1,1,21,10,0.0110242,"\int \cosh (a+b x) \, dx","Integrate[Cosh[a + b*x],x]","\frac{\sinh (a) \cosh (b x)}{b}+\frac{\cosh (a) \sinh (b x)}{b}","\frac{\sinh (a+b x)}{b}",1,"(Cosh[b*x]*Sinh[a])/b + (Cosh[a]*Sinh[b*x])/b","B",1
2,1,23,25,0.0223773,"\int \cosh ^2(a+b x) \, dx","Integrate[Cosh[a + b*x]^2,x]","\frac{2 (a+b x)+\sinh (2 (a+b x))}{4 b}","\frac{\sinh (a+b x) \cosh (a+b x)}{2 b}+\frac{x}{2}",1,"(2*(a + b*x) + Sinh[2*(a + b*x)])/(4*b)","A",1
3,1,26,26,0.0080845,"\int \cosh ^3(a+b x) \, dx","Integrate[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",1
4,1,33,46,0.0452937,"\int \cosh ^4(a+b x) \, dx","Integrate[Cosh[a + b*x]^4,x]","\frac{12 (a+b x)+8 \sinh (2 (a+b x))+\sinh (4 (a+b x))}{32 b}","\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,"(12*(a + b*x) + 8*Sinh[2*(a + b*x)] + Sinh[4*(a + b*x)])/(32*b)","A",1
5,1,41,41,0.0153183,"\int \cosh ^5(a+b x) \, dx","Integrate[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",1
6,1,43,67,0.0411628,"\int \cosh ^6(a+b x) \, dx","Integrate[Cosh[a + b*x]^6,x]","\frac{45 \sinh (2 (a+b x))+9 \sinh (4 (a+b x))+\sinh (6 (a+b x))+60 a+60 b x}{192 b}","\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,"(60*a + 60*b*x + 45*Sinh[2*(a + b*x)] + 9*Sinh[4*(a + b*x)] + Sinh[6*(a + b*x)])/(192*b)","A",1
7,1,55,69,0.1164302,"\int \cosh ^{\frac{7}{2}}(a+b x) \, dx","Integrate[Cosh[a + b*x]^(7/2),x]","\frac{(23 \sinh (a+b x)+3 \sinh (3 (a+b x))) \sqrt{\cosh (a+b x)}-20 i F\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{42 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,"((-20*I)*EllipticF[(I/2)*(a + b*x), 2] + Sqrt[Cosh[a + b*x]]*(23*Sinh[a + b*x] + 3*Sinh[3*(a + b*x)]))/(42*b)","A",1
8,1,44,46,0.055763,"\int \cosh ^{\frac{5}{2}}(a+b x) \, dx","Integrate[Cosh[a + b*x]^(5/2),x]","\frac{\sinh (2 (a+b x)) \sqrt{\cosh (a+b x)}-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)*EllipticE[(I/2)*(a + b*x), 2] + Sqrt[Cosh[a + b*x]]*Sinh[2*(a + b*x)])/(5*b)","A",1
9,1,81,46,0.1122501,"\int \cosh ^{\frac{3}{2}}(a+b x) \, dx","Integrate[Cosh[a + b*x]^(3/2),x]","\frac{2 \sqrt{\sinh (2 (a+b x))+\cosh (2 (a+b x))+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\cosh (2 (a+b x))-\sinh (2 (a+b x))\right)+\sinh (2 (a+b x))}{3 b \sqrt{\cosh (a+b 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}",1,"(Sinh[2*(a + b*x)] + 2*Hypergeometric2F1[1/4, 1/2, 5/4, -Cosh[2*(a + b*x)] - Sinh[2*(a + b*x)]]*Sqrt[1 + Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)]])/(3*b*Sqrt[Cosh[a + b*x]])","C",1
10,1,20,20,0.0295327,"\int \sqrt{\cosh (a+b x)} \, dx","Integrate[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
11,1,20,20,0.0287482,"\int \frac{1}{\sqrt{\cosh (a+b x)}} \, dx","Integrate[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
12,1,42,42,0.0630222,"\int \frac{1}{\cosh ^{\frac{3}{2}}(a+b x)} \, dx","Integrate[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",1
13,1,84,46,0.0724826,"\int \frac{1}{\cosh ^{\frac{5}{2}}(a+b x)} \, dx","Integrate[Cosh[a + b*x]^(-5/2),x]","\frac{2 \left(\cosh (a+b x) \sqrt{\sinh (2 (a+b x))+\cosh (2 (a+b x))+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\cosh (2 (a+b x))-\sinh (2 (a+b x))\right)+\sinh (a+b x)\right)}{3 b \cosh ^{\frac{3}{2}}(a+b 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}",1,"(2*(Sinh[a + b*x] + Cosh[a + b*x]*Hypergeometric2F1[1/4, 1/2, 5/4, -Cosh[2*(a + b*x)] - Sinh[2*(a + b*x)]]*Sqrt[1 + Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)]]))/(3*b*Cosh[a + b*x]^(3/2))","C",1
14,1,63,69,0.1422492,"\int \frac{1}{\cosh ^{\frac{7}{2}}(a+b x)} \, dx","Integrate[Cosh[a + b*x]^(-7/2),x]","\frac{3 \sinh (2 (a+b x))+2 \tanh (a+b x)+6 i \cosh ^{\frac{3}{2}}(a+b x) E\left(\left.\frac{1}{2} i (a+b x)\right|2\right)}{5 b \cosh ^{\frac{3}{2}}(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)*Cosh[a + b*x]^(3/2)*EllipticE[(I/2)*(a + b*x), 2] + 3*Sinh[2*(a + b*x)] + 2*Tanh[a + b*x])/(5*b*Cosh[a + b*x]^(3/2))","A",1
15,1,53,65,0.0532446,"\int (a \cosh (x))^{7/2} \, dx","Integrate[(a*Cosh[x])^(7/2),x]","\frac{a^3 \sqrt{a \cosh (x)} \left((23 \sinh (x)+3 \sinh (3 x)) \sqrt{\cosh (x)}-20 i F\left(\left.\frac{i x}{2}\right|2\right)\right)}{42 \sqrt{\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{10}{21} a^3 \sinh (x) \sqrt{a \cosh (x)}+\frac{2}{7} a \sinh (x) (a \cosh (x))^{5/2}",1,"(a^3*Sqrt[a*Cosh[x]]*((-20*I)*EllipticF[(I/2)*x, 2] + Sqrt[Cosh[x]]*(23*Sinh[x] + 3*Sinh[3*x])))/(42*Sqrt[Cosh[x]])","A",1
16,1,41,48,0.0463958,"\int (a \cosh (x))^{5/2} \, dx","Integrate[(a*Cosh[x])^(5/2),x]","\frac{2 (a \cosh (x))^{5/2} \left(\sinh (x) \cosh ^{\frac{3}{2}}(x)-3 i E\left(\left.\frac{i x}{2}\right|2\right)\right)}{5 \cosh ^{\frac{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)}}",1,"(2*(a*Cosh[x])^(5/2)*((-3*I)*EllipticE[(I/2)*x, 2] + Cosh[x]^(3/2)*Sinh[x]))/(5*Cosh[x]^(5/2))","A",1
17,1,57,48,0.0639265,"\int (a \cosh (x))^{3/2} \, dx","Integrate[(a*Cosh[x])^(3/2),x]","\frac{2}{3} (a \cosh (x))^{3/2} \left(\text{sech}^2(x) \sqrt{\sinh (2 x)+\cosh (2 x)+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\cosh (2 x)-\sinh (2 x)\right)+\tanh (x)\right)","\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*(a*Cosh[x])^(3/2)*(Hypergeometric2F1[1/4, 1/2, 5/4, -Cosh[2*x] - Sinh[2*x]]*Sech[x]^2*Sqrt[1 + Cosh[2*x] + Sinh[2*x]] + Tanh[x]))/3","C",1
18,1,27,27,0.0100796,"\int \sqrt{a \cosh (x)} \, dx","Integrate[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",1
19,1,27,27,0.013474,"\int \frac{1}{\sqrt{a \cosh (x)}} \, dx","Integrate[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",1
20,1,34,46,0.0259737,"\int \frac{1}{(a \cosh (x))^{3/2}} \, dx","Integrate[(a*Cosh[x])^(-3/2),x]","\frac{2 \cosh (x) \left(\sinh (x)+i \sqrt{\cosh (x)} E\left(\left.\frac{i x}{2}\right|2\right)\right)}{(a \cosh (x))^{3/2}}","\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*Cosh[x]*(I*Sqrt[Cosh[x]]*EllipticE[(I/2)*x, 2] + Sinh[x]))/(a*Cosh[x])^(3/2)","A",1
21,1,56,50,0.043173,"\int \frac{1}{(a \cosh (x))^{5/2}} \, dx","Integrate[(a*Cosh[x])^(-5/2),x]","\frac{2 \left(\sqrt{\sinh (2 x)+\cosh (2 x)+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\cosh (2 x)-\sinh (2 x)\right)+\tanh (x)\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*(Hypergeometric2F1[1/4, 1/2, 5/4, -Cosh[2*x] - Sinh[2*x]]*Sqrt[1 + Cosh[2*x] + Sinh[2*x]] + Tanh[x]))/(3*a^2*Sqrt[a*Cosh[x]])","C",1
22,1,43,67,0.0505151,"\int \frac{1}{(a \cosh (x))^{7/2}} \, dx","Integrate[(a*Cosh[x])^(-7/2),x]","\frac{2 \left(\tanh (x)+3 i \cosh ^{\frac{3}{2}}(x) E\left(\left.\frac{i x}{2}\right|2\right)+3 \sinh (x) \cosh (x)\right)}{5 a^2 (a \cosh (x))^{3/2}}","\frac{6 i E\left(\left.\frac{i x}{2}\right|2\right) \sqrt{a \cosh (x)}}{5 a^4 \sqrt{\cosh (x)}}+\frac{6 \sinh (x)}{5 a^3 \sqrt{a \cosh (x)}}+\frac{2 \sinh (x)}{5 a (a \cosh (x))^{5/2}}",1,"(2*((3*I)*Cosh[x]^(3/2)*EllipticE[(I/2)*x, 2] + 3*Cosh[x]*Sinh[x] + Tanh[x]))/(5*a^2*(a*Cosh[x])^(3/2))","A",1
23,1,65,71,0.0673533,"\int (b \cosh (c+d x))^n \, dx","Integrate[(b*Cosh[c + d*x])^n,x]","\frac{\sqrt{-\sinh ^2(c+d x)} \coth (c+d x) (b \cosh (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cosh ^2(c+d x)\right)}{d (n+1)}","-\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])^n*Coth[c + d*x]*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Cosh[c + d*x]^2]*Sqrt[-Sinh[c + d*x]^2])/(d*(1 + n))","A",1
24,1,53,54,0.0862544,"\int \frac{\cosh ^4(x)}{a+a \cosh (x)} \, dx","Integrate[Cosh[x]^4/(a + a*Cosh[x]),x]","\frac{\text{sech}\left(\frac{x}{2}\right) \left(45 \sinh \left(\frac{x}{2}\right)+18 \sinh \left(\frac{3 x}{2}\right)-2 \sinh \left(\frac{5 x}{2}\right)+\sinh \left(\frac{7 x}{2}\right)-36 x \cosh \left(\frac{x}{2}\right)\right)}{24 a}","-\frac{3 x}{2 a}+\frac{4 \sinh ^3(x)}{3 a}+\frac{4 \sinh (x)}{a}-\frac{\sinh (x) \cosh ^3(x)}{a \cosh (x)+a}-\frac{3 \sinh (x) \cosh (x)}{2 a}",1,"(Sech[x/2]*(-36*x*Cosh[x/2] + 45*Sinh[x/2] + 18*Sinh[(3*x)/2] - 2*Sinh[(5*x)/2] + Sinh[(7*x)/2]))/(24*a)","A",1
25,1,45,43,0.0557767,"\int \frac{\cosh ^3(x)}{a+a \cosh (x)} \, dx","Integrate[Cosh[x]^3/(a + a*Cosh[x]),x]","\frac{\text{sech}\left(\frac{x}{2}\right) \left(-12 \sinh \left(\frac{x}{2}\right)-3 \sinh \left(\frac{3 x}{2}\right)+\sinh \left(\frac{5 x}{2}\right)+12 x \cosh \left(\frac{x}{2}\right)\right)}{8 a}","\frac{3 x}{2 a}-\frac{2 \sinh (x)}{a}-\frac{\sinh (x) \cosh ^2(x)}{a \cosh (x)+a}+\frac{3 \sinh (x) \cosh (x)}{2 a}",1,"(Sech[x/2]*(12*x*Cosh[x/2] - 12*Sinh[x/2] - 3*Sinh[(3*x)/2] + Sinh[(5*x)/2]))/(8*a)","A",1
26,1,32,25,0.0588583,"\int \frac{\cosh ^2(x)}{a+a \cosh (x)} \, dx","Integrate[Cosh[x]^2/(a + a*Cosh[x]),x]","\frac{-2 x+3 \tanh \left(\frac{x}{2}\right)+\sinh \left(\frac{3 x}{2}\right) \text{sech}\left(\frac{x}{2}\right)}{2 a}","-\frac{x}{a}+\frac{\sinh (x)}{a}+\frac{\sinh (x)}{a (\cosh (x)+1)}",1,"(-2*x + Sech[x/2]*Sinh[(3*x)/2] + 3*Tanh[x/2])/(2*a)","A",1
27,1,14,18,0.0291936,"\int \frac{\cosh (x)}{a+a \cosh (x)} \, dx","Integrate[Cosh[x]/(a + a*Cosh[x]),x]","\frac{x-\tanh \left(\frac{x}{2}\right)}{a}","\frac{x}{a}-\frac{\sinh (x)}{a \cosh (x)+a}",1,"(x - Tanh[x/2])/a","A",1
28,1,22,20,0.0264073,"\int \frac{\text{sech}(x)}{a+a \cosh (x)} \, dx","Integrate[Sech[x]/(a + a*Cosh[x]),x]","\frac{2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)-\tanh \left(\frac{x}{2}\right)}{a}","\frac{\tan ^{-1}(\sinh (x))}{a}-\frac{\sinh (x)}{a \cosh (x)+a}",1,"(2*ArcTan[Tanh[x/2]] - Tanh[x/2])/a","A",1
29,1,43,28,0.088167,"\int \frac{\text{sech}^2(x)}{a+a \cosh (x)} \, dx","Integrate[Sech[x]^2/(a + a*Cosh[x]),x]","\frac{2 \cosh \left(\frac{x}{2}\right) \left(\sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right) \left(\tanh (x)-2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)\right)\right)}{a (\cosh (x)+1)}","\frac{2 \tanh (x)}{a}-\frac{\tan ^{-1}(\sinh (x))}{a}-\frac{\tanh (x)}{a \cosh (x)+a}",1,"(2*Cosh[x/2]*(Sinh[x/2] + Cosh[x/2]*(-2*ArcTan[Tanh[x/2]] + Tanh[x])))/(a*(1 + Cosh[x]))","A",1
30,1,49,43,0.0917471,"\int \frac{\text{sech}^3(x)}{a+a \cosh (x)} \, dx","Integrate[Sech[x]^3/(a + a*Cosh[x]),x]","\frac{\cosh \left(\frac{x}{2}\right) \left(\cosh \left(\frac{x}{2}\right) \left(6 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+\tanh (x) (\text{sech}(x)-2)\right)-2 \sinh \left(\frac{x}{2}\right)\right)}{a (\cosh (x)+1)}","-\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,"(Cosh[x/2]*(-2*Sinh[x/2] + Cosh[x/2]*(6*ArcTan[Tanh[x/2]] + (-2 + Sech[x])*Tanh[x])))/(a*(1 + Cosh[x]))","A",1
31,1,60,56,0.1954759,"\int \frac{\text{sech}^4(x)}{a+a \cosh (x)} \, dx","Integrate[Sech[x]^4/(a + a*Cosh[x]),x]","\frac{\cosh \left(\frac{x}{2}\right) \left(6 \sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right) \left(\tanh (x) \left(2 \text{sech}^2(x)-3 \text{sech}(x)+10\right)-18 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)\right)\right)}{3 a (\cosh (x)+1)}","-\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,"(Cosh[x/2]*(6*Sinh[x/2] + Cosh[x/2]*(-18*ArcTan[Tanh[x/2]] + (10 - 3*Sech[x] + 2*Sech[x]^2)*Tanh[x])))/(3*a*(1 + Cosh[x]))","A",1
32,1,14,20,0.0171199,"\int \frac{1}{1+\cosh (c+d x)} \, dx","Integrate[(1 + Cosh[c + d*x])^(-1),x]","\frac{\tanh \left(\frac{1}{2} (c+d x)\right)}{d}","\frac{\sinh (c+d x)}{d (\cosh (c+d x)+1)}",1,"Tanh[(c + d*x)/2]/d","A",1
33,1,34,47,0.0307029,"\int \frac{1}{(1+\cosh (c+d x))^2} \, dx","Integrate[(1 + Cosh[c + d*x])^(-2),x]","\frac{4 \sinh (c+d x)+\sinh (2 (c+d x))}{6 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,"(4*Sinh[c + d*x] + Sinh[2*(c + d*x)])/(6*d*(1 + Cosh[c + d*x])^2)","A",1
34,1,44,70,0.0605734,"\int \frac{1}{(1+\cosh (c+d x))^3} \, dx","Integrate[(1 + Cosh[c + d*x])^(-3),x]","\frac{15 \sinh (c+d x)+6 \sinh (2 (c+d x))+\sinh (3 (c+d x))}{30 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,"(15*Sinh[c + d*x] + 6*Sinh[2*(c + d*x)] + Sinh[3*(c + d*x)])/(30*d*(1 + Cosh[c + d*x])^3)","A",1
35,1,54,93,0.087254,"\int \frac{1}{(1+\cosh (c+d x))^4} \, dx","Integrate[(1 + Cosh[c + d*x])^(-4),x]","\frac{56 \sinh (c+d x)+28 \sinh (2 (c+d x))+8 \sinh (3 (c+d x))+\sinh (4 (c+d x))}{140 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,"(56*Sinh[c + d*x] + 28*Sinh[2*(c + d*x)] + 8*Sinh[3*(c + d*x)] + Sinh[4*(c + d*x)])/(140*d*(1 + Cosh[c + d*x])^4)","A",1
36,1,14,23,0.0256973,"\int \frac{1}{1-\cosh (c+d x)} \, dx","Integrate[(1 - Cosh[c + d*x])^(-1),x]","\frac{\coth \left(\frac{1}{2} (c+d x)\right)}{d}","-\frac{\sinh (c+d x)}{d (1-\cosh (c+d x))}",1,"Coth[(c + d*x)/2]/d","A",1
37,1,31,51,0.0301706,"\int \frac{1}{(1-\cosh (c+d x))^2} \, dx","Integrate[(1 - Cosh[c + d*x])^(-2),x]","\frac{\sinh (c+d x) (\cosh (c+d x)-2)}{3 d (\cosh (c+d x)-1)^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,"((-2 + Cosh[c + d*x])*Sinh[c + d*x])/(3*d*(-1 + Cosh[c + d*x])^2)","A",1
38,1,41,76,0.0564582,"\int \frac{1}{(1-\cosh (c+d x))^3} \, dx","Integrate[(1 - Cosh[c + d*x])^(-3),x]","\frac{\sinh (c+d x) (-6 \cosh (c+d x)+\cosh (2 (c+d x))+8)}{15 d (\cosh (c+d x)-1)^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,"((8 - 6*Cosh[c + d*x] + Cosh[2*(c + d*x)])*Sinh[c + d*x])/(15*d*(-1 + Cosh[c + d*x])^3)","A",1
39,1,51,101,0.0802224,"\int \frac{1}{(1-\cosh (c+d x))^4} \, dx","Integrate[(1 - Cosh[c + d*x])^(-4),x]","\frac{\sinh (c+d x) (29 \cosh (c+d x)-8 \cosh (2 (c+d x))+\cosh (3 (c+d x))-32)}{70 d (\cosh (c+d x)-1)^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,"((-32 + 29*Cosh[c + d*x] - 8*Cosh[2*(c + d*x)] + Cosh[3*(c + d*x)])*Sinh[c + d*x])/(70*d*(-1 + Cosh[c + d*x])^4)","A",1
40,1,34,51,0.0228612,"\int \frac{\cosh (x)}{\sqrt{a+a \cosh (x)}} \, dx","Integrate[Cosh[x]/Sqrt[a + a*Cosh[x]],x]","-\frac{2 \cosh \left(\frac{x}{2}\right) \left(\tan ^{-1}\left(\sinh \left(\frac{x}{2}\right)\right)-2 \sinh \left(\frac{x}{2}\right)\right)}{\sqrt{a (\cosh (x)+1)}}","\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,"(-2*Cosh[x/2]*(ArcTan[Sinh[x/2]] - 2*Sinh[x/2]))/Sqrt[a*(1 + Cosh[x])]","A",1
41,1,35,53,0.0312631,"\int \frac{\cosh (x)}{\sqrt{a-a \cosh (x)}} \, dx","Integrate[Cosh[x]/Sqrt[a - a*Cosh[x]],x]","\frac{2 \sinh \left(\frac{x}{2}\right) \left(2 \cosh \left(\frac{x}{2}\right)+\log \left(\tanh \left(\frac{x}{4}\right)\right)\right)}{\sqrt{a-a \cosh (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}}",1,"(2*(2*Cosh[x/2] + Log[Tanh[x/4]])*Sinh[x/2])/Sqrt[a - a*Cosh[x]]","A",1
42,1,71,89,0.1346329,"\int (a+a \cosh (c+d x))^{5/2} \, dx","Integrate[(a + a*Cosh[c + d*x])^(5/2),x]","\frac{a^2 \left(150 \sinh \left(\frac{1}{2} (c+d x)\right)+25 \sinh \left(\frac{3}{2} (c+d x)\right)+3 \sinh \left(\frac{5}{2} (c+d x)\right)\right) \text{sech}\left(\frac{1}{2} (c+d x)\right) \sqrt{a (\cosh (c+d x)+1)}}{30 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,"(a^2*Sqrt[a*(1 + Cosh[c + d*x])]*Sech[(c + d*x)/2]*(150*Sinh[(c + d*x)/2] + 25*Sinh[(3*(c + d*x))/2] + 3*Sinh[(5*(c + d*x))/2]))/(30*d)","A",1
43,1,55,59,0.0667103,"\int (a+a \cosh (c+d x))^{3/2} \, dx","Integrate[(a + a*Cosh[c + d*x])^(3/2),x]","\frac{a \left(9 \sinh \left(\frac{1}{2} (c+d x)\right)+\sinh \left(\frac{3}{2} (c+d x)\right)\right) \text{sech}\left(\frac{1}{2} (c+d x)\right) \sqrt{a (\cosh (c+d x)+1)}}{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,"(a*Sqrt[a*(1 + Cosh[c + d*x])]*Sech[(c + d*x)/2]*(9*Sinh[(c + d*x)/2] + Sinh[(3*(c + d*x))/2]))/(3*d)","A",1
44,1,29,26,0.03278,"\int \sqrt{a+a \cosh (c+d x)} \, dx","Integrate[Sqrt[a + a*Cosh[c + d*x]],x]","\frac{2 \tanh \left(\frac{1}{2} (c+d x)\right) \sqrt{a (\cosh (c+d x)+1)}}{d}","\frac{2 a \sinh (c+d x)}{d \sqrt{a \cosh (c+d x)+a}}",1,"(2*Sqrt[a*(1 + Cosh[c + d*x])]*Tanh[(c + d*x)/2])/d","A",1
45,1,40,46,0.0168608,"\int \frac{1}{\sqrt{a+a \cosh (c+d x)}} \, dx","Integrate[1/Sqrt[a + a*Cosh[c + d*x]],x]","\frac{2 \cosh \left(\frac{1}{2} (c+d x)\right) \tan ^{-1}\left(\sinh \left(\frac{1}{2} (c+d x)\right)\right)}{d \sqrt{a (\cosh (c+d x)+1)}}","\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,"(2*ArcTan[Sinh[(c + d*x)/2]]*Cosh[(c + d*x)/2])/(d*Sqrt[a*(1 + Cosh[c + d*x])])","A",1
46,1,63,77,0.0899587,"\int \frac{1}{(a+a \cosh (c+d x))^{3/2}} \, dx","Integrate[(a + a*Cosh[c + d*x])^(-3/2),x]","\frac{\cosh ^2\left(\frac{1}{2} (c+d x)\right) \left(\tanh \left(\frac{1}{2} (c+d x)\right)+\cosh \left(\frac{1}{2} (c+d x)\right) \tan ^{-1}\left(\sinh \left(\frac{1}{2} (c+d x)\right)\right)\right)}{d (a (\cosh (c+d x)+1))^{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,"(Cosh[(c + d*x)/2]^2*(ArcTan[Sinh[(c + d*x)/2]]*Cosh[(c + d*x)/2] + Tanh[(c + d*x)/2]))/(d*(a*(1 + Cosh[c + d*x]))^(3/2))","A",1
47,1,91,107,0.2825488,"\int \frac{1}{(a+a \cosh (c+d x))^{5/2}} \, dx","Integrate[(a + a*Cosh[c + d*x])^(-5/2),x]","\frac{\cosh ^5\left(\frac{1}{2} (c+d x)\right) \left(32 \sinh ^5\left(\frac{1}{2} (c+d x)\right) \text{csch}^4(c+d x)+3 \left(\tan ^{-1}\left(\sinh \left(\frac{1}{2} (c+d x)\right)\right)+\tanh \left(\frac{1}{2} (c+d x)\right) \text{sech}\left(\frac{1}{2} (c+d x)\right)\right)\right)}{4 d (a (\cosh (c+d x)+1))^{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,"(Cosh[(c + d*x)/2]^5*(32*Csch[c + d*x]^4*Sinh[(c + d*x)/2]^5 + 3*(ArcTan[Sinh[(c + d*x)/2]] + Sech[(c + d*x)/2]*Tanh[(c + d*x)/2])))/(4*d*(a*(1 + Cosh[c + d*x]))^(5/2))","A",1
48,1,72,92,0.1446671,"\int (a-a \cosh (c+d x))^{5/2} \, dx","Integrate[(a - a*Cosh[c + d*x])^(5/2),x]","\frac{a^2 \left(150 \cosh \left(\frac{1}{2} (c+d x)\right)-25 \cosh \left(\frac{3}{2} (c+d x)\right)+3 \cosh \left(\frac{5}{2} (c+d x)\right)\right) \text{csch}\left(\frac{1}{2} (c+d x)\right) \sqrt{a-a \cosh (c+d x)}}{30 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,"(a^2*Sqrt[a - a*Cosh[c + d*x]]*(150*Cosh[(c + d*x)/2] - 25*Cosh[(3*(c + d*x))/2] + 3*Cosh[(5*(c + d*x))/2])*Csch[(c + d*x)/2])/(30*d)","A",1
49,1,56,61,0.0944257,"\int (a-a \cosh (c+d x))^{3/2} \, dx","Integrate[(a - a*Cosh[c + d*x])^(3/2),x]","-\frac{a \left(\cosh \left(\frac{3}{2} (c+d x)\right)-9 \cosh \left(\frac{1}{2} (c+d x)\right)\right) \text{csch}\left(\frac{1}{2} (c+d x)\right) \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,"-1/3*(a*Sqrt[a - a*Cosh[c + d*x]]*(-9*Cosh[(c + d*x)/2] + Cosh[(3*(c + d*x))/2])*Csch[(c + d*x)/2])/d","A",1
50,1,30,27,0.0348077,"\int \sqrt{a-a \cosh (c+d x)} \, dx","Integrate[Sqrt[a - a*Cosh[c + d*x]],x]","\frac{2 \coth \left(\frac{1}{2} (c+d x)\right) \sqrt{a-a \cosh (c+d x)}}{d}","-\frac{2 a \sinh (c+d x)}{d \sqrt{a-a \cosh (c+d x)}}",1,"(2*Sqrt[a - a*Cosh[c + d*x]]*Coth[(c + d*x)/2])/d","A",1
51,1,41,48,0.032253,"\int \frac{1}{\sqrt{a-a \cosh (c+d x)}} \, dx","Integrate[1/Sqrt[a - a*Cosh[c + d*x]],x]","\frac{2 \sinh \left(\frac{1}{2} (c+d x)\right) \log \left(\tanh \left(\frac{1}{4} (c+d x)\right)\right)}{d \sqrt{a-a \cosh (c+d 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}",1,"(2*Log[Tanh[(c + d*x)/4]]*Sinh[(c + d*x)/2])/(d*Sqrt[a - a*Cosh[c + d*x]])","A",1
52,1,85,79,0.1747635,"\int \frac{1}{(a-a \cosh (c+d x))^{3/2}} \, dx","Integrate[(a - a*Cosh[c + d*x])^(-3/2),x]","\frac{\sinh ^3\left(\frac{1}{2} (c+d x)\right) \left(\text{csch}^2\left(\frac{1}{4} (c+d x)\right)+\text{sech}^2\left(\frac{1}{4} (c+d x)\right)+4 \log \left(\tanh \left(\frac{1}{4} (c+d x)\right)\right)\right)}{4 a d (\cosh (c+d x)-1) \sqrt{a-a \cosh (c+d 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}}",1,"((Csch[(c + d*x)/4]^2 + 4*Log[Tanh[(c + d*x)/4]] + Sech[(c + d*x)/4]^2)*Sinh[(c + d*x)/2]^3)/(4*a*d*(-1 + Cosh[c + d*x])*Sqrt[a - a*Cosh[c + d*x]])","A",1
53,1,115,110,0.1992679,"\int \frac{1}{(a-a \cosh (c+d x))^{5/2}} \, dx","Integrate[(a - a*Cosh[c + d*x])^(-5/2),x]","\frac{\sinh ^5\left(\frac{1}{2} (c+d x)\right) \left(-\text{csch}^4\left(\frac{1}{4} (c+d x)\right)+6 \text{csch}^2\left(\frac{1}{4} (c+d x)\right)+\text{sech}^4\left(\frac{1}{4} (c+d x)\right)+6 \text{sech}^2\left(\frac{1}{4} (c+d x)\right)+24 \log \left(\tanh \left(\frac{1}{4} (c+d x)\right)\right)\right)}{32 a^2 d (\cosh (c+d x)-1)^2 \sqrt{a-a \cosh (c+d 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}}",1,"((6*Csch[(c + d*x)/4]^2 - Csch[(c + d*x)/4]^4 + 24*Log[Tanh[(c + d*x)/4]] + 6*Sech[(c + d*x)/4]^2 + Sech[(c + d*x)/4]^4)*Sinh[(c + d*x)/2]^5)/(32*a^2*d*(-1 + Cosh[c + d*x])^2*Sqrt[a - a*Cosh[c + d*x]])","A",1
54,1,99,112,0.2004837,"\int \frac{\cosh ^4(x)}{a+b \cosh (x)} \, dx","Integrate[Cosh[x]^4/(a + b*Cosh[x]),x]","\frac{-6 a x \left(2 a^2+b^2\right)+3 b \left(4 a^2+3 b^2\right) \sinh (x)-\frac{24 a^4 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}-3 a b^2 \sinh (2 x)+b^3 \sinh (3 x)}{12 b^4}","\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 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{a \sinh (x) \cosh (x)}{2 b^2}+\frac{\sinh (x) \cosh ^2(x)}{3 b}",1,"(-6*a*(2*a^2 + b^2)*x - (24*a^4*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2] + 3*b*(4*a^2 + 3*b^2)*Sinh[x] - 3*a*b^2*Sinh[2*x] + b^3*Sinh[3*x])/(12*b^4)","A",1
55,1,78,85,0.1319571,"\int \frac{\cosh ^3(x)}{a+b \cosh (x)} \, dx","Integrate[Cosh[x]^3/(a + b*Cosh[x]),x]","\frac{4 a^2 x+\frac{8 a^3 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}-4 a b \sinh (x)+2 b^2 x+b^2 \sinh (2 x)}{4 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{x \left(2 a^2+b^2\right)}{2 b^3}-\frac{a \sinh (x)}{b^2}+\frac{\sinh (x) \cosh (x)}{2 b}",1,"(4*a^2*x + 2*b^2*x + (8*a^3*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2] - 4*a*b*Sinh[x] + b^2*Sinh[2*x])/(4*b^3)","A",1
56,1,57,62,0.1126403,"\int \frac{\cosh ^2(x)}{a+b \cosh (x)} \, dx","Integrate[Cosh[x]^2/(a + b*Cosh[x]),x]","\frac{a \left(-\frac{2 a \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}-x\right)+b \sinh (x)}{b^2}","\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 - (2*a*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2]) + b*Sinh[x])/b^2","A",1
57,1,48,52,0.0477442,"\int \frac{\cosh (x)}{a+b \cosh (x)} \, dx","Integrate[Cosh[x]/(a + b*Cosh[x]),x]","\frac{\frac{2 a \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}+x}{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 + (2*a*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2])/b","A",1
58,1,54,54,0.0532929,"\int \frac{\text{sech}(x)}{a+b \cosh (x)} \, dx","Integrate[Sech[x]/(a + b*Cosh[x]),x]","\frac{2 \left(\frac{b \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}+\tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)\right)}{a}","\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,"(2*(ArcTan[Tanh[x/2]] + (b*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2]))/a","A",1
59,1,63,64,0.1101096,"\int \frac{\text{sech}^2(x)}{a+b \cosh (x)} \, dx","Integrate[Sech[x]^2/(a + b*Cosh[x]),x]","\frac{-\frac{2 b^2 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}+a \tanh (x)-2 b \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)}{a^2}","\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,"(-2*b*ArcTan[Tanh[x/2]] - (2*b^2*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2] + a*Tanh[x])/a^2","A",1
60,1,82,87,0.2104533,"\int \frac{\text{sech}^3(x)}{a+b \cosh (x)} \, dx","Integrate[Sech[x]^3/(a + b*Cosh[x]),x]","\frac{2 \left(a^2+2 b^2\right) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+\frac{4 b^3 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}+a \tanh (x) (a \text{sech}(x)-2 b)}{2 a^3}","-\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{b \tanh (x)}{a^2}+\frac{\left(a^2+2 b^2\right) \tan ^{-1}(\sinh (x))}{2 a^3}+\frac{\tanh (x) \text{sech}(x)}{2 a}",1,"(2*(a^2 + 2*b^2)*ArcTan[Tanh[x/2]] + (4*b^3*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2] + a*(-2*b + a*Sech[x])*Tanh[x])/(2*a^3)","A",1
61,1,101,114,0.4265661,"\int \frac{\text{sech}^4(x)}{a+b \cosh (x)} \, dx","Integrate[Sech[x]^4/(a + b*Cosh[x]),x]","\frac{-6 b \left(a^2+2 b^2\right) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+a \tanh (x) \left(2 a^2 \text{sech}^2(x)+4 a^2-3 a b \text{sech}(x)+6 b^2\right)-\frac{12 b^4 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}}{6 a^4}","\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{b \tanh (x) \text{sech}(x)}{2 a^2}-\frac{b \left(a^2+2 b^2\right) \tan ^{-1}(\sinh (x))}{2 a^4}+\frac{\left(2 a^2+3 b^2\right) \tanh (x)}{3 a^3}+\frac{\tanh (x) \text{sech}^2(x)}{3 a}",1,"(-6*b*(a^2 + 2*b^2)*ArcTan[Tanh[x/2]] - (12*b^4*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2] + a*(4*a^2 + 6*b^2 - 3*a*b*Sech[x] + 2*a^2*Sech[x]^2)*Tanh[x])/(6*a^4)","A",1
