1,1,11,0,0.0050338,"\int \text{sech}(a+b x) \, dx","Int[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",1,1,6,0.1667,1,"{3770}"
2,1,10,0,0.0100053,"\int \text{sech}^2(a+b x) \, dx","Int[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",2,2,8,0.2500,1,"{3767, 8}"
3,1,34,0,0.0156794,"\int \text{sech}^3(a+b x) \, dx","Int[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",2,2,8,0.2500,1,"{3768, 3770}"
4,1,26,0,0.011633,"\int \text{sech}^4(a+b x) \, dx","Int[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",2,1,8,0.1250,1,"{3767}"
5,1,55,0,0.027885,"\int \text{sech}^5(a+b x) \, dx","Int[Sech[a + b*x]^5,x]","\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}","\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]])/(8*b) + (3*Sech[a + b*x]*Tanh[a + b*x])/(8*b) + (Sech[a + b*x]^3*Tanh[a + b*x])/(4*b)","A",3,2,8,0.2500,1,"{3768, 3770}"
6,1,41,0,0.0147582,"\int \text{sech}^6(a+b x) \, dx","Int[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",2,1,8,0.1250,1,"{3767}"
7,1,19,0,0.0096991,"\int \text{sech}^4(7 x) \, dx","Int[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",2,1,6,0.1667,1,"{3767}"
8,1,35,0,0.013558,"\int \text{sech}^6(\pi  x) \, dx","Int[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",2,1,6,0.1667,1,"{3767}"
9,1,66,0,0.031515,"\int \text{sech}^{\frac{5}{2}}(a+b x) \, dx","Int[Sech[a + b*x]^(5/2),x]","\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}","\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*I)/3)*Sqrt[Cosh[a + b*x]]*EllipticF[(I/2)*(a + b*x), 2]*Sqrt[Sech[a + b*x]])/b + (2*Sech[a + b*x]^(3/2)*Sinh[a + b*x])/(3*b)","A",3,3,10,0.3000,1,"{3768, 3771, 2641}"
10,1,62,0,0.0300481,"\int \text{sech}^{\frac{3}{2}}(a+b x) \, dx","Int[Sech[a + b*x]^(3/2),x]","\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}","\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*I)*Sqrt[Cosh[a + b*x]]*EllipticE[(I/2)*(a + b*x), 2]*Sqrt[Sech[a + b*x]])/b + (2*Sqrt[Sech[a + b*x]]*Sinh[a + b*x])/b","A",3,3,10,0.3000,1,"{3768, 3771, 2639}"
11,1,40,0,0.0199072,"\int \sqrt{\text{sech}(a+b x)} \, dx","Int[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",2,2,10,0.2000,1,"{3771, 2641}"
12,1,40,0,0.0198356,"\int \frac{1}{\sqrt{\text{sech}(a+b x)}} \, dx","Int[1/Sqrt[Sech[a + b*x]],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}","-\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)*Sqrt[Cosh[a + b*x]]*EllipticE[(I/2)*(a + b*x), 2]*Sqrt[Sech[a + b*x]])/b","A",2,2,10,0.2000,1,"{3771, 2639}"
13,1,66,0,0.0316396,"\int \frac{1}{\text{sech}^{\frac{3}{2}}(a+b x)} \, dx","Int[Sech[a + b*x]^(-3/2),x]","\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}","\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,"(((-2*I)/3)*Sqrt[Cosh[a + b*x]]*EllipticF[(I/2)*(a + b*x), 2]*Sqrt[Sech[a + b*x]])/b + (2*Sinh[a + b*x])/(3*b*Sqrt[Sech[a + b*x]])","A",3,3,10,0.3000,1,"{3769, 3771, 2641}"
14,1,66,0,0.0329784,"\int \frac{1}{\text{sech}^{\frac{5}{2}}(a+b x)} \, dx","Int[Sech[a + b*x]^(-5/2),x]","\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}","\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,"(((-6*I)/5)*Sqrt[Cosh[a + b*x]]*EllipticE[(I/2)*(a + b*x), 2]*Sqrt[Sech[a + b*x]])/b + (2*Sinh[a + b*x])/(5*b*Sech[a + b*x]^(3/2))","A",3,3,10,0.3000,1,"{3769, 3771, 2639}"
15,1,102,0,0.0602533,"\int (b \text{sech}(c+d x))^{7/2} \, dx","Int[(b*Sech[c + d*x])^(7/2),x]","\frac{6 b^3 \sinh (c+d x) \sqrt{b \text{sech}(c+d x)}}{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{2 b \sinh (c+d x) (b \text{sech}(c+d x))^{5/2}}{5 d}","\frac{6 b^3 \sinh (c+d x) \sqrt{b \text{sech}(c+d x)}}{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{2 b \sinh (c+d x) (b \text{sech}(c+d x))^{5/2}}{5 d}",1,"(((6*I)/5)*b^4*EllipticE[(I/2)*(c + d*x), 2])/(d*Sqrt[Cosh[c + d*x]]*Sqrt[b*Sech[c + d*x]]) + (6*b^3*Sqrt[b*Sech[c + d*x]]*Sinh[c + d*x])/(5*d) + (2*b*(b*Sech[c + d*x])^(5/2)*Sinh[c + d*x])/(5*d)","A",4,3,12,0.2500,1,"{3768, 3771, 2639}"
16,1,74,0,0.0381697,"\int (b \text{sech}(c+d x))^{5/2} \, dx","Int[(b*Sech[c + d*x])^(5/2),x]","\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}","\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*I)/3)*b^2*Sqrt[Cosh[c + d*x]]*EllipticF[(I/2)*(c + d*x), 2]*Sqrt[b*Sech[c + d*x]])/d + (2*b*(b*Sech[c + d*x])^(3/2)*Sinh[c + d*x])/(3*d)","A",3,3,12,0.2500,1,"{3768, 3771, 2641}"
17,1,70,0,0.0383941,"\int (b \text{sech}(c+d x))^{3/2} \, dx","Int[(b*Sech[c + d*x])^(3/2),x]","\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)}}","\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*I)*b^2*EllipticE[(I/2)*(c + d*x), 2])/(d*Sqrt[Cosh[c + d*x]]*Sqrt[b*Sech[c + d*x]]) + (2*b*Sqrt[b*Sech[c + d*x]]*Sinh[c + d*x])/d","A",3,3,12,0.2500,1,"{3768, 3771, 2639}"
18,1,42,0,0.0215461,"\int \sqrt{b \text{sech}(c+d x)} \, dx","Int[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",2,2,12,0.1667,1,"{3771, 2641}"
19,1,42,0,0.0220029,"\int \frac{1}{\sqrt{b \text{sech}(c+d x)}} \, dx","Int[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",2,2,12,0.1667,1,"{3771, 2639}"
20,1,76,0,0.0388664,"\int \frac{1}{(b \text{sech}(c+d x))^{3/2}} \, dx","Int[(b*Sech[c + d*x])^(-3/2),x]","\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}","\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,"(((-2*I)/3)*Sqrt[Cosh[c + d*x]]*EllipticF[(I/2)*(c + d*x), 2]*Sqrt[b*Sech[c + d*x]])/(b^2*d) + (2*Sinh[c + d*x])/(3*b*d*Sqrt[b*Sech[c + d*x]])","A",3,3,12,0.2500,1,"{3769, 3771, 2641}"
21,1,76,0,0.0391326,"\int \frac{1}{(b \text{sech}(c+d x))^{5/2}} \, dx","Int[(b*Sech[c + d*x])^(-5/2),x]","\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)}}","\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,"(((-6*I)/5)*EllipticE[(I/2)*(c + d*x), 2])/(b^2*d*Sqrt[Cosh[c + d*x]]*Sqrt[b*Sech[c + d*x]]) + (2*Sinh[c + d*x])/(5*b*d*(b*Sech[c + d*x])^(3/2))","A",3,3,12,0.2500,1,"{3769, 3771, 2639}"
22,1,104,0,0.0581648,"\int \frac{1}{(b \text{sech}(c+d x))^{7/2}} \, dx","Int[(b*Sech[c + d*x])^(-7/2),x]","\frac{10 \sinh (c+d x)}{21 b^3 d \sqrt{b \text{sech}(c+d x)}}-\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{2 \sinh (c+d x)}{7 b d (b \text{sech}(c+d x))^{5/2}}","\frac{10 \sinh (c+d x)}{21 b^3 d \sqrt{b \text{sech}(c+d x)}}-\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{2 \sinh (c+d x)}{7 b d (b \text{sech}(c+d x))^{5/2}}",1,"(((-10*I)/21)*Sqrt[Cosh[c + d*x]]*EllipticF[(I/2)*(c + d*x), 2]*Sqrt[b*Sech[c + d*x]])/(b^4*d) + (2*Sinh[c + d*x])/(7*b*d*(b*Sech[c + d*x])^(5/2)) + (10*Sinh[c + d*x])/(21*b^3*d*Sqrt[b*Sech[c + d*x]])","A",4,3,12,0.2500,1,"{3769, 3771, 2641}"
23,1,75,0,0.0365971,"\int (b \text{sech}(c+d x))^n \, dx","Int[(b*Sech[c + d*x])^n,x]","-\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)}}","-\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,"-((b*Hypergeometric2F1[1/2, (1 - n)/2, (3 - n)/2, Cosh[c + d*x]^2]*(b*Sech[c + d*x])^(-1 + n)*Sinh[c + d*x])/(d*(1 - n)*Sqrt[-Sinh[c + d*x]^2]))","A",2,2,10,0.2000,1,"{3772, 2643}"
24,1,90,0,0.0297275,"\int \text{sech}^2(a+b x)^{7/2} \, dx","Int[(Sech[a + b*x]^2)^(7/2),x]","\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}","\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,"(5*ArcSin[Tanh[a + b*x]])/(16*b) + (5*Sqrt[Sech[a + b*x]^2]*Tanh[a + b*x])/(16*b) + (5*(Sech[a + b*x]^2)^(3/2)*Tanh[a + b*x])/(24*b) + ((Sech[a + b*x]^2)^(5/2)*Tanh[a + b*x])/(6*b)","A",5,3,12,0.2500,1,"{4122, 195, 216}"
25,1,65,0,0.0220126,"\int \text{sech}^2(a+b x)^{5/2} \, dx","Int[(Sech[a + b*x]^2)^(5/2),x]","\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}","\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,"(3*ArcSin[Tanh[a + b*x]])/(8*b) + (3*Sqrt[Sech[a + b*x]^2]*Tanh[a + b*x])/(8*b) + ((Sech[a + b*x]^2)^(3/2)*Tanh[a + b*x])/(4*b)","A",4,3,12,0.2500,1,"{4122, 195, 216}"
26,1,40,0,0.0168868,"\int \text{sech}^2(a+b x)^{3/2} \, dx","Int[(Sech[a + b*x]^2)^(3/2),x]","\frac{\sin ^{-1}(\tanh (a+b x))}{2 b}+\frac{\tanh (a+b x) \sqrt{\text{sech}^2(a+b x)}}{2 b}","\frac{\sin ^{-1}(\tanh (a+b x))}{2 b}+\frac{\tanh (a+b x) \sqrt{\text{sech}^2(a+b x)}}{2 b}",1,"ArcSin[Tanh[a + b*x]]/(2*b) + (Sqrt[Sech[a + b*x]^2]*Tanh[a + b*x])/(2*b)","A",3,3,12,0.2500,1,"{4122, 195, 216}"
27,1,11,0,0.0109753,"\int \sqrt{\text{sech}^2(a+b x)} \, dx","Int[Sqrt[Sech[a + b*x]^2],x]","\frac{\sin ^{-1}(\tanh (a+b x))}{b}","\frac{\sin ^{-1}(\tanh (a+b x))}{b}",1,"ArcSin[Tanh[a + b*x]]/b","A",2,2,12,0.1667,1,"{4122, 216}"
28,1,22,0,0.0164002,"\int \frac{1}{\sqrt{\text{sech}^2(a+b x)}} \, dx","Int[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",2,2,12,0.1667,1,"{4122, 191}"
29,1,51,0,0.0197899,"\int \frac{1}{\text{sech}^2(a+b x)^{3/2}} \, dx","Int[(Sech[a + b*x]^2)^(-3/2),x]","\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}}","\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,"Tanh[a + b*x]/(3*b*(Sech[a + b*x]^2)^(3/2)) + (2*Tanh[a + b*x])/(3*b*Sqrt[Sech[a + b*x]^2])","A",3,3,12,0.2500,1,"{4122, 192, 191}"
30,1,76,0,0.0266368,"\int \frac{1}{\text{sech}^2(a+b x)^{5/2}} \, dx","Int[(Sech[a + b*x]^2)^(-5/2),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}}","\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,"Tanh[a + b*x]/(5*b*(Sech[a + b*x]^2)^(5/2)) + (4*Tanh[a + b*x])/(15*b*(Sech[a + b*x]^2)^(3/2)) + (8*Tanh[a + b*x])/(15*b*Sqrt[Sech[a + b*x]^2])","A",4,3,12,0.2500,1,"{4122, 192, 191}"
31,1,101,0,0.0345122,"\int \frac{1}{\text{sech}^2(a+b x)^{7/2}} \, dx","Int[(Sech[a + b*x]^2)^(-7/2),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}}","\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,"Tanh[a + b*x]/(7*b*(Sech[a + b*x]^2)^(7/2)) + (6*Tanh[a + b*x])/(35*b*(Sech[a + b*x]^2)^(5/2)) + (8*Tanh[a + b*x])/(35*b*(Sech[a + b*x]^2)^(3/2)) + (16*Tanh[a + b*x])/(35*b*Sqrt[Sech[a + b*x]^2])","A",5,3,12,0.2500,1,"{4122, 192, 191}"
32,1,65,0,0.0336254,"\int \left(a \text{sech}^2(x)\right)^{5/2} \, dx","Int[(a*Sech[x]^2)^(5/2),x]","\frac{3}{8} a^2 \tanh (x) \sqrt{a \text{sech}^2(x)}+\frac{3}{8} a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a \text{sech}^2(x)}}\right)+\frac{1}{4} a \tanh (x) \left(a \text{sech}^2(x)\right)^{3/2}","\frac{3}{8} a^2 \tanh (x) \sqrt{a \text{sech}^2(x)}+\frac{3}{8} a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a \text{sech}^2(x)}}\right)+\frac{1}{4} a \tanh (x) \left(a \text{sech}^2(x)\right)^{3/2}",1,"(3*a^(5/2)*ArcTan[(Sqrt[a]*Tanh[x])/Sqrt[a*Sech[x]^2]])/8 + (3*a^2*Sqrt[a*Sech[x]^2]*Tanh[x])/8 + (a*(a*Sech[x]^2)^(3/2)*Tanh[x])/4","A",5,4,10,0.4000,1,"{4122, 195, 217, 203}"
33,1,46,0,0.0244867,"\int \left(a \text{sech}^2(x)\right)^{3/2} \, dx","Int[(a*Sech[x]^2)^(3/2),x]","\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)}","\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^(3/2)*ArcTan[(Sqrt[a]*Tanh[x])/Sqrt[a*Sech[x]^2]])/2 + (a*Sqrt[a*Sech[x]^2]*Tanh[x])/2","A",4,4,10,0.4000,1,"{4122, 195, 217, 203}"
34,1,25,0,0.0157782,"\int \sqrt{a \text{sech}^2(x)} \, dx","Int[Sqrt[a*Sech[x]^2],x]","\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a \text{sech}^2(x)}}\right)","\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a \text{sech}^2(x)}}\right)",1,"Sqrt[a]*ArcTan[(Sqrt[a]*Tanh[x])/Sqrt[a*Sech[x]^2]]","A",3,3,10,0.3000,1,"{4122, 217, 203}"
35,1,13,0,0.0285025,"\int \frac{1}{\sqrt{a \text{sech}^2(x)}} \, dx","Int[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",2,2,10,0.2000,1,"{4122, 191}"
36,1,36,0,0.0201417,"\int \frac{1}{\left(a \text{sech}^2(x)\right)^{3/2}} \, dx","Int[(a*Sech[x]^2)^(-3/2),x]","\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}}","\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,"Tanh[x]/(3*(a*Sech[x]^2)^(3/2)) + (2*Tanh[x])/(3*a*Sqrt[a*Sech[x]^2])","A",3,3,10,0.3000,1,"{4122, 192, 191}"
