1,1,89,0,0.0548921,"\int \sinh ^4(c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Sinh[c + d*x]^4*(a + b*Sinh[c + d*x]^2),x]","\frac{(6 a-5 b) \sinh ^3(c+d x) \cosh (c+d x)}{24 d}-\frac{(6 a-5 b) \sinh (c+d x) \cosh (c+d x)}{16 d}+\frac{1}{16} x (6 a-5 b)+\frac{b \sinh ^5(c+d x) \cosh (c+d x)}{6 d}","\frac{(6 a-5 b) \sinh ^3(c+d x) \cosh (c+d x)}{24 d}-\frac{(6 a-5 b) \sinh (c+d x) \cosh (c+d x)}{16 d}+\frac{1}{16} x (6 a-5 b)+\frac{b \sinh ^5(c+d x) \cosh (c+d x)}{6 d}",1,"((6*a - 5*b)*x)/16 - ((6*a - 5*b)*Cosh[c + d*x]*Sinh[c + d*x])/(16*d) + ((6*a - 5*b)*Cosh[c + d*x]*Sinh[c + d*x]^3)/(24*d) + (b*Cosh[c + d*x]*Sinh[c + d*x]^5)/(6*d)","A",4,3,21,0.1429,1,"{3014, 2635, 8}"
2,1,53,0,0.0557225,"\int \sinh ^3(c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Sinh[c + d*x]^3*(a + b*Sinh[c + d*x]^2),x]","\frac{(a-2 b) \cosh ^3(c+d x)}{3 d}-\frac{(a-b) \cosh (c+d x)}{d}+\frac{b \cosh ^5(c+d x)}{5 d}","\frac{(a-2 b) \cosh ^3(c+d x)}{3 d}-\frac{(a-b) \cosh (c+d x)}{d}+\frac{b \cosh ^5(c+d x)}{5 d}",1,"-(((a - b)*Cosh[c + d*x])/d) + ((a - 2*b)*Cosh[c + d*x]^3)/(3*d) + (b*Cosh[c + d*x]^5)/(5*d)","A",3,2,21,0.09524,1,"{3013, 373}"
3,1,61,0,0.0428877,"\int \sinh ^2(c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Sinh[c + d*x]^2*(a + b*Sinh[c + d*x]^2),x]","\frac{(4 a-3 b) \sinh (c+d x) \cosh (c+d x)}{8 d}-\frac{1}{8} x (4 a-3 b)+\frac{b \sinh ^3(c+d x) \cosh (c+d x)}{4 d}","\frac{(4 a-3 b) \sinh (c+d x) \cosh (c+d x)}{8 d}-\frac{1}{8} x (4 a-3 b)+\frac{b \sinh ^3(c+d x) \cosh (c+d x)}{4 d}",1,"-((4*a - 3*b)*x)/8 + ((4*a - 3*b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (b*Cosh[c + d*x]*Sinh[c + d*x]^3)/(4*d)","A",3,3,21,0.1429,1,"{3014, 2635, 8}"
4,1,32,0,0.0289156,"\int \sinh (c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Sinh[c + d*x]*(a + b*Sinh[c + d*x]^2),x]","\frac{(a-b) \cosh (c+d x)}{d}+\frac{b \cosh ^3(c+d x)}{3 d}","\frac{(a-b) \cosh (c+d x)}{d}+\frac{b \cosh ^3(c+d x)}{3 d}",1,"((a - b)*Cosh[c + d*x])/d + (b*Cosh[c + d*x]^3)/(3*d)","A",2,1,19,0.05263,1,"{3013}"
5,1,30,0,0.0160623,"\int \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[a + b*Sinh[c + d*x]^2,x]","a x+\frac{b \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{b x}{2}","a x+\frac{b \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{b x}{2}",1,"a*x - (b*x)/2 + (b*Cosh[c + d*x]*Sinh[c + d*x])/(2*d)","A",3,2,12,0.1667,1,"{2635, 8}"
6,1,25,0,0.0350184,"\int \text{csch}(c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Csch[c + d*x]*(a + b*Sinh[c + d*x]^2),x]","\frac{b \cosh (c+d x)}{d}-\frac{a \tanh ^{-1}(\cosh (c+d x))}{d}","\frac{b \cosh (c+d x)}{d}-\frac{a \tanh ^{-1}(\cosh (c+d x))}{d}",1,"-((a*ArcTanh[Cosh[c + d*x]])/d) + (b*Cosh[c + d*x])/d","A",2,2,19,0.1053,1,"{3014, 3770}"
7,1,16,0,0.0266243,"\int \text{csch}^2(c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Csch[c + d*x]^2*(a + b*Sinh[c + d*x]^2),x]","b x-\frac{a \coth (c+d x)}{d}","b x-\frac{a \coth (c+d x)}{d}",1,"b*x - (a*Coth[c + d*x])/d","A",2,2,21,0.09524,1,"{3012, 8}"
8,1,40,0,0.04142,"\int \text{csch}^3(c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Csch[c + d*x]^3*(a + b*Sinh[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{(a-2 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{a \coth (c+d x) \text{csch}(c+d x)}{2 d}",1,"((a - 2*b)*ArcTanh[Cosh[c + d*x]])/(2*d) - (a*Coth[c + d*x]*Csch[c + d*x])/(2*d)","A",2,2,21,0.09524,1,"{3012, 3770}"
9,1,43,0,0.0394368,"\int \text{csch}^4(c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Csch[c + d*x]^4*(a + b*Sinh[c + d*x]^2),x]","\frac{(2 a-3 b) \coth (c+d x)}{3 d}-\frac{a \coth (c+d x) \text{csch}^2(c+d x)}{3 d}","\frac{(2 a-3 b) \coth (c+d x)}{3 d}-\frac{a \coth (c+d x) \text{csch}^2(c+d x)}{3 d}",1,"((2*a - 3*b)*Coth[c + d*x])/(3*d) - (a*Coth[c + d*x]*Csch[c + d*x]^2)/(3*d)","A",3,3,21,0.1429,1,"{3012, 3767, 8}"
10,1,146,0,0.1803999,"\int \sinh ^4(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]^4*(a + b*Sinh[c + d*x]^2)^2,x]","\frac{\left(48 a^2-208 a b+139 b^2\right) \sinh (c+d x) \cosh ^3(c+d x)}{192 d}-\frac{\left(80 a^2-176 a b+93 b^2\right) \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{1}{128} x \left(48 a^2-80 a b+35 b^2\right)+\frac{b (16 a-13 b) \sinh (c+d x) \cosh ^5(c+d x)}{48 d}+\frac{b^2 \sinh ^5(c+d x) \cosh ^3(c+d x)}{8 d}","\frac{\left(48 a^2-208 a b+139 b^2\right) \sinh (c+d x) \cosh ^3(c+d x)}{192 d}-\frac{\left(80 a^2-176 a b+93 b^2\right) \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{1}{128} x \left(48 a^2-80 a b+35 b^2\right)+\frac{b (16 a-13 b) \sinh (c+d x) \cosh ^5(c+d x)}{48 d}+\frac{b^2 \sinh ^5(c+d x) \cosh ^3(c+d x)}{8 d}",1,"((48*a^2 - 80*a*b + 35*b^2)*x)/128 - ((80*a^2 - 176*a*b + 93*b^2)*Cosh[c + d*x]*Sinh[c + d*x])/(128*d) + ((48*a^2 - 208*a*b + 139*b^2)*Cosh[c + d*x]^3*Sinh[c + d*x])/(192*d) + ((16*a - 13*b)*b*Cosh[c + d*x]^5*Sinh[c + d*x])/(48*d) + (b^2*Cosh[c + d*x]^3*Sinh[c + d*x]^5)/(8*d)","A",6,6,23,0.2609,1,"{3187, 463, 455, 1157, 385, 206}"
11,1,85,0,0.0974927,"\int \sinh ^3(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]^3*(a + b*Sinh[c + d*x]^2)^2,x]","\frac{b (2 a-3 b) \cosh ^5(c+d x)}{5 d}+\frac{(a-3 b) (a-b) \cosh ^3(c+d x)}{3 d}-\frac{(a-b)^2 \cosh (c+d x)}{d}+\frac{b^2 \cosh ^7(c+d x)}{7 d}","\frac{b (2 a-3 b) \cosh ^5(c+d x)}{5 d}+\frac{(a-3 b) (a-b) \cosh ^3(c+d x)}{3 d}-\frac{(a-b)^2 \cosh (c+d x)}{d}+\frac{b^2 \cosh ^7(c+d x)}{7 d}",1,"-(((a - b)^2*Cosh[c + d*x])/d) + ((a - 3*b)*(a - b)*Cosh[c + d*x]^3)/(3*d) + ((2*a - 3*b)*b*Cosh[c + d*x]^5)/(5*d) + (b^2*Cosh[c + d*x]^7)/(7*d)","A",3,2,23,0.08696,1,"{3186, 373}"
12,1,117,0,0.1100673,"\int \sinh ^2(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]^2*(a + b*Sinh[c + d*x]^2)^2,x]","\frac{\left(16 a^2-36 a b+15 b^2\right) \sinh (c+d x) \cosh (c+d x)}{48 d}-\frac{1}{16} x \left(8 a^2-12 a b+5 b^2\right)+\frac{b (4 a-5 b) \sinh ^3(c+d x) \cosh (c+d x)}{24 d}+\frac{\sinh (c+d x) \cosh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^2}{6 d}","\frac{\left(8 a^2-20 a b+11 b^2\right) \sinh (c+d x) \cosh (c+d x)}{16 d}-\frac{1}{16} x \left(8 a^2-12 a b+5 b^2\right)+\frac{b (4 a-3 b) \sinh (c+d x) \cosh ^3(c+d x)}{8 d}+\frac{b^2 \sinh ^3(c+d x) \cosh ^3(c+d x)}{6 d}",1,"-((8*a^2 - 12*a*b + 5*b^2)*x)/16 + ((16*a^2 - 36*a*b + 15*b^2)*Cosh[c + d*x]*Sinh[c + d*x])/(48*d) + ((4*a - 5*b)*b*Cosh[c + d*x]*Sinh[c + d*x]^3)/(24*d) + (Cosh[c + d*x]*Sinh[c + d*x]*(a + b*Sinh[c + d*x]^2)^2)/(6*d)","A",2,2,23,0.08696,1,"{3170, 3169}"
13,1,57,0,0.0600295,"\int \sinh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]*(a + b*Sinh[c + d*x]^2)^2,x]","\frac{2 b (a-b) \cosh ^3(c+d x)}{3 d}+\frac{(a-b)^2 \cosh (c+d x)}{d}+\frac{b^2 \cosh ^5(c+d x)}{5 d}","\frac{2 b (a-b) \cosh ^3(c+d x)}{3 d}+\frac{(a-b)^2 \cosh (c+d x)}{d}+\frac{b^2 \cosh ^5(c+d x)}{5 d}",1,"((a - b)^2*Cosh[c + d*x])/d + (2*(a - b)*b*Cosh[c + d*x]^3)/(3*d) + (b^2*Cosh[c + d*x]^5)/(5*d)","A",3,2,21,0.09524,1,"{3186, 194}"
14,1,72,0,0.0217836,"\int \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[(a + b*Sinh[c + d*x]^2)^2,x]","\frac{1}{8} x \left(8 a^2-8 a b+3 b^2\right)+\frac{b (8 a-3 b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{b^2 \sinh ^3(c+d x) \cosh (c+d x)}{4 d}","\frac{1}{8} x \left(8 a^2-8 a b+3 b^2\right)+\frac{b (8 a-3 b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{b^2 \sinh ^3(c+d x) \cosh (c+d x)}{4 d}",1,"((8*a^2 - 8*a*b + 3*b^2)*x)/8 + ((8*a - 3*b)*b*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (b^2*Cosh[c + d*x]*Sinh[c + d*x]^3)/(4*d)","A",1,1,14,0.07143,1,"{3179}"
15,1,52,0,0.0657536,"\int \text{csch}(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]*(a + b*Sinh[c + d*x]^2)^2,x]","-\frac{a^2 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b (2 a-b) \cosh (c+d x)}{d}+\frac{b^2 \cosh ^3(c+d x)}{3 d}","-\frac{a^2 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b (2 a-b) \cosh (c+d x)}{d}+\frac{b^2 \cosh ^3(c+d x)}{3 d}",1,"-((a^2*ArcTanh[Cosh[c + d*x]])/d) + ((2*a - b)*b*Cosh[c + d*x])/d + (b^2*Cosh[c + d*x]^3)/(3*d)","A",4,3,21,0.1429,1,"{3186, 390, 206}"
16,1,64,0,0.0813633,"\int \text{csch}^2(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^2*(a + b*Sinh[c + d*x]^2)^2,x]","\frac{\left(2 a^2+b^2\right) \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{a^2 \cosh ^2(c+d x) \coth (c+d x)}{d}+\frac{1}{2} b x (4 a-b)","-\frac{a^2 \coth (c+d x)}{d}+\frac{1}{2} b x (4 a-b)+\frac{b^2 \sinh (c+d x) \cosh (c+d x)}{2 d}",1,"((4*a - b)*b*x)/2 - (a^2*Cosh[c + d*x]^2*Coth[c + d*x])/d + ((2*a^2 + b^2)*Cosh[c + d*x]*Sinh[c + d*x])/(2*d)","A",4,4,23,0.1739,1,"{3187, 462, 385, 206}"
17,1,56,0,0.0880729,"\int \text{csch}^3(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^3*(a + b*Sinh[c + d*x]^2)^2,x]","-\frac{a^2 \coth (c+d x) \text{csch}(c+d x)}{2 d}+\frac{a (a-4 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}+\frac{b^2 \cosh (c+d x)}{d}","-\frac{a^2 \coth (c+d x) \text{csch}(c+d x)}{2 d}+\frac{a (a-4 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}+\frac{b^2 \cosh (c+d x)}{d}",1,"(a*(a - 4*b)*ArcTanh[Cosh[c + d*x]])/(2*d) + (b^2*Cosh[c + d*x])/d - (a^2*Coth[c + d*x]*Csch[c + d*x])/(2*d)","A",5,4,23,0.1739,1,"{3186, 390, 385, 206}"
18,1,40,0,0.0741049,"\int \text{csch}^4(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^4*(a + b*Sinh[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}+b^2 x","-\frac{a^2 \coth ^3(c+d x)}{3 d}+\frac{a (a-2 b) \coth (c+d x)}{d}+b^2 x",1,"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,"{3187, 461, 207}"
19,1,261,0,0.429778,"\int \sinh ^4(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]^4*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{\left(-272 a^2 b+48 a^3+314 a b^2-105 b^3\right) \sinh (c+d x) \cosh ^3(c+d x)}{640 d}-\frac{\left(-1744 a^2 b+576 a^3+1678 a b^2-525 b^3\right) \sinh (c+d x) \cosh (c+d x)}{1280 d}+\frac{3}{256} x (4 a-3 b) \left(8 a^2-14 a b+7 b^2\right)+\frac{\sinh ^3(c+d x) \cosh ^7(c+d x) \left(a-(a-b) \tanh ^2(c+d x)\right)^3}{10 d}+\frac{3 (2 a-3 b) \sinh ^3(c+d x) \cosh ^5(c+d x) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}{80 d}-\frac{b \sinh ^3(c+d x) \cosh ^3(c+d x) \left(a (14 a-9 b)-(22 a-21 b) (a-b) \tanh ^2(c+d x)\right)}{160 d}","\frac{\left(-272 a^2 b+48 a^3+314 a b^2-105 b^3\right) \sinh (c+d x) \cosh ^3(c+d x)}{640 d}-\frac{\left(-1744 a^2 b+576 a^3+1678 a b^2-525 b^3\right) \sinh (c+d x) \cosh (c+d x)}{1280 d}+\frac{3}{256} x (4 a-3 b) \left(8 a^2-14 a b+7 b^2\right)+\frac{\sinh ^3(c+d x) \cosh ^7(c+d x) \left(a-(a-b) \tanh ^2(c+d x)\right)^3}{10 d}+\frac{3 (2 a-3 b) \sinh ^3(c+d x) \cosh ^5(c+d x) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}{80 d}-\frac{b \sinh ^3(c+d x) \cosh ^3(c+d x) \left(a (14 a-9 b)-(22 a-21 b) (a-b) \tanh ^2(c+d x)\right)}{160 d}",1,"(3*(4*a - 3*b)*(8*a^2 - 14*a*b + 7*b^2)*x)/256 - ((576*a^3 - 1744*a^2*b + 1678*a*b^2 - 525*b^3)*Cosh[c + d*x]*Sinh[c + d*x])/(1280*d) + ((48*a^3 - 272*a^2*b + 314*a*b^2 - 105*b^3)*Cosh[c + d*x]^3*Sinh[c + d*x])/(640*d) + (3*(2*a - 3*b)*Cosh[c + d*x]^5*Sinh[c + d*x]^3*(a - (a - b)*Tanh[c + d*x]^2)^2)/(80*d) + (Cosh[c + d*x]^7*Sinh[c + d*x]^3*(a - (a - b)*Tanh[c + d*x]^2)^3)/(10*d) - (b*Cosh[c + d*x]^3*Sinh[c + d*x]^3*(a*(14*a - 9*b) - (22*a - 21*b)*(a - b)*Tanh[c + d*x]^2))/(160*d)","A",7,6,23,0.2609,1,"{3187, 467, 577, 455, 385, 206}"
20,1,115,0,0.1291727,"\int \sinh ^3(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]^3*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{b^2 (3 a-4 b) \cosh ^7(c+d x)}{7 d}+\frac{3 b (a-2 b) (a-b) \cosh ^5(c+d x)}{5 d}+\frac{(a-4 b) (a-b)^2 \cosh ^3(c+d x)}{3 d}-\frac{(a-b)^3 \cosh (c+d x)}{d}+\frac{b^3 \cosh ^9(c+d x)}{9 d}","\frac{b^2 (3 a-4 b) \cosh ^7(c+d x)}{7 d}+\frac{3 b (a-2 b) (a-b) \cosh ^5(c+d x)}{5 d}+\frac{(a-4 b) (a-b)^2 \cosh ^3(c+d x)}{3 d}-\frac{(a-b)^3 \cosh (c+d x)}{d}+\frac{b^3 \cosh ^9(c+d x)}{9 d}",1,"-(((a - b)^3*Cosh[c + d*x])/d) + ((a - 4*b)*(a - b)^2*Cosh[c + d*x]^3)/(3*d) + (3*(a - 2*b)*(a - b)*b*Cosh[c + d*x]^5)/(5*d) + ((3*a - 4*b)*b^2*Cosh[c + d*x]^7)/(7*d) + (b^3*Cosh[c + d*x]^9)/(9*d)","A",3,2,23,0.08696,1,"{3186, 373}"
21,1,181,0,0.1927769,"\int \sinh ^2(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]^2*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{b \left(24 a^2-64 a b+35 b^2\right) \sinh ^3(c+d x) \cosh (c+d x)}{192 d}+\frac{\left(-376 a^2 b+96 a^3+360 a b^2-105 b^3\right) \sinh (c+d x) \cosh (c+d x)}{384 d}-\frac{1}{128} x \left(-144 a^2 b+64 a^3+120 a b^2-35 b^3\right)+\frac{\sinh (c+d x) \cosh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^3}{8 d}+\frac{(6 a-7 b) \sinh (c+d x) \cosh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^2}{48 d}","\frac{b \left(24 a^2-64 a b+35 b^2\right) \sinh ^3(c+d x) \cosh (c+d x)}{192 d}+\frac{\left(-376 a^2 b+96 a^3+360 a b^2-105 b^3\right) \sinh (c+d x) \cosh (c+d x)}{384 d}-\frac{1}{128} x \left(-144 a^2 b+64 a^3+120 a b^2-35 b^3\right)+\frac{\sinh (c+d x) \cosh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^3}{8 d}+\frac{(6 a-7 b) \sinh (c+d x) \cosh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^2}{48 d}",1,"-((64*a^3 - 144*a^2*b + 120*a*b^2 - 35*b^3)*x)/128 + ((96*a^3 - 376*a^2*b + 360*a*b^2 - 105*b^3)*Cosh[c + d*x]*Sinh[c + d*x])/(384*d) + (b*(24*a^2 - 64*a*b + 35*b^2)*Cosh[c + d*x]*Sinh[c + d*x]^3)/(192*d) + ((6*a - 7*b)*Cosh[c + d*x]*Sinh[c + d*x]*(a + b*Sinh[c + d*x]^2)^2)/(48*d) + (Cosh[c + d*x]*Sinh[c + d*x]*(a + b*Sinh[c + d*x]^2)^3)/(8*d)","A",3,2,23,0.08696,1,"{3170, 3169}"
22,1,79,0,0.0873647,"\int \sinh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{3 b^2 (a-b) \cosh ^5(c+d x)}{5 d}+\frac{b (a-b)^2 \cosh ^3(c+d x)}{d}+\frac{(a-b)^3 \cosh (c+d x)}{d}+\frac{b^3 \cosh ^7(c+d x)}{7 d}","\frac{3 b^2 (a-b) \cosh ^5(c+d x)}{5 d}+\frac{b (a-b)^2 \cosh ^3(c+d x)}{d}+\frac{(a-b)^3 \cosh (c+d x)}{d}+\frac{b^3 \cosh ^7(c+d x)}{7 d}",1,"((a - b)^3*Cosh[c + d*x])/d + ((a - b)^2*b*Cosh[c + d*x]^3)/d + (3*(a - b)*b^2*Cosh[c + d*x]^5)/(5*d) + (b^3*Cosh[c + d*x]^7)/(7*d)","A",3,2,21,0.09524,1,"{3186, 194}"
23,1,128,0,0.1000851,"\int \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[(a + b*Sinh[c + d*x]^2)^3,x]","\frac{b \left(64 a^2-54 a b+15 b^2\right) \sinh (c+d x) \cosh (c+d x)}{48 d}+\frac{1}{16} x (2 a-b) \left(8 a^2-8 a b+5 b^2\right)+\frac{5 b^2 (2 a-b) \sinh ^3(c+d x) \cosh (c+d x)}{24 d}+\frac{b \sinh (c+d x) \cosh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^2}{6 d}","\frac{b \left(64 a^2-54 a b+15 b^2\right) \sinh (c+d x) \cosh (c+d x)}{48 d}+\frac{1}{16} x (2 a-b) \left(8 a^2-8 a b+5 b^2\right)+\frac{5 b^2 (2 a-b) \sinh ^3(c+d x) \cosh (c+d x)}{24 d}+\frac{b \sinh (c+d x) \cosh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^2}{6 d}",1,"((2*a - b)*(8*a^2 - 8*a*b + 5*b^2)*x)/16 + (b*(64*a^2 - 54*a*b + 15*b^2)*Cosh[c + d*x]*Sinh[c + d*x])/(48*d) + (5*(2*a - b)*b^2*Cosh[c + d*x]*Sinh[c + d*x]^3)/(24*d) + (b*Cosh[c + d*x]*Sinh[c + d*x]*(a + b*Sinh[c + d*x]^2)^2)/(6*d)","A",2,2,14,0.1429,1,"{3180, 3169}"
24,1,83,0,0.0869544,"\int \text{csch}(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{b \left(3 a^2-3 a b+b^2\right) \cosh (c+d x)}{d}-\frac{a^3 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b^2 (3 a-2 b) \cosh ^3(c+d x)}{3 d}+\frac{b^3 \cosh ^5(c+d x)}{5 d}","\frac{b \left(3 a^2-3 a b+b^2\right) \cosh (c+d x)}{d}-\frac{a^3 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b^2 (3 a-2 b) \cosh ^3(c+d x)}{3 d}+\frac{b^3 \cosh ^5(c+d x)}{5 d}",1,"-((a^3*ArcTanh[Cosh[c + d*x]])/d) + (b*(3*a^2 - 3*a*b + b^2)*Cosh[c + d*x])/d + ((3*a - 2*b)*b^2*Cosh[c + d*x]^3)/(3*d) + (b^3*Cosh[c + d*x]^5)/(5*d)","A",4,3,21,0.1429,1,"{3186, 390, 206}"
25,1,137,0,0.1919366,"\int \text{csch}^2(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^2*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{3}{8} b x \left(8 a^2-4 a b+b^2\right)-\frac{a (2 a+b) (4 a+b) \coth (c+d x)}{8 d}+\frac{b \cosh ^4(c+d x) \coth (c+d x) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}{4 d}+\frac{b \cosh ^2(c+d x) \coth (c+d x) \left(a (4 a+b)-(4 a-3 b) (a-b) \tanh ^2(c+d x)\right)}{8 d}","\frac{3}{8} b x \left(8 a^2-4 a b+b^2\right)-\frac{a (2 a+b) (4 a+b) \coth (c+d x)}{8 d}+\frac{b \cosh ^4(c+d x) \coth (c+d x) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}{4 d}+\frac{b \cosh ^2(c+d x) \coth (c+d x) \left(a (4 a+b)-(4 a-3 b) (a-b) \tanh ^2(c+d x)\right)}{8 d}",1,"(3*b*(8*a^2 - 4*a*b + b^2)*x)/8 - (a*(2*a + b)*(4*a + b)*Coth[c + d*x])/(8*d) + (b*Cosh[c + d*x]^4*Coth[c + d*x]*(a - (a - b)*Tanh[c + d*x]^2)^2)/(4*d) + (b*Cosh[c + d*x]^2*Coth[c + d*x]*(a*(4*a + b) - (4*a - 3*b)*(a - b)*Tanh[c + d*x]^2))/(8*d)","A",5,5,23,0.2174,1,"{3187, 468, 577, 453, 206}"
26,1,83,0,0.1068447,"\int \text{csch}^3(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^3*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{a^2 (a-6 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{a^3 \coth (c+d x) \text{csch}(c+d x)}{2 d}+\frac{b^2 (3 a-b) \cosh (c+d x)}{d}+\frac{b^3 \cosh ^3(c+d x)}{3 d}","\frac{a^2 (a-6 b) \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{a^3 \coth (c+d x) \text{csch}(c+d x)}{2 d}+\frac{b^2 (3 a-b) \cosh (c+d x)}{d}+\frac{b^3 \cosh ^3(c+d x)}{3 d}",1,"(a^2*(a - 6*b)*ArcTanh[Cosh[c + d*x]])/(2*d) + ((3*a - b)*b^2*Cosh[c + d*x])/d + (b^3*Cosh[c + d*x]^3)/(3*d) - (a^3*Coth[c + d*x]*Csch[c + d*x])/(2*d)","A",5,4,23,0.1739,1,"{3186, 390, 385, 206}"
27,1,113,0,0.1413871,"\int \text{csch}^4(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^4*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{a \left(2 a^2-5 a b-2 b^2\right) \coth (c+d x)}{2 d}-\frac{a^2 (2 a+3 b) \coth ^3(c+d x)}{6 d}+\frac{1}{2} b^2 x (6 a-b)+\frac{b \cosh ^2(c+d x) \coth ^3(c+d x) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}{2 d}","\frac{a \left(2 a^2-5 a b-2 b^2\right) \coth (c+d x)}{2 d}-\frac{a^2 (2 a+3 b) \coth ^3(c+d x)}{6 d}+\frac{1}{2} b^2 x (6 a-b)+\frac{b \cosh ^2(c+d x) \coth ^3(c+d x) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}{2 d}",1,"((6*a - b)*b^2*x)/2 + (a*(2*a^2 - 5*a*b - 2*b^2)*Coth[c + d*x])/(2*d) - (a^2*(2*a + 3*b)*Coth[c + d*x]^3)/(6*d) + (b*Cosh[c + d*x]^2*Coth[c + d*x]^3*(a - (a - b)*Tanh[c + d*x]^2)^2)/(2*d)","A",5,4,23,0.1739,1,"{3187, 468, 570, 207}"
28,1,109,0,0.149371,"\int \frac{\sinh ^7(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Sinh[c + d*x]^7/(a + b*Sinh[c + d*x]^2),x]","\frac{\left(a^2+a b+b^2\right) \cosh (c+d x)}{b^3 d}-\frac{a^3 \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{b^{7/2} d \sqrt{a-b}}-\frac{(a+2 b) \cosh ^3(c+d x)}{3 b^2 d}+\frac{\cosh ^5(c+d x)}{5 b d}","\frac{\left(a^2+a b+b^2\right) \cosh (c+d x)}{b^3 d}-\frac{a^3 \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{b^{7/2} d \sqrt{a-b}}-\frac{(a+2 b) \cosh ^3(c+d x)}{3 b^2 d}+\frac{\cosh ^5(c+d x)}{5 b d}",1,"-((a^3*ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]])/(Sqrt[a - b]*b^(7/2)*d)) + ((a^2 + a*b + b^2)*Cosh[c + d*x])/(b^3*d) - ((a + 2*b)*Cosh[c + d*x]^3)/(3*b^2*d) + Cosh[c + d*x]^5/(5*b*d)","A",4,3,23,0.1304,1,"{3186, 390, 205}"
29,1,121,0,0.235035,"\int \frac{\sinh ^6(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Sinh[c + d*x]^6/(a + b*Sinh[c + d*x]^2),x]","-\frac{a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{b^3 d \sqrt{a-b}}+\frac{x \left(8 a^2+4 a b+3 b^2\right)}{8 b^3}-\frac{(4 a+3 b) \sinh (c+d x) \cosh (c+d x)}{8 b^2 d}+\frac{\sinh ^3(c+d x) \cosh (c+d x)}{4 b d}","-\frac{a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{b^3 d \sqrt{a-b}}+\frac{x \left(8 a^2+4 a b+3 b^2\right)}{8 b^3}-\frac{(4 a+3 b) \sinh (c+d x) \cosh (c+d x)}{8 b^2 d}+\frac{\sinh ^3(c+d x) \cosh (c+d x)}{4 b d}",1,"((8*a^2 + 4*a*b + 3*b^2)*x)/(8*b^3) - (a^(5/2)*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(Sqrt[a - b]*b^3*d) - ((4*a + 3*b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*b^2*d) + (Cosh[c + d*x]*Sinh[c + d*x]^3)/(4*b*d)","A",6,6,23,0.2609,1,"{3187, 470, 578, 522, 206, 208}"
30,1,79,0,0.1080277,"\int \frac{\sinh ^5(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Sinh[c + d*x]^5/(a + b*Sinh[c + d*x]^2),x]","\frac{a^2 \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{b^{5/2} d \sqrt{a-b}}-\frac{(a+b) \cosh (c+d x)}{b^2 d}+\frac{\cosh ^3(c+d x)}{3 b d}","\frac{a^2 \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{b^{5/2} d \sqrt{a-b}}-\frac{(a+b) \cosh (c+d x)}{b^2 d}+\frac{\cosh ^3(c+d x)}{3 b d}",1,"(a^2*ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]])/(Sqrt[a - b]*b^(5/2)*d) - ((a + b)*Cosh[c + d*x])/(b^2*d) + Cosh[c + d*x]^3/(3*b*d)","A",4,3,23,0.1304,1,"{3186, 390, 205}"
31,1,79,0,0.1213247,"\int \frac{\sinh ^4(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Sinh[c + d*x]^4/(a + b*Sinh[c + d*x]^2),x]","\frac{a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{b^2 d \sqrt{a-b}}-\frac{x (2 a+b)}{2 b^2}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 b d}","\frac{a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{b^2 d \sqrt{a-b}}-\frac{x (2 a+b)}{2 b^2}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 b d}",1,"-((2*a + b)*x)/(2*b^2) + (a^(3/2)*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(Sqrt[a - b]*b^2*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*b*d)","A",5,5,23,0.2174,1,"{3187, 470, 522, 206, 208}"