62,1,133,183,0.3665229,"\int (a+b \cosh (c+d x))^5 \, dx","Integrate[(a + b*Cosh[c + d*x])^5,x]","\frac{600 a b^2 \left(2 a^2+b^2\right) \sinh (2 (c+d x))+50 b^3 \left(8 a^2+b^2\right) \sinh (3 (c+d x))+60 a \left(8 a^4+40 a^2 b^2+15 b^4\right) (c+d x)+300 b \left(8 a^4+12 a^2 b^2+b^4\right) \sinh (c+d x)+75 a b^4 \sinh (4 (c+d x))+6 b^5 \sinh (5 (c+d x))}{480 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{b \left(107 a^4+192 a^2 b^2+16 b^4\right) \sinh (c+d x)}{30 d}+\frac{1}{8} a x \left(8 a^4+40 a^2 b^2+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,"(60*a*(8*a^4 + 40*a^2*b^2 + 15*b^4)*(c + d*x) + 300*b*(8*a^4 + 12*a^2*b^2 + b^4)*Sinh[c + d*x] + 600*a*b^2*(2*a^2 + b^2)*Sinh[2*(c + d*x)] + 50*b^3*(8*a^2 + b^2)*Sinh[3*(c + d*x)] + 75*a*b^4*Sinh[4*(c + d*x)] + 6*b^5*Sinh[5*(c + d*x)])/(480*d)","A",1
63,1,104,137,0.2234082,"\int (a+b \cosh (c+d x))^4 \, dx","Integrate[(a + b*Cosh[c + d*x])^4,x]","\frac{24 b^2 \left(6 a^2+b^2\right) \sinh (2 (c+d x))+96 a b \left(4 a^2+3 b^2\right) \sinh (c+d x)+12 \left(8 a^4+24 a^2 b^2+3 b^4\right) (c+d x)+32 a b^3 \sinh (3 (c+d x))+3 b^4 \sinh (4 (c+d x))}{96 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(8 a^4+24 a^2 b^2+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,"(12*(8*a^4 + 24*a^2*b^2 + 3*b^4)*(c + d*x) + 96*a*b*(4*a^2 + 3*b^2)*Sinh[c + d*x] + 24*b^2*(6*a^2 + b^2)*Sinh[2*(c + d*x)] + 32*a*b^3*Sinh[3*(c + d*x)] + 3*b^4*Sinh[4*(c + d*x)])/(96*d)","A",1
64,1,80,90,0.1315015,"\int (a+b \cosh (c+d x))^3 \, dx","Integrate[(a + b*Cosh[c + d*x])^3,x]","\frac{12 a^3 c+12 a^3 d x+9 b \left(4 a^2+b^2\right) \sinh (c+d x)+9 a b^2 \sinh (2 (c+d x))+18 a b^2 c+18 a b^2 d x+b^3 \sinh (3 (c+d x))}{12 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,"(12*a^3*c + 18*a*b^2*c + 12*a^3*d*x + 18*a*b^2*d*x + 9*b*(4*a^2 + b^2)*Sinh[c + d*x] + 9*a*b^2*Sinh[2*(c + d*x)] + b^3*Sinh[3*(c + d*x)])/(12*d)","A",1
65,1,46,50,0.0791308,"\int (a+b \cosh (c+d x))^2 \, dx","Integrate[(a + b*Cosh[c + d*x])^2,x]","\frac{2 \left(2 a^2+b^2\right) (c+d x)+8 a b \sinh (c+d x)+b^2 \sinh (2 (c+d x))}{4 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*(2*a^2 + b^2)*(c + d*x) + 8*a*b*Sinh[c + d*x] + b^2*Sinh[2*(c + d*x)])/(4*d)","A",1
66,1,26,15,0.0086802,"\int (a+b \cosh (c+d x)) \, dx","Integrate[a + b*Cosh[c + d*x],x]","a x+\frac{b \sinh (c) \cosh (d x)}{d}+\frac{b \cosh (c) \sinh (d x)}{d}","a x+\frac{b \sinh (c+d x)}{d}",1,"a*x + (b*Cosh[d*x]*Sinh[c])/d + (b*Cosh[c]*Sinh[d*x])/d","A",1
67,1,48,49,0.0531141,"\int \frac{1}{a+b \cosh (c+d x)} \, dx","Integrate[(a + b*Cosh[c + d*x])^(-1),x]","-\frac{2 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{b^2-a^2}}\right)}{d \sqrt{b^2-a^2}}","\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*ArcTan[((a - b)*Tanh[(c + d*x)/2])/Sqrt[-a^2 + b^2]])/(Sqrt[-a^2 + b^2]*d)","A",1
68,1,84,86,0.2271993,"\int \frac{1}{(a+b \cosh (c+d x))^2} \, dx","Integrate[(a + b*Cosh[c + d*x])^(-2),x]","\frac{\frac{2 a \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{b^2-a^2}}\right)}{\left(b^2-a^2\right)^{3/2}}-\frac{b \sinh (c+d x)}{(a-b) (a+b) (a+b \cosh (c+d x))}}{d}","\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*ArcTan[((a - b)*Tanh[(c + d*x)/2])/Sqrt[-a^2 + b^2]])/(-a^2 + b^2)^(3/2) - (b*Sinh[c + d*x])/((a - b)*(a + b)*(a + b*Cosh[c + d*x])))/d","A",1
69,1,113,133,0.4103045,"\int \frac{1}{(a+b \cosh (c+d x))^3} \, dx","Integrate[(a + b*Cosh[c + d*x])^(-3),x]","\frac{\frac{b \sinh (c+d x) \left(-4 a^2-3 a b \cosh (c+d x)+b^2\right)}{(a-b)^2 (a+b)^2 (a+b \cosh (c+d x))^2}-\frac{2 \left(2 a^2+b^2\right) \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{b^2-a^2}}\right)}{\left(b^2-a^2\right)^{5/2}}}{2 d}","\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*(2*a^2 + b^2)*ArcTan[((a - b)*Tanh[(c + d*x)/2])/Sqrt[-a^2 + b^2]])/(-a^2 + b^2)^(5/2) + (b*(-4*a^2 + b^2 - 3*a*b*Cosh[c + d*x])*Sinh[c + d*x])/((a - b)^2*(a + b)^2*(a + b*Cosh[c + d*x])^2))/(2*d)","A",1
70,1,160,184,1.100994,"\int \frac{1}{(a+b \cosh (c+d x))^4} \, dx","Integrate[(a + b*Cosh[c + d*x])^(-4),x]","\frac{\frac{6 a \left(2 a^2+3 b^2\right) \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{b^2-a^2}}\right)}{\left(b^2-a^2\right)^{7/2}}-\frac{b \sinh (c+d x) \left(36 a^4+6 a b \left(9 a^2+b^2\right) \cosh (c+d x)+a^2 b^2+\left(11 a^2 b^2+4 b^4\right) \cosh (2 (c+d x))+8 b^4\right)}{2 (a-b)^3 (a+b)^3 (a+b \cosh (c+d x))^3}}{6 d}","\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,"((6*a*(2*a^2 + 3*b^2)*ArcTan[((a - b)*Tanh[(c + d*x)/2])/Sqrt[-a^2 + b^2]])/(-a^2 + b^2)^(7/2) - (b*(36*a^4 + a^2*b^2 + 8*b^4 + 6*a*b*(9*a^2 + b^2)*Cosh[c + d*x] + (11*a^2*b^2 + 4*b^4)*Cosh[2*(c + d*x)])*Sinh[c + d*x])/(2*(a - b)^3*(a + b)^3*(a + b*Cosh[c + d*x])^3))/(6*d)","A",1
71,1,23,22,0.0385113,"\int \frac{1}{3+5 \cosh (c+d x)} \, dx","Integrate[(3 + 5*Cosh[c + d*x])^(-1),x]","-\frac{\tan ^{-1}\left(2 \coth \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}{2 d}","\frac{\tan ^{-1}\left(\frac{1}{2} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{2 d}",1,"-1/2*ArcTan[2*Coth[c/2 + (d*x)/2]]/d","A",1
72,1,45,48,0.1054454,"\int \frac{1}{(3+5 \cosh (c+d x))^2} \, dx","Integrate[(3 + 5*Cosh[c + d*x])^(-2),x]","\frac{\frac{10 \sinh (c+d x)}{5 \cosh (c+d x)+3}-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] + (10*Sinh[c + d*x])/(3 + 5*Cosh[c + d*x]))/(32*d)","A",1
73,1,55,73,0.1649317,"\int \frac{1}{(3+5 \cosh (c+d x))^3} \, dx","Integrate[(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)-\frac{10 \sinh (c+d x) (45 \cosh (c+d x)+11)}{(5 \cosh (c+d x)+3)^2}}{1024 d}","\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] - (10*(11 + 45*Cosh[c + d*x])*Sinh[c + d*x])/(3 + 5*Cosh[c + d*x])^2)/(1024*d)","A",1
74,1,65,98,0.2733671,"\int \frac{1}{(3+5 \cosh (c+d x))^4} \, dx","Integrate[(3 + 5*Cosh[c + d*x])^(-4),x]","\frac{\frac{5 \sinh (c+d x) (9540 \cosh (c+d x)+4975 \cosh (2 (c+d x))+8141)}{(5 \cosh (c+d x)+3)^3}-837 \tan ^{-1}\left(\frac{1}{2} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{49152 d}","-\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,"(-837*ArcTan[Tanh[(c + d*x)/2]/2] + (5*(8141 + 9540*Cosh[c + d*x] + 4975*Cosh[2*(c + d*x)])*Sinh[c + d*x])/(3 + 5*Cosh[c + d*x])^3)/(49152*d)","A",1
75,1,77,31,0.0323424,"\int \frac{1}{5+3 \cosh (c+d x)} \, dx","Integrate[(5 + 3*Cosh[c + d*x])^(-1),x]","\frac{\log \left(\sinh \left(\frac{c}{2}+\frac{d x}{2}\right)+2 \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}{4 d}-\frac{\log \left(2 \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)-\sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}{4 d}","\frac{x}{4}-\frac{\tanh ^{-1}\left(\frac{\sinh (c+d x)}{\cosh (c+d x)+3}\right)}{2 d}",1,"-1/4*Log[2*Cosh[c/2 + (d*x)/2] - Sinh[c/2 + (d*x)/2]]/d + Log[2*Cosh[c/2 + (d*x)/2] + Sinh[c/2 + (d*x)/2]]/(4*d)","B",1
76,1,45,56,0.1213517,"\int \frac{1}{(5+3 \cosh (c+d x))^2} \, dx","Integrate[(5 + 3*Cosh[c + d*x])^(-2),x]","\frac{5 \tanh ^{-1}\left(\frac{1}{2} \tanh \left(\frac{1}{2} (c+d x)\right)\right)-\frac{6 \sinh (c+d x)}{3 \cosh (c+d x)+5}}{32 d}","-\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*ArcTanh[Tanh[(c + d*x)/2]/2] - (6*Sinh[c + d*x])/(5 + 3*Cosh[c + d*x]))/(32*d)","A",1
77,1,58,81,0.1989811,"\int \frac{1}{(5+3 \cosh (c+d x))^3} \, dx","Integrate[(5 + 3*Cosh[c + d*x])^(-3),x]","\frac{59 \tanh ^{-1}\left(\frac{1}{2} \tanh \left(\frac{1}{2} (c+d x)\right)\right)-\frac{3 (182 \sinh (c+d x)+45 \sinh (2 (c+d x)))}{(3 \cosh (c+d x)+5)^2}}{1024 d}","-\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*ArcTanh[Tanh[(c + d*x)/2]/2] - (3*(182*Sinh[c + d*x] + 45*Sinh[2*(c + d*x)]))/(5 + 3*Cosh[c + d*x])^2)/(1024*d)","A",1
78,1,68,106,0.2654776,"\int \frac{1}{(5+3 \cosh (c+d x))^4} \, dx","Integrate[(5 + 3*Cosh[c + d*x])^(-4),x]","\frac{770 \tanh ^{-1}\left(\frac{1}{2} \tanh \left(\frac{1}{2} (c+d x)\right)\right)-\frac{9 (4883 \sinh (c+d x)+2340 \sinh (2 (c+d x))+311 \sinh (3 (c+d x)))}{(3 \cosh (c+d x)+5)^3}}{32768 d}","-\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,"(770*ArcTanh[Tanh[(c + d*x)/2]/2] - (9*(4883*Sinh[c + d*x] + 2340*Sinh[2*(c + d*x)] + 311*Sinh[3*(c + d*x)]))/(5 + 3*Cosh[c + d*x])^3)/(32768*d)","A",1
79,1,150,153,0.5469094,"\int (a+b \cosh (x))^{5/2} \, dx","Integrate[(a + b*Cosh[x])^(5/2),x]","\frac{b \sinh (x) \left(22 a^2+28 a b \cosh (x)+3 b^2 \cosh (2 x)+3 b^2\right)+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)-2 i \left(23 a^3+23 a^2 b+9 a b^2+9 b^3\right) \sqrt{\frac{a+b \cosh (x)}{a+b}} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{15 \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)*(23*a^3 + 23*a^2*b + 9*a*b^2 + 9*b^3)*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticE[(I/2)*x, (2*b)/(a + b)] + (16*I)*a*(a^2 - b^2)*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticF[(I/2)*x, (2*b)/(a + b)] + b*(22*a^2 + 3*b^2 + 28*a*b*Cosh[x] + 3*b^2*Cosh[2*x])*Sinh[x])/(15*Sqrt[a + b*Cosh[x]])","A",1
80,1,111,124,0.2440614,"\int (a+b \cosh (x))^{3/2} \, dx","Integrate[(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)+2 b \sinh (x) (a+b \cosh (x))-8 i a (a+b) \sqrt{\frac{a+b \cosh (x)}{a+b}} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 \sqrt{a+b \cosh (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}}}",1,"((-8*I)*a*(a + b)*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticE[(I/2)*x, (2*b)/(a + b)] + (2*I)*(a^2 - b^2)*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticF[(I/2)*x, (2*b)/(a + b)] + 2*b*(a + b*Cosh[x])*Sinh[x])/(3*Sqrt[a + b*Cosh[x]])","A",1
81,1,61,61,0.0930389,"\int \sqrt{a+b \cosh (c+d x)} \, dx","Integrate[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",1
82,1,46,46,0.0389194,"\int \frac{1}{\sqrt{a+b \cosh (x)}} \, dx","Integrate[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",1
83,1,68,84,0.1282506,"\int \frac{1}{(a+b \cosh (x))^{3/2}} \, dx","Integrate[(a + b*Cosh[x])^(-3/2),x]","-\frac{2 \left(b \sinh (x)+i (a+b) \sqrt{\frac{a+b \cosh (x)}{a+b}} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)\right)}{(a-b) (a+b) \sqrt{a+b \cosh (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}}}",1,"(-2*(I*(a + b)*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticE[(I/2)*x, (2*b)/(a + b)] + b*Sinh[x]))/((a - b)*(a + b)*Sqrt[a + b*Cosh[x]])","A",1
84,1,135,177,0.5736359,"\int \frac{1}{(a+b \cosh (x))^{5/2}} \, dx","Integrate[(a + b*Cosh[x])^(-5/2),x]","\frac{2 b \sinh (x) \left(-5 a^2-4 a b \cosh (x)+b^2\right)+2 i (a-b) (a+b)^2 \left(\frac{a+b \cosh (x)}{a+b}\right)^{3/2} F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)-8 i a (a+b)^2 \left(\frac{a+b \cosh (x)}{a+b}\right)^{3/2} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{3 (a-b)^2 (a+b)^2 (a+b \cosh (x))^{3/2}}","-\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)*a*(a + b)^2*((a + b*Cosh[x])/(a + b))^(3/2)*EllipticE[(I/2)*x, (2*b)/(a + b)] + (2*I)*(a - b)*(a + b)^2*((a + b*Cosh[x])/(a + b))^(3/2)*EllipticF[(I/2)*x, (2*b)/(a + b)] + 2*b*(-5*a^2 + b^2 - 4*a*b*Cosh[x])*Sinh[x])/(3*(a - b)^2*(a + b)^2*(a + b*Cosh[x])^(3/2))","A",1
85,1,165,227,0.7192229,"\int \frac{1}{(a+b \cosh (x))^{7/2}} \, dx","Integrate[(a + b*Cosh[x])^(-7/2),x]","\frac{2 \left(\frac{b \sinh (x) \left(34 a^4+b^2 \left(23 a^2+9 b^2\right) \cosh ^2(x)+2 a b \left(27 a^2+5 b^2\right) \cosh (x)-5 a^2 b^2+3 b^4\right)}{\left(b^2-a^2\right)^3}-\frac{i \left(\frac{a+b \cosh (x)}{a+b}\right)^{5/2} \left(\left(23 a^2+9 b^2\right) E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)+8 a (b-a) F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)\right)}{(a-b)^3}\right)}{15 (a+b \cosh (x))^{5/2}}","-\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)*((a + b*Cosh[x])/(a + b))^(5/2)*((23*a^2 + 9*b^2)*EllipticE[(I/2)*x, (2*b)/(a + b)] + 8*a*(-a + b)*EllipticF[(I/2)*x, (2*b)/(a + b)]))/(a - b)^3 + (b*(34*a^4 - 5*a^2*b^2 + 3*b^4 + 2*a*b*(27*a^2 + 5*b^2)*Cosh[x] + b^2*(23*a^2 + 9*b^2)*Cosh[x]^2)*Sinh[x])/(-a^2 + b^2)^3))/(15*(a + b*Cosh[x])^(5/2))","A",1
86,1,73,100,0.3825925,"\int \frac{\cosh (x)}{\sqrt{a+b \cosh (x)}} \, dx","Integrate[Cosh[x]/Sqrt[a + b*Cosh[x]],x]","-\frac{2 i \sqrt{\frac{a+b \cosh (x)}{a+b}} \left((a+b) E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)-a F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)\right)}{b \sqrt{a+b \cosh (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}}}",1,"((-2*I)*Sqrt[(a + b*Cosh[x])/(a + b)]*((a + b)*EllipticE[(I/2)*x, (2*b)/(a + b)] - a*EllipticF[(I/2)*x, (2*b)/(a + b)]))/(b*Sqrt[a + b*Cosh[x]])","A",1
87,1,60,94,0.1345632,"\int (a+a \cosh (x))^{5/2} (A+B \cosh (x)) \, dx","Integrate[(a + a*Cosh[x])^(5/2)*(A + B*Cosh[x]),x]","\frac{1}{210} a^2 \tanh \left(\frac{x}{2}\right) \sqrt{a (\cosh (x)+1)} ((392 A+505 B) \cosh (x)+6 (7 A+20 B) \cosh (2 x)+1246 A+15 B \cosh (3 x)+1040 B)","\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,"(a^2*Sqrt[a*(1 + Cosh[x])]*(1246*A + 1040*B + (392*A + 505*B)*Cosh[x] + 6*(7*A + 20*B)*Cosh[2*x] + 15*B*Cosh[3*x])*Tanh[x/2])/210","A",1
88,1,46,68,0.0926233,"\int (a+a \cosh (x))^{3/2} (A+B \cosh (x)) \, dx","Integrate[(a + a*Cosh[x])^(3/2)*(A + B*Cosh[x]),x]","\frac{1}{15} a \tanh \left(\frac{x}{2}\right) \sqrt{a (\cosh (x)+1)} (2 (5 A+9 B) \cosh (x)+50 A+3 B \cosh (2 x)+39 B)","\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,"(a*Sqrt[a*(1 + Cosh[x])]*(50*A + 39*B + 2*(5*A + 9*B)*Cosh[x] + 3*B*Cosh[2*x])*Tanh[x/2])/15","A",1
89,1,31,40,0.0400438,"\int \sqrt{a+a \cosh (x)} (A+B \cosh (x)) \, dx","Integrate[Sqrt[a + a*Cosh[x]]*(A + B*Cosh[x]),x]","\frac{2}{3} \tanh \left(\frac{x}{2}\right) \sqrt{a (\cosh (x)+1)} (3 A+B \cosh (x)+2 B)","\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*Sqrt[a*(1 + Cosh[x])]*(3*A + 2*B + B*Cosh[x])*Tanh[x/2])/3","A",1
90,1,61,98,0.1477466,"\int (a-a \cosh (x))^{5/2} (A+B \cosh (x)) \, dx","Integrate[(a - a*Cosh[x])^(5/2)*(A + B*Cosh[x]),x]","\frac{1}{210} a^2 \coth \left(\frac{x}{2}\right) \sqrt{a-a \cosh (x)} ((505 B-392 A) \cosh (x)+6 (7 A-20 B) \cosh (2 x)+1246 A+15 B \cosh (3 x)-1040 B)","-\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,"(a^2*Sqrt[a - a*Cosh[x]]*(1246*A - 1040*B + (-392*A + 505*B)*Cosh[x] + 6*(7*A - 20*B)*Cosh[2*x] + 15*B*Cosh[3*x])*Coth[x/2])/210","A",1
91,1,47,71,0.1059953,"\int (a-a \cosh (x))^{3/2} (A+B \cosh (x)) \, dx","Integrate[(a - a*Cosh[x])^(3/2)*(A + B*Cosh[x]),x]","-\frac{1}{15} a \coth \left(\frac{x}{2}\right) \sqrt{a-a \cosh (x)} (2 (5 A-9 B) \cosh (x)-50 A+3 B \cosh (2 x)+39 B)","-\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,"-1/15*(a*Sqrt[a - a*Cosh[x]]*(-50*A + 39*B + 2*(5*A - 9*B)*Cosh[x] + 3*B*Cosh[2*x])*Coth[x/2])","A",1
92,1,32,44,0.0553286,"\int \sqrt{a-a \cosh (x)} (A+B \cosh (x)) \, dx","Integrate[Sqrt[a - a*Cosh[x]]*(A + B*Cosh[x]),x]","\frac{2}{3} \coth \left(\frac{x}{2}\right) \sqrt{a-a \cosh (x)} (3 A+B \cosh (x)-2 B)","\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*Sqrt[a - a*Cosh[x]]*(3*A - 2*B + B*Cosh[x])*Coth[x/2])/3","A",1
93,1,23,18,0.0588723,"\int \frac{A+B \cosh (x)}{1+\cosh (x)} \, dx","Integrate[(A + B*Cosh[x])/(1 + Cosh[x]),x]","\frac{\sinh (x) \left(A+B x \coth \left(\frac{x}{2}\right)-B\right)}{\cosh (x)+1}","\frac{(A-B) \sinh (x)}{\cosh (x)+1}+B x",1,"((A - B + B*x*Coth[x/2])*Sinh[x])/(1 + Cosh[x])","A",1
94,1,25,35,0.0592933,"\int \frac{A+B \cosh (x)}{(1+\cosh (x))^2} \, dx","Integrate[(A + B*Cosh[x])/(1 + Cosh[x])^2,x]","\frac{\sinh (x) ((A+2 B) \cosh (x)+2 A+B)}{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,"((2*A + B + (A + 2*B)*Cosh[x])*Sinh[x])/(3*(1 + Cosh[x])^2)","A",1
95,1,42,56,0.0954027,"\int \frac{A+B \cosh (x)}{(1+\cosh (x))^3} \, dx","Integrate[(A + B*Cosh[x])/(1 + Cosh[x])^3,x]","\frac{\sinh (x) (6 (2 A+3 B) \cosh (x)+(2 A+3 B) \cosh (2 x)+16 A+9 B)}{30 (\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,"((16*A + 9*B + 6*(2*A + 3*B)*Cosh[x] + (2*A + 3*B)*Cosh[2*x])*Sinh[x])/(30*(1 + Cosh[x])^3)","A",1
96,1,57,75,0.1110675,"\int \frac{A+B \cosh (x)}{(1+\cosh (x))^4} \, dx","Integrate[(A + B*Cosh[x])/(1 + Cosh[x])^4,x]","\frac{\sinh (x) (29 (3 A+4 B) \cosh (x)+8 (3 A+4 B) \cosh (2 x)+3 A \cosh (3 x)+96 A+4 B \cosh (3 x)+58 B)}{210 (\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,"((96*A + 58*B + 29*(3*A + 4*B)*Cosh[x] + 8*(3*A + 4*B)*Cosh[2*x] + 3*A*Cosh[3*x] + 4*B*Cosh[3*x])*Sinh[x])/(210*(1 + Cosh[x])^4)","A",1
97,1,35,20,0.0577793,"\int \frac{A+B \cosh (x)}{1-\cosh (x)} \, dx","Integrate[(A + B*Cosh[x])/(1 - Cosh[x]),x]","\frac{2 \sinh \left(\frac{x}{2}\right) \left((A+B) \cosh \left(\frac{x}{2}\right)-B x \sinh \left(\frac{x}{2}\right)\right)}{\cosh (x)-1}","-\frac{(A+B) \sinh (x)}{1-\cosh (x)}-B x",1,"(2*Sinh[x/2]*((A + B)*Cosh[x/2] - B*x*Sinh[x/2]))/(-1 + Cosh[x])","A",1
98,1,25,37,0.0587422,"\int \frac{A+B \cosh (x)}{(1-\cosh (x))^2} \, dx","Integrate[(A + B*Cosh[x])/(1 - Cosh[x])^2,x]","\frac{\sinh (x) ((A-2 B) \cosh (x)-2 A+B)}{3 (\cosh (x)-1)^2}","-\frac{(A-2 B) \sinh (x)}{3 (1-\cosh (x))}-\frac{(A+B) \sinh (x)}{3 (1-\cosh (x))^2}",1,"((-2*A + B + (A - 2*B)*Cosh[x])*Sinh[x])/(3*(-1 + Cosh[x])^2)","A",1
99,1,42,60,0.0850416,"\int \frac{A+B \cosh (x)}{(1-\cosh (x))^3} \, dx","Integrate[(A + B*Cosh[x])/(1 - Cosh[x])^3,x]","\frac{\sinh (x) (-6 (2 A-3 B) \cosh (x)+(2 A-3 B) \cosh (2 x)+16 A-9 B)}{30 (\cosh (x)-1)^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,"((16*A - 9*B - 6*(2*A - 3*B)*Cosh[x] + (2*A - 3*B)*Cosh[2*x])*Sinh[x])/(30*(-1 + Cosh[x])^3)","A",1
100,1,57,81,0.1035055,"\int \frac{A+B \cosh (x)}{(1-\cosh (x))^4} \, dx","Integrate[(A + B*Cosh[x])/(1 - Cosh[x])^4,x]","\frac{\sinh (x) (29 (3 A-4 B) \cosh (x)-8 (3 A-4 B) \cosh (2 x)+3 A \cosh (3 x)-96 A-4 B \cosh (3 x)+58 B)}{210 (\cosh (x)-1)^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,"((-96*A + 58*B + 29*(3*A - 4*B)*Cosh[x] - 8*(3*A - 4*B)*Cosh[2*x] + 3*A*Cosh[3*x] - 4*B*Cosh[3*x])*Sinh[x])/(210*(-1 + Cosh[x])^4)","A",1
101,1,41,56,0.0367307,"\int \frac{A+B \cosh (x)}{\sqrt{a+a \cosh (x)}} \, dx","Integrate[(A + B*Cosh[x])/Sqrt[a + a*Cosh[x]],x]","\frac{2 \cosh \left(\frac{x}{2}\right) \left((A-B) \tan ^{-1}\left(\sinh \left(\frac{x}{2}\right)\right)+2 B \sinh \left(\frac{x}{2}\right)\right)}{\sqrt{a (\cosh (x)+1)}}","\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,"(2*Cosh[x/2]*((A - B)*ArcTan[Sinh[x/2]] + 2*B*Sinh[x/2]))/Sqrt[a*(1 + Cosh[x])]","A",1
102,1,44,65,0.083995,"\int \frac{A+B \cosh (x)}{(a+a \cosh (x))^{3/2}} \, dx","Integrate[(A + B*Cosh[x])/(a + a*Cosh[x])^(3/2),x]","\frac{\frac{1}{2} (A-B) \sinh (x)+(A+3 B) \cosh ^3\left(\frac{x}{2}\right) \tan ^{-1}\left(\sinh \left(\frac{x}{2}\right)\right)}{(a (\cosh (x)+1))^{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[Sinh[x/2]]*Cosh[x/2]^3 + ((A - B)*Sinh[x])/2)/(a*(1 + Cosh[x]))^(3/2)","A",1
103,1,57,93,0.1700068,"\int \frac{A+B \cosh (x)}{(a+a \cosh (x))^{5/2}} \, dx","Integrate[(A + B*Cosh[x])/(a + a*Cosh[x])^(5/2),x]","\frac{\sinh (x) ((3 A+5 B) \cosh (x)+7 A+B)+4 (3 A+5 B) \cosh ^5\left(\frac{x}{2}\right) \tan ^{-1}\left(\sinh \left(\frac{x}{2}\right)\right)}{16 (a (\cosh (x)+1))^{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,"(4*(3*A + 5*B)*ArcTan[Sinh[x/2]]*Cosh[x/2]^5 + (7*A + B + (3*A + 5*B)*Cosh[x])*Sinh[x])/(16*(a*(1 + Cosh[x]))^(5/2))","A",1
104,1,40,57,0.0601215,"\int \frac{A+B \cosh (x)}{\sqrt{a-a \cosh (x)}} \, dx","Integrate[(A + B*Cosh[x])/Sqrt[a - a*Cosh[x]],x]","\frac{2 \sinh \left(\frac{x}{2}\right) \left((A+B) \log \left(\tanh \left(\frac{x}{4}\right)\right)+2 B \cosh \left(\frac{x}{2}\right)\right)}{\sqrt{a-a \cosh (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}}",1,"(2*(2*B*Cosh[x/2] + (A + B)*Log[Tanh[x/4]])*Sinh[x/2])/Sqrt[a - a*Cosh[x]]","A",1
105,1,71,65,0.1620531,"\int \frac{A+B \cosh (x)}{(a-a \cosh (x))^{3/2}} \, dx","Integrate[(A + B*Cosh[x])/(a - a*Cosh[x])^(3/2),x]","\frac{\sinh ^3\left(\frac{x}{2}\right) \left((A+B) \text{csch}^2\left(\frac{x}{4}\right)+(A+B) \text{sech}^2\left(\frac{x}{4}\right)+4 (A-3 B) \log \left(\tanh \left(\frac{x}{4}\right)\right)\right)}{4 a (\cosh (x)-1) \sqrt{a-a \cosh (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}}",1,"(((A + B)*Csch[x/4]^2 + 4*(A - 3*B)*Log[Tanh[x/4]] + (A + B)*Sech[x/4]^2)*Sinh[x/2]^3)/(4*a*(-1 + Cosh[x])*Sqrt[a - a*Cosh[x]])","A",1
106,1,108,94,0.3869777,"\int \frac{A+B \cosh (x)}{(a-a \cosh (x))^{5/2}} \, dx","Integrate[(A + B*Cosh[x])/(a - a*Cosh[x])^(5/2),x]","\frac{\sinh ^5\left(\frac{x}{2}\right) \left(-\left((A+B) \text{csch}^4\left(\frac{x}{4}\right)\right)+2 (3 A-5 B) \text{csch}^2\left(\frac{x}{4}\right)+(A+B) \text{sech}^4\left(\frac{x}{4}\right)+2 (3 A-5 B) \text{sech}^2\left(\frac{x}{4}\right)+8 (3 A-5 B) \log \left(\tanh \left(\frac{x}{4}\right)\right)\right)}{32 a^2 (\cosh (x)-1)^2 \sqrt{a-a \cosh (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}}",1,"((2*(3*A - 5*B)*Csch[x/4]^2 - (A + B)*Csch[x/4]^4 + 8*(3*A - 5*B)*Log[Tanh[x/4]] + 2*(3*A - 5*B)*Sech[x/4]^2 + (A + B)*Sech[x/4]^4)*Sinh[x/2]^5)/(32*a^2*(-1 + Cosh[x])^2*Sqrt[a - a*Cosh[x]])","A",1
107,1,203,233,0.6262331,"\int (a+b \cosh (x))^{5/2} (A+B \cosh (x)) \, dx","Integrate[(a + b*Cosh[x])^(5/2)*(A + B*Cosh[x]),x]","\frac{\sinh (x) (a+b \cosh (x)) \left(90 a^2 B+6 b \cosh (x) (15 a B+7 A b)+154 a A b+15 b^2 B \cosh (2 x)+65 b^2 B\right)-\frac{2 i \sqrt{\frac{a+b \cosh (x)}{a+b}} \left(b \left(105 a^3 A+135 a^2 b B+119 a A b^2+25 b^3 B\right) F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)+\left(15 a^3 B+161 a^2 A b+145 a b^2 B+63 A b^3\right) \left((a+b) E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)-a F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)\right)\right)}{b}}{105 \sqrt{a+b \cosh (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(15 a^3 B+161 a^2 A 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)*Sqrt[(a + b*Cosh[x])/(a + b)]*(b*(105*a^3*A + 119*a*A*b^2 + 135*a^2*b*B + 25*b^3*B)*EllipticF[(I/2)*x, (2*b)/(a + b)] + (161*a^2*A*b + 63*A*b^3 + 15*a^3*B + 145*a*b^2*B)*((a + b)*EllipticE[(I/2)*x, (2*b)/(a + b)] - a*EllipticF[(I/2)*x, (2*b)/(a + b)])))/b + (a + b*Cosh[x])*(154*a*A*b + 90*a^2*B + 65*b^2*B + 6*b*(7*A*b + 15*a*B)*Cosh[x] + 15*b^2*B*Cosh[2*x])*Sinh[x])/(105*Sqrt[a + b*Cosh[x]])","A",1
108,1,124,181,0.704527,"\int (a+b \cosh (x))^{3/2} (A+B \cosh (x)) \, dx","Integrate[(a + b*Cosh[x])^(3/2)*(A + B*Cosh[x]),x]","\frac{2}{15} \sqrt{a+b \cosh (x)} \left(\sinh (x) (6 a B+5 A b+3 b B \cosh (x))-\frac{i \left(\left(3 a^2 B+20 a A b+9 b^2 B\right) E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)-(a-b) (3 a B+5 A b) F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)\right)}{b \sqrt{\frac{a+b \cosh (x)}{a+b}}}\right)","\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*Sqrt[a + b*Cosh[x]]*(((-I)*((20*a*A*b + 3*a^2*B + 9*b^2*B)*EllipticE[(I/2)*x, (2*b)/(a + b)] - (a - b)*(5*A*b + 3*a*B)*EllipticF[(I/2)*x, (2*b)/(a + b)]))/(b*Sqrt[(a + b*Cosh[x])/(a + b)]) + (5*A*b + 6*a*B + 3*b*B*Cosh[x])*Sinh[x]))/15","A",1
109,1,123,138,0.3541877,"\int \sqrt{a+b \cosh (x)} (A+B \cosh (x)) \, dx","Integrate[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)-2 i (a+b) (a B+3 A b) \sqrt{\frac{a+b \cosh (x)}{a+b}} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)+2 b B \sinh (x) (a+b \cosh (x))}{3 b \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)*(a + b)*(3*A*b + a*B)*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticE[(I/2)*x, (2*b)/(a + b)] + (2*I)*(a^2 - b^2)*B*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticF[(I/2)*x, (2*b)/(a + b)] + 2*b*B*(a + b*Cosh[x])*Sinh[x])/(3*b*Sqrt[a + b*Cosh[x]])","A",1
110,1,59,60,0.1033405,"\int \frac{A+B \cosh (x)}{a+b \cosh (x)} \, dx","Integrate[(A + B*Cosh[x])/(a + b*Cosh[x]),x]","\frac{2 (a B-A b) \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{b \sqrt{b^2-a^2}}+\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)*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/(b*Sqrt[-a^2 + b^2])","A",1
111,1,81,82,0.2008552,"\int \frac{A+B \cosh (x)}{(a+b \cosh (x))^2} \, dx","Integrate[(A + B*Cosh[x])/(a + b*Cosh[x])^2,x]","\frac{2 (a A-b B) \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\left(b^2-a^2\right)^{3/2}}+\frac{\sinh (x) (a B-A b)}{(a-b) (a+b) (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)*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/(-a^2 + b^2)^(3/2) + ((-(A*b) + a*B)*Sinh[x])/((a - b)*(a + b)*(a + b*Cosh[x]))","A",1
112,1,134,135,0.4284647,"\int \frac{A+B \cosh (x)}{(a+b \cosh (x))^3} \, dx","Integrate[(A + B*Cosh[x])/(a + b*Cosh[x])^3,x]","\frac{1}{2} \left(-\frac{2 \left(2 a^2 A-3 a b B+A b^2\right) \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\left(b^2-a^2\right)^{5/2}}+\frac{\sinh (x) \left(a^2 B-3 a A b+2 b^2 B\right)}{(a-b)^2 (a+b)^2 (a+b \cosh (x))}+\frac{\sinh (x) (a B-A b)}{(a-b) (a+b) (a+b \cosh (x))^2}\right)","\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*(2*a^2*A + A*b^2 - 3*a*b*B)*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/(-a^2 + b^2)^(5/2) + ((-(A*b) + a*B)*Sinh[x])/((a - b)*(a + b)*(a + b*Cosh[x])^2) + ((-3*a*A*b + a^2*B + 2*b^2*B)*Sinh[x])/((a - b)^2*(a + b)^2*(a + b*Cosh[x])))/2","A",1
