1,1,10,0,0.0048472,"\int \cosh (a+b x) \, dx","Int[Cosh[a + b*x],x]","\frac{\sinh (a+b x)}{b}","\frac{\sinh (a+b x)}{b}",1,"Sinh[a + b*x]/b","A",1,1,6,0.1667,1,"{2637}"
2,1,25,0,0.0096989,"\int \cosh ^2(a+b x) \, dx","Int[Cosh[a + b*x]^2,x]","\frac{\sinh (a+b x) \cosh (a+b x)}{2 b}+\frac{x}{2}","\frac{\sinh (a+b x) \cosh (a+b x)}{2 b}+\frac{x}{2}",1,"x/2 + (Cosh[a + b*x]*Sinh[a + b*x])/(2*b)","A",2,2,8,0.2500,1,"{2635, 8}"
3,1,26,0,0.0117305,"\int \cosh ^3(a+b x) \, dx","Int[Cosh[a + b*x]^3,x]","\frac{\sinh ^3(a+b x)}{3 b}+\frac{\sinh (a+b x)}{b}","\frac{\sinh ^3(a+b x)}{3 b}+\frac{\sinh (a+b x)}{b}",1,"Sinh[a + b*x]/b + Sinh[a + b*x]^3/(3*b)","A",2,1,8,0.1250,1,"{2633}"
4,1,46,0,0.0199424,"\int \cosh ^4(a+b x) \, dx","Int[Cosh[a + b*x]^4,x]","\frac{\sinh (a+b x) \cosh ^3(a+b x)}{4 b}+\frac{3 \sinh (a+b x) \cosh (a+b x)}{8 b}+\frac{3 x}{8}","\frac{\sinh (a+b x) \cosh ^3(a+b x)}{4 b}+\frac{3 \sinh (a+b x) \cosh (a+b x)}{8 b}+\frac{3 x}{8}",1,"(3*x)/8 + (3*Cosh[a + b*x]*Sinh[a + b*x])/(8*b) + (Cosh[a + b*x]^3*Sinh[a + b*x])/(4*b)","A",3,2,8,0.2500,1,"{2635, 8}"
5,1,41,0,0.0132193,"\int \cosh ^5(a+b x) \, dx","Int[Cosh[a + b*x]^5,x]","\frac{\sinh ^5(a+b x)}{5 b}+\frac{2 \sinh ^3(a+b x)}{3 b}+\frac{\sinh (a+b x)}{b}","\frac{\sinh ^5(a+b x)}{5 b}+\frac{2 \sinh ^3(a+b x)}{3 b}+\frac{\sinh (a+b x)}{b}",1,"Sinh[a + b*x]/b + (2*Sinh[a + b*x]^3)/(3*b) + Sinh[a + b*x]^5/(5*b)","A",2,1,8,0.1250,1,"{2633}"
6,1,67,0,0.0329988,"\int \cosh ^6(a+b x) \, dx","Int[Cosh[a + b*x]^6,x]","\frac{\sinh (a+b x) \cosh ^5(a+b x)}{6 b}+\frac{5 \sinh (a+b x) \cosh ^3(a+b x)}{24 b}+\frac{5 \sinh (a+b x) \cosh (a+b x)}{16 b}+\frac{5 x}{16}","\frac{\sinh (a+b x) \cosh ^5(a+b x)}{6 b}+\frac{5 \sinh (a+b x) \cosh ^3(a+b x)}{24 b}+\frac{5 \sinh (a+b x) \cosh (a+b x)}{16 b}+\frac{5 x}{16}",1,"(5*x)/16 + (5*Cosh[a + b*x]*Sinh[a + b*x])/(16*b) + (5*Cosh[a + b*x]^3*Sinh[a + b*x])/(24*b) + (Cosh[a + b*x]^5*Sinh[a + b*x])/(6*b)","A",4,2,8,0.2500,1,"{2635, 8}"
7,1,69,0,0.0328581,"\int \cosh ^{\frac{7}{2}}(a+b x) \, dx","Int[Cosh[a + b*x]^(7/2),x]","-\frac{10 i F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{21 b}+\frac{2 \sinh (a+b x) \cosh ^{\frac{5}{2}}(a+b x)}{7 b}+\frac{10 \sinh (a+b x) \sqrt{\cosh (a+b x)}}{21 b}","-\frac{10 i F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{21 b}+\frac{2 \sinh (a+b x) \cosh ^{\frac{5}{2}}(a+b x)}{7 b}+\frac{10 \sinh (a+b x) \sqrt{\cosh (a+b x)}}{21 b}",1,"(((-10*I)/21)*EllipticF[(I/2)*(a + b*x), 2])/b + (10*Sqrt[Cosh[a + b*x]]*Sinh[a + b*x])/(21*b) + (2*Cosh[a + b*x]^(5/2)*Sinh[a + b*x])/(7*b)","A",3,2,10,0.2000,1,"{2635, 2641}"
8,1,46,0,0.0196099,"\int \cosh ^{\frac{5}{2}}(a+b x) \, dx","Int[Cosh[a + b*x]^(5/2),x]","\frac{2 \sinh (a+b x) \cosh ^{\frac{3}{2}}(a+b x)}{5 b}-\frac{6 i E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{5 b}","\frac{2 \sinh (a+b x) \cosh ^{\frac{3}{2}}(a+b x)}{5 b}-\frac{6 i E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{5 b}",1,"(((-6*I)/5)*EllipticE[(I/2)*(a + b*x), 2])/b + (2*Cosh[a + b*x]^(3/2)*Sinh[a + b*x])/(5*b)","A",2,2,10,0.2000,1,"{2635, 2639}"
9,1,46,0,0.0194128,"\int \cosh ^{\frac{3}{2}}(a+b x) \, dx","Int[Cosh[a + b*x]^(3/2),x]","\frac{2 \sinh (a+b x) \sqrt{\cosh (a+b x)}}{3 b}-\frac{2 i F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{3 b}","\frac{2 \sinh (a+b x) \sqrt{\cosh (a+b x)}}{3 b}-\frac{2 i F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{3 b}",1,"(((-2*I)/3)*EllipticF[(I/2)*(a + b*x), 2])/b + (2*Sqrt[Cosh[a + b*x]]*Sinh[a + b*x])/(3*b)","A",2,2,10,0.2000,1,"{2635, 2641}"
10,1,20,0,0.0089143,"\int \sqrt{\cosh (a+b x)} \, dx","Int[Sqrt[Cosh[a + b*x]],x]","-\frac{2 i E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{b}","-\frac{2 i E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{b}",1,"((-2*I)*EllipticE[(I/2)*(a + b*x), 2])/b","A",1,1,10,0.1000,1,"{2639}"
11,1,20,0,0.0086202,"\int \frac{1}{\sqrt{\cosh (a+b x)}} \, dx","Int[1/Sqrt[Cosh[a + b*x]],x]","-\frac{2 i F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{b}","-\frac{2 i F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{b}",1,"((-2*I)*EllipticF[(I/2)*(a + b*x), 2])/b","A",1,1,10,0.1000,1,"{2641}"
12,1,42,0,0.0185497,"\int \frac{1}{\cosh ^{\frac{3}{2}}(a+b x)} \, dx","Int[Cosh[a + b*x]^(-3/2),x]","\frac{2 \sinh (a+b x)}{b \sqrt{\cosh (a+b x)}}+\frac{2 i E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{b}","\frac{2 \sinh (a+b x)}{b \sqrt{\cosh (a+b x)}}+\frac{2 i E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{b}",1,"((2*I)*EllipticE[(I/2)*(a + b*x), 2])/b + (2*Sinh[a + b*x])/(b*Sqrt[Cosh[a + b*x]])","A",2,2,10,0.2000,1,"{2636, 2639}"
13,1,46,0,0.0191879,"\int \frac{1}{\cosh ^{\frac{5}{2}}(a+b x)} \, dx","Int[Cosh[a + b*x]^(-5/2),x]","\frac{2 \sinh (a+b x)}{3 b \cosh ^{\frac{3}{2}}(a+b x)}-\frac{2 i F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{3 b}","\frac{2 \sinh (a+b x)}{3 b \cosh ^{\frac{3}{2}}(a+b x)}-\frac{2 i F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{3 b}",1,"(((-2*I)/3)*EllipticF[(I/2)*(a + b*x), 2])/b + (2*Sinh[a + b*x])/(3*b*Cosh[a + b*x]^(3/2))","A",2,2,10,0.2000,1,"{2636, 2641}"
14,1,69,0,0.03007,"\int \frac{1}{\cosh ^{\frac{7}{2}}(a+b x)} \, dx","Int[Cosh[a + b*x]^(-7/2),x]","\frac{6 i E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{5 b}+\frac{2 \sinh (a+b x)}{5 b \cosh ^{\frac{5}{2}}(a+b x)}+\frac{6 \sinh (a+b x)}{5 b \sqrt{\cosh (a+b x)}}","\frac{6 i E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{5 b}+\frac{2 \sinh (a+b x)}{5 b \cosh ^{\frac{5}{2}}(a+b x)}+\frac{6 \sinh (a+b x)}{5 b \sqrt{\cosh (a+b x)}}",1,"(((6*I)/5)*EllipticE[(I/2)*(a + b*x), 2])/b + (2*Sinh[a + b*x])/(5*b*Cosh[a + b*x]^(5/2)) + (6*Sinh[a + b*x])/(5*b*Sqrt[Cosh[a + b*x]])","A",3,2,10,0.2000,1,"{2636, 2639}"
15,1,65,0,0.0374672,"\int (a \cosh (x))^{7/2} \, dx","Int[(a*Cosh[x])^(7/2),x]","\frac{10}{21} a^3 \sinh (x) \sqrt{a \cosh (x)}-\frac{10 i a^4 \sqrt{\cosh (x)} F\left(\left.\frac{i x}{2}\right|2\right)}{21 \sqrt{a \cosh (x)}}+\frac{2}{7} a \sinh (x) (a \cosh (x))^{5/2}","\frac{10}{21} a^3 \sinh (x) \sqrt{a \cosh (x)}-\frac{10 i a^4 \sqrt{\cosh (x)} F\left(\left.\frac{i x}{2}\right|2\right)}{21 \sqrt{a \cosh (x)}}+\frac{2}{7} a \sinh (x) (a \cosh (x))^{5/2}",1,"(((-10*I)/21)*a^4*Sqrt[Cosh[x]]*EllipticF[(I/2)*x, 2])/Sqrt[a*Cosh[x]] + (10*a^3*Sqrt[a*Cosh[x]]*Sinh[x])/21 + (2*a*(a*Cosh[x])^(5/2)*Sinh[x])/7","A",4,3,8,0.3750,1,"{2635, 2642, 2641}"
16,1,48,0,0.0252784,"\int (a \cosh (x))^{5/2} \, dx","Int[(a*Cosh[x])^(5/2),x]","\frac{2}{5} a \sinh (x) (a \cosh (x))^{3/2}-\frac{6 i a^2 E\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \cosh (x)}}{5 \sqrt{\cosh (x)}}","\frac{2}{5} a \sinh (x) (a \cosh (x))^{3/2}-\frac{6 i a^2 E\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \cosh (x)}}{5 \sqrt{\cosh (x)}}",1,"(((-6*I)/5)*a^2*Sqrt[a*Cosh[x]]*EllipticE[(I/2)*x, 2])/Sqrt[Cosh[x]] + (2*a*(a*Cosh[x])^(3/2)*Sinh[x])/5","A",3,3,8,0.3750,1,"{2635, 2640, 2639}"
17,1,48,0,0.0243887,"\int (a \cosh (x))^{3/2} \, dx","Int[(a*Cosh[x])^(3/2),x]","\frac{2}{3} a \sinh (x) \sqrt{a \cosh (x)}-\frac{2 i a^2 \sqrt{\cosh (x)} F\left(\left.\frac{i x}{2}\right|2\right)}{3 \sqrt{a \cosh (x)}}","\frac{2}{3} a \sinh (x) \sqrt{a \cosh (x)}-\frac{2 i a^2 \sqrt{\cosh (x)} F\left(\left.\frac{i x}{2}\right|2\right)}{3 \sqrt{a \cosh (x)}}",1,"(((-2*I)/3)*a^2*Sqrt[Cosh[x]]*EllipticF[(I/2)*x, 2])/Sqrt[a*Cosh[x]] + (2*a*Sqrt[a*Cosh[x]]*Sinh[x])/3","A",3,3,8,0.3750,1,"{2635, 2642, 2641}"
18,1,27,0,0.0150689,"\int \sqrt{a \cosh (x)} \, dx","Int[Sqrt[a*Cosh[x]],x]","-\frac{2 i E\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \cosh (x)}}{\sqrt{\cosh (x)}}","-\frac{2 i E\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \cosh (x)}}{\sqrt{\cosh (x)}}",1,"((-2*I)*Sqrt[a*Cosh[x]]*EllipticE[(I/2)*x, 2])/Sqrt[Cosh[x]]","A",2,2,8,0.2500,1,"{2640, 2639}"
19,1,27,0,0.014622,"\int \frac{1}{\sqrt{a \cosh (x)}} \, dx","Int[1/Sqrt[a*Cosh[x]],x]","-\frac{2 i \sqrt{\cosh (x)} F\left(\left.\frac{i x}{2}\right|2\right)}{\sqrt{a \cosh (x)}}","-\frac{2 i \sqrt{\cosh (x)} F\left(\left.\frac{i x}{2}\right|2\right)}{\sqrt{a \cosh (x)}}",1,"((-2*I)*Sqrt[Cosh[x]]*EllipticF[(I/2)*x, 2])/Sqrt[a*Cosh[x]]","A",2,2,8,0.2500,1,"{2642, 2641}"
20,1,46,0,0.0253687,"\int \frac{1}{(a \cosh (x))^{3/2}} \, dx","Int[(a*Cosh[x])^(-3/2),x]","\frac{2 \sinh (x)}{a \sqrt{a \cosh (x)}}+\frac{2 i E\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \cosh (x)}}{a^2 \sqrt{\cosh (x)}}","\frac{2 \sinh (x)}{a \sqrt{a \cosh (x)}}+\frac{2 i E\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \cosh (x)}}{a^2 \sqrt{\cosh (x)}}",1,"((2*I)*Sqrt[a*Cosh[x]]*EllipticE[(I/2)*x, 2])/(a^2*Sqrt[Cosh[x]]) + (2*Sinh[x])/(a*Sqrt[a*Cosh[x]])","A",3,3,8,0.3750,1,"{2636, 2640, 2639}"
21,1,50,0,0.0267797,"\int \frac{1}{(a \cosh (x))^{5/2}} \, dx","Int[(a*Cosh[x])^(-5/2),x]","\frac{2 \sinh (x)}{3 a (a \cosh (x))^{3/2}}-\frac{2 i \sqrt{\cosh (x)} F\left(\left.\frac{i x}{2}\right|2\right)}{3 a^2 \sqrt{a \cosh (x)}}","\frac{2 \sinh (x)}{3 a (a \cosh (x))^{3/2}}-\frac{2 i \sqrt{\cosh (x)} F\left(\left.\frac{i x}{2}\right|2\right)}{3 a^2 \sqrt{a \cosh (x)}}",1,"(((-2*I)/3)*Sqrt[Cosh[x]]*EllipticF[(I/2)*x, 2])/(a^2*Sqrt[a*Cosh[x]]) + (2*Sinh[x])/(3*a*(a*Cosh[x])^(3/2))","A",3,3,8,0.3750,1,"{2636, 2642, 2641}"
22,1,67,0,0.0387202,"\int \frac{1}{(a \cosh (x))^{7/2}} \, dx","Int[(a*Cosh[x])^(-7/2),x]","\frac{6 \sinh (x)}{5 a^3 \sqrt{a \cosh (x)}}+\frac{6 i E\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \cosh (x)}}{5 a^4 \sqrt{\cosh (x)}}+\frac{2 \sinh (x)}{5 a (a \cosh (x))^{5/2}}","\frac{6 \sinh (x)}{5 a^3 \sqrt{a \cosh (x)}}+\frac{6 i E\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \cosh (x)}}{5 a^4 \sqrt{\cosh (x)}}+\frac{2 \sinh (x)}{5 a (a \cosh (x))^{5/2}}",1,"(((6*I)/5)*Sqrt[a*Cosh[x]]*EllipticE[(I/2)*x, 2])/(a^4*Sqrt[Cosh[x]]) + (2*Sinh[x])/(5*a*(a*Cosh[x])^(5/2)) + (6*Sinh[x])/(5*a^3*Sqrt[a*Cosh[x]])","A",4,3,8,0.3750,1,"{2636, 2640, 2639}"
23,1,71,0,0.01884,"\int (b \cosh (c+d x))^n \, dx","Int[(b*Cosh[c + d*x])^n,x]","-\frac{\sinh (c+d x) (b \cosh (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cosh ^2(c+d x)\right)}{b d (n+1) \sqrt{-\sinh ^2(c+d x)}}","-\frac{\sinh (c+d x) (b \cosh (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cosh ^2(c+d x)\right)}{b d (n+1) \sqrt{-\sinh ^2(c+d x)}}",1,"-(((b*Cosh[c + d*x])^(1 + n)*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Cosh[c + d*x]^2]*Sinh[c + d*x])/(b*d*(1 + n)*Sqrt[-Sinh[c + d*x]^2]))","A",1,1,10,0.1000,1,"{2643}"
24,1,54,0,0.0758203,"\int \frac{\cosh ^4(x)}{a+a \cosh (x)} \, dx","Int[Cosh[x]^4/(a + a*Cosh[x]),x]","-\frac{3 x}{2 a}+\frac{4 \sinh ^3(x)}{3 a}+\frac{4 \sinh (x)}{a}-\frac{\sinh (x) \cosh ^3(x)}{a \cosh (x)+a}-\frac{3 \sinh (x) \cosh (x)}{2 a}","-\frac{3 x}{2 a}+\frac{4 \sinh ^3(x)}{3 a}+\frac{4 \sinh (x)}{a}-\frac{\sinh (x) \cosh ^3(x)}{a \cosh (x)+a}-\frac{3 \sinh (x) \cosh (x)}{2 a}",1,"(-3*x)/(2*a) + (4*Sinh[x])/a - (3*Cosh[x]*Sinh[x])/(2*a) - (Cosh[x]^3*Sinh[x])/(a + a*Cosh[x]) + (4*Sinh[x]^3)/(3*a)","A",6,5,13,0.3846,1,"{2767, 2748, 2635, 8, 2633}"
25,1,43,0,0.0512014,"\int \frac{\cosh ^3(x)}{a+a \cosh (x)} \, dx","Int[Cosh[x]^3/(a + a*Cosh[x]),x]","\frac{3 x}{2 a}-\frac{2 \sinh (x)}{a}-\frac{\sinh (x) \cosh ^2(x)}{a \cosh (x)+a}+\frac{3 \sinh (x) \cosh (x)}{2 a}","\frac{3 x}{2 a}-\frac{2 \sinh (x)}{a}-\frac{\sinh (x) \cosh ^2(x)}{a \cosh (x)+a}+\frac{3 \sinh (x) \cosh (x)}{2 a}",1,"(3*x)/(2*a) - (2*Sinh[x])/a + (3*Cosh[x]*Sinh[x])/(2*a) - (Cosh[x]^2*Sinh[x])/(a + a*Cosh[x])","A",2,2,13,0.1538,1,"{2767, 2734}"
26,1,25,0,0.0693868,"\int \frac{\cosh ^2(x)}{a+a \cosh (x)} \, dx","Int[Cosh[x]^2/(a + a*Cosh[x]),x]","-\frac{x}{a}+\frac{\sinh (x)}{a}+\frac{\sinh (x)}{a (\cosh (x)+1)}","-\frac{x}{a}+\frac{\sinh (x)}{a}+\frac{\sinh (x)}{a (\cosh (x)+1)}",1,"-(x/a) + Sinh[x]/a + Sinh[x]/(a*(1 + Cosh[x]))","A",4,4,13,0.3077,1,"{2746, 12, 2735, 2648}"
27,1,18,0,0.0315345,"\int \frac{\cosh (x)}{a+a \cosh (x)} \, dx","Int[Cosh[x]/(a + a*Cosh[x]),x]","\frac{x}{a}-\frac{\sinh (x)}{a \cosh (x)+a}","\frac{x}{a}-\frac{\sinh (x)}{a \cosh (x)+a}",1,"x/a - Sinh[x]/(a + a*Cosh[x])","A",2,2,11,0.1818,1,"{2735, 2648}"
28,1,20,0,0.0415903,"\int \frac{\text{sech}(x)}{a+a \cosh (x)} \, dx","Int[Sech[x]/(a + a*Cosh[x]),x]","\frac{\tan ^{-1}(\sinh (x))}{a}-\frac{\sinh (x)}{a \cosh (x)+a}","\frac{\tan ^{-1}(\sinh (x))}{a}-\frac{\sinh (x)}{a \cosh (x)+a}",1,"ArcTan[Sinh[x]]/a - Sinh[x]/(a + a*Cosh[x])","A",3,3,11,0.2727,1,"{2747, 3770, 2648}"
29,1,28,0,0.0683189,"\int \frac{\text{sech}^2(x)}{a+a \cosh (x)} \, dx","Int[Sech[x]^2/(a + a*Cosh[x]),x]","\frac{2 \tanh (x)}{a}-\frac{\tan ^{-1}(\sinh (x))}{a}-\frac{\tanh (x)}{a \cosh (x)+a}","\frac{2 \tanh (x)}{a}-\frac{\tan ^{-1}(\sinh (x))}{a}-\frac{\tanh (x)}{a \cosh (x)+a}",1,"-(ArcTan[Sinh[x]]/a) + (2*Tanh[x])/a - Tanh[x]/(a + a*Cosh[x])","A",5,5,13,0.3846,1,"{2768, 2748, 3767, 8, 3770}"
30,1,43,0,0.0744833,"\int \frac{\text{sech}^3(x)}{a+a \cosh (x)} \, dx","Int[Sech[x]^3/(a + a*Cosh[x]),x]","-\frac{2 \tanh (x)}{a}+\frac{3 \tan ^{-1}(\sinh (x))}{2 a}+\frac{3 \tanh (x) \text{sech}(x)}{2 a}-\frac{\tanh (x) \text{sech}(x)}{a \cosh (x)+a}","-\frac{2 \tanh (x)}{a}+\frac{3 \tan ^{-1}(\sinh (x))}{2 a}+\frac{3 \tanh (x) \text{sech}(x)}{2 a}-\frac{\tanh (x) \text{sech}(x)}{a \cosh (x)+a}",1,"(3*ArcTan[Sinh[x]])/(2*a) - (2*Tanh[x])/a + (3*Sech[x]*Tanh[x])/(2*a) - (Sech[x]*Tanh[x])/(a + a*Cosh[x])","A",6,6,13,0.4615,1,"{2768, 2748, 3768, 3770, 3767, 8}"
31,1,56,0,0.0769904,"\int \frac{\text{sech}^4(x)}{a+a \cosh (x)} \, dx","Int[Sech[x]^4/(a + a*Cosh[x]),x]","-\frac{4 \tanh ^3(x)}{3 a}+\frac{4 \tanh (x)}{a}-\frac{3 \tan ^{-1}(\sinh (x))}{2 a}-\frac{3 \tanh (x) \text{sech}(x)}{2 a}-\frac{\tanh (x) \text{sech}^2(x)}{a \cosh (x)+a}","-\frac{4 \tanh ^3(x)}{3 a}+\frac{4 \tanh (x)}{a}-\frac{3 \tan ^{-1}(\sinh (x))}{2 a}-\frac{3 \tanh (x) \text{sech}(x)}{2 a}-\frac{\tanh (x) \text{sech}^2(x)}{a \cosh (x)+a}",1,"(-3*ArcTan[Sinh[x]])/(2*a) + (4*Tanh[x])/a - (3*Sech[x]*Tanh[x])/(2*a) - (Sech[x]^2*Tanh[x])/(a + a*Cosh[x]) - (4*Tanh[x]^3)/(3*a)","A",6,5,13,0.3846,1,"{2768, 2748, 3767, 3768, 3770}"
32,1,20,0,0.0100075,"\int \frac{1}{1+\cosh (c+d x)} \, dx","Int[(1 + Cosh[c + d*x])^(-1),x]","\frac{\sinh (c+d x)}{d (\cosh (c+d x)+1)}","\frac{\sinh (c+d x)}{d (\cosh (c+d x)+1)}",1,"Sinh[c + d*x]/(d*(1 + Cosh[c + d*x]))","A",1,1,10,0.1000,1,"{2648}"
33,1,47,0,0.0223655,"\int \frac{1}{(1+\cosh (c+d x))^2} \, dx","Int[(1 + Cosh[c + d*x])^(-2),x]","\frac{\sinh (c+d x)}{3 d (\cosh (c+d x)+1)}+\frac{\sinh (c+d x)}{3 d (\cosh (c+d x)+1)^2}","\frac{\sinh (c+d x)}{3 d (\cosh (c+d x)+1)}+\frac{\sinh (c+d x)}{3 d (\cosh (c+d x)+1)^2}",1,"Sinh[c + d*x]/(3*d*(1 + Cosh[c + d*x])^2) + Sinh[c + d*x]/(3*d*(1 + Cosh[c + d*x]))","A",2,2,10,0.2000,1,"{2650, 2648}"
34,1,70,0,0.036479,"\int \frac{1}{(1+\cosh (c+d x))^3} \, dx","Int[(1 + Cosh[c + d*x])^(-3),x]","\frac{2 \sinh (c+d x)}{15 d (\cosh (c+d x)+1)}+\frac{2 \sinh (c+d x)}{15 d (\cosh (c+d x)+1)^2}+\frac{\sinh (c+d x)}{5 d (\cosh (c+d x)+1)^3}","\frac{2 \sinh (c+d x)}{15 d (\cosh (c+d x)+1)}+\frac{2 \sinh (c+d x)}{15 d (\cosh (c+d x)+1)^2}+\frac{\sinh (c+d x)}{5 d (\cosh (c+d x)+1)^3}",1,"Sinh[c + d*x]/(5*d*(1 + Cosh[c + d*x])^3) + (2*Sinh[c + d*x])/(15*d*(1 + Cosh[c + d*x])^2) + (2*Sinh[c + d*x])/(15*d*(1 + Cosh[c + d*x]))","A",3,2,10,0.2000,1,"{2650, 2648}"
35,1,93,0,0.0535939,"\int \frac{1}{(1+\cosh (c+d x))^4} \, dx","Int[(1 + Cosh[c + d*x])^(-4),x]","\frac{2 \sinh (c+d x)}{35 d (\cosh (c+d x)+1)}+\frac{2 \sinh (c+d x)}{35 d (\cosh (c+d x)+1)^2}+\frac{3 \sinh (c+d x)}{35 d (\cosh (c+d x)+1)^3}+\frac{\sinh (c+d x)}{7 d (\cosh (c+d x)+1)^4}","\frac{2 \sinh (c+d x)}{35 d (\cosh (c+d x)+1)}+\frac{2 \sinh (c+d x)}{35 d (\cosh (c+d x)+1)^2}+\frac{3 \sinh (c+d x)}{35 d (\cosh (c+d x)+1)^3}+\frac{\sinh (c+d x)}{7 d (\cosh (c+d x)+1)^4}",1,"Sinh[c + d*x]/(7*d*(1 + Cosh[c + d*x])^4) + (3*Sinh[c + d*x])/(35*d*(1 + Cosh[c + d*x])^3) + (2*Sinh[c + d*x])/(35*d*(1 + Cosh[c + d*x])^2) + (2*Sinh[c + d*x])/(35*d*(1 + Cosh[c + d*x]))","A",4,2,10,0.2000,1,"{2650, 2648}"
36,1,23,0,0.0109634,"\int \frac{1}{1-\cosh (c+d x)} \, dx","Int[(1 - Cosh[c + d*x])^(-1),x]","-\frac{\sinh (c+d x)}{d (1-\cosh (c+d x))}","-\frac{\sinh (c+d x)}{d (1-\cosh (c+d x))}",1,"-(Sinh[c + d*x]/(d*(1 - Cosh[c + d*x])))","A",1,1,12,0.08333,1,"{2648}"
37,1,51,0,0.0248098,"\int \frac{1}{(1-\cosh (c+d x))^2} \, dx","Int[(1 - Cosh[c + d*x])^(-2),x]","-\frac{\sinh (c+d x)}{3 d (1-\cosh (c+d x))}-\frac{\sinh (c+d x)}{3 d (1-\cosh (c+d x))^2}","-\frac{\sinh (c+d x)}{3 d (1-\cosh (c+d x))}-\frac{\sinh (c+d x)}{3 d (1-\cosh (c+d x))^2}",1,"-Sinh[c + d*x]/(3*d*(1 - Cosh[c + d*x])^2) - Sinh[c + d*x]/(3*d*(1 - Cosh[c + d*x]))","A",2,2,12,0.1667,1,"{2650, 2648}"
38,1,76,0,0.0403379,"\int \frac{1}{(1-\cosh (c+d x))^3} \, dx","Int[(1 - Cosh[c + d*x])^(-3),x]","-\frac{2 \sinh (c+d x)}{15 d (1-\cosh (c+d x))}-\frac{2 \sinh (c+d x)}{15 d (1-\cosh (c+d x))^2}-\frac{\sinh (c+d x)}{5 d (1-\cosh (c+d x))^3}","-\frac{2 \sinh (c+d x)}{15 d (1-\cosh (c+d x))}-\frac{2 \sinh (c+d x)}{15 d (1-\cosh (c+d x))^2}-\frac{\sinh (c+d x)}{5 d (1-\cosh (c+d x))^3}",1,"-Sinh[c + d*x]/(5*d*(1 - Cosh[c + d*x])^3) - (2*Sinh[c + d*x])/(15*d*(1 - Cosh[c + d*x])^2) - (2*Sinh[c + d*x])/(15*d*(1 - Cosh[c + d*x]))","A",3,2,12,0.1667,1,"{2650, 2648}"
39,1,101,0,0.0571527,"\int \frac{1}{(1-\cosh (c+d x))^4} \, dx","Int[(1 - Cosh[c + d*x])^(-4),x]","-\frac{2 \sinh (c+d x)}{35 d (1-\cosh (c+d x))}-\frac{2 \sinh (c+d x)}{35 d (1-\cosh (c+d x))^2}-\frac{3 \sinh (c+d x)}{35 d (1-\cosh (c+d x))^3}-\frac{\sinh (c+d x)}{7 d (1-\cosh (c+d x))^4}","-\frac{2 \sinh (c+d x)}{35 d (1-\cosh (c+d x))}-\frac{2 \sinh (c+d x)}{35 d (1-\cosh (c+d x))^2}-\frac{3 \sinh (c+d x)}{35 d (1-\cosh (c+d x))^3}-\frac{\sinh (c+d x)}{7 d (1-\cosh (c+d x))^4}",1,"-Sinh[c + d*x]/(7*d*(1 - Cosh[c + d*x])^4) - (3*Sinh[c + d*x])/(35*d*(1 - Cosh[c + d*x])^3) - (2*Sinh[c + d*x])/(35*d*(1 - Cosh[c + d*x])^2) - (2*Sinh[c + d*x])/(35*d*(1 - Cosh[c + d*x]))","A",4,2,12,0.1667,1,"{2650, 2648}"
40,1,51,0,0.0452953,"\int \frac{\cosh (x)}{\sqrt{a+a \cosh (x)}} \, dx","Int[Cosh[x]/Sqrt[a + a*Cosh[x]],x]","\frac{2 \sinh (x)}{\sqrt{a \cosh (x)+a}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{a} \sinh (x)}{\sqrt{2} \sqrt{a \cosh (x)+a}}\right)}{\sqrt{a}}","\frac{2 \sinh (x)}{\sqrt{a \cosh (x)+a}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{a} \sinh (x)}{\sqrt{2} \sqrt{a \cosh (x)+a}}\right)}{\sqrt{a}}",1,"-((Sqrt[2]*ArcTan[(Sqrt[a]*Sinh[x])/(Sqrt[2]*Sqrt[a + a*Cosh[x]])])/Sqrt[a]) + (2*Sinh[x])/Sqrt[a + a*Cosh[x]]","A",3,3,13,0.2308,1,"{2751, 2649, 206}"
41,1,53,0,0.0493212,"\int \frac{\cosh (x)}{\sqrt{a-a \cosh (x)}} \, dx","Int[Cosh[x]/Sqrt[a - a*Cosh[x]],x]","\frac{2 \sinh (x)}{\sqrt{a-a \cosh (x)}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{a} \sinh (x)}{\sqrt{2} \sqrt{a-a \cosh (x)}}\right)}{\sqrt{a}}","\frac{2 \sinh (x)}{\sqrt{a-a \cosh (x)}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{a} \sinh (x)}{\sqrt{2} \sqrt{a-a \cosh (x)}}\right)}{\sqrt{a}}",1,"-((Sqrt[2]*ArcTan[(Sqrt[a]*Sinh[x])/(Sqrt[2]*Sqrt[a - a*Cosh[x]])])/Sqrt[a]) + (2*Sinh[x])/Sqrt[a - a*Cosh[x]]","A",3,3,14,0.2143,1,"{2751, 2649, 206}"
42,1,89,0,0.0468435,"\int (a+a \cosh (c+d x))^{5/2} \, dx","Int[(a + a*Cosh[c + d*x])^(5/2),x]","\frac{64 a^3 \sinh (c+d x)}{15 d \sqrt{a \cosh (c+d x)+a}}+\frac{16 a^2 \sinh (c+d x) \sqrt{a \cosh (c+d x)+a}}{15 d}+\frac{2 a \sinh (c+d x) (a \cosh (c+d x)+a)^{3/2}}{5 d}","\frac{64 a^3 \sinh (c+d x)}{15 d \sqrt{a \cosh (c+d x)+a}}+\frac{16 a^2 \sinh (c+d x) \sqrt{a \cosh (c+d x)+a}}{15 d}+\frac{2 a \sinh (c+d x) (a \cosh (c+d x)+a)^{3/2}}{5 d}",1,"(64*a^3*Sinh[c + d*x])/(15*d*Sqrt[a + a*Cosh[c + d*x]]) + (16*a^2*Sqrt[a + a*Cosh[c + d*x]]*Sinh[c + d*x])/(15*d) + (2*a*(a + a*Cosh[c + d*x])^(3/2)*Sinh[c + d*x])/(5*d)","A",3,2,14,0.1429,1,"{2647, 2646}"
43,1,59,0,0.0287345,"\int (a+a \cosh (c+d x))^{3/2} \, dx","Int[(a + a*Cosh[c + d*x])^(3/2),x]","\frac{8 a^2 \sinh (c+d x)}{3 d \sqrt{a \cosh (c+d x)+a}}+\frac{2 a \sinh (c+d x) \sqrt{a \cosh (c+d x)+a}}{3 d}","\frac{8 a^2 \sinh (c+d x)}{3 d \sqrt{a \cosh (c+d x)+a}}+\frac{2 a \sinh (c+d x) \sqrt{a \cosh (c+d x)+a}}{3 d}",1,"(8*a^2*Sinh[c + d*x])/(3*d*Sqrt[a + a*Cosh[c + d*x]]) + (2*a*Sqrt[a + a*Cosh[c + d*x]]*Sinh[c + d*x])/(3*d)","A",2,2,14,0.1429,1,"{2647, 2646}"
44,1,26,0,0.013316,"\int \sqrt{a+a \cosh (c+d x)} \, dx","Int[Sqrt[a + a*Cosh[c + d*x]],x]","\frac{2 a \sinh (c+d x)}{d \sqrt{a \cosh (c+d x)+a}}","\frac{2 a \sinh (c+d x)}{d \sqrt{a \cosh (c+d x)+a}}",1,"(2*a*Sinh[c + d*x])/(d*Sqrt[a + a*Cosh[c + d*x]])","A",1,1,14,0.07143,1,"{2646}"
45,1,46,0,0.0225107,"\int \frac{1}{\sqrt{a+a \cosh (c+d x)}} \, dx","Int[1/Sqrt[a + a*Cosh[c + d*x]],x]","\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{2} \sqrt{a \cosh (c+d x)+a}}\right)}{\sqrt{a} d}","\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{2} \sqrt{a \cosh (c+d x)+a}}\right)}{\sqrt{a} d}",1,"(Sqrt[2]*ArcTan[(Sqrt[a]*Sinh[c + d*x])/(Sqrt[2]*Sqrt[a + a*Cosh[c + d*x]])])/(Sqrt[a]*d)","A",2,2,14,0.1429,1,"{2649, 206}"
46,1,77,0,0.0414038,"\int \frac{1}{(a+a \cosh (c+d x))^{3/2}} \, dx","Int[(a + a*Cosh[c + d*x])^(-3/2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{2} \sqrt{a \cosh (c+d x)+a}}\right)}{2 \sqrt{2} a^{3/2} d}+\frac{\sinh (c+d x)}{2 d (a \cosh (c+d x)+a)^{3/2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{2} \sqrt{a \cosh (c+d x)+a}}\right)}{2 \sqrt{2} a^{3/2} d}+\frac{\sinh (c+d x)}{2 d (a \cosh (c+d x)+a)^{3/2}}",1,"ArcTan[(Sqrt[a]*Sinh[c + d*x])/(Sqrt[2]*Sqrt[a + a*Cosh[c + d*x]])]/(2*Sqrt[2]*a^(3/2)*d) + Sinh[c + d*x]/(2*d*(a + a*Cosh[c + d*x])^(3/2))","A",3,3,14,0.2143,1,"{2650, 2649, 206}"
47,1,107,0,0.0624466,"\int \frac{1}{(a+a \cosh (c+d x))^{5/2}} \, dx","Int[(a + a*Cosh[c + d*x])^(-5/2),x]","\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{2} \sqrt{a \cosh (c+d x)+a}}\right)}{16 \sqrt{2} a^{5/2} d}+\frac{3 \sinh (c+d x)}{16 a d (a \cosh (c+d x)+a)^{3/2}}+\frac{\sinh (c+d x)}{4 d (a \cosh (c+d x)+a)^{5/2}}","\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{2} \sqrt{a \cosh (c+d x)+a}}\right)}{16 \sqrt{2} a^{5/2} d}+\frac{3 \sinh (c+d x)}{16 a d (a \cosh (c+d x)+a)^{3/2}}+\frac{\sinh (c+d x)}{4 d (a \cosh (c+d x)+a)^{5/2}}",1,"(3*ArcTan[(Sqrt[a]*Sinh[c + d*x])/(Sqrt[2]*Sqrt[a + a*Cosh[c + d*x]])])/(16*Sqrt[2]*a^(5/2)*d) + Sinh[c + d*x]/(4*d*(a + a*Cosh[c + d*x])^(5/2)) + (3*Sinh[c + d*x])/(16*a*d*(a + a*Cosh[c + d*x])^(3/2))","A",4,3,14,0.2143,1,"{2650, 2649, 206}"
48,1,92,0,0.0520059,"\int (a-a \cosh (c+d x))^{5/2} \, dx","Int[(a - a*Cosh[c + d*x])^(5/2),x]","-\frac{64 a^3 \sinh (c+d x)}{15 d \sqrt{a-a \cosh (c+d x)}}-\frac{16 a^2 \sinh (c+d x) \sqrt{a-a \cosh (c+d x)}}{15 d}-\frac{2 a \sinh (c+d x) (a-a \cosh (c+d x))^{3/2}}{5 d}","-\frac{64 a^3 \sinh (c+d x)}{15 d \sqrt{a-a \cosh (c+d x)}}-\frac{16 a^2 \sinh (c+d x) \sqrt{a-a \cosh (c+d x)}}{15 d}-\frac{2 a \sinh (c+d x) (a-a \cosh (c+d x))^{3/2}}{5 d}",1,"(-64*a^3*Sinh[c + d*x])/(15*d*Sqrt[a - a*Cosh[c + d*x]]) - (16*a^2*Sqrt[a - a*Cosh[c + d*x]]*Sinh[c + d*x])/(15*d) - (2*a*(a - a*Cosh[c + d*x])^(3/2)*Sinh[c + d*x])/(5*d)","A",3,2,15,0.1333,1,"{2647, 2646}"
49,1,61,0,0.031382,"\int (a-a \cosh (c+d x))^{3/2} \, dx","Int[(a - a*Cosh[c + d*x])^(3/2),x]","-\frac{8 a^2 \sinh (c+d x)}{3 d \sqrt{a-a \cosh (c+d x)}}-\frac{2 a \sinh (c+d x) \sqrt{a-a \cosh (c+d x)}}{3 d}","-\frac{8 a^2 \sinh (c+d x)}{3 d \sqrt{a-a \cosh (c+d x)}}-\frac{2 a \sinh (c+d x) \sqrt{a-a \cosh (c+d x)}}{3 d}",1,"(-8*a^2*Sinh[c + d*x])/(3*d*Sqrt[a - a*Cosh[c + d*x]]) - (2*a*Sqrt[a - a*Cosh[c + d*x]]*Sinh[c + d*x])/(3*d)","A",2,2,15,0.1333,1,"{2647, 2646}"
50,1,27,0,0.0144789,"\int \sqrt{a-a \cosh (c+d x)} \, dx","Int[Sqrt[a - a*Cosh[c + d*x]],x]","-\frac{2 a \sinh (c+d x)}{d \sqrt{a-a \cosh (c+d x)}}","-\frac{2 a \sinh (c+d x)}{d \sqrt{a-a \cosh (c+d x)}}",1,"(-2*a*Sinh[c + d*x])/(d*Sqrt[a - a*Cosh[c + d*x]])","A",1,1,15,0.06667,1,"{2646}"
51,1,48,0,0.0254998,"\int \frac{1}{\sqrt{a-a \cosh (c+d x)}} \, dx","Int[1/Sqrt[a - a*Cosh[c + d*x]],x]","-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{2} \sqrt{a-a \cosh (c+d x)}}\right)}{\sqrt{a} d}","-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{2} \sqrt{a-a \cosh (c+d x)}}\right)}{\sqrt{a} d}",1,"-((Sqrt[2]*ArcTan[(Sqrt[a]*Sinh[c + d*x])/(Sqrt[2]*Sqrt[a - a*Cosh[c + d*x]])])/(Sqrt[a]*d))","A",2,2,15,0.1333,1,"{2649, 206}"
52,1,79,0,0.0414287,"\int \frac{1}{(a-a \cosh (c+d x))^{3/2}} \, dx","Int[(a - a*Cosh[c + d*x])^(-3/2),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{2} \sqrt{a-a \cosh (c+d x)}}\right)}{2 \sqrt{2} a^{3/2} d}-\frac{\sinh (c+d x)}{2 d (a-a \cosh (c+d x))^{3/2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{2} \sqrt{a-a \cosh (c+d x)}}\right)}{2 \sqrt{2} a^{3/2} d}-\frac{\sinh (c+d x)}{2 d (a-a \cosh (c+d x))^{3/2}}",1,"-ArcTan[(Sqrt[a]*Sinh[c + d*x])/(Sqrt[2]*Sqrt[a - a*Cosh[c + d*x]])]/(2*Sqrt[2]*a^(3/2)*d) - Sinh[c + d*x]/(2*d*(a - a*Cosh[c + d*x])^(3/2))","A",3,3,15,0.2000,1,"{2650, 2649, 206}"
53,1,110,0,0.062987,"\int \frac{1}{(a-a \cosh (c+d x))^{5/2}} \, dx","Int[(a - a*Cosh[c + d*x])^(-5/2),x]","-\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{2} \sqrt{a-a \cosh (c+d x)}}\right)}{16 \sqrt{2} a^{5/2} d}-\frac{3 \sinh (c+d x)}{16 a d (a-a \cosh (c+d x))^{3/2}}-\frac{\sinh (c+d x)}{4 d (a-a \cosh (c+d x))^{5/2}}","-\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{2} \sqrt{a-a \cosh (c+d x)}}\right)}{16 \sqrt{2} a^{5/2} d}-\frac{3 \sinh (c+d x)}{16 a d (a-a \cosh (c+d x))^{3/2}}-\frac{\sinh (c+d x)}{4 d (a-a \cosh (c+d x))^{5/2}}",1,"(-3*ArcTan[(Sqrt[a]*Sinh[c + d*x])/(Sqrt[2]*Sqrt[a - a*Cosh[c + d*x]])])/(16*Sqrt[2]*a^(5/2)*d) - Sinh[c + d*x]/(4*d*(a - a*Cosh[c + d*x])^(5/2)) - (3*Sinh[c + d*x])/(16*a*d*(a - a*Cosh[c + d*x])^(3/2))","A",4,3,15,0.2000,1,"{2650, 2649, 206}"
54,1,112,0,0.3089758,"\int \frac{\cosh ^4(x)}{a+b \cosh (x)} \, dx","Int[Cosh[x]^4/(a + b*Cosh[x]),x]","-\frac{a x \left(2 a^2+b^2\right)}{2 b^4}+\frac{\left(3 a^2+2 b^2\right) \sinh (x)}{3 b^3}+\frac{2 a^4 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b^4 \sqrt{a-b} \sqrt{a+b}}-\frac{a \sinh (x) \cosh (x)}{2 b^2}+\frac{\sinh (x) \cosh ^2(x)}{3 b}","-\frac{a x \left(2 a^2+b^2\right)}{2 b^4}+\frac{\left(3 a^2+2 b^2\right) \sinh (x)}{3 b^3}+\frac{2 a^4 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b^4 \sqrt{a-b} \sqrt{a+b}}-\frac{a \sinh (x) \cosh (x)}{2 b^2}+\frac{\sinh (x) \cosh ^2(x)}{3 b}",1,"-(a*(2*a^2 + b^2)*x)/(2*b^4) + (2*a^4*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(Sqrt[a - b]*b^4*Sqrt[a + b]) + ((3*a^2 + 2*b^2)*Sinh[x])/(3*b^3) - (a*Cosh[x]*Sinh[x])/(2*b^2) + (Cosh[x]^2*Sinh[x])/(3*b)","A",6,6,13,0.4615,1,"{2793, 3049, 3023, 2735, 2659, 208}"
55,1,85,0,0.1686118,"\int \frac{\cosh ^3(x)}{a+b \cosh (x)} \, dx","Int[Cosh[x]^3/(a + b*Cosh[x]),x]","\frac{x \left(2 a^2+b^2\right)}{2 b^3}-\frac{2 a^3 \tanh ^{-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{a \sinh (x)}{b^2}+\frac{\sinh (x) \cosh (x)}{2 b}","\frac{x \left(2 a^2+b^2\right)}{2 b^3}-\frac{2 a^3 \tanh ^{-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{a \sinh (x)}{b^2}+\frac{\sinh (x) \cosh (x)}{2 b}",1,"((2*a^2 + b^2)*x)/(2*b^3) - (2*a^3*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(Sqrt[a - b]*b^3*Sqrt[a + b]) - (a*Sinh[x])/b^2 + (Cosh[x]*Sinh[x])/(2*b)","A",5,5,13,0.3846,1,"{2793, 3023, 2735, 2659, 208}"
56,1,62,0,0.1062289,"\int \frac{\cosh ^2(x)}{a+b \cosh (x)} \, dx","Int[Cosh[x]^2/(a + b*Cosh[x]),x]","\frac{2 a^2 \tanh ^{-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 x}{b^2}+\frac{\sinh (x)}{b}","\frac{2 a^2 \tanh ^{-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 x}{b^2}+\frac{\sinh (x)}{b}",1,"-((a*x)/b^2) + (2*a^2*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(Sqrt[a - b]*b^2*Sqrt[a + b]) + Sinh[x]/b","A",5,5,13,0.3846,1,"{2746, 12, 2735, 2659, 208}"
57,1,52,0,0.0525138,"\int \frac{\cosh (x)}{a+b \cosh (x)} \, dx","Int[Cosh[x]/(a + b*Cosh[x]),x]","\frac{x}{b}-\frac{2 a \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b \sqrt{a-b} \sqrt{a+b}}","\frac{x}{b}-\frac{2 a \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b \sqrt{a-b} \sqrt{a+b}}",1,"x/b - (2*a*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(Sqrt[a - b]*b*Sqrt[a + b])","A",3,3,11,0.2727,1,"{2735, 2659, 208}"
58,1,54,0,0.067154,"\int \frac{\text{sech}(x)}{a+b \cosh (x)} \, dx","Int[Sech[x]/(a + b*Cosh[x]),x]","\frac{\tan ^{-1}(\sinh (x))}{a}-\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a \sqrt{a-b} \sqrt{a+b}}","\frac{\tan ^{-1}(\sinh (x))}{a}-\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a \sqrt{a-b} \sqrt{a+b}}",1,"ArcTan[Sinh[x]]/a - (2*b*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(a*Sqrt[a - b]*Sqrt[a + b])","A",4,4,11,0.3636,1,"{2747, 3770, 2659, 208}"
59,1,64,0,0.1166936,"\int \frac{\text{sech}^2(x)}{a+b \cosh (x)} \, dx","Int[Sech[x]^2/(a + b*Cosh[x]),x]","\frac{2 b^2 \tanh ^{-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 \tan ^{-1}(\sinh (x))}{a^2}+\frac{\tanh (x)}{a}","\frac{2 b^2 \tanh ^{-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 \tan ^{-1}(\sinh (x))}{a^2}+\frac{\tanh (x)}{a}",1,"-((b*ArcTan[Sinh[x]])/a^2) + (2*b^2*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(a^2*Sqrt[a - b]*Sqrt[a + b]) + Tanh[x]/a","A",6,6,13,0.4615,1,"{2802, 12, 2747, 3770, 2659, 208}"
60,1,87,0,0.2996321,"\int \frac{\text{sech}^3(x)}{a+b \cosh (x)} \, dx","Int[Sech[x]^3/(a + b*Cosh[x]),x]","-\frac{2 b^3 \tanh ^{-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{\left(a^2+2 b^2\right) \tan ^{-1}(\sinh (x))}{2 a^3}-\frac{b \tanh (x)}{a^2}+\frac{\tanh (x) \text{sech}(x)}{2 a}","-\frac{2 b^3 \tanh ^{-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{\left(a^2+2 b^2\right) \tan ^{-1}(\sinh (x))}{2 a^3}-\frac{b \tanh (x)}{a^2}+\frac{\tanh (x) \text{sech}(x)}{2 a}",1,"((a^2 + 2*b^2)*ArcTan[Sinh[x]])/(2*a^3) - (2*b^3*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(a^3*Sqrt[a - b]*Sqrt[a + b]) - (b*Tanh[x])/a^2 + (Sech[x]*Tanh[x])/(2*a)","A",6,6,13,0.4615,1,"{2802, 3055, 3001, 3770, 2659, 208}"
61,1,114,0,0.4719658,"\int \frac{\text{sech}^4(x)}{a+b \cosh (x)} \, dx","Int[Sech[x]^4/(a + b*Cosh[x]),x]","\frac{2 b^4 \tanh ^{-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{\left(2 a^2+3 b^2\right) \tanh (x)}{3 a^3}-\frac{b \left(a^2+2 b^2\right) \tan ^{-1}(\sinh (x))}{2 a^4}-\frac{b \tanh (x) \text{sech}(x)}{2 a^2}+\frac{\tanh (x) \text{sech}^2(x)}{3 a}","\frac{2 b^4 \tanh ^{-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{\left(2 a^2+3 b^2\right) \tanh (x)}{3 a^3}-\frac{b \left(a^2+2 b^2\right) \tan ^{-1}(\sinh (x))}{2 a^4}-\frac{b \tanh (x) \text{sech}(x)}{2 a^2}+\frac{\tanh (x) \text{sech}^2(x)}{3 a}",1,"-(b*(a^2 + 2*b^2)*ArcTan[Sinh[x]])/(2*a^4) + (2*b^4*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(a^4*Sqrt[a - b]*Sqrt[a + b]) + ((2*a^2 + 3*b^2)*Tanh[x])/(3*a^3) - (b*Sech[x]*Tanh[x])/(2*a^2) + (Sech[x]^2*Tanh[x])/(3*a)","A",7,6,13,0.4615,1,"{2802, 3055, 3001, 3770, 2659, 208}"
