1,1,70,0,0.0808843,"\int \left(a+b \text{sech}^2(c+d x)\right) \sinh ^4(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)*Sinh[c + d*x]^4,x]","-\frac{(5 a-4 b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{3}{8} x (a-4 b)+\frac{a \sinh (c+d x) \cosh ^3(c+d x)}{4 d}+\frac{b \tanh (c+d x)}{d}","-\frac{(5 a-4 b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{3}{8} x (a-4 b)+\frac{a \sinh (c+d x) \cosh ^3(c+d x)}{4 d}+\frac{b \tanh (c+d x)}{d}",1,"(3*(a - 4*b)*x)/8 - ((5*a - 4*b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (a*Cosh[c + d*x]^3*Sinh[c + d*x])/(4*d) + (b*Tanh[c + d*x])/d","A",5,5,21,0.2381,1,"{4132, 455, 1157, 388, 206}"
2,1,44,0,0.0560561,"\int \left(a+b \text{sech}^2(c+d x)\right) \sinh ^3(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)*Sinh[c + d*x]^3,x]","-\frac{(a-b) \cosh (c+d x)}{d}+\frac{a \cosh ^3(c+d x)}{3 d}+\frac{b \text{sech}(c+d x)}{d}","-\frac{(a-b) \cosh (c+d x)}{d}+\frac{a \cosh ^3(c+d x)}{3 d}+\frac{b \text{sech}(c+d x)}{d}",1,"-(((a - b)*Cosh[c + d*x])/d) + (a*Cosh[c + d*x]^3)/(3*d) + (b*Sech[c + d*x])/d","A",3,2,21,0.09524,1,"{4133, 448}"
3,1,43,0,0.0561302,"\int \left(a+b \text{sech}^2(c+d x)\right) \sinh ^2(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)*Sinh[c + d*x]^2,x]","-\frac{1}{2} x (a-2 b)+\frac{a \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{b \tanh (c+d x)}{d}","-\frac{1}{2} x (a-2 b)+\frac{a \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{b \tanh (c+d x)}{d}",1,"-((a - 2*b)*x)/2 + (a*Cosh[c + d*x]*Sinh[c + d*x])/(2*d) - (b*Tanh[c + d*x])/d","A",4,4,21,0.1905,1,"{4132, 455, 388, 206}"
4,1,24,0,0.0326643,"\int \left(a+b \text{sech}^2(c+d x)\right) \sinh (c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)*Sinh[c + d*x],x]","\frac{a \cosh (c+d x)}{d}-\frac{b \text{sech}(c+d x)}{d}","\frac{a \cosh (c+d x)}{d}-\frac{b \text{sech}(c+d x)}{d}",1,"(a*Cosh[c + d*x])/d - (b*Sech[c + d*x])/d","A",3,2,19,0.1053,1,"{4133, 14}"
5,1,27,0,0.044651,"\int \text{csch}(c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Csch[c + d*x]*(a + b*Sech[c + d*x]^2),x]","\frac{b \text{sech}(c+d x)}{d}-\frac{(a+b) \tanh ^{-1}(\cosh (c+d x))}{d}","\frac{b \text{sech}(c+d x)}{d}-\frac{(a+b) \tanh ^{-1}(\cosh (c+d x))}{d}",1,"-(((a + b)*ArcTanh[Cosh[c + d*x]])/d) + (b*Sech[c + d*x])/d","A",3,3,19,0.1579,1,"{4133, 453, 206}"
6,1,27,0,0.0460427,"\int \text{csch}^2(c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Csch[c + d*x]^2*(a + b*Sech[c + d*x]^2),x]","-\frac{(a+b) \coth (c+d x)}{d}-\frac{b \tanh (c+d x)}{d}","-\frac{(a+b) \coth (c+d x)}{d}-\frac{b \tanh (c+d x)}{d}",1,"-(((a + b)*Coth[c + d*x])/d) - (b*Tanh[c + d*x])/d","A",3,2,21,0.09524,1,"{4132, 14}"
7,1,54,0,0.0713326,"\int \text{csch}^3(c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Csch[c + d*x]^3*(a + b*Sech[c + d*x]^2),x]","\frac{(a+3 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{(a+b) \coth (c+d x) \text{csch}(c+d x)}{2 d}-\frac{b \text{sech}(c+d x)}{d}","\frac{(a+3 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{(a+b) \coth (c+d x) \text{csch}(c+d x)}{2 d}-\frac{b \text{sech}(c+d x)}{d}",1,"((a + 3*b)*ArcTanh[Cosh[c + d*x]])/(2*d) - ((a + b)*Coth[c + d*x]*Csch[c + d*x])/(2*d) - (b*Sech[c + d*x])/d","A",4,4,21,0.1905,1,"{4133, 456, 453, 206}"
8,1,45,0,0.0579728,"\int \text{csch}^4(c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Csch[c + d*x]^4*(a + b*Sech[c + d*x]^2),x]","-\frac{(a+b) \coth ^3(c+d x)}{3 d}+\frac{(a+2 b) \coth (c+d x)}{d}+\frac{b \tanh (c+d x)}{d}","-\frac{(a+b) \coth ^3(c+d x)}{3 d}+\frac{(a+2 b) \coth (c+d x)}{d}+\frac{b \tanh (c+d x)}{d}",1,"((a + 2*b)*Coth[c + d*x])/d - ((a + b)*Coth[c + d*x]^3)/(3*d) + (b*Tanh[c + d*x])/d","A",3,2,21,0.09524,1,"{4132, 448}"
9,1,114,0,0.1383741,"\int \left(a+b \text{sech}^2(c+d x)\right)^2 \sinh ^4(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)^2*Sinh[c + d*x]^4,x]","-\frac{\left(a^2-8 a b+4 b^2\right) \tanh (c+d x)}{4 d}+\frac{1}{8} x \left(3 a^2-24 a b+8 b^2\right)+\frac{a^2 \sinh ^4(c+d x) \tanh (c+d x)}{4 d}-\frac{a (a-8 b) \sinh (c+d x) \cosh (c+d x)}{8 d}-\frac{b^2 \tanh ^3(c+d x)}{3 d}","-\frac{\left(a^2-8 a b+4 b^2\right) \tanh (c+d x)}{4 d}+\frac{1}{8} x \left(3 a^2-24 a b+8 b^2\right)+\frac{a^2 \sinh ^4(c+d x) \tanh (c+d x)}{4 d}-\frac{a (a-8 b) \sinh (c+d x) \cosh (c+d x)}{8 d}-\frac{b^2 \tanh ^3(c+d x)}{3 d}",1,"((3*a^2 - 24*a*b + 8*b^2)*x)/8 - (a*(a - 8*b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) - ((a^2 - 8*a*b + 4*b^2)*Tanh[c + d*x])/(4*d) + (a^2*Sinh[c + d*x]^4*Tanh[c + d*x])/(4*d) - (b^2*Tanh[c + d*x]^3)/(3*d)","A",6,5,23,0.2174,1,"{4132, 463, 455, 1153, 206}"
10,1,72,0,0.0865373,"\int \left(a+b \text{sech}^2(c+d x)\right)^2 \sinh ^3(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)^2*Sinh[c + d*x]^3,x]","\frac{a^2 \cosh ^3(c+d x)}{3 d}-\frac{a (a-2 b) \cosh (c+d x)}{d}+\frac{b (2 a-b) \text{sech}(c+d x)}{d}+\frac{b^2 \text{sech}^3(c+d x)}{3 d}","\frac{a^2 \cosh ^3(c+d x)}{3 d}-\frac{a (a-2 b) \cosh (c+d x)}{d}+\frac{b (2 a-b) \text{sech}(c+d x)}{d}+\frac{b^2 \text{sech}^3(c+d x)}{3 d}",1,"-((a*(a - 2*b)*Cosh[c + d*x])/d) + (a^2*Cosh[c + d*x]^3)/(3*d) + ((2*a - b)*b*Sech[c + d*x])/d + (b^2*Sech[c + d*x]^3)/(3*d)","A",3,2,23,0.08696,1,"{4133, 448}"
11,1,73,0,0.1074279,"\int \left(a+b \text{sech}^2(c+d x)\right)^2 \sinh ^2(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)^2*Sinh[c + d*x]^2,x]","\frac{a^2 \sinh ^2(c+d x) \tanh (c+d x)}{2 d}+\frac{a (a-4 b) \tanh (c+d x)}{2 d}-\frac{1}{2} a x (a-4 b)+\frac{b^2 \tanh ^3(c+d x)}{3 d}","\frac{a^2 \sinh ^2(c+d x) \tanh (c+d x)}{2 d}+\frac{a (a-4 b) \tanh (c+d x)}{2 d}-\frac{1}{2} a x (a-4 b)+\frac{b^2 \tanh ^3(c+d x)}{3 d}",1,"-(a*(a - 4*b)*x)/2 + (a*(a - 4*b)*Tanh[c + d*x])/(2*d) + (a^2*Sinh[c + d*x]^2*Tanh[c + d*x])/(2*d) + (b^2*Tanh[c + d*x]^3)/(3*d)","A",5,5,23,0.2174,1,"{4132, 463, 459, 321, 206}"
12,1,45,0,0.0457674,"\int \left(a+b \text{sech}^2(c+d x)\right)^2 \sinh (c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)^2*Sinh[c + d*x],x]","\frac{a^2 \cosh (c+d x)}{d}-\frac{2 a b \text{sech}(c+d x)}{d}-\frac{b^2 \text{sech}^3(c+d x)}{3 d}","\frac{a^2 \cosh (c+d x)}{d}-\frac{2 a b \text{sech}(c+d x)}{d}-\frac{b^2 \text{sech}^3(c+d x)}{3 d}",1,"(a^2*Cosh[c + d*x])/d - (2*a*b*Sech[c + d*x])/d - (b^2*Sech[c + d*x]^3)/(3*d)","A",3,2,21,0.09524,1,"{4133, 270}"
13,1,52,0,0.0771389,"\int \text{csch}(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]*(a + b*Sech[c + d*x]^2)^2,x]","\frac{b (2 a+b) \text{sech}(c+d x)}{d}-\frac{(a+b)^2 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b^2 \text{sech}^3(c+d x)}{3 d}","\frac{b (2 a+b) \text{sech}(c+d x)}{d}-\frac{(a+b)^2 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b^2 \text{sech}^3(c+d x)}{3 d}",1,"-(((a + b)^2*ArcTanh[Cosh[c + d*x]])/d) + (b*(2*a + b)*Sech[c + d*x])/d + (b^2*Sech[c + d*x]^3)/(3*d)","A",4,3,21,0.1429,1,"{4133, 461, 207}"
14,1,50,0,0.0622623,"\int \text{csch}^2(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^2*(a + b*Sech[c + d*x]^2)^2,x]","-\frac{2 b (a+b) \tanh (c+d x)}{d}-\frac{(a+b)^2 \coth (c+d x)}{d}+\frac{b^2 \tanh ^3(c+d x)}{3 d}","-\frac{2 b (a+b) \tanh (c+d x)}{d}-\frac{(a+b)^2 \coth (c+d x)}{d}+\frac{b^2 \tanh ^3(c+d x)}{3 d}",1,"-(((a + b)^2*Coth[c + d*x])/d) - (2*b*(a + b)*Tanh[c + d*x])/d + (b^2*Tanh[c + d*x]^3)/(3*d)","A",3,2,23,0.08696,1,"{4132, 270}"
15,1,104,0,0.1357151,"\int \text{csch}^3(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^3*(a + b*Sech[c + d*x]^2)^2,x]","-\frac{\left(3 a^2+6 a b+5 b^2\right) \coth (c+d x) \text{csch}(c+d x)}{6 d}-\frac{b (6 a+5 b) \text{sech}(c+d x)}{3 d}+\frac{(a+b) (a+5 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}+\frac{b^2 \text{csch}^2(c+d x) \text{sech}^3(c+d x)}{3 d}","-\frac{\left(3 a^2+6 a b+5 b^2\right) \coth (c+d x) \text{csch}(c+d x)}{6 d}-\frac{b (6 a+5 b) \text{sech}(c+d x)}{3 d}+\frac{(a+b) (a+5 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}+\frac{b^2 \text{csch}^2(c+d x) \text{sech}^3(c+d x)}{3 d}",1,"((a + b)*(a + 5*b)*ArcTanh[Cosh[c + d*x]])/(2*d) - ((3*a^2 + 6*a*b + 5*b^2)*Coth[c + d*x]*Csch[c + d*x])/(6*d) - (b*(6*a + 5*b)*Sech[c + d*x])/(3*d) + (b^2*Csch[c + d*x]^2*Sech[c + d*x]^3)/(3*d)","A",5,5,23,0.2174,1,"{4133, 462, 456, 453, 206}"
16,1,75,0,0.083351,"\int \text{csch}^4(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^4*(a + b*Sech[c + d*x]^2)^2,x]","\frac{b (2 a+3 b) \tanh (c+d x)}{d}-\frac{(a+b)^2 \coth ^3(c+d x)}{3 d}+\frac{(a+b) (a+3 b) \coth (c+d x)}{d}-\frac{b^2 \tanh ^3(c+d x)}{3 d}","\frac{b (2 a+3 b) \tanh (c+d x)}{d}-\frac{(a+b)^2 \coth ^3(c+d x)}{3 d}+\frac{(a+b) (a+3 b) \coth (c+d x)}{d}-\frac{b^2 \tanh ^3(c+d x)}{3 d}",1,"((a + b)*(a + 3*b)*Coth[c + d*x])/d - ((a + b)^2*Coth[c + d*x]^3)/(3*d) + (b*(2*a + 3*b)*Tanh[c + d*x])/d - (b^2*Tanh[c + d*x]^3)/(3*d)","A",3,2,23,0.08696,1,"{4132, 448}"
17,1,182,0,0.2315558,"\int \left(a+b \text{sech}^2(c+d x)\right)^3 \sinh ^4(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)^3*Sinh[c + d*x]^4,x]","\frac{b \left(6 a^2-23 a b-8 b^2\right) \tanh ^3(c+d x)}{8 d}-\frac{3 a \left(a^2-12 a b+8 b^2\right) \tanh (c+d x)}{8 d}+\frac{3}{8} a x \left(a^2-12 a b+8 b^2\right)-\frac{3 b^2 (5 a-16 b) \tanh ^5(c+d x)}{40 d}-\frac{3 (a-2 b) \sinh ^2(c+d x) \tanh (c+d x) \left(a-b \tanh ^2(c+d x)+b\right)^2}{8 d}+\frac{\sinh ^3(c+d x) \cosh (c+d x) \left(a-b \tanh ^2(c+d x)+b\right)^3}{4 d}","\frac{b \left(6 a^2-23 a b-8 b^2\right) \tanh ^3(c+d x)}{8 d}-\frac{3 a \left(a^2-12 a b+8 b^2\right) \tanh (c+d x)}{8 d}+\frac{3}{8} a x \left(a^2-12 a b+8 b^2\right)-\frac{3 b^2 (5 a-16 b) \tanh ^5(c+d x)}{40 d}-\frac{3 (a-2 b) \sinh ^2(c+d x) \tanh (c+d x) \left(a-b \tanh ^2(c+d x)+b\right)^2}{8 d}+\frac{\sinh ^3(c+d x) \cosh (c+d x) \left(a-b \tanh ^2(c+d x)+b\right)^3}{4 d}",1,"(3*a*(a^2 - 12*a*b + 8*b^2)*x)/8 - (3*a*(a^2 - 12*a*b + 8*b^2)*Tanh[c + d*x])/(8*d) + (b*(6*a^2 - 23*a*b - 8*b^2)*Tanh[c + d*x]^3)/(8*d) - (3*(5*a - 16*b)*b^2*Tanh[c + d*x]^5)/(40*d) - (3*(a - 2*b)*Sinh[c + d*x]^2*Tanh[c + d*x]*(a + b - b*Tanh[c + d*x]^2)^2)/(8*d) + (Cosh[c + d*x]*Sinh[c + d*x]^3*(a + b - b*Tanh[c + d*x]^2)^3)/(4*d)","A",6,5,23,0.2174,1,"{4132, 467, 577, 570, 206}"
18,1,99,0,0.1107055,"\int \left(a+b \text{sech}^2(c+d x)\right)^3 \sinh ^3(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)^3*Sinh[c + d*x]^3,x]","-\frac{a^2 (a-3 b) \cosh (c+d x)}{d}+\frac{a^3 \cosh ^3(c+d x)}{3 d}+\frac{b^2 (3 a-b) \text{sech}^3(c+d x)}{3 d}+\frac{3 a b (a-b) \text{sech}(c+d x)}{d}+\frac{b^3 \text{sech}^5(c+d x)}{5 d}","-\frac{a^2 (a-3 b) \cosh (c+d x)}{d}+\frac{a^3 \cosh ^3(c+d x)}{3 d}+\frac{b^2 (3 a-b) \text{sech}^3(c+d x)}{3 d}+\frac{3 a b (a-b) \text{sech}(c+d x)}{d}+\frac{b^3 \text{sech}^5(c+d x)}{5 d}",1,"-((a^2*(a - 3*b)*Cosh[c + d*x])/d) + (a^3*Cosh[c + d*x]^3)/(3*d) + (3*a*(a - b)*b*Sech[c + d*x])/d + ((3*a - b)*b^2*Sech[c + d*x]^3)/(3*d) + (b^3*Sech[c + d*x]^5)/(5*d)","A",3,2,23,0.08696,1,"{4133, 448}"
19,1,143,0,0.1927418,"\int \left(a+b \text{sech}^2(c+d x)\right)^3 \sinh ^2(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)^3*Sinh[c + d*x]^2,x]","-\frac{b \left(81 a^2-28 a b-4 b^2\right) \tanh (c+d x)}{30 d}-\frac{1}{2} a^2 x (a-6 b)-\frac{7 b \tanh (c+d x) \left(a-b \tanh ^2(c+d x)+b\right)^2}{10 d}-\frac{b (33 a-2 b) \tanh (c+d x) \left(a-b \tanh ^2(c+d x)+b\right)}{30 d}+\frac{\sinh (c+d x) \cosh (c+d x) \left(a-b \tanh ^2(c+d x)+b\right)^3}{2 d}","-\frac{3 a^2 b \tanh (c+d x)}{d}-\frac{1}{2} a^2 x (a-6 b)+\frac{a^3}{4 d (1-\tanh (c+d x))}-\frac{a^3}{4 d (\tanh (c+d x)+1)}+\frac{b^2 (3 a+b) \tanh ^3(c+d x)}{3 d}-\frac{b^3 \tanh ^5(c+d x)}{5 d}",1,"-(a^2*(a - 6*b)*x)/2 - (b*(81*a^2 - 28*a*b - 4*b^2)*Tanh[c + d*x])/(30*d) - ((33*a - 2*b)*b*Tanh[c + d*x]*(a + b - b*Tanh[c + d*x]^2))/(30*d) - (7*b*Tanh[c + d*x]*(a + b - b*Tanh[c + d*x]^2)^2)/(10*d) + (Cosh[c + d*x]*Sinh[c + d*x]*(a + b - b*Tanh[c + d*x]^2)^3)/(2*d)","A",6,5,23,0.2174,1,"{4132, 467, 528, 388, 206}"
20,1,64,0,0.0592691,"\int \left(a+b \text{sech}^2(c+d x)\right)^3 \sinh (c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)^3*Sinh[c + d*x],x]","-\frac{3 a^2 b \text{sech}(c+d x)}{d}+\frac{a^3 \cosh (c+d x)}{d}-\frac{a b^2 \text{sech}^3(c+d x)}{d}-\frac{b^3 \text{sech}^5(c+d x)}{5 d}","-\frac{3 a^2 b \text{sech}(c+d x)}{d}+\frac{a^3 \cosh (c+d x)}{d}-\frac{a b^2 \text{sech}^3(c+d x)}{d}-\frac{b^3 \text{sech}^5(c+d x)}{5 d}",1,"(a^3*Cosh[c + d*x])/d - (3*a^2*b*Sech[c + d*x])/d - (a*b^2*Sech[c + d*x]^3)/d - (b^3*Sech[c + d*x]^5)/(5*d)","A",3,2,21,0.09524,1,"{4133, 270}"
21,1,83,0,0.1003298,"\int \text{csch}(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]*(a + b*Sech[c + d*x]^2)^3,x]","\frac{b \left(3 a^2+3 a b+b^2\right) \text{sech}(c+d x)}{d}+\frac{b^2 (3 a+b) \text{sech}^3(c+d x)}{3 d}-\frac{(a+b)^3 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b^3 \text{sech}^5(c+d x)}{5 d}","\frac{b \left(3 a^2+3 a b+b^2\right) \text{sech}(c+d x)}{d}+\frac{b^2 (3 a+b) \text{sech}^3(c+d x)}{3 d}-\frac{(a+b)^3 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b^3 \text{sech}^5(c+d x)}{5 d}",1,"-(((a + b)^3*ArcTanh[Cosh[c + d*x]])/d) + (b*(3*a^2 + 3*a*b + b^2)*Sech[c + d*x])/d + (b^2*(3*a + b)*Sech[c + d*x]^3)/(3*d) + (b^3*Sech[c + d*x]^5)/(5*d)","A",4,3,21,0.1429,1,"{4133, 461, 207}"
22,1,70,0,0.0734432,"\int \text{csch}^2(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^2*(a + b*Sech[c + d*x]^2)^3,x]","\frac{b^2 (a+b) \tanh ^3(c+d x)}{d}-\frac{3 b (a+b)^2 \tanh (c+d x)}{d}-\frac{(a+b)^3 \coth (c+d x)}{d}-\frac{b^3 \tanh ^5(c+d x)}{5 d}","\frac{b^2 (a+b) \tanh ^3(c+d x)}{d}-\frac{3 b (a+b)^2 \tanh (c+d x)}{d}-\frac{(a+b)^3 \coth (c+d x)}{d}-\frac{b^3 \tanh ^5(c+d x)}{5 d}",1,"-(((a + b)^3*Coth[c + d*x])/d) - (3*b*(a + b)^2*Tanh[c + d*x])/d + (b^2*(a + b)*Tanh[c + d*x]^3)/d - (b^3*Tanh[c + d*x]^5)/(5*d)","A",3,2,23,0.08696,1,"{4132, 270}"
23,1,144,0,0.1782483,"\int \text{csch}^3(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^3*(a + b*Sech[c + d*x]^2)^3,x]","-\frac{b \left(6 a^2+15 a b+7 b^2\right) \text{sech}^3(c+d x)}{6 d}-\frac{b^2 (5 a+7 b) \text{sech}^5(c+d x)}{10 d}-\frac{(a+b)^2 (a+7 b) \text{sech}(c+d x)}{2 d}+\frac{(a+b)^2 (a+7 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{(a+b) \text{csch}^2(c+d x) \text{sech}^5(c+d x) \left(a \cosh ^2(c+d x)+b\right)^2}{2 d}","-\frac{b \left(6 a^2+15 a b+7 b^2\right) \text{sech}^3(c+d x)}{6 d}-\frac{b^2 (5 a+7 b) \text{sech}^5(c+d x)}{10 d}-\frac{(a+b)^2 (a+7 b) \text{sech}(c+d x)}{2 d}+\frac{(a+b)^2 (a+7 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{(a+b) \text{csch}^2(c+d x) \text{sech}^5(c+d x) \left(a \cosh ^2(c+d x)+b\right)^2}{2 d}",1,"((a + b)^2*(a + 7*b)*ArcTanh[Cosh[c + d*x]])/(2*d) - ((a + b)^2*(a + 7*b)*Sech[c + d*x])/(2*d) - (b*(6*a^2 + 15*a*b + 7*b^2)*Sech[c + d*x]^3)/(6*d) - (b^2*(5*a + 7*b)*Sech[c + d*x]^5)/(10*d) - ((a + b)*(b + a*Cosh[c + d*x]^2)^2*Csch[c + d*x]^2*Sech[c + d*x]^5)/(2*d)","A",5,4,23,0.1739,1,"{4133, 468, 570, 207}"
24,1,104,0,0.1050493,"\int \text{csch}^4(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^4*(a + b*Sech[c + d*x]^2)^3,x]","-\frac{b^2 (3 a+4 b) \tanh ^3(c+d x)}{3 d}+\frac{3 b (a+b) (a+2 b) \tanh (c+d x)}{d}-\frac{(a+b)^3 \coth ^3(c+d x)}{3 d}+\frac{(a+b)^2 (a+4 b) \coth (c+d x)}{d}+\frac{b^3 \tanh ^5(c+d x)}{5 d}","-\frac{b^2 (3 a+4 b) \tanh ^3(c+d x)}{3 d}+\frac{3 b (a+b) (a+2 b) \tanh (c+d x)}{d}-\frac{(a+b)^3 \coth ^3(c+d x)}{3 d}+\frac{(a+b)^2 (a+4 b) \coth (c+d x)}{d}+\frac{b^3 \tanh ^5(c+d x)}{5 d}",1,"((a + b)^2*(a + 4*b)*Coth[c + d*x])/d - ((a + b)^3*Coth[c + d*x]^3)/(3*d) + (3*b*(a + b)*(a + 2*b)*Tanh[c + d*x])/d - (b^2*(3*a + 4*b)*Tanh[c + d*x]^3)/(3*d) + (b^3*Tanh[c + d*x]^5)/(5*d)","A",3,2,23,0.08696,1,"{4132, 448}"
25,1,117,0,0.1955114,"\int \frac{\sinh ^4(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Sinh[c + d*x]^4/(a + b*Sech[c + d*x]^2),x]","\frac{x \left(3 a^2+12 a b+8 b^2\right)}{8 a^3}-\frac{\sqrt{b} (a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a^3 d}-\frac{(5 a+4 b) \sinh (c+d x) \cosh (c+d x)}{8 a^2 d}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 a d}","\frac{x \left(3 a^2+12 a b+8 b^2\right)}{8 a^3}-\frac{\sqrt{b} (a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a^3 d}-\frac{(5 a+4 b) \sinh (c+d x) \cosh (c+d x)}{8 a^2 d}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 a d}",1,"((3*a^2 + 12*a*b + 8*b^2)*x)/(8*a^3) - (Sqrt[b]*(a + b)^(3/2)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(a^3*d) - ((5*a + 4*b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*a^2*d) + (Cosh[c + d*x]^3*Sinh[c + d*x])/(4*a*d)","A",6,6,23,0.2609,1,"{4132, 470, 527, 522, 206, 208}"
26,1,71,0,0.1046803,"\int \frac{\sinh ^3(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Sinh[c + d*x]^3/(a + b*Sech[c + d*x]^2),x]","-\frac{(a+b) \cosh (c+d x)}{a^2 d}+\frac{\sqrt{b} (a+b) \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{a^{5/2} d}+\frac{\cosh ^3(c+d x)}{3 a d}","-\frac{(a+b) \cosh (c+d x)}{a^2 d}+\frac{\sqrt{b} (a+b) \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{a^{5/2} d}+\frac{\cosh ^3(c+d x)}{3 a d}",1,"(Sqrt[b]*(a + b)*ArcTan[(Sqrt[a]*Cosh[c + d*x])/Sqrt[b]])/(a^(5/2)*d) - ((a + b)*Cosh[c + d*x])/(a^2*d) + Cosh[c + d*x]^3/(3*a*d)","A",4,4,23,0.1739,1,"{4133, 459, 321, 205}"
27,1,75,0,0.1104282,"\int \frac{\sinh ^2(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Sinh[c + d*x]^2/(a + b*Sech[c + d*x]^2),x]","\frac{\sqrt{b} \sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a^2 d}-\frac{x (a+2 b)}{2 a^2}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 a d}","\frac{\sqrt{b} \sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a^2 d}-\frac{x (a+2 b)}{2 a^2}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 a d}",1,"-((a + 2*b)*x)/(2*a^2) + (Sqrt[b]*Sqrt[a + b]*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(a^2*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*a*d)","A",5,5,23,0.2174,1,"{4132, 471, 522, 206, 208}"
28,1,47,0,0.0484901,"\int \frac{\sinh (c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Sinh[c + d*x]/(a + b*Sech[c + d*x]^2),x]","\frac{\cosh (c+d x)}{a d}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{a^{3/2} d}","\frac{\cosh (c+d x)}{a d}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{a^{3/2} d}",1,"-((Sqrt[b]*ArcTan[(Sqrt[a]*Cosh[c + d*x])/Sqrt[b]])/(a^(3/2)*d)) + Cosh[c + d*x]/(a*d)","A",3,3,21,0.1429,1,"{4133, 321, 205}"
29,1,55,0,0.081834,"\int \frac{\text{csch}(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Csch[c + d*x]/(a + b*Sech[c + d*x]^2),x]","\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{\sqrt{a} d (a+b)}-\frac{\tanh ^{-1}(\cosh (c+d x))}{d (a+b)}","\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{\sqrt{a} d (a+b)}-\frac{\tanh ^{-1}(\cosh (c+d x))}{d (a+b)}",1,"(Sqrt[b]*ArcTan[(Sqrt[a]*Cosh[c + d*x])/Sqrt[b]])/(Sqrt[a]*(a + b)*d) - ArcTanh[Cosh[c + d*x]]/((a + b)*d)","A",4,4,21,0.1905,1,"{4133, 481, 206, 205}"
30,1,53,0,0.0709458,"\int \frac{\text{csch}^2(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Csch[c + d*x]^2/(a + b*Sech[c + d*x]^2),x]","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{d (a+b)^{3/2}}-\frac{\coth (c+d x)}{d (a+b)}","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{d (a+b)^{3/2}}-\frac{\coth (c+d x)}{d (a+b)}",1,"(Sqrt[b]*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/((a + b)^(3/2)*d) - Coth[c + d*x]/((a + b)*d)","A",3,3,23,0.1304,1,"{4132, 325, 208}"