113,1,196,197,0.8297093,"\int \frac{A+B \cosh (x)}{(a+b \cosh (x))^4} \, dx","Integrate[(A + B*Cosh[x])/(a + b*Cosh[x])^4,x]","\frac{1}{6} \left(\frac{\sinh (x) \left(2 a^2 B-5 a A b+3 b^2 B\right)}{(a-b)^2 (a+b)^2 (a+b \cosh (x))^2}+\frac{6 \left(2 a^3 A-4 a^2 b B+3 a A b^2-b^3 B\right) \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\left(b^2-a^2\right)^{7/2}}+\frac{\sinh (x) \left(2 a^3 B-11 a^2 A b+13 a b^2 B-4 A b^3\right)}{(a-b)^3 (a+b)^3 (a+b \cosh (x))}+\frac{2 \sinh (x) (a B-A b)}{(a-b) (a+b) (a+b \cosh (x))^3}\right)","-\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(-2 a^3 B+11 a^2 A b-13 a b^2 B+4 A b^3\right)}{6 \left(a^2-b^2\right)^3 (a+b \cosh (x))}",1,"((6*(2*a^3*A + 3*a*A*b^2 - 4*a^2*b*B - b^3*B)*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/(-a^2 + b^2)^(7/2) + (2*(-(A*b) + a*B)*Sinh[x])/((a - b)*(a + b)*(a + b*Cosh[x])^3) + ((-5*a*A*b + 2*a^2*B + 3*b^2*B)*Sinh[x])/((a - b)^2*(a + b)^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])/((a - b)^3*(a + b)^3*(a + b*Cosh[x])))/6","A",1
114,1,56,56,0.0752701,"\int \frac{\frac{b B}{a}+B \cosh (x)}{a+b \cosh (x)} \, dx","Integrate[((b*B)/a + B*Cosh[x])/(a + b*Cosh[x]),x]","\frac{B \left(\frac{2 \sqrt{b^2-a^2} \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{b}+\frac{a x}{b}\right)}{a}","\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*((a*x)/b + (2*Sqrt[-a^2 + b^2]*ArcTan[((-a + b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/b))/a","A",1
115,1,6,6,0.0004751,"\int \frac{\frac{a B}{b}+B \cosh (x)}{a+b \cosh (x)} \, dx","Integrate[((a*B)/b + B*Cosh[x])/(a + b*Cosh[x]),x]","\frac{B x}{b}","\frac{B x}{b}",1,"(B*x)/b","A",1
116,1,11,11,0.0537301,"\int \frac{a+b \cosh (x)}{(b+a \cosh (x))^2} \, dx","Integrate[(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",1
117,1,24,36,0.0772098,"\int \frac{3+\cosh (x)}{2-\cosh (x)} \, dx","Integrate[(3 + Cosh[x])/(2 - Cosh[x]),x]","\frac{10 \tanh ^{-1}\left(\sqrt{3} \tanh \left(\frac{x}{2}\right)\right)}{\sqrt{3}}-x","\frac{5 x}{\sqrt{3}}-x+\frac{10 \tanh ^{-1}\left(\frac{\sinh (x)}{-\cosh (x)+\sqrt{3}+2}\right)}{\sqrt{3}}",1,"-x + (10*ArcTanh[Sqrt[3]*Tanh[x/2]])/Sqrt[3]","A",1
118,1,80,108,0.483542,"\int \frac{A+B \cosh (x)}{\sqrt{a+b \cosh (x)}} \, dx","Integrate[(A + B*Cosh[x])/Sqrt[a + b*Cosh[x]],x]","-\frac{2 i \sqrt{\frac{a+b \cosh (x)}{a+b}} \left((A b-a B) F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)+B (a+b) E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)\right)}{b \sqrt{a+b \cosh (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}}}",1,"((-2*I)*Sqrt[(a + b*Cosh[x])/(a + b)]*((a + b)*B*EllipticE[(I/2)*x, (2*b)/(a + b)] + (A*b - a*B)*EllipticF[(I/2)*x, (2*b)/(a + b)]))/(b*Sqrt[a + b*Cosh[x]])","A",1
119,1,133,152,0.3812998,"\int \frac{A+B \cosh (x)}{(a+b \cosh (x))^{3/2}} \, dx","Integrate[(A + B*Cosh[x])/(a + b*Cosh[x])^(3/2),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)+2 b \sinh (x) (a B-A b)+2 i (a+b) (a B-A b) \sqrt{\frac{a+b \cosh (x)}{a+b}} E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)}{b (a-b) (a+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) + a*B)*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticE[(I/2)*x, (2*b)/(a + b)] - (2*I)*(a^2 - b^2)*B*Sqrt[(a + b*Cosh[x])/(a + b)]*EllipticF[(I/2)*x, (2*b)/(a + b)] + 2*b*(-(A*b) + a*B)*Sinh[x])/((a - b)*b*(a + b)*Sqrt[a + b*Cosh[x]])","A",1
120,1,172,231,0.9222893,"\int \frac{A+B \cosh (x)}{(a+b \cosh (x))^{5/2}} \, dx","Integrate[(A + B*Cosh[x])/(a + b*Cosh[x])^(5/2),x]","\frac{2 \left(\frac{\sinh (x) \left(2 a^3 B+b \cosh (x) \left(a^2 B-4 a A b+3 b^2 B\right)-5 a^2 A b+2 a b^2 B+A b^3\right)}{\left(a^2-b^2\right)^2}+\frac{i \left(\frac{a+b \cosh (x)}{a+b}\right)^{3/2} \left(\left(a^2 B-4 a A b+3 b^2 B\right) E\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)-(a-b) (a B-A b) F\left(\frac{i x}{2}|\frac{2 b}{a+b}\right)\right)}{b (a-b)^2}\right)}{3 (a+b \cosh (x))^{3/2}}","-\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*((a + b*Cosh[x])/(a + b))^(3/2)*((-4*a*A*b + a^2*B + 3*b^2*B)*EllipticE[(I/2)*x, (2*b)/(a + b)] - (a - b)*(-(A*b) + a*B)*EllipticF[(I/2)*x, (2*b)/(a + b)]))/((a - b)^2*b) + ((-5*a^2*A*b + A*b^3 + 2*a^3*B + 2*a*b^2*B + b*(-4*a*A*b + a^2*B + 3*b^2*B)*Cosh[x])*Sinh[x])/(a^2 - b^2)^2))/(3*(a + b*Cosh[x])^(3/2))","A",1
121,1,42,72,0.0270376,"\int \left(a \cosh ^2(x)\right)^{7/2} \, dx","Integrate[(a*Cosh[x]^2)^(7/2),x]","\frac{a^3 (1225 \sinh (x)+245 \sinh (3 x)+49 \sinh (5 x)+5 \sinh (7 x)) \text{sech}(x) \sqrt{a \cosh ^2(x)}}{2240}","\frac{16}{35} a^3 \tanh (x) \sqrt{a \cosh ^2(x)}+\frac{8}{35} a^2 \tanh (x) \left(a \cosh ^2(x)\right)^{3/2}+\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,"(a^3*Sqrt[a*Cosh[x]^2]*Sech[x]*(1225*Sinh[x] + 245*Sinh[3*x] + 49*Sinh[5*x] + 5*Sinh[7*x]))/2240","A",1
122,1,36,53,0.0187352,"\int \left(a \cosh ^2(x)\right)^{5/2} \, dx","Integrate[(a*Cosh[x]^2)^(5/2),x]","\frac{1}{240} a^2 (150 \sinh (x)+25 \sinh (3 x)+3 \sinh (5 x)) \text{sech}(x) \sqrt{a \cosh ^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}",1,"(a^2*Sqrt[a*Cosh[x]^2]*Sech[x]*(150*Sinh[x] + 25*Sinh[3*x] + 3*Sinh[5*x]))/240","A",1
123,1,26,34,0.0094601,"\int \left(a \cosh ^2(x)\right)^{3/2} \, dx","Integrate[(a*Cosh[x]^2)^(3/2),x]","\frac{1}{12} a (9 \sinh (x)+\sinh (3 x)) \text{sech}(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,"(a*Sqrt[a*Cosh[x]^2]*Sech[x]*(9*Sinh[x] + Sinh[3*x]))/12","A",1
124,1,13,13,0.0042631,"\int \sqrt{a \cosh ^2(x)} \, dx","Integrate[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",1
125,1,21,16,0.0067854,"\int \frac{1}{\sqrt{a \cosh ^2(x)}} \, dx","Integrate[1/Sqrt[a*Cosh[x]^2],x]","\frac{2 \cosh (x) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)}{\sqrt{a \cosh ^2(x)}}","\frac{\cosh (x) \tan ^{-1}(\sinh (x))}{\sqrt{a \cosh ^2(x)}}",1,"(2*ArcTan[Tanh[x/2]]*Cosh[x])/Sqrt[a*Cosh[x]^2]","A",1
126,1,31,42,0.0157786,"\int \frac{1}{\left(a \cosh ^2(x)\right)^{3/2}} \, dx","Integrate[(a*Cosh[x]^2)^(-3/2),x]","\frac{\tanh (x)+2 \cosh (x) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)}{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,"(2*ArcTan[Tanh[x/2]]*Cosh[x] + Tanh[x])/(2*a*Sqrt[a*Cosh[x]^2])","A",1
127,1,40,61,0.0374898,"\int \frac{1}{\left(a \cosh ^2(x)\right)^{5/2}} \, dx","Integrate[(a*Cosh[x]^2)^(-5/2),x]","\frac{\tanh (x) \left(2 \text{sech}^2(x)+3\right)+6 \cosh (x) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)}{8 a^2 \sqrt{a \cosh ^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}}",1,"(6*ArcTan[Tanh[x/2]]*Cosh[x] + (3 + 2*Sech[x]^2)*Tanh[x])/(8*a^2*Sqrt[a*Cosh[x]^2])","A",1
128,1,65,121,0.1211972,"\int \left(a \cosh ^3(x)\right)^{5/2} \, dx","Integrate[(a*Cosh[x]^3)^(5/2),x]","\frac{a \left(a \cosh ^3(x)\right)^{3/2} \left((15465 \sinh (x)+3657 \sinh (3 x)+749 \sinh (5 x)+77 \sinh (7 x)) \sqrt{\cosh (x)}-12480 i F\left(\left.\frac{i x}{2}\right|2\right)\right)}{36960 \cosh ^{\frac{9}{2}}(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)}",1,"(a*(a*Cosh[x]^3)^(3/2)*((-12480*I)*EllipticF[(I/2)*x, 2] + Sqrt[Cosh[x]]*(15465*Sinh[x] + 3657*Sinh[3*x] + 749*Sinh[5*x] + 77*Sinh[7*x])))/(36960*Cosh[x]^(9/2))","A",1
129,1,54,71,0.0750104,"\int \left(a \cosh ^3(x)\right)^{3/2} \, dx","Integrate[(a*Cosh[x]^3)^(3/2),x]","\frac{\left(a \cosh ^3(x)\right)^{3/2} \left((38 \sinh (2 x)+5 \sinh (4 x)) \sqrt{\cosh (x)}-168 i E\left(\left.\frac{i x}{2}\right|2\right)\right)}{180 \cosh ^{\frac{9}{2}}(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)}",1,"((a*Cosh[x]^3)^(3/2)*((-168*I)*EllipticE[(I/2)*x, 2] + Sqrt[Cosh[x]]*(38*Sinh[2*x] + 5*Sinh[4*x])))/(180*Cosh[x]^(9/2))","A",1
130,1,59,48,0.0458612,"\int \sqrt{a \cosh ^3(x)} \, dx","Integrate[Sqrt[a*Cosh[x]^3],x]","\frac{2}{3} \sqrt{a \cosh ^3(x)} \left(\text{sech}^2(x) \sqrt{\sinh (2 x)+\cosh (2 x)+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\cosh (2 x)-\sinh (2 x)\right)+\tanh (x)\right)","\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*Sqrt[a*Cosh[x]^3]*(Hypergeometric2F1[1/4, 1/2, 5/4, -Cosh[2*x] - Sinh[2*x]]*Sech[x]^2*Sqrt[1 + Cosh[2*x] + Sinh[2*x]] + Tanh[x]))/3","C",1
131,1,36,46,0.0232823,"\int \frac{1}{\sqrt{a \cosh ^3(x)}} \, dx","Integrate[1/Sqrt[a*Cosh[x]^3],x]","\frac{2 \cosh (x) \left(\sinh (x)+i \sqrt{\cosh (x)} E\left(\left.\frac{i x}{2}\right|2\right)\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*Cosh[x]*(I*Sqrt[Cosh[x]]*EllipticE[(I/2)*x, 2] + Sinh[x]))/Sqrt[a*Cosh[x]^3]","A",1
132,1,48,75,0.0636411,"\int \frac{1}{\left(a \cosh ^3(x)\right)^{3/2}} \, dx","Integrate[(a*Cosh[x]^3)^(-3/2),x]","\frac{2 \cosh ^2(x) \left(3 \tanh (x)-5 i \cosh ^{\frac{5}{2}}(x) F\left(\left.\frac{i x}{2}\right|2\right)+5 \sinh (x) \cosh (x)\right)}{21 \left(a \cosh ^3(x)\right)^{3/2}}","\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,"(2*Cosh[x]^2*((-5*I)*Cosh[x]^(5/2)*EllipticF[(I/2)*x, 2] + 5*Cosh[x]*Sinh[x] + 3*Tanh[x]))/(21*(a*Cosh[x]^3)^(3/2))","A",1
133,1,61,121,0.1086058,"\int \frac{1}{\left(a \cosh ^3(x)\right)^{5/2}} \, dx","Integrate[(a*Cosh[x]^3)^(-5/2),x]","\frac{462 i \cosh ^{\frac{3}{2}}(x) E\left(\left.\frac{i x}{2}\right|2\right)+462 \sinh (x) \cosh (x)+2 \tanh (x) \left(45 \text{sech}^4(x)+55 \text{sech}^2(x)+77\right)}{585 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,"((462*I)*Cosh[x]^(3/2)*EllipticE[(I/2)*x, 2] + 462*Cosh[x]*Sinh[x] + 2*(77 + 55*Sech[x]^2 + 45*Sech[x]^4)*Tanh[x])/(585*a^2*Sqrt[a*Cosh[x]^3])","A",1
134,1,53,132,0.1247074,"\int \left(a \cosh ^4(x)\right)^{5/2} \, dx","Integrate[(a*Cosh[x]^4)^(5/2),x]","\frac{a (2520 x+2100 \sinh (2 x)+600 \sinh (4 x)+150 \sinh (6 x)+25 \sinh (8 x)+2 \sinh (10 x)) \text{sech}^6(x) \left(a \cosh ^4(x)\right)^{3/2}}{10240}","\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)}",1,"(a*(a*Cosh[x]^4)^(3/2)*Sech[x]^6*(2520*x + 2100*Sinh[2*x] + 600*Sinh[4*x] + 150*Sinh[6*x] + 25*Sinh[8*x] + 2*Sinh[10*x]))/10240","A",1
135,1,38,78,0.0702409,"\int \left(a \cosh ^4(x)\right)^{3/2} \, dx","Integrate[(a*Cosh[x]^4)^(3/2),x]","\frac{1}{192} (60 x+45 \sinh (2 x)+9 \sinh (4 x)+\sinh (6 x)) \text{sech}^6(x) \left(a \cosh ^4(x)\right)^{3/2}","\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)}",1,"((a*Cosh[x]^4)^(3/2)*Sech[x]^6*(60*x + 45*Sinh[2*x] + 9*Sinh[4*x] + Sinh[6*x]))/192","A",1
136,1,25,36,0.014796,"\int \sqrt{a \cosh ^4(x)} \, dx","Integrate[Sqrt[a*Cosh[x]^4],x]","\frac{1}{2} \text{sech}^2(x) \sqrt{a \cosh ^4(x)} (x+\sinh (x) \cosh (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,"(Sqrt[a*Cosh[x]^4]*Sech[x]^2*(x + Cosh[x]*Sinh[x]))/2","A",1
137,1,15,15,0.005682,"\int \frac{1}{\sqrt{a \cosh ^4(x)}} \, dx","Integrate[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",1
138,1,30,67,0.0282643,"\int \frac{1}{\left(a \cosh ^4(x)\right)^{3/2}} \, dx","Integrate[(a*Cosh[x]^4)^(-3/2),x]","\frac{\sinh (x) \cosh (x) (6 \cosh (2 x)+\cosh (4 x)+8)}{15 \left(a \cosh ^4(x)\right)^{3/2}}","\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]*(8 + 6*Cosh[2*x] + Cosh[4*x])*Sinh[x])/(15*(a*Cosh[x]^4)^(3/2))","A",1
139,1,47,117,0.0496096,"\int \frac{1}{\left(a \cosh ^4(x)\right)^{5/2}} \, dx","Integrate[(a*Cosh[x]^4)^(-5/2),x]","\frac{(130 \cosh (2 x)+46 \cosh (4 x)+10 \cosh (6 x)+\cosh (8 x)+128) \tanh (x) \text{sech}^6(x)}{315 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,"((128 + 130*Cosh[2*x] + 46*Cosh[4*x] + 10*Cosh[6*x] + Cosh[8*x])*Sech[x]^6*Tanh[x])/(315*a^2*Sqrt[a*Cosh[x]^4])","A",1
140,1,12,8,0.0110063,"\int \frac{\sinh (x)}{(1+\cosh (x))^2} \, dx","Integrate[Sinh[x]/(1 + Cosh[x])^2,x]","-\frac{1}{2} \text{sech}^2\left(\frac{x}{2}\right)","-\frac{1}{\cosh (x)+1}",1,"-1/2*Sech[x/2]^2","A",1
141,1,12,8,0.0101238,"\int \frac{\sinh (x)}{(1-\cosh (x))^2} \, dx","Integrate[Sinh[x]/(1 - Cosh[x])^2,x]","-\frac{1}{2} \text{csch}^2\left(\frac{x}{2}\right)","\frac{1}{1-\cosh (x)}",1,"-1/2*Csch[x/2]^2","A",1
142,1,18,12,0.0065182,"\int \frac{\sinh ^2(x)}{(1+\cosh (x))^2} \, dx","Integrate[Sinh[x]^2/(1 + Cosh[x])^2,x]","2 \tanh ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)-2 \tanh \left(\frac{x}{2}\right)","x-\frac{2 \sinh (x)}{\cosh (x)+1}",1,"2*ArcTanh[Tanh[x/2]] - 2*Tanh[x/2]","A",1
143,1,24,14,0.0107393,"\int \frac{\sinh ^2(x)}{(1-\cosh (x))^2} \, dx","Integrate[Sinh[x]^2/(1 - Cosh[x])^2,x]","-2 \coth \left(\frac{x}{2}\right) \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};\tanh ^2\left(\frac{x}{2}\right)\right)","x+\frac{2 \sinh (x)}{1-\cosh (x)}",1,"-2*Coth[x/2]*Hypergeometric2F1[-1/2, 1, 1/2, Tanh[x/2]^2]","C",1
144,1,13,10,0.0198443,"\int \frac{\sinh ^3(x)}{(1+\cosh (x))^2} \, dx","Integrate[Sinh[x]^3/(1 + Cosh[x])^2,x]","\cosh (x)-4 \log \left(\cosh \left(\frac{x}{2}\right)\right)-1","\cosh (x)-2 \log (\cosh (x)+1)",1,"-1 + Cosh[x] - 4*Log[Cosh[x/2]]","A",1
145,1,13,12,0.0183985,"\int \frac{\sinh ^3(x)}{(1-\cosh (x))^2} \, dx","Integrate[Sinh[x]^3/(1 - Cosh[x])^2,x]","\cosh (x)+4 \log \left(\sinh \left(\frac{x}{2}\right)\right)-1","\cosh (x)+2 \log (1-\cosh (x))",1,"-1 + Cosh[x] + 4*Log[Sinh[x/2]]","A",1
146,1,12,10,0.0099085,"\int \frac{\sinh (x)}{(1+\cosh (x))^3} \, dx","Integrate[Sinh[x]/(1 + Cosh[x])^3,x]","-\frac{1}{8} \text{sech}^4\left(\frac{x}{2}\right)","-\frac{1}{2 (\cosh (x)+1)^2}",1,"-1/8*Sech[x/2]^4","A",1
147,1,12,12,0.0115486,"\int \frac{\sinh (x)}{(1-\cosh (x))^3} \, dx","Integrate[Sinh[x]/(1 - Cosh[x])^3,x]","\frac{1}{8} \text{csch}^4\left(\frac{x}{2}\right)","\frac{1}{2 (1-\cosh (x))^2}",1,"Csch[x/2]^4/8","A",1
148,1,12,14,0.0279363,"\int \frac{\sinh ^2(x)}{(1+\cosh (x))^3} \, dx","Integrate[Sinh[x]^2/(1 + Cosh[x])^3,x]","\frac{1}{3} \tanh ^3\left(\frac{x}{2}\right)","\frac{\sinh ^3(x)}{3 (\cosh (x)+1)^3}",1,"Tanh[x/2]^3/3","A",1
149,1,12,16,0.0293809,"\int \frac{\sinh ^2(x)}{(1-\cosh (x))^3} \, dx","Integrate[Sinh[x]^2/(1 - Cosh[x])^3,x]","\frac{1}{3} \coth ^3\left(\frac{x}{2}\right)","-\frac{\sinh ^3(x)}{3 (1-\cosh (x))^3}",1,"Coth[x/2]^3/3","A",1
150,1,20,14,0.0101187,"\int \frac{\sinh ^3(x)}{(1+\cosh (x))^3} \, dx","Integrate[Sinh[x]^3/(1 + Cosh[x])^3,x]","2 \log \left(\cosh \left(\frac{x}{2}\right)\right)-\tanh ^2\left(\frac{x}{2}\right)","\frac{2}{\cosh (x)+1}+\log (\cosh (x)+1)",1,"2*Log[Cosh[x/2]] - Tanh[x/2]^2","A",1
151,1,27,20,0.0141874,"\int \frac{\sinh ^3(x)}{(1-\cosh (x))^3} \, dx","Integrate[Sinh[x]^3/(1 - Cosh[x])^3,x]","\coth ^2\left(\frac{x}{2}\right)-2 \log \left(\tanh \left(\frac{x}{2}\right)\right)-2 \log \left(\cosh \left(\frac{x}{2}\right)\right)","-\frac{2}{1-\cosh (x)}-\log (1-\cosh (x))",1,"Coth[x/2]^2 - 2*Log[Cosh[x/2]] - 2*Log[Tanh[x/2]]","A",1
152,1,51,57,0.0718898,"\int \frac{\sinh ^8(x)}{a+a \cosh (x)} \, dx","Integrate[Sinh[x]^8/(a + a*Cosh[x]),x]","\frac{420 x-105 \sinh (x)-315 \sinh (2 x)+63 \sinh (3 x)+63 \sinh (4 x)-21 \sinh (5 x)-7 \sinh (6 x)+3 \sinh (7 x)}{1344 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,"(420*x - 105*Sinh[x] - 315*Sinh[2*x] + 63*Sinh[3*x] + 63*Sinh[4*x] - 21*Sinh[5*x] - 7*Sinh[6*x] + 3*Sinh[7*x])/(1344*a)","A",1
153,1,27,46,0.0327984,"\int \frac{\sinh ^7(x)}{a+a \cosh (x)} \, dx","Integrate[Sinh[x]^7/(a + a*Cosh[x]),x]","\frac{4 \sinh ^8\left(\frac{x}{2}\right) (28 \cosh (x)+5 \cosh (2 x)+27)}{15 a}","\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,"(4*(27 + 28*Cosh[x] + 5*Cosh[2*x])*Sinh[x/2]^8)/(15*a)","A",1
154,1,39,44,0.0554679,"\int \frac{\sinh ^6(x)}{a+a \cosh (x)} \, dx","Integrate[Sinh[x]^6/(a + a*Cosh[x]),x]","\frac{-60 x+20 \sinh (x)+40 \sinh (2 x)-10 \sinh (3 x)-5 \sinh (4 x)+2 \sinh (5 x)}{160 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,"(-60*x + 20*Sinh[x] + 40*Sinh[2*x] - 10*Sinh[3*x] - 5*Sinh[4*x] + 2*Sinh[5*x])/(160*a)","A",1
155,1,21,33,0.0215192,"\int \frac{\sinh ^5(x)}{a+a \cosh (x)} \, dx","Integrate[Sinh[x]^5/(a + a*Cosh[x]),x]","\frac{2 \sinh ^6\left(\frac{x}{2}\right) (3 \cosh (x)+5)}{3 a}","\frac{(a-a \cosh (x))^4}{4 a^5}-\frac{2 (a-a \cosh (x))^3}{3 a^4}",1,"(2*(5 + 3*Cosh[x])*Sinh[x/2]^6)/(3*a)","A",1
156,1,25,31,0.0370784,"\int \frac{\sinh ^4(x)}{a+a \cosh (x)} \, dx","Integrate[Sinh[x]^4/(a + a*Cosh[x]),x]","\frac{6 x-3 \sinh (x)-3 \sinh (2 x)+\sinh (3 x)}{12 a}","\frac{x}{2 a}+\frac{\sinh ^3(x)}{3 a}-\frac{\sinh (x) \cosh (x)}{2 a}",1,"(6*x - 3*Sinh[x] - 3*Sinh[2*x] + Sinh[3*x])/(12*a)","A",1
157,1,13,19,0.0132396,"\int \frac{\sinh ^3(x)}{a+a \cosh (x)} \, dx","Integrate[Sinh[x]^3/(a + a*Cosh[x]),x]","\frac{2 \sinh ^4\left(\frac{x}{2}\right)}{a}","\frac{\cosh ^2(x)}{2 a}-\frac{\cosh (x)}{a}",1,"(2*Sinh[x/2]^4)/a","A",1
158,1,17,13,0.0090356,"\int \frac{\sinh ^2(x)}{a+a \cosh (x)} \, dx","Integrate[Sinh[x]^2/(a + a*Cosh[x]),x]","\frac{2 \left(\frac{\sinh (x)}{2}-\frac{x}{2}\right)}{a}","\frac{\sinh (x)}{a}-\frac{x}{a}",1,"(2*(-1/2*x + Sinh[x]/2))/a","A",1
159,1,12,9,0.0063482,"\int \frac{\sinh (x)}{a+a \cosh (x)} \, dx","Integrate[Sinh[x]/(a + a*Cosh[x]),x]","\frac{2 \log \left(\cosh \left(\frac{x}{2}\right)\right)}{a}","\frac{\log (\cosh (x)+1)}{a}",1,"(2*Log[Cosh[x/2]])/a","A",1
160,1,42,23,0.0320953,"\int \frac{\text{csch}(x)}{a+a \cosh (x)} \, dx","Integrate[Csch[x]/(a + a*Cosh[x]),x]","\frac{1-2 \cosh ^2\left(\frac{x}{2}\right) \left(\log \left(\cosh \left(\frac{x}{2}\right)\right)-\log \left(\sinh \left(\frac{x}{2}\right)\right)\right)}{2 a (\cosh (x)+1)}","\frac{1}{2 (a \cosh (x)+a)}-\frac{\tanh ^{-1}(\cosh (x))}{2 a}",1,"(1 - 2*Cosh[x/2]^2*(Log[Cosh[x/2]] - Log[Sinh[x/2]]))/(2*a*(1 + Cosh[x]))","A",1
161,1,30,24,0.0500826,"\int \frac{\text{csch}^2(x)}{a+a \cosh (x)} \, dx","Integrate[Csch[x]^2/(a + a*Cosh[x]),x]","-\frac{(2 \cosh (x)+\cosh (2 x)) \text{csch}\left(\frac{x}{2}\right) \text{sech}^3\left(\frac{x}{2}\right)}{12 a}","\frac{\text{csch}(x)}{3 (a \cosh (x)+a)}-\frac{2 \coth (x)}{3 a}",1,"-1/12*((2*Cosh[x] + Cosh[2*x])*Csch[x/2]*Sech[x/2]^3)/a","A",1
162,1,60,49,0.1701773,"\int \frac{\text{csch}^3(x)}{a+a \cosh (x)} \, dx","Integrate[Csch[x]^3/(a + a*Cosh[x]),x]","-\frac{2 \coth ^2\left(\frac{x}{2}\right)+\text{sech}^2\left(\frac{x}{2}\right)-12 \cosh ^2\left(\frac{x}{2}\right) \left(\log \left(\cosh \left(\frac{x}{2}\right)\right)-\log \left(\sinh \left(\frac{x}{2}\right)\right)\right)+4}{16 a (\cosh (x)+1)}","-\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,"-1/16*(4 + 2*Coth[x/2]^2 - 12*Cosh[x/2]^2*(Log[Cosh[x/2]] - Log[Sinh[x/2]]) + Sech[x/2]^2)/(a*(1 + Cosh[x]))","A",1
163,1,38,37,0.05673,"\int \frac{\text{csch}^4(x)}{a+a \cosh (x)} \, dx","Integrate[Csch[x]^4/(a + a*Cosh[x]),x]","\frac{(-6 \cosh (x)-2 \cosh (2 x)+2 \cosh (3 x)+\cosh (4 x)) \text{csch}^3(x)}{15 a (\cosh (x)+1)}","-\frac{4 \coth ^3(x)}{15 a}+\frac{4 \coth (x)}{5 a}+\frac{\text{csch}^3(x)}{5 (a \cosh (x)+a)}",1,"((-6*Cosh[x] - 2*Cosh[2*x] + 2*Cosh[3*x] + Cosh[4*x])*Csch[x]^3)/(15*a*(1 + Cosh[x]))","A",1
164,1,89,78,0.2868423,"\int \frac{\text{csch}^5(x)}{a+a \cosh (x)} \, dx","Integrate[Csch[x]^5/(a + a*Cosh[x]),x]","\frac{\cosh ^2\left(\frac{x}{2}\right) \left(-3 \text{csch}^4\left(\frac{x}{2}\right)+24 \text{csch}^2\left(\frac{x}{2}\right)+2 \text{sech}^6\left(\frac{x}{2}\right)+9 \text{sech}^4\left(\frac{x}{2}\right)+36 \text{sech}^2\left(\frac{x}{2}\right)+120 \log \left(\sinh \left(\frac{x}{2}\right)\right)-120 \log \left(\cosh \left(\frac{x}{2}\right)\right)\right)}{192 (a \cosh (x)+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,"(Cosh[x/2]^2*(24*Csch[x/2]^2 - 3*Csch[x/2]^4 - 120*Log[Cosh[x/2]] + 120*Log[Sinh[x/2]] + 36*Sech[x/2]^2 + 9*Sech[x/2]^4 + 2*Sech[x/2]^6))/(192*(a + a*Cosh[x]))","A",1
165,1,144,140,0.1865383,"\int \frac{\sinh ^7(x)}{a+b \cosh (x)} \, dx","Integrate[Sinh[x]^7/(a + b*Cosh[x]),x]","\frac{960 \left(a^2-b^2\right)^3 \log (a+b \cosh (x))-30 b^4 \left(2 b^2-a^2\right) \cosh (4 x)+15 b^2 \left(16 a^4-40 a^2 b^2+29 b^4\right) \cosh (2 x)-120 a b \left(8 a^4-22 a^2 b^2+19 b^4\right) \cosh (x)-12 a b^5 \cosh (5 x)-20 a b^3 (2 a-3 b) (2 a+3 b) \cosh (3 x)+5 b^6 \cosh (6 x)}{960 b^7}","\frac{\left(a^2-b^2\right)^3 \log (a+b \cosh (x))}{b^7}-\frac{a \left(a^2-3 b^2\right) \cosh ^3(x)}{3 b^4}+\frac{\left(a^2-3 b^2\right) \cosh ^4(x)}{4 b^3}-\frac{a \left(a^4-3 a^2 b^2+3 b^4\right) \cosh (x)}{b^6}+\frac{\left(a^4-3 a^2 b^2+3 b^4\right) \cosh ^2(x)}{2 b^5}-\frac{a \cosh ^5(x)}{5 b^2}+\frac{\cosh ^6(x)}{6 b}",1,"(-120*a*b*(8*a^4 - 22*a^2*b^2 + 19*b^4)*Cosh[x] + 15*b^2*(16*a^4 - 40*a^2*b^2 + 29*b^4)*Cosh[2*x] - 20*a*(2*a - 3*b)*b^3*(2*a + 3*b)*Cosh[3*x] - 30*b^4*(-a^2 + 2*b^2)*Cosh[4*x] - 12*a*b^5*Cosh[5*x] + 5*b^6*Cosh[6*x] + 960*(a^2 - b^2)^3*Log[a + b*Cosh[x]])/(960*b^7)","A",1
166,1,154,154,0.2437352,"\int \frac{\sinh ^6(x)}{a+b \cosh (x)} \, dx","Integrate[Sinh[x]^6/(a + b*Cosh[x]),x]","\frac{-120 a b^2 \left(a^2-2 b^2\right) \sinh (2 x)+960 \left(b^2-a^2\right)^{5/2} \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)-10 b^3 \left(7 b^2-4 a^2\right) \sinh (3 x)-60 a x \left(8 a^4-20 a^2 b^2+15 b^4\right)+60 b \left(8 a^4-18 a^2 b^2+11 b^4\right) \sinh (x)-15 a b^4 \sinh (4 x)+6 b^5 \sinh (5 x)}{480 b^6}","\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{\sinh ^3(x) \left(4 \left(a^2-b^2\right)-3 a b \cosh (x)\right)}{12 b^3}-\frac{a x \left(8 a^4-20 a^2 b^2+15 b^4\right)}{8 b^6}+\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,"(-60*a*(8*a^4 - 20*a^2*b^2 + 15*b^4)*x + 960*(-a^2 + b^2)^(5/2)*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]] + 60*b*(8*a^4 - 18*a^2*b^2 + 11*b^4)*Sinh[x] - 120*a*b^2*(a^2 - 2*b^2)*Sinh[2*x] - 10*b^3*(-4*a^2 + 7*b^2)*Sinh[3*x] - 15*a*b^4*Sinh[4*x] + 6*b^5*Sinh[5*x])/(480*b^6)","A",1
167,1,84,83,0.1153622,"\int \frac{\sinh ^5(x)}{a+b \cosh (x)} \, dx","Integrate[Sinh[x]^5/(a + b*Cosh[x]),x]","\frac{-12 b^2 \left(3 b^2-2 a^2\right) \cosh (2 x)-24 a b \left(4 a^2-7 b^2\right) \cosh (x)+96 \left(a^2-b^2\right)^2 \log (a+b \cosh (x))-8 a b^3 \cosh (3 x)+3 b^4 \cosh (4 x)}{96 b^5}","\frac{\left(a^2-b^2\right)^2 \log (a+b \cosh (x))}{b^5}-\frac{a \left(a^2-2 b^2\right) \cosh (x)}{b^4}+\frac{\left(a^2-2 b^2\right) \cosh ^2(x)}{2 b^3}-\frac{a \cosh ^3(x)}{3 b^2}+\frac{\cosh ^4(x)}{4 b}",1,"(-24*a*b*(4*a^2 - 7*b^2)*Cosh[x] - 12*b^2*(-2*a^2 + 3*b^2)*Cosh[2*x] - 8*a*b^3*Cosh[3*x] + 3*b^4*Cosh[4*x] + 96*(a^2 - b^2)^2*Log[a + b*Cosh[x]])/(96*b^5)","A",1
168,1,95,104,0.1898384,"\int \frac{\sinh ^4(x)}{a+b \cosh (x)} \, dx","Integrate[Sinh[x]^4/(a + b*Cosh[x]),x]","\frac{-12 a^3 x-24 \left(b^2-a^2\right)^{3/2} \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)+12 a^2 b \sinh (x)+18 a b^2 x-3 a b^2 \sinh (2 x)-15 b^3 \sinh (x)+b^3 \sinh (3 x)}{12 b^4}","-\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,"(-12*a^3*x + 18*a*b^2*x - 24*(-a^2 + b^2)^(3/2)*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]] + 12*a^2*b*Sinh[x] - 15*b^3*Sinh[x] - 3*a*b^2*Sinh[2*x] + b^3*Sinh[3*x])/(12*b^4)","A",1
169,1,40,40,0.0597678,"\int \frac{\sinh ^3(x)}{a+b \cosh (x)} \, dx","Integrate[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)}{4 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[2*x]/(4*b) + ((a^2 - b^2)*Log[a + b*Cosh[x]])/b^3","A",1
170,1,54,59,0.0860399,"\int \frac{\sinh ^2(x)}{a+b \cosh (x)} \, dx","Integrate[Sinh[x]^2/(a + b*Cosh[x]),x]","\frac{2 \sqrt{b^2-a^2} \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)-a x+b \sinh (x)}{b^2}","-\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) + 2*Sqrt[-a^2 + b^2]*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]] + b*Sinh[x])/b^2","A",1
171,1,11,11,0.015772,"\int \frac{\sinh (x)}{a+b \cosh (x)} \, dx","Integrate[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",1
172,1,37,53,0.0706345,"\int \frac{\text{csch}(x)}{a+b \cosh (x)} \, dx","Integrate[Csch[x]/(a + b*Cosh[x]),x]","\frac{b \log (a+b \cosh (x))+a \log \left(\tanh \left(\frac{x}{2}\right)\right)-b \log (\sinh (x))}{a^2-b^2}","\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,"(b*Log[a + b*Cosh[x]] - b*Log[Sinh[x]] + a*Log[Tanh[x/2]])/(a^2 - b^2)","A",1
173,1,77,67,0.2115289,"\int \frac{\text{csch}^2(x)}{a+b \cosh (x)} \, dx","Integrate[Csch[x]^2/(a + b*Cosh[x]),x]","\frac{2 b^2 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\left(b^2-a^2\right)^{3/2}}-\frac{\tanh \left(\frac{x}{2}\right)}{2 (a-b)}-\frac{\coth \left(\frac{x}{2}\right)}{2 (a+b)}","\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*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/(-a^2 + b^2)^(3/2) - Coth[x/2]/(2*(a + b)) - Tanh[x/2]/(2*(a - b))","A",1