37,1,55,0,0.0291431,"\int \frac{1}{\left(a \text{sech}^2(x)\right)^{5/2}} \, dx","Int[(a*Sech[x]^2)^(-5/2),x]","\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}}","\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,"Tanh[x]/(5*(a*Sech[x]^2)^(5/2)) + (4*Tanh[x])/(15*a*(a*Sech[x]^2)^(3/2)) + (8*Tanh[x])/(15*a^2*Sqrt[a*Sech[x]^2])","A",4,3,10,0.3000,1,"{4122, 192, 191}"
38,1,74,0,0.0403825,"\int \frac{1}{\left(a \text{sech}^2(x)\right)^{7/2}} \, dx","Int[(a*Sech[x]^2)^(-7/2),x]","\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}}","\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,"Tanh[x]/(7*(a*Sech[x]^2)^(7/2)) + (6*Tanh[x])/(35*a*(a*Sech[x]^2)^(5/2)) + (8*Tanh[x])/(35*a^2*(a*Sech[x]^2)^(3/2)) + (16*Tanh[x])/(35*a^3*Sqrt[a*Sech[x]^2])","A",5,3,10,0.3000,1,"{4122, 192, 191}"
39,1,121,0,0.0600378,"\int \left(a \text{sech}^3(x)\right)^{5/2} \, dx","Int[(a*Sech[x]^3)^(5/2),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}{585} a^2 \tanh (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)}","\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}{585} a^2 \tanh (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,"((154*I)/195)*a^2*Cosh[x]^(3/2)*EllipticE[(I/2)*x, 2]*Sqrt[a*Sech[x]^3] + (154*a^2*Cosh[x]*Sqrt[a*Sech[x]^3]*Sinh[x])/195 + (154*a^2*Sqrt[a*Sech[x]^3]*Tanh[x])/585 + (22*a^2*Sech[x]^2*Sqrt[a*Sech[x]^3]*Tanh[x])/117 + (2*a^2*Sech[x]^4*Sqrt[a*Sech[x]^3]*Tanh[x])/13","A",7,4,10,0.4000,1,"{4123, 3768, 3771, 2639}"
40,1,69,0,0.0398334,"\int \left(a \text{sech}^3(x)\right)^{3/2} \, dx","Int[(a*Sech[x]^3)^(3/2),x]","\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)}","\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,"((-10*I)/21)*a*Cosh[x]^(3/2)*EllipticF[(I/2)*x, 2]*Sqrt[a*Sech[x]^3] + (10*a*Sqrt[a*Sech[x]^3]*Sinh[x])/21 + (2*a*Sech[x]*Sqrt[a*Sech[x]^3]*Tanh[x])/7","A",5,4,10,0.4000,1,"{4123, 3768, 3771, 2641}"
41,1,46,0,0.0342023,"\int \sqrt{a \text{sech}^3(x)} \, dx","Int[Sqrt[a*Sech[x]^3],x]","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)}","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*I)*Cosh[x]^(3/2)*EllipticE[(I/2)*x, 2]*Sqrt[a*Sech[x]^3] + 2*Cosh[x]*Sqrt[a*Sech[x]^3]*Sinh[x]","A",4,4,10,0.4000,1,"{4123, 3768, 3771, 2639}"
42,1,48,0,0.031463,"\int \frac{1}{\sqrt{a \text{sech}^3(x)}} \, dx","Int[1/Sqrt[a*Sech[x]^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)}}","\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)/3)*EllipticF[(I/2)*x, 2])/(Cosh[x]^(3/2)*Sqrt[a*Sech[x]^3]) + (2*Tanh[x])/(3*Sqrt[a*Sech[x]^3])","A",4,4,10,0.4000,1,"{4123, 3769, 3771, 2641}"
43,1,77,0,0.0441274,"\int \frac{1}{\left(a \text{sech}^3(x)\right)^{3/2}} \, dx","Int[(a*Sech[x]^3)^(-3/2),x]","\frac{14 \sinh (x)}{45 a \sqrt{a \text{sech}^3(x)}}+\frac{2 \sinh (x) \cosh ^2(x)}{9 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{14 \sinh (x)}{45 a \sqrt{a \text{sech}^3(x)}}+\frac{2 \sinh (x) \cosh ^2(x)}{9 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)}}",1,"(((-14*I)/15)*EllipticE[(I/2)*x, 2])/(a*Cosh[x]^(3/2)*Sqrt[a*Sech[x]^3]) + (14*Sinh[x])/(45*a*Sqrt[a*Sech[x]^3]) + (2*Cosh[x]^2*Sinh[x])/(9*a*Sqrt[a*Sech[x]^3])","A",5,4,10,0.4000,1,"{4123, 3769, 3771, 2639}"
44,1,121,0,0.0642417,"\int \frac{1}{\left(a \text{sech}^3(x)\right)^{5/2}} \, dx","Int[(a*Sech[x]^3)^(-5/2),x]","\frac{26 \tanh (x)}{77 a^2 \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{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{78 \sinh (x) \cosh (x)}{385 a^2 \sqrt{a \text{sech}^3(x)}}","\frac{26 \tanh (x)}{77 a^2 \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{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{78 \sinh (x) \cosh (x)}{385 a^2 \sqrt{a \text{sech}^3(x)}}",1,"(((-26*I)/77)*EllipticF[(I/2)*x, 2])/(a^2*Cosh[x]^(3/2)*Sqrt[a*Sech[x]^3]) + (78*Cosh[x]*Sinh[x])/(385*a^2*Sqrt[a*Sech[x]^3]) + (26*Cosh[x]^3*Sinh[x])/(165*a^2*Sqrt[a*Sech[x]^3]) + (2*Cosh[x]^5*Sinh[x])/(15*a^2*Sqrt[a*Sech[x]^3]) + (26*Tanh[x])/(77*a^2*Sqrt[a*Sech[x]^3])","A",7,4,10,0.4000,1,"{4123, 3769, 3771, 2641}"
45,1,163,0,0.0448859,"\int \left(a \text{sech}^4(x)\right)^{7/2} \, dx","Int[(a*Sech[x]^4)^(7/2),x]","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)}","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,"a^3*Cosh[x]*Sqrt[a*Sech[x]^4]*Sinh[x] - 2*a^3*Sqrt[a*Sech[x]^4]*Sinh[x]^2*Tanh[x] + 3*a^3*Sqrt[a*Sech[x]^4]*Sinh[x]^2*Tanh[x]^3 - (20*a^3*Sqrt[a*Sech[x]^4]*Sinh[x]^2*Tanh[x]^5)/7 + (5*a^3*Sqrt[a*Sech[x]^4]*Sinh[x]^2*Tanh[x]^7)/3 - (6*a^3*Sqrt[a*Sech[x]^4]*Sinh[x]^2*Tanh[x]^9)/11 + (a^3*Sqrt[a*Sech[x]^4]*Sinh[x]^2*Tanh[x]^11)/13","A",3,2,10,0.2000,1,"{4123, 3767}"
46,1,117,0,0.0351459,"\int \left(a \text{sech}^4(x)\right)^{5/2} \, dx","Int[(a*Sech[x]^4)^(5/2),x]","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)}","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,"a^2*Cosh[x]*Sqrt[a*Sech[x]^4]*Sinh[x] - (4*a^2*Sqrt[a*Sech[x]^4]*Sinh[x]^2*Tanh[x])/3 + (6*a^2*Sqrt[a*Sech[x]^4]*Sinh[x]^2*Tanh[x]^3)/5 - (4*a^2*Sqrt[a*Sech[x]^4]*Sinh[x]^2*Tanh[x]^5)/7 + (a^2*Sqrt[a*Sech[x]^4]*Sinh[x]^2*Tanh[x]^7)/9","A",3,2,10,0.2000,1,"{4123, 3767}"
47,1,61,0,0.0234475,"\int \left(a \text{sech}^4(x)\right)^{3/2} \, dx","Int[(a*Sech[x]^4)^(3/2),x]","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)}","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,"a*Cosh[x]*Sqrt[a*Sech[x]^4]*Sinh[x] - (2*a*Sqrt[a*Sech[x]^4]*Sinh[x]^2*Tanh[x])/3 + (a*Sqrt[a*Sech[x]^4]*Sinh[x]^2*Tanh[x]^3)/5","A",3,2,10,0.2000,1,"{4123, 3767}"
48,1,15,0,0.0166341,"\int \sqrt{a \text{sech}^4(x)} \, dx","Int[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",3,3,10,0.3000,1,"{4123, 3767, 8}"
49,1,36,0,0.0162538,"\int \frac{1}{\sqrt{a \text{sech}^4(x)}} \, dx","Int[1/Sqrt[a*Sech[x]^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)}}","\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)/(2*Sqrt[a*Sech[x]^4]) + Tanh[x]/(2*Sqrt[a*Sech[x]^4])","A",3,3,10,0.3000,1,"{4123, 2635, 8}"
50,1,86,0,0.035756,"\int \frac{1}{\left(a \text{sech}^4(x)\right)^{3/2}} \, dx","Int[(a*Sech[x]^4)^(-3/2),x]","\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)}}","\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,"(5*x*Sech[x]^2)/(16*a*Sqrt[a*Sech[x]^4]) + (5*Cosh[x]*Sinh[x])/(24*a*Sqrt[a*Sech[x]^4]) + (Cosh[x]^3*Sinh[x])/(6*a*Sqrt[a*Sech[x]^4]) + (5*Tanh[x])/(16*a*Sqrt[a*Sech[x]^4])","A",5,3,10,0.3000,1,"{4123, 2635, 8}"
51,1,132,0,0.0561511,"\int \frac{1}{\left(a \text{sech}^4(x)\right)^{5/2}} \, dx","Int[(a*Sech[x]^4)^(-5/2),x]","\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)}}","\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,"(63*x*Sech[x]^2)/(256*a^2*Sqrt[a*Sech[x]^4]) + (21*Cosh[x]*Sinh[x])/(128*a^2*Sqrt[a*Sech[x]^4]) + (21*Cosh[x]^3*Sinh[x])/(160*a^2*Sqrt[a*Sech[x]^4]) + (9*Cosh[x]^5*Sinh[x])/(80*a^2*Sqrt[a*Sech[x]^4]) + (Cosh[x]^7*Sinh[x])/(10*a^2*Sqrt[a*Sech[x]^4]) + (63*Tanh[x])/(256*a^2*Sqrt[a*Sech[x]^4])","A",7,3,10,0.3000,1,"{4123, 2635, 8}"
52,1,44,0,0.1390334,"\int \frac{\sinh ^4(x)}{a+a \text{sech}(x)} \, dx","Int[Sinh[x]^4/(a + a*Sech[x]),x]","-\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}","-\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,"-x/(8*a) - (Cosh[x]*Sinh[x])/(8*a) + (Cosh[x]^3*Sinh[x])/(4*a) - Sinh[x]^3/(3*a)","A",7,7,13,0.5385,1,"{3872, 2839, 2564, 30, 2568, 2635, 8}"
53,1,23,0,0.1220564,"\int \frac{\sinh ^3(x)}{a+a \text{sech}(x)} \, dx","Int[Sinh[x]^3/(a + a*Sech[x]),x]","\frac{\cosh ^3(x)}{3 a}-\frac{\sinh ^2(x)}{2 a}","\frac{\cosh ^3(x)}{3 a}-\frac{\sinh ^2(x)}{2 a}",1,"Cosh[x]^3/(3*a) - Sinh[x]^2/(2*a)","A",6,5,13,0.3846,1,"{3872, 2835, 2564, 30, 2565}"
54,1,27,0,0.1005306,"\int \frac{\sinh ^2(x)}{a+a \text{sech}(x)} \, dx","Int[Sinh[x]^2/(a + a*Sech[x]),x]","\frac{x}{2 a}-\frac{\sinh (x)}{a}+\frac{\sinh (x) \cosh (x)}{2 a}","\frac{x}{2 a}-\frac{\sinh (x)}{a}+\frac{\sinh (x) \cosh (x)}{2 a}",1,"x/(2*a) - Sinh[x]/a + (Cosh[x]*Sinh[x])/(2*a)","A",5,5,13,0.3846,1,"{3872, 2839, 2637, 2635, 8}"
55,1,17,0,0.0730798,"\int \frac{\sinh (x)}{a+a \text{sech}(x)} \, dx","Int[Sinh[x]/(a + a*Sech[x]),x]","\frac{\cosh (x)}{a}-\frac{\log (\cosh (x)+1)}{a}","\frac{\cosh (x)}{a}-\frac{\log (\cosh (x)+1)}{a}",1,"Cosh[x]/a - Log[1 + Cosh[x]]/a","A",5,4,11,0.3636,1,"{3872, 2833, 12, 43}"
56,1,33,0,0.0979849,"\int \frac{\text{csch}(x)}{a+a \text{sech}(x)} \, dx","Int[Csch[x]/(a + a*Sech[x]),x]","\frac{\text{csch}^2(x)}{2 a}-\frac{\tanh ^{-1}(\cosh (x))}{2 a}-\frac{\coth (x) \text{csch}(x)}{2 a}","\frac{\text{csch}^2(x)}{2 a}-\frac{\tanh ^{-1}(\cosh (x))}{2 a}-\frac{\coth (x) \text{csch}(x)}{2 a}",1,"-ArcTanh[Cosh[x]]/(2*a) - (Coth[x]*Csch[x])/(2*a) + Csch[x]^2/(2*a)","A",6,6,11,0.5455,1,"{3872, 2706, 2606, 30, 2611, 3770}"
57,1,23,0,0.1389086,"\int \frac{\text{csch}^2(x)}{a+a \text{sech}(x)} \, dx","Int[Csch[x]^2/(a + a*Sech[x]),x]","\frac{\text{csch}^3(x)}{3 a}-\frac{\coth ^3(x)}{3 a}","\frac{\text{csch}^3(x)}{3 a}-\frac{\coth ^3(x)}{3 a}",1,"-Coth[x]^3/(3*a) + Csch[x]^3/(3*a)","A",6,5,13,0.3846,1,"{3872, 2839, 2606, 30, 2607}"
58,1,46,0,0.1946623,"\int \frac{\text{csch}^3(x)}{a+a \text{sech}(x)} \, dx","Int[Csch[x]^3/(a + a*Sech[x]),x]","\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}","\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,"ArcTanh[Cosh[x]]/(8*a) - (Coth[x]*Csch[x])/(8*a) - (Coth[x]*Csch[x]^3)/(4*a) + Csch[x]^4/(4*a)","A",7,7,13,0.5385,1,"{3872, 2835, 2606, 30, 2611, 3768, 3770}"
59,1,34,0,0.1462519,"\int \frac{\text{csch}^4(x)}{a+a \text{sech}(x)} \, dx","Int[Csch[x]^4/(a + a*Sech[x]),x]","-\frac{\coth ^5(x)}{5 a}+\frac{\coth ^3(x)}{3 a}+\frac{\text{csch}^5(x)}{5 a}","-\frac{\coth ^5(x)}{5 a}+\frac{\coth ^3(x)}{3 a}+\frac{\text{csch}^5(x)}{5 a}",1,"Coth[x]^3/(3*a) - Coth[x]^5/(5*a) + Csch[x]^5/(5*a)","A",7,6,13,0.4615,1,"{3872, 2839, 2606, 30, 2607, 14}"
60,1,132,0,0.3697266,"\int \frac{\sinh ^4(x)}{a+b \text{sech}(x)} \, dx","Int[Sinh[x]^4/(a + b*Sech[x]),x]","\frac{x \left(-12 a^2 b^2+3 a^4+8 b^4\right)}{8 a^5}+\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{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{x \left(-12 a^2 b^2+3 a^4+8 b^4\right)}{8 a^5}+\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{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}",1,"((3*a^4 - 12*a^2*b^2 + 8*b^4)*x)/(8*a^5) - (2*(a - b)^(3/2)*b*(a + b)^(3/2)*ArcTan[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/a^5 + ((8*b*(a^2 - b^2) - a*(3*a^2 - 4*b^2)*Cosh[x])*Sinh[x])/(8*a^4) - ((4*b - 3*a*Cosh[x])*Sinh[x]^3)/(12*a^2)","A",6,5,13,0.3846,1,"{3872, 2865, 2735, 2659, 205}"
61,1,61,0,0.1801632,"\int \frac{\sinh ^3(x)}{a+b \text{sech}(x)} \, dx","Int[Sinh[x]^3/(a + b*Sech[x]),x]","-\frac{\left(a^2-b^2\right) \cosh (x)}{a^3}+\frac{b \left(a^2-b^2\right) \log (a \cosh (x)+b)}{a^4}-\frac{b \cosh ^2(x)}{2 a^2}+\frac{\cosh ^3(x)}{3 a}","-\frac{\left(a^2-b^2\right) \cosh (x)}{a^3}+\frac{b \left(a^2-b^2\right) \log (a \cosh (x)+b)}{a^4}-\frac{b \cosh ^2(x)}{2 a^2}+\frac{\cosh ^3(x)}{3 a}",1,"-(((a^2 - b^2)*Cosh[x])/a^3) - (b*Cosh[x]^2)/(2*a^2) + Cosh[x]^3/(3*a) + (b*(a^2 - b^2)*Log[b + a*Cosh[x]])/a^4","A",5,4,13,0.3077,1,"{3872, 2837, 12, 772}"
62,1,82,0,0.2121166,"\int \frac{\sinh ^2(x)}{a+b \text{sech}(x)} \, dx","Int[Sinh[x]^2/(a + b*Sech[x]),x]","-\frac{x \left(a^2-2 b^2\right)}{2 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}+\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}",1,"-((a^2 - 2*b^2)*x)/(2*a^3) + (2*Sqrt[a - b]*b*Sqrt[a + b]*ArcTan[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/a^3 - ((2*b - a*Cosh[x])*Sinh[x])/(2*a^2)","A",5,5,13,0.3846,1,"{3872, 2865, 2735, 2659, 205}"
