1,1,73,0,0.0757167,"\int \sinh ^4(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Sinh[c + d*x]^4*(a + b*Tanh[c + d*x]^2),x]","\frac{(a+b) \sinh (c+d x) \cosh ^3(c+d x)}{4 d}-\frac{(5 a+9 b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{3}{8} x (a+5 b)-\frac{b \tanh (c+d x)}{d}","\frac{(a+b) \sinh (c+d x) \cosh ^3(c+d x)}{4 d}-\frac{(5 a+9 b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{3}{8} x (a+5 b)-\frac{b \tanh (c+d x)}{d}",1,"(3*(a + 5*b)*x)/8 - ((5*a + 9*b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + ((a + b)*Cosh[c + d*x]^3*Sinh[c + d*x])/(4*d) - (b*Tanh[c + d*x])/d","A",5,5,21,0.2381,1,"{3663, 455, 1157, 388, 206}"
2,1,47,0,0.0546025,"\int \sinh ^3(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Sinh[c + d*x]^3*(a + b*Tanh[c + d*x]^2),x]","\frac{(a+b) \cosh ^3(c+d x)}{3 d}-\frac{(a+2 b) \cosh (c+d x)}{d}-\frac{b \text{sech}(c+d x)}{d}","\frac{(a+b) \cosh ^3(c+d x)}{3 d}-\frac{(a+2 b) \cosh (c+d x)}{d}-\frac{b \text{sech}(c+d x)}{d}",1,"-(((a + 2*b)*Cosh[c + d*x])/d) + ((a + b)*Cosh[c + d*x]^3)/(3*d) - (b*Sech[c + d*x])/d","A",3,2,21,0.09524,1,"{3664, 448}"
3,1,44,0,0.0507793,"\int \sinh ^2(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Sinh[c + d*x]^2*(a + b*Tanh[c + d*x]^2),x]","\frac{(a+b) \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{1}{2} x (a+3 b)+\frac{b \tanh (c+d x)}{d}","\frac{(a+b) \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{1}{2} x (a+3 b)+\frac{b \tanh (c+d x)}{d}",1,"-((a + 3*b)*x)/2 + ((a + b)*Cosh[c + d*x]*Sinh[c + d*x])/(2*d) + (b*Tanh[c + d*x])/d","A",4,4,21,0.1905,1,"{3663, 455, 388, 206}"
4,1,25,0,0.0320672,"\int \sinh (c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Sinh[c + d*x]*(a + b*Tanh[c + d*x]^2),x]","\frac{(a+b) \cosh (c+d x)}{d}+\frac{b \text{sech}(c+d x)}{d}","\frac{(a+b) \cosh (c+d x)}{d}+\frac{b \text{sech}(c+d x)}{d}",1,"((a + b)*Cosh[c + d*x])/d + (b*Sech[c + d*x])/d","A",3,2,19,0.1053,1,"{3664, 14}"
5,1,26,0,0.0332959,"\int \text{csch}(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Csch[c + d*x]*(a + b*Tanh[c + d*x]^2),x]","-\frac{a \tanh ^{-1}(\cosh (c+d x))}{d}-\frac{b \text{sech}(c+d x)}{d}","-\frac{a \tanh ^{-1}(\cosh (c+d x))}{d}-\frac{b \text{sech}(c+d x)}{d}",1,"-((a*ArcTanh[Cosh[c + d*x]])/d) - (b*Sech[c + d*x])/d","A",3,3,19,0.1579,1,"{3664, 388, 207}"
6,1,24,0,0.0327757,"\int \text{csch}^2(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Csch[c + d*x]^2*(a + b*Tanh[c + d*x]^2),x]","\frac{b \tanh (c+d x)}{d}-\frac{a \coth (c+d x)}{d}","\frac{b \tanh (c+d x)}{d}-\frac{a \coth (c+d x)}{d}",1,"-((a*Coth[c + d*x])/d) + (b*Tanh[c + d*x])/d","A",3,2,21,0.09524,1,"{3663, 14}"
7,1,51,0,0.0588961,"\int \text{csch}^3(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Csch[c + d*x]^3*(a + b*Tanh[c + d*x]^2),x]","\frac{(a-2 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{a \coth (c+d x) \text{csch}(c+d x)}{2 d}+\frac{b \text{sech}(c+d x)}{d}","\frac{(a-2 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{a \coth (c+d x) \text{csch}(c+d x)}{2 d}+\frac{b \text{sech}(c+d x)}{d}",1,"((a - 2*b)*ArcTanh[Cosh[c + d*x]])/(2*d) - (a*Coth[c + d*x]*Csch[c + d*x])/(2*d) + (b*Sech[c + d*x])/d","A",4,4,21,0.1905,1,"{3664, 455, 388, 207}"
8,1,44,0,0.0431187,"\int \text{csch}^4(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Csch[c + d*x]^4*(a + b*Tanh[c + d*x]^2),x]","\frac{(a-b) \coth (c+d x)}{d}-\frac{a \coth ^3(c+d x)}{3 d}-\frac{b \tanh (c+d x)}{d}","\frac{(a-b) \coth (c+d x)}{d}-\frac{a \coth ^3(c+d x)}{3 d}-\frac{b \tanh (c+d x)}{d}",1,"((a - b)*Coth[c + d*x])/d - (a*Coth[c + d*x]^3)/(3*d) - (b*Tanh[c + d*x])/d","A",3,2,21,0.09524,1,"{3663, 448}"
9,1,118,0,0.1325788,"\int \sinh ^4(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]^4*(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{\left(a^2+10 a b+13 b^2\right) \tanh (c+d x)}{4 d}+\frac{1}{8} x \left(3 a^2+30 a b+35 b^2\right)+\frac{(a+b)^2 \sinh ^4(c+d x) \tanh (c+d x)}{4 d}-\frac{(a+b) (a+9 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+10 a b+13 b^2\right) \tanh (c+d x)}{4 d}+\frac{1}{8} x \left(3 a^2+30 a b+35 b^2\right)+\frac{(a+b)^2 \sinh ^4(c+d x) \tanh (c+d x)}{4 d}-\frac{(a+b) (a+9 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 + 30*a*b + 35*b^2)*x)/8 - ((a + b)*(a + 9*b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) - ((a^2 + 10*a*b + 13*b^2)*Tanh[c + d*x])/(4*d) + ((a + b)^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,"{3663, 463, 455, 1153, 206}"
10,1,77,0,0.0978984,"\int \sinh ^3(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]^3*(a + b*Tanh[c + d*x]^2)^2,x]","\frac{(a+b)^2 \cosh ^3(c+d x)}{3 d}-\frac{(a+b) (a+3 b) \cosh (c+d x)}{d}-\frac{b (2 a+3 b) \text{sech}(c+d x)}{d}+\frac{b^2 \text{sech}^3(c+d x)}{3 d}","\frac{(a+b)^2 \cosh ^3(c+d x)}{3 d}-\frac{(a+b) (a+3 b) \cosh (c+d x)}{d}-\frac{b (2 a+3 b) \text{sech}(c+d x)}{d}+\frac{b^2 \text{sech}^3(c+d x)}{3 d}",1,"-(((a + b)*(a + 3*b)*Cosh[c + d*x])/d) + ((a + b)^2*Cosh[c + d*x]^3)/(3*d) - (b*(2*a + 3*b)*Sech[c + d*x])/d + (b^2*Sech[c + d*x]^3)/(3*d)","A",3,2,23,0.08696,1,"{3664, 448}"
11,1,79,0,0.1106722,"\int \sinh ^2(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]^2*(a + b*Tanh[c + d*x]^2)^2,x]","\frac{(a+b) (a+5 b) \tanh (c+d x)}{2 d}+\frac{(a+b)^2 \sinh ^2(c+d x) \tanh (c+d x)}{2 d}-\frac{1}{2} x (a+b) (a+5 b)+\frac{b^2 \tanh ^3(c+d x)}{3 d}","\frac{(a+b) (a+5 b) \tanh (c+d x)}{2 d}+\frac{(a+b)^2 \sinh ^2(c+d x) \tanh (c+d x)}{2 d}-\frac{1}{2} x (a+b) (a+5 b)+\frac{b^2 \tanh ^3(c+d x)}{3 d}",1,"-((a + b)*(a + 5*b)*x)/2 + ((a + b)*(a + 5*b)*Tanh[c + d*x])/(2*d) + ((a + b)^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,"{3663, 463, 459, 321, 206}"
12,1,49,0,0.0532368,"\int \sinh (c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]*(a + b*Tanh[c + d*x]^2)^2,x]","\frac{(a+b)^2 \cosh (c+d x)}{d}+\frac{2 b (a+b) \text{sech}(c+d x)}{d}-\frac{b^2 \text{sech}^3(c+d x)}{3 d}","\frac{(a+b)^2 \cosh (c+d x)}{d}+\frac{2 b (a+b) \text{sech}(c+d x)}{d}-\frac{b^2 \text{sech}^3(c+d x)}{3 d}",1,"((a + b)^2*Cosh[c + d*x])/d + (2*b*(a + b)*Sech[c + d*x])/d - (b^2*Sech[c + d*x]^3)/(3*d)","A",3,2,21,0.09524,1,"{3664, 270}"
13,1,51,0,0.0645143,"\int \text{csch}(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]*(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{a^2 \tanh ^{-1}(\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 \tanh ^{-1}(\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^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,"{3664, 390, 207}"
14,1,46,0,0.0567826,"\int \text{csch}^2(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^2*(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{a^2 \coth (c+d x)}{d}+\frac{2 a b \tanh (c+d x)}{d}+\frac{b^2 \tanh ^3(c+d x)}{3 d}","-\frac{a^2 \coth (c+d x)}{d}+\frac{2 a b \tanh (c+d x)}{d}+\frac{b^2 \tanh ^3(c+d x)}{3 d}",1,"-((a^2*Coth[c + d*x])/d) + (2*a*b*Tanh[c + d*x])/d + (b^2*Tanh[c + d*x]^3)/(3*d)","A",3,2,23,0.08696,1,"{3663, 270}"
15,1,82,0,0.1194295,"\int \text{csch}^3(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^3*(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{a^2 \text{csch}^2(c+d x) \text{sech}(c+d x)}{2 d}-\frac{a (a-4 b) \text{sech}(c+d x)}{2 d}+\frac{a (a-4 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{b^2 \text{sech}^3(c+d x)}{3 d}","-\frac{a^2 \text{csch}^2(c+d x) \text{sech}(c+d x)}{2 d}-\frac{a (a-4 b) \text{sech}(c+d x)}{2 d}+\frac{a (a-4 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{b^2 \text{sech}^3(c+d x)}{3 d}",1,"(a*(a - 4*b)*ArcTanh[Cosh[c + d*x]])/(2*d) - (a*(a - 4*b)*Sech[c + d*x])/(2*d) - (a^2*Csch[c + d*x]^2*Sech[c + d*x])/(2*d) - (b^2*Sech[c + d*x]^3)/(3*d)","A",5,5,23,0.2174,1,"{3664, 463, 459, 321, 207}"
16,1,72,0,0.0789086,"\int \text{csch}^4(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^4*(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{a^2 \coth ^3(c+d x)}{3 d}-\frac{b (2 a-b) \tanh (c+d x)}{d}+\frac{a (a-2 b) \coth (c+d x)}{d}-\frac{b^2 \tanh ^3(c+d x)}{3 d}","-\frac{a^2 \coth ^3(c+d x)}{3 d}-\frac{b (2 a-b) \tanh (c+d x)}{d}+\frac{a (a-2 b) \coth (c+d x)}{d}-\frac{b^2 \tanh ^3(c+d x)}{3 d}",1,"(a*(a - 2*b)*Coth[c + d*x])/d - (a^2*Coth[c + d*x]^3)/(3*d) - ((2*a - b)*b*Tanh[c + d*x])/d - (b^2*Tanh[c + d*x]^3)/(3*d)","A",3,2,23,0.08696,1,"{3663, 448}"
17,1,182,0,0.2216804,"\int \sinh ^4(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]^4*(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{b \left(6 a^2+35 a b+21 b^2\right) \tanh ^3(c+d x)}{8 d}-\frac{3 (a+b) \left(a^2+14 a b+21 b^2\right) \tanh (c+d x)}{8 d}+\frac{3}{8} x (a+b) \left(a^2+14 a b+21 b^2\right)-\frac{3 b^2 (5 a+21 b) \tanh ^5(c+d x)}{40 d}-\frac{3 (a+3 b) \sinh ^2(c+d x) \tanh (c+d x) \left(a+b \tanh ^2(c+d x)\right)^2}{8 d}+\frac{\sinh ^3(c+d x) \cosh (c+d x) \left(a+b \tanh ^2(c+d x)\right)^3}{4 d}","-\frac{b \left(6 a^2+35 a b+21 b^2\right) \tanh ^3(c+d x)}{8 d}-\frac{3 (a+b) \left(a^2+14 a b+21 b^2\right) \tanh (c+d x)}{8 d}+\frac{3}{8} x (a+b) \left(a^2+14 a b+21 b^2\right)-\frac{3 b^2 (5 a+21 b) \tanh ^5(c+d x)}{40 d}-\frac{3 (a+3 b) \sinh ^2(c+d x) \tanh (c+d x) \left(a+b \tanh ^2(c+d x)\right)^2}{8 d}+\frac{\sinh ^3(c+d x) \cosh (c+d x) \left(a+b \tanh ^2(c+d x)\right)^3}{4 d}",1,"(3*(a + b)*(a^2 + 14*a*b + 21*b^2)*x)/8 - (3*(a + b)*(a^2 + 14*a*b + 21*b^2)*Tanh[c + d*x])/(8*d) - (b*(6*a^2 + 35*a*b + 21*b^2)*Tanh[c + d*x]^3)/(8*d) - (3*b^2*(5*a + 21*b)*Tanh[c + d*x]^5)/(40*d) - (3*(a + 3*b)*Sinh[c + d*x]^2*Tanh[c + d*x]*(a + b*Tanh[c + d*x]^2)^2)/(8*d) + (Cosh[c + d*x]*Sinh[c + d*x]^3*(a + b*Tanh[c + d*x]^2)^3)/(4*d)","A",6,5,23,0.2174,1,"{3663, 467, 577, 570, 206}"
18,1,105,0,0.1225802,"\int \sinh ^3(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]^3*(a + b*Tanh[c + d*x]^2)^3,x]","\frac{b^2 (3 a+4 b) \text{sech}^3(c+d x)}{3 d}+\frac{(a+b)^3 \cosh ^3(c+d x)}{3 d}-\frac{(a+b)^2 (a+4 b) \cosh (c+d x)}{d}-\frac{3 b (a+b) (a+2 b) \text{sech}(c+d x)}{d}-\frac{b^3 \text{sech}^5(c+d x)}{5 d}","\frac{b^2 (3 a+4 b) \text{sech}^3(c+d x)}{3 d}+\frac{(a+b)^3 \cosh ^3(c+d x)}{3 d}-\frac{(a+b)^2 (a+4 b) \cosh (c+d x)}{d}-\frac{3 b (a+b) (a+2 b) \text{sech}(c+d x)}{d}-\frac{b^3 \text{sech}^5(c+d x)}{5 d}",1,"-(((a + b)^2*(a + 4*b)*Cosh[c + d*x])/d) + ((a + b)^3*Cosh[c + d*x]^3)/(3*d) - (3*b*(a + b)*(a + 2*b)*Sech[c + d*x])/d + (b^2*(3*a + 4*b)*Sech[c + d*x]^3)/(3*d) - (b^3*Sech[c + d*x]^5)/(5*d)","A",3,2,23,0.08696,1,"{3664, 448}"
19,1,139,0,0.1851461,"\int \sinh ^2(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]^2*(a + b*Tanh[c + d*x]^2)^3,x]","\frac{b \left(81 a^2+190 a b+105 b^2\right) \tanh (c+d x)}{30 d}+\frac{7 b \tanh (c+d x) \left(a+b \tanh ^2(c+d x)\right)^2}{10 d}+\frac{b (33 a+35 b) \tanh (c+d x) \left(a+b \tanh ^2(c+d x)\right)}{30 d}+\frac{\sinh (c+d x) \cosh (c+d x) \left(a+b \tanh ^2(c+d x)\right)^3}{2 d}-\frac{1}{2} x (a+b)^2 (a+7 b)","\frac{b^2 (3 a+2 b) \tanh ^3(c+d x)}{3 d}+\frac{3 b (a+b)^2 \tanh (c+d x)}{d}+\frac{(a+b)^3}{4 d (1-\tanh (c+d x))}-\frac{(a+b)^3}{4 d (\tanh (c+d x)+1)}-\frac{1}{2} x (a+b)^2 (a+7 b)+\frac{b^3 \tanh ^5(c+d x)}{5 d}",1,"-((a + b)^2*(a + 7*b)*x)/2 + (b*(81*a^2 + 190*a*b + 105*b^2)*Tanh[c + d*x])/(30*d) + (b*(33*a + 35*b)*Tanh[c + d*x]*(a + b*Tanh[c + d*x]^2))/(30*d) + (7*b*Tanh[c + d*x]*(a + b*Tanh[c + d*x]^2)^2)/(10*d) + (Cosh[c + d*x]*Sinh[c + d*x]*(a + b*Tanh[c + d*x]^2)^3)/(2*d)","A",6,5,23,0.2174,1,"{3663, 467, 528, 388, 206}"
20,1,70,0,0.0684337,"\int \sinh (c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]*(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{b^2 (a+b) \text{sech}^3(c+d x)}{d}+\frac{(a+b)^3 \cosh (c+d x)}{d}+\frac{3 b (a+b)^2 \text{sech}(c+d x)}{d}+\frac{b^3 \text{sech}^5(c+d x)}{5 d}","-\frac{b^2 (a+b) \text{sech}^3(c+d x)}{d}+\frac{(a+b)^3 \cosh (c+d x)}{d}+\frac{3 b (a+b)^2 \text{sech}(c+d x)}{d}+\frac{b^3 \text{sech}^5(c+d x)}{5 d}",1,"((a + b)^3*Cosh[c + d*x])/d + (3*b*(a + b)^2*Sech[c + d*x])/d - (b^2*(a + b)*Sech[c + d*x]^3)/d + (b^3*Sech[c + d*x]^5)/(5*d)","A",3,2,21,0.09524,1,"{3664, 270}"
21,1,84,0,0.0839635,"\int \text{csch}(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]*(a + b*Tanh[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{a^3 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b^2 (3 a+2 b) \text{sech}^3(c+d x)}{3 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{a^3 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b^2 (3 a+2 b) \text{sech}^3(c+d x)}{3 d}-\frac{b^3 \text{sech}^5(c+d x)}{5 d}",1,"-((a^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 + 2*b)*Sech[c + d*x]^3)/(3*d) - (b^3*Sech[c + d*x]^5)/(5*d)","A",4,3,21,0.1429,1,"{3664, 390, 207}"
22,1,64,0,0.0639957,"\int \text{csch}^2(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^2*(a + b*Tanh[c + d*x]^2)^3,x]","\frac{3 a^2 b \tanh (c+d x)}{d}-\frac{a^3 \coth (c+d x)}{d}+\frac{a b^2 \tanh ^3(c+d x)}{d}+\frac{b^3 \tanh ^5(c+d x)}{5 d}","\frac{3 a^2 b \tanh (c+d x)}{d}-\frac{a^3 \coth (c+d x)}{d}+\frac{a b^2 \tanh ^3(c+d x)}{d}+\frac{b^3 \tanh ^5(c+d x)}{5 d}",1,"-((a^3*Coth[c + d*x])/d) + (3*a^2*b*Tanh[c + d*x])/d + (a*b^2*Tanh[c + d*x]^3)/d + (b^3*Tanh[c + d*x]^5)/(5*d)","A",3,2,23,0.08696,1,"{3663, 270}"
23,1,152,0,0.2250327,"\int \text{csch}^3(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^3*(a + b*Tanh[c + d*x]^2)^3,x]","\frac{b \left(81 a^2-28 a b-4 b^2\right) \text{sech}(c+d x)}{30 d}+\frac{a^2 (a-6 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}+\frac{7 b \text{sech}(c+d x) \left(a-b \text{sech}^2(c+d x)+b\right)^2}{10 d}+\frac{b (33 a-2 b) \text{sech}(c+d x) \left(a-b \text{sech}^2(c+d x)+b\right)}{30 d}-\frac{\coth (c+d x) \text{csch}(c+d x) \left(a-b \text{sech}^2(c+d x)+b\right)^3}{2 d}","\frac{b \left(81 a^2-28 a b-4 b^2\right) \text{sech}(c+d x)}{30 d}+\frac{a^2 (a-6 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}+\frac{7 b \text{sech}(c+d x) \left(a-b \text{sech}^2(c+d x)+b\right)^2}{10 d}+\frac{b (33 a-2 b) \text{sech}(c+d x) \left(a-b \text{sech}^2(c+d x)+b\right)}{30 d}-\frac{\coth (c+d x) \text{csch}(c+d x) \left(a-b \text{sech}^2(c+d x)+b\right)^3}{2 d}",1,"(a^2*(a - 6*b)*ArcTanh[Cosh[c + d*x]])/(2*d) + (b*(81*a^2 - 28*a*b - 4*b^2)*Sech[c + d*x])/(30*d) + ((33*a - 2*b)*b*Sech[c + d*x]*(a + b - b*Sech[c + d*x]^2))/(30*d) + (7*b*Sech[c + d*x]*(a + b - b*Sech[c + d*x]^2)^2)/(10*d) - (Coth[c + d*x]*Csch[c + d*x]*(a + b - b*Sech[c + d*x]^2)^3)/(2*d)","A",6,5,23,0.2174,1,"{3664, 467, 528, 388, 207}"
24,1,98,0,0.0965718,"\int \text{csch}^4(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^4*(a + b*Tanh[c + d*x]^2)^3,x]","\frac{a^2 (a-3 b) \coth (c+d x)}{d}-\frac{a^3 \coth ^3(c+d x)}{3 d}-\frac{b^2 (3 a-b) \tanh ^3(c+d x)}{3 d}-\frac{3 a b (a-b) \tanh (c+d x)}{d}-\frac{b^3 \tanh ^5(c+d x)}{5 d}","\frac{a^2 (a-3 b) \coth (c+d x)}{d}-\frac{a^3 \coth ^3(c+d x)}{3 d}-\frac{b^2 (3 a-b) \tanh ^3(c+d x)}{3 d}-\frac{3 a b (a-b) \tanh (c+d x)}{d}-\frac{b^3 \tanh ^5(c+d x)}{5 d}",1,"(a^2*(a - 3*b)*Coth[c + d*x])/d - (a^3*Coth[c + d*x]^3)/(3*d) - (3*a*(a - b)*b*Tanh[c + d*x])/d - ((3*a - b)*b^2*Tanh[c + d*x]^3)/(3*d) - (b^3*Tanh[c + d*x]^5)/(5*d)","A",3,2,23,0.08696,1,"{3663, 448}"
25,1,118,0,0.1717064,"\int \frac{\sinh ^4(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Sinh[c + d*x]^4/(a + b*Tanh[c + d*x]^2),x]","\frac{x \left(3 a^2-6 a b-b^2\right)}{8 (a+b)^3}+\frac{a^{3/2} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{d (a+b)^3}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 d (a+b)}-\frac{(5 a+b) \sinh (c+d x) \cosh (c+d x)}{8 d (a+b)^2}","\frac{x \left(3 a^2-6 a b-b^2\right)}{8 (a+b)^3}+\frac{a^{3/2} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{d (a+b)^3}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 d (a+b)}-\frac{(5 a+b) \sinh (c+d x) \cosh (c+d x)}{8 d (a+b)^2}",1,"((3*a^2 - 6*a*b - b^2)*x)/(8*(a + b)^3) + (a^(3/2)*Sqrt[b]*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/((a + b)^3*d) - ((5*a + b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*(a + b)^2*d) + (Cosh[c + d*x]^3*Sinh[c + d*x])/(4*(a + b)*d)","A",6,6,23,0.2609,1,"{3663, 470, 527, 522, 206, 205}"
26,1,75,0,0.128102,"\int \frac{\sinh ^3(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Sinh[c + d*x]^3/(a + b*Tanh[c + d*x]^2),x]","\frac{\cosh ^3(c+d x)}{3 d (a+b)}-\frac{a \cosh (c+d x)}{d (a+b)^2}+\frac{a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{d (a+b)^{5/2}}","\frac{\cosh ^3(c+d x)}{3 d (a+b)}-\frac{a \cosh (c+d x)}{d (a+b)^2}+\frac{a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{d (a+b)^{5/2}}",1,"(a*Sqrt[b]*ArcTanh[(Sqrt[b]*Sech[c + d*x])/Sqrt[a + b]])/((a + b)^(5/2)*d) - (a*Cosh[c + d*x])/((a + b)^2*d) + Cosh[c + d*x]^3/(3*(a + b)*d)","A",4,4,23,0.1739,1,"{3664, 453, 325, 208}"
27,1,78,0,0.1044039,"\int \frac{\sinh ^2(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Sinh[c + d*x]^2/(a + b*Tanh[c + d*x]^2),x]","-\frac{\sqrt{a} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{d (a+b)^2}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 d (a+b)}-\frac{x (a-b)}{2 (a+b)^2}","-\frac{\sqrt{a} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{d (a+b)^2}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 d (a+b)}-\frac{x (a-b)}{2 (a+b)^2}",1,"-((a - b)*x)/(2*(a + b)^2) - (Sqrt[a]*Sqrt[b]*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/((a + b)^2*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*(a + b)*d)","A",5,5,23,0.2174,1,"{3663, 471, 522, 206, 205}"
28,1,53,0,0.0626703,"\int \frac{\sinh (c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Sinh[c + d*x]/(a + b*Tanh[c + d*x]^2),x]","\frac{\cosh (c+d x)}{d (a+b)}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{d (a+b)^{3/2}}","\frac{\cosh (c+d x)}{d (a+b)}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{d (a+b)^{3/2}}",1,"-((Sqrt[b]*ArcTanh[(Sqrt[b]*Sech[c + d*x])/Sqrt[a + b]])/((a + b)^(3/2)*d)) + Cosh[c + d*x]/((a + b)*d)","A",3,3,21,0.1429,1,"{3664, 325, 208}"
29,1,55,0,0.078118,"\int \frac{\text{csch}(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Csch[c + d*x]/(a + b*Tanh[c + d*x]^2),x]","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{a d \sqrt{a+b}}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a d}","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{a d \sqrt{a+b}}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a d}",1,"-(ArcTanh[Cosh[c + d*x]]/(a*d)) + (Sqrt[b]*ArcTanh[(Sqrt[b]*Sech[c + d*x])/Sqrt[a + b]])/(a*Sqrt[a + b]*d)","A",4,4,21,0.1905,1,"{3664, 391, 207, 208}"
30,1,48,0,0.062818,"\int \frac{\text{csch}^2(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Csch[c + d*x]^2/(a + b*Tanh[c + d*x]^2),x]","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{a^{3/2} d}-\frac{\coth (c+d x)}{a d}","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{a^{3/2} d}-\frac{\coth (c+d x)}{a d}",1,"-((Sqrt[b]*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(a^(3/2)*d)) - Coth[c + d*x]/(a*d)","A",3,3,23,0.1304,1,"{3663, 325, 205}"
31,1,85,0,0.1187275,"\int \frac{\text{csch}^3(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Csch[c + d*x]^3/(a + b*Tanh[c + d*x]^2),x]","\frac{(a+2 b) \tanh ^{-1}(\cosh (c+d x))}{2 a^2 d}-\frac{\sqrt{b} \sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{a^2 d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d}","\frac{(a+2 b) \tanh ^{-1}(\cosh (c+d x))}{2 a^2 d}-\frac{\sqrt{b} \sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{a^2 d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d}",1,"((a + 2*b)*ArcTanh[Cosh[c + d*x]])/(2*a^2*d) - (Sqrt[b]*Sqrt[a + b]*ArcTanh[(Sqrt[b]*Sech[c + d*x])/Sqrt[a + b]])/(a^2*d) - (Coth[c + d*x]*Csch[c + d*x])/(2*a*d)","A",5,5,23,0.2174,1,"{3664, 471, 522, 207, 208}"
32,1,70,0,0.0875878,"\int \frac{\text{csch}^4(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Csch[c + d*x]^4/(a + b*Tanh[c + d*x]^2),x]","\frac{(a+b) \coth (c+d x)}{a^2 d}+\frac{\sqrt{b} (a+b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{a^{5/2} d}-\frac{\coth ^3(c+d x)}{3 a d}","\frac{(a+b) \coth (c+d x)}{a^2 d}+\frac{\sqrt{b} (a+b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{a^{5/2} d}-\frac{\coth ^3(c+d x)}{3 a d}",1,"(Sqrt[b]*(a + b)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(a^(5/2)*d) + ((a + b)*Coth[c + d*x])/(a^2*d) - Coth[c + d*x]^3/(3*a*d)","A",4,4,23,0.1739,1,"{3663, 453, 325, 205}"
33,1,192,0,0.2523526,"\int \frac{\sinh ^4(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^4/(a + b*Tanh[c + d*x]^2)^2,x]","\frac{3 x \left(a^2-6 a b+b^2\right)}{8 (a+b)^4}+\frac{3 b (3 a-b) \tanh (c+d x)}{8 d (a+b)^3 \left(a+b \tanh ^2(c+d x)\right)}+\frac{3 \sqrt{a} \sqrt{b} (a-b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 d (a+b)^4}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 d (a+b) \left(a+b \tanh ^2(c+d x)\right)}-\frac{(5 a-b) \sinh (c+d x) \cosh (c+d x)}{8 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}","\frac{3 x \left(a^2-6 a b+b^2\right)}{8 (a+b)^4}+\frac{3 b (3 a-b) \tanh (c+d x)}{8 d (a+b)^3 \left(a+b \tanh ^2(c+d x)\right)}+\frac{3 \sqrt{a} \sqrt{b} (a-b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 d (a+b)^4}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 d (a+b) \left(a+b \tanh ^2(c+d x)\right)}-\frac{(5 a-b) \sinh (c+d x) \cosh (c+d x)}{8 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}",1,"(3*(a^2 - 6*a*b + b^2)*x)/(8*(a + b)^4) + (3*Sqrt[a]*(a - b)*Sqrt[b]*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(2*(a + b)^4*d) - ((5*a - b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*(a + b)^2*d*(a + b*Tanh[c + d*x]^2)) + (Cosh[c + d*x]^3*Sinh[c + d*x])/(4*(a + b)*d*(a + b*Tanh[c + d*x]^2)) + (3*(3*a - b)*b*Tanh[c + d*x])/(8*(a + b)^3*d*(a + b*Tanh[c + d*x]^2))","A",7,6,23,0.2609,1,"{3663, 470, 527, 522, 206, 205}"
34,1,124,0,0.2183719,"\int \frac{\sinh ^3(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^3/(a + b*Tanh[c + d*x]^2)^2,x]","\frac{\cosh ^3(c+d x)}{3 d (a+b)^2}-\frac{(a-b) \cosh (c+d x)}{d (a+b)^3}+\frac{a b \text{sech}(c+d x)}{2 d (a+b)^3 \left(a-b \text{sech}^2(c+d x)+b\right)}+\frac{\sqrt{b} (3 a-2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{2 d (a+b)^{7/2}}","\frac{\cosh ^3(c+d x)}{3 d (a+b)^2}-\frac{(a-b) \cosh (c+d x)}{d (a+b)^3}+\frac{a b \text{sech}(c+d x)}{2 d (a+b)^3 \left(a-b \text{sech}^2(c+d x)+b\right)}+\frac{\sqrt{b} (3 a-2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{2 d (a+b)^{7/2}}",1,"((3*a - 2*b)*Sqrt[b]*ArcTanh[(Sqrt[b]*Sech[c + d*x])/Sqrt[a + b]])/(2*(a + b)^(7/2)*d) - ((a - b)*Cosh[c + d*x])/((a + b)^3*d) + Cosh[c + d*x]^3/(3*(a + b)^2*d) + (a*b*Sech[c + d*x])/(2*(a + b)^3*d*(a + b - b*Sech[c + d*x]^2))","A",5,4,23,0.1739,1,"{3664, 456, 1261, 208}"
35,1,132,0,0.165343,"\int \frac{\sinh ^2(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^2/(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{b \tanh (c+d x)}{d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}-\frac{\sqrt{b} (3 a-b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 \sqrt{a} d (a+b)^3}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)}-\frac{x (a-3 b)}{2 (a+b)^3}","-\frac{b \tanh (c+d x)}{d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}-\frac{\sqrt{b} (3 a-b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 \sqrt{a} d (a+b)^3}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)}-\frac{x (a-3 b)}{2 (a+b)^3}",1,"-((a - 3*b)*x)/(2*(a + b)^3) - ((3*a - b)*Sqrt[b]*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(2*Sqrt[a]*(a + b)^3*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*(a + b)*d*(a + b*Tanh[c + d*x]^2)) - (b*Tanh[c + d*x])/((a + b)^2*d*(a + b*Tanh[c + d*x]^2))","A",6,6,23,0.2609,1,"{3663, 471, 527, 522, 206, 205}"
36,1,92,0,0.0746356,"\int \frac{\sinh (c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]/(a + b*Tanh[c + d*x]^2)^2,x]","\frac{3 \cosh (c+d x)}{2 d (a+b)^2}-\frac{\cosh (c+d x)}{2 d (a+b) \left(a-b \text{sech}^2(c+d x)+b\right)}-\frac{3 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{2 d (a+b)^{5/2}}","\frac{3 \cosh (c+d x)}{2 d (a+b)^2}-\frac{\cosh (c+d x)}{2 d (a+b) \left(a-b \text{sech}^2(c+d x)+b\right)}-\frac{3 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{2 d (a+b)^{5/2}}",1,"(-3*Sqrt[b]*ArcTanh[(Sqrt[b]*Sech[c + d*x])/Sqrt[a + b]])/(2*(a + b)^(5/2)*d) + (3*Cosh[c + d*x])/(2*(a + b)^2*d) - Cosh[c + d*x]/(2*(a + b)*d*(a + b - b*Sech[c + d*x]^2))","A",4,4,21,0.1905,1,"{3664, 290, 325, 208}"