174,1,100,91,0.2804752,"\int \frac{\text{csch}^3(x)}{a+b \cosh (x)} \, dx","Integrate[Csch[x]^3/(a + b*Cosh[x]),x]","-\frac{4 a^3 \log \left(\tanh \left(\frac{x}{2}\right)\right)-8 b^3 \log (a+b \cosh (x))-12 a b^2 \log \left(\tanh \left(\frac{x}{2}\right)\right)+(a-b)^2 (a+b) \text{csch}^2\left(\frac{x}{2}\right)+(a-b) (a+b)^2 \text{sech}^2\left(\frac{x}{2}\right)+8 b^3 \log (\sinh (x))}{8 (a-b)^2 (a+b)^2}","\frac{\text{csch}^2(x) (b-a \cosh (x))}{2 \left(a^2-b^2\right)}+\frac{b^3 \log (a+b \cosh (x))}{\left(a^2-b^2\right)^2}-\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,"-1/8*((a - b)^2*(a + b)*Csch[x/2]^2 - 8*b^3*Log[a + b*Cosh[x]] + 8*b^3*Log[Sinh[x]] + 4*a^3*Log[Tanh[x/2]] - 12*a*b^2*Log[Tanh[x/2]] + (a - b)*(a + b)^2*Sech[x/2]^2)/((a - b)^2*(a + b)^2)","A",1
175,1,141,110,0.570681,"\int \frac{\text{csch}^4(x)}{a+b \cosh (x)} \, dx","Integrate[Csch[x]^4/(a + b*Cosh[x]),x]","\frac{1}{24} \left(-\frac{48 b^4 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\left(b^2-a^2\right)^{5/2}}-\frac{14 b \tanh \left(\frac{x}{2}\right)}{(a-b)^2}+\frac{8 a \tanh \left(\frac{x}{2}\right)}{(a-b)^2}+\frac{2 (4 a+7 b) \coth \left(\frac{x}{2}\right)}{(a+b)^2}-\frac{\sinh (x) \text{csch}^4\left(\frac{x}{2}\right)}{2 (a+b)}+\frac{8 \sinh ^4\left(\frac{x}{2}\right) \text{csch}^3(x)}{a-b}\right)","\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,"((-48*b^4*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/(-a^2 + b^2)^(5/2) + (2*(4*a + 7*b)*Coth[x/2])/(a + b)^2 + (8*Csch[x]^3*Sinh[x/2]^4)/(a - b) - (Csch[x/2]^4*Sinh[x])/(2*(a + b)) + (8*a*Tanh[x/2])/(a - b)^2 - (14*b*Tanh[x/2])/(a - b)^2)/24","A",1
176,1,148,151,0.9100316,"\int \frac{\text{csch}^5(x)}{a+b \cosh (x)} \, dx","Integrate[Csch[x]^5/(a + b*Cosh[x]),x]","\frac{1}{64} \left(\frac{2 \left(3 a^2-8 a b+5 b^2\right) \text{sech}^2\left(\frac{x}{2}\right)+\frac{8 \left(a \left(3 a^4-10 a^2 b^2+15 b^4\right) \log \left(\tanh \left(\frac{x}{2}\right)\right)+8 b^5 \log (a+b \cosh (x))-8 b^5 \log (\sinh (x))\right)}{(a+b)^3}+(a-b)^2 \text{sech}^4\left(\frac{x}{2}\right)}{(a-b)^3}-\frac{\text{csch}^4\left(\frac{x}{2}\right)}{a+b}+\frac{2 (3 a+5 b) \text{csch}^2\left(\frac{x}{2}\right)}{(a+b)^2}\right)","\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{b^5 \log (a+b \cosh (x))}{\left(a^2-b^2\right)^3}+\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,"((2*(3*a + 5*b)*Csch[x/2]^2)/(a + b)^2 - Csch[x/2]^4/(a + b) + ((8*(8*b^5*Log[a + b*Cosh[x]] - 8*b^5*Log[Sinh[x]] + a*(3*a^4 - 10*a^2*b^2 + 15*b^4)*Log[Tanh[x/2]]))/(a + b)^3 + 2*(3*a^2 - 8*a*b + 5*b^2)*Sech[x/2]^2 + (a - b)^2*Sech[x/2]^4)/(a - b)^3)/64","A",1
177,1,201,159,1.8132161,"\int \frac{\text{csch}^6(x)}{a+b \cosh (x)} \, dx","Integrate[Csch[x]^6/(a + b*Cosh[x]),x]","\frac{1}{480} \left(-\frac{2 \left(64 a^2-183 a b+149 b^2\right) \tanh \left(\frac{x}{2}\right)}{(a-b)^3}-\frac{2 \left(64 a^2+183 a b+149 b^2\right) \coth \left(\frac{x}{2}\right)}{(a+b)^3}+\frac{960 b^6 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\left(b^2-a^2\right)^{7/2}}-\frac{3 \sinh (x) \text{csch}^6\left(\frac{x}{2}\right)}{2 (a+b)}-\frac{96 \sinh ^6\left(\frac{x}{2}\right) \text{csch}^5(x)}{a-b}+\frac{(19 a+29 b) \sinh (x) \text{csch}^4\left(\frac{x}{2}\right)}{2 (a+b)^2}-\frac{8 (19 a-29 b) \sinh ^4\left(\frac{x}{2}\right) \text{csch}^3(x)}{(a-b)^2}\right)","\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(8 a^4-26 a^2 b^2+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,"((960*b^6*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/(-a^2 + b^2)^(7/2) - (2*(64*a^2 + 183*a*b + 149*b^2)*Coth[x/2])/(a + b)^3 - (8*(19*a - 29*b)*Csch[x]^3*Sinh[x/2]^4)/(a - b)^2 - (96*Csch[x]^5*Sinh[x/2]^6)/(a - b) + ((19*a + 29*b)*Csch[x/2]^4*Sinh[x])/(2*(a + b)^2) - (3*Csch[x/2]^6*Sinh[x])/(2*(a + b)) - (2*(64*a^2 - 183*a*b + 149*b^2)*Tanh[x/2])/(a - b)^3)/480","A",1
178,1,61,67,0.109158,"\int \frac{\sinh ^2(x)}{(a+b \cosh (x))^2} \, dx","Integrate[Sinh[x]^2/(a + b*Cosh[x])^2,x]","\frac{\frac{2 a \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}-\frac{b \sinh (x)}{a+b \cosh (x)}+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 + (2*a*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2] - (b*Sinh[x])/(a + b*Cosh[x]))/b^2","A",1
179,1,100,113,0.4438198,"\int \frac{\tanh ^4(x)}{a+b \cosh (x)} \, dx","Integrate[Tanh[x]^4/(a + b*Cosh[x]),x]","\frac{-12 \left(b^2-a^2\right)^{3/2} \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)+6 b \left(3 a^2-2 b^2\right) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+a \tanh (x) \left(2 a^2 \text{sech}^2(x)-8 a^2-3 a b \text{sech}(x)+6 b^2\right)}{6 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{b \left(3 a^2-2 b^2\right) \tan ^{-1}(\sinh (x))}{2 a^4}-\frac{\left(4 a^2-3 b^2\right) \tanh (x)}{3 a^3}+\frac{\tanh (x) \text{sech}^2(x)}{3 a}",1,"(6*b*(3*a^2 - 2*b^2)*ArcTan[Tanh[x/2]] - 12*(-a^2 + b^2)^(3/2)*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]] + a*(-8*a^2 + 6*b^2 - 3*a*b*Sech[x] + 2*a^2*Sech[x]^2)*Tanh[x])/(6*a^4)","A",1
180,1,46,57,0.1043214,"\int \frac{\tanh ^3(x)}{a+b \cosh (x)} \, dx","Integrate[Tanh[x]^3/(a + b*Cosh[x]),x]","\frac{2 \left(a^2-b^2\right) (\log (\cosh (x))-\log (a+b \cosh (x)))+a^2 \text{sech}^2(x)-2 a b \text{sech}(x)}{2 a^3}","-\frac{b \text{sech}(x)}{a^2}+\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{\text{sech}^2(x)}{2 a}",1,"(2*(a^2 - b^2)*(Log[Cosh[x]] - Log[a + b*Cosh[x]]) - 2*a*b*Sech[x] + a^2*Sech[x]^2)/(2*a^3)","A",1
181,1,61,61,0.1213217,"\int \frac{\tanh ^2(x)}{a+b \cosh (x)} \, dx","Integrate[Tanh[x]^2/(a + b*Cosh[x]),x]","\frac{2 \sqrt{b^2-a^2} \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)-a \tanh (x)+2 b \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)}{a^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)}{a^2}+\frac{b \tan ^{-1}(\sinh (x))}{a^2}-\frac{\tanh (x)}{a}",1,"(2*b*ArcTan[Tanh[x/2]] + 2*Sqrt[-a^2 + b^2]*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]] - a*Tanh[x])/a^2","A",1
182,1,20,20,0.0093285,"\int \frac{\tanh (x)}{a+b \cosh (x)} \, dx","Integrate[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",1
183,1,38,54,0.0736874,"\int \frac{\coth (x)}{a+b \cosh (x)} \, dx","Integrate[Coth[x]/(a + b*Cosh[x]),x]","-\frac{a \log (a+b \cosh (x))-a \log (\sinh (x))+b \log \left(\tanh \left(\frac{x}{2}\right)\right)}{a^2-b^2}","-\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,"-((a*Log[a + b*Cosh[x]] - a*Log[Sinh[x]] + b*Log[Tanh[x/2]])/(a^2 - b^2))","A",1
184,1,77,77,0.2068873,"\int \frac{\coth ^2(x)}{a+b \cosh (x)} \, dx","Integrate[Coth[x]^2/(a + b*Cosh[x]),x]","\frac{2 a^2 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\left(b^2-a^2\right)^{3/2}}-\frac{\tanh \left(\frac{x}{2}\right)}{2 (a-b)}-\frac{\coth \left(\frac{x}{2}\right)}{2 (a+b)}","-\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*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/(-a^2 + b^2)^(3/2) - Coth[x/2]/(2*(a + b)) - Tanh[x/2]/(2*(a - b))","A",1
185,1,101,94,0.2246736,"\int \frac{\coth ^3(x)}{a+b \cosh (x)} \, dx","Integrate[Coth[x]^3/(a + b*Cosh[x]),x]","\frac{-8 a^3 \log (a+b \cosh (x))+8 a^3 \log (\sinh (x))-12 a^2 b \log \left(\tanh \left(\frac{x}{2}\right)\right)-(a-b)^2 (a+b) \text{csch}^2\left(\frac{x}{2}\right)+(a-b) (a+b)^2 \text{sech}^2\left(\frac{x}{2}\right)+4 b^3 \log \left(\tanh \left(\frac{x}{2}\right)\right)}{8 (a-b)^2 (a+b)^2}","-\frac{\text{csch}^2(x) (a-b \cosh (x))}{2 \left(a^2-b^2\right)}-\frac{a^3 \log (a+b \cosh (x))}{\left(a^2-b^2\right)^2}+\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)^2*(a + b)*Csch[x/2]^2) - 8*a^3*Log[a + b*Cosh[x]] + 8*a^3*Log[Sinh[x]] - 12*a^2*b*Log[Tanh[x/2]] + 4*b^3*Log[Tanh[x/2]] + (a - b)*(a + b)^2*Sech[x/2]^2)/(8*(a - b)^2*(a + b)^2)","A",1
186,1,131,137,0.5420112,"\int \frac{\coth ^4(x)}{a+b \cosh (x)} \, dx","Integrate[Coth[x]^4/(a + b*Cosh[x]),x]","\frac{1}{24} \left(-\frac{48 a^4 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\left(b^2-a^2\right)^{5/2}}+\frac{2 (5 b-8 a) \tanh \left(\frac{x}{2}\right)}{(a-b)^2}-\frac{2 (8 a+5 b) \coth \left(\frac{x}{2}\right)}{(a+b)^2}-\frac{\sinh (x) \text{csch}^4\left(\frac{x}{2}\right)}{2 (a+b)}+\frac{8 \sinh ^4\left(\frac{x}{2}\right) \text{csch}^3(x)}{a-b}\right)","\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{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{a^3 \coth (x)}{\left(a^2-b^2\right)^2}",1,"((-48*a^4*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/(-a^2 + b^2)^(5/2) - (2*(8*a + 5*b)*Coth[x/2])/(a + b)^2 + (8*Csch[x]^3*Sinh[x/2]^4)/(a - b) - (Csch[x/2]^4*Sinh[x])/(2*(a + b)) + (2*(-8*a + 5*b)*Tanh[x/2])/(a - b)^2)/24","A",1
187,1,58,46,0.0912674,"\int \frac{\tanh ^6(x)}{a+a \cosh (x)} \, dx","Integrate[Tanh[x]^6/(a + a*Cosh[x]),x]","\frac{\cosh ^2\left(\frac{x}{2}\right) \left(30 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+\tanh (x) \left(-8 \text{sech}^4(x)+10 \text{sech}^3(x)+16 \text{sech}^2(x)-25 \text{sech}(x)-8\right)\right)}{20 a (\cosh (x)+1)}","-\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,"(Cosh[x/2]^2*(30*ArcTan[Tanh[x/2]] + (-8 - 25*Sech[x] + 16*Sech[x]^2 + 10*Sech[x]^3 - 8*Sech[x]^4)*Tanh[x]))/(20*a*(1 + Cosh[x]))","A",1
188,1,25,30,0.0297443,"\int \frac{\tanh ^5(x)}{a+a \cosh (x)} \, dx","Integrate[Tanh[x]^5/(a + a*Cosh[x]),x]","\frac{2 \sinh ^6\left(\frac{x}{2}\right) (5 \cosh (x)+3) \text{sech}^4(x)}{3 a}","-\frac{\tanh ^4(x)}{4 a}+\frac{\text{sech}^3(x)}{3 a}-\frac{\text{sech}(x)}{a}",1,"(2*(3 + 5*Cosh[x])*Sech[x]^4*Sinh[x/2]^6)/(3*a)","A",1
189,1,46,33,0.0646984,"\int \frac{\tanh ^4(x)}{a+a \cosh (x)} \, dx","Integrate[Tanh[x]^4/(a + a*Cosh[x]),x]","\frac{\cosh ^2\left(\frac{x}{2}\right) \left(6 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+\tanh (x) \left(2 \text{sech}^2(x)-3 \text{sech}(x)-2\right)\right)}{3 a (\cosh (x)+1)}","-\frac{\tanh ^3(x)}{3 a}+\frac{\tan ^{-1}(\sinh (x))}{2 a}-\frac{\tanh (x) \text{sech}(x)}{2 a}",1,"(Cosh[x/2]^2*(6*ArcTan[Tanh[x/2]] + (-2 - 3*Sech[x] + 2*Sech[x]^2)*Tanh[x]))/(3*a*(1 + Cosh[x]))","A",1
190,1,17,19,0.0233622,"\int \frac{\tanh ^3(x)}{a+a \cosh (x)} \, dx","Integrate[Tanh[x]^3/(a + a*Cosh[x]),x]","\frac{2 \sinh ^4\left(\frac{x}{2}\right) \text{sech}^2(x)}{a}","\frac{\text{sech}^2(x)}{2 a}-\frac{\text{sech}(x)}{a}",1,"(2*Sech[x]^2*Sinh[x/2]^4)/a","A",1
191,1,18,15,0.0499678,"\int \frac{\tanh ^2(x)}{a+a \cosh (x)} \, dx","Integrate[Tanh[x]^2/(a + a*Cosh[x]),x]","\frac{2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)-\tanh (x)}{a}","\frac{\tan ^{-1}(\sinh (x))}{a}-\frac{\tanh (x)}{a}",1,"(2*ArcTan[Tanh[x/2]] - Tanh[x])/a","A",1
192,1,12,18,0.0193235,"\int \frac{\tanh (x)}{a+a \cosh (x)} \, dx","Integrate[Tanh[x]/(a + a*Cosh[x]),x]","-\frac{2 \tanh ^{-1}(2 \cosh (x)+1)}{a}","\frac{\log (\cosh (x))}{a}-\frac{\log (\cosh (x)+1)}{a}",1,"(-2*ArcTanh[1 + 2*Cosh[x]])/a","A",1
193,1,42,33,0.0428904,"\int \frac{\coth (x)}{a+a \cosh (x)} \, dx","Integrate[Coth[x]/(a + a*Cosh[x]),x]","-\frac{2 \cosh ^2\left(\frac{x}{2}\right) \left(\log \left(\cosh \left(\frac{x}{2}\right)\right)-\log \left(\sinh \left(\frac{x}{2}\right)\right)\right)+1}{2 a (\cosh (x)+1)}","\frac{\text{csch}^2(x)}{2 a}-\frac{\tanh ^{-1}(\cosh (x))}{2 a}-\frac{\coth (x) \text{csch}(x)}{2 a}",1,"-1/2*(1 + 2*Cosh[x/2]^2*(Log[Cosh[x/2]] - Log[Sinh[x/2]]))/(a*(1 + Cosh[x]))","A",1
194,1,25,30,0.0518504,"\int \frac{\coth ^2(x)}{a+a \cosh (x)} \, dx","Integrate[Coth[x]^2/(a + a*Cosh[x]),x]","\frac{(-4 \cosh (x)+\cosh (2 x)-3) \text{csch}(x)}{6 a (\cosh (x)+1)}","\frac{\coth ^3(x)}{3 a}-\frac{\text{csch}^3(x)}{3 a}-\frac{\text{csch}(x)}{a}",1,"((-3 - 4*Cosh[x] + Cosh[2*x])*Csch[x])/(6*a*(1 + Cosh[x]))","A",1
195,1,60,46,0.134199,"\int \frac{\coth ^3(x)}{a+a \cosh (x)} \, dx","Integrate[Coth[x]^3/(a + a*Cosh[x]),x]","\frac{-2 \coth ^2\left(\frac{x}{2}\right)+\text{sech}^2\left(\frac{x}{2}\right)-12 \cosh ^2\left(\frac{x}{2}\right) \left(\log \left(\cosh \left(\frac{x}{2}\right)\right)-\log \left(\sinh \left(\frac{x}{2}\right)\right)\right)-8}{16 a (\cosh (x)+1)}","\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,"(-8 - 2*Coth[x/2]^2 - 12*Cosh[x/2]^2*(Log[Cosh[x/2]] - Log[Sinh[x/2]]) + Sech[x/2]^2)/(16*a*(1 + Cosh[x]))","A",1
196,1,41,41,0.0779501,"\int \frac{\coth ^4(x)}{a+a \cosh (x)} \, dx","Integrate[Coth[x]^4/(a + a*Cosh[x]),x]","-\frac{(8 \cosh (x)+36 \cosh (2 x)+24 \cosh (3 x)-3 \cosh (4 x)-25) \text{csch}^3(x)}{120 a (\cosh (x)+1)}","\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,"-1/120*((-25 + 8*Cosh[x] + 36*Cosh[2*x] + 24*Cosh[3*x] - 3*Cosh[4*x])*Csch[x]^3)/(a*(1 + Cosh[x]))","A",1
197,1,37,37,0.0236173,"\int \sqrt{a+b \cosh (x)} \tanh (x) \, dx","Integrate[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",1
198,1,24,24,0.011736,"\int \frac{\tanh (x)}{\sqrt{a+b \cosh (x)}} \, dx","Integrate[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",1
199,1,55,56,0.0910589,"\int \frac{A+B \sinh (x)}{a+b \cosh (x)} \, dx","Integrate[(A + B*Sinh[x])/(a + b*Cosh[x]),x]","\frac{B \log (a+b \cosh (x))}{b}-\frac{2 A \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^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 (a+b \cosh (x))}{b}",1,"(-2*A*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2] + (B*Log[a + b*Cosh[x]])/b","A",1
200,1,19,18,0.0353732,"\int \frac{A+B \sinh (x)}{1+\cosh (x)} \, dx","Integrate[(A + B*Sinh[x])/(1 + Cosh[x]),x]","A \tanh \left(\frac{x}{2}\right)+2 B \log \left(\cosh \left(\frac{x}{2}\right)\right)","\frac{A \sinh (x)}{\cosh (x)+1}+B \log (\cosh (x)+1)",1,"2*B*Log[Cosh[x/2]] + A*Tanh[x/2]","A",1
201,1,19,24,0.0499862,"\int \frac{A+B \sinh (x)}{1-\cosh (x)} \, dx","Integrate[(A + B*Sinh[x])/(1 - Cosh[x]),x]","A \coth \left(\frac{x}{2}\right)-2 B \log \left(\sinh \left(\frac{x}{2}\right)\right)","-\frac{A \sinh (x)}{1-\cosh (x)}-B \log (1-\cosh (x))",1,"A*Coth[x/2] - 2*B*Log[Sinh[x/2]]","A",1
202,1,61,65,0.1584361,"\int \frac{A+B \tanh (x)}{a+b \cosh (x)} \, dx","Integrate[(A + B*Tanh[x])/(a + b*Cosh[x]),x]","\frac{B (\log (\cosh (x))-\log (a+b \cosh (x)))}{a}-\frac{2 A \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^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 (a+b \cosh (x))}{a}+\frac{B \log (\cosh (x))}{a}",1,"(-2*A*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2] + (B*(Log[Cosh[x]] - Log[a + b*Cosh[x]]))/a","A",1
203,1,81,100,0.2619535,"\int \frac{A+B \coth (x)}{a+b \cosh (x)} \, dx","Integrate[(A + B*Coth[x])/(a + b*Cosh[x]),x]","\frac{B \left(a \log (a+b \cosh (x))-a \log (\sinh (x))+b \log \left(\tanh \left(\frac{x}{2}\right)\right)\right)}{b^2-a^2}-\frac{2 A \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}","-\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*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2] + (B*(a*Log[a + b*Cosh[x]] - a*Log[Sinh[x]] + b*Log[Tanh[x/2]]))/(-a^2 + b^2)","A",1
204,1,63,62,0.1252499,"\int \frac{A+B \text{sech}(x)}{a+b \cosh (x)} \, dx","Integrate[(A + B*Sech[x])/(a + b*Cosh[x]),x]","\frac{2 \left(\frac{(b B-a A) \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}+B \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)\right)}{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,"(2*(B*ArcTan[Tanh[x/2]] + ((-(a*A) + b*B)*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2]))/a","A",1
205,1,81,99,0.1999768,"\int \frac{A+B \text{csch}(x)}{a+b \cosh (x)} \, dx","Integrate[(A + B*Csch[x])/(a + b*Cosh[x]),x]","\frac{B \left(b \log (a+b \cosh (x))+a \log \left(\tanh \left(\frac{x}{2}\right)\right)-b \log (\sinh (x))\right)}{a^2-b^2}-\frac{2 A \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}","\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*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2] + (B*(b*Log[a + b*Cosh[x]] - b*Log[Sinh[x]] + a*Log[Tanh[x/2]]))/(a^2 - b^2)","A",1
206,1,81,86,0.2562424,"\int \frac{A+B \cosh (d+e x)+C \sinh (d+e x)}{a+b \cosh (d+e x)} \, dx","Integrate[(A + B*Cosh[d + e*x] + C*Sinh[d + e*x])/(a + b*Cosh[d + e*x]),x]","\frac{\frac{2 (a B-A b) \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}+C \log (a+b \cosh (d+e x))+B (d+e x)}{b e}","\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*(d + e*x) + (2*(-(A*b) + a*B)*ArcTan[((a - b)*Tanh[(d + e*x)/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2] + C*Log[a + b*Cosh[d + e*x]])/(b*e)","A",1
207,1,115,121,0.4456999,"\int \frac{A+B \cosh (d+e x)+C \sinh (d+e x)}{(a+b \cosh (d+e x))^2} \, dx","Integrate[(A + B*Cosh[d + e*x] + C*Sinh[d + e*x])/(a + b*Cosh[d + e*x])^2,x]","\frac{\frac{C \left(b^2-a^2\right)-b (A b-a B) \sinh (d+e x)}{b (a-b) (a+b) (a+b \cosh (d+e x))}+\frac{2 (a A-b B) \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{b^2-a^2}}\right)}{\left(b^2-a^2\right)^{3/2}}}{e}","-\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)*ArcTan[((a - b)*Tanh[(d + e*x)/2])/Sqrt[-a^2 + b^2]])/(-a^2 + b^2)^(3/2) + ((-a^2 + b^2)*C - b*(A*b - a*B)*Sinh[d + e*x])/((a - b)*b*(a + b)*(a + b*Cosh[d + e*x])))/e","A",1
208,1,175,187,0.8492972,"\int \frac{A+B \cosh (d+e x)+C \sinh (d+e x)}{(a+b \cosh (d+e x))^3} \, dx","Integrate[(A + B*Cosh[d + e*x] + C*Sinh[d + e*x])/(a + b*Cosh[d + e*x])^3,x]","\frac{\frac{C \left(b^2-a^2\right)-b (A b-a B) \sinh (d+e x)}{b (a-b) (a+b) (a+b \cosh (d+e x))^2}-\frac{2 \left(2 a^2 A-3 a b B+A b^2\right) \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{b^2-a^2}}\right)}{\left(b^2-a^2\right)^{5/2}}+\frac{\left(a^2 B-3 a A b+2 b^2 B\right) \sinh (d+e x)}{(a-b)^2 (a+b)^2 (a+b \cosh (d+e x))}}{2 e}","\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*(2*a^2*A + A*b^2 - 3*a*b*B)*ArcTan[((a - b)*Tanh[(d + e*x)/2])/Sqrt[-a^2 + b^2]])/(-a^2 + b^2)^(5/2) + ((-3*a*A*b + a^2*B + 2*b^2*B)*Sinh[d + e*x])/((a - b)^2*(a + b)^2*(a + b*Cosh[d + e*x])) + ((-a^2 + b^2)*C - b*(A*b - a*B)*Sinh[d + e*x])/((a - b)*b*(a + b)*(a + b*Cosh[d + e*x])^2))/(2*e)","A",1
209,1,245,260,2.5736746,"\int \frac{A+B \cosh (d+e x)+C \sinh (d+e x)}{(a+b \cosh (d+e x))^4} \, dx","Integrate[(A + B*Cosh[d + e*x] + C*Sinh[d + e*x])/(a + b*Cosh[d + e*x])^4,x]","\frac{\frac{2 C \left(b^2-a^2\right)-2 b (A b-a B) \sinh (d+e x)}{b (a-b) (a+b) (a+b \cosh (d+e x))^3}+\frac{\left(2 a^2 B-5 a A b+3 b^2 B\right) \sinh (d+e x)}{(a-b)^2 (a+b)^2 (a+b \cosh (d+e x))^2}+\frac{6 \left(2 a^3 A-4 a^2 b B+3 a A b^2-b^3 B\right) \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{b^2-a^2}}\right)}{\left(b^2-a^2\right)^{7/2}}+\frac{\left(2 a^3 B-11 a^2 A b+13 a b^2 B-4 A b^3\right) \sinh (d+e x)}{(a-b)^3 (a+b)^3 (a+b \cosh (d+e x))}}{6 e}","-\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{\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(-2 a^3 B+11 a^2 A 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{C}{3 b e (a+b \cosh (d+e x))^3}",1,"((6*(2*a^3*A + 3*a*A*b^2 - 4*a^2*b*B - b^3*B)*ArcTan[((a - b)*Tanh[(d + e*x)/2])/Sqrt[-a^2 + b^2]])/(-a^2 + b^2)^(7/2) + ((-5*a*A*b + 2*a^2*B + 3*b^2*B)*Sinh[d + e*x])/((a - b)^2*(a + b)^2*(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])/((a - b)^3*(a + b)^3*(a + b*Cosh[d + e*x])) + (2*(-a^2 + b^2)*C - 2*b*(A*b - a*B)*Sinh[d + e*x])/((a - b)*b*(a + b)*(a + b*Cosh[d + e*x])^3))/(6*e)","A",1
210,1,536,191,0.6344392,"\int \frac{x}{a+b \cosh ^2(x)} \, dx","Integrate[x/(a + b*Cosh[x]^2),x]","-\frac{i \left(\text{Li}_2\left(\frac{\left(2 a+b-2 i \sqrt{-a (a+b)}\right) \left(a+b-i \sqrt{-a (a+b)} \tanh (x)\right)}{b \left(a+b+i \sqrt{-a (a+b)} \tanh (x)\right)}\right)-\text{Li}_2\left(\frac{\left(2 a+b+2 i \sqrt{-a (a+b)}\right) \left(a+b-i \sqrt{-a (a+b)} \tanh (x)\right)}{b \left(a+b+i \sqrt{-a (a+b)} \tanh (x)\right)}\right)\right)+4 x \tan ^{-1}\left(\frac{(a+b) \coth (x)}{\sqrt{-a (a+b)}}\right)+2 i \cos ^{-1}\left(-\frac{2 a}{b}-1\right) \tan ^{-1}\left(\frac{a \tanh (x)}{\sqrt{-a (a+b)}}\right)-\log \left(\frac{2 (a+b) \left(a+i \sqrt{-a (a+b)}\right) (\tanh (x)-1)}{b \left(i \sqrt{-a (a+b)} \tanh (x)+a+b\right)}\right) \left(\cos ^{-1}\left(-\frac{2 a}{b}-1\right)-2 \tan ^{-1}\left(\frac{a \tanh (x)}{\sqrt{-a (a+b)}}\right)\right)-\log \left(\frac{2 i (a+b) \left(\sqrt{-a (a+b)}+i a\right) (\tanh (x)+1)}{b \left(i \sqrt{-a (a+b)} \tanh (x)+a+b\right)}\right) \left(2 \tan ^{-1}\left(\frac{a \tanh (x)}{\sqrt{-a (a+b)}}\right)+\cos ^{-1}\left(-\frac{2 a}{b}-1\right)\right)+\log \left(\frac{\sqrt{2} e^{-x} \sqrt{-a (a+b)}}{\sqrt{b} \sqrt{2 a+b \cosh (2 x)+b}}\right) \left(-2 \tan ^{-1}\left(\frac{a \tanh (x)}{\sqrt{-a (a+b)}}\right)+2 \tan ^{-1}\left(\frac{(a+b) \coth (x)}{\sqrt{-a (a+b)}}\right)+\cos ^{-1}\left(-\frac{2 a}{b}-1\right)\right)+\log \left(\frac{\sqrt{2} e^x \sqrt{-a (a+b)}}{\sqrt{b} \sqrt{2 a+b \cosh (2 x)+b}}\right) \left(2 \tan ^{-1}\left(\frac{a \tanh (x)}{\sqrt{-a (a+b)}}\right)-2 \tan ^{-1}\left(\frac{(a+b) \coth (x)}{\sqrt{-a (a+b)}}\right)+\cos ^{-1}\left(-\frac{2 a}{b}-1\right)\right)}{4 \sqrt{-a (a+b)}}","\frac{\text{Li}_2\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a+b} \sqrt{a}+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{\text{Li}_2\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a+b} \sqrt{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,"-1/4*(4*x*ArcTan[((a + b)*Coth[x])/Sqrt[-(a*(a + b))]] + (2*I)*ArcCos[-1 - (2*a)/b]*ArcTan[(a*Tanh[x])/Sqrt[-(a*(a + b))]] + (ArcCos[-1 - (2*a)/b] + 2*ArcTan[((a + b)*Coth[x])/Sqrt[-(a*(a + b))]] - 2*ArcTan[(a*Tanh[x])/Sqrt[-(a*(a + b))]])*Log[(Sqrt[2]*Sqrt[-(a*(a + b))])/(Sqrt[b]*E^x*Sqrt[2*a + b + b*Cosh[2*x]])] + (ArcCos[-1 - (2*a)/b] - 2*ArcTan[((a + b)*Coth[x])/Sqrt[-(a*(a + b))]] + 2*ArcTan[(a*Tanh[x])/Sqrt[-(a*(a + b))]])*Log[(Sqrt[2]*Sqrt[-(a*(a + b))]*E^x)/(Sqrt[b]*Sqrt[2*a + b + b*Cosh[2*x]])] - (ArcCos[-1 - (2*a)/b] - 2*ArcTan[(a*Tanh[x])/Sqrt[-(a*(a + b))]])*Log[(2*(a + b)*(a + I*Sqrt[-(a*(a + b))])*(-1 + Tanh[x]))/(b*(a + b + I*Sqrt[-(a*(a + b))]*Tanh[x]))] - (ArcCos[-1 - (2*a)/b] + 2*ArcTan[(a*Tanh[x])/Sqrt[-(a*(a + b))]])*Log[((2*I)*(a + b)*(I*a + Sqrt[-(a*(a + b))])*(1 + Tanh[x]))/(b*(a + b + I*Sqrt[-(a*(a + b))]*Tanh[x]))] + I*(PolyLog[2, ((2*a + b - (2*I)*Sqrt[-(a*(a + b))])*(a + b - I*Sqrt[-(a*(a + b))]*Tanh[x]))/(b*(a + b + I*Sqrt[-(a*(a + b))]*Tanh[x]))] - PolyLog[2, ((2*a + b + (2*I)*Sqrt[-(a*(a + b))])*(a + b - I*Sqrt[-(a*(a + b))]*Tanh[x]))/(b*(a + b + I*Sqrt[-(a*(a + b))]*Tanh[x]))]))/Sqrt[-(a*(a + b))]","C",1
211,1,221,291,0.7742918,"\int \frac{x^2}{a+b \cosh ^2(x)} \, dx","Integrate[x^2/(a + b*Cosh[x]^2),x]","\frac{2 x \text{Li}_2\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a+b} \sqrt{a}+b}\right)-2 x \text{Li}_2\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a+b} \sqrt{a}+b}\right)-\text{Li}_3\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a+b} \sqrt{a}+b}\right)+\text{Li}_3\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a+b} \sqrt{a}+b}\right)+2 x^2 \log \left(\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}+1\right)-2 x^2 \log \left(\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}+1\right)}{4 \sqrt{a} \sqrt{a+b}}","\frac{x \text{Li}_2\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a+b} \sqrt{a}+b}\right)}{2 \sqrt{a} \sqrt{a+b}}-\frac{x \text{Li}_2\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a+b} \sqrt{a}+b}\right)}{2 \sqrt{a} \sqrt{a+b}}-\frac{\text{Li}_3\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a+b} \sqrt{a}+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{\text{Li}_3\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a+b} \sqrt{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,"(2*x^2*Log[1 + (b*E^(2*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])] - 2*x^2*Log[1 + (b*E^(2*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])] + 2*x*PolyLog[2, -((b*E^(2*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b]))] - 2*x*PolyLog[2, -((b*E^(2*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b]))] - PolyLog[3, -((b*E^(2*x))/(2*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])","A",1
212,1,295,391,0.6927913,"\int \frac{x^3}{a+b \cosh ^2(x)} \, dx","Integrate[x^3/(a + b*Cosh[x]^2),x]","\frac{6 x^2 \text{Li}_2\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a+b} \sqrt{a}+b}\right)-6 x^2 \text{Li}_2\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a+b} \sqrt{a}+b}\right)-6 x \text{Li}_3\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a+b} \sqrt{a}+b}\right)+6 x \text{Li}_3\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a+b} \sqrt{a}+b}\right)+3 \text{Li}_4\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a+b} \sqrt{a}+b}\right)-3 \text{Li}_4\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a+b} \sqrt{a}+b}\right)+4 x^3 \log \left(\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}+1\right)-4 x^3 \log \left(\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}+1\right)}{8 \sqrt{a} \sqrt{a+b}}","\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a+b} \sqrt{a}+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a+b} \sqrt{a}+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{3 x \text{Li}_3\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a+b} \sqrt{a}+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 x \text{Li}_3\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a+b} \sqrt{a}+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 \text{Li}_4\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a+b} \sqrt{a}+b}\right)}{8 \sqrt{a} \sqrt{a+b}}-\frac{3 \text{Li}_4\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a+b} \sqrt{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,"(4*x^3*Log[1 + (b*E^(2*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])] - 4*x^3*Log[1 + (b*E^(2*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])] + 6*x^2*PolyLog[2, -((b*E^(2*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b]))] - 6*x^2*PolyLog[2, -((b*E^(2*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b]))] - 6*x*PolyLog[3, -((b*E^(2*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b]))] + 6*x*PolyLog[3, -((b*E^(2*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b]))] + 3*PolyLog[4, -((b*E^(2*x))/(2*a + b - 2*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",1