63,1,20,0,0.0880297,"\int \frac{\sinh (x)}{a+b \text{sech}(x)} \, dx","Int[Sinh[x]/(a + b*Sech[x]),x]","\frac{\cosh (x)}{a}-\frac{b \log (a \cosh (x)+b)}{a^2}","\frac{\cosh (x)}{a}-\frac{b \log (a \cosh (x)+b)}{a^2}",1,"Cosh[x]/a - (b*Log[b + a*Cosh[x]])/a^2","A",5,4,11,0.3636,1,"{3872, 2833, 12, 43}"
64,1,53,0,0.1184485,"\int \frac{\text{csch}(x)}{a+b \text{sech}(x)} \, dx","Int[Csch[x]/(a + b*Sech[x]),x]","\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)}","\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,"Log[1 - Cosh[x]]/(2*(a + b)) - Log[1 + Cosh[x]]/(2*(a - b)) + (b*Log[b + a*Cosh[x]])/(a^2 - b^2)","A",4,3,11,0.2727,1,"{3872, 2721, 801}"
65,1,66,0,0.1325519,"\int \frac{\text{csch}^2(x)}{a+b \text{sech}(x)} \, dx","Int[Csch[x]^2/(a + b*Sech[x]),x]","\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}}","\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,"(2*a*b*ArcTan[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/((a - b)^(3/2)*(a + b)^(3/2)) + ((b - a*Cosh[x])*Csch[x])/(a^2 - b^2)","A",5,5,13,0.3846,1,"{3872, 2866, 12, 2659, 205}"
66,1,85,0,0.2381265,"\int \frac{\text{csch}^3(x)}{a+b \text{sech}(x)} \, dx","Int[Csch[x]^3/(a + b*Sech[x]),x]","-\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}","-\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,"((b - a*Cosh[x])*Csch[x]^2)/(2*(a^2 - b^2)) - (a*Log[1 - Cosh[x]])/(4*(a + b)^2) + (a*Log[1 + Cosh[x]])/(4*(a - b)^2) - (a^2*b*Log[b + a*Cosh[x]])/(a^2 - b^2)^2","A",6,5,13,0.3846,1,"{3872, 2837, 12, 823, 801}"
67,1,111,0,0.3035564,"\int \frac{\text{csch}^4(x)}{a+b \text{sech}(x)} \, dx","Int[Csch[x]^4/(a + b*Sech[x]),x]","\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}-\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}-\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}}",1,"(-2*a^3*b*ArcTan[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/((a - b)^(5/2)*(a + b)^(5/2)) - ((3*a^2*b - a*(2*a^2 + b^2)*Cosh[x])*Csch[x])/(3*(a^2 - b^2)^2) + ((b - a*Cosh[x])*Csch[x]^3)/(3*(a^2 - b^2))","A",6,5,13,0.3846,1,"{3872, 2866, 12, 2659, 205}"
68,1,67,0,0.0961097,"\int \frac{\cosh ^4(x)}{a+a \text{sech}(x)} \, dx","Int[Cosh[x]^4/(a + a*Sech[x]),x]","\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}","\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,"(15*x)/(8*a) - (4*Sinh[x])/a + (15*Cosh[x]*Sinh[x])/(8*a) + (5*Cosh[x]^3*Sinh[x])/(4*a) - (Cosh[x]^3*Sinh[x])/(a + a*Sech[x]) - (4*Sinh[x]^3)/(3*a)","A",7,5,13,0.3846,1,"{3819, 3787, 2635, 8, 2633}"
69,1,54,0,0.0864547,"\int \frac{\cosh ^3(x)}{a+a \text{sech}(x)} \, dx","Int[Cosh[x]^3/(a + a*Sech[x]),x]","-\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}","-\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,"(-3*x)/(2*a) + (4*Sinh[x])/a - (3*Cosh[x]*Sinh[x])/(2*a) - (Cosh[x]^2*Sinh[x])/(a + a*Sech[x]) + (4*Sinh[x]^3)/(3*a)","A",6,5,13,0.3846,1,"{3819, 3787, 2633, 2635, 8}"
70,1,41,0,0.0796549,"\int \frac{\cosh ^2(x)}{a+a \text{sech}(x)} \, dx","Int[Cosh[x]^2/(a + a*Sech[x]),x]","\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}","\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,"(3*x)/(2*a) - (2*Sinh[x])/a + (3*Cosh[x]*Sinh[x])/(2*a) - (Cosh[x]*Sinh[x])/(a + a*Sech[x])","A",5,5,13,0.3846,1,"{3819, 3787, 2635, 8, 2637}"
71,1,26,0,0.0568475,"\int \frac{\cosh (x)}{a+a \text{sech}(x)} \, dx","Int[Cosh[x]/(a + a*Sech[x]),x]","-\frac{x}{a}+\frac{2 \sinh (x)}{a}-\frac{\sinh (x)}{a \text{sech}(x)+a}","-\frac{x}{a}+\frac{2 \sinh (x)}{a}-\frac{\sinh (x)}{a \text{sech}(x)+a}",1,"-(x/a) + (2*Sinh[x])/a - Sinh[x]/(a + a*Sech[x])","A",4,4,11,0.3636,1,"{3819, 3787, 2637, 8}"
72,1,11,0,0.0242042,"\int \frac{\text{sech}(x)}{a+a \text{sech}(x)} \, dx","Int[Sech[x]/(a + a*Sech[x]),x]","\frac{\tanh (x)}{a \text{sech}(x)+a}","\frac{\tanh (x)}{a \text{sech}(x)+a}",1,"Tanh[x]/(a + a*Sech[x])","A",1,1,11,0.09091,1,"{3794}"
73,1,20,0,0.0658841,"\int \frac{\text{sech}^2(x)}{a+a \text{sech}(x)} \, dx","Int[Sech[x]^2/(a + a*Sech[x]),x]","\frac{\tan ^{-1}(\sinh (x))}{a}-\frac{\tanh (x)}{a \text{sech}(x)+a}","\frac{\tan ^{-1}(\sinh (x))}{a}-\frac{\tanh (x)}{a \text{sech}(x)+a}",1,"ArcTan[Sinh[x]]/a - Tanh[x]/(a + a*Sech[x])","A",3,3,13,0.2308,1,"{3789, 3770, 3794}"
74,1,26,0,0.1010519,"\int \frac{\text{sech}^3(x)}{a+a \text{sech}(x)} \, dx","Int[Sech[x]^3/(a + a*Sech[x]),x]","\frac{\tanh (x)}{a}-\frac{\tan ^{-1}(\sinh (x))}{a}+\frac{\tanh (x)}{a \text{sech}(x)+a}","\frac{\tanh (x)}{a}-\frac{\tan ^{-1}(\sinh (x))}{a}+\frac{\tanh (x)}{a \text{sech}(x)+a}",1,"-(ArcTan[Sinh[x]]/a) + Tanh[x]/a + Tanh[x]/(a + a*Sech[x])","A",4,4,13,0.3077,1,"{3790, 3789, 3770, 3794}"
75,1,45,0,0.0849706,"\int \frac{\text{sech}^4(x)}{a+a \text{sech}(x)} \, dx","Int[Sech[x]^4/(a + a*Sech[x]),x]","-\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}","-\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,"(3*ArcTan[Sinh[x]])/(2*a) - (2*Tanh[x])/a + (3*Sech[x]*Tanh[x])/(2*a) - (Sech[x]^2*Tanh[x])/(a + a*Sech[x])","A",6,6,13,0.4615,1,"{3818, 3787, 3767, 8, 3768, 3770}"
76,1,29,0,0.0154826,"\int \frac{1}{a+a \text{sech}(c+d x)} \, dx","Int[(a + a*Sech[c + d*x])^(-1),x]","\frac{x}{a}-\frac{\tanh (c+d x)}{d (a \text{sech}(c+d x)+a)}","\frac{x}{a}-\frac{\tanh (c+d x)}{d (a \text{sech}(c+d x)+a)}",1,"x/a - Tanh[c + d*x]/(d*(a + a*Sech[c + d*x]))","A",2,2,12,0.1667,1,"{3777, 8}"
77,1,30,0,0.0154844,"\int \frac{1}{a-a \text{sech}(c+d x)} \, dx","Int[(a - a*Sech[c + d*x])^(-1),x]","\frac{x}{a}-\frac{\tanh (c+d x)}{d (a-a \text{sech}(c+d x))}","\frac{x}{a}-\frac{\tanh (c+d x)}{d (a-a \text{sech}(c+d x))}",1,"x/a - Tanh[c + d*x]/(d*(a - a*Sech[c + d*x]))","A",2,2,13,0.1538,1,"{3777, 8}"
78,1,98,0,0.1203183,"\int (a+a \text{sech}(c+d x))^{5/2} \, dx","Int[(a + a*Sech[c + d*x])^(5/2),x]","\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}","\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,"(2*a^(5/2)*ArcTanh[(Sqrt[a]*Tanh[c + d*x])/Sqrt[a + a*Sech[c + d*x]]])/d + (14*a^3*Tanh[c + d*x])/(3*d*Sqrt[a + a*Sech[c + d*x]]) + (2*a^2*Sqrt[a + a*Sech[c + d*x]]*Tanh[c + d*x])/(3*d)","A",5,5,14,0.3571,1,"{3775, 3915, 3774, 203, 3792}"
79,1,66,0,0.0420447,"\int (a+a \text{sech}(c+d x))^{3/2} \, dx","Int[(a + a*Sech[c + d*x])^(3/2),x]","\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}}","\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,"(2*a^(3/2)*ArcTanh[(Sqrt[a]*Tanh[c + d*x])/Sqrt[a + a*Sech[c + d*x]]])/d + (2*a^2*Tanh[c + d*x])/(d*Sqrt[a + a*Sech[c + d*x]])","A",4,4,14,0.2857,1,"{3775, 21, 3774, 203}"
80,1,37,0,0.0185252,"\int \sqrt{a+a \text{sech}(c+d x)} \, dx","Int[Sqrt[a + a*Sech[c + d*x]],x]","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{a \text{sech}(c+d x)+a}}\right)}{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,"(2*Sqrt[a]*ArcTanh[(Sqrt[a]*Tanh[c + d*x])/Sqrt[a + a*Sech[c + d*x]]])/d","A",2,2,14,0.1429,1,"{3774, 203}"
81,1,85,0,0.0736925,"\int \frac{1}{\sqrt{a+a \text{sech}(c+d x)}} \, dx","Int[1/Sqrt[a + a*Sech[c + d*x]],x]","\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}","\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,"(2*ArcTanh[(Sqrt[a]*Tanh[c + d*x])/Sqrt[a + a*Sech[c + d*x]]])/(Sqrt[a]*d) - (Sqrt[2]*ArcTanh[(Sqrt[a]*Tanh[c + d*x])/(Sqrt[2]*Sqrt[a + a*Sech[c + d*x]])])/(Sqrt[a]*d)","A",5,4,14,0.2857,1,"{3776, 3774, 203, 3795}"
82,1,114,0,0.1276545,"\int \frac{1}{(a+a \text{sech}(c+d x))^{3/2}} \, dx","Int[(a + a*Sech[c + d*x])^(-3/2),x]","\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}}","\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,"(2*ArcTanh[(Sqrt[a]*Tanh[c + d*x])/Sqrt[a + a*Sech[c + d*x]]])/(a^(3/2)*d) - (5*ArcTanh[(Sqrt[a]*Tanh[c + d*x])/(Sqrt[2]*Sqrt[a + a*Sech[c + d*x]])])/(2*Sqrt[2]*a^(3/2)*d) - Tanh[c + d*x]/(2*d*(a + a*Sech[c + d*x])^(3/2))","A",6,5,14,0.3571,1,"{3777, 3920, 3774, 203, 3795}"
83,1,38,0,0.0232803,"\int \sqrt{a-a \text{sech}(c+d x)} \, dx","Int[Sqrt[a - a*Sech[c + d*x]],x]","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{a-a \text{sech}(c+d x)}}\right)}{d}","\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,"(2*Sqrt[a]*ArcTanh[(Sqrt[a]*Tanh[c + d*x])/Sqrt[a - a*Sech[c + d*x]]])/d","A",2,2,15,0.1333,1,"{3774, 203}"
84,1,87,0,0.079209,"\int \frac{1}{\sqrt{a-a \text{sech}(c+d x)}} \, dx","Int[1/Sqrt[a - a*Sech[c + d*x]],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}","\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,"(2*ArcTanh[(Sqrt[a]*Tanh[c + d*x])/Sqrt[a - a*Sech[c + d*x]]])/(Sqrt[a]*d) - (Sqrt[2]*ArcTanh[(Sqrt[a]*Tanh[c + d*x])/(Sqrt[2]*Sqrt[a - a*Sech[c + d*x]])])/(Sqrt[a]*d)","A",5,4,15,0.2667,1,"{3776, 3774, 203, 3795}"
85,1,19,0,0.0173795,"\int \sqrt{3+3 \text{sech}(x)} \, dx","Int[Sqrt[3 + 3*Sech[x]],x]","2 \sqrt{3} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{\text{sech}(x)+1}}\right)","2 \sqrt{3} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{\text{sech}(x)+1}}\right)",1,"2*Sqrt[3]*ArcTanh[Tanh[x]/Sqrt[1 + Sech[x]]]","A",2,2,10,0.2000,1,"{3774, 203}"
86,1,21,0,0.0186269,"\int \sqrt{3-3 \text{sech}(x)} \, dx","Int[Sqrt[3 - 3*Sech[x]],x]","2 \sqrt{3} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-\text{sech}(x)}}\right)","2 \sqrt{3} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{1-\text{sech}(x)}}\right)",1,"2*Sqrt[3]*ArcTanh[Tanh[x]/Sqrt[1 - Sech[x]]]","A",2,2,10,0.2000,1,"{3774, 203}"
87,1,107,0,0.1237987,"\int (a+b \text{sech}(c+d x))^4 \, dx","Int[(a + b*Sech[c + d*x])^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}+a^4 x+\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}","\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}+a^4 x+\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,"a^4*x + (2*a*b*(2*a^2 + b^2)*ArcTan[Sinh[c + d*x]])/d + (b^2*(17*a^2 + 2*b^2)*Tanh[c + d*x])/(3*d) + (4*a*b^3*Sech[c + d*x]*Tanh[c + d*x])/(3*d) + (b^2*(a + b*Sech[c + d*x])^2*Tanh[c + d*x])/(3*d)","A",6,5,12,0.4167,1,"{3782, 4048, 3770, 3767, 8}"
88,1,73,0,0.0516835,"\int (a+b \text{sech}(c+d x))^3 \, dx","Int[(a + b*Sech[c + d*x])^3,x]","\frac{b \left(6 a^2+b^2\right) \tan ^{-1}(\sinh (c+d x))}{2 d}+a^3 x+\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}","\frac{b \left(6 a^2+b^2\right) \tan ^{-1}(\sinh (c+d x))}{2 d}+a^3 x+\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,"a^3*x + (b*(6*a^2 + b^2)*ArcTan[Sinh[c + d*x]])/(2*d) + (5*a*b^2*Tanh[c + d*x])/(2*d) + (b^2*(a + b*Sech[c + d*x])*Tanh[c + d*x])/(2*d)","A",5,4,12,0.3333,1,"{3782, 3770, 3767, 8}"
89,1,33,0,0.0280215,"\int (a+b \text{sech}(c+d x))^2 \, dx","Int[(a + b*Sech[c + d*x])^2,x]","a^2 x+\frac{2 a b \tan ^{-1}(\sinh (c+d x))}{d}+\frac{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^2*x + (2*a*b*ArcTan[Sinh[c + d*x]])/d + (b^2*Tanh[c + d*x])/d","A",4,4,12,0.3333,1,"{3773, 3770, 3767, 8}"
90,1,16,0,0.009225,"\int (a+b \text{sech}(c+d x)) \, dx","Int[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",2,1,10,0.1000,1,"{3770}"
91,1,59,0,0.0553858,"\int \frac{1}{a+b \text{sech}(c+d x)} \, dx","Int[(a + b*Sech[c + d*x])^(-1),x]","\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}}","\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,"x/a - (2*b*ArcTan[(Sqrt[a - b]*Tanh[(c + d*x)/2])/Sqrt[a + b]])/(a*Sqrt[a - b]*Sqrt[a + b]*d)","A",3,3,12,0.2500,1,"{3783, 2659, 208}"
92,1,109,0,0.1589863,"\int \frac{1}{(a+b \text{sech}(c+d x))^2} \, dx","Int[(a + b*Sech[c + d*x])^(-2),x]","-\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}","-\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,"x/a^2 - (2*b*(2*a^2 - b^2)*ArcTan[(Sqrt[a - b]*Tanh[(c + d*x)/2])/Sqrt[a + b]])/(a^2*(a - b)^(3/2)*(a + b)^(3/2)*d) + (b^2*Tanh[c + d*x])/(a*(a^2 - b^2)*d*(a + b*Sech[c + d*x]))","A",5,5,12,0.4167,1,"{3785, 3919, 3831, 2659, 208}"