62,1,183,0,0.2600913,"\int (a+b \cosh (c+d x))^5 \, dx","Int[(a + b*Cosh[c + d*x])^5,x]","\frac{b \left(192 a^2 b^2+107 a^4+16 b^4\right) \sinh (c+d x)}{30 d}+\frac{b \left(47 a^2+16 b^2\right) \sinh (c+d x) (a+b \cosh (c+d x))^2}{60 d}+\frac{7 a b^2 \left(22 a^2+23 b^2\right) \sinh (c+d x) \cosh (c+d x)}{120 d}+\frac{1}{8} a x \left(40 a^2 b^2+8 a^4+15 b^4\right)+\frac{b \sinh (c+d x) (a+b \cosh (c+d x))^4}{5 d}+\frac{9 a b \sinh (c+d x) (a+b \cosh (c+d x))^3}{20 d}","\frac{b \left(192 a^2 b^2+107 a^4+16 b^4\right) \sinh (c+d x)}{30 d}+\frac{b \left(47 a^2+16 b^2\right) \sinh (c+d x) (a+b \cosh (c+d x))^2}{60 d}+\frac{7 a b^2 \left(22 a^2+23 b^2\right) \sinh (c+d x) \cosh (c+d x)}{120 d}+\frac{1}{8} a x \left(40 a^2 b^2+8 a^4+15 b^4\right)+\frac{b \sinh (c+d x) (a+b \cosh (c+d x))^4}{5 d}+\frac{9 a b \sinh (c+d x) (a+b \cosh (c+d x))^3}{20 d}",1,"(a*(8*a^4 + 40*a^2*b^2 + 15*b^4)*x)/8 + (b*(107*a^4 + 192*a^2*b^2 + 16*b^4)*Sinh[c + d*x])/(30*d) + (7*a*b^2*(22*a^2 + 23*b^2)*Cosh[c + d*x]*Sinh[c + d*x])/(120*d) + (b*(47*a^2 + 16*b^2)*(a + b*Cosh[c + d*x])^2*Sinh[c + d*x])/(60*d) + (9*a*b*(a + b*Cosh[c + d*x])^3*Sinh[c + d*x])/(20*d) + (b*(a + b*Cosh[c + d*x])^4*Sinh[c + d*x])/(5*d)","A",4,3,12,0.2500,1,"{2656, 2753, 2734}"
63,1,137,0,0.1507634,"\int (a+b \cosh (c+d x))^4 \, dx","Int[(a + b*Cosh[c + d*x])^4,x]","\frac{a b \left(19 a^2+16 b^2\right) \sinh (c+d x)}{6 d}+\frac{b^2 \left(26 a^2+9 b^2\right) \sinh (c+d x) \cosh (c+d x)}{24 d}+\frac{1}{8} x \left(24 a^2 b^2+8 a^4+3 b^4\right)+\frac{b \sinh (c+d x) (a+b \cosh (c+d x))^3}{4 d}+\frac{7 a b \sinh (c+d x) (a+b \cosh (c+d x))^2}{12 d}","\frac{a b \left(19 a^2+16 b^2\right) \sinh (c+d x)}{6 d}+\frac{b^2 \left(26 a^2+9 b^2\right) \sinh (c+d x) \cosh (c+d x)}{24 d}+\frac{1}{8} x \left(24 a^2 b^2+8 a^4+3 b^4\right)+\frac{b \sinh (c+d x) (a+b \cosh (c+d x))^3}{4 d}+\frac{7 a b \sinh (c+d x) (a+b \cosh (c+d x))^2}{12 d}",1,"((8*a^4 + 24*a^2*b^2 + 3*b^4)*x)/8 + (a*b*(19*a^2 + 16*b^2)*Sinh[c + d*x])/(6*d) + (b^2*(26*a^2 + 9*b^2)*Cosh[c + d*x]*Sinh[c + d*x])/(24*d) + (7*a*b*(a + b*Cosh[c + d*x])^2*Sinh[c + d*x])/(12*d) + (b*(a + b*Cosh[c + d*x])^3*Sinh[c + d*x])/(4*d)","A",3,3,12,0.2500,1,"{2656, 2753, 2734}"
64,1,90,0,0.0682165,"\int (a+b \cosh (c+d x))^3 \, dx","Int[(a + b*Cosh[c + d*x])^3,x]","\frac{2 b \left(4 a^2+b^2\right) \sinh (c+d x)}{3 d}+\frac{1}{2} a x \left(2 a^2+3 b^2\right)+\frac{5 a b^2 \sinh (c+d x) \cosh (c+d x)}{6 d}+\frac{b \sinh (c+d x) (a+b \cosh (c+d x))^2}{3 d}","\frac{2 b \left(4 a^2+b^2\right) \sinh (c+d x)}{3 d}+\frac{1}{2} a x \left(2 a^2+3 b^2\right)+\frac{5 a b^2 \sinh (c+d x) \cosh (c+d x)}{6 d}+\frac{b \sinh (c+d x) (a+b \cosh (c+d x))^2}{3 d}",1,"(a*(2*a^2 + 3*b^2)*x)/2 + (2*b*(4*a^2 + b^2)*Sinh[c + d*x])/(3*d) + (5*a*b^2*Cosh[c + d*x]*Sinh[c + d*x])/(6*d) + (b*(a + b*Cosh[c + d*x])^2*Sinh[c + d*x])/(3*d)","A",2,2,12,0.1667,1,"{2656, 2734}"
65,1,50,0,0.0172046,"\int (a+b \cosh (c+d x))^2 \, dx","Int[(a + b*Cosh[c + d*x])^2,x]","\frac{1}{2} x \left(2 a^2+b^2\right)+\frac{2 a b \sinh (c+d x)}{d}+\frac{b^2 \sinh (c+d x) \cosh (c+d x)}{2 d}","\frac{1}{2} x \left(2 a^2+b^2\right)+\frac{2 a b \sinh (c+d x)}{d}+\frac{b^2 \sinh (c+d x) \cosh (c+d x)}{2 d}",1,"((2*a^2 + b^2)*x)/2 + (2*a*b*Sinh[c + d*x])/d + (b^2*Cosh[c + d*x]*Sinh[c + d*x])/(2*d)","A",1,1,12,0.08333,1,"{2644}"
66,1,15,0,0.0084691,"\int (a+b \cosh (c+d x)) \, dx","Int[a + b*Cosh[c + d*x],x]","a x+\frac{b \sinh (c+d x)}{d}","a x+\frac{b \sinh (c+d x)}{d}",1,"a*x + (b*Sinh[c + d*x])/d","A",2,1,10,0.1000,1,"{2637}"
67,1,49,0,0.035172,"\int \frac{1}{a+b \cosh (c+d x)} \, dx","Int[(a + b*Cosh[c + d*x])^(-1),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a+b}}\right)}{d \sqrt{a-b} \sqrt{a+b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a+b}}\right)}{d \sqrt{a-b} \sqrt{a+b}}",1,"(2*ArcTanh[(Sqrt[a - b]*Tanh[(c + d*x)/2])/Sqrt[a + b]])/(Sqrt[a - b]*Sqrt[a + b]*d)","A",2,2,12,0.1667,1,"{2659, 205}"
68,1,86,0,0.0840867,"\int \frac{1}{(a+b \cosh (c+d x))^2} \, dx","Int[(a + b*Cosh[c + d*x])^(-2),x]","\frac{2 a \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a+b}}\right)}{d (a-b)^{3/2} (a+b)^{3/2}}-\frac{b \sinh (c+d x)}{d \left(a^2-b^2\right) (a+b \cosh (c+d x))}","\frac{2 a \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a+b}}\right)}{d (a-b)^{3/2} (a+b)^{3/2}}-\frac{b \sinh (c+d x)}{d \left(a^2-b^2\right) (a+b \cosh (c+d x))}",1,"(2*a*ArcTanh[(Sqrt[a - b]*Tanh[(c + d*x)/2])/Sqrt[a + b]])/((a - b)^(3/2)*(a + b)^(3/2)*d) - (b*Sinh[c + d*x])/((a^2 - b^2)*d*(a + b*Cosh[c + d*x]))","A",4,4,12,0.3333,1,"{2664, 12, 2659, 205}"
69,1,133,0,0.1465912,"\int \frac{1}{(a+b \cosh (c+d x))^3} \, dx","Int[(a + b*Cosh[c + d*x])^(-3),x]","\frac{\left(2 a^2+b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a+b}}\right)}{d (a-b)^{5/2} (a+b)^{5/2}}-\frac{3 a b \sinh (c+d x)}{2 d \left(a^2-b^2\right)^2 (a+b \cosh (c+d x))}-\frac{b \sinh (c+d x)}{2 d \left(a^2-b^2\right) (a+b \cosh (c+d x))^2}","\frac{\left(2 a^2+b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a+b}}\right)}{d (a-b)^{5/2} (a+b)^{5/2}}-\frac{3 a b \sinh (c+d x)}{2 d \left(a^2-b^2\right)^2 (a+b \cosh (c+d x))}-\frac{b \sinh (c+d x)}{2 d \left(a^2-b^2\right) (a+b \cosh (c+d x))^2}",1,"((2*a^2 + b^2)*ArcTanh[(Sqrt[a - b]*Tanh[(c + d*x)/2])/Sqrt[a + b]])/((a - b)^(5/2)*(a + b)^(5/2)*d) - (b*Sinh[c + d*x])/(2*(a^2 - b^2)*d*(a + b*Cosh[c + d*x])^2) - (3*a*b*Sinh[c + d*x])/(2*(a^2 - b^2)^2*d*(a + b*Cosh[c + d*x]))","A",5,5,12,0.4167,1,"{2664, 2754, 12, 2659, 205}"
70,1,184,0,0.2531106,"\int \frac{1}{(a+b \cosh (c+d x))^4} \, dx","Int[(a + b*Cosh[c + d*x])^(-4),x]","\frac{a \left(2 a^2+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a+b}}\right)}{d (a-b)^{7/2} (a+b)^{7/2}}-\frac{b \left(11 a^2+4 b^2\right) \sinh (c+d x)}{6 d \left(a^2-b^2\right)^3 (a+b \cosh (c+d x))}-\frac{5 a b \sinh (c+d x)}{6 d \left(a^2-b^2\right)^2 (a+b \cosh (c+d x))^2}-\frac{b \sinh (c+d x)}{3 d \left(a^2-b^2\right) (a+b \cosh (c+d x))^3}","\frac{a \left(2 a^2+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a+b}}\right)}{d (a-b)^{7/2} (a+b)^{7/2}}-\frac{b \left(11 a^2+4 b^2\right) \sinh (c+d x)}{6 d \left(a^2-b^2\right)^3 (a+b \cosh (c+d x))}-\frac{5 a b \sinh (c+d x)}{6 d \left(a^2-b^2\right)^2 (a+b \cosh (c+d x))^2}-\frac{b \sinh (c+d x)}{3 d \left(a^2-b^2\right) (a+b \cosh (c+d x))^3}",1,"(a*(2*a^2 + 3*b^2)*ArcTanh[(Sqrt[a - b]*Tanh[(c + d*x)/2])/Sqrt[a + b]])/((a - b)^(7/2)*(a + b)^(7/2)*d) - (b*Sinh[c + d*x])/(3*(a^2 - b^2)*d*(a + b*Cosh[c + d*x])^3) - (5*a*b*Sinh[c + d*x])/(6*(a^2 - b^2)^2*d*(a + b*Cosh[c + d*x])^2) - (b*(11*a^2 + 4*b^2)*Sinh[c + d*x])/(6*(a^2 - b^2)^3*d*(a + b*Cosh[c + d*x]))","A",6,5,12,0.4167,1,"{2664, 2754, 12, 2659, 205}"
71,1,22,0,0.0147783,"\int \frac{1}{3+5 \cosh (c+d x)} \, dx","Int[(3 + 5*Cosh[c + d*x])^(-1),x]","\frac{\tan ^{-1}\left(\frac{1}{2} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{2 d}","\frac{\tan ^{-1}\left(\frac{1}{2} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{2 d}",1,"ArcTan[Tanh[(c + d*x)/2]/2]/(2*d)","A",2,2,12,0.1667,1,"{2659, 206}"
72,1,48,0,0.0316992,"\int \frac{1}{(3+5 \cosh (c+d x))^2} \, dx","Int[(3 + 5*Cosh[c + d*x])^(-2),x]","\frac{5 \sinh (c+d x)}{16 d (5 \cosh (c+d x)+3)}-\frac{3 \tan ^{-1}\left(\frac{1}{2} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{32 d}","\frac{5 \sinh (c+d x)}{16 d (5 \cosh (c+d x)+3)}-\frac{3 \tan ^{-1}\left(\frac{1}{2} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{32 d}",1,"(-3*ArcTan[Tanh[(c + d*x)/2]/2])/(32*d) + (5*Sinh[c + d*x])/(16*d*(3 + 5*Cosh[c + d*x]))","A",4,4,12,0.3333,1,"{2664, 12, 2659, 206}"
73,1,73,0,0.0646426,"\int \frac{1}{(3+5 \cosh (c+d x))^3} \, dx","Int[(3 + 5*Cosh[c + d*x])^(-3),x]","\frac{43 \tan ^{-1}\left(\frac{1}{2} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{1024 d}-\frac{45 \sinh (c+d x)}{512 d (5 \cosh (c+d x)+3)}+\frac{5 \sinh (c+d x)}{32 d (5 \cosh (c+d x)+3)^2}","\frac{43 \tan ^{-1}\left(\frac{1}{2} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{1024 d}-\frac{45 \sinh (c+d x)}{512 d (5 \cosh (c+d x)+3)}+\frac{5 \sinh (c+d x)}{32 d (5 \cosh (c+d x)+3)^2}",1,"(43*ArcTan[Tanh[(c + d*x)/2]/2])/(1024*d) + (5*Sinh[c + d*x])/(32*d*(3 + 5*Cosh[c + d*x])^2) - (45*Sinh[c + d*x])/(512*d*(3 + 5*Cosh[c + d*x]))","A",5,5,12,0.4167,1,"{2664, 2754, 12, 2659, 206}"
74,1,98,0,0.097106,"\int \frac{1}{(3+5 \cosh (c+d x))^4} \, dx","Int[(3 + 5*Cosh[c + d*x])^(-4),x]","-\frac{279 \tan ^{-1}\left(\frac{1}{2} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{16384 d}+\frac{995 \sinh (c+d x)}{24576 d (5 \cosh (c+d x)+3)}-\frac{25 \sinh (c+d x)}{512 d (5 \cosh (c+d x)+3)^2}+\frac{5 \sinh (c+d x)}{48 d (5 \cosh (c+d x)+3)^3}","-\frac{279 \tan ^{-1}\left(\frac{1}{2} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{16384 d}+\frac{995 \sinh (c+d x)}{24576 d (5 \cosh (c+d x)+3)}-\frac{25 \sinh (c+d x)}{512 d (5 \cosh (c+d x)+3)^2}+\frac{5 \sinh (c+d x)}{48 d (5 \cosh (c+d x)+3)^3}",1,"(-279*ArcTan[Tanh[(c + d*x)/2]/2])/(16384*d) + (5*Sinh[c + d*x])/(48*d*(3 + 5*Cosh[c + d*x])^3) - (25*Sinh[c + d*x])/(512*d*(3 + 5*Cosh[c + d*x])^2) + (995*Sinh[c + d*x])/(24576*d*(3 + 5*Cosh[c + d*x]))","A",6,5,12,0.4167,1,"{2664, 2754, 12, 2659, 206}"
75,1,31,0,0.0128323,"\int \frac{1}{5+3 \cosh (c+d x)} \, dx","Int[(5 + 3*Cosh[c + d*x])^(-1),x]","\frac{x}{4}-\frac{\tanh ^{-1}\left(\frac{\sinh (c+d x)}{\cosh (c+d x)+3}\right)}{2 d}","\frac{x}{4}-\frac{\tanh ^{-1}\left(\frac{\sinh (c+d x)}{\cosh (c+d x)+3}\right)}{2 d}",1,"x/4 - ArcTanh[Sinh[c + d*x]/(3 + Cosh[c + d*x])]/(2*d)","A",1,1,12,0.08333,1,"{2657}"
76,1,56,0,0.0358887,"\int \frac{1}{(5+3 \cosh (c+d x))^2} \, dx","Int[(5 + 3*Cosh[c + d*x])^(-2),x]","-\frac{3 \sinh (c+d x)}{16 d (3 \cosh (c+d x)+5)}-\frac{5 \tanh ^{-1}\left(\frac{\sinh (c+d x)}{\cosh (c+d x)+3}\right)}{32 d}+\frac{5 x}{64}","-\frac{3 \sinh (c+d x)}{16 d (3 \cosh (c+d x)+5)}-\frac{5 \tanh ^{-1}\left(\frac{\sinh (c+d x)}{\cosh (c+d x)+3}\right)}{32 d}+\frac{5 x}{64}",1,"(5*x)/64 - (5*ArcTanh[Sinh[c + d*x]/(3 + Cosh[c + d*x])])/(32*d) - (3*Sinh[c + d*x])/(16*d*(5 + 3*Cosh[c + d*x]))","A",3,3,12,0.2500,1,"{2664, 12, 2657}"
77,1,81,0,0.0631422,"\int \frac{1}{(5+3 \cosh (c+d x))^3} \, dx","Int[(5 + 3*Cosh[c + d*x])^(-3),x]","-\frac{45 \sinh (c+d x)}{512 d (3 \cosh (c+d x)+5)}-\frac{3 \sinh (c+d x)}{32 d (3 \cosh (c+d x)+5)^2}-\frac{59 \tanh ^{-1}\left(\frac{\sinh (c+d x)}{\cosh (c+d x)+3}\right)}{1024 d}+\frac{59 x}{2048}","-\frac{45 \sinh (c+d x)}{512 d (3 \cosh (c+d x)+5)}-\frac{3 \sinh (c+d x)}{32 d (3 \cosh (c+d x)+5)^2}-\frac{59 \tanh ^{-1}\left(\frac{\sinh (c+d x)}{\cosh (c+d x)+3}\right)}{1024 d}+\frac{59 x}{2048}",1,"(59*x)/2048 - (59*ArcTanh[Sinh[c + d*x]/(3 + Cosh[c + d*x])])/(1024*d) - (3*Sinh[c + d*x])/(32*d*(5 + 3*Cosh[c + d*x])^2) - (45*Sinh[c + d*x])/(512*d*(5 + 3*Cosh[c + d*x]))","A",4,4,12,0.3333,1,"{2664, 2754, 12, 2657}"
78,1,106,0,0.0965579,"\int \frac{1}{(5+3 \cosh (c+d x))^4} \, dx","Int[(5 + 3*Cosh[c + d*x])^(-4),x]","-\frac{311 \sinh (c+d x)}{8192 d (3 \cosh (c+d x)+5)}-\frac{25 \sinh (c+d x)}{512 d (3 \cosh (c+d x)+5)^2}-\frac{\sinh (c+d x)}{16 d (3 \cosh (c+d x)+5)^3}-\frac{385 \tanh ^{-1}\left(\frac{\sinh (c+d x)}{\cosh (c+d x)+3}\right)}{16384 d}+\frac{385 x}{32768}","-\frac{311 \sinh (c+d x)}{8192 d (3 \cosh (c+d x)+5)}-\frac{25 \sinh (c+d x)}{512 d (3 \cosh (c+d x)+5)^2}-\frac{\sinh (c+d x)}{16 d (3 \cosh (c+d x)+5)^3}-\frac{385 \tanh ^{-1}\left(\frac{\sinh (c+d x)}{\cosh (c+d x)+3}\right)}{16384 d}+\frac{385 x}{32768}",1,"(385*x)/32768 - (385*ArcTanh[Sinh[c + d*x]/(3 + Cosh[c + d*x])])/(16384*d) - Sinh[c + d*x]/(16*d*(5 + 3*Cosh[c + d*x])^3) - (25*Sinh[c + d*x])/(512*d*(5 + 3*Cosh[c + d*x])^2) - (311*Sinh[c + d*x])/(8192*d*(5 + 3*Cosh[c + d*x]))","A",5,4,12,0.3333,1,"{2664, 2754, 12, 2657}"
79,1,153,0,0.2440198,"\int (a+b \cosh (x))^{5/2} \, dx","Int[(a + b*Cosh[x])^(5/2),x]","\frac{16 i a \left(a^2-b^2\right) \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{15 \sqrt{a+b \cosh (x)}}-\frac{2 i \left(23 a^2+9 b^2\right) \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{15 \sqrt{\frac{a+b \cosh (x)}{a+b}}}+\frac{2}{5} b \sinh (x) (a+b \cosh (x))^{3/2}+\frac{16}{15} a b \sinh (x) \sqrt{a+b \cosh (x)}","\frac{16 i a \left(a^2-b^2\right) \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{15 \sqrt{a+b \cosh (x)}}-\frac{2 i \left(23 a^2+9 b^2\right) \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{15 \sqrt{\frac{a+b \cosh (x)}{a+b}}}+\frac{2}{5} b \sinh (x) (a+b \cosh (x))^{3/2}+\frac{16}{15} a b \sinh (x) \sqrt{a+b \cosh (x)}",1,"(((-2*I)/15)*(23*a^2 + 9*b^2)*Sqrt[a + b*Cosh[x]]*EllipticE[(I/2)*x, (2*b)/(a + b)])/Sqrt[(a + b*Cosh[x])/(a + b)] + (((16*I)/15)*a*(a^2 - b^2)*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticF[(I/2)*x, (2*b)/(a + b)])/Sqrt[a + b*Cosh[x]] + (16*a*b*Sqrt[a + b*Cosh[x]]*Sinh[x])/15 + (2*b*(a + b*Cosh[x])^(3/2)*Sinh[x])/5","A",7,7,10,0.7000,1,"{2656, 2753, 2752, 2663, 2661, 2655, 2653}"
80,1,124,0,0.1565116,"\int (a+b \cosh (x))^{3/2} \, dx","Int[(a + b*Cosh[x])^(3/2),x]","\frac{2 i \left(a^2-b^2\right) \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 \sqrt{a+b \cosh (x)}}+\frac{2}{3} b \sinh (x) \sqrt{a+b \cosh (x)}-\frac{8 i a \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 \sqrt{\frac{a+b \cosh (x)}{a+b}}}","\frac{2 i \left(a^2-b^2\right) \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 \sqrt{a+b \cosh (x)}}+\frac{2}{3} b \sinh (x) \sqrt{a+b \cosh (x)}-\frac{8 i a \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 \sqrt{\frac{a+b \cosh (x)}{a+b}}}",1,"(((-8*I)/3)*a*Sqrt[a + b*Cosh[x]]*EllipticE[(I/2)*x, (2*b)/(a + b)])/Sqrt[(a + b*Cosh[x])/(a + b)] + (((2*I)/3)*(a^2 - b^2)*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticF[(I/2)*x, (2*b)/(a + b)])/Sqrt[a + b*Cosh[x]] + (2*b*Sqrt[a + b*Cosh[x]]*Sinh[x])/3","A",6,6,10,0.6000,1,"{2656, 2752, 2663, 2661, 2655, 2653}"
81,1,61,0,0.0394434,"\int \sqrt{a+b \cosh (c+d x)} \, dx","Int[Sqrt[a + b*Cosh[c + d*x]],x]","-\frac{2 i \sqrt{a+b \cosh (c+d x)} E\left(\frac{1}{2} i (c+d x)|\frac{2 b}{a+b}\right)}{d \sqrt{\frac{a+b \cosh (c+d x)}{a+b}}}","-\frac{2 i \sqrt{a+b \cosh (c+d x)} E\left(\frac{1}{2} i (c+d x)|\frac{2 b}{a+b}\right)}{d \sqrt{\frac{a+b \cosh (c+d x)}{a+b}}}",1,"((-2*I)*Sqrt[a + b*Cosh[c + d*x]]*EllipticE[(I/2)*(c + d*x), (2*b)/(a + b)])/(d*Sqrt[(a + b*Cosh[c + d*x])/(a + b)])","A",2,2,14,0.1429,1,"{2655, 2653}"
82,1,46,0,0.0341934,"\int \frac{1}{\sqrt{a+b \cosh (x)}} \, dx","Int[1/Sqrt[a + b*Cosh[x]],x]","-\frac{2 i \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{\sqrt{a+b \cosh (x)}}","-\frac{2 i \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{\sqrt{a+b \cosh (x)}}",1,"((-2*I)*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticF[(I/2)*x, (2*b)/(a + b)])/Sqrt[a + b*Cosh[x]]","A",2,2,10,0.2000,1,"{2663, 2661}"
83,1,84,0,0.0570477,"\int \frac{1}{(a+b \cosh (x))^{3/2}} \, dx","Int[(a + b*Cosh[x])^(-3/2),x]","-\frac{2 b \sinh (x)}{\left(a^2-b^2\right) \sqrt{a+b \cosh (x)}}-\frac{2 i \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{\left(a^2-b^2\right) \sqrt{\frac{a+b \cosh (x)}{a+b}}}","-\frac{2 b \sinh (x)}{\left(a^2-b^2\right) \sqrt{a+b \cosh (x)}}-\frac{2 i \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{\left(a^2-b^2\right) \sqrt{\frac{a+b \cosh (x)}{a+b}}}",1,"((-2*I)*Sqrt[a + b*Cosh[x]]*EllipticE[(I/2)*x, (2*b)/(a + b)])/((a^2 - b^2)*Sqrt[(a + b*Cosh[x])/(a + b)]) - (2*b*Sinh[x])/((a^2 - b^2)*Sqrt[a + b*Cosh[x]])","A",4,4,10,0.4000,1,"{2664, 21, 2655, 2653}"
84,1,177,0,0.2069606,"\int \frac{1}{(a+b \cosh (x))^{5/2}} \, dx","Int[(a + b*Cosh[x])^(-5/2),x]","-\frac{8 a b \sinh (x)}{3 \left(a^2-b^2\right)^2 \sqrt{a+b \cosh (x)}}-\frac{2 b \sinh (x)}{3 \left(a^2-b^2\right) (a+b \cosh (x))^{3/2}}+\frac{2 i \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 \left(a^2-b^2\right) \sqrt{a+b \cosh (x)}}-\frac{8 i a \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 \left(a^2-b^2\right)^2 \sqrt{\frac{a+b \cosh (x)}{a+b}}}","-\frac{8 a b \sinh (x)}{3 \left(a^2-b^2\right)^2 \sqrt{a+b \cosh (x)}}-\frac{2 b \sinh (x)}{3 \left(a^2-b^2\right) (a+b \cosh (x))^{3/2}}+\frac{2 i \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 \left(a^2-b^2\right) \sqrt{a+b \cosh (x)}}-\frac{8 i a \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 \left(a^2-b^2\right)^2 \sqrt{\frac{a+b \cosh (x)}{a+b}}}",1,"(((-8*I)/3)*a*Sqrt[a + b*Cosh[x]]*EllipticE[(I/2)*x, (2*b)/(a + b)])/((a^2 - b^2)^2*Sqrt[(a + b*Cosh[x])/(a + b)]) + (((2*I)/3)*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticF[(I/2)*x, (2*b)/(a + b)])/((a^2 - b^2)*Sqrt[a + b*Cosh[x]]) - (2*b*Sinh[x])/(3*(a^2 - b^2)*(a + b*Cosh[x])^(3/2)) - (8*a*b*Sinh[x])/(3*(a^2 - b^2)^2*Sqrt[a + b*Cosh[x]])","A",7,7,10,0.7000,1,"{2664, 2754, 2752, 2663, 2661, 2655, 2653}"
85,1,227,0,0.3128708,"\int \frac{1}{(a+b \cosh (x))^{7/2}} \, dx","Int[(a + b*Cosh[x])^(-7/2),x]","-\frac{2 b \left(23 a^2+9 b^2\right) \sinh (x)}{15 \left(a^2-b^2\right)^3 \sqrt{a+b \cosh (x)}}-\frac{16 a b \sinh (x)}{15 \left(a^2-b^2\right)^2 (a+b \cosh (x))^{3/2}}-\frac{2 b \sinh (x)}{5 \left(a^2-b^2\right) (a+b \cosh (x))^{5/2}}+\frac{16 i a \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{15 \left(a^2-b^2\right)^2 \sqrt{a+b \cosh (x)}}-\frac{2 i \left(23 a^2+9 b^2\right) \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{15 \left(a^2-b^2\right)^3 \sqrt{\frac{a+b \cosh (x)}{a+b}}}","-\frac{2 b \left(23 a^2+9 b^2\right) \sinh (x)}{15 \left(a^2-b^2\right)^3 \sqrt{a+b \cosh (x)}}-\frac{16 a b \sinh (x)}{15 \left(a^2-b^2\right)^2 (a+b \cosh (x))^{3/2}}-\frac{2 b \sinh (x)}{5 \left(a^2-b^2\right) (a+b \cosh (x))^{5/2}}+\frac{16 i a \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{15 \left(a^2-b^2\right)^2 \sqrt{a+b \cosh (x)}}-\frac{2 i \left(23 a^2+9 b^2\right) \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{15 \left(a^2-b^2\right)^3 \sqrt{\frac{a+b \cosh (x)}{a+b}}}",1,"(((-2*I)/15)*(23*a^2 + 9*b^2)*Sqrt[a + b*Cosh[x]]*EllipticE[(I/2)*x, (2*b)/(a + b)])/((a^2 - b^2)^3*Sqrt[(a + b*Cosh[x])/(a + b)]) + (((16*I)/15)*a*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticF[(I/2)*x, (2*b)/(a + b)])/((a^2 - b^2)^2*Sqrt[a + b*Cosh[x]]) - (2*b*Sinh[x])/(5*(a^2 - b^2)*(a + b*Cosh[x])^(5/2)) - (16*a*b*Sinh[x])/(15*(a^2 - b^2)^2*(a + b*Cosh[x])^(3/2)) - (2*b*(23*a^2 + 9*b^2)*Sinh[x])/(15*(a^2 - b^2)^3*Sqrt[a + b*Cosh[x]])","A",8,7,10,0.7000,1,"{2664, 2754, 2752, 2663, 2661, 2655, 2653}"
86,1,100,0,0.1066678,"\int \frac{\cosh (x)}{\sqrt{a+b \cosh (x)}} \, dx","Int[Cosh[x]/Sqrt[a + b*Cosh[x]],x]","\frac{2 i a \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{b \sqrt{a+b \cosh (x)}}-\frac{2 i \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{b \sqrt{\frac{a+b \cosh (x)}{a+b}}}","\frac{2 i a \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{b \sqrt{a+b \cosh (x)}}-\frac{2 i \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{b \sqrt{\frac{a+b \cosh (x)}{a+b}}}",1,"((-2*I)*Sqrt[a + b*Cosh[x]]*EllipticE[(I/2)*x, (2*b)/(a + b)])/(b*Sqrt[(a + b*Cosh[x])/(a + b)]) + ((2*I)*a*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticF[(I/2)*x, (2*b)/(a + b)])/(b*Sqrt[a + b*Cosh[x]])","A",5,5,13,0.3846,1,"{2752, 2663, 2661, 2655, 2653}"
87,1,94,0,0.0922257,"\int (a+a \cosh (x))^{5/2} (A+B \cosh (x)) \, dx","Int[(a + a*Cosh[x])^(5/2)*(A + B*Cosh[x]),x]","\frac{64 a^3 (7 A+5 B) \sinh (x)}{105 \sqrt{a \cosh (x)+a}}+\frac{16}{105} a^2 (7 A+5 B) \sinh (x) \sqrt{a \cosh (x)+a}+\frac{2}{35} a (7 A+5 B) \sinh (x) (a \cosh (x)+a)^{3/2}+\frac{2}{7} B \sinh (x) (a \cosh (x)+a)^{5/2}","\frac{64 a^3 (7 A+5 B) \sinh (x)}{105 \sqrt{a \cosh (x)+a}}+\frac{16}{105} a^2 (7 A+5 B) \sinh (x) \sqrt{a \cosh (x)+a}+\frac{2}{35} a (7 A+5 B) \sinh (x) (a \cosh (x)+a)^{3/2}+\frac{2}{7} B \sinh (x) (a \cosh (x)+a)^{5/2}",1,"(64*a^3*(7*A + 5*B)*Sinh[x])/(105*Sqrt[a + a*Cosh[x]]) + (16*a^2*(7*A + 5*B)*Sqrt[a + a*Cosh[x]]*Sinh[x])/105 + (2*a*(7*A + 5*B)*(a + a*Cosh[x])^(3/2)*Sinh[x])/35 + (2*B*(a + a*Cosh[x])^(5/2)*Sinh[x])/7","A",4,3,17,0.1765,1,"{2751, 2647, 2646}"
88,1,68,0,0.0738993,"\int (a+a \cosh (x))^{3/2} (A+B \cosh (x)) \, dx","Int[(a + a*Cosh[x])^(3/2)*(A + B*Cosh[x]),x]","\frac{8 a^2 (5 A+3 B) \sinh (x)}{15 \sqrt{a \cosh (x)+a}}+\frac{2}{15} a (5 A+3 B) \sinh (x) \sqrt{a \cosh (x)+a}+\frac{2}{5} B \sinh (x) (a \cosh (x)+a)^{3/2}","\frac{8 a^2 (5 A+3 B) \sinh (x)}{15 \sqrt{a \cosh (x)+a}}+\frac{2}{15} a (5 A+3 B) \sinh (x) \sqrt{a \cosh (x)+a}+\frac{2}{5} B \sinh (x) (a \cosh (x)+a)^{3/2}",1,"(8*a^2*(5*A + 3*B)*Sinh[x])/(15*Sqrt[a + a*Cosh[x]]) + (2*a*(5*A + 3*B)*Sqrt[a + a*Cosh[x]]*Sinh[x])/15 + (2*B*(a + a*Cosh[x])^(3/2)*Sinh[x])/5","A",3,3,17,0.1765,1,"{2751, 2647, 2646}"
89,1,40,0,0.0524759,"\int \sqrt{a+a \cosh (x)} (A+B \cosh (x)) \, dx","Int[Sqrt[a + a*Cosh[x]]*(A + B*Cosh[x]),x]","\frac{2 a (3 A+B) \sinh (x)}{3 \sqrt{a \cosh (x)+a}}+\frac{2}{3} B \sinh (x) \sqrt{a \cosh (x)+a}","\frac{2 a (3 A+B) \sinh (x)}{3 \sqrt{a \cosh (x)+a}}+\frac{2}{3} B \sinh (x) \sqrt{a \cosh (x)+a}",1,"(2*a*(3*A + B)*Sinh[x])/(3*Sqrt[a + a*Cosh[x]]) + (2*B*Sqrt[a + a*Cosh[x]]*Sinh[x])/3","A",2,2,17,0.1176,1,"{2751, 2646}"
90,1,98,0,0.1035536,"\int (a-a \cosh (x))^{5/2} (A+B \cosh (x)) \, dx","Int[(a - a*Cosh[x])^(5/2)*(A + B*Cosh[x]),x]","-\frac{64 a^3 (7 A-5 B) \sinh (x)}{105 \sqrt{a-a \cosh (x)}}-\frac{16}{105} a^2 (7 A-5 B) \sinh (x) \sqrt{a-a \cosh (x)}-\frac{2}{35} a (7 A-5 B) \sinh (x) (a-a \cosh (x))^{3/2}+\frac{2}{7} B \sinh (x) (a-a \cosh (x))^{5/2}","-\frac{64 a^3 (7 A-5 B) \sinh (x)}{105 \sqrt{a-a \cosh (x)}}-\frac{16}{105} a^2 (7 A-5 B) \sinh (x) \sqrt{a-a \cosh (x)}-\frac{2}{35} a (7 A-5 B) \sinh (x) (a-a \cosh (x))^{3/2}+\frac{2}{7} B \sinh (x) (a-a \cosh (x))^{5/2}",1,"(-64*a^3*(7*A - 5*B)*Sinh[x])/(105*Sqrt[a - a*Cosh[x]]) - (16*a^2*(7*A - 5*B)*Sqrt[a - a*Cosh[x]]*Sinh[x])/105 - (2*a*(7*A - 5*B)*(a - a*Cosh[x])^(3/2)*Sinh[x])/35 + (2*B*(a - a*Cosh[x])^(5/2)*Sinh[x])/7","A",4,3,18,0.1667,1,"{2751, 2647, 2646}"
91,1,71,0,0.0802921,"\int (a-a \cosh (x))^{3/2} (A+B \cosh (x)) \, dx","Int[(a - a*Cosh[x])^(3/2)*(A + B*Cosh[x]),x]","-\frac{8 a^2 (5 A-3 B) \sinh (x)}{15 \sqrt{a-a \cosh (x)}}-\frac{2}{15} a (5 A-3 B) \sinh (x) \sqrt{a-a \cosh (x)}+\frac{2}{5} B \sinh (x) (a-a \cosh (x))^{3/2}","-\frac{8 a^2 (5 A-3 B) \sinh (x)}{15 \sqrt{a-a \cosh (x)}}-\frac{2}{15} a (5 A-3 B) \sinh (x) \sqrt{a-a \cosh (x)}+\frac{2}{5} B \sinh (x) (a-a \cosh (x))^{3/2}",1,"(-8*a^2*(5*A - 3*B)*Sinh[x])/(15*Sqrt[a - a*Cosh[x]]) - (2*a*(5*A - 3*B)*Sqrt[a - a*Cosh[x]]*Sinh[x])/15 + (2*B*(a - a*Cosh[x])^(3/2)*Sinh[x])/5","A",3,3,18,0.1667,1,"{2751, 2647, 2646}"
92,1,44,0,0.0576204,"\int \sqrt{a-a \cosh (x)} (A+B \cosh (x)) \, dx","Int[Sqrt[a - a*Cosh[x]]*(A + B*Cosh[x]),x]","\frac{2}{3} B \sinh (x) \sqrt{a-a \cosh (x)}-\frac{2 a (3 A-B) \sinh (x)}{3 \sqrt{a-a \cosh (x)}}","\frac{2}{3} B \sinh (x) \sqrt{a-a \cosh (x)}-\frac{2 a (3 A-B) \sinh (x)}{3 \sqrt{a-a \cosh (x)}}",1,"(-2*a*(3*A - B)*Sinh[x])/(3*Sqrt[a - a*Cosh[x]]) + (2*B*Sqrt[a - a*Cosh[x]]*Sinh[x])/3","A",2,2,18,0.1111,1,"{2751, 2646}"
93,1,18,0,0.0359926,"\int \frac{A+B \cosh (x)}{1+\cosh (x)} \, dx","Int[(A + B*Cosh[x])/(1 + Cosh[x]),x]","\frac{(A-B) \sinh (x)}{\cosh (x)+1}+B x","\frac{(A-B) \sinh (x)}{\cosh (x)+1}+B x",1,"B*x + ((A - B)*Sinh[x])/(1 + Cosh[x])","A",2,2,13,0.1538,1,"{2735, 2648}"
94,1,35,0,0.0375198,"\int \frac{A+B \cosh (x)}{(1+\cosh (x))^2} \, dx","Int[(A + B*Cosh[x])/(1 + Cosh[x])^2,x]","\frac{(A+2 B) \sinh (x)}{3 (\cosh (x)+1)}+\frac{(A-B) \sinh (x)}{3 (\cosh (x)+1)^2}","\frac{(A+2 B) \sinh (x)}{3 (\cosh (x)+1)}+\frac{(A-B) \sinh (x)}{3 (\cosh (x)+1)^2}",1,"((A - B)*Sinh[x])/(3*(1 + Cosh[x])^2) + ((A + 2*B)*Sinh[x])/(3*(1 + Cosh[x]))","A",2,2,13,0.1538,1,"{2750, 2648}"
95,1,56,0,0.0482171,"\int \frac{A+B \cosh (x)}{(1+\cosh (x))^3} \, dx","Int[(A + B*Cosh[x])/(1 + Cosh[x])^3,x]","\frac{(2 A+3 B) \sinh (x)}{15 (\cosh (x)+1)}+\frac{(2 A+3 B) \sinh (x)}{15 (\cosh (x)+1)^2}+\frac{(A-B) \sinh (x)}{5 (\cosh (x)+1)^3}","\frac{(2 A+3 B) \sinh (x)}{15 (\cosh (x)+1)}+\frac{(2 A+3 B) \sinh (x)}{15 (\cosh (x)+1)^2}+\frac{(A-B) \sinh (x)}{5 (\cosh (x)+1)^3}",1,"((A - B)*Sinh[x])/(5*(1 + Cosh[x])^3) + ((2*A + 3*B)*Sinh[x])/(15*(1 + Cosh[x])^2) + ((2*A + 3*B)*Sinh[x])/(15*(1 + Cosh[x]))","A",3,3,13,0.2308,1,"{2750, 2650, 2648}"
96,1,75,0,0.0594869,"\int \frac{A+B \cosh (x)}{(1+\cosh (x))^4} \, dx","Int[(A + B*Cosh[x])/(1 + Cosh[x])^4,x]","\frac{2 (3 A+4 B) \sinh (x)}{105 (\cosh (x)+1)}+\frac{2 (3 A+4 B) \sinh (x)}{105 (\cosh (x)+1)^2}+\frac{(3 A+4 B) \sinh (x)}{35 (\cosh (x)+1)^3}+\frac{(A-B) \sinh (x)}{7 (\cosh (x)+1)^4}","\frac{2 (3 A+4 B) \sinh (x)}{105 (\cosh (x)+1)}+\frac{2 (3 A+4 B) \sinh (x)}{105 (\cosh (x)+1)^2}+\frac{(3 A+4 B) \sinh (x)}{35 (\cosh (x)+1)^3}+\frac{(A-B) \sinh (x)}{7 (\cosh (x)+1)^4}",1,"((A - B)*Sinh[x])/(7*(1 + Cosh[x])^4) + ((3*A + 4*B)*Sinh[x])/(35*(1 + Cosh[x])^3) + (2*(3*A + 4*B)*Sinh[x])/(105*(1 + Cosh[x])^2) + (2*(3*A + 4*B)*Sinh[x])/(105*(1 + Cosh[x]))","A",4,3,13,0.2308,1,"{2750, 2650, 2648}"
97,1,20,0,0.0395878,"\int \frac{A+B \cosh (x)}{1-\cosh (x)} \, dx","Int[(A + B*Cosh[x])/(1 - Cosh[x]),x]","-\frac{(A+B) \sinh (x)}{1-\cosh (x)}-B x","-\frac{(A+B) \sinh (x)}{1-\cosh (x)}-B x",1,"-(B*x) - ((A + B)*Sinh[x])/(1 - Cosh[x])","A",2,2,15,0.1333,1,"{2735, 2648}"
98,1,37,0,0.0408369,"\int \frac{A+B \cosh (x)}{(1-\cosh (x))^2} \, dx","Int[(A + B*Cosh[x])/(1 - Cosh[x])^2,x]","-\frac{(A-2 B) \sinh (x)}{3 (1-\cosh (x))}-\frac{(A+B) \sinh (x)}{3 (1-\cosh (x))^2}","-\frac{(A-2 B) \sinh (x)}{3 (1-\cosh (x))}-\frac{(A+B) \sinh (x)}{3 (1-\cosh (x))^2}",1,"-((A + B)*Sinh[x])/(3*(1 - Cosh[x])^2) - ((A - 2*B)*Sinh[x])/(3*(1 - Cosh[x]))","A",2,2,15,0.1333,1,"{2750, 2648}"
99,1,60,0,0.0550135,"\int \frac{A+B \cosh (x)}{(1-\cosh (x))^3} \, dx","Int[(A + B*Cosh[x])/(1 - Cosh[x])^3,x]","-\frac{(2 A-3 B) \sinh (x)}{15 (1-\cosh (x))}-\frac{(2 A-3 B) \sinh (x)}{15 (1-\cosh (x))^2}-\frac{(A+B) \sinh (x)}{5 (1-\cosh (x))^3}","-\frac{(2 A-3 B) \sinh (x)}{15 (1-\cosh (x))}-\frac{(2 A-3 B) \sinh (x)}{15 (1-\cosh (x))^2}-\frac{(A+B) \sinh (x)}{5 (1-\cosh (x))^3}",1,"-((A + B)*Sinh[x])/(5*(1 - Cosh[x])^3) - ((2*A - 3*B)*Sinh[x])/(15*(1 - Cosh[x])^2) - ((2*A - 3*B)*Sinh[x])/(15*(1 - Cosh[x]))","A",3,3,15,0.2000,1,"{2750, 2650, 2648}"
100,1,81,0,0.0664045,"\int \frac{A+B \cosh (x)}{(1-\cosh (x))^4} \, dx","Int[(A + B*Cosh[x])/(1 - Cosh[x])^4,x]","-\frac{2 (3 A-4 B) \sinh (x)}{105 (1-\cosh (x))}-\frac{2 (3 A-4 B) \sinh (x)}{105 (1-\cosh (x))^2}-\frac{(3 A-4 B) \sinh (x)}{35 (1-\cosh (x))^3}-\frac{(A+B) \sinh (x)}{7 (1-\cosh (x))^4}","-\frac{2 (3 A-4 B) \sinh (x)}{105 (1-\cosh (x))}-\frac{2 (3 A-4 B) \sinh (x)}{105 (1-\cosh (x))^2}-\frac{(3 A-4 B) \sinh (x)}{35 (1-\cosh (x))^3}-\frac{(A+B) \sinh (x)}{7 (1-\cosh (x))^4}",1,"-((A + B)*Sinh[x])/(7*(1 - Cosh[x])^4) - ((3*A - 4*B)*Sinh[x])/(35*(1 - Cosh[x])^3) - (2*(3*A - 4*B)*Sinh[x])/(105*(1 - Cosh[x])^2) - (2*(3*A - 4*B)*Sinh[x])/(105*(1 - Cosh[x]))","A",4,3,15,0.2000,1,"{2750, 2650, 2648}"
101,1,56,0,0.0655941,"\int \frac{A+B \cosh (x)}{\sqrt{a+a \cosh (x)}} \, dx","Int[(A + B*Cosh[x])/Sqrt[a + a*Cosh[x]],x]","\frac{\sqrt{2} (A-B) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (x)}{\sqrt{2} \sqrt{a \cosh (x)+a}}\right)}{\sqrt{a}}+\frac{2 B \sinh (x)}{\sqrt{a \cosh (x)+a}}","\frac{\sqrt{2} (A-B) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (x)}{\sqrt{2} \sqrt{a \cosh (x)+a}}\right)}{\sqrt{a}}+\frac{2 B \sinh (x)}{\sqrt{a \cosh (x)+a}}",1,"(Sqrt[2]*(A - B)*ArcTan[(Sqrt[a]*Sinh[x])/(Sqrt[2]*Sqrt[a + a*Cosh[x]])])/Sqrt[a] + (2*B*Sinh[x])/Sqrt[a + a*Cosh[x]]","A",3,3,17,0.1765,1,"{2751, 2649, 206}"
102,1,65,0,0.0681411,"\int \frac{A+B \cosh (x)}{(a+a \cosh (x))^{3/2}} \, dx","Int[(A + B*Cosh[x])/(a + a*Cosh[x])^(3/2),x]","\frac{(A+3 B) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (x)}{\sqrt{2} \sqrt{a \cosh (x)+a}}\right)}{2 \sqrt{2} a^{3/2}}+\frac{(A-B) \sinh (x)}{2 (a \cosh (x)+a)^{3/2}}","\frac{(A+3 B) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (x)}{\sqrt{2} \sqrt{a \cosh (x)+a}}\right)}{2 \sqrt{2} a^{3/2}}+\frac{(A-B) \sinh (x)}{2 (a \cosh (x)+a)^{3/2}}",1,"((A + 3*B)*ArcTan[(Sqrt[a]*Sinh[x])/(Sqrt[2]*Sqrt[a + a*Cosh[x]])])/(2*Sqrt[2]*a^(3/2)) + ((A - B)*Sinh[x])/(2*(a + a*Cosh[x])^(3/2))","A",3,3,17,0.1765,1,"{2750, 2649, 206}"
103,1,93,0,0.0885073,"\int \frac{A+B \cosh (x)}{(a+a \cosh (x))^{5/2}} \, dx","Int[(A + B*Cosh[x])/(a + a*Cosh[x])^(5/2),x]","\frac{(3 A+5 B) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (x)}{\sqrt{2} \sqrt{a \cosh (x)+a}}\right)}{16 \sqrt{2} a^{5/2}}+\frac{(3 A+5 B) \sinh (x)}{16 a (a \cosh (x)+a)^{3/2}}+\frac{(A-B) \sinh (x)}{4 (a \cosh (x)+a)^{5/2}}","\frac{(3 A+5 B) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (x)}{\sqrt{2} \sqrt{a \cosh (x)+a}}\right)}{16 \sqrt{2} a^{5/2}}+\frac{(3 A+5 B) \sinh (x)}{16 a (a \cosh (x)+a)^{3/2}}+\frac{(A-B) \sinh (x)}{4 (a \cosh (x)+a)^{5/2}}",1,"((3*A + 5*B)*ArcTan[(Sqrt[a]*Sinh[x])/(Sqrt[2]*Sqrt[a + a*Cosh[x]])])/(16*Sqrt[2]*a^(5/2)) + ((A - B)*Sinh[x])/(4*(a + a*Cosh[x])^(5/2)) + ((3*A + 5*B)*Sinh[x])/(16*a*(a + a*Cosh[x])^(3/2))","A",4,4,17,0.2353,1,"{2750, 2650, 2649, 206}"
104,1,57,0,0.0653115,"\int \frac{A+B \cosh (x)}{\sqrt{a-a \cosh (x)}} \, dx","Int[(A + B*Cosh[x])/Sqrt[a - a*Cosh[x]],x]","\frac{2 B \sinh (x)}{\sqrt{a-a \cosh (x)}}-\frac{\sqrt{2} (A+B) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (x)}{\sqrt{2} \sqrt{a-a \cosh (x)}}\right)}{\sqrt{a}}","\frac{2 B \sinh (x)}{\sqrt{a-a \cosh (x)}}-\frac{\sqrt{2} (A+B) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (x)}{\sqrt{2} \sqrt{a-a \cosh (x)}}\right)}{\sqrt{a}}",1,"-((Sqrt[2]*(A + B)*ArcTan[(Sqrt[a]*Sinh[x])/(Sqrt[2]*Sqrt[a - a*Cosh[x]])])/Sqrt[a]) + (2*B*Sinh[x])/Sqrt[a - a*Cosh[x]]","A",3,3,18,0.1667,1,"{2751, 2649, 206}"
105,1,65,0,0.0728487,"\int \frac{A+B \cosh (x)}{(a-a \cosh (x))^{3/2}} \, dx","Int[(A + B*Cosh[x])/(a - a*Cosh[x])^(3/2),x]","-\frac{(A-3 B) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (x)}{\sqrt{2} \sqrt{a-a \cosh (x)}}\right)}{2 \sqrt{2} a^{3/2}}-\frac{(A+B) \sinh (x)}{2 (a-a \cosh (x))^{3/2}}","-\frac{(A-3 B) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (x)}{\sqrt{2} \sqrt{a-a \cosh (x)}}\right)}{2 \sqrt{2} a^{3/2}}-\frac{(A+B) \sinh (x)}{2 (a-a \cosh (x))^{3/2}}",1,"-((A - 3*B)*ArcTan[(Sqrt[a]*Sinh[x])/(Sqrt[2]*Sqrt[a - a*Cosh[x]])])/(2*Sqrt[2]*a^(3/2)) - ((A + B)*Sinh[x])/(2*(a - a*Cosh[x])^(3/2))","A",3,3,18,0.1667,1,"{2750, 2649, 206}"