213,1,55,58,0.0839354,"\int \frac{\cosh ^3\left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Integrate[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)-\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]] - CoshIntegral[(3*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/(4*a)","A",1
214,1,57,58,0.0378062,"\int \frac{\cosh ^2\left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Integrate[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 (1-a x)}{4 a}+\frac{\log (a x+1)}{4 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,"-1/2*CoshIntegral[(2*Sqrt[1 - a*x])/Sqrt[1 + a*x]]/a - Log[1 - a*x]/(4*a) + Log[1 + a*x]/(4*a)","A",1
215,1,26,26,0.035359,"\int \frac{\cosh \left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Integrate[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",1
216,0,0,40,6.3373361,"\int \frac{\text{sech}\left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Integrate[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,"Integrate[Sech[Sqrt[1 - a*x]/Sqrt[1 + a*x]]/(1 - a^2*x^2), x]","A",-1
217,0,0,42,26.1408656,"\int \frac{\text{sech}^2\left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Integrate[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,"Integrate[Sech[Sqrt[1 - a*x]/Sqrt[1 + a*x]]^2/(1 - a^2*x^2), x]","A",-1
218,1,59,60,0.1358044,"\int \frac{x \sinh (x)}{(a+b \cosh (x))^2} \, dx","Integrate[(x*Sinh[x])/(a + b*Cosh[x])^2,x]","-\frac{2 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{b \sqrt{b^2-a^2}}-\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*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/(b*Sqrt[-a^2 + b^2]) - x/(b*(a + b*Cosh[x]))","A",1
219,1,87,87,0.263544,"\int \frac{x \sinh (x)}{(a+b \cosh (x))^3} \, dx","Integrate[(x*Sinh[x])/(a + b*Cosh[x])^3,x]","\frac{1}{2} \left(\frac{\frac{2 a \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\left(b^2-a^2\right)^{3/2}}-\frac{x}{(a+b \cosh (x))^2}}{b}-\frac{\sinh (x)}{(a-b) (a+b) (a+b \cosh (x))}\right)","-\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,"(((2*a*ArcTan[((a - b)*Tanh[x/2])/Sqrt[-a^2 + b^2]])/(-a^2 + b^2)^(3/2) - x/(a + b*Cosh[x])^2)/b - Sinh[x]/((a - b)*(a + b)*(a + b*Cosh[x])))/2","A",1
220,1,41,47,0.1133866,"\int \frac{\left(2+\cosh ^2(a+b x)\right) \sinh (a+b x)}{x} \, dx","Integrate[((2 + Cosh[a + b*x]^2)*Sinh[a + b*x])/x,x]","\frac{1}{4} (9 \sinh (a) \text{Chi}(b x)+\sinh (3 a) \text{Chi}(3 b x)+9 \cosh (a) \text{Shi}(b x)+\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] + CoshIntegral[3*b*x]*Sinh[3*a] + 9*Cosh[a]*SinhIntegral[b*x] + Cosh[3*a]*SinhIntegral[3*b*x])/4","A",1
221,0,0,25,5.5277501,"\int \frac{x^m \sinh (c+d x)}{a+b \cosh (c+d x)} \, dx","Integrate[(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,"Integrate[(x^m*Sinh[c + d*x])/(a + b*Cosh[c + d*x]), x]","A",-1
222,1,326,327,0.0355828,"\int \frac{x^3 \sinh (c+d x)}{a+b \cosh (c+d x)} \, dx","Integrate[(x^3*Sinh[c + d*x])/(a + b*Cosh[c + d*x]),x]","\frac{6 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}-a}\right)}{b d^4}+\frac{6 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b d^4}-\frac{6 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^3}-\frac{6 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b d^3}+\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}+\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b d^2}+\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{6 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^4}+\frac{6 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b d^4}-\frac{6 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^3}-\frac{6 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b d^3}+\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}+\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b d^2}+\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,"-1/4*x^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",1
223,1,244,245,0.0228438,"\int \frac{x^2 \sinh (c+d x)}{a+b \cosh (c+d x)} \, dx","Integrate[(x^2*Sinh[c + d*x])/(a + b*Cosh[c + d*x]),x]","-\frac{2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}-a}\right)}{b d^3}-\frac{2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b d^3}+\frac{2 x \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}+\frac{2 x \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b d^2}+\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 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^3}-\frac{2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b d^3}+\frac{2 x \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}+\frac{2 x \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b d^2}+\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,"-1/3*x^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",1
224,1,160,161,0.0130075,"\int \frac{x \sinh (c+d x)}{a+b \cosh (c+d x)} \, dx","Integrate[(x*Sinh[c + d*x])/(a + b*Cosh[c + d*x]),x]","\frac{\text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}-a}\right)}{b d^2}+\frac{\text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\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{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}+\frac{\text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\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,"-1/2*x^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",1
225,1,18,18,0.0380013,"\int \frac{\sinh (c+d x)}{a+b \cosh (c+d x)} \, dx","Integrate[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",1
226,0,0,25,14.2138647,"\int \frac{\sinh (c+d x)}{x (a+b \cosh (c+d x))} \, dx","Integrate[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,"Integrate[Sinh[c + d*x]/(x*(a + b*Cosh[c + d*x])), x]","A",-1
227,0,0,27,25.213252,"\int \frac{x^m \sinh ^2(c+d x)}{a+b \cosh (c+d x)} \, dx","Integrate[(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,"Integrate[(x^m*Sinh[c + d*x]^2)/(a + b*Cosh[c + d*x]), x]","A",-1
228,1,386,495,1.5131561,"\int \frac{x^3 \sinh ^2(c+d x)}{a+b \cosh (c+d x)} \, dx","Integrate[(x^3*Sinh[c + d*x]^2)/(a + b*Cosh[c + d*x]),x]","\frac{4 \sqrt{a^2-b^2} \left(d^3 x^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)-d^3 x^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)+3 d^2 x^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}-a}\right)-3 d^2 x^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)-6 d x \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}-a}\right)+6 d x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)+6 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}-a}\right)-6 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)\right)-a d^4 x^4+4 b \cosh (d x) \left(d x \sinh (c) \left(d^2 x^2+6\right)-3 \cosh (c) \left(d^2 x^2+2\right)\right)+4 b \sinh (d x) \left(d x \cosh (c) \left(d^2 x^2+6\right)-3 \sinh (c) \left(d^2 x^2+2\right)\right)}{4 b^2 d^4}","\frac{6 \sqrt{a^2-b^2} \text{Li}_4\left(-\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{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b^2 d^4}-\frac{6 x \sqrt{a^2-b^2} \text{Li}_3\left(-\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{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b^2 d^3}+\frac{3 x^2 \sqrt{a^2-b^2} \text{Li}_2\left(-\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{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b^2 d^2}+\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{6 \cosh (c+d x)}{b d^4}+\frac{6 x \sinh (c+d x)}{b d^3}-\frac{3 x^2 \cosh (c+d x)}{b d^2}+\frac{x^3 \sinh (c+d x)}{b d}",1,"(-(a*d^4*x^4) + 4*Sqrt[a^2 - b^2]*(d^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 - b^2])] - d^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 - b^2])] + 3*d^2*x^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 - b^2])] - 3*d^2*x^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))] - 6*d*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 - b^2])] + 6*d*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))] + 6*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 - b^2])] - 6*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))]) + 4*b*Cosh[d*x]*(-3*(2 + d^2*x^2)*Cosh[c] + d*x*(6 + d^2*x^2)*Sinh[c]) + 4*b*(d*x*(6 + d^2*x^2)*Cosh[c] - 3*(2 + d^2*x^2)*Sinh[c])*Sinh[d*x])/(4*b^2*d^4)","A",1
229,1,293,370,1.3047988,"\int \frac{x^2 \sinh ^2(c+d x)}{a+b \cosh (c+d x)} \, dx","Integrate[(x^2*Sinh[c + d*x]^2)/(a + b*Cosh[c + d*x]),x]","\frac{3 \sqrt{a^2-b^2} \left(d^2 x^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)-d^2 x^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)+2 d x \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}-a}\right)-2 d x \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)-2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}-a}\right)+2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)\right)-a d^3 x^3+3 b \cosh (d x) \left(\sinh (c) \left(d^2 x^2+2\right)-2 d x \cosh (c)\right)+3 b \sinh (d x) \left(\cosh (c) \left(d^2 x^2+2\right)-2 d x \sinh (c)\right)}{3 b^2 d^3}","-\frac{2 \sqrt{a^2-b^2} \text{Li}_3\left(-\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{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b^2 d^3}+\frac{2 x \sqrt{a^2-b^2} \text{Li}_2\left(-\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{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b^2 d^2}+\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*d^3*x^3) + 3*Sqrt[a^2 - b^2]*(d^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 - b^2])] - d^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 - b^2])] + 2*d*x*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 - b^2])] - 2*d*x*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))] - 2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 - b^2])] + 2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))]) + 3*b*Cosh[d*x]*(-2*d*x*Cosh[c] + (2 + d^2*x^2)*Sinh[c]) + 3*b*((2 + d^2*x^2)*Cosh[c] - 2*d*x*Sinh[c])*Sinh[d*x])/(3*b^2*d^3)","A",1
230,1,187,244,1.0295031,"\int \frac{x \sinh ^2(c+d x)}{a+b \cosh (c+d x)} \, dx","Integrate[(x*Sinh[c + d*x]^2)/(a + b*Cosh[c + d*x]),x]","\frac{2 \sqrt{a^2-b^2} \left(\text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}-a}\right)-\text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)+d x \left(\log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}+1\right)-\log \left(\frac{b e^{c+d x}}{\sqrt{a^2-b^2}+a}+1\right)\right)\right)+a (c-d x) (c+d x)+2 b d x \sinh (c+d x)-2 b \cosh (c+d x)}{2 b^2 d^2}","\frac{\sqrt{a^2-b^2} \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2}-\frac{\sqrt{a^2-b^2} \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\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*(c - d*x)*(c + d*x) - 2*b*Cosh[c + d*x] + 2*Sqrt[a^2 - b^2]*(d*x*(Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 - b^2])] - Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 - b^2])]) + PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 - b^2])] - PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 - b^2]))]) + 2*b*d*x*Sinh[c + d*x])/(2*b^2*d^2)","A",1
231,1,69,73,0.1801609,"\int \frac{\sinh ^2(c+d x)}{a+b \cosh (c+d x)} \, dx","Integrate[Sinh[c + d*x]^2/(a + b*Cosh[c + d*x]),x]","\frac{2 \sqrt{b^2-a^2} \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{b^2-a^2}}\right)-a (c+d x)+b \sinh (c+d x)}{b^2 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*(c + d*x)) + 2*Sqrt[-a^2 + b^2]*ArcTan[((a - b)*Tanh[(c + d*x)/2])/Sqrt[-a^2 + b^2]] + b*Sinh[c + d*x])/(b^2*d)","A",1
232,0,0,27,116.7278111,"\int \frac{\sinh ^2(c+d x)}{x (a+b \cosh (c+d x))} \, dx","Integrate[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,"Integrate[Sinh[c + d*x]^2/(x*(a + b*Cosh[c + d*x])), x]","A",-1
233,0,0,27,32.312815,"\int \frac{x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx","Integrate[(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,"Integrate[(x^m*Sinh[c + d*x]^3)/(a + b*Cosh[c + d*x]), x]","A",-1
234,1,1082,586,11.5721638,"\int \frac{x^3 \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx","Integrate[(x^3*Sinh[c + d*x]^3)/(a + b*Cosh[c + d*x]),x]","-\frac{(b-a) (a+b) \cosh \left(\frac{c}{2}\right) \text{sech}(c) \sinh \left(\frac{c}{2}\right) x^4}{2 b^3}-\frac{a \cosh (d x) \left(d^3 \cosh (c) x^3-3 d^2 \sinh (c) x^2+6 d \cosh (c) x-6 \sinh (c)\right)}{b^2 d^4}+\frac{\cosh (2 d x) \left(4 d^3 \cosh (2 c) x^3-6 d^2 \sinh (2 c) x^2+6 d \cosh (2 c) x-3 \sinh (2 c)\right)}{16 b d^4}-\frac{a \left(d^3 \sinh (c) x^3-3 d^2 \cosh (c) x^2+6 d \sinh (c) x-6 \cosh (c)\right) \sinh (d x)}{b^2 d^4}+\frac{\left(4 d^3 \sinh (2 c) x^3-6 d^2 \cosh (2 c) x^2+6 d \sinh (2 c) x-3 \cosh (2 c)\right) \sinh (2 d x)}{16 b d^4}+\frac{\left(b^2-a^2\right) \left(-x^4+\frac{2 b^2 \left(d^3 \log \left(\frac{\left(a-\sqrt{a^2-b^2}\right) (\cosh (c+d x)-\sinh (c+d x))}{b}+1\right) x^3-3 d^2 \text{Li}_2\left(\frac{\left(\sqrt{a^2-b^2}-a\right) (\cosh (c+d x)-\sinh (c+d x))}{b}\right) x^2-6 d \text{Li}_3\left(\frac{\left(\sqrt{a^2-b^2}-a\right) (\cosh (c+d x)-\sinh (c+d x))}{b}\right) x-6 \text{Li}_4\left(\frac{\left(\sqrt{a^2-b^2}-a\right) (\cosh (c+d x)-\sinh (c+d x))}{b}\right)\right) (\cosh (2 c)+\sinh (2 c)+1)}{\sqrt{a^2-b^2} \left(\sqrt{a^2-b^2}-a\right) d^4}+\frac{2 b^2 \left(d^3 \log \left(\frac{\left(a+\sqrt{a^2-b^2}\right) (\cosh (c+d x)-\sinh (c+d x))}{b}+1\right) x^3-3 d^2 \text{Li}_2\left(\frac{\left(a+\sqrt{a^2-b^2}\right) (\sinh (c+d x)-\cosh (c+d x))}{b}\right) x^2-6 d \text{Li}_3\left(\frac{\left(a+\sqrt{a^2-b^2}\right) (\sinh (c+d x)-\cosh (c+d x))}{b}\right) x-6 \text{Li}_4\left(\frac{\left(a+\sqrt{a^2-b^2}\right) (\sinh (c+d x)-\cosh (c+d x))}{b}\right)\right) (\cosh (2 c)+\sinh (2 c)+1)}{\sqrt{a^2-b^2} \left(a+\sqrt{a^2-b^2}\right) d^4}+\frac{2 a \left(d^3 \log \left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a-\sqrt{a^2-b^2}}+1\right) x^3+3 d^2 \text{Li}_2\left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2-b^2}-a}\right) x^2-6 d \text{Li}_3\left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2-b^2}-a}\right) x+6 \text{Li}_4\left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2-b^2}-a}\right)\right) (\cosh (2 c)+\sinh (2 c)+1)}{\sqrt{a^2-b^2} d^4}-\frac{2 a \left(d^3 \log \left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2-b^2}}+1\right) x^3+3 d^2 \text{Li}_2\left(-\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2-b^2}}\right) x^2-6 d \text{Li}_3\left(-\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2-b^2}}\right) x+6 \text{Li}_4\left(-\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2-b^2}}\right)\right) (\cosh (2 c)+\sinh (2 c)+1)}{\sqrt{a^2-b^2} d^4}\right) (1-\tanh (c))}{4 b^3}","\frac{6 \left(a^2-b^2\right) \text{Li}_4\left(-\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{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b^3 d^4}-\frac{6 x \left(a^2-b^2\right) \text{Li}_3\left(-\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{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b^3 d^3}+\frac{3 x^2 \left(a^2-b^2\right) \text{Li}_2\left(-\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{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b^3 d^2}+\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{6 a \sinh (c+d x)}{b^2 d^4}-\frac{6 a x \cosh (c+d x)}{b^2 d^3}+\frac{3 a x^2 \sinh (c+d x)}{b^2 d^2}-\frac{a x^3 \cosh (c+d x)}{b^2 d}-\frac{3 \sinh (c+d x) \cosh (c+d x)}{8 b d^4}+\frac{3 x \sinh ^2(c+d x)}{4 b d^3}-\frac{3 x^2 \sinh (c+d x) \cosh (c+d x)}{4 b d^2}+\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,"-1/2*((-a + b)*(a + b)*x^4*Cosh[c/2]*Sech[c]*Sinh[c/2])/b^3 - (a*Cosh[d*x]*(6*d*x*Cosh[c] + d^3*x^3*Cosh[c] - 6*Sinh[c] - 3*d^2*x^2*Sinh[c]))/(b^2*d^4) + (Cosh[2*d*x]*(6*d*x*Cosh[2*c] + 4*d^3*x^3*Cosh[2*c] - 3*Sinh[2*c] - 6*d^2*x^2*Sinh[2*c]))/(16*b*d^4) - (a*(-6*Cosh[c] - 3*d^2*x^2*Cosh[c] + 6*d*x*Sinh[c] + d^3*x^3*Sinh[c])*Sinh[d*x])/(b^2*d^4) + ((-3*Cosh[2*c] - 6*d^2*x^2*Cosh[2*c] + 6*d*x*Sinh[2*c] + 4*d^3*x^3*Sinh[2*c])*Sinh[2*d*x])/(16*b*d^4) + ((-a^2 + b^2)*(-x^4 + (2*b^2*(d^3*x^3*Log[1 + ((a - Sqrt[a^2 - b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 3*d^2*x^2*PolyLog[2, ((-a + Sqrt[a^2 - b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 6*d*x*PolyLog[3, ((-a + Sqrt[a^2 - b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 6*PolyLog[4, ((-a + Sqrt[a^2 - b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b])*(1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 - b^2]*(-a + Sqrt[a^2 - b^2])*d^4) + (2*b^2*(d^3*x^3*Log[1 + ((a + Sqrt[a^2 - b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 3*d^2*x^2*PolyLog[2, ((a + Sqrt[a^2 - b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b] - 6*d*x*PolyLog[3, ((a + Sqrt[a^2 - b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b] - 6*PolyLog[4, ((a + Sqrt[a^2 - b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b])*(1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 - b^2]*(a + Sqrt[a^2 - b^2])*d^4) + (2*a*(d^3*x^3*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 - b^2])] + 3*d^2*x^2*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 - b^2])] - 6*d*x*PolyLog[3, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 - b^2])] + 6*PolyLog[4, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 - b^2])])*(1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 - b^2]*d^4) - (2*a*(d^3*x^3*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 - b^2])] + 3*d^2*x^2*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 - b^2]))] - 6*d*x*PolyLog[3, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 - b^2]))] + 6*PolyLog[4, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 - b^2]))])*(1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 - b^2]*d^4))*(1 - Tanh[c]))/(4*b^3)","A",1
235,1,831,432,8.4228459,"\int \frac{x^2 \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx","Integrate[(x^2*Sinh[c + d*x]^3)/(a + b*Cosh[c + d*x]),x]","\frac{8 \left(a^2-b^2\right) \tanh (c) x^3-\frac{24 a b \cosh (d x) \left(\left(d^2 x^2+2\right) \cosh (c)-2 d x \sinh (c)\right)}{d^3}+\frac{3 b^2 \cosh (2 d x) \left(\left(2 d^2 x^2+1\right) \cosh (2 c)-2 d x \sinh (2 c)\right)}{d^3}-\frac{24 a b \left(\left(d^2 x^2+2\right) \sinh (c)-2 d x \cosh (c)\right) \sinh (d x)}{d^3}+\frac{3 b^2 \left(\left(2 d^2 x^2+1\right) \sinh (2 c)-2 d x \cosh (2 c)\right) \sinh (2 d x)}{d^3}+4 \left(b^2-a^2\right) \left(-2 x^3+\frac{3 b^2 \left(d^2 \log \left(\frac{\left(a-\sqrt{a^2-b^2}\right) (\cosh (c+d x)-\sinh (c+d x))}{b}+1\right) x^2-2 d \text{Li}_2\left(\frac{\left(\sqrt{a^2-b^2}-a\right) (\cosh (c+d x)-\sinh (c+d x))}{b}\right) x-2 \text{Li}_3\left(\frac{\left(\sqrt{a^2-b^2}-a\right) (\cosh (c+d x)-\sinh (c+d x))}{b}\right)\right) (\cosh (2 c)+\sinh (2 c)+1)}{\sqrt{a^2-b^2} \left(\sqrt{a^2-b^2}-a\right) d^3}+\frac{3 b^2 \left(d^2 \log \left(\frac{\left(a+\sqrt{a^2-b^2}\right) (\cosh (c+d x)-\sinh (c+d x))}{b}+1\right) x^2-2 d \text{Li}_2\left(\frac{\left(a+\sqrt{a^2-b^2}\right) (\sinh (c+d x)-\cosh (c+d x))}{b}\right) x-2 \text{Li}_3\left(\frac{\left(a+\sqrt{a^2-b^2}\right) (\sinh (c+d x)-\cosh (c+d x))}{b}\right)\right) (\cosh (2 c)+\sinh (2 c)+1)}{\sqrt{a^2-b^2} \left(a+\sqrt{a^2-b^2}\right) d^3}+\frac{3 a \left(d^2 \log \left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a-\sqrt{a^2-b^2}}+1\right) x^2+2 d \text{Li}_2\left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2-b^2}-a}\right) x-2 \text{Li}_3\left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2-b^2}-a}\right)\right) (\cosh (2 c)+\sinh (2 c)+1)}{\sqrt{a^2-b^2} d^3}-\frac{3 a \left(d^2 \log \left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2-b^2}}+1\right) x^2+2 d \text{Li}_2\left(-\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2-b^2}}\right) x-2 \text{Li}_3\left(-\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2-b^2}}\right)\right) (\cosh (2 c)+\sinh (2 c)+1)}{\sqrt{a^2-b^2} d^3}\right) (1-\tanh (c))}{24 b^3}","-\frac{2 \left(a^2-b^2\right) \text{Li}_3\left(-\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{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b^3 d^3}+\frac{2 x \left(a^2-b^2\right) \text{Li}_2\left(-\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{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\right)}{b^3 d^2}+\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 \cosh (c+d x)}{b^2 d^3}+\frac{2 a x \sinh (c+d x)}{b^2 d^2}-\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,"((-24*a*b*Cosh[d*x]*((2 + d^2*x^2)*Cosh[c] - 2*d*x*Sinh[c]))/d^3 + (3*b^2*Cosh[2*d*x]*((1 + 2*d^2*x^2)*Cosh[2*c] - 2*d*x*Sinh[2*c]))/d^3 - (24*a*b*(-2*d*x*Cosh[c] + (2 + d^2*x^2)*Sinh[c])*Sinh[d*x])/d^3 + (3*b^2*(-2*d*x*Cosh[2*c] + (1 + 2*d^2*x^2)*Sinh[2*c])*Sinh[2*d*x])/d^3 + 4*(-a^2 + b^2)*(-2*x^3 + (3*b^2*(d^2*x^2*Log[1 + ((a - Sqrt[a^2 - b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*d*x*PolyLog[2, ((-a + Sqrt[a^2 - b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*PolyLog[3, ((-a + Sqrt[a^2 - b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b])*(1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 - b^2]*(-a + Sqrt[a^2 - b^2])*d^3) + (3*b^2*(d^2*x^2*Log[1 + ((a + Sqrt[a^2 - b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*d*x*PolyLog[2, ((a + Sqrt[a^2 - b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b] - 2*PolyLog[3, ((a + Sqrt[a^2 - b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b])*(1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 - b^2]*(a + Sqrt[a^2 - b^2])*d^3) + (3*a*(d^2*x^2*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 - b^2])] + 2*d*x*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 - b^2])] - 2*PolyLog[3, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 - b^2])])*(1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 - b^2]*d^3) - (3*a*(d^2*x^2*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 - b^2])] + 2*d*x*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 - b^2]))] - 2*PolyLog[3, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 - b^2]))])*(1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 - b^2]*d^3))*(1 - Tanh[c]) + 8*(a^2 - b^2)*x^3*Tanh[c])/(24*b^3)","A",1
236,1,414,288,2.9612135,"\int \frac{x \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx","Integrate[(x*Sinh[c + d*x]^3)/(a + b*Cosh[c + d*x]),x]","\frac{4 \left(a^2-b^2\right) \left(2 \text{Li}_2\left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2-b^2}-a}\right)+2 \text{Li}_2\left(-\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2-b^2}}\right)+2 (c+d x) \log \left(\frac{b (\sinh (c+d x)+\cosh (c+d x))}{a-\sqrt{a^2-b^2}}+1\right)+2 (c+d x) \log \left(\frac{b (\sinh (c+d x)+\cosh (c+d x))}{\sqrt{a^2-b^2}+a}+1\right)+\frac{4 a c \sqrt{-\left(a^2-b^2\right)^2} \tan ^{-1}\left(\frac{a+b \sinh (c+d x)+b \cosh (c+d x)}{\sqrt{b^2-a^2}}\right)}{\left(a^2-b^2\right)^{3/2}}+\frac{4 a c \sqrt{-\left(a^2-b^2\right)^2} \tanh ^{-1}\left(\frac{a+b \sinh (c+d x)+b \cosh (c+d x)}{\sqrt{a^2-b^2}}\right)}{\left(b^2-a^2\right)^{3/2}}-2 c \log (2 (\sinh (c+d x)+\cosh (c+d x)) (a+b \cosh (c+d x)))-(c+d x)^2+2 c (c+d x)\right)+8 a b \sinh (c+d x)-8 a b d x \cosh (c+d x)-b^2 \sinh (2 (c+d x))+2 b^2 d x \cosh (2 (c+d x))}{8 b^3 d^2}","\frac{\left(a^2-b^2\right) \text{Li}_2\left(-\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{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2-b^2}}\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,"(-8*a*b*d*x*Cosh[c + d*x] + 2*b^2*d*x*Cosh[2*(c + d*x)] + 4*(a^2 - b^2)*(2*c*(c + d*x) - (c + d*x)^2 + (4*a*Sqrt[-(a^2 - b^2)^2]*c*ArcTan[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[-a^2 + b^2]])/(a^2 - b^2)^(3/2) + (4*a*Sqrt[-(a^2 - b^2)^2]*c*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 - b^2]])/(-a^2 + b^2)^(3/2) - 2*c*Log[2*(a + b*Cosh[c + d*x])*(Cosh[c + d*x] + Sinh[c + d*x])] + 2*(c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 - b^2])] + 2*(c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 - b^2])] + 2*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 - b^2])] + 2*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 - b^2]))]) + 8*a*b*Sinh[c + d*x] - b^2*Sinh[2*(c + d*x)])/(8*b^3*d^2)","A",1