31,1,87,0,0.1184096,"\int \frac{\text{csch}^3(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Csch[c + d*x]^3/(a + b*Sech[c + d*x]^2),x]","-\frac{\sqrt{a} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{d (a+b)^2}+\frac{(a-b) \tanh ^{-1}(\cosh (c+d x))}{2 d (a+b)^2}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 d (a+b)}","-\frac{\sqrt{a} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{d (a+b)^2}+\frac{(a-b) \tanh ^{-1}(\cosh (c+d x))}{2 d (a+b)^2}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 d (a+b)}",1,"-((Sqrt[a]*Sqrt[b]*ArcTan[(Sqrt[a]*Cosh[c + d*x])/Sqrt[b]])/((a + b)^2*d)) + ((a - b)*ArcTanh[Cosh[c + d*x]])/(2*(a + b)^2*d) - (Coth[c + d*x]*Csch[c + d*x])/(2*(a + b)*d)","A",5,5,23,0.2174,1,"{4133, 471, 522, 206, 205}"
32,1,75,0,0.0989715,"\int \frac{\text{csch}^4(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Csch[c + d*x]^4/(a + b*Sech[c + d*x]^2),x]","-\frac{a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{d (a+b)^{5/2}}-\frac{\coth ^3(c+d x)}{3 d (a+b)}+\frac{a \coth (c+d x)}{d (a+b)^2}","-\frac{a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{d (a+b)^{5/2}}-\frac{\coth ^3(c+d x)}{3 d (a+b)}+\frac{a \coth (c+d x)}{d (a+b)^2}",1,"-((a*Sqrt[b]*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/((a + b)^(5/2)*d)) + (a*Coth[c + d*x])/((a + b)^2*d) - Coth[c + d*x]^3/(3*(a + b)*d)","A",4,4,23,0.1739,1,"{4132, 453, 325, 208}"
33,1,194,0,0.2732753,"\int \frac{\sinh ^4(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^4/(a + b*Sech[c + d*x]^2)^2,x]","\frac{3 x \left(a^2+8 a b+8 b^2\right)}{8 a^4}-\frac{3 \sqrt{b} \sqrt{a+b} (a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 a^4 d}-\frac{3 b (3 a+4 b) \tanh (c+d x)}{8 a^3 d \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{(5 a+6 b) \sinh (c+d x) \cosh (c+d x)}{8 a^2 d \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 a d \left(a-b \tanh ^2(c+d x)+b\right)}","\frac{3 x \left(a^2+8 a b+8 b^2\right)}{8 a^4}-\frac{3 \sqrt{b} \sqrt{a+b} (a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 a^4 d}-\frac{3 b (3 a+4 b) \tanh (c+d x)}{8 a^3 d \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{(5 a+6 b) \sinh (c+d x) \cosh (c+d x)}{8 a^2 d \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 a d \left(a-b \tanh ^2(c+d x)+b\right)}",1,"(3*(a^2 + 8*a*b + 8*b^2)*x)/(8*a^4) - (3*Sqrt[b]*Sqrt[a + b]*(a + 2*b)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(2*a^4*d) - ((5*a + 6*b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*a^2*d*(a + b - b*Tanh[c + d*x]^2)) + (Cosh[c + d*x]^3*Sinh[c + d*x])/(4*a*d*(a + b - b*Tanh[c + d*x]^2)) - (3*b*(3*a + 4*b)*Tanh[c + d*x])/(8*a^3*d*(a + b - b*Tanh[c + d*x]^2))","A",7,6,23,0.2609,1,"{4132, 470, 527, 522, 206, 208}"
34,1,114,0,0.1442447,"\int \frac{\sinh ^3(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^3/(a + b*Sech[c + d*x]^2)^2,x]","-\frac{b (a+b) \cosh (c+d x)}{2 a^3 d \left(a \cosh ^2(c+d x)+b\right)}-\frac{(a+2 b) \cosh (c+d x)}{a^3 d}+\frac{\sqrt{b} (3 a+5 b) \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{2 a^{7/2} d}+\frac{\cosh ^3(c+d x)}{3 a^2 d}","-\frac{b (a+b) \cosh (c+d x)}{2 a^3 d \left(a \cosh ^2(c+d x)+b\right)}-\frac{(a+2 b) \cosh (c+d x)}{a^3 d}+\frac{\sqrt{b} (3 a+5 b) \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{2 a^{7/2} d}+\frac{\cosh ^3(c+d x)}{3 a^2 d}",1,"(Sqrt[b]*(3*a + 5*b)*ArcTan[(Sqrt[a]*Cosh[c + d*x])/Sqrt[b]])/(2*a^(7/2)*d) - ((a + 2*b)*Cosh[c + d*x])/(a^3*d) + Cosh[c + d*x]^3/(3*a^2*d) - (b*(a + b)*Cosh[c + d*x])/(2*a^3*d*(b + a*Cosh[c + d*x]^2))","A",5,4,23,0.1739,1,"{4133, 455, 1153, 205}"
35,1,131,0,0.1964695,"\int \frac{\sinh ^2(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^2/(a + b*Sech[c + d*x]^2)^2,x]","\frac{\sqrt{b} (3 a+4 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 a^3 d \sqrt{a+b}}+\frac{b \tanh (c+d x)}{a^2 d \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{x (a+4 b)}{2 a^3}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 a d \left(a-b \tanh ^2(c+d x)+b\right)}","\frac{\sqrt{b} (3 a+4 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 a^3 d \sqrt{a+b}}+\frac{b \tanh (c+d x)}{a^2 d \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{x (a+4 b)}{2 a^3}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 a d \left(a-b \tanh ^2(c+d x)+b\right)}",1,"-((a + 4*b)*x)/(2*a^3) + (Sqrt[b]*(3*a + 4*b)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(2*a^3*Sqrt[a + b]*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*a*d*(a + b - b*Tanh[c + d*x]^2)) + (b*Tanh[c + d*x])/(a^2*d*(a + b - b*Tanh[c + d*x]^2))","A",6,6,23,0.2609,1,"{4132, 471, 527, 522, 206, 208}"
36,1,84,0,0.0647587,"\int \frac{\sinh (c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]/(a + b*Sech[c + d*x]^2)^2,x]","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{2 a^{5/2} d}+\frac{3 \cosh (c+d x)}{2 a^2 d}-\frac{\cosh ^3(c+d x)}{2 a d \left(a \cosh ^2(c+d x)+b\right)}","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{2 a^{5/2} d}+\frac{3 \cosh (c+d x)}{2 a^2 d}-\frac{\cosh ^3(c+d x)}{2 a d \left(a \cosh ^2(c+d x)+b\right)}",1,"(-3*Sqrt[b]*ArcTan[(Sqrt[a]*Cosh[c + d*x])/Sqrt[b]])/(2*a^(5/2)*d) + (3*Cosh[c + d*x])/(2*a^2*d) - Cosh[c + d*x]^3/(2*a*d*(b + a*Cosh[c + d*x]^2))","A",4,4,21,0.1905,1,"{4133, 288, 321, 205}"
37,1,99,0,0.1299056,"\int \frac{\text{csch}(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Csch[c + d*x]/(a + b*Sech[c + d*x]^2)^2,x]","\frac{\sqrt{b} (3 a+b) \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{2 a^{3/2} d (a+b)^2}-\frac{b \cosh (c+d x)}{2 a d (a+b) \left(a \cosh ^2(c+d x)+b\right)}-\frac{\tanh ^{-1}(\cosh (c+d x))}{d (a+b)^2}","\frac{\sqrt{b} (3 a+b) \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{2 a^{3/2} d (a+b)^2}-\frac{b \cosh (c+d x)}{2 a d (a+b) \left(a \cosh ^2(c+d x)+b\right)}-\frac{\tanh ^{-1}(\cosh (c+d x))}{d (a+b)^2}",1,"(Sqrt[b]*(3*a + b)*ArcTan[(Sqrt[a]*Cosh[c + d*x])/Sqrt[b]])/(2*a^(3/2)*(a + b)^2*d) - ArcTanh[Cosh[c + d*x]]/((a + b)^2*d) - (b*Cosh[c + d*x])/(2*a*(a + b)*d*(b + a*Cosh[c + d*x]^2))","A",5,5,21,0.2381,1,"{4133, 470, 522, 206, 205}"
38,1,92,0,0.0844725,"\int \frac{\text{csch}^2(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Csch[c + d*x]^2/(a + b*Sech[c + d*x]^2)^2,x]","\frac{3 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 d (a+b)^{5/2}}-\frac{3 \coth (c+d x)}{2 d (a+b)^2}+\frac{\coth (c+d x)}{2 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}","\frac{3 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 d (a+b)^{5/2}}-\frac{3 \coth (c+d x)}{2 d (a+b)^2}+\frac{\coth (c+d x)}{2 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}",1,"(3*Sqrt[b]*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(2*(a + b)^(5/2)*d) - (3*Coth[c + d*x])/(2*(a + b)^2*d) + Coth[c + d*x]/(2*(a + b)*d*(a + b - b*Tanh[c + d*x]^2))","A",4,4,23,0.1739,1,"{4132, 290, 325, 208}"
39,1,147,0,0.2056583,"\int \frac{\text{csch}^3(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Csch[c + d*x]^3/(a + b*Sech[c + d*x]^2)^2,x]","-\frac{(a-b) \cosh (c+d x)}{2 d (a+b)^2 \left(a \cosh ^2(c+d x)+b\right)}-\frac{\sqrt{b} (3 a-b) \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{2 \sqrt{a} d (a+b)^3}+\frac{(a-3 b) \tanh ^{-1}(\cosh (c+d x))}{2 d (a+b)^3}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 d (a+b) \left(a \cosh ^2(c+d x)+b\right)}","-\frac{(a-b) \cosh (c+d x)}{2 d (a+b)^2 \left(a \cosh ^2(c+d x)+b\right)}-\frac{\sqrt{b} (3 a-b) \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{2 \sqrt{a} d (a+b)^3}+\frac{(a-3 b) \tanh ^{-1}(\cosh (c+d x))}{2 d (a+b)^3}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 d (a+b) \left(a \cosh ^2(c+d x)+b\right)}",1,"-((3*a - b)*Sqrt[b]*ArcTan[(Sqrt[a]*Cosh[c + d*x])/Sqrt[b]])/(2*Sqrt[a]*(a + b)^3*d) + ((a - 3*b)*ArcTanh[Cosh[c + d*x]])/(2*(a + b)^3*d) - ((a - b)*Cosh[c + d*x])/(2*(a + b)^2*d*(b + a*Cosh[c + d*x]^2)) - (Coth[c + d*x]*Csch[c + d*x])/(2*(a + b)*d*(b + a*Cosh[c + d*x]^2))","A",6,6,23,0.2609,1,"{4133, 470, 527, 522, 206, 205}"
40,1,123,0,0.1950587,"\int \frac{\text{csch}^4(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Csch[c + d*x]^4/(a + b*Sech[c + d*x]^2)^2,x]","-\frac{\sqrt{b} (3 a-2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 d (a+b)^{7/2}}-\frac{a b \tanh (c+d x)}{2 d (a+b)^3 \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{\coth ^3(c+d x)}{3 d (a+b)^2}+\frac{(a-b) \coth (c+d x)}{d (a+b)^3}","-\frac{\sqrt{b} (3 a-2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 d (a+b)^{7/2}}-\frac{a b \tanh (c+d x)}{2 d (a+b)^3 \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{\coth ^3(c+d x)}{3 d (a+b)^2}+\frac{(a-b) \coth (c+d x)}{d (a+b)^3}",1,"-((3*a - 2*b)*Sqrt[b]*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(2*(a + b)^(7/2)*d) + ((a - b)*Coth[c + d*x])/((a + b)^3*d) - Coth[c + d*x]^3/(3*(a + b)^2*d) - (a*b*Tanh[c + d*x])/(2*(a + b)^3*d*(a + b - b*Tanh[c + d*x]^2))","A",5,4,23,0.1739,1,"{4132, 456, 1261, 208}"
41,1,242,0,0.3991496,"\int \frac{\sinh ^4(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^4/(a + b*Sech[c + d*x]^2)^3,x]","-\frac{3 \sqrt{b} \left(5 a^2+20 a b+16 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^5 d \sqrt{a+b}}+\frac{3 x \left(a^2+12 a b+16 b^2\right)}{8 a^5}-\frac{3 b (a+2 b) \tanh (c+d x)}{2 a^4 d \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{b (7 a+12 b) \tanh (c+d x)}{8 a^3 d \left(a-b \tanh ^2(c+d x)+b\right)^2}-\frac{(5 a+8 b) \sinh (c+d x) \cosh (c+d x)}{8 a^2 d \left(a-b \tanh ^2(c+d x)+b\right)^2}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 a d \left(a-b \tanh ^2(c+d x)+b\right)^2}","-\frac{3 \sqrt{b} \left(5 a^2+20 a b+16 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^5 d \sqrt{a+b}}+\frac{3 x \left(a^2+12 a b+16 b^2\right)}{8 a^5}-\frac{3 b (a+2 b) \tanh (c+d x)}{2 a^4 d \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{b (7 a+12 b) \tanh (c+d x)}{8 a^3 d \left(a-b \tanh ^2(c+d x)+b\right)^2}-\frac{(5 a+8 b) \sinh (c+d x) \cosh (c+d x)}{8 a^2 d \left(a-b \tanh ^2(c+d x)+b\right)^2}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 a d \left(a-b \tanh ^2(c+d x)+b\right)^2}",1,"(3*(a^2 + 12*a*b + 16*b^2)*x)/(8*a^5) - (3*Sqrt[b]*(5*a^2 + 20*a*b + 16*b^2)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(8*a^5*Sqrt[a + b]*d) - ((5*a + 8*b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*a^2*d*(a + b - b*Tanh[c + d*x]^2)^2) + (Cosh[c + d*x]^3*Sinh[c + d*x])/(4*a*d*(a + b - b*Tanh[c + d*x]^2)^2) - (b*(7*a + 12*b)*Tanh[c + d*x])/(8*a^3*d*(a + b - b*Tanh[c + d*x]^2)^2) - (3*b*(a + 2*b)*Tanh[c + d*x])/(2*a^4*d*(a + b - b*Tanh[c + d*x]^2))","A",8,6,23,0.2609,1,"{4132, 470, 527, 522, 206, 208}"
42,1,154,0,0.2179894,"\int \frac{\sinh ^3(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^3/(a + b*Sech[c + d*x]^2)^3,x]","\frac{b^2 (a+b) \cosh (c+d x)}{4 a^4 d \left(a \cosh ^2(c+d x)+b\right)^2}-\frac{b (9 a+13 b) \cosh (c+d x)}{8 a^4 d \left(a \cosh ^2(c+d x)+b\right)}-\frac{(a+3 b) \cosh (c+d x)}{a^4 d}+\frac{5 \sqrt{b} (3 a+7 b) \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{8 a^{9/2} d}+\frac{\cosh ^3(c+d x)}{3 a^3 d}","\frac{b^2 (a+b) \cosh (c+d x)}{4 a^4 d \left(a \cosh ^2(c+d x)+b\right)^2}-\frac{b (9 a+13 b) \cosh (c+d x)}{8 a^4 d \left(a \cosh ^2(c+d x)+b\right)}-\frac{(a+3 b) \cosh (c+d x)}{a^4 d}+\frac{5 \sqrt{b} (3 a+7 b) \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{8 a^{9/2} d}+\frac{\cosh ^3(c+d x)}{3 a^3 d}",1,"(5*Sqrt[b]*(3*a + 7*b)*ArcTan[(Sqrt[a]*Cosh[c + d*x])/Sqrt[b]])/(8*a^(9/2)*d) - ((a + 3*b)*Cosh[c + d*x])/(a^4*d) + Cosh[c + d*x]^3/(3*a^3*d) + (b^2*(a + b)*Cosh[c + d*x])/(4*a^4*d*(b + a*Cosh[c + d*x]^2)^2) - (b*(9*a + 13*b)*Cosh[c + d*x])/(8*a^4*d*(b + a*Cosh[c + d*x]^2))","A",6,5,23,0.2174,1,"{4133, 455, 1814, 1153, 205}"
43,1,187,0,0.2917619,"\int \frac{\sinh ^2(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^2/(a + b*Sech[c + d*x]^2)^3,x]","\frac{\sqrt{b} \left(15 a^2+40 a b+24 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^4 d (a+b)^{3/2}}+\frac{b (11 a+12 b) \tanh (c+d x)}{8 a^3 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{3 b \tanh (c+d x)}{4 a^2 d \left(a-b \tanh ^2(c+d x)+b\right)^2}-\frac{x (a+6 b)}{2 a^4}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 a d \left(a-b \tanh ^2(c+d x)+b\right)^2}","\frac{\sqrt{b} \left(15 a^2+40 a b+24 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^4 d (a+b)^{3/2}}+\frac{b (11 a+12 b) \tanh (c+d x)}{8 a^3 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{3 b \tanh (c+d x)}{4 a^2 d \left(a-b \tanh ^2(c+d x)+b\right)^2}-\frac{x (a+6 b)}{2 a^4}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 a d \left(a-b \tanh ^2(c+d x)+b\right)^2}",1,"-((a + 6*b)*x)/(2*a^4) + (Sqrt[b]*(15*a^2 + 40*a*b + 24*b^2)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(8*a^4*(a + b)^(3/2)*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*a*d*(a + b - b*Tanh[c + d*x]^2)^2) + (3*b*Tanh[c + d*x])/(4*a^2*d*(a + b - b*Tanh[c + d*x]^2)^2) + (b*(11*a + 12*b)*Tanh[c + d*x])/(8*a^3*(a + b)*d*(a + b - b*Tanh[c + d*x]^2))","A",7,6,23,0.2609,1,"{4132, 471, 527, 522, 206, 208}"
44,1,116,0,0.0841521,"\int \frac{\sinh (c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]/(a + b*Sech[c + d*x]^2)^3,x]","-\frac{5 \cosh ^3(c+d x)}{8 a^2 d \left(a \cosh ^2(c+d x)+b\right)}-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{8 a^{7/2} d}+\frac{15 \cosh (c+d x)}{8 a^3 d}-\frac{\cosh ^5(c+d x)}{4 a d \left(a \cosh ^2(c+d x)+b\right)^2}","-\frac{5 \cosh ^3(c+d x)}{8 a^2 d \left(a \cosh ^2(c+d x)+b\right)}-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{8 a^{7/2} d}+\frac{15 \cosh (c+d x)}{8 a^3 d}-\frac{\cosh ^5(c+d x)}{4 a d \left(a \cosh ^2(c+d x)+b\right)^2}",1,"(-15*Sqrt[b]*ArcTan[(Sqrt[a]*Cosh[c + d*x])/Sqrt[b]])/(8*a^(7/2)*d) + (15*Cosh[c + d*x])/(8*a^3*d) - Cosh[c + d*x]^5/(4*a*d*(b + a*Cosh[c + d*x]^2)^2) - (5*Cosh[c + d*x]^3)/(8*a^2*d*(b + a*Cosh[c + d*x]^2))","A",5,4,21,0.1905,1,"{4133, 288, 321, 205}"
45,1,154,0,0.2228612,"\int \frac{\text{csch}(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Csch[c + d*x]/(a + b*Sech[c + d*x]^2)^3,x]","\frac{\sqrt{b} \left(15 a^2+10 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{8 a^{5/2} d (a+b)^3}-\frac{b (7 a+3 b) \cosh (c+d x)}{8 a^2 d (a+b)^2 \left(a \cosh ^2(c+d x)+b\right)}-\frac{b \cosh ^3(c+d x)}{4 a d (a+b) \left(a \cosh ^2(c+d x)+b\right)^2}-\frac{\tanh ^{-1}(\cosh (c+d x))}{d (a+b)^3}","\frac{\sqrt{b} \left(15 a^2+10 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{8 a^{5/2} d (a+b)^3}-\frac{b (7 a+3 b) \cosh (c+d x)}{8 a^2 d (a+b)^2 \left(a \cosh ^2(c+d x)+b\right)}-\frac{b \cosh ^3(c+d x)}{4 a d (a+b) \left(a \cosh ^2(c+d x)+b\right)^2}-\frac{\tanh ^{-1}(\cosh (c+d x))}{d (a+b)^3}",1,"(Sqrt[b]*(15*a^2 + 10*a*b + 3*b^2)*ArcTan[(Sqrt[a]*Cosh[c + d*x])/Sqrt[b]])/(8*a^(5/2)*(a + b)^3*d) - ArcTanh[Cosh[c + d*x]]/((a + b)^3*d) - (b*Cosh[c + d*x]^3)/(4*a*(a + b)*d*(b + a*Cosh[c + d*x]^2)^2) - (b*(7*a + 3*b)*Cosh[c + d*x])/(8*a^2*(a + b)^2*d*(b + a*Cosh[c + d*x]^2))","A",6,6,21,0.2857,1,"{4133, 470, 578, 522, 206, 205}"
46,1,126,0,0.1003399,"\int \frac{\text{csch}^2(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Csch[c + d*x]^2/(a + b*Sech[c + d*x]^2)^3,x]","\frac{15 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 d (a+b)^{7/2}}-\frac{15 \coth (c+d x)}{8 d (a+b)^3}+\frac{5 \coth (c+d x)}{8 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{\coth (c+d x)}{4 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^2}","\frac{15 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 d (a+b)^{7/2}}-\frac{15 \coth (c+d x)}{8 d (a+b)^3}+\frac{5 \coth (c+d x)}{8 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{\coth (c+d x)}{4 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^2}",1,"(15*Sqrt[b]*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(8*(a + b)^(7/2)*d) - (15*Coth[c + d*x])/(8*(a + b)^3*d) + Coth[c + d*x]/(4*(a + b)*d*(a + b - b*Tanh[c + d*x]^2)^2) + (5*Coth[c + d*x])/(8*(a + b)^2*d*(a + b - b*Tanh[c + d*x]^2))","A",5,4,23,0.1739,1,"{4132, 290, 325, 208}"
47,1,213,0,0.3422278,"\int \frac{\text{csch}^3(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Csch[c + d*x]^3/(a + b*Sech[c + d*x]^2)^3,x]","-\frac{\left(4 a^2-9 a b-b^2\right) \cosh (c+d x)}{8 a d (a+b)^3 \left(a \cosh ^2(c+d x)+b\right)}-\frac{\sqrt{b} \left(15 a^2-10 a b-b^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{8 a^{3/2} d (a+b)^4}+\frac{b (2 a-b) \cosh (c+d x)}{4 a d (a+b)^2 \left(a \cosh ^2(c+d x)+b\right)^2}-\frac{\cosh (c+d x) \coth ^2(c+d x)}{2 d (a+b) \left(a \cosh ^2(c+d x)+b\right)^2}+\frac{(a-5 b) \tanh ^{-1}(\cosh (c+d x))}{2 d (a+b)^4}","-\frac{\left(4 a^2-9 a b-b^2\right) \cosh (c+d x)}{8 a d (a+b)^3 \left(a \cosh ^2(c+d x)+b\right)}-\frac{\sqrt{b} \left(15 a^2-10 a b-b^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{b}}\right)}{8 a^{3/2} d (a+b)^4}+\frac{b (2 a-b) \cosh (c+d x)}{4 a d (a+b)^2 \left(a \cosh ^2(c+d x)+b\right)^2}-\frac{\cosh (c+d x) \coth ^2(c+d x)}{2 d (a+b) \left(a \cosh ^2(c+d x)+b\right)^2}+\frac{(a-5 b) \tanh ^{-1}(\cosh (c+d x))}{2 d (a+b)^4}",1,"-(Sqrt[b]*(15*a^2 - 10*a*b - b^2)*ArcTan[(Sqrt[a]*Cosh[c + d*x])/Sqrt[b]])/(8*a^(3/2)*(a + b)^4*d) + ((a - 5*b)*ArcTanh[Cosh[c + d*x]])/(2*(a + b)^4*d) + ((2*a - b)*b*Cosh[c + d*x])/(4*a*(a + b)^2*d*(b + a*Cosh[c + d*x]^2)^2) - ((4*a^2 - 9*a*b - b^2)*Cosh[c + d*x])/(8*a*(a + b)^3*d*(b + a*Cosh[c + d*x]^2)) - (Cosh[c + d*x]*Coth[c + d*x]^2)/(2*(a + b)*d*(b + a*Cosh[c + d*x]^2)^2)","A",7,7,23,0.3043,1,"{4133, 470, 578, 527, 522, 206, 205}"
48,1,165,0,0.2726442,"\int \frac{\text{csch}^4(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Csch[c + d*x]^4/(a + b*Sech[c + d*x]^2)^3,x]","-\frac{5 \sqrt{b} (3 a-4 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 d (a+b)^{9/2}}-\frac{b (7 a-4 b) \tanh (c+d x)}{8 d (a+b)^4 \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{a b \tanh (c+d x)}{4 d (a+b)^3 \left(a-b \tanh ^2(c+d x)+b\right)^2}-\frac{\coth ^3(c+d x)}{3 d (a+b)^3}+\frac{(a-2 b) \coth (c+d x)}{d (a+b)^4}","-\frac{5 \sqrt{b} (3 a-4 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 d (a+b)^{9/2}}-\frac{b (7 a-4 b) \tanh (c+d x)}{8 d (a+b)^4 \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{a b \tanh (c+d x)}{4 d (a+b)^3 \left(a-b \tanh ^2(c+d x)+b\right)^2}-\frac{\coth ^3(c+d x)}{3 d (a+b)^3}+\frac{(a-2 b) \coth (c+d x)}{d (a+b)^4}",1,"(-5*(3*a - 4*b)*Sqrt[b]*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(8*(a + b)^(9/2)*d) + ((a - 2*b)*Coth[c + d*x])/((a + b)^4*d) - Coth[c + d*x]^3/(3*(a + b)^3*d) - (a*b*Tanh[c + d*x])/(4*(a + b)^3*d*(a + b - b*Tanh[c + d*x]^2)^2) - ((7*a - 4*b)*b*Tanh[c + d*x])/(8*(a + b)^4*d*(a + b - b*Tanh[c + d*x]^2))","A",6,5,23,0.2174,1,"{4132, 456, 1259, 1261, 208}"
49,1,61,0,0.0458518,"\int \cosh ^4(c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Cosh[c + d*x]^4*(a + b*Sech[c + d*x]^2),x]","\frac{(3 a+4 b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{1}{8} x (3 a+4 b)+\frac{a \sinh (c+d x) \cosh ^3(c+d x)}{4 d}","\frac{(3 a+4 b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{1}{8} x (3 a+4 b)+\frac{a \sinh (c+d x) \cosh ^3(c+d x)}{4 d}",1,"((3*a + 4*b)*x)/8 + ((3*a + 4*b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (a*Cosh[c + d*x]^3*Sinh[c + d*x])/(4*d)","A",3,3,21,0.1429,1,"{4045, 2635, 8}"