32,1,56,0,0.0851327,"\int \frac{\sinh ^3(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Sinh[c + d*x]^3/(a + b*Sinh[c + d*x]^2),x]","\frac{\cosh (c+d x)}{b d}-\frac{a \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{b^{3/2} d \sqrt{a-b}}","\frac{\cosh (c+d x)}{b d}-\frac{a \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{b^{3/2} d \sqrt{a-b}}",1,"-((a*ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]])/(Sqrt[a - b]*b^(3/2)*d)) + Cosh[c + d*x]/(b*d)","A",3,3,23,0.1304,1,"{3186, 388, 205}"
33,1,50,0,0.0871054,"\int \frac{\sinh ^2(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Sinh[c + d*x]^2/(a + b*Sinh[c + d*x]^2),x]","\frac{x}{b}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{b d \sqrt{a-b}}","\frac{x}{b}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{b d \sqrt{a-b}}",1,"x/b - (Sqrt[a]*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(Sqrt[a - b]*b*d)","A",3,3,23,0.1304,1,"{3171, 3181, 208}"
34,1,40,0,0.0468252,"\int \frac{\sinh (c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Sinh[c + d*x]/(a + b*Sinh[c + d*x]^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{\sqrt{b} d \sqrt{a-b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{\sqrt{b} d \sqrt{a-b}}",1,"ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]]/(Sqrt[a - b]*Sqrt[b]*d)","A",2,2,21,0.09524,1,"{3186, 205}"
35,1,40,0,0.0270021,"\int \frac{1}{a+b \sinh ^2(c+d x)} \, dx","Int[(a + b*Sinh[c + d*x]^2)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d \sqrt{a-b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d \sqrt{a-b}}",1,"ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]]/(Sqrt[a]*Sqrt[a - b]*d)","A",2,2,14,0.1429,1,"{3181, 208}"
36,1,60,0,0.0742426,"\int \frac{\text{csch}(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Csch[c + d*x]/(a + b*Sinh[c + d*x]^2),x]","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{a d \sqrt{a-b}}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a d}","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{a d \sqrt{a-b}}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a d}",1,"-((Sqrt[b]*ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]])/(a*Sqrt[a - b]*d)) - ArcTanh[Cosh[c + d*x]]/(a*d)","A",4,4,21,0.1905,1,"{3186, 391, 206, 205}"
37,1,57,0,0.0808976,"\int \frac{\text{csch}^2(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Csch[c + d*x]^2/(a + b*Sinh[c + d*x]^2),x]","-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{a^{3/2} d \sqrt{a-b}}-\frac{\coth (c+d x)}{a d}","-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{a^{3/2} d \sqrt{a-b}}-\frac{\coth (c+d x)}{a d}",1,"-((b*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(a^(3/2)*Sqrt[a - b]*d)) - Coth[c + d*x]/(a*d)","A",3,3,23,0.1304,1,"{3187, 453, 208}"
38,1,88,0,0.1234933,"\int \frac{\text{csch}^3(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Csch[c + d*x]^3/(a + b*Sinh[c + d*x]^2),x]","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{a^2 d \sqrt{a-b}}+\frac{(a+2 b) \tanh ^{-1}(\cosh (c+d x))}{2 a^2 d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d}","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{a^2 d \sqrt{a-b}}+\frac{(a+2 b) \tanh ^{-1}(\cosh (c+d x))}{2 a^2 d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d}",1,"(b^(3/2)*ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]])/(a^2*Sqrt[a - b]*d) + ((a + 2*b)*ArcTanh[Cosh[c + d*x]])/(2*a^2*d) - (Coth[c + d*x]*Csch[c + d*x])/(2*a*d)","A",5,5,23,0.2174,1,"{3186, 414, 522, 206, 205}"
39,1,78,0,0.1203927,"\int \frac{\text{csch}^4(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Csch[c + d*x]^4/(a + b*Sinh[c + d*x]^2),x]","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{a^{5/2} d \sqrt{a-b}}+\frac{(a+b) \coth (c+d x)}{a^2 d}-\frac{\coth ^3(c+d x)}{3 a d}","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{a^{5/2} d \sqrt{a-b}}+\frac{(a+b) \coth (c+d x)}{a^2 d}-\frac{\coth ^3(c+d x)}{3 a d}",1,"(b^2*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(a^(5/2)*Sqrt[a - b]*d) + ((a + b)*Coth[c + d*x])/(a^2*d) - Coth[c + d*x]^3/(3*a*d)","A",4,3,23,0.1304,1,"{3187, 461, 208}"
40,1,130,0,0.2035446,"\int \frac{\text{csch}^5(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Csch[c + d*x]^5/(a + b*Sinh[c + d*x]^2),x]","-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{a^3 d \sqrt{a-b}}-\frac{\left(3 a^2+4 a b+8 b^2\right) \tanh ^{-1}(\cosh (c+d x))}{8 a^3 d}+\frac{(3 a+4 b) \coth (c+d x) \text{csch}(c+d x)}{8 a^2 d}-\frac{\coth (c+d x) \text{csch}^3(c+d x)}{4 a d}","-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{a^3 d \sqrt{a-b}}-\frac{\left(3 a^2+4 a b+8 b^2\right) \tanh ^{-1}(\cosh (c+d x))}{8 a^3 d}+\frac{(3 a+4 b) \coth (c+d x) \text{csch}(c+d x)}{8 a^2 d}-\frac{\coth (c+d x) \text{csch}^3(c+d x)}{4 a d}",1,"-((b^(5/2)*ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]])/(a^3*Sqrt[a - b]*d)) - ((3*a^2 + 4*a*b + 8*b^2)*ArcTanh[Cosh[c + d*x]])/(8*a^3*d) + ((3*a + 4*b)*Coth[c + d*x]*Csch[c + d*x])/(8*a^2*d) - (Coth[c + d*x]*Csch[c + d*x]^3)/(4*a*d)","A",6,6,23,0.2609,1,"{3186, 414, 527, 522, 206, 205}"
41,1,110,0,0.1355373,"\int \frac{\text{csch}^6(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Csch[c + d*x]^6/(a + b*Sinh[c + d*x]^2),x]","-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{a^{7/2} d \sqrt{a-b}}-\frac{\left(a^2+a b+b^2\right) \coth (c+d x)}{a^3 d}+\frac{(2 a+b) \coth ^3(c+d x)}{3 a^2 d}-\frac{\coth ^5(c+d x)}{5 a d}","-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{a^{7/2} d \sqrt{a-b}}-\frac{\left(a^2+a b+b^2\right) \coth (c+d x)}{a^3 d}+\frac{(2 a+b) \coth ^3(c+d x)}{3 a^2 d}-\frac{\coth ^5(c+d x)}{5 a d}",1,"-((b^3*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(a^(7/2)*Sqrt[a - b]*d)) - ((a^2 + a*b + b^2)*Coth[c + d*x])/(a^3*d) + ((2*a + b)*Coth[c + d*x]^3)/(3*a^2*d) - Coth[c + d*x]^5/(5*a*d)","A",4,3,23,0.1304,1,"{3187, 461, 208}"
42,1,102,0,0.169097,"\int \frac{\sinh ^4(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^4/(a + b*Sinh[c + d*x]^2)^2,x]","-\frac{\sqrt{a} (2 a-3 b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 b^2 d (a-b)^{3/2}}-\frac{a \tanh (c+d x)}{2 b d (a-b) \left(a-(a-b) \tanh ^2(c+d x)\right)}+\frac{x}{b^2}","-\frac{\sqrt{a} (2 a-3 b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 b^2 d (a-b)^{3/2}}-\frac{a \tanh (c+d x)}{2 b d (a-b) \left(a-(a-b) \tanh ^2(c+d x)\right)}+\frac{x}{b^2}",1,"x/b^2 - (Sqrt[a]*(2*a - 3*b)*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(2*(a - b)^(3/2)*b^2*d) - (a*Tanh[c + d*x])/(2*(a - b)*b*d*(a - (a - b)*Tanh[c + d*x]^2))","A",5,5,23,0.2174,1,"{3187, 470, 522, 206, 208}"
43,1,90,0,0.1125233,"\int \frac{\sinh ^3(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^3/(a + b*Sinh[c + d*x]^2)^2,x]","\frac{(a-2 b) \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{2 b^{3/2} d (a-b)^{3/2}}-\frac{a \cosh (c+d x)}{2 b d (a-b) \left(a+b \cosh ^2(c+d x)-b\right)}","\frac{(a-2 b) \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{2 b^{3/2} d (a-b)^{3/2}}-\frac{a \cosh (c+d x)}{2 b d (a-b) \left(a+b \cosh ^2(c+d x)-b\right)}",1,"((a - 2*b)*ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]])/(2*(a - b)^(3/2)*b^(3/2)*d) - (a*Cosh[c + d*x])/(2*(a - b)*b*d*(a - b + b*Cosh[c + d*x]^2))","A",3,3,23,0.1304,1,"{3186, 385, 205}"
44,1,84,0,0.0861296,"\int \frac{\sinh ^2(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^2/(a + b*Sinh[c + d*x]^2)^2,x]","\frac{\sinh (c+d x) \cosh (c+d x)}{2 d (a-b) \left(a+b \sinh ^2(c+d x)\right)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 \sqrt{a} d (a-b)^{3/2}}","\frac{\sinh (c+d x) \cosh (c+d x)}{2 d (a-b) \left(a+b \sinh ^2(c+d x)\right)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 \sqrt{a} d (a-b)^{3/2}}",1,"-ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]]/(2*Sqrt[a]*(a - b)^(3/2)*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*(a - b)*d*(a + b*Sinh[c + d*x]^2))","A",4,4,23,0.1739,1,"{3173, 12, 3181, 208}"
45,1,81,0,0.0654572,"\int \frac{\sinh (c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]/(a + b*Sinh[c + d*x]^2)^2,x]","\frac{\cosh (c+d x)}{2 d (a-b) \left(a+b \cosh ^2(c+d x)-b\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{2 \sqrt{b} d (a-b)^{3/2}}","\frac{\cosh (c+d x)}{2 d (a-b) \left(a+b \cosh ^2(c+d x)-b\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{2 \sqrt{b} d (a-b)^{3/2}}",1,"ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]]/(2*(a - b)^(3/2)*Sqrt[b]*d) + Cosh[c + d*x]/(2*(a - b)*d*(a - b + b*Cosh[c + d*x]^2))","A",3,3,21,0.1429,1,"{3186, 199, 205}"
46,1,95,0,0.0694698,"\int \frac{1}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[(a + b*Sinh[c + d*x]^2)^(-2),x]","\frac{(2 a-b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a-b)^{3/2}}-\frac{b \sinh (c+d x) \cosh (c+d x)}{2 a d (a-b) \left(a+b \sinh ^2(c+d x)\right)}","\frac{(2 a-b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a-b)^{3/2}}-\frac{b \sinh (c+d x) \cosh (c+d x)}{2 a d (a-b) \left(a+b \sinh ^2(c+d x)\right)}",1,"((2*a - b)*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*(a - b)^(3/2)*d) - (b*Cosh[c + d*x]*Sinh[c + d*x])/(2*a*(a - b)*d*(a + b*Sinh[c + d*x]^2))","A",4,4,14,0.2857,1,"{3184, 12, 3181, 208}"
47,1,110,0,0.1493268,"\int \frac{\text{csch}(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Csch[c + d*x]/(a + b*Sinh[c + d*x]^2)^2,x]","-\frac{\sqrt{b} (3 a-2 b) \tan ^{-1}\left(\frac{\sqrt{b} \cosh (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 \cosh (c+d x)}{2 a d (a-b) \left(a+b \cosh ^2(c+d x)-b\right)}","-\frac{\sqrt{b} (3 a-2 b) \tan ^{-1}\left(\frac{\sqrt{b} \cosh (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 \cosh (c+d x)}{2 a d (a-b) \left(a+b \cosh ^2(c+d x)-b\right)}",1,"-((3*a - 2*b)*Sqrt[b]*ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]])/(2*a^2*(a - b)^(3/2)*d) - ArcTanh[Cosh[c + d*x]]/(a^2*d) - (b*Cosh[c + d*x])/(2*a*(a - b)*d*(a - b + b*Cosh[c + d*x]^2))","A",5,5,21,0.2381,1,"{3186, 414, 522, 206, 205}"
48,1,142,0,0.1533887,"\int \frac{\text{csch}^2(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Csch[c + d*x]^2/(a + b*Sinh[c + d*x]^2)^2,x]","\frac{\left(2 a^2-4 a b+3 b^2\right) \tanh (c+d x)}{2 a^2 d (a-b) \left(a-(a-b) \tanh ^2(c+d x)\right)}-\frac{b (4 a-3 b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{5/2} d (a-b)^{3/2}}-\frac{\coth (c+d x)}{a d \left(a-(a-b) \tanh ^2(c+d x)\right)}","\frac{\left(2 a^2-4 a b+3 b^2\right) \tanh (c+d x)}{2 a^2 d (a-b) \left(a-(a-b) \tanh ^2(c+d x)\right)}-\frac{b (4 a-3 b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{5/2} d (a-b)^{3/2}}-\frac{\coth (c+d x)}{a d \left(a-(a-b) \tanh ^2(c+d x)\right)}",1,"-((4*a - 3*b)*b*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(2*a^(5/2)*(a - b)^(3/2)*d) - Coth[c + d*x]/(a*d*(a - (a - b)*Tanh[c + d*x]^2)) + ((2*a^2 - 4*a*b + 3*b^2)*Tanh[c + d*x])/(2*a^2*(a - b)*d*(a - (a - b)*Tanh[c + d*x]^2))","A",4,4,23,0.1739,1,"{3187, 462, 385, 208}"
49,1,161,0,0.2729159,"\int \frac{\text{csch}^3(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Csch[c + d*x]^3/(a + b*Sinh[c + d*x]^2)^2,x]","\frac{b^{3/2} (5 a-4 b) \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{2 a^3 d (a-b)^{3/2}}-\frac{b (a-2 b) \cosh (c+d x)}{2 a^2 d (a-b) \left(a+b \cosh ^2(c+d x)-b\right)}+\frac{(a+4 b) \tanh ^{-1}(\cosh (c+d x))}{2 a^3 d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d \left(a+b \cosh ^2(c+d x)-b\right)}","\frac{b^{3/2} (5 a-4 b) \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{2 a^3 d (a-b)^{3/2}}-\frac{b (a-2 b) \cosh (c+d x)}{2 a^2 d (a-b) \left(a+b \cosh ^2(c+d x)-b\right)}+\frac{(a+4 b) \tanh ^{-1}(\cosh (c+d x))}{2 a^3 d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d \left(a+b \cosh ^2(c+d x)-b\right)}",1,"((5*a - 4*b)*b^(3/2)*ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]])/(2*a^3*(a - b)^(3/2)*d) + ((a + 4*b)*ArcTanh[Cosh[c + d*x]])/(2*a^3*d) - ((a - 2*b)*b*Cosh[c + d*x])/(2*a^2*(a - b)*d*(a - b + b*Cosh[c + d*x]^2)) - (Coth[c + d*x]*Csch[c + d*x])/(2*a*d*(a - b + b*Cosh[c + d*x]^2))","A",6,6,23,0.2609,1,"{3186, 414, 527, 522, 206, 205}"
50,1,174,0,0.2063684,"\int \frac{\text{csch}^4(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Csch[c + d*x]^4/(a + b*Sinh[c + d*x]^2)^2,x]","\frac{b^2 (6 a-5 b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{7/2} d (a-b)^{3/2}}+\frac{\left(2 a^2+a b-5 b^2\right) \coth (c+d x)}{2 a^3 d (a-b)}-\frac{(2 a-5 b) \coth ^3(c+d x)}{6 a^2 d (a-b)}-\frac{b \text{csch}^3(c+d x) \text{sech}(c+d x)}{2 a d (a-b) \left(a-(a-b) \tanh ^2(c+d x)\right)}","\frac{b^2 (6 a-5 b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{7/2} d (a-b)^{3/2}}+\frac{\left(2 a^2+a b-5 b^2\right) \coth (c+d x)}{2 a^3 d (a-b)}-\frac{(2 a-5 b) \coth ^3(c+d x)}{6 a^2 d (a-b)}-\frac{b \text{csch}^3(c+d x) \text{sech}(c+d x)}{2 a d (a-b) \left(a-(a-b) \tanh ^2(c+d x)\right)}",1,"((6*a - 5*b)*b^2*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(2*a^(7/2)*(a - b)^(3/2)*d) + ((2*a^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*Csch[c + d*x]^3*Sech[c + d*x])/(2*a*(a - b)*d*(a - (a - b)*Tanh[c + d*x]^2))","A",5,4,23,0.1739,1,"{3187, 468, 570, 208}"
51,1,124,0,0.1230645,"\int \frac{\sinh ^4(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^4/(a + b*Sinh[c + d*x]^2)^3,x]","\frac{\tanh ^3(c+d x)}{4 d (a-b) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}-\frac{3 \tanh (c+d x)}{8 d (a-b)^2 \left(a-(a-b) \tanh ^2(c+d x)\right)}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 \sqrt{a} d (a-b)^{5/2}}","\frac{\tanh ^3(c+d x)}{4 d (a-b) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}-\frac{3 \tanh (c+d x)}{8 d (a-b)^2 \left(a-(a-b) \tanh ^2(c+d x)\right)}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 \sqrt{a} d (a-b)^{5/2}}",1,"(3*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(8*Sqrt[a]*(a - b)^(5/2)*d) + Tanh[c + d*x]^3/(4*(a - b)*d*(a - (a - b)*Tanh[c + d*x]^2)^2) - (3*Tanh[c + d*x])/(8*(a - b)^2*d*(a - (a - b)*Tanh[c + d*x]^2))","A",4,3,23,0.1304,1,"{3187, 288, 208}"
52,1,135,0,0.1411052,"\int \frac{\sinh ^3(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^3/(a + b*Sinh[c + d*x]^2)^3,x]","\frac{(a-4 b) \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{8 b^{3/2} d (a-b)^{5/2}}+\frac{(a-4 b) \cosh (c+d x)}{8 b d (a-b)^2 \left(a+b \cosh ^2(c+d x)-b\right)}-\frac{a \cosh (c+d x)}{4 b d (a-b) \left(a+b \cosh ^2(c+d x)-b\right)^2}","\frac{(a-4 b) \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{8 b^{3/2} d (a-b)^{5/2}}+\frac{(a-4 b) \cosh (c+d x)}{8 b d (a-b)^2 \left(a+b \cosh ^2(c+d x)-b\right)}-\frac{a \cosh (c+d x)}{4 b d (a-b) \left(a+b \cosh ^2(c+d x)-b\right)^2}",1,"((a - 4*b)*ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]])/(8*(a - b)^(5/2)*b^(3/2)*d) - (a*Cosh[c + d*x])/(4*(a - b)*b*d*(a - b + b*Cosh[c + d*x]^2)^2) + ((a - 4*b)*Cosh[c + d*x])/(8*(a - b)^2*b*d*(a - b + b*Cosh[c + d*x]^2))","A",4,4,23,0.1739,1,"{3186, 385, 199, 205}"
53,1,139,0,0.1565308,"\int \frac{\sinh ^2(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^2/(a + b*Sinh[c + d*x]^2)^3,x]","-\frac{(4 a-b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{3/2} d (a-b)^{5/2}}+\frac{(2 a+b) \sinh (c+d x) \cosh (c+d x)}{8 a d (a-b)^2 \left(a+b \sinh ^2(c+d x)\right)}+\frac{\sinh (c+d x) \cosh (c+d x)}{4 d (a-b) \left(a+b \sinh ^2(c+d x)\right)^2}","-\frac{(4 a-b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{3/2} d (a-b)^{5/2}}+\frac{(2 a+b) \sinh (c+d x) \cosh (c+d x)}{8 a d (a-b)^2 \left(a+b \sinh ^2(c+d x)\right)}+\frac{\sinh (c+d x) \cosh (c+d x)}{4 d (a-b) \left(a+b \sinh ^2(c+d x)\right)^2}",1,"-((4*a - b)*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(3/2)*(a - b)^(5/2)*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(4*(a - b)*d*(a + b*Sinh[c + d*x]^2)^2) + ((2*a + b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*a*(a - b)^2*d*(a + b*Sinh[c + d*x]^2))","A",5,4,23,0.1739,1,"{3173, 12, 3181, 208}"
54,1,118,0,0.0831678,"\int \frac{\sinh (c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]/(a + b*Sinh[c + d*x]^2)^3,x]","\frac{3 \cosh (c+d x)}{8 d (a-b)^2 \left(a+b \cosh ^2(c+d x)-b\right)}+\frac{\cosh (c+d x)}{4 d (a-b) \left(a+b \cosh ^2(c+d x)-b\right)^2}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{8 \sqrt{b} d (a-b)^{5/2}}","\frac{3 \cosh (c+d x)}{8 d (a-b)^2 \left(a+b \cosh ^2(c+d x)-b\right)}+\frac{\cosh (c+d x)}{4 d (a-b) \left(a+b \cosh ^2(c+d x)-b\right)^2}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{8 \sqrt{b} d (a-b)^{5/2}}",1,"(3*ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]])/(8*(a - b)^(5/2)*Sqrt[b]*d) + Cosh[c + d*x]/(4*(a - b)*d*(a - b + b*Cosh[c + d*x]^2)^2) + (3*Cosh[c + d*x])/(8*(a - b)^2*d*(a - b + b*Cosh[c + d*x]^2))","A",4,3,21,0.1429,1,"{3186, 199, 205}"
55,1,154,0,0.1546459,"\int \frac{1}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[(a + b*Sinh[c + d*x]^2)^(-3),x]","\frac{\left(8 a^2-8 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (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) \cosh (c+d x)}{8 a^2 d (a-b)^2 \left(a+b \sinh ^2(c+d x)\right)}-\frac{b \sinh (c+d x) \cosh (c+d x)}{4 a d (a-b) \left(a+b \sinh ^2(c+d x)\right)^2}","\frac{\left(8 a^2-8 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (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) \cosh (c+d x)}{8 a^2 d (a-b)^2 \left(a+b \sinh ^2(c+d x)\right)}-\frac{b \sinh (c+d x) \cosh (c+d x)}{4 a d (a-b) \left(a+b \sinh ^2(c+d x)\right)^2}",1,"((8*a^2 - 8*a*b + 3*b^2)*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*(a - b)^(5/2)*d) - (b*Cosh[c + d*x]*Sinh[c + d*x])/(4*a*(a - b)*d*(a + b*Sinh[c + d*x]^2)^2) - (3*(2*a - b)*b*Cosh[c + d*x]*Sinh[c + d*x])/(8*a^2*(a - b)^2*d*(a + b*Sinh[c + d*x]^2))","A",5,5,14,0.3571,1,"{3184, 3173, 12, 3181, 208}"
56,1,166,0,0.2665359,"\int \frac{\text{csch}(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Csch[c + d*x]/(a + b*Sinh[c + d*x]^2)^3,x]","-\frac{\sqrt{b} \left(15 a^2-20 a b+8 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{8 a^3 d (a-b)^{5/2}}-\frac{b (7 a-4 b) \cosh (c+d x)}{8 a^2 d (a-b)^2 \left(a+b \cosh ^2(c+d x)-b\right)}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a^3 d}-\frac{b \cosh (c+d x)}{4 a d (a-b) \left(a+b \cosh ^2(c+d x)-b\right)^2}","-\frac{\sqrt{b} \left(15 a^2-20 a b+8 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{8 a^3 d (a-b)^{5/2}}-\frac{b (7 a-4 b) \cosh (c+d x)}{8 a^2 d (a-b)^2 \left(a+b \cosh ^2(c+d x)-b\right)}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a^3 d}-\frac{b \cosh (c+d x)}{4 a d (a-b) \left(a+b \cosh ^2(c+d x)-b\right)^2}",1,"-(Sqrt[b]*(15*a^2 - 20*a*b + 8*b^2)*ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]])/(8*a^3*(a - b)^(5/2)*d) - ArcTanh[Cosh[c + d*x]]/(a^3*d) - (b*Cosh[c + d*x])/(4*a*(a - b)*d*(a - b + b*Cosh[c + d*x]^2)^2) - ((7*a - 4*b)*b*Cosh[c + d*x])/(8*a^2*(a - b)^2*d*(a - b + b*Cosh[c + d*x]^2))","A",6,6,21,0.2857,1,"{3186, 414, 527, 522, 206, 205}"
57,1,215,0,0.2871694,"\int \frac{\text{csch}^2(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Csch[c + d*x]^2/(a + b*Sinh[c + d*x]^2)^3,x]","-\frac{3 b \left(8 a^2-12 a b+5 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{7/2} d (a-b)^{5/2}}-\frac{(4 a-5 b) (2 a-3 b) \coth (c+d x)}{8 a^3 d (a-b)^2}-\frac{b \coth (c+d x) \left(-(4 a-b) \tanh ^2(c+d x)+4 a-5 b\right)}{8 a^2 d (a-b)^2 \left(a-(a-b) \tanh ^2(c+d x)\right)}-\frac{b \text{csch}(c+d x) \text{sech}^3(c+d x)}{4 a d (a-b) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}","-\frac{3 b \left(8 a^2-12 a b+5 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{7/2} d (a-b)^{5/2}}-\frac{(4 a-5 b) (2 a-3 b) \coth (c+d x)}{8 a^3 d (a-b)^2}-\frac{b \coth (c+d x) \left(-(4 a-b) \tanh ^2(c+d x)+4 a-5 b\right)}{8 a^2 d (a-b)^2 \left(a-(a-b) \tanh ^2(c+d x)\right)}-\frac{b \text{csch}(c+d x) \text{sech}^3(c+d x)}{4 a d (a-b) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}",1,"(-3*b*(8*a^2 - 12*a*b + 5*b^2)*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(7/2)*(a - b)^(5/2)*d) - ((4*a - 5*b)*(2*a - 3*b)*Coth[c + d*x])/(8*a^3*(a - b)^2*d) - (b*Csch[c + d*x]*Sech[c + d*x]^3)/(4*a*(a - b)*d*(a - (a - b)*Tanh[c + d*x]^2)^2) - (b*Coth[c + d*x]*(4*a - 5*b - (4*a - b)*Tanh[c + d*x]^2))/(8*a^2*(a - b)^2*d*(a - (a - b)*Tanh[c + d*x]^2))","A",5,5,23,0.2174,1,"{3187, 468, 577, 453, 208}"
