frac{2 \tanh (x)-\frac{2 i F\left(\left.\frac{i x}{2}\right|2\right)}{\cosh ^{\frac{3}{2}}(x)}}{3 \sqrt{a \text{sech}^3(x)}}","\frac{2 \tanh (x)}{3 \sqrt{a \text{sech}^3(x)}}-\frac{2 i F\left(\left.\frac{i x}{2}\right|2\right)}{3 \cosh ^{\frac{3}{2}}(x) \sqrt{a \text{sech}^3(x)}}",1,"(((-2*I)*EllipticF[(I/2)*x, 2])/Cosh[x]^(3/2) + 2*Tanh[x])/(3*Sqrt[a*Sech[x]^3])","A",1
43,1,47,77,0.0937449,"\int \frac{1}{\left(a \text{sech}^3(x)\right)^{3/2}} \, dx","Integrate[(a*Sech[x]^3)^(-3/2),x]","\frac{33 \sinh (x)+5 \sinh (3 x)-\frac{84 i E\left(\left.\frac{i x}{2}\right|2\right)}{\cosh ^{\frac{3}{2}}(x)}}{90 a \sqrt{a \text{sech}^3(x)}}","\frac{14 \sinh (x)}{45 a \sqrt{a \text{sech}^3(x)}}-\frac{14 i E\left(\left.\frac{i x}{2}\right|2\right)}{15 a \cosh ^{\frac{3}{2}}(x) \sqrt{a \text{sech}^3(x)}}+\frac{2 \sinh (x) \cosh ^2(x)}{9 a \sqrt{a \text{sech}^3(x)}}",1,"(((-84*I)*EllipticE[(I/2)*x, 2])/Cosh[x]^(3/2) + 33*Sinh[x] + 5*Sinh[3*x])/(90*a*Sqrt[a*Sech[x]^3])","A",1
44,1,63,121,0.0979511,"\int \frac{1}{\left(a \text{sech}^3(x)\right)^{5/2}} \, dx","Integrate[(a*Sech[x]^3)^(-5/2),x]","\frac{\cosh (x) \sqrt{a \text{sech}^3(x)} \left(19122 \sinh (2 x)+4406 \sinh (4 x)+826 \sinh (6 x)+77 \sinh (8 x)-24960 i \sqrt{\cosh (x)} F\left(\left.\frac{i x}{2}\right|2\right)\right)}{73920 a^3}","\frac{26 \tanh (x)}{77 a^2 \sqrt{a \text{sech}^3(x)}}-\frac{26 i F\left(\left.\frac{i x}{2}\right|2\right)}{77 a^2 \cosh ^{\frac{3}{2}}(x) \sqrt{a \text{sech}^3(x)}}+\frac{2 \sinh (x) \cosh ^5(x)}{15 a^2 \sqrt{a \text{sech}^3(x)}}+\frac{26 \sinh (x) \cosh ^3(x)}{165 a^2 \sqrt{a \text{sech}^3(x)}}+\frac{78 \sinh (x) \cosh (x)}{385 a^2 \sqrt{a \text{sech}^3(x)}}",1,"(Cosh[x]*Sqrt[a*Sech[x]^3]*((-24960*I)*Sqrt[Cosh[x]]*EllipticF[(I/2)*x, 2] + 19122*Sinh[2*x] + 4406*Sinh[4*x] + 826*Sinh[6*x] + 77*Sinh[8*x]))/(73920*a^3)","A",1
45,1,54,163,0.1709362,"\int \left(a \text{sech}^4(x)\right)^{7/2} \, dx","Integrate[(a*Sech[x]^4)^(7/2),x]","\frac{\sinh (x) \cosh (x) (2380 \cosh (2 x)+1093 \cosh (4 x)+378 \cosh (6 x)+92 \cosh (8 x)+14 \cosh (10 x)+\cosh (12 x)+2048) \left(a \text{sech}^4(x)\right)^{7/2}}{6006}","a^3 \sinh (x) \cosh (x) \sqrt{a \text{sech}^4(x)}+\frac{1}{13} a^3 \sinh ^2(x) \tanh ^{11}(x) \sqrt{a \text{sech}^4(x)}-\frac{6}{11} a^3 \sinh ^2(x) \tanh ^9(x) \sqrt{a \text{sech}^4(x)}+\frac{5}{3} a^3 \sinh ^2(x) \tanh ^7(x) \sqrt{a \text{sech}^4(x)}-\frac{20}{7} a^3 \sinh ^2(x) \tanh ^5(x) \sqrt{a \text{sech}^4(x)}+3 a^3 \sinh ^2(x) \tanh ^3(x) \sqrt{a \text{sech}^4(x)}-2 a^3 \sinh ^2(x) \tanh (x) \sqrt{a \text{sech}^4(x)}",1,"(Cosh[x]*(2048 + 2380*Cosh[2*x] + 1093*Cosh[4*x] + 378*Cosh[6*x] + 92*Cosh[8*x] + 14*Cosh[10*x] + Cosh[12*x])*(a*Sech[x]^4)^(7/2)*Sinh[x])/6006","A",1
46,1,42,117,0.0964585,"\int \left(a \text{sech}^4(x)\right)^{5/2} \, dx","Integrate[(a*Sech[x]^4)^(5/2),x]","\frac{1}{315} \sinh (x) \cosh (x) (130 \cosh (2 x)+46 \cosh (4 x)+10 \cosh (6 x)+\cosh (8 x)+128) \left(a \text{sech}^4(x)\right)^{5/2}","a^2 \sinh (x) \cosh (x) \sqrt{a \text{sech}^4(x)}+\frac{1}{9} a^2 \sinh ^2(x) \tanh ^7(x) \sqrt{a \text{sech}^4(x)}-\frac{4}{7} a^2 \sinh ^2(x) \tanh ^5(x) \sqrt{a \text{sech}^4(x)}+\frac{6}{5} a^2 \sinh ^2(x) \tanh ^3(x) \sqrt{a \text{sech}^4(x)}-\frac{4}{3} a^2 \sinh ^2(x) \tanh (x) \sqrt{a \text{sech}^4(x)}",1,"(Cosh[x]*(128 + 130*Cosh[2*x] + 46*Cosh[4*x] + 10*Cosh[6*x] + Cosh[8*x])*(a*Sech[x]^4)^(5/2)*Sinh[x])/315","A",1
47,1,30,61,0.0583054,"\int \left(a \text{sech}^4(x)\right)^{3/2} \, dx","Integrate[(a*Sech[x]^4)^(3/2),x]","\frac{1}{15} \sinh (x) \cosh (x) (6 \cosh (2 x)+\cosh (4 x)+8) \left(a \text{sech}^4(x)\right)^{3/2}","a \sinh (x) \cosh (x) \sqrt{a \text{sech}^4(x)}+\frac{1}{5} a \sinh ^2(x) \tanh ^3(x) \sqrt{a \text{sech}^4(x)}-\frac{2}{3} a \sinh ^2(x) \tanh (x) \sqrt{a \text{sech}^4(x)}",1,"(Cosh[x]*(8 + 6*Cosh[2*x] + Cosh[4*x])*(a*Sech[x]^4)^(3/2)*Sinh[x])/15","A",1
48,1,15,15,0.0061939,"\int \sqrt{a \text{sech}^4(x)} \, dx","Integrate[Sqrt[a*Sech[x]^4],x]","\sinh (x) \cosh (x) \sqrt{a \text{sech}^4(x)}","\sinh (x) \cosh (x) \sqrt{a \text{sech}^4(x)}",1,"Cosh[x]*Sqrt[a*Sech[x]^4]*Sinh[x]","A",1
49,1,23,36,0.0233956,"\int \frac{1}{\sqrt{a \text{sech}^4(x)}} \, dx","Integrate[1/Sqrt[a*Sech[x]^4],x]","\frac{\tanh (x)+x \text{sech}^2(x)}{2 \sqrt{a \text{sech}^4(x)}}","\frac{x \text{sech}^2(x)}{2 \sqrt{a \text{sech}^4(x)}}+\frac{\tanh (x)}{2 \sqrt{a \text{sech}^4(x)}}",1,"(x*Sech[x]^2 + Tanh[x])/(2*Sqrt[a*Sech[x]^4])","A",1
50,1,38,86,0.0374582,"\int \frac{1}{\left(a \text{sech}^4(x)\right)^{3/2}} \, dx","Integrate[(a*Sech[x]^4)^(-3/2),x]","\frac{(60 x+45 \sinh (2 x)+9 \sinh (4 x)+\sinh (6 x)) \text{sech}^6(x)}{192 \left(a \text{sech}^4(x)\right)^{3/2}}","\frac{5 x \text{sech}^2(x)}{16 a \sqrt{a \text{sech}^4(x)}}+\frac{5 \tanh (x)}{16 a \sqrt{a \text{sech}^4(x)}}+\frac{\sinh (x) \cosh ^3(x)}{6 a \sqrt{a \text{sech}^4(x)}}+\frac{5 \sinh (x) \cosh (x)}{24 a \sqrt{a \text{sech}^4(x)}}",1,"(Sech[x]^6*(60*x + 45*Sinh[2*x] + 9*Sinh[4*x] + Sinh[6*x]))/(192*(a*Sech[x]^4)^(3/2))","A",1
51,1,55,132,0.0791974,"\int \frac{1}{\left(a \text{sech}^4(x)\right)^{5/2}} \, dx","Integrate[(a*Sech[x]^4)^(-5/2),x]","\frac{(2520 x+2100 \sinh (2 x)+600 \sinh (4 x)+150 \sinh (6 x)+25 \sinh (8 x)+2 \sinh (10 x)) \cosh ^2(x) \sqrt{a \text{sech}^4(x)}}{10240 a^3}","\frac{63 x \text{sech}^2(x)}{256 a^2 \sqrt{a \text{sech}^4(x)}}+\frac{63 \tanh (x)}{256 a^2 \sqrt{a \text{sech}^4(x)}}+\frac{\sinh (x) \cosh ^7(x)}{10 a^2 \sqrt{a \text{sech}^4(x)}}+\frac{9 \sinh (x) \cosh ^5(x)}{80 a^2 \sqrt{a \text{sech}^4(x)}}+\frac{21 \sinh (x) \cosh ^3(x)}{160 a^2 \sqrt{a \text{sech}^4(x)}}+\frac{21 \sinh (x) \cosh (x)}{128 a^2 \sqrt{a \text{sech}^4(x)}}",1,"(Cosh[x]^2*Sqrt[a*Sech[x]^4]*(2520*x + 2100*Sinh[2*x] + 600*Sinh[4*x] + 150*Sinh[6*x] + 25*Sinh[8*x] + 2*Sinh[10*x]))/(10240*a^3)","A",1
52,1,28,44,0.1036668,"\int \frac{\sinh ^4(x)}{a+a \text{sech}(x)} \, dx","Integrate[Sinh[x]^4/(a + a*Sech[x]),x]","\frac{24 \sinh (x)-8 \sinh (3 x)+3 (\sinh (4 x)-4 x)}{96 a}","-\frac{x}{8 a}-\frac{\sinh ^3(x)}{3 a}+\frac{\sinh (x) \cosh ^3(x)}{4 a}-\frac{\sinh (x) \cosh (x)}{8 a}",1,"(24*Sinh[x] - 8*Sinh[3*x] + 3*(-4*x + Sinh[4*x]))/(96*a)","A",1
53,1,23,23,0.0480903,"\int \frac{\sinh ^3(x)}{a+a \text{sech}(x)} \, dx","Integrate[Sinh[x]^3/(a + a*Sech[x]),x]","\frac{3 \cosh (x)-3 \cosh (2 x)+\cosh (3 x)-7}{12 a}","\frac{\cosh ^3(x)}{3 a}-\frac{\sinh ^2(x)}{2 a}",1,"(-7 + 3*Cosh[x] - 3*Cosh[2*x] + Cosh[3*x])/(12*a)","A",1
54,1,16,27,0.0665796,"\int \frac{\sinh ^2(x)}{a+a \text{sech}(x)} \, dx","Integrate[Sinh[x]^2/(a + a*Sech[x]),x]","\frac{x+\sinh (x) (\cosh (x)-2)}{2 a}","\frac{x}{2 a}-\frac{\sinh (x)}{a}+\frac{\sinh (x) \cosh (x)}{2 a}",1,"(x + (-2 + Cosh[x])*Sinh[x])/(2*a)","A",1
55,1,16,17,0.0198077,"\int \frac{\sinh (x)}{a+a \text{sech}(x)} \, dx","Integrate[Sinh[x]/(a + a*Sech[x]),x]","\frac{\cosh (x)-2 \log \left(\cosh \left(\frac{x}{2}\right)\right)}{a}","\frac{\cosh (x)}{a}-\frac{\log (\cosh (x)+1)}{a}",1,"(Cosh[x] - 2*Log[Cosh[x/2]])/a","A",1
56,1,44,33,0.0551705,"\int \frac{\text{csch}(x)}{a+a \text{sech}(x)} \, dx","Integrate[Csch[x]/(a + a*Sech[x]),x]","-\frac{\text{sech}(x) \left(2 \cosh ^2\left(\frac{x}{2}\right) \left(\log \left(\cosh \left(\frac{x}{2}\right)\right)-\log \left(\sinh \left(\frac{x}{2}\right)\right)\right)+1\right)}{2 a (\text{sech}(x)+1)}","\frac{\text{csch}^2(x)}{2 a}-\frac{\tanh ^{-1}(\cosh (x))}{2 a}-\frac{\coth (x) \text{csch}(x)}{2 a}",1,"-1/2*((1 + 2*Cosh[x/2]^2*(Log[Cosh[x/2]] - Log[Sinh[x/2]]))*Sech[x])/(a*(1 + Sech[x]))","A",1
57,1,25,23,0.0408621,"\int \frac{\text{csch}^2(x)}{a+a \text{sech}(x)} \, dx","Integrate[Csch[x]^2/(a + a*Sech[x]),x]","-\frac{(2 \cosh (x)+\cosh (2 x)+3) \text{csch}(x)}{6 a (\cosh (x)+1)}","\frac{\text{csch}^3(x)}{3 a}-\frac{\coth ^3(x)}{3 a}",1,"-1/6*((3 + 2*Cosh[x] + Cosh[2*x])*Csch[x])/(a*(1 + Cosh[x]))","A",1
58,1,59,46,0.2195689,"\int \frac{\text{csch}^3(x)}{a+a \text{sech}(x)} \, dx","Integrate[Csch[x]^3/(a + a*Sech[x]),x]","\frac{\cosh ^2\left(\frac{x}{2}\right) \text{sech}(x) \left(-2 \text{csch}^2\left(\frac{x}{2}\right)+\text{sech}^4\left(\frac{x}{2}\right)-4 \log \left(\sinh \left(\frac{x}{2}\right)\right)+4 \log \left(\cosh \left(\frac{x}{2}\right)\right)\right)}{16 (a \text{sech}(x)+a)}","\frac{\text{csch}^4(x)}{4 a}+\frac{\tanh ^{-1}(\cosh (x))}{8 a}-\frac{\coth (x) \text{csch}^3(x)}{4 a}-\frac{\coth (x) \text{csch}(x)}{8 a}",1,"(Cosh[x/2]^2*(-2*Csch[x/2]^2 + 4*Log[Cosh[x/2]] - 4*Log[Sinh[x/2]] + Sech[x/2]^4)*Sech[x])/(16*(a + a*Sech[x]))","A",1
59,1,39,34,0.0643908,"\int \frac{\text{csch}^4(x)}{a+a \text{sech}(x)} \, dx","Integrate[Csch[x]^4/(a + a*Sech[x]),x]","\frac{(-6 \cosh (x)-2 \cosh (2 x)+2 \cosh (3 x)+\cosh (4 x)-15) \text{csch}^3(x)}{60 a (\cosh (x)+1)}","-\frac{\coth ^5(x)}{5 a}+\frac{\coth ^3(x)}{3 a}+\frac{\text{csch}^5(x)}{5 a}",1,"((-15 - 6*Cosh[x] - 2*Cosh[2*x] + 2*Cosh[3*x] + Cosh[4*x])*Csch[x]^3)/(60*a*(1 + Cosh[x]))","A",1
60,1,219,132,0.736358,"\int \frac{\sinh ^4(x)}{a+b \text{sech}(x)} \, dx","Integrate[Sinh[x]^4/(a + b*Sech[x]),x]","\frac{36 a^4 x+3 a^4 \sinh (4 x)-8 a^3 b \sinh (3 x)-144 a^2 b^2 x+24 a b \left(5 a^2-4 b^2\right) \sinh (x)-24 a^2 \left(a^2-b^2\right) \sinh (2 x)+\frac{192 b^5 \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}-\frac{384 a^2 b^3 \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+\frac{192 a^4 b \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+96 b^4 x}{96 a^5}","-\frac{2 b (a-b)^{3/2} (a+b)^{3/2} \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a^5}-\frac{\sinh ^3(x) (4 b-3 a \cosh (x))}{12 a^2}+\frac{\sinh (x) \left(8 b \left(a^2-b^2\right)-a \left(3 a^2-4 b^2\right) \cosh (x)\right)}{8 a^4}+\frac{x \left(3 a^4-12 a^2 b^2+8 b^4\right)}{8 a^5}",1,"(36*a^4*x - 144*a^2*b^2*x + 96*b^4*x + (192*a^4*b*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/Sqrt[a^2 - b^2] - (384*a^2*b^3*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/Sqrt[a^2 - b^2] + (192*b^5*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/Sqrt[a^2 - b^2] + 24*a*b*(5*a^2 - 4*b^2)*Sinh[x] - 24*a^2*(a^2 - b^2)*Sinh[2*x] - 8*a^3*b*Sinh[3*x] + 3*a^4*Sinh[4*x])/(96*a^5)","A",1
61,1,66,61,0.1352492,"\int \frac{\sinh ^3(x)}{a+b \text{sech}(x)} \, dx","Integrate[Sinh[x]^3/(a + b*Sech[x]),x]","\frac{\left(12 a b^2-9 a^3\right) \cosh (x)+a^3 \cosh (3 x)-3 a^2 b \cosh (2 x)+12 a^2 b \log (a \cosh (x)+b)-12 b^3 \log (a \cosh (x)+b)}{12 a^4}","-\frac{b \cosh ^2(x)}{2 a^2}+\frac{b \left(a^2-b^2\right) \log (a \cosh (x)+b)}{a^4}-\frac{\left(a^2-b^2\right) \cosh (x)}{a^3}+\frac{\cosh ^3(x)}{3 a}",1,"((-9*a^3 + 12*a*b^2)*Cosh[x] - 3*a^2*b*Cosh[2*x] + a^3*Cosh[3*x] + 12*a^2*b*Log[b + a*Cosh[x]] - 12*b^3*Log[b + a*Cosh[x]])/(12*a^4)","A",1
62,1,76,82,0.1950817,"\int \frac{\sinh ^2(x)}{a+b \text{sech}(x)} \, dx","Integrate[Sinh[x]^2/(a + b*Sech[x]),x]","\frac{-8 b \sqrt{a^2-b^2} \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)-2 a^2 x+a^2 \sinh (2 x)-4 a b \sinh (x)+4 b^2 x}{4 a^3}","\frac{2 b \sqrt{a-b} \sqrt{a+b} \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a^3}-\frac{\sinh (x) (2 b-a \cosh (x))}{2 a^2}-\frac{x \left(a^2-2 b^2\right)}{2 a^3}",1,"(-2*a^2*x + 4*b^2*x - 8*b*Sqrt[a^2 - b^2]*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]] - 4*a*b*Sinh[x] + a^2*Sinh[2*x])/(4*a^3)","A",1
63,1,19,20,0.0107356,"\int \frac{\sinh (x)}{a+b \text{sech}(x)} \, dx","Integrate[Sinh[x]/(a + b*Sech[x]),x]","\frac{a \cosh (x)-b \log (a \cosh (x)+b)}{a^2}","\frac{\cosh (x)}{a}-\frac{b \log (a \cosh (x)+b)}{a^2}",1,"(a*Cosh[x] - b*Log[b + a*Cosh[x]])/a^2","A",1
64,1,37,53,0.0739787,"\int \frac{\text{csch}(x)}{a+b \text{sech}(x)} \, dx","Integrate[Csch[x]/(a + b*Sech[x]),x]","\frac{b \log (a \cosh (x)+b)+a \log \left(\tanh \left(\frac{x}{2}\right)\right)-b \log (\sinh (x))}{a^2-b^2}","\frac{b \log (a \cosh (x)+b)}{a^2-b^2}+\frac{\log (1-\cosh (x))}{2 (a+b)}-\frac{\log (\cosh (x)+1)}{2 (a-b)}",1,"(b*Log[b + a*Cosh[x]] - b*Log[Sinh[x]] + a*Log[Tanh[x/2]])/(a^2 - b^2)","A",1
65,1,75,66,0.2614856,"\int \frac{\text{csch}^2(x)}{a+b \text{sech}(x)} \, dx","Integrate[Csch[x]^2/(a + b*Sech[x]),x]","\frac{1}{2} \left(-\frac{4 a b \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2}}+\frac{\tanh \left(\frac{x}{2}\right)}{b-a}-\frac{\coth \left(\frac{x}{2}\right)}{a+b}\right)","\frac{\text{csch}(x) (b-a \cosh (x))}{a^2-b^2}+\frac{2 a b \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{(a-b)^{3/2} (a+b)^{3/2}}",1,"((-4*a*b*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/(a^2 - b^2)^(3/2) - Coth[x/2]/(a + b) + Tanh[x/2]/(-a + b))/2","A",1
66,1,86,85,0.3465108,"\int \frac{\text{csch}^3(x)}{a+b \text{sech}(x)} \, dx","Integrate[Csch[x]^3/(a + b*Sech[x]),x]","\frac{1}{8} \left(-\frac{4 a \left(\left(a^2+b^2\right) \log \left(\tanh \left(\frac{x}{2}\right)\right)-2 a b \log (\sinh (x))+2 a b \log (a \cosh (x)+b)\right)}{(a-b)^2 (a+b)^2}-\frac{\text{csch}^2\left(\frac{x}{2}\right)}{a+b}-\frac{\text{sech}^2\left(\frac{x}{2}\right)}{a-b}\right)","-\frac{a^2 b \log (a \cosh (x)+b)}{\left(a^2-b^2\right)^2}+\frac{\text{csch}^2(x) (b-a \cosh (x))}{2 \left(a^2-b^2\right)}-\frac{a \log (1-\cosh (x))}{4 (a+b)^2}+\frac{a \log (\cosh (x)+1)}{4 (a-b)^2}",1,"(-(Csch[x/2]^2/(a + b)) - (4*a*(2*a*b*Log[b + a*Cosh[x]] - 2*a*b*Log[Sinh[x]] + (a^2 + b^2)*Log[Tanh[x/2]]))/((a - b)^2*(a + b)^2) - Sech[x/2]^2/(a - b))/8","A",1
67,1,156,111,0.5977602,"\int \frac{\text{csch}^4(x)}{a+b \text{sech}(x)} \, dx","Integrate[Csch[x]^4/(a + b*Sech[x]),x]","\frac{\text{sech}(x) (a \cosh (x)+b) \left(\frac{48 a^3 b \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}-\frac{2 b \tanh \left(\frac{x}{2}\right)}{(a-b)^2}+\frac{8 a \tanh \left(\frac{x}{2}\right)}{(a-b)^2}+\frac{2 (4 a+b) \coth \left(\frac{x}{2}\right)}{(a+b)^2}-\frac{\sinh (x) \text{csch}^4\left(\frac{x}{2}\right)}{2 (a+b)}+\frac{8 \sinh ^4\left(\frac{x}{2}\right) \text{csch}^3(x)}{a-b}\right)}{24 (a+b \text{sech}(x))}","-\frac{2 a^3 b \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{(a-b)^{5/2} (a+b)^{5/2}}+\frac{\text{csch}^3(x) (b-a \cosh (x))}{3 \left(a^2-b^2\right)}-\frac{\text{csch}(x) \left(3 a^2 b-a \left(2 a^2+b^2\right) \cosh (x)\right)}{3 \left(a^2-b^2\right)^2}",1,"((b + a*Cosh[x])*Sech[x]*((48*a^3*b*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/(a^2 - b^2)^(5/2) + (2*(4*a + b)*Coth[x/2])/(a + b)^2 + (8*Csch[x]^3*Sinh[x/2]^4)/(a - b) - (Csch[x/2]^4*Sinh[x])/(2*(a + b)) + (8*a*Tanh[x/2])/(a - b)^2 - (2*b*Tanh[x/2])/(a - b)^2))/(24*(a + b*Sech[x]))","A",1
68,1,63,67,0.0893848,"\int \frac{\cosh ^4(x)}{a+a \text{sech}(x)} \, dx","Integrate[Cosh[x]^4/(a + a*Sech[x]),x]","\frac{\text{sech}\left(\frac{x}{2}\right) \left(-360 \sinh \left(\frac{x}{2}\right)-120 \sinh \left(\frac{3 x}{2}\right)+40 \sinh \left(\frac{5 x}{2}\right)-5 \sinh \left(\frac{7 x}{2}\right)+3 \sinh \left(\frac{9 x}{2}\right)+360 x \cosh \left(\frac{x}{2}\right)\right)}{192 a}","\frac{15 x}{8 a}-\frac{4 \sinh ^3(x)}{3 a}-\frac{4 \sinh (x)}{a}+\frac{5 \sinh (x) \cosh ^3(x)}{4 a}+\frac{15 \sinh (x) \cosh (x)}{8 a}-\frac{\sinh (x) \cosh ^3(x)}{a \text{sech}(x)+a}",1,"(Sech[x/2]*(360*x*Cosh[x/2] - 360*Sinh[x/2] - 120*Sinh[(3*x)/2] + 40*Sinh[(5*x)/2] - 5*Sinh[(7*x)/2] + 3*Sinh[(9*x)/2]))/(192*a)","A",1