106,1,94,0,0.095537,"\int \frac{A+B \cosh (x)}{(a-a \cosh (x))^{5/2}} \, dx","Int[(A + B*Cosh[x])/(a - a*Cosh[x])^(5/2),x]","-\frac{(3 A-5 B) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (x)}{\sqrt{2} \sqrt{a-a \cosh (x)}}\right)}{16 \sqrt{2} a^{5/2}}-\frac{(3 A-5 B) \sinh (x)}{16 a (a-a \cosh (x))^{3/2}}-\frac{(A+B) \sinh (x)}{4 (a-a \cosh (x))^{5/2}}","-\frac{(3 A-5 B) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (x)}{\sqrt{2} \sqrt{a-a \cosh (x)}}\right)}{16 \sqrt{2} a^{5/2}}-\frac{(3 A-5 B) \sinh (x)}{16 a (a-a \cosh (x))^{3/2}}-\frac{(A+B) \sinh (x)}{4 (a-a \cosh (x))^{5/2}}",1,"-((3*A - 5*B)*ArcTan[(Sqrt[a]*Sinh[x])/(Sqrt[2]*Sqrt[a - a*Cosh[x]])])/(16*Sqrt[2]*a^(5/2)) - ((A + B)*Sinh[x])/(4*(a - a*Cosh[x])^(5/2)) - ((3*A - 5*B)*Sinh[x])/(16*a*(a - a*Cosh[x])^(3/2))","A",4,4,18,0.2222,1,"{2750, 2650, 2649, 206}"
107,1,233,0,0.4540976,"\int (a+b \cosh (x))^{5/2} (A+B \cosh (x)) \, dx","Int[(a + b*Cosh[x])^(5/2)*(A + B*Cosh[x]),x]","\frac{2}{105} \sinh (x) \left(15 a^2 B+56 a A b+25 b^2 B\right) \sqrt{a+b \cosh (x)}+\frac{2 i \left(a^2-b^2\right) \left(15 a^2 B+56 a A b+25 b^2 B\right) \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{105 b \sqrt{a+b \cosh (x)}}-\frac{2 i \left(161 a^2 A b+15 a^3 B+145 a b^2 B+63 A b^3\right) \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{105 b \sqrt{\frac{a+b \cosh (x)}{a+b}}}+\frac{2}{35} \sinh (x) (5 a B+7 A b) (a+b \cosh (x))^{3/2}+\frac{2}{7} B \sinh (x) (a+b \cosh (x))^{5/2}","\frac{2}{105} \sinh (x) \left(15 a^2 B+56 a A b+25 b^2 B\right) \sqrt{a+b \cosh (x)}+\frac{2 i \left(a^2-b^2\right) \left(15 a^2 B+56 a A b+25 b^2 B\right) \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{105 b \sqrt{a+b \cosh (x)}}-\frac{2 i \left(161 a^2 A b+15 a^3 B+145 a b^2 B+63 A b^3\right) \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{105 b \sqrt{\frac{a+b \cosh (x)}{a+b}}}+\frac{2}{35} \sinh (x) (5 a B+7 A b) (a+b \cosh (x))^{3/2}+\frac{2}{7} B \sinh (x) (a+b \cosh (x))^{5/2}",1,"(((-2*I)/105)*(161*a^2*A*b + 63*A*b^3 + 15*a^3*B + 145*a*b^2*B)*Sqrt[a + b*Cosh[x]]*EllipticE[(I/2)*x, (2*b)/(a + b)])/(b*Sqrt[(a + b*Cosh[x])/(a + b)]) + (((2*I)/105)*(a^2 - b^2)*(56*a*A*b + 15*a^2*B + 25*b^2*B)*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticF[(I/2)*x, (2*b)/(a + b)])/(b*Sqrt[a + b*Cosh[x]]) + (2*(56*a*A*b + 15*a^2*B + 25*b^2*B)*Sqrt[a + b*Cosh[x]]*Sinh[x])/105 + (2*(7*A*b + 5*a*B)*(a + b*Cosh[x])^(3/2)*Sinh[x])/35 + (2*B*(a + b*Cosh[x])^(5/2)*Sinh[x])/7","A",8,6,17,0.3529,1,"{2753, 2752, 2663, 2661, 2655, 2653}"
108,1,181,0,0.3221563,"\int (a+b \cosh (x))^{3/2} (A+B \cosh (x)) \, dx","Int[(a + b*Cosh[x])^(3/2)*(A + B*Cosh[x]),x]","\frac{2 i \left(a^2-b^2\right) (3 a B+5 A b) \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{15 b \sqrt{a+b \cosh (x)}}-\frac{2 i \left(3 a^2 B+20 a A b+9 b^2 B\right) \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{15 b \sqrt{\frac{a+b \cosh (x)}{a+b}}}+\frac{2}{15} \sinh (x) (3 a B+5 A b) \sqrt{a+b \cosh (x)}+\frac{2}{5} B \sinh (x) (a+b \cosh (x))^{3/2}","\frac{2 i \left(a^2-b^2\right) (3 a B+5 A b) \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{15 b \sqrt{a+b \cosh (x)}}-\frac{2 i \left(3 a^2 B+20 a A b+9 b^2 B\right) \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{15 b \sqrt{\frac{a+b \cosh (x)}{a+b}}}+\frac{2}{15} \sinh (x) (3 a B+5 A b) \sqrt{a+b \cosh (x)}+\frac{2}{5} B \sinh (x) (a+b \cosh (x))^{3/2}",1,"(((-2*I)/15)*(20*a*A*b + 3*a^2*B + 9*b^2*B)*Sqrt[a + b*Cosh[x]]*EllipticE[(I/2)*x, (2*b)/(a + b)])/(b*Sqrt[(a + b*Cosh[x])/(a + b)]) + (((2*I)/15)*(a^2 - b^2)*(5*A*b + 3*a*B)*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticF[(I/2)*x, (2*b)/(a + b)])/(b*Sqrt[a + b*Cosh[x]]) + (2*(5*A*b + 3*a*B)*Sqrt[a + b*Cosh[x]]*Sinh[x])/15 + (2*B*(a + b*Cosh[x])^(3/2)*Sinh[x])/5","A",7,6,17,0.3529,1,"{2753, 2752, 2663, 2661, 2655, 2653}"
109,1,138,0,0.2062767,"\int \sqrt{a+b \cosh (x)} (A+B \cosh (x)) \, dx","Int[Sqrt[a + b*Cosh[x]]*(A + B*Cosh[x]),x]","\frac{2 i B \left(a^2-b^2\right) \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 b \sqrt{a+b \cosh (x)}}-\frac{2 i (a B+3 A b) \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 b \sqrt{\frac{a+b \cosh (x)}{a+b}}}+\frac{2}{3} B \sinh (x) \sqrt{a+b \cosh (x)}","\frac{2 i B \left(a^2-b^2\right) \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 b \sqrt{a+b \cosh (x)}}-\frac{2 i (a B+3 A b) \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 b \sqrt{\frac{a+b \cosh (x)}{a+b}}}+\frac{2}{3} B \sinh (x) \sqrt{a+b \cosh (x)}",1,"(((-2*I)/3)*(3*A*b + a*B)*Sqrt[a + b*Cosh[x]]*EllipticE[(I/2)*x, (2*b)/(a + b)])/(b*Sqrt[(a + b*Cosh[x])/(a + b)]) + (((2*I)/3)*(a^2 - b^2)*B*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticF[(I/2)*x, (2*b)/(a + b)])/(b*Sqrt[a + b*Cosh[x]]) + (2*B*Sqrt[a + b*Cosh[x]]*Sinh[x])/3","A",6,6,17,0.3529,1,"{2753, 2752, 2663, 2661, 2655, 2653}"
110,1,60,0,0.0676142,"\int \frac{A+B \cosh (x)}{a+b \cosh (x)} \, dx","Int[(A + B*Cosh[x])/(a + b*Cosh[x]),x]","\frac{2 (A b-a B) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b \sqrt{a-b} \sqrt{a+b}}+\frac{B x}{b}","\frac{2 (A b-a B) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b \sqrt{a-b} \sqrt{a+b}}+\frac{B x}{b}",1,"(B*x)/b + (2*(A*b - a*B)*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(Sqrt[a - b]*b*Sqrt[a + b])","A",3,3,15,0.2000,1,"{2735, 2659, 208}"
111,1,82,0,0.0782561,"\int \frac{A+B \cosh (x)}{(a+b \cosh (x))^2} \, dx","Int[(A + B*Cosh[x])/(a + b*Cosh[x])^2,x]","\frac{2 (a A-b B) \tanh ^{-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{\sinh (x) (A b-a B)}{\left(a^2-b^2\right) (a+b \cosh (x))}","\frac{2 (a A-b B) \tanh ^{-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{\sinh (x) (A b-a B)}{\left(a^2-b^2\right) (a+b \cosh (x))}",1,"(2*(a*A - b*B)*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/((a - b)^(3/2)*(a + b)^(3/2)) - ((A*b - a*B)*Sinh[x])/((a^2 - b^2)*(a + b*Cosh[x]))","A",4,4,15,0.2667,1,"{2754, 12, 2659, 208}"
112,1,135,0,0.1693595,"\int \frac{A+B \cosh (x)}{(a+b \cosh (x))^3} \, dx","Int[(A + B*Cosh[x])/(a + b*Cosh[x])^3,x]","\frac{\left(2 a^2 A-3 a b B+A b^2\right) \tanh ^{-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{\sinh (x) \left(a^2 (-B)+3 a A b-2 b^2 B\right)}{2 \left(a^2-b^2\right)^2 (a+b \cosh (x))}-\frac{\sinh (x) (A b-a B)}{2 \left(a^2-b^2\right) (a+b \cosh (x))^2}","\frac{\left(2 a^2 A-3 a b B+A b^2\right) \tanh ^{-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{\sinh (x) \left(a^2 (-B)+3 a A b-2 b^2 B\right)}{2 \left(a^2-b^2\right)^2 (a+b \cosh (x))}-\frac{\sinh (x) (A b-a B)}{2 \left(a^2-b^2\right) (a+b \cosh (x))^2}",1,"((2*a^2*A + A*b^2 - 3*a*b*B)*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/((a - b)^(5/2)*(a + b)^(5/2)) - ((A*b - a*B)*Sinh[x])/(2*(a^2 - b^2)*(a + b*Cosh[x])^2) - ((3*a*A*b - a^2*B - 2*b^2*B)*Sinh[x])/(2*(a^2 - b^2)^2*(a + b*Cosh[x]))","A",5,4,15,0.2667,1,"{2754, 12, 2659, 208}"
113,1,197,0,0.3477373,"\int \frac{A+B \cosh (x)}{(a+b \cosh (x))^4} \, dx","Int[(A + B*Cosh[x])/(a + b*Cosh[x])^4,x]","\frac{\left(2 a^3 A-4 a^2 b B+3 a A b^2-b^3 B\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{(a-b)^{7/2} (a+b)^{7/2}}-\frac{\sinh (x) \left(11 a^2 A b-2 a^3 B-13 a b^2 B+4 A b^3\right)}{6 \left(a^2-b^2\right)^3 (a+b \cosh (x))}-\frac{\sinh (x) \left(-2 a^2 B+5 a A b-3 b^2 B\right)}{6 \left(a^2-b^2\right)^2 (a+b \cosh (x))^2}-\frac{\sinh (x) (A b-a B)}{3 \left(a^2-b^2\right) (a+b \cosh (x))^3}","\frac{\left(2 a^3 A-4 a^2 b B+3 a A b^2-b^3 B\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{(a-b)^{7/2} (a+b)^{7/2}}-\frac{\sinh (x) \left(11 a^2 A b-2 a^3 B-13 a b^2 B+4 A b^3\right)}{6 \left(a^2-b^2\right)^3 (a+b \cosh (x))}-\frac{\sinh (x) \left(-2 a^2 B+5 a A b-3 b^2 B\right)}{6 \left(a^2-b^2\right)^2 (a+b \cosh (x))^2}-\frac{\sinh (x) (A b-a B)}{3 \left(a^2-b^2\right) (a+b \cosh (x))^3}",1,"((2*a^3*A + 3*a*A*b^2 - 4*a^2*b*B - b^3*B)*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/((a - b)^(7/2)*(a + b)^(7/2)) - ((A*b - a*B)*Sinh[x])/(3*(a^2 - b^2)*(a + b*Cosh[x])^3) - ((5*a*A*b - 2*a^2*B - 3*b^2*B)*Sinh[x])/(6*(a^2 - b^2)^2*(a + b*Cosh[x])^2) - ((11*a^2*A*b + 4*A*b^3 - 2*a^3*B - 13*a*b^2*B)*Sinh[x])/(6*(a^2 - b^2)^3*(a + b*Cosh[x]))","A",6,4,15,0.2667,1,"{2754, 12, 2659, 208}"
114,1,56,0,0.0784398,"\int \frac{\frac{b B}{a}+B \cosh (x)}{a+b \cosh (x)} \, dx","Int[((b*B)/a + B*Cosh[x])/(a + b*Cosh[x]),x]","\frac{B x}{b}-\frac{2 B \sqrt{a-b} \sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a b}","\frac{B x}{b}-\frac{2 B \sqrt{a-b} \sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a b}",1,"(B*x)/b - (2*Sqrt[a - b]*Sqrt[a + b]*B*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(a*b)","A",3,3,20,0.1500,1,"{2735, 2659, 208}"
115,1,6,0,0.0013082,"\int \frac{\frac{a B}{b}+B \cosh (x)}{a+b \cosh (x)} \, dx","Int[((a*B)/b + B*Cosh[x])/(a + b*Cosh[x]),x]","\frac{B x}{b}","\frac{B x}{b}",1,"(B*x)/b","A",2,2,20,0.1000,1,"{21, 8}"
116,1,11,0,0.029401,"\int \frac{a+b \cosh (x)}{(b+a \cosh (x))^2} \, dx","Int[(a + b*Cosh[x])/(b + a*Cosh[x])^2,x]","\frac{\sinh (x)}{a \cosh (x)+b}","\frac{\sinh (x)}{a \cosh (x)+b}",1,"Sinh[x]/(b + a*Cosh[x])","A",2,2,15,0.1333,1,"{2754, 8}"
117,1,36,0,0.049653,"\int \frac{3+\cosh (x)}{2-\cosh (x)} \, dx","Int[(3 + Cosh[x])/(2 - Cosh[x]),x]","\frac{5 x}{\sqrt{3}}-x+\frac{10 \tanh ^{-1}\left(\frac{\sinh (x)}{-\cosh (x)+\sqrt{3}+2}\right)}{\sqrt{3}}","\frac{5 x}{\sqrt{3}}-x+\frac{10 \tanh ^{-1}\left(\frac{\sinh (x)}{-\cosh (x)+\sqrt{3}+2}\right)}{\sqrt{3}}",1,"-x + (5*x)/Sqrt[3] + (10*ArcTanh[Sinh[x]/(2 + Sqrt[3] - Cosh[x])])/Sqrt[3]","A",2,2,13,0.1538,1,"{2735, 2657}"
118,1,108,0,0.111749,"\int \frac{A+B \cosh (x)}{\sqrt{a+b \cosh (x)}} \, dx","Int[(A + B*Cosh[x])/Sqrt[a + b*Cosh[x]],x]","-\frac{2 i (A b-a B) \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{b \sqrt{a+b \cosh (x)}}-\frac{2 i B \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{b \sqrt{\frac{a+b \cosh (x)}{a+b}}}","-\frac{2 i (A b-a B) \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{b \sqrt{a+b \cosh (x)}}-\frac{2 i B \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{b \sqrt{\frac{a+b \cosh (x)}{a+b}}}",1,"((-2*I)*B*Sqrt[a + b*Cosh[x]]*EllipticE[(I/2)*x, (2*b)/(a + b)])/(b*Sqrt[(a + b*Cosh[x])/(a + b)]) - ((2*I)*(A*b - a*B)*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticF[(I/2)*x, (2*b)/(a + b)])/(b*Sqrt[a + b*Cosh[x]])","A",5,5,17,0.2941,1,"{2752, 2663, 2661, 2655, 2653}"
119,1,152,0,0.204889,"\int \frac{A+B \cosh (x)}{(a+b \cosh (x))^{3/2}} \, dx","Int[(A + B*Cosh[x])/(a + b*Cosh[x])^(3/2),x]","-\frac{2 \sinh (x) (A b-a B)}{\left(a^2-b^2\right) \sqrt{a+b \cosh (x)}}-\frac{2 i (A b-a B) \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{b \left(a^2-b^2\right) \sqrt{\frac{a+b \cosh (x)}{a+b}}}-\frac{2 i B \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{b \sqrt{a+b \cosh (x)}}","-\frac{2 \sinh (x) (A b-a B)}{\left(a^2-b^2\right) \sqrt{a+b \cosh (x)}}-\frac{2 i (A b-a B) \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{b \left(a^2-b^2\right) \sqrt{\frac{a+b \cosh (x)}{a+b}}}-\frac{2 i B \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{b \sqrt{a+b \cosh (x)}}",1,"((-2*I)*(A*b - a*B)*Sqrt[a + b*Cosh[x]]*EllipticE[(I/2)*x, (2*b)/(a + b)])/(b*(a^2 - b^2)*Sqrt[(a + b*Cosh[x])/(a + b)]) - ((2*I)*B*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticF[(I/2)*x, (2*b)/(a + b)])/(b*Sqrt[a + b*Cosh[x]]) - (2*(A*b - a*B)*Sinh[x])/((a^2 - b^2)*Sqrt[a + b*Cosh[x]])","A",6,6,17,0.3529,1,"{2754, 2752, 2663, 2661, 2655, 2653}"
120,1,231,0,0.3498325,"\int \frac{A+B \cosh (x)}{(a+b \cosh (x))^{5/2}} \, dx","Int[(A + B*Cosh[x])/(a + b*Cosh[x])^(5/2),x]","-\frac{2 \sinh (x) \left(a^2 (-B)+4 a A b-3 b^2 B\right)}{3 \left(a^2-b^2\right)^2 \sqrt{a+b \cosh (x)}}-\frac{2 \sinh (x) (A b-a B)}{3 \left(a^2-b^2\right) (a+b \cosh (x))^{3/2}}+\frac{2 i (A b-a B) \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 b \left(a^2-b^2\right) \sqrt{a+b \cosh (x)}}-\frac{2 i \left(a^2 (-B)+4 a A b-3 b^2 B\right) \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 b \left(a^2-b^2\right)^2 \sqrt{\frac{a+b \cosh (x)}{a+b}}}","-\frac{2 \sinh (x) \left(a^2 (-B)+4 a A b-3 b^2 B\right)}{3 \left(a^2-b^2\right)^2 \sqrt{a+b \cosh (x)}}-\frac{2 \sinh (x) (A b-a B)}{3 \left(a^2-b^2\right) (a+b \cosh (x))^{3/2}}+\frac{2 i (A b-a B) \sqrt{\frac{a+b \cosh (x)}{a+b}} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 b \left(a^2-b^2\right) \sqrt{a+b \cosh (x)}}-\frac{2 i \left(a^2 (-B)+4 a A b-3 b^2 B\right) \sqrt{a+b \cosh (x)} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 b \left(a^2-b^2\right)^2 \sqrt{\frac{a+b \cosh (x)}{a+b}}}",1,"(((-2*I)/3)*(4*a*A*b - a^2*B - 3*b^2*B)*Sqrt[a + b*Cosh[x]]*EllipticE[(I/2)*x, (2*b)/(a + b)])/(b*(a^2 - b^2)^2*Sqrt[(a + b*Cosh[x])/(a + b)]) + (((2*I)/3)*(A*b - a*B)*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticF[(I/2)*x, (2*b)/(a + b)])/(b*(a^2 - b^2)*Sqrt[a + b*Cosh[x]]) - (2*(A*b - a*B)*Sinh[x])/(3*(a^2 - b^2)*(a + b*Cosh[x])^(3/2)) - (2*(4*a*A*b - a^2*B - 3*b^2*B)*Sinh[x])/(3*(a^2 - b^2)^2*Sqrt[a + b*Cosh[x]])","A",7,6,17,0.3529,1,"{2754, 2752, 2663, 2661, 2655, 2653}"
121,1,72,0,0.0549499,"\int \left(a \cosh ^2(x)\right)^{7/2} \, dx","Int[(a*Cosh[x]^2)^(7/2),x]","\frac{8}{35} a^2 \tanh (x) \left(a \cosh ^2(x)\right)^{3/2}+\frac{16}{35} a^3 \tanh (x) \sqrt{a \cosh ^2(x)}+\frac{1}{7} \tanh (x) \left(a \cosh ^2(x)\right)^{7/2}+\frac{6}{35} a \tanh (x) \left(a \cosh ^2(x)\right)^{5/2}","\frac{8}{35} a^2 \tanh (x) \left(a \cosh ^2(x)\right)^{3/2}+\frac{16}{35} a^3 \tanh (x) \sqrt{a \cosh ^2(x)}+\frac{1}{7} \tanh (x) \left(a \cosh ^2(x)\right)^{7/2}+\frac{6}{35} a \tanh (x) \left(a \cosh ^2(x)\right)^{5/2}",1,"(16*a^3*Sqrt[a*Cosh[x]^2]*Tanh[x])/35 + (8*a^2*(a*Cosh[x]^2)^(3/2)*Tanh[x])/35 + (6*a*(a*Cosh[x]^2)^(5/2)*Tanh[x])/35 + ((a*Cosh[x]^2)^(7/2)*Tanh[x])/7","A",5,3,10,0.3000,1,"{3203, 3207, 2637}"
122,1,53,0,0.0356787,"\int \left(a \cosh ^2(x)\right)^{5/2} \, dx","Int[(a*Cosh[x]^2)^(5/2),x]","\frac{8}{15} a^2 \tanh (x) \sqrt{a \cosh ^2(x)}+\frac{1}{5} \tanh (x) \left(a \cosh ^2(x)\right)^{5/2}+\frac{4}{15} a \tanh (x) \left(a \cosh ^2(x)\right)^{3/2}","\frac{8}{15} a^2 \tanh (x) \sqrt{a \cosh ^2(x)}+\frac{1}{5} \tanh (x) \left(a \cosh ^2(x)\right)^{5/2}+\frac{4}{15} a \tanh (x) \left(a \cosh ^2(x)\right)^{3/2}",1,"(8*a^2*Sqrt[a*Cosh[x]^2]*Tanh[x])/15 + (4*a*(a*Cosh[x]^2)^(3/2)*Tanh[x])/15 + ((a*Cosh[x]^2)^(5/2)*Tanh[x])/5","A",4,3,10,0.3000,1,"{3203, 3207, 2637}"
123,1,34,0,0.0225666,"\int \left(a \cosh ^2(x)\right)^{3/2} \, dx","Int[(a*Cosh[x]^2)^(3/2),x]","\frac{1}{3} \tanh (x) \left(a \cosh ^2(x)\right)^{3/2}+\frac{2}{3} a \tanh (x) \sqrt{a \cosh ^2(x)}","\frac{1}{3} \tanh (x) \left(a \cosh ^2(x)\right)^{3/2}+\frac{2}{3} a \tanh (x) \sqrt{a \cosh ^2(x)}",1,"(2*a*Sqrt[a*Cosh[x]^2]*Tanh[x])/3 + ((a*Cosh[x]^2)^(3/2)*Tanh[x])/3","A",3,3,10,0.3000,1,"{3203, 3207, 2637}"
124,1,13,0,0.0122538,"\int \sqrt{a \cosh ^2(x)} \, dx","Int[Sqrt[a*Cosh[x]^2],x]","\tanh (x) \sqrt{a \cosh ^2(x)}","\tanh (x) \sqrt{a \cosh ^2(x)}",1,"Sqrt[a*Cosh[x]^2]*Tanh[x]","A",2,2,10,0.2000,1,"{3207, 2637}"
125,1,16,0,0.0149485,"\int \frac{1}{\sqrt{a \cosh ^2(x)}} \, dx","Int[1/Sqrt[a*Cosh[x]^2],x]","\frac{\cosh (x) \tan ^{-1}(\sinh (x))}{\sqrt{a \cosh ^2(x)}}","\frac{\cosh (x) \tan ^{-1}(\sinh (x))}{\sqrt{a \cosh ^2(x)}}",1,"(ArcTan[Sinh[x]]*Cosh[x])/Sqrt[a*Cosh[x]^2]","A",2,2,10,0.2000,1,"{3207, 3770}"
126,1,42,0,0.0248997,"\int \frac{1}{\left(a \cosh ^2(x)\right)^{3/2}} \, dx","Int[(a*Cosh[x]^2)^(-3/2),x]","\frac{\tanh (x)}{2 a \sqrt{a \cosh ^2(x)}}+\frac{\cosh (x) \tan ^{-1}(\sinh (x))}{2 a \sqrt{a \cosh ^2(x)}}","\frac{\tanh (x)}{2 a \sqrt{a \cosh ^2(x)}}+\frac{\cosh (x) \tan ^{-1}(\sinh (x))}{2 a \sqrt{a \cosh ^2(x)}}",1,"(ArcTan[Sinh[x]]*Cosh[x])/(2*a*Sqrt[a*Cosh[x]^2]) + Tanh[x]/(2*a*Sqrt[a*Cosh[x]^2])","A",3,3,10,0.3000,1,"{3204, 3207, 3770}"
127,1,61,0,0.0385913,"\int \frac{1}{\left(a \cosh ^2(x)\right)^{5/2}} \, dx","Int[(a*Cosh[x]^2)^(-5/2),x]","\frac{3 \tanh (x)}{8 a^2 \sqrt{a \cosh ^2(x)}}+\frac{3 \cosh (x) \tan ^{-1}(\sinh (x))}{8 a^2 \sqrt{a \cosh ^2(x)}}+\frac{\tanh (x)}{4 a \left(a \cosh ^2(x)\right)^{3/2}}","\frac{3 \tanh (x)}{8 a^2 \sqrt{a \cosh ^2(x)}}+\frac{3 \cosh (x) \tan ^{-1}(\sinh (x))}{8 a^2 \sqrt{a \cosh ^2(x)}}+\frac{\tanh (x)}{4 a \left(a \cosh ^2(x)\right)^{3/2}}",1,"(3*ArcTan[Sinh[x]]*Cosh[x])/(8*a^2*Sqrt[a*Cosh[x]^2]) + Tanh[x]/(4*a*(a*Cosh[x]^2)^(3/2)) + (3*Tanh[x])/(8*a^2*Sqrt[a*Cosh[x]^2])","A",4,3,10,0.3000,1,"{3204, 3207, 3770}"
128,1,121,0,0.0538256,"\int \left(a \cosh ^3(x)\right)^{5/2} \, dx","Int[(a*Cosh[x]^3)^(5/2),x]","\frac{2}{15} a^2 \sinh (x) \cosh ^5(x) \sqrt{a \cosh ^3(x)}+\frac{26}{165} a^2 \sinh (x) \cosh ^3(x) \sqrt{a \cosh ^3(x)}+\frac{78}{385} a^2 \sinh (x) \cosh (x) \sqrt{a \cosh ^3(x)}+\frac{26}{77} a^2 \tanh (x) \sqrt{a \cosh ^3(x)}-\frac{26 i a^2 F\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \cosh ^3(x)}}{77 \cosh ^{\frac{3}{2}}(x)}","\frac{2}{15} a^2 \sinh (x) \cosh ^5(x) \sqrt{a \cosh ^3(x)}+\frac{26}{165} a^2 \sinh (x) \cosh ^3(x) \sqrt{a \cosh ^3(x)}+\frac{78}{385} a^2 \sinh (x) \cosh (x) \sqrt{a \cosh ^3(x)}+\frac{26}{77} a^2 \tanh (x) \sqrt{a \cosh ^3(x)}-\frac{26 i a^2 F\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \cosh ^3(x)}}{77 \cosh ^{\frac{3}{2}}(x)}",1,"(((-26*I)/77)*a^2*Sqrt[a*Cosh[x]^3]*EllipticF[(I/2)*x, 2])/Cosh[x]^(3/2) + (78*a^2*Cosh[x]*Sqrt[a*Cosh[x]^3]*Sinh[x])/385 + (26*a^2*Cosh[x]^3*Sqrt[a*Cosh[x]^3]*Sinh[x])/165 + (2*a^2*Cosh[x]^5*Sqrt[a*Cosh[x]^3]*Sinh[x])/15 + (26*a^2*Sqrt[a*Cosh[x]^3]*Tanh[x])/77","A",6,3,10,0.3000,1,"{3207, 2635, 2641}"
129,1,71,0,0.0338387,"\int \left(a \cosh ^3(x)\right)^{3/2} \, dx","Int[(a*Cosh[x]^3)^(3/2),x]","\frac{2}{9} a \sinh (x) \cosh ^2(x) \sqrt{a \cosh ^3(x)}+\frac{14}{45} a \sinh (x) \sqrt{a \cosh ^3(x)}-\frac{14 i a E\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \cosh ^3(x)}}{15 \cosh ^{\frac{3}{2}}(x)}","\frac{2}{9} a \sinh (x) \cosh ^2(x) \sqrt{a \cosh ^3(x)}+\frac{14}{45} a \sinh (x) \sqrt{a \cosh ^3(x)}-\frac{14 i a E\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \cosh ^3(x)}}{15 \cosh ^{\frac{3}{2}}(x)}",1,"(((-14*I)/15)*a*Sqrt[a*Cosh[x]^3]*EllipticE[(I/2)*x, 2])/Cosh[x]^(3/2) + (14*a*Sqrt[a*Cosh[x]^3]*Sinh[x])/45 + (2*a*Cosh[x]^2*Sqrt[a*Cosh[x]^3]*Sinh[x])/9","A",4,3,10,0.3000,1,"{3207, 2635, 2639}"
130,1,48,0,0.0240773,"\int \sqrt{a \cosh ^3(x)} \, dx","Int[Sqrt[a*Cosh[x]^3],x]","\frac{2}{3} \tanh (x) \sqrt{a \cosh ^3(x)}-\frac{2 i F\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \cosh ^3(x)}}{3 \cosh ^{\frac{3}{2}}(x)}","\frac{2}{3} \tanh (x) \sqrt{a \cosh ^3(x)}-\frac{2 i F\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \cosh ^3(x)}}{3 \cosh ^{\frac{3}{2}}(x)}",1,"(((-2*I)/3)*Sqrt[a*Cosh[x]^3]*EllipticF[(I/2)*x, 2])/Cosh[x]^(3/2) + (2*Sqrt[a*Cosh[x]^3]*Tanh[x])/3","A",3,3,10,0.3000,1,"{3207, 2635, 2641}"
131,1,46,0,0.0238207,"\int \frac{1}{\sqrt{a \cosh ^3(x)}} \, dx","Int[1/Sqrt[a*Cosh[x]^3],x]","\frac{2 \sinh (x) \cosh (x)}{\sqrt{a \cosh ^3(x)}}+\frac{2 i \cosh ^{\frac{3}{2}}(x) E\left(\left.\frac{i x}{2}\right|2\right)}{\sqrt{a \cosh ^3(x)}}","\frac{2 \sinh (x) \cosh (x)}{\sqrt{a \cosh ^3(x)}}+\frac{2 i \cosh ^{\frac{3}{2}}(x) E\left(\left.\frac{i x}{2}\right|2\right)}{\sqrt{a \cosh ^3(x)}}",1,"((2*I)*Cosh[x]^(3/2)*EllipticE[(I/2)*x, 2])/Sqrt[a*Cosh[x]^3] + (2*Cosh[x]*Sinh[x])/Sqrt[a*Cosh[x]^3]","A",3,3,10,0.3000,1,"{3207, 2636, 2639}"
132,1,75,0,0.0342725,"\int \frac{1}{\left(a \cosh ^3(x)\right)^{3/2}} \, dx","Int[(a*Cosh[x]^3)^(-3/2),x]","\frac{10 \sinh (x)}{21 a \sqrt{a \cosh ^3(x)}}-\frac{10 i \cosh ^{\frac{3}{2}}(x) F\left(\left.\frac{i x}{2}\right|2\right)}{21 a \sqrt{a \cosh ^3(x)}}+\frac{2 \tanh (x) \text{sech}(x)}{7 a \sqrt{a \cosh ^3(x)}}","\frac{10 \sinh (x)}{21 a \sqrt{a \cosh ^3(x)}}-\frac{10 i \cosh ^{\frac{3}{2}}(x) F\left(\left.\frac{i x}{2}\right|2\right)}{21 a \sqrt{a \cosh ^3(x)}}+\frac{2 \tanh (x) \text{sech}(x)}{7 a \sqrt{a \cosh ^3(x)}}",1,"(((-10*I)/21)*Cosh[x]^(3/2)*EllipticF[(I/2)*x, 2])/(a*Sqrt[a*Cosh[x]^3]) + (10*Sinh[x])/(21*a*Sqrt[a*Cosh[x]^3]) + (2*Sech[x]*Tanh[x])/(7*a*Sqrt[a*Cosh[x]^3])","A",4,3,10,0.3000,1,"{3207, 2636, 2641}"
133,1,121,0,0.051845,"\int \frac{1}{\left(a \cosh ^3(x)\right)^{5/2}} \, dx","Int[(a*Cosh[x]^3)^(-5/2),x]","\frac{154 \sinh (x) \cosh (x)}{195 a^2 \sqrt{a \cosh ^3(x)}}+\frac{154 \tanh (x)}{585 a^2 \sqrt{a \cosh ^3(x)}}+\frac{154 i \cosh ^{\frac{3}{2}}(x) E\left(\left.\frac{i x}{2}\right|2\right)}{195 a^2 \sqrt{a \cosh ^3(x)}}+\frac{2 \tanh (x) \text{sech}^4(x)}{13 a^2 \sqrt{a \cosh ^3(x)}}+\frac{22 \tanh (x) \text{sech}^2(x)}{117 a^2 \sqrt{a \cosh ^3(x)}}","\frac{154 \sinh (x) \cosh (x)}{195 a^2 \sqrt{a \cosh ^3(x)}}+\frac{154 \tanh (x)}{585 a^2 \sqrt{a \cosh ^3(x)}}+\frac{154 i \cosh ^{\frac{3}{2}}(x) E\left(\left.\frac{i x}{2}\right|2\right)}{195 a^2 \sqrt{a \cosh ^3(x)}}+\frac{2 \tanh (x) \text{sech}^4(x)}{13 a^2 \sqrt{a \cosh ^3(x)}}+\frac{22 \tanh (x) \text{sech}^2(x)}{117 a^2 \sqrt{a \cosh ^3(x)}}",1,"(((154*I)/195)*Cosh[x]^(3/2)*EllipticE[(I/2)*x, 2])/(a^2*Sqrt[a*Cosh[x]^3]) + (154*Cosh[x]*Sinh[x])/(195*a^2*Sqrt[a*Cosh[x]^3]) + (154*Tanh[x])/(585*a^2*Sqrt[a*Cosh[x]^3]) + (22*Sech[x]^2*Tanh[x])/(117*a^2*Sqrt[a*Cosh[x]^3]) + (2*Sech[x]^4*Tanh[x])/(13*a^2*Sqrt[a*Cosh[x]^3])","A",6,3,10,0.3000,1,"{3207, 2636, 2639}"
134,1,132,0,0.0529856,"\int \left(a \cosh ^4(x)\right)^{5/2} \, dx","Int[(a*Cosh[x]^4)^(5/2),x]","\frac{1}{10} a^2 \sinh (x) \cosh ^7(x) \sqrt{a \cosh ^4(x)}+\frac{9}{80} a^2 \sinh (x) \cosh ^5(x) \sqrt{a \cosh ^4(x)}+\frac{21}{160} a^2 \sinh (x) \cosh ^3(x) \sqrt{a \cosh ^4(x)}+\frac{21}{128} a^2 \sinh (x) \cosh (x) \sqrt{a \cosh ^4(x)}+\frac{63}{256} a^2 \tanh (x) \sqrt{a \cosh ^4(x)}+\frac{63}{256} a^2 x \text{sech}^2(x) \sqrt{a \cosh ^4(x)}","\frac{1}{10} a^2 \sinh (x) \cosh ^7(x) \sqrt{a \cosh ^4(x)}+\frac{9}{80} a^2 \sinh (x) \cosh ^5(x) \sqrt{a \cosh ^4(x)}+\frac{21}{160} a^2 \sinh (x) \cosh ^3(x) \sqrt{a \cosh ^4(x)}+\frac{21}{128} a^2 \sinh (x) \cosh (x) \sqrt{a \cosh ^4(x)}+\frac{63}{256} a^2 \tanh (x) \sqrt{a \cosh ^4(x)}+\frac{63}{256} a^2 x \text{sech}^2(x) \sqrt{a \cosh ^4(x)}",1,"(63*a^2*x*Sqrt[a*Cosh[x]^4]*Sech[x]^2)/256 + (21*a^2*Cosh[x]*Sqrt[a*Cosh[x]^4]*Sinh[x])/128 + (21*a^2*Cosh[x]^3*Sqrt[a*Cosh[x]^4]*Sinh[x])/160 + (9*a^2*Cosh[x]^5*Sqrt[a*Cosh[x]^4]*Sinh[x])/80 + (a^2*Cosh[x]^7*Sqrt[a*Cosh[x]^4]*Sinh[x])/10 + (63*a^2*Sqrt[a*Cosh[x]^4]*Tanh[x])/256","A",7,3,10,0.3000,1,"{3207, 2635, 8}"
135,1,78,0,0.0352139,"\int \left(a \cosh ^4(x)\right)^{3/2} \, dx","Int[(a*Cosh[x]^4)^(3/2),x]","\frac{1}{6} a \sinh (x) \cosh ^3(x) \sqrt{a \cosh ^4(x)}+\frac{5}{24} a \sinh (x) \cosh (x) \sqrt{a \cosh ^4(x)}+\frac{5}{16} a \tanh (x) \sqrt{a \cosh ^4(x)}+\frac{5}{16} a x \text{sech}^2(x) \sqrt{a \cosh ^4(x)}","\frac{1}{6} a \sinh (x) \cosh ^3(x) \sqrt{a \cosh ^4(x)}+\frac{5}{24} a \sinh (x) \cosh (x) \sqrt{a \cosh ^4(x)}+\frac{5}{16} a \tanh (x) \sqrt{a \cosh ^4(x)}+\frac{5}{16} a x \text{sech}^2(x) \sqrt{a \cosh ^4(x)}",1,"(5*a*x*Sqrt[a*Cosh[x]^4]*Sech[x]^2)/16 + (5*a*Cosh[x]*Sqrt[a*Cosh[x]^4]*Sinh[x])/24 + (a*Cosh[x]^3*Sqrt[a*Cosh[x]^4]*Sinh[x])/6 + (5*a*Sqrt[a*Cosh[x]^4]*Tanh[x])/16","A",5,3,10,0.3000,1,"{3207, 2635, 8}"
136,1,36,0,0.0159334,"\int \sqrt{a \cosh ^4(x)} \, dx","Int[Sqrt[a*Cosh[x]^4],x]","\frac{1}{2} \tanh (x) \sqrt{a \cosh ^4(x)}+\frac{1}{2} x \text{sech}^2(x) \sqrt{a \cosh ^4(x)}","\frac{1}{2} \tanh (x) \sqrt{a \cosh ^4(x)}+\frac{1}{2} x \text{sech}^2(x) \sqrt{a \cosh ^4(x)}",1,"(x*Sqrt[a*Cosh[x]^4]*Sech[x]^2)/2 + (Sqrt[a*Cosh[x]^4]*Tanh[x])/2","A",3,3,10,0.3000,1,"{3207, 2635, 8}"
137,1,15,0,0.0166324,"\int \frac{1}{\sqrt{a \cosh ^4(x)}} \, dx","Int[1/Sqrt[a*Cosh[x]^4],x]","\frac{\sinh (x) \cosh (x)}{\sqrt{a \cosh ^4(x)}}","\frac{\sinh (x) \cosh (x)}{\sqrt{a \cosh ^4(x)}}",1,"(Cosh[x]*Sinh[x])/Sqrt[a*Cosh[x]^4]","A",3,3,10,0.3000,1,"{3207, 3767, 8}"
138,1,67,0,0.025165,"\int \frac{1}{\left(a \cosh ^4(x)\right)^{3/2}} \, dx","Int[(a*Cosh[x]^4)^(-3/2),x]","\frac{\sinh (x) \cosh (x)}{a \sqrt{a \cosh ^4(x)}}+\frac{\sinh ^2(x) \tanh ^3(x)}{5 a \sqrt{a \cosh ^4(x)}}-\frac{2 \sinh ^2(x) \tanh (x)}{3 a \sqrt{a \cosh ^4(x)}}","\frac{\sinh (x) \cosh (x)}{a \sqrt{a \cosh ^4(x)}}+\frac{\sinh ^2(x) \tanh ^3(x)}{5 a \sqrt{a \cosh ^4(x)}}-\frac{2 \sinh ^2(x) \tanh (x)}{3 a \sqrt{a \cosh ^4(x)}}",1,"(Cosh[x]*Sinh[x])/(a*Sqrt[a*Cosh[x]^4]) - (2*Sinh[x]^2*Tanh[x])/(3*a*Sqrt[a*Cosh[x]^4]) + (Sinh[x]^2*Tanh[x]^3)/(5*a*Sqrt[a*Cosh[x]^4])","A",3,2,10,0.2000,1,"{3207, 3767}"
139,1,117,0,0.0351632,"\int \frac{1}{\left(a \cosh ^4(x)\right)^{5/2}} \, dx","Int[(a*Cosh[x]^4)^(-5/2),x]","\frac{\sinh (x) \cosh (x)}{a^2 \sqrt{a \cosh ^4(x)}}+\frac{\sinh ^2(x) \tanh ^7(x)}{9 a^2 \sqrt{a \cosh ^4(x)}}-\frac{4 \sinh ^2(x) \tanh ^5(x)}{7 a^2 \sqrt{a \cosh ^4(x)}}+\frac{6 \sinh ^2(x) \tanh ^3(x)}{5 a^2 \sqrt{a \cosh ^4(x)}}-\frac{4 \sinh ^2(x) \tanh (x)}{3 a^2 \sqrt{a \cosh ^4(x)}}","\frac{\sinh (x) \cosh (x)}{a^2 \sqrt{a \cosh ^4(x)}}+\frac{\sinh ^2(x) \tanh ^7(x)}{9 a^2 \sqrt{a \cosh ^4(x)}}-\frac{4 \sinh ^2(x) \tanh ^5(x)}{7 a^2 \sqrt{a \cosh ^4(x)}}+\frac{6 \sinh ^2(x) \tanh ^3(x)}{5 a^2 \sqrt{a \cosh ^4(x)}}-\frac{4 \sinh ^2(x) \tanh (x)}{3 a^2 \sqrt{a \cosh ^4(x)}}",1,"(Cosh[x]*Sinh[x])/(a^2*Sqrt[a*Cosh[x]^4]) - (4*Sinh[x]^2*Tanh[x])/(3*a^2*Sqrt[a*Cosh[x]^4]) + (6*Sinh[x]^2*Tanh[x]^3)/(5*a^2*Sqrt[a*Cosh[x]^4]) - (4*Sinh[x]^2*Tanh[x]^5)/(7*a^2*Sqrt[a*Cosh[x]^4]) + (Sinh[x]^2*Tanh[x]^7)/(9*a^2*Sqrt[a*Cosh[x]^4])","A",3,2,10,0.2000,1,"{3207, 3767}"
140,1,8,0,0.0209781,"\int \frac{\sinh (x)}{(1+\cosh (x))^2} \, dx","Int[Sinh[x]/(1 + Cosh[x])^2,x]","-\frac{1}{\cosh (x)+1}","-\frac{1}{\cosh (x)+1}",1,"-(1 + Cosh[x])^(-1)","A",2,2,9,0.2222,1,"{2667, 32}"
141,1,8,0,0.0216567,"\int \frac{\sinh (x)}{(1-\cosh (x))^2} \, dx","Int[Sinh[x]/(1 - Cosh[x])^2,x]","\frac{1}{1-\cosh (x)}","\frac{1}{1-\cosh (x)}",1,"(1 - Cosh[x])^(-1)","A",2,2,11,0.1818,1,"{2667, 32}"
142,1,12,0,0.0314202,"\int \frac{\sinh ^2(x)}{(1+\cosh (x))^2} \, dx","Int[Sinh[x]^2/(1 + Cosh[x])^2,x]","x-\frac{2 \sinh (x)}{\cosh (x)+1}","x-\frac{2 \sinh (x)}{\cosh (x)+1}",1,"x - (2*Sinh[x])/(1 + Cosh[x])","A",2,2,11,0.1818,1,"{2680, 8}"
143,1,14,0,0.0311489,"\int \frac{\sinh ^2(x)}{(1-\cosh (x))^2} \, dx","Int[Sinh[x]^2/(1 - Cosh[x])^2,x]","x+\frac{2 \sinh (x)}{1-\cosh (x)}","x+\frac{2 \sinh (x)}{1-\cosh (x)}",1,"x + (2*Sinh[x])/(1 - Cosh[x])","A",2,2,13,0.1538,1,"{2680, 8}"
144,1,10,0,0.0383399,"\int \frac{\sinh ^3(x)}{(1+\cosh (x))^2} \, dx","Int[Sinh[x]^3/(1 + Cosh[x])^2,x]","\cosh (x)-2 \log (\cosh (x)+1)","\cosh (x)-2 \log (\cosh (x)+1)",1,"Cosh[x] - 2*Log[1 + Cosh[x]]","A",3,2,11,0.1818,1,"{2667, 43}"
145,1,12,0,0.0372116,"\int \frac{\sinh ^3(x)}{(1-\cosh (x))^2} \, dx","Int[Sinh[x]^3/(1 - Cosh[x])^2,x]","\cosh (x)+2 \log (1-\cosh (x))","\cosh (x)+2 \log (1-\cosh (x))",1,"Cosh[x] + 2*Log[1 - Cosh[x]]","A",3,2,13,0.1538,1,"{2667, 43}"
146,1,10,0,0.0205692,"\int \frac{\sinh (x)}{(1+\cosh (x))^3} \, dx","Int[Sinh[x]/(1 + Cosh[x])^3,x]","-\frac{1}{2 (\cosh (x)+1)^2}","-\frac{1}{2 (\cosh (x)+1)^2}",1,"-1/(2*(1 + Cosh[x])^2)","A",2,2,9,0.2222,1,"{2667, 32}"
147,1,12,0,0.0211197,"\int \frac{\sinh (x)}{(1-\cosh (x))^3} \, dx","Int[Sinh[x]/(1 - Cosh[x])^3,x]","\frac{1}{2 (1-\cosh (x))^2}","\frac{1}{2 (1-\cosh (x))^2}",1,"1/(2*(1 - Cosh[x])^2)","A",2,2,11,0.1818,1,"{2667, 32}"
148,1,14,0,0.0322497,"\int \frac{\sinh ^2(x)}{(1+\cosh (x))^3} \, dx","Int[Sinh[x]^2/(1 + Cosh[x])^3,x]","\frac{\sinh ^3(x)}{3 (\cosh (x)+1)^3}","\frac{\sinh ^3(x)}{3 (\cosh (x)+1)^3}",1,"Sinh[x]^3/(3*(1 + Cosh[x])^3)","A",1,1,11,0.09091,1,"{2671}"
149,1,16,0,0.0328942,"\int \frac{\sinh ^2(x)}{(1-\cosh (x))^3} \, dx","Int[Sinh[x]^2/(1 - Cosh[x])^3,x]","-\frac{\sinh ^3(x)}{3 (1-\cosh (x))^3}","-\frac{\sinh ^3(x)}{3 (1-\cosh (x))^3}",1,"-Sinh[x]^3/(3*(1 - Cosh[x])^3)","A",1,1,13,0.07692,1,"{2671}"
150,1,14,0,0.0402647,"\int \frac{\sinh ^3(x)}{(1+\cosh (x))^3} \, dx","Int[Sinh[x]^3/(1 + Cosh[x])^3,x]","\frac{2}{\cosh (x)+1}+\log (\cosh (x)+1)","\frac{2}{\cosh (x)+1}+\log (\cosh (x)+1)",1,"2/(1 + Cosh[x]) + Log[1 + Cosh[x]]","A",3,2,11,0.1818,1,"{2667, 43}"
151,1,20,0,0.0404257,"\int \frac{\sinh ^3(x)}{(1-\cosh (x))^3} \, dx","Int[Sinh[x]^3/(1 - Cosh[x])^3,x]","-\frac{2}{1-\cosh (x)}-\log (1-\cosh (x))","-\frac{2}{1-\cosh (x)}-\log (1-\cosh (x))",1,"-2/(1 - Cosh[x]) - Log[1 - Cosh[x]]","A",3,2,13,0.1538,1,"{2667, 43}"
152,1,57,0,0.059228,"\int \frac{\sinh ^8(x)}{a+a \cosh (x)} \, dx","Int[Sinh[x]^8/(a + a*Cosh[x]),x]","\frac{5 x}{16 a}+\frac{\sinh ^7(x)}{7 a}-\frac{\sinh ^5(x) \cosh (x)}{6 a}+\frac{5 \sinh ^3(x) \cosh (x)}{24 a}-\frac{5 \sinh (x) \cosh (x)}{16 a}","\frac{5 x}{16 a}+\frac{\sinh ^7(x)}{7 a}-\frac{\sinh ^5(x) \cosh (x)}{6 a}+\frac{5 \sinh ^3(x) \cosh (x)}{24 a}-\frac{5 \sinh (x) \cosh (x)}{16 a}",1,"(5*x)/(16*a) - (5*Cosh[x]*Sinh[x])/(16*a) + (5*Cosh[x]*Sinh[x]^3)/(24*a) - (Cosh[x]*Sinh[x]^5)/(6*a) + Sinh[x]^7/(7*a)","A",5,3,13,0.2308,1,"{2682, 2635, 8}"
153,1,46,0,0.0649232,"\int \frac{\sinh ^7(x)}{a+a \cosh (x)} \, dx","Int[Sinh[x]^7/(a + a*Cosh[x]),x]","\frac{(a-a \cosh (x))^6}{6 a^7}-\frac{4 (a-a \cosh (x))^5}{5 a^6}+\frac{(a-a \cosh (x))^4}{a^5}","\frac{(a-a \cosh (x))^6}{6 a^7}-\frac{4 (a-a \cosh (x))^5}{5 a^6}+\frac{(a-a \cosh (x))^4}{a^5}",1,"(a - a*Cosh[x])^4/a^5 - (4*(a - a*Cosh[x])^5)/(5*a^6) + (a - a*Cosh[x])^6/(6*a^7)","A",3,2,13,0.1538,1,"{2667, 43}"
154,1,44,0,0.0544319,"\int \frac{\sinh ^6(x)}{a+a \cosh (x)} \, dx","Int[Sinh[x]^6/(a + a*Cosh[x]),x]","-\frac{3 x}{8 a}+\frac{\sinh ^5(x)}{5 a}-\frac{\sinh ^3(x) \cosh (x)}{4 a}+\frac{3 \sinh (x) \cosh (x)}{8 a}","-\frac{3 x}{8 a}+\frac{\sinh ^5(x)}{5 a}-\frac{\sinh ^3(x) \cosh (x)}{4 a}+\frac{3 \sinh (x) \cosh (x)}{8 a}",1,"(-3*x)/(8*a) + (3*Cosh[x]*Sinh[x])/(8*a) - (Cosh[x]*Sinh[x]^3)/(4*a) + Sinh[x]^5/(5*a)","A",4,3,13,0.2308,1,"{2682, 2635, 8}"
155,1,33,0,0.0556596,"\int \frac{\sinh ^5(x)}{a+a \cosh (x)} \, dx","Int[Sinh[x]^5/(a + a*Cosh[x]),x]","\frac{(a-a \cosh (x))^4}{4 a^5}-\frac{2 (a-a \cosh (x))^3}{3 a^4}","\frac{(a-a \cosh (x))^4}{4 a^5}-\frac{2 (a-a \cosh (x))^3}{3 a^4}",1,"(-2*(a - a*Cosh[x])^3)/(3*a^4) + (a - a*Cosh[x])^4/(4*a^5)","A",3,2,13,0.1538,1,"{2667, 43}"
156,1,31,0,0.0459738,"\int \frac{\sinh ^4(x)}{a+a \cosh (x)} \, dx","Int[Sinh[x]^4/(a + a*Cosh[x]),x]","\frac{x}{2 a}+\frac{\sinh ^3(x)}{3 a}-\frac{\sinh (x) \cosh (x)}{2 a}","\frac{x}{2 a}+\frac{\sinh ^3(x)}{3 a}-\frac{\sinh (x) \cosh (x)}{2 a}",1,"x/(2*a) - (Cosh[x]*Sinh[x])/(2*a) + Sinh[x]^3/(3*a)","A",3,3,13,0.2308,1,"{2682, 2635, 8}"
157,1,19,0,0.0432605,"\int \frac{\sinh ^3(x)}{a+a \cosh (x)} \, dx","Int[Sinh[x]^3/(a + a*Cosh[x]),x]","\frac{\cosh ^2(x)}{2 a}-\frac{\cosh (x)}{a}","\frac{\cosh ^2(x)}{2 a}-\frac{\cosh (x)}{a}",1,"-(Cosh[x]/a) + Cosh[x]^2/(2*a)","A",2,1,13,0.07692,1,"{2667}"