237,1,55,61,0.1098322,"\int \frac{\sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx","Integrate[Sinh[c + d*x]^3/(a + b*Cosh[c + d*x]),x]","\frac{4 \left(a^2-b^2\right) \log (a+b \cosh (c+d x))-4 a b \cosh (c+d x)+b^2 \cosh (2 (c+d x))}{4 b^3 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,"(-4*a*b*Cosh[c + d*x] + b^2*Cosh[2*(c + d*x)] + 4*(a^2 - b^2)*Log[a + b*Cosh[c + d*x]])/(4*b^3*d)","A",1
238,-1,0,27,180.0003392,"\int \frac{\sinh ^3(c+d x)}{x (a+b \cosh (c+d x))} \, dx","Integrate[Sinh[c + d*x]^3/(x*(a + b*Cosh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh ^3(c+d x)}{x (a+b \cosh (c+d x))},x\right)",0,"$Aborted","F",-1
239,1,41,54,0.072403,"\int \cosh \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Cosh[a + b*Log[c*x^n]],x]","\frac{x \left(b n \sinh \left(a+b \log \left(c x^n\right)\right)-\cosh \left(a+b \log \left(c x^n\right)\right)\right)}{b^2 n^2-1}","\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]] + b*n*Sinh[a + b*Log[c*x^n]]))/(-1 + b^2*n^2)","A",1
240,1,56,88,0.1060286,"\int \cosh ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Cosh[a + b*Log[c*x^n]]^2,x]","\frac{x \left(2 b n \sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)-\cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+4 b^2 n^2-1\right)}{8 b^2 n^2-2}","\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,"(x*(-1 + 4*b^2*n^2 - Cosh[2*(a + b*Log[c*x^n])] + 2*b*n*Sinh[2*(a + b*Log[c*x^n])]))/(-2 + 8*b^2*n^2)","A",1
241,1,117,149,0.5615233,"\int \cosh ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Cosh[a + b*Log[c*x^n]]^3,x]","\frac{x \left(\left(3-27 b^2 n^2\right) \cosh \left(a+b \log \left(c x^n\right)\right)+\left(1-b^2 n^2\right) \cosh \left(3 \left(a+b \log \left(c x^n\right)\right)\right)+6 b n \sinh \left(a+b \log \left(c x^n\right)\right) \left(\left(b^2 n^2-1\right) \cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+5 b^2 n^2-1\right)\right)}{36 b^4 n^4-40 b^2 n^2+4}","\frac{x \cosh ^3\left(a+b \log \left(c x^n\right)\right)}{1-9 b^2 n^2}-\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^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{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}",1,"(x*((3 - 27*b^2*n^2)*Cosh[a + b*Log[c*x^n]] + (1 - b^2*n^2)*Cosh[3*(a + b*Log[c*x^n])] + 6*b*n*(-1 + 5*b^2*n^2 + (-1 + b^2*n^2)*Cosh[2*(a + b*Log[c*x^n])])*Sinh[a + b*Log[c*x^n]]))/(4 - 40*b^2*n^2 + 36*b^4*n^4)","A",1
242,1,167,191,0.4480068,"\int \cosh ^4\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Cosh[a + b*Log[c*x^n]]^4,x]","\frac{x \left(128 b^3 n^3 \sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+16 b^3 n^3 \sinh \left(4 \left(a+b \log \left(c x^n\right)\right)\right)+\left(4-64 b^2 n^2\right) \cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+\left(1-4 b^2 n^2\right) \cosh \left(4 \left(a+b \log \left(c x^n\right)\right)\right)-8 b n \sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)-4 b n \sinh \left(4 \left(a+b \log \left(c x^n\right)\right)\right)+192 b^4 n^4-60 b^2 n^2+3\right)}{8 \left(64 b^4 n^4-20 b^2 n^2+1\right)}","\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{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{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,"(x*(3 - 60*b^2*n^2 + 192*b^4*n^4 + (4 - 64*b^2*n^2)*Cosh[2*(a + b*Log[c*x^n])] + (1 - 4*b^2*n^2)*Cosh[4*(a + b*Log[c*x^n])] - 8*b*n*Sinh[2*(a + b*Log[c*x^n])] + 128*b^3*n^3*Sinh[2*(a + b*Log[c*x^n])] - 4*b*n*Sinh[4*(a + b*Log[c*x^n])] + 16*b^3*n^3*Sinh[4*(a + b*Log[c*x^n])]))/(8*(1 - 20*b^2*n^2 + 64*b^4*n^4))","A",1
243,1,54,73,0.1410325,"\int x^m \cosh \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^m*Cosh[a + b*Log[c*x^n]],x]","\frac{x^{m+1} \left((m+1) \cosh \left(a+b \log \left(c x^n\right)\right)-b n \sinh \left(a+b \log \left(c x^n\right)\right)\right)}{(-b n+m+1) (b n+m+1)}","\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,"(x^(1 + m)*((1 + m)*Cosh[a + b*Log[c*x^n]] - b*n*Sinh[a + b*Log[c*x^n]]))/((1 + m - b*n)*(1 + m + b*n))","A",1
244,1,87,120,0.3028104,"\int x^m \cosh ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^m*Cosh[a + b*Log[c*x^n]]^2,x]","\frac{x^{m+1} \left(-2 b (m+1) n \sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+(m+1)^2 \cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)-4 b^2 n^2+m^2+2 m+1\right)}{2 (m+1) (-2 b n+m+1) (2 b n+m+1)}","\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,"(x^(1 + m)*(1 + 2*m + m^2 - 4*b^2*n^2 + (1 + m)^2*Cosh[2*(a + b*Log[c*x^n])] - 2*b*(1 + m)*n*Sinh[2*(a + b*Log[c*x^n])]))/(2*(1 + m)*(1 + m - 2*b*n)*(1 + m + 2*b*n))","A",1
245,1,292,203,1.4804531,"\int x^m \cosh ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^m*Cosh[a + b*Log[c*x^n]]^3,x]","\frac{1}{4} x^{m+1} \left(\frac{3 \sinh (b n \log (x)) \left((m+1) \sinh \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-b n \cosh \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)}{(-b n+m+1) (b n+m+1)}+\frac{3 \cosh (b n \log (x)) \left((m+1) \cosh \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-b n \sinh \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)}{(-b n+m+1) (b n+m+1)}+\frac{\sinh (3 b n \log (x)) \left((m+1) \sinh \left(3 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)-3 b n \cosh \left(3 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)\right)}{(-3 b n+m+1) (3 b n+m+1)}+\frac{\cosh (3 b n \log (x)) \left((m+1) \cosh \left(3 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)-3 b n \sinh \left(3 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)\right)}{(-3 b n+m+1) (3 b n+m+1)}\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}+\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)}",1,"(x^(1 + m)*((3*Sinh[b*n*Log[x]]*(-(b*n*Cosh[a - b*n*Log[x] + b*Log[c*x^n]]) + (1 + m)*Sinh[a - b*n*Log[x] + b*Log[c*x^n]]))/((1 + m - b*n)*(1 + m + b*n)) + (3*Cosh[b*n*Log[x]]*((1 + m)*Cosh[a - b*n*Log[x] + b*Log[c*x^n]] - b*n*Sinh[a - b*n*Log[x] + b*Log[c*x^n]]))/((1 + m - b*n)*(1 + m + b*n)) + (Sinh[3*b*n*Log[x]]*(-3*b*n*Cosh[3*(a - b*n*Log[x] + b*Log[c*x^n])] + (1 + m)*Sinh[3*(a - b*n*Log[x] + b*Log[c*x^n])]))/((1 + m - 3*b*n)*(1 + m + 3*b*n)) + (Cosh[3*b*n*Log[x]]*((1 + m)*Cosh[3*(a - b*n*Log[x] + b*Log[c*x^n])] - 3*b*n*Sinh[3*(a - b*n*Log[x] + b*Log[c*x^n])]))/((1 + m - 3*b*n)*(1 + m + 3*b*n))))/4","A",1
246,1,311,266,3.4446422,"\int x^m \cosh ^4\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^m*Cosh[a + b*Log[c*x^n]]^4,x]","\frac{1}{8} x^{m+1} \left(\frac{4 \sinh (2 b n \log (x)) \left((m+1) \sinh \left(2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)-2 b n \cosh \left(2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)\right)}{(-2 b n+m+1) (2 b n+m+1)}+\frac{4 \cosh (2 b n \log (x)) \left((m+1) \cosh \left(2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)-2 b n \sinh \left(2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)\right)}{(-2 b n+m+1) (2 b n+m+1)}+\frac{\sinh (4 b n \log (x)) \left((m+1) \sinh \left(4 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)-4 b n \cosh \left(4 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)\right)}{(-4 b n+m+1) (4 b n+m+1)}+\frac{\cosh (4 b n \log (x)) \left((m+1) \cosh \left(4 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)-4 b n \sinh \left(4 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)\right)}{(-4 b n+m+1) (4 b n+m+1)}+\frac{3}{m+1}\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,"(x^(1 + m)*(3/(1 + m) + (4*Sinh[2*b*n*Log[x]]*(-2*b*n*Cosh[2*(a - b*n*Log[x] + b*Log[c*x^n])] + (1 + m)*Sinh[2*(a - b*n*Log[x] + b*Log[c*x^n])]))/((1 + m - 2*b*n)*(1 + m + 2*b*n)) + (4*Cosh[2*b*n*Log[x]]*((1 + m)*Cosh[2*(a - b*n*Log[x] + b*Log[c*x^n])] - 2*b*n*Sinh[2*(a - b*n*Log[x] + b*Log[c*x^n])]))/((1 + m - 2*b*n)*(1 + m + 2*b*n)) + (Sinh[4*b*n*Log[x]]*(-4*b*n*Cosh[4*(a - b*n*Log[x] + b*Log[c*x^n])] + (1 + m)*Sinh[4*(a - b*n*Log[x] + b*Log[c*x^n])]))/((1 + m - 4*b*n)*(1 + m + 4*b*n)) + (Cosh[4*b*n*Log[x]]*((1 + m)*Cosh[4*(a - b*n*Log[x] + b*Log[c*x^n])] - 4*b*n*Sinh[4*(a - b*n*Log[x] + b*Log[c*x^n])]))/((1 + m - 4*b*n)*(1 + m + 4*b*n))))/8","A",1
247,1,37,18,0.0138213,"\int \frac{\cosh \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Cosh[a + b*Log[c*x^n]]/x,x]","\frac{\sinh (a) \cosh \left(b \log \left(c x^n\right)\right)}{b n}+\frac{\cosh (a) \sinh \left(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,"(Cosh[b*Log[c*x^n]]*Sinh[a])/(b*n) + (Cosh[a]*Sinh[b*Log[c*x^n]])/(b*n)","B",1
248,1,36,39,0.0253989,"\int \frac{\cosh ^2\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Cosh[a + b*Log[c*x^n]]^2/x,x]","\frac{2 \left(a+b \log \left(c x^n\right)\right)+\sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)}{4 b n}","\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,"(2*(a + b*Log[c*x^n]) + Sinh[2*(a + b*Log[c*x^n])])/(4*b*n)","A",1
249,1,42,42,0.0096831,"\int \frac{\cosh ^3\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[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",1
250,1,51,73,0.0472306,"\int \frac{\cosh ^4\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Cosh[a + b*Log[c*x^n]]^4/x,x]","\frac{12 \left(a+b \log \left(c x^n\right)\right)+8 \sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+\sinh \left(4 \left(a+b \log \left(c x^n\right)\right)\right)}{32 b n}","\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,"(12*(a + b*Log[c*x^n]) + 8*Sinh[2*(a + b*Log[c*x^n])] + Sinh[4*(a + b*Log[c*x^n])])/(32*b*n)","A",1
251,1,65,65,0.0197259,"\int \frac{\cosh ^5\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[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",1
252,1,62,67,0.0563887,"\int \frac{\cosh ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Cosh[a + b*Log[c*x^n]]^(5/2)/x,x]","\frac{\sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right) \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)}-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)*EllipticE[(I/2)*(a + b*Log[c*x^n]), 2] + Sqrt[Cosh[a + b*Log[c*x^n]]]*Sinh[2*(a + b*Log[c*x^n])])/(5*b*n)","A",1
253,1,114,67,0.1310974,"\int \frac{\cosh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Cosh[a + b*Log[c*x^n]]^(3/2)/x,x]","\frac{2 \sqrt{\sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+\cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)-\sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)\right)+\sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)}{3 b n \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)}}","\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,"(Sinh[2*(a + b*Log[c*x^n])] + 2*Hypergeometric2F1[1/4, 1/2, 5/4, -Cosh[2*(a + b*Log[c*x^n])] - Sinh[2*(a + b*Log[c*x^n])]]*Sqrt[1 + Cosh[2*(a + b*Log[c*x^n])] + Sinh[2*(a + b*Log[c*x^n])]])/(3*b*n*Sqrt[Cosh[a + b*Log[c*x^n]]])","C",1
254,1,28,28,0.0226022,"\int \frac{\sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)}}{x} \, dx","Integrate[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",1
255,1,28,28,0.0207783,"\int \frac{1}{x \sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)}} \, dx","Integrate[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",1
256,1,58,63,0.0592449,"\int \frac{1}{x \cosh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x*Cosh[a + b*Log[c*x^n]]^(3/2)),x]","\frac{2 \left(\frac{\sinh \left(a+b \log \left(c x^n\right)\right)}{\sqrt{\cosh \left(a+b \log \left(c x^n\right)\right)}}+i E\left(\left.\frac{1}{2} i \left(a+b \log \left(c x^n\right)\right)\right|2\right)\right)}{b n}","\frac{2 \sinh \left(a+b \log \left(c x^n\right)\right)}{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] + Sinh[a + b*Log[c*x^n]]/Sqrt[Cosh[a + b*Log[c*x^n]]]))/(b*n)","A",1
257,1,122,67,0.0872544,"\int \frac{1}{x \cosh ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x*Cosh[a + b*Log[c*x^n]]^(5/2)),x]","\frac{2 \left(\cosh \left(a+b \log \left(c x^n\right)\right) \sqrt{\sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+\cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-\cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)-\sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)\right)+\sinh \left(a+b \log \left(c x^n\right)\right)\right)}{3 b n \cosh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}","\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*(Sinh[a + b*Log[c*x^n]] + Cosh[a + b*Log[c*x^n]]*Hypergeometric2F1[1/4, 1/2, 5/4, -Cosh[2*(a + b*Log[c*x^n])] - Sinh[2*(a + b*Log[c*x^n])]]*Sqrt[1 + Cosh[2*(a + b*Log[c*x^n])] + Sinh[2*(a + b*Log[c*x^n])]]))/(3*b*n*Cosh[a + b*Log[c*x^n]]^(3/2))","C",1
258,1,85,206,0.485202,"\int \cosh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right) \, dx","Integrate[Cosh[a + (2*Log[c*x^n])/n]^(5/2),x]","\frac{1}{14} e^{2 a} x \left(c x^n\right)^{4/n} \left(e^{2 a} \left(c x^n\right)^{4/n}+1\right) \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};e^{2 a} \left(c x^n\right)^{4/n}+1\right) \cosh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)","\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,"(E^(2*a)*x*(c*x^n)^(4/n)*(1 + E^(2*a)*(c*x^n)^(4/n))*Cosh[a + (2*Log[c*x^n])/n]^(5/2)*Hypergeometric2F1[2, 7/2, 9/2, 1 + E^(2*a)*(c*x^n)^(4/n)])/14","C",0
259,1,74,102,0.3314343,"\int \sqrt{\cosh \left(a+\frac{2 \log \left(c x^n\right)}{n}\right)} \, dx","Integrate[Sqrt[Cosh[a + (2*Log[c*x^n])/n]],x]","\frac{1}{2} x \left(1-\frac{\tanh ^{-1}\left(\sqrt{e^{2 a} \left(c x^n\right)^{4/n}+1}\right)}{\sqrt{e^{2 a} \left(c x^n\right)^{4/n}+1}}\right) \sqrt{\cosh \left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}","\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*(1 - ArcTanh[Sqrt[1 + E^(2*a)*(c*x^n)^(4/n)]]/Sqrt[1 + E^(2*a)*(c*x^n)^(4/n)])*Sqrt[Cosh[a + (2*Log[c*x^n])/n]])/2","A",0
260,1,61,42,0.1562064,"\int \frac{1}{\cosh ^{\frac{3}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)} \, dx","Integrate[Cosh[a + (2*Log[c*x^n])/n]^(-3/2),x]","\frac{\sinh \left(a+\frac{2 \log \left(c x^n\right)}{n}-2 \log (x)\right)-\cosh \left(a+\frac{2 \log \left(c x^n\right)}{n}-2 \log (x)\right)}{x \sqrt{\cosh \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,"(-Cosh[a - 2*Log[x] + (2*Log[c*x^n])/n] + Sinh[a - 2*Log[x] + (2*Log[c*x^n])/n])/(x*Sqrt[Cosh[a + (2*Log[c*x^n])/n]])","A",1
261,1,121,101,0.2666225,"\int \frac{1}{\cosh ^{\frac{7}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)} \, dx","Integrate[Cosh[a + (2*Log[c*x^n])/n]^(-7/2),x]","\frac{\left(\left(5 x^4-2\right) \sinh \left(a+\frac{2 \log \left(c x^n\right)}{n}-2 \log (x)\right)+\left(5 x^4+2\right) \cosh \left(a+\frac{2 \log \left(c x^n\right)}{n}-2 \log (x)\right)\right) \left(\sinh \left(2 a+\frac{4 \log \left(c x^n\right)}{n}-4 \log (x)\right)-\cosh \left(2 a+\frac{4 \log \left(c x^n\right)}{n}-4 \log (x)\right)\right)}{15 x^5 \cosh ^{\frac{5}{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,"(((2 + 5*x^4)*Cosh[a - 2*Log[x] + (2*Log[c*x^n])/n] + (-2 + 5*x^4)*Sinh[a - 2*Log[x] + (2*Log[c*x^n])/n])*(-Cosh[2*a - 4*Log[x] + (4*Log[c*x^n])/n] + Sinh[2*a - 4*Log[x] + (4*Log[c*x^n])/n]))/(15*x^5*Cosh[a + (2*Log[c*x^n])/n]^(5/2))","A",1
262,1,373,101,0.3686394,"\int \cosh \left(\frac{a+b x}{c+d x}\right) \, dx","Integrate[Cosh[(a + b*x)/(c + d*x)],x]","\frac{(b c-a d) \left(\sinh \left(\frac{b}{d}\right)-\cosh \left(\frac{b}{d}\right)\right) \text{Chi}\left(\frac{b c-a d}{x d^2+c d}\right)+(b c-a d) \left(\sinh \left(\frac{b}{d}\right)+\cosh \left(\frac{b}{d}\right)\right) \text{Chi}\left(\frac{a d-b c}{d (c+d x)}\right)-a d \sinh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{b c-a d}{x d^2+c d}\right)+b c \sinh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{b c-a d}{x d^2+c d}\right)+a d \cosh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{b c-a d}{x d^2+c d}\right)-b c \cosh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{b c-a d}{x d^2+c d}\right)+2 d^2 x \cosh \left(\frac{a+b x}{c+d x}\right)-a d \sinh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{a d-b c}{d (c+d x)}\right)+b c \sinh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{a d-b c}{d (c+d x)}\right)-a d \cosh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{a d-b c}{d (c+d x)}\right)+b c \cosh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{a d-b c}{d (c+d x)}\right)+2 c d \cosh \left(\frac{a+b x}{c+d x}\right)}{2 d^2}","\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,"(2*c*d*Cosh[(a + b*x)/(c + d*x)] + 2*d^2*x*Cosh[(a + b*x)/(c + d*x)] + (b*c - a*d)*CoshIntegral[(b*c - a*d)/(c*d + d^2*x)]*(-Cosh[b/d] + Sinh[b/d]) + (b*c - a*d)*CoshIntegral[(-(b*c) + a*d)/(d*(c + d*x))]*(Cosh[b/d] + Sinh[b/d]) + b*c*Cosh[b/d]*SinhIntegral[(-(b*c) + a*d)/(d*(c + d*x))] - a*d*Cosh[b/d]*SinhIntegral[(-(b*c) + a*d)/(d*(c + d*x))] + b*c*Sinh[b/d]*SinhIntegral[(-(b*c) + a*d)/(d*(c + d*x))] - a*d*Sinh[b/d]*SinhIntegral[(-(b*c) + a*d)/(d*(c + d*x))] - b*c*Cosh[b/d]*SinhIntegral[(b*c - a*d)/(c*d + d^2*x)] + a*d*Cosh[b/d]*SinhIntegral[(b*c - a*d)/(c*d + d^2*x)] + b*c*Sinh[b/d]*SinhIntegral[(b*c - a*d)/(c*d + d^2*x)] - a*d*Sinh[b/d]*SinhIntegral[(b*c - a*d)/(c*d + d^2*x)])/(2*d^2)","B",1
263,1,111,107,0.3092373,"\int \cosh ^2\left(\frac{a+b x}{c+d x}\right) \, dx","Integrate[Cosh[(a + b*x)/(c + d*x)]^2,x]","\frac{2 \sinh \left(\frac{2 b}{d}\right) (b c-a d) \text{Chi}\left(\frac{2 (a d-b c)}{d (c+d x)}\right)+2 \cosh \left(\frac{2 b}{d}\right) (b c-a d) \text{Shi}\left(\frac{2 (a d-b c)}{d (c+d x)}\right)+d \left((c+d x) \cosh \left(\frac{2 (a+b x)}{c+d x}\right)+d x\right)}{2 d^2}","\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,"(d*(d*x + (c + d*x)*Cosh[(2*(a + b*x))/(c + d*x)]) + 2*(b*c - a*d)*CoshIntegral[(2*(-(b*c) + a*d))/(d*(c + d*x))]*Sinh[(2*b)/d] + 2*(b*c - a*d)*Cosh[(2*b)/d]*SinhIntegral[(2*(-(b*c) + a*d))/(d*(c + d*x))])/(2*d^2)","A",1
264,1,62,83,0.0467287,"\int e^{a+b x} \cosh ^4(a+b x) \, dx","Integrate[E^(a + b*x)*Cosh[a + b*x]^4,x]","\frac{e^{-3 (a+b x)} \left(-60 e^{2 (a+b x)}+90 e^{4 (a+b x)}+20 e^{6 (a+b x)}+3 e^{8 (a+b x)}-5\right)}{240 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,"(-5 - 60*E^(2*(a + b*x)) + 90*E^(4*(a + b*x)) + 20*E^(6*(a + b*x)) + 3*E^(8*(a + b*x)))/(240*b*E^(3*(a + b*x)))","A",1
265,1,47,57,0.0411891,"\int e^{a+b x} \cosh ^3(a+b x) \, dx","Integrate[E^(a + b*x)*Cosh[a + b*x]^3,x]","\frac{-e^{-2 (a+b x)}+3 e^{2 (a+b x)}+\frac{1}{2} e^{4 (a+b x)}+6 b x}{16 b}","-\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 + b*x)) + 3*E^(2*(a + b*x)) + E^(4*(a + b*x))/2 + 6*b*x)/(16*b)","A",1
266,1,39,49,0.0227235,"\int e^{a+b x} \cosh ^2(a+b x) \, dx","Integrate[E^(a + b*x)*Cosh[a + b*x]^2,x]","\frac{e^{-a-b x} \left(6 e^{2 (a+b x)}+e^{4 (a+b x)}-3\right)}{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)*(-3 + 6*E^(2*(a + b*x)) + E^(4*(a + b*x))))/(12*b)","A",1
267,1,23,23,0.0134018,"\int e^{a+b x} \cosh (a+b x) \, dx","Integrate[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",1
268,1,17,17,0.0151315,"\int e^{a+b x} \text{sech}(a+b x) \, dx","Integrate[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",1
269,1,36,40,0.0667444,"\int e^{a+b x} \text{sech}^2(a+b x) \, dx","Integrate[E^(a + b*x)*Sech[a + b*x]^2,x]","\frac{2 \left(\tan ^{-1}\left(e^{a+b x}\right)-\frac{e^{a+b x}}{e^{2 (a+b x)}+1}\right)}{b}","\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)/(1 + E^(2*(a + b*x)))) + ArcTan[E^(a + b*x)]))/b","A",1
270,1,29,29,0.0188583,"\int e^{a+b x} \text{sech}^3(a+b x) \, dx","Integrate[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",1
271,1,64,95,0.0909567,"\int e^{a+b x} \text{sech}^4(a+b x) \, dx","Integrate[E^(a + b*x)*Sech[a + b*x]^4,x]","\frac{e^{a+b x} \left(-8 e^{2 (a+b x)}+3 e^{4 (a+b x)}-3\right)}{3 b \left(e^{2 (a+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,"(E^(a + b*x)*(-3 - 8*E^(2*(a + b*x)) + 3*E^(4*(a + b*x))))/(3*b*(1 + E^(2*(a + b*x)))^3) + ArcTan[E^(a + b*x)]/b","A",1
272,1,44,60,0.0371764,"\int e^{a+b x} \text{sech}^5(a+b x) \, dx","Integrate[E^(a + b*x)*Sech[a + b*x]^5,x]","-\frac{4 \left(4 e^{2 (a+b x)}+6 e^{4 (a+b x)}+1\right)}{3 b \left(e^{2 (a+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*(1 + 4*E^(2*(a + b*x)) + 6*E^(4*(a + b*x))))/(3*b*(1 + E^(2*(a + b*x)))^4)","A",1
273,1,26,26,0.0152058,"\int e^x \cosh ^2(2 x) \, dx","Integrate[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*1/E^(3*x) + E^x/2 + E^(5*x)/20","A",1
274,1,16,19,0.0098974,"\int e^x \cosh (2 x) \, dx","Integrate[E^x*Cosh[2*x],x]","\frac{1}{6} e^{-x} \left(e^{4 x}-3\right)","\frac{e^{3 x}}{6}-\frac{e^{-x}}{2}",1,"(-3 + E^(4*x))/(6*E^x)","A",1
275,1,24,92,0.0105919,"\int e^x \text{sech}(2 x) \, dx","Integrate[E^x*Sech[2*x],x]","\frac{2}{3} e^{3 x} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-e^{4 x}\right)","\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,"(2*E^(3*x)*Hypergeometric2F1[3/4, 1, 7/4, -E^(4*x)])/3","C",1
276,1,106,111,0.0931872,"\int e^x \text{sech}^2(2 x) \, dx","Integrate[E^x*Sech[2*x]^2,x]","\frac{1}{8} \left(-\frac{8 e^x}{e^{4 x}+1}-\sqrt{2} \log \left(-\sqrt{2} e^x+e^{2 x}+1\right)+\sqrt{2} \log \left(\sqrt{2} e^x+e^{2 x}+1\right)-2 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} e^x\right)+2 \sqrt{2} \tan ^{-1}\left(\sqrt{2} e^x+1\right)\right)","-\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,"((-8*E^x)/(1 + E^(4*x)) - 2*Sqrt[2]*ArcTan[1 - Sqrt[2]*E^x] + 2*Sqrt[2]*ArcTan[1 + Sqrt[2]*E^x] - Sqrt[2]*Log[1 - Sqrt[2]*E^x + E^(2*x)] + Sqrt[2]*Log[1 + Sqrt[2]*E^x + E^(2*x)])/8","A",1
277,1,26,26,0.0174179,"\int e^x \cosh ^2(3 x) \, dx","Integrate[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*1/E^(5*x) + E^x/2 + E^(7*x)/28","A",1
278,1,16,19,0.0105195,"\int e^x \cosh (3 x) \, dx","Integrate[E^x*Cosh[3*x],x]","\frac{1}{8} e^{-2 x} \left(e^{6 x}-2\right)","\frac{e^{4 x}}{8}-\frac{1}{4} e^{-2 x}",1,"(-2 + E^(6*x))/(8*E^(2*x))","A",1
279,1,24,55,0.0121077,"\int e^x \text{sech}(3 x) \, dx","Integrate[E^x*Sech[3*x],x]","\frac{1}{2} e^{4 x} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-e^{6 x}\right)","-\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,"(E^(4*x)*Hypergeometric2F1[2/3, 1, 5/3, -E^(6*x)])/2","C",1
280,1,34,110,0.0217361,"\int e^x \text{sech}^2(3 x) \, dx","Integrate[E^x*Sech[3*x]^2,x]","\frac{2}{3} e^x \left(\, _2F_1\left(\frac{1}{6},1;\frac{7}{6};-e^{6 x}\right)-\frac{1}{e^{6 x}+1}\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*(-(1 + E^(6*x))^(-1) + Hypergeometric2F1[1/6, 1, 7/6, -E^(6*x)]))/3","C",1
281,1,26,26,0.0170123,"\int e^x \cosh ^2(4 x) \, dx","Integrate[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*1/E^(7*x) + E^x/2 + E^(9*x)/36","A",1
282,1,19,19,0.0108945,"\int e^x \cosh (4 x) \, dx","Integrate[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*1/E^(3*x) + E^(5*x)/10","A",1
283,1,24,371,0.0113024,"\int e^x \text{sech}(4 x) \, dx","Integrate[E^x*Sech[4*x],x]","\frac{2}{5} e^{5 x} \, _2F_1\left(\frac{5}{8},1;\frac{13}{8};-e^{8 x}\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,"(2*E^(5*x)*Hypergeometric2F1[5/8, 1, 13/8, -E^(8*x)])/5","C",1
284,1,34,379,0.0222823,"\int e^x \text{sech}^2(4 x) \, dx","Integrate[E^x*Sech[4*x]^2,x]","\frac{1}{2} e^x \left(\, _2F_1\left(\frac{1}{8},1;\frac{9}{8};-e^{8 x}\right)-\frac{1}{e^{8 x}+1}\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*(-(1 + E^(8*x))^(-1) + Hypergeometric2F1[1/8, 1, 9/8, -E^(8*x)]))/2","C",1
285,1,159,202,0.7023085,"\int F^{c (a+b x)} \cosh ^3(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Cosh[d + e*x]^3,x]","\frac{F^{c (a+b x)} \left(3 \cosh (d+e x) \left(b^3 c^3 \log ^3(F)-9 b c e^2 \log (F)\right)+\cosh (3 (d+e x)) \left(b^3 c^3 \log ^3(F)-b c e^2 \log (F)\right)+6 e \sinh (d+e x) \left(\cosh (2 (d+e x)) \left(e^2-b^2 c^2 \log ^2(F)\right)-b^2 c^2 \log ^2(F)+5 e^2\right)\right)}{4 \left(b^4 c^4 \log ^4(F)-10 b^2 c^2 e^2 \log ^2(F)+9 e^4\right)}","-\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{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 b c e^2 \log (F) \cosh (d+e x) F^{c (a+b x)}}{b^4 c^4 \log ^4(F)-10 b^2 c^2 e^2 \log ^2(F)+9 e^4}+\frac{6 e^3 \sinh (d+e x) F^{c (a+b x)}}{b^4 c^4 \log ^4(F)-10 b^2 c^2 e^2 \log ^2(F)+9 e^4}",1,"(F^(c*(a + b*x))*(3*Cosh[d + e*x]*(-9*b*c*e^2*Log[F] + b^3*c^3*Log[F]^3) + Cosh[3*(d + e*x)]*(-(b*c*e^2*Log[F]) + b^3*c^3*Log[F]^3) + 6*e*(5*e^2 - b^2*c^2*Log[F]^2 + Cosh[2*(d + e*x)]*(e^2 - b^2*c^2*Log[F]^2))*Sinh[d + e*x]))/(4*(9*e^4 - 10*b^2*c^2*e^2*Log[F]^2 + b^4*c^4*Log[F]^4))","A",1