69,1,53,54,0.0771902,"\int \frac{\cosh ^3(x)}{a+a \text{sech}(x)} \, dx","Integrate[Cosh[x]^3/(a + a*Sech[x]),x]","\frac{\text{sech}\left(\frac{x}{2}\right) \left(45 \sinh \left(\frac{x}{2}\right)+18 \sinh \left(\frac{3 x}{2}\right)-2 \sinh \left(\frac{5 x}{2}\right)+\sinh \left(\frac{7 x}{2}\right)-36 x \cosh \left(\frac{x}{2}\right)\right)}{24 a}","-\frac{3 x}{2 a}+\frac{4 \sinh ^3(x)}{3 a}+\frac{4 \sinh (x)}{a}-\frac{3 \sinh (x) \cosh (x)}{2 a}-\frac{\sinh (x) \cosh ^2(x)}{a \text{sech}(x)+a}",1,"(Sech[x/2]*(-36*x*Cosh[x/2] + 45*Sinh[x/2] + 18*Sinh[(3*x)/2] - 2*Sinh[(5*x)/2] + Sinh[(7*x)/2]))/(24*a)","A",1
70,1,45,41,0.0513004,"\int \frac{\cosh ^2(x)}{a+a \text{sech}(x)} \, dx","Integrate[Cosh[x]^2/(a + a*Sech[x]),x]","\frac{\text{sech}\left(\frac{x}{2}\right) \left(-12 \sinh \left(\frac{x}{2}\right)-3 \sinh \left(\frac{3 x}{2}\right)+\sinh \left(\frac{5 x}{2}\right)+12 x \cosh \left(\frac{x}{2}\right)\right)}{8 a}","\frac{3 x}{2 a}-\frac{2 \sinh (x)}{a}+\frac{3 \sinh (x) \cosh (x)}{2 a}-\frac{\sinh (x) \cosh (x)}{a \text{sech}(x)+a}",1,"(Sech[x/2]*(12*x*Cosh[x/2] - 12*Sinh[x/2] - 3*Sinh[(3*x)/2] + Sinh[(5*x)/2]))/(8*a)","A",1
71,1,32,26,0.0633555,"\int \frac{\cosh (x)}{a+a \text{sech}(x)} \, dx","Integrate[Cosh[x]/(a + a*Sech[x]),x]","\frac{-2 x+3 \tanh \left(\frac{x}{2}\right)+\sinh \left(\frac{3 x}{2}\right) \text{sech}\left(\frac{x}{2}\right)}{2 a}","-\frac{x}{a}+\frac{2 \sinh (x)}{a}-\frac{\sinh (x)}{a \text{sech}(x)+a}",1,"(-2*x + Sech[x/2]*Sinh[(3*x)/2] + 3*Tanh[x/2])/(2*a)","A",1
72,1,10,11,0.0077444,"\int \frac{\text{sech}(x)}{a+a \text{sech}(x)} \, dx","Integrate[Sech[x]/(a + a*Sech[x]),x]","\frac{\tanh \left(\frac{x}{2}\right)}{a}","\frac{\tanh (x)}{a \text{sech}(x)+a}",1,"Tanh[x/2]/a","A",1
73,1,22,20,0.0293207,"\int \frac{\text{sech}^2(x)}{a+a \text{sech}(x)} \, dx","Integrate[Sech[x]^2/(a + a*Sech[x]),x]","\frac{2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)-\tanh \left(\frac{x}{2}\right)}{a}","\frac{\tan ^{-1}(\sinh (x))}{a}-\frac{\tanh (x)}{a \text{sech}(x)+a}",1,"(2*ArcTan[Tanh[x/2]] - Tanh[x/2])/a","A",1
74,1,45,26,0.085546,"\int \frac{\text{sech}^3(x)}{a+a \text{sech}(x)} \, dx","Integrate[Sech[x]^3/(a + a*Sech[x]),x]","\frac{2 \cosh \left(\frac{x}{2}\right) \text{sech}(x) \left(\sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right) \left(\tanh (x)-2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)\right)\right)}{a (\text{sech}(x)+1)}","\frac{\tanh (x)}{a}-\frac{\tan ^{-1}(\sinh (x))}{a}+\frac{\tanh (x)}{a \text{sech}(x)+a}",1,"(2*Cosh[x/2]*Sech[x]*(Sinh[x/2] + Cosh[x/2]*(-2*ArcTan[Tanh[x/2]] + Tanh[x])))/(a*(1 + Sech[x]))","A",1
75,1,51,45,0.087318,"\int \frac{\text{sech}^4(x)}{a+a \text{sech}(x)} \, dx","Integrate[Sech[x]^4/(a + a*Sech[x]),x]","\frac{\cosh \left(\frac{x}{2}\right) \text{sech}(x) \left(\cosh \left(\frac{x}{2}\right) \left(6 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+\tanh (x) (\text{sech}(x)-2)\right)-2 \sinh \left(\frac{x}{2}\right)\right)}{a (\text{sech}(x)+1)}","-\frac{2 \tanh (x)}{a}+\frac{3 \tan ^{-1}(\sinh (x))}{2 a}-\frac{\tanh (x) \text{sech}^2(x)}{a \text{sech}(x)+a}+\frac{3 \tanh (x) \text{sech}(x)}{2 a}",1,"(Cosh[x/2]*Sech[x]*(-2*Sinh[x/2] + Cosh[x/2]*(6*ArcTan[Tanh[x/2]] + (-2 + Sech[x])*Tanh[x])))/(a*(1 + Sech[x]))","A",1
76,1,58,29,0.1426353,"\int \frac{1}{a+a \text{sech}(c+d x)} \, dx","Integrate[(a + a*Sech[c + d*x])^(-1),x]","\frac{\text{sech}\left(\frac{c}{2}\right) \text{sech}\left(\frac{1}{2} (c+d x)\right) \left(d x \cosh \left(c+\frac{d x}{2}\right)-2 \sinh \left(\frac{d x}{2}\right)+d x \cosh \left(\frac{d x}{2}\right)\right)}{2 a d}","\frac{x}{a}-\frac{\tanh (c+d x)}{d (a \text{sech}(c+d x)+a)}",1,"(Sech[c/2]*Sech[(c + d*x)/2]*(d*x*Cosh[(d*x)/2] + d*x*Cosh[c + (d*x)/2] - 2*Sinh[(d*x)/2]))/(2*a*d)","A",1
77,1,59,30,0.1459877,"\int \frac{1}{a-a \text{sech}(c+d x)} \, dx","Integrate[(a - a*Sech[c + d*x])^(-1),x]","\frac{\text{csch}\left(\frac{c}{2}\right) \text{csch}\left(\frac{1}{2} (c+d x)\right) \left(d x \cosh \left(c+\frac{d x}{2}\right)+2 \sinh \left(\frac{d x}{2}\right)-d x \cosh \left(\frac{d x}{2}\right)\right)}{2 a d}","\frac{x}{a}-\frac{\tanh (c+d x)}{d (a-a \text{sech}(c+d x))}",1,"(Csch[c/2]*Csch[(c + d*x)/2]*(-(d*x*Cosh[(d*x)/2]) + d*x*Cosh[c + (d*x)/2] + 2*Sinh[(d*x)/2]))/(2*a*d)","A",1
78,1,99,98,0.3378076,"\int (a+a \text{sech}(c+d x))^{5/2} \, dx","Integrate[(a + a*Sech[c + d*x])^(5/2),x]","\frac{a^2 \text{sech}\left(\frac{1}{2} (c+d x)\right) \text{sech}(c+d x) \sqrt{a (\text{sech}(c+d x)+1)} \left(-6 \sinh \left(\frac{1}{2} (c+d x)\right)+8 \sinh \left(\frac{3}{2} (c+d x)\right)+3 \sqrt{2} \sinh ^{-1}\left(\sqrt{2} \sinh \left(\frac{1}{2} (c+d x)\right)\right) \cosh ^{\frac{3}{2}}(c+d x)\right)}{3 d}","\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{a \text{sech}(c+d x)+a}}\right)}{d}+\frac{14 a^3 \tanh (c+d x)}{3 d \sqrt{a \text{sech}(c+d x)+a}}+\frac{2 a^2 \tanh (c+d x) \sqrt{a \text{sech}(c+d x)+a}}{3 d}",1,"(a^2*Sech[(c + d*x)/2]*Sech[c + d*x]*Sqrt[a*(1 + Sech[c + d*x])]*(3*Sqrt[2]*ArcSinh[Sqrt[2]*Sinh[(c + d*x)/2]]*Cosh[c + d*x]^(3/2) - 6*Sinh[(c + d*x)/2] + 8*Sinh[(3*(c + d*x))/2]))/(3*d)","A",1
79,1,75,66,0.2003144,"\int (a+a \text{sech}(c+d x))^{3/2} \, dx","Integrate[(a + a*Sech[c + d*x])^(3/2),x]","\frac{a \text{sech}\left(\frac{1}{2} (c+d x)\right) \sqrt{a (\text{sech}(c+d x)+1)} \left(2 \sinh \left(\frac{1}{2} (c+d x)\right)+\sqrt{2} \sinh ^{-1}\left(\sqrt{2} \sinh \left(\frac{1}{2} (c+d x)\right)\right) \sqrt{\cosh (c+d x)}\right)}{d}","\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{a \text{sech}(c+d x)+a}}\right)}{d}+\frac{2 a^2 \tanh (c+d x)}{d \sqrt{a \text{sech}(c+d x)+a}}",1,"(a*Sech[(c + d*x)/2]*Sqrt[a*(1 + Sech[c + d*x])]*(Sqrt[2]*ArcSinh[Sqrt[2]*Sinh[(c + d*x)/2]]*Sqrt[Cosh[c + d*x]] + 2*Sinh[(c + d*x)/2]))/d","A",1
80,1,60,37,0.0916708,"\int \sqrt{a+a \text{sech}(c+d x)} \, dx","Integrate[Sqrt[a + a*Sech[c + d*x]],x]","\frac{\sqrt{2} \sinh ^{-1}\left(\sqrt{2} \sinh \left(\frac{1}{2} (c+d x)\right)\right) \sqrt{\cosh (c+d x)} \text{sech}\left(\frac{1}{2} (c+d x)\right) \sqrt{a (\text{sech}(c+d x)+1)}}{d}","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{a \text{sech}(c+d x)+a}}\right)}{d}",1,"(Sqrt[2]*ArcSinh[Sqrt[2]*Sinh[(c + d*x)/2]]*Sqrt[Cosh[c + d*x]]*Sech[(c + d*x)/2]*Sqrt[a*(1 + Sech[c + d*x])])/d","A",1
81,1,118,85,1.2056836,"\int \frac{1}{\sqrt{a+a \text{sech}(c+d x)}} \, dx","Integrate[1/Sqrt[a + a*Sech[c + d*x]],x]","\frac{\left(e^{c+d x}+1\right) \left(\sqrt{2} \sinh ^{-1}\left(e^{c+d x}\right)-2 \tanh ^{-1}\left(\frac{e^{c+d x}-1}{\sqrt{2} \sqrt{e^{2 (c+d x)}+1}}\right)-\sqrt{2} \tanh ^{-1}\left(\sqrt{e^{2 (c+d x)}+1}\right)\right)}{\sqrt{2} d \sqrt{e^{2 (c+d x)}+1} \sqrt{a (\text{sech}(c+d x)+1)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{a \text{sech}(c+d x)+a}}\right)}{\sqrt{a} d}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{2} \sqrt{a \text{sech}(c+d x)+a}}\right)}{\sqrt{a} d}",1,"((1 + E^(c + d*x))*(Sqrt[2]*ArcSinh[E^(c + d*x)] - 2*ArcTanh[(-1 + E^(c + d*x))/(Sqrt[2]*Sqrt[1 + E^(2*(c + d*x))])] - Sqrt[2]*ArcTanh[Sqrt[1 + E^(2*(c + d*x))]]))/(Sqrt[2]*d*Sqrt[1 + E^(2*(c + d*x))]*Sqrt[a*(1 + Sech[c + d*x])])","A",1
82,1,177,114,4.7736224,"\int \frac{1}{(a+a \text{sech}(c+d x))^{3/2}} \, dx","Integrate[(a + a*Sech[c + d*x])^(-3/2),x]","\frac{\cosh ^2\left(\frac{1}{2} (c+d x)\right) \text{sech}(c+d x) \left(4 \left(e^{c+d x}+1\right) \sinh ^{-1}\left(e^{c+d x}\right)+5 \sqrt{2} \left(e^{c+d x}+1\right) \tanh ^{-1}\left(\frac{1-e^{c+d x}}{\sqrt{2} \sqrt{e^{2 (c+d x)}+1}}\right)-4 \left(e^{c+d x}+1\right) \tanh ^{-1}\left(\sqrt{e^{2 (c+d x)}+1}\right)-2 \sqrt{e^{2 (c+d x)}+1} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{2 d \sqrt{e^{2 (c+d x)}+1} (a (\text{sech}(c+d x)+1))^{3/2}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{a \text{sech}(c+d x)+a}}\right)}{a^{3/2} d}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{2} \sqrt{a \text{sech}(c+d x)+a}}\right)}{2 \sqrt{2} a^{3/2} d}-\frac{\tanh (c+d x)}{2 d (a \text{sech}(c+d x)+a)^{3/2}}",1,"(Cosh[(c + d*x)/2]^2*Sech[c + d*x]*(4*(1 + E^(c + d*x))*ArcSinh[E^(c + d*x)] + 5*Sqrt[2]*(1 + E^(c + d*x))*ArcTanh[(1 - E^(c + d*x))/(Sqrt[2]*Sqrt[1 + E^(2*(c + d*x))])] - 4*(1 + E^(c + d*x))*ArcTanh[Sqrt[1 + E^(2*(c + d*x))]] - 2*Sqrt[1 + E^(2*(c + d*x))]*Tanh[(c + d*x)/2]))/(2*d*Sqrt[1 + E^(2*(c + d*x))]*(a*(1 + Sech[c + d*x]))^(3/2))","A",1
83,1,70,38,2.3826538,"\int \sqrt{a-a \text{sech}(c+d x)} \, dx","Integrate[Sqrt[a - a*Sech[c + d*x]],x]","\frac{\sqrt{e^{2 (c+d x)}+1} \sqrt{a-a \text{sech}(c+d x)} \left(\sinh ^{-1}\left(e^{c+d x}\right)+\tanh ^{-1}\left(\sqrt{e^{2 (c+d x)}+1}\right)\right)}{d \left(e^{c+d x}-1\right)}","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{a-a \text{sech}(c+d x)}}\right)}{d}",1,"(Sqrt[1 + E^(2*(c + d*x))]*(ArcSinh[E^(c + d*x)] + ArcTanh[Sqrt[1 + E^(2*(c + d*x))]])*Sqrt[a - a*Sech[c + d*x]])/(d*(-1 + E^(c + d*x)))","A",1
84,1,118,87,2.2323027,"\int \frac{1}{\sqrt{a-a \text{sech}(c+d x)}} \, dx","Integrate[1/Sqrt[a - a*Sech[c + d*x]],x]","\frac{\left(e^{c+d x}-1\right) \left(\sqrt{2} \sinh ^{-1}\left(e^{c+d x}\right)-2 \tanh ^{-1}\left(\frac{e^{c+d x}+1}{\sqrt{2} \sqrt{e^{2 (c+d x)}+1}}\right)+\sqrt{2} \tanh ^{-1}\left(\sqrt{e^{2 (c+d x)}+1}\right)\right)}{\sqrt{2} d \sqrt{e^{2 (c+d x)}+1} \sqrt{a-a \text{sech}(c+d x)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{a-a \text{sech}(c+d x)}}\right)}{\sqrt{a} d}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{2} \sqrt{a-a \text{sech}(c+d x)}}\right)}{\sqrt{a} d}",1,"((-1 + E^(c + d*x))*(Sqrt[2]*ArcSinh[E^(c + d*x)] - 2*ArcTanh[(1 + E^(c + d*x))/(Sqrt[2]*Sqrt[1 + E^(2*(c + d*x))])] + Sqrt[2]*ArcTanh[Sqrt[1 + E^(2*(c + d*x))]]))/(Sqrt[2]*d*Sqrt[1 + E^(2*(c + d*x))]*Sqrt[a - a*Sech[c + d*x]])","A",1
85,1,39,19,0.0422947,"\int \sqrt{3+3 \text{sech}(x)} \, dx","Integrate[Sqrt[3 + 3*Sech[x]],x]","\sqrt{6} \sinh ^{-1}\left(\sqrt{2} \sinh \left(\frac{x}{2}\right)\right) \sqrt{\cosh (x)} \text{sech}\left(\frac{x}{2}\right) \sqrt{\text{sech}(x)+1}","2 \sqrt{3} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{\text{sech}(x)+1}}\right)",1,"Sqrt[6]*ArcSinh[Sqrt[2]*Sinh[x/2]]*Sqrt[Cosh[x]]*Sech[x/2]*Sqrt[1 + Sech[x]]","B",1
86,1,51,21,0.5652628,"\int \sqrt{3-3 \text{sech}(x)} \, dx","Integrate[Sqrt[3 - 3*Sech[x]],x]","\frac{\sqrt{3} \sqrt{e^{2 x}+1} \sqrt{1-\text{sech}(x)} \left(\sinh ^{-1}\left(e^x\right)+\tanh ^{-1}\left(\sqrt{e^{2 x}+1}\right)\right)}{e^x-1}","2 \sqrt{3} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-\text{sech}(x)}}\right)",1,"(Sqrt[3]*Sqrt[1 + E^(2*x)]*(ArcSinh[E^x] + ArcTanh[Sqrt[1 + E^(2*x)]])*Sqrt[1 - Sech[x]])/(-1 + E^x)","B",1
87,1,78,107,0.2534268,"\int (a+b \text{sech}(c+d x))^4 \, dx","Integrate[(a + b*Sech[c + d*x])^4,x]","\frac{3 a^4 d x+6 a b \left(2 a^2+b^2\right) \tan ^{-1}(\sinh (c+d x))+3 b^2 \tanh (c+d x) \left(6 a^2+2 a b \text{sech}(c+d x)+b^2\right)-b^4 \tanh ^3(c+d x)}{3 d}","a^4 x+\frac{b^2 \left(17 a^2+2 b^2\right) \tanh (c+d x)}{3 d}+\frac{2 a b \left(2 a^2+b^2\right) \tan ^{-1}(\sinh (c+d x))}{d}+\frac{4 a b^3 \tanh (c+d x) \text{sech}(c+d x)}{3 d}+\frac{b^2 \tanh (c+d x) (a+b \text{sech}(c+d x))^2}{3 d}",1,"(3*a^4*d*x + 6*a*b*(2*a^2 + b^2)*ArcTan[Sinh[c + d*x]] + 3*b^2*(6*a^2 + b^2 + 2*a*b*Sech[c + d*x])*Tanh[c + d*x] - b^4*Tanh[c + d*x]^3)/(3*d)","A",1
88,1,55,73,0.134944,"\int (a+b \text{sech}(c+d x))^3 \, dx","Integrate[(a + b*Sech[c + d*x])^3,x]","\frac{2 a^3 d x+b \left(6 a^2+b^2\right) \tan ^{-1}(\sinh (c+d x))+b^2 \tanh (c+d x) (6 a+b \text{sech}(c+d x))}{2 d}","a^3 x+\frac{b \left(6 a^2+b^2\right) \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{5 a b^2 \tanh (c+d x)}{2 d}+\frac{b^2 \tanh (c+d x) (a+b \text{sech}(c+d x))}{2 d}",1,"(2*a^3*d*x + b*(6*a^2 + b^2)*ArcTan[Sinh[c + d*x]] + b^2*(6*a + b*Sech[c + d*x])*Tanh[c + d*x])/(2*d)","A",1
89,1,32,33,0.0659189,"\int (a+b \text{sech}(c+d x))^2 \, dx","Integrate[(a + b*Sech[c + d*x])^2,x]","\frac{a \left(a d x+2 b \tan ^{-1}(\sinh (c+d x))\right)+b^2 \tanh (c+d x)}{d}","a^2 x+\frac{2 a b \tan ^{-1}(\sinh (c+d x))}{d}+\frac{b^2 \tanh (c+d x)}{d}",1,"(a*(a*d*x + 2*b*ArcTan[Sinh[c + d*x]]) + b^2*Tanh[c + d*x])/d","A",1
90,1,16,16,0.001937,"\int (a+b \text{sech}(c+d x)) \, dx","Integrate[a + b*Sech[c + d*x],x]","a x+\frac{b \tan ^{-1}(\sinh (c+d x))}{d}","a x+\frac{b \tan ^{-1}(\sinh (c+d x))}{d}",1,"a*x + (b*ArcTan[Sinh[c + d*x]])/d","A",1
91,1,60,59,0.1109477,"\int \frac{1}{a+b \text{sech}(c+d x)} \, dx","Integrate[(a + b*Sech[c + d*x])^(-1),x]","\frac{\frac{2 b \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2-b^2}}\right)}{d \sqrt{a^2-b^2}}+\frac{c}{d}+x}{a}","\frac{x}{a}-\frac{2 b \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a+b}}\right)}{a d \sqrt{a-b} \sqrt{a+b}}",1,"(c/d + x + (2*b*ArcTan[((-a + b)*Tanh[(c + d*x)/2])/Sqrt[a^2 - b^2]])/(Sqrt[a^2 - b^2]*d))/a","A",1
92,1,203,109,0.4110082,"\int \frac{1}{(a+b \text{sech}(c+d x))^2} \, dx","Integrate[(a + b*Sech[c + d*x])^(-2),x]","\frac{b \left(\left(a^2-b^2\right)^{3/2} (c+d x)+a b \sqrt{a^2-b^2} \sinh (c+d x)+\left(4 a^2 b-2 b^3\right) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2-b^2}}\right)\right)+a \cosh (c+d x) \left(\left(a^2-b^2\right)^{3/2} (c+d x)+\left(4 a^2 b-2 b^3\right) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2-b^2}}\right)\right)}{a^2 d (a-b) (a+b) \sqrt{a^2-b^2} (a \cosh (c+d x)+b)}","-\frac{2 b \left(2 a^2-b^2\right) \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a+b}}\right)}{a^2 d (a-b)^{3/2} (a+b)^{3/2}}+\frac{b^2 \tanh (c+d x)}{a d \left(a^2-b^2\right) (a+b \text{sech}(c+d x))}+\frac{x}{a^2}",1,"(a*((a^2 - b^2)^(3/2)*(c + d*x) + (4*a^2*b - 2*b^3)*ArcTan[((-a + b)*Tanh[(c + d*x)/2])/Sqrt[a^2 - b^2]])*Cosh[c + d*x] + b*((a^2 - b^2)^(3/2)*(c + d*x) + (4*a^2*b - 2*b^3)*ArcTan[((-a + b)*Tanh[(c + d*x)/2])/Sqrt[a^2 - b^2]] + a*b*Sqrt[a^2 - b^2]*Sinh[c + d*x]))/(a^2*(a - b)*(a + b)*Sqrt[a^2 - b^2]*d*(b + a*Cosh[c + d*x]))","A",1
93,1,205,173,0.7351831,"\int \frac{1}{(a+b \text{sech}(c+d x))^3} \, dx","Integrate[(a + b*Sech[c + d*x])^(-3),x]","\frac{\text{sech}^3(c+d x) (a \cosh (c+d x)+b) \left(\frac{3 a b^2 \left(2 a^2-b^2\right) \sinh (c+d x) (a \cosh (c+d x)+b)}{(a-b)^2 (a+b)^2}+\frac{2 b \left(6 a^4-5 a^2 b^2+2 b^4\right) (a \cosh (c+d x)+b)^2 \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{5/2}}+\frac{a b^3 \sinh (c+d x)}{(b-a) (a+b)}+2 (c+d x) (a \cosh (c+d x)+b)^2\right)}{2 a^3 d (a+b \text{sech}(c+d x))^3}","\frac{x}{a^3}+\frac{b^2 \left(5 a^2-2 b^2\right) \tanh (c+d x)}{2 a^2 d \left(a^2-b^2\right)^2 (a+b \text{sech}(c+d x))}+\frac{b^2 \tanh (c+d x)}{2 a d \left(a^2-b^2\right) (a+b \text{sech}(c+d x))^2}-\frac{b \left(6 a^4-5 a^2 b^2+2 b^4\right) \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a+b}}\right)}{a^3 d (a-b)^{5/2} (a+b)^{5/2}}",1,"((b + a*Cosh[c + d*x])*Sech[c + d*x]^3*(2*(c + d*x)*(b + a*Cosh[c + d*x])^2 + (2*b*(6*a^4 - 5*a^2*b^2 + 2*b^4)*ArcTan[((-a + b)*Tanh[(c + d*x)/2])/Sqrt[a^2 - b^2]]*(b + a*Cosh[c + d*x])^2)/(a^2 - b^2)^(5/2) + (a*b^3*Sinh[c + d*x])/((-a + b)*(a + b)) + (3*a*b^2*(2*a^2 - b^2)*(b + a*Cosh[c + d*x])*Sinh[c + d*x])/((a - b)^2*(a + b)^2)))/(2*a^3*d*(a + b*Sech[c + d*x])^3)","A",1