37,1,103,0,0.143505,"\int \frac{\text{csch}(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Csch[c + d*x]/(a + b*Tanh[c + d*x]^2)^2,x]","\frac{\sqrt{b} (3 a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{2 a^2 d (a+b)^{3/2}}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a^2 d}+\frac{b \text{sech}(c+d x)}{2 a d (a+b) \left(a-b \text{sech}^2(c+d x)+b\right)}","\frac{\sqrt{b} (3 a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{2 a^2 d (a+b)^{3/2}}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a^2 d}+\frac{b \text{sech}(c+d x)}{2 a d (a+b) \left(a-b \text{sech}^2(c+d x)+b\right)}",1,"-(ArcTanh[Cosh[c + d*x]]/(a^2*d)) + (Sqrt[b]*(3*a + 2*b)*ArcTanh[(Sqrt[b]*Sech[c + d*x])/Sqrt[a + b]])/(2*a^2*(a + b)^(3/2)*d) + (b*Sech[c + d*x])/(2*a*(a + b)*d*(a + b - b*Sech[c + d*x]^2))","A",5,5,21,0.2381,1,"{3664, 414, 522, 207, 208}"
38,1,82,0,0.0764964,"\int \frac{\text{csch}^2(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Csch[c + d*x]^2/(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{5/2} d}-\frac{3 \coth (c+d x)}{2 a^2 d}+\frac{\coth (c+d x)}{2 a d \left(a+b \tanh ^2(c+d x)\right)}","-\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{5/2} d}-\frac{3 \coth (c+d x)}{2 a^2 d}+\frac{\coth (c+d x)}{2 a d \left(a+b \tanh ^2(c+d x)\right)}",1,"(-3*Sqrt[b]*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(2*a^(5/2)*d) - (3*Coth[c + d*x])/(2*a^2*d) + Coth[c + d*x]/(2*a*d*(a + b*Tanh[c + d*x]^2))","A",4,4,23,0.1739,1,"{3663, 290, 325, 205}"
39,1,141,0,0.2090259,"\int \frac{\text{csch}^3(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Csch[c + d*x]^3/(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{b \text{sech}(c+d x)}{a^2 d \left(a-b \text{sech}^2(c+d x)+b\right)}+\frac{(a+4 b) \tanh ^{-1}(\cosh (c+d x))}{2 a^3 d}-\frac{\sqrt{b} (3 a+4 b) \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{2 a^3 d \sqrt{a+b}}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d \left(a-b \text{sech}^2(c+d x)+b\right)}","-\frac{b \text{sech}(c+d x)}{a^2 d \left(a-b \text{sech}^2(c+d x)+b\right)}+\frac{(a+4 b) \tanh ^{-1}(\cosh (c+d x))}{2 a^3 d}-\frac{\sqrt{b} (3 a+4 b) \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{2 a^3 d \sqrt{a+b}}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d \left(a-b \text{sech}^2(c+d x)+b\right)}",1,"((a + 4*b)*ArcTanh[Cosh[c + d*x]])/(2*a^3*d) - (Sqrt[b]*(3*a + 4*b)*ArcTanh[(Sqrt[b]*Sech[c + d*x])/Sqrt[a + b]])/(2*a^3*Sqrt[a + b]*d) - (Coth[c + d*x]*Csch[c + d*x])/(2*a*d*(a + b - b*Sech[c + d*x]^2)) - (b*Sech[c + d*x])/(a^2*d*(a + b - b*Sech[c + d*x]^2))","A",6,6,23,0.2609,1,"{3664, 471, 527, 522, 207, 208}"
40,1,113,0,0.1538732,"\int \frac{\text{csch}^4(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Csch[c + d*x]^4/(a + b*Tanh[c + d*x]^2)^2,x]","\frac{b (a+b) \tanh (c+d x)}{2 a^3 d \left(a+b \tanh ^2(c+d x)\right)}+\frac{(a+2 b) \coth (c+d x)}{a^3 d}+\frac{\sqrt{b} (3 a+5 b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{7/2} d}-\frac{\coth ^3(c+d x)}{3 a^2 d}","\frac{b (a+b) \tanh (c+d x)}{2 a^3 d \left(a+b \tanh ^2(c+d x)\right)}+\frac{(a+2 b) \coth (c+d x)}{a^3 d}+\frac{\sqrt{b} (3 a+5 b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{7/2} d}-\frac{\coth ^3(c+d x)}{3 a^2 d}",1,"(Sqrt[b]*(3*a + 5*b)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(2*a^(7/2)*d) + ((a + 2*b)*Coth[c + d*x])/(a^3*d) - Coth[c + d*x]^3/(3*a^2*d) + (b*(a + b)*Tanh[c + d*x])/(2*a^3*d*(a + b*Tanh[c + d*x]^2))","A",5,4,23,0.1739,1,"{3663, 456, 1261, 205}"
41,1,240,0,0.3450647,"\int \frac{\sinh ^4(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^4/(a + b*Tanh[c + d*x]^2)^3,x]","\frac{3 \sqrt{b} \left(5 a^2-10 a b+b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 \sqrt{a} d (a+b)^5}+\frac{3 x \left(a^2-10 a b+5 b^2\right)}{8 (a+b)^5}+\frac{3 b (a-b) \tanh (c+d x)}{2 d (a+b)^4 \left(a+b \tanh ^2(c+d x)\right)}+\frac{b (7 a-5 b) \tanh (c+d x)}{8 d (a+b)^3 \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}-\frac{(5 a-3 b) \sinh (c+d x) \cosh (c+d x)}{8 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)^2}","\frac{3 \sqrt{b} \left(5 a^2-10 a b+b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 \sqrt{a} d (a+b)^5}+\frac{3 x \left(a^2-10 a b+5 b^2\right)}{8 (a+b)^5}+\frac{3 b (a-b) \tanh (c+d x)}{2 d (a+b)^4 \left(a+b \tanh ^2(c+d x)\right)}+\frac{b (7 a-5 b) \tanh (c+d x)}{8 d (a+b)^3 \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}-\frac{(5 a-3 b) \sinh (c+d x) \cosh (c+d x)}{8 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)^2}",1,"(3*(a^2 - 10*a*b + 5*b^2)*x)/(8*(a + b)^5) + (3*Sqrt[b]*(5*a^2 - 10*a*b + b^2)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(8*Sqrt[a]*(a + b)^5*d) - ((5*a - 3*b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*(a + b)^2*d*(a + b*Tanh[c + d*x]^2)^2) + (Cosh[c + d*x]^3*Sinh[c + d*x])/(4*(a + b)*d*(a + b*Tanh[c + d*x]^2)^2) + ((7*a - 5*b)*b*Tanh[c + d*x])/(8*(a + b)^3*d*(a + b*Tanh[c + d*x]^2)^2) + (3*(a - b)*b*Tanh[c + d*x])/(2*(a + b)^4*d*(a + b*Tanh[c + d*x]^2))","A",8,6,23,0.2609,1,"{3663, 470, 527, 522, 206, 205}"
42,1,166,0,0.2861736,"\int \frac{\sinh ^3(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^3/(a + b*Tanh[c + d*x]^2)^3,x]","\frac{\cosh ^3(c+d x)}{3 d (a+b)^3}-\frac{(a-2 b) \cosh (c+d x)}{d (a+b)^4}+\frac{b (7 a-4 b) \text{sech}(c+d x)}{8 d (a+b)^4 \left(a-b \text{sech}^2(c+d x)+b\right)}+\frac{a b \text{sech}(c+d x)}{4 d (a+b)^3 \left(a-b \text{sech}^2(c+d x)+b\right)^2}+\frac{5 \sqrt{b} (3 a-4 b) \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{8 d (a+b)^{9/2}}","\frac{\cosh ^3(c+d x)}{3 d (a+b)^3}-\frac{(a-2 b) \cosh (c+d x)}{d (a+b)^4}+\frac{b (7 a-4 b) \text{sech}(c+d x)}{8 d (a+b)^4 \left(a-b \text{sech}^2(c+d x)+b\right)}+\frac{a b \text{sech}(c+d x)}{4 d (a+b)^3 \left(a-b \text{sech}^2(c+d x)+b\right)^2}+\frac{5 \sqrt{b} (3 a-4 b) \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{8 d (a+b)^{9/2}}",1,"(5*(3*a - 4*b)*Sqrt[b]*ArcTanh[(Sqrt[b]*Sech[c + d*x])/Sqrt[a + b]])/(8*(a + b)^(9/2)*d) - ((a - 2*b)*Cosh[c + d*x])/((a + b)^4*d) + Cosh[c + d*x]^3/(3*(a + b)^3*d) + (a*b*Sech[c + d*x])/(4*(a + b)^3*d*(a + b - b*Sech[c + d*x]^2)^2) + ((7*a - 4*b)*b*Sech[c + d*x])/(8*(a + b)^4*d*(a + b - b*Sech[c + d*x]^2))","A",6,5,23,0.2174,1,"{3664, 456, 1259, 1261, 208}"
43,1,185,0,0.2508351,"\int \frac{\sinh ^2(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^2/(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{\sqrt{b} \left(15 a^2-10 a b-b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{3/2} d (a+b)^4}-\frac{b (11 a-b) \tanh (c+d x)}{8 a d (a+b)^3 \left(a+b \tanh ^2(c+d x)\right)}-\frac{3 b \tanh (c+d x)}{4 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}-\frac{x (a-5 b)}{2 (a+b)^4}","-\frac{\sqrt{b} \left(15 a^2-10 a b-b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{3/2} d (a+b)^4}-\frac{b (11 a-b) \tanh (c+d x)}{8 a d (a+b)^3 \left(a+b \tanh ^2(c+d x)\right)}-\frac{3 b \tanh (c+d x)}{4 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}-\frac{x (a-5 b)}{2 (a+b)^4}",1,"-((a - 5*b)*x)/(2*(a + b)^4) - (Sqrt[b]*(15*a^2 - 10*a*b - b^2)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(3/2)*(a + b)^4*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*(a + b)*d*(a + b*Tanh[c + d*x]^2)^2) - (3*b*Tanh[c + d*x])/(4*(a + b)^2*d*(a + b*Tanh[c + d*x]^2)^2) - ((11*a - b)*b*Tanh[c + d*x])/(8*a*(a + b)^3*d*(a + b*Tanh[c + d*x]^2))","A",7,6,23,0.2609,1,"{3663, 471, 527, 522, 206, 205}"
44,1,126,0,0.0966862,"\int \frac{\sinh (c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]/(a + b*Tanh[c + d*x]^2)^3,x]","\frac{15 \cosh (c+d x)}{8 d (a+b)^3}-\frac{5 \cosh (c+d x)}{8 d (a+b)^2 \left(a-b \text{sech}^2(c+d x)+b\right)}-\frac{\cosh (c+d x)}{4 d (a+b) \left(a-b \text{sech}^2(c+d x)+b\right)^2}-\frac{15 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{8 d (a+b)^{7/2}}","\frac{15 \cosh (c+d x)}{8 d (a+b)^3}-\frac{5 \cosh (c+d x)}{8 d (a+b)^2 \left(a-b \text{sech}^2(c+d x)+b\right)}-\frac{\cosh (c+d x)}{4 d (a+b) \left(a-b \text{sech}^2(c+d x)+b\right)^2}-\frac{15 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{8 d (a+b)^{7/2}}",1,"(-15*Sqrt[b]*ArcTanh[(Sqrt[b]*Sech[c + d*x])/Sqrt[a + b]])/(8*(a + b)^(7/2)*d) + (15*Cosh[c + d*x])/(8*(a + b)^3*d) - Cosh[c + d*x]/(4*(a + b)*d*(a + b - b*Sech[c + d*x]^2)^2) - (5*Cosh[c + d*x])/(8*(a + b)^2*d*(a + b - b*Sech[c + d*x]^2))","A",5,4,21,0.1905,1,"{3664, 290, 325, 208}"
45,1,156,0,0.2538498,"\int \frac{\text{csch}(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Csch[c + d*x]/(a + b*Tanh[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} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{8 a^3 d (a+b)^{5/2}}+\frac{b (7 a+4 b) \text{sech}(c+d x)}{8 a^2 d (a+b)^2 \left(a-b \text{sech}^2(c+d x)+b\right)}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a^3 d}+\frac{b \text{sech}(c+d x)}{4 a d (a+b) \left(a-b \text{sech}^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} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{8 a^3 d (a+b)^{5/2}}+\frac{b (7 a+4 b) \text{sech}(c+d x)}{8 a^2 d (a+b)^2 \left(a-b \text{sech}^2(c+d x)+b\right)}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a^3 d}+\frac{b \text{sech}(c+d x)}{4 a d (a+b) \left(a-b \text{sech}^2(c+d x)+b\right)^2}",1,"-(ArcTanh[Cosh[c + d*x]]/(a^3*d)) + (Sqrt[b]*(15*a^2 + 20*a*b + 8*b^2)*ArcTanh[(Sqrt[b]*Sech[c + d*x])/Sqrt[a + b]])/(8*a^3*(a + b)^(5/2)*d) + (b*Sech[c + d*x])/(4*a*(a + b)*d*(a + b - b*Sech[c + d*x]^2)^2) + (b*(7*a + 4*b)*Sech[c + d*x])/(8*a^2*(a + b)^2*d*(a + b - b*Sech[c + d*x]^2))","A",6,6,21,0.2857,1,"{3664, 414, 527, 522, 207, 208}"
46,1,112,0,0.086946,"\int \frac{\text{csch}^2(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Csch[c + d*x]^2/(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{7/2} d}+\frac{5 \coth (c+d x)}{8 a^2 d \left(a+b \tanh ^2(c+d x)\right)}-\frac{15 \coth (c+d x)}{8 a^3 d}+\frac{\coth (c+d x)}{4 a d \left(a+b \tanh ^2(c+d x)\right)^2}","-\frac{15 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{7/2} d}+\frac{5 \coth (c+d x)}{8 a^2 d \left(a+b \tanh ^2(c+d x)\right)}-\frac{15 \coth (c+d x)}{8 a^3 d}+\frac{\coth (c+d x)}{4 a d \left(a+b \tanh ^2(c+d x)\right)^2}",1,"(-15*Sqrt[b]*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(7/2)*d) - (15*Coth[c + d*x])/(8*a^3*d) + Coth[c + d*x]/(4*a*d*(a + b*Tanh[c + d*x]^2)^2) + (5*Coth[c + d*x])/(8*a^2*d*(a + b*Tanh[c + d*x]^2))","A",5,4,23,0.1739,1,"{3663, 290, 325, 205}"
47,1,196,0,0.3340247,"\int \frac{\text{csch}^3(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Csch[c + d*x]^3/(a + b*Tanh[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} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{8 a^4 d (a+b)^{3/2}}-\frac{b (11 a+12 b) \text{sech}(c+d x)}{8 a^3 d (a+b) \left(a-b \text{sech}^2(c+d x)+b\right)}-\frac{3 b \text{sech}(c+d x)}{4 a^2 d \left(a-b \text{sech}^2(c+d x)+b\right)^2}+\frac{(a+6 b) \tanh ^{-1}(\cosh (c+d x))}{2 a^4 d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d \left(a-b \text{sech}^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} \text{sech}(c+d x)}{\sqrt{a+b}}\right)}{8 a^4 d (a+b)^{3/2}}-\frac{b (11 a+12 b) \text{sech}(c+d x)}{8 a^3 d (a+b) \left(a-b \text{sech}^2(c+d x)+b\right)}-\frac{3 b \text{sech}(c+d x)}{4 a^2 d \left(a-b \text{sech}^2(c+d x)+b\right)^2}+\frac{(a+6 b) \tanh ^{-1}(\cosh (c+d x))}{2 a^4 d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d \left(a-b \text{sech}^2(c+d x)+b\right)^2}",1,"((a + 6*b)*ArcTanh[Cosh[c + d*x]])/(2*a^4*d) - (Sqrt[b]*(15*a^2 + 40*a*b + 24*b^2)*ArcTanh[(Sqrt[b]*Sech[c + d*x])/Sqrt[a + b]])/(8*a^4*(a + b)^(3/2)*d) - (Coth[c + d*x]*Csch[c + d*x])/(2*a*d*(a + b - b*Sech[c + d*x]^2)^2) - (3*b*Sech[c + d*x])/(4*a^2*d*(a + b - b*Sech[c + d*x]^2)^2) - (b*(11*a + 12*b)*Sech[c + d*x])/(8*a^3*(a + b)*d*(a + b - b*Sech[c + d*x]^2))","A",7,6,23,0.2609,1,"{3664, 471, 527, 522, 207, 208}"
48,1,151,0,0.2005535,"\int \frac{\text{csch}^4(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Csch[c + d*x]^4/(a + b*Tanh[c + d*x]^2)^3,x]","\frac{b (7 a+11 b) \tanh (c+d x)}{8 a^4 d \left(a+b \tanh ^2(c+d x)\right)}+\frac{b (a+b) \tanh (c+d x)}{4 a^3 d \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{(a+3 b) \coth (c+d x)}{a^4 d}+\frac{5 \sqrt{b} (3 a+7 b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{9/2} d}-\frac{\coth ^3(c+d x)}{3 a^3 d}","\frac{b (7 a+11 b) \tanh (c+d x)}{8 a^4 d \left(a+b \tanh ^2(c+d x)\right)}+\frac{b (a+b) \tanh (c+d x)}{4 a^3 d \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{(a+3 b) \coth (c+d x)}{a^4 d}+\frac{5 \sqrt{b} (3 a+7 b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{9/2} d}-\frac{\coth ^3(c+d x)}{3 a^3 d}",1,"(5*Sqrt[b]*(3*a + 7*b)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(9/2)*d) + ((a + 3*b)*Coth[c + d*x])/(a^4*d) - Coth[c + d*x]^3/(3*a^3*d) + (b*(a + b)*Tanh[c + d*x])/(4*a^3*d*(a + b*Tanh[c + d*x]^2)^2) + (b*(7*a + 11*b)*Tanh[c + d*x])/(8*a^4*d*(a + b*Tanh[c + d*x]^2))","A",6,5,23,0.2174,1,"{3663, 456, 1259, 1261, 205}"
49,1,132,0,0.1724932,"\int \sinh ^4(c+d x) \left(a+b \tanh ^3(c+d x)\right) \, dx","Int[Sinh[c + d*x]^4*(a + b*Tanh[c + d*x]^3),x]","-\frac{3 (a+8 b) \log (1-\tanh (c+d x))}{16 d}+\frac{3 (a-8 b) \log (\tanh (c+d x)+1)}{16 d}+\frac{\sinh ^4(c+d x) (a \tanh (c+d x)+b)}{4 d}-\frac{\sinh ^2(c+d x) \tanh (c+d x) (a+8 b \tanh (c+d x))}{8 d}-\frac{3 a \tanh (c+d x)}{8 d}-\frac{3 b \tanh ^2(c+d x)}{2 d}","-\frac{3 (a+8 b) \log (1-\tanh (c+d x))}{16 d}+\frac{3 (a-8 b) \log (\tanh (c+d x)+1)}{16 d}+\frac{\sinh ^4(c+d x) (a \tanh (c+d x)+b)}{4 d}-\frac{\sinh ^2(c+d x) \tanh (c+d x) (a+8 b \tanh (c+d x))}{8 d}-\frac{3 a \tanh (c+d x)}{8 d}-\frac{3 b \tanh ^2(c+d x)}{2 d}",1,"(-3*(a + 8*b)*Log[1 - Tanh[c + d*x]])/(16*d) + (3*(a - 8*b)*Log[1 + Tanh[c + d*x]])/(16*d) - (3*a*Tanh[c + d*x])/(8*d) - (3*b*Tanh[c + d*x]^2)/(2*d) + (Sinh[c + d*x]^4*(b + a*Tanh[c + d*x]))/(4*d) - (Sinh[c + d*x]^2*Tanh[c + d*x]*(a + 8*b*Tanh[c + d*x]))/(8*d)","A",8,5,21,0.2381,1,"{3663, 1804, 801, 633, 31}"
50,1,98,0,0.1196972,"\int \sinh ^3(c+d x) \left(a+b \tanh ^3(c+d x)\right) \, dx","Int[Sinh[c + d*x]^3*(a + b*Tanh[c + d*x]^3),x]","\frac{a \cosh ^3(c+d x)}{3 d}-\frac{a \cosh (c+d x)}{d}+\frac{5 b \sinh ^3(c+d x)}{6 d}-\frac{5 b \sinh (c+d x)}{2 d}-\frac{b \sinh ^3(c+d x) \tanh ^2(c+d x)}{2 d}+\frac{5 b \tan ^{-1}(\sinh (c+d x))}{2 d}","\frac{a \cosh ^3(c+d x)}{3 d}-\frac{a \cosh (c+d x)}{d}+\frac{5 b \sinh ^3(c+d x)}{6 d}-\frac{5 b \sinh (c+d x)}{2 d}-\frac{b \sinh ^3(c+d x) \tanh ^2(c+d x)}{2 d}+\frac{5 b \tan ^{-1}(\sinh (c+d x))}{2 d}",1,"(5*b*ArcTan[Sinh[c + d*x]])/(2*d) - (a*Cosh[c + d*x])/d + (a*Cosh[c + d*x]^3)/(3*d) - (5*b*Sinh[c + d*x])/(2*d) + (5*b*Sinh[c + d*x]^3)/(6*d) - (b*Sinh[c + d*x]^3*Tanh[c + d*x]^2)/(2*d)","A",9,6,21,0.2857,1,"{3666, 2633, 2592, 288, 302, 203}"
51,1,100,0,0.1174258,"\int \sinh ^2(c+d x) \left(a+b \tanh ^3(c+d x)\right) \, dx","Int[Sinh[c + d*x]^2*(a + b*Tanh[c + d*x]^3),x]","\frac{(a+4 b) \log (1-\tanh (c+d x))}{4 d}-\frac{(a-4 b) \log (\tanh (c+d x)+1)}{4 d}+\frac{\sinh ^2(c+d x) (a \tanh (c+d x)+b)}{2 d}+\frac{a \tanh (c+d x)}{2 d}+\frac{b \tanh ^2(c+d x)}{2 d}","\frac{(a+4 b) \log (1-\tanh (c+d x))}{4 d}-\frac{(a-4 b) \log (\tanh (c+d x)+1)}{4 d}+\frac{\sinh ^2(c+d x) (a \tanh (c+d x)+b)}{2 d}+\frac{a \tanh (c+d x)}{2 d}+\frac{b \tanh ^2(c+d x)}{2 d}",1,"((a + 4*b)*Log[1 - Tanh[c + d*x]])/(4*d) - ((a - 4*b)*Log[1 + Tanh[c + d*x]])/(4*d) + (a*Tanh[c + d*x])/(2*d) + (b*Tanh[c + d*x]^2)/(2*d) + (Sinh[c + d*x]^2*(b + a*Tanh[c + d*x]))/(2*d)","A",7,5,21,0.2381,1,"{3663, 1804, 1802, 633, 31}"
52,1,63,0,0.0761299,"\int \sinh (c+d x) \left(a+b \tanh ^3(c+d x)\right) \, dx","Int[Sinh[c + d*x]*(a + b*Tanh[c + d*x]^3),x]","\frac{a \cosh (c+d x)}{d}+\frac{3 b \sinh (c+d x)}{2 d}-\frac{3 b \tan ^{-1}(\sinh (c+d x))}{2 d}-\frac{b \sinh (c+d x) \tanh ^2(c+d x)}{2 d}","\frac{a \cosh (c+d x)}{d}+\frac{3 b \sinh (c+d x)}{2 d}-\frac{3 b \tan ^{-1}(\sinh (c+d x))}{2 d}-\frac{b \sinh (c+d x) \tanh ^2(c+d x)}{2 d}",1,"(-3*b*ArcTan[Sinh[c + d*x]])/(2*d) + (a*Cosh[c + d*x])/d + (3*b*Sinh[c + d*x])/(2*d) - (b*Sinh[c + d*x]*Tanh[c + d*x]^2)/(2*d)","A",7,6,19,0.3158,1,"{3666, 2638, 2592, 288, 321, 203}"
53,1,49,0,0.0743924,"\int \text{csch}(c+d x) \left(a+b \tanh ^3(c+d x)\right) \, dx","Int[Csch[c + d*x]*(a + b*Tanh[c + d*x]^3),x]","-\frac{a \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b \tan ^{-1}(\sinh (c+d x))}{2 d}-\frac{b \tanh (c+d x) \text{sech}(c+d x)}{2 d}","-\frac{a \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b \tan ^{-1}(\sinh (c+d x))}{2 d}-\frac{b \tanh (c+d x) \text{sech}(c+d x)}{2 d}",1,"(b*ArcTan[Sinh[c + d*x]])/(2*d) - (a*ArcTanh[Cosh[c + d*x]])/d - (b*Sech[c + d*x]*Tanh[c + d*x])/(2*d)","A",5,3,19,0.1579,1,"{3666, 3770, 2611}"
54,1,29,0,0.0341582,"\int \text{csch}^2(c+d x) \left(a+b \tanh ^3(c+d x)\right) \, dx","Int[Csch[c + d*x]^2*(a + b*Tanh[c + d*x]^3),x]","\frac{b \tanh ^2(c+d x)}{2 d}-\frac{a \coth (c+d x)}{d}","\frac{b \tanh ^2(c+d x)}{2 d}-\frac{a \coth (c+d x)}{d}",1,"-((a*Coth[c + d*x])/d) + (b*Tanh[c + d*x]^2)/(2*d)","A",3,2,21,0.09524,1,"{3663, 14}"
55,1,71,0,0.0904974,"\int \text{csch}^3(c+d x) \left(a+b \tanh ^3(c+d x)\right) \, dx","Int[Csch[c + d*x]^3*(a + b*Tanh[c + d*x]^3),x]","\frac{a \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{a \coth (c+d x) \text{csch}(c+d x)}{2 d}+\frac{b \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{b \tanh (c+d x) \text{sech}(c+d x)}{2 d}","\frac{a \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{a \coth (c+d x) \text{csch}(c+d x)}{2 d}+\frac{b \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{b \tanh (c+d x) \text{sech}(c+d x)}{2 d}",1,"(b*ArcTan[Sinh[c + d*x]])/(2*d) + (a*ArcTanh[Cosh[c + d*x]])/(2*d) - (a*Coth[c + d*x]*Csch[c + d*x])/(2*d) + (b*Sech[c + d*x]*Tanh[c + d*x])/(2*d)","A",6,3,21,0.1429,1,"{3666, 3768, 3770}"
56,1,56,0,0.0582295,"\int \text{csch}^4(c+d x) \left(a+b \tanh ^3(c+d x)\right) \, dx","Int[Csch[c + d*x]^4*(a + b*Tanh[c + d*x]^3),x]","-\frac{a \coth ^3(c+d x)}{3 d}+\frac{a \coth (c+d x)}{d}-\frac{b \tanh ^2(c+d x)}{2 d}+\frac{b \log (\tanh (c+d x))}{d}","-\frac{a \coth ^3(c+d x)}{3 d}+\frac{a \coth (c+d x)}{d}-\frac{b \tanh ^2(c+d x)}{2 d}+\frac{b \log (\tanh (c+d x))}{d}",1,"(a*Coth[c + d*x])/d - (a*Coth[c + d*x]^3)/(3*d) + (b*Log[Tanh[c + d*x]])/d - (b*Tanh[c + d*x]^2)/(2*d)","A",3,2,21,0.09524,1,"{3663, 1802}"
57,1,206,0,0.2966058,"\int \sinh ^4(c+d x) \left(a+b \tanh ^3(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]^4*(a + b*Tanh[c + d*x]^3)^2,x]","-\frac{3 \left(a^2+21 b^2\right) \tanh (c+d x)}{8 d}-\frac{3 \left(a^2+16 a b+21 b^2\right) \log (1-\tanh (c+d x))}{16 d}+\frac{3 \left(a^2-16 a b+21 b^2\right) \log (\tanh (c+d x)+1)}{16 d}-\frac{\sinh ^2(c+d x) \tanh (c+d x) \left(a^2+16 a b \tanh (c+d x)+13 b^2\right)}{8 d}+\frac{\sinh ^4(c+d x) \left(\left(a^2+b^2\right) \tanh (c+d x)+2 a b\right)}{4 d}-\frac{3 a b \tanh ^2(c+d x)}{d}-\frac{b^2 \tanh ^5(c+d x)}{5 d}-\frac{b^2 \tanh ^3(c+d x)}{d}","\frac{\sinh (c+d x) \cosh ^3(c+d x) \left(a^2+2 a b \tanh (c+d x)+b^2\right)}{4 d}-\frac{\sinh (c+d x) \cosh (c+d x) \left(5 a^2+20 a b \tanh (c+d x)+17 b^2\right)}{8 d}+\frac{3}{8} x \left(a^2+21 b^2\right)-\frac{a b \tanh ^2(c+d x)}{d}+\frac{6 a b \log (\cosh (c+d x))}{d}-\frac{b^2 \tanh ^5(c+d x)}{5 d}-\frac{b^2 \tanh ^3(c+d x)}{d}-\frac{6 b^2 \tanh (c+d x)}{d}",1,"(-3*(a^2 + 16*a*b + 21*b^2)*Log[1 - Tanh[c + d*x]])/(16*d) + (3*(a^2 - 16*a*b + 21*b^2)*Log[1 + Tanh[c + d*x]])/(16*d) - (3*(a^2 + 21*b^2)*Tanh[c + d*x])/(8*d) - (3*a*b*Tanh[c + d*x]^2)/d - (b^2*Tanh[c + d*x]^3)/d - (b^2*Tanh[c + d*x]^5)/(5*d) - (Sinh[c + d*x]^2*Tanh[c + d*x]*(a^2 + 13*b^2 + 16*a*b*Tanh[c + d*x]))/(8*d) + (Sinh[c + d*x]^4*(2*a*b + (a^2 + b^2)*Tanh[c + d*x]))/(4*d)","A",8,5,23,0.2174,1,"{3663, 1804, 1802, 633, 31}"
58,1,182,0,0.2248279,"\int \sinh ^3(c+d x) \left(a+b \tanh ^3(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]^3*(a + b*Tanh[c + d*x]^3)^2,x]","\frac{a^2 \cosh ^3(c+d x)}{3 d}-\frac{a^2 \cosh (c+d x)}{d}+\frac{5 a b \sinh ^3(c+d x)}{3 d}-\frac{5 a b \sinh (c+d x)}{d}-\frac{a b \sinh ^3(c+d x) \tanh ^2(c+d x)}{d}+\frac{5 a b \tan ^{-1}(\sinh (c+d x))}{d}+\frac{b^2 \cosh ^3(c+d x)}{3 d}-\frac{4 b^2 \cosh (c+d x)}{d}-\frac{b^2 \text{sech}^5(c+d x)}{5 d}+\frac{4 b^2 \text{sech}^3(c+d x)}{3 d}-\frac{6 b^2 \text{sech}(c+d x)}{d}","\frac{a^2 \cosh ^3(c+d x)}{3 d}-\frac{a^2 \cosh (c+d x)}{d}+\frac{5 a b \sinh ^3(c+d x)}{3 d}-\frac{5 a b \sinh (c+d x)}{d}-\frac{a b \sinh ^3(c+d x) \tanh ^2(c+d x)}{d}+\frac{5 a b \tan ^{-1}(\sinh (c+d x))}{d}+\frac{b^2 \cosh ^3(c+d x)}{3 d}-\frac{4 b^2 \cosh (c+d x)}{d}-\frac{b^2 \text{sech}^5(c+d x)}{5 d}+\frac{4 b^2 \text{sech}^3(c+d x)}{3 d}-\frac{6 b^2 \text{sech}(c+d x)}{d}",1,"(5*a*b*ArcTan[Sinh[c + d*x]])/d - (a^2*Cosh[c + d*x])/d - (4*b^2*Cosh[c + d*x])/d + (a^2*Cosh[c + d*x]^3)/(3*d) + (b^2*Cosh[c + d*x]^3)/(3*d) - (6*b^2*Sech[c + d*x])/d + (4*b^2*Sech[c + d*x]^3)/(3*d) - (b^2*Sech[c + d*x]^5)/(5*d) - (5*a*b*Sinh[c + d*x])/d + (5*a*b*Sinh[c + d*x]^3)/(3*d) - (a*b*Sinh[c + d*x]^3*Tanh[c + d*x]^2)/d","A",12,8,23,0.3478,1,"{3666, 2633, 2592, 288, 302, 203, 2590, 270}"
59,1,159,0,0.2051087,"\int \sinh ^2(c+d x) \left(a+b \tanh ^3(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]^2*(a + b*Tanh[c + d*x]^3)^2,x]","\frac{\left(a^2+7 b^2\right) \tanh (c+d x)}{2 d}+\frac{\sinh ^2(c+d x) \left(\left(a^2+b^2\right) \tanh (c+d x)+2 a b\right)}{2 d}+\frac{a b \tanh ^2(c+d x)}{d}+\frac{(a+b) (a+7 b) \log (1-\tanh (c+d x))}{4 d}-\frac{(a-7 b) (a-b) \log (\tanh (c+d x)+1)}{4 d}+\frac{b^2 \tanh ^5(c+d x)}{5 d}+\frac{2 b^2 \tanh ^3(c+d x)}{3 d}","\frac{\sinh (c+d x) \cosh (c+d x) \left(a^2+2 a b \tanh (c+d x)+b^2\right)}{2 d}-\frac{1}{2} x \left(a^2+7 b^2\right)+\frac{a b \tanh ^2(c+d x)}{d}-\frac{4 a b \log (\cosh (c+d x))}{d}+\frac{b^2 \tanh ^5(c+d x)}{5 d}+\frac{2 b^2 \tanh ^3(c+d x)}{3 d}+\frac{3 b^2 \tanh (c+d x)}{d}",1,"((a + b)*(a + 7*b)*Log[1 - Tanh[c + d*x]])/(4*d) - ((a - 7*b)*(a - b)*Log[1 + Tanh[c + d*x]])/(4*d) + ((a^2 + 7*b^2)*Tanh[c + d*x])/(2*d) + (a*b*Tanh[c + d*x]^2)/d + (2*b^2*Tanh[c + d*x]^3)/(3*d) + (b^2*Tanh[c + d*x]^5)/(5*d) + (Sinh[c + d*x]^2*(2*a*b + (a^2 + b^2)*Tanh[c + d*x]))/(2*d)","A",7,5,23,0.2174,1,"{3663, 1804, 1802, 633, 31}"
60,1,123,0,0.1466091,"\int \sinh (c+d x) \left(a+b \tanh ^3(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]*(a + b*Tanh[c + d*x]^3)^2,x]","\frac{a^2 \cosh (c+d x)}{d}+\frac{3 a b \sinh (c+d x)}{d}-\frac{3 a b \tan ^{-1}(\sinh (c+d x))}{d}-\frac{a b \sinh (c+d x) \tanh ^2(c+d x)}{d}+\frac{b^2 \cosh (c+d x)}{d}+\frac{b^2 \text{sech}^5(c+d x)}{5 d}-\frac{b^2 \text{sech}^3(c+d x)}{d}+\frac{3 b^2 \text{sech}(c+d x)}{d}","\frac{a^2 \cosh (c+d x)}{d}+\frac{3 a b \sinh (c+d x)}{d}-\frac{3 a b \tan ^{-1}(\sinh (c+d x))}{d}-\frac{a b \sinh (c+d x) \tanh ^2(c+d x)}{d}+\frac{b^2 \cosh (c+d x)}{d}+\frac{b^2 \text{sech}^5(c+d x)}{5 d}-\frac{b^2 \text{sech}^3(c+d x)}{d}+\frac{3 b^2 \text{sech}(c+d x)}{d}",1,"(-3*a*b*ArcTan[Sinh[c + d*x]])/d + (a^2*Cosh[c + d*x])/d + (b^2*Cosh[c + d*x])/d + (3*b^2*Sech[c + d*x])/d - (b^2*Sech[c + d*x]^3)/d + (b^2*Sech[c + d*x]^5)/(5*d) + (3*a*b*Sinh[c + d*x])/d - (a*b*Sinh[c + d*x]*Tanh[c + d*x]^2)/d","A",10,8,21,0.3810,1,"{3666, 2638, 2592, 288, 321, 203, 2590, 270}"
61,1,98,0,0.1362024,"\int \text{csch}(c+d x) \left(a+b \tanh ^3(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]*(a + b*Tanh[c + d*x]^3)^2,x]","-\frac{a^2 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{a b \tan ^{-1}(\sinh (c+d x))}{d}-\frac{a b \tanh (c+d x) \text{sech}(c+d x)}{d}-\frac{b^2 \text{sech}^5(c+d x)}{5 d}+\frac{2 b^2 \text{sech}^3(c+d x)}{3 d}-\frac{b^2 \text{sech}(c+d x)}{d}","-\frac{a^2 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{a b \tan ^{-1}(\sinh (c+d x))}{d}-\frac{a b \tanh (c+d x) \text{sech}(c+d x)}{d}-\frac{b^2 \text{sech}^5(c+d x)}{5 d}+\frac{2 b^2 \text{sech}^3(c+d x)}{3 d}-\frac{b^2 \text{sech}(c+d x)}{d}",1,"(a*b*ArcTan[Sinh[c + d*x]])/d - (a^2*ArcTanh[Cosh[c + d*x]])/d - (b^2*Sech[c + d*x])/d + (2*b^2*Sech[c + d*x]^3)/(3*d) - (b^2*Sech[c + d*x]^5)/(5*d) - (a*b*Sech[c + d*x]*Tanh[c + d*x])/d","A",8,5,21,0.2381,1,"{3666, 3770, 2611, 2606, 194}"