93,1,173,0,0.3084906,"\int \frac{1}{(a+b \text{sech}(c+d x))^3} \, dx","Int[(a + b*Sech[c + d*x])^(-3),x]","-\frac{b \left(-5 a^2 b^2+6 a^4+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}}+\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{x}{a^3}","-\frac{b \left(-5 a^2 b^2+6 a^4+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}}+\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{x}{a^3}",1,"x/a^3 - (b*(6*a^4 - 5*a^2*b^2 + 2*b^4)*ArcTan[(Sqrt[a - b]*Tanh[(c + d*x)/2])/Sqrt[a + b]])/(a^3*(a - b)^(5/2)*(a + b)^(5/2)*d) + (b^2*Tanh[c + d*x])/(2*a*(a^2 - b^2)*d*(a + b*Sech[c + d*x])^2) + (b^2*(5*a^2 - 2*b^2)*Tanh[c + d*x])/(2*a^2*(a^2 - b^2)^2*d*(a + b*Sech[c + d*x]))","A",6,6,12,0.5000,1,"{3785, 4060, 3919, 3831, 2659, 208}"
94,1,106,0,0.0292714,"\int \frac{1}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Int[1/Sqrt[a + b*Sech[c + d*x]],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}","\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*Sqrt[a + b]*Coth[c + d*x]*EllipticPi[(a + b)/a, ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a*d)","A",1,1,14,0.07143,1,"{3784}"
95,1,146,0,0.6573261,"\int \frac{\cosh ^4(x)}{a+b \text{sech}(x)} \, dx","Int[Cosh[x]^4/(a + b*Sech[x]),x]","\frac{x \left(4 a^2 b^2+3 a^4+8 b^4\right)}{8 a^5}-\frac{b \left(2 a^2+3 b^2\right) \sinh (x)}{3 a^4}-\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{\left(3 a^2+4 b^2\right) \sinh (x) \cosh (x)}{8 a^3}-\frac{b \sinh (x) \cosh ^2(x)}{3 a^2}+\frac{\sinh (x) \cosh ^3(x)}{4 a}","\frac{x \left(4 a^2 b^2+3 a^4+8 b^4\right)}{8 a^5}-\frac{b \left(2 a^2+3 b^2\right) \sinh (x)}{3 a^4}-\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{\left(3 a^2+4 b^2\right) \sinh (x) \cosh (x)}{8 a^3}-\frac{b \sinh (x) \cosh ^2(x)}{3 a^2}+\frac{\sinh (x) \cosh ^3(x)}{4 a}",1,"((3*a^4 + 4*a^2*b^2 + 8*b^4)*x)/(8*a^5) - (2*b^5*ArcTan[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(a^5*Sqrt[a - b]*Sqrt[a + b]) - (b*(2*a^2 + 3*b^2)*Sinh[x])/(3*a^4) + ((3*a^2 + 4*b^2)*Cosh[x]*Sinh[x])/(8*a^3) - (b*Cosh[x]^2*Sinh[x])/(3*a^2) + (Cosh[x]^3*Sinh[x])/(4*a)","A",8,6,13,0.4615,1,"{3853, 4104, 3919, 3831, 2659, 205}"
96,1,112,0,0.4234137,"\int \frac{\cosh ^3(x)}{a+b \text{sech}(x)} \, dx","Int[Cosh[x]^3/(a + b*Sech[x]),x]","-\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{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{\sinh (x) \cosh ^2(x)}{3 a}","-\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{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{\sinh (x) \cosh ^2(x)}{3 a}",1,"-(b*(a^2 + 2*b^2)*x)/(2*a^4) + (2*b^4*ArcTan[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(a^4*Sqrt[a - b]*Sqrt[a + b]) + ((2*a^2 + 3*b^2)*Sinh[x])/(3*a^3) - (b*Cosh[x]*Sinh[x])/(2*a^2) + (Cosh[x]^2*Sinh[x])/(3*a)","A",7,6,13,0.4615,1,"{3853, 4104, 3919, 3831, 2659, 205}"
97,1,85,0,0.2646636,"\int \frac{\cosh ^2(x)}{a+b \text{sech}(x)} \, dx","Int[Cosh[x]^2/(a + b*Sech[x]),x]","\frac{x \left(a^2+2 b^2\right)}{2 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{\sinh (x) \cosh (x)}{2 a}","\frac{x \left(a^2+2 b^2\right)}{2 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{\sinh (x) \cosh (x)}{2 a}",1,"((a^2 + 2*b^2)*x)/(2*a^3) - (2*b^3*ArcTan[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(a^3*Sqrt[a - b]*Sqrt[a + b]) - (b*Sinh[x])/a^2 + (Cosh[x]*Sinh[x])/(2*a)","A",6,6,13,0.4615,1,"{3853, 4104, 3919, 3831, 2659, 205}"
98,1,62,0,0.0924905,"\int \frac{\cosh (x)}{a+b \text{sech}(x)} \, dx","Int[Cosh[x]/(a + b*Sech[x]),x]","\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}","\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)/a^2) + (2*b^2*ArcTan[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(a^2*Sqrt[a - b]*Sqrt[a + b]) + Sinh[x]/a","A",5,5,11,0.4545,1,"{3853, 12, 3783, 2659, 205}"
99,1,42,0,0.0550791,"\int \frac{\text{sech}(x)}{a+b \text{sech}(x)} \, dx","Int[Sech[x]/(a + b*Sech[x]),x]","\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}}","\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[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(Sqrt[a - b]*Sqrt[a + b])","A",3,3,11,0.2727,1,"{3831, 2659, 205}"
100,1,54,0,0.0995088,"\int \frac{\text{sech}^2(x)}{a+b \text{sech}(x)} \, dx","Int[Sech[x]^2/(a + b*Sech[x]),x]","\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}}","\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,"ArcTan[Sinh[x]]/b - (2*a*ArcTan[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(Sqrt[a - b]*b*Sqrt[a + b])","A",5,5,13,0.3846,1,"{3789, 3770, 3831, 2659, 205}"
101,1,64,0,0.1402696,"\int \frac{\text{sech}^3(x)}{a+b \text{sech}(x)} \, dx","Int[Sech[x]^3/(a + b*Sech[x]),x]","\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}","\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,"-((a*ArcTan[Sinh[x]])/b^2) + (2*a^2*ArcTan[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(Sqrt[a - b]*b^2*Sqrt[a + b]) + Tanh[x]/b","A",6,6,13,0.4615,1,"{3790, 3789, 3770, 3831, 2659, 205}"
102,1,87,0,0.2420758,"\int \frac{\text{sech}^4(x)}{a+b \text{sech}(x)} \, dx","Int[Sech[x]^4/(a + b*Sech[x]),x]","-\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}","-\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*a^2 + b^2)*ArcTan[Sinh[x]])/(2*b^3) - (2*a^3*ArcTan[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(Sqrt[a - b]*b^3*Sqrt[a + b]) - (a*Tanh[x])/b^2 + (Sech[x]*Tanh[x])/(2*b)","A",7,7,13,0.5385,1,"{3851, 4082, 3998, 3770, 3831, 2659, 205}"
103,1,48,0,0.0967035,"\int \frac{\tanh ^6(x)}{a+a \text{sech}(x)} \, dx","Int[Tanh[x]^6/(a + a*Sech[x]),x]","\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}","\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,"x/a - (3*ArcTan[Sinh[x]])/(8*a) - ((8 - 3*Sech[x])*Tanh[x])/(8*a) - ((4 - 3*Sech[x])*Tanh[x]^3)/(12*a)","A",5,3,13,0.2308,1,"{3888, 3881, 3770}"
104,1,36,0,0.0591837,"\int \frac{\tanh ^5(x)}{a+a \text{sech}(x)} \, dx","Int[Tanh[x]^5/(a + a*Sech[x]),x]","-\frac{\text{sech}^3(x)}{3 a}+\frac{\text{sech}^2(x)}{2 a}+\frac{\text{sech}(x)}{a}+\frac{\log (\cosh (x))}{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,"Log[Cosh[x]]/a + Sech[x]/a + Sech[x]^2/(2*a) - Sech[x]^3/(3*a)","A",3,2,13,0.1538,1,"{3879, 75}"
105,1,31,0,0.0703507,"\int \frac{\tanh ^4(x)}{a+a \text{sech}(x)} \, dx","Int[Tanh[x]^4/(a + a*Sech[x]),x]","\frac{x}{a}-\frac{\tan ^{-1}(\sinh (x))}{2 a}-\frac{\tanh (x) (2-\text{sech}(x))}{2 a}","\frac{x}{a}-\frac{\tan ^{-1}(\sinh (x))}{2 a}-\frac{\tanh (x) (2-\text{sech}(x))}{2 a}",1,"x/a - ArcTan[Sinh[x]]/(2*a) - ((2 - Sech[x])*Tanh[x])/(2*a)","A",4,3,13,0.2308,1,"{3888, 3881, 3770}"
106,1,14,0,0.0483187,"\int \frac{\tanh ^3(x)}{a+a \text{sech}(x)} \, dx","Int[Tanh[x]^3/(a + a*Sech[x]),x]","\frac{\text{sech}(x)}{a}+\frac{\log (\cosh (x))}{a}","\frac{\text{sech}(x)}{a}+\frac{\log (\cosh (x))}{a}",1,"Log[Cosh[x]]/a + Sech[x]/a","A",3,2,13,0.1538,1,"{3879, 43}"
107,1,14,0,0.0457572,"\int \frac{\tanh ^2(x)}{a+a \text{sech}(x)} \, dx","Int[Tanh[x]^2/(a + a*Sech[x]),x]","\frac{x}{a}-\frac{\tan ^{-1}(\sinh (x))}{a}","\frac{x}{a}-\frac{\tan ^{-1}(\sinh (x))}{a}",1,"x/a - ArcTan[Sinh[x]]/a","A",3,2,13,0.1538,1,"{3888, 3770}"
108,1,9,0,0.0266844,"\int \frac{\tanh (x)}{a+a \text{sech}(x)} \, dx","Int[Tanh[x]/(a + a*Sech[x]),x]","\frac{\log (\cosh (x)+1)}{a}","\frac{\log (\cosh (x)+1)}{a}",1,"Log[1 + Cosh[x]]/a","A",2,2,11,0.1818,1,"{3879, 31}"
109,1,40,0,0.0581539,"\int \frac{\coth (x)}{a+a \text{sech}(x)} \, dx","Int[Coth[x]/(a + a*Sech[x]),x]","\frac{1}{2 a (\cosh (x)+1)}+\frac{\log (1-\cosh (x))}{4 a}+\frac{3 \log (\cosh (x)+1)}{4 a}","\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*a*(1 + Cosh[x])) + Log[1 - Cosh[x]]/(4*a) + (3*Log[1 + Cosh[x]])/(4*a)","A",3,2,11,0.1818,1,"{3879, 88}"
110,1,38,0,0.0893435,"\int \frac{\coth ^2(x)}{a+a \text{sech}(x)} \, dx","Int[Coth[x]^2/(a + a*Sech[x]),x]","\frac{x}{a}-\frac{\coth ^3(x) (1-\text{sech}(x))}{3 a}-\frac{\coth (x) (3-2 \text{sech}(x))}{3 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,"x/a - (Coth[x]*(3 - 2*Sech[x]))/(3*a) - (Coth[x]^3*(1 - Sech[x]))/(3*a)","A",4,3,13,0.2308,1,"{3888, 3882, 8}"
111,1,68,0,0.0857017,"\int \frac{\coth ^3(x)}{a+a \text{sech}(x)} \, dx","Int[Coth[x]^3/(a + a*Sech[x]),x]","\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}","\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,"1/(8*a*(1 - Cosh[x])) - 1/(8*a*(1 + Cosh[x])^2) + 3/(4*a*(1 + Cosh[x])) + (5*Log[1 - Cosh[x]])/(16*a) + (11*Log[1 + Cosh[x]])/(16*a)","A",3,2,13,0.1538,1,"{3879, 88}"
112,1,55,0,0.1204914,"\int \frac{\coth ^4(x)}{a+a \text{sech}(x)} \, dx","Int[Coth[x]^4/(a + a*Sech[x]),x]","\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}","\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,"x/a - (Coth[x]*(15 - 8*Sech[x]))/(15*a) - (Coth[x]^3*(5 - 4*Sech[x]))/(15*a) - (Coth[x]^5*(1 - Sech[x]))/(5*a)","A",5,3,13,0.2308,1,"{3888, 3882, 8}"
113,1,121,0,0.1493961,"\int \frac{\tanh ^7(x)}{a+b \text{sech}(x)} \, dx","Int[Tanh[x]^7/(a + b*Sech[x]),x]","\frac{\left(a^2-3 b^2\right) \text{sech}^3(x)}{3 b^3}-\frac{a \left(a^2-3 b^2\right) \text{sech}^2(x)}{2 b^4}+\frac{\left(-3 a^2 b^2+a^4+3 b^4\right) \text{sech}(x)}{b^5}-\frac{\left(a^2-b^2\right)^3 \log (a+b \text{sech}(x))}{a b^6}-\frac{a \text{sech}^4(x)}{4 b^2}+\frac{\log (\cosh (x))}{a}+\frac{\text{sech}^5(x)}{5 b}","\frac{\left(a^2-3 b^2\right) \text{sech}^3(x)}{3 b^3}-\frac{a \left(a^2-3 b^2\right) \text{sech}^2(x)}{2 b^4}+\frac{\left(-3 a^2 b^2+a^4+3 b^4\right) \text{sech}(x)}{b^5}-\frac{\left(a^2-b^2\right)^3 \log (a+b \text{sech}(x))}{a b^6}-\frac{a \text{sech}^4(x)}{4 b^2}+\frac{\log (\cosh (x))}{a}+\frac{\text{sech}^5(x)}{5 b}",1,"Log[Cosh[x]]/a - ((a^2 - b^2)^3*Log[a + b*Sech[x]])/(a*b^6) + ((a^4 - 3*a^2*b^2 + 3*b^4)*Sech[x])/b^5 - (a*(a^2 - 3*b^2)*Sech[x]^2)/(2*b^4) + ((a^2 - 3*b^2)*Sech[x]^3)/(3*b^3) - (a*Sech[x]^4)/(4*b^2) + Sech[x]^5/(5*b)","A",3,2,13,0.1538,1,"{3885, 894}"
114,1,187,0,0.2934511,"\int \frac{\tanh ^6(x)}{a+b \text{sech}(x)} \, dx","Int[Tanh[x]^6/(a + b*Sech[x]),x]","\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(-3 a^2 b^2+a^4+3 b^4\right) \tan ^{-1}(\sinh (x))}{b^5}-\frac{\left(a^2-3 b^2\right) \tanh (x) \text{sech}(x)}{2 b^3}-\frac{a \tanh ^3(x)}{3 b^2}+\frac{a \tanh (x)}{b^2}+\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{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}","\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(-3 a^2 b^2+a^4+3 b^4\right) \tan ^{-1}(\sinh (x))}{b^5}-\frac{\left(a^2-3 b^2\right) \tanh (x) \text{sech}(x)}{2 b^3}-\frac{a \tanh ^3(x)}{3 b^2}+\frac{a \tanh (x)}{b^2}+\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{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,"x/a - (3*ArcTan[Sinh[x]])/(8*b) - ((a^2 - 3*b^2)*ArcTan[Sinh[x]])/(2*b^3) - ((a^4 - 3*a^2*b^2 + 3*b^4)*ArcTan[Sinh[x]])/b^5 + (2*(a - b)^(5/2)*(a + b)^(5/2)*ArcTan[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(a*b^5) + (a*Tanh[x])/b^2 + (a*(a^2 - 3*b^2)*Tanh[x])/b^4 - (3*Sech[x]*Tanh[x])/(8*b) - ((a^2 - 3*b^2)*Sech[x]*Tanh[x])/(2*b^3) - (Sech[x]^3*Tanh[x])/(4*b) - (a*Tanh[x]^3)/(3*b^2)","A",15,8,13,0.6154,1,"{3898, 2897, 2659, 205, 3770, 3767, 8, 3768}"