94,1,168,106,2.4684004,"\int \frac{1}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Integrate[1/Sqrt[a + b*Sech[c + d*x]],x]","\frac{2 b \tanh \left(\frac{1}{2} (c+d x)\right) \sqrt{a \cosh (c+d x)+b} \sqrt{\frac{b (\text{sech}(c+d x)+1)}{b-a}} \Pi \left(\frac{a+b}{a};\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a+b} \sqrt{a \cosh (c+d x)}}\right)|\frac{a+b}{a-b}\right)}{\sqrt{a} d \sqrt{a+b} \sqrt{a \cosh (c+d x)} \sqrt{-\frac{b (\text{sech}(c+d x)-1)}{a+b}} \sqrt{a+b \text{sech}(c+d x)}}","\frac{2 \sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} \Pi \left(\frac{a+b}{a};\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{a d}",1,"(2*b*Sqrt[b + a*Cosh[c + d*x]]*EllipticPi[(a + b)/a, ArcSin[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a + b]*Sqrt[a*Cosh[c + d*x]])], (a + b)/(a - b)]*Sqrt[(b*(1 + Sech[c + d*x]))/(-a + b)]*Tanh[(c + d*x)/2])/(Sqrt[a]*Sqrt[a + b]*d*Sqrt[a*Cosh[c + d*x]]*Sqrt[-((b*(-1 + Sech[c + d*x]))/(a + b))]*Sqrt[a + b*Sech[c + d*x]])","A",1
95,1,126,146,0.2831017,"\int \frac{\cosh ^4(x)}{a+b \text{sech}(x)} \, dx","Integrate[Cosh[x]^4/(a + b*Sech[x]),x]","\frac{3 a^4 \sinh (4 x)-8 a^3 b \sinh (3 x)-24 a b \left(3 a^2+4 b^2\right) \sinh (x)+24 a^2 \left(a^2+b^2\right) \sinh (2 x)+\frac{192 b^5 \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+12 x \left(3 a^4+4 a^2 b^2+8 b^4\right)}{96 a^5}","-\frac{2 b^5 \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a^5 \sqrt{a-b} \sqrt{a+b}}-\frac{b \sinh (x) \cosh ^2(x)}{3 a^2}-\frac{b \left(2 a^2+3 b^2\right) \sinh (x)}{3 a^4}+\frac{\left(3 a^2+4 b^2\right) \sinh (x) \cosh (x)}{8 a^3}+\frac{x \left(3 a^4+4 a^2 b^2+8 b^4\right)}{8 a^5}+\frac{\sinh (x) \cosh ^3(x)}{4 a}",1,"(12*(3*a^4 + 4*a^2*b^2 + 8*b^4)*x + (192*b^5*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/Sqrt[a^2 - b^2] - 24*a*b*(3*a^2 + 4*b^2)*Sinh[x] + 24*a^2*(a^2 + b^2)*Sinh[2*x] - 8*a^3*b*Sinh[3*x] + 3*a^4*Sinh[4*x])/(96*a^5)","A",1
96,1,99,112,0.1665088,"\int \frac{\cosh ^3(x)}{a+b \text{sech}(x)} \, dx","Integrate[Cosh[x]^3/(a + b*Sech[x]),x]","\frac{a^3 \sinh (3 x)-6 b x \left(a^2+2 b^2\right)+3 a \left(3 a^2+4 b^2\right) \sinh (x)-\frac{24 b^4 \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}-3 a^2 b \sinh (2 x)}{12 a^4}","\frac{2 b^4 \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a^4 \sqrt{a-b} \sqrt{a+b}}-\frac{b \sinh (x) \cosh (x)}{2 a^2}-\frac{b x \left(a^2+2 b^2\right)}{2 a^4}+\frac{\left(2 a^2+3 b^2\right) \sinh (x)}{3 a^3}+\frac{\sinh (x) \cosh ^2(x)}{3 a}",1,"(-6*b*(a^2 + 2*b^2)*x - (24*b^4*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/Sqrt[a^2 - b^2] + 3*a*(3*a^2 + 4*b^2)*Sinh[x] - 3*a^2*b*Sinh[2*x] + a^3*Sinh[3*x])/(12*a^4)","A",1
97,1,78,85,0.128819,"\int \frac{\cosh ^2(x)}{a+b \text{sech}(x)} \, dx","Integrate[Cosh[x]^2/(a + b*Sech[x]),x]","\frac{\frac{8 b^3 \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+2 a^2 x+a^2 \sinh (2 x)-4 a b \sinh (x)+4 b^2 x}{4 a^3}","-\frac{2 b^3 \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a^3 \sqrt{a-b} \sqrt{a+b}}-\frac{b \sinh (x)}{a^2}+\frac{x \left(a^2+2 b^2\right)}{2 a^3}+\frac{\sinh (x) \cosh (x)}{2 a}",1,"(2*a^2*x + 4*b^2*x + (8*b^3*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/Sqrt[a^2 - b^2] - 4*a*b*Sinh[x] + a^2*Sinh[2*x])/(4*a^3)","A",1
98,1,57,62,0.1184993,"\int \frac{\cosh (x)}{a+b \text{sech}(x)} \, dx","Integrate[Cosh[x]/(a + b*Sech[x]),x]","\frac{b \left(-\frac{2 b \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}-x\right)+a \sinh (x)}{a^2}","\frac{2 b^2 \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a^2 \sqrt{a-b} \sqrt{a+b}}-\frac{b x}{a^2}+\frac{\sinh (x)}{a}",1,"(b*(-x - (2*b*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/Sqrt[a^2 - b^2]) + a*Sinh[x])/a^2","A",1
99,1,41,42,0.0260168,"\int \frac{\text{sech}(x)}{a+b \text{sech}(x)} \, dx","Integrate[Sech[x]/(a + b*Sech[x]),x]","-\frac{2 \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{\sqrt{a-b} \sqrt{a+b}}",1,"(-2*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/Sqrt[a^2 - b^2]","A",1
100,1,54,54,0.0530698,"\int \frac{\text{sech}^2(x)}{a+b \text{sech}(x)} \, dx","Integrate[Sech[x]^2/(a + b*Sech[x]),x]","\frac{2 \left(\frac{a \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+\tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)\right)}{b}","\frac{\tan ^{-1}(\sinh (x))}{b}-\frac{2 a \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b \sqrt{a-b} \sqrt{a+b}}",1,"(2*(ArcTan[Tanh[x/2]] + (a*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/Sqrt[a^2 - b^2]))/b","A",1
101,1,63,64,0.108677,"\int \frac{\text{sech}^3(x)}{a+b \text{sech}(x)} \, dx","Integrate[Sech[x]^3/(a + b*Sech[x]),x]","\frac{-\frac{2 a^2 \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}-2 a \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+b \tanh (x)}{b^2}","\frac{2 a^2 \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b^2 \sqrt{a-b} \sqrt{a+b}}-\frac{a \tan ^{-1}(\sinh (x))}{b^2}+\frac{\tanh (x)}{b}",1,"(-2*a*ArcTan[Tanh[x/2]] - (2*a^2*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/Sqrt[a^2 - b^2] + b*Tanh[x])/b^2","A",1
102,1,82,87,0.225829,"\int \frac{\text{sech}^4(x)}{a+b \text{sech}(x)} \, dx","Integrate[Sech[x]^4/(a + b*Sech[x]),x]","\frac{2 \left(2 a^2+b^2\right) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+\frac{4 a^3 \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+b \tanh (x) (b \text{sech}(x)-2 a)}{2 b^3}","-\frac{2 a^3 \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b^3 \sqrt{a-b} \sqrt{a+b}}+\frac{\left(2 a^2+b^2\right) \tan ^{-1}(\sinh (x))}{2 b^3}-\frac{a \tanh (x)}{b^2}+\frac{\tanh (x) \text{sech}(x)}{2 b}",1,"(2*(2*a^2 + b^2)*ArcTan[Tanh[x/2]] + (4*a^3*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/Sqrt[a^2 - b^2] + b*(-2*a + b*Sech[x])*Tanh[x])/(2*b^3)","A",1
103,1,60,48,0.1211498,"\int \frac{\tanh ^6(x)}{a+a \text{sech}(x)} \, dx","Integrate[Tanh[x]^6/(a + a*Sech[x]),x]","\frac{\cosh ^2\left(\frac{x}{2}\right) \text{sech}(x) \left(6 \left(4 x-3 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)\right)+\tanh (x) \left(-6 \text{sech}^3(x)+8 \text{sech}^2(x)+15 \text{sech}(x)-32\right)\right)}{12 a (\text{sech}(x)+1)}","\frac{x}{a}-\frac{3 \tan ^{-1}(\sinh (x))}{8 a}-\frac{\tanh ^3(x) (4-3 \text{sech}(x))}{12 a}-\frac{\tanh (x) (8-3 \text{sech}(x))}{8 a}",1,"(Cosh[x/2]^2*Sech[x]*(6*(4*x - 3*ArcTan[Tanh[x/2]]) + (-32 + 15*Sech[x] + 8*Sech[x]^2 - 6*Sech[x]^3)*Tanh[x]))/(12*a*(1 + Sech[x]))","A",1
104,1,38,36,0.0736192,"\int \frac{\tanh ^5(x)}{a+a \text{sech}(x)} \, dx","Integrate[Tanh[x]^5/(a + a*Sech[x]),x]","\frac{\text{sech}^3(x) (6 \cosh (2 x)+3 \cosh (3 x) \log (\cosh (x))+\cosh (x) (9 \log (\cosh (x))+6)+2)}{12 a}","-\frac{\text{sech}^3(x)}{3 a}+\frac{\text{sech}^2(x)}{2 a}+\frac{\text{sech}(x)}{a}+\frac{\log (\cosh (x))}{a}",1,"((2 + 6*Cosh[2*x] + 3*Cosh[3*x]*Log[Cosh[x]] + Cosh[x]*(6 + 9*Log[Cosh[x]]))*Sech[x]^3)/(12*a)","A",1
105,1,41,31,0.0591169,"\int \frac{\tanh ^4(x)}{a+a \text{sech}(x)} \, dx","Integrate[Tanh[x]^4/(a + a*Sech[x]),x]","\frac{\cosh ^2\left(\frac{x}{2}\right) \text{sech}(x) \left(2 \left(x-\tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)\right)+\tanh (x) (\text{sech}(x)-2)\right)}{a (\text{sech}(x)+1)}","\frac{x}{a}-\frac{\tan ^{-1}(\sinh (x))}{2 a}-\frac{\tanh (x) (2-\text{sech}(x))}{2 a}",1,"(Cosh[x/2]^2*Sech[x]*(2*(x - ArcTan[Tanh[x/2]]) + (-2 + Sech[x])*Tanh[x]))/(a*(1 + Sech[x]))","A",1
106,1,10,14,0.0362059,"\int \frac{\tanh ^3(x)}{a+a \text{sech}(x)} \, dx","Integrate[Tanh[x]^3/(a + a*Sech[x]),x]","\frac{\text{sech}(x)+\log (\cosh (x))}{a}","\frac{\text{sech}(x)}{a}+\frac{\log (\cosh (x))}{a}",1,"(Log[Cosh[x]] + Sech[x])/a","A",1
107,1,15,14,0.0301201,"\int \frac{\tanh ^2(x)}{a+a \text{sech}(x)} \, dx","Integrate[Tanh[x]^2/(a + a*Sech[x]),x]","\frac{x-2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)}{a}","\frac{x}{a}-\frac{\tan ^{-1}(\sinh (x))}{a}",1,"(x - 2*ArcTan[Tanh[x/2]])/a","A",1
108,1,12,9,0.0072237,"\int \frac{\tanh (x)}{a+a \text{sech}(x)} \, dx","Integrate[Tanh[x]/(a + a*Sech[x]),x]","\frac{2 \log \left(\cosh \left(\frac{x}{2}\right)\right)}{a}","\frac{\log (\cosh (x)+1)}{a}",1,"(2*Log[Cosh[x/2]])/a","A",1
109,1,44,40,0.0527056,"\int \frac{\coth (x)}{a+a \text{sech}(x)} \, dx","Integrate[Coth[x]/(a + a*Sech[x]),x]","\frac{\text{sech}(x) \left(2 \cosh ^2\left(\frac{x}{2}\right) \left(\log \left(\sinh \left(\frac{x}{2}\right)\right)+3 \log \left(\cosh \left(\frac{x}{2}\right)\right)\right)+1\right)}{2 a (\text{sech}(x)+1)}","\frac{1}{2 a (\cosh (x)+1)}+\frac{\log (1-\cosh (x))}{4 a}+\frac{3 \log (\cosh (x)+1)}{4 a}",1,"((1 + 2*Cosh[x/2]^2*(3*Log[Cosh[x/2]] + Log[Sinh[x/2]]))*Sech[x])/(2*a*(1 + Sech[x]))","A",1
110,1,33,38,0.0769895,"\int \frac{\coth ^2(x)}{a+a \text{sech}(x)} \, dx","Integrate[Coth[x]^2/(a + a*Sech[x]),x]","\frac{6 x-4 \tanh (x)-4 \coth (x)-2 \text{csch}(x)+6 x \text{sech}(x)}{6 a \text{sech}(x)+6 a}","\frac{x}{a}-\frac{\coth ^3(x) (1-\text{sech}(x))}{3 a}-\frac{\coth (x) (3-2 \text{sech}(x))}{3 a}",1,"(6*x - 4*Coth[x] - 2*Csch[x] + 6*x*Sech[x] - 4*Tanh[x])/(6*a + 6*a*Sech[x])","A",1
111,1,66,68,0.1859432,"\int \frac{\coth ^3(x)}{a+a \text{sech}(x)} \, dx","Integrate[Coth[x]^3/(a + a*Sech[x]),x]","\frac{\text{sech}(x) \left(-2 \coth ^2\left(\frac{x}{2}\right)-\text{sech}^2\left(\frac{x}{2}\right)+4 \cosh ^2\left(\frac{x}{2}\right) \left(5 \log \left(\sinh \left(\frac{x}{2}\right)\right)+11 \log \left(\cosh \left(\frac{x}{2}\right)\right)\right)+12\right)}{16 a (\text{sech}(x)+1)}","\frac{1}{8 a (1-\cosh (x))}+\frac{3}{4 a (\cosh (x)+1)}-\frac{1}{8 a (\cosh (x)+1)^2}+\frac{5 \log (1-\cosh (x))}{16 a}+\frac{11 \log (\cosh (x)+1)}{16 a}",1,"((12 - 2*Coth[x/2]^2 + 4*Cosh[x/2]^2*(11*Log[Cosh[x/2]] + 5*Log[Sinh[x/2]]) - Sech[x/2]^2)*Sech[x])/(16*a*(1 + Sech[x]))","A",1
112,1,69,55,0.1046401,"\int \frac{\coth ^4(x)}{a+a \text{sech}(x)} \, dx","Integrate[Coth[x]^4/(a + a*Sech[x]),x]","\frac{\text{csch}^3(x) \text{sech}(x) (-90 x \sinh (x)-30 x \sinh (2 x)+30 x \sinh (3 x)+15 x \sinh (4 x)+8 \cosh (x)+16 \cosh (2 x)-16 \cosh (3 x)-23 \cosh (4 x)-25)}{120 a (\text{sech}(x)+1)}","\frac{x}{a}-\frac{\coth ^5(x) (1-\text{sech}(x))}{5 a}-\frac{\coth ^3(x) (5-4 \text{sech}(x))}{15 a}-\frac{\coth (x) (15-8 \text{sech}(x))}{15 a}",1,"(Csch[x]^3*Sech[x]*(-25 + 8*Cosh[x] + 16*Cosh[2*x] - 16*Cosh[3*x] - 23*Cosh[4*x] - 90*x*Sinh[x] - 30*x*Sinh[2*x] + 30*x*Sinh[3*x] + 15*x*Sinh[4*x]))/(120*a*(1 + Sech[x]))","A",1
113,1,132,121,0.3362117,"\int \frac{\tanh ^7(x)}{a+b \text{sech}(x)} \, dx","Integrate[Tanh[x]^7/(a + b*Sech[x]),x]","\frac{-30 a b^2 \left(a^2-3 b^2\right) \text{sech}^2(x)-\frac{60 \left(a^2-b^2\right)^3 \log (a \cosh (x)+b)}{a}+20 b^3 \left(a^2-3 b^2\right) \text{sech}^3(x)+60 b \left(a^4-3 a^2 b^2+3 b^4\right) \text{sech}(x)+60 a \left(a^4-3 a^2 b^2+3 b^4\right) \log (\cosh (x))-15 a b^4 \text{sech}^4(x)+12 b^5 \text{sech}^5(x)}{60 b^6}","-\frac{\left(a^2-b^2\right)^3 \log (a+b \text{sech}(x))}{a b^6}-\frac{a \left(a^2-3 b^2\right) \text{sech}^2(x)}{2 b^4}+\frac{\left(a^2-3 b^2\right) \text{sech}^3(x)}{3 b^3}+\frac{\left(a^4-3 a^2 b^2+3 b^4\right) \text{sech}(x)}{b^5}-\frac{a \text{sech}^4(x)}{4 b^2}+\frac{\log (\cosh (x))}{a}+\frac{\text{sech}^5(x)}{5 b}",1,"(60*a*(a^4 - 3*a^2*b^2 + 3*b^4)*Log[Cosh[x]] - (60*(a^2 - b^2)^3*Log[b + a*Cosh[x]])/a + 60*b*(a^4 - 3*a^2*b^2 + 3*b^4)*Sech[x] - 30*a*b^2*(a^2 - 3*b^2)*Sech[x]^2 + 20*b^3*(a^2 - 3*b^2)*Sech[x]^3 - 15*a*b^4*Sech[x]^4 + 12*b^5*Sech[x]^5)/(60*b^6)","A",1
114,1,185,187,0.6159972,"\int \frac{\tanh ^6(x)}{a+b \text{sech}(x)} \, dx","Integrate[Tanh[x]^6/(a + b*Sech[x]),x]","\frac{\frac{48 \left(b^5 x \sqrt{a^2-b^2}-2 \left(a^2-b^2\right)^3 \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)\right)}{a \sqrt{a^2-b^2}}-12 \left(8 a^4-20 a^2 b^2+15 b^4\right) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+b \tanh (x) \text{sech}^3(x) \left(12 a^3 \cosh (3 x)+4 a \left(9 a^2-17 b^2\right) \cosh (x)+3 b \left(9 b^2-4 a^2\right) \cosh (2 x)-12 a^2 b-28 a b^2 \cosh (3 x)+15 b^3\right)}{48 b^5}","\frac{a \left(a^2-3 b^2\right) \tanh (x)}{b^4}-\frac{\left(a^2-3 b^2\right) \tan ^{-1}(\sinh (x))}{2 b^3}-\frac{\left(a^2-3 b^2\right) \tanh (x) \text{sech}(x)}{2 b^3}-\frac{\left(a^4-3 a^2 b^2+3 b^4\right) \tan ^{-1}(\sinh (x))}{b^5}+\frac{2 (a-b)^{5/2} (a+b)^{5/2} \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a b^5}-\frac{a \tanh ^3(x)}{3 b^2}+\frac{a \tanh (x)}{b^2}+\frac{x}{a}-\frac{3 \tan ^{-1}(\sinh (x))}{8 b}-\frac{\tanh (x) \text{sech}^3(x)}{4 b}-\frac{3 \tanh (x) \text{sech}(x)}{8 b}",1,"(-12*(8*a^4 - 20*a^2*b^2 + 15*b^4)*ArcTan[Tanh[x/2]] + (48*(b^5*Sqrt[a^2 - b^2]*x - 2*(a^2 - b^2)^3*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]]))/(a*Sqrt[a^2 - b^2]) + b*(-12*a^2*b + 15*b^3 + 4*a*(9*a^2 - 17*b^2)*Cosh[x] + 3*b*(-4*a^2 + 9*b^2)*Cosh[2*x] + 12*a^3*Cosh[3*x] - 28*a*b^2*Cosh[3*x])*Sech[x]^3*Tanh[x])/(48*b^5)","A",1
115,1,85,72,0.1850966,"\int \frac{\tanh ^5(x)}{a+b \text{sech}(x)} \, dx","Integrate[Tanh[x]^5/(a + b*Sech[x]),x]","\frac{3 a^2 b^2 \text{sech}^2(x)-6 a b \left(a^2-2 b^2\right) \text{sech}(x)-6 a^2 \left(a^2-2 b^2\right) \log (\cosh (x))+6 \left(a^2-b^2\right)^2 \log (a \cosh (x)+b)-2 a b^3 \text{sech}^3(x)}{6 a b^4}","\frac{\left(a^2-b^2\right)^2 \log (a+b \text{sech}(x))}{a b^4}-\frac{\left(a^2-2 b^2\right) \text{sech}(x)}{b^3}+\frac{a \text{sech}^2(x)}{2 b^2}+\frac{\log (\cosh (x))}{a}-\frac{\text{sech}^3(x)}{3 b}",1,"(-6*a^2*(a^2 - 2*b^2)*Log[Cosh[x]] + 6*(a^2 - b^2)^2*Log[b + a*Cosh[x]] - 6*a*b*(a^2 - 2*b^2)*Sech[x] + 3*a^2*b^2*Sech[x]^2 - 2*a*b^3*Sech[x]^3)/(6*a*b^4)","A",1
116,1,113,94,0.4192339,"\int \frac{\tanh ^4(x)}{a+b \text{sech}(x)} \, dx","Integrate[Tanh[x]^4/(a + b*Sech[x]),x]","\frac{\text{sech}^2(x) (a \cosh (x)+b) \left(2 \cosh (x) \left(a \left(2 a^2-3 b^2\right) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+2 \left(a^2-b^2\right)^{3/2} \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)+b^3 x\right)+a b (b \tanh (x)-2 a \sinh (x))\right)}{2 a b^3 (a+b \text{sech}(x))}","\frac{\left(2 a^2-3 b^2\right) \tan ^{-1}(\sinh (x))}{2 b^3}-\frac{2 (a-b)^{3/2} (a+b)^{3/2} \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a b^3}-\frac{a \tanh (x)}{b^2}+\frac{x}{a}+\frac{\tanh (x) \text{sech}(x)}{2 b}",1,"((b + a*Cosh[x])*Sech[x]^2*(2*(b^3*x + a*(2*a^2 - 3*b^2)*ArcTan[Tanh[x/2]] + 2*(a^2 - b^2)^(3/2)*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])*Cosh[x] + a*b*(-2*a*Sinh[x] + b*Tanh[x])))/(2*a*b^3*(a + b*Sech[x]))","A",1
117,1,37,35,0.0870824,"\int \frac{\tanh ^3(x)}{a+b \text{sech}(x)} \, dx","Integrate[Tanh[x]^3/(a + b*Sech[x]),x]","\frac{\left(b^2-a^2\right) \log (a \cosh (x)+b)+a^2 \log (\cosh (x))+a b \text{sech}(x)}{a b^2}","\frac{\left(1-\frac{a^2}{b^2}\right) \log (a+b \text{sech}(x))}{a}+\frac{\log (\cosh (x))}{a}+\frac{\text{sech}(x)}{b}",1,"(a^2*Log[Cosh[x]] + (-a^2 + b^2)*Log[b + a*Cosh[x]] + a*b*Sech[x])/(a*b^2)","A",1
118,1,62,62,0.0857305,"\int \frac{\tanh ^2(x)}{a+b \text{sech}(x)} \, dx","Integrate[Tanh[x]^2/(a + b*Sech[x]),x]","\frac{-2 \sqrt{a^2-b^2} \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)-2 a \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+b x}{a b}","\frac{2 \sqrt{a-b} \sqrt{a+b} \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a b}+\frac{x}{a}-\frac{\tan ^{-1}(\sinh (x))}{b}",1,"(b*x - 2*a*ArcTan[Tanh[x/2]] - 2*Sqrt[a^2 - b^2]*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/(a*b)","A",1