158,1,13,0,0.0392258,"\int \frac{\sinh ^2(x)}{a+a \cosh (x)} \, dx","Int[Sinh[x]^2/(a + a*Cosh[x]),x]","\frac{\sinh (x)}{a}-\frac{x}{a}","\frac{\sinh (x)}{a}-\frac{x}{a}",1,"-(x/a) + Sinh[x]/a","A",2,2,13,0.1538,1,"{2682, 8}"
159,1,9,0,0.0236929,"\int \frac{\sinh (x)}{a+a \cosh (x)} \, dx","Int[Sinh[x]/(a + a*Cosh[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,"{2667, 31}"
160,1,23,0,0.052373,"\int \frac{\text{csch}(x)}{a+a \cosh (x)} \, dx","Int[Csch[x]/(a + a*Cosh[x]),x]","\frac{1}{2 (a \cosh (x)+a)}-\frac{\tanh ^{-1}(\cosh (x))}{2 a}","\frac{1}{2 (a \cosh (x)+a)}-\frac{\tanh ^{-1}(\cosh (x))}{2 a}",1,"-ArcTanh[Cosh[x]]/(2*a) + 1/(2*(a + a*Cosh[x]))","A",4,3,11,0.2727,1,"{2667, 44, 206}"
161,1,24,0,0.0483311,"\int \frac{\text{csch}^2(x)}{a+a \cosh (x)} \, dx","Int[Csch[x]^2/(a + a*Cosh[x]),x]","\frac{\text{csch}(x)}{3 (a \cosh (x)+a)}-\frac{2 \coth (x)}{3 a}","\frac{\text{csch}(x)}{3 (a \cosh (x)+a)}-\frac{2 \coth (x)}{3 a}",1,"(-2*Coth[x])/(3*a) + Csch[x]/(3*(a + a*Cosh[x]))","A",3,3,13,0.2308,1,"{2672, 3767, 8}"
162,1,49,0,0.0811718,"\int \frac{\text{csch}^3(x)}{a+a \cosh (x)} \, dx","Int[Csch[x]^3/(a + a*Cosh[x]),x]","-\frac{a}{8 (a \cosh (x)+a)^2}+\frac{1}{8 (a-a \cosh (x))}-\frac{1}{4 (a \cosh (x)+a)}+\frac{3 \tanh ^{-1}(\cosh (x))}{8 a}","-\frac{a}{8 (a \cosh (x)+a)^2}+\frac{1}{8 (a-a \cosh (x))}-\frac{1}{4 (a \cosh (x)+a)}+\frac{3 \tanh ^{-1}(\cosh (x))}{8 a}",1,"(3*ArcTanh[Cosh[x]])/(8*a) + 1/(8*(a - a*Cosh[x])) - a/(8*(a + a*Cosh[x])^2) - 1/(4*(a + a*Cosh[x]))","A",4,3,13,0.2308,1,"{2667, 44, 206}"
163,1,37,0,0.0507936,"\int \frac{\text{csch}^4(x)}{a+a \cosh (x)} \, dx","Int[Csch[x]^4/(a + a*Cosh[x]),x]","-\frac{4 \coth ^3(x)}{15 a}+\frac{4 \coth (x)}{5 a}+\frac{\text{csch}^3(x)}{5 (a \cosh (x)+a)}","-\frac{4 \coth ^3(x)}{15 a}+\frac{4 \coth (x)}{5 a}+\frac{\text{csch}^3(x)}{5 (a \cosh (x)+a)}",1,"(4*Coth[x])/(5*a) - (4*Coth[x]^3)/(15*a) + Csch[x]^3/(5*(a + a*Cosh[x]))","A",3,2,13,0.1538,1,"{2672, 3767}"
164,1,78,0,0.1063554,"\int \frac{\text{csch}^5(x)}{a+a \cosh (x)} \, dx","Int[Csch[x]^5/(a + a*Cosh[x]),x]","\frac{a^2}{24 (a \cosh (x)+a)^3}-\frac{a}{32 (a-a \cosh (x))^2}+\frac{3 a}{32 (a \cosh (x)+a)^2}-\frac{1}{8 (a-a \cosh (x))}+\frac{3}{16 (a \cosh (x)+a)}-\frac{5 \tanh ^{-1}(\cosh (x))}{16 a}","\frac{a^2}{24 (a \cosh (x)+a)^3}-\frac{a}{32 (a-a \cosh (x))^2}+\frac{3 a}{32 (a \cosh (x)+a)^2}-\frac{1}{8 (a-a \cosh (x))}+\frac{3}{16 (a \cosh (x)+a)}-\frac{5 \tanh ^{-1}(\cosh (x))}{16 a}",1,"(-5*ArcTanh[Cosh[x]])/(16*a) - a/(32*(a - a*Cosh[x])^2) - 1/(8*(a - a*Cosh[x])) + a^2/(24*(a + a*Cosh[x])^3) + (3*a)/(32*(a + a*Cosh[x])^2) + 3/(16*(a + a*Cosh[x]))","A",4,3,13,0.2308,1,"{2667, 44, 206}"
165,1,140,0,0.1670115,"\int \frac{\sinh ^7(x)}{a+b \cosh (x)} \, dx","Int[Sinh[x]^7/(a + b*Cosh[x]),x]","\frac{\left(a^2-3 b^2\right) \cosh ^4(x)}{4 b^3}-\frac{a \left(a^2-3 b^2\right) \cosh ^3(x)}{3 b^4}+\frac{\left(-3 a^2 b^2+a^4+3 b^4\right) \cosh ^2(x)}{2 b^5}-\frac{a \left(-3 a^2 b^2+a^4+3 b^4\right) \cosh (x)}{b^6}+\frac{\left(a^2-b^2\right)^3 \log (a+b \cosh (x))}{b^7}-\frac{a \cosh ^5(x)}{5 b^2}+\frac{\cosh ^6(x)}{6 b}","\frac{\left(a^2-3 b^2\right) \cosh ^4(x)}{4 b^3}-\frac{a \left(a^2-3 b^2\right) \cosh ^3(x)}{3 b^4}+\frac{\left(-3 a^2 b^2+a^4+3 b^4\right) \cosh ^2(x)}{2 b^5}-\frac{a \left(-3 a^2 b^2+a^4+3 b^4\right) \cosh (x)}{b^6}+\frac{\left(a^2-b^2\right)^3 \log (a+b \cosh (x))}{b^7}-\frac{a \cosh ^5(x)}{5 b^2}+\frac{\cosh ^6(x)}{6 b}",1,"-((a*(a^4 - 3*a^2*b^2 + 3*b^4)*Cosh[x])/b^6) + ((a^4 - 3*a^2*b^2 + 3*b^4)*Cosh[x]^2)/(2*b^5) - (a*(a^2 - 3*b^2)*Cosh[x]^3)/(3*b^4) + ((a^2 - 3*b^2)*Cosh[x]^4)/(4*b^3) - (a*Cosh[x]^5)/(5*b^2) + Cosh[x]^6/(6*b) + ((a^2 - b^2)^3*Log[a + b*Cosh[x]])/b^7","A",3,2,13,0.1538,1,"{2668, 697}"
166,1,154,0,0.4251075,"\int \frac{\sinh ^6(x)}{a+b \cosh (x)} \, dx","Int[Sinh[x]^6/(a + b*Cosh[x]),x]","-\frac{a x \left(-20 a^2 b^2+8 a^4+15 b^4\right)}{8 b^6}+\frac{\sinh ^3(x) \left(4 \left(a^2-b^2\right)-3 a b \cosh (x)\right)}{12 b^3}+\frac{\sinh (x) \left(8 \left(a^2-b^2\right)^2-a b \left(4 a^2-7 b^2\right) \cosh (x)\right)}{8 b^5}+\frac{2 (a-b)^{5/2} (a+b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b^6}+\frac{\sinh ^5(x)}{5 b}","-\frac{a x \left(-20 a^2 b^2+8 a^4+15 b^4\right)}{8 b^6}+\frac{\sinh ^3(x) \left(4 \left(a^2-b^2\right)-3 a b \cosh (x)\right)}{12 b^3}+\frac{\sinh (x) \left(8 \left(a^2-b^2\right)^2-a b \left(4 a^2-7 b^2\right) \cosh (x)\right)}{8 b^5}+\frac{2 (a-b)^{5/2} (a+b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b^6}+\frac{\sinh ^5(x)}{5 b}",1,"-(a*(8*a^4 - 20*a^2*b^2 + 15*b^4)*x)/(8*b^6) + (2*(a - b)^(5/2)*(a + b)^(5/2)*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/b^6 + ((8*(a^2 - b^2)^2 - a*b*(4*a^2 - 7*b^2)*Cosh[x])*Sinh[x])/(8*b^5) + ((4*(a^2 - b^2) - 3*a*b*Cosh[x])*Sinh[x]^3)/(12*b^3) + Sinh[x]^5/(5*b)","A",6,5,13,0.3846,1,"{2695, 2865, 2735, 2659, 208}"
167,1,83,0,0.1072384,"\int \frac{\sinh ^5(x)}{a+b \cosh (x)} \, dx","Int[Sinh[x]^5/(a + b*Cosh[x]),x]","\frac{\left(a^2-2 b^2\right) \cosh ^2(x)}{2 b^3}-\frac{a \left(a^2-2 b^2\right) \cosh (x)}{b^4}+\frac{\left(a^2-b^2\right)^2 \log (a+b \cosh (x))}{b^5}-\frac{a \cosh ^3(x)}{3 b^2}+\frac{\cosh ^4(x)}{4 b}","\frac{\left(a^2-2 b^2\right) \cosh ^2(x)}{2 b^3}-\frac{a \left(a^2-2 b^2\right) \cosh (x)}{b^4}+\frac{\left(a^2-b^2\right)^2 \log (a+b \cosh (x))}{b^5}-\frac{a \cosh ^3(x)}{3 b^2}+\frac{\cosh ^4(x)}{4 b}",1,"-((a*(a^2 - 2*b^2)*Cosh[x])/b^4) + ((a^2 - 2*b^2)*Cosh[x]^2)/(2*b^3) - (a*Cosh[x]^3)/(3*b^2) + Cosh[x]^4/(4*b) + ((a^2 - b^2)^2*Log[a + b*Cosh[x]])/b^5","A",3,2,13,0.1538,1,"{2668, 697}"
168,1,104,0,0.2407632,"\int \frac{\sinh ^4(x)}{a+b \cosh (x)} \, dx","Int[Sinh[x]^4/(a + b*Cosh[x]),x]","-\frac{a x \left(2 a^2-3 b^2\right)}{2 b^4}+\frac{\sinh (x) \left(2 \left(a^2-b^2\right)-a b \cosh (x)\right)}{2 b^3}+\frac{2 (a-b)^{3/2} (a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b^4}+\frac{\sinh ^3(x)}{3 b}","-\frac{a x \left(2 a^2-3 b^2\right)}{2 b^4}+\frac{\sinh (x) \left(2 \left(a^2-b^2\right)-a b \cosh (x)\right)}{2 b^3}+\frac{2 (a-b)^{3/2} (a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b^4}+\frac{\sinh ^3(x)}{3 b}",1,"-(a*(2*a^2 - 3*b^2)*x)/(2*b^4) + (2*(a - b)^(3/2)*(a + b)^(3/2)*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/b^4 + ((2*(a^2 - b^2) - a*b*Cosh[x])*Sinh[x])/(2*b^3) + Sinh[x]^3/(3*b)","A",5,5,13,0.3846,1,"{2695, 2865, 2735, 2659, 208}"
169,1,40,0,0.0689581,"\int \frac{\sinh ^3(x)}{a+b \cosh (x)} \, dx","Int[Sinh[x]^3/(a + b*Cosh[x]),x]","\frac{\left(a^2-b^2\right) \log (a+b \cosh (x))}{b^3}-\frac{a \cosh (x)}{b^2}+\frac{\cosh ^2(x)}{2 b}","\frac{\left(a^2-b^2\right) \log (a+b \cosh (x))}{b^3}-\frac{a \cosh (x)}{b^2}+\frac{\cosh ^2(x)}{2 b}",1,"-((a*Cosh[x])/b^2) + Cosh[x]^2/(2*b) + ((a^2 - b^2)*Log[a + b*Cosh[x]])/b^3","A",3,2,13,0.1538,1,"{2668, 697}"
170,1,59,0,0.112383,"\int \frac{\sinh ^2(x)}{a+b \cosh (x)} \, dx","Int[Sinh[x]^2/(a + b*Cosh[x]),x]","-\frac{a x}{b^2}+\frac{2 \sqrt{a-b} \sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b^2}+\frac{\sinh (x)}{b}","-\frac{a x}{b^2}+\frac{2 \sqrt{a-b} \sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b^2}+\frac{\sinh (x)}{b}",1,"-((a*x)/b^2) + (2*Sqrt[a - b]*Sqrt[a + b]*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/b^2 + Sinh[x]/b","A",4,4,13,0.3077,1,"{2695, 2735, 2659, 208}"
171,1,11,0,0.0265945,"\int \frac{\sinh (x)}{a+b \cosh (x)} \, dx","Int[Sinh[x]/(a + b*Cosh[x]),x]","\frac{\log (a+b \cosh (x))}{b}","\frac{\log (a+b \cosh (x))}{b}",1,"Log[a + b*Cosh[x]]/b","A",2,2,11,0.1818,1,"{2668, 31}"
172,1,53,0,0.0770954,"\int \frac{\text{csch}(x)}{a+b \cosh (x)} \, dx","Int[Csch[x]/(a + b*Cosh[x]),x]","\frac{b \log (a+b \cosh (x))}{a^2-b^2}+\frac{\log (1-\cosh (x))}{2 (a+b)}-\frac{\log (\cosh (x)+1)}{2 (a-b)}","\frac{b \log (a+b \cosh (x))}{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[a + b*Cosh[x]])/(a^2 - b^2)","A",6,4,11,0.3636,1,"{2668, 706, 31, 633}"
173,1,67,0,0.0898146,"\int \frac{\text{csch}^2(x)}{a+b \cosh (x)} \, dx","Int[Csch[x]^2/(a + b*Cosh[x]),x]","\frac{\text{csch}(x) (b-a \cosh (x))}{a^2-b^2}+\frac{2 b^2 \tanh ^{-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 b^2 \tanh ^{-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*b^2*ArcTanh[(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",4,4,13,0.3077,1,"{2696, 12, 2659, 208}"
174,1,91,0,0.1592303,"\int \frac{\text{csch}^3(x)}{a+b \cosh (x)} \, dx","Int[Csch[x]^3/(a + b*Cosh[x]),x]","\frac{b^3 \log (a+b \cosh (x))}{\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+2 b) \log (1-\cosh (x))}{4 (a+b)^2}+\frac{(a-2 b) \log (\cosh (x)+1)}{4 (a-b)^2}","\frac{b^3 \log (a+b \cosh (x))}{\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+2 b) \log (1-\cosh (x))}{4 (a+b)^2}+\frac{(a-2 b) \log (\cosh (x)+1)}{4 (a-b)^2}",1,"((b - a*Cosh[x])*Csch[x]^2)/(2*(a^2 - b^2)) - ((a + 2*b)*Log[1 - Cosh[x]])/(4*(a + b)^2) + ((a - 2*b)*Log[1 + Cosh[x]])/(4*(a - b)^2) + (b^3*Log[a + b*Cosh[x]])/(a^2 - b^2)^2","A",4,3,13,0.2308,1,"{2668, 741, 801}"
175,1,110,0,0.2458708,"\int \frac{\text{csch}^4(x)}{a+b \cosh (x)} \, dx","Int[Csch[x]^4/(a + b*Cosh[x]),x]","\frac{\text{csch}^3(x) (b-a \cosh (x))}{3 \left(a^2-b^2\right)}+\frac{\text{csch}(x) \left(a \left(2 a^2-5 b^2\right) \cosh (x)+3 b^3\right)}{3 \left(a^2-b^2\right)^2}+\frac{2 b^4 \tanh ^{-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(a \left(2 a^2-5 b^2\right) \cosh (x)+3 b^3\right)}{3 \left(a^2-b^2\right)^2}+\frac{2 b^4 \tanh ^{-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*b^4*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/((a - b)^(5/2)*(a + b)^(5/2)) + ((3*b^3 + a*(2*a^2 - 5*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",5,5,13,0.3846,1,"{2696, 2866, 12, 2659, 208}"
176,1,151,0,0.2535785,"\int \frac{\text{csch}^5(x)}{a+b \cosh (x)} \, dx","Int[Csch[x]^5/(a + b*Cosh[x]),x]","\frac{b^5 \log (a+b \cosh (x))}{\left(a^2-b^2\right)^3}+\frac{\left(3 a^2+9 a b+8 b^2\right) \log (1-\cosh (x))}{16 (a+b)^3}-\frac{\left(3 a^2-9 a b+8 b^2\right) \log (\cosh (x)+1)}{16 (a-b)^3}+\frac{\text{csch}^4(x) (b-a \cosh (x))}{4 \left(a^2-b^2\right)}+\frac{\text{csch}^2(x) \left(a \left(3 a^2-7 b^2\right) \cosh (x)+4 b^3\right)}{8 \left(a^2-b^2\right)^2}","\frac{b^5 \log (a+b \cosh (x))}{\left(a^2-b^2\right)^3}+\frac{\left(3 a^2+9 a b+8 b^2\right) \log (1-\cosh (x))}{16 (a+b)^3}-\frac{\left(3 a^2-9 a b+8 b^2\right) \log (\cosh (x)+1)}{16 (a-b)^3}+\frac{\text{csch}^4(x) (b-a \cosh (x))}{4 \left(a^2-b^2\right)}+\frac{\text{csch}^2(x) \left(a \left(3 a^2-7 b^2\right) \cosh (x)+4 b^3\right)}{8 \left(a^2-b^2\right)^2}",1,"((4*b^3 + a*(3*a^2 - 7*b^2)*Cosh[x])*Csch[x]^2)/(8*(a^2 - b^2)^2) + ((b - a*Cosh[x])*Csch[x]^4)/(4*(a^2 - b^2)) + ((3*a^2 + 9*a*b + 8*b^2)*Log[1 - Cosh[x]])/(16*(a + b)^3) - ((3*a^2 - 9*a*b + 8*b^2)*Log[1 + Cosh[x]])/(16*(a - b)^3) + (b^5*Log[a + b*Cosh[x]])/(a^2 - b^2)^3","A",5,4,13,0.3077,1,"{2668, 741, 823, 801}"
177,1,159,0,0.4768459,"\int \frac{\text{csch}^6(x)}{a+b \cosh (x)} \, dx","Int[Csch[x]^6/(a + b*Cosh[x]),x]","\frac{\text{csch}^5(x) (b-a \cosh (x))}{5 \left(a^2-b^2\right)}+\frac{\text{csch}^3(x) \left(a \left(4 a^2-9 b^2\right) \cosh (x)+5 b^3\right)}{15 \left(a^2-b^2\right)^2}+\frac{\text{csch}(x) \left(15 b^5-a \left(-26 a^2 b^2+8 a^4+33 b^4\right) \cosh (x)\right)}{15 \left(a^2-b^2\right)^3}+\frac{2 b^6 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{(a-b)^{7/2} (a+b)^{7/2}}","\frac{\text{csch}^5(x) (b-a \cosh (x))}{5 \left(a^2-b^2\right)}+\frac{\text{csch}^3(x) \left(a \left(4 a^2-9 b^2\right) \cosh (x)+5 b^3\right)}{15 \left(a^2-b^2\right)^2}+\frac{\text{csch}(x) \left(15 b^5-a \left(-26 a^2 b^2+8 a^4+33 b^4\right) \cosh (x)\right)}{15 \left(a^2-b^2\right)^3}+\frac{2 b^6 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{(a-b)^{7/2} (a+b)^{7/2}}",1,"(2*b^6*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/((a - b)^(7/2)*(a + b)^(7/2)) + ((15*b^5 - a*(8*a^4 - 26*a^2*b^2 + 33*b^4)*Cosh[x])*Csch[x])/(15*(a^2 - b^2)^3) + ((5*b^3 + a*(4*a^2 - 9*b^2)*Cosh[x])*Csch[x]^3)/(15*(a^2 - b^2)^2) + ((b - a*Cosh[x])*Csch[x]^5)/(5*(a^2 - b^2))","A",6,5,13,0.3846,1,"{2696, 2866, 12, 2659, 208}"
178,1,67,0,0.1041575,"\int \frac{\sinh ^2(x)}{(a+b \cosh (x))^2} \, dx","Int[Sinh[x]^2/(a + b*Cosh[x])^2,x]","-\frac{2 a \tanh ^{-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{\sinh (x)}{b (a+b \cosh (x))}+\frac{x}{b^2}","-\frac{2 a \tanh ^{-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{\sinh (x)}{b (a+b \cosh (x))}+\frac{x}{b^2}",1,"x/b^2 - (2*a*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(Sqrt[a - b]*b^2*Sqrt[a + b]) - Sinh[x]/(b*(a + b*Cosh[x]))","A",4,4,13,0.3077,1,"{2693, 2735, 2659, 208}"
179,1,113,0,0.4056091,"\int \frac{\tanh ^4(x)}{a+b \cosh (x)} \, dx","Int[Tanh[x]^4/(a + b*Cosh[x]),x]","-\frac{\left(4 a^2-3 b^2\right) \tanh (x)}{3 a^3}+\frac{b \left(3 a^2-2 b^2\right) \tan ^{-1}(\sinh (x))}{2 a^4}+\frac{2 (a-b)^{3/2} (a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a^4}-\frac{b \tanh (x) \text{sech}(x)}{2 a^2}+\frac{\tanh (x) \text{sech}^2(x)}{3 a}","-\frac{\left(4 a^2-3 b^2\right) \tanh (x)}{3 a^3}+\frac{b \left(3 a^2-2 b^2\right) \tan ^{-1}(\sinh (x))}{2 a^4}+\frac{2 (a-b)^{3/2} (a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a^4}-\frac{b \tanh (x) \text{sech}(x)}{2 a^2}+\frac{\tanh (x) \text{sech}^2(x)}{3 a}",1,"(b*(3*a^2 - 2*b^2)*ArcTan[Sinh[x]])/(2*a^4) + (2*(a - b)^(3/2)*(a + b)^(3/2)*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/a^4 - ((4*a^2 - 3*b^2)*Tanh[x])/(3*a^3) - (b*Sech[x]*Tanh[x])/(2*a^2) + (Sech[x]^2*Tanh[x])/(3*a)","A",6,6,13,0.4615,1,"{2725, 3055, 3001, 3770, 2659, 208}"
180,1,57,0,0.0988762,"\int \frac{\tanh ^3(x)}{a+b \cosh (x)} \, dx","Int[Tanh[x]^3/(a + b*Cosh[x]),x]","\frac{\left(a^2-b^2\right) \log (\cosh (x))}{a^3}-\frac{\left(a^2-b^2\right) \log (a+b \cosh (x))}{a^3}-\frac{b \text{sech}(x)}{a^2}+\frac{\text{sech}^2(x)}{2 a}","\frac{\left(a^2-b^2\right) \log (\cosh (x))}{a^3}-\frac{\left(a^2-b^2\right) \log (a+b \cosh (x))}{a^3}-\frac{b \text{sech}(x)}{a^2}+\frac{\text{sech}^2(x)}{2 a}",1,"((a^2 - b^2)*Log[Cosh[x]])/a^3 - ((a^2 - b^2)*Log[a + b*Cosh[x]])/a^3 - (b*Sech[x])/a^2 + Sech[x]^2/(2*a)","A",3,2,13,0.1538,1,"{2721, 894}"
181,1,61,0,0.2318969,"\int \frac{\tanh ^2(x)}{a+b \cosh (x)} \, dx","Int[Tanh[x]^2/(a + b*Cosh[x]),x]","\frac{2 \sqrt{a-b} \sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a^2}+\frac{b \tan ^{-1}(\sinh (x))}{a^2}-\frac{\tanh (x)}{a}","\frac{2 \sqrt{a-b} \sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a^2}+\frac{b \tan ^{-1}(\sinh (x))}{a^2}-\frac{\tanh (x)}{a}",1,"(b*ArcTan[Sinh[x]])/a^2 + (2*Sqrt[a - b]*Sqrt[a + b]*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/a^2 - Tanh[x]/a","A",6,6,13,0.4615,1,"{2723, 3056, 3001, 3770, 2659, 208}"
182,1,20,0,0.0423172,"\int \frac{\tanh (x)}{a+b \cosh (x)} \, dx","Int[Tanh[x]/(a + b*Cosh[x]),x]","\frac{\log (\cosh (x))}{a}-\frac{\log (a+b \cosh (x))}{a}","\frac{\log (\cosh (x))}{a}-\frac{\log (a+b \cosh (x))}{a}",1,"Log[Cosh[x]]/a - Log[a + b*Cosh[x]]/a","A",4,4,11,0.3636,1,"{2721, 36, 29, 31}"
183,1,54,0,0.0704049,"\int \frac{\coth (x)}{a+b \cosh (x)} \, dx","Int[Coth[x]/(a + b*Cosh[x]),x]","-\frac{a \log (a+b \cosh (x))}{a^2-b^2}+\frac{\log (1-\cosh (x))}{2 (a+b)}+\frac{\log (\cosh (x)+1)}{2 (a-b)}","-\frac{a \log (a+b \cosh (x))}{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)) - (a*Log[a + b*Cosh[x]])/(a^2 - b^2)","A",3,2,11,0.1818,1,"{2721, 801}"
184,1,77,0,0.0935763,"\int \frac{\coth ^2(x)}{a+b \cosh (x)} \, dx","Int[Coth[x]^2/(a + b*Cosh[x]),x]","-\frac{a \coth (x)}{a^2-b^2}+\frac{b \text{csch}(x)}{a^2-b^2}+\frac{2 a^2 \tanh ^{-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{a \coth (x)}{a^2-b^2}+\frac{b \text{csch}(x)}{a^2-b^2}+\frac{2 a^2 \tanh ^{-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^2*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/((a - b)^(3/2)*(a + b)^(3/2)) - (a*Coth[x])/(a^2 - b^2) + (b*Csch[x])/(a^2 - b^2)","A",7,6,13,0.4615,1,"{2727, 3767, 8, 2606, 2659, 208}"
185,1,94,0,0.1994258,"\int \frac{\coth ^3(x)}{a+b \cosh (x)} \, dx","Int[Coth[x]^3/(a + b*Cosh[x]),x]","-\frac{a^3 \log (a+b \cosh (x))}{\left(a^2-b^2\right)^2}-\frac{\text{csch}^2(x) (a-b \cosh (x))}{2 \left(a^2-b^2\right)}+\frac{(2 a+b) \log (1-\cosh (x))}{4 (a+b)^2}+\frac{(2 a-b) \log (\cosh (x)+1)}{4 (a-b)^2}","-\frac{a^3 \log (a+b \cosh (x))}{\left(a^2-b^2\right)^2}-\frac{\text{csch}^2(x) (a-b \cosh (x))}{2 \left(a^2-b^2\right)}+\frac{(2 a+b) \log (1-\cosh (x))}{4 (a+b)^2}+\frac{(2 a-b) \log (\cosh (x)+1)}{4 (a-b)^2}",1,"-((a - b*Cosh[x])*Csch[x]^2)/(2*(a^2 - b^2)) + ((2*a + b)*Log[1 - Cosh[x]])/(4*(a + b)^2) + ((2*a - b)*Log[1 + Cosh[x]])/(4*(a - b)^2) - (a^3*Log[a + b*Cosh[x]])/(a^2 - b^2)^2","A",4,3,13,0.2308,1,"{2721, 1647, 801}"
186,1,137,0,0.1957797,"\int \frac{\coth ^4(x)}{a+b \cosh (x)} \, dx","Int[Coth[x]^4/(a + b*Cosh[x]),x]","-\frac{a \coth ^3(x)}{3 \left(a^2-b^2\right)}-\frac{a^3 \coth (x)}{\left(a^2-b^2\right)^2}+\frac{b \text{csch}^3(x)}{3 \left(a^2-b^2\right)}+\frac{a^2 b \text{csch}(x)}{\left(a^2-b^2\right)^2}+\frac{b \text{csch}(x)}{a^2-b^2}+\frac{2 a^4 \tanh ^{-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{a \coth ^3(x)}{3 \left(a^2-b^2\right)}-\frac{a^3 \coth (x)}{\left(a^2-b^2\right)^2}+\frac{b \text{csch}^3(x)}{3 \left(a^2-b^2\right)}+\frac{a^2 b \text{csch}(x)}{\left(a^2-b^2\right)^2}+\frac{b \text{csch}(x)}{a^2-b^2}+\frac{2 a^4 \tanh ^{-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^4*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/((a - b)^(5/2)*(a + b)^(5/2)) - (a^3*Coth[x])/(a^2 - b^2)^2 - (a*Coth[x]^3)/(3*(a^2 - b^2)) + (a^2*b*Csch[x])/(a^2 - b^2)^2 + (b*Csch[x])/(a^2 - b^2) + (b*Csch[x]^3)/(3*(a^2 - b^2))","A",12,8,13,0.6154,1,"{2727, 2607, 30, 2606, 3767, 8, 2659, 208}"
187,1,46,0,0.0928183,"\int \frac{\tanh ^6(x)}{a+a \cosh (x)} \, dx","Int[Tanh[x]^6/(a + a*Cosh[x]),x]","-\frac{\tanh ^5(x)}{5 a}+\frac{3 \tan ^{-1}(\sinh (x))}{8 a}-\frac{\tanh ^3(x) \text{sech}(x)}{4 a}-\frac{3 \tanh (x) \text{sech}(x)}{8 a}","-\frac{\tanh ^5(x)}{5 a}+\frac{3 \tan ^{-1}(\sinh (x))}{8 a}-\frac{\tanh ^3(x) \text{sech}(x)}{4 a}-\frac{3 \tanh (x) \text{sech}(x)}{8 a}",1,"(3*ArcTan[Sinh[x]])/(8*a) - (3*Sech[x]*Tanh[x])/(8*a) - (Sech[x]*Tanh[x]^3)/(4*a) - Tanh[x]^5/(5*a)","A",6,5,13,0.3846,1,"{2706, 2607, 30, 2611, 3770}"
188,1,30,0,0.0858699,"\int \frac{\tanh ^5(x)}{a+a \cosh (x)} \, dx","Int[Tanh[x]^5/(a + a*Cosh[x]),x]","-\frac{\tanh ^4(x)}{4 a}+\frac{\text{sech}^3(x)}{3 a}-\frac{\text{sech}(x)}{a}","-\frac{\tanh ^4(x)}{4 a}+\frac{\text{sech}^3(x)}{3 a}-\frac{\text{sech}(x)}{a}",1,"-(Sech[x]/a) + Sech[x]^3/(3*a) - Tanh[x]^4/(4*a)","A",5,4,13,0.3077,1,"{2706, 2607, 30, 2606}"
189,1,33,0,0.0797613,"\int \frac{\tanh ^4(x)}{a+a \cosh (x)} \, dx","Int[Tanh[x]^4/(a + a*Cosh[x]),x]","-\frac{\tanh ^3(x)}{3 a}+\frac{\tan ^{-1}(\sinh (x))}{2 a}-\frac{\tanh (x) \text{sech}(x)}{2 a}","-\frac{\tanh ^3(x)}{3 a}+\frac{\tan ^{-1}(\sinh (x))}{2 a}-\frac{\tanh (x) \text{sech}(x)}{2 a}",1,"ArcTan[Sinh[x]]/(2*a) - (Sech[x]*Tanh[x])/(2*a) - Tanh[x]^3/(3*a)","A",5,5,13,0.3846,1,"{2706, 2607, 30, 2611, 3770}"
190,1,19,0,0.0659567,"\int \frac{\tanh ^3(x)}{a+a \cosh (x)} \, dx","Int[Tanh[x]^3/(a + a*Cosh[x]),x]","\frac{\text{sech}^2(x)}{2 a}-\frac{\text{sech}(x)}{a}","\frac{\text{sech}^2(x)}{2 a}-\frac{\text{sech}(x)}{a}",1,"-(Sech[x]/a) + Sech[x]^2/(2*a)","A",5,4,13,0.3077,1,"{2706, 2606, 30, 8}"
191,1,15,0,0.0488648,"\int \frac{\tanh ^2(x)}{a+a \cosh (x)} \, dx","Int[Tanh[x]^2/(a + a*Cosh[x]),x]","\frac{\tan ^{-1}(\sinh (x))}{a}-\frac{\tanh (x)}{a}","\frac{\tan ^{-1}(\sinh (x))}{a}-\frac{\tanh (x)}{a}",1,"ArcTan[Sinh[x]]/a - Tanh[x]/a","A",4,4,13,0.3077,1,"{2706, 3767, 8, 3770}"
192,1,18,0,0.0399798,"\int \frac{\tanh (x)}{a+a \cosh (x)} \, dx","Int[Tanh[x]/(a + a*Cosh[x]),x]","\frac{\log (\cosh (x))}{a}-\frac{\log (\cosh (x)+1)}{a}","\frac{\log (\cosh (x))}{a}-\frac{\log (\cosh (x)+1)}{a}",1,"Log[Cosh[x]]/a - Log[1 + Cosh[x]]/a","A",4,4,11,0.3636,1,"{2707, 36, 29, 31}"
193,1,33,0,0.0651714,"\int \frac{\coth (x)}{a+a \cosh (x)} \, dx","Int[Coth[x]/(a + a*Cosh[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",5,5,11,0.4545,1,"{2706, 2606, 30, 2611, 3770}"
194,1,30,0,0.0785009,"\int \frac{\coth ^2(x)}{a+a \cosh (x)} \, dx","Int[Coth[x]^2/(a + a*Cosh[x]),x]","\frac{\coth ^3(x)}{3 a}-\frac{\text{csch}^3(x)}{3 a}-\frac{\text{csch}(x)}{a}","\frac{\coth ^3(x)}{3 a}-\frac{\text{csch}^3(x)}{3 a}-\frac{\text{csch}(x)}{a}",1,"Coth[x]^3/(3*a) - Csch[x]/a - Csch[x]^3/(3*a)","A",5,4,13,0.3077,1,"{2706, 2607, 30, 2606}"
195,1,46,0,0.1068647,"\int \frac{\coth ^3(x)}{a+a \cosh (x)} \, dx","Int[Coth[x]^3/(a + a*Cosh[x]),x]","\frac{\coth ^4(x)}{4 a}-\frac{3 \tanh ^{-1}(\cosh (x))}{8 a}-\frac{\coth ^3(x) \text{csch}(x)}{4 a}-\frac{3 \coth (x) \text{csch}(x)}{8 a}","\frac{\coth ^4(x)}{4 a}-\frac{3 \tanh ^{-1}(\cosh (x))}{8 a}-\frac{\coth ^3(x) \text{csch}(x)}{4 a}-\frac{3 \coth (x) \text{csch}(x)}{8 a}",1,"(-3*ArcTanh[Cosh[x]])/(8*a) + Coth[x]^4/(4*a) - (3*Coth[x]*Csch[x])/(8*a) - (Coth[x]^3*Csch[x])/(4*a)","A",6,5,13,0.3846,1,"{2706, 2607, 30, 2611, 3770}"
196,1,41,0,0.0807787,"\int \frac{\coth ^4(x)}{a+a \cosh (x)} \, dx","Int[Coth[x]^4/(a + a*Cosh[x]),x]","\frac{\coth ^5(x)}{5 a}-\frac{\text{csch}^5(x)}{5 a}-\frac{2 \text{csch}^3(x)}{3 a}-\frac{\text{csch}(x)}{a}","\frac{\coth ^5(x)}{5 a}-\frac{\text{csch}^5(x)}{5 a}-\frac{2 \text{csch}^3(x)}{3 a}-\frac{\text{csch}(x)}{a}",1,"Coth[x]^5/(5*a) - Csch[x]/a - (2*Csch[x]^3)/(3*a) - Csch[x]^5/(5*a)","A",6,5,13,0.3846,1,"{2706, 2607, 30, 2606, 194}"
197,1,37,0,0.0626052,"\int \sqrt{a+b \cosh (x)} \tanh (x) \, dx","Int[Sqrt[a + b*Cosh[x]]*Tanh[x],x]","2 \sqrt{a+b \cosh (x)}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \cosh (x)}}{\sqrt{a}}\right)","2 \sqrt{a+b \cosh (x)}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \cosh (x)}}{\sqrt{a}}\right)",1,"-2*Sqrt[a]*ArcTanh[Sqrt[a + b*Cosh[x]]/Sqrt[a]] + 2*Sqrt[a + b*Cosh[x]]","A",4,4,13,0.3077,1,"{2721, 50, 63, 207}"
198,1,24,0,0.0570442,"\int \frac{\tanh (x)}{\sqrt{a+b \cosh (x)}} \, dx","Int[Tanh[x]/Sqrt[a + b*Cosh[x]],x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \cosh (x)}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \cosh (x)}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(-2*ArcTanh[Sqrt[a + b*Cosh[x]]/Sqrt[a]])/Sqrt[a]","A",3,3,13,0.2308,1,"{2721, 63, 207}"
199,1,56,0,0.1277994,"\int \frac{A+B \sinh (x)}{a+b \cosh (x)} \, dx","Int[(A + B*Sinh[x])/(a + b*Cosh[x]),x]","\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{\sqrt{a-b} \sqrt{a+b}}+\frac{B \log (a+b \cosh (x))}{b}","\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{\sqrt{a-b} \sqrt{a+b}}+\frac{B \log (a+b \cosh (x))}{b}",1,"(2*A*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(Sqrt[a - b]*Sqrt[a + b]) + (B*Log[a + b*Cosh[x]])/b","A",6,5,15,0.3333,1,"{4401, 2659, 208, 2668, 31}"
200,1,18,0,0.0765717,"\int \frac{A+B \sinh (x)}{1+\cosh (x)} \, dx","Int[(A + B*Sinh[x])/(1 + Cosh[x]),x]","\frac{A \sinh (x)}{\cosh (x)+1}+B \log (\cosh (x)+1)","\frac{A \sinh (x)}{\cosh (x)+1}+B \log (\cosh (x)+1)",1,"B*Log[1 + Cosh[x]] + (A*Sinh[x])/(1 + Cosh[x])","A",5,4,13,0.3077,1,"{4401, 2648, 2667, 31}"
201,1,24,0,0.0859135,"\int \frac{A+B \sinh (x)}{1-\cosh (x)} \, dx","Int[(A + B*Sinh[x])/(1 - Cosh[x]),x]","-\frac{A \sinh (x)}{1-\cosh (x)}-B \log (1-\cosh (x))","-\frac{A \sinh (x)}{1-\cosh (x)}-B \log (1-\cosh (x))",1,"-(B*Log[1 - Cosh[x]]) - (A*Sinh[x])/(1 - Cosh[x])","A",5,4,15,0.2667,1,"{4401, 2648, 2667, 31}"
202,1,65,0,0.1479946,"\int \frac{A+B \tanh (x)}{a+b \cosh (x)} \, dx","Int[(A + B*Tanh[x])/(a + b*Cosh[x]),x]","\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{\sqrt{a-b} \sqrt{a+b}}-\frac{B \log (a+b \cosh (x))}{a}+\frac{B \log (\cosh (x))}{a}","\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{\sqrt{a-b} \sqrt{a+b}}-\frac{B \log (a+b \cosh (x))}{a}+\frac{B \log (\cosh (x))}{a}",1,"(2*A*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(Sqrt[a - b]*Sqrt[a + b]) + (B*Log[Cosh[x]])/a - (B*Log[a + b*Cosh[x]])/a","A",8,7,15,0.4667,1,"{4401, 2659, 208, 2721, 36, 29, 31}"
203,1,100,0,0.1663084,"\int \frac{A+B \coth (x)}{a+b \cosh (x)} \, dx","Int[(A + B*Coth[x])/(a + b*Cosh[x]),x]","-\frac{a B \log (a+b \cosh (x))}{a^2-b^2}+\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{\sqrt{a-b} \sqrt{a+b}}+\frac{B \log (1-\cosh (x))}{2 (a+b)}+\frac{B \log (\cosh (x)+1)}{2 (a-b)}","-\frac{a B \log (a+b \cosh (x))}{a^2-b^2}+\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{\sqrt{a-b} \sqrt{a+b}}+\frac{B \log (1-\cosh (x))}{2 (a+b)}+\frac{B \log (\cosh (x)+1)}{2 (a-b)}",1,"(2*A*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(Sqrt[a - b]*Sqrt[a + b]) + (B*Log[1 - Cosh[x]])/(2*(a + b)) + (B*Log[1 + Cosh[x]])/(2*(a - b)) - (a*B*Log[a + b*Cosh[x]])/(a^2 - b^2)","A",7,5,15,0.3333,1,"{4401, 2659, 208, 2721, 801}"
204,1,62,0,0.1332071,"\int \frac{A+B \text{sech}(x)}{a+b \cosh (x)} \, dx","Int[(A + B*Sech[x])/(a + b*Cosh[x]),x]","\frac{2 (a A-b B) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a \sqrt{a-b} \sqrt{a+b}}+\frac{B \tan ^{-1}(\sinh (x))}{a}","\frac{2 (a A-b B) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{a \sqrt{a-b} \sqrt{a+b}}+\frac{B \tan ^{-1}(\sinh (x))}{a}",1,"(B*ArcTan[Sinh[x]])/a + (2*(a*A - b*B)*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(a*Sqrt[a - b]*Sqrt[a + b])","A",5,5,15,0.3333,1,"{2828, 3001, 3770, 2659, 208}"
205,1,99,0,0.3050511,"\int \frac{A+B \text{csch}(x)}{a+b \cosh (x)} \, dx","Int[(A + B*Csch[x])/(a + b*Cosh[x]),x]","\frac{b B \log (a+b \cosh (x))}{a^2-b^2}+\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{\sqrt{a-b} \sqrt{a+b}}+\frac{B \log (1-\cosh (x))}{2 (a+b)}-\frac{B \log (\cosh (x)+1)}{2 (a-b)}","\frac{b B \log (a+b \cosh (x))}{a^2-b^2}+\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{\sqrt{a-b} \sqrt{a+b}}+\frac{B \log (1-\cosh (x))}{2 (a+b)}-\frac{B \log (\cosh (x)+1)}{2 (a-b)}",1,"(2*A*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(Sqrt[a - b]*Sqrt[a + b]) + (B*Log[1 - Cosh[x]])/(2*(a + b)) - (B*Log[1 + Cosh[x]])/(2*(a - b)) + (b*B*Log[a + b*Cosh[x]])/(a^2 - b^2)","A",11,8,15,0.5333,1,"{4225, 4401, 2659, 208, 2668, 706, 31, 633}"
206,1,86,0,0.1539646,"\int \frac{A+B \cosh (d+e x)+C \sinh (d+e x)}{a+b \cosh (d+e x)} \, dx","Int[(A + B*Cosh[d + e*x] + C*Sinh[d + e*x])/(a + b*Cosh[d + e*x]),x]","\frac{2 (A b-a B) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{a+b}}\right)}{b e \sqrt{a-b} \sqrt{a+b}}+\frac{C \log (a+b \cosh (d+e x))}{b e}+\frac{B x}{b}","\frac{2 (A b-a B) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{a+b}}\right)}{b e \sqrt{a-b} \sqrt{a+b}}+\frac{C \log (a+b \cosh (d+e x))}{b e}+\frac{B x}{b}",1,"(B*x)/b + (2*(A*b - a*B)*ArcTanh[(Sqrt[a - b]*Tanh[(d + e*x)/2])/Sqrt[a + b]])/(Sqrt[a - b]*b*Sqrt[a + b]*e) + (C*Log[a + b*Cosh[d + e*x]])/(b*e)","A",6,6,31,0.1935,1,"{4377, 2735, 2659, 205, 2668, 31}"
207,1,121,0,0.1761729,"\int \frac{A+B \cosh (d+e x)+C \sinh (d+e x)}{(a+b \cosh (d+e x))^2} \, dx","Int[(A + B*Cosh[d + e*x] + C*Sinh[d + e*x])/(a + b*Cosh[d + e*x])^2,x]","-\frac{(A b-a B) \sinh (d+e x)}{e \left(a^2-b^2\right) (a+b \cosh (d+e x))}+\frac{2 (a A-b B) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{a+b}}\right)}{e (a-b)^{3/2} (a+b)^{3/2}}-\frac{C}{b e (a+b \cosh (d+e x))}","-\frac{(A b-a B) \sinh (d+e x)}{e \left(a^2-b^2\right) (a+b \cosh (d+e x))}+\frac{2 (a A-b B) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{a+b}}\right)}{e (a-b)^{3/2} (a+b)^{3/2}}-\frac{C}{b e (a+b \cosh (d+e x))}",1,"(2*(a*A - b*B)*ArcTanh[(Sqrt[a - b]*Tanh[(d + e*x)/2])/Sqrt[a + b]])/((a - b)^(3/2)*(a + b)^(3/2)*e) - C/(b*e*(a + b*Cosh[d + e*x])) - ((A*b - a*B)*Sinh[d + e*x])/((a^2 - b^2)*e*(a + b*Cosh[d + e*x]))","A",7,7,31,0.2258,1,"{4377, 2754, 12, 2659, 205, 2668, 32}"
208,1,187,0,0.2641406,"\int \frac{A+B \cosh (d+e x)+C \sinh (d+e x)}{(a+b \cosh (d+e x))^3} \, dx","Int[(A + B*Cosh[d + e*x] + C*Sinh[d + e*x])/(a + b*Cosh[d + e*x])^3,x]","\frac{\left(2 a^2 A-3 a b B+A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{a+b}}\right)}{e (a-b)^{5/2} (a+b)^{5/2}}-\frac{\left(a^2 (-B)+3 a A b-2 b^2 B\right) \sinh (d+e x)}{2 e \left(a^2-b^2\right)^2 (a+b \cosh (d+e x))}-\frac{(A b-a B) \sinh (d+e x)}{2 e \left(a^2-b^2\right) (a+b \cosh (d+e x))^2}-\frac{C}{2 b e (a+b \cosh (d+e x))^2}","\frac{\left(2 a^2 A-3 a b B+A b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{a+b}}\right)}{e (a-b)^{5/2} (a+b)^{5/2}}-\frac{\left(a^2 (-B)+3 a A b-2 b^2 B\right) \sinh (d+e x)}{2 e \left(a^2-b^2\right)^2 (a+b \cosh (d+e x))}-\frac{(A b-a B) \sinh (d+e x)}{2 e \left(a^2-b^2\right) (a+b \cosh (d+e x))^2}-\frac{C}{2 b e (a+b \cosh (d+e x))^2}",1,"((2*a^2*A + A*b^2 - 3*a*b*B)*ArcTanh[(Sqrt[a - b]*Tanh[(d + e*x)/2])/Sqrt[a + b]])/((a - b)^(5/2)*(a + b)^(5/2)*e) - C/(2*b*e*(a + b*Cosh[d + e*x])^2) - ((A*b - a*B)*Sinh[d + e*x])/(2*(a^2 - b^2)*e*(a + b*Cosh[d + e*x])^2) - ((3*a*A*b - a^2*B - 2*b^2*B)*Sinh[d + e*x])/(2*(a^2 - b^2)^2*e*(a + b*Cosh[d + e*x]))","A",8,7,31,0.2258,1,"{4377, 2754, 12, 2659, 205, 2668, 32}"
209,1,260,0,0.4479674,"\int \frac{A+B \cosh (d+e x)+C \sinh (d+e x)}{(a+b \cosh (d+e x))^4} \, dx","Int[(A + B*Cosh[d + e*x] + C*Sinh[d + e*x])/(a + b*Cosh[d + e*x])^4,x]","\frac{\left(2 a^3 A-4 a^2 b B+3 a A b^2-b^3 B\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{a+b}}\right)}{e (a-b)^{7/2} (a+b)^{7/2}}-\frac{\left(11 a^2 A b-2 a^3 B-13 a b^2 B+4 A b^3\right) \sinh (d+e x)}{6 e \left(a^2-b^2\right)^3 (a+b \cosh (d+e x))}-\frac{\left(-2 a^2 B+5 a A b-3 b^2 B\right) \sinh (d+e x)}{6 e \left(a^2-b^2\right)^2 (a+b \cosh (d+e x))^2}-\frac{(A b-a B) \sinh (d+e x)}{3 e \left(a^2-b^2\right) (a+b \cosh (d+e x))^3}-\frac{C}{3 b e (a+b \cosh (d+e x))^3}","\frac{\left(2 a^3 A-4 a^2 b B+3 a A b^2-b^3 B\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{a+b}}\right)}{e (a-b)^{7/2} (a+b)^{7/2}}-\frac{\left(11 a^2 A b-2 a^3 B-13 a b^2 B+4 A b^3\right) \sinh (d+e x)}{6 e \left(a^2-b^2\right)^3 (a+b \cosh (d+e x))}-\frac{\left(-2 a^2 B+5 a A b-3 b^2 B\right) \sinh (d+e x)}{6 e \left(a^2-b^2\right)^2 (a+b \cosh (d+e x))^2}-\frac{(A b-a B) \sinh (d+e x)}{3 e \left(a^2-b^2\right) (a+b \cosh (d+e x))^3}-\frac{C}{3 b e (a+b \cosh (d+e x))^3}",1,"((2*a^3*A + 3*a*A*b^2 - 4*a^2*b*B - b^3*B)*ArcTanh[(Sqrt[a - b]*Tanh[(d + e*x)/2])/Sqrt[a + b]])/((a - b)^(7/2)*(a + b)^(7/2)*e) - C/(3*b*e*(a + b*Cosh[d + e*x])^3) - ((A*b - a*B)*Sinh[d + e*x])/(3*(a^2 - b^2)*e*(a + b*Cosh[d + e*x])^3) - ((5*a*A*b - 2*a^2*B - 3*b^2*B)*Sinh[d + e*x])/(6*(a^2 - b^2)^2*e*(a + b*Cosh[d + e*x])^2) - ((11*a^2*A*b + 4*A*b^3 - 2*a^3*B - 13*a*b^2*B)*Sinh[d + e*x])/(6*(a^2 - b^2)^3*e*(a + b*Cosh[d + e*x]))","A",9,7,31,0.2258,1,"{4377, 2754, 12, 2659, 205, 2668, 32}"