58,1,224,0,0.4387401,"\int \frac{\text{csch}^3(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Csch[c + d*x]^3/(a + b*Sinh[c + d*x]^2)^3,x]","\frac{b^{3/2} \left(35 a^2-56 a b+24 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{8 a^4 d (a-b)^{5/2}}-\frac{b (a-4 b) (4 a-3 b) \cosh (c+d x)}{8 a^3 d (a-b)^2 \left(a+b \cosh ^2(c+d x)-b\right)}-\frac{b (2 a-3 b) \cosh (c+d x)}{4 a^2 d (a-b) \left(a+b \cosh ^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 \cosh ^2(c+d x)-b\right)^2}","\frac{b^{3/2} \left(35 a^2-56 a b+24 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \cosh (c+d x)}{\sqrt{a-b}}\right)}{8 a^4 d (a-b)^{5/2}}-\frac{b (a-4 b) (4 a-3 b) \cosh (c+d x)}{8 a^3 d (a-b)^2 \left(a+b \cosh ^2(c+d x)-b\right)}-\frac{b (2 a-3 b) \cosh (c+d x)}{4 a^2 d (a-b) \left(a+b \cosh ^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 \cosh ^2(c+d x)-b\right)^2}",1,"(b^(3/2)*(35*a^2 - 56*a*b + 24*b^2)*ArcTan[(Sqrt[b]*Cosh[c + d*x])/Sqrt[a - b]])/(8*a^4*(a - b)^(5/2)*d) + ((a + 6*b)*ArcTanh[Cosh[c + d*x]])/(2*a^4*d) - ((2*a - 3*b)*b*Cosh[c + d*x])/(4*a^2*(a - b)*d*(a - b + b*Cosh[c + d*x]^2)^2) - ((a - 4*b)*(4*a - 3*b)*b*Cosh[c + d*x])/(8*a^3*(a - b)^2*d*(a - b + b*Cosh[c + d*x]^2)) - (Coth[c + d*x]*Csch[c + d*x])/(2*a*d*(a - b + b*Cosh[c + d*x]^2)^2)","A",7,6,23,0.2609,1,"{3186, 414, 527, 522, 206, 205}"
59,1,259,0,0.3379813,"\int \frac{\text{csch}^4(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Csch[c + d*x]^4/(a + b*Sinh[c + d*x]^2)^3,x]","\frac{b^2 \left(48 a^2-80 a b+35 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{9/2} d (a-b)^{5/2}}-\frac{\left(8 a^2-52 a b+35 b^2\right) \coth ^3(c+d x)}{24 a^3 d (a-b)^2}+\frac{\left(-4 a^2 b+8 a^3-45 a b^2+35 b^3\right) \coth (c+d x)}{8 a^4 d (a-b)^2}-\frac{b (10 a-7 b) \text{csch}^3(c+d x) \text{sech}(c+d x)}{8 a^2 d (a-b)^2 \left(a-(a-b) \tanh ^2(c+d x)\right)}-\frac{b \text{csch}^3(c+d x) \text{sech}^3(c+d x)}{4 a d (a-b) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}","\frac{b^2 \left(48 a^2-80 a b+35 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{9/2} d (a-b)^{5/2}}-\frac{\left(8 a^2-52 a b+35 b^2\right) \coth ^3(c+d x)}{24 a^3 d (a-b)^2}+\frac{\left(-4 a^2 b+8 a^3-45 a b^2+35 b^3\right) \coth (c+d x)}{8 a^4 d (a-b)^2}-\frac{b (10 a-7 b) \text{csch}^3(c+d x) \text{sech}(c+d x)}{8 a^2 d (a-b)^2 \left(a-(a-b) \tanh ^2(c+d x)\right)}-\frac{b \text{csch}^3(c+d x) \text{sech}^3(c+d x)}{4 a d (a-b) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}",1,"(b^2*(48*a^2 - 80*a*b + 35*b^2)*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(9/2)*(a - b)^(5/2)*d) + ((8*a^3 - 4*a^2*b - 45*a*b^2 + 35*b^3)*Coth[c + d*x])/(8*a^4*(a - b)^2*d) - ((8*a^2 - 52*a*b + 35*b^2)*Coth[c + d*x]^3)/(24*a^3*(a - b)^2*d) - (b*Csch[c + d*x]^3*Sech[c + d*x]^3)/(4*a*(a - b)*d*(a - (a - b)*Tanh[c + d*x]^2)^2) - ((10*a - 7*b)*b*Csch[c + d*x]^3*Sech[c + d*x])/(8*a^2*(a - b)^2*d*(a - (a - b)*Tanh[c + d*x]^2))","A",6,5,23,0.2174,1,"{3187, 468, 577, 570, 208}"
60,1,2,0,0.0163758,"\int \frac{1}{1+\sinh ^2(x)} \, dx","Int[(1 + Sinh[x]^2)^(-1),x]","\tanh (x)","\tanh (x)",1,"Tanh[x]","A",3,3,8,0.3750,1,"{3175, 3767, 8}"
61,1,11,0,0.0190848,"\int \frac{1}{\left(1+\sinh ^2(x)\right)^2} \, dx","Int[(1 + Sinh[x]^2)^(-2),x]","\tanh (x)-\frac{\tanh ^3(x)}{3}","\tanh (x)-\frac{\tanh ^3(x)}{3}",1,"Tanh[x] - Tanh[x]^3/3","A",3,2,8,0.2500,1,"{3175, 3767}"
62,1,19,0,0.0201132,"\int \frac{1}{\left(1+\sinh ^2(x)\right)^3} \, dx","Int[(1 + Sinh[x]^2)^(-3),x]","\frac{\tanh ^5(x)}{5}-\frac{2 \tanh ^3(x)}{3}+\tanh (x)","\frac{\tanh ^5(x)}{5}-\frac{2 \tanh ^3(x)}{3}+\tanh (x)",1,"Tanh[x] - (2*Tanh[x]^3)/3 + Tanh[x]^5/5","A",3,2,8,0.2500,1,"{3175, 3767}"
63,1,15,0,0.0127272,"\int \frac{1}{1-\sinh ^2(x)} \, dx","Int[(1 - Sinh[x]^2)^(-1),x]","\frac{\tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{\sqrt{2}}","\frac{\tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{\sqrt{2}}",1,"ArcTanh[Sqrt[2]*Tanh[x]]/Sqrt[2]","A",2,2,10,0.2000,1,"{3181, 206}"
64,1,37,0,0.0268138,"\int \frac{1}{\left(1-\sinh ^2(x)\right)^2} \, dx","Int[(1 - Sinh[x]^2)^(-2),x]","\frac{3 \tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{4 \sqrt{2}}+\frac{\sinh (x) \cosh (x)}{4 \left(1-\sinh ^2(x)\right)}","\frac{3 \tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{4 \sqrt{2}}+\frac{\sinh (x) \cosh (x)}{4 \left(1-\sinh ^2(x)\right)}",1,"(3*ArcTanh[Sqrt[2]*Tanh[x]])/(4*Sqrt[2]) + (Cosh[x]*Sinh[x])/(4*(1 - Sinh[x]^2))","A",4,4,10,0.4000,1,"{3184, 12, 3181, 206}"
65,1,55,0,0.0581055,"\int \frac{1}{\left(1-\sinh ^2(x)\right)^3} \, dx","Int[(1 - Sinh[x]^2)^(-3),x]","\frac{19 \tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{32 \sqrt{2}}+\frac{9 \sinh (x) \cosh (x)}{32 \left(1-\sinh ^2(x)\right)}+\frac{\sinh (x) \cosh (x)}{8 \left(1-\sinh ^2(x)\right)^2}","\frac{19 \tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{32 \sqrt{2}}+\frac{9 \sinh (x) \cosh (x)}{32 \left(1-\sinh ^2(x)\right)}+\frac{\sinh (x) \cosh (x)}{8 \left(1-\sinh ^2(x)\right)^2}",1,"(19*ArcTanh[Sqrt[2]*Tanh[x]])/(32*Sqrt[2]) + (Cosh[x]*Sinh[x])/(8*(1 - Sinh[x]^2)^2) + (9*Cosh[x]*Sinh[x])/(32*(1 - Sinh[x]^2))","A",5,5,10,0.5000,1,"{3184, 3173, 12, 3181, 206}"
66,1,130,0,0.1483483,"\int \sinh ^3(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Sinh[e + f*x]^3*Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{(a-b) (a+3 b) \tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{8 b^{3/2} f}+\frac{\cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}{4 b f}-\frac{(a+3 b) \cosh (e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{8 b f}","-\frac{(a-b) (a+3 b) \tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{8 b^{3/2} f}+\frac{\cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}{4 b f}-\frac{(a+3 b) \cosh (e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{8 b f}",1,"-((a - b)*(a + 3*b)*ArcTanh[(Sqrt[b]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/(8*b^(3/2)*f) - ((a + 3*b)*Cosh[e + f*x]*Sqrt[a - b + b*Cosh[e + f*x]^2])/(8*b*f) + (Cosh[e + f*x]*(a - b + b*Cosh[e + f*x]^2)^(3/2))/(4*b*f)","A",5,5,25,0.2000,1,"{3186, 388, 195, 217, 206}"
67,1,82,0,0.0702846,"\int \sinh (e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\cosh (e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{2 f}+\frac{(a-b) \tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{2 \sqrt{b} f}","\frac{\cosh (e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{2 f}+\frac{(a-b) \tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{2 \sqrt{b} f}",1,"((a - b)*ArcTanh[(Sqrt[b]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/(2*Sqrt[b]*f) + (Cosh[e + f*x]*Sqrt[a - b + b*Cosh[e + f*x]^2])/(2*f)","A",4,4,23,0.1739,1,"{3186, 195, 217, 206}"
68,1,84,0,0.1050758,"\int \text{csch}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Csch[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{f}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{f}","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{f}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{f}",1,"-((Sqrt[a]*ArcTanh[(Sqrt[a]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/f) + (Sqrt[b]*ArcTanh[(Sqrt[b]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/f","A",6,5,23,0.2174,1,"{3186, 402, 217, 206, 377}"
69,1,88,0,0.1180455,"\int \text{csch}^3(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Csch[e + f*x]^3*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{(a-b) \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{2 \sqrt{a} f}-\frac{\coth (e+f x) \text{csch}(e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{2 f}","\frac{(a-b) \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{2 \sqrt{a} f}-\frac{\coth (e+f x) \text{csch}(e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{2 f}",1,"((a - b)*ArcTanh[(Sqrt[a]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/(2*Sqrt[a]*f) - (Sqrt[a - b + b*Cosh[e + f*x]^2]*Coth[e + f*x]*Csch[e + f*x])/(2*f)","A",4,4,25,0.1600,1,"{3186, 378, 377, 206}"
70,1,144,0,0.1500171,"\int \text{csch}^5(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Csch[e + f*x]^5*Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{(a-b) (3 a+b) \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{8 a^{3/2} f}-\frac{\coth (e+f x) \text{csch}^3(e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}{4 a f}+\frac{(3 a+b) \coth (e+f x) \text{csch}(e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{8 a f}","-\frac{(a-b) (3 a+b) \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{8 a^{3/2} f}-\frac{\coth (e+f x) \text{csch}^3(e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}{4 a f}+\frac{(3 a+b) \coth (e+f x) \text{csch}(e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{8 a f}",1,"-((a - b)*(3*a + b)*ArcTanh[(Sqrt[a]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/(8*a^(3/2)*f) + ((3*a + b)*Sqrt[a - b + b*Cosh[e + f*x]^2]*Coth[e + f*x]*Csch[e + f*x])/(8*a*f) - ((a - b + b*Cosh[e + f*x]^2)^(3/2)*Coth[e + f*x]*Csch[e + f*x]^3)/(4*a*f)","A",5,5,25,0.2000,1,"{3186, 382, 378, 377, 206}"
71,1,300,0,0.3270357,"\int \sinh ^4(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Sinh[e + f*x]^4*Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{\left(2 a^2+3 a b-8 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{15 b^2 f}+\frac{\left(2 a^2+3 a b-8 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{15 b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{\sinh ^3(e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{5 f}+\frac{(a-4 b) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{15 b f}-\frac{(a-4 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{15 b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","-\frac{\left(2 a^2+3 a b-8 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{15 b^2 f}+\frac{\left(2 a^2+3 a b-8 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{15 b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{\sinh ^3(e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{5 f}+\frac{(a-4 b) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{15 b f}-\frac{(a-4 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{15 b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"((a - 4*b)*Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(15*b*f) + (Cosh[e + f*x]*Sinh[e + f*x]^3*Sqrt[a + b*Sinh[e + f*x]^2])/(5*f) + ((2*a^2 + 3*a*b - 8*b^2)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(15*b^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - ((a - 4*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(15*b*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - ((2*a^2 + 3*a*b - 8*b^2)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(15*b^2*f)","A",7,7,25,0.2800,1,"{3188, 478, 582, 531, 418, 492, 411}"
72,1,177,0,0.2133076,"\int \sinh ^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Sinh[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{i a (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 b f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{i (a-2 b) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 b f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}","\frac{\sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{i a (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 b f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{i (a-2 b) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 b f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}",1,"(Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f) - ((I/3)*(a - 2*b)*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/(b*f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a]) + ((I/3)*a*(a - b)*EllipticF[I*e + I*f*x, b/a]*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])/(b*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",6,6,25,0.2400,1,"{3170, 3172, 3178, 3177, 3183, 3182}"
73,1,60,0,0.0363792,"\int \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{i \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}","-\frac{i \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}",1,"((-I)*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/(f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])","A",2,2,16,0.1250,1,"{3178, 3177}"
74,1,199,0,0.1818183,"\int \text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Csch[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}-\frac{\coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{\tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}-\frac{\coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"-((Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/f) - (EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (b*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/f","A",7,7,25,0.2800,1,"{3188, 475, 21, 422, 418, 492, 411}"
75,1,276,0,0.281847,"\int \text{csch}^4(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Csch[e + f*x]^4*Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{(2 a-b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a f}+\frac{(2 a-b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a f}-\frac{\coth (e+f x) \text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{(2 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","-\frac{(2 a-b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a f}+\frac{(2 a-b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a f}-\frac{\coth (e+f x) \text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{(2 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"((2*a - b)*Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*f) - (Coth[e + f*x]*Csch[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f) + ((2*a - b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (b*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - ((2*a - b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*a*f)","A",7,7,25,0.2800,1,"{3188, 475, 583, 531, 418, 492, 411}"
76,1,177,0,0.1814809,"\int \sinh ^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Sinh[e + f*x]^3*(a + b*Sinh[e + f*x]^2)^(3/2),x]","-\frac{(a-b)^2 (a+5 b) \tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{16 b^{3/2} f}+\frac{\cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{5/2}}{6 b f}-\frac{(a+5 b) \cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}{24 b f}-\frac{(a-b) (a+5 b) \cosh (e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{16 b f}","-\frac{(a-b)^2 (a+5 b) \tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{16 b^{3/2} f}+\frac{\cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{5/2}}{6 b f}-\frac{(a+5 b) \cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}{24 b f}-\frac{(a-b) (a+5 b) \cosh (e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{16 b f}",1,"-((a - b)^2*(a + 5*b)*ArcTanh[(Sqrt[b]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/(16*b^(3/2)*f) - ((a - b)*(a + 5*b)*Cosh[e + f*x]*Sqrt[a - b + b*Cosh[e + f*x]^2])/(16*b*f) - ((a + 5*b)*Cosh[e + f*x]*(a - b + b*Cosh[e + f*x]^2)^(3/2))/(24*b*f) + (Cosh[e + f*x]*(a - b + b*Cosh[e + f*x]^2)^(5/2))/(6*b*f)","A",6,5,25,0.2000,1,"{3186, 388, 195, 217, 206}"
77,1,121,0,0.096654,"\int \sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{3 (a-b) \cosh (e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{8 f}+\frac{\cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}{4 f}+\frac{3 (a-b)^2 \tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{8 \sqrt{b} f}","\frac{3 (a-b) \cosh (e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{8 f}+\frac{\cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}{4 f}+\frac{3 (a-b)^2 \tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{8 \sqrt{b} f}",1,"(3*(a - b)^2*ArcTanh[(Sqrt[b]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/(8*Sqrt[b]*f) + (3*(a - b)*Cosh[e + f*x]*Sqrt[a - b + b*Cosh[e + f*x]^2])/(8*f) + (Cosh[e + f*x]*(a - b + b*Cosh[e + f*x]^2)^(3/2))/(4*f)","A",5,4,23,0.1739,1,"{3186, 195, 217, 206}"
78,1,127,0,0.1649704,"\int \text{csch}(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Csch[e + f*x]*(a + b*Sinh[e + f*x]^2)^(3/2),x]","-\frac{a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{f}+\frac{b \cosh (e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{2 f}+\frac{\sqrt{b} (3 a-b) \tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{2 f}","-\frac{a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{f}+\frac{b \cosh (e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{2 f}+\frac{\sqrt{b} (3 a-b) \tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{2 f}",1,"-((a^(3/2)*ArcTanh[(Sqrt[a]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/f) + ((3*a - b)*Sqrt[b]*ArcTanh[(Sqrt[b]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/(2*f) + (b*Cosh[e + f*x]*Sqrt[a - b + b*Cosh[e + f*x]^2])/(2*f)","A",7,6,23,0.2609,1,"{3186, 416, 523, 217, 206, 377}"
79,1,130,0,0.1682347,"\int \text{csch}^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Csch[e + f*x]^3*(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{f}+\frac{\sqrt{a} (a-3 b) \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{2 f}-\frac{a \coth (e+f x) \text{csch}(e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{2 f}","\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{f}+\frac{\sqrt{a} (a-3 b) \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{2 f}-\frac{a \coth (e+f x) \text{csch}(e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{2 f}",1,"(Sqrt[a]*(a - 3*b)*ArcTanh[(Sqrt[a]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/(2*f) + (b^(3/2)*ArcTanh[(Sqrt[b]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/f - (a*Sqrt[a - b + b*Cosh[e + f*x]^2]*Coth[e + f*x]*Csch[e + f*x])/(2*f)","A",7,6,25,0.2400,1,"{3186, 413, 523, 217, 206, 377}"
80,1,135,0,0.1406036,"\int \text{csch}^5(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Csch[e + f*x]^5*(a + b*Sinh[e + f*x]^2)^(3/2),x]","-\frac{3 (a-b)^2 \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{8 \sqrt{a} f}-\frac{\coth (e+f x) \text{csch}^3(e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}{4 f}+\frac{3 (a-b) \coth (e+f x) \text{csch}(e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{8 f}","-\frac{3 (a-b)^2 \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{8 \sqrt{a} f}-\frac{\coth (e+f x) \text{csch}^3(e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}{4 f}+\frac{3 (a-b) \coth (e+f x) \text{csch}(e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{8 f}",1,"(-3*(a - b)^2*ArcTanh[(Sqrt[a]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/(8*Sqrt[a]*f) + (3*(a - b)*Sqrt[a - b + b*Cosh[e + f*x]^2]*Coth[e + f*x]*Csch[e + f*x])/(8*f) - ((a - b + b*Cosh[e + f*x]^2)^(3/2)*Coth[e + f*x]*Csch[e + f*x]^3)/(4*f)","A",5,4,25,0.1600,1,"{3186, 378, 377, 206}"
81,1,199,0,0.199041,"\int \text{csch}^7(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Csch[e + f*x]^7*(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{(a-b)^2 (5 a+b) \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{16 a^{3/2} f}-\frac{\coth (e+f x) \text{csch}^5(e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{5/2}}{6 a f}+\frac{(5 a+b) \coth (e+f x) \text{csch}^3(e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}{24 a f}-\frac{(a-b) (5 a+b) \coth (e+f x) \text{csch}(e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{16 a f}","\frac{(a-b)^2 (5 a+b) \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{16 a^{3/2} f}-\frac{\coth (e+f x) \text{csch}^5(e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{5/2}}{6 a f}+\frac{(5 a+b) \coth (e+f x) \text{csch}^3(e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}{24 a f}-\frac{(a-b) (5 a+b) \coth (e+f x) \text{csch}(e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{16 a f}",1,"((a - b)^2*(5*a + b)*ArcTanh[(Sqrt[a]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/(16*a^(3/2)*f) - ((a - b)*(5*a + b)*Sqrt[a - b + b*Cosh[e + f*x]^2]*Coth[e + f*x]*Csch[e + f*x])/(16*a*f) + ((5*a + b)*(a - b + b*Cosh[e + f*x]^2)^(3/2)*Coth[e + f*x]*Csch[e + f*x]^3)/(24*a*f) - ((a - b + b*Cosh[e + f*x]^2)^(5/2)*Coth[e + f*x]*Csch[e + f*x]^5)/(6*a*f)","A",6,5,25,0.2000,1,"{3186, 382, 378, 377, 206}"
82,1,367,0,0.4708341,"\int \sinh ^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Sinh[e + f*x]^4*(a + b*Sinh[e + f*x]^2)^(3/2),x]","-\frac{2 (a-2 b) \left(a^2+4 a b-4 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{35 b^2 f}+\frac{\left(a^2-11 a b+8 b^2\right) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{35 b f}-\frac{\left(a^2-11 a b+8 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{35 b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{2 (a-2 b) \left(a^2+4 a b-4 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{35 b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{b \sinh ^5(e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{7 f}+\frac{2 (4 a-3 b) \sinh ^3(e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{35 f}","-\frac{2 (a-2 b) \left(a^2+4 a b-4 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{35 b^2 f}+\frac{\left(a^2-11 a b+8 b^2\right) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{35 b f}-\frac{\left(a^2-11 a b+8 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{35 b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{2 (a-2 b) \left(a^2+4 a b-4 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{35 b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{b \sinh ^5(e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{7 f}+\frac{2 (4 a-3 b) \sinh ^3(e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{35 f}",1,"((a^2 - 11*a*b + 8*b^2)*Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(35*b*f) + (2*(4*a - 3*b)*Cosh[e + f*x]*Sinh[e + f*x]^3*Sqrt[a + b*Sinh[e + f*x]^2])/(35*f) + (b*Cosh[e + f*x]*Sinh[e + f*x]^5*Sqrt[a + b*Sinh[e + f*x]^2])/(7*f) + (2*(a - 2*b)*(a^2 + 4*a*b - 4*b^2)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(35*b^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - ((a^2 - 11*a*b + 8*b^2)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(35*b*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (2*(a - 2*b)*(a^2 + 4*a*b - 4*b^2)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(35*b^2*f)","A",8,7,25,0.2800,1,"{3188, 477, 582, 531, 418, 492, 411}"