115,1,72,0,0.0970659,"\int \frac{\tanh ^5(x)}{a+b \text{sech}(x)} \, dx","Int[Tanh[x]^5/(a + b*Sech[x]),x]","-\frac{\left(a^2-2 b^2\right) \text{sech}(x)}{b^3}+\frac{\left(a^2-b^2\right)^2 \log (a+b \text{sech}(x))}{a b^4}+\frac{a \text{sech}^2(x)}{2 b^2}+\frac{\log (\cosh (x))}{a}-\frac{\text{sech}^3(x)}{3 b}","-\frac{\left(a^2-2 b^2\right) \text{sech}(x)}{b^3}+\frac{\left(a^2-b^2\right)^2 \log (a+b \text{sech}(x))}{a b^4}+\frac{a \text{sech}^2(x)}{2 b^2}+\frac{\log (\cosh (x))}{a}-\frac{\text{sech}^3(x)}{3 b}",1,"Log[Cosh[x]]/a + ((a^2 - b^2)^2*Log[a + b*Sech[x]])/(a*b^4) - ((a^2 - 2*b^2)*Sech[x])/b^3 + (a*Sech[x]^2)/(2*b^2) - Sech[x]^3/(3*b)","A",3,2,13,0.1538,1,"{3885, 894}"
116,1,94,0,0.3188661,"\int \frac{\tanh ^4(x)}{a+b \text{sech}(x)} \, dx","Int[Tanh[x]^4/(a + b*Sech[x]),x]","\frac{\left(2 a^2-3 b^2\right) \tan ^{-1}(\sinh (x))}{2 b^3}-\frac{a \tanh (x)}{b^2}-\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{x}{a}+\frac{\tanh (x) \text{sech}(x)}{2 b}","\frac{\left(2 a^2-3 b^2\right) \tan ^{-1}(\sinh (x))}{2 b^3}-\frac{a \tanh (x)}{b^2}-\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{x}{a}+\frac{\tanh (x) \text{sech}(x)}{2 b}",1,"x/a + ((2*a^2 - 3*b^2)*ArcTan[Sinh[x]])/(2*b^3) - (2*(a - b)^(3/2)*(a + b)^(3/2)*ArcTan[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(a*b^3) - (a*Tanh[x])/b^2 + (Sech[x]*Tanh[x])/(2*b)","A",6,6,13,0.4615,1,"{3898, 2893, 3057, 2659, 205, 3770}"
117,1,35,0,0.0750012,"\int \frac{\tanh ^3(x)}{a+b \text{sech}(x)} \, dx","Int[Tanh[x]^3/(a + b*Sech[x]),x]","\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}","\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,"Log[Cosh[x]]/a + ((1 - a^2/b^2)*Log[a + b*Sech[x]])/a + Sech[x]/b","A",3,2,13,0.1538,1,"{3885, 894}"
118,1,62,0,0.1712661,"\int \frac{\tanh ^2(x)}{a+b \text{sech}(x)} \, dx","Int[Tanh[x]^2/(a + b*Sech[x]),x]","\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}","\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,"x/a - ArcTan[Sinh[x]]/b + (2*Sqrt[a - b]*Sqrt[a + b]*ArcTan[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(a*b)","A",7,7,13,0.5385,1,"{3894, 4051, 3770, 3919, 3831, 2659, 205}"
119,1,19,0,0.0316895,"\int \frac{\tanh (x)}{a+b \text{sech}(x)} \, dx","Int[Tanh[x]/(a + b*Sech[x]),x]","\frac{\log (a+b \text{sech}(x))}{a}+\frac{\log (\cosh (x))}{a}","\frac{\log (a+b \text{sech}(x))}{a}+\frac{\log (\cosh (x))}{a}",1,"Log[Cosh[x]]/a + Log[a + b*Sech[x]]/a","A",4,4,11,0.3636,1,"{3885, 36, 29, 31}"
120,1,66,0,0.1063987,"\int \frac{\coth (x)}{a+b \text{sech}(x)} \, dx","Int[Coth[x]/(a + b*Sech[x]),x]","-\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}","-\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,"Log[Cosh[x]]/a + Log[1 - Sech[x]]/(2*(a + b)) + Log[1 + Sech[x]]/(2*(a - b)) - (b^2*Log[a + b*Sech[x]])/(a*(a^2 - b^2))","A",3,2,11,0.1818,1,"{3885, 894}"
121,1,114,0,0.2049895,"\int \frac{\coth ^2(x)}{a+b \text{sech}(x)} \, dx","Int[Coth[x]^2/(a + b*Sech[x]),x]","-\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}}","-\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*x)/(a^2 - b^2) - (b^2*x)/(a*(a^2 - b^2)) + (2*b^3*ArcTan[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(a*(a - b)^(3/2)*(a + b)^(3/2)) - (a*Coth[x])/(a^2 - b^2) + (b*Csch[x])/(a^2 - b^2)","A",9,8,13,0.6154,1,"{3898, 2902, 2606, 8, 3473, 2735, 2659, 205}"
122,1,113,0,0.1904958,"\int \frac{\coth ^3(x)}{a+b \text{sech}(x)} \, dx","Int[Coth[x]^3/(a + b*Sech[x]),x]","\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}","\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,"Log[Cosh[x]]/a + ((2*a + 3*b)*Log[1 - Sech[x]])/(4*(a + b)^2) + ((2*a - 3*b)*Log[1 + Sech[x]])/(4*(a - b)^2) + (b^4*Log[a + b*Sech[x]])/(a*(a^2 - b^2)^2) - 1/(4*(a + b)*(1 - Sech[x])) - 1/(4*(a - b)*(1 + Sech[x]))","A",3,2,13,0.1538,1,"{3885, 894}"
123,1,207,0,0.329422,"\int \frac{\coth ^4(x)}{a+b \text{sech}(x)} \, dx","Int[Coth[x]^4/(a + b*Sech[x]),x]","\frac{b^4 x}{a \left(a^2-b^2\right)^2}-\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^3 \text{csch}(x)}{\left(a^2-b^2\right)^2}+\frac{b \text{csch}(x)}{a^2-b^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}}","\frac{b^4 x}{a \left(a^2-b^2\right)^2}-\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^3 \text{csch}(x)}{\left(a^2-b^2\right)^2}+\frac{b \text{csch}(x)}{a^2-b^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,"-((a*b^2*x)/(a^2 - b^2)^2) + (b^4*x)/(a*(a^2 - b^2)^2) + (a*x)/(a^2 - b^2) - (2*b^5*ArcTan[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(a*(a - b)^(5/2)*(a + b)^(5/2)) + (a*b^2*Coth[x])/(a^2 - b^2)^2 - (a*Coth[x])/(a^2 - b^2) - (a*Coth[x]^3)/(3*(a^2 - b^2)) - (b^3*Csch[x])/(a^2 - b^2)^2 + (b*Csch[x])/(a^2 - b^2) + (b*Csch[x]^3)/(3*(a^2 - b^2))","A",15,8,13,0.6154,1,"{3898, 2902, 2606, 3473, 8, 2735, 2659, 205}"
124,1,178,0,0.3201371,"\int \frac{\coth ^5(x)}{a+b \text{sech}(x)} \, dx","Int[Coth[x]^5/(a + b*Sech[x]),x]","-\frac{b^6 \log (a+b \text{sech}(x))}{a \left(a^2-b^2\right)^3}+\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{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}","-\frac{b^6 \log (a+b \text{sech}(x))}{a \left(a^2-b^2\right)^3}+\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{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,"Log[Cosh[x]]/a + ((8*a^2 + 21*a*b + 15*b^2)*Log[1 - Sech[x]])/(16*(a + b)^3) + ((8*a^2 - 21*a*b + 15*b^2)*Log[1 + Sech[x]])/(16*(a - b)^3) - (b^6*Log[a + b*Sech[x]])/(a*(a^2 - b^2)^3) - 1/(16*(a + b)*(1 - Sech[x])^2) - (5*a + 7*b)/(16*(a + b)^2*(1 - Sech[x])) - 1/(16*(a - b)*(1 + Sech[x])^2) - (5*a - 7*b)/(16*(a - b)^2*(1 + Sech[x]))","A",3,2,13,0.1538,1,"{3885, 894}"
125,1,169,0,0.1940279,"\int \sqrt{a+b \text{sech}(c+d x)} \tanh ^5(c+d x) \, dx","Int[Sqrt[a + b*Sech[c + d*x]]*Tanh[c + d*x]^5,x]","-\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}","-\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]*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a]])/d - (2*Sqrt[a + b*Sech[c + d*x]])/d + (2*a*(a^2 - 2*b^2)*(a + b*Sech[c + d*x])^(3/2))/(3*b^4*d) - (2*(3*a^2 - 2*b^2)*(a + b*Sech[c + d*x])^(5/2))/(5*b^4*d) + (6*a*(a + b*Sech[c + d*x])^(7/2))/(7*b^4*d) - (2*(a + b*Sech[c + d*x])^(9/2))/(9*b^4*d)","A",5,4,23,0.1739,1,"{3885, 898, 1261, 207}"
126,1,100,0,0.1219071,"\int \sqrt{a+b \text{sech}(c+d x)} \tanh ^3(c+d x) \, dx","Int[Sqrt[a + b*Sech[c + d*x]]*Tanh[c + d*x]^3,x]","\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}","\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]*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a]])/d - (2*Sqrt[a + b*Sech[c + d*x]])/d - (2*a*(a + b*Sech[c + d*x])^(3/2))/(3*b^2*d) + (2*(a + b*Sech[c + d*x])^(5/2))/(5*b^2*d)","A",5,4,23,0.1739,1,"{3885, 898, 1261, 207}"
127,1,51,0,0.0535916,"\int \sqrt{a+b \text{sech}(c+d x)} \tanh (c+d x) \, dx","Int[Sqrt[a + b*Sech[c + d*x]]*Tanh[c + d*x],x]","\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}","\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*Sqrt[a]*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a]])/d - (2*Sqrt[a + b*Sech[c + d*x]])/d","A",4,4,21,0.1905,1,"{3885, 50, 63, 207}"
128,1,106,0,0.1747904,"\int \coth (c+d x) \sqrt{a+b \text{sech}(c+d x)} \, dx","Int[Coth[c + d*x]*Sqrt[a + b*Sech[c + d*x]],x]","\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}","\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,"(2*Sqrt[a]*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a]])/d - (Sqrt[a - b]*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a - b]])/d - (Sqrt[a + b]*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]])/d","A",7,5,21,0.2381,1,"{3885, 898, 1287, 206, 207}"
129,1,217,0,0.3270922,"\int \coth ^3(c+d x) \sqrt{a+b \text{sech}(c+d x)} \, dx","Int[Coth[c + d*x]^3*Sqrt[a + b*Sech[c + d*x]],x]","-\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}}","-\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,"(2*Sqrt[a]*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a]])/d - (a*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a - b]])/(Sqrt[a - b]*d) + (3*b*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a - b]])/(4*Sqrt[a - b]*d) - (a*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]])/(Sqrt[a + b]*d) - (3*b*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]])/(4*Sqrt[a + b]*d) - (Coth[c + d*x]^2*Sqrt[a + b*Sech[c + d*x]])/(2*d)","A",13,9,23,0.3913,1,"{3885, 898, 1315, 1178, 12, 1093, 206, 1170, 207}"
130,1,344,0,0.3924315,"\int \sqrt{a+b \text{sech}(c+d x)} \tanh ^2(c+d x) \, dx","Int[Sqrt[a + b*Sech[c + d*x]]*Tanh[c + d*x]^2,x]","-\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}","-\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,"(-2*a*(a - b)*Sqrt[a + b]*Coth[c + d*x]*EllipticE[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(3*b^2*d) - (2*Sqrt[a + b]*(a + 2*b)*Coth[c + d*x]*EllipticF[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(3*b*d) + (2*Sqrt[a + b]*Coth[c + d*x]*EllipticPi[(a + b)/a, ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/d - (2*Sqrt[a + b*Sech[c + d*x]]*Tanh[c + d*x])/(3*d)","A",7,7,23,0.3043,1,"{3894, 4057, 4058, 3921, 3784, 3832, 4004}"
131,1,125,0,0.0259978,"\int \sqrt{a+b \text{sech}(c+d x)} \, dx","Int[Sqrt[a + b*Sech[c + d*x]],x]","\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}}","\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,"(2*Coth[c + d*x]*EllipticPi[a/(a + b), ArcSin[Sqrt[a + b]/Sqrt[a + b*Sech[c + d*x]]], (a - b)/(a + b)]*Sqrt[-((b*(1 - Sech[c + d*x]))/(a + b*Sech[c + d*x]))]*Sqrt[(b*(1 + Sech[c + d*x]))/(a + b*Sech[c + d*x])]*(a + b*Sech[c + d*x]))/(Sqrt[a + b]*d)","A",1,1,14,0.07143,1,"{3780}"
132,1,246,0,0.2154038,"\int \coth ^2(c+d x) \sqrt{a+b \text{sech}(c+d x)} \, dx","Int[Coth[c + d*x]^2*Sqrt[a + b*Sech[c + d*x]],x]","-\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}}","-\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,"(Sqrt[a + b]*Coth[c + d*x]*EllipticF[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/d - (Coth[c + d*x]*Sqrt[a + b*Sech[c + d*x]])/d + (2*Coth[c + d*x]*EllipticPi[a/(a + b), ArcSin[Sqrt[a + b]/Sqrt[a + b*Sech[c + d*x]]], (a - b)/(a + b)]*Sqrt[-((b*(1 - Sech[c + d*x]))/(a + b*Sech[c + d*x]))]*Sqrt[(b*(1 + Sech[c + d*x]))/(a + b*Sech[c + d*x])]*(a + b*Sech[c + d*x]))/(Sqrt[a + b]*d)","A",5,4,23,0.1739,1,"{3896, 3780, 3875, 3832}"
133,1,148,0,0.1649094,"\int \frac{\tanh ^5(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Int[Tanh[c + d*x]^5/Sqrt[a + b*Sech[c + d*x]],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}","-\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*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a]])/(Sqrt[a]*d) + (2*a*(a^2 - 2*b^2)*Sqrt[a + b*Sech[c + d*x]])/(b^4*d) - (2*(3*a^2 - 2*b^2)*(a + b*Sech[c + d*x])^(3/2))/(3*b^4*d) + (6*a*(a + b*Sech[c + d*x])^(5/2))/(5*b^4*d) - (2*(a + b*Sech[c + d*x])^(7/2))/(7*b^4*d)","A",5,4,23,0.1739,1,"{3885, 898, 1153, 207}"
134,1,79,0,0.1083014,"\int \frac{\tanh ^3(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Int[Tanh[c + d*x]^3/Sqrt[a + b*Sech[c + d*x]],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}","\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*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a]])/(Sqrt[a]*d) - (2*a*Sqrt[a + b*Sech[c + d*x]])/(b^2*d) + (2*(a + b*Sech[c + d*x])^(3/2))/(3*b^2*d)","A",5,4,23,0.1739,1,"{3885, 898, 1153, 207}"
135,1,31,0,0.0469297,"\int \frac{\tanh (c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Int[Tanh[c + d*x]/Sqrt[a + b*Sech[c + d*x]],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{\sqrt{a} d}",1,"(2*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a]])/(Sqrt[a]*d)","A",3,3,21,0.1429,1,"{3885, 63, 207}"