210,1,191,0,0.3766043,"\int \frac{x}{a+b \cosh ^2(x)} \, dx","Int[x/(a + b*Cosh[x]^2),x]","\frac{\text{PolyLog}\left(2,-\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{\text{PolyLog}\left(2,-\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{x \log \left(\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}+1\right)}{2 \sqrt{a} \sqrt{a+b}}-\frac{x \log \left(\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}+1\right)}{2 \sqrt{a} \sqrt{a+b}}","\frac{\text{PolyLog}\left(2,-\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{\text{PolyLog}\left(2,-\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{x \log \left(\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}+1\right)}{2 \sqrt{a} \sqrt{a+b}}-\frac{x \log \left(\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}+1\right)}{2 \sqrt{a} \sqrt{a+b}}",1,"(x*Log[1 + (b*E^(2*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(2*Sqrt[a]*Sqrt[a + b]) - (x*Log[1 + (b*E^(2*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(2*Sqrt[a]*Sqrt[a + b]) + PolyLog[2, -((b*E^(2*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b]))]/(4*Sqrt[a]*Sqrt[a + b]) - PolyLog[2, -((b*E^(2*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b]))]/(4*Sqrt[a]*Sqrt[a + b])","A",9,6,12,0.5000,1,"{5630, 3320, 2264, 2190, 2279, 2391}"
211,1,291,0,0.5668054,"\int \frac{x^2}{a+b \cosh ^2(x)} \, dx","Int[x^2/(a + b*Cosh[x]^2),x]","\frac{x \text{PolyLog}\left(2,-\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}-\frac{x \text{PolyLog}\left(2,-\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}-\frac{\text{PolyLog}\left(3,-\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{\text{PolyLog}\left(3,-\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{x^2 \log \left(\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}+1\right)}{2 \sqrt{a} \sqrt{a+b}}-\frac{x^2 \log \left(\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}+1\right)}{2 \sqrt{a} \sqrt{a+b}}","\frac{x \text{PolyLog}\left(2,-\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}-\frac{x \text{PolyLog}\left(2,-\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}-\frac{\text{PolyLog}\left(3,-\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{\text{PolyLog}\left(3,-\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{x^2 \log \left(\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}+1\right)}{2 \sqrt{a} \sqrt{a+b}}-\frac{x^2 \log \left(\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}+1\right)}{2 \sqrt{a} \sqrt{a+b}}",1,"(x^2*Log[1 + (b*E^(2*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(2*Sqrt[a]*Sqrt[a + b]) - (x^2*Log[1 + (b*E^(2*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(2*Sqrt[a]*Sqrt[a + b]) + (x*PolyLog[2, -((b*E^(2*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b]))])/(2*Sqrt[a]*Sqrt[a + b]) - (x*PolyLog[2, -((b*E^(2*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b]))])/(2*Sqrt[a]*Sqrt[a + b]) - PolyLog[3, -((b*E^(2*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b]))]/(4*Sqrt[a]*Sqrt[a + b]) + PolyLog[3, -((b*E^(2*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b]))]/(4*Sqrt[a]*Sqrt[a + b])","A",11,7,14,0.5000,1,"{5630, 3320, 2264, 2190, 2531, 2282, 6589}"
212,1,391,0,0.5991441,"\int \frac{x^3}{a+b \cosh ^2(x)} \, dx","Int[x^3/(a + b*Cosh[x]^2),x]","\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{3 x \text{PolyLog}\left(3,-\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 x \text{PolyLog}\left(3,-\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 \text{PolyLog}\left(4,-\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 \sqrt{a} \sqrt{a+b}}-\frac{3 \text{PolyLog}\left(4,-\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 \sqrt{a} \sqrt{a+b}}+\frac{x^3 \log \left(\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}+1\right)}{2 \sqrt{a} \sqrt{a+b}}-\frac{x^3 \log \left(\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}+1\right)}{2 \sqrt{a} \sqrt{a+b}}","\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{3 x \text{PolyLog}\left(3,-\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 x \text{PolyLog}\left(3,-\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 \text{PolyLog}\left(4,-\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 \sqrt{a} \sqrt{a+b}}-\frac{3 \text{PolyLog}\left(4,-\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 \sqrt{a} \sqrt{a+b}}+\frac{x^3 \log \left(\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}+1\right)}{2 \sqrt{a} \sqrt{a+b}}-\frac{x^3 \log \left(\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}+1\right)}{2 \sqrt{a} \sqrt{a+b}}",1,"(x^3*Log[1 + (b*E^(2*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(2*Sqrt[a]*Sqrt[a + b]) - (x^3*Log[1 + (b*E^(2*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(2*Sqrt[a]*Sqrt[a + b]) + (3*x^2*PolyLog[2, -((b*E^(2*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b]))])/(4*Sqrt[a]*Sqrt[a + b]) - (3*x^2*PolyLog[2, -((b*E^(2*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b]))])/(4*Sqrt[a]*Sqrt[a + b]) - (3*x*PolyLog[3, -((b*E^(2*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b]))])/(4*Sqrt[a]*Sqrt[a + b]) + (3*x*PolyLog[3, -((b*E^(2*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b]))])/(4*Sqrt[a]*Sqrt[a + b]) + (3*PolyLog[4, -((b*E^(2*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b]))])/(8*Sqrt[a]*Sqrt[a + b]) - (3*PolyLog[4, -((b*E^(2*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b]))])/(8*Sqrt[a]*Sqrt[a + b])","A",13,8,14,0.5714,1,"{5630, 3320, 2264, 2190, 2531, 6609, 2282, 6589}"
213,1,58,0,0.1188761,"\int \frac{\cosh ^3\left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Int[Cosh[Sqrt[1 - a*x]/Sqrt[1 + a*x]]^3/(1 - a^2*x^2),x]","-\frac{3 \text{Chi}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)}{4 a}-\frac{\text{Chi}\left(\frac{3 \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{4 a}","-\frac{3 \text{Chi}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)}{4 a}-\frac{\text{Chi}\left(\frac{3 \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{4 a}",1,"(-3*CoshIntegral[Sqrt[1 - a*x]/Sqrt[1 + a*x]])/(4*a) - CoshIntegral[(3*Sqrt[1 - a*x])/Sqrt[1 + a*x]]/(4*a)","A",5,3,36,0.08333,1,"{6681, 3312, 3301}"
214,1,58,0,0.0813098,"\int \frac{\cosh ^2\left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Int[Cosh[Sqrt[1 - a*x]/Sqrt[1 + a*x]]^2/(1 - a^2*x^2),x]","-\frac{\text{Chi}\left(\frac{2 \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}-\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}","-\frac{\text{Chi}\left(\frac{2 \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}-\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}",1,"-CoshIntegral[(2*Sqrt[1 - a*x])/Sqrt[1 + a*x]]/(2*a) - Log[Sqrt[1 - a*x]/Sqrt[1 + a*x]]/(2*a)","A",4,3,36,0.08333,1,"{6681, 3312, 3301}"
215,1,26,0,0.038764,"\int \frac{\cosh \left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Int[Cosh[Sqrt[1 - a*x]/Sqrt[1 + a*x]]/(1 - a^2*x^2),x]","-\frac{\text{Chi}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}","-\frac{\text{Chi}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}",1,"-(CoshIntegral[Sqrt[1 - a*x]/Sqrt[1 + a*x]]/a)","A",2,2,34,0.05882,1,"{6681, 3301}"
216,0,0,0,0.0375866,"\int \frac{\text{sech}\left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Int[Sech[Sqrt[1 - a*x]/Sqrt[1 + a*x]]/(1 - a^2*x^2),x]","\int \frac{\text{sech}\left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","\text{Int}\left(\frac{\text{sech}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)}{(1-a x) (a x+1)},x\right)",0,"-(Defer[Subst][Defer[Int][Sech[x]/x, x], x, Sqrt[1 - a*x]/Sqrt[1 + a*x]]/a)","A",0,0,0,0,-1,"{}"
217,0,0,0,0.0798475,"\int \frac{\text{sech}^2\left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Int[Sech[Sqrt[1 - a*x]/Sqrt[1 + a*x]]^2/(1 - a^2*x^2),x]","\int \frac{\text{sech}^2\left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","\text{Int}\left(\frac{\text{sech}^2\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)}{(1-a x) (a x+1)},x\right)",0,"-(Defer[Subst][Defer[Int][Sech[x]^2/x, x], x, Sqrt[1 - a*x]/Sqrt[1 + a*x]]/a)","A",0,0,0,0,-1,"{}"
218,1,60,0,0.0568916,"\int \frac{x \sinh (x)}{(a+b \cosh (x))^2} \, dx","Int[(x*Sinh[x])/(a + b*Cosh[x])^2,x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b \sqrt{a-b} \sqrt{a+b}}-\frac{x}{b (a+b \cosh (x))}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b \sqrt{a-b} \sqrt{a+b}}-\frac{x}{b (a+b \cosh (x))}",1,"(2*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/(Sqrt[a - b]*b*Sqrt[a + b]) - x/(b*(a + b*Cosh[x]))","A",3,3,12,0.2500,1,"{5465, 2659, 208}"
219,1,87,0,0.0892023,"\int \frac{x \sinh (x)}{(a+b \cosh (x))^3} \, dx","Int[(x*Sinh[x])/(a + b*Cosh[x])^3,x]","-\frac{\sinh (x)}{2 \left(a^2-b^2\right) (a+b \cosh (x))}-\frac{x}{2 b (a+b \cosh (x))^2}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b (a-b)^{3/2} (a+b)^{3/2}}","-\frac{\sinh (x)}{2 \left(a^2-b^2\right) (a+b \cosh (x))}-\frac{x}{2 b (a+b \cosh (x))^2}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{b (a-b)^{3/2} (a+b)^{3/2}}",1,"(a*ArcTanh[(Sqrt[a - b]*Tanh[x/2])/Sqrt[a + b]])/((a - b)^(3/2)*b*(a + b)^(3/2)) - x/(2*b*(a + b*Cosh[x])^2) - Sinh[x]/(2*(a^2 - b^2)*(a + b*Cosh[x]))","A",5,5,12,0.4167,1,"{5465, 2664, 12, 2659, 208}"
220,1,47,0,0.4623277,"\int \frac{\left(2+\cosh ^2(a+b x)\right) \sinh (a+b x)}{x} \, dx","Int[((2 + Cosh[a + b*x]^2)*Sinh[a + b*x])/x,x]","\frac{9}{4} \sinh (a) \text{Chi}(b x)+\frac{1}{4} \sinh (3 a) \text{Chi}(3 b x)+\frac{9}{4} \cosh (a) \text{Shi}(b x)+\frac{1}{4} \cosh (3 a) \text{Shi}(3 b x)","\frac{9}{4} \sinh (a) \text{Chi}(b x)+\frac{1}{4} \sinh (3 a) \text{Chi}(3 b x)+\frac{9}{4} \cosh (a) \text{Shi}(b x)+\frac{1}{4} \cosh (3 a) \text{Shi}(3 b x)",1,"(9*CoshIntegral[b*x]*Sinh[a])/4 + (CoshIntegral[3*b*x]*Sinh[3*a])/4 + (9*Cosh[a]*SinhIntegral[b*x])/4 + (Cosh[3*a]*SinhIntegral[3*b*x])/4","A",13,5,20,0.2500,1,"{6742, 3303, 3298, 3301, 5448}"
221,0,0,0,0.0381827,"\int \frac{x^m \sinh (c+d x)}{a+b \cosh (c+d x)} \, dx","Int[(x^m*Sinh[c + d*x])/(a + b*Cosh[c + d*x]),x]","\int \frac{x^m \sinh (c+d x)}{a+b \cosh (c+d x)} \, dx","\text{Int}\left(\frac{x^m \sinh (c+d x)}{a+b \cosh (c+d x)},x\right)",0,"Defer[Int][(x^m*Sinh[c + d*x])/(a + b*Cosh[c + d*x]), x]","A",0,0,0,0,-1,"{}"
222,1,327,0,0.4794926,"\int \frac{x^3 \sinh (c+d x)}{a+b \cosh (c+d x)} \, dx","Int[(x^3*Sinh[c + d*x])/(a + b*Cosh[c + d*x]),x]","\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}+\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b d^2}-\frac{6 x \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^3}-\frac{6 x \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b d^3}+\frac{6 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^4}+\frac{6 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b d^4}+\frac{x^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b d}+\frac{x^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b d}-\frac{x^4}{4 b}","\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}+\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b d^2}-\frac{6 x \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^3}-\frac{6 x \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b d^3}+\frac{6 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^4}+\frac{6 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b d^4}+\frac{x^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b d}+\frac{x^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b d}-\frac{x^4}{4 b}",1,"-x^4/(4*b) + (x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 - b^2])])/(b*d) + (x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 - b^2])])/(b*d) + (3*x^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b*d^2) + (3*x^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b*d^2) - (6*x*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b*d^3) - (6*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b*d^3) + (6*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b*d^4) + (6*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b*d^4)","A",11,6,22,0.2727,1,"{5562, 2190, 2531, 6609, 2282, 6589}"
223,1,245,0,0.3901857,"\int \frac{x^2 \sinh (c+d x)}{a+b \cosh (c+d x)} \, dx","Int[(x^2*Sinh[c + d*x])/(a + b*Cosh[c + d*x]),x]","\frac{2 x \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}+\frac{2 x \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b d^2}-\frac{2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^3}-\frac{2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b d^3}+\frac{x^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b d}+\frac{x^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b d}-\frac{x^3}{3 b}","\frac{2 x \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}+\frac{2 x \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b d^2}-\frac{2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^3}-\frac{2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b d^3}+\frac{x^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b d}+\frac{x^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b d}-\frac{x^3}{3 b}",1,"-x^3/(3*b) + (x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 - b^2])])/(b*d) + (x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 - b^2])])/(b*d) + (2*x*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b*d^2) + (2*x*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b*d^2) - (2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b*d^3) - (2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b*d^3)","A",9,5,22,0.2273,1,"{5562, 2190, 2531, 2282, 6589}"
224,1,161,0,0.2416702,"\int \frac{x \sinh (c+d x)}{a+b \cosh (c+d x)} \, dx","Int[(x*Sinh[c + d*x])/(a + b*Cosh[c + d*x]),x]","\frac{\text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}+\frac{\text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b d^2}+\frac{x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b d}+\frac{x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b d}-\frac{x^2}{2 b}","\frac{\text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}+\frac{\text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b d^2}+\frac{x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b d}+\frac{x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b d}-\frac{x^2}{2 b}",1,"-x^2/(2*b) + (x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 - b^2])])/(b*d) + (x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 - b^2])])/(b*d) + PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))]/(b*d^2) + PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))]/(b*d^2)","A",7,4,20,0.2000,1,"{5562, 2190, 2279, 2391}"
225,1,18,0,0.0318788,"\int \frac{\sinh (c+d x)}{a+b \cosh (c+d x)} \, dx","Int[Sinh[c + d*x]/(a + b*Cosh[c + d*x]),x]","\frac{\log (a+b \cosh (c+d x))}{b d}","\frac{\log (a+b \cosh (c+d x))}{b d}",1,"Log[a + b*Cosh[c + d*x]]/(b*d)","A",2,2,19,0.1053,1,"{2668, 31}"
226,0,0,0,0.0364959,"\int \frac{\sinh (c+d x)}{x (a+b \cosh (c+d x))} \, dx","Int[Sinh[c + d*x]/(x*(a + b*Cosh[c + d*x])),x]","\int \frac{\sinh (c+d x)}{x (a+b \cosh (c+d x))} \, dx","\text{Int}\left(\frac{\sinh (c+d x)}{x (a+b \cosh (c+d x))},x\right)",0,"Defer[Int][Sinh[c + d*x]/(x*(a + b*Cosh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
227,0,0,0,0.0608897,"\int \frac{x^m \sinh ^2(c+d x)}{a+b \cosh (c+d x)} \, dx","Int[(x^m*Sinh[c + d*x]^2)/(a + b*Cosh[c + d*x]),x]","\int \frac{x^m \sinh ^2(c+d x)}{a+b \cosh (c+d x)} \, dx","\text{Int}\left(\frac{x^m \sinh ^2(c+d x)}{a+b \cosh (c+d x)},x\right)",0,"Defer[Int][(x^m*Sinh[c + d*x]^2)/(a + b*Cosh[c + d*x]), x]","A",0,0,0,0,-1,"{}"
228,1,495,0,0.8385888,"\int \frac{x^3 \sinh ^2(c+d x)}{a+b \cosh (c+d x)} \, dx","Int[(x^3*Sinh[c + d*x]^2)/(a + b*Cosh[c + d*x]),x]","\frac{3 x^2 \sqrt{a^2-b^2} \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2}-\frac{3 x^2 \sqrt{a^2-b^2} \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2}-\frac{6 x \sqrt{a^2-b^2} \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^3}+\frac{6 x \sqrt{a^2-b^2} \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^3}+\frac{6 \sqrt{a^2-b^2} \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^4}-\frac{6 \sqrt{a^2-b^2} \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^4}+\frac{x^3 \sqrt{a^2-b^2} \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b^2 d}-\frac{x^3 \sqrt{a^2-b^2} \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b^2 d}-\frac{a x^4}{4 b^2}-\frac{3 x^2 \cosh (c+d x)}{b d^2}+\frac{6 x \sinh (c+d x)}{b d^3}-\frac{6 \cosh (c+d x)}{b d^4}+\frac{x^3 \sinh (c+d x)}{b d}","\frac{3 x^2 \sqrt{a^2-b^2} \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2}-\frac{3 x^2 \sqrt{a^2-b^2} \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2}-\frac{6 x \sqrt{a^2-b^2} \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^3}+\frac{6 x \sqrt{a^2-b^2} \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^3}+\frac{6 \sqrt{a^2-b^2} \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^4}-\frac{6 \sqrt{a^2-b^2} \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^4}+\frac{x^3 \sqrt{a^2-b^2} \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b^2 d}-\frac{x^3 \sqrt{a^2-b^2} \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b^2 d}-\frac{a x^4}{4 b^2}-\frac{3 x^2 \cosh (c+d x)}{b d^2}+\frac{6 x \sinh (c+d x)}{b d^3}-\frac{6 \cosh (c+d x)}{b d^4}+\frac{x^3 \sinh (c+d x)}{b d}",1,"-(a*x^4)/(4*b^2) - (6*Cosh[c + d*x])/(b*d^4) - (3*x^2*Cosh[c + d*x])/(b*d^2) + (Sqrt[a^2 - b^2]*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 - b^2])])/(b^2*d) - (Sqrt[a^2 - b^2]*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 - b^2])])/(b^2*d) + (3*Sqrt[a^2 - b^2]*x^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b^2*d^2) - (3*Sqrt[a^2 - b^2]*x^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b^2*d^2) - (6*Sqrt[a^2 - b^2]*x*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b^2*d^3) + (6*Sqrt[a^2 - b^2]*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b^2*d^3) + (6*Sqrt[a^2 - b^2]*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b^2*d^4) - (6*Sqrt[a^2 - b^2]*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b^2*d^4) + (6*x*Sinh[c + d*x])/(b*d^3) + (x^3*Sinh[c + d*x])/(b*d)","A",18,11,24,0.4583,1,"{5566, 30, 3296, 2638, 3320, 2264, 2190, 2531, 6609, 2282, 6589}"
229,1,370,0,0.7041182,"\int \frac{x^2 \sinh ^2(c+d x)}{a+b \cosh (c+d x)} \, dx","Int[(x^2*Sinh[c + d*x]^2)/(a + b*Cosh[c + d*x]),x]","\frac{2 x \sqrt{a^2-b^2} \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2}-\frac{2 x \sqrt{a^2-b^2} \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2}-\frac{2 \sqrt{a^2-b^2} \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^3}+\frac{2 \sqrt{a^2-b^2} \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^3}+\frac{x^2 \sqrt{a^2-b^2} \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b^2 d}-\frac{x^2 \sqrt{a^2-b^2} \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b^2 d}-\frac{a x^3}{3 b^2}+\frac{2 \sinh (c+d x)}{b d^3}-\frac{2 x \cosh (c+d x)}{b d^2}+\frac{x^2 \sinh (c+d x)}{b d}","\frac{2 x \sqrt{a^2-b^2} \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2}-\frac{2 x \sqrt{a^2-b^2} \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2}-\frac{2 \sqrt{a^2-b^2} \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^3}+\frac{2 \sqrt{a^2-b^2} \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^3}+\frac{x^2 \sqrt{a^2-b^2} \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b^2 d}-\frac{x^2 \sqrt{a^2-b^2} \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b^2 d}-\frac{a x^3}{3 b^2}+\frac{2 \sinh (c+d x)}{b d^3}-\frac{2 x \cosh (c+d x)}{b d^2}+\frac{x^2 \sinh (c+d x)}{b d}",1,"-(a*x^3)/(3*b^2) - (2*x*Cosh[c + d*x])/(b*d^2) + (Sqrt[a^2 - b^2]*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 - b^2])])/(b^2*d) - (Sqrt[a^2 - b^2]*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 - b^2])])/(b^2*d) + (2*Sqrt[a^2 - b^2]*x*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b^2*d^2) - (2*Sqrt[a^2 - b^2]*x*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b^2*d^2) - (2*Sqrt[a^2 - b^2]*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b^2*d^3) + (2*Sqrt[a^2 - b^2]*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b^2*d^3) + (2*Sinh[c + d*x])/(b*d^3) + (x^2*Sinh[c + d*x])/(b*d)","A",15,10,24,0.4167,1,"{5566, 30, 3296, 2637, 3320, 2264, 2190, 2531, 2282, 6589}"
230,1,244,0,0.4175872,"\int \frac{x \sinh ^2(c+d x)}{a+b \cosh (c+d x)} \, dx","Int[(x*Sinh[c + d*x]^2)/(a + b*Cosh[c + d*x]),x]","\frac{\sqrt{a^2-b^2} \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2}-\frac{\sqrt{a^2-b^2} \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2}+\frac{x \sqrt{a^2-b^2} \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b^2 d}-\frac{x \sqrt{a^2-b^2} \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b^2 d}-\frac{a x^2}{2 b^2}-\frac{\cosh (c+d x)}{b d^2}+\frac{x \sinh (c+d x)}{b d}","\frac{\sqrt{a^2-b^2} \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2}-\frac{\sqrt{a^2-b^2} \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2}+\frac{x \sqrt{a^2-b^2} \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b^2 d}-\frac{x \sqrt{a^2-b^2} \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b^2 d}-\frac{a x^2}{2 b^2}-\frac{\cosh (c+d x)}{b d^2}+\frac{x \sinh (c+d x)}{b d}",1,"-(a*x^2)/(2*b^2) - Cosh[c + d*x]/(b*d^2) + (Sqrt[a^2 - b^2]*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 - b^2])])/(b^2*d) - (Sqrt[a^2 - b^2]*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 - b^2])])/(b^2*d) + (Sqrt[a^2 - b^2]*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b^2*d^2) - (Sqrt[a^2 - b^2]*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b^2*d^2) + (x*Sinh[c + d*x])/(b*d)","A",12,9,22,0.4091,1,"{5566, 30, 3296, 2638, 3320, 2264, 2190, 2279, 2391}"
231,1,73,0,0.1234181,"\int \frac{\sinh ^2(c+d x)}{a+b \cosh (c+d x)} \, dx","Int[Sinh[c + d*x]^2/(a + b*Cosh[c + d*x]),x]","\frac{2 \sqrt{a-b} \sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a+b}}\right)}{b^2 d}-\frac{a x}{b^2}+\frac{\sinh (c+d x)}{b d}","\frac{2 \sqrt{a-b} \sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a+b}}\right)}{b^2 d}-\frac{a x}{b^2}+\frac{\sinh (c+d x)}{b d}",1,"-((a*x)/b^2) + (2*Sqrt[a - b]*Sqrt[a + b]*ArcTanh[(Sqrt[a - b]*Tanh[(c + d*x)/2])/Sqrt[a + b]])/(b^2*d) + Sinh[c + d*x]/(b*d)","A",4,4,21,0.1905,1,"{2695, 2735, 2659, 205}"
232,0,0,0,0.0569911,"\int \frac{\sinh ^2(c+d x)}{x (a+b \cosh (c+d x))} \, dx","Int[Sinh[c + d*x]^2/(x*(a + b*Cosh[c + d*x])),x]","\int \frac{\sinh ^2(c+d x)}{x (a+b \cosh (c+d x))} \, dx","\text{Int}\left(\frac{\sinh ^2(c+d x)}{x (a+b \cosh (c+d x))},x\right)",0,"Defer[Int][Sinh[c + d*x]^2/(x*(a + b*Cosh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
233,0,0,0,0.0637631,"\int \frac{x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx","Int[(x^m*Sinh[c + d*x]^3)/(a + b*Cosh[c + d*x]),x]","\int \frac{x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx","\text{Int}\left(\frac{x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)},x\right)",0,"Defer[Int][(x^m*Sinh[c + d*x]^3)/(a + b*Cosh[c + d*x]), x]","A",0,0,0,0,-1,"{}"
234,1,586,0,0.6863921,"\int \frac{x^3 \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx","Int[(x^3*Sinh[c + d*x]^3)/(a + b*Cosh[c + d*x]),x]","\frac{3 x^2 \left(a^2-b^2\right) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^2}+\frac{3 x^2 \left(a^2-b^2\right) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^2}-\frac{6 x \left(a^2-b^2\right) \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^3}-\frac{6 x \left(a^2-b^2\right) \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^3}+\frac{6 \left(a^2-b^2\right) \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^4}+\frac{6 \left(a^2-b^2\right) \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^4}+\frac{x^3 \left(a^2-b^2\right) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b^3 d}+\frac{x^3 \left(a^2-b^2\right) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b^3 d}-\frac{x^4 \left(a^2-b^2\right)}{4 b^3}+\frac{3 a x^2 \sinh (c+d x)}{b^2 d^2}+\frac{6 a \sinh (c+d x)}{b^2 d^4}-\frac{6 a x \cosh (c+d x)}{b^2 d^3}-\frac{a x^3 \cosh (c+d x)}{b^2 d}-\frac{3 x^2 \sinh (c+d x) \cosh (c+d x)}{4 b d^2}+\frac{3 x \sinh ^2(c+d x)}{4 b d^3}-\frac{3 \sinh (c+d x) \cosh (c+d x)}{8 b d^4}+\frac{x^3 \sinh ^2(c+d x)}{2 b d}+\frac{3 x}{8 b d^3}+\frac{x^3}{4 b d}","\frac{3 x^2 \left(a^2-b^2\right) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^2}+\frac{3 x^2 \left(a^2-b^2\right) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^2}-\frac{6 x \left(a^2-b^2\right) \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^3}-\frac{6 x \left(a^2-b^2\right) \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^3}+\frac{6 \left(a^2-b^2\right) \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^4}+\frac{6 \left(a^2-b^2\right) \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^4}+\frac{x^3 \left(a^2-b^2\right) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b^3 d}+\frac{x^3 \left(a^2-b^2\right) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b^3 d}-\frac{x^4 \left(a^2-b^2\right)}{4 b^3}+\frac{3 a x^2 \sinh (c+d x)}{b^2 d^2}+\frac{6 a \sinh (c+d x)}{b^2 d^4}-\frac{6 a x \cosh (c+d x)}{b^2 d^3}-\frac{a x^3 \cosh (c+d x)}{b^2 d}-\frac{3 x^2 \sinh (c+d x) \cosh (c+d x)}{4 b d^2}+\frac{3 x \sinh ^2(c+d x)}{4 b d^3}-\frac{3 \sinh (c+d x) \cosh (c+d x)}{8 b d^4}+\frac{x^3 \sinh ^2(c+d x)}{2 b d}+\frac{3 x}{8 b d^3}+\frac{x^3}{4 b d}",1,"(3*x)/(8*b*d^3) + x^3/(4*b*d) - ((a^2 - b^2)*x^4)/(4*b^3) - (6*a*x*Cosh[c + d*x])/(b^2*d^3) - (a*x^3*Cosh[c + d*x])/(b^2*d) + ((a^2 - b^2)*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 - b^2])])/(b^3*d) + ((a^2 - b^2)*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 - b^2])])/(b^3*d) + (3*(a^2 - b^2)*x^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b^3*d^2) + (3*(a^2 - b^2)*x^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b^3*d^2) - (6*(a^2 - b^2)*x*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b^3*d^3) - (6*(a^2 - b^2)*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b^3*d^3) + (6*(a^2 - b^2)*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b^3*d^4) + (6*(a^2 - b^2)*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b^3*d^4) + (6*a*Sinh[c + d*x])/(b^2*d^4) + (3*a*x^2*Sinh[c + d*x])/(b^2*d^2) - (3*Cosh[c + d*x]*Sinh[c + d*x])/(8*b*d^4) - (3*x^2*Cosh[c + d*x]*Sinh[c + d*x])/(4*b*d^2) + (3*x*Sinh[c + d*x]^2)/(4*b*d^3) + (x^3*Sinh[c + d*x]^2)/(2*b*d)","A",21,14,24,0.5833,1,"{5566, 3296, 2637, 5372, 3311, 30, 2635, 8, 5562, 2190, 2531, 6609, 2282, 6589}"
235,1,432,0,0.5632868,"\int \frac{x^2 \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx","Int[(x^2*Sinh[c + d*x]^3)/(a + b*Cosh[c + d*x]),x]","\frac{2 x \left(a^2-b^2\right) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^2}+\frac{2 x \left(a^2-b^2\right) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^2}-\frac{2 \left(a^2-b^2\right) \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^3}-\frac{2 \left(a^2-b^2\right) \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^3}+\frac{x^2 \left(a^2-b^2\right) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b^3 d}+\frac{x^2 \left(a^2-b^2\right) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b^3 d}-\frac{x^3 \left(a^2-b^2\right)}{3 b^3}+\frac{2 a x \sinh (c+d x)}{b^2 d^2}-\frac{2 a \cosh (c+d x)}{b^2 d^3}-\frac{a x^2 \cosh (c+d x)}{b^2 d}+\frac{\sinh ^2(c+d x)}{4 b d^3}-\frac{x \sinh (c+d x) \cosh (c+d x)}{2 b d^2}+\frac{x^2 \sinh ^2(c+d x)}{2 b d}+\frac{x^2}{4 b d}","\frac{2 x \left(a^2-b^2\right) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^2}+\frac{2 x \left(a^2-b^2\right) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^2}-\frac{2 \left(a^2-b^2\right) \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^3}-\frac{2 \left(a^2-b^2\right) \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^3}+\frac{x^2 \left(a^2-b^2\right) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b^3 d}+\frac{x^2 \left(a^2-b^2\right) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b^3 d}-\frac{x^3 \left(a^2-b^2\right)}{3 b^3}+\frac{2 a x \sinh (c+d x)}{b^2 d^2}-\frac{2 a \cosh (c+d x)}{b^2 d^3}-\frac{a x^2 \cosh (c+d x)}{b^2 d}+\frac{\sinh ^2(c+d x)}{4 b d^3}-\frac{x \sinh (c+d x) \cosh (c+d x)}{2 b d^2}+\frac{x^2 \sinh ^2(c+d x)}{2 b d}+\frac{x^2}{4 b d}",1,"x^2/(4*b*d) - ((a^2 - b^2)*x^3)/(3*b^3) - (2*a*Cosh[c + d*x])/(b^2*d^3) - (a*x^2*Cosh[c + d*x])/(b^2*d) + ((a^2 - b^2)*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 - b^2])])/(b^3*d) + ((a^2 - b^2)*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 - b^2])])/(b^3*d) + (2*(a^2 - b^2)*x*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b^3*d^2) + (2*(a^2 - b^2)*x*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b^3*d^2) - (2*(a^2 - b^2)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b^3*d^3) - (2*(a^2 - b^2)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b^3*d^3) + (2*a*x*Sinh[c + d*x])/(b^2*d^2) - (x*Cosh[c + d*x]*Sinh[c + d*x])/(2*b*d^2) + Sinh[c + d*x]^2/(4*b*d^3) + (x^2*Sinh[c + d*x]^2)/(2*b*d)","A",16,11,24,0.4583,1,"{5566, 3296, 2638, 5372, 3310, 30, 5562, 2190, 2531, 2282, 6589}"
236,1,288,0,0.336127,"\int \frac{x \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx","Int[(x*Sinh[c + d*x]^3)/(a + b*Cosh[c + d*x]),x]","\frac{\left(a^2-b^2\right) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^2}+\frac{\left(a^2-b^2\right) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^2}+\frac{x \left(a^2-b^2\right) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b^3 d}+\frac{x \left(a^2-b^2\right) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b^3 d}-\frac{x^2 \left(a^2-b^2\right)}{2 b^3}+\frac{a \sinh (c+d x)}{b^2 d^2}-\frac{a x \cosh (c+d x)}{b^2 d}-\frac{\sinh (c+d x) \cosh (c+d x)}{4 b d^2}+\frac{x \sinh ^2(c+d x)}{2 b d}+\frac{x}{4 b d}","\frac{\left(a^2-b^2\right) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^2}+\frac{\left(a^2-b^2\right) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^2}+\frac{x \left(a^2-b^2\right) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)}{b^3 d}+\frac{x \left(a^2-b^2\right) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)}{b^3 d}-\frac{x^2 \left(a^2-b^2\right)}{2 b^3}+\frac{a \sinh (c+d x)}{b^2 d^2}-\frac{a x \cosh (c+d x)}{b^2 d}-\frac{\sinh (c+d x) \cosh (c+d x)}{4 b d^2}+\frac{x \sinh ^2(c+d x)}{2 b d}+\frac{x}{4 b d}",1,"x/(4*b*d) - ((a^2 - b^2)*x^2)/(2*b^3) - (a*x*Cosh[c + d*x])/(b^2*d) + ((a^2 - b^2)*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 - b^2])])/(b^3*d) + ((a^2 - b^2)*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 - b^2])])/(b^3*d) + ((a^2 - b^2)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 - b^2]))])/(b^3*d^2) + ((a^2 - b^2)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))])/(b^3*d^2) + (a*Sinh[c + d*x])/(b^2*d^2) - (Cosh[c + d*x]*Sinh[c + d*x])/(4*b*d^2) + (x*Sinh[c + d*x]^2)/(2*b*d)","A",13,10,22,0.4545,1,"{5566, 3296, 2637, 5372, 2635, 8, 5562, 2190, 2279, 2391}"