119,1,11,19,0.0193778,"\int \frac{\tanh (x)}{a+b \text{sech}(x)} \, dx","Integrate[Tanh[x]/(a + b*Sech[x]),x]","\frac{\log (a \cosh (x)+b)}{a}","\frac{\log (a+b \text{sech}(x))}{a}+\frac{\log (\cosh (x))}{a}",1,"Log[b + a*Cosh[x]]/a","A",1
120,1,44,66,0.0902751,"\int \frac{\coth (x)}{a+b \text{sech}(x)} \, dx","Integrate[Coth[x]/(a + b*Sech[x]),x]","-\frac{a^2 (-\log (\sinh (x)))+b^2 \log (a \cosh (x)+b)+a b \log \left(\tanh \left(\frac{x}{2}\right)\right)}{a^3-a b^2}","-\frac{b^2 \log (a+b \text{sech}(x))}{a \left(a^2-b^2\right)}+\frac{\log (1-\text{sech}(x))}{2 (a+b)}+\frac{\log (\text{sech}(x)+1)}{2 (a-b)}+\frac{\log (\cosh (x))}{a}",1,"-((b^2*Log[b + a*Cosh[x]] - a^2*Log[Sinh[x]] + a*b*Log[Tanh[x/2]])/(a^3 - a*b^2))","A",1
121,1,81,114,0.3488922,"\int \frac{\coth ^2(x)}{a+b \text{sech}(x)} \, dx","Integrate[Coth[x]^2/(a + b*Sech[x]),x]","\frac{\frac{2 b^3 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+a^2 x-a^2 \coth (x)+a b \text{csch}(x)-b^2 x}{a^3-a b^2}","-\frac{b^2 x}{a \left(a^2-b^2\right)}+\frac{a x}{a^2-b^2}-\frac{a \coth (x)}{a^2-b^2}+\frac{b \text{csch}(x)}{a^2-b^2}+\frac{2 b^3 \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a (a-b)^{3/2} (a+b)^{3/2}}",1,"(a^2*x - b^2*x + (2*b^3*ArcTan[((a - b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/Sqrt[a^2 - b^2] - a^2*Coth[x] + a*b*Csch[x])/(a^3 - a*b^2)","A",1
122,1,112,113,0.3227555,"\int \frac{\coth ^3(x)}{a+b \text{sech}(x)} \, dx","Integrate[Coth[x]^3/(a + b*Sech[x]),x]","\frac{4 a \left(2 a \left(a^2-2 b^2\right) \log (\sinh (x))+b \left(3 b^2-a^2\right) \log \left(\tanh \left(\frac{x}{2}\right)\right)\right)+8 b^4 \log (a \cosh (x)+b)-a (a-b)^2 (a+b) \text{csch}^2\left(\frac{x}{2}\right)+a (a-b) (a+b)^2 \text{sech}^2\left(\frac{x}{2}\right)}{8 a (a-b)^2 (a+b)^2}","\frac{b^4 \log (a+b \text{sech}(x))}{a \left(a^2-b^2\right)^2}-\frac{1}{4 (a+b) (1-\text{sech}(x))}-\frac{1}{4 (a-b) (\text{sech}(x)+1)}+\frac{(2 a+3 b) \log (1-\text{sech}(x))}{4 (a+b)^2}+\frac{(2 a-3 b) \log (\text{sech}(x)+1)}{4 (a-b)^2}+\frac{\log (\cosh (x))}{a}",1,"(-(a*(a - b)^2*(a + b)*Csch[x/2]^2) + 8*b^4*Log[b + a*Cosh[x]] + 4*a*(2*a*(a^2 - 2*b^2)*Log[Sinh[x]] + b*(-a^2 + 3*b^2)*Log[Tanh[x/2]]) + a*(a - b)*(a + b)^2*Sech[x/2]^2)/(8*a*(a - b)^2*(a + b)^2)","A",1
123,1,166,207,0.7778284,"\int \frac{\coth ^4(x)}{a+b \text{sech}(x)} \, dx","Integrate[Coth[x]^4/(a + b*Sech[x]),x]","\frac{\text{sech}(x) (a \cosh (x)+b) \left(\frac{48 b^5 \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{a \left(a^2-b^2\right)^{5/2}}+\frac{22 b \tanh \left(\frac{x}{2}\right)}{(a-b)^2}-\frac{16 a \tanh \left(\frac{x}{2}\right)}{(a-b)^2}-\frac{2 (8 a+11 b) \coth \left(\frac{x}{2}\right)}{(a+b)^2}-\frac{\sinh (x) \text{csch}^4\left(\frac{x}{2}\right)}{2 (a+b)}+\frac{8 \sinh ^4\left(\frac{x}{2}\right) \text{csch}^3(x)}{a-b}+\frac{24 x}{a}\right)}{24 (a+b \text{sech}(x))}","-\frac{a b^2 x}{\left(a^2-b^2\right)^2}+\frac{a x}{a^2-b^2}-\frac{a \coth ^3(x)}{3 \left(a^2-b^2\right)}+\frac{a b^2 \coth (x)}{\left(a^2-b^2\right)^2}-\frac{a \coth (x)}{a^2-b^2}+\frac{b \text{csch}^3(x)}{3 \left(a^2-b^2\right)}+\frac{b \text{csch}(x)}{a^2-b^2}+\frac{b^4 x}{a \left(a^2-b^2\right)^2}-\frac{b^3 \text{csch}(x)}{\left(a^2-b^2\right)^2}-\frac{2 b^5 \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a (a-b)^{5/2} (a+b)^{5/2}}",1,"((b + a*Cosh[x])*Sech[x]*((24*x)/a + (48*b^5*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[a^2 - b^2]])/(a*(a^2 - b^2)^(5/2)) - (2*(8*a + 11*b)*Coth[x/2])/(a + b)^2 + (8*Csch[x]^3*Sinh[x/2]^4)/(a - b) - (Csch[x/2]^4*Sinh[x])/(2*(a + b)) - (16*a*Tanh[x/2])/(a - b)^2 + (22*b*Tanh[x/2])/(a - b)^2))/(24*(a + b*Sech[x]))","A",1
124,1,167,178,1.0333321,"\int \frac{\coth ^5(x)}{a+b \text{sech}(x)} \, dx","Integrate[Coth[x]^5/(a + b*Sech[x]),x]","\frac{1}{64} \left(-\frac{8 \left(a \left(b \left(3 a^4-10 a^2 b^2+15 b^4\right) \log \left(\tanh \left(\frac{x}{2}\right)\right)-8 a \left(a^4-3 a^2 b^2+3 b^4\right) \log (\sinh (x))\right)+8 b^6 \log (a \cosh (x)+b)\right)}{a (a-b)^3 (a+b)^3}-\frac{\text{csch}^4\left(\frac{x}{2}\right)}{a+b}-\frac{2 (7 a+9 b) \text{csch}^2\left(\frac{x}{2}\right)}{(a+b)^2}-\frac{\text{sech}^4\left(\frac{x}{2}\right)}{a-b}+\frac{2 (7 a-9 b) \text{sech}^2\left(\frac{x}{2}\right)}{(a-b)^2}\right)","\frac{\left(8 a^2+21 a b+15 b^2\right) \log (1-\text{sech}(x))}{16 (a+b)^3}+\frac{\left(8 a^2-21 a b+15 b^2\right) \log (\text{sech}(x)+1)}{16 (a-b)^3}-\frac{b^6 \log (a+b \text{sech}(x))}{a \left(a^2-b^2\right)^3}-\frac{5 a+7 b}{16 (a+b)^2 (1-\text{sech}(x))}-\frac{5 a-7 b}{16 (a-b)^2 (\text{sech}(x)+1)}-\frac{1}{16 (a+b) (1-\text{sech}(x))^2}-\frac{1}{16 (a-b) (\text{sech}(x)+1)^2}+\frac{\log (\cosh (x))}{a}",1,"((-2*(7*a + 9*b)*Csch[x/2]^2)/(a + b)^2 - Csch[x/2]^4/(a + b) - (8*(8*b^6*Log[b + a*Cosh[x]] + a*(-8*a*(a^4 - 3*a^2*b^2 + 3*b^4)*Log[Sinh[x]] + b*(3*a^4 - 10*a^2*b^2 + 15*b^4)*Log[Tanh[x/2]])))/(a*(a - b)^3*(a + b)^3) + (2*(7*a - 9*b)*Sech[x/2]^2)/(a - b)^2 - Sech[x/2]^4/(a - b))/64","A",1
125,1,160,169,5.1245886,"\int \sqrt{a+b \text{sech}(c+d x)} \tanh ^5(c+d x) \, dx","Integrate[Sqrt[a + b*Sech[c + d*x]]*Tanh[c + d*x]^5,x]","\frac{2 \sqrt{a+b \text{sech}(c+d x)} \left(\frac{16 a^4}{b^4}+\left(\frac{42 a}{b}-\frac{8 a^3}{b^3}\right) \text{sech}(c+d x)+\left(\frac{6 a^2}{b^2}+126\right) \text{sech}^2(c+d x)-\frac{84 a^2}{b^2}-\frac{5 a \text{sech}^3(c+d x)}{b}+\frac{315 \sqrt{a \cosh (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{a \cosh (c+d x)+b}}{\sqrt{a \cosh (c+d x)}}\right)}{\sqrt{a \cosh (c+d x)+b}}-35 \text{sech}^4(c+d x)-315\right)}{315 d}","-\frac{2 \left(3 a^2-2 b^2\right) (a+b \text{sech}(c+d x))^{5/2}}{5 b^4 d}+\frac{2 a \left(a^2-2 b^2\right) (a+b \text{sech}(c+d x))^{3/2}}{3 b^4 d}-\frac{2 (a+b \text{sech}(c+d x))^{9/2}}{9 b^4 d}+\frac{6 a (a+b \text{sech}(c+d x))^{7/2}}{7 b^4 d}-\frac{2 \sqrt{a+b \text{sech}(c+d x)}}{d}+\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{d}",1,"(2*Sqrt[a + b*Sech[c + d*x]]*(-315 + (16*a^4)/b^4 - (84*a^2)/b^2 + (315*ArcTanh[Sqrt[b + a*Cosh[c + d*x]]/Sqrt[a*Cosh[c + d*x]]]*Sqrt[a*Cosh[c + d*x]])/Sqrt[b + a*Cosh[c + d*x]] + ((-8*a^3)/b^3 + (42*a)/b)*Sech[c + d*x] + (126 + (6*a^2)/b^2)*Sech[c + d*x]^2 - (5*a*Sech[c + d*x]^3)/b - 35*Sech[c + d*x]^4))/(315*d)","A",1
126,1,108,100,0.9892412,"\int \sqrt{a+b \text{sech}(c+d x)} \tanh ^3(c+d x) \, dx","Integrate[Sqrt[a + b*Sech[c + d*x]]*Tanh[c + d*x]^3,x]","\frac{2 \sqrt{a+b \text{sech}(c+d x)} \left(-\frac{2 a^2}{b^2}+\frac{a \text{sech}(c+d x)}{b}+\frac{15 \sqrt{a \cosh (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{a \cosh (c+d x)+b}}{\sqrt{a \cosh (c+d x)}}\right)}{\sqrt{a \cosh (c+d x)+b}}+3 \text{sech}^2(c+d x)-15\right)}{15 d}","\frac{2 (a+b \text{sech}(c+d x))^{5/2}}{5 b^2 d}-\frac{2 a (a+b \text{sech}(c+d x))^{3/2}}{3 b^2 d}-\frac{2 \sqrt{a+b \text{sech}(c+d x)}}{d}+\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{d}",1,"(2*Sqrt[a + b*Sech[c + d*x]]*(-15 - (2*a^2)/b^2 + (15*ArcTanh[Sqrt[b + a*Cosh[c + d*x]]/Sqrt[a*Cosh[c + d*x]]]*Sqrt[a*Cosh[c + d*x]])/Sqrt[b + a*Cosh[c + d*x]] + (a*Sech[c + d*x])/b + 3*Sech[c + d*x]^2))/(15*d)","A",1
127,1,90,51,0.1521702,"\int \sqrt{a+b \text{sech}(c+d x)} \tanh (c+d x) \, dx","Integrate[Sqrt[a + b*Sech[c + d*x]]*Tanh[c + d*x],x]","-\frac{2 \sqrt{a+b \text{sech}(c+d x)} \left(\sqrt{a \cosh (c+d x)+b}-\sqrt{a \cosh (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{a \cosh (c+d x)+b}}{\sqrt{a \cosh (c+d x)}}\right)\right)}{d \sqrt{a \cosh (c+d x)+b}}","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{d}-\frac{2 \sqrt{a+b \text{sech}(c+d x)}}{d}",1,"(-2*(-(ArcTanh[Sqrt[b + a*Cosh[c + d*x]]/Sqrt[a*Cosh[c + d*x]]]*Sqrt[a*Cosh[c + d*x]]) + Sqrt[b + a*Cosh[c + d*x]])*Sqrt[a + b*Sech[c + d*x]])/(d*Sqrt[b + a*Cosh[c + d*x]])","A",1
128,1,195,106,1.8278826,"\int \coth (c+d x) \sqrt{a+b \text{sech}(c+d x)} \, dx","Integrate[Coth[c + d*x]*Sqrt[a + b*Sech[c + d*x]],x]","\frac{\sqrt{a \cosh (c+d x)} \sqrt{a+b \text{sech}(c+d x)} \left(2 \sqrt{a} \log \left(\sqrt{a \cosh (c+d x)+b}+\sqrt{a \cosh (c+d x)}\right)-\sqrt{-a-b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{a \cosh (c+d x)+b}}{\sqrt{-a-b} \sqrt{a \cosh (c+d x)}}\right)-\sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{a \cosh (c+d x)+b}}{\sqrt{a-b} \sqrt{a \cosh (c+d x)}}\right)\right)}{\sqrt{a} d \sqrt{a \cosh (c+d x)+b}}","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{d}-\frac{\sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a-b}}\right)}{d}-\frac{\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)}{d}",1,"(Sqrt[a*Cosh[c + d*x]]*(-(Sqrt[-a - b]*ArcTan[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[-a - b]*Sqrt[a*Cosh[c + d*x]])]) - Sqrt[a - b]*ArcTanh[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a - b]*Sqrt[a*Cosh[c + d*x]])] + 2*Sqrt[a]*Log[Sqrt[a*Cosh[c + d*x]] + Sqrt[b + a*Cosh[c + d*x]]])*Sqrt[a + b*Sech[c + d*x]])/(Sqrt[a]*d*Sqrt[b + a*Cosh[c + d*x]])","A",1
129,1,518,217,20.6856245,"\int \coth ^3(c+d x) \sqrt{a+b \text{sech}(c+d x)} \, dx","Integrate[Coth[c + d*x]^3*Sqrt[a + b*Sech[c + d*x]],x]","\frac{\sqrt{a+b \text{sech}(c+d x)} \left(\frac{8 \sqrt{-a \cosh (c+d x)} \tan ^{-1}\left(\frac{\sqrt{a \cosh (c+d x)+b}}{\sqrt{-a \cosh (c+d x)}}\right)}{\sqrt{a \cosh (c+d x)+b}}-\frac{2 \sqrt{a} \sqrt{-a \cosh (c+d x)} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{a \cosh (c+d x)+b}}{\sqrt{a-b} \sqrt{-a \cosh (c+d x)}}\right)}{\sqrt{a-b} \sqrt{a \cosh (c+d x)+b}}-\frac{2 \sqrt{a} \sqrt{-a \cosh (c+d x)} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{a \cosh (c+d x)+b}}{\sqrt{a+b} \sqrt{-a \cosh (c+d x)}}\right)}{\sqrt{a+b} \sqrt{a \cosh (c+d x)+b}}+\frac{3 b \sqrt{a \cosh (c+d x)} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{a \cosh (c+d x)+b}}{\sqrt{-a-b} \sqrt{a \cosh (c+d x)}}\right)}{\sqrt{a} \sqrt{-a-b} \sqrt{a \cosh (c+d x)+b}}-\frac{(2 a-3 b) \sqrt{a \cosh (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{a \cosh (c+d x)+b}}{\sqrt{a-b} \sqrt{a \cosh (c+d x)}}\right)}{\sqrt{a} \sqrt{a-b} \sqrt{a \cosh (c+d x)+b}}-\frac{2 \sqrt{a} \sqrt{a \cosh (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{a \cosh (c+d x)+b}}{\sqrt{a+b} \sqrt{a \cosh (c+d x)}}\right)}{\sqrt{a+b} \sqrt{a \cosh (c+d x)+b}}-2 \coth ^2(c+d x)\right)}{4 d}","-\frac{\coth ^2(c+d x) \sqrt{a+b \text{sech}(c+d x)}}{2 d}+\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{d}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a-b}}\right)}{4 d \sqrt{a-b}}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a-b}}\right)}{d \sqrt{a-b}}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)}{d \sqrt{a+b}}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)}{4 d \sqrt{a+b}}",1,"(((8*ArcTan[Sqrt[b + a*Cosh[c + d*x]]/Sqrt[-(a*Cosh[c + d*x])]]*Sqrt[-(a*Cosh[c + d*x])])/Sqrt[b + a*Cosh[c + d*x]] - (2*Sqrt[a]*ArcTan[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a - b]*Sqrt[-(a*Cosh[c + d*x])])]*Sqrt[-(a*Cosh[c + d*x])])/(Sqrt[a - b]*Sqrt[b + a*Cosh[c + d*x]]) - (2*Sqrt[a]*ArcTan[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a + b]*Sqrt[-(a*Cosh[c + d*x])])]*Sqrt[-(a*Cosh[c + d*x])])/(Sqrt[a + b]*Sqrt[b + a*Cosh[c + d*x]]) + (3*b*ArcTan[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[-a - b]*Sqrt[a*Cosh[c + d*x]])]*Sqrt[a*Cosh[c + d*x]])/(Sqrt[a]*Sqrt[-a - b]*Sqrt[b + a*Cosh[c + d*x]]) - ((2*a - 3*b)*ArcTanh[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a - b]*Sqrt[a*Cosh[c + d*x]])]*Sqrt[a*Cosh[c + d*x]])/(Sqrt[a]*Sqrt[a - b]*Sqrt[b + a*Cosh[c + d*x]]) - (2*Sqrt[a]*ArcTanh[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a + b]*Sqrt[a*Cosh[c + d*x]])]*Sqrt[a*Cosh[c + d*x]])/(Sqrt[a + b]*Sqrt[b + a*Cosh[c + d*x]]) - 2*Coth[c + d*x]^2)*Sqrt[a + b*Sech[c + d*x]])/(4*d)","B",1
130,-1,0,344,180.0023401,"\int \sqrt{a+b \text{sech}(c+d x)} \tanh ^2(c+d x) \, dx","Integrate[Sqrt[a + b*Sech[c + d*x]]*Tanh[c + d*x]^2,x]","\text{\$Aborted}","-\frac{2 a (a-b) \sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} E\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{3 b^2 d}-\frac{2 \tanh (c+d x) \sqrt{a+b \text{sech}(c+d x)}}{3 d}-\frac{2 \sqrt{a+b} (a+2 b) \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{3 b d}+\frac{2 \sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} \Pi \left(\frac{a+b}{a};\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{d}",1,"$Aborted","F",-1
131,0,0,125,7.8554275,"\int \sqrt{a+b \text{sech}(c+d x)} \, dx","Integrate[Sqrt[a + b*Sech[c + d*x]],x]","\int \sqrt{a+b \text{sech}(c+d x)} \, dx","\frac{2 \coth (c+d x) \sqrt{-\frac{b (1-\text{sech}(c+d x))}{a+b \text{sech}(c+d x)}} \sqrt{\frac{b (\text{sech}(c+d x)+1)}{a+b \text{sech}(c+d x)}} (a+b \text{sech}(c+d x)) \Pi \left(\frac{a}{a+b};\sin ^{-1}\left(\frac{\sqrt{a+b}}{\sqrt{a+b \text{sech}(c+d x)}}\right)|\frac{a-b}{a+b}\right)}{d \sqrt{a+b}}",1,"Integrate[Sqrt[a + b*Sech[c + d*x]], x]","F",-1
132,1,539,246,18.2265893,"\int \coth ^2(c+d x) \sqrt{a+b \text{sech}(c+d x)} \, dx","Integrate[Coth[c + d*x]^2*Sqrt[a + b*Sech[c + d*x]],x]","\frac{\sqrt{a+b \text{sech}(c+d x)} \left(\frac{2 \sqrt{b} \sinh (c+d x) (a-a \cosh (c+d x))^{3/2} \sqrt{\frac{(a+b) (a \cosh (c+d x)+a)}{(a-b) (a-a \cosh (c+d x))}} F\left(\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{b} \sqrt{a-a \cosh (c+d x)}}\right)|-\frac{2 b}{a-b}\right)}{a^{3/2} \sqrt{\cosh (c+d x)-1} \sqrt{\cosh (c+d x)+1} \sqrt{\text{sech}(c+d x)} \left(-\frac{a-a \cosh (c+d x)}{a}\right)^{3/2} \sqrt{\frac{a \cosh (c+d x)+a}{a}} \sqrt{-\frac{a (a+b) \cosh (c+d x)}{b (a-a \cosh (c+d x))}}}-\frac{4 b \sinh (c+d x) (a-a \cosh (c+d x)) \sqrt{-\frac{b \text{sech}(c+d x) (a \cosh (c+d x)+a)}{a (a-b)}} \Pi \left(\frac{a+b}{a};\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a+b} \sqrt{a \cosh (c+d x)}}\right)|\frac{a+b}{a-b}\right)}{\sqrt{a} \sqrt{a+b} \sqrt{\cosh (c+d x)-1} \sqrt{\cosh (c+d x)+1} \sqrt{\text{sech}(c+d x)} \sqrt{a \cosh (c+d x)} \sqrt{-\frac{a-a \cosh (c+d x)}{a}} \sqrt{\frac{a \cosh (c+d x)+a}{a}} \sqrt{-\frac{b \text{sech}(c+d x) (a-a \cosh (c+d x))}{a (a+b)}}}\right)}{2 d \sqrt{\text{sech}(c+d x)} \sqrt{a \cosh (c+d x)+b}}-\frac{\coth (c+d x) \sqrt{a+b \text{sech}(c+d x)}}{d}","-\frac{\coth (c+d x) \sqrt{a+b \text{sech}(c+d x)}}{d}+\frac{\sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{d}+\frac{2 \coth (c+d x) \sqrt{-\frac{b (1-\text{sech}(c+d x))}{a+b \text{sech}(c+d x)}} \sqrt{\frac{b (\text{sech}(c+d x)+1)}{a+b \text{sech}(c+d x)}} (a+b \text{sech}(c+d x)) \Pi \left(\frac{a}{a+b};\sin ^{-1}\left(\frac{\sqrt{a+b}}{\sqrt{a+b \text{sech}(c+d x)}}\right)|\frac{a-b}{a+b}\right)}{d \sqrt{a+b}}",1,"-((Coth[c + d*x]*Sqrt[a + b*Sech[c + d*x]])/d) + (Sqrt[a + b*Sech[c + d*x]]*((2*Sqrt[b]*(a - a*Cosh[c + d*x])^(3/2)*Sqrt[((a + b)*(a + a*Cosh[c + d*x]))/((a - b)*(a - a*Cosh[c + d*x]))]*EllipticF[ArcSin[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[b]*Sqrt[a - a*Cosh[c + d*x]])], (-2*b)/(a - b)]*Sinh[c + d*x])/(a^(3/2)*Sqrt[-1 + Cosh[c + d*x]]*Sqrt[1 + Cosh[c + d*x]]*Sqrt[-((a*(a + b)*Cosh[c + d*x])/(b*(a - a*Cosh[c + d*x])))]*(-((a - a*Cosh[c + d*x])/a))^(3/2)*Sqrt[(a + a*Cosh[c + d*x])/a]*Sqrt[Sech[c + d*x]]) - (4*b*(a - a*Cosh[c + d*x])*EllipticPi[(a + b)/a, ArcSin[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a + b]*Sqrt[a*Cosh[c + d*x]])], (a + b)/(a - b)]*Sqrt[-((b*(a + a*Cosh[c + d*x])*Sech[c + d*x])/(a*(a - b)))]*Sinh[c + d*x])/(Sqrt[a]*Sqrt[a + b]*Sqrt[-1 + Cosh[c + d*x]]*Sqrt[a*Cosh[c + d*x]]*Sqrt[1 + Cosh[c + d*x]]*Sqrt[-((a - a*Cosh[c + d*x])/a)]*Sqrt[(a + a*Cosh[c + d*x])/a]*Sqrt[Sech[c + d*x]]*Sqrt[-((b*(a - a*Cosh[c + d*x])*Sech[c + d*x])/(a*(a + b)))])))/(2*d*Sqrt[b + a*Cosh[c + d*x]]*Sqrt[Sech[c + d*x]])","B",1