62,1,47,0,0.0581107,"\int \text{csch}^2(c+d x) \left(a+b \tanh ^3(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^2*(a + b*Tanh[c + d*x]^3)^2,x]","-\frac{a^2 \coth (c+d x)}{d}+\frac{a b \tanh ^2(c+d x)}{d}+\frac{b^2 \tanh ^5(c+d x)}{5 d}","-\frac{a^2 \coth (c+d x)}{d}+\frac{a b \tanh ^2(c+d x)}{d}+\frac{b^2 \tanh ^5(c+d x)}{5 d}",1,"-((a^2*Coth[c + d*x])/d) + (a*b*Tanh[c + d*x]^2)/d + (b^2*Tanh[c + d*x]^5)/(5*d)","A",3,2,23,0.08696,1,"{3663, 270}"
63,1,107,0,0.1599023,"\int \text{csch}^3(c+d x) \left(a+b \tanh ^3(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^3*(a + b*Tanh[c + d*x]^3)^2,x]","\frac{a^2 \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{a^2 \coth (c+d x) \text{csch}(c+d x)}{2 d}+\frac{a b \tan ^{-1}(\sinh (c+d x))}{d}+\frac{a b \tanh (c+d x) \text{sech}(c+d x)}{d}+\frac{b^2 \text{sech}^5(c+d x)}{5 d}-\frac{b^2 \text{sech}^3(c+d x)}{3 d}","\frac{a^2 \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{a^2 \coth (c+d x) \text{csch}(c+d x)}{2 d}+\frac{a b \tan ^{-1}(\sinh (c+d x))}{d}+\frac{a b \tanh (c+d x) \text{sech}(c+d x)}{d}+\frac{b^2 \text{sech}^5(c+d x)}{5 d}-\frac{b^2 \text{sech}^3(c+d x)}{3 d}",1,"(a*b*ArcTan[Sinh[c + d*x]])/d + (a^2*ArcTanh[Cosh[c + d*x]])/(2*d) - (a^2*Coth[c + d*x]*Csch[c + d*x])/(2*d) - (b^2*Sech[c + d*x]^3)/(3*d) + (b^2*Sech[c + d*x]^5)/(5*d) + (a*b*Sech[c + d*x]*Tanh[c + d*x])/d","A",9,5,23,0.2174,1,"{3666, 3768, 3770, 2606, 14}"
64,1,97,0,0.0980367,"\int \text{csch}^4(c+d x) \left(a+b \tanh ^3(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^4*(a + b*Tanh[c + d*x]^3)^2,x]","-\frac{a^2 \coth ^3(c+d x)}{3 d}+\frac{a^2 \coth (c+d x)}{d}-\frac{a b \tanh ^2(c+d x)}{d}+\frac{2 a b \log (\tanh (c+d x))}{d}-\frac{b^2 \tanh ^5(c+d x)}{5 d}+\frac{b^2 \tanh ^3(c+d x)}{3 d}","-\frac{a^2 \coth ^3(c+d x)}{3 d}+\frac{a^2 \coth (c+d x)}{d}-\frac{a b \tanh ^2(c+d x)}{d}+\frac{2 a b \log (\tanh (c+d x))}{d}-\frac{b^2 \tanh ^5(c+d x)}{5 d}+\frac{b^2 \tanh ^3(c+d x)}{3 d}",1,"(a^2*Coth[c + d*x])/d - (a^2*Coth[c + d*x]^3)/(3*d) + (2*a*b*Log[Tanh[c + d*x]])/d - (a*b*Tanh[c + d*x]^2)/d + (b^2*Tanh[c + d*x]^3)/(3*d) - (b^2*Tanh[c + d*x]^5)/(5*d)","A",3,2,23,0.08696,1,"{3663, 1802}"
65,1,306,0,0.4936729,"\int \sinh ^4(c+d x) \left(a+b \tanh ^3(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]^4*(a + b*Tanh[c + d*x]^3)^3,x]","-\frac{3 b \left(3 a^2+5 b^2\right) \tanh ^2(c+d x)}{2 d}-\frac{3 a \left(a^2+63 b^2\right) \tanh (c+d x)}{8 d}-\frac{3 (a+b) \left(a^2+23 a b+40 b^2\right) \log (1-\tanh (c+d x))}{16 d}+\frac{3 (a-b) \left(a^2-23 a b+40 b^2\right) \log (\tanh (c+d x)+1)}{16 d}-\frac{\sinh ^2(c+d x) \tanh (c+d x) \left(4 b \left(6 a^2+5 b^2\right) \tanh (c+d x)+a \left(a^2+39 b^2\right)\right)}{8 d}+\frac{\sinh ^4(c+d x) \left(a \left(a^2+3 b^2\right) \tanh (c+d x)+b \left(3 a^2+b^2\right)\right)}{4 d}-\frac{3 a b^2 \tanh ^5(c+d x)}{5 d}-\frac{3 a b^2 \tanh ^3(c+d x)}{d}-\frac{b^3 \tanh ^8(c+d x)}{8 d}-\frac{b^3 \tanh ^6(c+d x)}{2 d}-\frac{3 b^3 \tanh ^4(c+d x)}{2 d}","-\frac{b \left(3 a^2+10 b^2\right) \tanh ^2(c+d x)}{2 d}+\frac{3 b \left(3 a^2+5 b^2\right) \log (\cosh (c+d x))}{d}+\frac{\sinh (c+d x) \cosh ^3(c+d x) \left(b \left(3 a^2+b^2\right) \tanh (c+d x)+a \left(a^2+3 b^2\right)\right)}{4 d}-\frac{\sinh (c+d x) \cosh (c+d x) \left(2 b \left(15 a^2+11 b^2\right) \tanh (c+d x)+a \left(5 a^2+51 b^2\right)\right)}{8 d}+\frac{3}{8} a x \left(a^2+63 b^2\right)-\frac{3 a b^2 \tanh ^5(c+d x)}{5 d}-\frac{3 a b^2 \tanh ^3(c+d x)}{d}-\frac{18 a b^2 \tanh (c+d x)}{d}-\frac{b^3 \tanh ^8(c+d x)}{8 d}-\frac{b^3 \tanh ^6(c+d x)}{2 d}-\frac{3 b^3 \tanh ^4(c+d x)}{2 d}",1,"(-3*(a + b)*(a^2 + 23*a*b + 40*b^2)*Log[1 - Tanh[c + d*x]])/(16*d) + (3*(a - b)*(a^2 - 23*a*b + 40*b^2)*Log[1 + Tanh[c + d*x]])/(16*d) - (3*a*(a^2 + 63*b^2)*Tanh[c + d*x])/(8*d) - (3*b*(3*a^2 + 5*b^2)*Tanh[c + d*x]^2)/(2*d) - (3*a*b^2*Tanh[c + d*x]^3)/d - (3*b^3*Tanh[c + d*x]^4)/(2*d) - (3*a*b^2*Tanh[c + d*x]^5)/(5*d) - (b^3*Tanh[c + d*x]^6)/(2*d) - (b^3*Tanh[c + d*x]^8)/(8*d) + (Sinh[c + d*x]^4*(b*(3*a^2 + b^2) + a*(a^2 + 3*b^2)*Tanh[c + d*x]))/(4*d) - (Sinh[c + d*x]^2*Tanh[c + d*x]*(a*(a^2 + 39*b^2) + 4*b*(6*a^2 + 5*b^2)*Tanh[c + d*x]))/(8*d)","A",8,5,23,0.2174,1,"{3663, 1804, 1802, 633, 31}"
66,1,351,0,0.3499004,"\int \sinh ^3(c+d x) \left(a+b \tanh ^3(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]^3*(a + b*Tanh[c + d*x]^3)^3,x]","\frac{5 a^2 b \sinh ^3(c+d x)}{2 d}-\frac{15 a^2 b \sinh (c+d x)}{2 d}-\frac{3 a^2 b \sinh ^3(c+d x) \tanh ^2(c+d x)}{2 d}+\frac{15 a^2 b \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{a^3 \cosh ^3(c+d x)}{3 d}-\frac{a^3 \cosh (c+d x)}{d}+\frac{a b^2 \cosh ^3(c+d x)}{d}-\frac{12 a b^2 \cosh (c+d x)}{d}-\frac{3 a b^2 \text{sech}^5(c+d x)}{5 d}+\frac{4 a b^2 \text{sech}^3(c+d x)}{d}-\frac{18 a b^2 \text{sech}(c+d x)}{d}+\frac{385 b^3 \sinh ^3(c+d x)}{128 d}-\frac{1155 b^3 \sinh (c+d x)}{128 d}-\frac{b^3 \sinh ^3(c+d x) \tanh ^8(c+d x)}{8 d}-\frac{11 b^3 \sinh ^3(c+d x) \tanh ^6(c+d x)}{48 d}-\frac{33 b^3 \sinh ^3(c+d x) \tanh ^4(c+d x)}{64 d}-\frac{231 b^3 \sinh ^3(c+d x) \tanh ^2(c+d x)}{128 d}+\frac{1155 b^3 \tan ^{-1}(\sinh (c+d x))}{128 d}","\frac{5 a^2 b \sinh ^3(c+d x)}{2 d}-\frac{15 a^2 b \sinh (c+d x)}{2 d}-\frac{3 a^2 b \sinh ^3(c+d x) \tanh ^2(c+d x)}{2 d}+\frac{15 a^2 b \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{a^3 \cosh ^3(c+d x)}{3 d}-\frac{a^3 \cosh (c+d x)}{d}+\frac{a b^2 \cosh ^3(c+d x)}{d}-\frac{12 a b^2 \cosh (c+d x)}{d}-\frac{3 a b^2 \text{sech}^5(c+d x)}{5 d}+\frac{4 a b^2 \text{sech}^3(c+d x)}{d}-\frac{18 a b^2 \text{sech}(c+d x)}{d}+\frac{385 b^3 \sinh ^3(c+d x)}{128 d}-\frac{1155 b^3 \sinh (c+d x)}{128 d}-\frac{b^3 \sinh ^3(c+d x) \tanh ^8(c+d x)}{8 d}-\frac{11 b^3 \sinh ^3(c+d x) \tanh ^6(c+d x)}{48 d}-\frac{33 b^3 \sinh ^3(c+d x) \tanh ^4(c+d x)}{64 d}-\frac{231 b^3 \sinh ^3(c+d x) \tanh ^2(c+d x)}{128 d}+\frac{1155 b^3 \tan ^{-1}(\sinh (c+d x))}{128 d}",1,"(15*a^2*b*ArcTan[Sinh[c + d*x]])/(2*d) + (1155*b^3*ArcTan[Sinh[c + d*x]])/(128*d) - (a^3*Cosh[c + d*x])/d - (12*a*b^2*Cosh[c + d*x])/d + (a^3*Cosh[c + d*x]^3)/(3*d) + (a*b^2*Cosh[c + d*x]^3)/d - (18*a*b^2*Sech[c + d*x])/d + (4*a*b^2*Sech[c + d*x]^3)/d - (3*a*b^2*Sech[c + d*x]^5)/(5*d) - (15*a^2*b*Sinh[c + d*x])/(2*d) - (1155*b^3*Sinh[c + d*x])/(128*d) + (5*a^2*b*Sinh[c + d*x]^3)/(2*d) + (385*b^3*Sinh[c + d*x]^3)/(128*d) - (3*a^2*b*Sinh[c + d*x]^3*Tanh[c + d*x]^2)/(2*d) - (231*b^3*Sinh[c + d*x]^3*Tanh[c + d*x]^2)/(128*d) - (33*b^3*Sinh[c + d*x]^3*Tanh[c + d*x]^4)/(64*d) - (11*b^3*Sinh[c + d*x]^3*Tanh[c + d*x]^6)/(48*d) - (b^3*Sinh[c + d*x]^3*Tanh[c + d*x]^8)/(8*d)","A",20,8,23,0.3478,1,"{3666, 2633, 2592, 288, 302, 203, 2590, 270}"
67,1,241,0,0.3148377,"\int \sinh ^2(c+d x) \left(a+b \tanh ^3(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]^2*(a + b*Tanh[c + d*x]^3)^3,x]","\frac{b \left(3 a^2+4 b^2\right) \tanh ^2(c+d x)}{2 d}+\frac{a \left(a^2+21 b^2\right) \tanh (c+d x)}{2 d}+\frac{\sinh ^2(c+d x) \left(a \left(a^2+3 b^2\right) \tanh (c+d x)+b \left(3 a^2+b^2\right)\right)}{2 d}+\frac{3 a b^2 \tanh ^5(c+d x)}{5 d}+\frac{2 a b^2 \tanh ^3(c+d x)}{d}+\frac{(a+b)^2 (a+10 b) \log (1-\tanh (c+d x))}{4 d}-\frac{(a-10 b) (a-b)^2 \log (\tanh (c+d x)+1)}{4 d}+\frac{b^3 \tanh ^8(c+d x)}{8 d}+\frac{b^3 \tanh ^6(c+d x)}{3 d}+\frac{3 b^3 \tanh ^4(c+d x)}{4 d}","\frac{b \left(3 a^2+4 b^2\right) \tanh ^2(c+d x)}{2 d}-\frac{b \left(6 a^2+5 b^2\right) \log (\cosh (c+d x))}{d}+\frac{\sinh (c+d x) \cosh (c+d x) \left(b \left(3 a^2+b^2\right) \tanh (c+d x)+a \left(a^2+3 b^2\right)\right)}{2 d}-\frac{1}{2} a x \left(a^2+21 b^2\right)+\frac{3 a b^2 \tanh ^5(c+d x)}{5 d}+\frac{2 a b^2 \tanh ^3(c+d x)}{d}+\frac{9 a b^2 \tanh (c+d x)}{d}+\frac{b^3 \tanh ^8(c+d x)}{8 d}+\frac{b^3 \tanh ^6(c+d x)}{3 d}+\frac{3 b^3 \tanh ^4(c+d x)}{4 d}",1,"((a + b)^2*(a + 10*b)*Log[1 - Tanh[c + d*x]])/(4*d) - ((a - 10*b)*(a - b)^2*Log[1 + Tanh[c + d*x]])/(4*d) + (a*(a^2 + 21*b^2)*Tanh[c + d*x])/(2*d) + (b*(3*a^2 + 4*b^2)*Tanh[c + d*x]^2)/(2*d) + (2*a*b^2*Tanh[c + d*x]^3)/d + (3*b^3*Tanh[c + d*x]^4)/(4*d) + (3*a*b^2*Tanh[c + d*x]^5)/(5*d) + (b^3*Tanh[c + d*x]^6)/(3*d) + (b^3*Tanh[c + d*x]^8)/(8*d) + (Sinh[c + d*x]^2*(b*(3*a^2 + b^2) + a*(a^2 + 3*b^2)*Tanh[c + d*x]))/(2*d)","A",7,5,23,0.2174,1,"{3663, 1804, 1802, 633, 31}"
68,1,269,0,0.2491599,"\int \sinh (c+d x) \left(a+b \tanh ^3(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]*(a + b*Tanh[c + d*x]^3)^3,x]","\frac{9 a^2 b \sinh (c+d x)}{2 d}-\frac{9 a^2 b \tan ^{-1}(\sinh (c+d x))}{2 d}-\frac{3 a^2 b \sinh (c+d x) \tanh ^2(c+d x)}{2 d}+\frac{a^3 \cosh (c+d x)}{d}+\frac{3 a b^2 \cosh (c+d x)}{d}+\frac{3 a b^2 \text{sech}^5(c+d x)}{5 d}-\frac{3 a b^2 \text{sech}^3(c+d x)}{d}+\frac{9 a b^2 \text{sech}(c+d x)}{d}+\frac{315 b^3 \sinh (c+d x)}{128 d}-\frac{315 b^3 \tan ^{-1}(\sinh (c+d x))}{128 d}-\frac{b^3 \sinh (c+d x) \tanh ^8(c+d x)}{8 d}-\frac{3 b^3 \sinh (c+d x) \tanh ^6(c+d x)}{16 d}-\frac{21 b^3 \sinh (c+d x) \tanh ^4(c+d x)}{64 d}-\frac{105 b^3 \sinh (c+d x) \tanh ^2(c+d x)}{128 d}","\frac{9 a^2 b \sinh (c+d x)}{2 d}-\frac{9 a^2 b \tan ^{-1}(\sinh (c+d x))}{2 d}-\frac{3 a^2 b \sinh (c+d x) \tanh ^2(c+d x)}{2 d}+\frac{a^3 \cosh (c+d x)}{d}+\frac{3 a b^2 \cosh (c+d x)}{d}+\frac{3 a b^2 \text{sech}^5(c+d x)}{5 d}-\frac{3 a b^2 \text{sech}^3(c+d x)}{d}+\frac{9 a b^2 \text{sech}(c+d x)}{d}+\frac{315 b^3 \sinh (c+d x)}{128 d}-\frac{315 b^3 \tan ^{-1}(\sinh (c+d x))}{128 d}-\frac{b^3 \sinh (c+d x) \tanh ^8(c+d x)}{8 d}-\frac{3 b^3 \sinh (c+d x) \tanh ^6(c+d x)}{16 d}-\frac{21 b^3 \sinh (c+d x) \tanh ^4(c+d x)}{64 d}-\frac{105 b^3 \sinh (c+d x) \tanh ^2(c+d x)}{128 d}",1,"(-9*a^2*b*ArcTan[Sinh[c + d*x]])/(2*d) - (315*b^3*ArcTan[Sinh[c + d*x]])/(128*d) + (a^3*Cosh[c + d*x])/d + (3*a*b^2*Cosh[c + d*x])/d + (9*a*b^2*Sech[c + d*x])/d - (3*a*b^2*Sech[c + d*x]^3)/d + (3*a*b^2*Sech[c + d*x]^5)/(5*d) + (9*a^2*b*Sinh[c + d*x])/(2*d) + (315*b^3*Sinh[c + d*x])/(128*d) - (3*a^2*b*Sinh[c + d*x]*Tanh[c + d*x]^2)/(2*d) - (105*b^3*Sinh[c + d*x]*Tanh[c + d*x]^2)/(128*d) - (21*b^3*Sinh[c + d*x]*Tanh[c + d*x]^4)/(64*d) - (3*b^3*Sinh[c + d*x]*Tanh[c + d*x]^6)/(16*d) - (b^3*Sinh[c + d*x]*Tanh[c + d*x]^8)/(8*d)","A",17,8,21,0.3810,1,"{3666, 2638, 2592, 288, 321, 203, 2590, 270}"
69,1,219,0,0.2635001,"\int \text{csch}(c+d x) \left(a+b \tanh ^3(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]*(a + b*Tanh[c + d*x]^3)^3,x]","\frac{3 a^2 b \tan ^{-1}(\sinh (c+d x))}{2 d}-\frac{3 a^2 b \tanh (c+d x) \text{sech}(c+d x)}{2 d}-\frac{a^3 \tanh ^{-1}(\cosh (c+d x))}{d}-\frac{3 a b^2 \text{sech}^5(c+d x)}{5 d}+\frac{2 a b^2 \text{sech}^3(c+d x)}{d}-\frac{3 a b^2 \text{sech}(c+d x)}{d}+\frac{35 b^3 \tan ^{-1}(\sinh (c+d x))}{128 d}-\frac{b^3 \tanh ^7(c+d x) \text{sech}(c+d x)}{8 d}-\frac{7 b^3 \tanh ^5(c+d x) \text{sech}(c+d x)}{48 d}-\frac{35 b^3 \tanh ^3(c+d x) \text{sech}(c+d x)}{192 d}-\frac{35 b^3 \tanh (c+d x) \text{sech}(c+d x)}{128 d}","\frac{3 a^2 b \tan ^{-1}(\sinh (c+d x))}{2 d}-\frac{3 a^2 b \tanh (c+d x) \text{sech}(c+d x)}{2 d}-\frac{a^3 \tanh ^{-1}(\cosh (c+d x))}{d}-\frac{3 a b^2 \text{sech}^5(c+d x)}{5 d}+\frac{2 a b^2 \text{sech}^3(c+d x)}{d}-\frac{3 a b^2 \text{sech}(c+d x)}{d}+\frac{35 b^3 \tan ^{-1}(\sinh (c+d x))}{128 d}-\frac{b^3 \tanh ^7(c+d x) \text{sech}(c+d x)}{8 d}-\frac{7 b^3 \tanh ^5(c+d x) \text{sech}(c+d x)}{48 d}-\frac{35 b^3 \tanh ^3(c+d x) \text{sech}(c+d x)}{192 d}-\frac{35 b^3 \tanh (c+d x) \text{sech}(c+d x)}{128 d}",1,"(3*a^2*b*ArcTan[Sinh[c + d*x]])/(2*d) + (35*b^3*ArcTan[Sinh[c + d*x]])/(128*d) - (a^3*ArcTanh[Cosh[c + d*x]])/d - (3*a*b^2*Sech[c + d*x])/d + (2*a*b^2*Sech[c + d*x]^3)/d - (3*a*b^2*Sech[c + d*x]^5)/(5*d) - (3*a^2*b*Sech[c + d*x]*Tanh[c + d*x])/(2*d) - (35*b^3*Sech[c + d*x]*Tanh[c + d*x])/(128*d) - (35*b^3*Sech[c + d*x]*Tanh[c + d*x]^3)/(192*d) - (7*b^3*Sech[c + d*x]*Tanh[c + d*x]^5)/(48*d) - (b^3*Sech[c + d*x]*Tanh[c + d*x]^7)/(8*d)","A",13,5,21,0.2381,1,"{3666, 3770, 2611, 2606, 194}"
70,1,71,0,0.0645756,"\int \text{csch}^2(c+d x) \left(a+b \tanh ^3(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^2*(a + b*Tanh[c + d*x]^3)^3,x]","\frac{3 a^2 b \tanh ^2(c+d x)}{2 d}-\frac{a^3 \coth (c+d x)}{d}+\frac{3 a b^2 \tanh ^5(c+d x)}{5 d}+\frac{b^3 \tanh ^8(c+d x)}{8 d}","\frac{3 a^2 b \tanh ^2(c+d x)}{2 d}-\frac{a^3 \coth (c+d x)}{d}+\frac{3 a b^2 \tanh ^5(c+d x)}{5 d}+\frac{b^3 \tanh ^8(c+d x)}{8 d}",1,"-((a^3*Coth[c + d*x])/d) + (3*a^2*b*Tanh[c + d*x]^2)/(2*d) + (3*a*b^2*Tanh[c + d*x]^5)/(5*d) + (b^3*Tanh[c + d*x]^8)/(8*d)","A",3,2,23,0.08696,1,"{3663, 270}"
71,1,232,0,0.3160708,"\int \text{csch}^3(c+d x) \left(a+b \tanh ^3(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^3*(a + b*Tanh[c + d*x]^3)^3,x]","\frac{3 a^2 b \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{3 a^2 b \tanh (c+d x) \text{sech}(c+d x)}{2 d}+\frac{a^3 \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{a^3 \coth (c+d x) \text{csch}(c+d x)}{2 d}+\frac{3 a b^2 \text{sech}^5(c+d x)}{5 d}-\frac{a b^2 \text{sech}^3(c+d x)}{d}+\frac{5 b^3 \tan ^{-1}(\sinh (c+d x))}{128 d}-\frac{b^3 \tanh ^5(c+d x) \text{sech}^3(c+d x)}{8 d}-\frac{5 b^3 \tanh ^3(c+d x) \text{sech}^3(c+d x)}{48 d}-\frac{5 b^3 \tanh (c+d x) \text{sech}^3(c+d x)}{64 d}+\frac{5 b^3 \tanh (c+d x) \text{sech}(c+d x)}{128 d}","\frac{3 a^2 b \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{3 a^2 b \tanh (c+d x) \text{sech}(c+d x)}{2 d}+\frac{a^3 \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{a^3 \coth (c+d x) \text{csch}(c+d x)}{2 d}+\frac{3 a b^2 \text{sech}^5(c+d x)}{5 d}-\frac{a b^2 \text{sech}^3(c+d x)}{d}+\frac{5 b^3 \tan ^{-1}(\sinh (c+d x))}{128 d}-\frac{b^3 \tanh ^5(c+d x) \text{sech}^3(c+d x)}{8 d}-\frac{5 b^3 \tanh ^3(c+d x) \text{sech}^3(c+d x)}{48 d}-\frac{5 b^3 \tanh (c+d x) \text{sech}^3(c+d x)}{64 d}+\frac{5 b^3 \tanh (c+d x) \text{sech}(c+d x)}{128 d}",1,"(3*a^2*b*ArcTan[Sinh[c + d*x]])/(2*d) + (5*b^3*ArcTan[Sinh[c + d*x]])/(128*d) + (a^3*ArcTanh[Cosh[c + d*x]])/(2*d) - (a^3*Coth[c + d*x]*Csch[c + d*x])/(2*d) - (a*b^2*Sech[c + d*x]^3)/d + (3*a*b^2*Sech[c + d*x]^5)/(5*d) + (3*a^2*b*Sech[c + d*x]*Tanh[c + d*x])/(2*d) + (5*b^3*Sech[c + d*x]*Tanh[c + d*x])/(128*d) - (5*b^3*Sech[c + d*x]^3*Tanh[c + d*x])/(64*d) - (5*b^3*Sech[c + d*x]^3*Tanh[c + d*x]^3)/(48*d) - (b^3*Sech[c + d*x]^3*Tanh[c + d*x]^5)/(8*d)","A",14,6,23,0.2609,1,"{3666, 3768, 3770, 2606, 14, 2611}"
72,1,138,0,0.1150983,"\int \text{csch}^4(c+d x) \left(a+b \tanh ^3(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^4*(a + b*Tanh[c + d*x]^3)^3,x]","-\frac{3 a^2 b \tanh ^2(c+d x)}{2 d}+\frac{3 a^2 b \log (\tanh (c+d x))}{d}-\frac{a^3 \coth ^3(c+d x)}{3 d}+\frac{a^3 \coth (c+d x)}{d}-\frac{3 a b^2 \tanh ^5(c+d x)}{5 d}+\frac{a b^2 \tanh ^3(c+d x)}{d}-\frac{b^3 \tanh ^8(c+d x)}{8 d}+\frac{b^3 \tanh ^6(c+d x)}{6 d}","-\frac{3 a^2 b \tanh ^2(c+d x)}{2 d}+\frac{3 a^2 b \log (\tanh (c+d x))}{d}-\frac{a^3 \coth ^3(c+d x)}{3 d}+\frac{a^3 \coth (c+d x)}{d}-\frac{3 a b^2 \tanh ^5(c+d x)}{5 d}+\frac{a b^2 \tanh ^3(c+d x)}{d}-\frac{b^3 \tanh ^8(c+d x)}{8 d}+\frac{b^3 \tanh ^6(c+d x)}{6 d}",1,"(a^3*Coth[c + d*x])/d - (a^3*Coth[c + d*x]^3)/(3*d) + (3*a^2*b*Log[Tanh[c + d*x]])/d - (3*a^2*b*Tanh[c + d*x]^2)/(2*d) + (a*b^2*Tanh[c + d*x]^3)/d - (3*a*b^2*Tanh[c + d*x]^5)/(5*d) + (b^3*Tanh[c + d*x]^6)/(6*d) - (b^3*Tanh[c + d*x]^8)/(8*d)","A",3,2,23,0.08696,1,"{3663, 1802}"
73,1,491,0,0.8915486,"\int \frac{\sinh ^4(c+d x)}{a+b \tanh ^3(c+d x)} \, dx","Int[Sinh[c + d*x]^4/(a + b*Tanh[c + d*x]^3),x]","-\frac{a^2 b \left(a^2+2 b^2\right) \log \left(a+b \tanh ^3(c+d x)\right)}{d \left(a^2-b^2\right)^3}+\frac{a^{2/3} \sqrt[3]{b} \left(7 a^2 b^2+3 a^{2/3} b^{4/3} \left(2 a^2+b^2\right)+a^4+b^4\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \tanh (c+d x)+b^{2/3} \tanh ^2(c+d x)\right)}{6 d \left(a^2-b^2\right)^3}-\frac{a^{2/3} \sqrt[3]{b} \left(7 a^2 b^2+3 a^{2/3} b^{4/3} \left(2 a^2+b^2\right)+a^4+b^4\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} \tanh (c+d x)\right)}{3 d \left(a^2-b^2\right)^3}-\frac{a^{2/3} \sqrt[3]{b} \left(3 a^{4/3} b^{2/3}+a^2-b^2\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \tanh (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} d \left(a^{2/3} b^{2/3}+a^{4/3}+b^{4/3}\right)^3}-\frac{5 a-b}{16 d (a+b)^2 (1-\tanh (c+d x))}+\frac{5 a+b}{16 d (a-b)^2 (\tanh (c+d x)+1)}+\frac{1}{16 d (a+b) (1-\tanh (c+d x))^2}-\frac{1}{16 d (a-b) (\tanh (c+d x)+1)^2}-\frac{3 a (a-5 b) \log (1-\tanh (c+d x))}{16 d (a+b)^3}+\frac{3 a (a+5 b) \log (\tanh (c+d x)+1)}{16 d (a-b)^3}","-\frac{a^2 b \left(a^2+2 b^2\right) \log \left(a+b \tanh ^3(c+d x)\right)}{d \left(a^2-b^2\right)^3}+\frac{a^{2/3} \sqrt[3]{b} \left(7 a^2 b^2+3 a^{2/3} b^{4/3} \left(2 a^2+b^2\right)+a^4+b^4\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \tanh (c+d x)+b^{2/3} \tanh ^2(c+d x)\right)}{6 d \left(a^2-b^2\right)^3}-\frac{a^{2/3} \sqrt[3]{b} \left(7 a^2 b^2+3 a^{2/3} b^{4/3} \left(2 a^2+b^2\right)+a^4+b^4\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} \tanh (c+d x)\right)}{3 d \left(a^2-b^2\right)^3}-\frac{a^{2/3} \sqrt[3]{b} \left(3 a^{4/3} b^{2/3}+a^2-b^2\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \tanh (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} d \left(a^{2/3} b^{2/3}+a^{4/3}+b^{4/3}\right)^3}-\frac{5 a-b}{16 d (a+b)^2 (1-\tanh (c+d x))}+\frac{5 a+b}{16 d (a-b)^2 (\tanh (c+d x)+1)}+\frac{1}{16 d (a+b) (1-\tanh (c+d x))^2}-\frac{1}{16 d (a-b) (\tanh (c+d x)+1)^2}-\frac{3 a (a-5 b) \log (1-\tanh (c+d x))}{16 d (a+b)^3}+\frac{3 a (a+5 b) \log (\tanh (c+d x)+1)}{16 d (a-b)^3}",1,"-((a^(2/3)*b^(1/3)*(a^2 + 3*a^(4/3)*b^(2/3) - b^2)*ArcTan[(a^(1/3) - 2*b^(1/3)*Tanh[c + d*x])/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*(a^(4/3) + a^(2/3)*b^(2/3) + b^(4/3))^3*d)) - (3*a*(a - 5*b)*Log[1 - Tanh[c + d*x]])/(16*(a + b)^3*d) + (3*a*(a + 5*b)*Log[1 + Tanh[c + d*x]])/(16*(a - b)^3*d) - (a^(2/3)*b^(1/3)*(a^4 + 7*a^2*b^2 + b^4 + 3*a^(2/3)*b^(4/3)*(2*a^2 + b^2))*Log[a^(1/3) + b^(1/3)*Tanh[c + d*x]])/(3*(a^2 - b^2)^3*d) + (a^(2/3)*b^(1/3)*(a^4 + 7*a^2*b^2 + b^4 + 3*a^(2/3)*b^(4/3)*(2*a^2 + b^2))*Log[a^(2/3) - a^(1/3)*b^(1/3)*Tanh[c + d*x] + b^(2/3)*Tanh[c + d*x]^2])/(6*(a^2 - b^2)^3*d) - (a^2*b*(a^2 + 2*b^2)*Log[a + b*Tanh[c + d*x]^3])/((a^2 - b^2)^3*d) + 1/(16*(a + b)*d*(1 - Tanh[c + d*x])^2) - (5*a - b)/(16*(a + b)^2*d*(1 - Tanh[c + d*x])) - 1/(16*(a - b)*d*(1 + Tanh[c + d*x])^2) + (5*a + b)/(16*(a - b)^2*d*(1 + Tanh[c + d*x]))","A",11,10,23,0.4348,1,"{3663, 6725, 1871, 1860, 31, 634, 617, 204, 628, 260}"
74,0,0,0,0.0461342,"\int \frac{\sinh ^3(c+d x)}{a+b \tanh ^3(c+d x)} \, dx","Int[Sinh[c + d*x]^3/(a + b*Tanh[c + d*x]^3),x]","\int \frac{\sinh ^3(c+d x)}{a+b \tanh ^3(c+d x)} \, dx","i \text{Int}\left(-\frac{i \sinh ^3(c+d x)}{a+b \tanh ^3(c+d x)},x\right)",0,"I*Defer[Int][((-I)*Sinh[c + d*x]^3)/(a + b*Tanh[c + d*x]^3), x]","A",0,0,0,0,-1,"{}"
75,1,384,0,0.629447,"\int \frac{\sinh ^2(c+d x)}{a+b \tanh ^3(c+d x)} \, dx","Int[Sinh[c + d*x]^2/(a + b*Tanh[c + d*x]^3),x]","-\frac{a^{2/3} \sqrt[3]{b} \left(3 a^{2/3} b^{4/3}+a^2+2 b^2\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \tanh (c+d x)+b^{2/3} \tanh ^2(c+d x)\right)}{6 d \left(a^2-b^2\right)^2}+\frac{b \left(2 a^2+b^2\right) \log \left(a+b \tanh ^3(c+d x)\right)}{3 d \left(a^2-b^2\right)^2}+\frac{a^{2/3} \sqrt[3]{b} \left(3 a^{2/3} b^{4/3}+a^2+2 b^2\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} \tanh (c+d x)\right)}{3 d \left(a^2-b^2\right)^2}+\frac{a^{2/3} \sqrt[3]{b} \left(-3 a^{2/3} b^{4/3}+a^2+2 b^2\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \tanh (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} d \left(a^2-b^2\right)^2}+\frac{1}{4 d (a+b) (1-\tanh (c+d x))}-\frac{1}{4 d (a-b) (\tanh (c+d x)+1)}+\frac{(a-2 b) \log (1-\tanh (c+d x))}{4 d (a+b)^2}-\frac{(a+2 b) \log (\tanh (c+d x)+1)}{4 d (a-b)^2}","-\frac{a^{2/3} \sqrt[3]{b} \left(3 a^{2/3} b^{4/3}+a^2+2 b^2\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \tanh (c+d x)+b^{2/3} \tanh ^2(c+d x)\right)}{6 d \left(a^2-b^2\right)^2}+\frac{b \left(2 a^2+b^2\right) \log \left(a+b \tanh ^3(c+d x)\right)}{3 d \left(a^2-b^2\right)^2}+\frac{a^{2/3} \sqrt[3]{b} \left(3 a^{2/3} b^{4/3}+a^2+2 b^2\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} \tanh (c+d x)\right)}{3 d \left(a^2-b^2\right)^2}+\frac{a^{2/3} \sqrt[3]{b} \left(-3 a^{2/3} b^{4/3}+a^2+2 b^2\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \tanh (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} d \left(a^2-b^2\right)^2}+\frac{1}{4 d (a+b) (1-\tanh (c+d x))}-\frac{1}{4 d (a-b) (\tanh (c+d x)+1)}+\frac{(a-2 b) \log (1-\tanh (c+d x))}{4 d (a+b)^2}-\frac{(a+2 b) \log (\tanh (c+d x)+1)}{4 d (a-b)^2}",1,"(a^(2/3)*b^(1/3)*(a^2 - 3*a^(2/3)*b^(4/3) + 2*b^2)*ArcTan[(a^(1/3) - 2*b^(1/3)*Tanh[c + d*x])/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*(a^2 - b^2)^2*d) + ((a - 2*b)*Log[1 - Tanh[c + d*x]])/(4*(a + b)^2*d) - ((a + 2*b)*Log[1 + Tanh[c + d*x]])/(4*(a - b)^2*d) + (a^(2/3)*b^(1/3)*(a^2 + 3*a^(2/3)*b^(4/3) + 2*b^2)*Log[a^(1/3) + b^(1/3)*Tanh[c + d*x]])/(3*(a^2 - b^2)^2*d) - (a^(2/3)*b^(1/3)*(a^2 + 3*a^(2/3)*b^(4/3) + 2*b^2)*Log[a^(2/3) - a^(1/3)*b^(1/3)*Tanh[c + d*x] + b^(2/3)*Tanh[c + d*x]^2])/(6*(a^2 - b^2)^2*d) + (b*(2*a^2 + b^2)*Log[a + b*Tanh[c + d*x]^3])/(3*(a^2 - b^2)^2*d) + 1/(4*(a + b)*d*(1 - Tanh[c + d*x])) - 1/(4*(a - b)*d*(1 + Tanh[c + d*x]))","A",11,10,23,0.4348,1,"{3663, 6725, 1871, 1860, 31, 634, 617, 204, 628, 260}"
76,0,0,0,0.0276825,"\int \frac{\sinh (c+d x)}{a+b \tanh ^3(c+d x)} \, dx","Int[Sinh[c + d*x]/(a + b*Tanh[c + d*x]^3),x]","\int \frac{\sinh (c+d x)}{a+b \tanh ^3(c+d x)} \, dx","-i \text{Int}\left(\frac{i \sinh (c+d x)}{a+b \tanh ^3(c+d x)},x\right)",0,"(-I)*Defer[Int][(I*Sinh[c + d*x])/(a + b*Tanh[c + d*x]^3), x]","A",0,0,0,0,-1,"{}"
77,0,0,0,0.0408265,"\int \frac{\text{csch}(c+d x)}{a+b \tanh ^3(c+d x)} \, dx","Int[Csch[c + d*x]/(a + b*Tanh[c + d*x]^3),x]","\int \frac{\text{csch}(c+d x)}{a+b \tanh ^3(c+d x)} \, dx","i \text{Int}\left(-\frac{i \text{csch}(c+d x)}{a+b \tanh ^3(c+d x)},x\right)",0,"I*Defer[Int][((-I)*Csch[c + d*x])/(a + b*Tanh[c + d*x]^3), x]","A",0,0,0,0,-1,"{}"
78,1,157,0,0.1403491,"\int \frac{\text{csch}^2(c+d x)}{a+b \tanh ^3(c+d x)} \, dx","Int[Csch[c + d*x]^2/(a + b*Tanh[c + d*x]^3),x]","-\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \tanh (c+d x)+b^{2/3} \tanh ^2(c+d x)\right)}{6 a^{4/3} d}+\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \tanh (c+d x)\right)}{3 a^{4/3} d}+\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \tanh (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} d}-\frac{\coth (c+d x)}{a d}","-\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \tanh (c+d x)+b^{2/3} \tanh ^2(c+d x)\right)}{6 a^{4/3} d}+\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \tanh (c+d x)\right)}{3 a^{4/3} d}+\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \tanh (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} d}-\frac{\coth (c+d x)}{a d}",1,"(b^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*Tanh[c + d*x])/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)*d) - Coth[c + d*x]/(a*d) + (b^(1/3)*Log[a^(1/3) + b^(1/3)*Tanh[c + d*x]])/(3*a^(4/3)*d) - (b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*Tanh[c + d*x] + b^(2/3)*Tanh[c + d*x]^2])/(6*a^(4/3)*d)","A",8,8,23,0.3478,1,"{3663, 325, 292, 31, 634, 617, 204, 628}"
79,0,0,0,0.0471116,"\int \frac{\text{csch}^3(c+d x)}{a+b \tanh ^3(c+d x)} \, dx","Int[Csch[c + d*x]^3/(a + b*Tanh[c + d*x]^3),x]","\int \frac{\text{csch}^3(c+d x)}{a+b \tanh ^3(c+d x)} \, dx","-i \text{Int}\left(\frac{i \text{csch}^3(c+d x)}{a+b \tanh ^3(c+d x)},x\right)",0,"(-I)*Defer[Int][(I*Csch[c + d*x]^3)/(a + b*Tanh[c + d*x]^3), x]","A",0,0,0,0,-1,"{}"