50,1,30,0,0.0502306,"\int \cosh ^3(c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Cosh[c + d*x]^3*(a + b*Sech[c + d*x]^2),x]","\frac{(a+b) \sinh (c+d x)}{d}+\frac{a \sinh ^3(c+d x)}{3 d}","\frac{(a+b) \sinh (c+d x)}{d}+\frac{a \sinh ^3(c+d x)}{3 d}",1,"((a + b)*Sinh[c + d*x])/d + (a*Sinh[c + d*x]^3)/(3*d)","A",3,2,21,0.09524,1,"{4044, 3013}"
51,1,31,0,0.0314004,"\int \cosh ^2(c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Cosh[c + d*x]^2*(a + b*Sech[c + d*x]^2),x]","\frac{1}{2} x (a+2 b)+\frac{a \sinh (c+d x) \cosh (c+d x)}{2 d}","\frac{1}{2} x (a+2 b)+\frac{a \sinh (c+d x) \cosh (c+d x)}{2 d}",1,"((a + 2*b)*x)/2 + (a*Cosh[c + d*x]*Sinh[c + d*x])/(2*d)","A",2,2,21,0.09524,1,"{4045, 8}"
52,1,24,0,0.0298312,"\int \cosh (c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Cosh[c + d*x]*(a + b*Sech[c + d*x]^2),x]","\frac{a \sinh (c+d x)}{d}+\frac{b \tan ^{-1}(\sinh (c+d x))}{d}","\frac{a \sinh (c+d x)}{d}+\frac{b \tan ^{-1}(\sinh (c+d x))}{d}",1,"(b*ArcTan[Sinh[c + d*x]])/d + (a*Sinh[c + d*x])/d","A",2,2,19,0.1053,1,"{4045, 3770}"
53,1,40,0,0.0265989,"\int \text{sech}(c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Sech[c + d*x]*(a + b*Sech[c + d*x]^2),x]","\frac{(2 a+b) \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{b \tanh (c+d x) \text{sech}(c+d x)}{2 d}","\frac{(2 a+b) \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{b \tanh (c+d x) \text{sech}(c+d x)}{2 d}",1,"((2*a + b)*ArcTan[Sinh[c + d*x]])/(2*d) + (b*Sech[c + d*x]*Tanh[c + d*x])/(2*d)","A",2,2,19,0.1053,1,"{4046, 3770}"
54,1,43,0,0.0402439,"\int \text{sech}^2(c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Sech[c + d*x]^2*(a + b*Sech[c + d*x]^2),x]","\frac{(3 a+2 b) \tanh (c+d x)}{3 d}+\frac{b \tanh (c+d x) \text{sech}^2(c+d x)}{3 d}","\frac{(a+b) \tanh (c+d x)}{d}-\frac{b \tanh ^3(c+d x)}{3 d}",1,"((3*a + 2*b)*Tanh[c + d*x])/(3*d) + (b*Sech[c + d*x]^2*Tanh[c + d*x])/(3*d)","A",3,3,21,0.1429,1,"{4046, 3767, 8}"
55,1,70,0,0.0502423,"\int \text{sech}^3(c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Sech[c + d*x]^3*(a + b*Sech[c + d*x]^2),x]","\frac{(4 a+3 b) \tan ^{-1}(\sinh (c+d x))}{8 d}+\frac{(4 a+3 b) \tanh (c+d x) \text{sech}(c+d x)}{8 d}+\frac{b \tanh (c+d x) \text{sech}^3(c+d x)}{4 d}","\frac{(4 a+3 b) \tan ^{-1}(\sinh (c+d x))}{8 d}+\frac{(4 a+3 b) \tanh (c+d x) \text{sech}(c+d x)}{8 d}+\frac{b \tanh (c+d x) \text{sech}^3(c+d x)}{4 d}",1,"((4*a + 3*b)*ArcTan[Sinh[c + d*x]])/(8*d) + ((4*a + 3*b)*Sech[c + d*x]*Tanh[c + d*x])/(8*d) + (b*Sech[c + d*x]^3*Tanh[c + d*x])/(4*d)","A",3,3,21,0.1429,1,"{4046, 3768, 3770}"
56,1,65,0,0.0460788,"\int \text{sech}^4(c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Sech[c + d*x]^4*(a + b*Sech[c + d*x]^2),x]","-\frac{(5 a+4 b) \tanh ^3(c+d x)}{15 d}+\frac{(5 a+4 b) \tanh (c+d x)}{5 d}+\frac{b \tanh (c+d x) \text{sech}^4(c+d x)}{5 d}","-\frac{(a+2 b) \tanh ^3(c+d x)}{3 d}+\frac{(a+b) \tanh (c+d x)}{d}+\frac{b \tanh ^5(c+d x)}{5 d}",1,"((5*a + 4*b)*Tanh[c + d*x])/(5*d) + (b*Sech[c + d*x]^4*Tanh[c + d*x])/(5*d) - ((5*a + 4*b)*Tanh[c + d*x]^3)/(15*d)","A",3,2,21,0.09524,1,"{4046, 3767}"
57,1,82,0,0.0929244,"\int \cosh ^4(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Cosh[c + d*x]^4*(a + b*Sech[c + d*x]^2)^2,x]","\frac{1}{8} x \left(3 a^2+8 a b+8 b^2\right)+\frac{3 a (a+2 b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{a \sinh (c+d x) \cosh ^3(c+d x) \left(a-b \tanh ^2(c+d x)+b\right)}{4 d}","\frac{1}{8} x \left(3 a^2+8 a b+8 b^2\right)+\frac{3 a (a+2 b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{a \sinh (c+d x) \cosh ^3(c+d x) \left(a-b \tanh ^2(c+d x)+b\right)}{4 d}",1,"((3*a^2 + 8*a*b + 8*b^2)*x)/8 + (3*a*(a + 2*b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (a*Cosh[c + d*x]^3*Sinh[c + d*x]*(a + b - b*Tanh[c + d*x]^2))/(4*d)","A",4,4,23,0.1739,1,"{4146, 413, 385, 206}"
58,1,49,0,0.0592035,"\int \cosh ^3(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Cosh[c + d*x]^3*(a + b*Sech[c + d*x]^2)^2,x]","\frac{a^2 \sinh ^3(c+d x)}{3 d}+\frac{a (a+2 b) \sinh (c+d x)}{d}+\frac{b^2 \tan ^{-1}(\sinh (c+d x))}{d}","\frac{a^2 \sinh ^3(c+d x)}{3 d}+\frac{a (a+2 b) \sinh (c+d x)}{d}+\frac{b^2 \tan ^{-1}(\sinh (c+d x))}{d}",1,"(b^2*ArcTan[Sinh[c + d*x]])/d + (a*(a + 2*b)*Sinh[c + d*x])/d + (a^2*Sinh[c + d*x]^3)/(3*d)","A",4,3,23,0.1304,1,"{4147, 390, 203}"
59,1,47,0,0.0784786,"\int \cosh ^2(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Cosh[c + d*x]^2*(a + b*Sech[c + d*x]^2)^2,x]","\frac{a^2 \sinh (c+d x) \cosh (c+d x)}{2 d}+\frac{1}{2} a x (a+4 b)+\frac{b^2 \tanh (c+d x)}{d}","\frac{a^2 \sinh (c+d x) \cosh (c+d x)}{2 d}+\frac{1}{2} a x (a+4 b)+\frac{b^2 \tanh (c+d x)}{d}",1,"(a*(a + 4*b)*x)/2 + (a^2*Cosh[c + d*x]*Sinh[c + d*x])/(2*d) + (b^2*Tanh[c + d*x])/d","A",5,4,23,0.1739,1,"{4146, 390, 385, 206}"
60,1,56,0,0.0678789,"\int \cosh (c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Cosh[c + d*x]*(a + b*Sech[c + d*x]^2)^2,x]","\frac{a^2 \sinh (c+d x)}{d}+\frac{b (4 a+b) \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{b^2 \tanh (c+d x) \text{sech}(c+d x)}{2 d}","\frac{a^2 \sinh (c+d x)}{d}+\frac{b (4 a+b) \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{b^2 \tanh (c+d x) \text{sech}(c+d x)}{2 d}",1,"(b*(4*a + b)*ArcTan[Sinh[c + d*x]])/(2*d) + (a^2*Sinh[c + d*x])/d + (b^2*Sech[c + d*x]*Tanh[c + d*x])/(2*d)","A",5,4,21,0.1905,1,"{4147, 390, 385, 203}"
61,1,90,0,0.0838808,"\int \text{sech}(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Sech[c + d*x]*(a + b*Sech[c + d*x]^2)^2,x]","\frac{\left(8 a^2+8 a b+3 b^2\right) \tan ^{-1}(\sinh (c+d x))}{8 d}+\frac{3 b (2 a+b) \tanh (c+d x) \text{sech}(c+d x)}{8 d}+\frac{b \tanh (c+d x) \text{sech}^3(c+d x) \left(a \sinh ^2(c+d x)+a+b\right)}{4 d}","\frac{\left(8 a^2+8 a b+3 b^2\right) \tan ^{-1}(\sinh (c+d x))}{8 d}+\frac{3 b (2 a+b) \tanh (c+d x) \text{sech}(c+d x)}{8 d}+\frac{b \tanh (c+d x) \text{sech}^3(c+d x) \left(a \sinh ^2(c+d x)+a+b\right)}{4 d}",1,"((8*a^2 + 8*a*b + 3*b^2)*ArcTan[Sinh[c + d*x]])/(8*d) + (3*b*(2*a + b)*Sech[c + d*x]*Tanh[c + d*x])/(8*d) + (b*Sech[c + d*x]^3*(a + b + a*Sinh[c + d*x]^2)*Tanh[c + d*x])/(4*d)","A",4,4,21,0.1905,1,"{4147, 413, 385, 203}"
62,1,53,0,0.0656931,"\int \text{sech}^2(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Sech[c + d*x]^2*(a + b*Sech[c + d*x]^2)^2,x]","-\frac{2 b (a+b) \tanh ^3(c+d x)}{3 d}+\frac{(a+b)^2 \tanh (c+d x)}{d}+\frac{b^2 \tanh ^5(c+d x)}{5 d}","-\frac{2 b (a+b) \tanh ^3(c+d x)}{3 d}+\frac{(a+b)^2 \tanh (c+d x)}{d}+\frac{b^2 \tanh ^5(c+d x)}{5 d}",1,"((a + b)^2*Tanh[c + d*x])/d - (2*b*(a + b)*Tanh[c + d*x]^3)/(3*d) + (b^2*Tanh[c + d*x]^5)/(5*d)","A",3,2,23,0.08696,1,"{4146, 194}"
63,1,128,0,0.1494483,"\int \text{sech}^3(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Sech[c + d*x]^3*(a + b*Sech[c + d*x]^2)^2,x]","\frac{\left(8 a^2+12 a b+5 b^2\right) \tan ^{-1}(\sinh (c+d x))}{16 d}+\frac{\left(8 a^2+12 a b+5 b^2\right) \tanh (c+d x) \text{sech}(c+d x)}{16 d}+\frac{b (8 a+5 b) \tanh (c+d x) \text{sech}^3(c+d x)}{24 d}+\frac{b \tanh (c+d x) \text{sech}^5(c+d x) \left(a \sinh ^2(c+d x)+a+b\right)}{6 d}","\frac{\left(8 a^2+12 a b+5 b^2\right) \tan ^{-1}(\sinh (c+d x))}{16 d}+\frac{\left(8 a^2+12 a b+5 b^2\right) \tanh (c+d x) \text{sech}(c+d x)}{16 d}+\frac{b (8 a+5 b) \tanh (c+d x) \text{sech}^3(c+d x)}{24 d}+\frac{b \tanh (c+d x) \text{sech}^5(c+d x) \left(a \sinh ^2(c+d x)+a+b\right)}{6 d}",1,"((8*a^2 + 12*a*b + 5*b^2)*ArcTan[Sinh[c + d*x]])/(16*d) + ((8*a^2 + 12*a*b + 5*b^2)*Sech[c + d*x]*Tanh[c + d*x])/(16*d) + (b*(8*a + 5*b)*Sech[c + d*x]^3*Tanh[c + d*x])/(24*d) + (b*Sech[c + d*x]^5*(a + b + a*Sinh[c + d*x]^2)*Tanh[c + d*x])/(6*d)","A",5,5,23,0.2174,1,"{4147, 413, 385, 199, 203}"
64,1,80,0,0.076328,"\int \text{sech}^4(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Sech[c + d*x]^4*(a + b*Sech[c + d*x]^2)^2,x]","\frac{b (2 a+3 b) \tanh ^5(c+d x)}{5 d}-\frac{(a+b) (a+3 b) \tanh ^3(c+d x)}{3 d}+\frac{(a+b)^2 \tanh (c+d x)}{d}-\frac{b^2 \tanh ^7(c+d x)}{7 d}","\frac{b (2 a+3 b) \tanh ^5(c+d x)}{5 d}-\frac{(a+b) (a+3 b) \tanh ^3(c+d x)}{3 d}+\frac{(a+b)^2 \tanh (c+d x)}{d}-\frac{b^2 \tanh ^7(c+d x)}{7 d}",1,"((a + b)^2*Tanh[c + d*x])/d - ((a + b)*(a + 3*b)*Tanh[c + d*x]^3)/(3*d) + (b*(2*a + 3*b)*Tanh[c + d*x]^5)/(5*d) - (b^2*Tanh[c + d*x]^7)/(7*d)","A",3,2,23,0.08696,1,"{4146, 373}"
65,1,84,0,0.1111958,"\int \cosh ^4(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Cosh[c + d*x]^4*(a + b*Sech[c + d*x]^2)^3,x]","\frac{3}{8} a x \left(a^2+4 a b+8 b^2\right)+\frac{3 a^2 (a+4 b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{a^3 \sinh (c+d x) \cosh ^3(c+d x)}{4 d}+\frac{b^3 \tanh (c+d x)}{d}","\frac{3}{8} a x \left(a^2+4 a b+8 b^2\right)+\frac{3 a^2 (a+4 b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{a^3 \sinh (c+d x) \cosh ^3(c+d x)}{4 d}+\frac{b^3 \tanh (c+d x)}{d}",1,"(3*a*(a^2 + 4*a*b + 8*b^2)*x)/8 + (3*a^2*(a + 4*b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (a^3*Cosh[c + d*x]^3*Sinh[c + d*x])/(4*d) + (b^3*Tanh[c + d*x])/d","A",6,5,23,0.2174,1,"{4146, 390, 1157, 385, 206}"
66,1,81,0,0.0931799,"\int \cosh ^3(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Cosh[c + d*x]^3*(a + b*Sech[c + d*x]^2)^3,x]","\frac{a^2 (a+3 b) \sinh (c+d x)}{d}+\frac{a^3 \sinh ^3(c+d x)}{3 d}+\frac{b^2 (6 a+b) \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{b^3 \tanh (c+d x) \text{sech}(c+d x)}{2 d}","\frac{a^2 (a+3 b) \sinh (c+d x)}{d}+\frac{a^3 \sinh ^3(c+d x)}{3 d}+\frac{b^2 (6 a+b) \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{b^3 \tanh (c+d x) \text{sech}(c+d x)}{2 d}",1,"(b^2*(6*a + b)*ArcTan[Sinh[c + d*x]])/(2*d) + (a^2*(a + 3*b)*Sinh[c + d*x])/d + (a^3*Sinh[c + d*x]^3)/(3*d) + (b^3*Sech[c + d*x]*Tanh[c + d*x])/(2*d)","A",5,4,23,0.1739,1,"{4147, 390, 385, 203}"
67,1,72,0,0.0923167,"\int \cosh ^2(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Cosh[c + d*x]^2*(a + b*Sech[c + d*x]^2)^3,x]","\frac{1}{2} a^2 x (a+6 b)+\frac{a^3 \sinh (c+d x) \cosh (c+d x)}{2 d}+\frac{b^2 (3 a+b) \tanh (c+d x)}{d}-\frac{b^3 \tanh ^3(c+d x)}{3 d}","\frac{1}{2} a^2 x (a+6 b)+\frac{a^3 \sinh (c+d x) \cosh (c+d x)}{2 d}+\frac{b^2 (3 a+b) \tanh (c+d x)}{d}-\frac{b^3 \tanh ^3(c+d x)}{3 d}",1,"(a^2*(a + 6*b)*x)/2 + (a^3*Cosh[c + d*x]*Sinh[c + d*x])/(2*d) + (b^2*(3*a + b)*Tanh[c + d*x])/d - (b^3*Tanh[c + d*x]^3)/(3*d)","A",5,4,23,0.1739,1,"{4146, 390, 385, 206}"
68,1,93,0,0.1026811,"\int \cosh (c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Cosh[c + d*x]*(a + b*Sech[c + d*x]^2)^3,x]","\frac{3 b \left(8 a^2+4 a b+b^2\right) \tan ^{-1}(\sinh (c+d x))}{8 d}+\frac{a^3 \sinh (c+d x)}{d}+\frac{3 b^2 (4 a+b) \tanh (c+d x) \text{sech}(c+d x)}{8 d}+\frac{b^3 \tanh (c+d x) \text{sech}^3(c+d x)}{4 d}","\frac{3 b \left(8 a^2+4 a b+b^2\right) \tan ^{-1}(\sinh (c+d x))}{8 d}+\frac{a^3 \sinh (c+d x)}{d}+\frac{3 b^2 (4 a+b) \tanh (c+d x) \text{sech}(c+d x)}{8 d}+\frac{b^3 \tanh (c+d x) \text{sech}^3(c+d x)}{4 d}",1,"(3*b*(8*a^2 + 4*a*b + b^2)*ArcTan[Sinh[c + d*x]])/(8*d) + (a^3*Sinh[c + d*x])/d + (3*b^2*(4*a + b)*Sech[c + d*x]*Tanh[c + d*x])/(8*d) + (b^3*Sech[c + d*x]^3*Tanh[c + d*x])/(4*d)","A",6,5,21,0.2381,1,"{4147, 390, 1157, 385, 203}"
69,1,147,0,0.1428098,"\int \text{sech}(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Sech[c + d*x]*(a + b*Sech[c + d*x]^2)^3,x]","\frac{(2 a+b) \left(8 a^2+8 a b+5 b^2\right) \tan ^{-1}(\sinh (c+d x))}{16 d}+\frac{b \left(44 a^2+44 a b+15 b^2\right) \tanh (c+d x) \text{sech}(c+d x)}{48 d}+\frac{b \tanh (c+d x) \text{sech}^5(c+d x) \left(a \sinh ^2(c+d x)+a+b\right)^2}{6 d}+\frac{5 b (2 a+b) \tanh (c+d x) \text{sech}^3(c+d x) \left(a \sinh ^2(c+d x)+a+b\right)}{24 d}","\frac{(2 a+b) \left(8 a^2+8 a b+5 b^2\right) \tan ^{-1}(\sinh (c+d x))}{16 d}+\frac{b \left(44 a^2+44 a b+15 b^2\right) \tanh (c+d x) \text{sech}(c+d x)}{48 d}+\frac{b \tanh (c+d x) \text{sech}^5(c+d x) \left(a \sinh ^2(c+d x)+a+b\right)^2}{6 d}+\frac{5 b (2 a+b) \tanh (c+d x) \text{sech}^3(c+d x) \left(a \sinh ^2(c+d x)+a+b\right)}{24 d}",1,"((2*a + b)*(8*a^2 + 8*a*b + 5*b^2)*ArcTan[Sinh[c + d*x]])/(16*d) + (b*(44*a^2 + 44*a*b + 15*b^2)*Sech[c + d*x]*Tanh[c + d*x])/(48*d) + (5*b*(2*a + b)*Sech[c + d*x]^3*(a + b + a*Sinh[c + d*x]^2)*Tanh[c + d*x])/(24*d) + (b*Sech[c + d*x]^5*(a + b + a*Sinh[c + d*x]^2)^2*Tanh[c + d*x])/(6*d)","A",5,5,21,0.2381,1,"{4147, 413, 526, 385, 203}"
70,1,74,0,0.079839,"\int \text{sech}^2(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Sech[c + d*x]^2*(a + b*Sech[c + d*x]^2)^3,x]","\frac{3 b^2 (a+b) \tanh ^5(c+d x)}{5 d}-\frac{b (a+b)^2 \tanh ^3(c+d x)}{d}+\frac{(a+b)^3 \tanh (c+d x)}{d}-\frac{b^3 \tanh ^7(c+d x)}{7 d}","\frac{3 b^2 (a+b) \tanh ^5(c+d x)}{5 d}-\frac{b (a+b)^2 \tanh ^3(c+d x)}{d}+\frac{(a+b)^3 \tanh (c+d x)}{d}-\frac{b^3 \tanh ^7(c+d x)}{7 d}",1,"((a + b)^3*Tanh[c + d*x])/d - (b*(a + b)^2*Tanh[c + d*x]^3)/d + (3*b^2*(a + b)*Tanh[c + d*x]^5)/(5*d) - (b^3*Tanh[c + d*x]^7)/(7*d)","A",3,2,23,0.08696,1,"{4146, 194}"
71,1,196,0,0.2320288,"\int \text{sech}^3(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Sech[c + d*x]^3*(a + b*Sech[c + d*x]^2)^3,x]","\frac{\left(144 a^2 b+64 a^3+120 a b^2+35 b^3\right) \tan ^{-1}(\sinh (c+d x))}{128 d}+\frac{b \left(72 a^2+92 a b+35 b^2\right) \tanh (c+d x) \text{sech}^3(c+d x)}{192 d}+\frac{\left(144 a^2 b+64 a^3+120 a b^2+35 b^3\right) \tanh (c+d x) \text{sech}(c+d x)}{128 d}+\frac{b \tanh (c+d x) \text{sech}^7(c+d x) \left(a \sinh ^2(c+d x)+a+b\right)^2}{8 d}+\frac{b (12 a+7 b) \tanh (c+d x) \text{sech}^5(c+d x) \left(a \sinh ^2(c+d x)+a+b\right)}{48 d}","\frac{\left(144 a^2 b+64 a^3+120 a b^2+35 b^3\right) \tan ^{-1}(\sinh (c+d x))}{128 d}+\frac{b \left(72 a^2+92 a b+35 b^2\right) \tanh (c+d x) \text{sech}^3(c+d x)}{192 d}+\frac{\left(144 a^2 b+64 a^3+120 a b^2+35 b^3\right) \tanh (c+d x) \text{sech}(c+d x)}{128 d}+\frac{b \tanh (c+d x) \text{sech}^7(c+d x) \left(a \sinh ^2(c+d x)+a+b\right)^2}{8 d}+\frac{b (12 a+7 b) \tanh (c+d x) \text{sech}^5(c+d x) \left(a \sinh ^2(c+d x)+a+b\right)}{48 d}",1,"((64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*ArcTan[Sinh[c + d*x]])/(128*d) + ((64*a^3 + 144*a^2*b + 120*a*b^2 + 35*b^3)*Sech[c + d*x]*Tanh[c + d*x])/(128*d) + (b*(72*a^2 + 92*a*b + 35*b^2)*Sech[c + d*x]^3*Tanh[c + d*x])/(192*d) + (b*(12*a + 7*b)*Sech[c + d*x]^5*(a + b + a*Sinh[c + d*x]^2)*Tanh[c + d*x])/(48*d) + (b*Sech[c + d*x]^7*(a + b + a*Sinh[c + d*x]^2)^2*Tanh[c + d*x])/(8*d)","A",6,6,23,0.2609,1,"{4147, 413, 526, 385, 199, 203}"
72,1,108,0,0.0937486,"\int \text{sech}^4(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Sech[c + d*x]^4*(a + b*Sech[c + d*x]^2)^3,x]","-\frac{b^2 (3 a+4 b) \tanh ^7(c+d x)}{7 d}+\frac{3 b (a+b) (a+2 b) \tanh ^5(c+d x)}{5 d}-\frac{(a+b)^2 (a+4 b) \tanh ^3(c+d x)}{3 d}+\frac{(a+b)^3 \tanh (c+d x)}{d}+\frac{b^3 \tanh ^9(c+d x)}{9 d}","-\frac{b^2 (3 a+4 b) \tanh ^7(c+d x)}{7 d}+\frac{3 b (a+b) (a+2 b) \tanh ^5(c+d x)}{5 d}-\frac{(a+b)^2 (a+4 b) \tanh ^3(c+d x)}{3 d}+\frac{(a+b)^3 \tanh (c+d x)}{d}+\frac{b^3 \tanh ^9(c+d x)}{9 d}",1,"((a + b)^3*Tanh[c + d*x])/d - ((a + b)^2*(a + 4*b)*Tanh[c + d*x]^3)/(3*d) + (3*b*(a + b)*(a + 2*b)*Tanh[c + d*x]^5)/(5*d) - (b^2*(3*a + 4*b)*Tanh[c + d*x]^7)/(7*d) + (b^3*Tanh[c + d*x]^9)/(9*d)","A",3,2,23,0.08696,1,"{4146, 373}"
73,1,117,0,0.1892815,"\int \frac{\cosh ^4(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Cosh[c + d*x]^4/(a + b*Sech[c + d*x]^2),x]","-\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a^3 d \sqrt{a+b}}+\frac{x \left(3 a^2-4 a b+8 b^2\right)}{8 a^3}+\frac{(3 a-4 b) \sinh (c+d x) \cosh (c+d x)}{8 a^2 d}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 a d}","-\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a^3 d \sqrt{a+b}}+\frac{x \left(3 a^2-4 a b+8 b^2\right)}{8 a^3}+\frac{(3 a-4 b) \sinh (c+d x) \cosh (c+d x)}{8 a^2 d}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 a d}",1,"((3*a^2 - 4*a*b + 8*b^2)*x)/(8*a^3) - (b^(5/2)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(a^3*Sqrt[a + b]*d) + ((3*a - 4*b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*a^2*d) + (Cosh[c + d*x]^3*Sinh[c + d*x])/(4*a*d)","A",6,6,23,0.2609,1,"{4146, 414, 527, 522, 206, 208}"
74,1,76,0,0.09035,"\int \frac{\cosh ^3(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Cosh[c + d*x]^3/(a + b*Sech[c + d*x]^2),x]","\frac{b^2 \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{a^{5/2} d \sqrt{a+b}}+\frac{(a-b) \sinh (c+d x)}{a^2 d}+\frac{\sinh ^3(c+d x)}{3 a d}","\frac{b^2 \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{a^{5/2} d \sqrt{a+b}}+\frac{(a-b) \sinh (c+d x)}{a^2 d}+\frac{\sinh ^3(c+d x)}{3 a d}",1,"(b^2*ArcTan[(Sqrt[a]*Sinh[c + d*x])/Sqrt[a + b]])/(a^(5/2)*Sqrt[a + b]*d) + ((a - b)*Sinh[c + d*x])/(a^2*d) + Sinh[c + d*x]^3/(3*a*d)","A",4,3,23,0.1304,1,"{4147, 390, 205}"
75,1,75,0,0.1155012,"\int \frac{\cosh ^2(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Cosh[c + d*x]^2/(a + b*Sech[c + d*x]^2),x]","\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a^2 d \sqrt{a+b}}+\frac{x (a-2 b)}{2 a^2}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 a d}","\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a^2 d \sqrt{a+b}}+\frac{x (a-2 b)}{2 a^2}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 a d}",1,"((a - 2*b)*x)/(2*a^2) + (b^(3/2)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(a^2*Sqrt[a + b]*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*a*d)","A",5,5,23,0.2174,1,"{4146, 414, 522, 206, 208}"
76,1,52,0,0.061165,"\int \frac{\cosh (c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Cosh[c + d*x]/(a + b*Sech[c + d*x]^2),x]","\frac{\sinh (c+d x)}{a d}-\frac{b \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{a^{3/2} d \sqrt{a+b}}","\frac{\sinh (c+d x)}{a d}-\frac{b \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{a^{3/2} d \sqrt{a+b}}",1,"-((b*ArcTan[(Sqrt[a]*Sinh[c + d*x])/Sqrt[a + b]])/(a^(3/2)*Sqrt[a + b]*d)) + Sinh[c + d*x]/(a*d)","A",3,3,21,0.1429,1,"{4147, 388, 205}"
77,1,36,0,0.0415728,"\int \frac{\text{sech}(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Sech[c + d*x]/(a + b*Sech[c + d*x]^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{\sqrt{a} d \sqrt{a+b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{\sqrt{a} d \sqrt{a+b}}",1,"ArcTan[(Sqrt[a]*Sinh[c + d*x])/Sqrt[a + b]]/(Sqrt[a]*Sqrt[a + b]*d)","A",2,2,21,0.09524,1,"{4147, 205}"
78,1,36,0,0.0605388,"\int \frac{\text{sech}^2(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Sech[c + d*x]^2/(a + b*Sech[c + d*x]^2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{\sqrt{b} d \sqrt{a+b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{\sqrt{b} d \sqrt{a+b}}",1,"ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]]/(Sqrt[b]*Sqrt[a + b]*d)","A",2,2,23,0.08696,1,"{4146, 208}"
79,1,55,0,0.0691455,"\int \frac{\text{sech}^3(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Sech[c + d*x]^3/(a + b*Sech[c + d*x]^2),x]","\frac{\tan ^{-1}(\sinh (c+d x))}{b d}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{b d \sqrt{a+b}}","\frac{\tan ^{-1}(\sinh (c+d x))}{b d}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{b d \sqrt{a+b}}",1,"ArcTan[Sinh[c + d*x]]/(b*d) - (Sqrt[a]*ArcTan[(Sqrt[a]*Sinh[c + d*x])/Sqrt[a + b]])/(b*Sqrt[a + b]*d)","A",4,4,23,0.1739,1,"{4147, 391, 203, 205}"