136,1,106,0,0.1477011,"\int \frac{\coth (c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Int[Coth[c + d*x]/Sqrt[a + b*Sech[c + d*x]],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}}","\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,"(2*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a]])/(Sqrt[a]*d) - ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a - b]]/(Sqrt[a - b]*d) - ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]]/(Sqrt[a + b]*d)","A",7,5,21,0.2381,1,"{3885, 898, 1170, 206, 207}"
137,1,262,0,0.2966687,"\int \frac{\coth ^3(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Int[Coth[c + d*x]^3/Sqrt[a + b*Sech[c + d*x]],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}}","-\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,"(2*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a]])/(Sqrt[a]*d) - ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a - b]]/(Sqrt[a - b]*d) + (b*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a - b]])/(4*(a - b)^(3/2)*d) - (b*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]])/(4*(a + b)^(3/2)*d) - ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]]/(Sqrt[a + b]*d) - Sqrt[a + b*Sech[c + d*x]]/(4*(a + b)*d*(1 - Sech[c + d*x])) - Sqrt[a + b*Sech[c + d*x]]/(4*(a - b)*d*(1 + Sech[c + d*x]))","A",11,6,23,0.2609,1,"{3885, 898, 1238, 206, 199, 207}"
138,1,610,0,0.7906063,"\int \frac{\tanh ^4(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Int[Tanh[c + d*x]^4/Sqrt[a + b*Sech[c + d*x]],x]","\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{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{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}","\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{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{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,"(-4*(a - b)*Sqrt[a + b]*Coth[c + d*x]*EllipticE[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(b^2*d) + (2*(a - b)*Sqrt[a + b]*(8*a^2 + 9*b^2)*Coth[c + d*x]*EllipticE[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(15*b^4*d) - (4*Sqrt[a + b]*Coth[c + d*x]*EllipticF[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(b*d) + (2*Sqrt[a + b]*(8*a^2 - 2*a*b + 9*b^2)*Coth[c + d*x]*EllipticF[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(15*b^3*d) + (2*Sqrt[a + b]*Coth[c + d*x]*EllipticPi[(a + b)/a, ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a*d) - (8*a*Sqrt[a + b*Sech[c + d*x]]*Tanh[c + d*x])/(15*b^2*d) + (2*Sech[c + d*x]*Sqrt[a + b*Sech[c + d*x]]*Tanh[c + d*x])/(5*b*d)","A",11,8,23,0.3478,1,"{3895, 3784, 3837, 3832, 4004, 3860, 4082, 4005}"
139,1,310,0,0.2583717,"\int \frac{\tanh ^2(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Int[Tanh[c + d*x]^2/Sqrt[a + b*Sech[c + d*x]],x]","-\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}","-\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,"(-2*(a - b)*Sqrt[a + b]*Coth[c + d*x]*EllipticE[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(b^2*d) - (2*Sqrt[a + b]*Coth[c + d*x]*EllipticF[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(b*d) + (2*Sqrt[a + b]*Coth[c + d*x]*EllipticPi[(a + b)/a, ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a*d)","A",6,6,23,0.2609,1,"{3894, 4059, 3921, 3784, 3832, 4004}"
140,1,106,0,0.0214469,"\int \frac{1}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Int[1/Sqrt[a + b*Sech[c + d*x]],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}","\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*Sqrt[a + b]*Coth[c + d*x]*EllipticPi[(a + b)/a, ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a*d)","A",1,1,14,0.07143,1,"{3784}"
141,1,362,0,0.436081,"\int \frac{\coth ^2(c+d x)}{\sqrt{a+b \text{sech}(c+d x)}} \, dx","Int[Coth[c + d*x]^2/Sqrt[a + b*Sech[c + d*x]],x]","-\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}","-\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,"(Coth[c + d*x]*EllipticE[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(Sqrt[a + b]*d) - (Coth[c + d*x]*EllipticF[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(Sqrt[a + b]*d) + (2*Sqrt[a + b]*Coth[c + d*x]*EllipticPi[(a + b)/a, ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a*d) - Coth[c + d*x]/(d*Sqrt[a + b*Sech[c + d*x]]) - (b^2*Tanh[c + d*x])/((a^2 - b^2)*d*Sqrt[a + b*Sech[c + d*x]])","A",9,8,23,0.3478,1,"{3896, 3784, 3875, 3833, 21, 3829, 3832, 4004}"
142,1,148,0,0.1911646,"\int \frac{\tanh ^5(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Int[Tanh[c + d*x]^5/(a + b*Sech[c + d*x])^(3/2),x]","-\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 \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}-\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}","-\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 \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}(c+d x)}}{\sqrt{a}}\right)}{a^{3/2} d}-\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*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a]])/(a^(3/2)*d) - (2*(a^2 - b^2)^2)/(a*b^4*d*Sqrt[a + b*Sech[c + d*x]]) - (2*(3*a^2 - 2*b^2)*Sqrt[a + b*Sech[c + d*x]])/(b^4*d) + (2*a*(a + b*Sech[c + d*x])^(3/2))/(b^4*d) - (2*(a + b*Sech[c + d*x])^(5/2))/(5*b^4*d)","A",5,4,23,0.1739,1,"{3885, 898, 1261, 206}"
143,1,88,0,0.1414037,"\int \frac{\tanh ^3(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Int[Tanh[c + d*x]^3/(a + b*Sech[c + d*x])^(3/2),x]","\frac{2 \left(a^2-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 \sqrt{a+b \text{sech}(c+d x)}}{b^2 d}","\frac{2 \left(a^2-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 \sqrt{a+b \text{sech}(c+d x)}}{b^2 d}",1,"(2*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a]])/(a^(3/2)*d) + (2*(a^2 - b^2))/(a*b^2*d*Sqrt[a + b*Sech[c + d*x]]) + (2*Sqrt[a + b*Sech[c + d*x]])/(b^2*d)","A",5,4,23,0.1739,1,"{3885, 898, 1261, 206}"
144,1,54,0,0.0622013,"\int \frac{\tanh (c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Int[Tanh[c + d*x]/(a + b*Sech[c + d*x])^(3/2),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)}}","\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*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a]])/(a^(3/2)*d) - 2/(a*d*Sqrt[a + b*Sech[c + d*x]])","A",4,4,21,0.1905,1,"{3885, 51, 63, 207}"
145,1,142,0,0.2166238,"\int \frac{\coth (c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Int[Coth[c + d*x]/(a + b*Sech[c + d*x])^(3/2),x]","\frac{2 b^2}{a d \left(a^2-b^2\right) \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{\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}}","\frac{2 b^2}{a d \left(a^2-b^2\right) \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{\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,"(2*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a]])/(a^(3/2)*d) - ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a - b]]/((a - b)^(3/2)*d) - ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]]/((a + b)^(3/2)*d) + (2*b^2)/(a*(a^2 - b^2)*d*Sqrt[a + b*Sech[c + d*x]])","A",7,4,21,0.1905,1,"{3885, 898, 1287, 206}"
146,1,316,0,0.4268416,"\int \frac{\coth ^3(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Int[Coth[c + d*x]^3/(a + b*Sech[c + d*x])^(3/2),x]","-\frac{2 b^4}{a d \left(a^2-b^2\right)^2 \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{\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}}","-\frac{2 b^4}{a d \left(a^2-b^2\right)^2 \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{\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,"(2*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a]])/(a^(3/2)*d) - ((2*a - 3*b)*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a - b]])/(2*(a - b)^(5/2)*d) + (b*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a - b]])/(4*(a - b)^(5/2)*d) - (b*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]])/(4*(a + b)^(5/2)*d) - ((2*a + 3*b)*ArcTanh[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]])/(2*(a + b)^(5/2)*d) - (2*b^4)/(a*(a^2 - b^2)^2*d*Sqrt[a + b*Sech[c + d*x]]) - Sqrt[a + b*Sech[c + d*x]]/(4*(a + b)^2*d*(1 - Sech[c + d*x])) - Sqrt[a + b*Sech[c + d*x]]/(4*(a - b)^2*d*(1 + Sech[c + d*x]))","A",11,5,23,0.2174,1,"{3885, 898, 1335, 206, 199}"
147,1,907,0,1.3663711,"\int \frac{\tanh ^4(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Int[Tanh[c + d*x]^4/(a + b*Sech[c + d*x])^(3/2),x]","-\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}","-\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,"(-2*Coth[c + d*x]*EllipticE[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a*Sqrt[a + b]*d) + (4*a*Coth[c + d*x]*EllipticE[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(b^2*Sqrt[a + b]*d) - (2*a*(8*a^2 - 5*b^2)*Coth[c + d*x]*EllipticE[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(3*b^4*Sqrt[a + b]*d) + (2*Coth[c + d*x]*EllipticF[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a*Sqrt[a + b]*d) + (4*Coth[c + d*x]*EllipticF[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(b*Sqrt[a + b]*d) - (2*(2*a + b)*(4*a + b)*Coth[c + d*x]*EllipticF[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(3*b^3*Sqrt[a + b]*d) + (2*Sqrt[a + b]*Coth[c + d*x]*EllipticPi[(a + b)/a, ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a^2*d) - (4*a*Tanh[c + d*x])/((a^2 - b^2)*d*Sqrt[a + b*Sech[c + d*x]]) + (2*b^2*Tanh[c + d*x])/(a*(a^2 - b^2)*d*Sqrt[a + b*Sech[c + d*x]]) - (2*a^2*Sech[c + d*x]*Tanh[c + d*x])/(b*(a^2 - b^2)*d*Sqrt[a + b*Sech[c + d*x]]) + (2*(4*a^2 - b^2)*Sqrt[a + b*Sech[c + d*x]]*Tanh[c + d*x])/(3*b^2*(a^2 - b^2)*d)","A",17,11,23,0.4783,1,"{3895, 3785, 4058, 3921, 3784, 3832, 4004, 3836, 4005, 3845, 4082}"
148,1,344,0,0.4202308,"\int \frac{\tanh ^2(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Int[Tanh[c + d*x]^2/(a + b*Sech[c + d*x])^(3/2),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 (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}","\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,"(2*(a - b)*Sqrt[a + b]*Coth[c + d*x]*EllipticE[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a*b^2*d) + (2*Sqrt[a + b]*Coth[c + d*x]*EllipticF[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a*b*d) + (2*Sqrt[a + b]*Coth[c + d*x]*EllipticPi[(a + b)/a, ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a^2*d) - (2*Tanh[c + d*x])/(a*d*Sqrt[a + b*Sech[c + d*x]])","A",7,7,23,0.3043,1,"{3894, 4061, 4059, 3921, 3784, 3832, 4004}"
149,1,347,0,0.3370431,"\int \frac{1}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Int[(a + b*Sech[c + d*x])^(-3/2),x]","\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}}","\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,"(-2*Coth[c + d*x]*EllipticE[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a*Sqrt[a + b]*d) + (2*Coth[c + d*x]*EllipticF[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a*Sqrt[a + b]*d) + (2*Sqrt[a + b]*Coth[c + d*x]*EllipticPi[(a + b)/a, ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a^2*d) + (2*b^2*Tanh[c + d*x])/(a*(a^2 - b^2)*d*Sqrt[a + b*Sech[c + d*x]])","A",6,6,14,0.4286,1,"{3785, 4058, 3921, 3784, 3832, 4004}"
150,1,665,0,0.9834903,"\int \frac{\coth ^2(c+d x)}{(a+b \text{sech}(c+d x))^{3/2}} \, dx","Int[Coth[c + d*x]^2/(a + b*Sech[c + d*x])^(3/2),x]","\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}}","\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,"(4*a*Coth[c + d*x]*EllipticE[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/((a - b)*(a + b)^(3/2)*d) - (2*Coth[c + d*x]*EllipticE[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a*Sqrt[a + b]*d) - ((3*a - b)*Coth[c + d*x]*EllipticF[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/((a - b)*(a + b)^(3/2)*d) + (2*Coth[c + d*x]*EllipticF[ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a*Sqrt[a + b]*d) + (2*Sqrt[a + b]*Coth[c + d*x]*EllipticPi[(a + b)/a, ArcSin[Sqrt[a + b*Sech[c + d*x]]/Sqrt[a + b]], (a + b)/(a - b)]*Sqrt[(b*(1 - Sech[c + d*x]))/(a + b)]*Sqrt[-((b*(1 + Sech[c + d*x]))/(a - b))])/(a^2*d) - Coth[c + d*x]/(d*(a + b*Sech[c + d*x])^(3/2)) - (b^2*Tanh[c + d*x])/((a^2 - b^2)*d*(a + b*Sech[c + d*x])^(3/2)) - (4*a*b^2*Tanh[c + d*x])/((a^2 - b^2)^2*d*Sqrt[a + b*Sech[c + d*x]]) + (2*b^2*Tanh[c + d*x])/(a*(a^2 - b^2)*d*Sqrt[a + b*Sech[c + d*x]])","A",14,11,23,0.4783,1,"{3896, 3785, 4058, 3921, 3784, 3832, 4004, 3875, 3833, 4003, 4005}"