80,1,215,0,0.2386585,"\int \frac{\text{csch}^4(c+d x)}{a+b \tanh ^3(c+d x)} \, dx","Int[Csch[c + d*x]^4/(a + b*Tanh[c + d*x]^3),x]","\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \tanh (c+d x)+b^{2/3} \tanh ^2(c+d x)\right)}{6 a^{4/3} d}+\frac{b \log \left(a+b \tanh ^3(c+d x)\right)}{3 a^2 d}-\frac{b \log (\tanh (c+d x))}{a^2 d}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \tanh (c+d x)\right)}{3 a^{4/3} d}-\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \tanh (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} d}-\frac{\coth ^3(c+d x)}{3 a d}+\frac{\coth (c+d x)}{a d}","\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \tanh (c+d x)+b^{2/3} \tanh ^2(c+d x)\right)}{6 a^{4/3} d}+\frac{b \log \left(a+b \tanh ^3(c+d x)\right)}{3 a^2 d}-\frac{b \log (\tanh (c+d x))}{a^2 d}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \tanh (c+d x)\right)}{3 a^{4/3} d}-\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \tanh (c+d x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} d}-\frac{\coth ^3(c+d x)}{3 a d}+\frac{\coth (c+d x)}{a d}",1,"-((b^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*Tanh[c + d*x])/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)*d)) + Coth[c + d*x]/(a*d) - Coth[c + d*x]^3/(3*a*d) - (b*Log[Tanh[c + d*x]])/(a^2*d) - (b^(1/3)*Log[a^(1/3) + b^(1/3)*Tanh[c + d*x]])/(3*a^(4/3)*d) + (b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*Tanh[c + d*x] + b^(2/3)*Tanh[c + d*x]^2])/(6*a^(4/3)*d) + (b*Log[a + b*Tanh[c + d*x]^3])/(3*a^2*d)","A",12,11,23,0.4783,1,"{3663, 1834, 1871, 12, 292, 31, 634, 617, 204, 628, 260}"
81,1,63,0,0.0496557,"\int \cosh ^4(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Cosh[c + d*x]^4*(a + b*Tanh[c + d*x]^2),x]","\frac{(a+b) \sinh (c+d x) \cosh ^3(c+d x)}{4 d}+\frac{(3 a-b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{1}{8} x (3 a-b)","\frac{(a+b) \sinh (c+d x) \cosh ^3(c+d x)}{4 d}+\frac{(3 a-b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{1}{8} x (3 a-b)",1,"((3*a - b)*x)/8 + ((3*a - b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + ((a + b)*Cosh[c + d*x]^3*Sinh[c + d*x])/(4*d)","A",4,4,21,0.1905,1,"{3675, 385, 199, 206}"
82,1,30,0,0.0355443,"\int \cosh ^3(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Cosh[c + d*x]^3*(a + b*Tanh[c + d*x]^2),x]","\frac{(a+b) \sinh ^3(c+d x)}{3 d}+\frac{a \sinh (c+d x)}{d}","\frac{(a+b) \sinh ^3(c+d x)}{3 d}+\frac{a \sinh (c+d x)}{d}",1,"(a*Sinh[c + d*x])/d + ((a + b)*Sinh[c + d*x]^3)/(3*d)","A",2,1,21,0.04762,1,"{3676}"
83,1,33,0,0.0390378,"\int \cosh ^2(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Cosh[c + d*x]^2*(a + b*Tanh[c + d*x]^2),x]","\frac{(a+b) \sinh (c+d x) \cosh (c+d x)}{2 d}+\frac{1}{2} x (a-b)","\frac{(a+b) \sinh (c+d x) \cosh (c+d x)}{2 d}+\frac{1}{2} x (a-b)",1,"((a - b)*x)/2 + ((a + b)*Cosh[c + d*x]*Sinh[c + d*x])/(2*d)","A",3,3,21,0.1429,1,"{3675, 385, 206}"
84,1,27,0,0.0319431,"\int \cosh (c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Cosh[c + d*x]*(a + b*Tanh[c + d*x]^2),x]","\frac{(a+b) \sinh (c+d x)}{d}-\frac{b \tan ^{-1}(\sinh (c+d x))}{d}","\frac{(a+b) \sinh (c+d x)}{d}-\frac{b \tan ^{-1}(\sinh (c+d x))}{d}",1,"-((b*ArcTan[Sinh[c + d*x]])/d) + ((a + b)*Sinh[c + d*x])/d","A",3,3,19,0.1579,1,"{3676, 388, 203}"
85,1,40,0,0.0310208,"\int \text{sech}(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Sech[c + d*x]*(a + b*Tanh[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",3,3,19,0.1579,1,"{3676, 385, 203}"
86,1,28,0,0.0293381,"\int \text{sech}^2(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Sech[c + d*x]^2*(a + b*Tanh[c + d*x]^2),x]","\frac{a \tanh (c+d x)}{d}+\frac{b \tanh ^3(c+d x)}{3 d}","\frac{a \tanh (c+d x)}{d}+\frac{b \tanh ^3(c+d x)}{3 d}",1,"(a*Tanh[c + d*x])/d + (b*Tanh[c + d*x]^3)/(3*d)","A",2,1,21,0.04762,1,"{3675}"
87,1,66,0,0.0455378,"\int \text{sech}^3(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Sech[c + d*x]^3*(a + b*Tanh[c + d*x]^2),x]","\frac{(4 a+b) \tan ^{-1}(\sinh (c+d x))}{8 d}+\frac{(4 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)}{4 d}","\frac{(4 a+b) \tan ^{-1}(\sinh (c+d x))}{8 d}+\frac{(4 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)}{4 d}",1,"((4*a + b)*ArcTan[Sinh[c + d*x]])/(8*d) + ((4*a + b)*Sech[c + d*x]*Tanh[c + d*x])/(8*d) - (b*Sech[c + d*x]^3*Tanh[c + d*x])/(4*d)","A",4,4,21,0.1905,1,"{3676, 385, 199, 203}"
88,1,48,0,0.0398919,"\int \text{sech}^4(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Sech[c + d*x]^4*(a + b*Tanh[c + d*x]^2),x]","-\frac{(a-b) \tanh ^3(c+d x)}{3 d}+\frac{a \tanh (c+d x)}{d}-\frac{b \tanh ^5(c+d x)}{5 d}","-\frac{(a-b) \tanh ^3(c+d x)}{3 d}+\frac{a \tanh (c+d x)}{d}-\frac{b \tanh ^5(c+d x)}{5 d}",1,"(a*Tanh[c + d*x])/d - ((a - b)*Tanh[c + d*x]^3)/(3*d) - (b*Tanh[c + d*x]^5)/(5*d)","A",3,2,21,0.09524,1,"{3675, 373}"
89,1,85,0,0.0868324,"\int \cosh ^4(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Cosh[c + d*x]^4*(a + b*Tanh[c + d*x]^2)^2,x]","\frac{3 \left(a^2-b^2\right) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{1}{8} x \left(3 a^2-2 a b+3 b^2\right)+\frac{(a+b) \sinh (c+d x) \cosh ^3(c+d x) \left(a+b \tanh ^2(c+d x)\right)}{4 d}","\frac{3 \left(a^2-b^2\right) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{1}{8} x \left(3 a^2-2 a b+3 b^2\right)+\frac{(a+b) \sinh (c+d x) \cosh ^3(c+d x) \left(a+b \tanh ^2(c+d x)\right)}{4 d}",1,"((3*a^2 - 2*a*b + 3*b^2)*x)/8 + (3*(a^2 - b^2)*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + ((a + b)*Cosh[c + d*x]^3*Sinh[c + d*x]*(a + b*Tanh[c + d*x]^2))/(4*d)","A",4,4,23,0.1739,1,"{3675, 413, 385, 206}"
90,1,54,0,0.0603328,"\int \cosh ^3(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Cosh[c + d*x]^3*(a + b*Tanh[c + d*x]^2)^2,x]","\frac{\left(a^2-b^2\right) \sinh (c+d x)}{d}+\frac{(a+b)^2 \sinh ^3(c+d x)}{3 d}+\frac{b^2 \tan ^{-1}(\sinh (c+d x))}{d}","\frac{\left(a^2-b^2\right) \sinh (c+d x)}{d}+\frac{(a+b)^2 \sinh ^3(c+d x)}{3 d}+\frac{b^2 \tan ^{-1}(\sinh (c+d x))}{d}",1,"(b^2*ArcTan[Sinh[c + d*x]])/d + ((a^2 - b^2)*Sinh[c + d*x])/d + ((a + b)^2*Sinh[c + d*x]^3)/(3*d)","A",4,3,23,0.1304,1,"{3676, 390, 203}"
91,1,51,0,0.0756621,"\int \cosh ^2(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Cosh[c + d*x]^2*(a + b*Tanh[c + d*x]^2)^2,x]","\frac{(a+b)^2 \sinh (c+d x) \cosh (c+d x)}{2 d}+\frac{1}{2} x (a-3 b) (a+b)+\frac{b^2 \tanh (c+d x)}{d}","\frac{(a+b)^2 \sinh (c+d x) \cosh (c+d x)}{2 d}+\frac{1}{2} x (a-3 b) (a+b)+\frac{b^2 \tanh (c+d x)}{d}",1,"((a - 3*b)*(a + b)*x)/2 + ((a + b)^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,"{3675, 390, 385, 206}"
92,1,60,0,0.0824405,"\int \cosh (c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Cosh[c + d*x]*(a + b*Tanh[c + d*x]^2)^2,x]","\frac{(a+b)^2 \sinh (c+d x)}{d}-\frac{b (4 a+3 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+b)^2 \sinh (c+d x)}{d}-\frac{b (4 a+3 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 + 3*b)*ArcTan[Sinh[c + d*x]])/(2*d) + ((a + b)^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,"{3676, 390, 385, 203}"
93,1,91,0,0.085125,"\int \text{sech}(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Sech[c + d*x]*(a + b*Tanh[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+b) \sinh ^2(c+d x)+a\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+b) \sinh ^2(c+d x)+a\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 + (a + b)*Sinh[c + d*x]^2)*Tanh[c + d*x])/(4*d)","A",4,4,21,0.1905,1,"{3676, 413, 385, 203}"
94,1,49,0,0.0530052,"\int \text{sech}^2(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Sech[c + d*x]^2*(a + b*Tanh[c + d*x]^2)^2,x]","\frac{a^2 \tanh (c+d x)}{d}+\frac{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}+\frac{2 a b \tanh ^3(c+d x)}{3 d}+\frac{b^2 \tanh ^5(c+d x)}{5 d}",1,"(a^2*Tanh[c + d*x])/d + (2*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,"{3675, 194}"
95,1,125,0,0.1519149,"\int \text{sech}^3(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Sech[c + d*x]^3*(a + b*Tanh[c + d*x]^2)^2,x]","\frac{\left(8 a^2+4 a b+b^2\right) \tan ^{-1}(\sinh (c+d x))}{16 d}+\frac{\left(8 a^2+4 a b+b^2\right) \tanh (c+d x) \text{sech}(c+d x)}{16 d}-\frac{b (8 a+3 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+b) \sinh ^2(c+d x)+a\right)}{6 d}","\frac{\left(8 a^2+4 a b+b^2\right) \tan ^{-1}(\sinh (c+d x))}{16 d}+\frac{\left(8 a^2+4 a b+b^2\right) \tanh (c+d x) \text{sech}(c+d x)}{16 d}-\frac{b (8 a+3 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+b) \sinh ^2(c+d x)+a\right)}{6 d}",1,"((8*a^2 + 4*a*b + b^2)*ArcTan[Sinh[c + d*x]])/(16*d) + ((8*a^2 + 4*a*b + b^2)*Sech[c + d*x]*Tanh[c + d*x])/(16*d) - (b*(8*a + 3*b)*Sech[c + d*x]^3*Tanh[c + d*x])/(24*d) - (b*Sech[c + d*x]^5*(a + (a + b)*Sinh[c + d*x]^2)*Tanh[c + d*x])/(6*d)","A",5,5,23,0.2174,1,"{3676, 413, 385, 199, 203}"
96,1,76,0,0.070226,"\int \text{sech}^4(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Sech[c + d*x]^4*(a + b*Tanh[c + d*x]^2)^2,x]","\frac{a^2 \tanh (c+d x)}{d}-\frac{b (2 a-b) \tanh ^5(c+d x)}{5 d}-\frac{a (a-2 b) \tanh ^3(c+d x)}{3 d}-\frac{b^2 \tanh ^7(c+d x)}{7 d}","\frac{a^2 \tanh (c+d x)}{d}-\frac{b (2 a-b) \tanh ^5(c+d x)}{5 d}-\frac{a (a-2 b) \tanh ^3(c+d x)}{3 d}-\frac{b^2 \tanh ^7(c+d x)}{7 d}",1,"(a^2*Tanh[c + d*x])/d - (a*(a - 2*b)*Tanh[c + d*x]^3)/(3*d) - ((2*a - b)*b*Tanh[c + d*x]^5)/(5*d) - (b^2*Tanh[c + d*x]^7)/(7*d)","A",3,2,23,0.08696,1,"{3675, 373}"
97,1,91,0,0.1303537,"\int \cosh ^4(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Cosh[c + d*x]^4*(a + b*Tanh[c + d*x]^2)^3,x]","\frac{3}{8} x (a+b) \left(a^2-2 a b+5 b^2\right)+\frac{(a+b)^3 \sinh (c+d x) \cosh ^3(c+d x)}{4 d}+\frac{3 (a-3 b) (a+b)^2 \sinh (c+d x) \cosh (c+d x)}{8 d}-\frac{b^3 \tanh (c+d x)}{d}","\frac{3}{8} x (a+b) \left(a^2-2 a b+5 b^2\right)+\frac{(a+b)^3 \sinh (c+d x) \cosh ^3(c+d x)}{4 d}+\frac{3 (a-3 b) (a+b)^2 \sinh (c+d x) \cosh (c+d x)}{8 d}-\frac{b^3 \tanh (c+d x)}{d}",1,"(3*(a + b)*(a^2 - 2*a*b + 5*b^2)*x)/8 + (3*(a - 3*b)*(a + b)^2*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + ((a + b)^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,"{3675, 390, 1157, 385, 206}"
98,1,87,0,0.1051084,"\int \cosh ^3(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Cosh[c + d*x]^3*(a + b*Tanh[c + d*x]^2)^3,x]","\frac{b^2 (6 a+5 b) \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{(a+b)^3 \sinh ^3(c+d x)}{3 d}+\frac{(a-2 b) (a+b)^2 \sinh (c+d x)}{d}-\frac{b^3 \tanh (c+d x) \text{sech}(c+d x)}{2 d}","\frac{b^2 (6 a+5 b) \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{(a+b)^3 \sinh ^3(c+d x)}{3 d}+\frac{(a-2 b) (a+b)^2 \sinh (c+d x)}{d}-\frac{b^3 \tanh (c+d x) \text{sech}(c+d x)}{2 d}",1,"(b^2*(6*a + 5*b)*ArcTan[Sinh[c + d*x]])/(2*d) + ((a - 2*b)*(a + b)^2*Sinh[c + d*x])/d + ((a + b)^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,"{3676, 390, 385, 203}"
99,1,78,0,0.089681,"\int \cosh ^2(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Cosh[c + d*x]^2*(a + b*Tanh[c + d*x]^2)^3,x]","\frac{b^2 (3 a+2 b) \tanh (c+d x)}{d}+\frac{(a+b)^3 \sinh (c+d x) \cosh (c+d x)}{2 d}+\frac{1}{2} x (a-5 b) (a+b)^2+\frac{b^3 \tanh ^3(c+d x)}{3 d}","\frac{b^2 (3 a+2 b) \tanh (c+d x)}{d}+\frac{(a+b)^3 \sinh (c+d x) \cosh (c+d x)}{2 d}+\frac{1}{2} x (a-5 b) (a+b)^2+\frac{b^3 \tanh ^3(c+d x)}{3 d}",1,"((a - 5*b)*(a + b)^2*x)/2 + ((a + b)^3*Cosh[c + d*x]*Sinh[c + d*x])/(2*d) + (b^2*(3*a + 2*b)*Tanh[c + d*x])/d + (b^3*Tanh[c + d*x]^3)/(3*d)","A",5,4,23,0.1739,1,"{3675, 390, 385, 206}"
100,1,99,0,0.1162974,"\int \cosh (c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Cosh[c + d*x]*(a + b*Tanh[c + d*x]^2)^3,x]","\frac{3 b^2 (4 a+3 b) \tanh (c+d x) \text{sech}(c+d x)}{8 d}+\frac{(a+b)^3 \sinh (c+d x)}{d}-\frac{3 b \left(4 (a+b)^2+(2 a+b)^2\right) \tan ^{-1}(\sinh (c+d x))}{8 d}-\frac{b^3 \tanh (c+d x) \text{sech}^3(c+d x)}{4 d}","\frac{3 b^2 (4 a+3 b) \tanh (c+d x) \text{sech}(c+d x)}{8 d}+\frac{(a+b)^3 \sinh (c+d x)}{d}-\frac{3 b \left(4 (a+b)^2+(2 a+b)^2\right) \tan ^{-1}(\sinh (c+d x))}{8 d}-\frac{b^3 \tanh (c+d x) \text{sech}^3(c+d x)}{4 d}",1,"(-3*b*(4*(a + b)^2 + (2*a + b)^2)*ArcTan[Sinh[c + d*x]])/(8*d) + ((a + b)^3*Sinh[c + d*x])/d + (3*b^2*(4*a + 3*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,"{3676, 390, 1157, 385, 203}"
101,1,149,0,0.1543914,"\int \text{sech}(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Sech[c + d*x]*(a + b*Tanh[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+b) \sinh ^2(c+d x)+a\right)^2}{6 d}-\frac{5 b (2 a+b) \tanh (c+d x) \text{sech}^3(c+d x) \left((a+b) \sinh ^2(c+d x)+a\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+b) \sinh ^2(c+d x)+a\right)^2}{6 d}-\frac{5 b (2 a+b) \tanh (c+d x) \text{sech}^3(c+d x) \left((a+b) \sinh ^2(c+d x)+a\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 + (a + b)*Sinh[c + d*x]^2)*Tanh[c + d*x])/(24*d) - (b*Sech[c + d*x]^5*(a + (a + b)*Sinh[c + d*x]^2)^2*Tanh[c + d*x])/(6*d)","A",5,5,21,0.2381,1,"{3676, 413, 526, 385, 203}"
102,1,67,0,0.0613605,"\int \text{sech}^2(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Sech[c + d*x]^2*(a + b*Tanh[c + d*x]^2)^3,x]","\frac{a^2 b \tanh ^3(c+d x)}{d}+\frac{a^3 \tanh (c+d x)}{d}+\frac{3 a b^2 \tanh ^5(c+d x)}{5 d}+\frac{b^3 \tanh ^7(c+d x)}{7 d}","\frac{a^2 b \tanh ^3(c+d x)}{d}+\frac{a^3 \tanh (c+d x)}{d}+\frac{3 a b^2 \tanh ^5(c+d x)}{5 d}+\frac{b^3 \tanh ^7(c+d x)}{7 d}",1,"(a^3*Tanh[c + d*x])/d + (a^2*b*Tanh[c + d*x]^3)/d + (3*a*b^2*Tanh[c + d*x]^5)/(5*d) + (b^3*Tanh[c + d*x]^7)/(7*d)","A",3,2,23,0.08696,1,"{3675, 194}"
103,1,198,0,0.2394664,"\int \text{sech}^3(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Sech[c + d*x]^3*(a + b*Tanh[c + d*x]^2)^3,x]","\frac{\left(48 a^2 b+64 a^3+24 a b^2+5 b^3\right) \tan ^{-1}(\sinh (c+d x))}{128 d}-\frac{b \left(72 a^2+52 a b+15 b^2\right) \tanh (c+d x) \text{sech}^3(c+d x)}{192 d}+\frac{\left(48 a^2 b+64 a^3+24 a b^2+5 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+b) \sinh ^2(c+d x)+a\right)^2}{8 d}-\frac{b (12 a+5 b) \tanh (c+d x) \text{sech}^5(c+d x) \left((a+b) \sinh ^2(c+d x)+a\right)}{48 d}","\frac{\left(48 a^2 b+64 a^3+24 a b^2+5 b^3\right) \tan ^{-1}(\sinh (c+d x))}{128 d}-\frac{b \left(72 a^2+52 a b+15 b^2\right) \tanh (c+d x) \text{sech}^3(c+d x)}{192 d}+\frac{\left(48 a^2 b+64 a^3+24 a b^2+5 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+b) \sinh ^2(c+d x)+a\right)^2}{8 d}-\frac{b (12 a+5 b) \tanh (c+d x) \text{sech}^5(c+d x) \left((a+b) \sinh ^2(c+d x)+a\right)}{48 d}",1,"((64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*ArcTan[Sinh[c + d*x]])/(128*d) + ((64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*Sech[c + d*x]*Tanh[c + d*x])/(128*d) - (b*(72*a^2 + 52*a*b + 15*b^2)*Sech[c + d*x]^3*Tanh[c + d*x])/(192*d) - (b*(12*a + 5*b)*Sech[c + d*x]^5*(a + (a + b)*Sinh[c + d*x]^2)*Tanh[c + d*x])/(48*d) - (b*Sech[c + d*x]^7*(a + (a + b)*Sinh[c + d*x]^2)^2*Tanh[c + d*x])/(8*d)","A",6,6,23,0.2609,1,"{3676, 413, 526, 385, 199, 203}"
104,1,102,0,0.0889386,"\int \text{sech}^4(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Sech[c + d*x]^4*(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{a^2 (a-3 b) \tanh ^3(c+d x)}{3 d}+\frac{a^3 \tanh (c+d x)}{d}-\frac{b^2 (3 a-b) \tanh ^7(c+d x)}{7 d}-\frac{3 a b (a-b) \tanh ^5(c+d x)}{5 d}-\frac{b^3 \tanh ^9(c+d x)}{9 d}","-\frac{a^2 (a-3 b) \tanh ^3(c+d x)}{3 d}+\frac{a^3 \tanh (c+d x)}{d}-\frac{b^2 (3 a-b) \tanh ^7(c+d x)}{7 d}-\frac{3 a b (a-b) \tanh ^5(c+d x)}{5 d}-\frac{b^3 \tanh ^9(c+d x)}{9 d}",1,"(a^3*Tanh[c + d*x])/d - (a^2*(a - 3*b)*Tanh[c + d*x]^3)/(3*d) - (3*a*(a - b)*b*Tanh[c + d*x]^5)/(5*d) - ((3*a - b)*b^2*Tanh[c + d*x]^7)/(7*d) - (b^3*Tanh[c + d*x]^9)/(9*d)","A",3,2,23,0.08696,1,"{3675, 373}"
105,1,120,0,0.1682741,"\int \frac{\cosh ^4(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Cosh[c + d*x]^4/(a + b*Tanh[c + d*x]^2),x]","\frac{x \left(3 a^2+10 a b+15 b^2\right)}{8 (a+b)^3}+\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a+b)^3}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 d (a+b)}+\frac{(3 a+7 b) \sinh (c+d x) \cosh (c+d x)}{8 d (a+b)^2}","\frac{x \left(3 a^2+10 a b+15 b^2\right)}{8 (a+b)^3}+\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a+b)^3}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 d (a+b)}+\frac{(3 a+7 b) \sinh (c+d x) \cosh (c+d x)}{8 d (a+b)^2}",1,"((3*a^2 + 10*a*b + 15*b^2)*x)/(8*(a + b)^3) + (b^(5/2)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(Sqrt[a]*(a + b)^3*d) + ((3*a + 7*b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*(a + b)^2*d) + (Cosh[c + d*x]^3*Sinh[c + d*x])/(4*(a + b)*d)","A",6,6,23,0.2609,1,"{3675, 414, 527, 522, 206, 205}"
106,1,80,0,0.1090619,"\int \frac{\cosh ^3(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Cosh[c + d*x]^3/(a + b*Tanh[c + d*x]^2),x]","\frac{b^2 \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a+b)^{5/2}}+\frac{\sinh ^3(c+d x)}{3 d (a+b)}+\frac{(a+2 b) \sinh (c+d x)}{d (a+b)^2}","\frac{b^2 \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a+b)^{5/2}}+\frac{\sinh ^3(c+d x)}{3 d (a+b)}+\frac{(a+2 b) \sinh (c+d x)}{d (a+b)^2}",1,"(b^2*ArcTan[(Sqrt[a + b]*Sinh[c + d*x])/Sqrt[a]])/(Sqrt[a]*(a + b)^(5/2)*d) + ((a + 2*b)*Sinh[c + d*x])/((a + b)^2*d) + Sinh[c + d*x]^3/(3*(a + b)*d)","A",4,3,23,0.1304,1,"{3676, 390, 205}"
107,1,77,0,0.102965,"\int \frac{\cosh ^2(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Cosh[c + d*x]^2/(a + b*Tanh[c + d*x]^2),x]","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a+b)^2}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 d (a+b)}+\frac{x (a+3 b)}{2 (a+b)^2}","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a+b)^2}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 d (a+b)}+\frac{x (a+3 b)}{2 (a+b)^2}",1,"((a + 3*b)*x)/(2*(a + b)^2) + (b^(3/2)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(Sqrt[a]*(a + b)^2*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*(a + b)*d)","A",5,5,23,0.2174,1,"{3675, 414, 522, 206, 205}"
108,1,53,0,0.0704951,"\int \frac{\cosh (c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Cosh[c + d*x]/(a + b*Tanh[c + d*x]^2),x]","\frac{\sinh (c+d x)}{d (a+b)}+\frac{b \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a+b)^{3/2}}","\frac{\sinh (c+d x)}{d (a+b)}+\frac{b \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a+b)^{3/2}}",1,"(b*ArcTan[(Sqrt[a + b]*Sinh[c + d*x])/Sqrt[a]])/(Sqrt[a]*(a + b)^(3/2)*d) + Sinh[c + d*x]/((a + b)*d)","A",3,3,21,0.1429,1,"{3676, 388, 205}"
109,1,36,0,0.0443204,"\int \frac{\text{sech}(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Sech[c + d*x]/(a + b*Tanh[c + d*x]^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d \sqrt{a+b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d \sqrt{a+b}}",1,"ArcTan[(Sqrt[a + b]*Sinh[c + d*x])/Sqrt[a]]/(Sqrt[a]*Sqrt[a + b]*d)","A",2,2,21,0.09524,1,"{3676, 205}"
110,1,32,0,0.056264,"\int \frac{\text{sech}^2(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Sech[c + d*x]^2/(a + b*Tanh[c + d*x]^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} d}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} d}",1,"ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]]/(Sqrt[a]*Sqrt[b]*d)","A",2,2,23,0.08696,1,"{3675, 205}"
111,1,55,0,0.0729596,"\int \frac{\text{sech}^3(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Sech[c + d*x]^3/(a + b*Tanh[c + d*x]^2),x]","\frac{\sqrt{a+b} \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b d}-\frac{\tan ^{-1}(\sinh (c+d x))}{b d}","\frac{\sqrt{a+b} \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b d}-\frac{\tan ^{-1}(\sinh (c+d x))}{b d}",1,"-(ArcTan[Sinh[c + d*x]]/(b*d)) + (Sqrt[a + b]*ArcTan[(Sqrt[a + b]*Sinh[c + d*x])/Sqrt[a]])/(Sqrt[a]*b*d)","A",4,4,23,0.1739,1,"{3676, 391, 203, 205}"
112,1,50,0,0.0695992,"\int \frac{\text{sech}^4(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Sech[c + d*x]^4/(a + b*Tanh[c + d*x]^2),x]","\frac{(a+b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2} d}-\frac{\tanh (c+d x)}{b d}","\frac{(a+b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2} d}-\frac{\tanh (c+d x)}{b d}",1,"((a + b)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(Sqrt[a]*b^(3/2)*d) - Tanh[c + d*x]/(b*d)","A",3,3,23,0.1304,1,"{3675, 388, 205}"
113,1,86,0,0.1204838,"\int \frac{\text{sech}^5(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Sech[c + d*x]^5/(a + b*Tanh[c + d*x]^2),x]","\frac{(a+b)^{3/2} \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b^2 d}-\frac{(2 a+3 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+b)^{3/2} \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b^2 d}-\frac{(2 a+3 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 + 3*b)*ArcTan[Sinh[c + d*x]])/(2*b^2*d) + ((a + b)^(3/2)*ArcTan[(Sqrt[a + b]*Sinh[c + d*x])/Sqrt[a]])/(Sqrt[a]*b^2*d) - (Sech[c + d*x]*Tanh[c + d*x])/(2*b*d)","A",5,5,23,0.2174,1,"{3676, 414, 522, 203, 205}"
114,1,75,0,0.0915841,"\int \frac{\text{sech}^6(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Sech[c + d*x]^6/(a + b*Tanh[c + d*x]^2),x]","-\frac{(a+2 b) \tanh (c+d x)}{b^2 d}+\frac{(a+b)^2 \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b^{5/2} d}+\frac{\tanh ^3(c+d x)}{3 b d}","-\frac{(a+2 b) \tanh (c+d x)}{b^2 d}+\frac{(a+b)^2 \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b^{5/2} d}+\frac{\tanh ^3(c+d x)}{3 b d}",1,"((a + b)^2*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(Sqrt[a]*b^(5/2)*d) - ((a + 2*b)*Tanh[c + d*x])/(b^2*d) + Tanh[c + d*x]^3/(3*b*d)","A",4,3,23,0.1304,1,"{3675, 390, 205}"
115,1,128,0,0.1815111,"\int \frac{\cosh ^3(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Cosh[c + d*x]^3/(a + b*Tanh[c + d*x]^2)^2,x]","\frac{b^2 (6 a+b) \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a+b)^{7/2}}+\frac{b^3 \sinh (c+d x)}{2 a d (a+b)^3 \left((a+b) \sinh ^2(c+d x)+a\right)}+\frac{\sinh ^3(c+d x)}{3 d (a+b)^2}+\frac{(a+3 b) \sinh (c+d x)}{d (a+b)^3}","\frac{b^2 (6 a+b) \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a+b)^{7/2}}+\frac{b^3 \sinh (c+d x)}{2 a d (a+b)^3 \left((a+b) \sinh ^2(c+d x)+a\right)}+\frac{\sinh ^3(c+d x)}{3 d (a+b)^2}+\frac{(a+3 b) \sinh (c+d x)}{d (a+b)^3}",1,"(b^2*(6*a + b)*ArcTan[(Sqrt[a + b]*Sinh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*(a + b)^(7/2)*d) + ((a + 3*b)*Sinh[c + d*x])/((a + b)^3*d) + Sinh[c + d*x]^3/(3*(a + b)^2*d) + (b^3*Sinh[c + d*x])/(2*a*(a + b)^3*d*(a + (a + b)*Sinh[c + d*x]^2))","A",5,4,23,0.1739,1,"{3676, 390, 385, 205}"
116,1,140,0,0.1937782,"\int \frac{\cosh ^2(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Cosh[c + d*x]^2/(a + b*Tanh[c + d*x]^2)^2,x]","\frac{b^{3/2} (5 a+b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a+b)^3}-\frac{b (a-b) \tanh (c+d x)}{2 a d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{x (a+5 b)}{2 (a+b)^3}","\frac{b^{3/2} (5 a+b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a+b)^3}-\frac{b (a-b) \tanh (c+d x)}{2 a d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{x (a+5 b)}{2 (a+b)^3}",1,"((a + 5*b)*x)/(2*(a + b)^3) + (b^(3/2)*(5*a + b)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*(a + b)^3*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*(a + b)*d*(a + b*Tanh[c + d*x]^2)) - ((a - b)*b*Tanh[c + d*x])/(2*a*(a + b)^2*d*(a + b*Tanh[c + d*x]^2))","A",6,6,23,0.2609,1,"{3675, 414, 527, 522, 206, 205}"
117,1,101,0,0.1391961,"\int \frac{\cosh (c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Cosh[c + d*x]/(a + b*Tanh[c + d*x]^2)^2,x]","\frac{b (4 a+b) \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a+b)^{5/2}}+\frac{b^2 \sinh (c+d x)}{2 a d (a+b)^2 \left((a+b) \sinh ^2(c+d x)+a\right)}+\frac{\sinh (c+d x)}{d (a+b)^2}","\frac{b (4 a+b) \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a+b)^{5/2}}+\frac{b^2 \sinh (c+d x)}{2 a d (a+b)^2 \left((a+b) \sinh ^2(c+d x)+a\right)}+\frac{\sinh (c+d x)}{d (a+b)^2}",1,"(b*(4*a + b)*ArcTan[(Sqrt[a + b]*Sinh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*(a + b)^(5/2)*d) + Sinh[c + d*x]/((a + b)^2*d) + (b^2*Sinh[c + d*x])/(2*a*(a + b)^2*d*(a + (a + b)*Sinh[c + d*x]^2))","A",5,4,21,0.1905,1,"{3676, 390, 385, 205}"
118,1,83,0,0.0708357,"\int \frac{\text{sech}(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]/(a + b*Tanh[c + d*x]^2)^2,x]","\frac{(2 a+b) \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a+b)^{3/2}}+\frac{b \sinh (c+d x)}{2 a d (a+b) \left((a+b) \sinh ^2(c+d x)+a\right)}","\frac{(2 a+b) \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a+b)^{3/2}}+\frac{b \sinh (c+d x)}{2 a d (a+b) \left((a+b) \sinh ^2(c+d x)+a\right)}",1,"((2*a + b)*ArcTan[(Sqrt[a + b]*Sinh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*(a + b)^(3/2)*d) + (b*Sinh[c + d*x])/(2*a*(a + b)*d*(a + (a + b)*Sinh[c + d*x]^2))","A",3,3,21,0.1429,1,"{3676, 385, 205}"