83,1,236,0,0.3254305,"\int \sinh ^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Sinh[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^(3/2),x]","-\frac{i \left(3 a^2-13 a b+8 b^2\right) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{15 b f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}+\frac{\sinh (e+f x) \cosh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{5 f}+\frac{(3 a-4 b) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{15 f}+\frac{i a (3 a-4 b) (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{15 b f \sqrt{a+b \sinh ^2(e+f x)}}","-\frac{i \left(3 a^2-13 a b+8 b^2\right) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{15 b f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}+\frac{\sinh (e+f x) \cosh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{5 f}+\frac{(3 a-4 b) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{15 f}+\frac{i a (3 a-4 b) (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{15 b f \sqrt{a+b \sinh ^2(e+f x)}}",1,"((3*a - 4*b)*Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(15*f) + (Cosh[e + f*x]*Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^(3/2))/(5*f) - ((I/15)*(3*a^2 - 13*a*b + 8*b^2)*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/(b*f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a]) + ((I/15)*a*(3*a - 4*b)*(a - b)*EllipticF[I*e + I*f*x, b/a]*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])/(b*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",7,6,25,0.2400,1,"{3170, 3172, 3178, 3177, 3183, 3182}"
84,1,174,0,0.1936972,"\int \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{b \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{i a (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{2 i (2 a-b) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}","\frac{b \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{i a (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{2 i (2 a-b) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}",1,"(b*Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f) - (((2*I)/3)*(2*a - b)*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/(f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a]) + ((I/3)*a*(a - b)*EllipticF[I*e + I*f*x, b/a]*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])/(f*Sqrt[a + b*Sinh[e + f*x]^2])","A",6,6,16,0.3750,1,"{3180, 3172, 3178, 3177, 3183, 3182}"
85,1,204,0,0.2114929,"\int \text{csch}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Csch[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{(a+b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}-\frac{a \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{2 b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{(a+b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}-\frac{a \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{2 b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"-((a*Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/f) - ((a + b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (2*b*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((a + b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/f","A",6,6,25,0.2400,1,"{3188, 474, 531, 418, 492, 411}"
86,1,267,0,0.3059408,"\int \text{csch}^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Csch[e + f*x]^4*(a + b*Sinh[e + f*x]^2)^(3/2),x]","-\frac{2 (a-2 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{2 (a-2 b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{a \coth (e+f x) \text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{b (a-3 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{2 (a-2 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","-\frac{2 (a-2 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{2 (a-2 b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{a \coth (e+f x) \text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{b (a-3 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{2 (a-2 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(2*(a - 2*b)*Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f) - (a*Coth[e + f*x]*Csch[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f) + (2*(a - 2*b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - ((a - 3*b)*b*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (2*(a - 2*b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*f)","A",7,7,25,0.2800,1,"{3188, 474, 583, 531, 418, 492, 411}"
87,1,232,0,0.303784,"\int \left(a+b \sinh ^2(c+d x)\right)^{5/2} \, dx","Int[(a + b*Sinh[c + d*x]^2)^(5/2),x]","-\frac{i \left(23 a^2-23 a b+8 b^2\right) \sqrt{a+b \sinh ^2(c+d x)} E\left(i c+i d x\left|\frac{b}{a}\right.\right)}{15 d \sqrt{\frac{b \sinh ^2(c+d x)}{a}+1}}+\frac{b \sinh (c+d x) \cosh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^{3/2}}{5 d}+\frac{4 b (2 a-b) \sinh (c+d x) \cosh (c+d x) \sqrt{a+b \sinh ^2(c+d x)}}{15 d}+\frac{4 i a (a-b) (2 a-b) \sqrt{\frac{b \sinh ^2(c+d x)}{a}+1} F\left(i c+i d x\left|\frac{b}{a}\right.\right)}{15 d \sqrt{a+b \sinh ^2(c+d x)}}","-\frac{i \left(23 a^2-23 a b+8 b^2\right) \sqrt{a+b \sinh ^2(c+d x)} E\left(i c+i d x\left|\frac{b}{a}\right.\right)}{15 d \sqrt{\frac{b \sinh ^2(c+d x)}{a}+1}}+\frac{b \sinh (c+d x) \cosh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^{3/2}}{5 d}+\frac{4 b (2 a-b) \sinh (c+d x) \cosh (c+d x) \sqrt{a+b \sinh ^2(c+d x)}}{15 d}+\frac{4 i a (a-b) (2 a-b) \sqrt{\frac{b \sinh ^2(c+d x)}{a}+1} F\left(i c+i d x\left|\frac{b}{a}\right.\right)}{15 d \sqrt{a+b \sinh ^2(c+d x)}}",1,"(4*(2*a - b)*b*Cosh[c + d*x]*Sinh[c + d*x]*Sqrt[a + b*Sinh[c + d*x]^2])/(15*d) + (b*Cosh[c + d*x]*Sinh[c + d*x]*(a + b*Sinh[c + d*x]^2)^(3/2))/(5*d) - ((I/15)*(23*a^2 - 23*a*b + 8*b^2)*EllipticE[I*c + I*d*x, b/a]*Sqrt[a + b*Sinh[c + d*x]^2])/(d*Sqrt[1 + (b*Sinh[c + d*x]^2)/a]) + (((4*I)/15)*a*(a - b)*(2*a - b)*EllipticF[I*c + I*d*x, b/a]*Sqrt[1 + (b*Sinh[c + d*x]^2)/a])/(d*Sqrt[a + b*Sinh[c + d*x]^2])","A",7,7,16,0.4375,1,"{3180, 3170, 3172, 3178, 3177, 3183, 3182}"
88,1,11,0,0.0239073,"\int \sqrt{1+\sinh ^2(x)} \, dx","Int[Sqrt[1 + Sinh[x]^2],x]","\sqrt{\cosh ^2(x)} \tanh (x)","\sqrt{\cosh ^2(x)} \tanh (x)",1,"Sqrt[Cosh[x]^2]*Tanh[x]","A",3,3,10,0.3000,1,"{3176, 3207, 2637}"
89,1,13,0,0.0256116,"\int \sqrt{-1-\sinh ^2(x)} \, dx","Int[Sqrt[-1 - Sinh[x]^2],x]","\sqrt{-\cosh ^2(x)} \tanh (x)","\sqrt{-\cosh ^2(x)} \tanh (x)",1,"Sqrt[-Cosh[x]^2]*Tanh[x]","A",3,3,12,0.2500,1,"{3176, 3207, 2637}"
90,1,11,0,0.0102307,"\int \sqrt{1-\sinh ^2(x)} \, dx","Int[Sqrt[1 - Sinh[x]^2],x]","-i E(i x|-1)","-i E(i x|-1)",1,"(-I)*EllipticE[I*x, -1]","A",1,1,12,0.08333,1,"{3177}"
91,1,33,0,0.0202611,"\int \sqrt{-1+\sinh ^2(x)} \, dx","Int[Sqrt[-1 + Sinh[x]^2],x]","-\frac{i \sqrt{\sinh ^2(x)-1} E(i x|-1)}{\sqrt{1-\sinh ^2(x)}}","-\frac{i \sqrt{\sinh ^2(x)-1} E(i x|-1)}{\sqrt{1-\sinh ^2(x)}}",1,"((-I)*EllipticE[I*x, -1]*Sqrt[-1 + Sinh[x]^2])/Sqrt[1 - Sinh[x]^2]","A",2,2,10,0.2000,1,"{3178, 3177}"
92,1,42,0,0.0317896,"\int \sqrt{a+b \sinh ^2(x)} \, dx","Int[Sqrt[a + b*Sinh[x]^2],x]","-\frac{i \sqrt{a+b \sinh ^2(x)} E\left(i x\left|\frac{b}{a}\right.\right)}{\sqrt{\frac{b \sinh ^2(x)}{a}+1}}","-\frac{i \sqrt{a+b \sinh ^2(x)} E\left(i x\left|\frac{b}{a}\right.\right)}{\sqrt{\frac{b \sinh ^2(x)}{a}+1}}",1,"((-I)*EllipticE[I*x, b/a]*Sqrt[a + b*Sinh[x]^2])/Sqrt[1 + (b*Sinh[x]^2)/a]","A",2,2,12,0.1667,1,"{3178, 3177}"
93,1,29,0,0.026434,"\int \left(1+\sinh ^2(x)\right)^{3/2} \, dx","Int[(1 + Sinh[x]^2)^(3/2),x]","\frac{1}{3} \cosh ^2(x)^{3/2} \tanh (x)+\frac{2}{3} \sqrt{\cosh ^2(x)} \tanh (x)","\frac{1}{3} \cosh ^2(x)^{3/2} \tanh (x)+\frac{2}{3} \sqrt{\cosh ^2(x)} \tanh (x)",1,"(2*Sqrt[Cosh[x]^2]*Tanh[x])/3 + ((Cosh[x]^2)^(3/2)*Tanh[x])/3","A",4,4,10,0.4000,1,"{3176, 3203, 3207, 2637}"
94,1,33,0,0.0293963,"\int \left(-1-\sinh ^2(x)\right)^{3/2} \, dx","Int[(-1 - Sinh[x]^2)^(3/2),x]","\frac{1}{3} \left(-\cosh ^2(x)\right)^{3/2} \tanh (x)-\frac{2}{3} \sqrt{-\cosh ^2(x)} \tanh (x)","\frac{1}{3} \left(-\cosh ^2(x)\right)^{3/2} \tanh (x)-\frac{2}{3} \sqrt{-\cosh ^2(x)} \tanh (x)",1,"(-2*Sqrt[-Cosh[x]^2]*Tanh[x])/3 + ((-Cosh[x]^2)^(3/2)*Tanh[x])/3","A",4,4,12,0.3333,1,"{3176, 3203, 3207, 2637}"
95,1,45,0,0.0635546,"\int \left(1-\sinh ^2(x)\right)^{3/2} \, dx","Int[(1 - Sinh[x]^2)^(3/2),x]","\frac{2}{3} i F(i x|-1)-2 i E(i x|-1)-\frac{1}{3} \sinh (x) \sqrt{1-\sinh ^2(x)} \cosh (x)","\frac{2}{3} i F(i x|-1)-2 i E(i x|-1)-\frac{1}{3} \sinh (x) \sqrt{1-\sinh ^2(x)} \cosh (x)",1,"(-2*I)*EllipticE[I*x, -1] + ((2*I)/3)*EllipticF[I*x, -1] - (Cosh[x]*Sinh[x]*Sqrt[1 - Sinh[x]^2])/3","A",4,4,12,0.3333,1,"{3180, 3172, 3177, 3182}"
96,1,87,0,0.0855633,"\int \left(-1+\sinh ^2(x)\right)^{3/2} \, dx","Int[(-1 + Sinh[x]^2)^(3/2),x]","\frac{1}{3} \sinh (x) \sqrt{\sinh ^2(x)-1} \cosh (x)+\frac{2 i \sqrt{1-\sinh ^2(x)} F(i x|-1)}{3 \sqrt{\sinh ^2(x)-1}}+\frac{2 i \sqrt{\sinh ^2(x)-1} E(i x|-1)}{\sqrt{1-\sinh ^2(x)}}","\frac{1}{3} \sinh (x) \sqrt{\sinh ^2(x)-1} \cosh (x)+\frac{2 i \sqrt{1-\sinh ^2(x)} F(i x|-1)}{3 \sqrt{\sinh ^2(x)-1}}+\frac{2 i \sqrt{\sinh ^2(x)-1} E(i x|-1)}{\sqrt{1-\sinh ^2(x)}}",1,"(((2*I)/3)*EllipticF[I*x, -1]*Sqrt[1 - Sinh[x]^2])/Sqrt[-1 + Sinh[x]^2] + (Cosh[x]*Sinh[x]*Sqrt[-1 + Sinh[x]^2])/3 + ((2*I)*EllipticE[I*x, -1]*Sqrt[-1 + Sinh[x]^2])/Sqrt[1 - Sinh[x]^2]","A",6,6,10,0.6000,1,"{3180, 3172, 3178, 3177, 3183, 3182}"
97,1,123,0,0.1628221,"\int \left(a+b \sinh ^2(x)\right)^{3/2} \, dx","Int[(a + b*Sinh[x]^2)^(3/2),x]","\frac{1}{3} b \sinh (x) \cosh (x) \sqrt{a+b \sinh ^2(x)}+\frac{i a (a-b) \sqrt{\frac{b \sinh ^2(x)}{a}+1} F\left(i x\left|\frac{b}{a}\right.\right)}{3 \sqrt{a+b \sinh ^2(x)}}-\frac{2 i (2 a-b) \sqrt{a+b \sinh ^2(x)} E\left(i x\left|\frac{b}{a}\right.\right)}{3 \sqrt{\frac{b \sinh ^2(x)}{a}+1}}","\frac{1}{3} b \sinh (x) \cosh (x) \sqrt{a+b \sinh ^2(x)}+\frac{i a (a-b) \sqrt{\frac{b \sinh ^2(x)}{a}+1} F\left(i x\left|\frac{b}{a}\right.\right)}{3 \sqrt{a+b \sinh ^2(x)}}-\frac{2 i (2 a-b) \sqrt{a+b \sinh ^2(x)} E\left(i x\left|\frac{b}{a}\right.\right)}{3 \sqrt{\frac{b \sinh ^2(x)}{a}+1}}",1,"(b*Cosh[x]*Sinh[x]*Sqrt[a + b*Sinh[x]^2])/3 - (((2*I)/3)*(2*a - b)*EllipticE[I*x, b/a]*Sqrt[a + b*Sinh[x]^2])/Sqrt[1 + (b*Sinh[x]^2)/a] + ((I/3)*a*(a - b)*EllipticF[I*x, b/a]*Sqrt[1 + (b*Sinh[x]^2)/a])/Sqrt[a + b*Sinh[x]^2]","A",6,6,12,0.5000,1,"{3180, 3172, 3178, 3177, 3183, 3182}"
98,1,83,0,0.0992391,"\int \frac{\sinh ^3(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Sinh[e + f*x]^3/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\cosh (e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{2 b f}-\frac{(a+b) \tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{2 b^{3/2} f}","\frac{\cosh (e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{2 b f}-\frac{(a+b) \tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{2 b^{3/2} f}",1,"-((a + b)*ArcTanh[(Sqrt[b]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/(2*b^(3/2)*f) + (Cosh[e + f*x]*Sqrt[a - b + b*Cosh[e + f*x]^2])/(2*b*f)","A",4,4,25,0.1600,1,"{3186, 388, 217, 206}"
99,1,41,0,0.0505043,"\int \frac{\sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Sinh[e + f*x]/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{\sqrt{b} f}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{\sqrt{b} f}",1,"ArcTanh[(Sqrt[b]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]]/(Sqrt[b]*f)","A",3,3,23,0.1304,1,"{3186, 217, 206}"
100,1,42,0,0.0802426,"\int \frac{\text{csch}(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Csch[e + f*x]/Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{\sqrt{a} f}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{\sqrt{a} f}",1,"-(ArcTanh[(Sqrt[a]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]]/(Sqrt[a]*f))","A",3,3,23,0.1304,1,"{3186, 377, 206}"
101,1,89,0,0.1148861,"\int \frac{\text{csch}^3(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Csch[e + f*x]^3/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{(a+b) \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{2 a^{3/2} f}-\frac{\coth (e+f x) \text{csch}(e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{2 a f}","\frac{(a+b) \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{2 a^{3/2} f}-\frac{\coth (e+f x) \text{csch}(e+f x) \sqrt{a+b \cosh ^2(e+f x)-b}}{2 a f}",1,"((a + b)*ArcTanh[(Sqrt[a]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/(2*a^(3/2)*f) - (Sqrt[a - b + b*Cosh[e + f*x]^2]*Coth[e + f*x]*Csch[e + f*x])/(2*a*f)","A",4,4,25,0.1600,1,"{3186, 382, 377, 206}"
102,1,229,0,0.217968,"\int \frac{\sinh ^4(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Sinh[e + f*x]^4/Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{2 (a+b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 b^2 f}+\frac{2 (a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{\sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 b f}-\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","-\frac{2 (a+b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 b^2 f}+\frac{2 (a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{\sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 b f}-\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*b*f) + (2*(a + b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*b^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*b*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (2*(a + b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*b^2*f)","A",6,6,25,0.2400,1,"{3188, 479, 531, 418, 492, 411}"
103,1,128,0,0.1358129,"\int \frac{\sinh ^2(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Sinh[e + f*x]^2/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{i a \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{b f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{i \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{b f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}","\frac{i a \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{b f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{i \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{b f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}",1,"((-I)*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/(b*f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a]) + (I*a*EllipticF[I*e + I*f*x, b/a]*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])/(b*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",5,5,25,0.2000,1,"{3172, 3178, 3177, 3183, 3182}"
104,1,60,0,0.0362947,"\int \frac{1}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[1/Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{i \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{f \sqrt{a+b \sinh ^2(e+f x)}}","-\frac{i \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{f \sqrt{a+b \sinh ^2(e+f x)}}",1,"((-I)*EllipticF[I*e + I*f*x, b/a]*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])/(f*Sqrt[a + b*Sinh[e + f*x]^2])","A",2,2,16,0.1250,1,"{3183, 3182}"
105,1,134,0,0.1489709,"\int \frac{\text{csch}^2(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Csch[e + f*x]^2/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a f}-\frac{\coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a f}-\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{\tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a f}-\frac{\coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a f}-\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"-((Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*f)) - (EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(a*f)","A",5,5,25,0.2000,1,"{3188, 480, 12, 492, 411}"
106,1,267,0,0.2835456,"\int \frac{\text{csch}^4(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Csch[e + f*x]^4/Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{2 (a+b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^2 f}+\frac{2 (a+b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^2 f}-\frac{b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{2 (a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{\coth (e+f x) \text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a f}","-\frac{2 (a+b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^2 f}+\frac{2 (a+b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^2 f}-\frac{b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{2 (a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{\coth (e+f x) \text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a f}",1,"(2*(a + b)*Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^2*f) - (Coth[e + f*x]*Csch[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*f) + (2*(a + b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (b*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (2*(a + b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*a^2*f)","A",7,7,25,0.2800,1,"{3188, 480, 583, 531, 418, 492, 411}"
107,1,83,0,0.1124542,"\int \frac{\sinh ^3(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Sinh[e + f*x]^3/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{b^{3/2} f}-\frac{a \cosh (e+f x)}{b f (a-b) \sqrt{a+b \cosh ^2(e+f x)-b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{b^{3/2} f}-\frac{a \cosh (e+f x)}{b f (a-b) \sqrt{a+b \cosh ^2(e+f x)-b}}",1,"ArcTanh[(Sqrt[b]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]]/(b^(3/2)*f) - (a*Cosh[e + f*x])/((a - b)*b*f*Sqrt[a - b + b*Cosh[e + f*x]^2])","A",4,4,25,0.1600,1,"{3186, 385, 217, 206}"
108,1,36,0,0.0526382,"\int \frac{\sinh (e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Sinh[e + f*x]/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{\cosh (e+f x)}{f (a-b) \sqrt{a+b \cosh ^2(e+f x)-b}}","\frac{\cosh (e+f x)}{f (a-b) \sqrt{a+b \cosh ^2(e+f x)-b}}",1,"Cosh[e + f*x]/((a - b)*f*Sqrt[a - b + b*Cosh[e + f*x]^2])","A",2,2,23,0.08696,1,"{3186, 191}"
109,1,84,0,0.1084403,"\int \frac{\text{csch}(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Csch[e + f*x]/(a + b*Sinh[e + f*x]^2)^(3/2),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{a^{3/2} f}-\frac{b \cosh (e+f x)}{a f (a-b) \sqrt{a+b \cosh ^2(e+f x)-b}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{a^{3/2} f}-\frac{b \cosh (e+f x)}{a f (a-b) \sqrt{a+b \cosh ^2(e+f x)-b}}",1,"-(ArcTanh[(Sqrt[a]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]]/(a^(3/2)*f)) - (b*Cosh[e + f*x])/(a*(a - b)*f*Sqrt[a - b + b*Cosh[e + f*x]^2])","A",4,4,23,0.1739,1,"{3186, 382, 377, 206}"
110,1,139,0,0.1818339,"\int \frac{\text{csch}^3(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Csch[e + f*x]^3/(a + b*Sinh[e + f*x]^2)^(3/2),x]","-\frac{b (a-3 b) \cosh (e+f x)}{2 a^2 f (a-b) \sqrt{a+b \cosh ^2(e+f x)-b}}+\frac{(a+3 b) \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{2 a^{5/2} f}-\frac{\coth (e+f x) \text{csch}(e+f x)}{2 a f \sqrt{a+b \cosh ^2(e+f x)-b}}","-\frac{b (a-3 b) \cosh (e+f x)}{2 a^2 f (a-b) \sqrt{a+b \cosh ^2(e+f x)-b}}+\frac{(a+3 b) \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{2 a^{5/2} f}-\frac{\coth (e+f x) \text{csch}(e+f x)}{2 a f \sqrt{a+b \cosh ^2(e+f x)-b}}",1,"((a + 3*b)*ArcTanh[(Sqrt[a]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]])/(2*a^(5/2)*f) - ((a - 3*b)*b*Cosh[e + f*x])/(2*a^2*(a - b)*f*Sqrt[a - b + b*Cosh[e + f*x]^2]) - (Coth[e + f*x]*Csch[e + f*x])/(2*a*f*Sqrt[a - b + b*Cosh[e + f*x]^2])","A",6,6,25,0.2400,1,"{3186, 414, 527, 12, 377, 206}"