151,1,191,0,0.2820128,"\int e^{c (a+b x)} \text{sech}^2(a c+b c x)^{7/2} \, dx","Int[E^(c*(a + b*x))*(Sech[a*c + b*c*x]^2)^(7/2),x]","-\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}","-\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,"(32*Cosh[a*c + b*c*x]*Sqrt[Sech[a*c + b*c*x]^2])/(3*b*c*(1 + E^(2*c*(a + b*x)))^6) - (192*Cosh[a*c + b*c*x]*Sqrt[Sech[a*c + b*c*x]^2])/(5*b*c*(1 + E^(2*c*(a + b*x)))^5) + (48*Cosh[a*c + b*c*x]*Sqrt[Sech[a*c + b*c*x]^2])/(b*c*(1 + E^(2*c*(a + b*x)))^4) - (64*Cosh[a*c + b*c*x]*Sqrt[Sech[a*c + b*c*x]^2])/(3*b*c*(1 + E^(2*c*(a + b*x)))^3)","A",6,5,25,0.2000,1,"{6720, 2282, 12, 266, 43}"
152,1,141,0,0.1668444,"\int e^{c (a+b x)} \text{sech}^2(a c+b c x)^{5/2} \, dx","Int[E^(c*(a + b*x))*(Sech[a*c + b*c*x]^2)^(5/2),x]","-\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}","-\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*Cosh[a*c + b*c*x]*Sqrt[Sech[a*c + b*c*x]^2])/(b*c*(1 + E^(2*c*(a + b*x)))^4) + (32*Cosh[a*c + b*c*x]*Sqrt[Sech[a*c + b*c*x]^2])/(3*b*c*(1 + E^(2*c*(a + b*x)))^3) - (8*Cosh[a*c + b*c*x]*Sqrt[Sech[a*c + b*c*x]^2])/(b*c*(1 + E^(2*c*(a + b*x)))^2)","A",6,5,25,0.2000,1,"{6720, 2282, 12, 266, 43}"
153,1,56,0,0.1128976,"\int e^{c (a+b x)} \text{sech}^2(a c+b c x)^{3/2} \, dx","Int[E^(c*(a + b*x))*(Sech[a*c + b*c*x]^2)^(3/2),x]","\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}","\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,"(2*E^(4*c*(a + b*x))*Cosh[a*c + b*c*x]*Sqrt[Sech[a*c + b*c*x]^2])/(b*c*(1 + E^(2*c*(a + b*x)))^2)","A",4,4,25,0.1600,1,"{6720, 2282, 12, 264}"
154,1,44,0,0.0869514,"\int e^{c (a+b x)} \sqrt{\text{sech}^2(a c+b c x)} \, dx","Int[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 (a c+b c x) \sqrt{\text{sech}^2(a c+b c 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[a*c + b*c*x]*Log[1 + E^(2*c*(a + b*x))]*Sqrt[Sech[a*c + b*c*x]^2])/(b*c)","A",4,4,25,0.1600,1,"{6720, 2282, 12, 260}"
155,1,74,0,0.1129695,"\int \frac{e^{c (a+b x)}}{\sqrt{\text{sech}^2(a c+b c x)}} \, dx","Int[E^(c*(a + b*x))/Sqrt[Sech[a*c + b*c*x]^2],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)}}","\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))*Sech[a*c + b*c*x])/(4*b*c*Sqrt[Sech[a*c + b*c*x]^2]) + (x*Sech[a*c + b*c*x])/(2*Sqrt[Sech[a*c + b*c*x]^2])","A",5,4,25,0.1600,1,"{6720, 2282, 12, 14}"
156,1,162,0,0.154983,"\int \frac{e^{c (a+b x)}}{\text{sech}^2(a c+b c x)^{3/2}} \, dx","Int[E^(c*(a + b*x))/(Sech[a*c + b*c*x]^2)^(3/2),x]","-\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)}}","-\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,"-Sech[a*c + b*c*x]/(16*b*c*E^(2*c*(a + b*x))*Sqrt[Sech[a*c + b*c*x]^2]) + (3*E^(2*c*(a + b*x))*Sech[a*c + b*c*x])/(16*b*c*Sqrt[Sech[a*c + b*c*x]^2]) + (E^(4*c*(a + b*x))*Sech[a*c + b*c*x])/(32*b*c*Sqrt[Sech[a*c + b*c*x]^2]) + (3*x*Sech[a*c + b*c*x])/(8*Sqrt[Sech[a*c + b*c*x]^2])","A",6,5,25,0.2000,1,"{6720, 2282, 12, 266, 43}"
157,1,250,0,0.1961593,"\int \frac{e^{c (a+b x)}}{\text{sech}^2(a c+b c x)^{5/2}} \, dx","Int[E^(c*(a + b*x))/(Sech[a*c + b*c*x]^2)^(5/2),x]","-\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)}}","-\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,"-Sech[a*c + b*c*x]/(128*b*c*E^(4*c*(a + b*x))*Sqrt[Sech[a*c + b*c*x]^2]) - (5*Sech[a*c + b*c*x])/(64*b*c*E^(2*c*(a + b*x))*Sqrt[Sech[a*c + b*c*x]^2]) + (5*E^(2*c*(a + b*x))*Sech[a*c + b*c*x])/(32*b*c*Sqrt[Sech[a*c + b*c*x]^2]) + (5*E^(4*c*(a + b*x))*Sech[a*c + b*c*x])/(128*b*c*Sqrt[Sech[a*c + b*c*x]^2]) + (E^(6*c*(a + b*x))*Sech[a*c + b*c*x])/(192*b*c*Sqrt[Sech[a*c + b*c*x]^2]) + (5*x*Sech[a*c + b*c*x])/(16*Sqrt[Sech[a*c + b*c*x]^2])","A",6,5,25,0.2000,1,"{6720, 2282, 12, 266, 43}"
158,1,108,0,0.0869211,"\int \frac{x^5}{\sqrt{\text{sech}(2 \log (c x))}} \, dx","Int[x^5/Sqrt[Sech[2*Log[c*x]]],x]","\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))}}","\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,"(2*x^2)/(21*c^4*Sqrt[Sech[2*Log[c*x]]]) + x^6/(7*Sqrt[Sech[2*Log[c*x]]]) + (Sqrt[(c^4 + x^(-4))/(c^2 + x^(-2))^2]*(c^2 + x^(-2))*EllipticF[2*ArcCot[c*x], 1/2])/(21*c^5*(c^4 + x^(-4))*x*Sqrt[Sech[2*Log[c*x]]])","A",6,6,15,0.4000,1,"{5551, 5549, 335, 277, 325, 220}"
159,1,28,0,0.0423691,"\int \frac{x^4}{\sqrt{\text{sech}(2 \log (c x))}} \, dx","Int[x^4/Sqrt[Sech[2*Log[c*x]]],x]","\frac{x^5 \left(c^4+\frac{1}{x^4}\right)}{6 c^4 \sqrt{\text{sech}(2 \log (c x))}}","\frac{x^5 \left(c^4+\frac{1}{x^4}\right)}{6 c^4 \sqrt{\text{sech}(2 \log (c x))}}",1,"((c^4 + x^(-4))*x^5)/(6*c^4*Sqrt[Sech[2*Log[c*x]]])","A",3,3,15,0.2000,1,"{5551, 5549, 264}"
160,1,203,0,0.129896,"\int \frac{x^3}{\sqrt{\text{sech}(2 \log (c x))}} \, dx","Int[x^3/Sqrt[Sech[2*Log[c*x]]],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{2}{5 c^4 \sqrt{\text{sech}(2 \log (c x))}}+\frac{x^4}{5 \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{2}{5 c^4 \sqrt{\text{sech}(2 \log (c x))}}+\frac{x^4}{5 \sqrt{\text{sech}(2 \log (c x))}}",1,"2/(5*c^4*Sqrt[Sech[2*Log[c*x]]]) - 2/(5*c^4*(c^2 + x^(-2))*x^2*Sqrt[Sech[2*Log[c*x]]]) + x^4/(5*Sqrt[Sech[2*Log[c*x]]]) + (2*Sqrt[(c^4 + x^(-4))/(c^2 + x^(-2))^2]*(c^2 + x^(-2))*EllipticE[2*ArcCot[c*x], 1/2])/(5*c^3*(c^4 + x^(-4))*x*Sqrt[Sech[2*Log[c*x]]]) - (Sqrt[(c^4 + x^(-4))/(c^2 + x^(-2))^2]*(c^2 + x^(-2))*EllipticF[2*ArcCot[c*x], 1/2])/(5*c^3*(c^4 + x^(-4))*x*Sqrt[Sech[2*Log[c*x]]])","A",8,8,15,0.5333,1,"{5551, 5549, 335, 277, 325, 305, 220, 1196}"
161,1,67,0,0.0549709,"\int \frac{x^2}{\sqrt{\text{sech}(2 \log (c x))}} \, dx","Int[x^2/Sqrt[Sech[2*Log[c*x]]],x]","\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))}}","\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^3/(4*Sqrt[Sech[2*Log[c*x]]]) + ArcTanh[Sqrt[1 + 1/(c^4*x^4)]]/(4*c^4*Sqrt[1 + 1/(c^4*x^4)]*x*Sqrt[Sech[2*Log[c*x]]])","A",6,6,15,0.4000,1,"{5551, 5549, 266, 47, 63, 207}"
162,1,87,0,0.0595054,"\int \frac{x}{\sqrt{\text{sech}(2 \log (c x))}} \, dx","Int[x/Sqrt[Sech[2*Log[c*x]]],x]","\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))}}","\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,"x^2/(3*Sqrt[Sech[2*Log[c*x]]]) - (Sqrt[(c^4 + x^(-4))/(c^2 + x^(-2))^2]*(c^2 + x^(-2))*EllipticF[2*ArcCot[c*x], 1/2])/(3*c*(c^4 + x^(-4))*x*Sqrt[Sech[2*Log[c*x]]])","A",5,5,13,0.3846,1,"{5551, 5549, 335, 277, 220}"
163,1,59,0,0.0326481,"\int \frac{1}{\sqrt{\text{sech}(2 \log (c x))}} \, dx","Int[1/Sqrt[Sech[2*Log[c*x]]],x]","\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))}}","\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[Sech[2*Log[c*x]]]) - ArcCsch[c^2*x^2]/(2*c^2*Sqrt[1 + 1/(c^4*x^4)]*x*Sqrt[Sech[2*Log[c*x]]])","A",6,6,11,0.5455,1,"{5545, 5543, 335, 275, 277, 215}"
164,1,36,0,0.0286682,"\int \frac{\sqrt{\text{sech}(2 \log (c x))}}{x} \, dx","Int[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",3,2,15,0.1333,1,"{3771, 2641}"
165,1,40,0,0.0450486,"\int \frac{\sqrt{\text{sech}(2 \log (c x))}}{x^2} \, dx","Int[Sqrt[Sech[2*Log[c*x]]]/x^2,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))}","-\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,"-(c^2*Sqrt[1 + 1/(c^4*x^4)]*x*ArcCsch[c^2*x^2]*Sqrt[Sech[2*Log[c*x]]])/2","A",5,5,15,0.3333,1,"{5551, 5549, 335, 275, 215}"
166,1,137,0,0.0992905,"\int \frac{\sqrt{\text{sech}(2 \log (c x))}}{x^3} \, dx","Int[Sqrt[Sech[2*Log[c*x]]]/x^3,x]","-\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)","-\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^4 + x^(-4))*Sqrt[Sech[2*Log[c*x]]])/(c^2 + x^(-2))) + c*Sqrt[(c^4 + x^(-4))/(c^2 + x^(-2))^2]*(c^2 + x^(-2))*x*EllipticE[2*ArcCot[c*x], 1/2]*Sqrt[Sech[2*Log[c*x]]] - (c*Sqrt[(c^4 + x^(-4))/(c^2 + x^(-2))^2]*(c^2 + x^(-2))*x*EllipticF[2*ArcCot[c*x], 1/2]*Sqrt[Sech[2*Log[c*x]]])/2","A",6,6,15,0.4000,1,"{5551, 5549, 335, 305, 220, 1196}"
167,1,23,0,0.0403995,"\int \frac{\sqrt{\text{sech}(2 \log (c x))}}{x^4} \, dx","Int[Sqrt[Sech[2*Log[c*x]]]/x^4,x]","-\frac{1}{2} x \left(c^4+\frac{1}{x^4}\right) \sqrt{\text{sech}(2 \log (c x))}","-\frac{1}{2} x \left(c^4+\frac{1}{x^4}\right) \sqrt{\text{sech}(2 \log (c x))}",1,"-((c^4 + x^(-4))*x*Sqrt[Sech[2*Log[c*x]]])/2","A",3,3,15,0.2000,1,"{5551, 5549, 261}"
168,1,80,0,0.0696465,"\int \frac{\sqrt{\text{sech}(2 \log (c x))}}{x^5} \, dx","Int[Sqrt[Sech[2*Log[c*x]]]/x^5,x]","\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))}","\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,"-((c^4 + x^(-4))*Sqrt[Sech[2*Log[c*x]]])/3 + (c^3*Sqrt[(c^4 + x^(-4))/(c^2 + x^(-2))^2]*(c^2 + x^(-2))*x*EllipticF[2*ArcCot[c*x], 1/2]*Sqrt[Sech[2*Log[c*x]]])/6","A",5,5,15,0.3333,1,"{5551, 5549, 335, 321, 220}"
169,1,122,0,0.0752549,"\int \frac{x^8}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Int[x^8/Sech[2*Log[c*x]]^(3/2),x]","\frac{x^5}{16 \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{x}{32 c^4 \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))}","\frac{x^5}{16 \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))}+\frac{x}{32 c^4 \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,"x/(32*c^4*(c^4 + x^(-4))*Sech[2*Log[c*x]]^(3/2)) + x^5/(16*(c^4 + x^(-4))*Sech[2*Log[c*x]]^(3/2)) + x^9/(12*Sech[2*Log[c*x]]^(3/2)) - ArcTanh[Sqrt[1 + 1/(c^4*x^4)]]/(32*c^12*(1 + 1/(c^4*x^4))^(3/2)*x^3*Sech[2*Log[c*x]]^(3/2))","A",8,7,15,0.4667,1,"{5551, 5549, 266, 47, 51, 63, 207}"
170,1,141,0,0.0979203,"\int \frac{x^7}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Int[x^7/Sech[2*Log[c*x]]^(3/2),x]","\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))}","\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,"4/(77*c^4*(c^4 + x^(-4))*Sech[2*Log[c*x]]^(3/2)) + (6*x^4)/(77*(c^4 + x^(-4))*Sech[2*Log[c*x]]^(3/2)) + x^8/(11*Sech[2*Log[c*x]]^(3/2)) + (2*Sqrt[(c^4 + x^(-4))/(c^2 + x^(-2))^2]*(c^2 + x^(-2))*EllipticF[2*ArcCot[c*x], 1/2])/(77*c^5*(c^4 + x^(-4))^2*x^3*Sech[2*Log[c*x]]^(3/2))","A",7,6,15,0.4000,1,"{5551, 5549, 335, 277, 325, 220}"
171,1,28,0,0.0434737,"\int \frac{x^6}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Int[x^6/Sech[2*Log[c*x]]^(3/2),x]","\frac{x^7 \left(c^4+\frac{1}{x^4}\right)}{10 c^4 \text{sech}^{\frac{3}{2}}(2 \log (c 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,"((c^4 + x^(-4))*x^7)/(10*c^4*Sech[2*Log[c*x]]^(3/2))","A",3,3,15,0.2000,1,"{5551, 5549, 264}"
172,1,251,0,0.1493297,"\int \frac{x^5}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Int[x^5/Sech[2*Log[c*x]]^(3/2),x]","\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))}","\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,"-4/(15*c^4*(c^4 + x^(-4))*(c^2 + x^(-2))*x^4*Sech[2*Log[c*x]]^(3/2)) + 4/(15*c^4*(c^4 + x^(-4))*x^2*Sech[2*Log[c*x]]^(3/2)) + (2*x^2)/(15*(c^4 + x^(-4))*Sech[2*Log[c*x]]^(3/2)) + x^6/(9*Sech[2*Log[c*x]]^(3/2)) + (4*Sqrt[(c^4 + x^(-4))/(c^2 + x^(-2))^2]*(c^2 + x^(-2))*EllipticE[2*ArcCot[c*x], 1/2])/(15*c^3*(c^4 + x^(-4))^2*x^3*Sech[2*Log[c*x]]^(3/2)) - (2*Sqrt[(c^4 + x^(-4))/(c^2 + x^(-2))^2]*(c^2 + x^(-2))*EllipticF[2*ArcCot[c*x], 1/2])/(15*c^3*(c^4 + x^(-4))^2*x^3*Sech[2*Log[c*x]]^(3/2))","A",9,8,15,0.5333,1,"{5551, 5549, 335, 277, 325, 305, 220, 1196}"