119,1,66,0,0.0660707,"\int \frac{\text{sech}^2(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]^2/(a + b*Tanh[c + d*x]^2)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} d}+\frac{\tanh (c+d x)}{2 a d \left(a+b \tanh ^2(c+d x)\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} d}+\frac{\tanh (c+d x)}{2 a d \left(a+b \tanh ^2(c+d x)\right)}",1,"ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]]/(2*a^(3/2)*Sqrt[b]*d) + Tanh[c + d*x]/(2*a*d*(a + b*Tanh[c + d*x]^2))","A",3,3,23,0.1304,1,"{3675, 199, 205}"
120,1,72,0,0.0765269,"\int \frac{\text{sech}^3(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]^3/(a + b*Tanh[c + d*x]^2)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d \sqrt{a+b}}+\frac{\sinh (c+d x)}{2 a d \left((a+b) \sinh ^2(c+d x)+a\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d \sqrt{a+b}}+\frac{\sinh (c+d x)}{2 a d \left((a+b) \sinh ^2(c+d x)+a\right)}",1,"ArcTan[(Sqrt[a + b]*Sinh[c + d*x])/Sqrt[a]]/(2*a^(3/2)*Sqrt[a + b]*d) + Sinh[c + d*x]/(2*a*d*(a + (a + b)*Sinh[c + d*x]^2))","A",3,3,23,0.1304,1,"{3676, 199, 205}"
121,1,77,0,0.0788741,"\int \frac{\text{sech}^4(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]^4/(a + b*Tanh[c + d*x]^2)^2,x]","\frac{(a+b) \tanh (c+d x)}{2 a b d \left(a+b \tanh ^2(c+d x)\right)}-\frac{(a-b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} b^{3/2} d}","\frac{(a+b) \tanh (c+d x)}{2 a b d \left(a+b \tanh ^2(c+d x)\right)}-\frac{(a-b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} b^{3/2} d}",1,"-((a - b)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*b^(3/2)*d) + ((a + b)*Tanh[c + d*x])/(2*a*b*d*(a + b*Tanh[c + d*x]^2))","A",3,3,23,0.1304,1,"{3675, 385, 205}"
122,1,102,0,0.1271035,"\int \frac{\text{sech}^5(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]^5/(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{(2 a-b) \sqrt{a+b} \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} b^2 d}+\frac{(a+b) \sinh (c+d x)}{2 a b d \left((a+b) \sinh ^2(c+d x)+a\right)}+\frac{\tan ^{-1}(\sinh (c+d x))}{b^2 d}","-\frac{(2 a-b) \sqrt{a+b} \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} b^2 d}+\frac{(a+b) \sinh (c+d x)}{2 a b d \left((a+b) \sinh ^2(c+d x)+a\right)}+\frac{\tan ^{-1}(\sinh (c+d x))}{b^2 d}",1,"ArcTan[Sinh[c + d*x]]/(b^2*d) - ((2*a - b)*Sqrt[a + b]*ArcTan[(Sqrt[a + b]*Sinh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*b^2*d) + ((a + b)*Sinh[c + d*x])/(2*a*b*d*(a + (a + b)*Sinh[c + d*x]^2))","A",5,5,23,0.2174,1,"{3676, 414, 522, 203, 205}"
123,1,97,0,0.1294996,"\int \frac{\text{sech}^6(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]^6/(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{(3 a-b) (a+b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} b^{5/2} d}+\frac{(a+b)^2 \tanh (c+d x)}{2 a b^2 d \left(a+b \tanh ^2(c+d x)\right)}+\frac{\tanh (c+d x)}{b^2 d}","-\frac{(3 a-b) (a+b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} b^{5/2} d}+\frac{(a+b)^2 \tanh (c+d x)}{2 a b^2 d \left(a+b \tanh ^2(c+d x)\right)}+\frac{\tanh (c+d x)}{b^2 d}",1,"-((3*a - b)*(a + b)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*b^(5/2)*d) + Tanh[c + d*x]/(b^2*d) + ((a + b)^2*Tanh[c + d*x])/(2*a*b^2*d*(a + b*Tanh[c + d*x]^2))","A",5,4,23,0.1739,1,"{3675, 390, 385, 205}"
124,1,155,0,0.24918,"\int \frac{\text{sech}^7(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]^7/(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{(4 a-b) (a+b)^{3/2} \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} b^3 d}+\frac{(2 a+b) (a+b) \sinh (c+d x)}{2 a b^2 d \left((a+b) \sinh ^2(c+d x)+a\right)}+\frac{(4 a+5 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+b) \sinh ^2(c+d x)+a\right)}","-\frac{(4 a-b) (a+b)^{3/2} \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} b^3 d}+\frac{(2 a+b) (a+b) \sinh (c+d x)}{2 a b^2 d \left((a+b) \sinh ^2(c+d x)+a\right)}+\frac{(4 a+5 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+b) \sinh ^2(c+d x)+a\right)}",1,"((4*a + 5*b)*ArcTan[Sinh[c + d*x]])/(2*b^3*d) - ((4*a - b)*(a + b)^(3/2)*ArcTan[(Sqrt[a + b]*Sinh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*b^3*d) + ((a + b)*(2*a + b)*Sinh[c + d*x])/(2*a*b^2*d*(a + (a + b)*Sinh[c + d*x]^2)) - (Sech[c + d*x]*Tanh[c + d*x])/(2*b*d*(a + (a + b)*Sinh[c + d*x]^2))","A",6,6,23,0.2609,1,"{3676, 414, 527, 522, 203, 205}"
125,1,198,0,0.3096665,"\int \frac{\cosh ^2(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Cosh[c + d*x]^2/(a + b*Tanh[c + d*x]^2)^3,x]","\frac{b^{3/2} \left(35 a^2+14 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a+b)^4}-\frac{b (a-3 b) (4 a+b) \tanh (c+d x)}{8 a^2 d (a+b)^3 \left(a+b \tanh ^2(c+d x)\right)}-\frac{b (2 a-b) \tanh (c+d x)}{4 a d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{x (a+7 b)}{2 (a+b)^4}","\frac{b^{3/2} \left(35 a^2+14 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a+b)^4}-\frac{b (a-3 b) (4 a+b) \tanh (c+d x)}{8 a^2 d (a+b)^3 \left(a+b \tanh ^2(c+d x)\right)}-\frac{b (2 a-b) \tanh (c+d x)}{4 a d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{x (a+7 b)}{2 (a+b)^4}",1,"((a + 7*b)*x)/(2*(a + b)^4) + (b^(3/2)*(35*a^2 + 14*a*b + 3*b^2)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*(a + b)^4*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*(a + b)*d*(a + b*Tanh[c + d*x]^2)^2) - ((2*a - b)*b*Tanh[c + d*x])/(4*a*(a + b)^2*d*(a + b*Tanh[c + d*x]^2)^2) - ((a - 3*b)*b*(4*a + b)*Tanh[c + d*x])/(8*a^2*(a + b)^3*d*(a + b*Tanh[c + d*x]^2))","A",7,6,23,0.2609,1,"{3675, 414, 527, 522, 206, 205}"
126,1,154,0,0.222993,"\int \frac{\cosh (c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Cosh[c + d*x]/(a + b*Tanh[c + d*x]^2)^3,x]","\frac{3 b^2 (4 a+b) \sinh (c+d x)}{8 a^2 d (a+b)^3 \left((a+b) \sinh ^2(c+d x)+a\right)}+\frac{3 b \left(8 a^2+4 a b+b^2\right) \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a+b)^{7/2}}+\frac{b^3 \sinh (c+d x)}{4 a d (a+b)^3 \left((a+b) \sinh ^2(c+d x)+a\right)^2}+\frac{\sinh (c+d x)}{d (a+b)^3}","\frac{3 b^2 (4 a+b) \sinh (c+d x)}{8 a^2 d (a+b)^3 \left((a+b) \sinh ^2(c+d x)+a\right)}+\frac{3 b \left(8 a^2+4 a b+b^2\right) \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a+b)^{7/2}}+\frac{b^3 \sinh (c+d x)}{4 a d (a+b)^3 \left((a+b) \sinh ^2(c+d x)+a\right)^2}+\frac{\sinh (c+d x)}{d (a+b)^3}",1,"(3*b*(8*a^2 + 4*a*b + b^2)*ArcTan[(Sqrt[a + b]*Sinh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*(a + b)^(7/2)*d) + Sinh[c + d*x]/((a + b)^3*d) + (b^3*Sinh[c + d*x])/(4*a*(a + b)^3*d*(a + (a + b)*Sinh[c + d*x]^2)^2) + (3*b^2*(4*a + b)*Sinh[c + d*x])/(8*a^2*(a + b)^3*d*(a + (a + b)*Sinh[c + d*x]^2))","A",6,5,21,0.2381,1,"{3676, 390, 1157, 385, 205}"
127,1,144,0,0.1414255,"\int \frac{\text{sech}(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]/(a + b*Tanh[c + d*x]^2)^3,x]","\frac{\left(8 a^2+8 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\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+b) \sinh ^2(c+d x)+a\right)}+\frac{b \sinh (c+d x) \cosh ^2(c+d x)}{4 a d (a+b) \left((a+b) \sinh ^2(c+d x)+a\right)^2}","\frac{\left(8 a^2+8 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\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+b) \sinh ^2(c+d x)+a\right)}+\frac{b \sinh (c+d x) \cosh ^2(c+d x)}{4 a d (a+b) \left((a+b) \sinh ^2(c+d x)+a\right)^2}",1,"((8*a^2 + 8*a*b + 3*b^2)*ArcTan[(Sqrt[a + b]*Sinh[c + d*x])/Sqrt[a]])/(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 + (a + b)*Sinh[c + d*x]^2)^2) + (3*b*(2*a + b)*Sinh[c + d*x])/(8*a^2*(a + b)^2*d*(a + (a + b)*Sinh[c + d*x]^2))","A",4,4,21,0.1905,1,"{3676, 413, 385, 205}"
128,1,96,0,0.0754865,"\int \frac{\text{sech}^2(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]^2/(a + b*Tanh[c + d*x]^2)^3,x]","\frac{3 \tanh (c+d x)}{8 a^2 d \left(a+b \tanh ^2(c+d x)\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} d}+\frac{\tanh (c+d x)}{4 a d \left(a+b \tanh ^2(c+d x)\right)^2}","\frac{3 \tanh (c+d x)}{8 a^2 d \left(a+b \tanh ^2(c+d x)\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} d}+\frac{\tanh (c+d x)}{4 a d \left(a+b \tanh ^2(c+d x)\right)^2}",1,"(3*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*Sqrt[b]*d) + Tanh[c + d*x]/(4*a*d*(a + b*Tanh[c + d*x]^2)^2) + (3*Tanh[c + d*x])/(8*a^2*d*(a + b*Tanh[c + d*x]^2))","A",4,3,23,0.1304,1,"{3675, 199, 205}"
129,1,129,0,0.1199727,"\int \frac{\text{sech}^3(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]^3/(a + b*Tanh[c + d*x]^2)^3,x]","\frac{(4 a+3 b) \sinh (c+d x)}{8 a^2 d (a+b) \left((a+b) \sinh ^2(c+d x)+a\right)}+\frac{(4 a+3 b) \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a+b)^{3/2}}+\frac{b \sinh (c+d x)}{4 a d (a+b) \left((a+b) \sinh ^2(c+d x)+a\right)^2}","\frac{(4 a+3 b) \sinh (c+d x)}{8 a^2 d (a+b) \left((a+b) \sinh ^2(c+d x)+a\right)}+\frac{(4 a+3 b) \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a+b)^{3/2}}+\frac{b \sinh (c+d x)}{4 a d (a+b) \left((a+b) \sinh ^2(c+d x)+a\right)^2}",1,"((4*a + 3*b)*ArcTan[(Sqrt[a + b]*Sinh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*(a + b)^(3/2)*d) + (b*Sinh[c + d*x])/(4*a*(a + b)*d*(a + (a + b)*Sinh[c + d*x]^2)^2) + ((4*a + 3*b)*Sinh[c + d*x])/(8*a^2*(a + b)*d*(a + (a + b)*Sinh[c + d*x]^2))","A",4,4,23,0.1739,1,"{3676, 385, 199, 205}"
130,1,115,0,0.0968225,"\int \frac{\text{sech}^4(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]^4/(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{(a-3 b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} b^{3/2} d}-\frac{(a-3 b) \tanh (c+d x)}{8 a^2 b d \left(a+b \tanh ^2(c+d x)\right)}+\frac{(a+b) \tanh (c+d x)}{4 a b d \left(a+b \tanh ^2(c+d x)\right)^2}","-\frac{(a-3 b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} b^{3/2} d}-\frac{(a-3 b) \tanh (c+d x)}{8 a^2 b d \left(a+b \tanh ^2(c+d x)\right)}+\frac{(a+b) \tanh (c+d x)}{4 a b d \left(a+b \tanh ^2(c+d x)\right)^2}",1,"-((a - 3*b)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*b^(3/2)*d) + ((a + b)*Tanh[c + d*x])/(4*a*b*d*(a + b*Tanh[c + d*x]^2)^2) - ((a - 3*b)*Tanh[c + d*x])/(8*a^2*b*d*(a + b*Tanh[c + d*x]^2))","A",4,4,23,0.1739,1,"{3675, 385, 199, 205}"
131,1,104,0,0.0905743,"\int \frac{\text{sech}^5(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]^5/(a + b*Tanh[c + d*x]^2)^3,x]","\frac{3 \sinh (c+d x)}{8 a^2 d \left((a+b) \sinh ^2(c+d x)+a\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d \sqrt{a+b}}+\frac{\sinh (c+d x)}{4 a d \left((a+b) \sinh ^2(c+d x)+a\right)^2}","\frac{3 \sinh (c+d x)}{8 a^2 d \left((a+b) \sinh ^2(c+d x)+a\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d \sqrt{a+b}}+\frac{\sinh (c+d x)}{4 a d \left((a+b) \sinh ^2(c+d x)+a\right)^2}",1,"(3*ArcTan[(Sqrt[a + b]*Sinh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*Sqrt[a + b]*d) + Sinh[c + d*x]/(4*a*d*(a + (a + b)*Sinh[c + d*x]^2)^2) + (3*Sinh[c + d*x])/(8*a^2*d*(a + (a + b)*Sinh[c + d*x]^2))","A",4,3,23,0.1304,1,"{3676, 199, 205}"
132,1,131,0,0.1238163,"\int \frac{\text{sech}^6(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]^6/(a + b*Tanh[c + d*x]^2)^3,x]","\frac{3 \left(\frac{1}{a^2}-\frac{1}{b^2}\right) \tanh (c+d x)}{8 d \left(a+b \tanh ^2(c+d x)\right)}+\frac{\left(3 a^2-2 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} b^{5/2} d}+\frac{(a+b) \tanh (c+d x) \text{sech}^2(c+d x)}{4 a b d \left(a+b \tanh ^2(c+d x)\right)^2}","\frac{3 \left(\frac{1}{a^2}-\frac{1}{b^2}\right) \tanh (c+d x)}{8 d \left(a+b \tanh ^2(c+d x)\right)}+\frac{\left(3 a^2-2 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} b^{5/2} d}+\frac{(a+b) \tanh (c+d x) \text{sech}^2(c+d x)}{4 a b d \left(a+b \tanh ^2(c+d x)\right)^2}",1,"((3*a^2 - 2*a*b + 3*b^2)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*b^(5/2)*d) + ((a + b)*Sech[c + d*x]^2*Tanh[c + d*x])/(4*a*b*d*(a + b*Tanh[c + d*x]^2)^2) + (3*(a^(-2) - b^(-2))*Tanh[c + d*x])/(8*d*(a + b*Tanh[c + d*x]^2))","A",4,4,23,0.1739,1,"{3675, 413, 385, 205}"
133,1,156,0,0.2279874,"\int \frac{\text{sech}^7(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]^7/(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{(4 a-3 b) (a+b) \sinh (c+d x)}{8 a^2 b^2 d \left((a+b) \sinh ^2(c+d x)+a\right)}+\frac{\sqrt{a+b} \left(8 a^2-4 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} b^3 d}+\frac{(a+b) \sinh (c+d x)}{4 a b d \left((a+b) \sinh ^2(c+d x)+a\right)^2}-\frac{\tan ^{-1}(\sinh (c+d x))}{b^3 d}","-\frac{(4 a-3 b) (a+b) \sinh (c+d x)}{8 a^2 b^2 d \left((a+b) \sinh ^2(c+d x)+a\right)}+\frac{\sqrt{a+b} \left(8 a^2-4 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a+b} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} b^3 d}+\frac{(a+b) \sinh (c+d x)}{4 a b d \left((a+b) \sinh ^2(c+d x)+a\right)^2}-\frac{\tan ^{-1}(\sinh (c+d x))}{b^3 d}",1,"-(ArcTan[Sinh[c + d*x]]/(b^3*d)) + (Sqrt[a + b]*(8*a^2 - 4*a*b + 3*b^2)*ArcTan[(Sqrt[a + b]*Sinh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*b^3*d) + ((a + b)*Sinh[c + d*x])/(4*a*b*d*(a + (a + b)*Sinh[c + d*x]^2)^2) - ((4*a - 3*b)*(a + b)*Sinh[c + d*x])/(8*a^2*b^2*d*(a + (a + b)*Sinh[c + d*x]^2))","A",6,6,23,0.2609,1,"{3676, 414, 527, 522, 203, 205}"
134,1,54,0,0.0519301,"\int \tanh ^4(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Tanh[c + d*x]^4*(a + b*Tanh[c + d*x]^2),x]","-\frac{(a+b) \tanh ^3(c+d x)}{3 d}-\frac{(a+b) \tanh (c+d x)}{d}+x (a+b)-\frac{b \tanh ^5(c+d x)}{5 d}","-\frac{(a+b) \tanh ^3(c+d x)}{3 d}-\frac{(a+b) \tanh (c+d x)}{d}+x (a+b)-\frac{b \tanh ^5(c+d x)}{5 d}",1,"(a + b)*x - ((a + b)*Tanh[c + d*x])/d - ((a + b)*Tanh[c + d*x]^3)/(3*d) - (b*Tanh[c + d*x]^5)/(5*d)","A",4,3,21,0.1429,1,"{3631, 3473, 8}"
135,1,49,0,0.0594662,"\int \tanh ^3(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Tanh[c + d*x]^3*(a + b*Tanh[c + d*x]^2),x]","-\frac{(a+b) \tanh ^2(c+d x)}{2 d}+\frac{(a+b) \log (\cosh (c+d x))}{d}-\frac{b \tanh ^4(c+d x)}{4 d}","-\frac{(a+b) \tanh ^2(c+d x)}{2 d}+\frac{(a+b) \log (\cosh (c+d x))}{d}-\frac{b \tanh ^4(c+d x)}{4 d}",1,"((a + b)*Log[Cosh[c + d*x]])/d - ((a + b)*Tanh[c + d*x]^2)/(2*d) - (b*Tanh[c + d*x]^4)/(4*d)","A",3,3,21,0.1429,1,"{3631, 3473, 3475}"
136,1,36,0,0.0396052,"\int \tanh ^2(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Tanh[c + d*x]^2*(a + b*Tanh[c + d*x]^2),x]","-\frac{(a+b) \tanh (c+d x)}{d}+x (a+b)-\frac{b \tanh ^3(c+d x)}{3 d}","-\frac{(a+b) \tanh (c+d x)}{d}+x (a+b)-\frac{b \tanh ^3(c+d x)}{3 d}",1,"(a + b)*x - ((a + b)*Tanh[c + d*x])/d - (b*Tanh[c + d*x]^3)/(3*d)","A",3,3,21,0.1429,1,"{3631, 3473, 8}"
137,1,31,0,0.0319005,"\int \tanh (c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Tanh[c + d*x]*(a + b*Tanh[c + d*x]^2),x]","\frac{(a+b) \log (\cosh (c+d x))}{d}-\frac{b \tanh ^2(c+d x)}{2 d}","\frac{(a+b) \log (\cosh (c+d x))}{d}-\frac{b \tanh ^2(c+d x)}{2 d}",1,"((a + b)*Log[Cosh[c + d*x]])/d - (b*Tanh[c + d*x]^2)/(2*d)","A",2,2,19,0.1053,1,"{3631, 3475}"
138,1,19,0,0.0132686,"\int \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[a + b*Tanh[c + d*x]^2,x]","a x-\frac{b \tanh (c+d x)}{d}+b x","a x-\frac{b \tanh (c+d x)}{d}+b x",1,"a*x + b*x - (b*Tanh[c + d*x])/d","A",3,2,12,0.1667,1,"{3473, 8}"
139,1,25,0,0.0412611,"\int \coth (c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Coth[c + d*x]*(a + b*Tanh[c + d*x]^2),x]","\frac{a \log (\sinh (c+d x))}{d}+\frac{b \log (\cosh (c+d x))}{d}","\frac{a \log (\sinh (c+d x))}{d}+\frac{b \log (\cosh (c+d x))}{d}",1,"(b*Log[Cosh[c + d*x]])/d + (a*Log[Sinh[c + d*x]])/d","A",3,2,19,0.1053,1,"{3625, 3475}"
140,1,18,0,0.0290586,"\int \coth ^2(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Coth[c + d*x]^2*(a + b*Tanh[c + d*x]^2),x]","x (a+b)-\frac{a \coth (c+d x)}{d}","x (a+b)-\frac{a \coth (c+d x)}{d}",1,"(a + b)*x - (a*Coth[c + d*x])/d","A",2,2,21,0.09524,1,"{3629, 8}"
141,1,31,0,0.0424706,"\int \coth ^3(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Coth[c + d*x]^3*(a + b*Tanh[c + d*x]^2),x]","\frac{(a+b) \log (\sinh (c+d x))}{d}-\frac{a \coth ^2(c+d x)}{2 d}","\frac{(a+b) \log (\sinh (c+d x))}{d}-\frac{a \coth ^2(c+d x)}{2 d}",1,"-(a*Coth[c + d*x]^2)/(2*d) + ((a + b)*Log[Sinh[c + d*x]])/d","A",3,3,21,0.1429,1,"{3629, 12, 3475}"
142,1,36,0,0.038836,"\int \coth ^4(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Coth[c + d*x]^4*(a + b*Tanh[c + d*x]^2),x]","-\frac{(a+b) \coth (c+d x)}{d}+x (a+b)-\frac{a \coth ^3(c+d x)}{3 d}","-\frac{(a+b) \coth (c+d x)}{d}+x (a+b)-\frac{a \coth ^3(c+d x)}{3 d}",1,"(a + b)*x - ((a + b)*Coth[c + d*x])/d - (a*Coth[c + d*x]^3)/(3*d)","A",4,4,21,0.1905,1,"{3629, 12, 3473, 8}"
143,1,49,0,0.0618572,"\int \coth ^5(c+d x) \left(a+b \tanh ^2(c+d x)\right) \, dx","Int[Coth[c + d*x]^5*(a + b*Tanh[c + d*x]^2),x]","-\frac{(a+b) \coth ^2(c+d x)}{2 d}+\frac{(a+b) \log (\sinh (c+d x))}{d}-\frac{a \coth ^4(c+d x)}{4 d}","-\frac{(a+b) \coth ^2(c+d x)}{2 d}+\frac{(a+b) \log (\sinh (c+d x))}{d}-\frac{a \coth ^4(c+d x)}{4 d}",1,"-((a + b)*Coth[c + d*x]^2)/(2*d) - (a*Coth[c + d*x]^4)/(4*d) + ((a + b)*Log[Sinh[c + d*x]])/d","A",4,4,21,0.1905,1,"{3629, 12, 3473, 3475}"
144,1,83,0,0.0788679,"\int \tanh ^4(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Tanh[c + d*x]^4*(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{b (2 a+b) \tanh ^5(c+d x)}{5 d}-\frac{(a+b)^2 \tanh ^3(c+d x)}{3 d}-\frac{(a+b)^2 \tanh (c+d x)}{d}+x (a+b)^2-\frac{b^2 \tanh ^7(c+d x)}{7 d}","-\frac{b (2 a+b) \tanh ^5(c+d x)}{5 d}-\frac{(a+b)^2 \tanh ^3(c+d x)}{3 d}-\frac{(a+b)^2 \tanh (c+d x)}{d}+x (a+b)^2-\frac{b^2 \tanh ^7(c+d x)}{7 d}",1,"(a + b)^2*x - ((a + b)^2*Tanh[c + d*x])/d - ((a + b)^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,"{3670, 461, 206}"
145,1,76,0,0.1096302,"\int \tanh ^3(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Tanh[c + d*x]^3*(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{b (2 a+b) \tanh ^4(c+d x)}{4 d}-\frac{(a+b)^2 \tanh ^2(c+d x)}{2 d}+\frac{(a+b)^2 \log (\cosh (c+d x))}{d}-\frac{b^2 \tanh ^6(c+d x)}{6 d}","-\frac{b (2 a+b) \tanh ^4(c+d x)}{4 d}-\frac{(a+b)^2 \tanh ^2(c+d x)}{2 d}+\frac{(a+b)^2 \log (\cosh (c+d x))}{d}-\frac{b^2 \tanh ^6(c+d x)}{6 d}",1,"((a + b)^2*Log[Cosh[c + d*x]])/d - ((a + b)^2*Tanh[c + d*x]^2)/(2*d) - (b*(2*a + b)*Tanh[c + d*x]^4)/(4*d) - (b^2*Tanh[c + d*x]^6)/(6*d)","A",4,3,23,0.1304,1,"{3670, 446, 77}"
146,1,63,0,0.0755494,"\int \tanh ^2(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Tanh[c + d*x]^2*(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{b (2 a+b) \tanh ^3(c+d x)}{3 d}-\frac{(a+b)^2 \tanh (c+d x)}{d}+x (a+b)^2-\frac{b^2 \tanh ^5(c+d x)}{5 d}","-\frac{b (2 a+b) \tanh ^3(c+d x)}{3 d}-\frac{(a+b)^2 \tanh (c+d x)}{d}+x (a+b)^2-\frac{b^2 \tanh ^5(c+d x)}{5 d}",1,"(a + b)^2*x - ((a + b)^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,"{3670, 461, 206}"
147,1,57,0,0.0733014,"\int \tanh (c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Tanh[c + d*x]*(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{b (a+b) \tanh ^2(c+d x)}{2 d}-\frac{\left(a+b \tanh ^2(c+d x)\right)^2}{4 d}+\frac{(a+b)^2 \log (\cosh (c+d x))}{d}","-\frac{b (a+b) \tanh ^2(c+d x)}{2 d}-\frac{\left(a+b \tanh ^2(c+d x)\right)^2}{4 d}+\frac{(a+b)^2 \log (\cosh (c+d x))}{d}",1,"((a + b)^2*Log[Cosh[c + d*x]])/d - (b*(a + b)*Tanh[c + d*x]^2)/(2*d) - (a + b*Tanh[c + d*x]^2)^2/(4*d)","A",4,3,21,0.1429,1,"{3670, 444, 43}"
148,1,43,0,0.0314103,"\int \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{b (2 a+b) \tanh (c+d x)}{d}+x (a+b)^2-\frac{b^2 \tanh ^3(c+d x)}{3 d}","-\frac{b (2 a+b) \tanh (c+d x)}{d}+x (a+b)^2-\frac{b^2 \tanh ^3(c+d x)}{3 d}",1,"(a + b)^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,"{3661, 390, 206}"
149,1,49,0,0.0769667,"\int \coth (c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Coth[c + d*x]*(a + b*Tanh[c + d*x]^2)^2,x]","\frac{a^2 \log (\tanh (c+d x))}{d}+\frac{(a+b)^2 \log (\cosh (c+d x))}{d}-\frac{b^2 \tanh ^2(c+d x)}{2 d}","\frac{a^2 \log (\tanh (c+d x))}{d}+\frac{(a+b)^2 \log (\cosh (c+d x))}{d}-\frac{b^2 \tanh ^2(c+d x)}{2 d}",1,"((a + b)^2*Log[Cosh[c + d*x]])/d + (a^2*Log[Tanh[c + d*x]])/d - (b^2*Tanh[c + d*x]^2)/(2*d)","A",4,3,21,0.1429,1,"{3670, 446, 72}"
150,1,36,0,0.0671894,"\int \coth ^2(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Coth[c + d*x]^2*(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{a^2 \coth (c+d x)}{d}+x (a+b)^2-\frac{b^2 \tanh (c+d x)}{d}","-\frac{a^2 \coth (c+d x)}{d}+x (a+b)^2-\frac{b^2 \tanh (c+d x)}{d}",1,"(a + b)^2*x - (a^2*Coth[c + d*x])/d - (b^2*Tanh[c + d*x])/d","A",4,3,23,0.1304,1,"{3670, 461, 207}"
151,1,52,0,0.0947188,"\int \coth ^3(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Coth[c + d*x]^3*(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{a^2 \coth ^2(c+d x)}{2 d}+\frac{a (a+2 b) \log (\tanh (c+d x))}{d}+\frac{(a+b)^2 \log (\cosh (c+d x))}{d}","-\frac{a^2 \coth ^2(c+d x)}{2 d}+\frac{a (a+2 b) \log (\tanh (c+d x))}{d}+\frac{(a+b)^2 \log (\cosh (c+d x))}{d}",1,"-(a^2*Coth[c + d*x]^2)/(2*d) + ((a + b)^2*Log[Cosh[c + d*x]])/d + (a*(a + 2*b)*Log[Tanh[c + d*x]])/d","A",4,3,23,0.1304,1,"{3670, 446, 88}"
152,1,43,0,0.0714495,"\int \coth ^4(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Coth[c + d*x]^4*(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{a^2 \coth ^3(c+d x)}{3 d}-\frac{a (a+2 b) \coth (c+d x)}{d}+x (a+b)^2","-\frac{a^2 \coth ^3(c+d x)}{3 d}-\frac{a (a+2 b) \coth (c+d x)}{d}+x (a+b)^2",1,"(a + b)^2*x - (a*(a + 2*b)*Coth[c + d*x])/d - (a^2*Coth[c + d*x]^3)/(3*d)","A",4,3,23,0.1304,1,"{3670, 461, 207}"
153,1,72,0,0.0988802,"\int \coth ^5(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Coth[c + d*x]^5*(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{a^2 \coth ^4(c+d x)}{4 d}-\frac{a (a+2 b) \coth ^2(c+d x)}{2 d}+\frac{(a+b)^2 \log (\tanh (c+d x))}{d}+\frac{(a+b)^2 \log (\cosh (c+d x))}{d}","-\frac{a^2 \coth ^4(c+d x)}{4 d}-\frac{a (a+2 b) \coth ^2(c+d x)}{2 d}+\frac{(a+b)^2 \log (\tanh (c+d x))}{d}+\frac{(a+b)^2 \log (\cosh (c+d x))}{d}",1,"-(a*(a + 2*b)*Coth[c + d*x]^2)/(2*d) - (a^2*Coth[c + d*x]^4)/(4*d) + ((a + b)^2*Log[Cosh[c + d*x]])/d + ((a + b)^2*Log[Tanh[c + d*x]])/d","A",4,3,23,0.1304,1,"{3670, 446, 88}"
154,1,63,0,0.0771258,"\int \coth ^6(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Coth[c + d*x]^6*(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{a^2 \coth ^5(c+d x)}{5 d}-\frac{a (a+2 b) \coth ^3(c+d x)}{3 d}-\frac{(a+b)^2 \coth (c+d x)}{d}+x (a+b)^2","-\frac{a^2 \coth ^5(c+d x)}{5 d}-\frac{a (a+2 b) \coth ^3(c+d x)}{3 d}-\frac{(a+b)^2 \coth (c+d x)}{d}+x (a+b)^2",1,"(a + b)^2*x - ((a + b)^2*Coth[c + d*x])/d - (a*(a + 2*b)*Coth[c + d*x]^3)/(3*d) - (a^2*Coth[c + d*x]^5)/(5*d)","A",4,3,23,0.1304,1,"{3670, 461, 207}"
155,1,92,0,0.1130832,"\int \coth ^7(c+d x) \left(a+b \tanh ^2(c+d x)\right)^2 \, dx","Int[Coth[c + d*x]^7*(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{a^2 \coth ^6(c+d x)}{6 d}-\frac{a (a+2 b) \coth ^4(c+d x)}{4 d}-\frac{(a+b)^2 \coth ^2(c+d x)}{2 d}+\frac{(a+b)^2 \log (\tanh (c+d x))}{d}+\frac{(a+b)^2 \log (\cosh (c+d x))}{d}","-\frac{a^2 \coth ^6(c+d x)}{6 d}-\frac{a (a+2 b) \coth ^4(c+d x)}{4 d}-\frac{(a+b)^2 \coth ^2(c+d x)}{2 d}+\frac{(a+b)^2 \log (\tanh (c+d x))}{d}+\frac{(a+b)^2 \log (\cosh (c+d x))}{d}",1,"-((a + b)^2*Coth[c + d*x]^2)/(2*d) - (a*(a + 2*b)*Coth[c + d*x]^4)/(4*d) - (a^2*Coth[c + d*x]^6)/(6*d) + ((a + b)^2*Log[Cosh[c + d*x]])/d + ((a + b)^2*Log[Tanh[c + d*x]])/d","A",4,3,23,0.1304,1,"{3670, 446, 88}"
156,1,114,0,0.1005231,"\int \tanh ^4(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Tanh[c + d*x]^4*(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{b \left(3 a^2+3 a b+b^2\right) \tanh ^5(c+d x)}{5 d}-\frac{b^2 (3 a+b) \tanh ^7(c+d x)}{7 d}-\frac{(a+b)^3 \tanh ^3(c+d x)}{3 d}-\frac{(a+b)^3 \tanh (c+d x)}{d}+x (a+b)^3-\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{b^2 (3 a+b) \tanh ^7(c+d x)}{7 d}-\frac{(a+b)^3 \tanh ^3(c+d x)}{3 d}-\frac{(a+b)^3 \tanh (c+d x)}{d}+x (a+b)^3-\frac{b^3 \tanh ^9(c+d x)}{9 d}",1,"(a + b)^3*x - ((a + b)^3*Tanh[c + d*x])/d - ((a + b)^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 + b)*Tanh[c + d*x]^7)/(7*d) - (b^3*Tanh[c + d*x]^9)/(9*d)","A",4,3,23,0.1304,1,"{3670, 461, 206}"