80,1,52,0,0.0703809,"\int \frac{\text{sech}^4(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Sech[c + d*x]^4/(a + b*Sech[c + d*x]^2),x]","\frac{\tanh (c+d x)}{b d}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{b^{3/2} d \sqrt{a+b}}","\frac{\tanh (c+d x)}{b d}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{b^{3/2} d \sqrt{a+b}}",1,"-((a*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(b^(3/2)*Sqrt[a + b]*d)) + Tanh[c + d*x]/(b*d)","A",3,3,23,0.1304,1,"{4146, 388, 208}"
81,1,86,0,0.1027588,"\int \frac{\text{sech}^5(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Sech[c + d*x]^5/(a + b*Sech[c + d*x]^2),x]","\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{b^2 d \sqrt{a+b}}-\frac{(2 a-b) \tan ^{-1}(\sinh (c+d x))}{2 b^2 d}+\frac{\tanh (c+d x) \text{sech}(c+d x)}{2 b d}","\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{b^2 d \sqrt{a+b}}-\frac{(2 a-b) \tan ^{-1}(\sinh (c+d x))}{2 b^2 d}+\frac{\tanh (c+d x) \text{sech}(c+d x)}{2 b d}",1,"-((2*a - b)*ArcTan[Sinh[c + d*x]])/(2*b^2*d) + (a^(3/2)*ArcTan[(Sqrt[a]*Sinh[c + d*x])/Sqrt[a + b]])/(b^2*Sqrt[a + b]*d) + (Sech[c + d*x]*Tanh[c + d*x])/(2*b*d)","A",5,5,23,0.2174,1,"{4147, 414, 522, 203, 205}"
82,1,77,0,0.0891387,"\int \frac{\text{sech}^6(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Sech[c + d*x]^6/(a + b*Sech[c + d*x]^2),x]","\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{b^{5/2} d \sqrt{a+b}}-\frac{(a-b) \tanh (c+d x)}{b^2 d}-\frac{\tanh ^3(c+d x)}{3 b d}","\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{b^{5/2} d \sqrt{a+b}}-\frac{(a-b) \tanh (c+d x)}{b^2 d}-\frac{\tanh ^3(c+d x)}{3 b d}",1,"(a^2*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(b^(5/2)*Sqrt[a + b]*d) - ((a - b)*Tanh[c + d*x])/(b^2*d) - Tanh[c + d*x]^3/(3*b*d)","A",4,3,23,0.1304,1,"{4146, 390, 208}"
83,1,125,0,0.1535556,"\int \frac{\cosh ^3(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Cosh[c + d*x]^3/(a + b*Sech[c + d*x]^2)^2,x]","-\frac{b^3 \sinh (c+d x)}{2 a^3 d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)}+\frac{b^2 (6 a+5 b) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{2 a^{7/2} d (a+b)^{3/2}}+\frac{(a-2 b) \sinh (c+d x)}{a^3 d}+\frac{\sinh ^3(c+d x)}{3 a^2 d}","-\frac{b^3 \sinh (c+d x)}{2 a^3 d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)}+\frac{b^2 (6 a+5 b) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{2 a^{7/2} d (a+b)^{3/2}}+\frac{(a-2 b) \sinh (c+d x)}{a^3 d}+\frac{\sinh ^3(c+d x)}{3 a^2 d}",1,"(b^2*(6*a + 5*b)*ArcTan[(Sqrt[a]*Sinh[c + d*x])/Sqrt[a + b]])/(2*a^(7/2)*(a + b)^(3/2)*d) + ((a - 2*b)*Sinh[c + d*x])/(a^3*d) + Sinh[c + d*x]^3/(3*a^2*d) - (b^3*Sinh[c + d*x])/(2*a^3*(a + b)*d*(a + b + a*Sinh[c + d*x]^2))","A",5,4,23,0.1739,1,"{4147, 390, 385, 205}"
84,1,144,0,0.2350704,"\int \frac{\cosh ^2(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Cosh[c + d*x]^2/(a + b*Sech[c + d*x]^2)^2,x]","\frac{b^{3/2} (5 a+4 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 a^3 d (a+b)^{3/2}}+\frac{b (a+2 b) \tanh (c+d x)}{2 a^2 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{x (a-4 b)}{2 a^3}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 a d \left(a-b \tanh ^2(c+d x)+b\right)}","\frac{b^{3/2} (5 a+4 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 a^3 d (a+b)^{3/2}}+\frac{b (a+2 b) \tanh (c+d x)}{2 a^2 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{x (a-4 b)}{2 a^3}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 a d \left(a-b \tanh ^2(c+d x)+b\right)}",1,"((a - 4*b)*x)/(2*a^3) + (b^(3/2)*(5*a + 4*b)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(2*a^3*(a + b)^(3/2)*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*a*d*(a + b - b*Tanh[c + d*x]^2)) + (b*(a + 2*b)*Tanh[c + d*x])/(2*a^2*(a + b)*d*(a + b - b*Tanh[c + d*x]^2))","A",6,6,23,0.2609,1,"{4146, 414, 527, 522, 206, 208}"
85,1,100,0,0.131521,"\int \frac{\cosh (c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Cosh[c + d*x]/(a + b*Sech[c + d*x]^2)^2,x]","\frac{b^2 \sinh (c+d x)}{2 a^2 d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)}-\frac{b (4 a+3 b) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{2 a^{5/2} d (a+b)^{3/2}}+\frac{\sinh (c+d x)}{a^2 d}","\frac{b^2 \sinh (c+d x)}{2 a^2 d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)}-\frac{b (4 a+3 b) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{2 a^{5/2} d (a+b)^{3/2}}+\frac{\sinh (c+d x)}{a^2 d}",1,"-(b*(4*a + 3*b)*ArcTan[(Sqrt[a]*Sinh[c + d*x])/Sqrt[a + b]])/(2*a^(5/2)*(a + b)^(3/2)*d) + Sinh[c + d*x]/(a^2*d) + (b^2*Sinh[c + d*x])/(2*a^2*(a + b)*d*(a + b + a*Sinh[c + d*x]^2))","A",5,4,21,0.1905,1,"{4147, 390, 385, 205}"
86,1,82,0,0.0655658,"\int \frac{\text{sech}(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]/(a + b*Sech[c + d*x]^2)^2,x]","\frac{(2 a+b) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{2 a^{3/2} d (a+b)^{3/2}}-\frac{b \sinh (c+d x)}{2 a d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)}","\frac{(2 a+b) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{2 a^{3/2} d (a+b)^{3/2}}-\frac{b \sinh (c+d x)}{2 a d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)}",1,"((2*a + b)*ArcTan[(Sqrt[a]*Sinh[c + d*x])/Sqrt[a + b]])/(2*a^(3/2)*(a + b)^(3/2)*d) - (b*Sinh[c + d*x])/(2*a*(a + b)*d*(a + b + a*Sinh[c + d*x]^2))","A",3,3,21,0.1429,1,"{4147, 385, 205}"
87,1,74,0,0.0735656,"\int \frac{\text{sech}^2(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]^2/(a + b*Sech[c + d*x]^2)^2,x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 \sqrt{b} d (a+b)^{3/2}}+\frac{\tanh (c+d x)}{2 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 \sqrt{b} d (a+b)^{3/2}}+\frac{\tanh (c+d x)}{2 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}",1,"ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]]/(2*Sqrt[b]*(a + b)^(3/2)*d) + Tanh[c + d*x]/(2*(a + b)*d*(a + b - b*Tanh[c + d*x]^2))","A",3,3,23,0.1304,1,"{4146, 199, 208}"
88,1,73,0,0.070761,"\int \frac{\text{sech}^3(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]^3/(a + b*Sech[c + d*x]^2)^2,x]","\frac{\sinh (c+d x)}{2 d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{2 \sqrt{a} d (a+b)^{3/2}}","\frac{\sinh (c+d x)}{2 d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{2 \sqrt{a} d (a+b)^{3/2}}",1,"ArcTan[(Sqrt[a]*Sinh[c + d*x])/Sqrt[a + b]]/(2*Sqrt[a]*(a + b)^(3/2)*d) + Sinh[c + d*x]/(2*(a + b)*d*(a + b + a*Sinh[c + d*x]^2))","A",3,3,23,0.1304,1,"{4147, 199, 205}"
89,1,83,0,0.0904603,"\int \frac{\text{sech}^4(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]^4/(a + b*Sech[c + d*x]^2)^2,x]","\frac{(a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 b^{3/2} d (a+b)^{3/2}}-\frac{a \tanh (c+d x)}{2 b d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}","\frac{(a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 b^{3/2} d (a+b)^{3/2}}-\frac{a \tanh (c+d x)}{2 b d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}",1,"((a + 2*b)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(2*b^(3/2)*(a + b)^(3/2)*d) - (a*Tanh[c + d*x])/(2*b*(a + b)*d*(a + b - b*Tanh[c + d*x]^2))","A",3,3,23,0.1304,1,"{4146, 385, 208}"
90,1,101,0,0.116827,"\int \frac{\text{sech}^5(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]^5/(a + b*Sech[c + d*x]^2)^2,x]","-\frac{\sqrt{a} (2 a+3 b) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{2 b^2 d (a+b)^{3/2}}-\frac{a \sinh (c+d x)}{2 b d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)}+\frac{\tan ^{-1}(\sinh (c+d x))}{b^2 d}","-\frac{\sqrt{a} (2 a+3 b) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{2 b^2 d (a+b)^{3/2}}-\frac{a \sinh (c+d x)}{2 b d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)}+\frac{\tan ^{-1}(\sinh (c+d x))}{b^2 d}",1,"ArcTan[Sinh[c + d*x]]/(b^2*d) - (Sqrt[a]*(2*a + 3*b)*ArcTan[(Sqrt[a]*Sinh[c + d*x])/Sqrt[a + b]])/(2*b^2*(a + b)^(3/2)*d) - (a*Sinh[c + d*x])/(2*b*(a + b)*d*(a + b + a*Sinh[c + d*x]^2))","A",5,5,23,0.2174,1,"{4147, 414, 522, 203, 205}"
91,1,101,0,0.141507,"\int \frac{\text{sech}^6(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]^6/(a + b*Sech[c + d*x]^2)^2,x]","\frac{a^2 \tanh (c+d x)}{2 b^2 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{a (3 a+4 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 b^{5/2} d (a+b)^{3/2}}+\frac{\tanh (c+d x)}{b^2 d}","\frac{a^2 \tanh (c+d x)}{2 b^2 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{a (3 a+4 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 b^{5/2} d (a+b)^{3/2}}+\frac{\tanh (c+d x)}{b^2 d}",1,"-(a*(3*a + 4*b)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(2*b^(5/2)*(a + b)^(3/2)*d) + Tanh[c + d*x]/(b^2*d) + (a^2*Tanh[c + d*x])/(2*b^2*(a + b)*d*(a + b - b*Tanh[c + d*x]^2))","A",5,4,23,0.1739,1,"{4146, 390, 385, 208}"
92,1,153,0,0.199911,"\int \frac{\text{sech}^7(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]^7/(a + b*Sech[c + d*x]^2)^2,x]","\frac{a^{3/2} (4 a+5 b) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{2 b^3 d (a+b)^{3/2}}+\frac{a (2 a+b) \sinh (c+d x)}{2 b^2 d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)}-\frac{(4 a-b) \tan ^{-1}(\sinh (c+d x))}{2 b^3 d}+\frac{\tanh (c+d x) \text{sech}(c+d x)}{2 b d \left(a \sinh ^2(c+d x)+a+b\right)}","\frac{a^{3/2} (4 a+5 b) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{2 b^3 d (a+b)^{3/2}}+\frac{a (2 a+b) \sinh (c+d x)}{2 b^2 d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)}-\frac{(4 a-b) \tan ^{-1}(\sinh (c+d x))}{2 b^3 d}+\frac{\tanh (c+d x) \text{sech}(c+d x)}{2 b d \left(a \sinh ^2(c+d x)+a+b\right)}",1,"-((4*a - b)*ArcTan[Sinh[c + d*x]])/(2*b^3*d) + (a^(3/2)*(4*a + 5*b)*ArcTan[(Sqrt[a]*Sinh[c + d*x])/Sqrt[a + b]])/(2*b^3*(a + b)^(3/2)*d) + (a*(2*a + b)*Sinh[c + d*x])/(2*b^2*(a + b)*d*(a + b + a*Sinh[c + d*x]^2)) + (Sech[c + d*x]*Tanh[c + d*x])/(2*b*d*(a + b + a*Sinh[c + d*x]^2))","A",6,6,23,0.2609,1,"{4147, 414, 527, 522, 203, 205}"
93,1,204,0,0.3772955,"\int \frac{\cosh ^2(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Cosh[c + d*x]^2/(a + b*Sech[c + d*x]^2)^3,x]","\frac{b^{3/2} \left(35 a^2+56 a b+24 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^4 d (a+b)^{5/2}}+\frac{b (4 a+3 b) (a+4 b) \tanh (c+d x)}{8 a^3 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{b (2 a+3 b) \tanh (c+d x)}{4 a^2 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^2}+\frac{x (a-6 b)}{2 a^4}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 a d \left(a-b \tanh ^2(c+d x)+b\right)^2}","\frac{b^{3/2} \left(35 a^2+56 a b+24 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^4 d (a+b)^{5/2}}+\frac{b (4 a+3 b) (a+4 b) \tanh (c+d x)}{8 a^3 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{b (2 a+3 b) \tanh (c+d x)}{4 a^2 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^2}+\frac{x (a-6 b)}{2 a^4}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 a d \left(a-b \tanh ^2(c+d x)+b\right)^2}",1,"((a - 6*b)*x)/(2*a^4) + (b^(3/2)*(35*a^2 + 56*a*b + 24*b^2)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(8*a^4*(a + b)^(5/2)*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*a*d*(a + b - b*Tanh[c + d*x]^2)^2) + (b*(2*a + 3*b)*Tanh[c + d*x])/(4*a^2*(a + b)*d*(a + b - b*Tanh[c + d*x]^2)^2) + (b*(4*a + 3*b)*(a + 4*b)*Tanh[c + d*x])/(8*a^3*(a + b)^2*d*(a + b - b*Tanh[c + d*x]^2))","A",7,6,23,0.2609,1,"{4146, 414, 527, 522, 206, 208}"
94,1,154,0,0.1848151,"\int \frac{\cosh (c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Cosh[c + d*x]/(a + b*Sech[c + d*x]^2)^3,x]","-\frac{b^3 \sinh (c+d x)}{4 a^3 d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)^2}+\frac{3 b^2 (4 a+3 b) \sinh (c+d x)}{8 a^3 d (a+b)^2 \left(a \sinh ^2(c+d x)+a+b\right)}-\frac{3 b \left(4 (a+b)^2+(2 a+b)^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{8 a^{7/2} d (a+b)^{5/2}}+\frac{\sinh (c+d x)}{a^3 d}","-\frac{b^3 \sinh (c+d x)}{4 a^3 d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)^2}+\frac{3 b^2 (4 a+3 b) \sinh (c+d x)}{8 a^3 d (a+b)^2 \left(a \sinh ^2(c+d x)+a+b\right)}-\frac{3 b \left(4 (a+b)^2+(2 a+b)^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{8 a^{7/2} d (a+b)^{5/2}}+\frac{\sinh (c+d x)}{a^3 d}",1,"(-3*b*(4*(a + b)^2 + (2*a + b)^2)*ArcTan[(Sqrt[a]*Sinh[c + d*x])/Sqrt[a + b]])/(8*a^(7/2)*(a + b)^(5/2)*d) + Sinh[c + d*x]/(a^3*d) - (b^3*Sinh[c + d*x])/(4*a^3*(a + b)*d*(a + b + a*Sinh[c + d*x]^2)^2) + (3*b^2*(4*a + 3*b)*Sinh[c + d*x])/(8*a^3*(a + b)^2*d*(a + b + a*Sinh[c + d*x]^2))","A",6,5,21,0.2381,1,"{4147, 390, 1157, 385, 205}"
95,1,142,0,0.1366803,"\int \frac{\text{sech}(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]/(a + b*Sech[c + d*x]^2)^3,x]","\frac{\left(8 a^2+8 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{8 a^{5/2} d (a+b)^{5/2}}-\frac{3 b (2 a+b) \sinh (c+d x)}{8 a^2 d (a+b)^2 \left(a \sinh ^2(c+d x)+a+b\right)}-\frac{b \sinh (c+d x) \cosh ^2(c+d x)}{4 a d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)^2}","\frac{\left(8 a^2+8 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{8 a^{5/2} d (a+b)^{5/2}}-\frac{3 b (2 a+b) \sinh (c+d x)}{8 a^2 d (a+b)^2 \left(a \sinh ^2(c+d x)+a+b\right)}-\frac{b \sinh (c+d x) \cosh ^2(c+d x)}{4 a d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)^2}",1,"((8*a^2 + 8*a*b + 3*b^2)*ArcTan[(Sqrt[a]*Sinh[c + d*x])/Sqrt[a + b]])/(8*a^(5/2)*(a + b)^(5/2)*d) - (b*Cosh[c + d*x]^2*Sinh[c + d*x])/(4*a*(a + b)*d*(a + b + a*Sinh[c + d*x]^2)^2) - (3*b*(2*a + b)*Sinh[c + d*x])/(8*a^2*(a + b)^2*d*(a + b + a*Sinh[c + d*x]^2))","A",4,4,21,0.1905,1,"{4147, 413, 385, 205}"
96,1,108,0,0.090436,"\int \frac{\text{sech}^2(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]^2/(a + b*Sech[c + d*x]^2)^3,x]","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 \sqrt{b} d (a+b)^{5/2}}+\frac{3 \tanh (c+d x)}{8 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{\tanh (c+d x)}{4 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^2}","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 \sqrt{b} d (a+b)^{5/2}}+\frac{3 \tanh (c+d x)}{8 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{\tanh (c+d x)}{4 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^2}",1,"(3*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(8*Sqrt[b]*(a + b)^(5/2)*d) + Tanh[c + d*x]/(4*(a + b)*d*(a + b - b*Tanh[c + d*x]^2)^2) + (3*Tanh[c + d*x])/(8*(a + b)^2*d*(a + b - b*Tanh[c + d*x]^2))","A",4,3,23,0.1304,1,"{4146, 199, 208}"
97,1,123,0,0.1083699,"\int \frac{\text{sech}^3(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]^3/(a + b*Sech[c + d*x]^2)^3,x]","\frac{(4 a+b) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{8 a^{3/2} d (a+b)^{5/2}}+\frac{(4 a+b) \sinh (c+d x)}{8 a d (a+b)^2 \left(a \sinh ^2(c+d x)+a+b\right)}-\frac{b \sinh (c+d x)}{4 a d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)^2}","\frac{(4 a+b) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{8 a^{3/2} d (a+b)^{5/2}}+\frac{(4 a+b) \sinh (c+d x)}{8 a d (a+b)^2 \left(a \sinh ^2(c+d x)+a+b\right)}-\frac{b \sinh (c+d x)}{4 a d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)^2}",1,"((4*a + b)*ArcTan[(Sqrt[a]*Sinh[c + d*x])/Sqrt[a + b]])/(8*a^(3/2)*(a + b)^(5/2)*d) - (b*Sinh[c + d*x])/(4*a*(a + b)*d*(a + b + a*Sinh[c + d*x]^2)^2) + ((4*a + b)*Sinh[c + d*x])/(8*a*(a + b)^2*d*(a + b + a*Sinh[c + d*x]^2))","A",4,4,23,0.1739,1,"{4147, 385, 199, 205}"
98,1,125,0,0.1073517,"\int \frac{\text{sech}^4(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]^4/(a + b*Sech[c + d*x]^2)^3,x]","\frac{(a+4 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 b^{3/2} d (a+b)^{5/2}}+\frac{(a+4 b) \tanh (c+d x)}{8 b d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{a \tanh (c+d x)}{4 b d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^2}","\frac{(a+4 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 b^{3/2} d (a+b)^{5/2}}+\frac{(a+4 b) \tanh (c+d x)}{8 b d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{a \tanh (c+d x)}{4 b d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^2}",1,"((a + 4*b)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(8*b^(3/2)*(a + b)^(5/2)*d) - (a*Tanh[c + d*x])/(4*b*(a + b)*d*(a + b - b*Tanh[c + d*x]^2)^2) + ((a + 4*b)*Tanh[c + d*x])/(8*b*(a + b)^2*d*(a + b - b*Tanh[c + d*x]^2))","A",4,4,23,0.1739,1,"{4146, 385, 199, 208}"
99,1,106,0,0.0921015,"\int \frac{\text{sech}^5(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]^5/(a + b*Sech[c + d*x]^2)^3,x]","\frac{3 \sinh (c+d x)}{8 d (a+b)^2 \left(a \sinh ^2(c+d x)+a+b\right)}+\frac{\sinh (c+d x)}{4 d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)^2}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{8 \sqrt{a} d (a+b)^{5/2}}","\frac{3 \sinh (c+d x)}{8 d (a+b)^2 \left(a \sinh ^2(c+d x)+a+b\right)}+\frac{\sinh (c+d x)}{4 d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)^2}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{8 \sqrt{a} d (a+b)^{5/2}}",1,"(3*ArcTan[(Sqrt[a]*Sinh[c + d*x])/Sqrt[a + b]])/(8*Sqrt[a]*(a + b)^(5/2)*d) + Sinh[c + d*x]/(4*(a + b)*d*(a + b + a*Sinh[c + d*x]^2)^2) + (3*Sinh[c + d*x])/(8*(a + b)^2*d*(a + b + a*Sinh[c + d*x]^2))","A",4,3,23,0.1304,1,"{4147, 199, 205}"
100,1,144,0,0.1423835,"\int \frac{\text{sech}^6(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]^6/(a + b*Sech[c + d*x]^2)^3,x]","\frac{\left(3 a^2+8 a b+8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 b^{5/2} d (a+b)^{5/2}}-\frac{3 a (a+2 b) \tanh (c+d x)}{8 b^2 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{a \tanh (c+d x) \text{sech}^2(c+d x)}{4 b d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^2}","\frac{\left(3 a^2+8 a b+8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 b^{5/2} d (a+b)^{5/2}}-\frac{3 a (a+2 b) \tanh (c+d x)}{8 b^2 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{a \tanh (c+d x) \text{sech}^2(c+d x)}{4 b d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^2}",1,"((3*a^2 + 8*a*b + 8*b^2)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(8*b^(5/2)*(a + b)^(5/2)*d) - (a*Sech[c + d*x]^2*Tanh[c + d*x])/(4*b*(a + b)*d*(a + b - b*Tanh[c + d*x]^2)^2) - (3*a*(a + 2*b)*Tanh[c + d*x])/(8*b^2*(a + b)^2*d*(a + b - b*Tanh[c + d*x]^2))","A",4,4,23,0.1739,1,"{4146, 413, 385, 208}"
101,1,153,0,0.2046831,"\int \frac{\text{sech}^7(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]^7/(a + b*Sech[c + d*x]^2)^3,x]","-\frac{\sqrt{a} \left(8 a^2+20 a b+15 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{8 b^3 d (a+b)^{5/2}}-\frac{a (4 a+7 b) \sinh (c+d x)}{8 b^2 d (a+b)^2 \left(a \sinh ^2(c+d x)+a+b\right)}-\frac{a \sinh (c+d x)}{4 b d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)^2}+\frac{\tan ^{-1}(\sinh (c+d x))}{b^3 d}","-\frac{\sqrt{a} \left(8 a^2+20 a b+15 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a} \sinh (c+d x)}{\sqrt{a+b}}\right)}{8 b^3 d (a+b)^{5/2}}-\frac{a (4 a+7 b) \sinh (c+d x)}{8 b^2 d (a+b)^2 \left(a \sinh ^2(c+d x)+a+b\right)}-\frac{a \sinh (c+d x)}{4 b d (a+b) \left(a \sinh ^2(c+d x)+a+b\right)^2}+\frac{\tan ^{-1}(\sinh (c+d x))}{b^3 d}",1,"ArcTan[Sinh[c + d*x]]/(b^3*d) - (Sqrt[a]*(8*a^2 + 20*a*b + 15*b^2)*ArcTan[(Sqrt[a]*Sinh[c + d*x])/Sqrt[a + b]])/(8*b^3*(a + b)^(5/2)*d) - (a*Sinh[c + d*x])/(4*b*(a + b)*d*(a + b + a*Sinh[c + d*x]^2)^2) - (a*(4*a + 7*b)*Sinh[c + d*x])/(8*b^2*(a + b)^2*d*(a + b + a*Sinh[c + d*x]^2))","A",6,6,23,0.2609,1,"{4147, 414, 527, 522, 203, 205}"