111,1,341,0,0.3406615,"\int \frac{\sinh ^6(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Sinh[e + f*x]^6/(a + b*Sinh[e + f*x]^2)^(3/2),x]","-\frac{\left(8 a^2-3 a b-2 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 b^3 f (a-b)}+\frac{\left(8 a^2-3 a b-2 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 b^3 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{(4 a-b) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 b^2 f (a-b)}-\frac{(4 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 b^2 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{a \sinh ^3(e+f x) \cosh (e+f x)}{b f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}","-\frac{\left(8 a^2-3 a b-2 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 b^3 f (a-b)}+\frac{\left(8 a^2-3 a b-2 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 b^3 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{(4 a-b) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 b^2 f (a-b)}-\frac{(4 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 b^2 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{a \sinh ^3(e+f x) \cosh (e+f x)}{b f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}",1,"-((a*Cosh[e + f*x]*Sinh[e + f*x]^3)/((a - b)*b*f*Sqrt[a + b*Sinh[e + f*x]^2])) + ((4*a - b)*Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*(a - b)*b^2*f) + ((8*a^2 - 3*a*b - 2*b^2)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*(a - b)*b^3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - ((4*a - b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*(a - b)*b^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - ((8*a^2 - 3*a*b - 2*b^2)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*(a - b)*b^3*f)","A",7,7,25,0.2800,1,"{3188, 470, 582, 531, 418, 492, 411}"
112,1,256,0,0.2350176,"\int \frac{\sinh ^4(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Sinh[e + f*x]^4/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{(2 a-b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{b^2 f (a-b)}-\frac{(2 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{b^2 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{a \sinh (e+f x) \cosh (e+f x)}{b f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}+\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{b f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{(2 a-b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{b^2 f (a-b)}-\frac{(2 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{b^2 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{a \sinh (e+f x) \cosh (e+f x)}{b f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}+\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{b f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"-((a*Cosh[e + f*x]*Sinh[e + f*x])/((a - b)*b*f*Sqrt[a + b*Sinh[e + f*x]^2])) - ((2*a - b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/((a - b)*b^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/((a - b)*b*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((2*a - b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/((a - b)*b^2*f)","A",6,6,25,0.2400,1,"{3188, 470, 531, 418, 492, 411}"
113,1,173,0,0.2120755,"\int \frac{\sinh ^2(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Sinh[e + f*x]^2/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{\sinh (e+f x) \cosh (e+f x)}{f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}-\frac{i \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{b f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{i \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{b f (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}","\frac{\sinh (e+f x) \cosh (e+f x)}{f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}-\frac{i \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{b f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{i \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{b f (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}",1,"(Cosh[e + f*x]*Sinh[e + f*x])/((a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2]) + (I*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/((a - b)*b*f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a]) - (I*EllipticF[I*e + I*f*x, b/a]*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])/(b*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",6,6,25,0.2400,1,"{3173, 3172, 3178, 3177, 3183, 3182}"
114,1,115,0,0.0616497,"\int \frac{1}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[(a + b*Sinh[e + f*x]^2)^(-3/2),x]","-\frac{b \sinh (e+f x) \cosh (e+f x)}{a f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}-\frac{i \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{a f (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}","-\frac{b \sinh (e+f x) \cosh (e+f x)}{a f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}-\frac{i \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{a f (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}",1,"-((b*Cosh[e + f*x]*Sinh[e + f*x])/(a*(a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2])) - (I*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*(a - b)*f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])","A",4,4,16,0.2500,1,"{3184, 21, 3178, 3177}"
115,1,290,0,0.3100076,"\int \frac{\text{csch}^2(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Csch[e + f*x]^2/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{(a-2 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a^2 f (a-b)}-\frac{(a-2 b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a^2 f (a-b)}-\frac{b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a^2 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a-2 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a^2 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{b \coth (e+f x)}{a f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}","\frac{(a-2 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a^2 f (a-b)}-\frac{(a-2 b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a^2 f (a-b)}-\frac{b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a^2 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a-2 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a^2 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{b \coth (e+f x)}{a f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}",1,"-((b*Coth[e + f*x])/(a*(a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2])) - ((a - 2*b)*Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a^2*(a - b)*f) - ((a - 2*b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a^2*(a - b)*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (b*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a^2*(a - b)*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((a - 2*b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(a^2*(a - b)*f)","A",7,7,25,0.2800,1,"{3188, 472, 583, 531, 418, 492, 411}"
116,1,143,0,0.1660951,"\int \frac{\sinh ^5(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Sinh[e + f*x]^5/(a + b*Sinh[e + f*x]^2)^(5/2),x]","-\frac{a (3 a-5 b) \cosh (e+f x)}{3 b^2 f (a-b)^2 \sqrt{a+b \cosh ^2(e+f x)-b}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{b^{5/2} f}-\frac{a \sinh ^2(e+f x) \cosh (e+f x)}{3 b f (a-b) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}","-\frac{a (3 a-5 b) \cosh (e+f x)}{3 b^2 f (a-b)^2 \sqrt{a+b \cosh ^2(e+f x)-b}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{b^{5/2} f}-\frac{a \sinh ^2(e+f x) \cosh (e+f x)}{3 b f (a-b) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}",1,"ArcTanh[(Sqrt[b]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]]/(b^(5/2)*f) - (a*(3*a - 5*b)*Cosh[e + f*x])/(3*(a - b)^2*b^2*f*Sqrt[a - b + b*Cosh[e + f*x]^2]) - (a*Cosh[e + f*x]*Sinh[e + f*x]^2)/(3*(a - b)*b*f*(a - b + b*Cosh[e + f*x]^2)^(3/2))","A",5,5,25,0.2000,1,"{3186, 413, 385, 217, 206}"
117,1,87,0,0.1072199,"\int \frac{\sinh ^3(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Sinh[e + f*x]^3/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{\sinh ^2(e+f x) \cosh (e+f x)}{3 f (a-b) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}-\frac{2 \cosh (e+f x)}{3 f (a-b)^2 \sqrt{a+b \cosh ^2(e+f x)-b}}","\frac{\sinh ^2(e+f x) \cosh (e+f x)}{3 f (a-b) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}-\frac{2 \cosh (e+f x)}{3 f (a-b)^2 \sqrt{a+b \cosh ^2(e+f x)-b}}",1,"(-2*Cosh[e + f*x])/(3*(a - b)^2*f*Sqrt[a - b + b*Cosh[e + f*x]^2]) + (Cosh[e + f*x]*Sinh[e + f*x]^2)/(3*(a - b)*f*(a - b + b*Cosh[e + f*x]^2)^(3/2))","A",3,3,25,0.1200,1,"{3186, 378, 191}"
118,1,79,0,0.0675662,"\int \frac{\sinh (e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Sinh[e + f*x]/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{2 \cosh (e+f x)}{3 f (a-b)^2 \sqrt{a+b \cosh ^2(e+f x)-b}}+\frac{\cosh (e+f x)}{3 f (a-b) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}","\frac{2 \cosh (e+f x)}{3 f (a-b)^2 \sqrt{a+b \cosh ^2(e+f x)-b}}+\frac{\cosh (e+f x)}{3 f (a-b) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}",1,"Cosh[e + f*x]/(3*(a - b)*f*(a - b + b*Cosh[e + f*x]^2)^(3/2)) + (2*Cosh[e + f*x])/(3*(a - b)^2*f*Sqrt[a - b + b*Cosh[e + f*x]^2])","A",3,3,23,0.1304,1,"{3186, 192, 191}"
119,1,136,0,0.1713864,"\int \frac{\text{csch}(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Csch[e + f*x]/(a + b*Sinh[e + f*x]^2)^(5/2),x]","-\frac{b (5 a-3 b) \cosh (e+f x)}{3 a^2 f (a-b)^2 \sqrt{a+b \cosh ^2(e+f x)-b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{a^{5/2} f}-\frac{b \cosh (e+f x)}{3 a f (a-b) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}","-\frac{b (5 a-3 b) \cosh (e+f x)}{3 a^2 f (a-b)^2 \sqrt{a+b \cosh ^2(e+f x)-b}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \cosh (e+f x)}{\sqrt{a+b \cosh ^2(e+f x)-b}}\right)}{a^{5/2} f}-\frac{b \cosh (e+f x)}{3 a f (a-b) \left(a+b \cosh ^2(e+f x)-b\right)^{3/2}}",1,"-(ArcTanh[(Sqrt[a]*Cosh[e + f*x])/Sqrt[a - b + b*Cosh[e + f*x]^2]]/(a^(5/2)*f)) - (b*Cosh[e + f*x])/(3*a*(a - b)*f*(a - b + b*Cosh[e + f*x]^2)^(3/2)) - ((5*a - 3*b)*b*Cosh[e + f*x])/(3*a^2*(a - b)^2*f*Sqrt[a - b + b*Cosh[e + f*x]^2])","A",6,6,23,0.2609,1,"{3186, 414, 527, 12, 377, 206}"
120,1,344,0,0.3664332,"\int \frac{\sinh ^6(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Sinh[e + f*x]^6/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{\left(8 a^2-13 a b+3 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 b^3 f (a-b)^2}-\frac{\left(8 a^2-13 a b+3 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 b^3 f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{2 a (2 a-3 b) \sinh (e+f x) \cosh (e+f x)}{3 b^2 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}+\frac{2 (2 a-3 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 b^2 f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{a \sinh ^3(e+f x) \cosh (e+f x)}{3 b f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}","\frac{\left(8 a^2-13 a b+3 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 b^3 f (a-b)^2}-\frac{\left(8 a^2-13 a b+3 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 b^3 f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{2 a (2 a-3 b) \sinh (e+f x) \cosh (e+f x)}{3 b^2 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}+\frac{2 (2 a-3 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 b^2 f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{a \sinh ^3(e+f x) \cosh (e+f x)}{3 b f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}",1,"-(a*Cosh[e + f*x]*Sinh[e + f*x]^3)/(3*(a - b)*b*f*(a + b*Sinh[e + f*x]^2)^(3/2)) - (2*a*(2*a - 3*b)*Cosh[e + f*x]*Sinh[e + f*x])/(3*(a - b)^2*b^2*f*Sqrt[a + b*Sinh[e + f*x]^2]) - ((8*a^2 - 13*a*b + 3*b^2)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*(a - b)^2*b^3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (2*(2*a - 3*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*(a - b)^2*b^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((8*a^2 - 13*a*b + 3*b^2)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*(a - b)^2*b^3*f)","A",7,7,25,0.2800,1,"{3188, 470, 578, 531, 418, 492, 411}"
121,1,244,0,0.2492294,"\int \frac{\sinh ^4(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Sinh[e + f*x]^4/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{2 \sqrt{a} (a-2 b) \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{3 b^{3/2} f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}-\frac{a \sinh (e+f x) \cosh (e+f x)}{3 b f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{(a-3 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a b f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{2 \sqrt{a} (a-2 b) \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{3 b^{3/2} f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}-\frac{a \sinh (e+f x) \cosh (e+f x)}{3 b f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{(a-3 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a b f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"-(a*Cosh[e + f*x]*Sinh[e + f*x])/(3*(a - b)*b*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + (2*Sqrt[a]*(a - 2*b)*Cosh[e + f*x]*EllipticE[ArcTan[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a]], 1 - a/b])/(3*(a - b)^2*b^(3/2)*f*Sqrt[(a*Cosh[e + f*x]^2)/(a + b*Sinh[e + f*x]^2)]*Sqrt[a + b*Sinh[e + f*x]^2]) - ((a - 3*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*(a - b)^2*b*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a])","A",5,5,25,0.2000,1,"{3188, 470, 525, 418, 411}"
122,1,241,0,0.3256951,"\int \frac{\sinh ^2(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Sinh[e + f*x]^2/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{(a+b) \sinh (e+f x) \cosh (e+f x)}{3 a f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}+\frac{\sinh (e+f x) \cosh (e+f x)}{3 f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{i \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 b f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}+\frac{i (a+b) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 a b f (a-b)^2 \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}","\frac{(a+b) \sinh (e+f x) \cosh (e+f x)}{3 a f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}+\frac{\sinh (e+f x) \cosh (e+f x)}{3 f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{i \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 b f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}+\frac{i (a+b) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 a b f (a-b)^2 \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}",1,"(Cosh[e + f*x]*Sinh[e + f*x])/(3*(a - b)*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + ((a + b)*Cosh[e + f*x]*Sinh[e + f*x])/(3*a*(a - b)^2*f*Sqrt[a + b*Sinh[e + f*x]^2]) + ((I/3)*(a + b)*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*(a - b)^2*b*f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a]) - ((I/3)*EllipticF[I*e + I*f*x, b/a]*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])/((a - b)*b*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",7,6,25,0.2400,1,"{3173, 3172, 3178, 3177, 3183, 3182}"
123,1,251,0,0.2796921,"\int \frac{1}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[(a + b*Sinh[e + f*x]^2)^(-5/2),x]","-\frac{2 b (2 a-b) \sinh (e+f x) \cosh (e+f x)}{3 a^2 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}-\frac{2 i (2 a-b) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 a^2 f (a-b)^2 \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}-\frac{b \sinh (e+f x) \cosh (e+f x)}{3 a f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}+\frac{i \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 a f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}","-\frac{2 b (2 a-b) \sinh (e+f x) \cosh (e+f x)}{3 a^2 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}-\frac{2 i (2 a-b) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 a^2 f (a-b)^2 \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}-\frac{b \sinh (e+f x) \cosh (e+f x)}{3 a f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}+\frac{i \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 a f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}",1,"-(b*Cosh[e + f*x]*Sinh[e + f*x])/(3*a*(a - b)*f*(a + b*Sinh[e + f*x]^2)^(3/2)) - (2*(2*a - b)*b*Cosh[e + f*x]*Sinh[e + f*x])/(3*a^2*(a - b)^2*f*Sqrt[a + b*Sinh[e + f*x]^2]) - (((2*I)/3)*(2*a - b)*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/(a^2*(a - b)^2*f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a]) + ((I/3)*EllipticF[I*e + I*f*x, b/a]*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])/(a*(a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",7,7,16,0.4375,1,"{3184, 3173, 3172, 3178, 3177, 3183, 3182}"
124,1,385,0,0.4562178,"\int \frac{\text{csch}^2(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Csch[e + f*x]^2/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{\left(3 a^2-13 a b+8 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^3 f (a-b)^2}-\frac{\left(3 a^2-13 a b+8 b^2\right) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^3 f (a-b)^2}-\frac{\left(3 a^2-13 a b+8 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^3 f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{2 b (3 a-2 b) \coth (e+f x)}{3 a^2 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}-\frac{2 b (3 a-2 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^3 f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{b \coth (e+f x)}{3 a f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}","\frac{\left(3 a^2-13 a b+8 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^3 f (a-b)^2}-\frac{\left(3 a^2-13 a b+8 b^2\right) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^3 f (a-b)^2}-\frac{\left(3 a^2-13 a b+8 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^3 f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{2 b (3 a-2 b) \coth (e+f x)}{3 a^2 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}-\frac{2 b (3 a-2 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^3 f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{b \coth (e+f x)}{3 a f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}",1,"-(b*Coth[e + f*x])/(3*a*(a - b)*f*(a + b*Sinh[e + f*x]^2)^(3/2)) - (2*(3*a - 2*b)*b*Coth[e + f*x])/(3*a^2*(a - b)^2*f*Sqrt[a + b*Sinh[e + f*x]^2]) - ((3*a^2 - 13*a*b + 8*b^2)*Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^3*(a - b)^2*f) - ((3*a^2 - 13*a*b + 8*b^2)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^3*(a - b)^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (2*(3*a - 2*b)*b*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^3*(a - b)^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((3*a^2 - 13*a*b + 8*b^2)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*a^3*(a - b)^2*f)","A",8,8,25,0.3200,1,"{3188, 472, 579, 583, 531, 418, 492, 411}"
125,1,14,0,0.0240236,"\int \frac{1}{\sqrt{1+\sinh ^2(x)}} \, dx","Int[1/Sqrt[1 + Sinh[x]^2],x]","\frac{\cosh (x) \tan ^{-1}(\sinh (x))}{\sqrt{\cosh ^2(x)}}","\frac{\cosh (x) \tan ^{-1}(\sinh (x))}{\sqrt{\cosh ^2(x)}}",1,"(ArcTan[Sinh[x]]*Cosh[x])/Sqrt[Cosh[x]^2]","A",3,3,10,0.3000,1,"{3176, 3207, 3770}"
126,1,11,0,0.0108332,"\int \frac{1}{\sqrt{1-\sinh ^2(x)}} \, dx","Int[1/Sqrt[1 - Sinh[x]^2],x]","-i F(i x|-1)","-i F(i x|-1)",1,"(-I)*EllipticF[I*x, -1]","A",1,1,12,0.08333,1,"{3182}"
127,1,33,0,0.021624,"\int \frac{1}{\sqrt{-1+\sinh ^2(x)}} \, dx","Int[1/Sqrt[-1 + Sinh[x]^2],x]","-\frac{i \sqrt{1-\sinh ^2(x)} F(i x|-1)}{\sqrt{\sinh ^2(x)-1}}","-\frac{i \sqrt{1-\sinh ^2(x)} F(i x|-1)}{\sqrt{\sinh ^2(x)-1}}",1,"((-I)*EllipticF[I*x, -1]*Sqrt[1 - Sinh[x]^2])/Sqrt[-1 + Sinh[x]^2]","A",2,2,10,0.2000,1,"{3183, 3182}"
128,1,16,0,0.0237084,"\int \frac{1}{\sqrt{-1-\sinh ^2(x)}} \, dx","Int[1/Sqrt[-1 - Sinh[x]^2],x]","\frac{\cosh (x) \tan ^{-1}(\sinh (x))}{\sqrt{-\cosh ^2(x)}}","\frac{\cosh (x) \tan ^{-1}(\sinh (x))}{\sqrt{-\cosh ^2(x)}}",1,"(ArcTan[Sinh[x]]*Cosh[x])/Sqrt[-Cosh[x]^2]","A",3,3,12,0.2500,1,"{3176, 3207, 3770}"
129,1,42,0,0.0329238,"\int \frac{1}{\sqrt{a+b \sinh ^2(x)}} \, dx","Int[1/Sqrt[a + b*Sinh[x]^2],x]","-\frac{i \sqrt{\frac{b \sinh ^2(x)}{a}+1} F\left(i x\left|\frac{b}{a}\right.\right)}{\sqrt{a+b \sinh ^2(x)}}","-\frac{i \sqrt{\frac{b \sinh ^2(x)}{a}+1} F\left(i x\left|\frac{b}{a}\right.\right)}{\sqrt{a+b \sinh ^2(x)}}",1,"((-I)*EllipticF[I*x, b/a]*Sqrt[1 + (b*Sinh[x]^2)/a])/Sqrt[a + b*Sinh[x]^2]","A",2,2,12,0.1667,1,"{3183, 3182}"
130,1,128,0,0.1161031,"\int (d \sinh (e+f x))^m \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[(d*Sinh[e + f*x])^m*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{d \cosh (e+f x) \left(-\sinh ^2(e+f x)\right)^{\frac{1-m}{2}} (d \sinh (e+f x))^{m-1} \left(a+b \cosh ^2(e+f x)-b\right)^p \left(\frac{b \cosh ^2(e+f x)}{a-b}+1\right)^{-p} F_1\left(\frac{1}{2};\frac{1-m}{2},-p;\frac{3}{2};\cosh ^2(e+f x),-\frac{b \cosh ^2(e+f x)}{a-b}\right)}{f}","\frac{d \cosh (e+f x) \left(-\sinh ^2(e+f x)\right)^{\frac{1-m}{2}} (d \sinh (e+f x))^{m-1} \left(a+b \cosh ^2(e+f x)-b\right)^p \left(\frac{b \cosh ^2(e+f x)}{a-b}+1\right)^{-p} F_1\left(\frac{1}{2};\frac{1-m}{2},-p;\frac{3}{2};\cosh ^2(e+f x),-\frac{b \cosh ^2(e+f x)}{a-b}\right)}{f}",1,"(d*AppellF1[1/2, (1 - m)/2, -p, 3/2, Cosh[e + f*x]^2, -((b*Cosh[e + f*x]^2)/(a - b))]*Cosh[e + f*x]*(a - b + b*Cosh[e + f*x]^2)^p*(d*Sinh[e + f*x])^(-1 + m)*(-Sinh[e + f*x]^2)^((1 - m)/2))/(f*(1 + (b*Cosh[e + f*x]^2)/(a - b))^p)","A",3,3,25,0.1200,1,"{3189, 430, 429}"