157,1,107,0,0.1522961,"\int \tanh ^3(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Tanh[c + d*x]^3*(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{b \left(3 a^2+3 a b+b^2\right) \tanh ^4(c+d x)}{4 d}-\frac{b^2 (3 a+b) \tanh ^6(c+d x)}{6 d}-\frac{(a+b)^3 \tanh ^2(c+d x)}{2 d}+\frac{(a+b)^3 \log (\cosh (c+d x))}{d}-\frac{b^3 \tanh ^8(c+d x)}{8 d}","-\frac{b \left(3 a^2+3 a b+b^2\right) \tanh ^4(c+d x)}{4 d}-\frac{b^2 (3 a+b) \tanh ^6(c+d x)}{6 d}-\frac{(a+b)^3 \tanh ^2(c+d x)}{2 d}+\frac{(a+b)^3 \log (\cosh (c+d x))}{d}-\frac{b^3 \tanh ^8(c+d x)}{8 d}",1,"((a + b)^3*Log[Cosh[c + d*x]])/d - ((a + b)^3*Tanh[c + d*x]^2)/(2*d) - (b*(3*a^2 + 3*a*b + b^2)*Tanh[c + d*x]^4)/(4*d) - (b^2*(3*a + b)*Tanh[c + d*x]^6)/(6*d) - (b^3*Tanh[c + d*x]^8)/(8*d)","A",4,3,23,0.1304,1,"{3670, 446, 77}"
158,1,94,0,0.0927085,"\int \tanh ^2(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Tanh[c + d*x]^2*(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{b \left(3 a^2+3 a b+b^2\right) \tanh ^3(c+d x)}{3 d}-\frac{b^2 (3 a+b) \tanh ^5(c+d x)}{5 d}-\frac{(a+b)^3 \tanh (c+d x)}{d}+x (a+b)^3-\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{b^2 (3 a+b) \tanh ^5(c+d x)}{5 d}-\frac{(a+b)^3 \tanh (c+d x)}{d}+x (a+b)^3-\frac{b^3 \tanh ^7(c+d x)}{7 d}",1,"(a + b)^3*x - ((a + b)^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 + b)*Tanh[c + d*x]^5)/(5*d) - (b^3*Tanh[c + d*x]^7)/(7*d)","A",4,3,23,0.1304,1,"{3670, 461, 206}"
159,1,83,0,0.1014411,"\int \tanh (c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Tanh[c + d*x]*(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{b (a+b)^2 \tanh ^2(c+d x)}{2 d}-\frac{(a+b) \left(a+b \tanh ^2(c+d x)\right)^2}{4 d}-\frac{\left(a+b \tanh ^2(c+d x)\right)^3}{6 d}+\frac{(a+b)^3 \log (\cosh (c+d x))}{d}","-\frac{b (a+b)^2 \tanh ^2(c+d x)}{2 d}-\frac{(a+b) \left(a+b \tanh ^2(c+d x)\right)^2}{4 d}-\frac{\left(a+b \tanh ^2(c+d x)\right)^3}{6 d}+\frac{(a+b)^3 \log (\cosh (c+d x))}{d}",1,"((a + b)^3*Log[Cosh[c + d*x]])/d - (b*(a + b)^2*Tanh[c + d*x]^2)/(2*d) - ((a + b)*(a + b*Tanh[c + d*x]^2)^2)/(4*d) - (a + b*Tanh[c + d*x]^2)^3/(6*d)","A",4,3,21,0.1429,1,"{3670, 444, 43}"
160,1,74,0,0.0458704,"\int \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{b \left(3 a^2+3 a b+b^2\right) \tanh (c+d x)}{d}-\frac{b^2 (3 a+b) \tanh ^3(c+d x)}{3 d}+x (a+b)^3-\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}-\frac{b^2 (3 a+b) \tanh ^3(c+d x)}{3 d}+x (a+b)^3-\frac{b^3 \tanh ^5(c+d x)}{5 d}",1,"(a + b)^3*x - (b*(3*a^2 + 3*a*b + b^2)*Tanh[c + d*x])/d - (b^2*(3*a + b)*Tanh[c + d*x]^3)/(3*d) - (b^3*Tanh[c + d*x]^5)/(5*d)","A",4,3,14,0.2143,1,"{3661, 390, 206}"
161,1,72,0,0.0984251,"\int \coth (c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Coth[c + d*x]*(a + b*Tanh[c + d*x]^2)^3,x]","\frac{a^3 \log (\tanh (c+d x))}{d}-\frac{b^2 (3 a+b) \tanh ^2(c+d x)}{2 d}+\frac{(a+b)^3 \log (\cosh (c+d x))}{d}-\frac{b^3 \tanh ^4(c+d x)}{4 d}","\frac{a^3 \log (\tanh (c+d x))}{d}-\frac{b^2 (3 a+b) \tanh ^2(c+d x)}{2 d}+\frac{(a+b)^3 \log (\cosh (c+d x))}{d}-\frac{b^3 \tanh ^4(c+d x)}{4 d}",1,"((a + b)^3*Log[Cosh[c + d*x]])/d + (a^3*Log[Tanh[c + d*x]])/d - (b^2*(3*a + b)*Tanh[c + d*x]^2)/(2*d) - (b^3*Tanh[c + d*x]^4)/(4*d)","A",4,3,21,0.1429,1,"{3670, 446, 72}"
162,1,59,0,0.0800658,"\int \coth ^2(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Coth[c + d*x]^2*(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{a^3 \coth (c+d x)}{d}-\frac{b^2 (3 a+b) \tanh (c+d x)}{d}+x (a+b)^3-\frac{b^3 \tanh ^3(c+d x)}{3 d}","-\frac{a^3 \coth (c+d x)}{d}-\frac{b^2 (3 a+b) \tanh (c+d x)}{d}+x (a+b)^3-\frac{b^3 \tanh ^3(c+d x)}{3 d}",1,"(a + b)^3*x - (a^3*Coth[c + d*x])/d - (b^2*(3*a + b)*Tanh[c + d*x])/d - (b^3*Tanh[c + d*x]^3)/(3*d)","A",4,3,23,0.1304,1,"{3670, 461, 207}"
163,1,72,0,0.1084806,"\int \coth ^3(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Coth[c + d*x]^3*(a + b*Tanh[c + d*x]^2)^3,x]","\frac{a^2 (a+3 b) \log (\tanh (c+d x))}{d}-\frac{a^3 \coth ^2(c+d x)}{2 d}+\frac{(a+b)^3 \log (\cosh (c+d x))}{d}-\frac{b^3 \tanh ^2(c+d x)}{2 d}","\frac{a^2 (a+3 b) \log (\tanh (c+d x))}{d}-\frac{a^3 \coth ^2(c+d x)}{2 d}+\frac{(a+b)^3 \log (\cosh (c+d x))}{d}-\frac{b^3 \tanh ^2(c+d x)}{2 d}",1,"-(a^3*Coth[c + d*x]^2)/(2*d) + ((a + b)^3*Log[Cosh[c + d*x]])/d + (a^2*(a + 3*b)*Log[Tanh[c + d*x]])/d - (b^3*Tanh[c + d*x]^2)/(2*d)","A",4,3,23,0.1304,1,"{3670, 446, 88}"
164,1,59,0,0.0812287,"\int \coth ^4(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Coth[c + d*x]^4*(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{a^2 (a+3 b) \coth (c+d x)}{d}-\frac{a^3 \coth ^3(c+d x)}{3 d}+x (a+b)^3-\frac{b^3 \tanh (c+d x)}{d}","-\frac{a^2 (a+3 b) \coth (c+d x)}{d}-\frac{a^3 \coth ^3(c+d x)}{3 d}+x (a+b)^3-\frac{b^3 \tanh (c+d x)}{d}",1,"(a + b)^3*x - (a^2*(a + 3*b)*Coth[c + d*x])/d - (a^3*Coth[c + d*x]^3)/(3*d) - (b^3*Tanh[c + d*x])/d","A",4,3,23,0.1304,1,"{3670, 461, 207}"
165,1,83,0,0.1173357,"\int \coth ^5(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Coth[c + d*x]^5*(a + b*Tanh[c + d*x]^2)^3,x]","\frac{a \left(a^2+3 a b+3 b^2\right) \log (\tanh (c+d x))}{d}-\frac{a^2 (a+3 b) \coth ^2(c+d x)}{2 d}-\frac{a^3 \coth ^4(c+d x)}{4 d}+\frac{(a+b)^3 \log (\cosh (c+d x))}{d}","\frac{a \left(a^2+3 a b+3 b^2\right) \log (\tanh (c+d x))}{d}-\frac{a^2 (a+3 b) \coth ^2(c+d x)}{2 d}-\frac{a^3 \coth ^4(c+d x)}{4 d}+\frac{(a+b)^3 \log (\cosh (c+d x))}{d}",1,"-(a^2*(a + 3*b)*Coth[c + d*x]^2)/(2*d) - (a^3*Coth[c + d*x]^4)/(4*d) + ((a + b)^3*Log[Cosh[c + d*x]])/d + (a*(a^2 + 3*a*b + 3*b^2)*Log[Tanh[c + d*x]])/d","A",4,3,23,0.1304,1,"{3670, 446, 88}"
166,1,74,0,0.088843,"\int \coth ^6(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Coth[c + d*x]^6*(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{a \left(a^2+3 a b+3 b^2\right) \coth (c+d x)}{d}-\frac{a^2 (a+3 b) \coth ^3(c+d x)}{3 d}-\frac{a^3 \coth ^5(c+d x)}{5 d}+x (a+b)^3","-\frac{a \left(a^2+3 a b+3 b^2\right) \coth (c+d x)}{d}-\frac{a^2 (a+3 b) \coth ^3(c+d x)}{3 d}-\frac{a^3 \coth ^5(c+d x)}{5 d}+x (a+b)^3",1,"(a + b)^3*x - (a*(a^2 + 3*a*b + 3*b^2)*Coth[c + d*x])/d - (a^2*(a + 3*b)*Coth[c + d*x]^3)/(3*d) - (a^3*Coth[c + d*x]^5)/(5*d)","A",4,3,23,0.1304,1,"{3670, 461, 207}"
167,1,103,0,0.1289685,"\int \coth ^7(c+d x) \left(a+b \tanh ^2(c+d x)\right)^3 \, dx","Int[Coth[c + d*x]^7*(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{a \left(a^2+3 a b+3 b^2\right) \coth ^2(c+d x)}{2 d}-\frac{a^2 (a+3 b) \coth ^4(c+d x)}{4 d}-\frac{a^3 \coth ^6(c+d x)}{6 d}+\frac{(a+b)^3 \log (\tanh (c+d x))}{d}+\frac{(a+b)^3 \log (\cosh (c+d x))}{d}","-\frac{a \left(a^2+3 a b+3 b^2\right) \coth ^2(c+d x)}{2 d}-\frac{a^2 (a+3 b) \coth ^4(c+d x)}{4 d}-\frac{a^3 \coth ^6(c+d x)}{6 d}+\frac{(a+b)^3 \log (\tanh (c+d x))}{d}+\frac{(a+b)^3 \log (\cosh (c+d x))}{d}",1,"-(a*(a^2 + 3*a*b + 3*b^2)*Coth[c + d*x]^2)/(2*d) - (a^2*(a + 3*b)*Coth[c + d*x]^4)/(4*d) - (a^3*Coth[c + d*x]^6)/(6*d) + ((a + b)^3*Log[Cosh[c + d*x]])/d + ((a + b)^3*Log[Tanh[c + d*x]])/d","A",4,3,23,0.1304,1,"{3670, 446, 88}"
168,1,110,0,0.070031,"\int \left(a+b \tanh ^2(c+d x)\right)^4 \, dx","Int[(a + b*Tanh[c + d*x]^2)^4,x]","-\frac{b^2 \left(6 a^2+4 a b+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}-\frac{b^3 (4 a+b) \tanh ^5(c+d x)}{5 d}+x (a+b)^4-\frac{b^4 \tanh ^7(c+d x)}{7 d}","-\frac{b^2 \left(6 a^2+4 a b+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}-\frac{b^3 (4 a+b) \tanh ^5(c+d x)}{5 d}+x (a+b)^4-\frac{b^4 \tanh ^7(c+d x)}{7 d}",1,"(a + b)^4*x - (b*(2*a + b)*(2*a^2 + 2*a*b + b^2)*Tanh[c + d*x])/d - (b^2*(6*a^2 + 4*a*b + b^2)*Tanh[c + d*x]^3)/(3*d) - (b^3*(4*a + b)*Tanh[c + d*x]^5)/(5*d) - (b^4*Tanh[c + d*x]^7)/(7*d)","A",4,3,14,0.2143,1,"{3661, 390, 206}"
169,1,160,0,0.0942217,"\int \left(a+b \tanh ^2(c+d x)\right)^5 \, dx","Int[(a + b*Tanh[c + d*x]^2)^5,x]","-\frac{b^3 \left(10 a^2+5 a b+b^2\right) \tanh ^5(c+d x)}{5 d}-\frac{b^2 \left(10 a^2 b+10 a^3+5 a b^2+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}-\frac{b^4 (5 a+b) \tanh ^7(c+d x)}{7 d}+x (a+b)^5-\frac{b^5 \tanh ^9(c+d x)}{9 d}","-\frac{b^3 \left(10 a^2+5 a b+b^2\right) \tanh ^5(c+d x)}{5 d}-\frac{b^2 \left(10 a^2 b+10 a^3+5 a b^2+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}-\frac{b^4 (5 a+b) \tanh ^7(c+d x)}{7 d}+x (a+b)^5-\frac{b^5 \tanh ^9(c+d x)}{9 d}",1,"(a + b)^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 + 10*a^2*b + 5*a*b^2 + b^3)*Tanh[c + d*x]^3)/(3*d) - (b^3*(10*a^2 + 5*a*b + b^2)*Tanh[c + d*x]^5)/(5*d) - (b^4*(5*a + b)*Tanh[c + d*x]^7)/(7*d) - (b^5*Tanh[c + d*x]^9)/(9*d)","A",4,3,14,0.2143,1,"{3661, 390, 206}"
170,1,66,0,0.1145798,"\int \frac{\tanh ^5(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Tanh[c + d*x]^5/(a + b*Tanh[c + d*x]^2),x]","\frac{a^2 \log \left(a+b \tanh ^2(c+d x)\right)}{2 b^2 d (a+b)}+\frac{\log (\cosh (c+d x))}{d (a+b)}-\frac{\tanh ^2(c+d x)}{2 b d}","\frac{a^2 \log \left(a+b \tanh ^2(c+d x)\right)}{2 b^2 d (a+b)}+\frac{\log (\cosh (c+d x))}{d (a+b)}-\frac{\tanh ^2(c+d x)}{2 b d}",1,"Log[Cosh[c + d*x]]/((a + b)*d) + (a^2*Log[a + b*Tanh[c + d*x]^2])/(2*b^2*(a + b)*d) - Tanh[c + d*x]^2/(2*b*d)","A",4,3,23,0.1304,1,"{3670, 446, 72}"
171,1,59,0,0.1079301,"\int \frac{\tanh ^4(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Tanh[c + d*x]^4/(a + b*Tanh[c + d*x]^2),x]","\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{b^{3/2} d (a+b)}+\frac{x}{a+b}-\frac{\tanh (c+d x)}{b d}","\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{b^{3/2} d (a+b)}+\frac{x}{a+b}-\frac{\tanh (c+d x)}{b d}",1,"x/(a + b) + (a^(3/2)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(b^(3/2)*(a + b)*d) - Tanh[c + d*x]/(b*d)","A",5,5,23,0.2174,1,"{3670, 479, 522, 206, 205}"
172,1,46,0,0.1036522,"\int \frac{\tanh ^3(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Tanh[c + d*x]^3/(a + b*Tanh[c + d*x]^2),x]","\frac{\log (\cosh (c+d x))}{d (a+b)}-\frac{a \log \left(a+b \tanh ^2(c+d x)\right)}{2 b d (a+b)}","\frac{\log (\cosh (c+d x))}{d (a+b)}-\frac{a \log \left(a+b \tanh ^2(c+d x)\right)}{2 b d (a+b)}",1,"Log[Cosh[c + d*x]]/((a + b)*d) - (a*Log[a + b*Tanh[c + d*x]^2])/(2*b*(a + b)*d)","A",4,3,23,0.1304,1,"{3670, 446, 72}"
173,1,46,0,0.083218,"\int \frac{\tanh ^2(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Tanh[c + d*x]^2/(a + b*Tanh[c + d*x]^2),x]","\frac{x}{a+b}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{b} d (a+b)}","\frac{x}{a+b}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{b} d (a+b)}",1,"x/(a + b) - (Sqrt[a]*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(Sqrt[b]*(a + b)*d)","A",4,4,23,0.1739,1,"{3670, 481, 206, 205}"
174,1,42,0,0.0612942,"\int \frac{\tanh (c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Tanh[c + d*x]/(a + b*Tanh[c + d*x]^2),x]","\frac{\log \left(a+b \tanh ^2(c+d x)\right)}{2 d (a+b)}+\frac{\log (\cosh (c+d x))}{d (a+b)}","\frac{\log \left(a+b \tanh ^2(c+d x)\right)}{2 d (a+b)}+\frac{\log (\cosh (c+d x))}{d (a+b)}",1,"Log[Cosh[c + d*x]]/((a + b)*d) + Log[a + b*Tanh[c + d*x]^2]/(2*(a + b)*d)","A",5,4,21,0.1905,1,"{3670, 444, 36, 31}"
175,1,45,0,0.0740487,"\int \frac{1}{a+b \tanh ^2(c+d x)} \, dx","Int[(a + b*Tanh[c + d*x]^2)^(-1),x]","\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a+b)}+\frac{x}{a+b}","\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a+b)}+\frac{x}{a+b}",1,"x/(a + b) + (Sqrt[b]*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(Sqrt[a]*(a + b)*d)","A",3,3,14,0.2143,1,"{3660, 3675, 205}"
176,1,60,0,0.1014971,"\int \frac{\coth (c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Coth[c + d*x]/(a + b*Tanh[c + d*x]^2),x]","-\frac{b \log \left(a+b \tanh ^2(c+d x)\right)}{2 a d (a+b)}+\frac{\log (\cosh (c+d x))}{d (a+b)}+\frac{\log (\tanh (c+d x))}{a d}","-\frac{b \log \left(a+b \tanh ^2(c+d x)\right)}{2 a d (a+b)}+\frac{\log (\cosh (c+d x))}{d (a+b)}+\frac{\log (\tanh (c+d x))}{a d}",1,"Log[Cosh[c + d*x]]/((a + b)*d) + Log[Tanh[c + d*x]]/(a*d) - (b*Log[a + b*Tanh[c + d*x]^2])/(2*a*(a + b)*d)","A",4,3,21,0.1429,1,"{3670, 446, 72}"
177,1,60,0,0.1061309,"\int \frac{\coth ^2(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Coth[c + d*x]^2/(a + b*Tanh[c + d*x]^2),x]","-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{a^{3/2} d (a+b)}+\frac{x}{a+b}-\frac{\coth (c+d x)}{a d}","-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{a^{3/2} d (a+b)}+\frac{x}{a+b}-\frac{\coth (c+d x)}{a d}",1,"x/(a + b) - (b^(3/2)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(a^(3/2)*(a + b)*d) - Coth[c + d*x]/(a*d)","A",5,5,23,0.2174,1,"{3670, 480, 522, 206, 205}"
178,1,85,0,0.1372221,"\int \frac{\coth ^3(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Coth[c + d*x]^3/(a + b*Tanh[c + d*x]^2),x]","\frac{b^2 \log \left(a+b \tanh ^2(c+d x)\right)}{2 a^2 d (a+b)}+\frac{(a-b) \log (\tanh (c+d x))}{a^2 d}+\frac{\log (\cosh (c+d x))}{d (a+b)}-\frac{\coth ^2(c+d x)}{2 a d}","\frac{b^2 \log \left(a+b \tanh ^2(c+d x)\right)}{2 a^2 d (a+b)}+\frac{(a-b) \log (\tanh (c+d x))}{a^2 d}+\frac{\log (\cosh (c+d x))}{d (a+b)}-\frac{\coth ^2(c+d x)}{2 a d}",1,"-Coth[c + d*x]^2/(2*a*d) + Log[Cosh[c + d*x]]/((a + b)*d) + ((a - b)*Log[Tanh[c + d*x]])/(a^2*d) + (b^2*Log[a + b*Tanh[c + d*x]^2])/(2*a^2*(a + b)*d)","A",4,3,23,0.1304,1,"{3670, 446, 72}"
179,1,82,0,0.1772027,"\int \frac{\coth ^4(c+d x)}{a+b \tanh ^2(c+d x)} \, dx","Int[Coth[c + d*x]^4/(a + b*Tanh[c + d*x]^2),x]","\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{a^{5/2} d (a+b)}-\frac{(a-b) \coth (c+d x)}{a^2 d}+\frac{x}{a+b}-\frac{\coth ^3(c+d x)}{3 a d}","\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{a^{5/2} d (a+b)}-\frac{(a-b) \coth (c+d x)}{a^2 d}+\frac{x}{a+b}-\frac{\coth ^3(c+d x)}{3 a d}",1,"x/(a + b) + (b^(5/2)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(a^(5/2)*(a + b)*d) - ((a - b)*Coth[c + d*x])/(a^2*d) - Coth[c + d*x]^3/(3*a*d)","A",6,6,23,0.2609,1,"{3670, 480, 583, 522, 206, 205}"
180,1,83,0,0.1500872,"\int \frac{\tanh ^5(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Tanh[c + d*x]^5/(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{a^2}{2 b^2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)}-\frac{a (a+2 b) \log \left(a+b \tanh ^2(c+d x)\right)}{2 b^2 d (a+b)^2}+\frac{\log (\cosh (c+d x))}{d (a+b)^2}","-\frac{a^2}{2 b^2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)}-\frac{a (a+2 b) \log \left(a+b \tanh ^2(c+d x)\right)}{2 b^2 d (a+b)^2}+\frac{\log (\cosh (c+d x))}{d (a+b)^2}",1,"Log[Cosh[c + d*x]]/((a + b)^2*d) - (a*(a + 2*b)*Log[a + b*Tanh[c + d*x]^2])/(2*b^2*(a + b)^2*d) - a^2/(2*b^2*(a + b)*d*(a + b*Tanh[c + d*x]^2))","A",4,3,23,0.1304,1,"{3670, 446, 88}"
181,1,89,0,0.1168312,"\int \frac{\tanh ^4(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Tanh[c + d*x]^4/(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{\sqrt{a} (a+3 b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 b^{3/2} d (a+b)^2}+\frac{a \tanh (c+d x)}{2 b d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{x}{(a+b)^2}","-\frac{\sqrt{a} (a+3 b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 b^{3/2} d (a+b)^2}+\frac{a \tanh (c+d x)}{2 b d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{x}{(a+b)^2}",1,"x/(a + b)^2 - (Sqrt[a]*(a + 3*b)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(2*b^(3/2)*(a + b)^2*d) + (a*Tanh[c + d*x])/(2*b*(a + b)*d*(a + b*Tanh[c + d*x]^2))","A",5,5,23,0.2174,1,"{3670, 470, 522, 206, 205}"
182,1,72,0,0.1182145,"\int \frac{\tanh ^3(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Tanh[c + d*x]^3/(a + b*Tanh[c + d*x]^2)^2,x]","\frac{a}{2 b d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{\log \left(a+b \tanh ^2(c+d x)\right)}{2 d (a+b)^2}+\frac{\log (\cosh (c+d x))}{d (a+b)^2}","\frac{a}{2 b d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{\log \left(a+b \tanh ^2(c+d x)\right)}{2 d (a+b)^2}+\frac{\log (\cosh (c+d x))}{d (a+b)^2}",1,"Log[Cosh[c + d*x]]/((a + b)^2*d) + Log[a + b*Tanh[c + d*x]^2]/(2*(a + b)^2*d) + a/(2*b*(a + b)*d*(a + b*Tanh[c + d*x]^2))","A",4,3,23,0.1304,1,"{3670, 446, 77}"
183,1,85,0,0.1079582,"\int \frac{\tanh ^2(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Tanh[c + d*x]^2/(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{\tanh (c+d x)}{2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)}-\frac{(a-b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} d (a+b)^2}+\frac{x}{(a+b)^2}","-\frac{\tanh (c+d x)}{2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)}-\frac{(a-b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} d (a+b)^2}+\frac{x}{(a+b)^2}",1,"x/(a + b)^2 - ((a - b)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(2*Sqrt[a]*Sqrt[b]*(a + b)^2*d) - Tanh[c + d*x]/(2*(a + b)*d*(a + b*Tanh[c + d*x]^2))","A",5,5,23,0.2174,1,"{3670, 471, 522, 206, 205}"
184,1,68,0,0.0857955,"\int \frac{\tanh (c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Tanh[c + d*x]/(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{1}{2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{\log \left(a+b \tanh ^2(c+d x)\right)}{2 d (a+b)^2}+\frac{\log (\cosh (c+d x))}{d (a+b)^2}","-\frac{1}{2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{\log \left(a+b \tanh ^2(c+d x)\right)}{2 d (a+b)^2}+\frac{\log (\cosh (c+d x))}{d (a+b)^2}",1,"Log[Cosh[c + d*x]]/((a + b)^2*d) + Log[a + b*Tanh[c + d*x]^2]/(2*(a + b)^2*d) - 1/(2*(a + b)*d*(a + b*Tanh[c + d*x]^2))","A",4,3,21,0.1429,1,"{3670, 444, 44}"
185,1,89,0,0.0882202,"\int \frac{1}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[(a + b*Tanh[c + d*x]^2)^(-2),x]","\frac{\sqrt{b} (3 a+b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a+b)^2}+\frac{b \tanh (c+d x)}{2 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{x}{(a+b)^2}","\frac{\sqrt{b} (3 a+b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a+b)^2}+\frac{b \tanh (c+d x)}{2 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{x}{(a+b)^2}",1,"x/(a + b)^2 + (Sqrt[b]*(3*a + b)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*(a + b)^2*d) + (b*Tanh[c + d*x])/(2*a*(a + b)*d*(a + b*Tanh[c + d*x]^2))","A",5,5,14,0.3571,1,"{3661, 414, 522, 206, 205}"
186,1,95,0,0.1490786,"\int \frac{\coth (c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Coth[c + d*x]/(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{b (2 a+b) \log \left(a+b \tanh ^2(c+d x)\right)}{2 a^2 d (a+b)^2}+\frac{\log (\tanh (c+d x))}{a^2 d}+\frac{b}{2 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{\log (\cosh (c+d x))}{d (a+b)^2}","-\frac{b (2 a+b) \log \left(a+b \tanh ^2(c+d x)\right)}{2 a^2 d (a+b)^2}+\frac{\log (\tanh (c+d x))}{a^2 d}+\frac{b}{2 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{\log (\cosh (c+d x))}{d (a+b)^2}",1,"Log[Cosh[c + d*x]]/((a + b)^2*d) + Log[Tanh[c + d*x]]/(a^2*d) - (b*(2*a + b)*Log[a + b*Tanh[c + d*x]^2])/(2*a^2*(a + b)^2*d) + b/(2*a*(a + b)*d*(a + b*Tanh[c + d*x]^2))","A",4,3,21,0.1429,1,"{3670, 446, 72}"
187,1,119,0,0.1940751,"\int \frac{\coth ^2(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Coth[c + d*x]^2/(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{b^{3/2} (5 a+3 b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{5/2} d (a+b)^2}-\frac{(2 a+3 b) \coth (c+d x)}{2 a^2 d (a+b)}+\frac{b \coth (c+d x)}{2 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{x}{(a+b)^2}","-\frac{b^{3/2} (5 a+3 b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{5/2} d (a+b)^2}-\frac{(2 a+3 b) \coth (c+d x)}{2 a^2 d (a+b)}+\frac{b \coth (c+d x)}{2 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{x}{(a+b)^2}",1,"x/(a + b)^2 - (b^(3/2)*(5*a + 3*b)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(2*a^(5/2)*(a + b)^2*d) - ((2*a + 3*b)*Coth[c + d*x])/(2*a^2*(a + b)*d) + (b*Coth[c + d*x])/(2*a*(a + b)*d*(a + b*Tanh[c + d*x]^2))","A",6,6,23,0.2609,1,"{3670, 472, 583, 522, 206, 205}"
188,1,124,0,0.188638,"\int \frac{\coth ^3(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Coth[c + d*x]^3/(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{b^2}{2 a^2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{b^2 (3 a+2 b) \log \left(a+b \tanh ^2(c+d x)\right)}{2 a^3 d (a+b)^2}+\frac{(a-2 b) \log (\tanh (c+d x))}{a^3 d}-\frac{\coth ^2(c+d x)}{2 a^2 d}+\frac{\log (\cosh (c+d x))}{d (a+b)^2}","-\frac{b^2}{2 a^2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{b^2 (3 a+2 b) \log \left(a+b \tanh ^2(c+d x)\right)}{2 a^3 d (a+b)^2}+\frac{(a-2 b) \log (\tanh (c+d x))}{a^3 d}-\frac{\coth ^2(c+d x)}{2 a^2 d}+\frac{\log (\cosh (c+d x))}{d (a+b)^2}",1,"-Coth[c + d*x]^2/(2*a^2*d) + Log[Cosh[c + d*x]]/((a + b)^2*d) + ((a - 2*b)*Log[Tanh[c + d*x]])/(a^3*d) + (b^2*(3*a + 2*b)*Log[a + b*Tanh[c + d*x]^2])/(2*a^3*(a + b)^2*d) - b^2/(2*a^2*(a + b)*d*(a + b*Tanh[c + d*x]^2))","A",4,3,23,0.1304,1,"{3670, 446, 88}"
189,1,159,0,0.2827773,"\int \frac{\coth ^4(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^2} \, dx","Int[Coth[c + d*x]^4/(a + b*Tanh[c + d*x]^2)^2,x]","-\frac{\left(2 a^2-2 a b-5 b^2\right) \coth (c+d x)}{2 a^3 d (a+b)}+\frac{b^{5/2} (7 a+5 b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{7/2} d (a+b)^2}-\frac{(2 a+5 b) \coth ^3(c+d x)}{6 a^2 d (a+b)}+\frac{b \coth ^3(c+d x)}{2 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{x}{(a+b)^2}","-\frac{\left(2 a^2-2 a b-5 b^2\right) \coth (c+d x)}{2 a^3 d (a+b)}+\frac{b^{5/2} (7 a+5 b) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{7/2} d (a+b)^2}-\frac{(2 a+5 b) \coth ^3(c+d x)}{6 a^2 d (a+b)}+\frac{b \coth ^3(c+d x)}{2 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)}+\frac{x}{(a+b)^2}",1,"x/(a + b)^2 + (b^(5/2)*(7*a + 5*b)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(2*a^(7/2)*(a + b)^2*d) - ((2*a^2 - 2*a*b - 5*b^2)*Coth[c + d*x])/(2*a^3*(a + b)*d) - ((2*a + 5*b)*Coth[c + d*x]^3)/(6*a^2*(a + b)*d) + (b*Coth[c + d*x]^3)/(2*a*(a + b)*d*(a + b*Tanh[c + d*x]^2))","A",7,6,23,0.2609,1,"{3670, 472, 583, 522, 206, 205}"
190,1,144,0,0.2082491,"\int \frac{\tanh ^6(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Tanh[c + d*x]^6/(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{\sqrt{a} \left(3 a^2+10 a b+15 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 b^{5/2} d (a+b)^3}+\frac{a (3 a+7 b) \tanh (c+d x)}{8 b^2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{a \tanh ^3(c+d x)}{4 b d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{x}{(a+b)^3}","-\frac{\sqrt{a} \left(3 a^2+10 a b+15 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 b^{5/2} d (a+b)^3}+\frac{a (3 a+7 b) \tanh (c+d x)}{8 b^2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{a \tanh ^3(c+d x)}{4 b d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{x}{(a+b)^3}",1,"x/(a + b)^3 - (Sqrt[a]*(3*a^2 + 10*a*b + 15*b^2)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(8*b^(5/2)*(a + b)^3*d) + (a*Tanh[c + d*x]^3)/(4*b*(a + b)*d*(a + b*Tanh[c + d*x]^2)^2) + (a*(3*a + 7*b)*Tanh[c + d*x])/(8*b^2*(a + b)^2*d*(a + b*Tanh[c + d*x]^2))","A",6,6,23,0.2609,1,"{3670, 470, 578, 522, 206, 205}"
191,1,109,0,0.1704202,"\int \frac{\tanh ^5(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Tanh[c + d*x]^5/(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{a^2}{4 b^2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{a (a+2 b)}{2 b^2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{\log \left(a+b \tanh ^2(c+d x)\right)}{2 d (a+b)^3}+\frac{\log (\cosh (c+d x))}{d (a+b)^3}","-\frac{a^2}{4 b^2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{a (a+2 b)}{2 b^2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{\log \left(a+b \tanh ^2(c+d x)\right)}{2 d (a+b)^3}+\frac{\log (\cosh (c+d x))}{d (a+b)^3}",1,"Log[Cosh[c + d*x]]/((a + b)^3*d) + Log[a + b*Tanh[c + d*x]^2]/(2*(a + b)^3*d) - a^2/(4*b^2*(a + b)*d*(a + b*Tanh[c + d*x]^2)^2) + (a*(a + 2*b))/(2*b^2*(a + b)^2*d*(a + b*Tanh[c + d*x]^2))","A",4,3,23,0.1304,1,"{3670, 446, 88}"
192,1,137,0,0.1954892,"\int \frac{\tanh ^4(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Tanh[c + d*x]^4/(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{\left(a^2+6 a b-3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 \sqrt{a} b^{3/2} d (a+b)^3}-\frac{(a+5 b) \tanh (c+d x)}{8 b d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{a \tanh (c+d x)}{4 b d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{x}{(a+b)^3}","-\frac{\left(a^2+6 a b-3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 \sqrt{a} b^{3/2} d (a+b)^3}-\frac{(a+5 b) \tanh (c+d x)}{8 b d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{a \tanh (c+d x)}{4 b d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{x}{(a+b)^3}",1,"x/(a + b)^3 - ((a^2 + 6*a*b - 3*b^2)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(8*Sqrt[a]*b^(3/2)*(a + b)^3*d) + (a*Tanh[c + d*x])/(4*b*(a + b)*d*(a + b*Tanh[c + d*x]^2)^2) - ((a + 5*b)*Tanh[c + d*x])/(8*b*(a + b)^2*d*(a + b*Tanh[c + d*x]^2))","A",6,6,23,0.2609,1,"{3670, 470, 527, 522, 206, 205}"