102,1,48,0,0.0638269,"\int \left(a+b \text{sech}^2(c+d x)\right) \tanh ^4(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)*Tanh[c + d*x]^4,x]","-\frac{a \tanh ^3(c+d x)}{3 d}-\frac{a \tanh (c+d x)}{d}+a x+\frac{b \tanh ^5(c+d x)}{5 d}","-\frac{a \tanh ^3(c+d x)}{3 d}-\frac{a \tanh (c+d x)}{d}+a x+\frac{b \tanh ^5(c+d x)}{5 d}",1,"a*x - (a*Tanh[c + d*x])/d - (a*Tanh[c + d*x]^3)/(3*d) + (b*Tanh[c + d*x]^5)/(5*d)","A",4,3,21,0.1429,1,"{4141, 1802, 206}"
103,1,49,0,0.0564093,"\int \left(a+b \text{sech}^2(c+d x)\right) \tanh ^3(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)*Tanh[c + d*x]^3,x]","\frac{(a-b) \text{sech}^2(c+d x)}{2 d}+\frac{a \log (\cosh (c+d x))}{d}+\frac{b \text{sech}^4(c+d x)}{4 d}","\frac{(a-b) \text{sech}^2(c+d x)}{2 d}+\frac{a \log (\cosh (c+d x))}{d}+\frac{b \text{sech}^4(c+d x)}{4 d}",1,"(a*Log[Cosh[c + d*x]])/d + ((a - b)*Sech[c + d*x]^2)/(2*d) + (b*Sech[c + d*x]^4)/(4*d)","A",4,3,21,0.1429,1,"{4138, 446, 76}"
104,1,32,0,0.0570871,"\int \left(a+b \text{sech}^2(c+d x)\right) \tanh ^2(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)*Tanh[c + d*x]^2,x]","-\frac{a \tanh (c+d x)}{d}+a x+\frac{b \tanh ^3(c+d x)}{3 d}","-\frac{a \tanh (c+d x)}{d}+a x+\frac{b \tanh ^3(c+d x)}{3 d}",1,"a*x - (a*Tanh[c + d*x])/d + (b*Tanh[c + d*x]^3)/(3*d)","A",4,3,21,0.1429,1,"{4141, 1802, 206}"
105,1,29,0,0.0283861,"\int \left(a+b \text{sech}^2(c+d x)\right) \tanh (c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)*Tanh[c + d*x],x]","\frac{a \log (\cosh (c+d x))}{d}-\frac{b \text{sech}^2(c+d x)}{2 d}","\frac{a \log (\cosh (c+d x))}{d}-\frac{b \text{sech}^2(c+d x)}{2 d}",1,"(a*Log[Cosh[c + d*x]])/d - (b*Sech[c + d*x]^2)/(2*d)","A",3,2,19,0.1053,1,"{4138, 14}"
106,1,15,0,0.0132529,"\int \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[a + b*Sech[c + d*x]^2,x]","a x+\frac{b \tanh (c+d x)}{d}","a x+\frac{b \tanh (c+d x)}{d}",1,"a*x + (b*Tanh[c + d*x])/d","A",3,2,12,0.1667,1,"{3767, 8}"
107,1,28,0,0.0514288,"\int \coth (c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Coth[c + d*x]*(a + b*Sech[c + d*x]^2),x]","\frac{(a+b) \log (\sinh (c+d x))}{d}-\frac{b \log (\cosh (c+d x))}{d}","\frac{(a+b) \log (\sinh (c+d x))}{d}-\frac{b \log (\cosh (c+d x))}{d}",1,"-((b*Log[Cosh[c + d*x]])/d) + ((a + b)*Log[Sinh[c + d*x]])/d","A",4,3,19,0.1579,1,"{4138, 446, 72}"
108,1,18,0,0.0585628,"\int \coth ^2(c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Coth[c + d*x]^2*(a + b*Sech[c + d*x]^2),x]","a x-\frac{(a+b) \coth (c+d x)}{d}","a x-\frac{(a+b) \coth (c+d x)}{d}",1,"a*x - ((a + b)*Coth[c + d*x])/d","A",4,3,21,0.1429,1,"{4141, 1802, 207}"
109,1,31,0,0.0565121,"\int \coth ^3(c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Coth[c + d*x]^3*(a + b*Sech[c + d*x]^2),x]","\frac{a \log (\sinh (c+d x))}{d}-\frac{(a+b) \text{csch}^2(c+d x)}{2 d}","\frac{a \log (\sinh (c+d x))}{d}-\frac{(a+b) \text{csch}^2(c+d x)}{2 d}",1,"-((a + b)*Csch[c + d*x]^2)/(2*d) + (a*Log[Sinh[c + d*x]])/d","A",4,3,21,0.1429,1,"{4138, 444, 43}"
110,1,34,0,0.0628673,"\int \coth ^4(c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Coth[c + d*x]^4*(a + b*Sech[c + d*x]^2),x]","-\frac{(a+b) \coth ^3(c+d x)}{3 d}-\frac{a \coth (c+d x)}{d}+a x","-\frac{(a+b) \coth ^3(c+d x)}{3 d}-\frac{a \coth (c+d x)}{d}+a x",1,"a*x - (a*Coth[c + d*x])/d - ((a + b)*Coth[c + d*x]^3)/(3*d)","A",4,3,21,0.1429,1,"{4141, 1802, 207}"
111,1,51,0,0.0781343,"\int \coth ^5(c+d x) \left(a+b \text{sech}^2(c+d x)\right) \, dx","Int[Coth[c + d*x]^5*(a + b*Sech[c + d*x]^2),x]","-\frac{(a+b) \text{csch}^4(c+d x)}{4 d}-\frac{(2 a+b) \text{csch}^2(c+d x)}{2 d}+\frac{a \log (\sinh (c+d x))}{d}","-\frac{(a+b) \text{csch}^4(c+d x)}{4 d}-\frac{(2 a+b) \text{csch}^2(c+d x)}{2 d}+\frac{a \log (\sinh (c+d x))}{d}",1,"-((2*a + b)*Csch[c + d*x]^2)/(2*d) - ((a + b)*Csch[c + d*x]^4)/(4*d) + (a*Log[Sinh[c + d*x]])/d","A",4,3,21,0.1429,1,"{4138, 446, 77}"
112,1,77,0,0.1046352,"\int \left(a+b \text{sech}^2(c+d x)\right)^2 \tanh ^4(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)^2*Tanh[c + d*x]^4,x]","-\frac{a^2 \tanh ^3(c+d x)}{3 d}-\frac{a^2 \tanh (c+d x)}{d}+a^2 x+\frac{b (2 a+b) \tanh ^5(c+d x)}{5 d}-\frac{b^2 \tanh ^7(c+d x)}{7 d}","-\frac{a^2 \tanh ^3(c+d x)}{3 d}-\frac{a^2 \tanh (c+d x)}{d}+a^2 x+\frac{b (2 a+b) \tanh ^5(c+d x)}{5 d}-\frac{b^2 \tanh ^7(c+d x)}{7 d}",1,"a^2*x - (a^2*Tanh[c + d*x])/d - (a^2*Tanh[c + d*x]^3)/(3*d) + (b*(2*a + b)*Tanh[c + d*x]^5)/(5*d) - (b^2*Tanh[c + d*x]^7)/(7*d)","A",4,3,23,0.1304,1,"{4141, 1802, 206}"
113,1,77,0,0.094726,"\int \left(a+b \text{sech}^2(c+d x)\right)^2 \tanh ^3(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)^2*Tanh[c + d*x]^3,x]","\frac{a^2 \log (\cosh (c+d x))}{d}+\frac{b (2 a-b) \text{sech}^4(c+d x)}{4 d}+\frac{a (a-2 b) \text{sech}^2(c+d x)}{2 d}+\frac{b^2 \text{sech}^6(c+d x)}{6 d}","\frac{a^2 \log (\cosh (c+d x))}{d}+\frac{b (2 a-b) \text{sech}^4(c+d x)}{4 d}+\frac{a (a-2 b) \text{sech}^2(c+d x)}{2 d}+\frac{b^2 \text{sech}^6(c+d x)}{6 d}",1,"(a^2*Log[Cosh[c + d*x]])/d + (a*(a - 2*b)*Sech[c + d*x]^2)/(2*d) + ((2*a - b)*b*Sech[c + d*x]^4)/(4*d) + (b^2*Sech[c + d*x]^6)/(6*d)","A",4,3,23,0.1304,1,"{4138, 446, 76}"
114,1,59,0,0.0980225,"\int \left(a+b \text{sech}^2(c+d x)\right)^2 \tanh ^2(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)^2*Tanh[c + d*x]^2,x]","-\frac{a^2 \tanh (c+d x)}{d}+a^2 x+\frac{b (2 a+b) \tanh ^3(c+d x)}{3 d}-\frac{b^2 \tanh ^5(c+d x)}{5 d}","-\frac{a^2 \tanh (c+d x)}{d}+a^2 x+\frac{b (2 a+b) \tanh ^3(c+d x)}{3 d}-\frac{b^2 \tanh ^5(c+d x)}{5 d}",1,"a^2*x - (a^2*Tanh[c + d*x])/d + (b*(2*a + b)*Tanh[c + d*x]^3)/(3*d) - (b^2*Tanh[c + d*x]^5)/(5*d)","A",4,3,23,0.1304,1,"{4141, 1802, 206}"
115,1,48,0,0.0500898,"\int \left(a+b \text{sech}^2(c+d x)\right)^2 \tanh (c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)^2*Tanh[c + d*x],x]","\frac{a^2 \log (\cosh (c+d x))}{d}-\frac{a b \text{sech}^2(c+d x)}{d}-\frac{b^2 \text{sech}^4(c+d x)}{4 d}","\frac{a^2 \log (\cosh (c+d x))}{d}-\frac{a b \text{sech}^2(c+d x)}{d}-\frac{b^2 \text{sech}^4(c+d x)}{4 d}",1,"(a^2*Log[Cosh[c + d*x]])/d - (a*b*Sech[c + d*x]^2)/d - (b^2*Sech[c + d*x]^4)/(4*d)","A",4,3,21,0.1429,1,"{4138, 266, 43}"
116,1,40,0,0.0341698,"\int \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[(a + b*Sech[c + d*x]^2)^2,x]","a^2 x+\frac{b (2 a+b) \tanh (c+d x)}{d}-\frac{b^2 \tanh ^3(c+d x)}{3 d}","a^2 x+\frac{b (2 a+b) \tanh (c+d x)}{d}-\frac{b^2 \tanh ^3(c+d x)}{3 d}",1,"a^2*x + (b*(2*a + b)*Tanh[c + d*x])/d - (b^2*Tanh[c + d*x]^3)/(3*d)","A",4,3,14,0.2143,1,"{4128, 390, 206}"
117,1,53,0,0.0801266,"\int \coth (c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Coth[c + d*x]*(a + b*Sech[c + d*x]^2)^2,x]","\frac{(a+b)^2 \log (\sinh (c+d x))}{d}-\frac{b (2 a+b) \log (\cosh (c+d x))}{d}+\frac{b^2 \text{sech}^2(c+d x)}{2 d}","\frac{(a+b)^2 \log (\sinh (c+d x))}{d}-\frac{b (2 a+b) \log (\cosh (c+d x))}{d}+\frac{b^2 \text{sech}^2(c+d x)}{2 d}",1,"-((b*(2*a + b)*Log[Cosh[c + d*x]])/d) + ((a + b)^2*Log[Sinh[c + d*x]])/d + (b^2*Sech[c + d*x]^2)/(2*d)","A",4,3,21,0.1429,1,"{4138, 446, 88}"
118,1,36,0,0.0851578,"\int \coth ^2(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Coth[c + d*x]^2*(a + b*Sech[c + d*x]^2)^2,x]","a^2 x-\frac{(a+b)^2 \coth (c+d x)}{d}-\frac{b^2 \tanh (c+d x)}{d}","a^2 x-\frac{(a+b)^2 \coth (c+d x)}{d}-\frac{b^2 \tanh (c+d x)}{d}",1,"a^2*x - ((a + b)^2*Coth[c + d*x])/d - (b^2*Tanh[c + d*x])/d","A",4,3,23,0.1304,1,"{4141, 1802, 207}"
119,1,55,0,0.089335,"\int \coth ^3(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Coth[c + d*x]^3*(a + b*Sech[c + d*x]^2)^2,x]","\frac{\left(a^2-b^2\right) \log (\sinh (c+d x))}{d}-\frac{(a+b)^2 \text{csch}^2(c+d x)}{2 d}+\frac{b^2 \log (\cosh (c+d x))}{d}","\frac{\left(a^2-b^2\right) \log (\sinh (c+d x))}{d}-\frac{(a+b)^2 \text{csch}^2(c+d x)}{2 d}+\frac{b^2 \log (\cosh (c+d x))}{d}",1,"-((a + b)^2*Csch[c + d*x]^2)/(2*d) + (b^2*Log[Cosh[c + d*x]])/d + ((a^2 - b^2)*Log[Sinh[c + d*x]])/d","A",4,3,23,0.1304,1,"{4138, 446, 88}"
120,1,46,0,0.0917147,"\int \coth ^4(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Coth[c + d*x]^4*(a + b*Sech[c + d*x]^2)^2,x]","-\frac{\left(a^2-b^2\right) \coth (c+d x)}{d}+a^2 x-\frac{(a+b)^2 \coth ^3(c+d x)}{3 d}","-\frac{\left(a^2-b^2\right) \coth (c+d x)}{d}+a^2 x-\frac{(a+b)^2 \coth ^3(c+d x)}{3 d}",1,"a^2*x - ((a^2 - b^2)*Coth[c + d*x])/d - ((a + b)^2*Coth[c + d*x]^3)/(3*d)","A",4,3,23,0.1304,1,"{4141, 1802, 207}"
121,1,52,0,0.0939137,"\int \coth ^5(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Coth[c + d*x]^5*(a + b*Sech[c + d*x]^2)^2,x]","\frac{a^2 \log (\sinh (c+d x))}{d}-\frac{(a+b)^2 \text{csch}^4(c+d x)}{4 d}-\frac{a (a+b) \text{csch}^2(c+d x)}{d}","\frac{a^2 \log (\sinh (c+d x))}{d}-\frac{(a+b)^2 \text{csch}^4(c+d x)}{4 d}-\frac{a (a+b) \text{csch}^2(c+d x)}{d}",1,"-((a*(a + b)*Csch[c + d*x]^2)/d) - ((a + b)^2*Csch[c + d*x]^4)/(4*d) + (a^2*Log[Sinh[c + d*x]])/d","A",4,3,23,0.1304,1,"{4138, 444, 43}"
122,1,64,0,0.0970039,"\int \coth ^6(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Coth[c + d*x]^6*(a + b*Sech[c + d*x]^2)^2,x]","-\frac{\left(a^2-b^2\right) \coth ^3(c+d x)}{3 d}-\frac{a^2 \coth (c+d x)}{d}+a^2 x-\frac{(a+b)^2 \coth ^5(c+d x)}{5 d}","-\frac{\left(a^2-b^2\right) \coth ^3(c+d x)}{3 d}-\frac{a^2 \coth (c+d x)}{d}+a^2 x-\frac{(a+b)^2 \coth ^5(c+d x)}{5 d}",1,"a^2*x - (a^2*Coth[c + d*x])/d - ((a^2 - b^2)*Coth[c + d*x]^3)/(3*d) - ((a + b)^2*Coth[c + d*x]^5)/(5*d)","A",4,3,23,0.1304,1,"{4141, 1802, 207}"
123,1,86,0,0.1248448,"\int \coth ^7(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^2 \, dx","Int[Coth[c + d*x]^7*(a + b*Sech[c + d*x]^2)^2,x]","\frac{a^2 \log (\sinh (c+d x))}{d}-\frac{(a+b)^2 \text{csch}^4(c+d x)}{4 d}-\frac{a (a+b) \text{csch}^2(c+d x)}{d}-\frac{\text{csch}^6(c+d x) \left(a \cosh ^2(c+d x)+b\right)^3}{6 d (a+b)}","\frac{a^2 \log (\sinh (c+d x))}{d}-\frac{(a+b)^2 \text{csch}^4(c+d x)}{4 d}-\frac{a (a+b) \text{csch}^2(c+d x)}{d}-\frac{\text{csch}^6(c+d x) \left(a \cosh ^2(c+d x)+b\right)^3}{6 d (a+b)}",1,"-((a*(a + b)*Csch[c + d*x]^2)/d) - ((a + b)^2*Csch[c + d*x]^4)/(4*d) - ((b + a*Cosh[c + d*x]^2)^3*Csch[c + d*x]^6)/(6*(a + b)*d) + (a^2*Log[Sinh[c + d*x]])/d","A",5,4,23,0.1739,1,"{4138, 446, 78, 43}"
124,1,110,0,0.1181629,"\int \left(a+b \text{sech}^2(c+d x)\right)^3 \tanh ^4(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)^3*Tanh[c + d*x]^4,x]","\frac{b \left(3 a^2+3 a b+b^2\right) \tanh ^5(c+d x)}{5 d}-\frac{a^3 \tanh ^3(c+d x)}{3 d}-\frac{a^3 \tanh (c+d x)}{d}+a^3 x-\frac{b^2 (3 a+2 b) \tanh ^7(c+d x)}{7 d}+\frac{b^3 \tanh ^9(c+d x)}{9 d}","\frac{b \left(3 a^2+3 a b+b^2\right) \tanh ^5(c+d x)}{5 d}-\frac{a^3 \tanh ^3(c+d x)}{3 d}-\frac{a^3 \tanh (c+d x)}{d}+a^3 x-\frac{b^2 (3 a+2 b) \tanh ^7(c+d x)}{7 d}+\frac{b^3 \tanh ^9(c+d x)}{9 d}",1,"a^3*x - (a^3*Tanh[c + d*x])/d - (a^3*Tanh[c + d*x]^3)/(3*d) + (b*(3*a^2 + 3*a*b + b^2)*Tanh[c + d*x]^5)/(5*d) - (b^2*(3*a + 2*b)*Tanh[c + d*x]^7)/(7*d) + (b^3*Tanh[c + d*x]^9)/(9*d)","A",4,3,23,0.1304,1,"{4141, 1802, 206}"
125,1,103,0,0.0976315,"\int \left(a+b \text{sech}^2(c+d x)\right)^3 \tanh ^3(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)^3*Tanh[c + d*x]^3,x]","-\frac{3 a^2 b \text{sech}^2(c+d x)}{2 d}+\frac{a^3 \log (\cosh (c+d x))}{d}-\frac{3 a b^2 \text{sech}^4(c+d x)}{4 d}+\frac{\text{sech}^8(c+d x) \left(a \cosh ^2(c+d x)+b\right)^4}{8 b d}-\frac{b^3 \text{sech}^6(c+d x)}{6 d}","-\frac{3 a^2 b \text{sech}^2(c+d x)}{2 d}+\frac{a^3 \log (\cosh (c+d x))}{d}-\frac{3 a b^2 \text{sech}^4(c+d x)}{4 d}+\frac{\text{sech}^8(c+d x) \left(a \cosh ^2(c+d x)+b\right)^4}{8 b d}-\frac{b^3 \text{sech}^6(c+d x)}{6 d}",1,"(a^3*Log[Cosh[c + d*x]])/d - (3*a^2*b*Sech[c + d*x]^2)/(2*d) - (3*a*b^2*Sech[c + d*x]^4)/(4*d) - (b^3*Sech[c + d*x]^6)/(6*d) + ((b + a*Cosh[c + d*x]^2)^4*Sech[c + d*x]^8)/(8*b*d)","A",5,4,23,0.1739,1,"{4138, 446, 78, 43}"
126,1,92,0,0.110217,"\int \left(a+b \text{sech}^2(c+d x)\right)^3 \tanh ^2(c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)^3*Tanh[c + d*x]^2,x]","\frac{b \left(3 a^2+3 a b+b^2\right) \tanh ^3(c+d x)}{3 d}-\frac{a^3 \tanh (c+d x)}{d}+a^3 x-\frac{b^2 (3 a+2 b) \tanh ^5(c+d x)}{5 d}+\frac{b^3 \tanh ^7(c+d x)}{7 d}","\frac{b \left(3 a^2+3 a b+b^2\right) \tanh ^3(c+d x)}{3 d}-\frac{a^3 \tanh (c+d x)}{d}+a^3 x-\frac{b^2 (3 a+2 b) \tanh ^5(c+d x)}{5 d}+\frac{b^3 \tanh ^7(c+d x)}{7 d}",1,"a^3*x - (a^3*Tanh[c + d*x])/d + (b*(3*a^2 + 3*a*b + b^2)*Tanh[c + d*x]^3)/(3*d) - (b^2*(3*a + 2*b)*Tanh[c + d*x]^5)/(5*d) + (b^3*Tanh[c + d*x]^7)/(7*d)","A",4,3,23,0.1304,1,"{4141, 1802, 206}"
127,1,71,0,0.0581538,"\int \left(a+b \text{sech}^2(c+d x)\right)^3 \tanh (c+d x) \, dx","Int[(a + b*Sech[c + d*x]^2)^3*Tanh[c + d*x],x]","-\frac{3 a^2 b \text{sech}^2(c+d x)}{2 d}+\frac{a^3 \log (\cosh (c+d x))}{d}-\frac{3 a b^2 \text{sech}^4(c+d x)}{4 d}-\frac{b^3 \text{sech}^6(c+d x)}{6 d}","-\frac{3 a^2 b \text{sech}^2(c+d x)}{2 d}+\frac{a^3 \log (\cosh (c+d x))}{d}-\frac{3 a b^2 \text{sech}^4(c+d x)}{4 d}-\frac{b^3 \text{sech}^6(c+d x)}{6 d}",1,"(a^3*Log[Cosh[c + d*x]])/d - (3*a^2*b*Sech[c + d*x]^2)/(2*d) - (3*a*b^2*Sech[c + d*x]^4)/(4*d) - (b^3*Sech[c + d*x]^6)/(6*d)","A",4,3,21,0.1429,1,"{4138, 266, 43}"
128,1,73,0,0.0469913,"\int \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[(a + b*Sech[c + d*x]^2)^3,x]","\frac{b \left(3 a^2+3 a b+b^2\right) \tanh (c+d x)}{d}+a^3 x-\frac{b^2 (3 a+2 b) \tanh ^3(c+d x)}{3 d}+\frac{b^3 \tanh ^5(c+d x)}{5 d}","\frac{b \left(3 a^2+3 a b+b^2\right) \tanh (c+d x)}{d}+a^3 x-\frac{b^2 (3 a+2 b) \tanh ^3(c+d x)}{3 d}+\frac{b^3 \tanh ^5(c+d x)}{5 d}",1,"a^3*x + (b*(3*a^2 + 3*a*b + b^2)*Tanh[c + d*x])/d - (b^2*(3*a + 2*b)*Tanh[c + d*x]^3)/(3*d) + (b^3*Tanh[c + d*x]^5)/(5*d)","A",4,3,14,0.2143,1,"{4128, 390, 206}"
129,1,84,0,0.1067829,"\int \coth (c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Coth[c + d*x]*(a + b*Sech[c + d*x]^2)^3,x]","-\frac{b \left(3 a^2+3 a b+b^2\right) \log (\cosh (c+d x))}{d}+\frac{b^2 (3 a+b) \text{sech}^2(c+d x)}{2 d}+\frac{(a+b)^3 \log (\sinh (c+d x))}{d}+\frac{b^3 \text{sech}^4(c+d x)}{4 d}","-\frac{b \left(3 a^2+3 a b+b^2\right) \log (\cosh (c+d x))}{d}+\frac{b^2 (3 a+b) \text{sech}^2(c+d x)}{2 d}+\frac{(a+b)^3 \log (\sinh (c+d x))}{d}+\frac{b^3 \text{sech}^4(c+d x)}{4 d}",1,"-((b*(3*a^2 + 3*a*b + b^2)*Log[Cosh[c + d*x]])/d) + ((a + b)^3*Log[Sinh[c + d*x]])/d + (b^2*(3*a + b)*Sech[c + d*x]^2)/(2*d) + (b^3*Sech[c + d*x]^4)/(4*d)","A",4,3,21,0.1429,1,"{4138, 446, 88}"
130,1,61,0,0.1025188,"\int \coth ^2(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Coth[c + d*x]^2*(a + b*Sech[c + d*x]^2)^3,x]","a^3 x-\frac{b^2 (3 a+2 b) \tanh (c+d x)}{d}-\frac{(a+b)^3 \coth (c+d x)}{d}+\frac{b^3 \tanh ^3(c+d x)}{3 d}","a^3 x-\frac{b^2 (3 a+2 b) \tanh (c+d x)}{d}-\frac{(a+b)^3 \coth (c+d x)}{d}+\frac{b^3 \tanh ^3(c+d x)}{3 d}",1,"a^3*x - ((a + b)^3*Coth[c + d*x])/d - (b^2*(3*a + 2*b)*Tanh[c + d*x])/d + (b^3*Tanh[c + d*x]^3)/(3*d)","A",4,3,23,0.1304,1,"{4141, 1802, 207}"
131,1,81,0,0.1164445,"\int \coth ^3(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Coth[c + d*x]^3*(a + b*Sech[c + d*x]^2)^3,x]","\frac{b^2 (3 a+2 b) \log (\cosh (c+d x))}{d}-\frac{(a+b)^3 \text{csch}^2(c+d x)}{2 d}+\frac{(a-2 b) (a+b)^2 \log (\sinh (c+d x))}{d}-\frac{b^3 \text{sech}^2(c+d x)}{2 d}","\frac{b^2 (3 a+2 b) \log (\cosh (c+d x))}{d}-\frac{(a+b)^3 \text{csch}^2(c+d x)}{2 d}+\frac{(a-2 b) (a+b)^2 \log (\sinh (c+d x))}{d}-\frac{b^3 \text{sech}^2(c+d x)}{2 d}",1,"-((a + b)^3*Csch[c + d*x]^2)/(2*d) + (b^2*(3*a + 2*b)*Log[Cosh[c + d*x]])/d + ((a - 2*b)*(a + b)^2*Log[Sinh[c + d*x]])/d - (b^3*Sech[c + d*x]^2)/(2*d)","A",4,3,23,0.1304,1,"{4138, 446, 88}"
132,1,60,0,0.1009462,"\int \coth ^4(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Coth[c + d*x]^4*(a + b*Sech[c + d*x]^2)^3,x]","a^3 x-\frac{(a+b)^3 \coth ^3(c+d x)}{3 d}-\frac{(a-2 b) (a+b)^2 \coth (c+d x)}{d}+\frac{b^3 \tanh (c+d x)}{d}","a^3 x-\frac{(a+b)^3 \coth ^3(c+d x)}{3 d}-\frac{(a-2 b) (a+b)^2 \coth (c+d x)}{d}+\frac{b^3 \tanh (c+d x)}{d}",1,"a^3*x - ((a - 2*b)*(a + b)^2*Coth[c + d*x])/d - ((a + b)^3*Coth[c + d*x]^3)/(3*d) + (b^3*Tanh[c + d*x])/d","A",4,3,23,0.1304,1,"{4141, 1802, 207}"
133,1,81,0,0.1209946,"\int \coth ^5(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Coth[c + d*x]^5*(a + b*Sech[c + d*x]^2)^3,x]","\frac{\left(a^3+b^3\right) \log (\sinh (c+d x))}{d}-\frac{(a+b)^3 \text{csch}^4(c+d x)}{4 d}-\frac{(2 a-b) (a+b)^2 \text{csch}^2(c+d x)}{2 d}-\frac{b^3 \log (\cosh (c+d x))}{d}","\frac{\left(a^3+b^3\right) \log (\sinh (c+d x))}{d}-\frac{(a+b)^3 \text{csch}^4(c+d x)}{4 d}-\frac{(2 a-b) (a+b)^2 \text{csch}^2(c+d x)}{2 d}-\frac{b^3 \log (\cosh (c+d x))}{d}",1,"-((2*a - b)*(a + b)^2*Csch[c + d*x]^2)/(2*d) - ((a + b)^3*Csch[c + d*x]^4)/(4*d) - (b^3*Log[Cosh[c + d*x]])/d + ((a^3 + b^3)*Log[Sinh[c + d*x]])/d","A",4,3,23,0.1304,1,"{4138, 446, 88}"
134,1,69,0,0.1093483,"\int \coth ^6(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Coth[c + d*x]^6*(a + b*Sech[c + d*x]^2)^3,x]","-\frac{\left(a^3+b^3\right) \coth (c+d x)}{d}+a^3 x-\frac{(a+b)^3 \coth ^5(c+d x)}{5 d}-\frac{(a-2 b) (a+b)^2 \coth ^3(c+d x)}{3 d}","-\frac{\left(a^3+b^3\right) \coth (c+d x)}{d}+a^3 x-\frac{(a+b)^3 \coth ^5(c+d x)}{5 d}-\frac{(a-2 b) (a+b)^2 \coth ^3(c+d x)}{3 d}",1,"a^3*x - ((a^3 + b^3)*Coth[c + d*x])/d - ((a - 2*b)*(a + b)^2*Coth[c + d*x]^3)/(3*d) - ((a + b)^3*Coth[c + d*x]^5)/(5*d)","A",4,3,23,0.1304,1,"{4141, 1802, 207}"
135,1,77,0,0.1210029,"\int \coth ^7(c+d x) \left(a+b \text{sech}^2(c+d x)\right)^3 \, dx","Int[Coth[c + d*x]^7*(a + b*Sech[c + d*x]^2)^3,x]","-\frac{3 a^2 (a+b) \text{csch}^2(c+d x)}{2 d}+\frac{a^3 \log (\sinh (c+d x))}{d}-\frac{(a+b)^3 \text{csch}^6(c+d x)}{6 d}-\frac{3 a (a+b)^2 \text{csch}^4(c+d x)}{4 d}","-\frac{3 a^2 (a+b) \text{csch}^2(c+d x)}{2 d}+\frac{a^3 \log (\sinh (c+d x))}{d}-\frac{(a+b)^3 \text{csch}^6(c+d x)}{6 d}-\frac{3 a (a+b)^2 \text{csch}^4(c+d x)}{4 d}",1,"(-3*a^2*(a + b)*Csch[c + d*x]^2)/(2*d) - (3*a*(a + b)^2*Csch[c + d*x]^4)/(4*d) - ((a + b)^3*Csch[c + d*x]^6)/(6*d) + (a^3*Log[Sinh[c + d*x]])/d","A",4,3,23,0.1304,1,"{4138, 444, 43}"
136,1,111,0,0.0700309,"\int \left(a+b \text{sech}^2(c+d x)\right)^4 \, dx","Int[(a + b*Sech[c + d*x]^2)^4,x]","-\frac{b^2 \left(6 a^2+8 a b+3 b^2\right) \tanh ^3(c+d x)}{3 d}+\frac{b (2 a+b) \left(2 a^2+2 a b+b^2\right) \tanh (c+d x)}{d}+a^4 x+\frac{b^3 (4 a+3 b) \tanh ^5(c+d x)}{5 d}-\frac{b^4 \tanh ^7(c+d x)}{7 d}","-\frac{b^2 \left(6 a^2+8 a b+3 b^2\right) \tanh ^3(c+d x)}{3 d}+\frac{b (2 a+b) \left(2 a^2+2 a b+b^2\right) \tanh (c+d x)}{d}+a^4 x+\frac{b^3 (4 a+3 b) \tanh ^5(c+d x)}{5 d}-\frac{b^4 \tanh ^7(c+d x)}{7 d}",1,"a^4*x + (b*(2*a + b)*(2*a^2 + 2*a*b + b^2)*Tanh[c + d*x])/d - (b^2*(6*a^2 + 8*a*b + 3*b^2)*Tanh[c + d*x]^3)/(3*d) + (b^3*(4*a + 3*b)*Tanh[c + d*x]^5)/(5*d) - (b^4*Tanh[c + d*x]^7)/(7*d)","A",4,3,14,0.2143,1,"{4128, 390, 206}"
137,1,163,0,0.0952181,"\int \left(a+b \text{sech}^2(c+d x)\right)^5 \, dx","Int[(a + b*Sech[c + d*x]^2)^5,x]","\frac{b^3 \left(10 a^2+15 a b+6 b^2\right) \tanh ^5(c+d x)}{5 d}-\frac{b^2 \left(20 a^2 b+10 a^3+15 a b^2+4 b^3\right) \tanh ^3(c+d x)}{3 d}+\frac{b \left(10 a^2 b^2+10 a^3 b+5 a^4+5 a b^3+b^4\right) \tanh (c+d x)}{d}+a^5 x-\frac{b^4 (5 a+4 b) \tanh ^7(c+d x)}{7 d}+\frac{b^5 \tanh ^9(c+d x)}{9 d}","\frac{b^3 \left(10 a^2+15 a b+6 b^2\right) \tanh ^5(c+d x)}{5 d}-\frac{b^2 \left(20 a^2 b+10 a^3+15 a b^2+4 b^3\right) \tanh ^3(c+d x)}{3 d}+\frac{b \left(10 a^2 b^2+10 a^3 b+5 a^4+5 a b^3+b^4\right) \tanh (c+d x)}{d}+a^5 x-\frac{b^4 (5 a+4 b) \tanh ^7(c+d x)}{7 d}+\frac{b^5 \tanh ^9(c+d x)}{9 d}",1,"a^5*x + (b*(5*a^4 + 10*a^3*b + 10*a^2*b^2 + 5*a*b^3 + b^4)*Tanh[c + d*x])/d - (b^2*(10*a^3 + 20*a^2*b + 15*a*b^2 + 4*b^3)*Tanh[c + d*x]^3)/(3*d) + (b^3*(10*a^2 + 15*a*b + 6*b^2)*Tanh[c + d*x]^5)/(5*d) - (b^4*(5*a + 4*b)*Tanh[c + d*x]^7)/(7*d) + (b^5*Tanh[c + d*x]^9)/(9*d)","A",4,3,14,0.2143,1,"{4128, 390, 206}"