131,1,226,0,0.2590804,"\int \sinh ^5(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Sinh[e + f*x]^5*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{\left(3 a^2+4 a b (p+1)+4 b^2 \left(p^2+3 p+2\right)\right) \cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^p \left(\frac{b \cosh ^2(e+f x)}{a-b}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b \cosh ^2(e+f x)}{a-b}\right)}{b^2 f (2 p+3) (2 p+5)}-\frac{(3 a+2 b (p+2)) \cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{p+1}}{b^2 f (2 p+3) (2 p+5)}+\frac{\sinh ^2(e+f x) \cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{p+1}}{b f (2 p+5)}","\frac{\left(3 a^2+4 a b (p+1)+4 b^2 \left(p^2+3 p+2\right)\right) \cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^p \left(\frac{b \cosh ^2(e+f x)}{a-b}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b \cosh ^2(e+f x)}{a-b}\right)}{b^2 f (2 p+3) (2 p+5)}-\frac{(3 a+2 b (p+2)) \cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{p+1}}{b^2 f (2 p+3) (2 p+5)}+\frac{\sinh ^2(e+f x) \cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{p+1}}{b f (2 p+5)}",1,"-(((3*a + 2*b*(2 + p))*Cosh[e + f*x]*(a - b + b*Cosh[e + f*x]^2)^(1 + p))/(b^2*f*(3 + 2*p)*(5 + 2*p))) + ((3*a^2 + 4*a*b*(1 + p) + 4*b^2*(2 + 3*p + p^2))*Cosh[e + f*x]*(a - b + b*Cosh[e + f*x]^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*Cosh[e + f*x]^2)/(a - b))])/(b^2*f*(3 + 2*p)*(5 + 2*p)*(1 + (b*Cosh[e + f*x]^2)/(a - b))^p) + (Cosh[e + f*x]*(a - b + b*Cosh[e + f*x]^2)^(1 + p)*Sinh[e + f*x]^2)/(b*f*(5 + 2*p))","A",5,5,23,0.2174,1,"{3186, 416, 388, 246, 245}"
132,1,137,0,0.1229334,"\int \sinh ^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Sinh[e + f*x]^3*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{\cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{p+1}}{b f (2 p+3)}-\frac{(a+2 b (p+1)) \cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^p \left(\frac{b \cosh ^2(e+f x)}{a-b}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b \cosh ^2(e+f x)}{a-b}\right)}{b f (2 p+3)}","\frac{\cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^{p+1}}{b f (2 p+3)}-\frac{(a+2 b (p+1)) \cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^p \left(\frac{b \cosh ^2(e+f x)}{a-b}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b \cosh ^2(e+f x)}{a-b}\right)}{b f (2 p+3)}",1,"(Cosh[e + f*x]*(a - b + b*Cosh[e + f*x]^2)^(1 + p))/(b*f*(3 + 2*p)) - ((a + 2*b*(1 + p))*Cosh[e + f*x]*(a - b + b*Cosh[e + f*x]^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*Cosh[e + f*x]^2)/(a - b))])/(b*f*(3 + 2*p)*(1 + (b*Cosh[e + f*x]^2)/(a - b))^p)","A",4,4,23,0.1739,1,"{3186, 388, 246, 245}"
133,1,78,0,0.057892,"\int \sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{\cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^p \left(\frac{b \cosh ^2(e+f x)}{a-b}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b \cosh ^2(e+f x)}{a-b}\right)}{f}","\frac{\cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^p \left(\frac{b \cosh ^2(e+f x)}{a-b}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b \cosh ^2(e+f x)}{a-b}\right)}{f}",1,"(Cosh[e + f*x]*(a - b + b*Cosh[e + f*x]^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((b*Cosh[e + f*x]^2)/(a - b))])/(f*(1 + (b*Cosh[e + f*x]^2)/(a - b))^p)","A",3,3,21,0.1429,1,"{3186, 246, 245}"
134,1,88,0,0.0878811,"\int \text{csch}(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Csch[e + f*x]*(a + b*Sinh[e + f*x]^2)^p,x]","-\frac{\cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^p \left(\frac{b \cosh ^2(e+f x)}{a-b}+1\right)^{-p} F_1\left(\frac{1}{2};1,-p;\frac{3}{2};\cosh ^2(e+f x),-\frac{b \cosh ^2(e+f x)}{a-b}\right)}{f}","-\frac{\cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^p \left(\frac{b \cosh ^2(e+f x)}{a-b}+1\right)^{-p} F_1\left(\frac{1}{2};1,-p;\frac{3}{2};\cosh ^2(e+f x),-\frac{b \cosh ^2(e+f x)}{a-b}\right)}{f}",1,"-((AppellF1[1/2, 1, -p, 3/2, Cosh[e + f*x]^2, -((b*Cosh[e + f*x]^2)/(a - b))]*Cosh[e + f*x]*(a - b + b*Cosh[e + f*x]^2)^p)/(f*(1 + (b*Cosh[e + f*x]^2)/(a - b))^p))","A",3,3,21,0.1429,1,"{3186, 430, 429}"
135,1,87,0,0.0968984,"\int \text{csch}^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Csch[e + f*x]^3*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{\cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^p \left(\frac{b \cosh ^2(e+f x)}{a-b}+1\right)^{-p} F_1\left(\frac{1}{2};2,-p;\frac{3}{2};\cosh ^2(e+f x),-\frac{b \cosh ^2(e+f x)}{a-b}\right)}{f}","\frac{\cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^p \left(\frac{b \cosh ^2(e+f x)}{a-b}+1\right)^{-p} F_1\left(\frac{1}{2};2,-p;\frac{3}{2};\cosh ^2(e+f x),-\frac{b \cosh ^2(e+f x)}{a-b}\right)}{f}",1,"(AppellF1[1/2, 2, -p, 3/2, Cosh[e + f*x]^2, -((b*Cosh[e + f*x]^2)/(a - b))]*Cosh[e + f*x]*(a - b + b*Cosh[e + f*x]^2)^p)/(f*(1 + (b*Cosh[e + f*x]^2)/(a - b))^p)","A",3,3,23,0.1304,1,"{3186, 430, 429}"
136,1,88,0,0.0970843,"\int \text{csch}^5(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Csch[e + f*x]^5*(a + b*Sinh[e + f*x]^2)^p,x]","-\frac{\cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^p \left(\frac{b \cosh ^2(e+f x)}{a-b}+1\right)^{-p} F_1\left(\frac{1}{2};3,-p;\frac{3}{2};\cosh ^2(e+f x),-\frac{b \cosh ^2(e+f x)}{a-b}\right)}{f}","-\frac{\cosh (e+f x) \left(a+b \cosh ^2(e+f x)-b\right)^p \left(\frac{b \cosh ^2(e+f x)}{a-b}+1\right)^{-p} F_1\left(\frac{1}{2};3,-p;\frac{3}{2};\cosh ^2(e+f x),-\frac{b \cosh ^2(e+f x)}{a-b}\right)}{f}",1,"-((AppellF1[1/2, 3, -p, 3/2, Cosh[e + f*x]^2, -((b*Cosh[e + f*x]^2)/(a - b))]*Cosh[e + f*x]*(a - b + b*Cosh[e + f*x]^2)^p)/(f*(1 + (b*Cosh[e + f*x]^2)/(a - b))^p))","A",3,3,23,0.1304,1,"{3186, 430, 429}"
137,1,103,0,0.1099662,"\int \sinh ^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Sinh[e + f*x]^4*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{\sinh ^4(e+f x) \sqrt{\cosh ^2(e+f x)} \tanh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{5}{2};\frac{1}{2},-p;\frac{7}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{5 f}","\frac{\sinh ^4(e+f x) \sqrt{\cosh ^2(e+f x)} \tanh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{5}{2};\frac{1}{2},-p;\frac{7}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{5 f}",1,"(AppellF1[5/2, 1/2, -p, 7/2, -Sinh[e + f*x]^2, -((b*Sinh[e + f*x]^2)/a)]*Sqrt[Cosh[e + f*x]^2]*Sinh[e + f*x]^4*(a + b*Sinh[e + f*x]^2)^p*Tanh[e + f*x])/(5*f*(1 + (b*Sinh[e + f*x]^2)/a)^p)","A",3,3,23,0.1304,1,"{3188, 511, 510}"
138,1,101,0,0.1924775,"\int \sinh ^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Sinh[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{\tanh ^3(e+f x) \text{sech}^2(e+f x)^p \left(a+b \sinh ^2(e+f x)\right)^p \left(1-\frac{(a-b) \tanh ^2(e+f x)}{a}\right)^{-p} F_1\left(\frac{3}{2};p+2,-p;\frac{5}{2};\tanh ^2(e+f x),\frac{(a-b) \tanh ^2(e+f x)}{a}\right)}{3 f}","\frac{\tanh ^3(e+f x) \text{sech}^2(e+f x)^p \left(a+b \sinh ^2(e+f x)\right)^p \left(1-\frac{(a-b) \tanh ^2(e+f x)}{a}\right)^{-p} F_1\left(\frac{3}{2};p+2,-p;\frac{5}{2};\tanh ^2(e+f x),\frac{(a-b) \tanh ^2(e+f x)}{a}\right)}{3 f}",1,"(AppellF1[3/2, 2 + p, -p, 5/2, Tanh[e + f*x]^2, ((a - b)*Tanh[e + f*x]^2)/a]*(Sech[e + f*x]^2)^p*(a + b*Sinh[e + f*x]^2)^p*Tanh[e + f*x]^3)/(3*f*(1 - ((a - b)*Tanh[e + f*x]^2)/a)^p)","A",3,3,23,0.1304,1,"{3174, 511, 510}"
139,1,99,0,0.1043912,"\int \text{csch}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Csch[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^p,x]","-\frac{\sqrt{\cosh ^2(e+f x)} \text{csch}(e+f x) \text{sech}(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(-\frac{1}{2};\frac{1}{2},-p;\frac{1}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}","-\frac{\sqrt{\cosh ^2(e+f x)} \text{csch}(e+f x) \text{sech}(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(-\frac{1}{2};\frac{1}{2},-p;\frac{1}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}",1,"-((AppellF1[-1/2, 1/2, -p, 1/2, -Sinh[e + f*x]^2, -((b*Sinh[e + f*x]^2)/a)]*Sqrt[Cosh[e + f*x]^2]*Csch[e + f*x]*Sech[e + f*x]*(a + b*Sinh[e + f*x]^2)^p)/(f*(1 + (b*Sinh[e + f*x]^2)/a)^p))","A",3,3,23,0.1304,1,"{3188, 511, 510}"
140,1,103,0,0.1047426,"\int \text{csch}^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Csch[e + f*x]^4*(a + b*Sinh[e + f*x]^2)^p,x]","-\frac{\sqrt{\cosh ^2(e+f x)} \text{csch}^3(e+f x) \text{sech}(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(-\frac{3}{2};\frac{1}{2},-p;-\frac{1}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{3 f}","-\frac{\sqrt{\cosh ^2(e+f x)} \text{csch}^3(e+f x) \text{sech}(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(-\frac{3}{2};\frac{1}{2},-p;-\frac{1}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{3 f}",1,"-(AppellF1[-3/2, 1/2, -p, -1/2, -Sinh[e + f*x]^2, -((b*Sinh[e + f*x]^2)/a)]*Sqrt[Cosh[e + f*x]^2]*Csch[e + f*x]^3*Sech[e + f*x]*(a + b*Sinh[e + f*x]^2)^p)/(3*f*(1 + (b*Sinh[e + f*x]^2)/a)^p)","A",3,3,23,0.1304,1,"{3188, 511, 510}"
141,1,106,0,0.0943742,"\int \sinh ^4(c+d x) \left(a+b \sinh ^3(c+d x)\right) \, dx","Int[Sinh[c + d*x]^4*(a + b*Sinh[c + d*x]^3),x]","\frac{a \sinh ^3(c+d x) \cosh (c+d x)}{4 d}-\frac{3 a \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{3 a x}{8}+\frac{b \cosh ^7(c+d x)}{7 d}-\frac{3 b \cosh ^5(c+d x)}{5 d}+\frac{b \cosh ^3(c+d x)}{d}-\frac{b \cosh (c+d x)}{d}","\frac{a \sinh ^3(c+d x) \cosh (c+d x)}{4 d}-\frac{3 a \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{3 a x}{8}+\frac{b \cosh ^7(c+d x)}{7 d}-\frac{3 b \cosh ^5(c+d x)}{5 d}+\frac{b \cosh ^3(c+d x)}{d}-\frac{b \cosh (c+d x)}{d}",1,"(3*a*x)/8 - (b*Cosh[c + d*x])/d + (b*Cosh[c + d*x]^3)/d - (3*b*Cosh[c + d*x]^5)/(5*d) + (b*Cosh[c + d*x]^7)/(7*d) - (3*a*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (a*Cosh[c + d*x]*Sinh[c + d*x]^3)/(4*d)","A",7,4,21,0.1905,1,"{3220, 2635, 8, 2633}"
142,1,99,0,0.1084718,"\int \sinh ^3(c+d x) \left(a+b \sinh ^3(c+d x)\right) \, dx","Int[Sinh[c + d*x]^3*(a + b*Sinh[c + d*x]^3),x]","\frac{a \cosh ^3(c+d x)}{3 d}-\frac{a \cosh (c+d x)}{d}+\frac{b \sinh ^5(c+d x) \cosh (c+d x)}{6 d}-\frac{5 b \sinh ^3(c+d x) \cosh (c+d x)}{24 d}+\frac{5 b \sinh (c+d x) \cosh (c+d x)}{16 d}-\frac{5 b x}{16}","\frac{a \cosh ^3(c+d x)}{3 d}-\frac{a \cosh (c+d x)}{d}+\frac{b \sinh ^5(c+d x) \cosh (c+d x)}{6 d}-\frac{5 b \sinh ^3(c+d x) \cosh (c+d x)}{24 d}+\frac{5 b \sinh (c+d x) \cosh (c+d x)}{16 d}-\frac{5 b x}{16}",1,"(-5*b*x)/16 - (a*Cosh[c + d*x])/d + (a*Cosh[c + d*x]^3)/(3*d) + (5*b*Cosh[c + d*x]*Sinh[c + d*x])/(16*d) - (5*b*Cosh[c + d*x]*Sinh[c + d*x]^3)/(24*d) + (b*Cosh[c + d*x]*Sinh[c + d*x]^5)/(6*d)","A",8,4,21,0.1905,1,"{3220, 2633, 2635, 8}"
143,1,70,0,0.0708939,"\int \sinh ^2(c+d x) \left(a+b \sinh ^3(c+d x)\right) \, dx","Int[Sinh[c + d*x]^2*(a + b*Sinh[c + d*x]^3),x]","\frac{a \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{a x}{2}+\frac{b \cosh ^5(c+d x)}{5 d}-\frac{2 b \cosh ^3(c+d x)}{3 d}+\frac{b \cosh (c+d x)}{d}","\frac{a \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{a x}{2}+\frac{b \cosh ^5(c+d x)}{5 d}-\frac{2 b \cosh ^3(c+d x)}{3 d}+\frac{b \cosh (c+d x)}{d}",1,"-(a*x)/2 + (b*Cosh[c + d*x])/d - (2*b*Cosh[c + d*x]^3)/(3*d) + (b*Cosh[c + d*x]^5)/(5*d) + (a*Cosh[c + d*x]*Sinh[c + d*x])/(2*d)","A",6,4,21,0.1905,1,"{3220, 2635, 8, 2633}"
144,1,60,0,0.0684057,"\int \sinh (c+d x) \left(a+b \sinh ^3(c+d x)\right) \, dx","Int[Sinh[c + d*x]*(a + b*Sinh[c + d*x]^3),x]","\frac{a \cosh (c+d x)}{d}+\frac{b \sinh ^3(c+d x) \cosh (c+d x)}{4 d}-\frac{3 b \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{3 b x}{8}","\frac{a \cosh (c+d x)}{d}+\frac{b \sinh ^3(c+d x) \cosh (c+d x)}{4 d}-\frac{3 b \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{3 b x}{8}",1,"(3*b*x)/8 + (a*Cosh[c + d*x])/d - (3*b*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (b*Cosh[c + d*x]*Sinh[c + d*x]^3)/(4*d)","A",6,4,19,0.2105,1,"{3220, 2638, 2635, 8}"
145,1,32,0,0.0211492,"\int \left(a+b \sinh ^3(c+d x)\right) \, dx","Int[a + b*Sinh[c + d*x]^3,x]","a x+\frac{b \cosh ^3(c+d x)}{3 d}-\frac{b \cosh (c+d x)}{d}","a x+\frac{b \cosh ^3(c+d x)}{3 d}-\frac{b \cosh (c+d x)}{d}",1,"a*x - (b*Cosh[c + d*x])/d + (b*Cosh[c + d*x]^3)/(3*d)","A",3,1,12,0.08333,1,"{2633}"
146,1,40,0,0.0559113,"\int \text{csch}(c+d x) \left(a+b \sinh ^3(c+d x)\right) \, dx","Int[Csch[c + d*x]*(a + b*Sinh[c + d*x]^3),x]","-\frac{a \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{b x}{2}","-\frac{a \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{b x}{2}",1,"-(b*x)/2 - (a*ArcTanh[Cosh[c + d*x]])/d + (b*Cosh[c + d*x]*Sinh[c + d*x])/(2*d)","A",5,4,19,0.2105,1,"{3220, 3770, 2635, 8}"
147,1,24,0,0.0500271,"\int \text{csch}^2(c+d x) \left(a+b \sinh ^3(c+d x)\right) \, dx","Int[Csch[c + d*x]^2*(a + b*Sinh[c + d*x]^3),x]","\frac{b \cosh (c+d x)}{d}-\frac{a \coth (c+d x)}{d}","\frac{b \cosh (c+d x)}{d}-\frac{a \coth (c+d x)}{d}",1,"(b*Cosh[c + d*x])/d - (a*Coth[c + d*x])/d","A",5,4,21,0.1905,1,"{3220, 3767, 8, 2638}"
148,1,39,0,0.0626266,"\int \text{csch}^3(c+d x) \left(a+b \sinh ^3(c+d x)\right) \, dx","Int[Csch[c + d*x]^3*(a + b*Sinh[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}+b x","\frac{a \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{a \coth (c+d x) \text{csch}(c+d x)}{2 d}+b x",1,"b*x + (a*ArcTanh[Cosh[c + d*x]])/(2*d) - (a*Coth[c + d*x]*Csch[c + d*x])/(2*d)","A",4,3,21,0.1429,1,"{3220, 3768, 3770}"
149,1,41,0,0.0571616,"\int \text{csch}^4(c+d x) \left(a+b \sinh ^3(c+d x)\right) \, dx","Int[Csch[c + d*x]^4*(a + b*Sinh[c + d*x]^3),x]","-\frac{a \coth ^3(c+d x)}{3 d}+\frac{a \coth (c+d x)}{d}-\frac{b \tanh ^{-1}(\cosh (c+d x))}{d}","-\frac{a \coth ^3(c+d x)}{3 d}+\frac{a \coth (c+d x)}{d}-\frac{b \tanh ^{-1}(\cosh (c+d x))}{d}",1,"-((b*ArcTanh[Cosh[c + d*x]])/d) + (a*Coth[c + d*x])/d - (a*Coth[c + d*x]^3)/(3*d)","A",5,3,21,0.1429,1,"{3220, 3770, 3767}"
150,1,192,0,0.1791611,"\int \sinh ^3(c+d x) \left(a+b \sinh ^3(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]^3*(a + b*Sinh[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{a b \sinh ^5(c+d x) \cosh (c+d x)}{3 d}-\frac{5 a b \sinh ^3(c+d x) \cosh (c+d x)}{12 d}+\frac{5 a b \sinh (c+d x) \cosh (c+d x)}{8 d}-\frac{5 a b x}{8}+\frac{b^2 \cosh ^9(c+d x)}{9 d}-\frac{4 b^2 \cosh ^7(c+d x)}{7 d}+\frac{6 b^2 \cosh ^5(c+d x)}{5 d}-\frac{4 b^2 \cosh ^3(c+d x)}{3 d}+\frac{b^2 \cosh (c+d x)}{d}","\frac{a^2 \cosh ^3(c+d x)}{3 d}-\frac{a^2 \cosh (c+d x)}{d}+\frac{a b \sinh ^5(c+d x) \cosh (c+d x)}{3 d}-\frac{5 a b \sinh ^3(c+d x) \cosh (c+d x)}{12 d}+\frac{5 a b \sinh (c+d x) \cosh (c+d x)}{8 d}-\frac{5 a b x}{8}+\frac{b^2 \cosh ^9(c+d x)}{9 d}-\frac{4 b^2 \cosh ^7(c+d x)}{7 d}+\frac{6 b^2 \cosh ^5(c+d x)}{5 d}-\frac{4 b^2 \cosh ^3(c+d x)}{3 d}+\frac{b^2 \cosh (c+d x)}{d}",1,"(-5*a*b*x)/8 - (a^2*Cosh[c + d*x])/d + (b^2*Cosh[c + d*x])/d + (a^2*Cosh[c + d*x]^3)/(3*d) - (4*b^2*Cosh[c + d*x]^3)/(3*d) + (6*b^2*Cosh[c + d*x]^5)/(5*d) - (4*b^2*Cosh[c + d*x]^7)/(7*d) + (b^2*Cosh[c + d*x]^9)/(9*d) + (5*a*b*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) - (5*a*b*Cosh[c + d*x]*Sinh[c + d*x]^3)/(12*d) + (a*b*Cosh[c + d*x]*Sinh[c + d*x]^5)/(3*d)","A",10,4,23,0.1739,1,"{3220, 2633, 2635, 8}"
151,1,180,0,0.154268,"\int \sinh ^2(c+d x) \left(a+b \sinh ^3(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]^2*(a + b*Sinh[c + d*x]^3)^2,x]","\frac{a^2 \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{a^2 x}{2}+\frac{2 a b \cosh ^5(c+d x)}{5 d}-\frac{4 a b \cosh ^3(c+d x)}{3 d}+\frac{2 a b \cosh (c+d x)}{d}+\frac{b^2 \sinh ^7(c+d x) \cosh (c+d x)}{8 d}-\frac{7 b^2 \sinh ^5(c+d x) \cosh (c+d x)}{48 d}+\frac{35 b^2 \sinh ^3(c+d x) \cosh (c+d x)}{192 d}-\frac{35 b^2 \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{35 b^2 x}{128}","\frac{a^2 \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{a^2 x}{2}+\frac{2 a b \cosh ^5(c+d x)}{5 d}-\frac{4 a b \cosh ^3(c+d x)}{3 d}+\frac{2 a b \cosh (c+d x)}{d}+\frac{b^2 \sinh ^7(c+d x) \cosh (c+d x)}{8 d}-\frac{7 b^2 \sinh ^5(c+d x) \cosh (c+d x)}{48 d}+\frac{35 b^2 \sinh ^3(c+d x) \cosh (c+d x)}{192 d}-\frac{35 b^2 \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{35 b^2 x}{128}",1,"-(a^2*x)/2 + (35*b^2*x)/128 + (2*a*b*Cosh[c + d*x])/d - (4*a*b*Cosh[c + d*x]^3)/(3*d) + (2*a*b*Cosh[c + d*x]^5)/(5*d) + (a^2*Cosh[c + d*x]*Sinh[c + d*x])/(2*d) - (35*b^2*Cosh[c + d*x]*Sinh[c + d*x])/(128*d) + (35*b^2*Cosh[c + d*x]*Sinh[c + d*x]^3)/(192*d) - (7*b^2*Cosh[c + d*x]*Sinh[c + d*x]^5)/(48*d) + (b^2*Cosh[c + d*x]*Sinh[c + d*x]^7)/(8*d)","A",11,4,23,0.1739,1,"{3220, 2635, 8, 2633}"
152,1,130,0,0.1189336,"\int \sinh (c+d x) \left(a+b \sinh ^3(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]*(a + b*Sinh[c + d*x]^3)^2,x]","\frac{a^2 \cosh (c+d x)}{d}+\frac{a b \sinh ^3(c+d x) \cosh (c+d x)}{2 d}-\frac{3 a b \sinh (c+d x) \cosh (c+d x)}{4 d}+\frac{3 a b x}{4}+\frac{b^2 \cosh ^7(c+d x)}{7 d}-\frac{3 b^2 \cosh ^5(c+d x)}{5 d}+\frac{b^2 \cosh ^3(c+d x)}{d}-\frac{b^2 \cosh (c+d x)}{d}","\frac{a^2 \cosh (c+d x)}{d}+\frac{a b \sinh ^3(c+d x) \cosh (c+d x)}{2 d}-\frac{3 a b \sinh (c+d x) \cosh (c+d x)}{4 d}+\frac{3 a b x}{4}+\frac{b^2 \cosh ^7(c+d x)}{7 d}-\frac{3 b^2 \cosh ^5(c+d x)}{5 d}+\frac{b^2 \cosh ^3(c+d x)}{d}-\frac{b^2 \cosh (c+d x)}{d}",1,"(3*a*b*x)/4 + (a^2*Cosh[c + d*x])/d - (b^2*Cosh[c + d*x])/d + (b^2*Cosh[c + d*x]^3)/d - (3*b^2*Cosh[c + d*x]^5)/(5*d) + (b^2*Cosh[c + d*x]^7)/(7*d) - (3*a*b*Cosh[c + d*x]*Sinh[c + d*x])/(4*d) + (a*b*Cosh[c + d*x]*Sinh[c + d*x]^3)/(2*d)","A",8,5,21,0.2381,1,"{3220, 2638, 2635, 8, 2633}"
153,1,114,0,0.0832559,"\int \left(a+b \sinh ^3(c+d x)\right)^2 \, dx","Int[(a + b*Sinh[c + d*x]^3)^2,x]","a^2 x+\frac{2 a b \cosh ^3(c+d x)}{3 d}-\frac{2 a b \cosh (c+d x)}{d}+\frac{b^2 \sinh ^5(c+d x) \cosh (c+d x)}{6 d}-\frac{5 b^2 \sinh ^3(c+d x) \cosh (c+d x)}{24 d}+\frac{5 b^2 \sinh (c+d x) \cosh (c+d x)}{16 d}-\frac{5 b^2 x}{16}","a^2 x+\frac{2 a b \cosh ^3(c+d x)}{3 d}-\frac{2 a b \cosh (c+d x)}{d}+\frac{b^2 \sinh ^5(c+d x) \cosh (c+d x)}{6 d}-\frac{5 b^2 \sinh ^3(c+d x) \cosh (c+d x)}{24 d}+\frac{5 b^2 \sinh (c+d x) \cosh (c+d x)}{16 d}-\frac{5 b^2 x}{16}",1,"a^2*x - (5*b^2*x)/16 - (2*a*b*Cosh[c + d*x])/d + (2*a*b*Cosh[c + d*x]^3)/(3*d) + (5*b^2*Cosh[c + d*x]*Sinh[c + d*x])/(16*d) - (5*b^2*Cosh[c + d*x]*Sinh[c + d*x]^3)/(24*d) + (b^2*Cosh[c + d*x]*Sinh[c + d*x]^5)/(6*d)","A",8,4,14,0.2857,1,"{3213, 2633, 2635, 8}"
154,1,88,0,0.1017467,"\int \text{csch}(c+d x) \left(a+b \sinh ^3(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]*(a + b*Sinh[c + d*x]^3)^2,x]","-\frac{a^2 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{a b \sinh (c+d x) \cosh (c+d x)}{d}-a b x+\frac{b^2 \cosh ^5(c+d x)}{5 d}-\frac{2 b^2 \cosh ^3(c+d x)}{3 d}+\frac{b^2 \cosh (c+d x)}{d}","-\frac{a^2 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{a b \sinh (c+d x) \cosh (c+d x)}{d}-a b x+\frac{b^2 \cosh ^5(c+d x)}{5 d}-\frac{2 b^2 \cosh ^3(c+d x)}{3 d}+\frac{b^2 \cosh (c+d x)}{d}",1,"-(a*b*x) - (a^2*ArcTanh[Cosh[c + d*x]])/d + (b^2*Cosh[c + d*x])/d - (2*b^2*Cosh[c + d*x]^3)/(3*d) + (b^2*Cosh[c + d*x]^5)/(5*d) + (a*b*Cosh[c + d*x]*Sinh[c + d*x])/d","A",7,5,21,0.2381,1,"{3220, 3770, 2635, 8, 2633}"
155,1,82,0,0.0979725,"\int \text{csch}^2(c+d x) \left(a+b \sinh ^3(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^2*(a + b*Sinh[c + d*x]^3)^2,x]","-\frac{a^2 \coth (c+d x)}{d}+\frac{2 a b \cosh (c+d x)}{d}+\frac{b^2 \sinh ^3(c+d x) \cosh (c+d x)}{4 d}-\frac{3 b^2 \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{3 b^2 x}{8}","-\frac{a^2 \coth (c+d x)}{d}+\frac{2 a b \cosh (c+d x)}{d}+\frac{b^2 \sinh ^3(c+d x) \cosh (c+d x)}{4 d}-\frac{3 b^2 \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{3 b^2 x}{8}",1,"(3*b^2*x)/8 + (2*a*b*Cosh[c + d*x])/d - (a^2*Coth[c + d*x])/d - (3*b^2*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (b^2*Cosh[c + d*x]*Sinh[c + d*x]^3)/(4*d)","A",8,5,23,0.2174,1,"{3220, 3767, 8, 2638, 2635}"
156,1,77,0,0.1053343,"\int \text{csch}^3(c+d x) \left(a+b \sinh ^3(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^3*(a + b*Sinh[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}+2 a b x+\frac{b^2 \cosh ^3(c+d x)}{3 d}-\frac{b^2 \cosh (c+d x)}{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}+2 a b x+\frac{b^2 \cosh ^3(c+d x)}{3 d}-\frac{b^2 \cosh (c+d x)}{d}",1,"2*a*b*x + (a^2*ArcTanh[Cosh[c + d*x]])/(2*d) - (b^2*Cosh[c + d*x])/d + (b^2*Cosh[c + d*x]^3)/(3*d) - (a^2*Coth[c + d*x]*Csch[c + d*x])/(2*d)","A",6,4,23,0.1739,1,"{3220, 3768, 3770, 2633}"
157,1,76,0,0.0910175,"\int \text{csch}^4(c+d x) \left(a+b \sinh ^3(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^4*(a + b*Sinh[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{2 a b \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b^2 \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{b^2 x}{2}","-\frac{a^2 \coth ^3(c+d x)}{3 d}+\frac{a^2 \coth (c+d x)}{d}-\frac{2 a b \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b^2 \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{b^2 x}{2}",1,"-(b^2*x)/2 - (2*a*b*ArcTanh[Cosh[c + d*x]])/d + (a^2*Coth[c + d*x])/d - (a^2*Coth[c + d*x]^3)/(3*d) + (b^2*Cosh[c + d*x]*Sinh[c + d*x])/(2*d)","A",7,5,23,0.2174,1,"{3220, 3770, 3767, 2635, 8}"