286,1,85,132,0.2363193,"\int F^{c (a+b x)} \cosh ^2(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Cosh[d + e*x]^2,x]","\frac{F^{c (a+b x)} \left(b^2 c^2 \log ^2(F) \cosh (2 (d+e x))+b^2 c^2 \log ^2(F)-2 b c e \log (F) \sinh (2 (d+e x))-4 e^2\right)}{2 b^3 c^3 \log ^3(F)-8 b c e^2 \log (F)}","-\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,"(F^(c*(a + b*x))*(-4*e^2 + b^2*c^2*Log[F]^2 + b^2*c^2*Cosh[2*(d + e*x)]*Log[F]^2 - 2*b*c*e*Log[F]*Sinh[2*(d + e*x)]))/(-8*b*c*e^2*Log[F] + 2*b^3*c^3*Log[F]^3)","A",1
287,1,50,75,0.1170239,"\int F^{c (a+b x)} \cosh (d+e x) \, dx","Integrate[F^(c*(a + b*x))*Cosh[d + e*x],x]","\frac{F^{c (a+b x)} (e \sinh (d+e x)-b c \log (F) \cosh (d+e x))}{(e-b c \log (F)) (b c \log (F)+e)}","\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,"(F^(c*(a + b*x))*(-(b*c*Cosh[d + e*x]*Log[F]) + e*Sinh[d + e*x]))/((e - b*c*Log[F])*(e + b*c*Log[F]))","A",1
288,1,70,68,0.0201164,"\int F^{c (a+b x)} \text{sech}(d+e x) \, dx","Integrate[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{b c \log (F)}{2 e}+\frac{1}{2};\frac{b c \log (F)}{2 e}+\frac{3}{2};-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, 1/2 + (b*c*Log[F])/(2*e), 3/2 + (b*c*Log[F])/(2*e), -E^(2*(d + e*x))])/(e + b*c*Log[F])","A",1
289,1,70,70,0.0170407,"\int F^{c (a+b x)} \text{sech}^2(d+e x) \, dx","Integrate[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
290,1,96,124,0.2550933,"\int F^{c (a+b x)} \text{sech}^3(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Sech[d + e*x]^3,x]","\frac{F^{c (a+b x)} \left(2 e^{d+e 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)+\text{sech}(d+e x) (b c \log (F)+e \tanh (d+e x))\right)}{2 e^2}","\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,"(F^(c*(a + b*x))*(2*E^(d + e*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]) + Sech[d + e*x]*(b*c*Log[F] + e*Tanh[d + e*x])))/(2*e^2)","A",1
291,1,101,133,0.2027345,"\int F^{c (a+b x)} \text{sech}^4(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Sech[d + e*x]^4,x]","\frac{F^{c (a+b x)} \left(4 e^{2 (d+e 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)+\text{sech}^2(d+e x) (b c \log (F)+2 e \tanh (d+e x))\right)}{6 e^2}","\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,"(F^(c*(a + b*x))*(4*E^(2*(d + e*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]) + Sech[d + e*x]^2*(b*c*Log[F] + 2*e*Tanh[d + e*x])))/(6*e^2)","A",1
292,1,106,250,0.106109,"\int e^{c (a+b x)} \cosh ^2(a c+b c x)^{5/2} \, dx","Integrate[E^(c*(a + b*x))*(Cosh[a*c + b*c*x]^2)^(5/2),x]","\frac{\left(-\frac{1}{2} e^{-4 c (a+b x)}-5 e^{-2 c (a+b x)}+10 e^{2 c (a+b x)}+\frac{5}{2} e^{4 c (a+b x)}+\frac{1}{3} e^{6 c (a+b x)}+20 b c x\right) \cosh ^2(c (a+b x))^{5/2} \text{sech}^5(c (a+b x))}{64 b c}","-\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,"((-1/2*1/E^(4*c*(a + b*x)) - 5/E^(2*c*(a + b*x)) + 10*E^(2*c*(a + b*x)) + (5*E^(4*c*(a + b*x)))/2 + E^(6*c*(a + b*x))/3 + 20*b*c*x)*(Cosh[c*(a + b*x)]^2)^(5/2)*Sech[c*(a + b*x)]^5)/(64*b*c)","A",1
293,1,78,162,0.1156781,"\int e^{c (a+b x)} \cosh ^2(a c+b c x)^{3/2} \, dx","Integrate[E^(c*(a + b*x))*(Cosh[a*c + b*c*x]^2)^(3/2),x]","\frac{\left(-e^{-2 c (a+b x)}+3 e^{2 c (a+b x)}+\frac{1}{2} e^{4 c (a+b x)}+6 b c x\right) \cosh ^2(c (a+b x))^{3/2} \text{sech}^3(c (a+b x))}{16 b c}","-\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,"((-E^(-2*c*(a + b*x)) + 3*E^(2*c*(a + b*x)) + E^(4*c*(a + b*x))/2 + 6*b*c*x)*(Cosh[c*(a + b*x)]^2)^(3/2)*Sech[c*(a + b*x)]^3)/(16*b*c)","A",1
294,1,48,74,0.0419435,"\int e^{c (a+b x)} \sqrt{\cosh ^2(a c+b c x)} \, dx","Integrate[E^(c*(a + b*x))*Sqrt[Cosh[a*c + b*c*x]^2],x]","\frac{\left(e^{2 c (a+b x)}+2 b c x\right) \sqrt{\cosh ^2(c (a+b x))} \text{sech}(c (a+b x))}{4 b c}","\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)) + 2*b*c*x)*Sqrt[Cosh[c*(a + b*x)]^2]*Sech[c*(a + b*x)])/(4*b*c)","A",1
295,1,42,44,0.0560489,"\int \frac{e^{c (a+b x)}}{\sqrt{\cosh ^2(a c+b c x)}} \, dx","Integrate[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 (c (a+b x))}{b c \sqrt{\cosh ^2(c (a+b 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[c*(a + b*x)]*Log[1 + E^(2*c*(a + b*x))])/(b*c*Sqrt[Cosh[c*(a + b*x)]^2])","A",1
296,1,46,56,0.0757462,"\int \frac{e^{c (a+b x)}}{\cosh ^2(a c+b c x)^{3/2}} \, dx","Integrate[E^(c*(a + b*x))/(Cosh[a*c + b*c*x]^2)^(3/2),x]","\frac{4 e^{5 c (a+b x)} \sqrt{\cosh ^2(c (a+b x))}}{b c \left(e^{2 c (a+b x)}+1\right)^3}","\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,"(4*E^(5*c*(a + b*x))*Sqrt[Cosh[c*(a + b*x)]^2])/(b*c*(1 + E^(2*c*(a + b*x)))^3)","A",1
297,1,72,141,0.0726202,"\int \frac{e^{c (a+b x)}}{\cosh ^2(a c+b c x)^{5/2}} \, dx","Integrate[E^(c*(a + b*x))/(Cosh[a*c + b*c*x]^2)^(5/2),x]","-\frac{4 \left(4 e^{2 c (a+b x)}+6 e^{4 c (a+b x)}+1\right) \cosh (c (a+b x))}{3 b c \left(e^{2 c (a+b x)}+1\right)^4 \sqrt{\cosh ^2(c (a+b 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*(1 + 4*E^(2*c*(a + b*x)) + 6*E^(4*c*(a + b*x)))*Cosh[c*(a + b*x)])/(3*b*c*(1 + E^(2*c*(a + b*x)))^4*Sqrt[Cosh[c*(a + b*x)]^2])","A",1
298,1,84,191,0.0855616,"\int \frac{e^{c (a+b x)}}{\cosh ^2(a c+b c x)^{7/2}} \, dx","Integrate[E^(c*(a + b*x))/(Cosh[a*c + b*c*x]^2)^(7/2),x]","-\frac{16 \left(6 e^{2 c (a+b x)}+15 e^{4 c (a+b x)}+20 e^{6 c (a+b x)}+1\right) \cosh (c (a+b x))}{15 b c \left(e^{2 c (a+b x)}+1\right)^6 \sqrt{\cosh ^2(c (a+b 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,"(-16*(1 + 6*E^(2*c*(a + b*x)) + 15*E^(4*c*(a + b*x)) + 20*E^(6*c*(a + b*x)))*Cosh[c*(a + b*x)])/(15*b*c*(1 + E^(2*c*(a + b*x)))^6*Sqrt[Cosh[c*(a + b*x)]^2])","A",1
299,1,28,41,0.0490918,"\int e^x \cosh (a+b x) \, dx","Integrate[E^x*Cosh[a + b*x],x]","\frac{e^x (b \sinh (a+b x)-\cosh (a+b x))}{b^2-1}","\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] + b*Sinh[a + b*x]))/(-1 + b^2)","A",1
300,1,79,85,0.082304,"\int e^x \cosh \left(a+c x^2\right) \, dx","Integrate[E^x*Cosh[a + c*x^2],x]","\frac{\sqrt{\pi } e^{\left.-\frac{1}{4}\right/c} \left(e^{\left.\frac{1}{2}\right/c} (\cosh (a)-\sinh (a)) \text{erf}\left(\frac{2 c x-1}{2 \sqrt{c}}\right)+(\sinh (a)+\cosh (a)) \text{erfi}\left(\frac{2 c x+1}{2 \sqrt{c}}\right)\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,"(Sqrt[Pi]*(E^(1/(2*c))*Erf[(-1 + 2*c*x)/(2*Sqrt[c])]*(Cosh[a] - Sinh[a]) + Erfi[(1 + 2*c*x)/(2*Sqrt[c])]*(Cosh[a] + Sinh[a])))/(4*Sqrt[c]*E^(1/(4*c)))","A",1
301,1,91,101,0.1541738,"\int e^x \cosh \left(a+b x+c x^2\right) \, dx","Integrate[E^x*Cosh[a + b*x + c*x^2],x]","\frac{\sqrt{\pi } e^{-\frac{(b+1)^2}{4 c}} \left(e^{\frac{b^2+1}{2 c}} (\cosh (a)-\sinh (a)) \text{erf}\left(\frac{b+2 c x-1}{2 \sqrt{c}}\right)+(\sinh (a)+\cosh (a)) \text{erfi}\left(\frac{b+2 c x+1}{2 \sqrt{c}}\right)\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,"(Sqrt[Pi]*(E^((1 + b^2)/(2*c))*Erf[(-1 + b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a] - Sinh[a]) + Erfi[(1 + b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a] + Sinh[a])))/(4*Sqrt[c]*E^((1 + b)^2/(4*c)))","A",1
302,1,51,65,0.0702932,"\int e^{x^2} \cosh (a+b x) \, dx","Integrate[E^x^2*Cosh[a + b*x],x]","\frac{1}{4} \sqrt{\pi } e^{-\frac{b^2}{4}} \left((\sinh (a)-\cosh (a)) \text{erfi}\left(\frac{b}{2}-x\right)+(\sinh (a)+\cosh (a)) \text{erfi}\left(\frac{b}{2}+x\right)\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,"(Sqrt[Pi]*(Erfi[b/2 - x]*(-Cosh[a] + Sinh[a]) + Erfi[b/2 + x]*(Cosh[a] + Sinh[a])))/(4*E^(b^2/4))","A",1
303,1,71,65,0.1017124,"\int e^{x^2} \cosh \left(a+c x^2\right) \, dx","Integrate[E^x^2*Cosh[a + c*x^2],x]","\frac{\sqrt{\pi } \left(\sqrt{c-1} (c+1) (\cosh (a)-\sinh (a)) \text{erf}\left(\sqrt{c-1} x\right)+(c-1) \sqrt{c+1} (\sinh (a)+\cosh (a)) \text{erfi}\left(\sqrt{c+1} x\right)\right)}{4 \left(c^2-1\right)}","\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]*(Sqrt[-1 + c]*(1 + c)*Erf[Sqrt[-1 + c]*x]*(Cosh[a] - Sinh[a]) + (-1 + c)*Sqrt[1 + c]*Erfi[Sqrt[1 + c]*x]*(Cosh[a] + Sinh[a])))/(4*(-1 + c^2))","A",1
304,1,122,115,0.3702661,"\int e^{x^2} \cosh \left(a+b x+c x^2\right) \, dx","Integrate[E^x^2*Cosh[a + b*x + c*x^2],x]","\frac{\sqrt{\pi } e^{-\frac{b^2}{4 c+4}} \left(\sqrt{c-1} (c+1) e^{\frac{b^2 c}{2 \left(c^2-1\right)}} (\cosh (a)-\sinh (a)) \text{erf}\left(\frac{b+2 (c-1) x}{2 \sqrt{c-1}}\right)+(c-1) \sqrt{c+1} (\sinh (a)+\cosh (a)) \text{erfi}\left(\frac{b+2 (c+1) x}{2 \sqrt{c+1}}\right)\right)}{4 \left(c^2-1\right)}","\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,"(Sqrt[Pi]*(Sqrt[-1 + c]*(1 + c)*E^((b^2*c)/(2*(-1 + c^2)))*Erf[(b + 2*(-1 + c)*x)/(2*Sqrt[-1 + c])]*(Cosh[a] - Sinh[a]) + (-1 + c)*Sqrt[1 + c]*Erfi[(b + 2*(1 + c)*x)/(2*Sqrt[1 + c])]*(Cosh[a] + Sinh[a])))/(4*(-1 + c^2)*E^(b^2/(4 + 4*c)))","A",1
305,1,102,110,0.1276286,"\int f^{a+b x} \cosh \left(d+f x^2\right) \, dx","Integrate[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}} \left(e^{\frac{b^2 \log ^2(f)}{2 f}} (\cosh (d)-\sinh (d)) \text{erf}\left(\frac{2 f x-b \log (f)}{2 \sqrt{f}}\right)+(\sinh (d)+\cosh (d)) \text{erfi}\left(\frac{b \log (f)+2 f x}{2 \sqrt{f}}\right)\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,"(f^(-1/2 + a)*Sqrt[Pi]*(E^((b^2*Log[f]^2)/(2*f))*Erf[(2*f*x - b*Log[f])/(2*Sqrt[f])]*(Cosh[d] - Sinh[d]) + Erfi[(2*f*x + b*Log[f])/(2*Sqrt[f])]*(Cosh[d] + Sinh[d])))/(4*E^((b^2*Log[f]^2)/(4*f)))","A",1
306,1,149,148,0.7000163,"\int f^{a+b x} \cosh ^2\left(d+f x^2\right) \, dx","Integrate[f^(a + b*x)*Cosh[d + f*x^2]^2,x]","\frac{1}{16} f^a \left(\frac{\sqrt{2 \pi } e^{\frac{b^2 \log ^2(f)}{8 f}} (\cosh (2 d)-\sinh (2 d)) \text{erf}\left(\frac{4 f x-b \log (f)}{2 \sqrt{2} \sqrt{f}}\right)}{\sqrt{f}}+\frac{\sqrt{2 \pi } e^{-\frac{b^2 \log ^2(f)}{8 f}} (\sinh (2 d)+\cosh (2 d)) \text{erfi}\left(\frac{b \log (f)+4 f x}{2 \sqrt{2} \sqrt{f}}\right)}{\sqrt{f}}+\frac{8 f^{b x}}{b \log (f)}\right)","\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,"(f^a*((8*f^(b*x))/(b*Log[f]) + (E^((b^2*Log[f]^2)/(8*f))*Sqrt[2*Pi]*Erf[(4*f*x - b*Log[f])/(2*Sqrt[2]*Sqrt[f])]*(Cosh[2*d] - Sinh[2*d]))/Sqrt[f] + (Sqrt[2*Pi]*Erfi[(4*f*x + b*Log[f])/(2*Sqrt[2]*Sqrt[f])]*(Cosh[2*d] + Sinh[2*d]))/(E^((b^2*Log[f]^2)/(8*f))*Sqrt[f])))/16","A",1
307,1,286,239,0.4294847,"\int f^{a+b x} \cosh ^3\left(d+f x^2\right) \, dx","Integrate[f^(a + b*x)*Cosh[d + f*x^2]^3,x]","\frac{1}{16} \sqrt{\frac{\pi }{3}} f^{a-\frac{1}{2}} e^{-\frac{b^2 \log ^2(f)}{4 f}} \left(3 \sqrt{3} e^{\frac{b^2 \log ^2(f)}{2 f}} (\cosh (d)-\sinh (d)) \text{erf}\left(\frac{2 f x-b \log (f)}{2 \sqrt{f}}\right)+e^{\frac{b^2 \log ^2(f)}{3 f}} (\cosh (3 d)-\sinh (3 d)) \text{erf}\left(\frac{6 f x-b \log (f)}{2 \sqrt{3} \sqrt{f}}\right)+\sinh (3 d) e^{\frac{b^2 \log ^2(f)}{6 f}} \text{erfi}\left(\frac{b \log (f)+6 f x}{2 \sqrt{3} \sqrt{f}}\right)+\cosh (3 d) e^{\frac{b^2 \log ^2(f)}{6 f}} \text{erfi}\left(\frac{b \log (f)+6 f x}{2 \sqrt{3} \sqrt{f}}\right)+3 \sqrt{3} \sinh (d) \text{erfi}\left(\frac{b \log (f)+2 f x}{2 \sqrt{f}}\right)+3 \sqrt{3} \cosh (d) \text{erfi}\left(\frac{b \log (f)+2 f x}{2 \sqrt{f}}\right)\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,"(f^(-1/2 + a)*Sqrt[Pi/3]*(3*Sqrt[3]*Cosh[d]*Erfi[(2*f*x + b*Log[f])/(2*Sqrt[f])] + E^((b^2*Log[f]^2)/(6*f))*Cosh[3*d]*Erfi[(6*f*x + b*Log[f])/(2*Sqrt[3]*Sqrt[f])] + 3*Sqrt[3]*E^((b^2*Log[f]^2)/(2*f))*Erf[(2*f*x - b*Log[f])/(2*Sqrt[f])]*(Cosh[d] - Sinh[d]) + 3*Sqrt[3]*Erfi[(2*f*x + b*Log[f])/(2*Sqrt[f])]*Sinh[d] + E^((b^2*Log[f]^2)/(3*f))*Erf[(6*f*x - b*Log[f])/(2*Sqrt[3]*Sqrt[f])]*(Cosh[3*d] - Sinh[3*d]) + E^((b^2*Log[f]^2)/(6*f))*Erfi[(6*f*x + b*Log[f])/(2*Sqrt[3]*Sqrt[f])]*Sinh[3*d]))/(16*E^((b^2*Log[f]^2)/(4*f)))","A",1
308,1,123,115,0.276429,"\int f^{a+b x} \cosh \left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x)*Cosh[d + e*x + f*x^2],x]","\frac{1}{4} \sqrt{\pi } f^{a-\frac{b e+f}{2 f}} e^{-\frac{b^2 \log ^2(f)+e^2}{4 f}} \left((\cosh (d)-\sinh (d)) e^{\frac{b^2 \log ^2(f)+e^2}{2 f}} \text{erf}\left(\frac{-b \log (f)+e+2 f x}{2 \sqrt{f}}\right)+(\sinh (d)+\cosh (d)) \text{erfi}\left(\frac{b \log (f)+e+2 f x}{2 \sqrt{f}}\right)\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,"(f^(a - (b*e + f)/(2*f))*Sqrt[Pi]*(E^((e^2 + b^2*Log[f]^2)/(2*f))*Erf[(e + 2*f*x - b*Log[f])/(2*Sqrt[f])]*(Cosh[d] - Sinh[d]) + Erfi[(e + 2*f*x + b*Log[f])/(2*Sqrt[f])]*(Cosh[d] + Sinh[d])))/(4*E^((e^2 + b^2*Log[f]^2)/(4*f)))","A",1
309,1,220,161,0.6489792,"\int f^{a+b x} \cosh ^2\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x)*Cosh[d + e*x + f*x^2]^2,x]","\frac{f^{a-\frac{b e+f}{2 f}} e^{-\frac{b^2 \log ^2(f)+4 e^2}{8 f}} \left(\sqrt{\pi } b \log (f) (\cosh (2 d)-\sinh (2 d)) e^{\frac{b^2 \log ^2(f)+4 e^2}{4 f}} \text{erf}\left(\frac{-b \log (f)+2 e+4 f x}{2 \sqrt{2} \sqrt{f}}\right)+4 \sqrt{2} f^{b \left(\frac{e}{2 f}+x\right)+\frac{1}{2}} e^{\frac{b^2 \log ^2(f)+4 e^2}{8 f}}+\sqrt{\pi } b \log (f) (\sinh (2 d)+\cosh (2 d)) \text{erfi}\left(\frac{b \log (f)+2 e+4 f x}{2 \sqrt{2} \sqrt{f}}\right)\right)}{8 \sqrt{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,"(f^(a - (b*e + f)/(2*f))*(4*Sqrt[2]*E^((4*e^2 + b^2*Log[f]^2)/(8*f))*f^(1/2 + b*(e/(2*f) + x)) + b*E^((4*e^2 + b^2*Log[f]^2)/(4*f))*Sqrt[Pi]*Erf[(2*e + 4*f*x - b*Log[f])/(2*Sqrt[2]*Sqrt[f])]*Log[f]*(Cosh[2*d] - Sinh[2*d]) + b*Sqrt[Pi]*Erfi[(2*e + 4*f*x + b*Log[f])/(2*Sqrt[2]*Sqrt[f])]*Log[f]*(Cosh[2*d] + Sinh[2*d])))/(8*Sqrt[2]*b*E^((4*e^2 + b^2*Log[f]^2)/(8*f))*Log[f])","A",1
310,1,353,257,0.7982804,"\int f^{a+b x} \cosh ^3\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x)*Cosh[d + e*x + f*x^2]^3,x]","\frac{1}{16} \sqrt{\frac{\pi }{3}} f^{a-\frac{b e+f}{2 f}} e^{-\frac{b^2 \log ^2(f)+3 e^2}{4 f}} \left(3 \sqrt{3} (\cosh (d)-\sinh (d)) e^{\frac{b^2 \log ^2(f)+2 e^2}{2 f}} \text{erf}\left(\frac{-b \log (f)+e+2 f x}{2 \sqrt{f}}\right)+(\cosh (3 d)-\sinh (3 d)) e^{\frac{2 b^2 \log ^2(f)+9 e^2}{6 f}} \text{erf}\left(\frac{-b \log (f)+3 e+6 f x}{2 \sqrt{3} \sqrt{f}}\right)+\sinh (3 d) e^{\frac{b^2 \log ^2(f)}{6 f}} \text{erfi}\left(\frac{b \log (f)+3 e+6 f x}{2 \sqrt{3} \sqrt{f}}\right)+\cosh (3 d) e^{\frac{b^2 \log ^2(f)}{6 f}} \text{erfi}\left(\frac{b \log (f)+3 e+6 f x}{2 \sqrt{3} \sqrt{f}}\right)+3 \sqrt{3} \sinh (d) e^{\frac{e^2}{2 f}} \text{erfi}\left(\frac{b \log (f)+e+2 f x}{2 \sqrt{f}}\right)+3 \sqrt{3} \cosh (d) e^{\frac{e^2}{2 f}} \text{erfi}\left(\frac{b \log (f)+e+2 f x}{2 \sqrt{f}}\right)\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,"(f^(a - (b*e + f)/(2*f))*Sqrt[Pi/3]*(3*Sqrt[3]*E^(e^2/(2*f))*Cosh[d]*Erfi[(e + 2*f*x + b*Log[f])/(2*Sqrt[f])] + E^((b^2*Log[f]^2)/(6*f))*Cosh[3*d]*Erfi[(3*e + 6*f*x + b*Log[f])/(2*Sqrt[3]*Sqrt[f])] + 3*Sqrt[3]*E^((2*e^2 + b^2*Log[f]^2)/(2*f))*Erf[(e + 2*f*x - b*Log[f])/(2*Sqrt[f])]*(Cosh[d] - Sinh[d]) + 3*Sqrt[3]*E^(e^2/(2*f))*Erfi[(e + 2*f*x + b*Log[f])/(2*Sqrt[f])]*Sinh[d] + E^((9*e^2 + 2*b^2*Log[f]^2)/(6*f))*Erf[(3*e + 6*f*x - b*Log[f])/(2*Sqrt[3]*Sqrt[f])]*(Cosh[3*d] - Sinh[3*d]) + E^((b^2*Log[f]^2)/(6*f))*Erfi[(3*e + 6*f*x + b*Log[f])/(2*Sqrt[3]*Sqrt[f])]*Sinh[3*d]))/(16*E^((3*e^2 + b^2*Log[f]^2)/(4*f)))","A",1
311,1,104,133,0.1527352,"\int f^{a+c x^2} \cosh (d+e x) \, dx","Integrate[f^(a + c*x^2)*Cosh[d + e*x],x]","\frac{\sqrt{\pi } f^a e^{-\frac{e^2}{4 c \log (f)}} \left((\cosh (d)-\sinh (d)) \text{erfi}\left(\frac{2 c x \log (f)-e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+(\sinh (d)+\cosh (d)) \text{erfi}\left(\frac{2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\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,"(f^a*Sqrt[Pi]*(Erfi[(-e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[d] - Sinh[d]) + Erfi[(e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[d] + Sinh[d])))/(4*Sqrt[c]*E^(e^2/(4*c*Log[f]))*Sqrt[Log[f]])","A",1
312,1,131,161,0.2301148,"\int f^{a+c x^2} \cosh ^2(d+e x) \, dx","Integrate[f^(a + c*x^2)*Cosh[d + e*x]^2,x]","\frac{\sqrt{\pi } f^a e^{-\frac{e^2}{c \log (f)}} \left((\cosh (2 d)-\sinh (2 d)) \text{erfi}\left(\frac{c x \log (f)-e}{\sqrt{c} \sqrt{\log (f)}}\right)+(\sinh (2 d)+\cosh (2 d)) \text{erfi}\left(\frac{c x \log (f)+e}{\sqrt{c} \sqrt{\log (f)}}\right)+2 e^{\frac{e^2}{c \log (f)}} \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)\right)}{8 \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]*(2*E^(e^2/(c*Log[f]))*Erfi[Sqrt[c]*x*Sqrt[Log[f]]] + Erfi[(-e + c*x*Log[f])/(Sqrt[c]*Sqrt[Log[f]])]*(Cosh[2*d] - Sinh[2*d]) + Erfi[(e + c*x*Log[f])/(Sqrt[c]*Sqrt[Log[f]])]*(Cosh[2*d] + Sinh[2*d])))/(8*Sqrt[c]*E^(e^2/(c*Log[f]))*Sqrt[Log[f]])","A",1
313,1,214,271,0.4680308,"\int f^{a+c x^2} \cosh ^3(d+e x) \, dx","Integrate[f^(a + c*x^2)*Cosh[d + e*x]^3,x]","\frac{\sqrt{\pi } f^a e^{-\frac{9 e^2}{4 c \log (f)}} \left((\sinh (d)+\cosh (d)) \left(3 (\cosh (2 d)-\sinh (2 d)) e^{\frac{2 e^2}{c \log (f)}} \text{erfi}\left(\frac{2 c x \log (f)-e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+(\sinh (2 d)+\cosh (2 d)) \text{erfi}\left(\frac{2 c x \log (f)+3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+3 e^{\frac{2 e^2}{c \log (f)}} \text{erfi}\left(\frac{2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)+(\cosh (3 d)-\sinh (3 d)) \text{erfi}\left(\frac{2 c x \log (f)-3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\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,"(f^a*Sqrt[Pi]*((Cosh[d] + Sinh[d])*(3*E^((2*e^2)/(c*Log[f]))*Erfi[(e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])] + 3*E^((2*e^2)/(c*Log[f]))*Erfi[(-e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[2*d] - Sinh[2*d]) + Erfi[(3*e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[2*d] + Sinh[2*d])) + Erfi[(-3*e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[3*d] - Sinh[3*d])))/(16*Sqrt[c]*E^((9*e^2)/(4*c*Log[f]))*Sqrt[Log[f]])","A",1
314,1,75,81,0.3334521,"\int f^{a+c x^2} \cosh \left(d+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Cosh[d + f*x^2],x]","\frac{1}{4} \sqrt{\pi } f^a \left(\frac{(\cosh (d)-\sinh (d)) \text{erf}\left(x \sqrt{f-c \log (f)}\right)}{\sqrt{f-c \log (f)}}+\frac{(\sinh (d)+\cosh (d)) \text{erfi}\left(x \sqrt{c \log (f)+f}\right)}{\sqrt{c \log (f)+f}}\right)","\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]]]*(Cosh[d] - Sinh[d]))/Sqrt[f - c*Log[f]] + (Erfi[x*Sqrt[f + c*Log[f]]]*(Cosh[d] + Sinh[d]))/Sqrt[f + c*Log[f]]))/4","A",1
315,1,179,128,0.5644827,"\int f^{a+c x^2} \cosh ^2\left(d+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Cosh[d + f*x^2]^2,x]","\frac{\sqrt{\pi } f^a \left(\left(2 c^2 \log ^2(f)-8 f^2\right) \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)+\sqrt{c} \sqrt{\log (f)} \left(\sqrt{2 f-c \log (f)} (c \log (f)+2 f) (\sinh (2 d)-\cosh (2 d)) \text{erf}\left(x \sqrt{2 f-c \log (f)}\right)-(2 f-c \log (f)) \sqrt{c \log (f)+2 f} (\sinh (2 d)+\cosh (2 d)) \text{erfi}\left(x \sqrt{c \log (f)+2 f}\right)\right)\right)}{8 \sqrt{c} \sqrt{\log (f)} \left(c^2 \log ^2(f)-4 f^2\right)}","\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]]]*(-8*f^2 + 2*c^2*Log[f]^2) + Sqrt[c]*Sqrt[Log[f]]*(Erf[x*Sqrt[2*f - c*Log[f]]]*Sqrt[2*f - c*Log[f]]*(2*f + c*Log[f])*(-Cosh[2*d] + Sinh[2*d]) - Erfi[x*Sqrt[2*f + c*Log[f]]]*(2*f - c*Log[f])*Sqrt[2*f + c*Log[f]]*(Cosh[2*d] + Sinh[2*d]))))/(8*Sqrt[c]*Sqrt[Log[f]]*(-4*f^2 + c^2*Log[f]^2))","A",1
316,1,270,171,1.2354586,"\int f^{a+c x^2} \cosh ^3\left(d+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Cosh[d + f*x^2]^3,x]","\frac{\sqrt{\pi } f^a \left((f-c \log (f)) \left(\sqrt{3 f-c \log (f)} \left(c^2 \log ^2(f)+4 c f \log (f)+3 f^2\right) (\cosh (3 d)-\sinh (3 d)) \text{erf}\left(x \sqrt{3 f-c \log (f)}\right)+(3 f-c \log (f)) \left(3 \sqrt{c \log (f)+f} (c \log (f)+3 f) (\sinh (d)+\cosh (d)) \text{erfi}\left(x \sqrt{c \log (f)+f}\right)+(c \log (f)+f) \sqrt{c \log (f)+3 f} (\sinh (3 d)+\cosh (3 d)) \text{erfi}\left(x \sqrt{c \log (f)+3 f}\right)\right)\right)+3 \sqrt{f-c \log (f)} \left(-c^3 \log ^3(f)-c^2 f \log ^2(f)+9 c f^2 \log (f)+9 f^3\right) (\cosh (d)-\sinh (d)) \text{erf}\left(x \sqrt{f-c \log (f)}\right)\right)}{16 \left(c^4 \log ^4(f)-10 c^2 f^2 \log ^2(f)+9 f^4\right)}","\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,"(f^a*Sqrt[Pi]*(3*Erf[x*Sqrt[f - c*Log[f]]]*Sqrt[f - c*Log[f]]*(9*f^3 + 9*c*f^2*Log[f] - c^2*f*Log[f]^2 - c^3*Log[f]^3)*(Cosh[d] - Sinh[d]) + (f - c*Log[f])*(Erf[x*Sqrt[3*f - c*Log[f]]]*Sqrt[3*f - c*Log[f]]*(3*f^2 + 4*c*f*Log[f] + c^2*Log[f]^2)*(Cosh[3*d] - Sinh[3*d]) + (3*f - c*Log[f])*(3*Erfi[x*Sqrt[f + c*Log[f]]]*Sqrt[f + c*Log[f]]*(3*f + c*Log[f])*(Cosh[d] + Sinh[d]) + Erfi[x*Sqrt[3*f + c*Log[f]]]*(f + c*Log[f])*Sqrt[3*f + c*Log[f]]*(Cosh[3*d] + Sinh[3*d])))))/(16*(9*f^4 - 10*c^2*f^2*Log[f]^2 + c^4*Log[f]^4))","A",1
317,1,165,140,0.6733638,"\int f^{a+c x^2} \cosh \left(d+e x+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Cosh[d + e*x + f*x^2],x]","\frac{\sqrt{\pi } f^a e^{-\frac{e^2}{4 (c \log (f)+f)}} \left(\sqrt{c \log (f)+f} (\cosh (d)-\sinh (d)) e^{\frac{e^2 f}{2 f^2-2 c^2 \log ^2(f)}} \text{erf}\left(\frac{-2 c x \log (f)+e+2 f x}{2 \sqrt{f-c \log (f)}}\right)+\sqrt{f-c \log (f)} (\sinh (d)+\cosh (d)) \text{erfi}\left(\frac{2 c x \log (f)+e+2 f x}{2 \sqrt{c \log (f)+f}}\right)\right)}{4 \sqrt{f-c \log (f)} \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,"(f^a*Sqrt[Pi]*(E^((e^2*f)/(2*f^2 - 2*c^2*Log[f]^2))*Erf[(e + 2*f*x - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Sqrt[f + c*Log[f]]*(Cosh[d] - Sinh[d]) + Erfi[(e + 2*f*x + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Sqrt[f - c*Log[f]]*(Cosh[d] + Sinh[d])))/(4*E^(e^2/(4*(f + c*Log[f])))*Sqrt[f - c*Log[f]]*Sqrt[f + c*Log[f]])","A",1
318,1,258,183,1.4888022,"\int f^{a+c x^2} \cosh ^2\left(d+e x+f x^2\right) \, dx","Integrate[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)}} \left(-\sqrt{c} \sqrt{\log (f)} \left((2 f-c \log (f)) \sqrt{c \log (f)+2 f} (\sinh (2 d)+\cosh (2 d)) e^{\frac{4 e^2 f}{c^2 \log ^2(f)-4 f^2}} \text{erfi}\left(\frac{c x \log (f)+e+2 f x}{\sqrt{c \log (f)+2 f}}\right)+\sqrt{2 f-c \log (f)} (c \log (f)+2 f) (\cosh (2 d)-\sinh (2 d)) \text{erf}\left(\frac{-c x \log (f)+e+2 f x}{\sqrt{2 f-c \log (f)}}\right)\right)-2 \left(4 f^2-c^2 \log ^2(f)\right) e^{\frac{e^2}{c \log (f)-2 f}} \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)\right)}{8 \sqrt{c} \sqrt{\log (f)} \left(c^2 \log ^2(f)-4 f^2\right)}","\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,"(E^(e^2/(2*f - c*Log[f]))*f^a*Sqrt[Pi]*(-2*E^(e^2/(-2*f + c*Log[f]))*Erfi[Sqrt[c]*x*Sqrt[Log[f]]]*(4*f^2 - c^2*Log[f]^2) - Sqrt[c]*Sqrt[Log[f]]*(Erf[(e + 2*f*x - c*x*Log[f])/Sqrt[2*f - c*Log[f]]]*Sqrt[2*f - c*Log[f]]*(2*f + c*Log[f])*(Cosh[2*d] - Sinh[2*d]) + E^((4*e^2*f)/(-4*f^2 + c^2*Log[f]^2))*Erfi[(e + 2*f*x + c*x*Log[f])/Sqrt[2*f + c*Log[f]]]*(2*f - c*Log[f])*Sqrt[2*f + c*Log[f]]*(Cosh[2*d] + Sinh[2*d]))))/(8*Sqrt[c]*Sqrt[Log[f]]*(-4*f^2 + c^2*Log[f]^2))","A",1
319,1,478,300,5.9975596,"\int f^{a+c x^2} \cosh ^3\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Cosh[d + e*x + f*x^2]^3,x]","\frac{\sqrt{\pi } f^a \exp \left(-\frac{1}{4} e^2 \left(\frac{9}{c \log (f)+3 f}+\frac{1}{c \log (f)+f}\right)\right) \left((f-c \log (f)) \left(\sqrt{3 f-c \log (f)} \left(c^2 \log ^2(f)+4 c f \log (f)+3 f^2\right) (\cosh (3 d)-\sinh (3 d)) \exp \left(\frac{1}{4} e^2 \left(\frac{1}{c \log (f)+f}+\frac{9}{c \log (f)+3 f}+\frac{9}{3 f-c \log (f)}\right)\right) \text{erf}\left(\frac{-2 c x \log (f)+3 e+6 f x}{2 \sqrt{3 f-c \log (f)}}\right)+(3 f-c \log (f)) \left(3 \sqrt{c \log (f)+f} (c \log (f)+3 f) (\sinh (d)+\cosh (d)) e^{\frac{9 e^2}{4 (c \log (f)+3 f)}} \text{erfi}\left(\frac{2 c x \log (f)+e+2 f x}{2 \sqrt{c \log (f)+f}}\right)+(c \log (f)+f) \sqrt{c \log (f)+3 f} (\sinh (3 d)+\cosh (3 d)) e^{\frac{e^2}{4 (c \log (f)+f)}} \text{erfi}\left(\frac{2 c x \log (f)+3 e+6 f x}{2 \sqrt{c \log (f)+3 f}}\right)\right)\right)+3 \sqrt{f-c \log (f)} \left(-c^3 \log ^3(f)-c^2 f \log ^2(f)+9 c f^2 \log (f)+9 f^3\right) (\cosh (d)-\sinh (d)) \exp \left(\frac{1}{4} e^2 \left(\frac{1}{c \log (f)+f}+\frac{9}{c \log (f)+3 f}+\frac{1}{f-c \log (f)}\right)\right) \text{erf}\left(\frac{-2 c x \log (f)+e+2 f x}{2 \sqrt{f-c \log (f)}}\right)\right)}{16 \left(c^4 \log ^4(f)-10 c^2 f^2 \log ^2(f)+9 f^4\right)}","\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,"(f^a*Sqrt[Pi]*(3*E^((e^2*((f - c*Log[f])^(-1) + (f + c*Log[f])^(-1) + 9/(3*f + c*Log[f])))/4)*Erf[(e + 2*f*x - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Sqrt[f - c*Log[f]]*(9*f^3 + 9*c*f^2*Log[f] - c^2*f*Log[f]^2 - c^3*Log[f]^3)*(Cosh[d] - Sinh[d]) + (f - c*Log[f])*(E^((e^2*(9/(3*f - c*Log[f]) + (f + c*Log[f])^(-1) + 9/(3*f + c*Log[f])))/4)*Erf[(3*e + 6*f*x - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Sqrt[3*f - c*Log[f]]*(3*f^2 + 4*c*f*Log[f] + c^2*Log[f]^2)*(Cosh[3*d] - Sinh[3*d]) + (3*f - c*Log[f])*(3*E^((9*e^2)/(4*(3*f + c*Log[f])))*Erfi[(e + 2*f*x + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Sqrt[f + c*Log[f]]*(3*f + c*Log[f])*(Cosh[d] + Sinh[d]) + E^(e^2/(4*(f + c*Log[f])))*Erfi[(3*e + 6*f*x + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*(f + c*Log[f])*Sqrt[3*f + c*Log[f]]*(Cosh[3*d] + Sinh[3*d])))))/(16*E^((e^2*((f + c*Log[f])^(-1) + 9/(3*f + c*Log[f])))/4)*(9*f^4 - 10*c^2*f^2*Log[f]^2 + c^4*Log[f]^4))","A",0