138,1,70,0,0.1115487,"\int \frac{\tanh ^5(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Tanh[c + d*x]^5/(a + b*Sech[c + d*x]^2),x]","\frac{(a+b)^2 \log \left(a \cosh ^2(c+d x)+b\right)}{2 a b^2 d}-\frac{(a+2 b) \log (\cosh (c+d x))}{b^2 d}-\frac{\text{sech}^2(c+d x)}{2 b d}","\frac{(a+b)^2 \log \left(a \cosh ^2(c+d x)+b\right)}{2 a b^2 d}-\frac{(a+2 b) \log (\cosh (c+d x))}{b^2 d}-\frac{\text{sech}^2(c+d x)}{2 b d}",1,"-(((a + 2*b)*Log[Cosh[c + d*x]])/(b^2*d)) + ((a + b)^2*Log[b + a*Cosh[c + d*x]^2])/(2*a*b^2*d) - Sech[c + d*x]^2/(2*b*d)","A",4,3,23,0.1304,1,"{4138, 446, 88}"
139,1,59,0,0.1781886,"\int \frac{\tanh ^4(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Tanh[c + d*x]^4/(a + b*Sech[c + d*x]^2),x]","-\frac{(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a b^{3/2} d}+\frac{x}{a}+\frac{\tanh (c+d x)}{b d}","-\frac{(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a b^{3/2} d}+\frac{x}{a}+\frac{\tanh (c+d x)}{b d}",1,"x/a - ((a + b)^(3/2)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(a*b^(3/2)*d) + Tanh[c + d*x]/(b*d)","A",6,6,23,0.2609,1,"{4141, 1975, 479, 522, 206, 208}"
140,1,45,0,0.0883408,"\int \frac{\tanh ^3(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Tanh[c + d*x]^3/(a + b*Sech[c + d*x]^2),x]","\frac{(a+b) \log \left(a \cosh ^2(c+d x)+b\right)}{2 a b d}-\frac{\log (\cosh (c+d x))}{b d}","\frac{(a+b) \log \left(a \cosh ^2(c+d x)+b\right)}{2 a b d}-\frac{\log (\cosh (c+d x))}{b d}",1,"-(Log[Cosh[c + d*x]]/(b*d)) + ((a + b)*Log[b + a*Cosh[c + d*x]^2])/(2*a*b*d)","A",4,3,23,0.1304,1,"{4138, 446, 72}"
141,1,46,0,0.1403978,"\int \frac{\tanh ^2(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Tanh[c + d*x]^2/(a + b*Sech[c + d*x]^2),x]","\frac{x}{a}-\frac{\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a \sqrt{b} d}","\frac{x}{a}-\frac{\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a \sqrt{b} d}",1,"x/a - (Sqrt[a + b]*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(a*Sqrt[b]*d)","A",5,5,23,0.2174,1,"{4141, 1975, 481, 206, 208}"
142,1,23,0,0.0347621,"\int \frac{\tanh (c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Tanh[c + d*x]/(a + b*Sech[c + d*x]^2),x]","\frac{\log \left(a \cosh ^2(c+d x)+b\right)}{2 a d}","\frac{\log \left(a \cosh ^2(c+d x)+b\right)}{2 a d}",1,"Log[b + a*Cosh[c + d*x]^2]/(2*a*d)","A",2,2,21,0.09524,1,"{4138, 260}"
143,1,46,0,0.0463049,"\int \frac{1}{a+b \text{sech}^2(c+d x)} \, dx","Int[(a + b*Sech[c + d*x]^2)^(-1),x]","\frac{x}{a}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a d \sqrt{a+b}}","\frac{x}{a}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a d \sqrt{a+b}}",1,"x/a - (Sqrt[b]*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(a*Sqrt[a + b]*d)","A",3,3,14,0.2143,1,"{4127, 3181, 208}"
144,1,46,0,0.087361,"\int \frac{\coth (c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Coth[c + d*x]/(a + b*Sech[c + d*x]^2),x]","\frac{\log (\sinh (c+d x))}{d (a+b)}+\frac{b \log \left(a \cosh ^2(c+d x)+b\right)}{2 a d (a+b)}","\frac{\log (\sinh (c+d x))}{d (a+b)}+\frac{b \log \left(a \cosh ^2(c+d x)+b\right)}{2 a d (a+b)}",1,"(b*Log[b + a*Cosh[c + d*x]^2])/(2*a*(a + b)*d) + Log[Sinh[c + d*x]]/((a + b)*d)","A",4,3,21,0.1429,1,"{4138, 446, 72}"
145,1,62,0,0.1796155,"\int \frac{\coth ^2(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Coth[c + d*x]^2/(a + b*Sech[c + d*x]^2),x]","-\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a d (a+b)^{3/2}}-\frac{\coth (c+d x)}{d (a+b)}+\frac{x}{a}","-\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a d (a+b)^{3/2}}-\frac{\coth (c+d x)}{d (a+b)}+\frac{x}{a}",1,"x/a - (b^(3/2)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(a*(a + b)^(3/2)*d) - Coth[c + d*x]/((a + b)*d)","A",6,6,23,0.2609,1,"{4141, 1975, 480, 522, 206, 208}"
146,1,73,0,0.1218258,"\int \frac{\coth ^3(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Coth[c + d*x]^3/(a + b*Sech[c + d*x]^2),x]","\frac{b^2 \log \left(a \cosh ^2(c+d x)+b\right)}{2 a d (a+b)^2}-\frac{\text{csch}^2(c+d x)}{2 d (a+b)}+\frac{(a+2 b) \log (\sinh (c+d x))}{d (a+b)^2}","\frac{b^2 \log \left(a \cosh ^2(c+d x)+b\right)}{2 a d (a+b)^2}-\frac{\text{csch}^2(c+d x)}{2 d (a+b)}+\frac{(a+2 b) \log (\sinh (c+d x))}{d (a+b)^2}",1,"-Csch[c + d*x]^2/(2*(a + b)*d) + (b^2*Log[b + a*Cosh[c + d*x]^2])/(2*a*(a + b)^2*d) + ((a + 2*b)*Log[Sinh[c + d*x]])/((a + b)^2*d)","A",4,3,23,0.1304,1,"{4138, 446, 88}"
147,1,87,0,0.2858954,"\int \frac{\coth ^4(c+d x)}{a+b \text{sech}^2(c+d x)} \, dx","Int[Coth[c + d*x]^4/(a + b*Sech[c + d*x]^2),x]","-\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a d (a+b)^{5/2}}-\frac{\coth ^3(c+d x)}{3 d (a+b)}-\frac{(a+2 b) \coth (c+d x)}{d (a+b)^2}+\frac{x}{a}","-\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{a d (a+b)^{5/2}}-\frac{\coth ^3(c+d x)}{3 d (a+b)}-\frac{(a+2 b) \coth (c+d x)}{d (a+b)^2}+\frac{x}{a}",1,"x/a - (b^(5/2)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(a*(a + b)^(5/2)*d) - ((a + 2*b)*Coth[c + d*x])/((a + b)^2*d) - Coth[c + d*x]^3/(3*(a + b)*d)","A",7,7,23,0.3043,1,"{4141, 1975, 480, 583, 522, 206, 208}"
148,1,76,0,0.1167793,"\int \frac{\tanh ^5(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Tanh[c + d*x]^5/(a + b*Sech[c + d*x]^2)^2,x]","\frac{\left(\frac{1}{a^2}-\frac{1}{b^2}\right) \log \left(a \cosh ^2(c+d x)+b\right)}{2 d}+\frac{(a+b)^2}{2 a^2 b d \left(a \cosh ^2(c+d x)+b\right)}+\frac{\log (\cosh (c+d x))}{b^2 d}","\frac{\left(\frac{1}{a^2}-\frac{1}{b^2}\right) \log \left(a \cosh ^2(c+d x)+b\right)}{2 d}+\frac{(a+b)^2}{2 a^2 b d \left(a \cosh ^2(c+d x)+b\right)}+\frac{\log (\cosh (c+d x))}{b^2 d}",1,"(a + b)^2/(2*a^2*b*d*(b + a*Cosh[c + d*x]^2)) + Log[Cosh[c + d*x]]/(b^2*d) + ((a^(-2) - b^(-2))*Log[b + a*Cosh[c + d*x]^2])/(2*d)","A",4,3,23,0.1304,1,"{4138, 446, 88}"
149,1,91,0,0.1940694,"\int \frac{\tanh ^4(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Tanh[c + d*x]^4/(a + b*Sech[c + d*x]^2)^2,x]","\frac{(a-2 b) \sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 a^2 b^{3/2} d}+\frac{x}{a^2}-\frac{(a+b) \tanh (c+d x)}{2 a b d \left(a-b \tanh ^2(c+d x)+b\right)}","\frac{(a-2 b) \sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 a^2 b^{3/2} d}+\frac{x}{a^2}-\frac{(a+b) \tanh (c+d x)}{2 a b d \left(a-b \tanh ^2(c+d x)+b\right)}",1,"x/a^2 + ((a - 2*b)*Sqrt[a + b]*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(2*a^2*b^(3/2)*d) - ((a + b)*Tanh[c + d*x])/(2*a*b*d*(a + b - b*Tanh[c + d*x]^2))","A",6,6,23,0.2609,1,"{4141, 1975, 470, 522, 206, 208}"
150,1,51,0,0.0898654,"\int \frac{\tanh ^3(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Tanh[c + d*x]^3/(a + b*Sech[c + d*x]^2)^2,x]","\frac{a+b}{2 a^2 d \left(a \cosh ^2(c+d x)+b\right)}+\frac{\log \left(a \cosh ^2(c+d x)+b\right)}{2 a^2 d}","\frac{a+b}{2 a^2 d \left(a \cosh ^2(c+d x)+b\right)}+\frac{\log \left(a \cosh ^2(c+d x)+b\right)}{2 a^2 d}",1,"(a + b)/(2*a^2*d*(b + a*Cosh[c + d*x]^2)) + Log[b + a*Cosh[c + d*x]^2]/(2*a^2*d)","A",4,3,23,0.1304,1,"{4138, 444, 43}"
151,1,85,0,0.1691089,"\int \frac{\tanh ^2(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Tanh[c + d*x]^2/(a + b*Sech[c + d*x]^2)^2,x]","-\frac{(a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 a^2 \sqrt{b} d \sqrt{a+b}}+\frac{x}{a^2}-\frac{\tanh (c+d x)}{2 a d \left(a-b \tanh ^2(c+d x)+b\right)}","-\frac{(a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 a^2 \sqrt{b} d \sqrt{a+b}}+\frac{x}{a^2}-\frac{\tanh (c+d x)}{2 a d \left(a-b \tanh ^2(c+d x)+b\right)}",1,"x/a^2 - ((a + 2*b)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(2*a^2*Sqrt[b]*Sqrt[a + b]*d) - Tanh[c + d*x]/(2*a*d*(a + b - b*Tanh[c + d*x]^2))","A",6,6,23,0.2609,1,"{4141, 1975, 471, 522, 206, 208}"
152,1,49,0,0.0624705,"\int \frac{\tanh (c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Tanh[c + d*x]/(a + b*Sech[c + d*x]^2)^2,x]","\frac{b}{2 a^2 d \left(a \cosh ^2(c+d x)+b\right)}+\frac{\log \left(a \cosh ^2(c+d x)+b\right)}{2 a^2 d}","\frac{b}{2 a^2 d \left(a \cosh ^2(c+d x)+b\right)}+\frac{\log \left(a \cosh ^2(c+d x)+b\right)}{2 a^2 d}",1,"b/(2*a^2*d*(b + a*Cosh[c + d*x]^2)) + Log[b + a*Cosh[c + d*x]^2]/(2*a^2*d)","A",4,3,21,0.1429,1,"{4138, 266, 43}"
153,1,93,0,0.0964635,"\int \frac{1}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[(a + b*Sech[c + d*x]^2)^(-2),x]","-\frac{\sqrt{b} (3 a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 a^2 d (a+b)^{3/2}}+\frac{x}{a^2}-\frac{b \tanh (c+d x)}{2 a d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}","-\frac{\sqrt{b} (3 a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 a^2 d (a+b)^{3/2}}+\frac{x}{a^2}-\frac{b \tanh (c+d x)}{2 a d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}",1,"x/a^2 - (Sqrt[b]*(3*a + 2*b)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(2*a^2*(a + b)^(3/2)*d) - (b*Tanh[c + d*x])/(2*a*(a + b)*d*(a + b - b*Tanh[c + d*x]^2))","A",5,5,14,0.3571,1,"{4128, 414, 522, 206, 208}"
154,1,83,0,0.1288665,"\int \frac{\coth (c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Coth[c + d*x]/(a + b*Sech[c + d*x]^2)^2,x]","\frac{b^2}{2 a^2 d (a+b) \left(a \cosh ^2(c+d x)+b\right)}+\frac{b (2 a+b) \log \left(a \cosh ^2(c+d x)+b\right)}{2 a^2 d (a+b)^2}+\frac{\log (\sinh (c+d x))}{d (a+b)^2}","\frac{b^2}{2 a^2 d (a+b) \left(a \cosh ^2(c+d x)+b\right)}+\frac{b (2 a+b) \log \left(a \cosh ^2(c+d x)+b\right)}{2 a^2 d (a+b)^2}+\frac{\log (\sinh (c+d x))}{d (a+b)^2}",1,"b^2/(2*a^2*(a + b)*d*(b + a*Cosh[c + d*x]^2)) + (b*(2*a + b)*Log[b + a*Cosh[c + d*x]^2])/(2*a^2*(a + b)^2*d) + Log[Sinh[c + d*x]]/((a + b)^2*d)","A",4,3,21,0.1429,1,"{4138, 446, 88}"
155,1,121,0,0.2841049,"\int \frac{\coth ^2(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Coth[c + d*x]^2/(a + b*Sech[c + d*x]^2)^2,x]","-\frac{b^{3/2} (5 a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 a^2 d (a+b)^{5/2}}+\frac{x}{a^2}-\frac{(2 a-b) \coth (c+d x)}{2 a d (a+b)^2}-\frac{b \coth (c+d x)}{2 a d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}","-\frac{b^{3/2} (5 a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 a^2 d (a+b)^{5/2}}+\frac{x}{a^2}-\frac{(2 a-b) \coth (c+d x)}{2 a d (a+b)^2}-\frac{b \coth (c+d x)}{2 a d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}",1,"x/a^2 - (b^(3/2)*(5*a + 2*b)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(2*a^2*(a + b)^(5/2)*d) - ((2*a - b)*Coth[c + d*x])/(2*a*(a + b)^2*d) - (b*Coth[c + d*x])/(2*a*(a + b)*d*(a + b - b*Tanh[c + d*x]^2))","A",7,7,23,0.3043,1,"{4141, 1975, 472, 583, 522, 206, 208}"
156,1,110,0,0.1745017,"\int \frac{\coth ^3(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Coth[c + d*x]^3/(a + b*Sech[c + d*x]^2)^2,x]","\frac{b^3}{2 a^2 d (a+b)^2 \left(a \cosh ^2(c+d x)+b\right)}+\frac{b^2 (3 a+b) \log \left(a \cosh ^2(c+d x)+b\right)}{2 a^2 d (a+b)^3}-\frac{\text{csch}^2(c+d x)}{2 d (a+b)^2}+\frac{(a+3 b) \log (\sinh (c+d x))}{d (a+b)^3}","\frac{b^3}{2 a^2 d (a+b)^2 \left(a \cosh ^2(c+d x)+b\right)}+\frac{b^2 (3 a+b) \log \left(a \cosh ^2(c+d x)+b\right)}{2 a^2 d (a+b)^3}-\frac{\text{csch}^2(c+d x)}{2 d (a+b)^2}+\frac{(a+3 b) \log (\sinh (c+d x))}{d (a+b)^3}",1,"b^3/(2*a^2*(a + b)^2*d*(b + a*Cosh[c + d*x]^2)) - Csch[c + d*x]^2/(2*(a + b)^2*d) + (b^2*(3*a + b)*Log[b + a*Cosh[c + d*x]^2])/(2*a^2*(a + b)^3*d) + ((a + 3*b)*Log[Sinh[c + d*x]])/((a + b)^3*d)","A",4,3,23,0.1304,1,"{4138, 446, 88}"
157,1,161,0,0.4113264,"\int \frac{\coth ^4(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^2} \, dx","Int[Coth[c + d*x]^4/(a + b*Sech[c + d*x]^2)^2,x]","-\frac{b^{5/2} (7 a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 a^2 d (a+b)^{7/2}}-\frac{\left(2 a^2+6 a b-b^2\right) \coth (c+d x)}{2 a d (a+b)^3}+\frac{x}{a^2}-\frac{(2 a-3 b) \coth ^3(c+d x)}{6 a d (a+b)^2}-\frac{b \coth ^3(c+d x)}{2 a d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}","-\frac{b^{5/2} (7 a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{2 a^2 d (a+b)^{7/2}}-\frac{\left(2 a^2+6 a b-b^2\right) \coth (c+d x)}{2 a d (a+b)^3}+\frac{x}{a^2}-\frac{(2 a-3 b) \coth ^3(c+d x)}{6 a d (a+b)^2}-\frac{b \coth ^3(c+d x)}{2 a d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}",1,"x/a^2 - (b^(5/2)*(7*a + 2*b)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(2*a^2*(a + b)^(7/2)*d) - ((2*a^2 + 6*a*b - b^2)*Coth[c + d*x])/(2*a*(a + b)^3*d) - ((2*a - 3*b)*Coth[c + d*x]^3)/(6*a*(a + b)^2*d) - (b*Coth[c + d*x]^3)/(2*a*(a + b)*d*(a + b - b*Tanh[c + d*x]^2))","A",8,7,23,0.3043,1,"{4141, 1975, 472, 583, 522, 206, 208}"
158,1,148,0,0.3195618,"\int \frac{\tanh ^6(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Tanh[c + d*x]^6/(a + b*Sech[c + d*x]^2)^3,x]","\frac{(3 a-4 b) (a+b) \tanh (c+d x)}{8 a^2 b^2 d \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{\sqrt{a+b} \left(3 a^2-4 a b+8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^3 b^{5/2} d}+\frac{x}{a^3}-\frac{(a+b) \tanh ^3(c+d x)}{4 a b d \left(a-b \tanh ^2(c+d x)+b\right)^2}","\frac{(3 a-4 b) (a+b) \tanh (c+d x)}{8 a^2 b^2 d \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{\sqrt{a+b} \left(3 a^2-4 a b+8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^3 b^{5/2} d}+\frac{x}{a^3}-\frac{(a+b) \tanh ^3(c+d x)}{4 a b d \left(a-b \tanh ^2(c+d x)+b\right)^2}",1,"x/a^3 - (Sqrt[a + b]*(3*a^2 - 4*a*b + 8*b^2)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(8*a^3*b^(5/2)*d) - ((a + b)*Tanh[c + d*x]^3)/(4*a*b*d*(a + b - b*Tanh[c + d*x]^2)^2) + ((3*a - 4*b)*(a + b)*Tanh[c + d*x])/(8*a^2*b^2*d*(a + b - b*Tanh[c + d*x]^2))","A",7,7,23,0.3043,1,"{4141, 1975, 470, 578, 522, 206, 208}"
159,1,77,0,0.1195916,"\int \frac{\tanh ^5(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Tanh[c + d*x]^5/(a + b*Sech[c + d*x]^2)^3,x]","-\frac{(a+b)^2}{4 a^3 d \left(a \cosh ^2(c+d x)+b\right)^2}+\frac{a+b}{a^3 d \left(a \cosh ^2(c+d x)+b\right)}+\frac{\log \left(a \cosh ^2(c+d x)+b\right)}{2 a^3 d}","-\frac{(a+b)^2}{4 a^3 d \left(a \cosh ^2(c+d x)+b\right)^2}+\frac{a+b}{a^3 d \left(a \cosh ^2(c+d x)+b\right)}+\frac{\log \left(a \cosh ^2(c+d x)+b\right)}{2 a^3 d}",1,"-(a + b)^2/(4*a^3*d*(b + a*Cosh[c + d*x]^2)^2) + (a + b)/(a^3*d*(b + a*Cosh[c + d*x]^2)) + Log[b + a*Cosh[c + d*x]^2]/(2*a^3*d)","A",4,3,23,0.1304,1,"{4138, 444, 43}"
160,1,139,0,0.2941066,"\int \frac{\tanh ^4(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Tanh[c + d*x]^4/(a + b*Sech[c + d*x]^2)^3,x]","\frac{\left(a^2-4 a b-8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^3 b^{3/2} d \sqrt{a+b}}+\frac{(a-4 b) \tanh (c+d x)}{8 a^2 b d \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{x}{a^3}-\frac{(a+b) \tanh (c+d x)}{4 a b d \left(a-b \tanh ^2(c+d x)+b\right)^2}","\frac{\left(a^2-4 a b-8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^3 b^{3/2} d \sqrt{a+b}}+\frac{(a-4 b) \tanh (c+d x)}{8 a^2 b d \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{x}{a^3}-\frac{(a+b) \tanh (c+d x)}{4 a b d \left(a-b \tanh ^2(c+d x)+b\right)^2}",1,"x/a^3 + ((a^2 - 4*a*b - 8*b^2)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(8*a^3*b^(3/2)*Sqrt[a + b]*d) - ((a + b)*Tanh[c + d*x])/(4*a*b*d*(a + b - b*Tanh[c + d*x]^2)^2) + ((a - 4*b)*Tanh[c + d*x])/(8*a^2*b*d*(a + b - b*Tanh[c + d*x]^2))","A",7,7,23,0.3043,1,"{4141, 1975, 470, 527, 522, 206, 208}"
161,1,81,0,0.1261362,"\int \frac{\tanh ^3(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Tanh[c + d*x]^3/(a + b*Sech[c + d*x]^2)^3,x]","-\frac{b (a+b)}{4 a^3 d \left(a \cosh ^2(c+d x)+b\right)^2}+\frac{a+2 b}{2 a^3 d \left(a \cosh ^2(c+d x)+b\right)}+\frac{\log \left(a \cosh ^2(c+d x)+b\right)}{2 a^3 d}","-\frac{b (a+b)}{4 a^3 d \left(a \cosh ^2(c+d x)+b\right)^2}+\frac{a+2 b}{2 a^3 d \left(a \cosh ^2(c+d x)+b\right)}+\frac{\log \left(a \cosh ^2(c+d x)+b\right)}{2 a^3 d}",1,"-(b*(a + b))/(4*a^3*d*(b + a*Cosh[c + d*x]^2)^2) + (a + 2*b)/(2*a^3*d*(b + a*Cosh[c + d*x]^2)) + Log[b + a*Cosh[c + d*x]^2]/(2*a^3*d)","A",4,3,23,0.1304,1,"{4138, 446, 77}"
162,1,139,0,0.2462678,"\int \frac{\tanh ^2(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Tanh[c + d*x]^2/(a + b*Sech[c + d*x]^2)^3,x]","-\frac{\left(3 a^2+12 a b+8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^3 \sqrt{b} d (a+b)^{3/2}}-\frac{(3 a+4 b) \tanh (c+d x)}{8 a^2 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{x}{a^3}-\frac{\tanh (c+d x)}{4 a d \left(a-b \tanh ^2(c+d x)+b\right)^2}","-\frac{\left(3 a^2+12 a b+8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^3 \sqrt{b} d (a+b)^{3/2}}-\frac{(3 a+4 b) \tanh (c+d x)}{8 a^2 d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{x}{a^3}-\frac{\tanh (c+d x)}{4 a d \left(a-b \tanh ^2(c+d x)+b\right)^2}",1,"x/a^3 - ((3*a^2 + 12*a*b + 8*b^2)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(8*a^3*Sqrt[b]*(a + b)^(3/2)*d) - Tanh[c + d*x]/(4*a*d*(a + b - b*Tanh[c + d*x]^2)^2) - ((3*a + 4*b)*Tanh[c + d*x])/(8*a^2*(a + b)*d*(a + b - b*Tanh[c + d*x]^2))","A",7,7,23,0.3043,1,"{4141, 1975, 471, 527, 522, 206, 208}"
163,1,73,0,0.082045,"\int \frac{\tanh (c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Tanh[c + d*x]/(a + b*Sech[c + d*x]^2)^3,x]","-\frac{b^2}{4 a^3 d \left(a \cosh ^2(c+d x)+b\right)^2}+\frac{b}{a^3 d \left(a \cosh ^2(c+d x)+b\right)}+\frac{\log \left(a \cosh ^2(c+d x)+b\right)}{2 a^3 d}","-\frac{b^2}{4 a^3 d \left(a \cosh ^2(c+d x)+b\right)^2}+\frac{b}{a^3 d \left(a \cosh ^2(c+d x)+b\right)}+\frac{\log \left(a \cosh ^2(c+d x)+b\right)}{2 a^3 d}",1,"-b^2/(4*a^3*d*(b + a*Cosh[c + d*x]^2)^2) + b/(a^3*d*(b + a*Cosh[c + d*x]^2)) + Log[b + a*Cosh[c + d*x]^2]/(2*a^3*d)","A",4,3,21,0.1429,1,"{4138, 266, 43}"
164,1,146,0,0.181249,"\int \frac{1}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[(a + b*Sech[c + d*x]^2)^(-3),x]","-\frac{\sqrt{b} \left(15 a^2+20 a b+8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^3 d (a+b)^{5/2}}-\frac{b (7 a+4 b) \tanh (c+d x)}{8 a^2 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{x}{a^3}-\frac{b \tanh (c+d x)}{4 a d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^2}","-\frac{\sqrt{b} \left(15 a^2+20 a b+8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^3 d (a+b)^{5/2}}-\frac{b (7 a+4 b) \tanh (c+d x)}{8 a^2 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{x}{a^3}-\frac{b \tanh (c+d x)}{4 a d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^2}",1,"x/a^3 - (Sqrt[b]*(15*a^2 + 20*a*b + 8*b^2)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(8*a^3*(a + b)^(5/2)*d) - (b*Tanh[c + d*x])/(4*a*(a + b)*d*(a + b - b*Tanh[c + d*x]^2)^2) - (b*(7*a + 4*b)*Tanh[c + d*x])/(8*a^2*(a + b)^2*d*(a + b - b*Tanh[c + d*x]^2))","A",6,6,14,0.4286,1,"{4128, 414, 527, 522, 206, 208}"