158,1,90,0,0.1324294,"\int \text{csch}^5(c+d x) \left(a+b \sinh ^3(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^5*(a + b*Sinh[c + d*x]^3)^2,x]","-\frac{3 a^2 \tanh ^{-1}(\cosh (c+d x))}{8 d}-\frac{a^2 \coth (c+d x) \text{csch}^3(c+d x)}{4 d}+\frac{3 a^2 \coth (c+d x) \text{csch}(c+d x)}{8 d}-\frac{2 a b \coth (c+d x)}{d}+\frac{b^2 \cosh (c+d x)}{d}","-\frac{3 a^2 \tanh ^{-1}(\cosh (c+d x))}{8 d}-\frac{a^2 \coth (c+d x) \text{csch}^3(c+d x)}{4 d}+\frac{3 a^2 \coth (c+d x) \text{csch}(c+d x)}{8 d}-\frac{2 a b \coth (c+d x)}{d}+\frac{b^2 \cosh (c+d x)}{d}",1,"(-3*a^2*ArcTanh[Cosh[c + d*x]])/(8*d) + (b^2*Cosh[c + d*x])/d - (2*a*b*Coth[c + d*x])/d + (3*a^2*Coth[c + d*x]*Csch[c + d*x])/(8*d) - (a^2*Coth[c + d*x]*Csch[c + d*x]^3)/(4*d)","A",8,6,23,0.2609,1,"{3220, 3767, 8, 3768, 3770, 2638}"
159,1,88,0,0.1025431,"\int \text{csch}^6(c+d x) \left(a+b \sinh ^3(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^6*(a + b*Sinh[c + d*x]^3)^2,x]","-\frac{a^2 \coth ^5(c+d x)}{5 d}+\frac{2 a^2 \coth ^3(c+d x)}{3 d}-\frac{a^2 \coth (c+d x)}{d}+\frac{a b \tanh ^{-1}(\cosh (c+d x))}{d}-\frac{a b \coth (c+d x) \text{csch}(c+d x)}{d}+b^2 x","-\frac{a^2 \coth ^5(c+d x)}{5 d}+\frac{2 a^2 \coth ^3(c+d x)}{3 d}-\frac{a^2 \coth (c+d x)}{d}+\frac{a b \tanh ^{-1}(\cosh (c+d x))}{d}-\frac{a b \coth (c+d x) \text{csch}(c+d x)}{d}+b^2 x",1,"b^2*x + (a*b*ArcTanh[Cosh[c + d*x]])/d - (a^2*Coth[c + d*x])/d + (2*a^2*Coth[c + d*x]^3)/(3*d) - (a^2*Coth[c + d*x]^5)/(5*d) - (a*b*Coth[c + d*x]*Csch[c + d*x])/d","A",6,4,23,0.1739,1,"{3220, 3768, 3770, 3767}"
160,1,133,0,0.1749642,"\int \text{csch}^7(c+d x) \left(a+b \sinh ^3(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^7*(a + b*Sinh[c + d*x]^3)^2,x]","\frac{5 a^2 \tanh ^{-1}(\cosh (c+d x))}{16 d}-\frac{a^2 \coth (c+d x) \text{csch}^5(c+d x)}{6 d}+\frac{5 a^2 \coth (c+d x) \text{csch}^3(c+d x)}{24 d}-\frac{5 a^2 \coth (c+d x) \text{csch}(c+d x)}{16 d}-\frac{2 a b \coth ^3(c+d x)}{3 d}+\frac{2 a b \coth (c+d x)}{d}-\frac{b^2 \tanh ^{-1}(\cosh (c+d x))}{d}","\frac{5 a^2 \tanh ^{-1}(\cosh (c+d x))}{16 d}-\frac{a^2 \coth (c+d x) \text{csch}^5(c+d x)}{6 d}+\frac{5 a^2 \coth (c+d x) \text{csch}^3(c+d x)}{24 d}-\frac{5 a^2 \coth (c+d x) \text{csch}(c+d x)}{16 d}-\frac{2 a b \coth ^3(c+d x)}{3 d}+\frac{2 a b \coth (c+d x)}{d}-\frac{b^2 \tanh ^{-1}(\cosh (c+d x))}{d}",1,"(5*a^2*ArcTanh[Cosh[c + d*x]])/(16*d) - (b^2*ArcTanh[Cosh[c + d*x]])/d + (2*a*b*Coth[c + d*x])/d - (2*a*b*Coth[c + d*x]^3)/(3*d) - (5*a^2*Coth[c + d*x]*Csch[c + d*x])/(16*d) + (5*a^2*Coth[c + d*x]*Csch[c + d*x]^3)/(24*d) - (a^2*Coth[c + d*x]*Csch[c + d*x]^5)/(6*d)","A",9,4,23,0.1739,1,"{3220, 3770, 3767, 3768}"
161,1,291,0,0.2086464,"\int \sinh ^2(c+d x) \left(a+b \sinh ^3(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]^2*(a + b*Sinh[c + d*x]^3)^3,x]","\frac{3 a^2 b \cosh ^5(c+d x)}{5 d}-\frac{2 a^2 b \cosh ^3(c+d x)}{d}+\frac{3 a^2 b \cosh (c+d x)}{d}+\frac{a^3 \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{a^3 x}{2}+\frac{3 a b^2 \sinh ^7(c+d x) \cosh (c+d x)}{8 d}-\frac{7 a b^2 \sinh ^5(c+d x) \cosh (c+d x)}{16 d}+\frac{35 a b^2 \sinh ^3(c+d x) \cosh (c+d x)}{64 d}-\frac{105 a b^2 \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{105}{128} a b^2 x+\frac{b^3 \cosh ^{11}(c+d x)}{11 d}-\frac{5 b^3 \cosh ^9(c+d x)}{9 d}+\frac{10 b^3 \cosh ^7(c+d x)}{7 d}-\frac{2 b^3 \cosh ^5(c+d x)}{d}+\frac{5 b^3 \cosh ^3(c+d x)}{3 d}-\frac{b^3 \cosh (c+d x)}{d}","\frac{3 a^2 b \cosh ^5(c+d x)}{5 d}-\frac{2 a^2 b \cosh ^3(c+d x)}{d}+\frac{3 a^2 b \cosh (c+d x)}{d}+\frac{a^3 \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{a^3 x}{2}+\frac{3 a b^2 \sinh ^7(c+d x) \cosh (c+d x)}{8 d}-\frac{7 a b^2 \sinh ^5(c+d x) \cosh (c+d x)}{16 d}+\frac{35 a b^2 \sinh ^3(c+d x) \cosh (c+d x)}{64 d}-\frac{105 a b^2 \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{105}{128} a b^2 x+\frac{b^3 \cosh ^{11}(c+d x)}{11 d}-\frac{5 b^3 \cosh ^9(c+d x)}{9 d}+\frac{10 b^3 \cosh ^7(c+d x)}{7 d}-\frac{2 b^3 \cosh ^5(c+d x)}{d}+\frac{5 b^3 \cosh ^3(c+d x)}{3 d}-\frac{b^3 \cosh (c+d x)}{d}",1,"-(a^3*x)/2 + (105*a*b^2*x)/128 + (3*a^2*b*Cosh[c + d*x])/d - (b^3*Cosh[c + d*x])/d - (2*a^2*b*Cosh[c + d*x]^3)/d + (5*b^3*Cosh[c + d*x]^3)/(3*d) + (3*a^2*b*Cosh[c + d*x]^5)/(5*d) - (2*b^3*Cosh[c + d*x]^5)/d + (10*b^3*Cosh[c + d*x]^7)/(7*d) - (5*b^3*Cosh[c + d*x]^9)/(9*d) + (b^3*Cosh[c + d*x]^11)/(11*d) + (a^3*Cosh[c + d*x]*Sinh[c + d*x])/(2*d) - (105*a*b^2*Cosh[c + d*x]*Sinh[c + d*x])/(128*d) + (35*a*b^2*Cosh[c + d*x]*Sinh[c + d*x]^3)/(64*d) - (7*a*b^2*Cosh[c + d*x]*Sinh[c + d*x]^5)/(16*d) + (3*a*b^2*Cosh[c + d*x]*Sinh[c + d*x]^7)/(8*d)","A",13,4,23,0.1739,1,"{3220, 2635, 8, 2633}"
162,1,267,0,0.2220528,"\int \sinh (c+d x) \left(a+b \sinh ^3(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]*(a + b*Sinh[c + d*x]^3)^3,x]","\frac{3 a^2 b \sinh ^3(c+d x) \cosh (c+d x)}{4 d}-\frac{9 a^2 b \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{9}{8} a^2 b x+\frac{a^3 \cosh (c+d x)}{d}+\frac{3 a b^2 \cosh ^7(c+d x)}{7 d}-\frac{9 a b^2 \cosh ^5(c+d x)}{5 d}+\frac{3 a b^2 \cosh ^3(c+d x)}{d}-\frac{3 a b^2 \cosh (c+d x)}{d}+\frac{b^3 \sinh ^9(c+d x) \cosh (c+d x)}{10 d}-\frac{9 b^3 \sinh ^7(c+d x) \cosh (c+d x)}{80 d}+\frac{21 b^3 \sinh ^5(c+d x) \cosh (c+d x)}{160 d}-\frac{21 b^3 \sinh ^3(c+d x) \cosh (c+d x)}{128 d}+\frac{63 b^3 \sinh (c+d x) \cosh (c+d x)}{256 d}-\frac{63 b^3 x}{256}","\frac{3 a^2 b \sinh ^3(c+d x) \cosh (c+d x)}{4 d}-\frac{9 a^2 b \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{9}{8} a^2 b x+\frac{a^3 \cosh (c+d x)}{d}+\frac{3 a b^2 \cosh ^7(c+d x)}{7 d}-\frac{9 a b^2 \cosh ^5(c+d x)}{5 d}+\frac{3 a b^2 \cosh ^3(c+d x)}{d}-\frac{3 a b^2 \cosh (c+d x)}{d}+\frac{b^3 \sinh ^9(c+d x) \cosh (c+d x)}{10 d}-\frac{9 b^3 \sinh ^7(c+d x) \cosh (c+d x)}{80 d}+\frac{21 b^3 \sinh ^5(c+d x) \cosh (c+d x)}{160 d}-\frac{21 b^3 \sinh ^3(c+d x) \cosh (c+d x)}{128 d}+\frac{63 b^3 \sinh (c+d x) \cosh (c+d x)}{256 d}-\frac{63 b^3 x}{256}",1,"(9*a^2*b*x)/8 - (63*b^3*x)/256 + (a^3*Cosh[c + d*x])/d - (3*a*b^2*Cosh[c + d*x])/d + (3*a*b^2*Cosh[c + d*x]^3)/d - (9*a*b^2*Cosh[c + d*x]^5)/(5*d) + (3*a*b^2*Cosh[c + d*x]^7)/(7*d) - (9*a^2*b*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (63*b^3*Cosh[c + d*x]*Sinh[c + d*x])/(256*d) + (3*a^2*b*Cosh[c + d*x]*Sinh[c + d*x]^3)/(4*d) - (21*b^3*Cosh[c + d*x]*Sinh[c + d*x]^3)/(128*d) + (21*b^3*Cosh[c + d*x]*Sinh[c + d*x]^5)/(160*d) - (9*b^3*Cosh[c + d*x]*Sinh[c + d*x]^7)/(80*d) + (b^3*Cosh[c + d*x]*Sinh[c + d*x]^9)/(10*d)","A",14,5,21,0.2381,1,"{3220, 2638, 2635, 8, 2633}"
163,1,204,0,0.1277541,"\int \left(a+b \sinh ^3(c+d x)\right)^3 \, dx","Int[(a + b*Sinh[c + d*x]^3)^3,x]","\frac{a^2 b \cosh ^3(c+d x)}{d}-\frac{3 a^2 b \cosh (c+d x)}{d}+a^3 x+\frac{a b^2 \sinh ^5(c+d x) \cosh (c+d x)}{2 d}-\frac{5 a b^2 \sinh ^3(c+d x) \cosh (c+d x)}{8 d}+\frac{15 a b^2 \sinh (c+d x) \cosh (c+d x)}{16 d}-\frac{15}{16} a b^2 x+\frac{b^3 \cosh ^9(c+d x)}{9 d}-\frac{4 b^3 \cosh ^7(c+d x)}{7 d}+\frac{6 b^3 \cosh ^5(c+d x)}{5 d}-\frac{4 b^3 \cosh ^3(c+d x)}{3 d}+\frac{b^3 \cosh (c+d x)}{d}","\frac{a^2 b \cosh ^3(c+d x)}{d}-\frac{3 a^2 b \cosh (c+d x)}{d}+a^3 x+\frac{a b^2 \sinh ^5(c+d x) \cosh (c+d x)}{2 d}-\frac{5 a b^2 \sinh ^3(c+d x) \cosh (c+d x)}{8 d}+\frac{15 a b^2 \sinh (c+d x) \cosh (c+d x)}{16 d}-\frac{15}{16} a b^2 x+\frac{b^3 \cosh ^9(c+d x)}{9 d}-\frac{4 b^3 \cosh ^7(c+d x)}{7 d}+\frac{6 b^3 \cosh ^5(c+d x)}{5 d}-\frac{4 b^3 \cosh ^3(c+d x)}{3 d}+\frac{b^3 \cosh (c+d x)}{d}",1,"a^3*x - (15*a*b^2*x)/16 - (3*a^2*b*Cosh[c + d*x])/d + (b^3*Cosh[c + d*x])/d + (a^2*b*Cosh[c + d*x]^3)/d - (4*b^3*Cosh[c + d*x]^3)/(3*d) + (6*b^3*Cosh[c + d*x]^5)/(5*d) - (4*b^3*Cosh[c + d*x]^7)/(7*d) + (b^3*Cosh[c + d*x]^9)/(9*d) + (15*a*b^2*Cosh[c + d*x]*Sinh[c + d*x])/(16*d) - (5*a*b^2*Cosh[c + d*x]*Sinh[c + d*x]^3)/(8*d) + (a*b^2*Cosh[c + d*x]*Sinh[c + d*x]^5)/(2*d)","A",10,4,14,0.2857,1,"{3213, 2633, 2635, 8}"
164,1,201,0,0.1887182,"\int \text{csch}(c+d x) \left(a+b \sinh ^3(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]*(a + b*Sinh[c + d*x]^3)^3,x]","\frac{3 a^2 b \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{3}{2} a^2 b x-\frac{a^3 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{3 a b^2 \cosh ^5(c+d x)}{5 d}-\frac{2 a b^2 \cosh ^3(c+d x)}{d}+\frac{3 a b^2 \cosh (c+d x)}{d}+\frac{b^3 \sinh ^7(c+d x) \cosh (c+d x)}{8 d}-\frac{7 b^3 \sinh ^5(c+d x) \cosh (c+d x)}{48 d}+\frac{35 b^3 \sinh ^3(c+d x) \cosh (c+d x)}{192 d}-\frac{35 b^3 \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{35 b^3 x}{128}","\frac{3 a^2 b \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{3}{2} a^2 b x-\frac{a^3 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{3 a b^2 \cosh ^5(c+d x)}{5 d}-\frac{2 a b^2 \cosh ^3(c+d x)}{d}+\frac{3 a b^2 \cosh (c+d x)}{d}+\frac{b^3 \sinh ^7(c+d x) \cosh (c+d x)}{8 d}-\frac{7 b^3 \sinh ^5(c+d x) \cosh (c+d x)}{48 d}+\frac{35 b^3 \sinh ^3(c+d x) \cosh (c+d x)}{192 d}-\frac{35 b^3 \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{35 b^3 x}{128}",1,"(-3*a^2*b*x)/2 + (35*b^3*x)/128 - (a^3*ArcTanh[Cosh[c + d*x]])/d + (3*a*b^2*Cosh[c + d*x])/d - (2*a*b^2*Cosh[c + d*x]^3)/d + (3*a*b^2*Cosh[c + d*x]^5)/(5*d) + (3*a^2*b*Cosh[c + d*x]*Sinh[c + d*x])/(2*d) - (35*b^3*Cosh[c + d*x]*Sinh[c + d*x])/(128*d) + (35*b^3*Cosh[c + d*x]*Sinh[c + d*x]^3)/(192*d) - (7*b^3*Cosh[c + d*x]*Sinh[c + d*x]^5)/(48*d) + (b^3*Cosh[c + d*x]*Sinh[c + d*x]^7)/(8*d)","A",12,5,21,0.2381,1,"{3220, 3770, 2635, 8, 2633}"
165,1,152,0,0.1383349,"\int \text{csch}^2(c+d x) \left(a+b \sinh ^3(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^2*(a + b*Sinh[c + d*x]^3)^3,x]","\frac{3 a^2 b \cosh (c+d x)}{d}-\frac{a^3 \coth (c+d x)}{d}+\frac{3 a b^2 \sinh ^3(c+d x) \cosh (c+d x)}{4 d}-\frac{9 a b^2 \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{9}{8} a b^2 x+\frac{b^3 \cosh ^7(c+d x)}{7 d}-\frac{3 b^3 \cosh ^5(c+d x)}{5 d}+\frac{b^3 \cosh ^3(c+d x)}{d}-\frac{b^3 \cosh (c+d x)}{d}","\frac{3 a^2 b \cosh (c+d x)}{d}-\frac{a^3 \coth (c+d x)}{d}+\frac{3 a b^2 \sinh ^3(c+d x) \cosh (c+d x)}{4 d}-\frac{9 a b^2 \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{9}{8} a b^2 x+\frac{b^3 \cosh ^7(c+d x)}{7 d}-\frac{3 b^3 \cosh ^5(c+d x)}{5 d}+\frac{b^3 \cosh ^3(c+d x)}{d}-\frac{b^3 \cosh (c+d x)}{d}",1,"(9*a*b^2*x)/8 + (3*a^2*b*Cosh[c + d*x])/d - (b^3*Cosh[c + d*x])/d + (b^3*Cosh[c + d*x]^3)/d - (3*b^3*Cosh[c + d*x]^5)/(5*d) + (b^3*Cosh[c + d*x]^7)/(7*d) - (a^3*Coth[c + d*x])/d - (9*a*b^2*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (3*a*b^2*Cosh[c + d*x]*Sinh[c + d*x]^3)/(4*d)","A",10,6,23,0.2609,1,"{3220, 3767, 8, 2638, 2635, 2633}"
166,1,156,0,0.1686014,"\int \text{csch}^3(c+d x) \left(a+b \sinh ^3(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^3*(a + b*Sinh[c + d*x]^3)^3,x]","3 a^2 b x+\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{a b^2 \cosh ^3(c+d x)}{d}-\frac{3 a b^2 \cosh (c+d x)}{d}+\frac{b^3 \sinh ^5(c+d x) \cosh (c+d x)}{6 d}-\frac{5 b^3 \sinh ^3(c+d x) \cosh (c+d x)}{24 d}+\frac{5 b^3 \sinh (c+d x) \cosh (c+d x)}{16 d}-\frac{5 b^3 x}{16}","3 a^2 b x+\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{a b^2 \cosh ^3(c+d x)}{d}-\frac{3 a b^2 \cosh (c+d x)}{d}+\frac{b^3 \sinh ^5(c+d x) \cosh (c+d x)}{6 d}-\frac{5 b^3 \sinh ^3(c+d x) \cosh (c+d x)}{24 d}+\frac{5 b^3 \sinh (c+d x) \cosh (c+d x)}{16 d}-\frac{5 b^3 x}{16}",1,"3*a^2*b*x - (5*b^3*x)/16 + (a^3*ArcTanh[Cosh[c + d*x]])/(2*d) - (3*a*b^2*Cosh[c + d*x])/d + (a*b^2*Cosh[c + d*x]^3)/d - (a^3*Coth[c + d*x]*Csch[c + d*x])/(2*d) + (5*b^3*Cosh[c + d*x]*Sinh[c + d*x])/(16*d) - (5*b^3*Cosh[c + d*x]*Sinh[c + d*x]^3)/(24*d) + (b^3*Cosh[c + d*x]*Sinh[c + d*x]^5)/(6*d)","A",10,6,23,0.2609,1,"{3220, 3768, 3770, 2633, 2635, 8}"
167,1,129,0,0.1204717,"\int \text{csch}^4(c+d x) \left(a+b \sinh ^3(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^4*(a + b*Sinh[c + d*x]^3)^3,x]","-\frac{3 a^2 b \tanh ^{-1}(\cosh (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 \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{3}{2} a b^2 x+\frac{b^3 \cosh ^5(c+d x)}{5 d}-\frac{2 b^3 \cosh ^3(c+d x)}{3 d}+\frac{b^3 \cosh (c+d x)}{d}","-\frac{3 a^2 b \tanh ^{-1}(\cosh (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 \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{3}{2} a b^2 x+\frac{b^3 \cosh ^5(c+d x)}{5 d}-\frac{2 b^3 \cosh ^3(c+d x)}{3 d}+\frac{b^3 \cosh (c+d x)}{d}",1,"(-3*a*b^2*x)/2 - (3*a^2*b*ArcTanh[Cosh[c + d*x]])/d + (b^3*Cosh[c + d*x])/d - (2*b^3*Cosh[c + d*x]^3)/(3*d) + (b^3*Cosh[c + d*x]^5)/(5*d) + (a^3*Coth[c + d*x])/d - (a^3*Coth[c + d*x]^3)/(3*d) + (3*a*b^2*Cosh[c + d*x]*Sinh[c + d*x])/(2*d)","A",9,6,23,0.2609,1,"{3220, 3770, 3767, 2635, 8, 2633}"
168,1,148,0,0.1726919,"\int \text{csch}^5(c+d x) \left(a+b \sinh ^3(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^5*(a + b*Sinh[c + d*x]^3)^3,x]","-\frac{3 a^2 b \coth (c+d x)}{d}-\frac{3 a^3 \tanh ^{-1}(\cosh (c+d x))}{8 d}-\frac{a^3 \coth (c+d x) \text{csch}^3(c+d x)}{4 d}+\frac{3 a^3 \coth (c+d x) \text{csch}(c+d x)}{8 d}+\frac{3 a b^2 \cosh (c+d x)}{d}+\frac{b^3 \sinh ^3(c+d x) \cosh (c+d x)}{4 d}-\frac{3 b^3 \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{3 b^3 x}{8}","-\frac{3 a^2 b \coth (c+d x)}{d}-\frac{3 a^3 \tanh ^{-1}(\cosh (c+d x))}{8 d}-\frac{a^3 \coth (c+d x) \text{csch}^3(c+d x)}{4 d}+\frac{3 a^3 \coth (c+d x) \text{csch}(c+d x)}{8 d}+\frac{3 a b^2 \cosh (c+d x)}{d}+\frac{b^3 \sinh ^3(c+d x) \cosh (c+d x)}{4 d}-\frac{3 b^3 \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{3 b^3 x}{8}",1,"(3*b^3*x)/8 - (3*a^3*ArcTanh[Cosh[c + d*x]])/(8*d) + (3*a*b^2*Cosh[c + d*x])/d - (3*a^2*b*Coth[c + d*x])/d + (3*a^3*Coth[c + d*x]*Csch[c + d*x])/(8*d) - (a^3*Coth[c + d*x]*Csch[c + d*x]^3)/(4*d) - (3*b^3*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (b^3*Cosh[c + d*x]*Sinh[c + d*x]^3)/(4*d)","A",11,7,23,0.3043,1,"{3220, 3767, 8, 3768, 3770, 2638, 2635}"
169,1,131,0,0.1249646,"\int \text{csch}^6(c+d x) \left(a+b \sinh ^3(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^6*(a + b*Sinh[c + d*x]^3)^3,x]","\frac{3 a^2 b \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{3 a^2 b \coth (c+d x) \text{csch}(c+d x)}{2 d}-\frac{a^3 \coth ^5(c+d x)}{5 d}+\frac{2 a^3 \coth ^3(c+d x)}{3 d}-\frac{a^3 \coth (c+d x)}{d}+3 a b^2 x+\frac{b^3 \cosh ^3(c+d x)}{3 d}-\frac{b^3 \cosh (c+d x)}{d}","\frac{3 a^2 b \tanh ^{-1}(\cosh (c+d x))}{2 d}-\frac{3 a^2 b \coth (c+d x) \text{csch}(c+d x)}{2 d}-\frac{a^3 \coth ^5(c+d x)}{5 d}+\frac{2 a^3 \coth ^3(c+d x)}{3 d}-\frac{a^3 \coth (c+d x)}{d}+3 a b^2 x+\frac{b^3 \cosh ^3(c+d x)}{3 d}-\frac{b^3 \cosh (c+d x)}{d}",1,"3*a*b^2*x + (3*a^2*b*ArcTanh[Cosh[c + d*x]])/(2*d) - (b^3*Cosh[c + d*x])/d + (b^3*Cosh[c + d*x]^3)/(3*d) - (a^3*Coth[c + d*x])/d + (2*a^3*Coth[c + d*x]^3)/(3*d) - (a^3*Coth[c + d*x]^5)/(5*d) - (3*a^2*b*Coth[c + d*x]*Csch[c + d*x])/(2*d)","A",8,5,23,0.2174,1,"{3220, 3768, 3770, 3767, 2633}"
170,1,166,0,0.1971019,"\int \text{csch}^7(c+d x) \left(a+b \sinh ^3(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^7*(a + b*Sinh[c + d*x]^3)^3,x]","-\frac{a^2 b \coth ^3(c+d x)}{d}+\frac{3 a^2 b \coth (c+d x)}{d}+\frac{5 a^3 \tanh ^{-1}(\cosh (c+d x))}{16 d}-\frac{a^3 \coth (c+d x) \text{csch}^5(c+d x)}{6 d}+\frac{5 a^3 \coth (c+d x) \text{csch}^3(c+d x)}{24 d}-\frac{5 a^3 \coth (c+d x) \text{csch}(c+d x)}{16 d}-\frac{3 a b^2 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b^3 \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{b^3 x}{2}","-\frac{a^2 b \coth ^3(c+d x)}{d}+\frac{3 a^2 b \coth (c+d x)}{d}+\frac{5 a^3 \tanh ^{-1}(\cosh (c+d x))}{16 d}-\frac{a^3 \coth (c+d x) \text{csch}^5(c+d x)}{6 d}+\frac{5 a^3 \coth (c+d x) \text{csch}^3(c+d x)}{24 d}-\frac{5 a^3 \coth (c+d x) \text{csch}(c+d x)}{16 d}-\frac{3 a b^2 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b^3 \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{b^3 x}{2}",1,"-(b^3*x)/2 + (5*a^3*ArcTanh[Cosh[c + d*x]])/(16*d) - (3*a*b^2*ArcTanh[Cosh[c + d*x]])/d + (3*a^2*b*Coth[c + d*x])/d - (a^2*b*Coth[c + d*x]^3)/d - (5*a^3*Coth[c + d*x]*Csch[c + d*x])/(16*d) + (5*a^3*Coth[c + d*x]*Csch[c + d*x]^3)/(24*d) - (a^3*Coth[c + d*x]*Csch[c + d*x]^5)/(6*d) + (b^3*Cosh[c + d*x]*Sinh[c + d*x])/(2*d)","A",11,6,23,0.2609,1,"{3220, 3770, 3767, 3768, 2635, 8}"
171,1,328,0,0.7385271,"\int \frac{\sinh ^6(c+d x)}{a+b \sinh ^3(c+d x)} \, dx","Int[Sinh[c + d*x]^6/(a + b*Sinh[c + d*x]^3),x]","-\frac{2 a^{4/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 b^2 d \sqrt{a^{2/3}+b^{2/3}}}-\frac{2 (-1)^{2/3} a^{4/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}\right)}{3 b^2 d \sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}-\frac{2 (-1)^{2/3} a^{4/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 b^2 d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}-\frac{a x}{b^2}+\frac{\cosh ^3(c+d x)}{3 b d}-\frac{\cosh (c+d x)}{b d}","-\frac{2 a^{4/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 b^2 d \sqrt{a^{2/3}+b^{2/3}}}-\frac{2 (-1)^{2/3} a^{4/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}\right)}{3 b^2 d \sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}-\frac{2 (-1)^{2/3} a^{4/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 b^2 d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}-\frac{a x}{b^2}+\frac{\cosh ^3(c+d x)}{3 b d}-\frac{\cosh (c+d x)}{b d}",1,"-((a*x)/b^2) - (2*(-1)^(2/3)*a^(4/3)*ArcTan[((-1)^(1/6)*((-1)^(1/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - (-1)^(2/3)*b^(2/3)]])/(3*Sqrt[(-1)^(1/3)*a^(2/3) - (-1)^(2/3)*b^(2/3)]*b^2*d) - (2*(-1)^(2/3)*a^(4/3)*ArcTan[((-1)^(1/6)*((-1)^(5/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]])/(3*Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]*b^2*d) - (2*a^(4/3)*ArcTanh[(b^(1/3) - a^(1/3)*Tanh[(c + d*x)/2])/Sqrt[a^(2/3) + b^(2/3)]])/(3*Sqrt[a^(2/3) + b^(2/3)]*b^2*d) - Cosh[c + d*x]/(b*d) + Cosh[c + d*x]^3/(3*b*d)","A",15,6,23,0.2609,1,"{3220, 2633, 3213, 2660, 618, 204}"
172,1,295,0,0.5586011,"\int \frac{\sinh ^5(c+d x)}{a+b \sinh ^3(c+d x)} \, dx","Int[Sinh[c + d*x]^5/(a + b*Sinh[c + d*x]^3),x]","\frac{2 a \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 b^{5/3} d \sqrt{a^{2/3}+b^{2/3}}}+\frac{2 a \tan ^{-1}\left(\frac{(-1)^{5/6} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{-(-1)^{2/3} a^{2/3}-b^{2/3}}}\right)}{3 b^{5/3} d \sqrt{-(-1)^{2/3} a^{2/3}-b^{2/3}}}+\frac{2 a \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 b^{5/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 b d}-\frac{x}{2 b}","\frac{2 a \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 b^{5/3} d \sqrt{a^{2/3}+b^{2/3}}}+\frac{2 a \tan ^{-1}\left(\frac{(-1)^{5/6} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{-(-1)^{2/3} a^{2/3}-b^{2/3}}}\right)}{3 b^{5/3} d \sqrt{-(-1)^{2/3} a^{2/3}-b^{2/3}}}+\frac{2 a \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 b^{5/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 b d}-\frac{x}{2 b}",1,"-x/(2*b) + (2*a*ArcTan[((-1)^(5/6)*((-1)^(1/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[-((-1)^(2/3)*a^(2/3)) - b^(2/3)]])/(3*Sqrt[-((-1)^(2/3)*a^(2/3)) - b^(2/3)]*b^(5/3)*d) + (2*a*ArcTan[((-1)^(1/6)*((-1)^(5/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]])/(3*Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]*b^(5/3)*d) + (2*a*ArcTanh[(b^(1/3) - a^(1/3)*Tanh[(c + d*x)/2])/Sqrt[a^(2/3) + b^(2/3)]])/(3*Sqrt[a^(2/3) + b^(2/3)]*b^(5/3)*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*b*d)","A",15,7,23,0.3043,1,"{3220, 2635, 8, 2660, 618, 206, 204}"
173,1,303,0,0.5449642,"\int \frac{\sinh ^4(c+d x)}{a+b \sinh ^3(c+d x)} \, dx","Int[Sinh[c + d*x]^4/(a + b*Sinh[c + d*x]^3),x]","-\frac{2 a^{2/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 b^{4/3} d \sqrt{a^{2/3}+b^{2/3}}}-\frac{2 a^{2/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}\right)}{3 b^{4/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}+\frac{2 \sqrt[3]{-1} a^{2/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 b^{4/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}+\frac{\cosh (c+d x)}{b d}","-\frac{2 a^{2/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 b^{4/3} d \sqrt{a^{2/3}+b^{2/3}}}-\frac{2 a^{2/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}\right)}{3 b^{4/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}+\frac{2 \sqrt[3]{-1} a^{2/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 b^{4/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}+\frac{\cosh (c+d x)}{b d}",1,"(-2*a^(2/3)*ArcTan[((-1)^(1/6)*((-1)^(1/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - (-1)^(2/3)*b^(2/3)]])/(3*Sqrt[(-1)^(1/3)*a^(2/3) - (-1)^(2/3)*b^(2/3)]*b^(4/3)*d) + (2*(-1)^(1/3)*a^(2/3)*ArcTan[((-1)^(1/6)*((-1)^(5/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]])/(3*Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]*b^(4/3)*d) - (2*a^(2/3)*ArcTanh[(b^(1/3) - a^(1/3)*Tanh[(c + d*x)/2])/Sqrt[a^(2/3) + b^(2/3)]])/(3*Sqrt[a^(2/3) + b^(2/3)]*b^(4/3)*d) + Cosh[c + d*x]/(b*d)","A",14,5,23,0.2174,1,"{3220, 2638, 2660, 618, 204}"