237,1,61,0,0.0727722,"\int \frac{\sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx","Int[Sinh[c + d*x]^3/(a + b*Cosh[c + d*x]),x]","\frac{\left(a^2-b^2\right) \log (a+b \cosh (c+d x))}{b^3 d}-\frac{a \cosh (c+d x)}{b^2 d}+\frac{\cosh ^2(c+d x)}{2 b d}","\frac{\left(a^2-b^2\right) \log (a+b \cosh (c+d x))}{b^3 d}-\frac{a \cosh (c+d x)}{b^2 d}+\frac{\cosh ^2(c+d x)}{2 b d}",1,"-((a*Cosh[c + d*x])/(b^2*d)) + Cosh[c + d*x]^2/(2*b*d) + ((a^2 - b^2)*Log[a + b*Cosh[c + d*x]])/(b^3*d)","A",3,2,21,0.09524,1,"{2668, 697}"
238,0,0,0,0.0550612,"\int \frac{\sinh ^3(c+d x)}{x (a+b \cosh (c+d x))} \, dx","Int[Sinh[c + d*x]^3/(x*(a + b*Cosh[c + d*x])),x]","\int \frac{\sinh ^3(c+d x)}{x (a+b \cosh (c+d x))} \, dx","\text{Int}\left(\frac{\sinh ^3(c+d x)}{x (a+b \cosh (c+d x))},x\right)",0,"Defer[Int][Sinh[c + d*x]^3/(x*(a + b*Cosh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
239,1,54,0,0.0119098,"\int \cosh \left(a+b \log \left(c x^n\right)\right) \, dx","Int[Cosh[a + b*Log[c*x^n]],x]","\frac{x \cosh \left(a+b \log \left(c x^n\right)\right)}{1-b^2 n^2}-\frac{b n x \sinh \left(a+b \log \left(c x^n\right)\right)}{1-b^2 n^2}","\frac{x \cosh \left(a+b \log \left(c x^n\right)\right)}{1-b^2 n^2}-\frac{b n x \sinh \left(a+b \log \left(c x^n\right)\right)}{1-b^2 n^2}",1,"(x*Cosh[a + b*Log[c*x^n]])/(1 - b^2*n^2) - (b*n*x*Sinh[a + b*Log[c*x^n]])/(1 - b^2*n^2)","A",1,1,11,0.09091,1,"{5518}"
240,1,88,0,0.0200897,"\int \cosh ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Cosh[a + b*Log[c*x^n]]^2,x]","\frac{x \cosh ^2\left(a+b \log \left(c x^n\right)\right)}{1-4 b^2 n^2}-\frac{2 b n x \sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{1-4 b^2 n^2}-\frac{2 b^2 n^2 x}{1-4 b^2 n^2}","\frac{x \cosh ^2\left(a+b \log \left(c x^n\right)\right)}{1-4 b^2 n^2}-\frac{2 b n x \sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{1-4 b^2 n^2}-\frac{2 b^2 n^2 x}{1-4 b^2 n^2}",1,"(-2*b^2*n^2*x)/(1 - 4*b^2*n^2) + (x*Cosh[a + b*Log[c*x^n]]^2)/(1 - 4*b^2*n^2) - (2*b*n*x*Cosh[a + b*Log[c*x^n]]*Sinh[a + b*Log[c*x^n]])/(1 - 4*b^2*n^2)","A",2,2,13,0.1538,1,"{5520, 8}"
241,1,149,0,0.0388181,"\int \cosh ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Cosh[a + b*Log[c*x^n]]^3,x]","\frac{6 b^3 n^3 x \sinh \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4-10 b^2 n^2+1}+\frac{x \cosh ^3\left(a+b \log \left(c x^n\right)\right)}{1-9 b^2 n^2}-\frac{6 b^2 n^2 x \cosh \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4-10 b^2 n^2+1}-\frac{3 b n x \sinh \left(a+b \log \left(c x^n\right)\right) \cosh ^2\left(a+b \log \left(c x^n\right)\right)}{1-9 b^2 n^2}","\frac{6 b^3 n^3 x \sinh \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4-10 b^2 n^2+1}+\frac{x \cosh ^3\left(a+b \log \left(c x^n\right)\right)}{1-9 b^2 n^2}-\frac{6 b^2 n^2 x \cosh \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4-10 b^2 n^2+1}-\frac{3 b n x \sinh \left(a+b \log \left(c x^n\right)\right) \cosh ^2\left(a+b \log \left(c x^n\right)\right)}{1-9 b^2 n^2}",1,"(-6*b^2*n^2*x*Cosh[a + b*Log[c*x^n]])/(1 - 10*b^2*n^2 + 9*b^4*n^4) + (x*Cosh[a + b*Log[c*x^n]]^3)/(1 - 9*b^2*n^2) + (6*b^3*n^3*x*Sinh[a + b*Log[c*x^n]])/(1 - 10*b^2*n^2 + 9*b^4*n^4) - (3*b*n*x*Cosh[a + b*Log[c*x^n]]^2*Sinh[a + b*Log[c*x^n]])/(1 - 9*b^2*n^2)","A",2,2,13,0.1538,1,"{5520, 5518}"
242,1,191,0,0.0509666,"\int \cosh ^4\left(a+b \log \left(c x^n\right)\right) \, dx","Int[Cosh[a + b*Log[c*x^n]]^4,x]","-\frac{12 b^2 n^2 x \cosh ^2\left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4-20 b^2 n^2+1}+\frac{x \cosh ^4\left(a+b \log \left(c x^n\right)\right)}{1-16 b^2 n^2}-\frac{4 b n x \sinh \left(a+b \log \left(c x^n\right)\right) \cosh ^3\left(a+b \log \left(c x^n\right)\right)}{1-16 b^2 n^2}+\frac{24 b^3 n^3 x \sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4-20 b^2 n^2+1}+\frac{24 b^4 n^4 x}{64 b^4 n^4-20 b^2 n^2+1}","-\frac{12 b^2 n^2 x \cosh ^2\left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4-20 b^2 n^2+1}+\frac{x \cosh ^4\left(a+b \log \left(c x^n\right)\right)}{1-16 b^2 n^2}-\frac{4 b n x \sinh \left(a+b \log \left(c x^n\right)\right) \cosh ^3\left(a+b \log \left(c x^n\right)\right)}{1-16 b^2 n^2}+\frac{24 b^3 n^3 x \sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4-20 b^2 n^2+1}+\frac{24 b^4 n^4 x}{64 b^4 n^4-20 b^2 n^2+1}",1,"(24*b^4*n^4*x)/(1 - 20*b^2*n^2 + 64*b^4*n^4) - (12*b^2*n^2*x*Cosh[a + b*Log[c*x^n]]^2)/(1 - 20*b^2*n^2 + 64*b^4*n^4) + (x*Cosh[a + b*Log[c*x^n]]^4)/(1 - 16*b^2*n^2) + (24*b^3*n^3*x*Cosh[a + b*Log[c*x^n]]*Sinh[a + b*Log[c*x^n]])/(1 - 20*b^2*n^2 + 64*b^4*n^4) - (4*b*n*x*Cosh[a + b*Log[c*x^n]]^3*Sinh[a + b*Log[c*x^n]])/(1 - 16*b^2*n^2)","A",3,2,13,0.1538,1,"{5520, 8}"
243,1,73,0,0.0225428,"\int x^m \cosh \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^m*Cosh[a + b*Log[c*x^n]],x]","\frac{(m+1) x^{m+1} \cosh \left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-b^2 n^2}-\frac{b n x^{m+1} \sinh \left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-b^2 n^2}","\frac{(m+1) x^{m+1} \cosh \left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-b^2 n^2}-\frac{b n x^{m+1} \sinh \left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-b^2 n^2}",1,"((1 + m)*x^(1 + m)*Cosh[a + b*Log[c*x^n]])/((1 + m)^2 - b^2*n^2) - (b*n*x^(1 + m)*Sinh[a + b*Log[c*x^n]])/((1 + m)^2 - b^2*n^2)","A",1,1,15,0.06667,1,"{5528}"
244,1,120,0,0.0481035,"\int x^m \cosh ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^m*Cosh[a + b*Log[c*x^n]]^2,x]","\frac{(m+1) x^{m+1} \cosh ^2\left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-4 b^2 n^2}-\frac{2 b n x^{m+1} \sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-4 b^2 n^2}-\frac{2 b^2 n^2 x^{m+1}}{(m+1) \left((m+1)^2-4 b^2 n^2\right)}","\frac{(m+1) x^{m+1} \cosh ^2\left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-4 b^2 n^2}-\frac{2 b n x^{m+1} \sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-4 b^2 n^2}-\frac{2 b^2 n^2 x^{m+1}}{(m+1) \left((m+1)^2-4 b^2 n^2\right)}",1,"(-2*b^2*n^2*x^(1 + m))/((1 + m)*((1 + m)^2 - 4*b^2*n^2)) + ((1 + m)*x^(1 + m)*Cosh[a + b*Log[c*x^n]]^2)/((1 + m)^2 - 4*b^2*n^2) - (2*b*n*x^(1 + m)*Cosh[a + b*Log[c*x^n]]*Sinh[a + b*Log[c*x^n]])/((1 + m)^2 - 4*b^2*n^2)","A",2,2,17,0.1176,1,"{5530, 30}"
245,1,197,0,0.0834603,"\int x^m \cosh ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^m*Cosh[a + b*Log[c*x^n]]^3,x]","\frac{6 b^3 n^3 x^{m+1} \sinh \left(a+b \log \left(c x^n\right)\right)}{-10 b^2 (m+1)^2 n^2+9 b^4 n^4+(m+1)^4}+\frac{(m+1) x^{m+1} \cosh ^3\left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-9 b^2 n^2}-\frac{6 b^2 (m+1) n^2 x^{m+1} \cosh \left(a+b \log \left(c x^n\right)\right)}{-10 b^2 (m+1)^2 n^2+9 b^4 n^4+(m+1)^4}-\frac{3 b n x^{m+1} \sinh \left(a+b \log \left(c x^n\right)\right) \cosh ^2\left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-9 b^2 n^2}","\frac{6 b^3 n^3 x^{m+1} \sinh \left(a+b \log \left(c x^n\right)\right)}{\left((m+1)^2-9 b^2 n^2\right) \left((m+1)^2-b^2 n^2\right)}+\frac{(m+1) x^{m+1} \cosh ^3\left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-9 b^2 n^2}-\frac{6 b^2 (m+1) n^2 x^{m+1} \cosh \left(a+b \log \left(c x^n\right)\right)}{\left((m+1)^2-9 b^2 n^2\right) \left((m+1)^2-b^2 n^2\right)}-\frac{3 b n x^{m+1} \sinh \left(a+b \log \left(c x^n\right)\right) \cosh ^2\left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-9 b^2 n^2}",1,"(-6*b^2*(1 + m)*n^2*x^(1 + m)*Cosh[a + b*Log[c*x^n]])/((1 + m)^4 - 10*b^2*(1 + m)^2*n^2 + 9*b^4*n^4) + ((1 + m)*x^(1 + m)*Cosh[a + b*Log[c*x^n]]^3)/((1 + m)^2 - 9*b^2*n^2) + (6*b^3*n^3*x^(1 + m)*Sinh[a + b*Log[c*x^n]])/((1 + m)^4 - 10*b^2*(1 + m)^2*n^2 + 9*b^4*n^4) - (3*b*n*x^(1 + m)*Cosh[a + b*Log[c*x^n]]^2*Sinh[a + b*Log[c*x^n]])/((1 + m)^2 - 9*b^2*n^2)","A",2,2,17,0.1176,1,"{5530, 5528}"
246,1,260,0,0.1275367,"\int x^m \cosh ^4\left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^m*Cosh[a + b*Log[c*x^n]]^4,x]","\frac{(m+1) x^{m+1} \cosh ^4\left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-16 b^2 n^2}-\frac{12 b^2 (m+1) n^2 x^{m+1} \cosh ^2\left(a+b \log \left(c x^n\right)\right)}{-20 b^2 (m+1)^2 n^2+64 b^4 n^4+(m+1)^4}-\frac{4 b n x^{m+1} \sinh \left(a+b \log \left(c x^n\right)\right) \cosh ^3\left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-16 b^2 n^2}+\frac{24 b^3 n^3 x^{m+1} \sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{-20 b^2 (m+1)^2 n^2+64 b^4 n^4+(m+1)^4}+\frac{24 b^4 n^4 x^{m+1}}{(m+1) \left((m+1)^2-16 b^2 n^2\right) \left((m+1)^2-4 b^2 n^2\right)}","\frac{(m+1) x^{m+1} \cosh ^4\left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-16 b^2 n^2}-\frac{12 b^2 (m+1) n^2 x^{m+1} \cosh ^2\left(a+b \log \left(c x^n\right)\right)}{\left((m+1)^2-16 b^2 n^2\right) \left((m+1)^2-4 b^2 n^2\right)}-\frac{4 b n x^{m+1} \sinh \left(a+b \log \left(c x^n\right)\right) \cosh ^3\left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-16 b^2 n^2}+\frac{24 b^3 n^3 x^{m+1} \sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{\left((m+1)^2-16 b^2 n^2\right) \left((m+1)^2-4 b^2 n^2\right)}+\frac{24 b^4 n^4 x^{m+1}}{(m+1) \left((m+1)^2-16 b^2 n^2\right) \left((m+1)^2-4 b^2 n^2\right)}",1,"(24*b^4*n^4*x^(1 + m))/((1 + m)*((1 + m)^2 - 16*b^2*n^2)*((1 + m)^2 - 4*b^2*n^2)) - (12*b^2*(1 + m)*n^2*x^(1 + m)*Cosh[a + b*Log[c*x^n]]^2)/((1 + m)^4 - 20*b^2*(1 + m)^2*n^2 + 64*b^4*n^4) + ((1 + m)*x^(1 + m)*Cosh[a + b*Log[c*x^n]]^4)/((1 + m)^2 - 16*b^2*n^2) + (24*b^3*n^3*x^(1 + m)*Cosh[a + b*Log[c*x^n]]*Sinh[a + b*Log[c*x^n]])/((1 + m)^4 - 20*b^2*(1 + m)^2*n^2 + 64*b^4*n^4) - (4*b*n*x^(1 + m)*Cosh[a + b*Log[c*x^n]]^3*Sinh[a + b*Log[c*x^n]])/((1 + m)^2 - 16*b^2*n^2)","A",3,2,17,0.1176,1,"{5530, 30}"
247,1,18,0,0.0160305,"\int \frac{\cosh \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cosh[a + b*Log[c*x^n]]/x,x]","\frac{\sinh \left(a+b \log \left(c x^n\right)\right)}{b n}","\frac{\sinh \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"Sinh[a + b*Log[c*x^n]]/(b*n)","A",2,1,15,0.06667,1,"{2637}"
248,1,39,0,0.031073,"\int \frac{\cosh ^2\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cosh[a + b*Log[c*x^n]]^2/x,x]","\frac{\sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{2 b n}+\frac{\log (x)}{2}","\frac{\sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{2 b n}+\frac{\log (x)}{2}",1,"Log[x]/2 + (Cosh[a + b*Log[c*x^n]]*Sinh[a + b*Log[c*x^n]])/(2*b*n)","A",3,2,17,0.1176,1,"{2635, 8}"
249,1,42,0,0.0324898,"\int \frac{\cosh ^3\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cosh[a + b*Log[c*x^n]]^3/x,x]","\frac{\sinh ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{\sinh \left(a+b \log \left(c x^n\right)\right)}{b n}","\frac{\sinh ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{\sinh \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"Sinh[a + b*Log[c*x^n]]/(b*n) + Sinh[a + b*Log[c*x^n]]^3/(3*b*n)","A",3,1,17,0.05882,1,"{2633}"
250,1,73,0,0.0471974,"\int \frac{\cosh ^4\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cosh[a + b*Log[c*x^n]]^4/x,x]","\frac{\sinh \left(a+b \log \left(c x^n\right)\right) \cosh ^3\left(a+b \log \left(c x^n\right)\right)}{4 b n}+\frac{3 \sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{8 b n}+\frac{3 \log (x)}{8}","\frac{\sinh \left(a+b \log \left(c x^n\right)\right) \cosh ^3\left(a+b \log \left(c x^n\right)\right)}{4 b n}+\frac{3 \sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{8 b n}+\frac{3 \log (x)}{8}",1,"(3*Log[x])/8 + (3*Cosh[a + b*Log[c*x^n]]*Sinh[a + b*Log[c*x^n]])/(8*b*n) + (Cosh[a + b*Log[c*x^n]]^3*Sinh[a + b*Log[c*x^n]])/(4*b*n)","A",4,2,17,0.1176,1,"{2635, 8}"
251,1,65,0,0.0372635,"\int \frac{\cosh ^5\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cosh[a + b*Log[c*x^n]]^5/x,x]","\frac{\sinh ^5\left(a+b \log \left(c x^n\right)\right)}{5 b n}+\frac{2 \sinh ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{\sinh \left(a+b \log \left(c x^n\right)\right)}{b n}","\frac{\sinh ^5\left(a+b \log \left(c x^n\right)\right)}{5 b n}+\frac{2 \sinh ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{\sinh \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"Sinh[a + b*Log[c*x^n]]/(b*n) + (2*Sinh[a + b*Log[c*x^n]]^3)/(3*b*n) + Sinh[a + b*Log[c*x^n]]^5/(5*b*n)","A",3,1,17,0.05882,1,"{2633}"
252,1,67,0,0.0444049,"\int \frac{\cosh ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cosh[a + b*Log[c*x^n]]^(5/2)/x,x]","\frac{2 \sinh \left(a+b \log \left(c x^n\right)\right) \cosh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{5 b n}-\frac{6 i 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) \cosh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{5 b n}-\frac{6 i 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)*EllipticE[(I/2)*(a + b*Log[c*x^n]), 2])/(b*n) + (2*Cosh[a + b*Log[c*x^n]]^(3/2)*Sinh[a + b*Log[c*x^n]])/(5*b*n)","A",3,2,19,0.1053,1,"{2635, 2639}"
253,1,67,0,0.0443683,"\int \frac{\cosh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[Cosh[a + b*Log[c*x^n]]^(3/2)/x,x]","\frac{2 \sinh \left(a+b \log \left(c x^n\right)\right) \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)}}{3 b n}-\frac{2 i 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) \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)}}{3 b n}-\frac{2 i 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)*EllipticF[(I/2)*(a + b*Log[c*x^n]), 2])/(b*n) + (2*Sqrt[Cosh[a + b*Log[c*x^n]]]*Sinh[a + b*Log[c*x^n]])/(3*b*n)","A",3,2,19,0.1053,1,"{2635, 2641}"
254,1,28,0,0.0275534,"\int \frac{\sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)}}{x} \, dx","Int[Sqrt[Cosh[a + b*Log[c*x^n]]]/x,x]","-\frac{2 i E\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}","-\frac{2 i E\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}",1,"((-2*I)*EllipticE[(I/2)*(a + b*Log[c*x^n]), 2])/(b*n)","A",2,1,19,0.05263,1,"{2639}"
255,1,28,0,0.0277238,"\int \frac{1}{x \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)}} \, dx","Int[1/(x*Sqrt[Cosh[a + b*Log[c*x^n]]]),x]","-\frac{2 i 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 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)*EllipticF[(I/2)*(a + b*Log[c*x^n]), 2])/(b*n)","A",2,1,19,0.05263,1,"{2641}"
256,1,63,0,0.0421568,"\int \frac{1}{x \cosh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Cosh[a + b*Log[c*x^n]]^(3/2)),x]","\frac{2 \sinh \left(a+b \log \left(c x^n\right)\right)}{b n \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)}}+\frac{2 i E\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}","\frac{2 \sinh \left(a+b \log \left(c x^n\right)\right)}{b n \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)}}+\frac{2 i E\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)}{b n}",1,"((2*I)*EllipticE[(I/2)*(a + b*Log[c*x^n]), 2])/(b*n) + (2*Sinh[a + b*Log[c*x^n]])/(b*n*Sqrt[Cosh[a + b*Log[c*x^n]]])","A",3,2,19,0.1053,1,"{2636, 2639}"
257,1,67,0,0.0421404,"\int \frac{1}{x \cosh ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Int[1/(x*Cosh[a + b*Log[c*x^n]]^(5/2)),x]","\frac{2 \sinh \left(a+b \log \left(c x^n\right)\right)}{3 b n \cosh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}-\frac{2 i 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 \cosh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}-\frac{2 i 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)*EllipticF[(I/2)*(a + b*Log[c*x^n]), 2])/(b*n) + (2*Sinh[a + b*Log[c*x^n]])/(3*b*n*Cosh[a + b*Log[c*x^n]]^(3/2))","A",3,2,19,0.1053,1,"{2636, 2641}"
258,1,206,0,0.1536957,"\int \cosh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right) \, dx","Int[Cosh[a + (2*Log[c*x^n])/n]^(5/2),x]","\frac{5 e^{-2 a} x \left(c x^n\right)^{-4/n} \cosh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}{4 \left(e^{-2 a} \left(c x^n\right)^{-4/n}+1\right)^2}-\frac{1}{4} x \cosh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)+\frac{5 x \cosh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}{12 \left(e^{-2 a} \left(c x^n\right)^{-4/n}+1\right)}-\frac{5 e^{-3 a} x \left(c x^n\right)^{-6/n} \text{csch}^{-1}\left(e^a \left(c x^n\right)^{2/n}\right) \cosh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}{4 \left(e^{-2 a} \left(c x^n\right)^{-4/n}+1\right)^{5/2}}","\frac{5 e^{-2 a} x \left(c x^n\right)^{-4/n} \cosh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}{4 \left(e^{-2 a} \left(c x^n\right)^{-4/n}+1\right)^2}-\frac{1}{4} x \cosh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)+\frac{5 x \cosh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}{12 \left(e^{-2 a} \left(c x^n\right)^{-4/n}+1\right)}-\frac{5 e^{-3 a} x \left(c x^n\right)^{-6/n} \text{csch}^{-1}\left(e^a \left(c x^n\right)^{2/n}\right) \cosh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}{4 \left(e^{-2 a} \left(c x^n\right)^{-4/n}+1\right)^{5/2}}",1,"-(x*Cosh[a + (2*Log[c*x^n])/n]^(5/2))/4 + (5*x*Cosh[a + (2*Log[c*x^n])/n]^(5/2))/(4*E^(2*a)*(c*x^n)^(4/n)*(1 + 1/(E^(2*a)*(c*x^n)^(4/n)))^2) + (5*x*Cosh[a + (2*Log[c*x^n])/n]^(5/2))/(12*(1 + 1/(E^(2*a)*(c*x^n)^(4/n)))) - (5*x*ArcCsch[E^a*(c*x^n)^(2/n)]*Cosh[a + (2*Log[c*x^n])/n]^(5/2))/(4*E^(3*a)*(c*x^n)^(6/n)*(1 + 1/(E^(2*a)*(c*x^n)^(4/n)))^(5/2))","A",8,8,18,0.4444,1,"{5526, 5534, 353, 349, 345, 242, 277, 215}"
259,1,102,0,0.0823893,"\int \sqrt{\cosh \left(a+\frac{2 \log \left(c x^n\right)}{n}\right)} \, dx","Int[Sqrt[Cosh[a + (2*Log[c*x^n])/n]],x]","\frac{1}{2} x \sqrt{\cosh \left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}-\frac{e^{-a} x \left(c x^n\right)^{-2/n} \text{csch}^{-1}\left(e^a \left(c x^n\right)^{2/n}\right) \sqrt{\cosh \left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}}{2 \sqrt{e^{-2 a} \left(c x^n\right)^{-4/n}+1}}","\frac{1}{2} x \sqrt{\cosh \left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}-\frac{e^{-a} x \left(c x^n\right)^{-2/n} \text{csch}^{-1}\left(e^a \left(c x^n\right)^{2/n}\right) \sqrt{\cosh \left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}}{2 \sqrt{e^{-2 a} \left(c x^n\right)^{-4/n}+1}}",1,"(x*Sqrt[Cosh[a + (2*Log[c*x^n])/n]])/2 - (x*ArcCsch[E^a*(c*x^n)^(2/n)]*Sqrt[Cosh[a + (2*Log[c*x^n])/n]])/(2*E^a*(c*x^n)^(2/n)*Sqrt[1 + 1/(E^(2*a)*(c*x^n)^(4/n))])","A",6,6,18,0.3333,1,"{5526, 5534, 345, 242, 277, 215}"
260,1,42,0,0.0498428,"\int \frac{1}{\cosh ^{\frac{3}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)} \, dx","Int[Cosh[a + (2*Log[c*x^n])/n]^(-3/2),x]","-\frac{x \left(e^{-2 a} \left(c x^n\right)^{-4/n}+1\right)}{2 \cosh ^{\frac{3}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}","-\frac{x \left(e^{-2 a} \left(c x^n\right)^{-4/n}+1\right)}{2 \cosh ^{\frac{3}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}",1,"-(x*(1 + 1/(E^(2*a)*(c*x^n)^(4/n))))/(2*Cosh[a + (2*Log[c*x^n])/n]^(3/2))","A",3,3,18,0.1667,1,"{5526, 5534, 264}"
261,1,101,0,0.0752656,"\int \frac{1}{\cosh ^{\frac{7}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)} \, dx","Int[Cosh[a + (2*Log[c*x^n])/n]^(-7/2),x]","-\frac{e^{-2 a} x \left(c x^n\right)^{-4/n} \left(e^{-2 a} \left(c x^n\right)^{-4/n}+1\right)}{15 \cosh ^{\frac{7}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}-\frac{x \left(e^{-2 a} \left(c x^n\right)^{-4/n}+1\right)}{6 \cosh ^{\frac{7}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}","-\frac{e^{-2 a} x \left(c x^n\right)^{-4/n} \left(e^{-2 a} \left(c x^n\right)^{-4/n}+1\right)}{15 \cosh ^{\frac{7}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}-\frac{x \left(e^{-2 a} \left(c x^n\right)^{-4/n}+1\right)}{6 \cosh ^{\frac{7}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}",1,"-(x*(1 + 1/(E^(2*a)*(c*x^n)^(4/n))))/(6*Cosh[a + (2*Log[c*x^n])/n]^(7/2)) - (x*(1 + 1/(E^(2*a)*(c*x^n)^(4/n))))/(15*E^(2*a)*(c*x^n)^(4/n)*Cosh[a + (2*Log[c*x^n])/n]^(7/2))","A",4,4,18,0.2222,1,"{5526, 5534, 271, 264}"
262,1,101,0,0.1766728,"\int \cosh \left(\frac{a+b x}{c+d x}\right) \, dx","Int[Cosh[(a + b*x)/(c + d*x)],x]","\frac{\sinh \left(\frac{b}{d}\right) (b c-a d) \text{Chi}\left(\frac{b c-a d}{d (c+d x)}\right)}{d^2}-\frac{\cosh \left(\frac{b}{d}\right) (b c-a d) \text{Shi}\left(\frac{b c-a d}{d (c+d x)}\right)}{d^2}+\frac{(c+d x) \cosh \left(\frac{a+b x}{c+d x}\right)}{d}","\frac{\sinh \left(\frac{b}{d}\right) (b c-a d) \text{Chi}\left(\frac{b c-a d}{d (c+d x)}\right)}{d^2}-\frac{\cosh \left(\frac{b}{d}\right) (b c-a d) \text{Shi}\left(\frac{b c-a d}{d (c+d x)}\right)}{d^2}+\frac{(c+d x) \cosh \left(\frac{a+b x}{c+d x}\right)}{d}",1,"((c + d*x)*Cosh[(a + b*x)/(c + d*x)])/d + ((b*c - a*d)*CoshIntegral[(b*c - a*d)/(d*(c + d*x))]*Sinh[b/d])/d^2 - ((b*c - a*d)*Cosh[b/d]*SinhIntegral[(b*c - a*d)/(d*(c + d*x))])/d^2","A",5,5,14,0.3571,1,"{5608, 3297, 3303, 3298, 3301}"
263,1,107,0,0.193896,"\int \cosh ^2\left(\frac{a+b x}{c+d x}\right) \, dx","Int[Cosh[(a + b*x)/(c + d*x)]^2,x]","\frac{\sinh \left(\frac{2 b}{d}\right) (b c-a d) \text{Chi}\left(\frac{2 (b c-a d)}{d (c+d x)}\right)}{d^2}-\frac{\cosh \left(\frac{2 b}{d}\right) (b c-a d) \text{Shi}\left(\frac{2 (b c-a d)}{d (c+d x)}\right)}{d^2}+\frac{(c+d x) \cosh ^2\left(\frac{a+b x}{c+d x}\right)}{d}","\frac{\sinh \left(\frac{2 b}{d}\right) (b c-a d) \text{Chi}\left(\frac{2 (b c-a d)}{d (c+d x)}\right)}{d^2}-\frac{\cosh \left(\frac{2 b}{d}\right) (b c-a d) \text{Shi}\left(\frac{2 (b c-a d)}{d (c+d x)}\right)}{d^2}+\frac{(c+d x) \cosh ^2\left(\frac{a+b x}{c+d x}\right)}{d}",1,"((c + d*x)*Cosh[(a + b*x)/(c + d*x)]^2)/d + ((b*c - a*d)*CoshIntegral[(2*(b*c - a*d))/(d*(c + d*x))]*Sinh[(2*b)/d])/d^2 - ((b*c - a*d)*Cosh[(2*b)/d]*SinhIntegral[(2*(b*c - a*d))/(d*(c + d*x))])/d^2","A",6,6,16,0.3750,1,"{5608, 3313, 12, 3303, 3298, 3301}"
264,1,83,0,0.0386232,"\int e^{a+b x} \cosh ^4(a+b x) \, dx","Int[E^(a + b*x)*Cosh[a + b*x]^4,x]","-\frac{e^{-3 a-3 b x}}{48 b}-\frac{e^{-a-b x}}{4 b}+\frac{3 e^{a+b x}}{8 b}+\frac{e^{3 a+3 b x}}{12 b}+\frac{e^{5 a+5 b x}}{80 b}","-\frac{e^{-3 a-3 b x}}{48 b}-\frac{e^{-a-b x}}{4 b}+\frac{3 e^{a+b x}}{8 b}+\frac{e^{3 a+3 b x}}{12 b}+\frac{e^{5 a+5 b x}}{80 b}",1,"-E^(-3*a - 3*b*x)/(48*b) - E^(-a - b*x)/(4*b) + (3*E^(a + b*x))/(8*b) + E^(3*a + 3*b*x)/(12*b) + E^(5*a + 5*b*x)/(80*b)","A",4,3,16,0.1875,1,"{2282, 12, 270}"
265,1,57,0,0.0367967,"\int e^{a+b x} \cosh ^3(a+b x) \, dx","Int[E^(a + b*x)*Cosh[a + b*x]^3,x]","-\frac{e^{-2 a-2 b x}}{16 b}+\frac{3 e^{2 a+2 b x}}{16 b}+\frac{e^{4 a+4 b x}}{32 b}+\frac{3 x}{8}","-\frac{e^{-2 a-2 b x}}{16 b}+\frac{3 e^{2 a+2 b x}}{16 b}+\frac{e^{4 a+4 b x}}{32 b}+\frac{3 x}{8}",1,"-E^(-2*a - 2*b*x)/(16*b) + (3*E^(2*a + 2*b*x))/(16*b) + E^(4*a + 4*b*x)/(32*b) + (3*x)/8","A",5,4,16,0.2500,1,"{2282, 12, 266, 43}"
266,1,49,0,0.029496,"\int e^{a+b x} \cosh ^2(a+b x) \, dx","Int[E^(a + b*x)*Cosh[a + b*x]^2,x]","-\frac{e^{-a-b x}}{4 b}+\frac{e^{a+b x}}{2 b}+\frac{e^{3 a+3 b x}}{12 b}","-\frac{e^{-a-b x}}{4 b}+\frac{e^{a+b x}}{2 b}+\frac{e^{3 a+3 b x}}{12 b}",1,"-E^(-a - b*x)/(4*b) + E^(a + b*x)/(2*b) + E^(3*a + 3*b*x)/(12*b)","A",4,3,16,0.1875,1,"{2282, 12, 270}"
267,1,23,0,0.0151755,"\int e^{a+b x} \cosh (a+b x) \, dx","Int[E^(a + b*x)*Cosh[a + b*x],x]","\frac{e^{2 a+2 b x}}{4 b}+\frac{x}{2}","\frac{e^{2 a+2 b x}}{4 b}+\frac{x}{2}",1,"E^(2*a + 2*b*x)/(4*b) + x/2","A",4,3,14,0.2143,1,"{2282, 12, 14}"
268,1,17,0,0.0173843,"\int e^{a+b x} \text{sech}(a+b x) \, dx","Int[E^(a + b*x)*Sech[a + b*x],x]","\frac{\log \left(e^{2 a+2 b x}+1\right)}{b}","\frac{\log \left(e^{2 a+2 b x}+1\right)}{b}",1,"Log[1 + E^(2*a + 2*b*x)]/b","A",3,3,14,0.2143,1,"{2282, 12, 260}"
269,1,40,0,0.0293319,"\int e^{a+b x} \text{sech}^2(a+b x) \, dx","Int[E^(a + b*x)*Sech[a + b*x]^2,x]","\frac{2 \tan ^{-1}\left(e^{a+b x}\right)}{b}-\frac{2 e^{a+b x}}{b \left(e^{2 a+2 b x}+1\right)}","\frac{2 \tan ^{-1}\left(e^{a+b x}\right)}{b}-\frac{2 e^{a+b x}}{b \left(e^{2 a+2 b x}+1\right)}",1,"(-2*E^(a + b*x))/(b*(1 + E^(2*a + 2*b*x))) + (2*ArcTan[E^(a + b*x)])/b","A",4,4,16,0.2500,1,"{2282, 12, 288, 203}"
270,1,29,0,0.0265666,"\int e^{a+b x} \text{sech}^3(a+b x) \, dx","Int[E^(a + b*x)*Sech[a + b*x]^3,x]","\frac{2 e^{4 a+4 b x}}{b \left(e^{2 a+2 b x}+1\right)^2}","\frac{2 e^{4 a+4 b x}}{b \left(e^{2 a+2 b x}+1\right)^2}",1,"(2*E^(4*a + 4*b*x))/(b*(1 + E^(2*a + 2*b*x))^2)","A",3,3,16,0.1875,1,"{2282, 12, 264}"
271,1,95,0,0.0467283,"\int e^{a+b x} \text{sech}^4(a+b x) \, dx","Int[E^(a + b*x)*Sech[a + b*x]^4,x]","\frac{e^{a+b x}}{b \left(e^{2 a+2 b x}+1\right)}-\frac{2 e^{a+b x}}{b \left(e^{2 a+2 b x}+1\right)^2}-\frac{8 e^{3 a+3 b x}}{3 b \left(e^{2 a+2 b x}+1\right)^3}+\frac{\tan ^{-1}\left(e^{a+b x}\right)}{b}","\frac{e^{a+b x}}{b \left(e^{2 a+2 b x}+1\right)}-\frac{2 e^{a+b x}}{b \left(e^{2 a+2 b x}+1\right)^2}-\frac{8 e^{3 a+3 b x}}{3 b \left(e^{2 a+2 b x}+1\right)^3}+\frac{\tan ^{-1}\left(e^{a+b x}\right)}{b}",1,"(-8*E^(3*a + 3*b*x))/(3*b*(1 + E^(2*a + 2*b*x))^3) - (2*E^(a + b*x))/(b*(1 + E^(2*a + 2*b*x))^2) + E^(a + b*x)/(b*(1 + E^(2*a + 2*b*x))) + ArcTan[E^(a + b*x)]/b","A",6,5,16,0.3125,1,"{2282, 12, 288, 199, 203}"
272,1,60,0,0.0477429,"\int e^{a+b x} \text{sech}^5(a+b x) \, dx","Int[E^(a + b*x)*Sech[a + b*x]^5,x]","-\frac{8}{b \left(e^{2 a+2 b x}+1\right)^2}+\frac{32}{3 b \left(e^{2 a+2 b x}+1\right)^3}-\frac{4}{b \left(e^{2 a+2 b x}+1\right)^4}","-\frac{8}{b \left(e^{2 a+2 b x}+1\right)^2}+\frac{32}{3 b \left(e^{2 a+2 b x}+1\right)^3}-\frac{4}{b \left(e^{2 a+2 b x}+1\right)^4}",1,"-4/(b*(1 + E^(2*a + 2*b*x))^4) + 32/(3*b*(1 + E^(2*a + 2*b*x))^3) - 8/(b*(1 + E^(2*a + 2*b*x))^2)","A",5,4,16,0.2500,1,"{2282, 12, 266, 43}"
273,1,26,0,0.0202289,"\int e^x \cosh ^2(2 x) \, dx","Int[E^x*Cosh[2*x]^2,x]","-\frac{1}{12} e^{-3 x}+\frac{e^x}{2}+\frac{e^{5 x}}{20}","-\frac{1}{12} e^{-3 x}+\frac{e^x}{2}+\frac{e^{5 x}}{20}",1,"-1/(12*E^(3*x)) + E^x/2 + E^(5*x)/20","A",4,3,10,0.3000,1,"{2282, 12, 270}"
274,1,19,0,0.0113203,"\int e^x \cosh (2 x) \, dx","Int[E^x*Cosh[2*x],x]","\frac{e^{3 x}}{6}-\frac{e^{-x}}{2}","\frac{e^{3 x}}{6}-\frac{e^{-x}}{2}",1,"-1/(2*E^x) + E^(3*x)/6","A",4,3,8,0.3750,1,"{2282, 12, 14}"
275,1,92,0,0.0635706,"\int e^x \text{sech}(2 x) \, dx","Int[E^x*Sech[2*x],x]","\frac{\log \left(-\sqrt{2} e^x+e^{2 x}+1\right)}{2 \sqrt{2}}-\frac{\log \left(\sqrt{2} e^x+e^{2 x}+1\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} e^x\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} e^x+1\right)}{\sqrt{2}}","\frac{\log \left(-\sqrt{2} e^x+e^{2 x}+1\right)}{2 \sqrt{2}}-\frac{\log \left(\sqrt{2} e^x+e^{2 x}+1\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} e^x\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} e^x+1\right)}{\sqrt{2}}",1,"-(ArcTan[1 - Sqrt[2]*E^x]/Sqrt[2]) + ArcTan[1 + Sqrt[2]*E^x]/Sqrt[2] + Log[1 - Sqrt[2]*E^x + E^(2*x)]/(2*Sqrt[2]) - Log[1 + Sqrt[2]*E^x + E^(2*x)]/(2*Sqrt[2])","A",11,8,8,1.000,1,"{2282, 12, 297, 1162, 617, 204, 1165, 628}"
276,1,111,0,0.0747904,"\int e^x \text{sech}^2(2 x) \, dx","Int[E^x*Sech[2*x]^2,x]","-\frac{e^x}{e^{4 x}+1}-\frac{\log \left(-\sqrt{2} e^x+e^{2 x}+1\right)}{4 \sqrt{2}}+\frac{\log \left(\sqrt{2} e^x+e^{2 x}+1\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} e^x\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} e^x+1\right)}{2 \sqrt{2}}","-\frac{e^x}{e^{4 x}+1}-\frac{\log \left(-\sqrt{2} e^x+e^{2 x}+1\right)}{4 \sqrt{2}}+\frac{\log \left(\sqrt{2} e^x+e^{2 x}+1\right)}{4 \sqrt{2}}-\frac{\tan ^{-1}\left(1-\sqrt{2} e^x\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} e^x+1\right)}{2 \sqrt{2}}",1,"-(E^x/(1 + E^(4*x))) - ArcTan[1 - Sqrt[2]*E^x]/(2*Sqrt[2]) + ArcTan[1 + Sqrt[2]*E^x]/(2*Sqrt[2]) - Log[1 - Sqrt[2]*E^x + E^(2*x)]/(4*Sqrt[2]) + Log[1 + Sqrt[2]*E^x + E^(2*x)]/(4*Sqrt[2])","A",12,9,10,0.9000,1,"{2282, 12, 288, 211, 1165, 628, 1162, 617, 204}"
277,1,26,0,0.0191598,"\int e^x \cosh ^2(3 x) \, dx","Int[E^x*Cosh[3*x]^2,x]","-\frac{1}{20} e^{-5 x}+\frac{e^x}{2}+\frac{e^{7 x}}{28}","-\frac{1}{20} e^{-5 x}+\frac{e^x}{2}+\frac{e^{7 x}}{28}",1,"-1/(20*E^(5*x)) + E^x/2 + E^(7*x)/28","A",4,3,10,0.3000,1,"{2282, 12, 270}"
278,1,19,0,0.0116903,"\int e^x \cosh (3 x) \, dx","Int[E^x*Cosh[3*x],x]","\frac{e^{4 x}}{8}-\frac{1}{4} e^{-2 x}","\frac{e^{4 x}}{8}-\frac{1}{4} e^{-2 x}",1,"-1/(4*E^(2*x)) + E^(4*x)/8","A",4,3,8,0.3750,1,"{2282, 12, 14}"
279,1,55,0,0.0584103,"\int e^x \text{sech}(3 x) \, dx","Int[E^x*Sech[3*x],x]","-\frac{1}{3} \log \left(e^{2 x}+1\right)+\frac{1}{6} \log \left(-e^{2 x}+e^{4 x}+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 e^{2 x}}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1}{3} \log \left(e^{2 x}+1\right)+\frac{1}{6} \log \left(-e^{2 x}+e^{4 x}+1\right)-\frac{\tan ^{-1}\left(\frac{1-2 e^{2 x}}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(ArcTan[(1 - 2*E^(2*x))/Sqrt[3]]/Sqrt[3]) - Log[1 + E^(2*x)]/3 + Log[1 - E^(2*x) + E^(4*x)]/6","A",9,9,8,1.125,1,"{2282, 12, 275, 292, 31, 634, 618, 204, 628}"
280,1,110,0,0.205163,"\int e^x \text{sech}^2(3 x) \, dx","Int[E^x*Sech[3*x]^2,x]","-\frac{2 e^x}{3 \left(e^{6 x}+1\right)}-\frac{\log \left(-\sqrt{3} e^x+e^{2 x}+1\right)}{6 \sqrt{3}}+\frac{\log \left(\sqrt{3} e^x+e^{2 x}+1\right)}{6 \sqrt{3}}+\frac{2}{9} \tan ^{-1}\left(e^x\right)-\frac{1}{9} \tan ^{-1}\left(\sqrt{3}-2 e^x\right)+\frac{1}{9} \tan ^{-1}\left(2 e^x+\sqrt{3}\right)","-\frac{2 e^x}{3 \left(e^{6 x}+1\right)}-\frac{\log \left(-\sqrt{3} e^x+e^{2 x}+1\right)}{6 \sqrt{3}}+\frac{\log \left(\sqrt{3} e^x+e^{2 x}+1\right)}{6 \sqrt{3}}+\frac{2}{9} \tan ^{-1}\left(e^x\right)-\frac{1}{9} \tan ^{-1}\left(\sqrt{3}-2 e^x\right)+\frac{1}{9} \tan ^{-1}\left(2 e^x+\sqrt{3}\right)",1,"(-2*E^x)/(3*(1 + E^(6*x))) + (2*ArcTan[E^x])/9 - ArcTan[Sqrt[3] - 2*E^x]/9 + ArcTan[Sqrt[3] + 2*E^x]/9 - Log[1 - Sqrt[3]*E^x + E^(2*x)]/(6*Sqrt[3]) + Log[1 + Sqrt[3]*E^x + E^(2*x)]/(6*Sqrt[3])","A",13,9,10,0.9000,1,"{2282, 12, 288, 209, 634, 618, 204, 628, 203}"
281,1,26,0,0.0190408,"\int e^x \cosh ^2(4 x) \, dx","Int[E^x*Cosh[4*x]^2,x]","-\frac{1}{28} e^{-7 x}+\frac{e^x}{2}+\frac{e^{9 x}}{36}","-\frac{1}{28} e^{-7 x}+\frac{e^x}{2}+\frac{e^{9 x}}{36}",1,"-1/(28*E^(7*x)) + E^x/2 + E^(9*x)/36","A",4,3,10,0.3000,1,"{2282, 12, 270}"
282,1,19,0,0.0113104,"\int e^x \cosh (4 x) \, dx","Int[E^x*Cosh[4*x],x]","\frac{e^{5 x}}{10}-\frac{1}{6} e^{-3 x}","\frac{e^{5 x}}{10}-\frac{1}{6} e^{-3 x}",1,"-1/(6*E^(3*x)) + E^(5*x)/10","A",4,3,8,0.3750,1,"{2282, 12, 14}"