133,1,167,148,4.4117324,"\int \frac{\tanh ^5(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Integrate[Tanh[c + d*x]^5/Sqrt[a + b*Sech[c + d*x]],x]","\frac{2 \left(48 a^4+\left(24 a^3 b-70 a b^3\right) \text{sech}(c+d x)-140 a^2 b^2+\left(70 b^4-6 a^2 b^2\right) \text{sech}^2(c+d x)+\frac{105 b^4 \sqrt{a \cosh (c+d x)+b} \tanh ^{-1}\left(\frac{\sqrt{a \cosh (c+d x)+b}}{\sqrt{a \cosh (c+d x)}}\right)}{\sqrt{a \cosh (c+d x)}}+3 a b^3 \text{sech}^3(c+d x)-15 b^4 \text{sech}^4(c+d x)\right)}{105 b^4 d \sqrt{a+b \text{sech}(c+d x)}}","-\frac{2 \left(3 a^2-2 b^2\right) (a+b \text{sech}(c+d x))^{3/2}}{3 b^4 d}+\frac{2 a \left(a^2-2 b^2\right) \sqrt{a+b \text{sech}(c+d x)}}{b^4 d}-\frac{2 (a+b \text{sech}(c+d x))^{7/2}}{7 b^4 d}+\frac{6 a (a+b \text{sech}(c+d x))^{5/2}}{5 b^4 d}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}",1,"(2*(48*a^4 - 140*a^2*b^2 + (105*b^4*ArcTanh[Sqrt[b + a*Cosh[c + d*x]]/Sqrt[a*Cosh[c + d*x]]]*Sqrt[b + a*Cosh[c + d*x]])/Sqrt[a*Cosh[c + d*x]] + (24*a^3*b - 70*a*b^3)*Sech[c + d*x] + (-6*a^2*b^2 + 70*b^4)*Sech[c + d*x]^2 + 3*a*b^3*Sech[c + d*x]^3 - 15*b^4*Sech[c + d*x]^4))/(105*b^4*d*Sqrt[a + b*Sech[c + d*x]])","A",1
134,1,111,79,0.6373298,"\int \frac{\tanh ^3(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Integrate[Tanh[c + d*x]^3/Sqrt[a + b*Sech[c + d*x]],x]","\frac{2 \left(-2 a^2+\frac{3 b^2 \sqrt{a \cosh (c+d x)+b} \tanh ^{-1}\left(\frac{\sqrt{a \cosh (c+d x)+b}}{\sqrt{a \cosh (c+d x)}}\right)}{\sqrt{a \cosh (c+d x)}}-a b \text{sech}(c+d x)+b^2 \text{sech}^2(c+d x)\right)}{3 b^2 d \sqrt{a+b \text{sech}(c+d x)}}","\frac{2 (a+b \text{sech}(c+d x))^{3/2}}{3 b^2 d}-\frac{2 a \sqrt{a+b \text{sech}(c+d x)}}{b^2 d}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}",1,"(2*(-2*a^2 + (3*b^2*ArcTanh[Sqrt[b + a*Cosh[c + d*x]]/Sqrt[a*Cosh[c + d*x]]]*Sqrt[b + a*Cosh[c + d*x]])/Sqrt[a*Cosh[c + d*x]] - a*b*Sech[c + d*x] + b^2*Sech[c + d*x]^2))/(3*b^2*d*Sqrt[a + b*Sech[c + d*x]])","A",1
135,1,73,31,0.1395047,"\int \frac{\tanh (c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Integrate[Tanh[c + d*x]/Sqrt[a + b*Sech[c + d*x]],x]","\frac{2 \sqrt{a \cosh (c+d x)+b} \tanh ^{-1}\left(\frac{\sqrt{a \cosh (c+d x)+b}}{\sqrt{a \cosh (c+d x)}}\right)}{d \sqrt{a \cosh (c+d x)} \sqrt{a+b \text{sech}(c+d x)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}",1,"(2*ArcTanh[Sqrt[b + a*Cosh[c + d*x]]/Sqrt[a*Cosh[c + d*x]]]*Sqrt[b + a*Cosh[c + d*x]])/(d*Sqrt[a*Cosh[c + d*x]]*Sqrt[a + b*Sech[c + d*x]])","B",1
136,1,226,106,3.6796145,"\int \frac{\coth (c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Integrate[Coth[c + d*x]/Sqrt[a + b*Sech[c + d*x]],x]","\frac{\sqrt{a \cosh (c+d x)+b} \left(\frac{\frac{2 \sqrt{b} \sqrt{\frac{a \cosh (c+d x)}{b}+1} \sinh ^{-1}\left(\frac{\sqrt{a} \sqrt{\cosh (c+d x)}}{\sqrt{b}}\right)}{\sqrt{a}}-\frac{\sqrt{-a \cosh (c+d x)-b} \tanh ^{-1}\left(\frac{\sqrt{-a-b} \sqrt{\cosh (c+d x)}}{\sqrt{-a \cosh (c+d x)-b}}\right)}{\sqrt{-a-b}}}{\sqrt{a \cosh (c+d x)+b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a-b} \sqrt{\cosh (c+d x)}}{\sqrt{a \cosh (c+d x)+b}}\right)}{\sqrt{a-b}}\right)}{d \sqrt{\cosh (c+d x)} \sqrt{a+b \text{sech}(c+d x)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a-b}}\right)}{d \sqrt{a-b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)}{d \sqrt{a+b}}",1,"(Sqrt[b + a*Cosh[c + d*x]]*(-(ArcTanh[(Sqrt[a - b]*Sqrt[Cosh[c + d*x]])/Sqrt[b + a*Cosh[c + d*x]]]/Sqrt[a - b]) + (-((ArcTanh[(Sqrt[-a - b]*Sqrt[Cosh[c + d*x]])/Sqrt[-b - a*Cosh[c + d*x]]]*Sqrt[-b - a*Cosh[c + d*x]])/Sqrt[-a - b]) + (2*Sqrt[b]*ArcSinh[(Sqrt[a]*Sqrt[Cosh[c + d*x]])/Sqrt[b]]*Sqrt[1 + (a*Cosh[c + d*x])/b])/Sqrt[a])/Sqrt[b + a*Cosh[c + d*x]]))/(d*Sqrt[Cosh[c + d*x]]*Sqrt[a + b*Sech[c + d*x]])","B",1
137,1,902,262,7.3960413,"\int \frac{\coth ^3(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Integrate[Coth[c + d*x]^3/Sqrt[a + b*Sech[c + d*x]],x]","\frac{\sqrt{b+a \cosh (c+d x)} \sqrt{\text{sech}(c+d x)} \left(\frac{\left(2 a^2-2 b^2\right) \left(\sqrt{a} \left(\sqrt{a+b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a-b} \sqrt{-a \cosh (c+d x)}}\right)+\sqrt{a-b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a+b} \sqrt{-a \cosh (c+d x)}}\right)\right)-4 \sqrt{a-b} \sqrt{a+b} \tan ^{-1}\left(\frac{\sqrt{b+a \cosh (c+d x)}}{\sqrt{-a \cosh (c+d x)}}\right)\right) \sqrt{-a \cosh (c+d x)} \sqrt{\frac{a \cosh (c+d x)-a}{\cosh (c+d x) a+a}} \cosh (2 (c+d x)) \sqrt{\text{sech}(c+d x)} (\cosh (c+d x) a+a)}{\sqrt{a-b} \sqrt{a+b} \sqrt{\cosh (c+d x)-1} \sqrt{\cosh (c+d x)+1} \left(a^2-2 b^2-2 (b+a \cosh (c+d x))^2+4 b (b+a \cosh (c+d x))\right)}-\frac{\left(2 a^2-3 b^2\right) \left(\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a-b} \sqrt{a \cosh (c+d x)}}\right)+\sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a+b} \sqrt{a \cosh (c+d x)}}\right)\right) \sqrt{a \cosh (c+d x)} \sqrt{\frac{a \cosh (c+d x)-a}{\cosh (c+d x) a+a}} \sqrt{\text{sech}(c+d x)} (\cosh (c+d x) a+a)}{a^{3/2} \sqrt{a-b} \sqrt{a+b} \sqrt{\cosh (c+d x)-1} \sqrt{\cosh (c+d x)+1}}+\frac{\sqrt{a} b \left(\sqrt{a-b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{-a-b} \sqrt{a \cosh (c+d x)}}\right)+\sqrt{-a-b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a-b} \sqrt{a \cosh (c+d x)}}\right)\right) \sqrt{\frac{a \cosh (c+d x)-a}{\cosh (c+d x) a+a}} (\cosh (c+d x) a+a)}{\sqrt{-a-b} \sqrt{a-b} \sqrt{\cosh (c+d x)-1} \sqrt{a \cosh (c+d x)} \sqrt{\cosh (c+d x)+1} \sqrt{\text{sech}(c+d x)}}\right)}{4 (a-b) (a+b) d \sqrt{a+b \text{sech}(c+d x)}}+\frac{(b+a \cosh (c+d x)) \left(\frac{(a-b \cosh (c+d x)) \text{csch}^2(c+d x)}{2 \left(b^2-a^2\right)}-\frac{a}{2 \left(a^2-b^2\right)}\right) \text{sech}(c+d x)}{d \sqrt{a+b \text{sech}(c+d x)}}","-\frac{\sqrt{a+b \text{sech}(c+d x)}}{4 d (a+b) (1-\text{sech}(c+d x))}-\frac{\sqrt{a+b \text{sech}(c+d x)}}{4 d (a-b) (\text{sech}(c+d x)+1)}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a-b}}\right)}{4 d (a-b)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a-b}}\right)}{d \sqrt{a-b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)}{d \sqrt{a+b}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)}{4 d (a+b)^{3/2}}",1,"(Sqrt[b + a*Cosh[c + d*x]]*((Sqrt[a]*b*(Sqrt[a - b]*ArcTan[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[-a - b]*Sqrt[a*Cosh[c + d*x]])] + Sqrt[-a - b]*ArcTanh[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a - b]*Sqrt[a*Cosh[c + d*x]])])*Sqrt[(-a + a*Cosh[c + d*x])/(a + a*Cosh[c + d*x])]*(a + a*Cosh[c + d*x]))/(Sqrt[-a - b]*Sqrt[a - b]*Sqrt[-1 + Cosh[c + d*x]]*Sqrt[a*Cosh[c + d*x]]*Sqrt[1 + Cosh[c + d*x]]*Sqrt[Sech[c + d*x]]) - ((2*a^2 - 3*b^2)*(Sqrt[a + b]*ArcTanh[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a - b]*Sqrt[a*Cosh[c + d*x]])] + Sqrt[a - b]*ArcTanh[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a + b]*Sqrt[a*Cosh[c + d*x]])])*Sqrt[a*Cosh[c + d*x]]*Sqrt[(-a + a*Cosh[c + d*x])/(a + a*Cosh[c + d*x])]*(a + a*Cosh[c + d*x])*Sqrt[Sech[c + d*x]])/(a^(3/2)*Sqrt[a - b]*Sqrt[a + b]*Sqrt[-1 + Cosh[c + d*x]]*Sqrt[1 + Cosh[c + d*x]]) + ((2*a^2 - 2*b^2)*(-4*Sqrt[a - b]*Sqrt[a + b]*ArcTan[Sqrt[b + a*Cosh[c + d*x]]/Sqrt[-(a*Cosh[c + d*x])]] + Sqrt[a]*(Sqrt[a + b]*ArcTan[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a - b]*Sqrt[-(a*Cosh[c + d*x])])] + Sqrt[a - b]*ArcTan[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a + b]*Sqrt[-(a*Cosh[c + d*x])])]))*Sqrt[-(a*Cosh[c + d*x])]*Sqrt[(-a + a*Cosh[c + d*x])/(a + a*Cosh[c + d*x])]*(a + a*Cosh[c + d*x])*Cosh[2*(c + d*x)]*Sqrt[Sech[c + d*x]])/(Sqrt[a - b]*Sqrt[a + b]*Sqrt[-1 + Cosh[c + d*x]]*Sqrt[1 + Cosh[c + d*x]]*(a^2 - 2*b^2 + 4*b*(b + a*Cosh[c + d*x]) - 2*(b + a*Cosh[c + d*x])^2)))*Sqrt[Sech[c + d*x]])/(4*(a - b)*(a + b)*d*Sqrt[a + b*Sech[c + d*x]]) + ((b + a*Cosh[c + d*x])*(-1/2*a/(a^2 - b^2) + ((a - b*Cosh[c + d*x])*Csch[c + d*x]^2)/(2*(-a^2 + b^2)))*Sech[c + d*x])/(d*Sqrt[a + b*Sech[c + d*x]])","B",1
138,-1,0,610,180.0013921,"\int \frac{\tanh ^4(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Integrate[Tanh[c + d*x]^4/Sqrt[a + b*Sech[c + d*x]],x]","\text{\$Aborted}","\frac{2 (a-b) \sqrt{a+b} \left(8 a^2+9 b^2\right) \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} E\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{15 b^4 d}+\frac{2 \sqrt{a+b} \left(8 a^2-2 a b+9 b^2\right) \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{15 b^3 d}-\frac{8 a \tanh (c+d x) \sqrt{a+b \text{sech}(c+d x)}}{15 b^2 d}-\frac{4 (a-b) \sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} E\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{b^2 d}+\frac{2 \tanh (c+d x) \text{sech}(c+d x) \sqrt{a+b \text{sech}(c+d x)}}{5 b d}-\frac{4 \sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{b d}+\frac{2 \sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} \Pi \left(\frac{a+b}{a};\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{a d}",1,"$Aborted","F",-1
139,-1,0,310,180.0012036,"\int \frac{\tanh ^2(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Integrate[Tanh[c + d*x]^2/Sqrt[a + b*Sech[c + d*x]],x]","\text{\$Aborted}","-\frac{2 (a-b) \sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} E\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{b^2 d}-\frac{2 \sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{b d}+\frac{2 \sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} \Pi \left(\frac{a+b}{a};\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{a d}",1,"$Aborted","F",-1
140,1,168,106,0.6335851,"\int \frac{1}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Integrate[1/Sqrt[a + b*Sech[c + d*x]],x]","\frac{2 b \tanh \left(\frac{1}{2} (c+d x)\right) \sqrt{a \cosh (c+d x)+b} \sqrt{\frac{b (\text{sech}(c+d x)+1)}{b-a}} \Pi \left(\frac{a+b}{a};\sin ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a+b} \sqrt{a \cosh (c+d x)}}\right)|\frac{a+b}{a-b}\right)}{\sqrt{a} d \sqrt{a+b} \sqrt{a \cosh (c+d x)} \sqrt{-\frac{b (\text{sech}(c+d x)-1)}{a+b}} \sqrt{a+b \text{sech}(c+d x)}}","\frac{2 \sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} \Pi \left(\frac{a+b}{a};\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{a d}",1,"(2*b*Sqrt[b + a*Cosh[c + d*x]]*EllipticPi[(a + b)/a, ArcSin[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a + b]*Sqrt[a*Cosh[c + d*x]])], (a + b)/(a - b)]*Sqrt[(b*(1 + Sech[c + d*x]))/(-a + b)]*Tanh[(c + d*x)/2])/(Sqrt[a]*Sqrt[a + b]*d*Sqrt[a*Cosh[c + d*x]]*Sqrt[-((b*(-1 + Sech[c + d*x]))/(a + b))]*Sqrt[a + b*Sech[c + d*x]])","A",1
141,0,0,362,91.3521973,"\int \frac{\coth ^2(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Integrate[Coth[c + d*x]^2/Sqrt[a + b*Sech[c + d*x]],x]","\int \frac{\coth ^2(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","-\frac{b^2 \tanh (c+d x)}{d \left(a^2-b^2\right) \sqrt{a+b \text{sech}(c+d x)}}-\frac{\coth (c+d x)}{d \sqrt{a+b \text{sech}(c+d x)}}-\frac{\coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{d \sqrt{a+b}}+\frac{\coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} E\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{d \sqrt{a+b}}+\frac{2 \sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} \Pi \left(\frac{a+b}{a};\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{a d}",1,"Integrate[Coth[c + d*x]^2/Sqrt[a + b*Sech[c + d*x]], x]","F",-1
142,1,155,148,3.1696616,"\int \frac{\tanh ^5(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Integrate[Tanh[c + d*x]^5/(a + b*Sech[c + d*x])^(3/2),x]","-\frac{2 \left(16 a^4-2 a^2 b^2 \text{sech}^2(c+d x)+2 a b \left(4 a^2-5 b^2\right) \text{sech}(c+d x)-20 a^2 b^2-\frac{5 b^4 \sqrt{a \cosh (c+d x)+b} \tanh ^{-1}\left(\frac{\sqrt{a \cosh (c+d x)+b}}{\sqrt{a \cosh (c+d x)}}\right)}{\sqrt{a \cosh (c+d x)}}+a b^3 \text{sech}^3(c+d x)+5 b^4\right)}{5 a b^4 d \sqrt{a+b \text{sech}(c+d x)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}-\frac{2 \left(3 a^2-2 b^2\right) \sqrt{a+b \text{sech}(c+d x)}}{b^4 d}-\frac{2 \left(a^2-b^2\right)^2}{a b^4 d \sqrt{a+b \text{sech}(c+d x)}}-\frac{2 (a+b \text{sech}(c+d x))^{5/2}}{5 b^4 d}+\frac{2 a (a+b \text{sech}(c+d x))^{3/2}}{b^4 d}",1,"(-2*(16*a^4 - 20*a^2*b^2 + 5*b^4 - (5*b^4*ArcTanh[Sqrt[b + a*Cosh[c + d*x]]/Sqrt[a*Cosh[c + d*x]]]*Sqrt[b + a*Cosh[c + d*x]])/Sqrt[a*Cosh[c + d*x]] + 2*a*b*(4*a^2 - 5*b^2)*Sech[c + d*x] - 2*a^2*b^2*Sech[c + d*x]^2 + a*b^3*Sech[c + d*x]^3))/(5*a*b^4*d*Sqrt[a + b*Sech[c + d*x]])","A",1
143,1,103,88,0.6728661,"\int \frac{\tanh ^3(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Integrate[Tanh[c + d*x]^3/(a + b*Sech[c + d*x])^(3/2),x]","\frac{2 \left(2 a^2+\frac{b^2 \sqrt{a \cosh (c+d x)+b} \tanh ^{-1}\left(\frac{\sqrt{a \cosh (c+d x)+b}}{\sqrt{a \cosh (c+d x)}}\right)}{\sqrt{a \cosh (c+d x)}}+a b \text{sech}(c+d x)-b^2\right)}{a b^2 d \sqrt{a+b \text{sech}(c+d x)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{2 \left(a^2-b^2\right)}{a b^2 d \sqrt{a+b \text{sech}(c+d x)}}+\frac{2 \sqrt{a+b \text{sech}(c+d x)}}{b^2 d}",1,"(2*(2*a^2 - b^2 + (b^2*ArcTanh[Sqrt[b + a*Cosh[c + d*x]]/Sqrt[a*Cosh[c + d*x]]]*Sqrt[b + a*Cosh[c + d*x]])/Sqrt[a*Cosh[c + d*x]] + a*b*Sech[c + d*x]))/(a*b^2*d*Sqrt[a + b*Sech[c + d*x]])","A",1
144,1,79,54,0.2455199,"\int \frac{\tanh (c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Integrate[Tanh[c + d*x]/(a + b*Sech[c + d*x])^(3/2),x]","\frac{2 \left(\frac{\sqrt{a \cosh (c+d x)+b} \tanh ^{-1}\left(\frac{\sqrt{a \cosh (c+d x)+b}}{\sqrt{a \cosh (c+d x)}}\right)}{\sqrt{a \cosh (c+d x)}}-1\right)}{a d \sqrt{a+b \text{sech}(c+d x)}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}-\frac{2}{a d \sqrt{a+b \text{sech}(c+d x)}}",1,"(2*(-1 + (ArcTanh[Sqrt[b + a*Cosh[c + d*x]]/Sqrt[a*Cosh[c + d*x]]]*Sqrt[b + a*Cosh[c + d*x]])/Sqrt[a*Cosh[c + d*x]]))/(a*d*Sqrt[a + b*Sech[c + d*x]])","A",1