193,1,98,0,0.1382908,"\int \frac{\tanh ^3(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Tanh[c + d*x]^3/(a + b*Tanh[c + d*x]^2)^3,x]","\frac{a}{4 b d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}-\frac{1}{2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{\log \left(a+b \tanh ^2(c+d x)\right)}{2 d (a+b)^3}+\frac{\log (\cosh (c+d x))}{d (a+b)^3}","\frac{a}{4 b d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}-\frac{1}{2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{\log \left(a+b \tanh ^2(c+d x)\right)}{2 d (a+b)^3}+\frac{\log (\cosh (c+d x))}{d (a+b)^3}",1,"Log[Cosh[c + d*x]]/((a + b)^3*d) + Log[a + b*Tanh[c + d*x]^2]/(2*(a + b)^3*d) + a/(4*b*(a + b)*d*(a + b*Tanh[c + d*x]^2)^2) - 1/(2*(a + b)^2*d*(a + b*Tanh[c + d*x]^2))","A",4,3,23,0.1304,1,"{3670, 446, 77}"
194,1,137,0,0.1570224,"\int \frac{\tanh ^2(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Tanh[c + d*x]^2/(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{\left(3 a^2-6 a b-b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{3/2} \sqrt{b} d (a+b)^3}-\frac{(3 a-b) \tanh (c+d x)}{8 a d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}-\frac{\tanh (c+d x)}{4 d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{x}{(a+b)^3}","-\frac{\left(3 a^2-6 a b-b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{3/2} \sqrt{b} d (a+b)^3}-\frac{(3 a-b) \tanh (c+d x)}{8 a d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}-\frac{\tanh (c+d x)}{4 d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{x}{(a+b)^3}",1,"x/(a + b)^3 - ((3*a^2 - 6*a*b - b^2)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(3/2)*Sqrt[b]*(a + b)^3*d) - Tanh[c + d*x]/(4*(a + b)*d*(a + b*Tanh[c + d*x]^2)^2) - ((3*a - b)*Tanh[c + d*x])/(8*a*(a + b)^2*d*(a + b*Tanh[c + d*x]^2))","A",6,6,23,0.2609,1,"{3670, 471, 527, 522, 206, 205}"
195,1,94,0,0.1045679,"\int \frac{\tanh (c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Tanh[c + d*x]/(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{1}{2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}-\frac{1}{4 d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{\log \left(a+b \tanh ^2(c+d x)\right)}{2 d (a+b)^3}+\frac{\log (\cosh (c+d x))}{d (a+b)^3}","-\frac{1}{2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}-\frac{1}{4 d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{\log \left(a+b \tanh ^2(c+d x)\right)}{2 d (a+b)^3}+\frac{\log (\cosh (c+d x))}{d (a+b)^3}",1,"Log[Cosh[c + d*x]]/((a + b)^3*d) + Log[a + b*Tanh[c + d*x]^2]/(2*(a + b)^3*d) - 1/(4*(a + b)*d*(a + b*Tanh[c + d*x]^2)^2) - 1/(2*(a + b)^2*d*(a + b*Tanh[c + d*x]^2))","A",4,3,21,0.1429,1,"{3670, 444, 44}"
196,1,142,0,0.1626853,"\int \frac{1}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[(a + b*Tanh[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{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a+b)^3}+\frac{b (7 a+3 b) \tanh (c+d x)}{8 a^2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{b \tanh (c+d x)}{4 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{x}{(a+b)^3}","\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}}\right)}{8 a^{5/2} d (a+b)^3}+\frac{b (7 a+3 b) \tanh (c+d x)}{8 a^2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{b \tanh (c+d x)}{4 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{x}{(a+b)^3}",1,"x/(a + b)^3 + (Sqrt[b]*(15*a^2 + 10*a*b + 3*b^2)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*(a + b)^3*d) + (b*Tanh[c + d*x])/(4*a*(a + b)*d*(a + b*Tanh[c + d*x]^2)^2) + (b*(7*a + 3*b)*Tanh[c + d*x])/(8*a^2*(a + b)^2*d*(a + b*Tanh[c + d*x]^2))","A",6,6,14,0.4286,1,"{3661, 414, 527, 522, 206, 205}"
197,1,138,0,0.2047054,"\int \frac{\coth (c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Coth[c + d*x]/(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{b \left(3 a^2+3 a b+b^2\right) \log \left(a+b \tanh ^2(c+d x)\right)}{2 a^3 d (a+b)^3}+\frac{b (2 a+b)}{2 a^2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{\log (\tanh (c+d x))}{a^3 d}+\frac{b}{4 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{\log (\cosh (c+d x))}{d (a+b)^3}","-\frac{b \left(3 a^2+3 a b+b^2\right) \log \left(a+b \tanh ^2(c+d x)\right)}{2 a^3 d (a+b)^3}+\frac{b (2 a+b)}{2 a^2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{\log (\tanh (c+d x))}{a^3 d}+\frac{b}{4 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{\log (\cosh (c+d x))}{d (a+b)^3}",1,"Log[Cosh[c + d*x]]/((a + b)^3*d) + Log[Tanh[c + d*x]]/(a^3*d) - (b*(3*a^2 + 3*a*b + b^2)*Log[a + b*Tanh[c + d*x]^2])/(2*a^3*(a + b)^3*d) + b/(4*a*(a + b)*d*(a + b*Tanh[c + d*x]^2)^2) + (b*(2*a + b))/(2*a^2*(a + b)^2*d*(a + b*Tanh[c + d*x]^2))","A",4,3,21,0.1429,1,"{3670, 446, 72}"
198,1,178,0,0.2908581,"\int \frac{\coth ^2(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Coth[c + d*x]^2/(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{\left(8 a^2+27 a b+15 b^2\right) \coth (c+d x)}{8 a^3 d (a+b)^2}-\frac{b^{3/2} \left(35 a^2+42 a b+15 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{7/2} d (a+b)^3}+\frac{b (9 a+5 b) \coth (c+d x)}{8 a^2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{b \coth (c+d x)}{4 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{x}{(a+b)^3}","-\frac{\left(8 a^2+27 a b+15 b^2\right) \coth (c+d x)}{8 a^3 d (a+b)^2}-\frac{b^{3/2} \left(35 a^2+42 a b+15 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{7/2} d (a+b)^3}+\frac{b (9 a+5 b) \coth (c+d x)}{8 a^2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{b \coth (c+d x)}{4 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{x}{(a+b)^3}",1,"x/(a + b)^3 - (b^(3/2)*(35*a^2 + 42*a*b + 15*b^2)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(7/2)*(a + b)^3*d) - ((8*a^2 + 27*a*b + 15*b^2)*Coth[c + d*x])/(8*a^3*(a + b)^2*d) + (b*Coth[c + d*x])/(4*a*(a + b)*d*(a + b*Tanh[c + d*x]^2)^2) + (b*(9*a + 5*b)*Coth[c + d*x])/(8*a^2*(a + b)^2*d*(a + b*Tanh[c + d*x]^2))","A",7,7,23,0.3043,1,"{3670, 472, 579, 583, 522, 206, 205}"
199,1,171,0,0.2618352,"\int \frac{\coth ^3(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Coth[c + d*x]^3/(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{b^2 (3 a+2 b)}{2 a^3 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}-\frac{b^2}{4 a^2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{b^2 \left(6 a^2+8 a b+3 b^2\right) \log \left(a+b \tanh ^2(c+d x)\right)}{2 a^4 d (a+b)^3}+\frac{(a-3 b) \log (\tanh (c+d x))}{a^4 d}-\frac{\coth ^2(c+d x)}{2 a^3 d}+\frac{\log (\cosh (c+d x))}{d (a+b)^3}","-\frac{b^2 (3 a+2 b)}{2 a^3 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}-\frac{b^2}{4 a^2 d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{b^2 \left(6 a^2+8 a b+3 b^2\right) \log \left(a+b \tanh ^2(c+d x)\right)}{2 a^4 d (a+b)^3}+\frac{(a-3 b) \log (\tanh (c+d x))}{a^4 d}-\frac{\coth ^2(c+d x)}{2 a^3 d}+\frac{\log (\cosh (c+d x))}{d (a+b)^3}",1,"-Coth[c + d*x]^2/(2*a^3*d) + Log[Cosh[c + d*x]]/((a + b)^3*d) + ((a - 3*b)*Log[Tanh[c + d*x]])/(a^4*d) + (b^2*(6*a^2 + 8*a*b + 3*b^2)*Log[a + b*Tanh[c + d*x]^2])/(2*a^4*(a + b)^3*d) - b^2/(4*a^2*(a + b)*d*(a + b*Tanh[c + d*x]^2)^2) - (b^2*(3*a + 2*b))/(2*a^3*(a + b)^2*d*(a + b*Tanh[c + d*x]^2))","A",4,3,23,0.1304,1,"{3670, 446, 88}"
200,1,228,0,0.3684722,"\int \frac{\coth ^4(c+d x)}{\left(a+b \tanh ^2(c+d x)\right)^3} \, dx","Int[Coth[c + d*x]^4/(a + b*Tanh[c + d*x]^2)^3,x]","-\frac{\left(8 a^2+55 a b+35 b^2\right) \coth ^3(c+d x)}{24 a^3 d (a+b)^2}-\frac{\left(-8 a^2 b+8 a^3-55 a b^2-35 b^3\right) \coth (c+d x)}{8 a^4 d (a+b)^2}+\frac{b^{5/2} \left(63 a^2+90 a b+35 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{9/2} d (a+b)^3}+\frac{b (11 a+7 b) \coth ^3(c+d x)}{8 a^2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{b \coth ^3(c+d x)}{4 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{x}{(a+b)^3}","-\frac{\left(8 a^2+55 a b+35 b^2\right) \coth ^3(c+d x)}{24 a^3 d (a+b)^2}-\frac{\left(-8 a^2 b+8 a^3-55 a b^2-35 b^3\right) \coth (c+d x)}{8 a^4 d (a+b)^2}+\frac{b^{5/2} \left(63 a^2+90 a b+35 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{9/2} d (a+b)^3}+\frac{b (11 a+7 b) \coth ^3(c+d x)}{8 a^2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)}+\frac{b \coth ^3(c+d x)}{4 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{x}{(a+b)^3}",1,"x/(a + b)^3 + (b^(5/2)*(63*a^2 + 90*a*b + 35*b^2)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(9/2)*(a + b)^3*d) - ((8*a^3 - 8*a^2*b - 55*a*b^2 - 35*b^3)*Coth[c + d*x])/(8*a^4*(a + b)^2*d) - ((8*a^2 + 55*a*b + 35*b^2)*Coth[c + d*x]^3)/(24*a^3*(a + b)^2*d) + (b*Coth[c + d*x]^3)/(4*a*(a + b)*d*(a + b*Tanh[c + d*x]^2)^2) + (b*(11*a + 7*b)*Coth[c + d*x]^3)/(8*a^2*(a + b)^2*d*(a + b*Tanh[c + d*x]^2))","A",8,7,23,0.3043,1,"{3670, 472, 579, 583, 522, 206, 205}"
201,1,201,0,0.2771353,"\int \frac{1}{\left(a+b \tanh ^2(c+d x)\right)^4} \, dx","Int[(a + b*Tanh[c + d*x]^2)^(-4),x]","\frac{b \left(19 a^2+16 a b+5 b^2\right) \tanh (c+d x)}{16 a^3 d (a+b)^3 \left(a+b \tanh ^2(c+d x)\right)}+\frac{\sqrt{b} \left(35 a^2 b+35 a^3+21 a b^2+5 b^3\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{16 a^{7/2} d (a+b)^4}+\frac{b (11 a+5 b) \tanh (c+d x)}{24 a^2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{b \tanh (c+d x)}{6 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)^3}+\frac{x}{(a+b)^4}","\frac{b \left(19 a^2+16 a b+5 b^2\right) \tanh (c+d x)}{16 a^3 d (a+b)^3 \left(a+b \tanh ^2(c+d x)\right)}+\frac{\sqrt{b} \left(35 a^2 b+35 a^3+21 a b^2+5 b^3\right) \tan ^{-1}\left(\frac{\sqrt{b} \tanh (c+d x)}{\sqrt{a}}\right)}{16 a^{7/2} d (a+b)^4}+\frac{b (11 a+5 b) \tanh (c+d x)}{24 a^2 d (a+b)^2 \left(a+b \tanh ^2(c+d x)\right)^2}+\frac{b \tanh (c+d x)}{6 a d (a+b) \left(a+b \tanh ^2(c+d x)\right)^3}+\frac{x}{(a+b)^4}",1,"x/(a + b)^4 + (Sqrt[b]*(35*a^3 + 35*a^2*b + 21*a*b^2 + 5*b^3)*ArcTan[(Sqrt[b]*Tanh[c + d*x])/Sqrt[a]])/(16*a^(7/2)*(a + b)^4*d) + (b*Tanh[c + d*x])/(6*a*(a + b)*d*(a + b*Tanh[c + d*x]^2)^3) + (b*(11*a + 5*b)*Tanh[c + d*x])/(24*a^2*(a + b)^2*d*(a + b*Tanh[c + d*x]^2)^2) + (b*(19*a^2 + 16*a*b + 5*b^2)*Tanh[c + d*x])/(16*a^3*(a + b)^3*d*(a + b*Tanh[c + d*x]^2))","A",7,6,14,0.4286,1,"{3661, 414, 527, 522, 206, 205}"
202,1,3,0,0.0165158,"\int \sqrt{1-\tanh ^2(x)} \, dx","Int[Sqrt[1 - Tanh[x]^2],x]","\sin ^{-1}(\tanh (x))","\sin ^{-1}(\tanh (x))",1,"ArcSin[Tanh[x]]","A",3,3,12,0.2500,1,"{3657, 4122, 216}"
203,1,16,0,0.0205394,"\int \sqrt{-1+\tanh ^2(x)} \, dx","Int[Sqrt[-1 + Tanh[x]^2],x]","-\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{-\text{sech}^2(x)}}\right)","-\tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{-\text{sech}^2(x)}}\right)",1,"-ArcTanh[Tanh[x]/Sqrt[-Sech[x]^2]]","A",4,4,10,0.4000,1,"{3657, 4122, 217, 206}"
204,1,22,0,0.0199402,"\int \left(1-\tanh ^2(x)\right)^{3/2} \, dx","Int[(1 - Tanh[x]^2)^(3/2),x]","\frac{1}{2} \sin ^{-1}(\tanh (x))+\frac{1}{2} \tanh (x) \sqrt{\text{sech}^2(x)}","\frac{1}{2} \sin ^{-1}(\tanh (x))+\frac{1}{2} \tanh (x) \sqrt{\text{sech}^2(x)}",1,"ArcSin[Tanh[x]]/2 + (Sqrt[Sech[x]^2]*Tanh[x])/2","A",4,4,12,0.3333,1,"{3657, 4122, 195, 216}"
205,1,35,0,0.0235295,"\int \left(-1+\tanh ^2(x)\right)^{3/2} \, dx","Int[(-1 + Tanh[x]^2)^(3/2),x]","\frac{1}{2} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{-\text{sech}^2(x)}}\right)-\frac{1}{2} \tanh (x) \sqrt{-\text{sech}^2(x)}","\frac{1}{2} \tanh ^{-1}\left(\frac{\tanh (x)}{\sqrt{-\text{sech}^2(x)}}\right)-\frac{1}{2} \tanh (x) \sqrt{-\text{sech}^2(x)}",1,"ArcTanh[Tanh[x]/Sqrt[-Sech[x]^2]]/2 - (Sqrt[-Sech[x]^2]*Tanh[x])/2","A",5,5,10,0.5000,1,"{3657, 4122, 195, 217, 206}"
206,1,11,0,0.0205086,"\int \frac{1}{\sqrt{1-\tanh ^2(x)}} \, dx","Int[1/Sqrt[1 - Tanh[x]^2],x]","\frac{\tanh (x)}{\sqrt{\text{sech}^2(x)}}","\frac{\tanh (x)}{\sqrt{\text{sech}^2(x)}}",1,"Tanh[x]/Sqrt[Sech[x]^2]","A",3,3,12,0.2500,1,"{3657, 4122, 191}"
207,1,13,0,0.0210973,"\int \frac{1}{\sqrt{-1+\tanh ^2(x)}} \, dx","Int[1/Sqrt[-1 + Tanh[x]^2],x]","\frac{\tanh (x)}{\sqrt{-\text{sech}^2(x)}}","\frac{\tanh (x)}{\sqrt{-\text{sech}^2(x)}}",1,"Tanh[x]/Sqrt[-Sech[x]^2]","A",3,3,10,0.3000,1,"{3657, 4122, 191}"
208,1,87,0,0.1609438,"\int \tanh ^5(x) \sqrt{a+b \tanh ^2(x)} \, dx","Int[Tanh[x]^5*Sqrt[a + b*Tanh[x]^2],x]","-\frac{\left(a+b \tanh ^2(x)\right)^{5/2}}{5 b^2}+\frac{(a-b) \left(a+b \tanh ^2(x)\right)^{3/2}}{3 b^2}-\sqrt{a+b \tanh ^2(x)}+\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)","-\frac{\left(a+b \tanh ^2(x)\right)^{5/2}}{5 b^2}+\frac{(a-b) \left(a+b \tanh ^2(x)\right)^{3/2}}{3 b^2}-\sqrt{a+b \tanh ^2(x)}+\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)",1,"Sqrt[a + b]*ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]] - Sqrt[a + b*Tanh[x]^2] + ((a - b)*(a + b*Tanh[x]^2)^(3/2))/(3*b^2) - (a + b*Tanh[x]^2)^(5/2)/(5*b^2)","A",7,6,17,0.3529,1,"{3670, 446, 88, 50, 63, 208}"
209,1,121,0,0.2002877,"\int \tanh ^4(x) \sqrt{a+b \tanh ^2(x)} \, dx","Int[Tanh[x]^4*Sqrt[a + b*Tanh[x]^2],x]","\frac{\left(a^2-4 a b-8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{8 b^{3/2}}-\frac{1}{4} \tanh ^3(x) \sqrt{a+b \tanh ^2(x)}-\frac{(a+4 b) \tanh (x) \sqrt{a+b \tanh ^2(x)}}{8 b}+\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)","\frac{\left(a^2-4 a b-8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{8 b^{3/2}}-\frac{1}{4} \tanh ^3(x) \sqrt{a+b \tanh ^2(x)}-\frac{(a+4 b) \tanh (x) \sqrt{a+b \tanh ^2(x)}}{8 b}+\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)",1,"((a^2 - 4*a*b - 8*b^2)*ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]])/(8*b^(3/2)) + Sqrt[a + b]*ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]] - ((a + 4*b)*Tanh[x]*Sqrt[a + b*Tanh[x]^2])/(8*b) - (Tanh[x]^3*Sqrt[a + b*Tanh[x]^2])/4","A",8,7,17,0.4118,1,"{3670, 478, 582, 523, 217, 206, 377}"
210,1,63,0,0.1194585,"\int \tanh ^3(x) \sqrt{a+b \tanh ^2(x)} \, dx","Int[Tanh[x]^3*Sqrt[a + b*Tanh[x]^2],x]","-\frac{\left(a+b \tanh ^2(x)\right)^{3/2}}{3 b}-\sqrt{a+b \tanh ^2(x)}+\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)","-\frac{\left(a+b \tanh ^2(x)\right)^{3/2}}{3 b}-\sqrt{a+b \tanh ^2(x)}+\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)",1,"Sqrt[a + b]*ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]] - Sqrt[a + b*Tanh[x]^2] - (a + b*Tanh[x]^2)^(3/2)/(3*b)","A",6,6,17,0.3529,1,"{3670, 446, 80, 50, 63, 208}"
211,1,85,0,0.1245182,"\int \tanh ^2(x) \sqrt{a+b \tanh ^2(x)} \, dx","Int[Tanh[x]^2*Sqrt[a + b*Tanh[x]^2],x]","-\frac{(a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{2 \sqrt{b}}+\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)-\frac{1}{2} \tanh (x) \sqrt{a+b \tanh ^2(x)}","-\frac{(a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{2 \sqrt{b}}+\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)-\frac{1}{2} \tanh (x) \sqrt{a+b \tanh ^2(x)}",1,"-((a + 2*b)*ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]])/(2*Sqrt[b]) + Sqrt[a + b]*ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]] - (Tanh[x]*Sqrt[a + b*Tanh[x]^2])/2","A",7,6,17,0.3529,1,"{3670, 478, 523, 217, 206, 377}"
212,1,44,0,0.0770792,"\int \tanh (x) \sqrt{a+b \tanh ^2(x)} \, dx","Int[Tanh[x]*Sqrt[a + b*Tanh[x]^2],x]","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)-\sqrt{a+b \tanh ^2(x)}","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)-\sqrt{a+b \tanh ^2(x)}",1,"Sqrt[a + b]*ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]] - Sqrt[a + b*Tanh[x]^2]","A",5,5,15,0.3333,1,"{3670, 444, 50, 63, 208}"
213,1,60,0,0.047025,"\int \sqrt{a+b \tanh ^2(x)} \, dx","Int[Sqrt[a + b*Tanh[x]^2],x]","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)-\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)-\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)",1,"-(Sqrt[b]*ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]) + Sqrt[a + b]*ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]","A",6,5,12,0.4167,1,"{3661, 402, 217, 206, 377}"
214,1,56,0,0.1119441,"\int \coth (x) \sqrt{a+b \tanh ^2(x)} \, dx","Int[Coth[x]*Sqrt[a + b*Tanh[x]^2],x]","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)-\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a}}\right)","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)-\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a}}\right)",1,"-(Sqrt[a]*ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a]]) + Sqrt[a + b]*ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]]","A",7,5,15,0.3333,1,"{3670, 446, 83, 63, 208}"
215,1,48,0,0.0926206,"\int \coth ^2(x) \sqrt{a+b \tanh ^2(x)} \, dx","Int[Coth[x]^2*Sqrt[a + b*Tanh[x]^2],x]","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)-\coth (x) \sqrt{a+b \tanh ^2(x)}","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)-\coth (x) \sqrt{a+b \tanh ^2(x)}",1,"Sqrt[a + b]*ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]] - Coth[x]*Sqrt[a + b*Tanh[x]^2]","A",5,5,17,0.2941,1,"{3670, 475, 12, 377, 206}"
216,1,83,0,0.1552081,"\int \coth ^3(x) \sqrt{a+b \tanh ^2(x)} \, dx","Int[Coth[x]^3*Sqrt[a + b*Tanh[x]^2],x]","-\frac{(2 a+b) \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a}}\right)}{2 \sqrt{a}}+\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)-\frac{1}{2} \coth ^2(x) \sqrt{a+b \tanh ^2(x)}","-\frac{(2 a+b) \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a}}\right)}{2 \sqrt{a}}+\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)-\frac{1}{2} \coth ^2(x) \sqrt{a+b \tanh ^2(x)}",1,"-((2*a + b)*ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a]])/(2*Sqrt[a]) + Sqrt[a + b]*ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]] - (Coth[x]^2*Sqrt[a + b*Tanh[x]^2])/2","A",8,6,17,0.3529,1,"{3670, 446, 99, 156, 63, 208}"
217,1,78,0,0.1459685,"\int \coth ^4(x) \sqrt{a+b \tanh ^2(x)} \, dx","Int[Coth[x]^4*Sqrt[a + b*Tanh[x]^2],x]","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)-\frac{1}{3} \coth ^3(x) \sqrt{a+b \tanh ^2(x)}-\frac{(3 a+b) \coth (x) \sqrt{a+b \tanh ^2(x)}}{3 a}","\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)-\frac{1}{3} \coth ^3(x) \sqrt{a+b \tanh ^2(x)}-\frac{(3 a+b) \coth (x) \sqrt{a+b \tanh ^2(x)}}{3 a}",1,"Sqrt[a + b]*ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]] - ((3*a + b)*Coth[x]*Sqrt[a + b*Tanh[x]^2])/(3*a) - (Coth[x]^3*Sqrt[a + b*Tanh[x]^2])/3","A",6,6,17,0.3529,1,"{3670, 475, 583, 12, 377, 206}"
218,1,121,0,0.2129804,"\int \coth ^5(x) \sqrt{a+b \tanh ^2(x)} \, dx","Int[Coth[x]^5*Sqrt[a + b*Tanh[x]^2],x]","-\frac{\left(8 a^2+4 a b-b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a}}\right)}{8 a^{3/2}}+\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)-\frac{1}{4} \coth ^4(x) \sqrt{a+b \tanh ^2(x)}-\frac{(4 a+b) \coth ^2(x) \sqrt{a+b \tanh ^2(x)}}{8 a}","-\frac{\left(8 a^2+4 a b-b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a}}\right)}{8 a^{3/2}}+\sqrt{a+b} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)-\frac{1}{4} \coth ^4(x) \sqrt{a+b \tanh ^2(x)}-\frac{(4 a+b) \coth ^2(x) \sqrt{a+b \tanh ^2(x)}}{8 a}",1,"-((8*a^2 + 4*a*b - b^2)*ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a]])/(8*a^(3/2)) + Sqrt[a + b]*ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]] - ((4*a + b)*Coth[x]^2*Sqrt[a + b*Tanh[x]^2])/(8*a) - (Coth[x]^4*Sqrt[a + b*Tanh[x]^2])/4","A",9,7,17,0.4118,1,"{3670, 446, 99, 151, 156, 63, 208}"
219,1,82,0,0.1520832,"\int \tanh ^3(x) \left(a+b \tanh ^2(x)\right)^{3/2} \, dx","Int[Tanh[x]^3*(a + b*Tanh[x]^2)^(3/2),x]","-\frac{\left(a+b \tanh ^2(x)\right)^{5/2}}{5 b}-\frac{1}{3} \left(a+b \tanh ^2(x)\right)^{3/2}-(a+b) \sqrt{a+b \tanh ^2(x)}+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)","-\frac{\left(a+b \tanh ^2(x)\right)^{5/2}}{5 b}-\frac{1}{3} \left(a+b \tanh ^2(x)\right)^{3/2}-(a+b) \sqrt{a+b \tanh ^2(x)}+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)",1,"(a + b)^(3/2)*ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]] - (a + b)*Sqrt[a + b*Tanh[x]^2] - (a + b*Tanh[x]^2)^(3/2)/3 - (a + b*Tanh[x]^2)^(5/2)/(5*b)","A",7,6,17,0.3529,1,"{3670, 446, 80, 50, 63, 208}"
220,1,123,0,0.2444138,"\int \tanh ^2(x) \left(a+b \tanh ^2(x)\right)^{3/2} \, dx","Int[Tanh[x]^2*(a + b*Tanh[x]^2)^(3/2),x]","-\frac{\left(3 a^2+12 a b+8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{8 \sqrt{b}}-\frac{1}{4} b \tanh ^3(x) \sqrt{a+b \tanh ^2(x)}-\frac{1}{8} (5 a+4 b) \tanh (x) \sqrt{a+b \tanh ^2(x)}+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)","-\frac{\left(3 a^2+12 a b+8 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{8 \sqrt{b}}-\frac{1}{4} b \tanh ^3(x) \sqrt{a+b \tanh ^2(x)}-\frac{1}{8} (5 a+4 b) \tanh (x) \sqrt{a+b \tanh ^2(x)}+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)",1,"-((3*a^2 + 12*a*b + 8*b^2)*ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]])/(8*Sqrt[b]) + (a + b)^(3/2)*ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]] - ((5*a + 4*b)*Tanh[x]*Sqrt[a + b*Tanh[x]^2])/8 - (b*Tanh[x]^3*Sqrt[a + b*Tanh[x]^2])/4","A",8,7,17,0.4118,1,"{3670, 477, 582, 523, 217, 206, 377}"
221,1,63,0,0.1014684,"\int \tanh (x) \left(a+b \tanh ^2(x)\right)^{3/2} \, dx","Int[Tanh[x]*(a + b*Tanh[x]^2)^(3/2),x]","(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)-(a+b) \sqrt{a+b \tanh ^2(x)}-\frac{1}{3} \left(a+b \tanh ^2(x)\right)^{3/2}","(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)-(a+b) \sqrt{a+b \tanh ^2(x)}-\frac{1}{3} \left(a+b \tanh ^2(x)\right)^{3/2}",1,"(a + b)^(3/2)*ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]] - (a + b)*Sqrt[a + b*Tanh[x]^2] - (a + b*Tanh[x]^2)^(3/2)/3","A",6,5,15,0.3333,1,"{3670, 444, 50, 63, 208}"
222,1,88,0,0.0852639,"\int \left(a+b \tanh ^2(x)\right)^{3/2} \, dx","Int[(a + b*Tanh[x]^2)^(3/2),x]","(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)-\frac{1}{2} \sqrt{b} (3 a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)-\frac{1}{2} b \tanh (x) \sqrt{a+b \tanh ^2(x)}","(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)-\frac{1}{2} \sqrt{b} (3 a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)-\frac{1}{2} b \tanh (x) \sqrt{a+b \tanh ^2(x)}",1,"-(Sqrt[b]*(3*a + 2*b)*ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]])/2 + (a + b)^(3/2)*ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]] - (b*Tanh[x]*Sqrt[a + b*Tanh[x]^2])/2","A",7,6,12,0.5000,1,"{3661, 416, 523, 217, 206, 377}"
223,1,71,0,0.1362509,"\int \coth (x) \left(a+b \tanh ^2(x)\right)^{3/2} \, dx","Int[Coth[x]*(a + b*Tanh[x]^2)^(3/2),x]","a^{3/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a}}\right)\right)+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)-b \sqrt{a+b \tanh ^2(x)}","a^{3/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a}}\right)\right)+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)-b \sqrt{a+b \tanh ^2(x)}",1,"-(a^(3/2)*ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a]]) + (a + b)^(3/2)*ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]] - b*Sqrt[a + b*Tanh[x]^2]","A",8,6,15,0.4000,1,"{3670, 446, 84, 156, 63, 208}"
224,1,77,0,0.1271269,"\int \coth ^2(x) \left(a+b \tanh ^2(x)\right)^{3/2} \, dx","Int[Coth[x]^2*(a + b*Tanh[x]^2)^(3/2),x]","b^{3/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)\right)+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)-a \coth (x) \sqrt{a+b \tanh ^2(x)}","b^{3/2} \left(-\tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)\right)+(a+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)-a \coth (x) \sqrt{a+b \tanh ^2(x)}",1,"-(b^(3/2)*ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]) + (a + b)^(3/2)*ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]] - a*Coth[x]*Sqrt[a + b*Tanh[x]^2]","A",7,6,17,0.3529,1,"{3670, 474, 523, 217, 206, 377}"