283,1,371,0,0.3210782,"\int e^x \text{sech}(4 x) \, dx","Int[E^x*Sech[4*x],x]","-\frac{\log \left(-\sqrt{2-\sqrt{2}} e^x+e^{2 x}+1\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\log \left(\sqrt{2-\sqrt{2}} e^x+e^{2 x}+1\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\log \left(-\sqrt{2+\sqrt{2}} e^x+e^{2 x}+1\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\log \left(\sqrt{2+\sqrt{2}} e^x+e^{2 x}+1\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 e^x}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 e^x}{\sqrt{2-\sqrt{2}}}\right)}{2 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 e^x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 e^x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{2 \sqrt{2 \left(2-\sqrt{2}\right)}}","-\frac{\log \left(-\sqrt{2-\sqrt{2}} e^x+e^{2 x}+1\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\log \left(\sqrt{2-\sqrt{2}} e^x+e^{2 x}+1\right)}{4 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\log \left(-\sqrt{2+\sqrt{2}} e^x+e^{2 x}+1\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\log \left(\sqrt{2+\sqrt{2}} e^x+e^{2 x}+1\right)}{4 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 e^x}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2 \left(2+\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 e^x}{\sqrt{2-\sqrt{2}}}\right)}{2 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{2 e^x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 e^x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{2 \sqrt{2 \left(2-\sqrt{2}\right)}}",1,"ArcTan[(Sqrt[2 - Sqrt[2]] - 2*E^x)/Sqrt[2 + Sqrt[2]]]/(2*Sqrt[2*(2 + Sqrt[2])]) - ArcTan[(Sqrt[2 + Sqrt[2]] - 2*E^x)/Sqrt[2 - Sqrt[2]]]/(2*Sqrt[2*(2 - Sqrt[2])]) - ArcTan[(Sqrt[2 - Sqrt[2]] + 2*E^x)/Sqrt[2 + Sqrt[2]]]/(2*Sqrt[2*(2 + Sqrt[2])]) + ArcTan[(Sqrt[2 + Sqrt[2]] + 2*E^x)/Sqrt[2 - Sqrt[2]]]/(2*Sqrt[2*(2 - Sqrt[2])]) - Log[1 - Sqrt[2 - Sqrt[2]]*E^x + E^(2*x)]/(4*Sqrt[2*(2 - Sqrt[2])]) + Log[1 + Sqrt[2 - Sqrt[2]]*E^x + E^(2*x)]/(4*Sqrt[2*(2 - Sqrt[2])]) + Log[1 - Sqrt[2 + Sqrt[2]]*E^x + E^(2*x)]/(4*Sqrt[2*(2 + Sqrt[2])]) - Log[1 + Sqrt[2 + Sqrt[2]]*E^x + E^(2*x)]/(4*Sqrt[2*(2 + Sqrt[2])])","A",21,9,8,1.125,1,"{2282, 12, 299, 1127, 1161, 618, 204, 1164, 628}"
284,1,379,0,0.3191494,"\int e^x \text{sech}^2(4 x) \, dx","Int[E^x*Sech[4*x]^2,x]","-\frac{e^x}{2 \left(e^{8 x}+1\right)}-\frac{1}{32} \sqrt{2-\sqrt{2}} \log \left(-\sqrt{2-\sqrt{2}} e^x+e^{2 x}+1\right)+\frac{1}{32} \sqrt{2-\sqrt{2}} \log \left(\sqrt{2-\sqrt{2}} e^x+e^{2 x}+1\right)-\frac{1}{32} \sqrt{2+\sqrt{2}} \log \left(-\sqrt{2+\sqrt{2}} e^x+e^{2 x}+1\right)+\frac{1}{32} \sqrt{2+\sqrt{2}} \log \left(\sqrt{2+\sqrt{2}} e^x+e^{2 x}+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 e^x}{\sqrt{2+\sqrt{2}}}\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 e^x}{\sqrt{2-\sqrt{2}}}\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 e^x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 e^x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}","-\frac{e^x}{2 \left(e^{8 x}+1\right)}-\frac{1}{32} \sqrt{2-\sqrt{2}} \log \left(-\sqrt{2-\sqrt{2}} e^x+e^{2 x}+1\right)+\frac{1}{32} \sqrt{2-\sqrt{2}} \log \left(\sqrt{2-\sqrt{2}} e^x+e^{2 x}+1\right)-\frac{1}{32} \sqrt{2+\sqrt{2}} \log \left(-\sqrt{2+\sqrt{2}} e^x+e^{2 x}+1\right)+\frac{1}{32} \sqrt{2+\sqrt{2}} \log \left(\sqrt{2+\sqrt{2}} e^x+e^{2 x}+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{2-\sqrt{2}}-2 e^x}{\sqrt{2+\sqrt{2}}}\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}-\frac{\tan ^{-1}\left(\frac{\sqrt{2+\sqrt{2}}-2 e^x}{\sqrt{2-\sqrt{2}}}\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 e^x+\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{8 \sqrt{2 \left(2-\sqrt{2}\right)}}+\frac{\tan ^{-1}\left(\frac{2 e^x+\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{8 \sqrt{2 \left(2+\sqrt{2}\right)}}",1,"-E^x/(2*(1 + E^(8*x))) - ArcTan[(Sqrt[2 - Sqrt[2]] - 2*E^x)/Sqrt[2 + Sqrt[2]]]/(8*Sqrt[2*(2 - Sqrt[2])]) - ArcTan[(Sqrt[2 + Sqrt[2]] - 2*E^x)/Sqrt[2 - Sqrt[2]]]/(8*Sqrt[2*(2 + Sqrt[2])]) + ArcTan[(Sqrt[2 - Sqrt[2]] + 2*E^x)/Sqrt[2 + Sqrt[2]]]/(8*Sqrt[2*(2 - Sqrt[2])]) + ArcTan[(Sqrt[2 + Sqrt[2]] + 2*E^x)/Sqrt[2 - Sqrt[2]]]/(8*Sqrt[2*(2 + Sqrt[2])]) - (Sqrt[2 - Sqrt[2]]*Log[1 - Sqrt[2 - Sqrt[2]]*E^x + E^(2*x)])/32 + (Sqrt[2 - Sqrt[2]]*Log[1 + Sqrt[2 - Sqrt[2]]*E^x + E^(2*x)])/32 - (Sqrt[2 + Sqrt[2]]*Log[1 - Sqrt[2 + Sqrt[2]]*E^x + E^(2*x)])/32 + (Sqrt[2 + Sqrt[2]]*Log[1 + Sqrt[2 + Sqrt[2]]*E^x + E^(2*x)])/32","A",22,9,10,0.9000,1,"{2282, 12, 288, 213, 1169, 634, 618, 204, 628}"
285,1,202,0,0.0781238,"\int F^{c (a+b x)} \cosh ^3(d+e x) \, dx","Int[F^(c*(a + b*x))*Cosh[d + e*x]^3,x]","\frac{6 e^3 \sinh (d+e x) F^{c (a+b x)}}{-10 b^2 c^2 e^2 \log ^2(F)+b^4 c^4 \log ^4(F)+9 e^4}-\frac{b c \log (F) \cosh ^3(d+e x) F^{c (a+b x)}}{9 e^2-b^2 c^2 \log ^2(F)}-\frac{6 b c e^2 \log (F) \cosh (d+e x) F^{c (a+b x)}}{-10 b^2 c^2 e^2 \log ^2(F)+b^4 c^4 \log ^4(F)+9 e^4}+\frac{3 e \sinh (d+e x) \cosh ^2(d+e x) F^{c (a+b x)}}{9 e^2-b^2 c^2 \log ^2(F)}","\frac{6 e^3 \sinh (d+e x) F^{c (a+b x)}}{-10 b^2 c^2 e^2 \log ^2(F)+b^4 c^4 \log ^4(F)+9 e^4}-\frac{b c \log (F) \cosh ^3(d+e x) F^{c (a+b x)}}{9 e^2-b^2 c^2 \log ^2(F)}-\frac{6 b c e^2 \log (F) \cosh (d+e x) F^{c (a+b x)}}{-10 b^2 c^2 e^2 \log ^2(F)+b^4 c^4 \log ^4(F)+9 e^4}+\frac{3 e \sinh (d+e x) \cosh ^2(d+e x) F^{c (a+b x)}}{9 e^2-b^2 c^2 \log ^2(F)}",1,"-((b*c*F^(c*(a + b*x))*Cosh[d + e*x]^3*Log[F])/(9*e^2 - b^2*c^2*Log[F]^2)) - (6*b*c*e^2*F^(c*(a + b*x))*Cosh[d + e*x]*Log[F])/(9*e^4 - 10*b^2*c^2*e^2*Log[F]^2 + b^4*c^4*Log[F]^4) + (3*e*F^(c*(a + b*x))*Cosh[d + e*x]^2*Sinh[d + e*x])/(9*e^2 - b^2*c^2*Log[F]^2) + (6*e^3*F^(c*(a + b*x))*Sinh[d + e*x])/(9*e^4 - 10*b^2*c^2*e^2*Log[F]^2 + b^4*c^4*Log[F]^4)","A",2,2,18,0.1111,1,"{5477, 5475}"
286,1,132,0,0.0528336,"\int F^{c (a+b x)} \cosh ^2(d+e x) \, dx","Int[F^(c*(a + b*x))*Cosh[d + e*x]^2,x]","-\frac{b c \log (F) \cosh ^2(d+e x) F^{c (a+b x)}}{4 e^2-b^2 c^2 \log ^2(F)}+\frac{2 e \sinh (d+e x) \cosh (d+e x) F^{c (a+b x)}}{4 e^2-b^2 c^2 \log ^2(F)}+\frac{2 e^2 F^{c (a+b x)}}{b c \log (F) \left(4 e^2-b^2 c^2 \log ^2(F)\right)}","-\frac{b c \log (F) \cosh ^2(d+e x) F^{c (a+b x)}}{4 e^2-b^2 c^2 \log ^2(F)}+\frac{2 e \sinh (d+e x) \cosh (d+e x) F^{c (a+b x)}}{4 e^2-b^2 c^2 \log ^2(F)}+\frac{2 e^2 F^{c (a+b x)}}{b c \log (F) \left(4 e^2-b^2 c^2 \log ^2(F)\right)}",1,"(2*e^2*F^(c*(a + b*x)))/(b*c*Log[F]*(4*e^2 - b^2*c^2*Log[F]^2)) - (b*c*F^(c*(a + b*x))*Cosh[d + e*x]^2*Log[F])/(4*e^2 - b^2*c^2*Log[F]^2) + (2*e*F^(c*(a + b*x))*Cosh[d + e*x]*Sinh[d + e*x])/(4*e^2 - b^2*c^2*Log[F]^2)","A",2,2,18,0.1111,1,"{5477, 2194}"
287,1,75,0,0.0182983,"\int F^{c (a+b x)} \cosh (d+e x) \, dx","Int[F^(c*(a + b*x))*Cosh[d + e*x],x]","\frac{e \sinh (d+e x) F^{c (a+b x)}}{e^2-b^2 c^2 \log ^2(F)}-\frac{b c \log (F) \cosh (d+e x) F^{c (a+b x)}}{e^2-b^2 c^2 \log ^2(F)}","\frac{e \sinh (d+e x) F^{c (a+b x)}}{e^2-b^2 c^2 \log ^2(F)}-\frac{b c \log (F) \cosh (d+e x) F^{c (a+b x)}}{e^2-b^2 c^2 \log ^2(F)}",1,"-((b*c*F^(c*(a + b*x))*Cosh[d + e*x]*Log[F])/(e^2 - b^2*c^2*Log[F]^2)) + (e*F^(c*(a + b*x))*Sinh[d + e*x])/(e^2 - b^2*c^2*Log[F]^2)","A",1,1,16,0.06250,1,"{5475}"
288,1,68,0,0.0217432,"\int F^{c (a+b x)} \text{sech}(d+e x) \, dx","Int[F^(c*(a + b*x))*Sech[d + e*x],x]","\frac{2 e^{d+e x} F^{c (a+b x)} \, _2F_1\left(1,\frac{e+b c \log (F)}{2 e};\frac{1}{2} \left(\frac{b c \log (F)}{e}+3\right);-e^{2 (d+e x)}\right)}{b c \log (F)+e}","\frac{2 e^{d+e x} F^{c (a+b x)} \, _2F_1\left(1,\frac{e+b c \log (F)}{2 e};\frac{1}{2} \left(\frac{b c \log (F)}{e}+3\right);-e^{2 (d+e x)}\right)}{b c \log (F)+e}",1,"(2*E^(d + e*x)*F^(c*(a + b*x))*Hypergeometric2F1[1, (e + b*c*Log[F])/(2*e), (3 + (b*c*Log[F])/e)/2, -E^(2*(d + e*x))])/(e + b*c*Log[F])","A",1,1,16,0.06250,1,"{5492}"
289,1,70,0,0.0292432,"\int F^{c (a+b x)} \text{sech}^2(d+e x) \, dx","Int[F^(c*(a + b*x))*Sech[d + e*x]^2,x]","\frac{4 e^{2 (d+e x)} F^{c (a+b x)} \, _2F_1\left(2,\frac{b c \log (F)}{2 e}+1;\frac{b c \log (F)}{2 e}+2;-e^{2 (d+e x)}\right)}{b c \log (F)+2 e}","\frac{4 e^{2 (d+e x)} F^{c (a+b x)} \, _2F_1\left(2,\frac{b c \log (F)}{2 e}+1;\frac{b c \log (F)}{2 e}+2;-e^{2 (d+e x)}\right)}{b c \log (F)+2 e}",1,"(4*E^(2*(d + e*x))*F^(c*(a + b*x))*Hypergeometric2F1[2, 1 + (b*c*Log[F])/(2*e), 2 + (b*c*Log[F])/(2*e), -E^(2*(d + e*x))])/(2*e + b*c*Log[F])","A",1,1,18,0.05556,1,"{5492}"
290,1,124,0,0.0524655,"\int F^{c (a+b x)} \text{sech}^3(d+e x) \, dx","Int[F^(c*(a + b*x))*Sech[d + e*x]^3,x]","\frac{e^{d+e x} F^{c (a+b x)} (e-b c \log (F)) \, _2F_1\left(1,\frac{e+b c \log (F)}{2 e};\frac{1}{2} \left(\frac{b c \log (F)}{e}+3\right);-e^{2 (d+e x)}\right)}{e^2}+\frac{b c \log (F) \text{sech}(d+e x) F^{c (a+b x)}}{2 e^2}+\frac{\tanh (d+e x) \text{sech}(d+e x) F^{c (a+b x)}}{2 e}","\frac{e^{d+e x} F^{c (a+b x)} (e-b c \log (F)) \, _2F_1\left(1,\frac{e+b c \log (F)}{2 e};\frac{1}{2} \left(\frac{b c \log (F)}{e}+3\right);-e^{2 (d+e x)}\right)}{e^2}+\frac{b c \log (F) \text{sech}(d+e x) F^{c (a+b x)}}{2 e^2}+\frac{\tanh (d+e x) \text{sech}(d+e x) F^{c (a+b x)}}{2 e}",1,"(E^(d + e*x)*F^(c*(a + b*x))*Hypergeometric2F1[1, (e + b*c*Log[F])/(2*e), (3 + (b*c*Log[F])/e)/2, -E^(2*(d + e*x))]*(e - b*c*Log[F]))/e^2 + (b*c*F^(c*(a + b*x))*Log[F]*Sech[d + e*x])/(2*e^2) + (F^(c*(a + b*x))*Sech[d + e*x]*Tanh[d + e*x])/(2*e)","A",2,2,18,0.1111,1,"{5490, 5492}"
291,1,133,0,0.0585902,"\int F^{c (a+b x)} \text{sech}^4(d+e x) \, dx","Int[F^(c*(a + b*x))*Sech[d + e*x]^4,x]","\frac{2 e^{2 (d+e x)} F^{c (a+b x)} (2 e-b c \log (F)) \, _2F_1\left(2,\frac{b c \log (F)}{2 e}+1;\frac{b c \log (F)}{2 e}+2;-e^{2 (d+e x)}\right)}{3 e^2}+\frac{b c \log (F) \text{sech}^2(d+e x) F^{c (a+b x)}}{6 e^2}+\frac{\tanh (d+e x) \text{sech}^2(d+e x) F^{c (a+b x)}}{3 e}","\frac{2 e^{2 (d+e x)} F^{c (a+b x)} (2 e-b c \log (F)) \, _2F_1\left(2,\frac{b c \log (F)}{2 e}+1;\frac{b c \log (F)}{2 e}+2;-e^{2 (d+e x)}\right)}{3 e^2}+\frac{b c \log (F) \text{sech}^2(d+e x) F^{c (a+b x)}}{6 e^2}+\frac{\tanh (d+e x) \text{sech}^2(d+e x) F^{c (a+b x)}}{3 e}",1,"(2*E^(2*(d + e*x))*F^(c*(a + b*x))*Hypergeometric2F1[2, 1 + (b*c*Log[F])/(2*e), 2 + (b*c*Log[F])/(2*e), -E^(2*(d + e*x))]*(2*e - b*c*Log[F]))/(3*e^2) + (b*c*F^(c*(a + b*x))*Log[F]*Sech[d + e*x]^2)/(6*e^2) + (F^(c*(a + b*x))*Sech[d + e*x]^2*Tanh[d + e*x])/(3*e)","A",2,2,18,0.1111,1,"{5490, 5492}"
292,1,250,0,0.2289176,"\int e^{c (a+b x)} \cosh ^2(a c+b c x)^{5/2} \, dx","Int[E^(c*(a + b*x))*(Cosh[a*c + b*c*x]^2)^(5/2),x]","-\frac{e^{-4 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{128 b c}-\frac{5 e^{-2 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{64 b c}+\frac{5 e^{2 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{32 b c}+\frac{5 e^{4 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{128 b c}+\frac{e^{6 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{192 b c}+\frac{5}{16} x \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)","-\frac{e^{-4 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{128 b c}-\frac{5 e^{-2 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{64 b c}+\frac{5 e^{2 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{32 b c}+\frac{5 e^{4 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{128 b c}+\frac{e^{6 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{192 b c}+\frac{5}{16} x \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)",1,"-(Sqrt[Cosh[a*c + b*c*x]^2]*Sech[a*c + b*c*x])/(128*b*c*E^(4*c*(a + b*x))) - (5*Sqrt[Cosh[a*c + b*c*x]^2]*Sech[a*c + b*c*x])/(64*b*c*E^(2*c*(a + b*x))) + (5*E^(2*c*(a + b*x))*Sqrt[Cosh[a*c + b*c*x]^2]*Sech[a*c + b*c*x])/(32*b*c) + (5*E^(4*c*(a + b*x))*Sqrt[Cosh[a*c + b*c*x]^2]*Sech[a*c + b*c*x])/(128*b*c) + (E^(6*c*(a + b*x))*Sqrt[Cosh[a*c + b*c*x]^2]*Sech[a*c + b*c*x])/(192*b*c) + (5*x*Sqrt[Cosh[a*c + b*c*x]^2]*Sech[a*c + b*c*x])/16","A",6,5,25,0.2000,1,"{6720, 2282, 12, 266, 43}"
293,1,162,0,0.1235124,"\int e^{c (a+b x)} \cosh ^2(a c+b c x)^{3/2} \, dx","Int[E^(c*(a + b*x))*(Cosh[a*c + b*c*x]^2)^(3/2),x]","-\frac{e^{-2 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{16 b c}+\frac{3 e^{2 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{16 b c}+\frac{e^{4 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{32 b c}+\frac{3}{8} x \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)","-\frac{e^{-2 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{16 b c}+\frac{3 e^{2 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{16 b c}+\frac{e^{4 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{32 b c}+\frac{3}{8} x \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)",1,"-(Sqrt[Cosh[a*c + b*c*x]^2]*Sech[a*c + b*c*x])/(16*b*c*E^(2*c*(a + b*x))) + (3*E^(2*c*(a + b*x))*Sqrt[Cosh[a*c + b*c*x]^2]*Sech[a*c + b*c*x])/(16*b*c) + (E^(4*c*(a + b*x))*Sqrt[Cosh[a*c + b*c*x]^2]*Sech[a*c + b*c*x])/(32*b*c) + (3*x*Sqrt[Cosh[a*c + b*c*x]^2]*Sech[a*c + b*c*x])/8","A",6,5,25,0.2000,1,"{6720, 2282, 12, 266, 43}"
294,1,74,0,0.0993262,"\int e^{c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \, dx","Int[E^(c*(a + b*x))*Sqrt[Cosh[a*c + b*c*x]^2],x]","\frac{e^{2 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{4 b c}+\frac{1}{2} x \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)","\frac{e^{2 c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)}{4 b c}+\frac{1}{2} x \sqrt{\cosh ^2(a c+b c x)} \text{sech}(a c+b c x)",1,"(E^(2*c*(a + b*x))*Sqrt[Cosh[a*c + b*c*x]^2]*Sech[a*c + b*c*x])/(4*b*c) + (x*Sqrt[Cosh[a*c + b*c*x]^2]*Sech[a*c + b*c*x])/2","A",5,4,25,0.1600,1,"{6720, 2282, 12, 14}"
295,1,44,0,0.1133155,"\int \frac{e^{c (a+b x)}}{\sqrt{\cosh ^2(a c+b c x)}} \, dx","Int[E^(c*(a + b*x))/Sqrt[Cosh[a*c + b*c*x]^2],x]","\frac{\log \left(e^{2 c (a+b x)}+1\right) \cosh (a c+b c x)}{b c \sqrt{\cosh ^2(a c+b c x)}}","\frac{\log \left(e^{2 c (a+b x)}+1\right) \cosh (a c+b c x)}{b c \sqrt{\cosh ^2(a c+b c x)}}",1,"(Cosh[a*c + b*c*x]*Log[1 + E^(2*c*(a + b*x))])/(b*c*Sqrt[Cosh[a*c + b*c*x]^2])","A",4,4,25,0.1600,1,"{6720, 2282, 12, 260}"
296,1,56,0,0.1287108,"\int \frac{e^{c (a+b x)}}{\cosh ^2(a c+b c x)^{3/2}} \, dx","Int[E^(c*(a + b*x))/(Cosh[a*c + b*c*x]^2)^(3/2),x]","\frac{2 e^{4 c (a+b x)} \cosh (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)^2 \sqrt{\cosh ^2(a c+b c x)}}","\frac{2 e^{4 c (a+b x)} \cosh (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)^2 \sqrt{\cosh ^2(a c+b c x)}}",1,"(2*E^(4*c*(a + b*x))*Cosh[a*c + b*c*x])/(b*c*(1 + E^(2*c*(a + b*x)))^2*Sqrt[Cosh[a*c + b*c*x]^2])","A",4,4,25,0.1600,1,"{6720, 2282, 12, 264}"
297,1,141,0,0.19712,"\int \frac{e^{c (a+b x)}}{\cosh ^2(a c+b c x)^{5/2}} \, dx","Int[E^(c*(a + b*x))/(Cosh[a*c + b*c*x]^2)^(5/2),x]","-\frac{8 \cosh (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)^2 \sqrt{\cosh ^2(a c+b c x)}}+\frac{32 \cosh (a c+b c x)}{3 b c \left(e^{2 c (a+b x)}+1\right)^3 \sqrt{\cosh ^2(a c+b c x)}}-\frac{4 \cosh (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)^4 \sqrt{\cosh ^2(a c+b c x)}}","-\frac{8 \cosh (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)^2 \sqrt{\cosh ^2(a c+b c x)}}+\frac{32 \cosh (a c+b c x)}{3 b c \left(e^{2 c (a+b x)}+1\right)^3 \sqrt{\cosh ^2(a c+b c x)}}-\frac{4 \cosh (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)^4 \sqrt{\cosh ^2(a c+b c x)}}",1,"(-4*Cosh[a*c + b*c*x])/(b*c*(1 + E^(2*c*(a + b*x)))^4*Sqrt[Cosh[a*c + b*c*x]^2]) + (32*Cosh[a*c + b*c*x])/(3*b*c*(1 + E^(2*c*(a + b*x)))^3*Sqrt[Cosh[a*c + b*c*x]^2]) - (8*Cosh[a*c + b*c*x])/(b*c*(1 + E^(2*c*(a + b*x)))^2*Sqrt[Cosh[a*c + b*c*x]^2])","A",6,5,25,0.2000,1,"{6720, 2282, 12, 266, 43}"
298,1,191,0,0.2587734,"\int \frac{e^{c (a+b x)}}{\cosh ^2(a c+b c x)^{7/2}} \, dx","Int[E^(c*(a + b*x))/(Cosh[a*c + b*c*x]^2)^(7/2),x]","-\frac{64 \cosh (a c+b c x)}{3 b c \left(e^{2 c (a+b x)}+1\right)^3 \sqrt{\cosh ^2(a c+b c x)}}+\frac{48 \cosh (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)^4 \sqrt{\cosh ^2(a c+b c x)}}-\frac{192 \cosh (a c+b c x)}{5 b c \left(e^{2 c (a+b x)}+1\right)^5 \sqrt{\cosh ^2(a c+b c x)}}+\frac{32 \cosh (a c+b c x)}{3 b c \left(e^{2 c (a+b x)}+1\right)^6 \sqrt{\cosh ^2(a c+b c x)}}","-\frac{64 \cosh (a c+b c x)}{3 b c \left(e^{2 c (a+b x)}+1\right)^3 \sqrt{\cosh ^2(a c+b c x)}}+\frac{48 \cosh (a c+b c x)}{b c \left(e^{2 c (a+b x)}+1\right)^4 \sqrt{\cosh ^2(a c+b c x)}}-\frac{192 \cosh (a c+b c x)}{5 b c \left(e^{2 c (a+b x)}+1\right)^5 \sqrt{\cosh ^2(a c+b c x)}}+\frac{32 \cosh (a c+b c x)}{3 b c \left(e^{2 c (a+b x)}+1\right)^6 \sqrt{\cosh ^2(a c+b c x)}}",1,"(32*Cosh[a*c + b*c*x])/(3*b*c*(1 + E^(2*c*(a + b*x)))^6*Sqrt[Cosh[a*c + b*c*x]^2]) - (192*Cosh[a*c + b*c*x])/(5*b*c*(1 + E^(2*c*(a + b*x)))^5*Sqrt[Cosh[a*c + b*c*x]^2]) + (48*Cosh[a*c + b*c*x])/(b*c*(1 + E^(2*c*(a + b*x)))^4*Sqrt[Cosh[a*c + b*c*x]^2]) - (64*Cosh[a*c + b*c*x])/(3*b*c*(1 + E^(2*c*(a + b*x)))^3*Sqrt[Cosh[a*c + b*c*x]^2])","A",6,5,25,0.2000,1,"{6720, 2282, 12, 266, 43}"
299,1,41,0,0.0133061,"\int e^x \cosh (a+b x) \, dx","Int[E^x*Cosh[a + b*x],x]","\frac{e^x \cosh (a+b x)}{1-b^2}-\frac{b e^x \sinh (a+b x)}{1-b^2}","\frac{e^x \cosh (a+b x)}{1-b^2}-\frac{b e^x \sinh (a+b x)}{1-b^2}",1,"(E^x*Cosh[a + b*x])/(1 - b^2) - (b*E^x*Sinh[a + b*x])/(1 - b^2)","A",1,1,10,0.1000,1,"{5475}"
300,1,85,0,0.0811729,"\int e^x \cosh \left(a+c x^2\right) \, dx","Int[E^x*Cosh[a + c*x^2],x]","\frac{\sqrt{\pi } e^{a-\frac{1}{4 c}} \text{Erfi}\left(\frac{2 c x+1}{2 \sqrt{c}}\right)}{4 \sqrt{c}}-\frac{\sqrt{\pi } e^{\frac{1}{4 c}-a} \text{Erf}\left(\frac{1-2 c x}{2 \sqrt{c}}\right)}{4 \sqrt{c}}","\frac{\sqrt{\pi } e^{a-\frac{1}{4 c}} \text{Erfi}\left(\frac{2 c x+1}{2 \sqrt{c}}\right)}{4 \sqrt{c}}-\frac{\sqrt{\pi } e^{\frac{1}{4 c}-a} \text{Erf}\left(\frac{1-2 c x}{2 \sqrt{c}}\right)}{4 \sqrt{c}}",1,"-(E^(-a + 1/(4*c))*Sqrt[Pi]*Erf[(1 - 2*c*x)/(2*Sqrt[c])])/(4*Sqrt[c]) + (E^(a - 1/(4*c))*Sqrt[Pi]*Erfi[(1 + 2*c*x)/(2*Sqrt[c])])/(4*Sqrt[c])","A",6,4,12,0.3333,1,"{5513, 2234, 2205, 2204}"
301,1,101,0,0.1254837,"\int e^x \cosh \left(a+b x+c x^2\right) \, dx","Int[E^x*Cosh[a + b*x + c*x^2],x]","\frac{\sqrt{\pi } e^{a-\frac{(b+1)^2}{4 c}} \text{Erfi}\left(\frac{b+2 c x+1}{2 \sqrt{c}}\right)}{4 \sqrt{c}}-\frac{\sqrt{\pi } e^{\frac{(1-b)^2}{4 c}-a} \text{Erf}\left(\frac{-b-2 c x+1}{2 \sqrt{c}}\right)}{4 \sqrt{c}}","\frac{\sqrt{\pi } e^{a-\frac{(b+1)^2}{4 c}} \text{Erfi}\left(\frac{b+2 c x+1}{2 \sqrt{c}}\right)}{4 \sqrt{c}}-\frac{\sqrt{\pi } e^{\frac{(1-b)^2}{4 c}-a} \text{Erf}\left(\frac{-b-2 c x+1}{2 \sqrt{c}}\right)}{4 \sqrt{c}}",1,"-(E^(-a + (1 - b)^2/(4*c))*Sqrt[Pi]*Erf[(1 - b - 2*c*x)/(2*Sqrt[c])])/(4*Sqrt[c]) + (E^(a - (1 + b)^2/(4*c))*Sqrt[Pi]*Erfi[(1 + b + 2*c*x)/(2*Sqrt[c])])/(4*Sqrt[c])","A",6,4,15,0.2667,1,"{5513, 2234, 2205, 2204}"
302,1,65,0,0.0644386,"\int e^{x^2} \cosh (a+b x) \, dx","Int[E^x^2*Cosh[a + b*x],x]","\frac{1}{4} \sqrt{\pi } e^{-a-\frac{b^2}{4}} \text{Erfi}\left(\frac{1}{2} (2 x-b)\right)+\frac{1}{4} \sqrt{\pi } e^{a-\frac{b^2}{4}} \text{Erfi}\left(\frac{1}{2} (b+2 x)\right)","\frac{1}{4} \sqrt{\pi } e^{-a-\frac{b^2}{4}} \text{Erfi}\left(\frac{1}{2} (2 x-b)\right)+\frac{1}{4} \sqrt{\pi } e^{a-\frac{b^2}{4}} \text{Erfi}\left(\frac{1}{2} (b+2 x)\right)",1,"(E^(-a - b^2/4)*Sqrt[Pi]*Erfi[(-b + 2*x)/2])/4 + (E^(a - b^2/4)*Sqrt[Pi]*Erfi[(b + 2*x)/2])/4","A",6,3,12,0.2500,1,"{5513, 2234, 2204}"
303,1,65,0,0.0789304,"\int e^{x^2} \cosh \left(a+c x^2\right) \, dx","Int[E^x^2*Cosh[a + c*x^2],x]","\frac{\sqrt{\pi } e^{-a} \text{Erfi}\left(\sqrt{1-c} x\right)}{4 \sqrt{1-c}}+\frac{\sqrt{\pi } e^a \text{Erfi}\left(\sqrt{c+1} x\right)}{4 \sqrt{c+1}}","\frac{\sqrt{\pi } e^{-a} \text{Erfi}\left(\sqrt{1-c} x\right)}{4 \sqrt{1-c}}+\frac{\sqrt{\pi } e^a \text{Erfi}\left(\sqrt{c+1} x\right)}{4 \sqrt{c+1}}",1,"(Sqrt[Pi]*Erfi[Sqrt[1 - c]*x])/(4*Sqrt[1 - c]*E^a) + (E^a*Sqrt[Pi]*Erfi[Sqrt[1 + c]*x])/(4*Sqrt[1 + c])","A",4,2,14,0.1429,1,"{5513, 2204}"
304,1,115,0,0.1585384,"\int e^{x^2} \cosh \left(a+b x+c x^2\right) \, dx","Int[E^x^2*Cosh[a + b*x + c*x^2],x]","\frac{\sqrt{\pi } e^{a-\frac{b^2}{4 (c+1)}} \text{Erfi}\left(\frac{b+2 (c+1) x}{2 \sqrt{c+1}}\right)}{4 \sqrt{c+1}}-\frac{\sqrt{\pi } e^{-a-\frac{b^2}{4 (1-c)}} \text{Erfi}\left(\frac{b-2 (1-c) x}{2 \sqrt{1-c}}\right)}{4 \sqrt{1-c}}","\frac{\sqrt{\pi } e^{a-\frac{b^2}{4 (c+1)}} \text{Erfi}\left(\frac{b+2 (c+1) x}{2 \sqrt{c+1}}\right)}{4 \sqrt{c+1}}-\frac{\sqrt{\pi } e^{-a-\frac{b^2}{4 (1-c)}} \text{Erfi}\left(\frac{b-2 (1-c) x}{2 \sqrt{1-c}}\right)}{4 \sqrt{1-c}}",1,"-(E^(-a - b^2/(4*(1 - c)))*Sqrt[Pi]*Erfi[(b - 2*(1 - c)*x)/(2*Sqrt[1 - c])])/(4*Sqrt[1 - c]) + (E^(a - b^2/(4*(1 + c)))*Sqrt[Pi]*Erfi[(b + 2*(1 + c)*x)/(2*Sqrt[1 + c])])/(4*Sqrt[1 + c])","A",6,3,17,0.1765,1,"{5513, 2234, 2204}"
305,1,110,0,0.148254,"\int f^{a+b x} \cosh \left(d+f x^2\right) \, dx","Int[f^(a + b*x)*Cosh[d + f*x^2],x]","\frac{1}{4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{b^2 \log ^2(f)}{4 f}-d} \text{Erf}\left(\frac{2 f x-b \log (f)}{2 \sqrt{f}}\right)+\frac{1}{4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{d-\frac{b^2 \log ^2(f)}{4 f}} \text{Erfi}\left(\frac{b \log (f)+2 f x}{2 \sqrt{f}}\right)","\frac{1}{4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{b^2 \log ^2(f)}{4 f}-d} \text{Erf}\left(\frac{2 f x-b \log (f)}{2 \sqrt{f}}\right)+\frac{1}{4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{d-\frac{b^2 \log ^2(f)}{4 f}} \text{Erfi}\left(\frac{b \log (f)+2 f x}{2 \sqrt{f}}\right)",1,"(E^(-d + (b^2*Log[f]^2)/(4*f))*f^(-1/2 + a)*Sqrt[Pi]*Erf[(2*f*x - b*Log[f])/(2*Sqrt[f])])/4 + (E^(d - (b^2*Log[f]^2)/(4*f))*f^(-1/2 + a)*Sqrt[Pi]*Erfi[(2*f*x + b*Log[f])/(2*Sqrt[f])])/4","A",8,5,16,0.3125,1,"{5513, 2287, 2234, 2205, 2204}"
306,1,148,0,0.1911347,"\int f^{a+b x} \cosh ^2\left(d+f x^2\right) \, dx","Int[f^(a + b*x)*Cosh[d + f*x^2]^2,x]","\frac{1}{8} \sqrt{\frac{\pi }{2}} f^{a-\frac{1}{2}} e^{\frac{b^2 \log ^2(f)}{8 f}-2 d} \text{Erf}\left(\frac{4 f x-b \log (f)}{2 \sqrt{2} \sqrt{f}}\right)+\frac{1}{8} \sqrt{\frac{\pi }{2}} f^{a-\frac{1}{2}} e^{2 d-\frac{b^2 \log ^2(f)}{8 f}} \text{Erfi}\left(\frac{b \log (f)+4 f x}{2 \sqrt{2} \sqrt{f}}\right)+\frac{f^{a+b x}}{2 b \log (f)}","\frac{1}{8} \sqrt{\frac{\pi }{2}} f^{a-\frac{1}{2}} e^{\frac{b^2 \log ^2(f)}{8 f}-2 d} \text{Erf}\left(\frac{4 f x-b \log (f)}{2 \sqrt{2} \sqrt{f}}\right)+\frac{1}{8} \sqrt{\frac{\pi }{2}} f^{a-\frac{1}{2}} e^{2 d-\frac{b^2 \log ^2(f)}{8 f}} \text{Erfi}\left(\frac{b \log (f)+4 f x}{2 \sqrt{2} \sqrt{f}}\right)+\frac{f^{a+b x}}{2 b \log (f)}",1,"(E^(-2*d + (b^2*Log[f]^2)/(8*f))*f^(-1/2 + a)*Sqrt[Pi/2]*Erf[(4*f*x - b*Log[f])/(2*Sqrt[2]*Sqrt[f])])/8 + (E^(2*d - (b^2*Log[f]^2)/(8*f))*f^(-1/2 + a)*Sqrt[Pi/2]*Erfi[(4*f*x + b*Log[f])/(2*Sqrt[2]*Sqrt[f])])/8 + f^(a + b*x)/(2*b*Log[f])","A",9,6,18,0.3333,1,"{5513, 2194, 2287, 2234, 2205, 2204}"
307,1,239,0,0.2857711,"\int f^{a+b x} \cosh ^3\left(d+f x^2\right) \, dx","Int[f^(a + b*x)*Cosh[d + f*x^2]^3,x]","\frac{3}{16} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{b^2 \log ^2(f)}{4 f}-d} \text{Erf}\left(\frac{2 f x-b \log (f)}{2 \sqrt{f}}\right)+\frac{1}{16} \sqrt{\frac{\pi }{3}} f^{a-\frac{1}{2}} e^{\frac{b^2 \log ^2(f)}{12 f}-3 d} \text{Erf}\left(\frac{6 f x-b \log (f)}{2 \sqrt{3} \sqrt{f}}\right)+\frac{3}{16} \sqrt{\pi } f^{a-\frac{1}{2}} e^{d-\frac{b^2 \log ^2(f)}{4 f}} \text{Erfi}\left(\frac{b \log (f)+2 f x}{2 \sqrt{f}}\right)+\frac{1}{16} \sqrt{\frac{\pi }{3}} f^{a-\frac{1}{2}} e^{3 d-\frac{b^2 \log ^2(f)}{12 f}} \text{Erfi}\left(\frac{b \log (f)+6 f x}{2 \sqrt{3} \sqrt{f}}\right)","\frac{3}{16} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{b^2 \log ^2(f)}{4 f}-d} \text{Erf}\left(\frac{2 f x-b \log (f)}{2 \sqrt{f}}\right)+\frac{1}{16} \sqrt{\frac{\pi }{3}} f^{a-\frac{1}{2}} e^{\frac{b^2 \log ^2(f)}{12 f}-3 d} \text{Erf}\left(\frac{6 f x-b \log (f)}{2 \sqrt{3} \sqrt{f}}\right)+\frac{3}{16} \sqrt{\pi } f^{a-\frac{1}{2}} e^{d-\frac{b^2 \log ^2(f)}{4 f}} \text{Erfi}\left(\frac{b \log (f)+2 f x}{2 \sqrt{f}}\right)+\frac{1}{16} \sqrt{\frac{\pi }{3}} f^{a-\frac{1}{2}} e^{3 d-\frac{b^2 \log ^2(f)}{12 f}} \text{Erfi}\left(\frac{b \log (f)+6 f x}{2 \sqrt{3} \sqrt{f}}\right)",1,"(3*E^(-d + (b^2*Log[f]^2)/(4*f))*f^(-1/2 + a)*Sqrt[Pi]*Erf[(2*f*x - b*Log[f])/(2*Sqrt[f])])/16 + (E^(-3*d + (b^2*Log[f]^2)/(12*f))*f^(-1/2 + a)*Sqrt[Pi/3]*Erf[(6*f*x - b*Log[f])/(2*Sqrt[3]*Sqrt[f])])/16 + (3*E^(d - (b^2*Log[f]^2)/(4*f))*f^(-1/2 + a)*Sqrt[Pi]*Erfi[(2*f*x + b*Log[f])/(2*Sqrt[f])])/16 + (E^(3*d - (b^2*Log[f]^2)/(12*f))*f^(-1/2 + a)*Sqrt[Pi/3]*Erfi[(6*f*x + b*Log[f])/(2*Sqrt[3]*Sqrt[f])])/16","A",14,5,18,0.2778,1,"{5513, 2287, 2234, 2205, 2204}"
308,1,115,0,0.2195096,"\int f^{a+b x} \cosh \left(d+e x+f x^2\right) \, dx","Int[f^(a + b*x)*Cosh[d + e*x + f*x^2],x]","\frac{1}{4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{(e-b \log (f))^2}{4 f}-d} \text{Erf}\left(\frac{-b \log (f)+e+2 f x}{2 \sqrt{f}}\right)+\frac{1}{4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{d-\frac{(b \log (f)+e)^2}{4 f}} \text{Erfi}\left(\frac{b \log (f)+e+2 f x}{2 \sqrt{f}}\right)","\frac{1}{4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{(e-b \log (f))^2}{4 f}-d} \text{Erf}\left(\frac{-b \log (f)+e+2 f x}{2 \sqrt{f}}\right)+\frac{1}{4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{d-\frac{(b \log (f)+e)^2}{4 f}} \text{Erfi}\left(\frac{b \log (f)+e+2 f x}{2 \sqrt{f}}\right)",1,"(E^(-d + (e - b*Log[f])^2/(4*f))*f^(-1/2 + a)*Sqrt[Pi]*Erf[(e + 2*f*x - b*Log[f])/(2*Sqrt[f])])/4 + (E^(d - (e + b*Log[f])^2/(4*f))*f^(-1/2 + a)*Sqrt[Pi]*Erfi[(e + 2*f*x + b*Log[f])/(2*Sqrt[f])])/4","A",8,5,19,0.2632,1,"{5513, 2287, 2234, 2205, 2204}"
309,1,161,0,0.2726946,"\int f^{a+b x} \cosh ^2\left(d+e x+f x^2\right) \, dx","Int[f^(a + b*x)*Cosh[d + e*x + f*x^2]^2,x]","\frac{1}{8} \sqrt{\frac{\pi }{2}} f^{a-\frac{1}{2}} e^{\frac{(2 e-b \log (f))^2}{8 f}-2 d} \text{Erf}\left(\frac{-b \log (f)+2 e+4 f x}{2 \sqrt{2} \sqrt{f}}\right)+\frac{1}{8} \sqrt{\frac{\pi }{2}} f^{a-\frac{1}{2}} e^{2 d-\frac{(b \log (f)+2 e)^2}{8 f}} \text{Erfi}\left(\frac{b \log (f)+2 e+4 f x}{2 \sqrt{2} \sqrt{f}}\right)+\frac{f^{a+b x}}{2 b \log (f)}","\frac{1}{8} \sqrt{\frac{\pi }{2}} f^{a-\frac{1}{2}} e^{\frac{(2 e-b \log (f))^2}{8 f}-2 d} \text{Erf}\left(\frac{-b \log (f)+2 e+4 f x}{2 \sqrt{2} \sqrt{f}}\right)+\frac{1}{8} \sqrt{\frac{\pi }{2}} f^{a-\frac{1}{2}} e^{2 d-\frac{(b \log (f)+2 e)^2}{8 f}} \text{Erfi}\left(\frac{b \log (f)+2 e+4 f x}{2 \sqrt{2} \sqrt{f}}\right)+\frac{f^{a+b x}}{2 b \log (f)}",1,"(E^(-2*d + (2*e - b*Log[f])^2/(8*f))*f^(-1/2 + a)*Sqrt[Pi/2]*Erf[(2*e + 4*f*x - b*Log[f])/(2*Sqrt[2]*Sqrt[f])])/8 + (E^(2*d - (2*e + b*Log[f])^2/(8*f))*f^(-1/2 + a)*Sqrt[Pi/2]*Erfi[(2*e + 4*f*x + b*Log[f])/(2*Sqrt[2]*Sqrt[f])])/8 + f^(a + b*x)/(2*b*Log[f])","A",9,6,21,0.2857,1,"{5513, 2194, 2287, 2234, 2205, 2204}"
310,1,257,0,0.4660396,"\int f^{a+b x} \cosh ^3\left(d+e x+f x^2\right) \, dx","Int[f^(a + b*x)*Cosh[d + e*x + f*x^2]^3,x]","\frac{3}{16} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{(e-b \log (f))^2}{4 f}-d} \text{Erf}\left(\frac{-b \log (f)+e+2 f x}{2 \sqrt{f}}\right)+\frac{1}{16} \sqrt{\frac{\pi }{3}} f^{a-\frac{1}{2}} e^{\frac{(3 e-b \log (f))^2}{12 f}-3 d} \text{Erf}\left(\frac{-b \log (f)+3 e+6 f x}{2 \sqrt{3} \sqrt{f}}\right)+\frac{3}{16} \sqrt{\pi } f^{a-\frac{1}{2}} e^{d-\frac{(b \log (f)+e)^2}{4 f}} \text{Erfi}\left(\frac{b \log (f)+e+2 f x}{2 \sqrt{f}}\right)+\frac{1}{16} \sqrt{\frac{\pi }{3}} f^{a-\frac{1}{2}} e^{3 d-\frac{(b \log (f)+3 e)^2}{12 f}} \text{Erfi}\left(\frac{b \log (f)+3 e+6 f x}{2 \sqrt{3} \sqrt{f}}\right)","\frac{3}{16} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{(e-b \log (f))^2}{4 f}-d} \text{Erf}\left(\frac{-b \log (f)+e+2 f x}{2 \sqrt{f}}\right)+\frac{1}{16} \sqrt{\frac{\pi }{3}} f^{a-\frac{1}{2}} e^{\frac{(3 e-b \log (f))^2}{12 f}-3 d} \text{Erf}\left(\frac{-b \log (f)+3 e+6 f x}{2 \sqrt{3} \sqrt{f}}\right)+\frac{3}{16} \sqrt{\pi } f^{a-\frac{1}{2}} e^{d-\frac{(b \log (f)+e)^2}{4 f}} \text{Erfi}\left(\frac{b \log (f)+e+2 f x}{2 \sqrt{f}}\right)+\frac{1}{16} \sqrt{\frac{\pi }{3}} f^{a-\frac{1}{2}} e^{3 d-\frac{(b \log (f)+3 e)^2}{12 f}} \text{Erfi}\left(\frac{b \log (f)+3 e+6 f x}{2 \sqrt{3} \sqrt{f}}\right)",1,"(3*E^(-d + (e - b*Log[f])^2/(4*f))*f^(-1/2 + a)*Sqrt[Pi]*Erf[(e + 2*f*x - b*Log[f])/(2*Sqrt[f])])/16 + (E^(-3*d + (3*e - b*Log[f])^2/(12*f))*f^(-1/2 + a)*Sqrt[Pi/3]*Erf[(3*e + 6*f*x - b*Log[f])/(2*Sqrt[3]*Sqrt[f])])/16 + (3*E^(d - (e + b*Log[f])^2/(4*f))*f^(-1/2 + a)*Sqrt[Pi]*Erfi[(e + 2*f*x + b*Log[f])/(2*Sqrt[f])])/16 + (E^(3*d - (3*e + b*Log[f])^2/(12*f))*f^(-1/2 + a)*Sqrt[Pi/3]*Erfi[(3*e + 6*f*x + b*Log[f])/(2*Sqrt[3]*Sqrt[f])])/16","A",14,5,21,0.2381,1,"{5513, 2287, 2234, 2205, 2204}"
311,1,133,0,0.1938487,"\int f^{a+c x^2} \cosh (d+e x) \, dx","Int[f^(a + c*x^2)*Cosh[d + e*x],x]","\frac{\sqrt{\pi } f^a e^{d-\frac{e^2}{4 c \log (f)}} \text{Erfi}\left(\frac{2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{-\frac{e^2}{4 c \log (f)}-d} \text{Erfi}\left(\frac{e-2 c x \log (f)}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}","\frac{\sqrt{\pi } f^a e^{d-\frac{e^2}{4 c \log (f)}} \text{Erfi}\left(\frac{2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{-\frac{e^2}{4 c \log (f)}-d} \text{Erfi}\left(\frac{e-2 c x \log (f)}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"-(E^(-d - e^2/(4*c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(e - 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])])/(4*Sqrt[c]*Sqrt[Log[f]]) + (E^(d - e^2/(4*c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])])/(4*Sqrt[c]*Sqrt[Log[f]])","A",8,4,16,0.2500,1,"{5513, 2287, 2234, 2204}"
312,1,161,0,0.21993,"\int f^{a+c x^2} \cosh ^2(d+e x) \, dx","Int[f^(a + c*x^2)*Cosh[d + e*x]^2,x]","-\frac{\sqrt{\pi } f^a e^{-\frac{e^2}{c \log (f)}-2 d} \text{Erfi}\left(\frac{e-c x \log (f)}{\sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{2 d-\frac{e^2}{c \log (f)}} \text{Erfi}\left(\frac{c x \log (f)+e}{\sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a \text{Erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{4 \sqrt{c} \sqrt{\log (f)}}","-\frac{\sqrt{\pi } f^a e^{-\frac{e^2}{c \log (f)}-2 d} \text{Erfi}\left(\frac{e-c x \log (f)}{\sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{2 d-\frac{e^2}{c \log (f)}} \text{Erfi}\left(\frac{c x \log (f)+e}{\sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a \text{Erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*Erfi[Sqrt[c]*x*Sqrt[Log[f]]])/(4*Sqrt[c]*Sqrt[Log[f]]) - (E^(-2*d - e^2/(c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(e - c*x*Log[f])/(Sqrt[c]*Sqrt[Log[f]])])/(8*Sqrt[c]*Sqrt[Log[f]]) + (E^(2*d - e^2/(c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(e + c*x*Log[f])/(Sqrt[c]*Sqrt[Log[f]])])/(8*Sqrt[c]*Sqrt[Log[f]])","A",9,4,18,0.2222,1,"{5513, 2204, 2287, 2234}"