145,1,904,142,7.367468,"\int \frac{\coth (c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Integrate[Coth[c + d*x]/(a + b*Sech[c + d*x])^(3/2),x]","\frac{(b+a \cosh (c+d x))^2 \left(-\frac{2 b^3}{a^2 \left(a^2-b^2\right) (b+a \cosh (c+d x))}-\frac{2 b^2}{a^2 \left(b^2-a^2\right)}\right) \text{sech}^2(c+d x)}{d (a+b \text{sech}(c+d x))^{3/2}}-\frac{(b+a \cosh (c+d x))^{3/2} \left(\frac{\left(a^2-b^2\right) \left(\sqrt{a} \left(\sqrt{a+b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a-b} \sqrt{-a \cosh (c+d x)}}\right)+\sqrt{a-b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a+b} \sqrt{-a \cosh (c+d x)}}\right)\right)-4 \sqrt{a-b} \sqrt{a+b} \tan ^{-1}\left(\frac{\sqrt{b+a \cosh (c+d x)}}{\sqrt{-a \cosh (c+d x)}}\right)\right) \sqrt{-a \cosh (c+d x)} \sqrt{\frac{a \cosh (c+d x)-a}{\cosh (c+d x) a+a}} \cosh (2 (c+d x)) \sqrt{\text{sech}(c+d x)} (\cosh (c+d x) a+a)}{\sqrt{a-b} \sqrt{a+b} \sqrt{\cosh (c+d x)-1} \sqrt{\cosh (c+d x)+1} \left(a^2-2 b^2-2 (b+a \cosh (c+d x))^2+4 b (b+a \cosh (c+d x))\right)}-\frac{\left(a^2+b^2\right) \left(\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a-b} \sqrt{a \cosh (c+d x)}}\right)+\sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a+b} \sqrt{a \cosh (c+d x)}}\right)\right) \sqrt{a \cosh (c+d x)} \sqrt{\frac{a \cosh (c+d x)-a}{\cosh (c+d x) a+a}} \sqrt{\text{sech}(c+d x)} (\cosh (c+d x) a+a)}{a^{3/2} \sqrt{a-b} \sqrt{a+b} \sqrt{\cosh (c+d x)-1} \sqrt{\cosh (c+d x)+1}}-\frac{2 \sqrt{a} b \left(\sqrt{a-b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{-a-b} \sqrt{a \cosh (c+d x)}}\right)+\sqrt{-a-b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a-b} \sqrt{a \cosh (c+d x)}}\right)\right) \sqrt{\frac{a \cosh (c+d x)-a}{\cosh (c+d x) a+a}} (\cosh (c+d x) a+a)}{\sqrt{-a-b} \sqrt{a-b} \sqrt{\cosh (c+d x)-1} \sqrt{a \cosh (c+d x)} \sqrt{\cosh (c+d x)+1} \sqrt{\text{sech}(c+d x)}}\right) \text{sech}^{\frac{3}{2}}(c+d x)}{2 a (b-a) (a+b) d (a+b \text{sech}(c+d x))^{3/2}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}+\frac{2 b^2}{a d \left(a^2-b^2\right) \sqrt{a+b \text{sech}(c+d x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a-b}}\right)}{d (a-b)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)}{d (a+b)^{3/2}}",1,"-1/2*((b + a*Cosh[c + d*x])^(3/2)*((-2*Sqrt[a]*b*(Sqrt[a - b]*ArcTan[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[-a - b]*Sqrt[a*Cosh[c + d*x]])] + Sqrt[-a - b]*ArcTanh[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a - b]*Sqrt[a*Cosh[c + d*x]])])*Sqrt[(-a + a*Cosh[c + d*x])/(a + a*Cosh[c + d*x])]*(a + a*Cosh[c + d*x]))/(Sqrt[-a - b]*Sqrt[a - b]*Sqrt[-1 + Cosh[c + d*x]]*Sqrt[a*Cosh[c + d*x]]*Sqrt[1 + Cosh[c + d*x]]*Sqrt[Sech[c + d*x]]) - ((a^2 + b^2)*(Sqrt[a + b]*ArcTanh[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a - b]*Sqrt[a*Cosh[c + d*x]])] + Sqrt[a - b]*ArcTanh[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a + b]*Sqrt[a*Cosh[c + d*x]])])*Sqrt[a*Cosh[c + d*x]]*Sqrt[(-a + a*Cosh[c + d*x])/(a + a*Cosh[c + d*x])]*(a + a*Cosh[c + d*x])*Sqrt[Sech[c + d*x]])/(a^(3/2)*Sqrt[a - b]*Sqrt[a + b]*Sqrt[-1 + Cosh[c + d*x]]*Sqrt[1 + Cosh[c + d*x]]) + ((a^2 - b^2)*(-4*Sqrt[a - b]*Sqrt[a + b]*ArcTan[Sqrt[b + a*Cosh[c + d*x]]/Sqrt[-(a*Cosh[c + d*x])]] + Sqrt[a]*(Sqrt[a + b]*ArcTan[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a - b]*Sqrt[-(a*Cosh[c + d*x])])] + Sqrt[a - b]*ArcTan[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a + b]*Sqrt[-(a*Cosh[c + d*x])])]))*Sqrt[-(a*Cosh[c + d*x])]*Sqrt[(-a + a*Cosh[c + d*x])/(a + a*Cosh[c + d*x])]*(a + a*Cosh[c + d*x])*Cosh[2*(c + d*x)]*Sqrt[Sech[c + d*x]])/(Sqrt[a - b]*Sqrt[a + b]*Sqrt[-1 + Cosh[c + d*x]]*Sqrt[1 + Cosh[c + d*x]]*(a^2 - 2*b^2 + 4*b*(b + a*Cosh[c + d*x]) - 2*(b + a*Cosh[c + d*x])^2)))*Sech[c + d*x]^(3/2))/(a*(-a + b)*(a + b)*d*(a + b*Sech[c + d*x])^(3/2)) + ((b + a*Cosh[c + d*x])^2*((-2*b^2)/(a^2*(-a^2 + b^2)) - (2*b^3)/(a^2*(a^2 - b^2)*(b + a*Cosh[c + d*x])))*Sech[c + d*x]^2)/(d*(a + b*Sech[c + d*x])^(3/2))","B",1
146,1,996,316,7.61197,"\int \frac{\coth ^3(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Integrate[Coth[c + d*x]^3/(a + b*Sech[c + d*x])^(3/2),x]","\frac{(b+a \cosh (c+d x))^2 \left(\frac{2 b^5}{a^2 \left(a^2-b^2\right)^2 (b+a \cosh (c+d x))}+\frac{\left(-a^2+2 b \cosh (c+d x) a-b^2\right) \text{csch}^2(c+d x)}{2 \left(b^2-a^2\right)^2}-\frac{a^4+b^2 a^2+4 b^4}{2 a^2 \left(b^2-a^2\right)^2}\right) \text{sech}^2(c+d x)}{d (a+b \text{sech}(c+d x))^{3/2}}+\frac{(b+a \cosh (c+d x))^{3/2} \left(\frac{\left(2 a^4-4 b^2 a^2+2 b^4\right) \left(\sqrt{a} \left(\sqrt{a+b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a-b} \sqrt{-a \cosh (c+d x)}}\right)+\sqrt{a-b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a+b} \sqrt{-a \cosh (c+d x)}}\right)\right)-4 \sqrt{a-b} \sqrt{a+b} \tan ^{-1}\left(\frac{\sqrt{b+a \cosh (c+d x)}}{\sqrt{-a \cosh (c+d x)}}\right)\right) \sqrt{-a \cosh (c+d x)} \sqrt{\frac{a \cosh (c+d x)-a}{\cosh (c+d x) a+a}} \cosh (2 (c+d x)) \sqrt{\text{sech}(c+d x)} (\cosh (c+d x) a+a)}{\sqrt{a-b} \sqrt{a+b} \sqrt{\cosh (c+d x)-1} \sqrt{\cosh (c+d x)+1} \left(a^2-2 b^2-2 (b+a \cosh (c+d x))^2+4 b (b+a \cosh (c+d x))\right)}-\frac{\left(2 a^4-6 b^2 a^2-2 b^4\right) \left(\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a-b} \sqrt{a \cosh (c+d x)}}\right)+\sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a+b} \sqrt{a \cosh (c+d x)}}\right)\right) \sqrt{a \cosh (c+d x)} \sqrt{\frac{a \cosh (c+d x)-a}{\cosh (c+d x) a+a}} \sqrt{\text{sech}(c+d x)} (\cosh (c+d x) a+a)}{a^{3/2} \sqrt{a-b} \sqrt{a+b} \sqrt{\cosh (c+d x)-1} \sqrt{\cosh (c+d x)+1}}+\frac{\left(7 a b^3-a^3 b\right) \left(\sqrt{a-b} \tan ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{-a-b} \sqrt{a \cosh (c+d x)}}\right)+\sqrt{-a-b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{b+a \cosh (c+d x)}}{\sqrt{a-b} \sqrt{a \cosh (c+d x)}}\right)\right) \sqrt{\frac{a \cosh (c+d x)-a}{\cosh (c+d x) a+a}} (\cosh (c+d x) a+a)}{\sqrt{a} \sqrt{-a-b} \sqrt{a-b} \sqrt{\cosh (c+d x)-1} \sqrt{a \cosh (c+d x)} \sqrt{\cosh (c+d x)+1} \sqrt{\text{sech}(c+d x)}}\right) \text{sech}^{\frac{3}{2}}(c+d x)}{4 a (a-b)^2 (a+b)^2 d (a+b \text{sech}(c+d x))^{3/2}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}-\frac{2 b^4}{a d \left(a^2-b^2\right)^2 \sqrt{a+b \text{sech}(c+d x)}}-\frac{\sqrt{a+b \text{sech}(c+d x)}}{4 d (a+b)^2 (1-\text{sech}(c+d x))}-\frac{\sqrt{a+b \text{sech}(c+d x)}}{4 d (a-b)^2 (\text{sech}(c+d x)+1)}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a-b}}\right)}{4 d (a-b)^{5/2}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)}{4 d (a+b)^{5/2}}-\frac{(2 a-3 b) \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a-b}}\right)}{2 d (a-b)^{5/2}}-\frac{(2 a+3 b) \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)}{2 d (a+b)^{5/2}}",1,"((b + a*Cosh[c + d*x])^(3/2)*(((-(a^3*b) + 7*a*b^3)*(Sqrt[a - b]*ArcTan[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[-a - b]*Sqrt[a*Cosh[c + d*x]])] + Sqrt[-a - b]*ArcTanh[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a - b]*Sqrt[a*Cosh[c + d*x]])])*Sqrt[(-a + a*Cosh[c + d*x])/(a + a*Cosh[c + d*x])]*(a + a*Cosh[c + d*x]))/(Sqrt[a]*Sqrt[-a - b]*Sqrt[a - b]*Sqrt[-1 + Cosh[c + d*x]]*Sqrt[a*Cosh[c + d*x]]*Sqrt[1 + Cosh[c + d*x]]*Sqrt[Sech[c + d*x]]) - ((2*a^4 - 6*a^2*b^2 - 2*b^4)*(Sqrt[a + b]*ArcTanh[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a - b]*Sqrt[a*Cosh[c + d*x]])] + Sqrt[a - b]*ArcTanh[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a + b]*Sqrt[a*Cosh[c + d*x]])])*Sqrt[a*Cosh[c + d*x]]*Sqrt[(-a + a*Cosh[c + d*x])/(a + a*Cosh[c + d*x])]*(a + a*Cosh[c + d*x])*Sqrt[Sech[c + d*x]])/(a^(3/2)*Sqrt[a - b]*Sqrt[a + b]*Sqrt[-1 + Cosh[c + d*x]]*Sqrt[1 + Cosh[c + d*x]]) + ((2*a^4 - 4*a^2*b^2 + 2*b^4)*(-4*Sqrt[a - b]*Sqrt[a + b]*ArcTan[Sqrt[b + a*Cosh[c + d*x]]/Sqrt[-(a*Cosh[c + d*x])]] + Sqrt[a]*(Sqrt[a + b]*ArcTan[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a - b]*Sqrt[-(a*Cosh[c + d*x])])] + Sqrt[a - b]*ArcTan[(Sqrt[a]*Sqrt[b + a*Cosh[c + d*x]])/(Sqrt[a + b]*Sqrt[-(a*Cosh[c + d*x])])]))*Sqrt[-(a*Cosh[c + d*x])]*Sqrt[(-a + a*Cosh[c + d*x])/(a + a*Cosh[c + d*x])]*(a + a*Cosh[c + d*x])*Cosh[2*(c + d*x)]*Sqrt[Sech[c + d*x]])/(Sqrt[a - b]*Sqrt[a + b]*Sqrt[-1 + Cosh[c + d*x]]*Sqrt[1 + Cosh[c + d*x]]*(a^2 - 2*b^2 + 4*b*(b + a*Cosh[c + d*x]) - 2*(b + a*Cosh[c + d*x])^2)))*Sech[c + d*x]^(3/2))/(4*a*(a - b)^2*(a + b)^2*d*(a + b*Sech[c + d*x])^(3/2)) + ((b + a*Cosh[c + d*x])^2*(-1/2*(a^4 + a^2*b^2 + 4*b^4)/(a^2*(-a^2 + b^2)^2) + (2*b^5)/(a^2*(a^2 - b^2)^2*(b + a*Cosh[c + d*x])) + ((-a^2 - b^2 + 2*a*b*Cosh[c + d*x])*Csch[c + d*x]^2)/(2*(-a^2 + b^2)^2))*Sech[c + d*x]^2)/(d*(a + b*Sech[c + d*x])^(3/2))","B",1
147,-1,0,907,180.0007554,"\int \frac{\tanh ^4(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Integrate[Tanh[c + d*x]^4/(a + b*Sech[c + d*x])^(3/2),x]","\text{\$Aborted}","-\frac{2 \text{sech}(c+d x) \tanh (c+d x) a^2}{b \left(a^2-b^2\right) d \sqrt{a+b \text{sech}(c+d x)}}-\frac{4 \tanh (c+d x) a}{\left(a^2-b^2\right) d \sqrt{a+b \text{sech}(c+d x)}}-\frac{2 \left(8 a^2-5 b^2\right) \coth (c+d x) E\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} a}{3 b^4 \sqrt{a+b} d}+\frac{4 \coth (c+d x) E\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} a}{b^2 \sqrt{a+b} d}+\frac{2 \left(4 a^2-b^2\right) \sqrt{a+b \text{sech}(c+d x)} \tanh (c+d x)}{3 b^2 \left(a^2-b^2\right) d}-\frac{2 (2 a+b) (4 a+b) \coth (c+d x) F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}}}{3 b^3 \sqrt{a+b} d}+\frac{4 \coth (c+d x) F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}}}{b \sqrt{a+b} d}+\frac{2 b^2 \tanh (c+d x)}{\left(a^2-b^2\right) d \sqrt{a+b \text{sech}(c+d x)} a}-\frac{2 \coth (c+d x) E\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}}}{\sqrt{a+b} d a}+\frac{2 \coth (c+d x) F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}}}{\sqrt{a+b} d a}+\frac{2 \sqrt{a+b} \coth (c+d x) \Pi \left(\frac{a+b}{a};\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}}}{d a^2}",1,"$Aborted","F",-1
148,-1,0,344,180.0009383,"\int \frac{\tanh ^2(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Integrate[Tanh[c + d*x]^2/(a + b*Sech[c + d*x])^(3/2),x]","\text{\$Aborted}","\frac{2 \sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} \Pi \left(\frac{a+b}{a};\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{a^2 d}+\frac{2 (a-b) \sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} E\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{a b^2 d}-\frac{2 \tanh (c+d x)}{a d \sqrt{a+b \text{sech}(c+d x)}}+\frac{2 \sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{a b d}",1,"$Aborted","F",-1
149,0,0,347,86.6686606,"\int \frac{1}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Integrate[(a + b*Sech[c + d*x])^(-3/2),x]","\int \frac{1}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","\frac{2 b^2 \tanh (c+d x)}{a d \left(a^2-b^2\right) \sqrt{a+b \text{sech}(c+d x)}}+\frac{2 \sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} \Pi \left(\frac{a+b}{a};\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{a^2 d}+\frac{2 \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{a d \sqrt{a+b}}-\frac{2 \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} E\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{a d \sqrt{a+b}}",1,"Integrate[(a + b*Sech[c + d*x])^(-3/2), x]","F",-1
150,0,0,665,110.5534007,"\int \frac{\coth ^2(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Integrate[Coth[c + d*x]^2/(a + b*Sech[c + d*x])^(3/2),x]","\int \frac{\coth ^2(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","\frac{2 b^2 \tanh (c+d x)}{a d \left(a^2-b^2\right) \sqrt{a+b \text{sech}(c+d x)}}-\frac{4 a b^2 \tanh (c+d x)}{d \left(a^2-b^2\right)^2 \sqrt{a+b \text{sech}(c+d x)}}-\frac{b^2 \tanh (c+d x)}{d \left(a^2-b^2\right) (a+b \text{sech}(c+d x))^{3/2}}+\frac{2 \sqrt{a+b} \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} \Pi \left(\frac{a+b}{a};\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{a^2 d}-\frac{\coth (c+d x)}{d (a+b \text{sech}(c+d x))^{3/2}}+\frac{2 \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{a d \sqrt{a+b}}-\frac{(3 a-b) \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} F\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{d (a-b) (a+b)^{3/2}}-\frac{2 \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} E\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{a d \sqrt{a+b}}+\frac{4 a \coth (c+d x) \sqrt{\frac{b (1-\text{sech}(c+d x))}{a+b}} \sqrt{-\frac{b (\text{sech}(c+d x)+1)}{a-b}} E\left(\sin ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a+b}}\right)|\frac{a+b}{a-b}\right)}{d (a-b) (a+b)^{3/2}}",1,"Integrate[Coth[c + d*x]^2/(a + b*Sech[c + d*x])^(3/2), x]","F",-1
151,1,84,191,0.0908712,"\int e^{c (a+b x)} \text{sech}^2(a c+b c x)^{7/2} \, dx","Integrate[E^(c*(a + b*x))*(Sech[a*c + b*c*x]^2)^(7/2),x]","-\frac{16 \left(6 e^{2 c (a+b x)}+15 e^{4 c (a+b x)}+20 e^{6 c (a+b x)}+1\right) \cosh (c (a+b x)) \sqrt{\text{sech}^2(c (a+b x))}}{15 b c \left(e^{2 c (a+b x)}+1\right)^6}","-\frac{64 \cosh (a c+b c x) \sqrt{\text{sech}^2(a c+b c x)}}{3 b c \left(e^{2 c (a+b x)}+1\right)^3}+\frac{48 \cosh (a c+b c x) \sqrt{\text{sech}^2(a c+b c x)}}{b c \left(e^{2 c (a+b x)}+1\right)^4}-\frac{192 \cosh (a c+b c x) \sqrt{\text{sech}^2(a c+b c x)}}{5 b c \left(e^{2 c (a+b x)}+1\right)^5}+\frac{32 \cosh (a c+b c x) \sqrt{\text{sech}^2(a c+b c x)}}{3 b c \left(e^{2 c (a+b x)}+1\right)^6}",1,"(-16*(1 + 6*E^(2*c*(a + b*x)) + 15*E^(4*c*(a + b*x)) + 20*E^(6*c*(a + b*x)))*Cosh[c*(a + b*x)]*Sqrt[Sech[c*(a + b*x)]^2])/(15*b*c*(1 + E^(2*c*(a + b*x)))^6)","A",1
152,1,72,141,0.0691276,"\int e^{c (a+b x)} \text{sech}^2(a c+b c x)^{5/2} \, dx","Integrate[E^(c*(a + b*x))*(Sech[a*c + b*c*x]^2)^(5/2),x]","-\frac{4 \left(4 e^{2 c (a+b x)}+6 e^{4 c (a+b x)}+1\right) \cosh (c (a+b x)) \sqrt{\text{sech}^2(c (a+b x))}}{3 b c \left(e^{2 c (a+b x)}+1\right)^4}","-\frac{8 \cosh (a c+b c x) \sqrt{\text{sech}^2(a c+b c x)}}{b c \left(e^{2 c (a+b x)}+1\right)^2}+\frac{32 \cosh (a c+b c x) \sqrt{\text{sech}^2(a c+b c x)}}{3 b c \left(e^{2 c (a+b x)}+1\right)^3}-\frac{4 \cosh (a c+b c x) \sqrt{\text{sech}^2(a c+b c x)}}{b c \left(e^{2 c (a+b x)}+1\right)^4}",1,"(-4*(1 + 4*E^(2*c*(a + b*x)) + 6*E^(4*c*(a + b*x)))*Cosh[c*(a + b*x)]*Sqrt[Sech[c*(a + b*x)]^2])/(3*b*c*(1 + E^(2*c*(a + b*x)))^4)","A",1
153,1,44,56,0.0586708,"\int e^{c (a+b x)} \text{sech}^2(a c+b c x)^{3/2} \, dx","Integrate[E^(c*(a + b*x))*(Sech[a*c + b*c*x]^2)^(3/2),x]","\frac{e^{3 c (a+b x)} \sqrt{\text{sech}^2(c (a+b x))}}{b c e^{2 c (a+b x)}+b c}","\frac{2 e^{4 c (a+b x)} \cosh (a c+b c x) \sqrt{\text{sech}^2(a c+b c x)}}{b c \left(e^{2 c (a+b x)}+1\right)^2}",1,"(E^(3*c*(a + b*x))*Sqrt[Sech[c*(a + b*x)]^2])/(b*c + b*c*E^(2*c*(a + b*x)))","A",1
154,1,42,44,0.0403032,"\int e^{c (a+b x)} \sqrt{\text{sech}^2(a c+b c x)} \, dx","Integrate[E^(c*(a + b*x))*Sqrt[Sech[a*c + b*c*x]^2],x]","\frac{\log \left(e^{2 c (a+b x)}+1\right) \cosh (c (a+b x)) \sqrt{\text{sech}^2(c (a+b x))}}{b c}","\frac{\log \left(e^{2 c (a+b x)}+1\right) \cosh (a c+b c x) \sqrt{\text{sech}^2(a c+b c x)}}{b c}",1,"(Cosh[c*(a + b*x)]*Log[1 + E^(2*c*(a + b*x))]*Sqrt[Sech[c*(a + b*x)]^2])/(b*c)","A",1
155,1,48,74,0.0525179,"\int \frac{e^{c (a+b x)}}{\sqrt{\text{sech}^2(a c+b c x)}} \, dx","Integrate[E^(c*(a + b*x))/Sqrt[Sech[a*c + b*c*x]^2],x]","\frac{\left(e^{2 c (a+b x)}+2 b c x\right) \text{sech}(c (a+b x))}{4 b c \sqrt{\text{sech}^2(c (a+b x))}}","\frac{e^{2 c (a+b x)} \text{sech}(a c+b c x)}{4 b c \sqrt{\text{sech}^2(a c+b c x)}}+\frac{x \text{sech}(a c+b c x)}{2 \sqrt{\text{sech}^2(a c+b c x)}}",1,"((E^(2*c*(a + b*x)) + 2*b*c*x)*Sech[c*(a + b*x)])/(4*b*c*Sqrt[Sech[c*(a + b*x)]^2])","A",1
156,1,78,162,0.0674719,"\int \frac{e^{c (a+b x)}}{\text{sech}^2(a c+b c x)^{3/2}} \, dx","Integrate[E^(c*(a + b*x))/(Sech[a*c + b*c*x]^2)^(3/2),x]","\frac{\left(-e^{-2 c (a+b x)}+3 e^{2 c (a+b x)}+\frac{1}{2} e^{4 c (a+b x)}+6 b c x\right) \text{sech}^3(c (a+b x))}{16 b c \text{sech}^2(c (a+b x))^{3/2}}","-\frac{e^{-2 c (a+b x)} \text{sech}(a c+b c x)}{16 b c \sqrt{\text{sech}^2(a c+b c x)}}+\frac{3 e^{2 c (a+b x)} \text{sech}(a c+b c x)}{16 b c \sqrt{\text{sech}^2(a c+b c x)}}+\frac{e^{4 c (a+b x)} \text{sech}(a c+b c x)}{32 b c \sqrt{\text{sech}^2(a c+b c x)}}+\frac{3 x \text{sech}(a c+b c x)}{8 \sqrt{\text{sech}^2(a c+b c x)}}",1,"((-E^(-2*c*(a + b*x)) + 3*E^(2*c*(a + b*x)) + E^(4*c*(a + b*x))/2 + 6*b*c*x)*Sech[c*(a + b*x)]^3)/(16*b*c*(Sech[c*(a + b*x)]^2)^(3/2))","A",1