225,1,31,0,0.0269331,"\int \sqrt{1+\tanh ^2(x)} \, dx","Int[Sqrt[1 + Tanh[x]^2],x]","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \tanh (x)}{\sqrt{\tanh ^2(x)+1}}\right)-\sinh ^{-1}(\tanh (x))","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \tanh (x)}{\sqrt{\tanh ^2(x)+1}}\right)-\sinh ^{-1}(\tanh (x))",1,"-ArcSinh[Tanh[x]] + Sqrt[2]*ArcTanh[(Sqrt[2]*Tanh[x])/Sqrt[1 + Tanh[x]^2]]","A",5,5,10,0.5000,1,"{3661, 402, 215, 377, 206}"
226,1,45,0,0.0345847,"\int \sqrt{-1-\tanh ^2(x)} \, dx","Int[Sqrt[-1 - Tanh[x]^2],x]","\tan ^{-1}\left(\frac{\tanh (x)}{\sqrt{-\tanh ^2(x)-1}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \tanh (x)}{\sqrt{-\tanh ^2(x)-1}}\right)","\tan ^{-1}\left(\frac{\tanh (x)}{\sqrt{-\tanh ^2(x)-1}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \tanh (x)}{\sqrt{-\tanh ^2(x)-1}}\right)",1,"ArcTan[Tanh[x]/Sqrt[-1 - Tanh[x]^2]] - Sqrt[2]*ArcTan[(Sqrt[2]*Tanh[x])/Sqrt[-1 - Tanh[x]^2]]","A",6,5,12,0.4167,1,"{3661, 402, 217, 203, 377}"
227,1,50,0,0.0388703,"\int \left(1+\tanh ^2(x)\right)^{3/2} \, dx","Int[(1 + Tanh[x]^2)^(3/2),x]","2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \tanh (x)}{\sqrt{\tanh ^2(x)+1}}\right)-\frac{1}{2} \tanh (x) \sqrt{\tanh ^2(x)+1}-\frac{5}{2} \sinh ^{-1}(\tanh (x))","2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \tanh (x)}{\sqrt{\tanh ^2(x)+1}}\right)-\frac{1}{2} \tanh (x) \sqrt{\tanh ^2(x)+1}-\frac{5}{2} \sinh ^{-1}(\tanh (x))",1,"(-5*ArcSinh[Tanh[x]])/2 + 2*Sqrt[2]*ArcTanh[(Sqrt[2]*Tanh[x])/Sqrt[1 + Tanh[x]^2]] - (Tanh[x]*Sqrt[1 + Tanh[x]^2])/2","A",6,6,10,0.6000,1,"{3661, 416, 523, 215, 377, 206}"
228,1,67,0,0.0473687,"\int \left(-1-\tanh ^2(x)\right)^{3/2} \, dx","Int[(-1 - Tanh[x]^2)^(3/2),x]","\frac{1}{2} \tanh (x) \sqrt{-\tanh ^2(x)-1}-\frac{5}{2} \tan ^{-1}\left(\frac{\tanh (x)}{\sqrt{-\tanh ^2(x)-1}}\right)+2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \tanh (x)}{\sqrt{-\tanh ^2(x)-1}}\right)","\frac{1}{2} \tanh (x) \sqrt{-\tanh ^2(x)-1}-\frac{5}{2} \tan ^{-1}\left(\frac{\tanh (x)}{\sqrt{-\tanh ^2(x)-1}}\right)+2 \sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2} \tanh (x)}{\sqrt{-\tanh ^2(x)-1}}\right)",1,"(-5*ArcTan[Tanh[x]/Sqrt[-1 - Tanh[x]^2]])/2 + 2*Sqrt[2]*ArcTan[(Sqrt[2]*Tanh[x])/Sqrt[-1 - Tanh[x]^2]] + (Tanh[x]*Sqrt[-1 - Tanh[x]^2])/2","A",7,6,12,0.5000,1,"{3661, 416, 523, 217, 203, 377}"
229,1,70,0,0.1360632,"\int \frac{\tanh ^5(x)}{\sqrt{a+b \tanh ^2(x)}} \, dx","Int[Tanh[x]^5/Sqrt[a + b*Tanh[x]^2],x]","-\frac{\left(a+b \tanh ^2(x)\right)^{3/2}}{3 b^2}+\frac{(a-b) \sqrt{a+b \tanh ^2(x)}}{b^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}","-\frac{\left(a+b \tanh ^2(x)\right)^{3/2}}{3 b^2}+\frac{(a-b) \sqrt{a+b \tanh ^2(x)}}{b^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}",1,"ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]]/Sqrt[a + b] + ((a - b)*Sqrt[a + b*Tanh[x]^2])/b^2 - (a + b*Tanh[x]^2)^(3/2)/(3*b^2)","A",6,5,17,0.2941,1,"{3670, 446, 88, 63, 208}"
230,1,88,0,0.1232224,"\int \frac{\tanh ^4(x)}{\sqrt{a+b \tanh ^2(x)}} \, dx","Int[Tanh[x]^4/Sqrt[a + b*Tanh[x]^2],x]","\frac{(a-2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{2 b^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{\sqrt{a+b}}-\frac{\tanh (x) \sqrt{a+b \tanh ^2(x)}}{2 b}","\frac{(a-2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{2 b^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{\sqrt{a+b}}-\frac{\tanh (x) \sqrt{a+b \tanh ^2(x)}}{2 b}",1,"((a - 2*b)*ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]])/(2*b^(3/2)) + ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/Sqrt[a + b] - (Tanh[x]*Sqrt[a + b*Tanh[x]^2])/(2*b)","A",7,6,17,0.3529,1,"{3670, 479, 523, 217, 206, 377}"
231,1,47,0,0.1056577,"\int \frac{\tanh ^3(x)}{\sqrt{a+b \tanh ^2(x)}} \, dx","Int[Tanh[x]^3/Sqrt[a + b*Tanh[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}-\frac{\sqrt{a+b \tanh ^2(x)}}{b}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}-\frac{\sqrt{a+b \tanh ^2(x)}}{b}",1,"ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]]/Sqrt[a + b] - Sqrt[a + b*Tanh[x]^2]/b","A",5,5,17,0.2941,1,"{3670, 446, 80, 63, 208}"
232,1,60,0,0.0932622,"\int \frac{\tanh ^2(x)}{\sqrt{a+b \tanh ^2(x)}} \, dx","Int[Tanh[x]^2/Sqrt[a + b*Tanh[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{\sqrt{a+b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{\sqrt{b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{\sqrt{a+b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{\sqrt{b}}",1,"-(ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/Sqrt[b]) + ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/Sqrt[a + b]","A",6,5,17,0.2941,1,"{3670, 483, 217, 206, 377}"
233,1,29,0,0.0643284,"\int \frac{\tanh (x)}{\sqrt{a+b \tanh ^2(x)}} \, dx","Int[Tanh[x]/Sqrt[a + b*Tanh[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}",1,"ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]]/Sqrt[a + b]","A",4,4,15,0.2667,1,"{3670, 444, 63, 208}"
234,1,31,0,0.0269137,"\int \frac{1}{\sqrt{a+b \tanh ^2(x)}} \, dx","Int[1/Sqrt[a + b*Tanh[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{\sqrt{a+b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{\sqrt{a+b}}",1,"ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/Sqrt[a + b]","A",3,3,12,0.2500,1,"{3661, 377, 206}"
235,1,56,0,0.1126076,"\int \frac{\coth (x)}{\sqrt{a+b \tanh ^2(x)}} \, dx","Int[Coth[x]/Sqrt[a + b*Tanh[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"-(ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a]]/Sqrt[a]) + ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]]/Sqrt[a + b]","A",7,5,15,0.3333,1,"{3670, 446, 86, 63, 208}"
236,1,51,0,0.0948034,"\int \frac{\coth ^2(x)}{\sqrt{a+b \tanh ^2(x)}} \, dx","Int[Coth[x]^2/Sqrt[a + b*Tanh[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{\sqrt{a+b}}-\frac{\coth (x) \sqrt{a+b \tanh ^2(x)}}{a}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{\sqrt{a+b}}-\frac{\coth (x) \sqrt{a+b \tanh ^2(x)}}{a}",1,"ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/Sqrt[a + b] - (Coth[x]*Sqrt[a + b*Tanh[x]^2])/a","A",5,5,17,0.2941,1,"{3670, 480, 12, 377, 206}"
237,1,88,0,0.1659488,"\int \frac{\coth ^3(x)}{\sqrt{a+b \tanh ^2(x)}} \, dx","Int[Coth[x]^3/Sqrt[a + b*Tanh[x]^2],x]","-\frac{(2 a-b) \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a}}\right)}{2 a^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}-\frac{\coth ^2(x) \sqrt{a+b \tanh ^2(x)}}{2 a}","-\frac{(2 a-b) \tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a}}\right)}{2 a^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{\sqrt{a+b}}-\frac{\coth ^2(x) \sqrt{a+b \tanh ^2(x)}}{2 a}",1,"-((2*a - b)*ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a]])/(2*a^(3/2)) + ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]]/Sqrt[a + b] - (Coth[x]^2*Sqrt[a + b*Tanh[x]^2])/(2*a)","A",8,6,17,0.3529,1,"{3670, 446, 103, 156, 63, 208}"
238,1,72,0,0.1633298,"\int \frac{\tanh ^5(x)}{\left(a+b \tanh ^2(x)\right)^{3/2}} \, dx","Int[Tanh[x]^5/(a + b*Tanh[x]^2)^(3/2),x]","-\frac{a^2}{b^2 (a+b) \sqrt{a+b \tanh ^2(x)}}-\frac{\sqrt{a+b \tanh ^2(x)}}{b^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{3/2}}","-\frac{a^2}{b^2 (a+b) \sqrt{a+b \tanh ^2(x)}}-\frac{\sqrt{a+b \tanh ^2(x)}}{b^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{3/2}}",1,"ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]]/(a + b)^(3/2) - a^2/(b^2*(a + b)*Sqrt[a + b*Tanh[x]^2]) - Sqrt[a + b*Tanh[x]^2]/b^2","A",6,5,17,0.2941,1,"{3670, 446, 87, 63, 208}"
239,1,84,0,0.1299035,"\int \frac{\tanh ^4(x)}{\left(a+b \tanh ^2(x)\right)^{3/2}} \, dx","Int[Tanh[x]^4/(a + b*Tanh[x]^2)^(3/2),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{b^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{3/2}}+\frac{a \tanh (x)}{b (a+b) \sqrt{a+b \tanh ^2(x)}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{b^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{3/2}}+\frac{a \tanh (x)}{b (a+b) \sqrt{a+b \tanh ^2(x)}}",1,"-(ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/b^(3/2)) + ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/(a + b)^(3/2) + (a*Tanh[x])/(b*(a + b)*Sqrt[a + b*Tanh[x]^2])","A",7,6,17,0.3529,1,"{3670, 470, 523, 217, 206, 377}"
240,1,52,0,0.123291,"\int \frac{\tanh ^3(x)}{\left(a+b \tanh ^2(x)\right)^{3/2}} \, dx","Int[Tanh[x]^3/(a + b*Tanh[x]^2)^(3/2),x]","\frac{a}{b (a+b) \sqrt{a+b \tanh ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{3/2}}","\frac{a}{b (a+b) \sqrt{a+b \tanh ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{3/2}}",1,"ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]]/(a + b)^(3/2) + a/(b*(a + b)*Sqrt[a + b*Tanh[x]^2])","A",5,5,17,0.2941,1,"{3670, 446, 78, 63, 208}"
241,1,53,0,0.0992793,"\int \frac{\tanh ^2(x)}{\left(a+b \tanh ^2(x)\right)^{3/2}} \, dx","Int[Tanh[x]^2/(a + b*Tanh[x]^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{3/2}}-\frac{\tanh (x)}{(a+b) \sqrt{a+b \tanh ^2(x)}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{3/2}}-\frac{\tanh (x)}{(a+b) \sqrt{a+b \tanh ^2(x)}}",1,"ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/(a + b)^(3/2) - Tanh[x]/((a + b)*Sqrt[a + b*Tanh[x]^2])","A",4,4,17,0.2353,1,"{3670, 471, 377, 206}"
242,1,49,0,0.0856056,"\int \frac{\tanh (x)}{\left(a+b \tanh ^2(x)\right)^{3/2}} \, dx","Int[Tanh[x]/(a + b*Tanh[x]^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{3/2}}-\frac{1}{(a+b) \sqrt{a+b \tanh ^2(x)}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{3/2}}-\frac{1}{(a+b) \sqrt{a+b \tanh ^2(x)}}",1,"ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]]/(a + b)^(3/2) - 1/((a + b)*Sqrt[a + b*Tanh[x]^2])","A",5,5,15,0.3333,1,"{3670, 444, 51, 63, 208}"
243,1,56,0,0.042802,"\int \frac{1}{\left(a+b \tanh ^2(x)\right)^{3/2}} \, dx","Int[(a + b*Tanh[x]^2)^(-3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{3/2}}+\frac{b \tanh (x)}{a (a+b) \sqrt{a+b \tanh ^2(x)}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{3/2}}+\frac{b \tanh (x)}{a (a+b) \sqrt{a+b \tanh ^2(x)}}",1,"ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/(a + b)^(3/2) + (b*Tanh[x])/(a*(a + b)*Sqrt[a + b*Tanh[x]^2])","A",4,4,12,0.3333,1,"{3661, 382, 377, 206}"
244,1,78,0,0.1464282,"\int \frac{\coth (x)}{\left(a+b \tanh ^2(x)\right)^{3/2}} \, dx","Int[Coth[x]/(a + b*Tanh[x]^2)^(3/2),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a}}\right)}{a^{3/2}}+\frac{b}{a (a+b) \sqrt{a+b \tanh ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{3/2}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a}}\right)}{a^{3/2}}+\frac{b}{a (a+b) \sqrt{a+b \tanh ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{3/2}}",1,"-(ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a]]/a^(3/2)) + ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]]/(a + b)^(3/2) + b/(a*(a + b)*Sqrt[a + b*Tanh[x]^2])","A",8,6,15,0.4000,1,"{3670, 446, 85, 156, 63, 208}"
245,1,85,0,0.1612388,"\int \frac{\coth ^2(x)}{\left(a+b \tanh ^2(x)\right)^{3/2}} \, dx","Int[Coth[x]^2/(a + b*Tanh[x]^2)^(3/2),x]","-\frac{(a+2 b) \coth (x) \sqrt{a+b \tanh ^2(x)}}{a^2 (a+b)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{3/2}}+\frac{b \coth (x)}{a (a+b) \sqrt{a+b \tanh ^2(x)}}","-\frac{(a+2 b) \coth (x) \sqrt{a+b \tanh ^2(x)}}{a^2 (a+b)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{3/2}}+\frac{b \coth (x)}{a (a+b) \sqrt{a+b \tanh ^2(x)}}",1,"ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/(a + b)^(3/2) + (b*Coth[x])/(a*(a + b)*Sqrt[a + b*Tanh[x]^2]) - ((a + 2*b)*Coth[x]*Sqrt[a + b*Tanh[x]^2])/(a^2*(a + b))","A",6,6,17,0.3529,1,"{3670, 472, 583, 12, 377, 206}"
246,1,118,0,0.2204506,"\int \frac{\tanh ^6(x)}{\left(a+b \tanh ^2(x)\right)^{5/2}} \, dx","Int[Tanh[x]^6/(a + b*Tanh[x]^2)^(5/2),x]","\frac{a (a+2 b) \tanh (x)}{b^2 (a+b)^2 \sqrt{a+b \tanh ^2(x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{b^{5/2}}+\frac{a \tanh ^3(x)}{3 b (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{5/2}}","\frac{a (a+2 b) \tanh (x)}{b^2 (a+b)^2 \sqrt{a+b \tanh ^2(x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{b^{5/2}}+\frac{a \tanh ^3(x)}{3 b (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{5/2}}",1,"-(ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/b^(5/2)) + ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/(a + b)^(5/2) + (a*Tanh[x]^3)/(3*b*(a + b)*(a + b*Tanh[x]^2)^(3/2)) + (a*(a + 2*b)*Tanh[x])/(b^2*(a + b)^2*Sqrt[a + b*Tanh[x]^2])","A",8,7,17,0.4118,1,"{3670, 470, 578, 523, 217, 206, 377}"
247,1,84,0,0.1805894,"\int \frac{\tanh ^5(x)}{\left(a+b \tanh ^2(x)\right)^{5/2}} \, dx","Int[Tanh[x]^5/(a + b*Tanh[x]^2)^(5/2),x]","-\frac{a^2}{3 b^2 (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}+\frac{a (a+2 b)}{b^2 (a+b)^2 \sqrt{a+b \tanh ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}","-\frac{a^2}{3 b^2 (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}+\frac{a (a+2 b)}{b^2 (a+b)^2 \sqrt{a+b \tanh ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}",1,"ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]]/(a + b)^(5/2) - a^2/(3*b^2*(a + b)*(a + b*Tanh[x]^2)^(3/2)) + (a*(a + 2*b))/(b^2*(a + b)^2*Sqrt[a + b*Tanh[x]^2])","A",6,5,17,0.2941,1,"{3670, 446, 87, 63, 208}"
248,1,90,0,0.1379772,"\int \frac{\tanh ^4(x)}{\left(a+b \tanh ^2(x)\right)^{5/2}} \, dx","Int[Tanh[x]^4/(a + b*Tanh[x]^2)^(5/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{5/2}}-\frac{(a+4 b) \tanh (x)}{3 b (a+b)^2 \sqrt{a+b \tanh ^2(x)}}+\frac{a \tanh (x)}{3 b (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{5/2}}-\frac{(a+4 b) \tanh (x)}{3 b (a+b)^2 \sqrt{a+b \tanh ^2(x)}}+\frac{a \tanh (x)}{3 b (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}",1,"ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/(a + b)^(5/2) + (a*Tanh[x])/(3*b*(a + b)*(a + b*Tanh[x]^2)^(3/2)) - ((a + 4*b)*Tanh[x])/(3*b*(a + b)^2*Sqrt[a + b*Tanh[x]^2])","A",6,6,17,0.3529,1,"{3670, 470, 527, 12, 377, 206}"
249,1,74,0,0.1440092,"\int \frac{\tanh ^3(x)}{\left(a+b \tanh ^2(x)\right)^{5/2}} \, dx","Int[Tanh[x]^3/(a + b*Tanh[x]^2)^(5/2),x]","\frac{a}{3 b (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}-\frac{1}{(a+b)^2 \sqrt{a+b \tanh ^2(x)}}","\frac{a}{3 b (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}-\frac{1}{(a+b)^2 \sqrt{a+b \tanh ^2(x)}}",1,"ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]]/(a + b)^(5/2) + a/(3*b*(a + b)*(a + b*Tanh[x]^2)^(3/2)) - 1/((a + b)^2*Sqrt[a + b*Tanh[x]^2])","A",6,6,17,0.3529,1,"{3670, 446, 78, 51, 63, 208}"
250,1,88,0,0.1318126,"\int \frac{\tanh ^2(x)}{\left(a+b \tanh ^2(x)\right)^{5/2}} \, dx","Int[Tanh[x]^2/(a + b*Tanh[x]^2)^(5/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{5/2}}-\frac{(2 a-b) \tanh (x)}{3 a (a+b)^2 \sqrt{a+b \tanh ^2(x)}}-\frac{\tanh (x)}{3 (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{5/2}}-\frac{(2 a-b) \tanh (x)}{3 a (a+b)^2 \sqrt{a+b \tanh ^2(x)}}-\frac{\tanh (x)}{3 (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}",1,"ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/(a + b)^(5/2) - Tanh[x]/(3*(a + b)*(a + b*Tanh[x]^2)^(3/2)) - ((2*a - b)*Tanh[x])/(3*a*(a + b)^2*Sqrt[a + b*Tanh[x]^2])","A",6,6,17,0.3529,1,"{3670, 471, 527, 12, 377, 206}"
251,1,70,0,0.1030771,"\int \frac{\tanh (x)}{\left(a+b \tanh ^2(x)\right)^{5/2}} \, dx","Int[Tanh[x]/(a + b*Tanh[x]^2)^(5/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}-\frac{1}{(a+b)^2 \sqrt{a+b \tanh ^2(x)}}-\frac{1}{3 (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}-\frac{1}{(a+b)^2 \sqrt{a+b \tanh ^2(x)}}-\frac{1}{3 (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}",1,"ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]]/(a + b)^(5/2) - 1/(3*(a + b)*(a + b*Tanh[x]^2)^(3/2)) - 1/((a + b)^2*Sqrt[a + b*Tanh[x]^2])","A",6,5,15,0.3333,1,"{3670, 444, 51, 63, 208}"
252,1,93,0,0.0852452,"\int \frac{1}{\left(a+b \tanh ^2(x)\right)^{5/2}} \, dx","Int[(a + b*Tanh[x]^2)^(-5/2),x]","\frac{b (5 a+2 b) \tanh (x)}{3 a^2 (a+b)^2 \sqrt{a+b \tanh ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{5/2}}+\frac{b \tanh (x)}{3 a (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}","\frac{b (5 a+2 b) \tanh (x)}{3 a^2 (a+b)^2 \sqrt{a+b \tanh ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{5/2}}+\frac{b \tanh (x)}{3 a (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}",1,"ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/(a + b)^(5/2) + (b*Tanh[x])/(3*a*(a + b)*(a + b*Tanh[x]^2)^(3/2)) + (b*(5*a + 2*b)*Tanh[x])/(3*a^2*(a + b)^2*Sqrt[a + b*Tanh[x]^2])","A",6,6,12,0.5000,1,"{3661, 414, 527, 12, 377, 206}"
253,1,108,0,0.2083737,"\int \frac{\coth (x)}{\left(a+b \tanh ^2(x)\right)^{5/2}} \, dx","Int[Coth[x]/(a + b*Tanh[x]^2)^(5/2),x]","\frac{b (2 a+b)}{a^2 (a+b)^2 \sqrt{a+b \tanh ^2(x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{b}{3 a (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}","\frac{b (2 a+b)}{a^2 (a+b)^2 \sqrt{a+b \tanh ^2(x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{b}{3 a (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \tanh ^2(x)}}{\sqrt{a+b}}\right)}{(a+b)^{5/2}}",1,"-(ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a]]/a^(5/2)) + ArcTanh[Sqrt[a + b*Tanh[x]^2]/Sqrt[a + b]]/(a + b)^(5/2) + b/(3*a*(a + b)*(a + b*Tanh[x]^2)^(3/2)) + (b*(2*a + b))/(a^2*(a + b)^2*Sqrt[a + b*Tanh[x]^2])","A",9,7,15,0.4667,1,"{3670, 446, 85, 152, 156, 63, 208}"
254,1,131,0,0.241572,"\int \frac{\coth ^2(x)}{\left(a+b \tanh ^2(x)\right)^{5/2}} \, dx","Int[Coth[x]^2/(a + b*Tanh[x]^2)^(5/2),x]","-\frac{(3 a+2 b) (a+4 b) \coth (x) \sqrt{a+b \tanh ^2(x)}}{3 a^3 (a+b)^2}+\frac{b (7 a+4 b) \coth (x)}{3 a^2 (a+b)^2 \sqrt{a+b \tanh ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{5/2}}+\frac{b \coth (x)}{3 a (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}","-\frac{(3 a+2 b) (a+4 b) \coth (x) \sqrt{a+b \tanh ^2(x)}}{3 a^3 (a+b)^2}+\frac{b (7 a+4 b) \coth (x)}{3 a^2 (a+b)^2 \sqrt{a+b \tanh ^2(x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b} \tanh (x)}{\sqrt{a+b \tanh ^2(x)}}\right)}{(a+b)^{5/2}}+\frac{b \coth (x)}{3 a (a+b) \left(a+b \tanh ^2(x)\right)^{3/2}}",1,"ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/(a + b)^(5/2) + (b*Coth[x])/(3*a*(a + b)*(a + b*Tanh[x]^2)^(3/2)) + (b*(7*a + 4*b)*Coth[x])/(3*a^2*(a + b)^2*Sqrt[a + b*Tanh[x]^2]) - ((3*a + 2*b)*(a + 4*b)*Coth[x]*Sqrt[a + b*Tanh[x]^2])/(3*a^3*(a + b)^2)","A",7,7,17,0.4118,1,"{3670, 472, 579, 583, 12, 377, 206}"
255,1,25,0,0.0185679,"\int \frac{1}{\sqrt{1+\tanh ^2(x)}} \, dx","Int[1/Sqrt[1 + Tanh[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \tanh (x)}{\sqrt{\tanh ^2(x)+1}}\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \tanh (x)}{\sqrt{\tanh ^2(x)+1}}\right)}{\sqrt{2}}",1,"ArcTanh[(Sqrt[2]*Tanh[x])/Sqrt[1 + Tanh[x]^2]]/Sqrt[2]","A",3,3,10,0.3000,1,"{3661, 377, 206}"
256,1,27,0,0.0201954,"\int \frac{1}{\sqrt{-1-\tanh ^2(x)}} \, dx","Int[1/Sqrt[-1 - Tanh[x]^2],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \tanh (x)}{\sqrt{-\tanh ^2(x)-1}}\right)}{\sqrt{2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \tanh (x)}{\sqrt{-\tanh ^2(x)-1}}\right)}{\sqrt{2}}",1,"ArcTan[(Sqrt[2]*Tanh[x])/Sqrt[-1 - Tanh[x]^2]]/Sqrt[2]","A",3,3,12,0.2500,1,"{3661, 377, 203}"
257,1,112,0,0.0749499,"\int \left(a+b \tanh ^3(c+d x)\right)^2 \, dx","Int[(a + b*Tanh[c + d*x]^3)^2,x]","-\frac{a b \tanh ^2(c+d x)}{d}-\frac{(a+b)^2 \log (1-\tanh (c+d x))}{2 d}+\frac{(a-b)^2 \log (\tanh (c+d x)+1)}{2 d}-\frac{b^2 \tanh ^5(c+d x)}{5 d}-\frac{b^2 \tanh ^3(c+d x)}{3 d}-\frac{b^2 \tanh (c+d x)}{d}","x \left(a^2+b^2\right)-\frac{a b \tanh ^2(c+d x)}{d}+\frac{2 a b \log (\cosh (c+d x))}{d}-\frac{b^2 \tanh ^5(c+d x)}{5 d}-\frac{b^2 \tanh ^3(c+d x)}{3 d}-\frac{b^2 \tanh (c+d x)}{d}",1,"-((a + b)^2*Log[1 - Tanh[c + d*x]])/(2*d) + ((a - b)^2*Log[1 + Tanh[c + d*x]])/(2*d) - (b^2*Tanh[c + d*x])/d - (a*b*Tanh[c + d*x]^2)/d - (b^2*Tanh[c + d*x]^3)/(3*d) - (b^2*Tanh[c + d*x]^5)/(5*d)","A",6,4,14,0.2857,1,"{3661, 1810, 633, 31}"
258,1,38,0,0.0662628,"\int \frac{1}{1+\tanh ^3(x)} \, dx","Int[(1 + Tanh[x]^3)^(-1),x]","\frac{x}{2}-\frac{1}{6 (\tanh (x)+1)}-\frac{2 \tan ^{-1}\left(\frac{1-2 \tanh (x)}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{x}{2}-\frac{1}{6 (\tanh (x)+1)}-\frac{2 \tan ^{-1}\left(\frac{1-2 \tanh (x)}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"x/2 - (2*ArcTan[(1 - 2*Tanh[x])/Sqrt[3]])/(3*Sqrt[3]) - 1/(6*(1 + Tanh[x]))","A",6,5,8,0.6250,1,"{3661, 2074, 207, 618, 204}"
259,1,124,0,0.2418081,"\int \tanh (x) \left(a+b \tanh ^4(x)\right)^{3/2} \, dx","Int[Tanh[x]*(a + b*Tanh[x]^4)^(3/2),x]","\frac{1}{2} (a+b)^{3/2} \tanh ^{-1}\left(\frac{a+b \tanh ^2(x)}{\sqrt{a+b} \sqrt{a+b \tanh ^4(x)}}\right)-\frac{1}{6} \left(a+b \tanh ^4(x)\right)^{3/2}-\frac{1}{4} \sqrt{b} (3 a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh ^2(x)}{\sqrt{a+b \tanh ^4(x)}}\right)-\frac{1}{4} \left(2 (a+b)+b \tanh ^2(x)\right) \sqrt{a+b \tanh ^4(x)}","\frac{1}{2} (a+b)^{3/2} \tanh ^{-1}\left(\frac{a+b \tanh ^2(x)}{\sqrt{a+b} \sqrt{a+b \tanh ^4(x)}}\right)-\frac{1}{6} \left(a+b \tanh ^4(x)\right)^{3/2}-\frac{1}{4} \sqrt{b} (3 a+2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \tanh ^2(x)}{\sqrt{a+b \tanh ^4(x)}}\right)-\frac{1}{4} \left(2 (a+b)+b \tanh ^2(x)\right) \sqrt{a+b \tanh ^4(x)}",1,"-(Sqrt[b]*(3*a + 2*b)*ArcTanh[(Sqrt[b]*Tanh[x]^2)/Sqrt[a + b*Tanh[x]^4]])/4 + ((a + b)^(3/2)*ArcTanh[(a + b*Tanh[x]^2)/(Sqrt[a + b]*Sqrt[a + b*Tanh[x]^4])])/2 - ((2*(a + b) + b*Tanh[x]^2)*Sqrt[a + b*Tanh[x]^4])/4 - (a + b*Tanh[x]^4)^(3/2)/6","A",9,8,15,0.5333,1,"{3670, 1248, 735, 815, 844, 217, 206, 725}"
260,1,89,0,0.1284024,"\int \tanh (x) \sqrt{a+b \tanh ^4(x)} \, dx","Int[Tanh[x]*Sqrt[a + b*Tanh[x]^4],x]","-\frac{1}{2} \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh ^2(x)}{\sqrt{a+b \tanh ^4(x)}}\right)+\frac{1}{2} \sqrt{a+b} \tanh ^{-1}\left(\frac{a+b \tanh ^2(x)}{\sqrt{a+b} \sqrt{a+b \tanh ^4(x)}}\right)-\frac{1}{2} \sqrt{a+b \tanh ^4(x)}","-\frac{1}{2} \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \tanh ^2(x)}{\sqrt{a+b \tanh ^4(x)}}\right)+\frac{1}{2} \sqrt{a+b} \tanh ^{-1}\left(\frac{a+b \tanh ^2(x)}{\sqrt{a+b} \sqrt{a+b \tanh ^4(x)}}\right)-\frac{1}{2} \sqrt{a+b \tanh ^4(x)}",1,"-(Sqrt[b]*ArcTanh[(Sqrt[b]*Tanh[x]^2)/Sqrt[a + b*Tanh[x]^4]])/2 + (Sqrt[a + b]*ArcTanh[(a + b*Tanh[x]^2)/(Sqrt[a + b]*Sqrt[a + b*Tanh[x]^4])])/2 - Sqrt[a + b*Tanh[x]^4]/2","A",8,7,15,0.4667,1,"{3670, 1248, 735, 844, 217, 206, 725}"
261,1,40,0,0.0782411,"\int \frac{\tanh (x)}{\sqrt{a+b \tanh ^4(x)}} \, dx","Int[Tanh[x]/Sqrt[a + b*Tanh[x]^4],x]","\frac{\tanh ^{-1}\left(\frac{a+b \tanh ^2(x)}{\sqrt{a+b} \sqrt{a+b \tanh ^4(x)}}\right)}{2 \sqrt{a+b}}","\frac{\tanh ^{-1}\left(\frac{a+b \tanh ^2(x)}{\sqrt{a+b} \sqrt{a+b \tanh ^4(x)}}\right)}{2 \sqrt{a+b}}",1,"ArcTanh[(a + b*Tanh[x]^2)/(Sqrt[a + b]*Sqrt[a + b*Tanh[x]^4])]/(2*Sqrt[a + b])","A",4,4,15,0.2667,1,"{3670, 1248, 725, 206}"
262,1,74,0,0.1228712,"\int \frac{\tanh (x)}{\left(a+b \tanh ^4(x)\right)^{3/2}} \, dx","Int[Tanh[x]/(a + b*Tanh[x]^4)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{a+b \tanh ^2(x)}{\sqrt{a+b} \sqrt{a+b \tanh ^4(x)}}\right)}{2 (a+b)^{3/2}}-\frac{a-b \tanh ^2(x)}{2 a (a+b) \sqrt{a+b \tanh ^4(x)}}","\frac{\tanh ^{-1}\left(\frac{a+b \tanh ^2(x)}{\sqrt{a+b} \sqrt{a+b \tanh ^4(x)}}\right)}{2 (a+b)^{3/2}}-\frac{a-b \tanh ^2(x)}{2 a (a+b) \sqrt{a+b \tanh ^4(x)}}",1,"ArcTanh[(a + b*Tanh[x]^2)/(Sqrt[a + b]*Sqrt[a + b*Tanh[x]^4])]/(2*(a + b)^(3/2)) - (a - b*Tanh[x]^2)/(2*a*(a + b)*Sqrt[a + b*Tanh[x]^4])","A",6,6,15,0.4000,1,"{3670, 1248, 741, 12, 725, 206}"
263,1,118,0,0.1987536,"\int \frac{\tanh (x)}{\left(a+b \tanh ^4(x)\right)^{5/2}} \, dx","Int[Tanh[x]/(a + b*Tanh[x]^4)^(5/2),x]","-\frac{3 a^2-b (5 a+2 b) \tanh ^2(x)}{6 a^2 (a+b)^2 \sqrt{a+b \tanh ^4(x)}}+\frac{\tanh ^{-1}\left(\frac{a+b \tanh ^2(x)}{\sqrt{a+b} \sqrt{a+b \tanh ^4(x)}}\right)}{2 (a+b)^{5/2}}-\frac{a-b \tanh ^2(x)}{6 a (a+b) \left(a+b \tanh ^4(x)\right)^{3/2}}","-\frac{3 a^2-b (5 a+2 b) \tanh ^2(x)}{6 a^2 (a+b)^2 \sqrt{a+b \tanh ^4(x)}}+\frac{\tanh ^{-1}\left(\frac{a+b \tanh ^2(x)}{\sqrt{a+b} \sqrt{a+b \tanh ^4(x)}}\right)}{2 (a+b)^{5/2}}-\frac{a-b \tanh ^2(x)}{6 a (a+b) \left(a+b \tanh ^4(x)\right)^{3/2}}",1,"ArcTanh[(a + b*Tanh[x]^2)/(Sqrt[a + b]*Sqrt[a + b*Tanh[x]^4])]/(2*(a + b)^(5/2)) - (a - b*Tanh[x]^2)/(6*a*(a + b)*(a + b*Tanh[x]^4)^(3/2)) - (3*a^2 - b*(5*a + 2*b)*Tanh[x]^2)/(6*a^2*(a + b)^2*Sqrt[a + b*Tanh[x]^4])","A",7,7,15,0.4667,1,"{3670, 1248, 741, 823, 12, 725, 206}"