313,1,271,0,0.3378812,"\int f^{a+c x^2} \cosh ^3(d+e x) \, dx","Int[f^(a + c*x^2)*Cosh[d + e*x]^3,x]","-\frac{3 \sqrt{\pi } f^a e^{-\frac{e^2}{4 c \log (f)}-d} \text{Erfi}\left(\frac{e-2 c x \log (f)}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{-\frac{9 e^2}{4 c \log (f)}-3 d} \text{Erfi}\left(\frac{3 e-2 c x \log (f)}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{3 \sqrt{\pi } f^a e^{d-\frac{e^2}{4 c \log (f)}} \text{Erfi}\left(\frac{2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{3 d-\frac{9 e^2}{4 c \log (f)}} \text{Erfi}\left(\frac{2 c x \log (f)+3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}","-\frac{3 \sqrt{\pi } f^a e^{-\frac{e^2}{4 c \log (f)}-d} \text{Erfi}\left(\frac{e-2 c x \log (f)}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{-\frac{9 e^2}{4 c \log (f)}-3 d} \text{Erfi}\left(\frac{3 e-2 c x \log (f)}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{3 \sqrt{\pi } f^a e^{d-\frac{e^2}{4 c \log (f)}} \text{Erfi}\left(\frac{2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{3 d-\frac{9 e^2}{4 c \log (f)}} \text{Erfi}\left(\frac{2 c x \log (f)+3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}",1,"(-3*E^(-d - e^2/(4*c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(e - 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])])/(16*Sqrt[c]*Sqrt[Log[f]]) - (E^(-3*d - (9*e^2)/(4*c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(3*e - 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])])/(16*Sqrt[c]*Sqrt[Log[f]]) + (3*E^(d - e^2/(4*c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])])/(16*Sqrt[c]*Sqrt[Log[f]]) + (E^(3*d - (9*e^2)/(4*c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(3*e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])])/(16*Sqrt[c]*Sqrt[Log[f]])","A",14,4,18,0.2222,1,"{5513, 2287, 2234, 2204}"
314,1,81,0,0.1581936,"\int f^{a+c x^2} \cosh \left(d+f x^2\right) \, dx","Int[f^(a + c*x^2)*Cosh[d + f*x^2],x]","\frac{\sqrt{\pi } e^{-d} f^a \text{Erf}\left(x \sqrt{f-c \log (f)}\right)}{4 \sqrt{f-c \log (f)}}+\frac{\sqrt{\pi } e^d f^a \text{Erfi}\left(x \sqrt{c \log (f)+f}\right)}{4 \sqrt{c \log (f)+f}}","\frac{\sqrt{\pi } e^{-d} f^a \text{Erf}\left(x \sqrt{f-c \log (f)}\right)}{4 \sqrt{f-c \log (f)}}+\frac{\sqrt{\pi } e^d f^a \text{Erfi}\left(x \sqrt{c \log (f)+f}\right)}{4 \sqrt{c \log (f)+f}}",1,"(f^a*Sqrt[Pi]*Erf[x*Sqrt[f - c*Log[f]]])/(4*E^d*Sqrt[f - c*Log[f]]) + (E^d*f^a*Sqrt[Pi]*Erfi[x*Sqrt[f + c*Log[f]]])/(4*Sqrt[f + c*Log[f]])","A",6,4,18,0.2222,1,"{5513, 2287, 2205, 2204}"
315,1,128,0,0.2034448,"\int f^{a+c x^2} \cosh ^2\left(d+f x^2\right) \, dx","Int[f^(a + c*x^2)*Cosh[d + f*x^2]^2,x]","\frac{\sqrt{\pi } e^{-2 d} f^a \text{Erf}\left(x \sqrt{2 f-c \log (f)}\right)}{8 \sqrt{2 f-c \log (f)}}+\frac{\sqrt{\pi } e^{2 d} f^a \text{Erfi}\left(x \sqrt{c \log (f)+2 f}\right)}{8 \sqrt{c \log (f)+2 f}}+\frac{\sqrt{\pi } f^a \text{Erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{4 \sqrt{c} \sqrt{\log (f)}}","\frac{\sqrt{\pi } e^{-2 d} f^a \text{Erf}\left(x \sqrt{2 f-c \log (f)}\right)}{8 \sqrt{2 f-c \log (f)}}+\frac{\sqrt{\pi } e^{2 d} f^a \text{Erfi}\left(x \sqrt{c \log (f)+2 f}\right)}{8 \sqrt{c \log (f)+2 f}}+\frac{\sqrt{\pi } f^a \text{Erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*Erfi[Sqrt[c]*x*Sqrt[Log[f]]])/(4*Sqrt[c]*Sqrt[Log[f]]) + (f^a*Sqrt[Pi]*Erf[x*Sqrt[2*f - c*Log[f]]])/(8*E^(2*d)*Sqrt[2*f - c*Log[f]]) + (E^(2*d)*f^a*Sqrt[Pi]*Erfi[x*Sqrt[2*f + c*Log[f]]])/(8*Sqrt[2*f + c*Log[f]])","A",7,4,20,0.2000,1,"{5513, 2204, 2287, 2205}"
316,1,171,0,0.2965675,"\int f^{a+c x^2} \cosh ^3\left(d+f x^2\right) \, dx","Int[f^(a + c*x^2)*Cosh[d + f*x^2]^3,x]","\frac{3 \sqrt{\pi } e^{-d} f^a \text{Erf}\left(x \sqrt{f-c \log (f)}\right)}{16 \sqrt{f-c \log (f)}}+\frac{\sqrt{\pi } e^{-3 d} f^a \text{Erf}\left(x \sqrt{3 f-c \log (f)}\right)}{16 \sqrt{3 f-c \log (f)}}+\frac{3 \sqrt{\pi } e^d f^a \text{Erfi}\left(x \sqrt{c \log (f)+f}\right)}{16 \sqrt{c \log (f)+f}}+\frac{\sqrt{\pi } e^{3 d} f^a \text{Erfi}\left(x \sqrt{c \log (f)+3 f}\right)}{16 \sqrt{c \log (f)+3 f}}","\frac{3 \sqrt{\pi } e^{-d} f^a \text{Erf}\left(x \sqrt{f-c \log (f)}\right)}{16 \sqrt{f-c \log (f)}}+\frac{\sqrt{\pi } e^{-3 d} f^a \text{Erf}\left(x \sqrt{3 f-c \log (f)}\right)}{16 \sqrt{3 f-c \log (f)}}+\frac{3 \sqrt{\pi } e^d f^a \text{Erfi}\left(x \sqrt{c \log (f)+f}\right)}{16 \sqrt{c \log (f)+f}}+\frac{\sqrt{\pi } e^{3 d} f^a \text{Erfi}\left(x \sqrt{c \log (f)+3 f}\right)}{16 \sqrt{c \log (f)+3 f}}",1,"(3*f^a*Sqrt[Pi]*Erf[x*Sqrt[f - c*Log[f]]])/(16*E^d*Sqrt[f - c*Log[f]]) + (f^a*Sqrt[Pi]*Erf[x*Sqrt[3*f - c*Log[f]]])/(16*E^(3*d)*Sqrt[3*f - c*Log[f]]) + (3*E^d*f^a*Sqrt[Pi]*Erfi[x*Sqrt[f + c*Log[f]]])/(16*Sqrt[f + c*Log[f]]) + (E^(3*d)*f^a*Sqrt[Pi]*Erfi[x*Sqrt[3*f + c*Log[f]]])/(16*Sqrt[3*f + c*Log[f]])","A",10,4,20,0.2000,1,"{5513, 2287, 2205, 2204}"
317,1,140,0,0.3107359,"\int f^{a+c x^2} \cosh \left(d+e x+f x^2\right) \, dx","Int[f^(a + c*x^2)*Cosh[d + e*x + f*x^2],x]","\frac{\sqrt{\pi } f^a e^{\frac{e^2}{4 f-4 c \log (f)}-d} \text{Erf}\left(\frac{2 x (f-c \log (f))+e}{2 \sqrt{f-c \log (f)}}\right)}{4 \sqrt{f-c \log (f)}}+\frac{\sqrt{\pi } f^a e^{d-\frac{e^2}{4 (c \log (f)+f)}} \text{Erfi}\left(\frac{2 x (c \log (f)+f)+e}{2 \sqrt{c \log (f)+f}}\right)}{4 \sqrt{c \log (f)+f}}","\frac{\sqrt{\pi } f^a e^{\frac{e^2}{4 f-4 c \log (f)}-d} \text{Erf}\left(\frac{2 x (f-c \log (f))+e}{2 \sqrt{f-c \log (f)}}\right)}{4 \sqrt{f-c \log (f)}}+\frac{\sqrt{\pi } f^a e^{d-\frac{e^2}{4 (c \log (f)+f)}} \text{Erfi}\left(\frac{2 x (c \log (f)+f)+e}{2 \sqrt{c \log (f)+f}}\right)}{4 \sqrt{c \log (f)+f}}",1,"(E^(-d + e^2/(4*f - 4*c*Log[f]))*f^a*Sqrt[Pi]*Erf[(e + 2*x*(f - c*Log[f]))/(2*Sqrt[f - c*Log[f]])])/(4*Sqrt[f - c*Log[f]]) + (E^(d - e^2/(4*(f + c*Log[f])))*f^a*Sqrt[Pi]*Erfi[(e + 2*x*(f + c*Log[f]))/(2*Sqrt[f + c*Log[f]])])/(4*Sqrt[f + c*Log[f]])","A",8,5,21,0.2381,1,"{5513, 2287, 2234, 2205, 2204}"
318,1,183,0,0.3321901,"\int f^{a+c x^2} \cosh ^2\left(d+e x+f x^2\right) \, dx","Int[f^(a + c*x^2)*Cosh[d + e*x + f*x^2]^2,x]","\frac{\sqrt{\pi } f^a e^{\frac{e^2}{2 f-c \log (f)}-2 d} \text{Erf}\left(\frac{x (2 f-c \log (f))+e}{\sqrt{2 f-c \log (f)}}\right)}{8 \sqrt{2 f-c \log (f)}}+\frac{\sqrt{\pi } f^a e^{2 d-\frac{e^2}{c \log (f)+2 f}} \text{Erfi}\left(\frac{x (c \log (f)+2 f)+e}{\sqrt{c \log (f)+2 f}}\right)}{8 \sqrt{c \log (f)+2 f}}+\frac{\sqrt{\pi } f^a \text{Erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{4 \sqrt{c} \sqrt{\log (f)}}","\frac{\sqrt{\pi } f^a e^{\frac{e^2}{2 f-c \log (f)}-2 d} \text{Erf}\left(\frac{x (2 f-c \log (f))+e}{\sqrt{2 f-c \log (f)}}\right)}{8 \sqrt{2 f-c \log (f)}}+\frac{\sqrt{\pi } f^a e^{2 d-\frac{e^2}{c \log (f)+2 f}} \text{Erfi}\left(\frac{x (c \log (f)+2 f)+e}{\sqrt{c \log (f)+2 f}}\right)}{8 \sqrt{c \log (f)+2 f}}+\frac{\sqrt{\pi } f^a \text{Erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*Erfi[Sqrt[c]*x*Sqrt[Log[f]]])/(4*Sqrt[c]*Sqrt[Log[f]]) + (E^(-2*d + e^2/(2*f - c*Log[f]))*f^a*Sqrt[Pi]*Erf[(e + x*(2*f - c*Log[f]))/Sqrt[2*f - c*Log[f]]])/(8*Sqrt[2*f - c*Log[f]]) + (E^(2*d - e^2/(2*f + c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(e + x*(2*f + c*Log[f]))/Sqrt[2*f + c*Log[f]]])/(8*Sqrt[2*f + c*Log[f]])","A",9,5,23,0.2174,1,"{5513, 2204, 2287, 2234, 2205}"
319,1,300,0,0.5811997,"\int f^{a+c x^2} \cosh ^3\left(d+e x+f x^2\right) \, dx","Int[f^(a + c*x^2)*Cosh[d + e*x + f*x^2]^3,x]","\frac{3 \sqrt{\pi } f^a e^{\frac{e^2}{4 f-4 c \log (f)}-d} \text{Erf}\left(\frac{2 x (f-c \log (f))+e}{2 \sqrt{f-c \log (f)}}\right)}{16 \sqrt{f-c \log (f)}}+\frac{\sqrt{\pi } f^a e^{\frac{9 e^2}{12 f-4 c \log (f)}-3 d} \text{Erf}\left(\frac{2 x (3 f-c \log (f))+3 e}{2 \sqrt{3 f-c \log (f)}}\right)}{16 \sqrt{3 f-c \log (f)}}+\frac{3 \sqrt{\pi } f^a e^{d-\frac{e^2}{4 (c \log (f)+f)}} \text{Erfi}\left(\frac{2 x (c \log (f)+f)+e}{2 \sqrt{c \log (f)+f}}\right)}{16 \sqrt{c \log (f)+f}}+\frac{\sqrt{\pi } f^a e^{3 d-\frac{9 e^2}{4 (c \log (f)+3 f)}} \text{Erfi}\left(\frac{2 x (c \log (f)+3 f)+3 e}{2 \sqrt{c \log (f)+3 f}}\right)}{16 \sqrt{c \log (f)+3 f}}","\frac{3 \sqrt{\pi } f^a e^{\frac{e^2}{4 f-4 c \log (f)}-d} \text{Erf}\left(\frac{2 x (f-c \log (f))+e}{2 \sqrt{f-c \log (f)}}\right)}{16 \sqrt{f-c \log (f)}}+\frac{\sqrt{\pi } f^a e^{\frac{9 e^2}{12 f-4 c \log (f)}-3 d} \text{Erf}\left(\frac{2 x (3 f-c \log (f))+3 e}{2 \sqrt{3 f-c \log (f)}}\right)}{16 \sqrt{3 f-c \log (f)}}+\frac{3 \sqrt{\pi } f^a e^{d-\frac{e^2}{4 (c \log (f)+f)}} \text{Erfi}\left(\frac{2 x (c \log (f)+f)+e}{2 \sqrt{c \log (f)+f}}\right)}{16 \sqrt{c \log (f)+f}}+\frac{\sqrt{\pi } f^a e^{3 d-\frac{9 e^2}{4 (c \log (f)+3 f)}} \text{Erfi}\left(\frac{2 x (c \log (f)+3 f)+3 e}{2 \sqrt{c \log (f)+3 f}}\right)}{16 \sqrt{c \log (f)+3 f}}",1,"(3*E^(-d + e^2/(4*f - 4*c*Log[f]))*f^a*Sqrt[Pi]*Erf[(e + 2*x*(f - c*Log[f]))/(2*Sqrt[f - c*Log[f]])])/(16*Sqrt[f - c*Log[f]]) + (E^(-3*d + (9*e^2)/(12*f - 4*c*Log[f]))*f^a*Sqrt[Pi]*Erf[(3*e + 2*x*(3*f - c*Log[f]))/(2*Sqrt[3*f - c*Log[f]])])/(16*Sqrt[3*f - c*Log[f]]) + (3*E^(d - e^2/(4*(f + c*Log[f])))*f^a*Sqrt[Pi]*Erfi[(e + 2*x*(f + c*Log[f]))/(2*Sqrt[f + c*Log[f]])])/(16*Sqrt[f + c*Log[f]]) + (E^(3*d - (9*e^2)/(4*(3*f + c*Log[f])))*f^a*Sqrt[Pi]*Erfi[(3*e + 2*x*(3*f + c*Log[f]))/(2*Sqrt[3*f + c*Log[f]])])/(16*Sqrt[3*f + c*Log[f]])","A",14,5,23,0.2174,1,"{5513, 2287, 2234, 2205, 2204}"
320,1,153,0,0.2910377,"\int f^{a+b x+c x^2} \cosh (d+e x) \, dx","Int[f^(a + b*x + c*x^2)*Cosh[d + e*x],x]","\frac{\sqrt{\pi } f^a e^{d-\frac{(b \log (f)+e)^2}{4 c \log (f)}} \text{Erfi}\left(\frac{b \log (f)+2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{-\frac{(e-b \log (f))^2}{4 c \log (f)}-d} \text{Erfi}\left(\frac{-b \log (f)-2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}","\frac{\sqrt{\pi } f^a e^{d-\frac{(b \log (f)+e)^2}{4 c \log (f)}} \text{Erfi}\left(\frac{b \log (f)+2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{-\frac{(e-b \log (f))^2}{4 c \log (f)}-d} \text{Erfi}\left(\frac{-b \log (f)-2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"-(E^(-d - (e - b*Log[f])^2/(4*c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(e - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])])/(4*Sqrt[c]*Sqrt[Log[f]]) + (E^(d - (e + b*Log[f])^2/(4*c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(e + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])])/(4*Sqrt[c]*Sqrt[Log[f]])","A",8,4,19,0.2105,1,"{5513, 2287, 2234, 2204}"
321,1,219,0,0.3687648,"\int f^{a+b x+c x^2} \cosh ^2(d+e x) \, dx","Int[f^(a + b*x + c*x^2)*Cosh[d + e*x]^2,x]","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{Erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{-\frac{(2 e-b \log (f))^2}{4 c \log (f)}-2 d} \text{Erfi}\left(\frac{-b \log (f)-2 c x \log (f)+2 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{2 d-\frac{(b \log (f)+2 e)^2}{4 c \log (f)}} \text{Erfi}\left(\frac{b \log (f)+2 c x \log (f)+2 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{Erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{-\frac{(2 e-b \log (f))^2}{4 c \log (f)}-2 d} \text{Erfi}\left(\frac{-b \log (f)-2 c x \log (f)+2 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{2 d-\frac{(b \log (f)+2 e)^2}{4 c \log (f)}} \text{Erfi}\left(\frac{b \log (f)+2 c x \log (f)+2 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}",1,"(f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(4*Sqrt[c]*Sqrt[Log[f]]) - (E^(-2*d - (2*e - b*Log[f])^2/(4*c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(2*e - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])])/(8*Sqrt[c]*Sqrt[Log[f]]) + (E^(2*d - (2*e + b*Log[f])^2/(4*c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(2*e + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])])/(8*Sqrt[c]*Sqrt[Log[f]])","A",10,4,21,0.1905,1,"{5513, 2234, 2204, 2287}"
322,1,315,0,0.4572587,"\int f^{a+b x+c x^2} \cosh ^3(d+e x) \, dx","Int[f^(a + b*x + c*x^2)*Cosh[d + e*x]^3,x]","-\frac{3 \sqrt{\pi } f^a e^{-\frac{(e-b \log (f))^2}{4 c \log (f)}-d} \text{Erfi}\left(\frac{-b \log (f)-2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{-\frac{(3 e-b \log (f))^2}{4 c \log (f)}-3 d} \text{Erfi}\left(\frac{-b \log (f)-2 c x \log (f)+3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{3 \sqrt{\pi } f^a e^{d-\frac{(b \log (f)+e)^2}{4 c \log (f)}} \text{Erfi}\left(\frac{b \log (f)+2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{3 d-\frac{(b \log (f)+3 e)^2}{4 c \log (f)}} \text{Erfi}\left(\frac{b \log (f)+2 c x \log (f)+3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}","-\frac{3 \sqrt{\pi } f^a e^{-\frac{(e-b \log (f))^2}{4 c \log (f)}-d} \text{Erfi}\left(\frac{-b \log (f)-2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{-\frac{(3 e-b \log (f))^2}{4 c \log (f)}-3 d} \text{Erfi}\left(\frac{-b \log (f)-2 c x \log (f)+3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{3 \sqrt{\pi } f^a e^{d-\frac{(b \log (f)+e)^2}{4 c \log (f)}} \text{Erfi}\left(\frac{b \log (f)+2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{3 d-\frac{(b \log (f)+3 e)^2}{4 c \log (f)}} \text{Erfi}\left(\frac{b \log (f)+2 c x \log (f)+3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}",1,"(-3*E^(-d - (e - b*Log[f])^2/(4*c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(e - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])])/(16*Sqrt[c]*Sqrt[Log[f]]) - (E^(-3*d - (3*e - b*Log[f])^2/(4*c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(3*e - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])])/(16*Sqrt[c]*Sqrt[Log[f]]) + (3*E^(d - (e + b*Log[f])^2/(4*c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(e + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])])/(16*Sqrt[c]*Sqrt[Log[f]]) + (E^(3*d - (3*e + b*Log[f])^2/(4*c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(3*e + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])])/(16*Sqrt[c]*Sqrt[Log[f]])","A",14,4,21,0.1905,1,"{5513, 2287, 2234, 2204}"
323,1,154,0,0.3205907,"\int f^{a+b x+c x^2} \cosh \left(d+f x^2\right) \, dx","Int[f^(a + b*x + c*x^2)*Cosh[d + f*x^2],x]","\frac{\sqrt{\pi } f^a e^{d-\frac{b^2 \log ^2(f)}{4 (c \log (f)+f)}} \text{Erfi}\left(\frac{b \log (f)+2 x (c \log (f)+f)}{2 \sqrt{c \log (f)+f}}\right)}{4 \sqrt{c \log (f)+f}}-\frac{\sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{4 f-4 c \log (f)}-d} \text{Erf}\left(\frac{b \log (f)-2 x (f-c \log (f))}{2 \sqrt{f-c \log (f)}}\right)}{4 \sqrt{f-c \log (f)}}","\frac{\sqrt{\pi } f^a e^{d-\frac{b^2 \log ^2(f)}{4 (c \log (f)+f)}} \text{Erfi}\left(\frac{b \log (f)+2 x (c \log (f)+f)}{2 \sqrt{c \log (f)+f}}\right)}{4 \sqrt{c \log (f)+f}}-\frac{\sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{4 f-4 c \log (f)}-d} \text{Erf}\left(\frac{b \log (f)-2 x (f-c \log (f))}{2 \sqrt{f-c \log (f)}}\right)}{4 \sqrt{f-c \log (f)}}",1,"-(E^(-d + (b^2*Log[f]^2)/(4*f - 4*c*Log[f]))*f^a*Sqrt[Pi]*Erf[(b*Log[f] - 2*x*(f - c*Log[f]))/(2*Sqrt[f - c*Log[f]])])/(4*Sqrt[f - c*Log[f]]) + (E^(d - (b^2*Log[f]^2)/(4*(f + c*Log[f])))*f^a*Sqrt[Pi]*Erfi[(b*Log[f] + 2*x*(f + c*Log[f]))/(2*Sqrt[f + c*Log[f]])])/(4*Sqrt[f + c*Log[f]])","A",8,5,21,0.2381,1,"{5513, 2287, 2234, 2205, 2204}"
324,1,225,0,0.3498369,"\int f^{a+b x+c x^2} \cosh ^2\left(d+f x^2\right) \, dx","Int[f^(a + b*x + c*x^2)*Cosh[d + f*x^2]^2,x]","-\frac{\sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{8 f-4 c \log (f)}-2 d} \text{Erf}\left(\frac{b \log (f)-2 x (2 f-c \log (f))}{2 \sqrt{2 f-c \log (f)}}\right)}{8 \sqrt{2 f-c \log (f)}}+\frac{\sqrt{\pi } f^a e^{2 d-\frac{b^2 \log ^2(f)}{4 c \log (f)+8 f}} \text{Erfi}\left(\frac{b \log (f)+2 x (c \log (f)+2 f)}{2 \sqrt{c \log (f)+2 f}}\right)}{8 \sqrt{c \log (f)+2 f}}+\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{Erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}","-\frac{\sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{8 f-4 c \log (f)}-2 d} \text{Erf}\left(\frac{b \log (f)-2 x (2 f-c \log (f))}{2 \sqrt{2 f-c \log (f)}}\right)}{8 \sqrt{2 f-c \log (f)}}+\frac{\sqrt{\pi } f^a e^{2 d-\frac{b^2 \log ^2(f)}{4 c \log (f)+8 f}} \text{Erfi}\left(\frac{b \log (f)+2 x (c \log (f)+2 f)}{2 \sqrt{c \log (f)+2 f}}\right)}{8 \sqrt{c \log (f)+2 f}}+\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{Erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(4*Sqrt[c]*Sqrt[Log[f]]) - (E^(-2*d + (b^2*Log[f]^2)/(8*f - 4*c*Log[f]))*f^a*Sqrt[Pi]*Erf[(b*Log[f] - 2*x*(2*f - c*Log[f]))/(2*Sqrt[2*f - c*Log[f]])])/(8*Sqrt[2*f - c*Log[f]]) + (E^(2*d - (b^2*Log[f]^2)/(8*f + 4*c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(b*Log[f] + 2*x*(2*f + c*Log[f]))/(2*Sqrt[2*f + c*Log[f]])])/(8*Sqrt[2*f + c*Log[f]])","A",10,5,23,0.2174,1,"{5513, 2234, 2204, 2287, 2205}"
325,1,323,0,0.5124603,"\int f^{a+b x+c x^2} \cosh ^3\left(d+f x^2\right) \, dx","Int[f^(a + b*x + c*x^2)*Cosh[d + f*x^2]^3,x]","-\frac{3 \sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{4 f-4 c \log (f)}-d} \text{Erf}\left(\frac{b \log (f)-2 x (f-c \log (f))}{2 \sqrt{f-c \log (f)}}\right)}{16 \sqrt{f-c \log (f)}}-\frac{\sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{12 f-4 c \log (f)}-3 d} \text{Erf}\left(\frac{b \log (f)-2 x (3 f-c \log (f))}{2 \sqrt{3 f-c \log (f)}}\right)}{16 \sqrt{3 f-c \log (f)}}+\frac{3 \sqrt{\pi } f^a e^{d-\frac{b^2 \log ^2(f)}{4 (c \log (f)+f)}} \text{Erfi}\left(\frac{b \log (f)+2 x (c \log (f)+f)}{2 \sqrt{c \log (f)+f}}\right)}{16 \sqrt{c \log (f)+f}}+\frac{\sqrt{\pi } f^a e^{3 d-\frac{b^2 \log ^2(f)}{4 (c \log (f)+3 f)}} \text{Erfi}\left(\frac{b \log (f)+2 x (c \log (f)+3 f)}{2 \sqrt{c \log (f)+3 f}}\right)}{16 \sqrt{c \log (f)+3 f}}","-\frac{3 \sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{4 f-4 c \log (f)}-d} \text{Erf}\left(\frac{b \log (f)-2 x (f-c \log (f))}{2 \sqrt{f-c \log (f)}}\right)}{16 \sqrt{f-c \log (f)}}-\frac{\sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{12 f-4 c \log (f)}-3 d} \text{Erf}\left(\frac{b \log (f)-2 x (3 f-c \log (f))}{2 \sqrt{3 f-c \log (f)}}\right)}{16 \sqrt{3 f-c \log (f)}}+\frac{3 \sqrt{\pi } f^a e^{d-\frac{b^2 \log ^2(f)}{4 (c \log (f)+f)}} \text{Erfi}\left(\frac{b \log (f)+2 x (c \log (f)+f)}{2 \sqrt{c \log (f)+f}}\right)}{16 \sqrt{c \log (f)+f}}+\frac{\sqrt{\pi } f^a e^{3 d-\frac{b^2 \log ^2(f)}{4 (c \log (f)+3 f)}} \text{Erfi}\left(\frac{b \log (f)+2 x (c \log (f)+3 f)}{2 \sqrt{c \log (f)+3 f}}\right)}{16 \sqrt{c \log (f)+3 f}}",1,"(-3*E^(-d + (b^2*Log[f]^2)/(4*f - 4*c*Log[f]))*f^a*Sqrt[Pi]*Erf[(b*Log[f] - 2*x*(f - c*Log[f]))/(2*Sqrt[f - c*Log[f]])])/(16*Sqrt[f - c*Log[f]]) - (E^(-3*d + (b^2*Log[f]^2)/(12*f - 4*c*Log[f]))*f^a*Sqrt[Pi]*Erf[(b*Log[f] - 2*x*(3*f - c*Log[f]))/(2*Sqrt[3*f - c*Log[f]])])/(16*Sqrt[3*f - c*Log[f]]) + (3*E^(d - (b^2*Log[f]^2)/(4*(f + c*Log[f])))*f^a*Sqrt[Pi]*Erfi[(b*Log[f] + 2*x*(f + c*Log[f]))/(2*Sqrt[f + c*Log[f]])])/(16*Sqrt[f + c*Log[f]]) + (E^(3*d - (b^2*Log[f]^2)/(4*(3*f + c*Log[f])))*f^a*Sqrt[Pi]*Erfi[(b*Log[f] + 2*x*(3*f + c*Log[f]))/(2*Sqrt[3*f + c*Log[f]])])/(16*Sqrt[3*f + c*Log[f]])","A",14,5,23,0.2174,1,"{5513, 2287, 2234, 2205, 2204}"
326,1,161,0,0.4257271,"\int f^{a+b x+c x^2} \cosh \left(d+e x+f x^2\right) \, dx","Int[f^(a + b*x + c*x^2)*Cosh[d + e*x + f*x^2],x]","\frac{\sqrt{\pi } f^a e^{\frac{(e-b \log (f))^2}{4 (f-c \log (f))}-d} \text{Erf}\left(\frac{-b \log (f)+2 x (f-c \log (f))+e}{2 \sqrt{f-c \log (f)}}\right)}{4 \sqrt{f-c \log (f)}}+\frac{\sqrt{\pi } f^a e^{d-\frac{(b \log (f)+e)^2}{4 (c \log (f)+f)}} \text{Erfi}\left(\frac{b \log (f)+2 x (c \log (f)+f)+e}{2 \sqrt{c \log (f)+f}}\right)}{4 \sqrt{c \log (f)+f}}","\frac{\sqrt{\pi } f^a e^{\frac{(e-b \log (f))^2}{4 (f-c \log (f))}-d} \text{Erf}\left(\frac{-b \log (f)+2 x (f-c \log (f))+e}{2 \sqrt{f-c \log (f)}}\right)}{4 \sqrt{f-c \log (f)}}+\frac{\sqrt{\pi } f^a e^{d-\frac{(b \log (f)+e)^2}{4 (c \log (f)+f)}} \text{Erfi}\left(\frac{b \log (f)+2 x (c \log (f)+f)+e}{2 \sqrt{c \log (f)+f}}\right)}{4 \sqrt{c \log (f)+f}}",1,"(E^(-d + (e - b*Log[f])^2/(4*(f - c*Log[f])))*f^a*Sqrt[Pi]*Erf[(e - b*Log[f] + 2*x*(f - c*Log[f]))/(2*Sqrt[f - c*Log[f]])])/(4*Sqrt[f - c*Log[f]]) + (E^(d - (e + b*Log[f])^2/(4*(f + c*Log[f])))*f^a*Sqrt[Pi]*Erfi[(e + b*Log[f] + 2*x*(f + c*Log[f]))/(2*Sqrt[f + c*Log[f]])])/(4*Sqrt[f + c*Log[f]])","A",8,5,24,0.2083,1,"{5513, 2287, 2234, 2205, 2204}"
327,1,239,0,0.5059054,"\int f^{a+b x+c x^2} \cosh ^2\left(d+e x+f x^2\right) \, dx","Int[f^(a + b*x + c*x^2)*Cosh[d + e*x + f*x^2]^2,x]","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{Erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a \exp \left(\frac{(2 e-b \log (f))^2}{8 f-4 c \log (f)}-2 d\right) \text{Erf}\left(\frac{-b \log (f)+2 x (2 f-c \log (f))+2 e}{2 \sqrt{2 f-c \log (f)}}\right)}{8 \sqrt{2 f-c \log (f)}}+\frac{\sqrt{\pi } f^a \exp \left(2 d-\frac{(b \log (f)+2 e)^2}{4 c \log (f)+8 f}\right) \text{Erfi}\left(\frac{b \log (f)+2 x (c \log (f)+2 f)+2 e}{2 \sqrt{c \log (f)+2 f}}\right)}{8 \sqrt{c \log (f)+2 f}}","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{Erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a \exp \left(\frac{(2 e-b \log (f))^2}{8 f-4 c \log (f)}-2 d\right) \text{Erf}\left(\frac{-b \log (f)+2 x (2 f-c \log (f))+2 e}{2 \sqrt{2 f-c \log (f)}}\right)}{8 \sqrt{2 f-c \log (f)}}+\frac{\sqrt{\pi } f^a \exp \left(2 d-\frac{(b \log (f)+2 e)^2}{4 c \log (f)+8 f}\right) \text{Erfi}\left(\frac{b \log (f)+2 x (c \log (f)+2 f)+2 e}{2 \sqrt{c \log (f)+2 f}}\right)}{8 \sqrt{c \log (f)+2 f}}",1,"(f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(4*Sqrt[c]*Sqrt[Log[f]]) + (E^(-2*d + (2*e - b*Log[f])^2/(8*f - 4*c*Log[f]))*f^a*Sqrt[Pi]*Erf[(2*e - b*Log[f] + 2*x*(2*f - c*Log[f]))/(2*Sqrt[2*f - c*Log[f]])])/(8*Sqrt[2*f - c*Log[f]]) + (E^(2*d - (2*e + b*Log[f])^2/(8*f + 4*c*Log[f]))*f^a*Sqrt[Pi]*Erfi[(2*e + b*Log[f] + 2*x*(2*f + c*Log[f]))/(2*Sqrt[2*f + c*Log[f]])])/(8*Sqrt[2*f + c*Log[f]])","A",10,5,26,0.1923,1,"{5513, 2234, 2204, 2287, 2205}"
328,1,344,0,0.7344411,"\int f^{a+b x+c x^2} \cosh ^3\left(d+e x+f x^2\right) \, dx","Int[f^(a + b*x + c*x^2)*Cosh[d + e*x + f*x^2]^3,x]","\frac{\sqrt{\pi } f^a \exp \left(\frac{(3 e-b \log (f))^2}{12 f-4 c \log (f)}-3 d\right) \text{Erf}\left(\frac{-b \log (f)+2 x (3 f-c \log (f))+3 e}{2 \sqrt{3 f-c \log (f)}}\right)}{16 \sqrt{3 f-c \log (f)}}+\frac{3 \sqrt{\pi } f^a e^{\frac{(e-b \log (f))^2}{4 (f-c \log (f))}-d} \text{Erf}\left(\frac{-b \log (f)+2 x (f-c \log (f))+e}{2 \sqrt{f-c \log (f)}}\right)}{16 \sqrt{f-c \log (f)}}+\frac{\sqrt{\pi } f^a \exp \left(3 d-\frac{(b \log (f)+3 e)^2}{4 (c \log (f)+3 f)}\right) \text{Erfi}\left(\frac{b \log (f)+2 x (c \log (f)+3 f)+3 e}{2 \sqrt{c \log (f)+3 f}}\right)}{16 \sqrt{c \log (f)+3 f}}+\frac{3 \sqrt{\pi } f^a e^{d-\frac{(b \log (f)+e)^2}{4 (c \log (f)+f)}} \text{Erfi}\left(\frac{b \log (f)+2 x (c \log (f)+f)+e}{2 \sqrt{c \log (f)+f}}\right)}{16 \sqrt{c \log (f)+f}}","\frac{\sqrt{\pi } f^a \exp \left(\frac{(3 e-b \log (f))^2}{12 f-4 c \log (f)}-3 d\right) \text{Erf}\left(\frac{-b \log (f)+2 x (3 f-c \log (f))+3 e}{2 \sqrt{3 f-c \log (f)}}\right)}{16 \sqrt{3 f-c \log (f)}}+\frac{3 \sqrt{\pi } f^a e^{\frac{(e-b \log (f))^2}{4 (f-c \log (f))}-d} \text{Erf}\left(\frac{-b \log (f)+2 x (f-c \log (f))+e}{2 \sqrt{f-c \log (f)}}\right)}{16 \sqrt{f-c \log (f)}}+\frac{\sqrt{\pi } f^a \exp \left(3 d-\frac{(b \log (f)+3 e)^2}{4 (c \log (f)+3 f)}\right) \text{Erfi}\left(\frac{b \log (f)+2 x (c \log (f)+3 f)+3 e}{2 \sqrt{c \log (f)+3 f}}\right)}{16 \sqrt{c \log (f)+3 f}}+\frac{3 \sqrt{\pi } f^a e^{d-\frac{(b \log (f)+e)^2}{4 (c \log (f)+f)}} \text{Erfi}\left(\frac{b \log (f)+2 x (c \log (f)+f)+e}{2 \sqrt{c \log (f)+f}}\right)}{16 \sqrt{c \log (f)+f}}",1,"(3*E^(-d + (e - b*Log[f])^2/(4*(f - c*Log[f])))*f^a*Sqrt[Pi]*Erf[(e - b*Log[f] + 2*x*(f - c*Log[f]))/(2*Sqrt[f - c*Log[f]])])/(16*Sqrt[f - c*Log[f]]) + (E^(-3*d + (3*e - b*Log[f])^2/(12*f - 4*c*Log[f]))*f^a*Sqrt[Pi]*Erf[(3*e - b*Log[f] + 2*x*(3*f - c*Log[f]))/(2*Sqrt[3*f - c*Log[f]])])/(16*Sqrt[3*f - c*Log[f]]) + (3*E^(d - (e + b*Log[f])^2/(4*(f + c*Log[f])))*f^a*Sqrt[Pi]*Erfi[(e + b*Log[f] + 2*x*(f + c*Log[f]))/(2*Sqrt[f + c*Log[f]])])/(16*Sqrt[f + c*Log[f]]) + (E^(3*d - (3*e + b*Log[f])^2/(4*(3*f + c*Log[f])))*f^a*Sqrt[Pi]*Erfi[(3*e + b*Log[f] + 2*x*(3*f + c*Log[f]))/(2*Sqrt[3*f + c*Log[f]])])/(16*Sqrt[3*f + c*Log[f]])","A",14,5,26,0.1923,1,"{5513, 2287, 2234, 2205, 2204}"
329,1,20,0,0.0498668,"\int \left(\frac{x}{\cosh ^{\frac{3}{2}}(x)}+x \sqrt{\cosh (x)}\right) \, dx","Int[x/Cosh[x]^(3/2) + x*Sqrt[Cosh[x]],x]","\frac{2 x \sinh (x)}{\sqrt{\cosh (x)}}-4 \sqrt{\cosh (x)}","\frac{2 x \sinh (x)}{\sqrt{\cosh (x)}}-4 \sqrt{\cosh (x)}",1,"-4*Sqrt[Cosh[x]] + (2*x*Sinh[x])/Sqrt[Cosh[x]]","A",2,1,17,0.05882,1,"{3315}"
330,1,24,0,0.0511449,"\int \left(\frac{x}{\cosh ^{\frac{5}{2}}(x)}-\frac{x}{3 \sqrt{\cosh (x)}}\right) \, dx","Int[x/Cosh[x]^(5/2) - x/(3*Sqrt[Cosh[x]]),x]","\frac{4}{3 \sqrt{\cosh (x)}}+\frac{2 x \sinh (x)}{3 \cosh ^{\frac{3}{2}}(x)}","\frac{4}{3 \sqrt{\cosh (x)}}+\frac{2 x \sinh (x)}{3 \cosh ^{\frac{3}{2}}(x)}",1,"4/(3*Sqrt[Cosh[x]]) + (2*x*Sinh[x])/(3*Cosh[x]^(3/2))","A",2,1,20,0.05000,1,"{3315}"
331,1,47,0,0.0708335,"\int \left(\frac{x}{\cosh ^{\frac{7}{2}}(x)}+\frac{3}{5} x \sqrt{\cosh (x)}\right) \, dx","Int[x/Cosh[x]^(7/2) + (3*x*Sqrt[Cosh[x]])/5,x]","\frac{4}{15 \cosh ^{\frac{3}{2}}(x)}-\frac{12 \sqrt{\cosh (x)}}{5}+\frac{2 x \sinh (x)}{5 \cosh ^{\frac{5}{2}}(x)}+\frac{6 x \sinh (x)}{5 \sqrt{\cosh (x)}}","\frac{4}{15 \cosh ^{\frac{3}{2}}(x)}-\frac{12 \sqrt{\cosh (x)}}{5}+\frac{2 x \sinh (x)}{5 \cosh ^{\frac{5}{2}}(x)}+\frac{6 x \sinh (x)}{5 \sqrt{\cosh (x)}}",1,"4/(15*Cosh[x]^(3/2)) - (12*Sqrt[Cosh[x]])/5 + (2*x*Sinh[x])/(5*Cosh[x]^(5/2)) + (6*x*Sinh[x])/(5*Sqrt[Cosh[x]])","A",3,1,20,0.05000,1,"{3315}"
332,1,36,0,0.0941286,"\int \left(\frac{x^2}{\cosh ^{\frac{3}{2}}(x)}+x^2 \sqrt{\cosh (x)}\right) \, dx","Int[x^2/Cosh[x]^(3/2) + x^2*Sqrt[Cosh[x]],x]","\frac{2 x^2 \sinh (x)}{\sqrt{\cosh (x)}}-8 x \sqrt{\cosh (x)}-16 i E\left(\left.\frac{i x}{2}\right|2\right)","\frac{2 x^2 \sinh (x)}{\sqrt{\cosh (x)}}-8 x \sqrt{\cosh (x)}-16 i E\left(\left.\frac{i x}{2}\right|2\right)",1,"-8*x*Sqrt[Cosh[x]] - (16*I)*EllipticE[(I/2)*x, 2] + (2*x^2*Sinh[x])/Sqrt[Cosh[x]]","A",3,2,21,0.09524,1,"{3316, 2639}"
333,1,30,0,0.038134,"\int (x+\cosh (x))^2 \, dx","Int[(x + Cosh[x])^2,x]","\frac{x^3}{3}+\frac{x}{2}+2 x \sinh (x)-2 \cosh (x)+\frac{1}{2} \sinh (x) \cosh (x)","\frac{x^3}{3}+\frac{x}{2}+2 x \sinh (x)-2 \cosh (x)+\frac{1}{2} \sinh (x) \cosh (x)",1,"x/2 + x^3/3 - 2*Cosh[x] + 2*x*Sinh[x] + (Cosh[x]*Sinh[x])/2","A",6,5,6,0.8333,1,"{6742, 3296, 2638, 2635, 8}"
334,1,56,0,0.0745582,"\int (x+\cosh (x))^3 \, dx","Int[(x + Cosh[x])^3,x]","\frac{x^4}{4}+\frac{3 x^2}{4}+3 x^2 \sinh (x)+\frac{\sinh ^3(x)}{3}+7 \sinh (x)-\frac{3 \cosh ^2(x)}{4}-6 x \cosh (x)+\frac{3}{2} x \sinh (x) \cosh (x)","\frac{x^4}{4}+\frac{3 x^2}{4}+3 x^2 \sinh (x)+\frac{\sinh ^3(x)}{3}+7 \sinh (x)-\frac{3 \cosh ^2(x)}{4}-6 x \cosh (x)+\frac{3}{2} x \sinh (x) \cosh (x)",1,"(3*x^2)/4 + x^4/4 - 6*x*Cosh[x] - (3*Cosh[x]^2)/4 + 7*Sinh[x] + 3*x^2*Sinh[x] + (3*x*Cosh[x]*Sinh[x])/2 + Sinh[x]^3/3","A",9,6,6,1.000,1,"{6742, 3296, 2637, 3310, 30, 2633}"
335,1,213,0,0.5233459,"\int \frac{\cosh (a+b x)}{c+d x^2} \, dx","Int[Cosh[a + b*x]/(c + d*x^2),x]","\frac{\cosh \left(a+\frac{b \sqrt{-c}}{\sqrt{d}}\right) \text{Chi}\left(\frac{b \sqrt{-c}}{\sqrt{d}}-b x\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\cosh \left(a-\frac{b \sqrt{-c}}{\sqrt{d}}\right) \text{Chi}\left(x b+\frac{\sqrt{-c} b}{\sqrt{d}}\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\sinh \left(a+\frac{b \sqrt{-c}}{\sqrt{d}}\right) \text{Shi}\left(\frac{b \sqrt{-c}}{\sqrt{d}}-b x\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\sinh \left(a-\frac{b \sqrt{-c}}{\sqrt{d}}\right) \text{Shi}\left(x b+\frac{\sqrt{-c} b}{\sqrt{d}}\right)}{2 \sqrt{-c} \sqrt{d}}","\frac{\cosh \left(a+\frac{b \sqrt{-c}}{\sqrt{d}}\right) \text{Chi}\left(\frac{b \sqrt{-c}}{\sqrt{d}}-b x\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\cosh \left(a-\frac{b \sqrt{-c}}{\sqrt{d}}\right) \text{Chi}\left(x b+\frac{\sqrt{-c} b}{\sqrt{d}}\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\sinh \left(a+\frac{b \sqrt{-c}}{\sqrt{d}}\right) \text{Shi}\left(\frac{b \sqrt{-c}}{\sqrt{d}}-b x\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\sinh \left(a-\frac{b \sqrt{-c}}{\sqrt{d}}\right) \text{Shi}\left(x b+\frac{\sqrt{-c} b}{\sqrt{d}}\right)}{2 \sqrt{-c} \sqrt{d}}",1,"(Cosh[a + (b*Sqrt[-c])/Sqrt[d]]*CoshIntegral[(b*Sqrt[-c])/Sqrt[d] - b*x])/(2*Sqrt[-c]*Sqrt[d]) - (Cosh[a - (b*Sqrt[-c])/Sqrt[d]]*CoshIntegral[(b*Sqrt[-c])/Sqrt[d] + b*x])/(2*Sqrt[-c]*Sqrt[d]) - (Sinh[a + (b*Sqrt[-c])/Sqrt[d]]*SinhIntegral[(b*Sqrt[-c])/Sqrt[d] - b*x])/(2*Sqrt[-c]*Sqrt[d]) - (Sinh[a - (b*Sqrt[-c])/Sqrt[d]]*SinhIntegral[(b*Sqrt[-c])/Sqrt[d] + b*x])/(2*Sqrt[-c]*Sqrt[d])","A",8,4,16,0.2500,1,"{5281, 3303, 3298, 3301}"
336,1,271,0,0.7505137,"\int \frac{\cosh (a+b x)}{c+d x+e x^2} \, dx","Int[Cosh[a + b*x]/(c + d*x + e*x^2),x]","\frac{\cosh \left(a-\frac{b \left(d-\sqrt{d^2-4 c e}\right)}{2 e}\right) \text{Chi}\left(\frac{b \left(d-\sqrt{d^2-4 c e}\right)}{2 e}+b x\right)}{\sqrt{d^2-4 c e}}-\frac{\cosh \left(a-\frac{b \left(\sqrt{d^2-4 c e}+d\right)}{2 e}\right) \text{Chi}\left(\frac{b \left(d+\sqrt{d^2-4 c e}\right)}{2 e}+b x\right)}{\sqrt{d^2-4 c e}}+\frac{\sinh \left(a-\frac{b \left(d-\sqrt{d^2-4 c e}\right)}{2 e}\right) \text{Shi}\left(\frac{b \left(d-\sqrt{d^2-4 c e}\right)}{2 e}+b x\right)}{\sqrt{d^2-4 c e}}-\frac{\sinh \left(a-\frac{b \left(\sqrt{d^2-4 c e}+d\right)}{2 e}\right) \text{Shi}\left(\frac{b \left(d+\sqrt{d^2-4 c e}\right)}{2 e}+b x\right)}{\sqrt{d^2-4 c e}}","\frac{\cosh \left(a-\frac{b \left(d-\sqrt{d^2-4 c e}\right)}{2 e}\right) \text{Chi}\left(\frac{b \left(d-\sqrt{d^2-4 c e}\right)}{2 e}+b x\right)}{\sqrt{d^2-4 c e}}-\frac{\cosh \left(a-\frac{b \left(\sqrt{d^2-4 c e}+d\right)}{2 e}\right) \text{Chi}\left(\frac{b \left(d+\sqrt{d^2-4 c e}\right)}{2 e}+b x\right)}{\sqrt{d^2-4 c e}}+\frac{\sinh \left(a-\frac{b \left(d-\sqrt{d^2-4 c e}\right)}{2 e}\right) \text{Shi}\left(\frac{b \left(d-\sqrt{d^2-4 c e}\right)}{2 e}+b x\right)}{\sqrt{d^2-4 c e}}-\frac{\sinh \left(a-\frac{b \left(\sqrt{d^2-4 c e}+d\right)}{2 e}\right) \text{Shi}\left(\frac{b \left(d+\sqrt{d^2-4 c e}\right)}{2 e}+b x\right)}{\sqrt{d^2-4 c e}}",1,"(Cosh[a - (b*(d - Sqrt[d^2 - 4*c*e]))/(2*e)]*CoshIntegral[(b*(d - Sqrt[d^2 - 4*c*e]))/(2*e) + b*x])/Sqrt[d^2 - 4*c*e] - (Cosh[a - (b*(d + Sqrt[d^2 - 4*c*e]))/(2*e)]*CoshIntegral[(b*(d + Sqrt[d^2 - 4*c*e]))/(2*e) + b*x])/Sqrt[d^2 - 4*c*e] + (Sinh[a - (b*(d - Sqrt[d^2 - 4*c*e]))/(2*e)]*SinhIntegral[(b*(d - Sqrt[d^2 - 4*c*e]))/(2*e) + b*x])/Sqrt[d^2 - 4*c*e] - (Sinh[a - (b*(d + Sqrt[d^2 - 4*c*e]))/(2*e)]*SinhIntegral[(b*(d + Sqrt[d^2 - 4*c*e]))/(2*e) + b*x])/Sqrt[d^2 - 4*c*e]","A",8,4,19,0.2105,1,"{6728, 3303, 3298, 3301}"