157,1,106,250,0.1058624,"\int \frac{e^{c (a+b x)}}{\text{sech}^2(a c+b c x)^{5/2}} \, dx","Integrate[E^(c*(a + b*x))/(Sech[a*c + b*c*x]^2)^(5/2),x]","\frac{\left(-\frac{1}{2} e^{-4 c (a+b x)}-5 e^{-2 c (a+b x)}+10 e^{2 c (a+b x)}+\frac{5}{2} e^{4 c (a+b x)}+\frac{1}{3} e^{6 c (a+b x)}+20 b c x\right) \text{sech}^5(c (a+b x))}{64 b c \text{sech}^2(c (a+b x))^{5/2}}","-\frac{e^{-4 c (a+b x)} \text{sech}(a c+b c x)}{128 b c \sqrt{\text{sech}^2(a c+b c x)}}-\frac{5 e^{-2 c (a+b x)} \text{sech}(a c+b c x)}{64 b c \sqrt{\text{sech}^2(a c+b c x)}}+\frac{5 e^{2 c (a+b x)} \text{sech}(a c+b c x)}{32 b c \sqrt{\text{sech}^2(a c+b c x)}}+\frac{5 e^{4 c (a+b x)} \text{sech}(a c+b c x)}{128 b c \sqrt{\text{sech}^2(a c+b c x)}}+\frac{e^{6 c (a+b x)} \text{sech}(a c+b c x)}{192 b c \sqrt{\text{sech}^2(a c+b c x)}}+\frac{5 x \text{sech}(a c+b c x)}{16 \sqrt{\text{sech}^2(a c+b c x)}}",1,"((-1/2*1/E^(4*c*(a + b*x)) - 5/E^(2*c*(a + b*x)) + 10*E^(2*c*(a + b*x)) + (5*E^(4*c*(a + b*x)))/2 + E^(6*c*(a + b*x))/3 + 20*b*c*x)*Sech[c*(a + b*x)]^5)/(64*b*c*(Sech[c*(a + b*x)]^2)^(5/2))","A",1
158,1,77,108,0.1783943,"\int \frac{x^5}{\sqrt{\text{sech}(2 \log (c x))}} \, dx","Integrate[x^5/Sqrt[Sech[2*Log[c*x]]],x]","\frac{\sqrt{c^4 x^4+1} \sqrt{\frac{c^2 x^2}{2 c^4 x^4+2}} \left(\left(c^4 x^4+1\right)^{3/2}-\, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-c^4 x^4\right)\right)}{7 c^6}","\frac{2 x^2}{21 c^4 \sqrt{\text{sech}(2 \log (c x))}}+\frac{\sqrt{\frac{c^4+\frac{1}{x^4}}{\left(c^2+\frac{1}{x^2}\right)^2}} \left(c^2+\frac{1}{x^2}\right) F\left(2 \cot ^{-1}(c x)|\frac{1}{2}\right)}{21 c^5 x \left(c^4+\frac{1}{x^4}\right) \sqrt{\text{sech}(2 \log (c x))}}+\frac{x^6}{7 \sqrt{\text{sech}(2 \log (c x))}}",1,"(Sqrt[1 + c^4*x^4]*Sqrt[(c^2*x^2)/(2 + 2*c^4*x^4)]*((1 + c^4*x^4)^(3/2) - Hypergeometric2F1[-1/2, 1/4, 5/4, -(c^4*x^4)]))/(7*c^6)","C",1
159,1,44,28,0.0473627,"\int \frac{x^4}{\sqrt{\text{sech}(2 \log (c x))}} \, dx","Integrate[x^4/Sqrt[Sech[2*Log[c*x]]],x]","\frac{\left(c^4 x^4+1\right)^2 \sqrt{\frac{c^2 x^2}{2 c^4 x^4+2}}}{6 c^6 x}","\frac{x^5 \left(c^4+\frac{1}{x^4}\right)}{6 c^4 \sqrt{\text{sech}(2 \log (c x))}}",1,"((1 + c^4*x^4)^2*Sqrt[(c^2*x^2)/(2 + 2*c^4*x^4)])/(6*c^6*x)","A",1
160,1,65,203,0.1153625,"\int \frac{x^3}{\sqrt{\text{sech}(2 \log (c x))}} \, dx","Integrate[x^3/Sqrt[Sech[2*Log[c*x]]],x]","\frac{\left(\frac{c^2 x^2}{c^4 x^4+1}\right)^{3/2} \left(c^4 x^4+1\right)^{3/2} \, _2F_1\left(-\frac{1}{2},\frac{3}{4};\frac{7}{4};-c^4 x^4\right)}{3 \sqrt{2} c^4}","\frac{2}{5 c^4 \sqrt{\text{sech}(2 \log (c x))}}-\frac{2}{5 c^4 x^2 \left(c^2+\frac{1}{x^2}\right) \sqrt{\text{sech}(2 \log (c x))}}-\frac{\sqrt{\frac{c^4+\frac{1}{x^4}}{\left(c^2+\frac{1}{x^2}\right)^2}} \left(c^2+\frac{1}{x^2}\right) F\left(2 \cot ^{-1}(c x)|\frac{1}{2}\right)}{5 c^3 x \left(c^4+\frac{1}{x^4}\right) \sqrt{\text{sech}(2 \log (c x))}}+\frac{2 \sqrt{\frac{c^4+\frac{1}{x^4}}{\left(c^2+\frac{1}{x^2}\right)^2}} \left(c^2+\frac{1}{x^2}\right) E\left(2 \cot ^{-1}(c x)|\frac{1}{2}\right)}{5 c^3 x \left(c^4+\frac{1}{x^4}\right) \sqrt{\text{sech}(2 \log (c x))}}+\frac{x^4}{5 \sqrt{\text{sech}(2 \log (c x))}}",1,"(((c^2*x^2)/(1 + c^4*x^4))^(3/2)*(1 + c^4*x^4)^(3/2)*Hypergeometric2F1[-1/2, 3/4, 7/4, -(c^4*x^4)])/(3*Sqrt[2]*c^4)","C",1
161,1,77,67,0.145943,"\int \frac{x^2}{\sqrt{\text{sech}(2 \log (c x))}} \, dx","Integrate[x^2/Sqrt[Sech[2*Log[c*x]]],x]","\frac{x \left(\sinh ^{-1}\left(c^2 x^2\right)+c^2 x^2 \sqrt{c^4 x^4+1}\right)}{4 \sqrt{2} c^2 \sqrt{\frac{c^2 x^2}{c^4 x^4+1}} \sqrt{c^4 x^4+1}}","\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{c^4 x^4}+1}\right)}{4 c^4 x \sqrt{\frac{1}{c^4 x^4}+1} \sqrt{\text{sech}(2 \log (c x))}}+\frac{x^3}{4 \sqrt{\text{sech}(2 \log (c x))}}",1,"(x*(c^2*x^2*Sqrt[1 + c^4*x^4] + ArcSinh[c^2*x^2]))/(4*Sqrt[2]*c^2*Sqrt[(c^2*x^2)/(1 + c^4*x^4)]*Sqrt[1 + c^4*x^4])","A",1
162,1,58,87,0.1043358,"\int \frac{x}{\sqrt{\text{sech}(2 \log (c x))}} \, dx","Integrate[x/Sqrt[Sech[2*Log[c*x]]],x]","\frac{\sqrt{c^4 x^4+1} \sqrt{\frac{c^2 x^2}{2 c^4 x^4+2}} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{5}{4};-c^4 x^4\right)}{c^2}","\frac{x^2}{3 \sqrt{\text{sech}(2 \log (c x))}}-\frac{\sqrt{\frac{c^4+\frac{1}{x^4}}{\left(c^2+\frac{1}{x^2}\right)^2}} \left(c^2+\frac{1}{x^2}\right) F\left(2 \cot ^{-1}(c x)|\frac{1}{2}\right)}{3 c x \left(c^4+\frac{1}{x^4}\right) \sqrt{\text{sech}(2 \log (c x))}}",1,"(Sqrt[1 + c^4*x^4]*Sqrt[(c^2*x^2)/(2 + 2*c^4*x^4)]*Hypergeometric2F1[-1/2, 1/4, 5/4, -(c^4*x^4)])/c^2","C",1
163,1,77,59,0.0958248,"\int \frac{1}{\sqrt{\text{sech}(2 \log (c x))}} \, dx","Integrate[1/Sqrt[Sech[2*Log[c*x]]],x]","\frac{x \left(2 \sqrt{c^4 x^4+1}-2 \tanh ^{-1}\left(\sqrt{c^4 x^4+1}\right)\right)}{4 \sqrt{2} \sqrt{\frac{c^2 x^2}{c^4 x^4+1}} \sqrt{c^4 x^4+1}}","\frac{x}{2 \sqrt{\text{sech}(2 \log (c x))}}-\frac{\text{csch}^{-1}\left(c^2 x^2\right)}{2 c^2 x \sqrt{\frac{1}{c^4 x^4}+1} \sqrt{\text{sech}(2 \log (c x))}}",1,"(x*(2*Sqrt[1 + c^4*x^4] - 2*ArcTanh[Sqrt[1 + c^4*x^4]]))/(4*Sqrt[2]*Sqrt[(c^2*x^2)/(1 + c^4*x^4)]*Sqrt[1 + c^4*x^4])","A",1
164,1,36,36,0.0580428,"\int \frac{\sqrt{\text{sech}(2 \log (c x))}}{x} \, dx","Integrate[Sqrt[Sech[2*Log[c*x]]]/x,x]","-i \sqrt{\text{sech}(2 \log (c x))} \sqrt{\cosh (2 \log (c x))} F(i \log (c x)|2)","-i \sqrt{\text{sech}(2 \log (c x))} \sqrt{\cosh (2 \log (c x))} F(i \log (c x)|2)",1,"(-I)*Sqrt[Cosh[2*Log[c*x]]]*EllipticF[I*Log[c*x], 2]*Sqrt[Sech[2*Log[c*x]]]","A",1
165,1,55,40,0.1223029,"\int \frac{\sqrt{\text{sech}(2 \log (c x))}}{x^2} \, dx","Integrate[Sqrt[Sech[2*Log[c*x]]]/x^2,x]","-\frac{\sqrt{c^4 x^4+1} \sqrt{\frac{c^2 x^2}{2 c^4 x^4+2}} \tanh ^{-1}\left(\sqrt{c^4 x^4+1}\right)}{x}","-\frac{1}{2} c^2 x \sqrt{\frac{1}{c^4 x^4}+1} \text{csch}^{-1}\left(c^2 x^2\right) \sqrt{\text{sech}(2 \log (c x))}",1,"-((Sqrt[1 + c^4*x^4]*Sqrt[(c^2*x^2)/(2 + 2*c^4*x^4)]*ArcTanh[Sqrt[1 + c^4*x^4]])/x)","A",1
166,1,59,137,0.1217473,"\int \frac{\sqrt{\text{sech}(2 \log (c x))}}{x^3} \, dx","Integrate[Sqrt[Sech[2*Log[c*x]]]/x^3,x]","-\frac{c^2 \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-c^4 x^4\right)}{\sqrt{c^4 x^4+1} \sqrt{\frac{c^2 x^2}{2 c^4 x^4+2}}}","-\frac{\left(c^4+\frac{1}{x^4}\right) \sqrt{\text{sech}(2 \log (c x))}}{c^2+\frac{1}{x^2}}-\frac{1}{2} c x \sqrt{\frac{c^4+\frac{1}{x^4}}{\left(c^2+\frac{1}{x^2}\right)^2}} \left(c^2+\frac{1}{x^2}\right) \sqrt{\text{sech}(2 \log (c x))} F\left(2 \cot ^{-1}(c x)|\frac{1}{2}\right)+c x \sqrt{\frac{c^4+\frac{1}{x^4}}{\left(c^2+\frac{1}{x^2}\right)^2}} \left(c^2+\frac{1}{x^2}\right) \sqrt{\text{sech}(2 \log (c x))} E\left(2 \cot ^{-1}(c x)|\frac{1}{2}\right)",1,"-((c^2*Hypergeometric2F1[-1/4, 1/2, 3/4, -(c^4*x^4)])/(Sqrt[1 + c^4*x^4]*Sqrt[(c^2*x^2)/(2 + 2*c^4*x^4)]))","C",1
167,1,33,23,0.0399796,"\int \frac{\sqrt{\text{sech}(2 \log (c x))}}{x^4} \, dx","Integrate[Sqrt[Sech[2*Log[c*x]]]/x^4,x]","-\frac{c^2}{2 x \sqrt{\frac{c^2 x^2}{2 c^4 x^4+2}}}","-\frac{1}{2} x \left(c^4+\frac{1}{x^4}\right) \sqrt{\text{sech}(2 \log (c x))}",1,"-1/2*c^2/(x*Sqrt[(c^2*x^2)/(2 + 2*c^4*x^4)])","A",1
168,1,65,80,0.1011645,"\int \frac{\sqrt{\text{sech}(2 \log (c x))}}{x^5} \, dx","Integrate[Sqrt[Sech[2*Log[c*x]]]/x^5,x]","-\frac{\sqrt{2} \sqrt{\frac{c^2 x^2}{c^4 x^4+1}} \sqrt{c^4 x^4+1} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};-c^4 x^4\right)}{3 x^4}","\frac{1}{6} c^3 x \sqrt{\frac{c^4+\frac{1}{x^4}}{\left(c^2+\frac{1}{x^2}\right)^2}} \left(c^2+\frac{1}{x^2}\right) \sqrt{\text{sech}(2 \log (c x))} F\left(2 \cot ^{-1}(c x)|\frac{1}{2}\right)-\frac{1}{3} \left(c^4+\frac{1}{x^4}\right) \sqrt{\text{sech}(2 \log (c x))}",1,"-1/3*(Sqrt[2]*Sqrt[(c^2*x^2)/(1 + c^4*x^4)]*Sqrt[1 + c^4*x^4]*Hypergeometric2F1[-3/4, 1/2, 1/4, -(c^4*x^4)])/x^4","C",1
169,1,98,122,0.1941153,"\int \frac{x^8}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[x^8/Sech[2*Log[c*x]]^(3/2),x]","\frac{c^3 x^3 \sqrt{c^4 x^4+1} \left(8 c^8 x^8+14 c^4 x^4+3\right)-3 c x \sinh ^{-1}\left(c^2 x^2\right)}{192 \sqrt{2} c^9 \sqrt{\frac{c^2 x^2}{c^4 x^4+1}} \sqrt{c^4 x^4+1}}","\frac{x}{32 c^4 \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{x^5}{16 \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))}-\frac{\tanh ^{-1}\left(\sqrt{\frac{1}{c^4 x^4}+1}\right)}{32 c^{12} x^3 \left(\frac{1}{c^4 x^4}+1\right)^{3/2} \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{x^9}{12 \text{sech}^{\frac{3}{2}}(2 \log (c x))}",1,"(c^3*x^3*Sqrt[1 + c^4*x^4]*(3 + 14*c^4*x^4 + 8*c^8*x^8) - 3*c*x*ArcSinh[c^2*x^2])/(192*Sqrt[2]*c^9*Sqrt[(c^2*x^2)/(1 + c^4*x^4)]*Sqrt[1 + c^4*x^4])","A",1
170,1,77,141,0.1838584,"\int \frac{x^7}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[x^7/Sech[2*Log[c*x]]^(3/2),x]","\frac{\sqrt{c^4 x^4+1} \sqrt{\frac{c^2 x^2}{2 c^4 x^4+2}} \left(\left(c^4 x^4+1\right)^{5/2}-\, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};-c^4 x^4\right)\right)}{22 c^8}","\frac{6 x^4}{77 \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{4}{77 c^4 \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{2 \sqrt{\frac{c^4+\frac{1}{x^4}}{\left(c^2+\frac{1}{x^2}\right)^2}} \left(c^2+\frac{1}{x^2}\right) F\left(2 \cot ^{-1}(c x)|\frac{1}{2}\right)}{77 c^5 x^3 \left(c^4+\frac{1}{x^4}\right)^2 \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{x^8}{11 \text{sech}^{\frac{3}{2}}(2 \log (c x))}",1,"(Sqrt[1 + c^4*x^4]*Sqrt[(c^2*x^2)/(2 + 2*c^4*x^4)]*((1 + c^4*x^4)^(5/2) - Hypergeometric2F1[-3/2, 1/4, 5/4, -(c^4*x^4)]))/(22*c^8)","C",1
171,1,44,28,0.0531813,"\int \frac{x^6}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[x^6/Sech[2*Log[c*x]]^(3/2),x]","\frac{\left(c^4 x^4+1\right)^3 \sqrt{\frac{c^2 x^2}{2 c^4 x^4+2}}}{20 c^8 x}","\frac{x^7 \left(c^4+\frac{1}{x^4}\right)}{10 c^4 \text{sech}^{\frac{3}{2}}(2 \log (c x))}",1,"((1 + c^4*x^4)^3*Sqrt[(c^2*x^2)/(2 + 2*c^4*x^4)])/(20*c^8*x)","A",1
172,1,65,251,0.1193333,"\int \frac{x^5}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[x^5/Sech[2*Log[c*x]]^(3/2),x]","\frac{\left(\frac{c^2 x^2}{c^4 x^4+1}\right)^{3/2} \left(c^4 x^4+1\right)^{3/2} \, _2F_1\left(-\frac{3}{2},\frac{3}{4};\frac{7}{4};-c^4 x^4\right)}{6 \sqrt{2} c^6}","\frac{2 x^2}{15 \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{4}{15 c^4 x^2 \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))}-\frac{4}{15 c^4 x^4 \left(c^4+\frac{1}{x^4}\right) \left(c^2+\frac{1}{x^2}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))}-\frac{2 \sqrt{\frac{c^4+\frac{1}{x^4}}{\left(c^2+\frac{1}{x^2}\right)^2}} \left(c^2+\frac{1}{x^2}\right) F\left(2 \cot ^{-1}(c x)|\frac{1}{2}\right)}{15 c^3 x^3 \left(c^4+\frac{1}{x^4}\right)^2 \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{4 \sqrt{\frac{c^4+\frac{1}{x^4}}{\left(c^2+\frac{1}{x^2}\right)^2}} \left(c^2+\frac{1}{x^2}\right) E\left(2 \cot ^{-1}(c x)|\frac{1}{2}\right)}{15 c^3 x^3 \left(c^4+\frac{1}{x^4}\right)^2 \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{x^6}{9 \text{sech}^{\frac{3}{2}}(2 \log (c x))}",1,"(((c^2*x^2)/(1 + c^4*x^4))^(3/2)*(1 + c^4*x^4)^(3/2)*Hypergeometric2F1[-3/2, 3/4, 7/4, -(c^4*x^4)])/(6*Sqrt[2]*c^6)","C",1
173,1,90,92,0.1722064,"\int \frac{x^4}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[x^4/Sech[2*Log[c*x]]^(3/2),x]","\frac{3 c x \sinh ^{-1}\left(c^2 x^2\right)+c^3 x^3 \sqrt{c^4 x^4+1} \left(2 c^4 x^4+5\right)}{32 \sqrt{2} c^5 \sqrt{\frac{c^2 x^2}{c^4 x^4+1}} \sqrt{c^4 x^4+1}}","\frac{3 x}{16 \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{3 \tanh ^{-1}\left(\sqrt{\frac{1}{c^4 x^4}+1}\right)}{16 c^8 x^3 \left(\frac{1}{c^4 x^4}+1\right)^{3/2} \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{x^5}{8 \text{sech}^{\frac{3}{2}}(2 \log (c x))}",1,"(c^3*x^3*Sqrt[1 + c^4*x^4]*(5 + 2*c^4*x^4) + 3*c*x*ArcSinh[c^2*x^2])/(32*Sqrt[2]*c^5*Sqrt[(c^2*x^2)/(1 + c^4*x^4)]*Sqrt[1 + c^4*x^4])","A",1
174,1,61,111,0.1115356,"\int \frac{x^3}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[x^3/Sech[2*Log[c*x]]^(3/2),x]","\frac{\sqrt{c^4 x^4+1} \sqrt{\frac{c^2 x^2}{2 c^4 x^4+2}} \, _2F_1\left(-\frac{3}{2},\frac{1}{4};\frac{5}{4};-c^4 x^4\right)}{2 c^4}","\frac{2}{7 \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))}-\frac{2 \sqrt{\frac{c^4+\frac{1}{x^4}}{\left(c^2+\frac{1}{x^2}\right)^2}} \left(c^2+\frac{1}{x^2}\right) F\left(2 \cot ^{-1}(c x)|\frac{1}{2}\right)}{7 c x^3 \left(c^4+\frac{1}{x^4}\right)^2 \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{x^4}{7 \text{sech}^{\frac{3}{2}}(2 \log (c x))}",1,"(Sqrt[1 + c^4*x^4]*Sqrt[(c^2*x^2)/(2 + 2*c^4*x^4)]*Hypergeometric2F1[-3/2, 1/4, 5/4, -(c^4*x^4)])/(2*c^4)","C",1
175,1,88,88,0.1683226,"\int \frac{x^2}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[x^2/Sech[2*Log[c*x]]^(3/2),x]","\frac{x \left(\sqrt{c^4 x^4+1} \left(c^4 x^4+4\right)-3 \tanh ^{-1}\left(\sqrt{c^4 x^4+1}\right)\right)}{12 \sqrt{2} c^2 \sqrt{\frac{c^2 x^2}{c^4 x^4+1}} \sqrt{c^4 x^4+1}}","\frac{1}{2 x \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))}-\frac{\text{csch}^{-1}\left(c^2 x^2\right)}{2 c^6 x^3 \left(\frac{1}{c^4 x^4}+1\right)^{3/2} \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{x^3}{6 \text{sech}^{\frac{3}{2}}(2 \log (c x))}",1,"(x*(Sqrt[1 + c^4*x^4]*(4 + c^4*x^4) - 3*ArcTanh[Sqrt[1 + c^4*x^4]]))/(12*Sqrt[2]*c^2*Sqrt[(c^2*x^2)/(1 + c^4*x^4)]*Sqrt[1 + c^4*x^4])","A",1
176,1,65,214,0.1148768,"\int \frac{x}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[x/Sech[2*Log[c*x]]^(3/2),x]","-\frac{\, _2F_1\left(-\frac{3}{2},-\frac{1}{4};\frac{3}{4};-c^4 x^4\right)}{2 \sqrt{2} c^2 \sqrt{\frac{c^2 x^2}{c^4 x^4+1}} \sqrt{c^4 x^4+1}}","\frac{6}{5 x^2 \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))}-\frac{12}{5 x^4 \left(c^4+\frac{1}{x^4}\right) \left(c^2+\frac{1}{x^2}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))}-\frac{6 c \sqrt{\frac{c^4+\frac{1}{x^4}}{\left(c^2+\frac{1}{x^2}\right)^2}} \left(c^2+\frac{1}{x^2}\right) F\left(2 \cot ^{-1}(c x)|\frac{1}{2}\right)}{5 x^3 \left(c^4+\frac{1}{x^4}\right)^2 \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{12 c \sqrt{\frac{c^4+\frac{1}{x^4}}{\left(c^2+\frac{1}{x^2}\right)^2}} \left(c^2+\frac{1}{x^2}\right) E\left(2 \cot ^{-1}(c x)|\frac{1}{2}\right)}{5 x^3 \left(c^4+\frac{1}{x^4}\right)^2 \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{x^2}{5 \text{sech}^{\frac{3}{2}}(2 \log (c x))}",1,"-1/2*Hypergeometric2F1[-3/2, -1/4, 3/4, -(c^4*x^4)]/(Sqrt[2]*c^2*Sqrt[(c^2*x^2)/(1 + c^4*x^4)]*Sqrt[1 + c^4*x^4])","C",1
177,1,64,92,0.0901427,"\int \frac{1}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Integrate[Sech[2*Log[c*x]]^(-3/2),x]","-\frac{\sqrt{c^4 x^4+1} \sqrt{\frac{c^2 x^2}{2 c^4 x^4+2}} \, _2F_1\left(-\frac{3}{2},-\frac{1}{2};\frac{1}{2};-c^4 x^4\right)}{4 c^4 x^3}","-\frac{3}{4 x^3 \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{3 \tanh ^{-1}\left(\sqrt{\frac{1}{c^4 x^4}+1}\right)}{4 c^4 x^3 \left(\frac{1}{c^4 x^4}+1\right)^{3/2} \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{x}{4 \text{sech}^{\frac{3}{2}}(2 \log (c x))}",1,"-1/4*(Sqrt[1 + c^4*x^4]*Sqrt[(c^2*x^2)/(2 + 2*c^4*x^4)]*Hypergeometric2F1[-3/2, -1/2, 1/2, -(c^4*x^4)])/(c^4*x^3)","C",1