320,1,134,153,0.3205031,"\int f^{a+b x+c x^2} \cosh (d+e x) \, dx","Integrate[f^(a + b*x + c*x^2)*Cosh[d + e*x],x]","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} e^{-\frac{e (2 b \log (f)+e)}{4 c \log (f)}} \left(e^{\frac{b e}{c}} (\cosh (d)-\sinh (d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)-e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+(\sinh (d)+\cosh (d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\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,"(f^(a - b^2/(4*c))*Sqrt[Pi]*(E^((b*e)/c)*Erfi[(-e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[d] - Sinh[d]) + Erfi[(e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[d] + Sinh[d])))/(4*Sqrt[c]*E^((e*(e + 2*b*Log[f]))/(4*c*Log[f]))*Sqrt[Log[f]])","A",1
321,1,183,219,0.5637819,"\int f^{a+b x+c x^2} \cosh ^2(d+e x) \, dx","Integrate[f^(a + b*x + c*x^2)*Cosh[d + e*x]^2,x]","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} e^{-\frac{e (b \log (f)+e)}{c \log (f)}} \left(e^{\frac{2 b e}{c}} (\cosh (2 d)-\sinh (2 d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)-2 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+(\sinh (2 d)+\cosh (2 d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)+2 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+2 e^{\frac{e (b \log (f)+e)}{c \log (f)}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)\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]*(2*E^((e*(e + b*Log[f]))/(c*Log[f]))*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])] + E^((2*b*e)/c)*Erfi[(-2*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[2*d] - Sinh[2*d]) + Erfi[(2*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[2*d] + Sinh[2*d])))/(8*Sqrt[c]*E^((e*(e + b*Log[f]))/(c*Log[f]))*Sqrt[Log[f]])","A",1
322,1,262,315,1.0230066,"\int f^{a+b x+c x^2} \cosh ^3(d+e x) \, dx","Integrate[f^(a + b*x + c*x^2)*Cosh[d + e*x]^3,x]","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} e^{-\frac{3 e (2 b \log (f)+3 e)}{4 c \log (f)}} \left((\sinh (d)+\cosh (d)) \left(3 (\cosh (2 d)-\sinh (2 d)) e^{\frac{2 e (b \log (f)+e)}{c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)-e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+(\sinh (2 d)+\cosh (2 d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)+3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+3 e^{\frac{e (b \log (f)+2 e)}{c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)+e^{\frac{3 b e}{c}} (\cosh (3 d)-\sinh (3 d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)-3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\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,"(f^(a - b^2/(4*c))*Sqrt[Pi]*((Cosh[d] + Sinh[d])*(3*E^((e*(2*e + b*Log[f]))/(c*Log[f]))*Erfi[(e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])] + 3*E^((2*e*(e + b*Log[f]))/(c*Log[f]))*Erfi[(-e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[2*d] - Sinh[2*d]) + Erfi[(3*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[2*d] + Sinh[2*d])) + E^((3*b*e)/c)*Erfi[(-3*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[3*d] - Sinh[3*d])))/(16*Sqrt[c]*E^((3*e*(3*e + 2*b*Log[f]))/(4*c*Log[f]))*Sqrt[Log[f]])","A",1
323,1,185,154,0.6787979,"\int f^{a+b x+c x^2} \cosh \left(d+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Cosh[d + f*x^2],x]","\frac{\sqrt{\pi } f^a e^{-\frac{b^2 \log ^2(f)}{4 (c \log (f)+f)}} \left(\sqrt{f-c \log (f)} (c \log (f)+f) (\cosh (d)-\sinh (d)) e^{\frac{b^2 f \log ^2(f)}{2 f^2-2 c^2 \log ^2(f)}} \text{erf}\left(\frac{2 f x-\log (f) (b+2 c x)}{2 \sqrt{f-c \log (f)}}\right)+(f-c \log (f)) \sqrt{c \log (f)+f} (\sinh (d)+\cosh (d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)+2 f x}{2 \sqrt{c \log (f)+f}}\right)\right)}{4 \left(f^2-c^2 \log ^2(f)\right)}","\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,"(f^a*Sqrt[Pi]*(E^((b^2*f*Log[f]^2)/(2*f^2 - 2*c^2*Log[f]^2))*Erf[(2*f*x - (b + 2*c*x)*Log[f])/(2*Sqrt[f - c*Log[f]])]*Sqrt[f - c*Log[f]]*(f + c*Log[f])*(Cosh[d] - Sinh[d]) + Erfi[(2*f*x + (b + 2*c*x)*Log[f])/(2*Sqrt[f + c*Log[f]])]*(f - c*Log[f])*Sqrt[f + c*Log[f]]*(Cosh[d] + Sinh[d])))/(4*E^((b^2*Log[f]^2)/(4*(f + c*Log[f])))*(f^2 - c^2*Log[f]^2))","A",1
324,1,257,225,2.2786325,"\int f^{a+b x+c x^2} \cosh ^2\left(d+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Cosh[d + f*x^2]^2,x]","\frac{1}{8} \sqrt{\pi } f^a \left(\frac{2 f^{-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{\sqrt{c} \sqrt{\log (f)}}-\frac{e^{-\frac{b^2 \log ^2(f)}{4 c \log (f)+8 f}} \left(\sqrt{2 f-c \log (f)} (c \log (f)+2 f) (\cosh (2 d)-\sinh (2 d)) e^{\frac{b^2 f \log ^2(f)}{4 f^2-c^2 \log ^2(f)}} \text{erf}\left(\frac{4 f x-\log (f) (b+2 c x)}{2 \sqrt{2 f-c \log (f)}}\right)+(2 f-c \log (f)) \sqrt{c \log (f)+2 f} (\sinh (2 d)+\cosh (2 d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)+4 f x}{2 \sqrt{c \log (f)+2 f}}\right)\right)}{c^2 \log ^2(f)-4 f^2}\right)","-\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*Sqrt[Pi]*((2*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(Sqrt[c]*f^(b^2/(4*c))*Sqrt[Log[f]]) - (E^((b^2*f*Log[f]^2)/(4*f^2 - c^2*Log[f]^2))*Erf[(4*f*x - (b + 2*c*x)*Log[f])/(2*Sqrt[2*f - c*Log[f]])]*Sqrt[2*f - c*Log[f]]*(2*f + c*Log[f])*(Cosh[2*d] - Sinh[2*d]) + Erfi[(4*f*x + (b + 2*c*x)*Log[f])/(2*Sqrt[2*f + c*Log[f]])]*(2*f - c*Log[f])*Sqrt[2*f + c*Log[f]]*(Cosh[2*d] + Sinh[2*d]))/(E^((b^2*Log[f]^2)/(8*f + 4*c*Log[f]))*(-4*f^2 + c^2*Log[f]^2))))/8","A",1
325,1,2511,323,6.5089877,"\int f^{a+b x+c x^2} \cosh ^3\left(d+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Cosh[d + f*x^2]^3,x]","\text{Result too large to show}","-\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,"(f^a*Sqrt[Pi]*(27*E^((b^2*Log[f]^2)/(4*(f - c*Log[f])))*f^3*Cosh[d]*Erf[(2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Sqrt[f - c*Log[f]] + 27*c*E^((b^2*Log[f]^2)/(4*(f - c*Log[f])))*f^2*Cosh[d]*Erf[(2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]*Sqrt[f - c*Log[f]] - 3*c^2*E^((b^2*Log[f]^2)/(4*(f - c*Log[f])))*f*Cosh[d]*Erf[(2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]^2*Sqrt[f - c*Log[f]] - 3*c^3*E^((b^2*Log[f]^2)/(4*(f - c*Log[f])))*Cosh[d]*Erf[(2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]^3*Sqrt[f - c*Log[f]] + 3*E^((b^2*Log[f]^2)/(4*(3*f - c*Log[f])))*f^3*Cosh[3*d]*Erf[(6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Sqrt[3*f - c*Log[f]] + c*E^((b^2*Log[f]^2)/(4*(3*f - c*Log[f])))*f^2*Cosh[3*d]*Erf[(6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]*Sqrt[3*f - c*Log[f]] - 3*c^2*E^((b^2*Log[f]^2)/(4*(3*f - c*Log[f])))*f*Cosh[3*d]*Erf[(6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]^2*Sqrt[3*f - c*Log[f]] - c^3*E^((b^2*Log[f]^2)/(4*(3*f - c*Log[f])))*Cosh[3*d]*Erf[(6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]^3*Sqrt[3*f - c*Log[f]] + (27*f^3*Cosh[d]*Erfi[(2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Sqrt[f + c*Log[f]])/E^((b^2*Log[f]^2)/(4*(f + c*Log[f]))) - (27*c*f^2*Cosh[d]*Erfi[(2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]*Sqrt[f + c*Log[f]])/E^((b^2*Log[f]^2)/(4*(f + c*Log[f]))) - (3*c^2*f*Cosh[d]*Erfi[(2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]^2*Sqrt[f + c*Log[f]])/E^((b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (3*c^3*Cosh[d]*Erfi[(2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]^3*Sqrt[f + c*Log[f]])/E^((b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (3*f^3*Cosh[3*d]*Erfi[(6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Sqrt[3*f + c*Log[f]])/E^((b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (c*f^2*Cosh[3*d]*Erfi[(6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]*Sqrt[3*f + c*Log[f]])/E^((b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (3*c^2*f*Cosh[3*d]*Erfi[(6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]^2*Sqrt[3*f + c*Log[f]])/E^((b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) + (c^3*Cosh[3*d]*Erfi[(6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]^3*Sqrt[3*f + c*Log[f]])/E^((b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - 27*E^((b^2*Log[f]^2)/(4*(f - c*Log[f])))*f^3*Erf[(2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Sqrt[f - c*Log[f]]*Sinh[d] - 27*c*E^((b^2*Log[f]^2)/(4*(f - c*Log[f])))*f^2*Erf[(2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]*Sqrt[f - c*Log[f]]*Sinh[d] + 3*c^2*E^((b^2*Log[f]^2)/(4*(f - c*Log[f])))*f*Erf[(2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]^2*Sqrt[f - c*Log[f]]*Sinh[d] + 3*c^3*E^((b^2*Log[f]^2)/(4*(f - c*Log[f])))*Erf[(2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]^3*Sqrt[f - c*Log[f]]*Sinh[d] + (27*f^3*Erfi[(2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Sqrt[f + c*Log[f]]*Sinh[d])/E^((b^2*Log[f]^2)/(4*(f + c*Log[f]))) - (27*c*f^2*Erfi[(2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]*Sqrt[f + c*Log[f]]*Sinh[d])/E^((b^2*Log[f]^2)/(4*(f + c*Log[f]))) - (3*c^2*f*Erfi[(2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]^2*Sqrt[f + c*Log[f]]*Sinh[d])/E^((b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (3*c^3*Erfi[(2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]^3*Sqrt[f + c*Log[f]]*Sinh[d])/E^((b^2*Log[f]^2)/(4*(f + c*Log[f]))) - 3*E^((b^2*Log[f]^2)/(4*(3*f - c*Log[f])))*f^3*Erf[(6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Sqrt[3*f - c*Log[f]]*Sinh[3*d] - c*E^((b^2*Log[f]^2)/(4*(3*f - c*Log[f])))*f^2*Erf[(6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]*Sqrt[3*f - c*Log[f]]*Sinh[3*d] + 3*c^2*E^((b^2*Log[f]^2)/(4*(3*f - c*Log[f])))*f*Erf[(6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]^2*Sqrt[3*f - c*Log[f]]*Sinh[3*d] + c^3*E^((b^2*Log[f]^2)/(4*(3*f - c*Log[f])))*Erf[(6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]^3*Sqrt[3*f - c*Log[f]]*Sinh[3*d] + (3*f^3*Erfi[(6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Sqrt[3*f + c*Log[f]]*Sinh[3*d])/E^((b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (c*f^2*Erfi[(6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]*Sqrt[3*f + c*Log[f]]*Sinh[3*d])/E^((b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (3*c^2*f*Erfi[(6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]^2*Sqrt[3*f + c*Log[f]]*Sinh[3*d])/E^((b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) + (c^3*Erfi[(6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]^3*Sqrt[3*f + c*Log[f]]*Sinh[3*d])/E^((b^2*Log[f]^2)/(4*(3*f + c*Log[f])))))/(16*(f - c*Log[f])*(3*f - c*Log[f])*(f + c*Log[f])*(3*f + c*Log[f]))","B",1
326,1,251,161,1.5140197,"\int f^{a+b x+c x^2} \cosh \left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Cosh[d + e*x + f*x^2],x]","\frac{\sqrt{\pi } e^{-\frac{b^2 \log ^2(f)+e^2}{4 (c \log (f)+f)}} f^{a+\frac{b e f}{c^2 \log ^2(f)-f^2}} \left(\sqrt{f-c \log (f)} (c \log (f)+f) (\cosh (d)-\sinh (d)) f^{\frac{b e}{2 (c \log (f)+f)}} \exp \left(\frac{f \left(b^2 \log ^2(f)+e^2\right)}{2 \left(f^2-c^2 \log ^2(f)\right)}\right) \text{erf}\left(\frac{-\log (f) (b+2 c x)+e+2 f x}{2 \sqrt{f-c \log (f)}}\right)+(f-c \log (f)) \sqrt{c \log (f)+f} (\sinh (d)+\cosh (d)) f^{\frac{b e}{2 f-2 c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)+e+2 f x}{2 \sqrt{c \log (f)+f}}\right)\right)}{4 \left(f^2-c^2 \log ^2(f)\right)}","\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,"(f^(a + (b*e*f)/(-f^2 + c^2*Log[f]^2))*Sqrt[Pi]*(E^((f*(e^2 + b^2*Log[f]^2))/(2*(f^2 - c^2*Log[f]^2)))*f^((b*e)/(2*(f + c*Log[f])))*Erf[(e + 2*f*x - (b + 2*c*x)*Log[f])/(2*Sqrt[f - c*Log[f]])]*Sqrt[f - c*Log[f]]*(f + c*Log[f])*(Cosh[d] - Sinh[d]) + f^((b*e)/(2*f - 2*c*Log[f]))*Erfi[(e + 2*f*x + (b + 2*c*x)*Log[f])/(2*Sqrt[f + c*Log[f]])]*(f - c*Log[f])*Sqrt[f + c*Log[f]]*(Cosh[d] + Sinh[d])))/(4*E^((e^2 + b^2*Log[f]^2)/(4*(f + c*Log[f])))*(f^2 - c^2*Log[f]^2))","A",0
327,1,339,239,6.1673066,"\int f^{a+b x+c x^2} \cosh ^2\left(d+e x+f x^2\right) \, dx","Integrate[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 } e^{-\frac{b^2 \log ^2(f)+4 e^2}{4 c \log (f)+8 f}} f^{a+\frac{4 b e f}{c^2 \log ^2(f)-4 f^2}} \left(\sqrt{2 f-c \log (f)} (c \log (f)+2 f) (\cosh (2 d)-\sinh (2 d)) f^{\frac{b e}{c \log (f)+2 f}} \exp \left(\frac{f \left(b^2 \log ^2(f)+4 e^2\right)}{4 f^2-c^2 \log ^2(f)}\right) \text{erf}\left(\frac{2 (e+2 f x)-\log (f) (b+2 c x)}{2 \sqrt{2 f-c \log (f)}}\right)+(2 f-c \log (f)) \sqrt{c \log (f)+2 f} (\sinh (2 d)+\cosh (2 d)) f^{\frac{b e}{2 f-c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)+2 (e+2 f x)}{2 \sqrt{c \log (f)+2 f}}\right)\right)}{8 \left(c^2 \log ^2(f)-4 f^2\right)}","\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]]) - (f^(a + (4*b*e*f)/(-4*f^2 + c^2*Log[f]^2))*Sqrt[Pi]*(E^((f*(4*e^2 + b^2*Log[f]^2))/(4*f^2 - c^2*Log[f]^2))*f^((b*e)/(2*f + c*Log[f]))*Erf[(2*(e + 2*f*x) - (b + 2*c*x)*Log[f])/(2*Sqrt[2*f - c*Log[f]])]*Sqrt[2*f - c*Log[f]]*(2*f + c*Log[f])*(Cosh[2*d] - Sinh[2*d]) + f^((b*e)/(2*f - c*Log[f]))*Erfi[(2*(e + 2*f*x) + (b + 2*c*x)*Log[f])/(2*Sqrt[2*f + c*Log[f]])]*(2*f - c*Log[f])*Sqrt[2*f + c*Log[f]]*(Cosh[2*d] + Sinh[2*d])))/(8*E^((4*e^2 + b^2*Log[f]^2)/(8*f + 4*c*Log[f]))*(-4*f^2 + c^2*Log[f]^2))","A",0
328,1,2991,344,6.6492132,"\int f^{a+b x+c x^2} \cosh ^3\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Cosh[d + e*x + f*x^2]^3,x]","\text{Result too large to show}","\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,"(f^a*Sqrt[Pi]*((27*f^3*Cosh[d]*Erf[(e + 2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Sqrt[f - c*Log[f]])/E^((-e^2 + 2*b*e*Log[f] - b^2*Log[f]^2)/(4*(f - c*Log[f]))) + (27*c*f^2*Cosh[d]*Erf[(e + 2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]*Sqrt[f - c*Log[f]])/E^((-e^2 + 2*b*e*Log[f] - b^2*Log[f]^2)/(4*(f - c*Log[f]))) - (3*c^2*f*Cosh[d]*Erf[(e + 2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]^2*Sqrt[f - c*Log[f]])/E^((-e^2 + 2*b*e*Log[f] - b^2*Log[f]^2)/(4*(f - c*Log[f]))) - (3*c^3*Cosh[d]*Erf[(e + 2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]^3*Sqrt[f - c*Log[f]])/E^((-e^2 + 2*b*e*Log[f] - b^2*Log[f]^2)/(4*(f - c*Log[f]))) + (3*f^3*Cosh[3*d]*Erf[(3*e + 6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Sqrt[3*f - c*Log[f]])/E^((-9*e^2 + 6*b*e*Log[f] - b^2*Log[f]^2)/(4*(3*f - c*Log[f]))) + (c*f^2*Cosh[3*d]*Erf[(3*e + 6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]*Sqrt[3*f - c*Log[f]])/E^((-9*e^2 + 6*b*e*Log[f] - b^2*Log[f]^2)/(4*(3*f - c*Log[f]))) - (3*c^2*f*Cosh[3*d]*Erf[(3*e + 6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]^2*Sqrt[3*f - c*Log[f]])/E^((-9*e^2 + 6*b*e*Log[f] - b^2*Log[f]^2)/(4*(3*f - c*Log[f]))) - (c^3*Cosh[3*d]*Erf[(3*e + 6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]^3*Sqrt[3*f - c*Log[f]])/E^((-9*e^2 + 6*b*e*Log[f] - b^2*Log[f]^2)/(4*(3*f - c*Log[f]))) + (27*f^3*Cosh[d]*Erfi[(e + 2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Sqrt[f + c*Log[f]])/E^((e^2 + 2*b*e*Log[f] + b^2*Log[f]^2)/(4*(f + c*Log[f]))) - (27*c*f^2*Cosh[d]*Erfi[(e + 2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]*Sqrt[f + c*Log[f]])/E^((e^2 + 2*b*e*Log[f] + b^2*Log[f]^2)/(4*(f + c*Log[f]))) - (3*c^2*f*Cosh[d]*Erfi[(e + 2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]^2*Sqrt[f + c*Log[f]])/E^((e^2 + 2*b*e*Log[f] + b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (3*c^3*Cosh[d]*Erfi[(e + 2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]^3*Sqrt[f + c*Log[f]])/E^((e^2 + 2*b*e*Log[f] + b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (3*f^3*Cosh[3*d]*Erfi[(3*e + 6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Sqrt[3*f + c*Log[f]])/E^((9*e^2 + 6*b*e*Log[f] + b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (c*f^2*Cosh[3*d]*Erfi[(3*e + 6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]*Sqrt[3*f + c*Log[f]])/E^((9*e^2 + 6*b*e*Log[f] + b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (3*c^2*f*Cosh[3*d]*Erfi[(3*e + 6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]^2*Sqrt[3*f + c*Log[f]])/E^((9*e^2 + 6*b*e*Log[f] + b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) + (c^3*Cosh[3*d]*Erfi[(3*e + 6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]^3*Sqrt[3*f + c*Log[f]])/E^((9*e^2 + 6*b*e*Log[f] + b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (27*f^3*Erf[(e + 2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Sqrt[f - c*Log[f]]*Sinh[d])/E^((-e^2 + 2*b*e*Log[f] - b^2*Log[f]^2)/(4*(f - c*Log[f]))) - (27*c*f^2*Erf[(e + 2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]*Sqrt[f - c*Log[f]]*Sinh[d])/E^((-e^2 + 2*b*e*Log[f] - b^2*Log[f]^2)/(4*(f - c*Log[f]))) + (3*c^2*f*Erf[(e + 2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]^2*Sqrt[f - c*Log[f]]*Sinh[d])/E^((-e^2 + 2*b*e*Log[f] - b^2*Log[f]^2)/(4*(f - c*Log[f]))) + (3*c^3*Erf[(e + 2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]^3*Sqrt[f - c*Log[f]]*Sinh[d])/E^((-e^2 + 2*b*e*Log[f] - b^2*Log[f]^2)/(4*(f - c*Log[f]))) + (27*f^3*Erfi[(e + 2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Sqrt[f + c*Log[f]]*Sinh[d])/E^((e^2 + 2*b*e*Log[f] + b^2*Log[f]^2)/(4*(f + c*Log[f]))) - (27*c*f^2*Erfi[(e + 2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]*Sqrt[f + c*Log[f]]*Sinh[d])/E^((e^2 + 2*b*e*Log[f] + b^2*Log[f]^2)/(4*(f + c*Log[f]))) - (3*c^2*f*Erfi[(e + 2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]^2*Sqrt[f + c*Log[f]]*Sinh[d])/E^((e^2 + 2*b*e*Log[f] + b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (3*c^3*Erfi[(e + 2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]^3*Sqrt[f + c*Log[f]]*Sinh[d])/E^((e^2 + 2*b*e*Log[f] + b^2*Log[f]^2)/(4*(f + c*Log[f]))) - (3*f^3*Erf[(3*e + 6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Sqrt[3*f - c*Log[f]]*Sinh[3*d])/E^((-9*e^2 + 6*b*e*Log[f] - b^2*Log[f]^2)/(4*(3*f - c*Log[f]))) - (c*f^2*Erf[(3*e + 6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]*Sqrt[3*f - c*Log[f]]*Sinh[3*d])/E^((-9*e^2 + 6*b*e*Log[f] - b^2*Log[f]^2)/(4*(3*f - c*Log[f]))) + (3*c^2*f*Erf[(3*e + 6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]^2*Sqrt[3*f - c*Log[f]]*Sinh[3*d])/E^((-9*e^2 + 6*b*e*Log[f] - b^2*Log[f]^2)/(4*(3*f - c*Log[f]))) + (c^3*Erf[(3*e + 6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]^3*Sqrt[3*f - c*Log[f]]*Sinh[3*d])/E^((-9*e^2 + 6*b*e*Log[f] - b^2*Log[f]^2)/(4*(3*f - c*Log[f]))) + (3*f^3*Erfi[(3*e + 6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Sqrt[3*f + c*Log[f]]*Sinh[3*d])/E^((9*e^2 + 6*b*e*Log[f] + b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (c*f^2*Erfi[(3*e + 6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]*Sqrt[3*f + c*Log[f]]*Sinh[3*d])/E^((9*e^2 + 6*b*e*Log[f] + b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (3*c^2*f*Erfi[(3*e + 6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]^2*Sqrt[3*f + c*Log[f]]*Sinh[3*d])/E^((9*e^2 + 6*b*e*Log[f] + b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) + (c^3*Erfi[(3*e + 6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]^3*Sqrt[3*f + c*Log[f]]*Sinh[3*d])/E^((9*e^2 + 6*b*e*Log[f] + b^2*Log[f]^2)/(4*(3*f + c*Log[f])))))/(16*(f - c*Log[f])*(3*f - c*Log[f])*(f + c*Log[f])*(3*f + c*Log[f]))","B",1
329,1,46,20,0.3615526,"\int \left(\frac{x}{\cosh ^{\frac{3}{2}}(x)}+x \sqrt{\cosh (x)}\right) \, dx","Integrate[x/Cosh[x]^(3/2) + x*Sqrt[Cosh[x]],x]","\frac{2 \sinh (x) \left(x-\frac{2 \sinh (x) \cosh (x) \sqrt{\tanh ^2\left(\frac{x}{2}\right)}}{(\cosh (x)-1)^{3/2} \sqrt{\cosh (x)+1}}\right)}{\sqrt{\cosh (x)}}","\frac{2 x \sinh (x)}{\sqrt{\cosh (x)}}-4 \sqrt{\cosh (x)}",1,"(2*Sinh[x]*(x - (2*Cosh[x]*Sinh[x]*Sqrt[Tanh[x/2]^2])/((-1 + Cosh[x])^(3/2)*Sqrt[1 + Cosh[x]])))/Sqrt[Cosh[x]]","B",0
330,1,16,24,0.0816507,"\int \left(\frac{x}{\cosh ^{\frac{5}{2}}(x)}-\frac{x}{3 \sqrt{\cosh (x)}}\right) \, dx","Integrate[x/Cosh[x]^(5/2) - x/(3*Sqrt[Cosh[x]]),x]","\frac{2 (x \tanh (x)+2)}{3 \sqrt{\cosh (x)}}","\frac{4}{3 \sqrt{\cosh (x)}}+\frac{2 x \sinh (x)}{3 \cosh ^{\frac{3}{2}}(x)}",1,"(2*(2 + x*Tanh[x]))/(3*Sqrt[Cosh[x]])","A",1
331,1,64,47,0.6102506,"\int \left(\frac{x}{\cosh ^{\frac{7}{2}}(x)}+\frac{3}{5} x \sqrt{\cosh (x)}\right) \, dx","Integrate[x/Cosh[x]^(7/2) + (3*x*Sqrt[Cosh[x]])/5,x]","\frac{1}{5} \sqrt{\cosh (x)} \left(6 x \tanh (x)+\left(2 x \tanh (x)+\frac{4}{3}\right) \text{sech}^2(x)-\frac{12 \sinh ^2(x)}{\sqrt{\cosh (x)-1} (\cosh (x)+1)^{3/2} \sqrt{\tanh ^2\left(\frac{x}{2}\right)}}\right)","\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,"(Sqrt[Cosh[x]]*((-12*Sinh[x]^2)/(Sqrt[-1 + Cosh[x]]*(1 + Cosh[x])^(3/2)*Sqrt[Tanh[x/2]^2]) + 6*x*Tanh[x] + Sech[x]^2*(4/3 + 2*x*Tanh[x])))/5","A",0
332,1,76,36,0.1889998,"\int \left(\frac{x^2}{\cosh ^{\frac{3}{2}}(x)}+x^2 \sqrt{\cosh (x)}\right) \, dx","Integrate[x^2/Cosh[x]^(3/2) + x^2*Sqrt[Cosh[x]],x]","\frac{4 \sqrt{\cosh (x)} (\sinh (x)+\cosh (x)) \left(8 \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-e^{2 x}\right) (\sinh (x)-\cosh (x)) \sqrt{\sinh (2 x)+\cosh (2 x)+1}+x^2 \sinh (x)-4 (x-2) \cosh (x)\right)}{e^{2 x}+1}","\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,"(4*Sqrt[Cosh[x]]*(Cosh[x] + Sinh[x])*(-4*(-2 + x)*Cosh[x] + x^2*Sinh[x] + 8*Hypergeometric2F1[-1/4, 1/2, 3/4, -E^(2*x)]*(-Cosh[x] + Sinh[x])*Sqrt[1 + Cosh[2*x] + Sinh[2*x]]))/(1 + E^(2*x))","C",1
333,1,26,30,0.0662955,"\int (x+\cosh (x))^2 \, dx","Integrate[(x + Cosh[x])^2,x]","\frac{1}{6} \left(x \left(2 x^2+12 \sinh (x)+3\right)+3 (\sinh (x)-4) \cosh (x)\right)","\frac{x^3}{3}+\frac{x}{2}+2 x \sinh (x)-2 \cosh (x)+\frac{1}{2} \sinh (x) \cosh (x)",1,"(3*Cosh[x]*(-4 + Sinh[x]) + x*(3 + 2*x^2 + 12*Sinh[x]))/6","A",1
334,1,51,56,0.0929011,"\int (x+\cosh (x))^3 \, dx","Integrate[(x + Cosh[x])^3,x]","\frac{1}{12} \left(3 x^4+9 x^2+9 \left(4 x^2+9\right) \sinh (x)+9 x \sinh (2 x)+\sinh (3 x)\right)-6 x \cosh (x)-\frac{3}{8} \cosh (2 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,"-6*x*Cosh[x] - (3*Cosh[2*x])/8 + (9*x^2 + 3*x^4 + 9*(9 + 4*x^2)*Sinh[x] + 9*x*Sinh[2*x] + Sinh[3*x])/12","A",1
335,1,180,213,0.2987301,"\int \frac{\cosh (a+b x)}{c+d x^2} \, dx","Integrate[Cosh[a + b*x]/(c + d*x^2),x]","\frac{i \left(\cosh \left(a-\frac{i b \sqrt{c}}{\sqrt{d}}\right) \text{Ci}\left(i b x-\frac{b \sqrt{c}}{\sqrt{d}}\right)-\cosh \left(a+\frac{i b \sqrt{c}}{\sqrt{d}}\right) \text{Ci}\left(i x b+\frac{\sqrt{c} b}{\sqrt{d}}\right)+i \left(\sinh \left(a-\frac{i b \sqrt{c}}{\sqrt{d}}\right) \text{Si}\left(\frac{b \sqrt{c}}{\sqrt{d}}-i b x\right)+\sinh \left(a+\frac{i b \sqrt{c}}{\sqrt{d}}\right) \text{Si}\left(i x b+\frac{\sqrt{c} b}{\sqrt{d}}\right)\right)\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,"((I/2)*(Cosh[a - (I*b*Sqrt[c])/Sqrt[d]]*CosIntegral[-((b*Sqrt[c])/Sqrt[d]) + I*b*x] - Cosh[a + (I*b*Sqrt[c])/Sqrt[d]]*CosIntegral[(b*Sqrt[c])/Sqrt[d] + I*b*x] + I*(Sinh[a - (I*b*Sqrt[c])/Sqrt[d]]*SinIntegral[(b*Sqrt[c])/Sqrt[d] - I*b*x] + Sinh[a + (I*b*Sqrt[c])/Sqrt[d]]*SinIntegral[(b*Sqrt[c])/Sqrt[d] + I*b*x])))/(Sqrt[c]*Sqrt[d])","C",0
336,1,248,271,0.4993618,"\int \frac{\cosh (a+b x)}{c+d x+e x^2} \, dx","Integrate[Cosh[a + b*x]/(c + d*x + e*x^2),x]","\frac{\cosh \left(a+\frac{b \left(\sqrt{d^2-4 c e}-d\right)}{2 e}\right) \text{Ci}\left(\frac{i b \left(d+2 e x-\sqrt{d^2-4 c e}\right)}{2 e}\right)-\cosh \left(a-\frac{b \left(\sqrt{d^2-4 c e}+d\right)}{2 e}\right) \text{Ci}\left(\frac{i b \left(d+2 e x+\sqrt{d^2-4 c e}\right)}{2 e}\right)-\sinh \left(a-\frac{b \left(\sqrt{d^2-4 c e}+d\right)}{2 e}\right) \text{Shi}\left(\frac{b \left(d+2 e x+\sqrt{d^2-4 c e}\right)}{2 e}\right)+i \sinh \left(a+\frac{b \left(\sqrt{d^2-4 c e}-d\right)}{2 e}\right) \text{Si}\left(\frac{i b \left(\sqrt{d^2-4 c e}-d\right)}{2 e}-i 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)]*CosIntegral[((I/2)*b*(d - Sqrt[d^2 - 4*c*e] + 2*e*x))/e] - Cosh[a - (b*(d + Sqrt[d^2 - 4*c*e]))/(2*e)]*CosIntegral[((I/2)*b*(d + Sqrt[d^2 - 4*c*e] + 2*e*x))/e] - Sinh[a - (b*(d + Sqrt[d^2 - 4*c*e]))/(2*e)]*SinhIntegral[(b*(d + Sqrt[d^2 - 4*c*e] + 2*e*x))/(2*e)] + I*Sinh[a + (b*(-d + Sqrt[d^2 - 4*c*e]))/(2*e)]*SinIntegral[((I/2)*b*(-d + Sqrt[d^2 - 4*c*e]))/e - I*b*x])/Sqrt[d^2 - 4*c*e]","C",0