165,1,130,0,0.1855432,"\int \frac{\coth (c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Coth[c + d*x]/(a + b*Sech[c + d*x]^2)^3,x]","-\frac{b^3}{4 a^3 d (a+b) \left(a \cosh ^2(c+d x)+b\right)^2}+\frac{b^2 (3 a+2 b)}{2 a^3 d (a+b)^2 \left(a \cosh ^2(c+d x)+b\right)}+\frac{b \left(3 a^2+3 a b+b^2\right) \log \left(a \cosh ^2(c+d x)+b\right)}{2 a^3 d (a+b)^3}+\frac{\log (\sinh (c+d x))}{d (a+b)^3}","-\frac{b^3}{4 a^3 d (a+b) \left(a \cosh ^2(c+d x)+b\right)^2}+\frac{b^2 (3 a+2 b)}{2 a^3 d (a+b)^2 \left(a \cosh ^2(c+d x)+b\right)}+\frac{b \left(3 a^2+3 a b+b^2\right) \log \left(a \cosh ^2(c+d x)+b\right)}{2 a^3 d (a+b)^3}+\frac{\log (\sinh (c+d x))}{d (a+b)^3}",1,"-b^3/(4*a^3*(a + b)*d*(b + a*Cosh[c + d*x]^2)^2) + (b^2*(3*a + 2*b))/(2*a^3*(a + b)^2*d*(b + a*Cosh[c + d*x]^2)) + (b*(3*a^2 + 3*a*b + b^2)*Log[b + a*Cosh[c + d*x]^2])/(2*a^3*(a + b)^3*d) + Log[Sinh[c + d*x]]/((a + b)^3*d)","A",4,3,21,0.1429,1,"{4138, 446, 88}"
166,1,182,0,0.4031537,"\int \frac{\coth ^2(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Coth[c + d*x]^2/(a + b*Sech[c + d*x]^2)^3,x]","-\frac{b^{3/2} \left(35 a^2+28 a b+8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^3 d (a+b)^{7/2}}-\frac{\left(8 a^2-11 a b-4 b^2\right) \coth (c+d x)}{8 a^2 d (a+b)^3}-\frac{b (9 a+4 b) \coth (c+d x)}{8 a^2 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{x}{a^3}-\frac{b \coth (c+d x)}{4 a d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^2}","-\frac{b^{3/2} \left(35 a^2+28 a b+8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^3 d (a+b)^{7/2}}-\frac{\left(8 a^2-11 a b-4 b^2\right) \coth (c+d x)}{8 a^2 d (a+b)^3}-\frac{b (9 a+4 b) \coth (c+d x)}{8 a^2 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{x}{a^3}-\frac{b \coth (c+d x)}{4 a d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^2}",1,"x/a^3 - (b^(3/2)*(35*a^2 + 28*a*b + 8*b^2)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(8*a^3*(a + b)^(7/2)*d) - ((8*a^2 - 11*a*b - 4*b^2)*Coth[c + d*x])/(8*a^2*(a + b)^3*d) - (b*Coth[c + d*x])/(4*a*(a + b)*d*(a + b - b*Tanh[c + d*x]^2)^2) - (b*(9*a + 4*b)*Coth[c + d*x])/(8*a^2*(a + b)^2*d*(a + b - b*Tanh[c + d*x]^2))","A",8,8,23,0.3478,1,"{4141, 1975, 472, 579, 583, 522, 206, 208}"
167,1,152,0,0.2429905,"\int \frac{\coth ^3(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Coth[c + d*x]^3/(a + b*Sech[c + d*x]^2)^3,x]","-\frac{b^4}{4 a^3 d (a+b)^2 \left(a \cosh ^2(c+d x)+b\right)^2}+\frac{b^3 (2 a+b)}{a^3 d (a+b)^3 \left(a \cosh ^2(c+d x)+b\right)}+\frac{b^2 \left(6 a^2+4 a b+b^2\right) \log \left(a \cosh ^2(c+d x)+b\right)}{2 a^3 d (a+b)^4}-\frac{\text{csch}^2(c+d x)}{2 d (a+b)^3}+\frac{(a+4 b) \log (\sinh (c+d x))}{d (a+b)^4}","-\frac{b^4}{4 a^3 d (a+b)^2 \left(a \cosh ^2(c+d x)+b\right)^2}+\frac{b^3 (2 a+b)}{a^3 d (a+b)^3 \left(a \cosh ^2(c+d x)+b\right)}+\frac{b^2 \left(6 a^2+4 a b+b^2\right) \log \left(a \cosh ^2(c+d x)+b\right)}{2 a^3 d (a+b)^4}-\frac{\text{csch}^2(c+d x)}{2 d (a+b)^3}+\frac{(a+4 b) \log (\sinh (c+d x))}{d (a+b)^4}",1,"-b^4/(4*a^3*(a + b)^2*d*(b + a*Cosh[c + d*x]^2)^2) + (b^3*(2*a + b))/(a^3*(a + b)^3*d*(b + a*Cosh[c + d*x]^2)) - Csch[c + d*x]^2/(2*(a + b)^3*d) + (b^2*(6*a^2 + 4*a*b + b^2)*Log[b + a*Cosh[c + d*x]^2])/(2*a^3*(a + b)^4*d) + ((a + 4*b)*Log[Sinh[c + d*x]])/((a + b)^4*d)","A",4,3,23,0.1304,1,"{4138, 446, 88}"
168,1,232,0,0.513631,"\int \frac{\coth ^4(c+d x)}{\left(a+b \text{sech}^2(c+d x)\right)^3} \, dx","Int[Coth[c + d*x]^4/(a + b*Sech[c + d*x]^2)^3,x]","-\frac{b^{5/2} \left(63 a^2+36 a b+8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^3 d (a+b)^{9/2}}-\frac{\left(8 a^2-39 a b-12 b^2\right) \coth ^3(c+d x)}{24 a^2 d (a+b)^3}-\frac{\left(32 a^2 b+8 a^3-15 a b^2-4 b^3\right) \coth (c+d x)}{8 a^2 d (a+b)^4}-\frac{b (11 a+4 b) \coth ^3(c+d x)}{8 a^2 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{x}{a^3}-\frac{b \coth ^3(c+d x)}{4 a d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^2}","-\frac{b^{5/2} \left(63 a^2+36 a b+8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{8 a^3 d (a+b)^{9/2}}-\frac{\left(8 a^2-39 a b-12 b^2\right) \coth ^3(c+d x)}{24 a^2 d (a+b)^3}-\frac{\left(32 a^2 b+8 a^3-15 a b^2-4 b^3\right) \coth (c+d x)}{8 a^2 d (a+b)^4}-\frac{b (11 a+4 b) \coth ^3(c+d x)}{8 a^2 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)}+\frac{x}{a^3}-\frac{b \coth ^3(c+d x)}{4 a d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^2}",1,"x/a^3 - (b^(5/2)*(63*a^2 + 36*a*b + 8*b^2)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(8*a^3*(a + b)^(9/2)*d) - ((8*a^3 + 32*a^2*b - 15*a*b^2 - 4*b^3)*Coth[c + d*x])/(8*a^2*(a + b)^4*d) - ((8*a^2 - 39*a*b - 12*b^2)*Coth[c + d*x]^3)/(24*a^2*(a + b)^3*d) - (b*Coth[c + d*x]^3)/(4*a*(a + b)*d*(a + b - b*Tanh[c + d*x]^2)^2) - (b*(11*a + 4*b)*Coth[c + d*x]^3)/(8*a^2*(a + b)^2*d*(a + b - b*Tanh[c + d*x]^2))","A",9,8,23,0.3478,1,"{4141, 1975, 472, 579, 583, 522, 206, 208}"
169,1,207,0,0.3456284,"\int \frac{1}{\left(a+b \text{sech}^2(c+d x)\right)^4} \, dx","Int[(a + b*Sech[c + d*x]^2)^(-4),x]","-\frac{\sqrt{b} \left(70 a^2 b+35 a^3+56 a b^2+16 b^3\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{16 a^4 d (a+b)^{7/2}}-\frac{b \left(19 a^2+22 a b+8 b^2\right) \tanh (c+d x)}{16 a^3 d (a+b)^3 \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{b (11 a+6 b) \tanh (c+d x)}{24 a^2 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)^2}+\frac{x}{a^4}-\frac{b \tanh (c+d x)}{6 a d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^3}","-\frac{\sqrt{b} \left(70 a^2 b+35 a^3+56 a b^2+16 b^3\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a+b}}\right)}{16 a^4 d (a+b)^{7/2}}-\frac{b \left(19 a^2+22 a b+8 b^2\right) \tanh (c+d x)}{16 a^3 d (a+b)^3 \left(a-b \tanh ^2(c+d x)+b\right)}-\frac{b (11 a+6 b) \tanh (c+d x)}{24 a^2 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)^2}+\frac{x}{a^4}-\frac{b \tanh (c+d x)}{6 a d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^3}",1,"x/a^4 - (Sqrt[b]*(35*a^3 + 70*a^2*b + 56*a*b^2 + 16*b^3)*ArcTanh[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b]])/(16*a^4*(a + b)^(7/2)*d) - (b*Tanh[c + d*x])/(6*a*(a + b)*d*(a + b - b*Tanh[c + d*x]^2)^3) - (b*(11*a + 6*b)*Tanh[c + d*x])/(24*a^2*(a + b)^2*d*(a + b - b*Tanh[c + d*x]^2)^2) - (b*(19*a^2 + 22*a*b + 8*b^2)*Tanh[c + d*x])/(16*a^3*(a + b)^3*d*(a + b - b*Tanh[c + d*x]^2))","A",7,6,14,0.4286,1,"{4128, 414, 527, 522, 206, 208}"
170,1,29,0,0.0310718,"\int \left(1-\text{sech}^2(x)\right)^{3/2} \, dx","Int[(1 - Sech[x]^2)^(3/2),x]","\sqrt{\tanh ^2(x)} \coth (x) \log (\cosh (x))-\frac{1}{2} \tanh ^2(x)^{3/2} \coth (x)","\sqrt{\tanh ^2(x)} \coth (x) \log (\cosh (x))-\frac{1}{2} \tanh ^2(x)^{3/2} \coth (x)",1,"Coth[x]*Log[Cosh[x]]*Sqrt[Tanh[x]^2] - (Coth[x]*(Tanh[x]^2)^(3/2))/2","A",4,4,12,0.3333,1,"{4121, 3658, 3473, 3475}"
171,1,14,0,0.0218037,"\int \sqrt{1-\text{sech}^2(x)} \, dx","Int[Sqrt[1 - Sech[x]^2],x]","\sqrt{\tanh ^2(x)} \coth (x) \log (\cosh (x))","\sqrt{\tanh ^2(x)} \coth (x) \log (\cosh (x))",1,"Coth[x]*Log[Cosh[x]]*Sqrt[Tanh[x]^2]","A",3,3,12,0.2500,1,"{4121, 3658, 3475}"
172,1,14,0,0.0243822,"\int \frac{1}{\sqrt{1-\text{sech}^2(x)}} \, dx","Int[1/Sqrt[1 - Sech[x]^2],x]","\frac{\tanh (x) \log (\sinh (x))}{\sqrt{\tanh ^2(x)}}","\frac{\tanh (x) \log (\sinh (x))}{\sqrt{\tanh ^2(x)}}",1,"(Log[Sinh[x]]*Tanh[x])/Sqrt[Tanh[x]^2]","A",3,3,12,0.2500,1,"{4121, 3658, 3475}"
173,1,34,0,0.0288396,"\int \left(-1+\text{sech}^2(x)\right)^{3/2} \, dx","Int[(-1 + Sech[x]^2)^(3/2),x]","\frac{1}{2} \tanh (x) \sqrt{-\tanh ^2(x)}-\sqrt{-\tanh ^2(x)} \coth (x) \log (\cosh (x))","\frac{1}{2} \tanh (x) \sqrt{-\tanh ^2(x)}-\sqrt{-\tanh ^2(x)} \coth (x) \log (\cosh (x))",1,"-(Coth[x]*Log[Cosh[x]]*Sqrt[-Tanh[x]^2]) + (Tanh[x]*Sqrt[-Tanh[x]^2])/2","A",4,4,10,0.4000,1,"{4121, 3658, 3473, 3475}"
174,1,16,0,0.0195109,"\int \sqrt{-1+\text{sech}^2(x)} \, dx","Int[Sqrt[-1 + Sech[x]^2],x]","\sqrt{-\tanh ^2(x)} \coth (x) \log (\cosh (x))","\sqrt{-\tanh ^2(x)} \coth (x) \log (\cosh (x))",1,"Coth[x]*Log[Cosh[x]]*Sqrt[-Tanh[x]^2]","A",3,3,10,0.3000,1,"{4121, 3658, 3475}"
175,1,16,0,0.0219229,"\int \frac{1}{\sqrt{-1+\text{sech}^2(x)}} \, dx","Int[1/Sqrt[-1 + Sech[x]^2],x]","\frac{\tanh (x) \log (\sinh (x))}{\sqrt{-\tanh ^2(x)}}","\frac{\tanh (x) \log (\sinh (x))}{\sqrt{-\tanh ^2(x)}}",1,"(Log[Sinh[x]]*Tanh[x])/Sqrt[-Tanh[x]^2]","A",3,3,10,0.3000,1,"{4121, 3658, 3475}"
176,1,83,0,0.1467305,"\int \sqrt{a+b \text{sech}^2(x)} \tanh ^5(x) \, dx","Int[Sqrt[a + b*Sech[x]^2]*Tanh[x]^5,x]","-\frac{\left(a+b \text{sech}^2(x)\right)^{5/2}}{5 b^2}+\frac{(a+2 b) \left(a+b \text{sech}^2(x)\right)^{3/2}}{3 b^2}-\sqrt{a+b \text{sech}^2(x)}+\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)","-\frac{\left(a+b \text{sech}^2(x)\right)^{5/2}}{5 b^2}+\frac{(a+2 b) \left(a+b \text{sech}^2(x)\right)^{3/2}}{3 b^2}-\sqrt{a+b \text{sech}^2(x)}+\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)",1,"Sqrt[a]*ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]] - Sqrt[a + b*Sech[x]^2] + ((a + 2*b)*(a + b*Sech[x]^2)^(3/2))/(3*b^2) - (a + b*Sech[x]^2)^(5/2)/(5*b^2)","A",7,6,17,0.3529,1,"{4139, 446, 88, 50, 63, 208}"
177,1,125,0,0.3127709,"\int \sqrt{a+b \text{sech}^2(x)} \tanh ^4(x) \, dx","Int[Sqrt[a + b*Sech[x]^2]*Tanh[x]^4,x]","-\frac{\left(a^2+6 a b-3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{8 b^{3/2}}-\frac{1}{4} \tanh ^3(x) \sqrt{a-b \tanh ^2(x)+b}+\frac{(a-3 b) \tanh (x) \sqrt{a-b \tanh ^2(x)+b}}{8 b}+\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)","-\frac{\left(a^2+6 a b-3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{8 b^{3/2}}-\frac{1}{4} \tanh ^3(x) \sqrt{a-b \tanh ^2(x)+b}+\frac{(a-3 b) \tanh (x) \sqrt{a-b \tanh ^2(x)+b}}{8 b}+\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)",1,"-((a^2 + 6*a*b - 3*b^2)*ArcTan[(Sqrt[b]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]])/(8*b^(3/2)) + Sqrt[a]*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]] + ((a - 3*b)*Tanh[x]*Sqrt[a + b - b*Tanh[x]^2])/(8*b) - (Tanh[x]^3*Sqrt[a + b - b*Tanh[x]^2])/4","A",9,9,17,0.5294,1,"{4141, 1975, 478, 582, 523, 217, 203, 377, 206}"
178,1,59,0,0.1066414,"\int \sqrt{a+b \text{sech}^2(x)} \tanh ^3(x) \, dx","Int[Sqrt[a + b*Sech[x]^2]*Tanh[x]^3,x]","\frac{\left(a+b \text{sech}^2(x)\right)^{3/2}}{3 b}-\sqrt{a+b \text{sech}^2(x)}+\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)","\frac{\left(a+b \text{sech}^2(x)\right)^{3/2}}{3 b}-\sqrt{a+b \text{sech}^2(x)}+\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)",1,"Sqrt[a]*ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]] - Sqrt[a + b*Sech[x]^2] + (a + b*Sech[x]^2)^(3/2)/(3*b)","A",6,6,17,0.3529,1,"{4139, 446, 80, 50, 63, 208}"
179,1,87,0,0.2180307,"\int \sqrt{a+b \text{sech}^2(x)} \tanh ^2(x) \, dx","Int[Sqrt[a + b*Sech[x]^2]*Tanh[x]^2,x]","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)-\frac{1}{2} \tanh (x) \sqrt{a-b \tanh ^2(x)+b}-\frac{(a-b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{2 \sqrt{b}}","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)-\frac{1}{2} \tanh (x) \sqrt{a-b \tanh ^2(x)+b}-\frac{(a-b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{2 \sqrt{b}}",1,"-((a - b)*ArcTan[(Sqrt[b]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]])/(2*Sqrt[b]) + Sqrt[a]*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]] - (Tanh[x]*Sqrt[a + b - b*Tanh[x]^2])/2","A",8,8,17,0.4706,1,"{4141, 1975, 478, 523, 217, 203, 377, 206}"
180,1,40,0,0.0630451,"\int \sqrt{a+b \text{sech}^2(x)} \tanh (x) \, dx","Int[Sqrt[a + b*Sech[x]^2]*Tanh[x],x]","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)-\sqrt{a+b \text{sech}^2(x)}","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)-\sqrt{a+b \text{sech}^2(x)}",1,"Sqrt[a]*ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]] - Sqrt[a + b*Sech[x]^2]","A",5,5,15,0.3333,1,"{4139, 266, 50, 63, 208}"
181,1,59,0,0.0454513,"\int \sqrt{a+b \text{sech}^2(x)} \, dx","Int[Sqrt[a + b*Sech[x]^2],x]","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)+\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)+\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)",1,"Sqrt[b]*ArcTan[(Sqrt[b]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]] + Sqrt[a]*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]","A",6,6,12,0.5000,1,"{4128, 402, 217, 203, 377, 206}"
182,1,56,0,0.1078926,"\int \coth (x) \sqrt{a+b \text{sech}^2(x)} \, dx","Int[Coth[x]*Sqrt[a + b*Sech[x]^2],x]","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)-\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a+b}}\right)","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)-\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a+b}}\right)",1,"Sqrt[a]*ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]] - Sqrt[a + b]*ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a + b]]","A",7,5,15,0.3333,1,"{4139, 446, 83, 63, 208}"
183,1,48,0,0.1776769,"\int \coth ^2(x) \sqrt{a+b \text{sech}^2(x)} \, dx","Int[Coth[x]^2*Sqrt[a + b*Sech[x]^2],x]","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)-\coth (x) \sqrt{a-b \tanh ^2(x)+b}","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)-\coth (x) \sqrt{a-b \tanh ^2(x)+b}",1,"Sqrt[a]*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]] - Coth[x]*Sqrt[a + b - b*Tanh[x]^2]","A",6,6,17,0.3529,1,"{4141, 1975, 475, 12, 377, 206}"
184,1,83,0,0.1432864,"\int \coth ^3(x) \sqrt{a+b \text{sech}^2(x)} \, dx","Int[Coth[x]^3*Sqrt[a + b*Sech[x]^2],x]","-\frac{1}{2} \coth ^2(x) \sqrt{a+b \text{sech}^2(x)}+\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)-\frac{(2 a+b) \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a+b}}\right)}{2 \sqrt{a+b}}","-\frac{1}{2} \coth ^2(x) \sqrt{a+b \text{sech}^2(x)}+\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)-\frac{(2 a+b) \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a+b}}\right)}{2 \sqrt{a+b}}",1,"Sqrt[a]*ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]] - ((2*a + b)*ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a + b]])/(2*Sqrt[a + b]) - (Coth[x]^2*Sqrt[a + b*Sech[x]^2])/2","A",8,6,17,0.3529,1,"{4139, 446, 99, 156, 63, 208}"
185,1,84,0,0.2484637,"\int \coth ^4(x) \sqrt{a+b \text{sech}^2(x)} \, dx","Int[Coth[x]^4*Sqrt[a + b*Sech[x]^2],x]","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)-\frac{1}{3} \coth ^3(x) \sqrt{a-b \tanh ^2(x)+b}-\frac{(3 a+2 b) \coth (x) \sqrt{a-b \tanh ^2(x)+b}}{3 (a+b)}","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)-\frac{1}{3} \coth ^3(x) \sqrt{a-b \tanh ^2(x)+b}-\frac{(3 a+2 b) \coth (x) \sqrt{a-b \tanh ^2(x)+b}}{3 (a+b)}",1,"Sqrt[a]*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]] - ((3*a + 2*b)*Coth[x]*Sqrt[a + b - b*Tanh[x]^2])/(3*(a + b)) - (Coth[x]^3*Sqrt[a + b - b*Tanh[x]^2])/3","A",7,7,17,0.4118,1,"{4141, 1975, 475, 583, 12, 377, 206}"
186,1,125,0,0.2206208,"\int \coth ^5(x) \sqrt{a+b \text{sech}^2(x)} \, dx","Int[Coth[x]^5*Sqrt[a + b*Sech[x]^2],x]","-\frac{\left(8 a^2+12 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a+b}}\right)}{8 (a+b)^{3/2}}-\frac{1}{4} \coth ^4(x) \sqrt{a+b \text{sech}^2(x)}-\frac{(4 a+3 b) \coth ^2(x) \sqrt{a+b \text{sech}^2(x)}}{8 (a+b)}+\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)","-\frac{\left(8 a^2+12 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a+b}}\right)}{8 (a+b)^{3/2}}-\frac{1}{4} \coth ^4(x) \sqrt{a+b \text{sech}^2(x)}-\frac{(4 a+3 b) \coth ^2(x) \sqrt{a+b \text{sech}^2(x)}}{8 (a+b)}+\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)",1,"Sqrt[a]*ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]] - ((8*a^2 + 12*a*b + 3*b^2)*ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a + b]])/(8*(a + b)^(3/2)) - ((4*a + 3*b)*Coth[x]^2*Sqrt[a + b*Sech[x]^2])/(8*(a + b)) - (Coth[x]^4*Sqrt[a + b*Sech[x]^2])/4","A",9,7,17,0.4118,1,"{4139, 446, 99, 151, 156, 63, 208}"
187,1,76,0,0.1276687,"\int \left(a+b \text{sech}^2(x)\right)^{3/2} \tanh ^3(x) \, dx","Int[(a + b*Sech[x]^2)^(3/2)*Tanh[x]^3,x]","a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)+\frac{\left(a+b \text{sech}^2(x)\right)^{5/2}}{5 b}-\frac{1}{3} \left(a+b \text{sech}^2(x)\right)^{3/2}-a \sqrt{a+b \text{sech}^2(x)}","a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)+\frac{\left(a+b \text{sech}^2(x)\right)^{5/2}}{5 b}-\frac{1}{3} \left(a+b \text{sech}^2(x)\right)^{3/2}-a \sqrt{a+b \text{sech}^2(x)}",1,"a^(3/2)*ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]] - a*Sqrt[a + b*Sech[x]^2] - (a + b*Sech[x]^2)^(3/2)/3 + (a + b*Sech[x]^2)^(5/2)/(5*b)","A",7,6,17,0.3529,1,"{4139, 446, 80, 50, 63, 208}"
188,1,125,0,0.3609662,"\int \left(a+b \text{sech}^2(x)\right)^{3/2} \tanh ^2(x) \, dx","Int[(a + b*Sech[x]^2)^(3/2)*Tanh[x]^2,x]","-\frac{\left(3 a^2-6 a b-b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{8 \sqrt{b}}+a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)+\frac{1}{4} b \tanh ^3(x) \sqrt{a-b \tanh ^2(x)+b}-\frac{1}{8} (5 a+b) \tanh (x) \sqrt{a-b \tanh ^2(x)+b}","-\frac{\left(3 a^2-6 a b-b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{8 \sqrt{b}}+a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)+\frac{1}{4} b \tanh ^3(x) \sqrt{a-b \tanh ^2(x)+b}-\frac{1}{8} (5 a+b) \tanh (x) \sqrt{a-b \tanh ^2(x)+b}",1,"-((3*a^2 - 6*a*b - b^2)*ArcTan[(Sqrt[b]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]])/(8*Sqrt[b]) + a^(3/2)*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]] - ((5*a + b)*Tanh[x]*Sqrt[a + b - b*Tanh[x]^2])/8 + (b*Tanh[x]^3*Sqrt[a + b - b*Tanh[x]^2])/4","A",9,9,17,0.5294,1,"{4141, 1975, 477, 582, 523, 217, 203, 377, 206}"
189,1,57,0,0.084093,"\int \left(a+b \text{sech}^2(x)\right)^{3/2} \tanh (x) \, dx","Int[(a + b*Sech[x]^2)^(3/2)*Tanh[x],x]","a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)-a \sqrt{a+b \text{sech}^2(x)}-\frac{1}{3} \left(a+b \text{sech}^2(x)\right)^{3/2}","a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)-a \sqrt{a+b \text{sech}^2(x)}-\frac{1}{3} \left(a+b \text{sech}^2(x)\right)^{3/2}",1,"a^(3/2)*ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]] - a*Sqrt[a + b*Sech[x]^2] - (a + b*Sech[x]^2)^(3/2)/3","A",6,5,15,0.3333,1,"{4139, 266, 50, 63, 208}"
190,1,88,0,0.0912239,"\int \left(a+b \text{sech}^2(x)\right)^{3/2} \, dx","Int[(a + b*Sech[x]^2)^(3/2),x]","a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)+\frac{1}{2} b \tanh (x) \sqrt{a-b \tanh ^2(x)+b}+\frac{1}{2} \sqrt{b} (3 a+b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)","a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)+\frac{1}{2} b \tanh (x) \sqrt{a-b \tanh ^2(x)+b}+\frac{1}{2} \sqrt{b} (3 a+b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)",1,"(Sqrt[b]*(3*a + b)*ArcTan[(Sqrt[b]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]])/2 + a^(3/2)*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]] + (b*Tanh[x]*Sqrt[a + b - b*Tanh[x]^2])/2","A",7,7,12,0.5833,1,"{4128, 416, 523, 217, 203, 377, 206}"
191,1,70,0,0.1319558,"\int \coth (x) \left(a+b \text{sech}^2(x)\right)^{3/2} \, dx","Int[Coth[x]*(a + b*Sech[x]^2)^(3/2),x]","a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)+b \sqrt{a+b \text{sech}^2(x)}-(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a+b}}\right)","a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)+b \sqrt{a+b \text{sech}^2(x)}-(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a+b}}\right)",1,"a^(3/2)*ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]] - (a + b)^(3/2)*ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a + b]] + b*Sqrt[a + b*Sech[x]^2]","A",8,6,15,0.4000,1,"{4139, 446, 84, 156, 63, 208}"