178,1,45,56,0.1079933,"\int \frac{\text{sech}^{\frac{3}{2}}(2 \log (c x))}{x} \, dx","Integrate[Sech[2*Log[c*x]]^(3/2)/x,x]","\frac{\tanh (2 \log (c x))+\frac{i E(i \log (c x)|2)}{\sqrt{\cosh (2 \log (c x))}}}{\sqrt{\text{sech}(2 \log (c x))}}","\sinh (2 \log (c x)) \sqrt{\text{sech}(2 \log (c x))}+i \sqrt{\text{sech}(2 \log (c x))} \sqrt{\cosh (2 \log (c x))} E(i \log (c x)|2)",1,"((I*EllipticE[I*Log[c*x], 2])/Sqrt[Cosh[2*Log[c*x]]] + Tanh[2*Log[c*x]])/Sqrt[Sech[2*Log[c*x]]]","A",1
179,1,32,25,0.0348538,"\int \frac{\text{sech}^{\frac{3}{2}}(2 \log (c x))}{x^2} \, dx","Integrate[Sech[2*Log[c*x]]^(3/2)/x^2,x]","\sqrt{2} c^2 x \sqrt{\frac{c^2 x^2}{c^4 x^4+1}}","\frac{1}{2} x^3 \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))",1,"Sqrt[2]*c^2*x*Sqrt[(c^2*x^2)/(1 + c^4*x^4)]","A",1
180,1,65,92,0.111556,"\int \frac{\text{sech}^{\frac{3}{2}}(2 \log (c x))}{x^3} \, dx","Integrate[Sech[2*Log[c*x]]^(3/2)/x^3,x]","\sqrt{2} c^2 \sqrt{\frac{c^2 x^2}{c^4 x^4+1}} \left(\sqrt{c^4 x^4+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-c^4 x^4\right)+1\right)","\frac{1}{2} x^2 \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))-\frac{x^3 \left(c^4+\frac{1}{x^4}\right) \sqrt{\frac{c^4+\frac{1}{x^4}}{\left(c^2+\frac{1}{x^2}\right)^2}} \left(c^2+\frac{1}{x^2}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x)) F\left(2 \cot ^{-1}(c x)|\frac{1}{2}\right)}{4 c}",1,"Sqrt[2]*c^2*Sqrt[(c^2*x^2)/(1 + c^4*x^4)]*(1 + Sqrt[1 + c^4*x^4]*Hypergeometric2F1[1/4, 1/2, 5/4, -(c^4*x^4)])","C",1
181,1,51,66,0.1108389,"\int \frac{\text{sech}^{\frac{3}{2}}(2 \log (c x))}{x^4} \, dx","Integrate[Sech[2*Log[c*x]]^(3/2)/x^4,x]","\frac{\sqrt{2} c^2 \sqrt{\frac{c^2 x^2}{c^4 x^4+1}} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};c^4 x^4+1\right)}{x}","\frac{1}{2} x \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))-\frac{1}{2} c^6 x^3 \left(\frac{1}{c^4 x^4}+1\right)^{3/2} \text{csch}^{-1}\left(c^2 x^2\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))",1,"(Sqrt[2]*c^2*Sqrt[(c^2*x^2)/(1 + c^4*x^4)]*Hypergeometric2F1[-1/2, 1, 1/2, 1 + c^4*x^4])/x","C",1
182,1,64,63,0.1510678,"\int \text{sech}\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Sech[a + b*Log[c*x^n]],x]","\frac{2 e^a x \left(c x^n\right)^b \, _2F_1\left(1,\frac{1}{2} \left(1+\frac{1}{b n}\right);\frac{1}{2} \left(3+\frac{1}{b n}\right);-e^{2 a} \left(c x^n\right)^{2 b}\right)}{b n+1}","\frac{2 e^a x \left(c x^n\right)^b \, _2F_1\left(1,\frac{b+\frac{1}{n}}{2 b};\frac{1}{2} \left(3+\frac{1}{b n}\right);-e^{2 a} \left(c x^n\right)^{2 b}\right)}{b n+1}",1,"(2*E^a*x*(c*x^n)^b*Hypergeometric2F1[1, (1 + 1/(b*n))/2, (3 + 1/(b*n))/2, -(E^(2*a)*(c*x^n)^(2*b))])/(1 + b*n)","A",1
183,1,126,69,5.552514,"\int \text{sech}^2\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Sech[a + b*Log[c*x^n]]^2,x]","\frac{x \left(-\frac{e^{2 a} \left(c x^n\right)^{2 b} \, _2F_1\left(1,1+\frac{1}{2 b n};2+\frac{1}{2 b n};-e^{2 a} \left(c x^n\right)^{2 b}\right)}{2 b n+1}+\, _2F_1\left(1,\frac{1}{2 b n};1+\frac{1}{2 b n};-e^{2 a} \left(c x^n\right)^{2 b}\right)+\tanh \left(a+b \log \left(c x^n\right)\right)\right)}{b n}","\frac{4 e^{2 a} x \left(c x^n\right)^{2 b} \, _2F_1\left(2,\frac{1}{2} \left(2+\frac{1}{b n}\right);\frac{1}{2} \left(4+\frac{1}{b n}\right);-e^{2 a} \left(c x^n\right)^{2 b}\right)}{2 b n+1}",1,"(x*(-((E^(2*a)*(c*x^n)^(2*b)*Hypergeometric2F1[1, 1 + 1/(2*b*n), 2 + 1/(2*b*n), -(E^(2*a)*(c*x^n)^(2*b))])/(1 + 2*b*n)) + Hypergeometric2F1[1, 1/(2*b*n), 1 + 1/(2*b*n), -(E^(2*a)*(c*x^n)^(2*b))] + Tanh[a + b*Log[c*x^n]]))/(b*n)","A",0
184,1,101,70,0.9034857,"\int \text{sech}^3\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Sech[a + b*Log[c*x^n]]^3,x]","\frac{x \left(2 e^a (b n-1) \left(c x^n\right)^b \, _2F_1\left(1,\frac{1}{2} \left(1+\frac{1}{b n}\right);\frac{1}{2} \left(3+\frac{1}{b n}\right);-e^{2 a} \left(c x^n\right)^{2 b}\right)+\left(b n \tanh \left(a+b \log \left(c x^n\right)\right)+1\right) \text{sech}\left(a+b \log \left(c x^n\right)\right)\right)}{2 b^2 n^2}","\frac{8 e^{3 a} x \left(c x^n\right)^{3 b} \, _2F_1\left(3,\frac{3 b+\frac{1}{n}}{2 b};\frac{1}{2} \left(5+\frac{1}{b n}\right);-e^{2 a} \left(c x^n\right)^{2 b}\right)}{3 b n+1}",1,"(x*(2*E^a*(-1 + b*n)*(c*x^n)^b*Hypergeometric2F1[1, (1 + 1/(b*n))/2, (3 + 1/(b*n))/2, -(E^(2*a)*(c*x^n)^(2*b))] + Sech[a + b*Log[c*x^n]]*(1 + b*n*Tanh[a + b*Log[c*x^n]])))/(2*b^2*n^2)","A",0
185,1,192,69,13.7008346,"\int \text{sech}^4\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Sech[a + b*Log[c*x^n]]^4,x]","\frac{x \left(\left(8 b^2 n^2-2\right) \, _2F_1\left(1,\frac{1}{2 b n};1+\frac{1}{2 b n};-e^{2 a} \left(c x^n\right)^{2 b}\right)+\text{sech}^2\left(a+b \log \left(c x^n\right)\right) \left(\tanh \left(a+b \log \left(c x^n\right)\right) \left(\left(4 b^2 n^2-1\right) \cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+8 b^2 n^2-1\right)+2 b n\right)-2 e^{2 a} (2 b n-1) \left(c x^n\right)^{2 b} \, _2F_1\left(1,1+\frac{1}{2 b n};2+\frac{1}{2 b n};-e^{2 a} \left(c x^n\right)^{2 b}\right)\right)}{12 b^3 n^3}","\frac{16 e^{4 a} x \left(c x^n\right)^{4 b} \, _2F_1\left(4,\frac{1}{2} \left(4+\frac{1}{b n}\right);\frac{1}{2} \left(6+\frac{1}{b n}\right);-e^{2 a} \left(c x^n\right)^{2 b}\right)}{4 b n+1}",1,"(x*(-2*E^(2*a)*(-1 + 2*b*n)*(c*x^n)^(2*b)*Hypergeometric2F1[1, 1 + 1/(2*b*n), 2 + 1/(2*b*n), -(E^(2*a)*(c*x^n)^(2*b))] + (-2 + 8*b^2*n^2)*Hypergeometric2F1[1, 1/(2*b*n), 1 + 1/(2*b*n), -(E^(2*a)*(c*x^n)^(2*b))] + Sech[a + b*Log[c*x^n]]^2*(2*b*n + (-1 + 8*b^2*n^2 + (-1 + 4*b^2*n^2)*Cosh[2*(a + b*Log[c*x^n])])*Tanh[a + b*Log[c*x^n]])))/(12*b^3*n^3)","B",0
186,1,29,40,0.3189258,"\int \left(\left(1-b^2 n^2\right) \text{sech}\left(a+b \log \left(c x^n\right)\right)+2 b^2 n^2 \text{sech}^3\left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[(1 - b^2*n^2)*Sech[a + b*Log[c*x^n]] + 2*b^2*n^2*Sech[a + b*Log[c*x^n]]^3,x]","x \left(b n \tanh \left(a+b \log \left(c x^n\right)\right)+1\right) \text{sech}\left(a+b \log \left(c x^n\right)\right)","x \text{sech}\left(a+b \log \left(c x^n\right)\right)+b n x \tanh \left(a+b \log \left(c x^n\right)\right) \text{sech}\left(a+b \log \left(c x^n\right)\right)",1,"x*Sech[a + b*Log[c*x^n]]*(1 + b*n*Tanh[a + b*Log[c*x^n]])","A",1
187,1,62,25,0.1288719,"\int \text{sech}^3\left(a+2 \log \left(c \sqrt{x}\right)\right) \, dx","Integrate[Sech[a + 2*Log[c*Sqrt[x]]]^3,x]","-\frac{2 (\cosh (a)-\sinh (a)) \left(\sinh ^2(a)+\cosh ^2(a)-2 \sinh (a) \cosh (a)+2 c^4 x^2\right)}{c^2 \left(\sinh (a) \left(c^4 x^2-1\right)+\cosh (a) \left(c^4 x^2+1\right)\right)^2}","\frac{2 e^{-a} c^6}{\left(\frac{e^{-2 a}}{x^2}+c^4\right)^2}",1,"(-2*(Cosh[a] - Sinh[a])*(2*c^4*x^2 + Cosh[a]^2 - 2*Cosh[a]*Sinh[a] + Sinh[a]^2))/(c^2*((1 + c^4*x^2)*Cosh[a] + (-1 + c^4*x^2)*Sinh[a])^2)","B",1
188,1,64,25,0.1082747,"\int \text{sech}^3\left(a+2 \log \left(\frac{c}{\sqrt{x}}\right)\right) \, dx","Integrate[Sech[a + 2*Log[c/Sqrt[x]]]^3,x]","-\frac{2 c^6 (\sinh (2 a)+\cosh (2 a)) \left(\sinh (a) \left(c^4-2 x^2\right)+\cosh (a) \left(c^4+2 x^2\right)\right)}{\left(\sinh (a) \left(c^4-x^2\right)+\cosh (a) \left(c^4+x^2\right)\right)^2}","\frac{2 e^{-3 a} c^2}{\left(e^{-2 a}+\frac{c^4}{x^2}\right)^2}",1,"(-2*c^6*((c^4 + 2*x^2)*Cosh[a] + (c^4 - 2*x^2)*Sinh[a])*(Cosh[2*a] + Sinh[2*a]))/((c^4 + x^2)*Cosh[a] + (c^4 - x^2)*Sinh[a])^2","B",1
189,1,57,89,0.7720243,"\int \text{sech}^p\left(a+\frac{\log \left(c x^n\right)}{n (-2+p)}\right) \, dx","Integrate[Sech[a + Log[c*x^n]/(n*(-2 + p))]^p,x]","\frac{(p-2) x \left(e^{2 a} \left(c x^n\right)^{\frac{2}{n (p-2)}}+1\right) \text{sech}^p\left(a+\frac{\log \left(c x^n\right)}{n (p-2)}\right)}{2 (p-1)}","\frac{e^{2 a} (2-p) x \left(c x^n\right)^{-\frac{2}{n (2-p)}} \left(e^{-2 a} \left(c x^n\right)^{\frac{2}{n (2-p)}}+1\right) \text{sech}^p\left(a-\frac{\log \left(c x^n\right)}{n (2-p)}\right)}{2 (1-p)}",1,"((-2 + p)*x*(1 + E^(2*a)*(c*x^n)^(2/(n*(-2 + p))))*Sech[a + Log[c*x^n]/(n*(-2 + p))]^p)/(2*(-1 + p))","A",1
190,1,62,65,0.8769327,"\int \text{sech}^p\left(a-\frac{\log \left(c x^n\right)}{n (-2+p)}\right) \, dx","Integrate[Sech[a - Log[c*x^n]/(n*(-2 + p))]^p,x]","\frac{e^{-2 a} (p-2) x \left(e^{2 a}+\left(c x^n\right)^{\frac{2}{n (p-2)}}\right) \text{sech}^p\left(a+\frac{\log \left(c x^n\right)}{2 n-n p}\right)}{2 (p-1)}","\frac{(2-p) x \left(e^{-2 a} \left(c x^n\right)^{-\frac{2}{n (2-p)}}+1\right) \text{sech}^p\left(a+\frac{\log \left(c x^n\right)}{n (2-p)}\right)}{2 (1-p)}",1,"((-2 + p)*x*(E^(2*a) + (c*x^n)^(2/(n*(-2 + p))))*Sech[a + Log[c*x^n]/(2*n - n*p)]^p)/(2*E^(2*a)*(-1 + p))","A",1
191,1,19,19,0.0487027,"\int \frac{\text{sech}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Sech[a + b*Log[c*x^n]]/x,x]","\frac{\tan ^{-1}\left(\sinh \left(a+b \log \left(c x^n\right)\right)\right)}{b n}","\frac{\tan ^{-1}\left(\sinh \left(a+b \log \left(c x^n\right)\right)\right)}{b n}",1,"ArcTan[Sinh[a + b*Log[c*x^n]]]/(b*n)","A",1
192,1,18,18,0.0601145,"\int \frac{\text{sech}^2\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Sech[a + b*Log[c*x^n]]^2/x,x]","\frac{\tanh \left(a+b \log \left(c x^n\right)\right)}{b n}","\frac{\tanh \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"Tanh[a + b*Log[c*x^n]]/(b*n)","A",1
193,1,55,55,0.0587975,"\int \frac{\text{sech}^3\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Sech[a + b*Log[c*x^n]]^3/x,x]","\frac{\tan ^{-1}\left(\sinh \left(a+b \log \left(c x^n\right)\right)\right)}{2 b n}+\frac{\tanh \left(a+b \log \left(c x^n\right)\right) \text{sech}\left(a+b \log \left(c x^n\right)\right)}{2 b n}","\frac{\tan ^{-1}\left(\sinh \left(a+b \log \left(c x^n\right)\right)\right)}{2 b n}+\frac{\tanh \left(a+b \log \left(c x^n\right)\right) \text{sech}\left(a+b \log \left(c x^n\right)\right)}{2 b n}",1,"ArcTan[Sinh[a + b*Log[c*x^n]]]/(2*b*n) + (Sech[a + b*Log[c*x^n]]*Tanh[a + b*Log[c*x^n]])/(2*b*n)","A",1
194,1,42,42,0.0490803,"\int \frac{\text{sech}^4\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Sech[a + b*Log[c*x^n]]^4/x,x]","\frac{\tanh \left(a+b \log \left(c x^n\right)\right)}{b n}-\frac{\tanh ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}","\frac{\tanh \left(a+b \log \left(c x^n\right)\right)}{b n}-\frac{\tanh ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}",1,"Tanh[a + b*Log[c*x^n]]/(b*n) - Tanh[a + b*Log[c*x^n]]^3/(3*b*n)","A",1
195,1,75,89,0.093525,"\int \frac{\text{sech}^5\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Sech[a + b*Log[c*x^n]]^5/x,x]","\frac{3 \tan ^{-1}\left(\sinh \left(a+b \log \left(c x^n\right)\right)\right)+2 \tanh \left(a+b \log \left(c x^n\right)\right) \text{sech}^3\left(a+b \log \left(c x^n\right)\right)+3 \tanh \left(a+b \log \left(c x^n\right)\right) \text{sech}\left(a+b \log \left(c x^n\right)\right)}{8 b n}","\frac{3 \tan ^{-1}\left(\sinh \left(a+b \log \left(c x^n\right)\right)\right)}{8 b n}+\frac{\tanh \left(a+b \log \left(c x^n\right)\right) \text{sech}^3\left(a+b \log \left(c x^n\right)\right)}{4 b n}+\frac{3 \tanh \left(a+b \log \left(c x^n\right)\right) \text{sech}\left(a+b \log \left(c x^n\right)\right)}{8 b n}",1,"(3*ArcTan[Sinh[a + b*Log[c*x^n]]] + 3*Sech[a + b*Log[c*x^n]]*Tanh[a + b*Log[c*x^n]] + 2*Sech[a + b*Log[c*x^n]]^3*Tanh[a + b*Log[c*x^n]])/(8*b*n)","A",1
196,1,74,97,0.1665061,"\int \frac{\text{sech}^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Sech[a + b*Log[c*x^n]]^(5/2)/x,x]","\frac{2 \text{sech}^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right) \left(\sinh \left(a+b \log \left(c x^n\right)\right)-i \cosh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right) F\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)\right)}{3 b n}","\frac{2 \sinh \left(a+b \log \left(c x^n\right)\right) \text{sech}^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{2 i \sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)} \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{3 b n}",1,"(2*Sech[a + b*Log[c*x^n]]^(3/2)*((-I)*Cosh[a + b*Log[c*x^n]]^(3/2)*EllipticF[(I/2)*(a + b*Log[c*x^n]), 2] + Sinh[a + b*Log[c*x^n]]))/(3*b*n)","A",1
197,1,72,93,0.0931921,"\int \frac{\text{sech}^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Sech[a + b*Log[c*x^n]]^(3/2)/x,x]","\frac{2 \sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)} \left(\sinh \left(a+b \log \left(c x^n\right)\right)+i \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)\right)}{b n}","\frac{2 \sinh \left(a+b \log \left(c x^n\right)\right) \sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)}}{b n}+\frac{2 i \sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)} \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}",1,"(2*Sqrt[Sech[a + b*Log[c*x^n]]]*(I*Sqrt[Cosh[a + b*Log[c*x^n]]]*EllipticE[(I/2)*(a + b*Log[c*x^n]), 2] + Sinh[a + b*Log[c*x^n]]))/(b*n)","A",1
198,1,58,58,0.0685851,"\int \frac{\sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)}}{x} \, dx","Integrate[Sqrt[Sech[a + b*Log[c*x^n]]]/x,x]","-\frac{2 i \sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)} \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}","-\frac{2 i \sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)} \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}",1,"((-2*I)*Sqrt[Cosh[a + b*Log[c*x^n]]]*EllipticF[(I/2)*(a + b*Log[c*x^n]), 2]*Sqrt[Sech[a + b*Log[c*x^n]]])/(b*n)","A",1
199,1,58,58,0.0755923,"\int \frac{1}{x \sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)}} \, dx","Integrate[1/(x*Sqrt[Sech[a + b*Log[c*x^n]]]),x]","-\frac{2 i E\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n \sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)} \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)}}","-\frac{2 i \sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)} \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}",1,"((-2*I)*EllipticE[(I/2)*(a + b*Log[c*x^n]), 2])/(b*n*Sqrt[Cosh[a + b*Log[c*x^n]]]*Sqrt[Sech[a + b*Log[c*x^n]]])","A",1
200,1,76,97,0.1143839,"\int \frac{1}{x \text{sech}^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x*Sech[a + b*Log[c*x^n]]^(3/2)),x]","\frac{\sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)} \left(\sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)-2 i \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)\right)}{3 b n}","\frac{2 \sinh \left(a+b \log \left(c x^n\right)\right)}{3 b n \sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)}}-\frac{2 i \sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)} \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{3 b n}",1,"(Sqrt[Sech[a + b*Log[c*x^n]]]*((-2*I)*Sqrt[Cosh[a + b*Log[c*x^n]]]*EllipticF[(I/2)*(a + b*Log[c*x^n]), 2] + Sinh[2*(a + b*Log[c*x^n])]))/(3*b*n)","A",1
201,1,87,97,0.1302154,"\int \frac{1}{x \text{sech}^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x*Sech[a + b*Log[c*x^n]]^(5/2)),x]","\frac{\sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)} \left(\sinh \left(a+b \log \left(c x^n\right)\right)+\sinh \left(3 \left(a+b \log \left(c x^n\right)\right)\right)-12 i \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)\right)}{10 b n}","\frac{2 \sinh \left(a+b \log \left(c x^n\right)\right)}{5 b n \text{sech}^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}-\frac{6 i \sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)} \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{5 b n}",1,"(Sqrt[Sech[a + b*Log[c*x^n]]]*((-12*I)*Sqrt[Cosh[a + b*Log[c*x^n]]]*EllipticE[(I/2)*(a + b*Log[c*x^n]), 2] + Sinh[a + b*Log[c*x^n]] + Sinh[3*(a + b*Log[c*x^n])]))/(10*b*n)","A",1