173,1,92,0,0.0658133,"\int \frac{x^4}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Int[x^4/Sech[2*Log[c*x]]^(3/2),x]","\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))}","\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,"(3*x)/(16*(c^4 + x^(-4))*Sech[2*Log[c*x]]^(3/2)) + x^5/(8*Sech[2*Log[c*x]]^(3/2)) + (3*ArcTanh[Sqrt[1 + 1/(c^4*x^4)]])/(16*c^8*(1 + 1/(c^4*x^4))^(3/2)*x^3*Sech[2*Log[c*x]]^(3/2))","A",7,6,15,0.4000,1,"{5551, 5549, 266, 47, 63, 207}"
174,1,111,0,0.0831317,"\int \frac{x^3}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Int[x^3/Sech[2*Log[c*x]]^(3/2),x]","\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))}","\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,"2/(7*(c^4 + x^(-4))*Sech[2*Log[c*x]]^(3/2)) + x^4/(7*Sech[2*Log[c*x]]^(3/2)) - (2*Sqrt[(c^4 + x^(-4))/(c^2 + x^(-2))^2]*(c^2 + x^(-2))*EllipticF[2*ArcCot[c*x], 1/2])/(7*c*(c^4 + x^(-4))^2*x^3*Sech[2*Log[c*x]]^(3/2))","A",6,5,15,0.3333,1,"{5551, 5549, 335, 277, 220}"
175,1,88,0,0.0670216,"\int \frac{x^2}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Int[x^2/Sech[2*Log[c*x]]^(3/2),x]","\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))}","\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,"1/(2*(c^4 + x^(-4))*x*Sech[2*Log[c*x]]^(3/2)) + x^3/(6*Sech[2*Log[c*x]]^(3/2)) - ArcCsch[c^2*x^2]/(2*c^6*(1 + 1/(c^4*x^4))^(3/2)*x^3*Sech[2*Log[c*x]]^(3/2))","A",7,6,15,0.4000,1,"{5551, 5549, 335, 275, 277, 215}"
176,1,214,0,0.1162871,"\int \frac{x}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Int[x/Sech[2*Log[c*x]]^(3/2),x]","\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))}","\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,"-12/(5*(c^4 + x^(-4))*(c^2 + x^(-2))*x^4*Sech[2*Log[c*x]]^(3/2)) + 6/(5*(c^4 + x^(-4))*x^2*Sech[2*Log[c*x]]^(3/2)) + x^2/(5*Sech[2*Log[c*x]]^(3/2)) + (12*c*Sqrt[(c^4 + x^(-4))/(c^2 + x^(-2))^2]*(c^2 + x^(-2))*EllipticE[2*ArcCot[c*x], 1/2])/(5*(c^4 + x^(-4))^2*x^3*Sech[2*Log[c*x]]^(3/2)) - (6*c*Sqrt[(c^4 + x^(-4))/(c^2 + x^(-2))^2]*(c^2 + x^(-2))*EllipticF[2*ArcCot[c*x], 1/2])/(5*(c^4 + x^(-4))^2*x^3*Sech[2*Log[c*x]]^(3/2))","A",8,7,13,0.5385,1,"{5551, 5549, 335, 277, 305, 220, 1196}"
177,1,92,0,0.0392663,"\int \frac{1}{\text{sech}^{\frac{3}{2}}(2 \log (c x))} \, dx","Int[Sech[2*Log[c*x]]^(-3/2),x]","-\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))}","-\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,"-3/(4*(c^4 + x^(-4))*x^3*Sech[2*Log[c*x]]^(3/2)) + x/(4*Sech[2*Log[c*x]]^(3/2)) + (3*ArcTanh[Sqrt[1 + 1/(c^4*x^4)]])/(4*c^4*(1 + 1/(c^4*x^4))^(3/2)*x^3*Sech[2*Log[c*x]]^(3/2))","A",7,7,11,0.6364,1,"{5545, 5543, 266, 47, 50, 63, 207}"
178,1,56,0,0.035545,"\int \frac{\text{sech}^{\frac{3}{2}}(2 \log (c x))}{x} \, dx","Int[Sech[2*Log[c*x]]^(3/2)/x,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)","\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*Sqrt[Cosh[2*Log[c*x]]]*EllipticE[I*Log[c*x], 2]*Sqrt[Sech[2*Log[c*x]]] + Sqrt[Sech[2*Log[c*x]]]*Sinh[2*Log[c*x]]","A",4,3,15,0.2000,1,"{3768, 3771, 2639}"
179,1,25,0,0.0395768,"\int \frac{\text{sech}^{\frac{3}{2}}(2 \log (c x))}{x^2} \, dx","Int[Sech[2*Log[c*x]]^(3/2)/x^2,x]","\frac{1}{2} x^3 \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))","\frac{1}{2} x^3 \left(c^4+\frac{1}{x^4}\right) \text{sech}^{\frac{3}{2}}(2 \log (c x))",1,"((c^4 + x^(-4))*x^3*Sech[2*Log[c*x]]^(3/2))/2","A",3,3,15,0.2000,1,"{5551, 5549, 261}"
180,1,92,0,0.0771525,"\int \frac{\text{sech}^{\frac{3}{2}}(2 \log (c x))}{x^3} \, dx","Int[Sech[2*Log[c*x]]^(3/2)/x^3,x]","\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}","\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,"((c^4 + x^(-4))*x^2*Sech[2*Log[c*x]]^(3/2))/2 - ((c^4 + x^(-4))*Sqrt[(c^4 + x^(-4))/(c^2 + x^(-2))^2]*(c^2 + x^(-2))*x^3*EllipticF[2*ArcCot[c*x], 1/2]*Sech[2*Log[c*x]]^(3/2))/(4*c)","A",5,5,15,0.3333,1,"{5551, 5549, 335, 288, 220}"
181,1,66,0,0.0574587,"\int \frac{\text{sech}^{\frac{3}{2}}(2 \log (c x))}{x^4} \, dx","Int[Sech[2*Log[c*x]]^(3/2)/x^4,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))","\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,"((c^4 + x^(-4))*x*Sech[2*Log[c*x]]^(3/2))/2 - (c^6*(1 + 1/(c^4*x^4))^(3/2)*x^3*ArcCsch[c^2*x^2]*Sech[2*Log[c*x]]^(3/2))/2","A",6,6,15,0.4000,1,"{5551, 5549, 335, 275, 288, 215}"
182,1,63,0,0.0586494,"\int \text{sech}\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sech[a + b*Log[c*x^n]],x]","\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}","\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, (b + n^(-1))/(2*b), (3 + 1/(b*n))/2, -(E^(2*a)*(c*x^n)^(2*b))])/(1 + b*n)","A",4,4,11,0.3636,1,"{5545, 5547, 263, 364}"
183,1,69,0,0.0698002,"\int \text{sech}^2\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sech[a + b*Log[c*x^n]]^2,x]","\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}","\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,"(4*E^(2*a)*x*(c*x^n)^(2*b)*Hypergeometric2F1[2, (2 + 1/(b*n))/2, (4 + 1/(b*n))/2, -(E^(2*a)*(c*x^n)^(2*b))])/(1 + 2*b*n)","A",4,4,13,0.3077,1,"{5545, 5547, 263, 364}"
184,1,70,0,0.070584,"\int \text{sech}^3\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sech[a + b*Log[c*x^n]]^3,x]","\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}","\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,"(8*E^(3*a)*x*(c*x^n)^(3*b)*Hypergeometric2F1[3, (3*b + n^(-1))/(2*b), (5 + 1/(b*n))/2, -(E^(2*a)*(c*x^n)^(2*b))])/(1 + 3*b*n)","A",4,4,13,0.3077,1,"{5545, 5547, 263, 364}"
185,1,69,0,0.0730036,"\int \text{sech}^4\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sech[a + b*Log[c*x^n]]^4,x]","\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}","\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,"(16*E^(4*a)*x*(c*x^n)^(4*b)*Hypergeometric2F1[4, (4 + 1/(b*n))/2, (6 + 1/(b*n))/2, -(E^(2*a)*(c*x^n)^(2*b))])/(1 + 4*b*n)","A",4,4,13,0.3077,1,"{5545, 5547, 263, 364}"
186,1,139,0,0.1353728,"\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","Int[(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]","\frac{16 e^{3 a} b^2 n^2 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}+2 e^a x (1-b n) \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)","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,"2*E^a*(1 - b*n)*x*(c*x^n)^b*Hypergeometric2F1[1, (b + n^(-1))/(2*b), (3 + 1/(b*n))/2, -(E^(2*a)*(c*x^n)^(2*b))] + (16*b^2*E^(3*a)*n^2*x*(c*x^n)^(3*b)*Hypergeometric2F1[3, (3*b + n^(-1))/(2*b), (5 + 1/(b*n))/2, -(E^(2*a)*(c*x^n)^(2*b))])/(1 + 3*b*n)","C",9,4,44,0.09091,0,"{5545, 5547, 263, 364}"
187,1,25,0,0.0389133,"\int \text{sech}^3\left(a+2 \log \left(c \sqrt{x}\right)\right) \, dx","Int[Sech[a + 2*Log[c*Sqrt[x]]]^3,x]","\frac{2 e^{-a} c^6}{\left(\frac{e^{-2 a}}{x^2}+c^4\right)^2}","\frac{2 e^{-a} c^6}{\left(\frac{e^{-2 a}}{x^2}+c^4\right)^2}",1,"(2*c^6)/(E^a*(c^4 + 1/(E^(2*a)*x^2))^2)","A",3,3,15,0.2000,1,"{5545, 5547, 261}"
188,1,25,0,0.0457748,"\int \text{sech}^3\left(a+2 \log \left(\frac{c}{\sqrt{x}}\right)\right) \, dx","Int[Sech[a + 2*Log[c/Sqrt[x]]]^3,x]","\frac{2 e^{-3 a} c^2}{\left(e^{-2 a}+\frac{c^4}{x^2}\right)^2}","\frac{2 e^{-3 a} c^2}{\left(e^{-2 a}+\frac{c^4}{x^2}\right)^2}",1,"(2*c^2)/(E^(3*a)*(E^(-2*a) + c^4/x^2)^2)","A",4,4,15,0.2667,1,"{5545, 5547, 263, 261}"
189,1,89,0,0.0894543,"\int \text{sech}^p\left(a+\frac{\log \left(c x^n\right)}{n (-2+p)}\right) \, dx","Int[Sech[a + Log[c*x^n]/(n*(-2 + p))]^p,x]","\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)}","\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,"(E^(2*a)*(2 - p)*x*(1 + (c*x^n)^(2/(n*(2 - p)))/E^(2*a))*Sech[a - Log[c*x^n]/(n*(2 - p))]^p)/(2*(1 - p)*(c*x^n)^(2/(n*(2 - p))))","A",3,3,20,0.1500,1,"{5545, 5549, 261}"
190,1,65,0,0.0758799,"\int \text{sech}^p\left(a-\frac{\log \left(c x^n\right)}{n (-2+p)}\right) \, dx","Int[Sech[a - Log[c*x^n]/(n*(-2 + p))]^p,x]","\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)}","\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*(1 + 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",3,3,21,0.1429,1,"{5545, 5549, 264}"
191,1,19,0,0.0162663,"\int \frac{\text{sech}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[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",2,1,15,0.06667,1,"{3770}"
192,1,18,0,0.0276421,"\int \frac{\text{sech}^2\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[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",3,2,17,0.1176,1,"{3767, 8}"
193,1,55,0,0.0396532,"\int \frac{\text{sech}^3\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[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",3,2,17,0.1176,1,"{3768, 3770}"
194,1,42,0,0.0337831,"\int \frac{\text{sech}^4\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[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",3,1,17,0.05882,1,"{3767}"
195,1,89,0,0.0571088,"\int \frac{\text{sech}^5\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[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)}{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}","\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]]])/(8*b*n) + (3*Sech[a + b*Log[c*x^n]]*Tanh[a + b*Log[c*x^n]])/(8*b*n) + (Sech[a + b*Log[c*x^n]]^3*Tanh[a + b*Log[c*x^n]])/(4*b*n)","A",4,2,17,0.1176,1,"{3768, 3770}"
196,1,97,0,0.0614106,"\int \frac{\text{sech}^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Sech[a + b*Log[c*x^n]]^(5/2)/x,x]","\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}","\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*I)/3)*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) + (2*Sech[a + b*Log[c*x^n]]^(3/2)*Sinh[a + b*Log[c*x^n]])/(3*b*n)","A",4,3,19,0.1579,1,"{3768, 3771, 2641}"
197,1,93,0,0.0721233,"\int \frac{\text{sech}^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Sech[a + b*Log[c*x^n]]^(3/2)/x,x]","\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}","\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*I)*Sqrt[Cosh[a + b*Log[c*x^n]]]*EllipticE[(I/2)*(a + b*Log[c*x^n]), 2]*Sqrt[Sech[a + b*Log[c*x^n]]])/(b*n) + (2*Sqrt[Sech[a + b*Log[c*x^n]]]*Sinh[a + b*Log[c*x^n]])/(b*n)","A",4,3,19,0.1579,1,"{3768, 3771, 2639}"
198,1,58,0,0.0692647,"\int \frac{\sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)}}{x} \, dx","Int[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",3,2,19,0.1053,1,"{3771, 2641}"
199,1,58,0,0.0557946,"\int \frac{1}{x \sqrt{\text{sech}\left(a+b \log \left(c x^n\right)\right)}} \, dx","Int[1/(x*Sqrt[Sech[a + b*Log[c*x^n]]]),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)} E\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)} 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)*Sqrt[Cosh[a + b*Log[c*x^n]]]*EllipticE[(I/2)*(a + b*Log[c*x^n]), 2]*Sqrt[Sech[a + b*Log[c*x^n]]])/(b*n)","A",3,2,19,0.1053,1,"{3771, 2639}"
200,1,97,0,0.0728327,"\int \frac{1}{x \text{sech}^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Sech[a + b*Log[c*x^n]]^(3/2)),x]","\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}","\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,"(((-2*I)/3)*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) + (2*Sinh[a + b*Log[c*x^n]])/(3*b*n*Sqrt[Sech[a + b*Log[c*x^n]]])","A",4,3,19,0.1579,1,"{3769, 3771, 2641}"
201,1,97,0,0.0702866,"\int \frac{1}{x \text{sech}^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Sech[a + b*Log[c*x^n]]^(5/2)),x]","\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}","\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,"(((-6*I)/5)*Sqrt[Cosh[a + b*Log[c*x^n]]]*EllipticE[(I/2)*(a + b*Log[c*x^n]), 2]*Sqrt[Sech[a + b*Log[c*x^n]]])/(b*n) + (2*Sinh[a + b*Log[c*x^n]])/(5*b*n*Sech[a + b*Log[c*x^n]]^(3/2))","A",4,3,19,0.1579,1,"{3769, 3771, 2639}"