192,1,81,0,0.2324783,"\int \coth ^2(x) \left(a+b \text{sech}^2(x)\right)^{3/2} \, dx","Int[Coth[x]^2*(a + b*Sech[x]^2)^(3/2),x]","a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)-b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)-(a+b) \coth (x) \sqrt{a-b \tanh ^2(x)+b}","a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)-b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)-(a+b) \coth (x) \sqrt{a-b \tanh ^2(x)+b}",1,"-(b^(3/2)*ArcTan[(Sqrt[b]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]) + a^(3/2)*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]] - (a + b)*Coth[x]*Sqrt[a + b - b*Tanh[x]^2]","A",8,8,17,0.4706,1,"{4141, 1975, 474, 523, 217, 203, 377, 206}"
193,1,170,0,0.1943539,"\int \left(a+b \text{sech}^2(c+d x)\right)^{5/2} \, dx","Int[(a + b*Sech[c + d*x]^2)^(5/2),x]","\frac{\sqrt{b} \left(15 a^2+10 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a-b \tanh ^2(c+d x)+b}}\right)}{8 d}+\frac{a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{a-b \tanh ^2(c+d x)+b}}\right)}{d}+\frac{b \tanh (c+d x) \left(a-b \tanh ^2(c+d x)+b\right)^{3/2}}{4 d}+\frac{b (7 a+3 b) \tanh (c+d x) \sqrt{a-b \tanh ^2(c+d x)+b}}{8 d}","\frac{\sqrt{b} \left(15 a^2+10 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a-b \tanh ^2(c+d x)+b}}\right)}{8 d}+\frac{a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{a-b \tanh ^2(c+d x)+b}}\right)}{d}+\frac{b \tanh (c+d x) \left(a-b \tanh ^2(c+d x)+b\right)^{3/2}}{4 d}+\frac{b (7 a+3 b) \tanh (c+d x) \sqrt{a-b \tanh ^2(c+d x)+b}}{8 d}",1,"(Sqrt[b]*(15*a^2 + 10*a*b + 3*b^2)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a + b - b*Tanh[c + d*x]^2]])/(8*d) + (a^(5/2)*ArcTanh[(Sqrt[a]*Tanh[c + d*x])/Sqrt[a + b - b*Tanh[c + d*x]^2]])/d + (b*(7*a + 3*b)*Tanh[c + d*x]*Sqrt[a + b - b*Tanh[c + d*x]^2])/(8*d) + (b*Tanh[c + d*x]*(a + b - b*Tanh[c + d*x]^2)^(3/2))/(4*d)","A",8,8,16,0.5000,1,"{4128, 416, 528, 523, 217, 203, 377, 206}"
194,1,66,0,0.1314203,"\int \frac{\tanh ^5(x)}{\sqrt{a+b \text{sech}^2(x)}} \, dx","Int[Tanh[x]^5/Sqrt[a + b*Sech[x]^2],x]","-\frac{\left(a+b \text{sech}^2(x)\right)^{3/2}}{3 b^2}+\frac{(a+2 b) \sqrt{a+b \text{sech}^2(x)}}{b^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{\left(a+b \text{sech}^2(x)\right)^{3/2}}{3 b^2}+\frac{(a+2 b) \sqrt{a+b \text{sech}^2(x)}}{b^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]]/Sqrt[a] + ((a + 2*b)*Sqrt[a + b*Sech[x]^2])/b^2 - (a + b*Sech[x]^2)^(3/2)/(3*b^2)","A",6,5,17,0.2941,1,"{4139, 446, 88, 63, 208}"
195,1,90,0,0.2283188,"\int \frac{\tanh ^4(x)}{\sqrt{a+b \text{sech}^2(x)}} \, dx","Int[Tanh[x]^4/Sqrt[a + b*Sech[x]^2],x]","-\frac{(a+3 b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{2 b^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{\sqrt{a}}+\frac{\tanh (x) \sqrt{a-b \tanh ^2(x)+b}}{2 b}","-\frac{(a+3 b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{2 b^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{\sqrt{a}}+\frac{\tanh (x) \sqrt{a-b \tanh ^2(x)+b}}{2 b}",1,"-((a + 3*b)*ArcTan[(Sqrt[b]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]])/(2*b^(3/2)) + ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/Sqrt[a] + (Tanh[x]*Sqrt[a + b - b*Tanh[x]^2])/(2*b)","A",8,8,17,0.4706,1,"{4141, 1975, 479, 523, 217, 203, 377, 206}"
196,1,42,0,0.0929296,"\int \frac{\tanh ^3(x)}{\sqrt{a+b \text{sech}^2(x)}} \, dx","Int[Tanh[x]^3/Sqrt[a + b*Sech[x]^2],x]","\frac{\sqrt{a+b \text{sech}^2(x)}}{b}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{\sqrt{a+b \text{sech}^2(x)}}{b}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]]/Sqrt[a] + Sqrt[a + b*Sech[x]^2]/b","A",5,5,17,0.2941,1,"{4139, 446, 80, 63, 208}"
197,1,60,0,0.1926459,"\int \frac{\tanh ^2(x)}{\sqrt{a+b \text{sech}^2(x)}} \, dx","Int[Tanh[x]^2/Sqrt[a + b*Sech[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{\sqrt{a}}-\frac{\tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{\sqrt{b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{\sqrt{a}}-\frac{\tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{\sqrt{b}}",1,"-(ArcTan[(Sqrt[b]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/Sqrt[b]) + ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/Sqrt[a]","A",7,7,17,0.4118,1,"{4141, 1975, 483, 217, 203, 377, 206}"
198,1,25,0,0.0532532,"\int \frac{\tanh (x)}{\sqrt{a+b \text{sech}^2(x)}} \, dx","Int[Tanh[x]/Sqrt[a + b*Sech[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]]/Sqrt[a]","A",4,4,15,0.2667,1,"{4139, 266, 63, 208}"
199,1,29,0,0.0254476,"\int \frac{1}{\sqrt{a+b \text{sech}^2(x)}} \, dx","Int[1/Sqrt[a + b*Sech[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{\sqrt{a}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{\sqrt{a}}",1,"ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/Sqrt[a]","A",3,3,12,0.2500,1,"{4128, 377, 206}"
200,1,56,0,0.102984,"\int \frac{\coth (x)}{\sqrt{a+b \text{sech}^2(x)}} \, dx","Int[Coth[x]/Sqrt[a + b*Sech[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}",1,"ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]]/Sqrt[a] - ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a + b]]/Sqrt[a + b]","A",7,5,15,0.3333,1,"{4139, 446, 86, 63, 208}"
201,1,53,0,0.1881423,"\int \frac{\coth ^2(x)}{\sqrt{a+b \text{sech}^2(x)}} \, dx","Int[Coth[x]^2/Sqrt[a + b*Sech[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{\sqrt{a}}-\frac{\coth (x) \sqrt{a-b \tanh ^2(x)+b}}{a+b}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{\sqrt{a}}-\frac{\coth (x) \sqrt{a-b \tanh ^2(x)+b}}{a+b}",1,"ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/Sqrt[a] - (Coth[x]*Sqrt[a + b - b*Tanh[x]^2])/(a + b)","A",6,6,17,0.3529,1,"{4141, 1975, 480, 12, 377, 206}"
202,1,90,0,0.1606256,"\int \frac{\coth ^3(x)}{\sqrt{a+b \text{sech}^2(x)}} \, dx","Int[Coth[x]^3/Sqrt[a + b*Sech[x]^2],x]","-\frac{\coth ^2(x) \sqrt{a+b \text{sech}^2(x)}}{2 (a+b)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{(2 a+3 b) \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a+b}}\right)}{2 (a+b)^{3/2}}","-\frac{\coth ^2(x) \sqrt{a+b \text{sech}^2(x)}}{2 (a+b)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{(2 a+3 b) \tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a+b}}\right)}{2 (a+b)^{3/2}}",1,"ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]]/Sqrt[a] - ((2*a + 3*b)*ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a + b]])/(2*(a + b)^(3/2)) - (Coth[x]^2*Sqrt[a + b*Sech[x]^2])/(2*(a + b))","A",8,6,17,0.3529,1,"{4139, 446, 103, 156, 63, 208}"
203,1,68,0,0.1473923,"\int \frac{\tanh ^5(x)}{\left(a+b \text{sech}^2(x)\right)^{3/2}} \, dx","Int[Tanh[x]^5/(a + b*Sech[x]^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{(a+b)^2}{a b^2 \sqrt{a+b \text{sech}^2(x)}}-\frac{\sqrt{a+b \text{sech}^2(x)}}{b^2}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{(a+b)^2}{a b^2 \sqrt{a+b \text{sech}^2(x)}}-\frac{\sqrt{a+b \text{sech}^2(x)}}{b^2}",1,"ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]]/a^(3/2) - (a + b)^2/(a*b^2*Sqrt[a + b*Sech[x]^2]) - Sqrt[a + b*Sech[x]^2]/b^2","A",6,5,17,0.2941,1,"{4139, 446, 87, 63, 208}"
204,1,86,0,0.2523477,"\int \frac{\tanh ^4(x)}{\left(a+b \text{sech}^2(x)\right)^{3/2}} \, dx","Int[Tanh[x]^4/(a + b*Sech[x]^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{3/2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{b^{3/2}}-\frac{(a+b) \tanh (x)}{a b \sqrt{a-b \tanh ^2(x)+b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{3/2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{b^{3/2}}-\frac{(a+b) \tanh (x)}{a b \sqrt{a-b \tanh ^2(x)+b}}",1,"ArcTan[(Sqrt[b]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/b^(3/2) + ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/a^(3/2) - ((a + b)*Tanh[x])/(a*b*Sqrt[a + b - b*Tanh[x]^2])","A",8,8,17,0.4706,1,"{4141, 1975, 470, 523, 217, 203, 377, 206}"
205,1,49,0,0.1146083,"\int \frac{\tanh ^3(x)}{\left(a+b \text{sech}^2(x)\right)^{3/2}} \, dx","Int[Tanh[x]^3/(a + b*Sech[x]^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{a+b}{a b \sqrt{a+b \text{sech}^2(x)}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{a+b}{a b \sqrt{a+b \text{sech}^2(x)}}",1,"ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]]/a^(3/2) - (a + b)/(a*b*Sqrt[a + b*Sech[x]^2])","A",5,5,17,0.2941,1,"{4139, 446, 78, 63, 208}"
206,1,51,0,0.2175833,"\int \frac{\tanh ^2(x)}{\left(a+b \text{sech}^2(x)\right)^{3/2}} \, dx","Int[Tanh[x]^2/(a + b*Sech[x]^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{3/2}}-\frac{\tanh (x)}{a \sqrt{a-b \tanh ^2(x)+b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{3/2}}-\frac{\tanh (x)}{a \sqrt{a-b \tanh ^2(x)+b}}",1,"ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/a^(3/2) - Tanh[x]/(a*Sqrt[a + b - b*Tanh[x]^2])","A",5,5,17,0.2941,1,"{4141, 1975, 471, 377, 206}"
207,1,43,0,0.0729075,"\int \frac{\tanh (x)}{\left(a+b \text{sech}^2(x)\right)^{3/2}} \, dx","Int[Tanh[x]/(a + b*Sech[x]^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{1}{a \sqrt{a+b \text{sech}^2(x)}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{1}{a \sqrt{a+b \text{sech}^2(x)}}",1,"ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]]/a^(3/2) - 1/(a*Sqrt[a + b*Sech[x]^2])","A",5,5,15,0.3333,1,"{4139, 266, 51, 63, 208}"
208,1,57,0,0.0451566,"\int \frac{1}{\left(a+b \text{sech}^2(x)\right)^{3/2}} \, dx","Int[(a + b*Sech[x]^2)^(-3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{3/2}}-\frac{b \tanh (x)}{a (a+b) \sqrt{a-b \tanh ^2(x)+b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{3/2}}-\frac{b \tanh (x)}{a (a+b) \sqrt{a-b \tanh ^2(x)+b}}",1,"ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/a^(3/2) - (b*Tanh[x])/(a*(a + b)*Sqrt[a + b - b*Tanh[x]^2])","A",4,4,12,0.3333,1,"{4128, 382, 377, 206}"
209,1,79,0,0.1402182,"\int \frac{\coth (x)}{\left(a+b \text{sech}^2(x)\right)^{3/2}} \, dx","Int[Coth[x]/(a + b*Sech[x]^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{b}{a (a+b) \sqrt{a+b \text{sech}^2(x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{3/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{b}{a (a+b) \sqrt{a+b \text{sech}^2(x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{3/2}}",1,"ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]]/a^(3/2) - ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a + b]]/(a + b)^(3/2) - b/(a*(a + b)*Sqrt[a + b*Sech[x]^2])","A",8,6,15,0.4000,1,"{4139, 446, 85, 156, 63, 208}"
210,1,88,0,0.274126,"\int \frac{\coth ^2(x)}{\left(a+b \text{sech}^2(x)\right)^{3/2}} \, dx","Int[Coth[x]^2/(a + b*Sech[x]^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{3/2}}-\frac{(a-b) \coth (x) \sqrt{a-b \tanh ^2(x)+b}}{a (a+b)^2}-\frac{b \coth (x)}{a (a+b) \sqrt{a-b \tanh ^2(x)+b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{3/2}}-\frac{(a-b) \coth (x) \sqrt{a-b \tanh ^2(x)+b}}{a (a+b)^2}-\frac{b \coth (x)}{a (a+b) \sqrt{a-b \tanh ^2(x)+b}}",1,"ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/a^(3/2) - (b*Coth[x])/(a*(a + b)*Sqrt[a + b - b*Tanh[x]^2]) - ((a - b)*Coth[x]*Sqrt[a + b - b*Tanh[x]^2])/(a*(a + b)^2)","A",7,7,17,0.4118,1,"{4141, 1975, 472, 583, 12, 377, 206}"
211,1,118,0,0.3388731,"\int \frac{\tanh ^6(x)}{\left(a+b \text{sech}^2(x)\right)^{5/2}} \, dx","Int[Tanh[x]^6/(a + b*Sech[x]^2)^(5/2),x]","-\frac{\left(\frac{1}{a^2}-\frac{1}{b^2}\right) \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{5/2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{b^{5/2}}-\frac{(a+b) \tanh ^3(x)}{3 a b \left(a-b \tanh ^2(x)+b\right)^{3/2}}","-\frac{\left(\frac{1}{a^2}-\frac{1}{b^2}\right) \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{5/2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{b^{5/2}}-\frac{(a+b) \tanh ^3(x)}{3 a b \left(a-b \tanh ^2(x)+b\right)^{3/2}}",1,"-(ArcTan[(Sqrt[b]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/b^(5/2)) + ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/a^(5/2) - ((a + b)*Tanh[x]^3)/(3*a*b*(a + b - b*Tanh[x]^2)^(3/2)) - ((a^(-2) - b^(-2))*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]","A",9,9,17,0.5294,1,"{4141, 1975, 470, 578, 523, 217, 203, 377, 206}"
212,1,76,0,0.157898,"\int \frac{\tanh ^5(x)}{\left(a+b \text{sech}^2(x)\right)^{5/2}} \, dx","Int[Tanh[x]^5/(a + b*Sech[x]^2)^(5/2),x]","-\frac{\frac{1}{a^2}-\frac{1}{b^2}}{\sqrt{a+b \text{sech}^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{(a+b)^2}{3 a b^2 \left(a+b \text{sech}^2(x)\right)^{3/2}}","-\frac{\frac{1}{a^2}-\frac{1}{b^2}}{\sqrt{a+b \text{sech}^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{(a+b)^2}{3 a b^2 \left(a+b \text{sech}^2(x)\right)^{3/2}}",1,"ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]]/a^(5/2) - (a + b)^2/(3*a*b^2*(a + b*Sech[x]^2)^(3/2)) - (a^(-2) - b^(-2))/Sqrt[a + b*Sech[x]^2]","A",6,5,17,0.2941,1,"{4139, 446, 87, 63, 208}"
213,1,90,0,0.2623493,"\int \frac{\tanh ^4(x)}{\left(a+b \text{sech}^2(x)\right)^{5/2}} \, dx","Int[Tanh[x]^4/(a + b*Sech[x]^2)^(5/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{5/2}}+\frac{(a-3 b) \tanh (x)}{3 a^2 b \sqrt{a-b \tanh ^2(x)+b}}-\frac{(a+b) \tanh (x)}{3 a b \left(a-b \tanh ^2(x)+b\right)^{3/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{5/2}}+\frac{(a-3 b) \tanh (x)}{3 a^2 b \sqrt{a-b \tanh ^2(x)+b}}-\frac{(a+b) \tanh (x)}{3 a b \left(a-b \tanh ^2(x)+b\right)^{3/2}}",1,"ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/a^(5/2) - ((a + b)*Tanh[x])/(3*a*b*(a + b - b*Tanh[x]^2)^(3/2)) + ((a - 3*b)*Tanh[x])/(3*a^2*b*Sqrt[a + b - b*Tanh[x]^2])","A",7,7,17,0.4118,1,"{4141, 1975, 470, 527, 12, 377, 206}"
214,1,68,0,0.1244406,"\int \frac{\tanh ^3(x)}{\left(a+b \text{sech}^2(x)\right)^{5/2}} \, dx","Int[Tanh[x]^3/(a + b*Sech[x]^2)^(5/2),x]","-\frac{1}{a^2 \sqrt{a+b \text{sech}^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{a+b}{3 a b \left(a+b \text{sech}^2(x)\right)^{3/2}}","-\frac{1}{a^2 \sqrt{a+b \text{sech}^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{a+b}{3 a b \left(a+b \text{sech}^2(x)\right)^{3/2}}",1,"ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]]/a^(5/2) - (a + b)/(3*a*b*(a + b*Sech[x]^2)^(3/2)) - 1/(a^2*Sqrt[a + b*Sech[x]^2])","A",6,6,17,0.3529,1,"{4139, 446, 78, 51, 63, 208}"
215,1,88,0,0.2479037,"\int \frac{\tanh ^2(x)}{\left(a+b \text{sech}^2(x)\right)^{5/2}} \, dx","Int[Tanh[x]^2/(a + b*Sech[x]^2)^(5/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{5/2}}-\frac{(2 a+3 b) \tanh (x)}{3 a^2 (a+b) \sqrt{a-b \tanh ^2(x)+b}}-\frac{\tanh (x)}{3 a \left(a-b \tanh ^2(x)+b\right)^{3/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{5/2}}-\frac{(2 a+3 b) \tanh (x)}{3 a^2 (a+b) \sqrt{a-b \tanh ^2(x)+b}}-\frac{\tanh (x)}{3 a \left(a-b \tanh ^2(x)+b\right)^{3/2}}",1,"ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/a^(5/2) - Tanh[x]/(3*a*(a + b - b*Tanh[x]^2)^(3/2)) - ((2*a + 3*b)*Tanh[x])/(3*a^2*(a + b)*Sqrt[a + b - b*Tanh[x]^2])","A",7,7,17,0.4118,1,"{4141, 1975, 471, 527, 12, 377, 206}"
216,1,62,0,0.0871114,"\int \frac{\tanh (x)}{\left(a+b \text{sech}^2(x)\right)^{5/2}} \, dx","Int[Tanh[x]/(a + b*Sech[x]^2)^(5/2),x]","-\frac{1}{a^2 \sqrt{a+b \text{sech}^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{1}{3 a \left(a+b \text{sech}^2(x)\right)^{3/2}}","-\frac{1}{a^2 \sqrt{a+b \text{sech}^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{1}{3 a \left(a+b \text{sech}^2(x)\right)^{3/2}}",1,"ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]]/a^(5/2) - 1/(3*a*(a + b*Sech[x]^2)^(3/2)) - 1/(a^2*Sqrt[a + b*Sech[x]^2])","A",6,5,15,0.3333,1,"{4139, 266, 51, 63, 208}"
217,1,95,0,0.0901705,"\int \frac{1}{\left(a+b \text{sech}^2(x)\right)^{5/2}} \, dx","Int[(a + b*Sech[x]^2)^(-5/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{5/2}}-\frac{b (5 a+3 b) \tanh (x)}{3 a^2 (a+b)^2 \sqrt{a-b \tanh ^2(x)+b}}-\frac{b \tanh (x)}{3 a (a+b) \left(a-b \tanh ^2(x)+b\right)^{3/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{5/2}}-\frac{b (5 a+3 b) \tanh (x)}{3 a^2 (a+b)^2 \sqrt{a-b \tanh ^2(x)+b}}-\frac{b \tanh (x)}{3 a (a+b) \left(a-b \tanh ^2(x)+b\right)^{3/2}}",1,"ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/a^(5/2) - (b*Tanh[x])/(3*a*(a + b)*(a + b - b*Tanh[x]^2)^(3/2)) - (b*(5*a + 3*b)*Tanh[x])/(3*a^2*(a + b)^2*Sqrt[a + b - b*Tanh[x]^2])","A",6,6,12,0.5000,1,"{4128, 414, 527, 12, 377, 206}"
218,1,109,0,0.1998933,"\int \frac{\coth (x)}{\left(a+b \text{sech}^2(x)\right)^{5/2}} \, dx","Int[Coth[x]/(a + b*Sech[x]^2)^(5/2),x]","-\frac{b (2 a+b)}{a^2 (a+b)^2 \sqrt{a+b \text{sech}^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{b}{3 a (a+b) \left(a+b \text{sech}^2(x)\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}","-\frac{b (2 a+b)}{a^2 (a+b)^2 \sqrt{a+b \text{sech}^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{b}{3 a (a+b) \left(a+b \text{sech}^2(x)\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \text{sech}^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}",1,"ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a]]/a^(5/2) - ArcTanh[Sqrt[a + b*Sech[x]^2]/Sqrt[a + b]]/(a + b)^(5/2) - b/(3*a*(a + b)*(a + b*Sech[x]^2)^(3/2)) - (b*(2*a + b))/(a^2*(a + b)^2*Sqrt[a + b*Sech[x]^2])","A",9,7,15,0.4667,1,"{4139, 446, 85, 152, 156, 63, 208}"
219,1,133,0,0.3759754,"\int \frac{\coth ^2(x)}{\left(a+b \text{sech}^2(x)\right)^{5/2}} \, dx","Int[Coth[x]^2/(a + b*Sech[x]^2)^(5/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{5/2}}-\frac{(a-3 b) (3 a+b) \coth (x) \sqrt{a-b \tanh ^2(x)+b}}{3 a^2 (a+b)^3}-\frac{b (7 a+3 b) \coth (x)}{3 a^2 (a+b)^2 \sqrt{a-b \tanh ^2(x)+b}}-\frac{b \coth (x)}{3 a (a+b) \left(a-b \tanh ^2(x)+b\right)^{3/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (x)}{\sqrt{a-b \tanh ^2(x)+b}}\right)}{a^{5/2}}-\frac{(a-3 b) (3 a+b) \coth (x) \sqrt{a-b \tanh ^2(x)+b}}{3 a^2 (a+b)^3}-\frac{b (7 a+3 b) \coth (x)}{3 a^2 (a+b)^2 \sqrt{a-b \tanh ^2(x)+b}}-\frac{b \coth (x)}{3 a (a+b) \left(a-b \tanh ^2(x)+b\right)^{3/2}}",1,"ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/a^(5/2) - (b*Coth[x])/(3*a*(a + b)*(a + b - b*Tanh[x]^2)^(3/2)) - (b*(7*a + 3*b)*Coth[x])/(3*a^2*(a + b)^2*Sqrt[a + b - b*Tanh[x]^2]) - ((a - 3*b)*(3*a + b)*Coth[x]*Sqrt[a + b - b*Tanh[x]^2])/(3*a^2*(a + b)^3)","A",8,8,17,0.4706,1,"{4141, 1975, 472, 579, 583, 12, 377, 206}"
220,1,183,0,0.1910893,"\int \frac{1}{\left(a+b \text{sech}^2(c+d x)\right)^{7/2}} \, dx","Int[(a + b*Sech[c + d*x]^2)^(-7/2),x]","-\frac{b \left(33 a^2+40 a b+15 b^2\right) \tanh (c+d x)}{15 a^3 d (a+b)^3 \sqrt{a-b \tanh ^2(c+d x)+b}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{a-b \tanh ^2(c+d x)+b}}\right)}{a^{7/2} d}-\frac{b (9 a+5 b) \tanh (c+d x)}{15 a^2 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)^{3/2}}-\frac{b \tanh (c+d x)}{5 a d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^{5/2}}","-\frac{b \left(33 a^2+40 a b+15 b^2\right) \tanh (c+d x)}{15 a^3 d (a+b)^3 \sqrt{a-b \tanh ^2(c+d x)+b}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \tanh (c+d x)}{\sqrt{a-b \tanh ^2(c+d x)+b}}\right)}{a^{7/2} d}-\frac{b (9 a+5 b) \tanh (c+d x)}{15 a^2 d (a+b)^2 \left(a-b \tanh ^2(c+d x)+b\right)^{3/2}}-\frac{b \tanh (c+d x)}{5 a d (a+b) \left(a-b \tanh ^2(c+d x)+b\right)^{5/2}}",1,"ArcTanh[(Sqrt[a]*Tanh[c + d*x])/Sqrt[a + b - b*Tanh[c + d*x]^2]]/(a^(7/2)*d) - (b*Tanh[c + d*x])/(5*a*(a + b)*d*(a + b - b*Tanh[c + d*x]^2)^(5/2)) - (b*(9*a + 5*b)*Tanh[c + d*x])/(15*a^2*(a + b)^2*d*(a + b - b*Tanh[c + d*x]^2)^(3/2)) - (b*(33*a^2 + 40*a*b + 15*b^2)*Tanh[c + d*x])/(15*a^3*(a + b)^3*d*Sqrt[a + b - b*Tanh[c + d*x]^2])","A",7,6,16,0.3750,1,"{4128, 414, 527, 12, 377, 206}"