174,1,294,0,0.4398972,"\int \frac{\sinh ^3(c+d x)}{a+b \sinh ^3(c+d x)} \, dx","Int[Sinh[c + d*x]^3/(a + b*Sinh[c + d*x]^3),x]","\frac{2 \sqrt[3]{a} \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 b d \sqrt{a^{2/3}+b^{2/3}}}+\frac{2 (-1)^{2/3} \sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}\right)}{3 b d \sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}+\frac{2 (-1)^{2/3} \sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 b d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}+\frac{x}{b}","\frac{2 \sqrt[3]{a} \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 b d \sqrt{a^{2/3}+b^{2/3}}}+\frac{2 (-1)^{2/3} \sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}\right)}{3 b d \sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}+\frac{2 (-1)^{2/3} \sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 b d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}+\frac{x}{b}",1,"x/b + (2*(-1)^(2/3)*a^(1/3)*ArcTan[((-1)^(1/6)*((-1)^(1/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - (-1)^(2/3)*b^(2/3)]])/(3*Sqrt[(-1)^(1/3)*a^(2/3) - (-1)^(2/3)*b^(2/3)]*b*d) + (2*(-1)^(2/3)*a^(1/3)*ArcTan[((-1)^(1/6)*((-1)^(5/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]])/(3*Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]*b*d) + (2*a^(1/3)*ArcTanh[(b^(1/3) - a^(1/3)*Tanh[(c + d*x)/2])/Sqrt[a^(2/3) + b^(2/3)]])/(3*Sqrt[a^(2/3) + b^(2/3)]*b*d)","A",13,5,23,0.2174,1,"{3220, 3213, 2660, 618, 204}"
175,1,262,0,0.2707453,"\int \frac{\sinh ^2(c+d x)}{a+b \sinh ^3(c+d x)} \, dx","Int[Sinh[c + d*x]^2/(a + b*Sinh[c + d*x]^3),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 b^{2/3} d \sqrt{a^{2/3}+b^{2/3}}}-\frac{2 \tan ^{-1}\left(\frac{(-1)^{5/6} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{-(-1)^{2/3} a^{2/3}-b^{2/3}}}\right)}{3 b^{2/3} d \sqrt{-(-1)^{2/3} a^{2/3}-b^{2/3}}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 b^{2/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 b^{2/3} d \sqrt{a^{2/3}+b^{2/3}}}-\frac{2 \tan ^{-1}\left(\frac{(-1)^{5/6} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{-(-1)^{2/3} a^{2/3}-b^{2/3}}}\right)}{3 b^{2/3} d \sqrt{-(-1)^{2/3} a^{2/3}-b^{2/3}}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 b^{2/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}",1,"(-2*ArcTan[((-1)^(5/6)*((-1)^(1/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[-((-1)^(2/3)*a^(2/3)) - b^(2/3)]])/(3*Sqrt[-((-1)^(2/3)*a^(2/3)) - b^(2/3)]*b^(2/3)*d) - (2*ArcTan[((-1)^(1/6)*((-1)^(5/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]])/(3*Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]*b^(2/3)*d) - (2*ArcTanh[(b^(1/3) - a^(1/3)*Tanh[(c + d*x)/2])/Sqrt[a^(2/3) + b^(2/3)]])/(3*Sqrt[a^(2/3) + b^(2/3)]*b^(2/3)*d)","A",11,5,23,0.2174,1,"{3220, 2660, 618, 206, 204}"
176,1,290,0,0.3357564,"\int \frac{\sinh (c+d x)}{a+b \sinh ^3(c+d x)} \, dx","Int[Sinh[c + d*x]/(a + b*Sinh[c + d*x]^3),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 \sqrt[3]{a} \sqrt[3]{b} d \sqrt{a^{2/3}+b^{2/3}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}\right)}{3 \sqrt[3]{a} \sqrt[3]{b} d \sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}-\frac{2 \sqrt[3]{-1} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 \sqrt[3]{a} \sqrt[3]{b} d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 \sqrt[3]{a} \sqrt[3]{b} d \sqrt{a^{2/3}+b^{2/3}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}\right)}{3 \sqrt[3]{a} \sqrt[3]{b} d \sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}-\frac{2 \sqrt[3]{-1} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 \sqrt[3]{a} \sqrt[3]{b} d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}",1,"(2*ArcTan[((-1)^(1/6)*((-1)^(1/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - (-1)^(2/3)*b^(2/3)]])/(3*a^(1/3)*Sqrt[(-1)^(1/3)*a^(2/3) - (-1)^(2/3)*b^(2/3)]*b^(1/3)*d) - (2*(-1)^(1/3)*ArcTan[((-1)^(1/6)*((-1)^(5/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]])/(3*a^(1/3)*Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]*b^(1/3)*d) + (2*ArcTanh[(b^(1/3) - a^(1/3)*Tanh[(c + d*x)/2])/Sqrt[a^(2/3) + b^(2/3)]])/(3*a^(1/3)*Sqrt[a^(2/3) + b^(2/3)]*b^(1/3)*d)","A",11,4,21,0.1905,1,"{3220, 2660, 618, 204}"
177,1,280,0,0.250961,"\int \frac{1}{a+b \sinh ^3(c+d x)} \, dx","Int[(a + b*Sinh[c + d*x]^3)^(-1),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 a^{2/3} d \sqrt{a^{2/3}+b^{2/3}}}-\frac{2 (-1)^{2/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}\right)}{3 a^{2/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}-\frac{2 (-1)^{2/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 a^{2/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 a^{2/3} d \sqrt{a^{2/3}+b^{2/3}}}-\frac{2 (-1)^{2/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}\right)}{3 a^{2/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}-\frac{2 (-1)^{2/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 a^{2/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}",1,"(-2*(-1)^(2/3)*ArcTan[((-1)^(1/6)*((-1)^(1/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - (-1)^(2/3)*b^(2/3)]])/(3*a^(2/3)*Sqrt[(-1)^(1/3)*a^(2/3) - (-1)^(2/3)*b^(2/3)]*d) - (2*(-1)^(2/3)*ArcTan[((-1)^(1/6)*((-1)^(5/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]])/(3*a^(2/3)*Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]*d) - (2*ArcTanh[(b^(1/3) - a^(1/3)*Tanh[(c + d*x)/2])/Sqrt[a^(2/3) + b^(2/3)]])/(3*a^(2/3)*Sqrt[a^(2/3) + b^(2/3)]*d)","A",11,4,14,0.2857,1,"{3213, 2660, 618, 204}"
178,1,286,0,0.4324141,"\int \frac{\text{csch}(c+d x)}{a+b \sinh ^3(c+d x)} \, dx","Int[Csch[c + d*x]/(a + b*Sinh[c + d*x]^3),x]","\frac{2 \sqrt[3]{b} \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 a d \sqrt{a^{2/3}+b^{2/3}}}+\frac{2 \sqrt[3]{b} \tan ^{-1}\left(\frac{(-1)^{5/6} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{-(-1)^{2/3} a^{2/3}-b^{2/3}}}\right)}{3 a d \sqrt{-(-1)^{2/3} a^{2/3}-b^{2/3}}}+\frac{2 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 a d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a d}","\frac{2 \sqrt[3]{b} \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 a d \sqrt{a^{2/3}+b^{2/3}}}+\frac{2 \sqrt[3]{b} \tan ^{-1}\left(\frac{(-1)^{5/6} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{-(-1)^{2/3} a^{2/3}-b^{2/3}}}\right)}{3 a d \sqrt{-(-1)^{2/3} a^{2/3}-b^{2/3}}}+\frac{2 \sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 a d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a d}",1,"(2*b^(1/3)*ArcTan[((-1)^(5/6)*((-1)^(1/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[-((-1)^(2/3)*a^(2/3)) - b^(2/3)]])/(3*a*Sqrt[-((-1)^(2/3)*a^(2/3)) - b^(2/3)]*d) + (2*b^(1/3)*ArcTan[((-1)^(1/6)*((-1)^(5/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]])/(3*a*Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]*d) - ArcTanh[Cosh[c + d*x]]/(a*d) + (2*b^(1/3)*ArcTanh[(b^(1/3) - a^(1/3)*Tanh[(c + d*x)/2])/Sqrt[a^(2/3) + b^(2/3)]])/(3*a*Sqrt[a^(2/3) + b^(2/3)]*d)","A",14,6,21,0.2857,1,"{3220, 3770, 2660, 618, 206, 204}"
179,1,304,0,0.4784693,"\int \frac{\text{csch}^2(c+d x)}{a+b \sinh ^3(c+d x)} \, dx","Int[Csch[c + d*x]^2/(a + b*Sinh[c + d*x]^3),x]","-\frac{2 b^{2/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 a^{4/3} d \sqrt{a^{2/3}+b^{2/3}}}-\frac{2 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}\right)}{3 a^{4/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}+\frac{2 \sqrt[3]{-1} b^{2/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 a^{4/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}-\frac{\coth (c+d x)}{a d}","-\frac{2 b^{2/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 a^{4/3} d \sqrt{a^{2/3}+b^{2/3}}}-\frac{2 b^{2/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}\right)}{3 a^{4/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}+\frac{2 \sqrt[3]{-1} b^{2/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 a^{4/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}-\frac{\coth (c+d x)}{a d}",1,"(-2*b^(2/3)*ArcTan[((-1)^(1/6)*((-1)^(1/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - (-1)^(2/3)*b^(2/3)]])/(3*a^(4/3)*Sqrt[(-1)^(1/3)*a^(2/3) - (-1)^(2/3)*b^(2/3)]*d) + (2*(-1)^(1/3)*b^(2/3)*ArcTan[((-1)^(1/6)*((-1)^(5/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]])/(3*a^(4/3)*Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]*d) - (2*b^(2/3)*ArcTanh[(b^(1/3) - a^(1/3)*Tanh[(c + d*x)/2])/Sqrt[a^(2/3) + b^(2/3)]])/(3*a^(4/3)*Sqrt[a^(2/3) + b^(2/3)]*d) - Coth[c + d*x]/(a*d)","A",15,6,23,0.2609,1,"{3220, 3767, 8, 2660, 618, 204}"
180,1,322,0,0.4573264,"\int \frac{\text{csch}^3(c+d x)}{a+b \sinh ^3(c+d x)} \, dx","Int[Csch[c + d*x]^3/(a + b*Sinh[c + d*x]^3),x]","\frac{2 b \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 a^{5/3} d \sqrt{a^{2/3}+b^{2/3}}}+\frac{2 (-1)^{2/3} b \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}\right)}{3 a^{5/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}+\frac{2 (-1)^{2/3} b \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 a^{5/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}+\frac{\tanh ^{-1}(\cosh (c+d x))}{2 a d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d}","\frac{2 b \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 a^{5/3} d \sqrt{a^{2/3}+b^{2/3}}}+\frac{2 (-1)^{2/3} b \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}\right)}{3 a^{5/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-(-1)^{2/3} b^{2/3}}}+\frac{2 (-1)^{2/3} b \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 a^{5/3} d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}+\frac{\tanh ^{-1}(\cosh (c+d x))}{2 a d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d}",1,"(2*(-1)^(2/3)*b*ArcTan[((-1)^(1/6)*((-1)^(1/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - (-1)^(2/3)*b^(2/3)]])/(3*a^(5/3)*Sqrt[(-1)^(1/3)*a^(2/3) - (-1)^(2/3)*b^(2/3)]*d) + (2*(-1)^(2/3)*b*ArcTan[((-1)^(1/6)*((-1)^(5/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]])/(3*a^(5/3)*Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]*d) + ArcTanh[Cosh[c + d*x]]/(2*a*d) + (2*b*ArcTanh[(b^(1/3) - a^(1/3)*Tanh[(c + d*x)/2])/Sqrt[a^(2/3) + b^(2/3)]])/(3*a^(5/3)*Sqrt[a^(2/3) + b^(2/3)]*d) - (Coth[c + d*x]*Csch[c + d*x])/(2*a*d)","A",15,7,23,0.3043,1,"{3220, 3768, 3770, 3213, 2660, 618, 204}"
181,1,317,0,0.4325009,"\int \frac{\text{csch}^4(c+d x)}{a+b \sinh ^3(c+d x)} \, dx","Int[Csch[c + d*x]^4/(a + b*Sinh[c + d*x]^3),x]","-\frac{2 b^{4/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 a^2 d \sqrt{a^{2/3}+b^{2/3}}}-\frac{2 b^{4/3} \tan ^{-1}\left(\frac{(-1)^{5/6} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{-(-1)^{2/3} a^{2/3}-b^{2/3}}}\right)}{3 a^2 d \sqrt{-(-1)^{2/3} a^{2/3}-b^{2/3}}}-\frac{2 b^{4/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 a^2 d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}+\frac{b \tanh ^{-1}(\cosh (c+d x))}{a^2 d}-\frac{\coth ^3(c+d x)}{3 a d}+\frac{\coth (c+d x)}{a d}","-\frac{2 b^{4/3} \tanh ^{-1}\left(\frac{\sqrt[3]{b}-\sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^{2/3}+b^{2/3}}}\right)}{3 a^2 d \sqrt{a^{2/3}+b^{2/3}}}-\frac{2 b^{4/3} \tan ^{-1}\left(\frac{(-1)^{5/6} \left(\sqrt[6]{-1} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{-(-1)^{2/3} a^{2/3}-b^{2/3}}}\right)}{3 a^2 d \sqrt{-(-1)^{2/3} a^{2/3}-b^{2/3}}}-\frac{2 b^{4/3} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \left((-1)^{5/6} \sqrt[3]{b}+i \sqrt[3]{a} \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{\sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}\right)}{3 a^2 d \sqrt{\sqrt[3]{-1} a^{2/3}-b^{2/3}}}+\frac{b \tanh ^{-1}(\cosh (c+d x))}{a^2 d}-\frac{\coth ^3(c+d x)}{3 a d}+\frac{\coth (c+d x)}{a d}",1,"(-2*b^(4/3)*ArcTan[((-1)^(5/6)*((-1)^(1/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[-((-1)^(2/3)*a^(2/3)) - b^(2/3)]])/(3*a^2*Sqrt[-((-1)^(2/3)*a^(2/3)) - b^(2/3)]*d) - (2*b^(4/3)*ArcTan[((-1)^(1/6)*((-1)^(5/6)*b^(1/3) + I*a^(1/3)*Tanh[(c + d*x)/2]))/Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]])/(3*a^2*Sqrt[(-1)^(1/3)*a^(2/3) - b^(2/3)]*d) + (b*ArcTanh[Cosh[c + d*x]])/(a^2*d) - (2*b^(4/3)*ArcTanh[(b^(1/3) - a^(1/3)*Tanh[(c + d*x)/2])/Sqrt[a^(2/3) + b^(2/3)]])/(3*a^2*Sqrt[a^(2/3) + b^(2/3)]*d) + Coth[c + d*x]/(a*d) - Coth[c + d*x]^3/(3*a*d)","A",16,7,23,0.3043,1,"{3220, 3770, 3767, 2660, 618, 206, 204}"
182,1,139,0,0.1878194,"\int \frac{1}{1+\sinh ^3(x)} \, dx","Int[(1 + Sinh[x]^3)^(-1),x]","-\frac{1}{3} \sqrt{2} \tanh ^{-1}\left(\frac{1-\tanh \left(\frac{x}{2}\right)}{\sqrt{2}}\right)-\frac{1}{3} \sqrt[6]{-1} \log \left(-\sqrt[6]{-1} \tanh \left(\frac{x}{2}\right)+(-1)^{5/6}+1\right)+\frac{1}{3} \sqrt[6]{-1} \log \left(\sqrt[3]{-1} \tanh \left(\frac{x}{2}\right)+\sqrt[6]{-1}+1\right)-\frac{2 \sqrt[6]{-1} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \tanh \left(\frac{x}{2}\right)+i}{\sqrt{1-\sqrt[3]{-1}}}\right)}{3 \sqrt{1-\sqrt[3]{-1}}}","-\frac{1}{3} \sqrt{2} \tanh ^{-1}\left(\frac{1-\tanh \left(\frac{x}{2}\right)}{\sqrt{2}}\right)-\frac{1}{3} \sqrt[6]{-1} \log \left(-\sqrt[6]{-1} \tanh \left(\frac{x}{2}\right)+(-1)^{5/6}+1\right)+\frac{1}{3} \sqrt[6]{-1} \log \left(\sqrt[3]{-1} \tanh \left(\frac{x}{2}\right)+\sqrt[6]{-1}+1\right)-\frac{2 \sqrt[6]{-1} \tan ^{-1}\left(\frac{\sqrt[6]{-1} \tanh \left(\frac{x}{2}\right)+i}{\sqrt{1-\sqrt[3]{-1}}}\right)}{3 \sqrt{1-\sqrt[3]{-1}}}",1,"(-2*(-1)^(1/6)*ArcTan[(I + (-1)^(1/6)*Tanh[x/2])/Sqrt[1 - (-1)^(1/3)]])/(3*Sqrt[1 - (-1)^(1/3)]) - (Sqrt[2]*ArcTanh[(1 - Tanh[x/2])/Sqrt[2]])/3 - ((-1)^(1/6)*Log[1 + (-1)^(5/6) - (-1)^(1/6)*Tanh[x/2]])/3 + ((-1)^(1/6)*Log[1 + (-1)^(1/6) + (-1)^(1/3)*Tanh[x/2]])/3","A",12,8,8,1.000,1,"{3213, 2660, 618, 204, 617, 206, 616, 31}"
183,1,133,0,0.1889515,"\int \frac{1}{1-\sinh ^3(x)} \, dx","Int[(1 - Sinh[x]^3)^(-1),x]","\frac{1}{3} \sqrt{2} \tanh ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right)+1}{\sqrt{2}}\right)-\frac{1}{3} (-1)^{5/6} \log \left((-1)^{2/3} \tanh \left(\frac{x}{2}\right)+(-1)^{5/6}+1\right)+\frac{1}{3} (-1)^{5/6} \log \left((-1)^{5/6} \tanh \left(\frac{x}{2}\right)+\sqrt[6]{-1}+1\right)+\frac{2 (-1)^{5/6} \tan ^{-1}\left(\frac{-(-1)^{5/6} \tanh \left(\frac{x}{2}\right)+i}{\sqrt{1+(-1)^{2/3}}}\right)}{3 \sqrt{1+(-1)^{2/3}}}","\frac{1}{3} \sqrt{2} \tanh ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right)+1}{\sqrt{2}}\right)-\frac{1}{3} (-1)^{5/6} \log \left((-1)^{2/3} \tanh \left(\frac{x}{2}\right)+(-1)^{5/6}+1\right)+\frac{1}{3} (-1)^{5/6} \log \left((-1)^{5/6} \tanh \left(\frac{x}{2}\right)+\sqrt[6]{-1}+1\right)+\frac{2 (-1)^{5/6} \tan ^{-1}\left(\frac{-(-1)^{5/6} \tanh \left(\frac{x}{2}\right)+i}{\sqrt{1+(-1)^{2/3}}}\right)}{3 \sqrt{1+(-1)^{2/3}}}",1,"(2*(-1)^(5/6)*ArcTan[(I - (-1)^(5/6)*Tanh[x/2])/Sqrt[1 + (-1)^(2/3)]])/(3*Sqrt[1 + (-1)^(2/3)]) + (Sqrt[2]*ArcTanh[(1 + Tanh[x/2])/Sqrt[2]])/3 - ((-1)^(5/6)*Log[1 + (-1)^(5/6) + (-1)^(2/3)*Tanh[x/2]])/3 + ((-1)^(5/6)*Log[1 + (-1)^(1/6) + (-1)^(5/6)*Tanh[x/2]])/3","A",12,8,10,0.8000,1,"{3213, 2660, 618, 204, 616, 31, 617, 206}"
184,1,111,0,0.1427963,"\int \sinh ^4(c+d x) \left(a+b \sinh ^4(c+d x)\right) \, dx","Int[Sinh[c + d*x]^4*(a + b*Sinh[c + d*x]^4),x]","\frac{(48 a+163 b) \sinh (c+d x) \cosh ^3(c+d x)}{192 d}-\frac{(80 a+93 b) \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{1}{128} x (48 a+35 b)+\frac{b \sinh (c+d x) \cosh ^7(c+d x)}{8 d}-\frac{25 b \sinh (c+d x) \cosh ^5(c+d x)}{48 d}","\frac{(48 a+163 b) \sinh (c+d x) \cosh ^3(c+d x)}{192 d}-\frac{(80 a+93 b) \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{1}{128} x (48 a+35 b)+\frac{b \sinh (c+d x) \cosh ^7(c+d x)}{8 d}-\frac{25 b \sinh (c+d x) \cosh ^5(c+d x)}{48 d}",1,"((48*a + 35*b)*x)/128 - ((80*a + 93*b)*Cosh[c + d*x]*Sinh[c + d*x])/(128*d) + ((48*a + 163*b)*Cosh[c + d*x]^3*Sinh[c + d*x])/(192*d) - (25*b*Cosh[c + d*x]^5*Sinh[c + d*x])/(48*d) + (b*Cosh[c + d*x]^7*Sinh[c + d*x])/(8*d)","A",6,6,21,0.2857,1,"{3217, 1257, 1814, 1157, 385, 206}"
185,1,67,0,0.0661279,"\int \sinh ^3(c+d x) \left(a+b \sinh ^4(c+d x)\right) \, dx","Int[Sinh[c + d*x]^3*(a + b*Sinh[c + d*x]^4),x]","\frac{(a+3 b) \cosh ^3(c+d x)}{3 d}-\frac{(a+b) \cosh (c+d x)}{d}+\frac{b \cosh ^7(c+d x)}{7 d}-\frac{3 b \cosh ^5(c+d x)}{5 d}","\frac{(a+3 b) \cosh ^3(c+d x)}{3 d}-\frac{(a+b) \cosh (c+d x)}{d}+\frac{b \cosh ^7(c+d x)}{7 d}-\frac{3 b \cosh ^5(c+d x)}{5 d}",1,"-(((a + b)*Cosh[c + d*x])/d) + ((a + 3*b)*Cosh[c + d*x]^3)/(3*d) - (3*b*Cosh[c + d*x]^5)/(5*d) + (b*Cosh[c + d*x]^7)/(7*d)","A",3,2,21,0.09524,1,"{3215, 1153}"
186,1,83,0,0.0976626,"\int \sinh ^2(c+d x) \left(a+b \sinh ^4(c+d x)\right) \, dx","Int[Sinh[c + d*x]^2*(a + b*Sinh[c + d*x]^4),x]","\frac{(8 a+11 b) \sinh (c+d x) \cosh (c+d x)}{16 d}-\frac{1}{16} x (8 a+5 b)+\frac{b \sinh (c+d x) \cosh ^5(c+d x)}{6 d}-\frac{13 b \sinh (c+d x) \cosh ^3(c+d x)}{24 d}","\frac{(8 a+11 b) \sinh (c+d x) \cosh (c+d x)}{16 d}-\frac{1}{16} x (8 a+5 b)+\frac{b \sinh (c+d x) \cosh ^5(c+d x)}{6 d}-\frac{13 b \sinh (c+d x) \cosh ^3(c+d x)}{24 d}",1,"-((8*a + 5*b)*x)/16 + ((8*a + 11*b)*Cosh[c + d*x]*Sinh[c + d*x])/(16*d) - (13*b*Cosh[c + d*x]^3*Sinh[c + d*x])/(24*d) + (b*Cosh[c + d*x]^5*Sinh[c + d*x])/(6*d)","A",5,5,21,0.2381,1,"{3217, 1257, 1157, 385, 206}"
187,1,46,0,0.0342356,"\int \sinh (c+d x) \left(a+b \sinh ^4(c+d x)\right) \, dx","Int[Sinh[c + d*x]*(a + b*Sinh[c + d*x]^4),x]","\frac{(a+b) \cosh (c+d x)}{d}+\frac{b \cosh ^5(c+d x)}{5 d}-\frac{2 b \cosh ^3(c+d x)}{3 d}","\frac{(a+b) \cosh (c+d x)}{d}+\frac{b \cosh ^5(c+d x)}{5 d}-\frac{2 b \cosh ^3(c+d x)}{3 d}",1,"((a + b)*Cosh[c + d*x])/d - (2*b*Cosh[c + d*x]^3)/(3*d) + (b*Cosh[c + d*x]^5)/(5*d)","A",2,1,19,0.05263,1,"{3215}"
188,1,52,0,0.0339566,"\int \left(a+b \sinh ^4(c+d x)\right) \, dx","Int[a + b*Sinh[c + d*x]^4,x]","a x+\frac{b \sinh ^3(c+d x) \cosh (c+d x)}{4 d}-\frac{3 b \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{3 b x}{8}","a x+\frac{b \sinh ^3(c+d x) \cosh (c+d x)}{4 d}-\frac{3 b \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{3 b x}{8}",1,"a*x + (3*b*x)/8 - (3*b*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (b*Cosh[c + d*x]*Sinh[c + d*x]^3)/(4*d)","A",4,2,12,0.1667,1,"{2635, 8}"
189,1,42,0,0.0433106,"\int \text{csch}(c+d x) \left(a+b \sinh ^4(c+d x)\right) \, dx","Int[Csch[c + d*x]*(a + b*Sinh[c + d*x]^4),x]","-\frac{a \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b \cosh ^3(c+d x)}{3 d}-\frac{b \cosh (c+d x)}{d}","-\frac{a \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b \cosh ^3(c+d x)}{3 d}-\frac{b \cosh (c+d x)}{d}",1,"-((a*ArcTanh[Cosh[c + d*x]])/d) - (b*Cosh[c + d*x])/d + (b*Cosh[c + d*x]^3)/(3*d)","A",4,3,19,0.1579,1,"{3215, 1153, 206}"
190,1,39,0,0.0522995,"\int \text{csch}^2(c+d x) \left(a+b \sinh ^4(c+d x)\right) \, dx","Int[Csch[c + d*x]^2*(a + b*Sinh[c + d*x]^4),x]","-\frac{a \coth (c+d x)}{d}+\frac{b \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{b x}{2}","-\frac{a \coth (c+d x)}{d}+\frac{b \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{b x}{2}",1,"-(b*x)/2 - (a*Coth[c + d*x])/d + (b*Cosh[c + d*x]*Sinh[c + d*x])/(2*d)","A",4,4,21,0.1905,1,"{3217, 1259, 453, 206}"
191,1,47,0,0.0539296,"\int \text{csch}^3(c+d x) \left(a+b \sinh ^4(c+d x)\right) \, dx","Int[Csch[c + d*x]^3*(a + b*Sinh[c + d*x]^4),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 \cosh (c+d x)}{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 \cosh (c+d x)}{d}",1,"(a*ArcTanh[Cosh[c + d*x]])/(2*d) + (b*Cosh[c + d*x])/d - (a*Coth[c + d*x]*Csch[c + d*x])/(2*d)","A",4,4,21,0.1905,1,"{3215, 1157, 388, 206}"
192,1,31,0,0.0498847,"\int \text{csch}^4(c+d x) \left(a+b \sinh ^4(c+d x)\right) \, dx","Int[Csch[c + d*x]^4*(a + b*Sinh[c + d*x]^4),x]","-\frac{a \coth ^3(c+d x)}{3 d}+\frac{a \coth (c+d x)}{d}+b x","-\frac{a \coth ^3(c+d x)}{3 d}+\frac{a \coth (c+d x)}{d}+b x",1,"b*x + (a*Coth[c + d*x])/d - (a*Coth[c + d*x]^3)/(3*d)","A",4,3,21,0.1429,1,"{3217, 1261, 207}"
193,1,64,0,0.0627252,"\int \text{csch}^5(c+d x) \left(a+b \sinh ^4(c+d x)\right) \, dx","Int[Csch[c + d*x]^5*(a + b*Sinh[c + d*x]^4),x]","-\frac{(3 a+8 b) \tanh ^{-1}(\cosh (c+d x))}{8 d}-\frac{a \coth (c+d x) \text{csch}^3(c+d x)}{4 d}+\frac{3 a \coth (c+d x) \text{csch}(c+d x)}{8 d}","-\frac{(3 a+8 b) \tanh ^{-1}(\cosh (c+d x))}{8 d}-\frac{a \coth (c+d x) \text{csch}^3(c+d x)}{4 d}+\frac{3 a \coth (c+d x) \text{csch}(c+d x)}{8 d}",1,"-((3*a + 8*b)*ArcTanh[Cosh[c + d*x]])/(8*d) + (3*a*Coth[c + d*x]*Csch[c + d*x])/(8*d) - (a*Coth[c + d*x]*Csch[c + d*x]^3)/(4*d)","A",4,4,21,0.1905,1,"{3215, 1157, 385, 206}"
194,1,47,0,0.0434493,"\int \text{csch}^6(c+d x) \left(a+b \sinh ^4(c+d x)\right) \, dx","Int[Csch[c + d*x]^6*(a + b*Sinh[c + d*x]^4),x]","-\frac{(a+b) \coth (c+d x)}{d}-\frac{a \coth ^5(c+d x)}{5 d}+\frac{2 a \coth ^3(c+d x)}{3 d}","-\frac{(a+b) \coth (c+d x)}{d}-\frac{a \coth ^5(c+d x)}{5 d}+\frac{2 a \coth ^3(c+d x)}{3 d}",1,"-(((a + b)*Coth[c + d*x])/d) + (2*a*Coth[c + d*x]^3)/(3*d) - (a*Coth[c + d*x]^5)/(5*d)","A",3,2,21,0.09524,1,"{3217, 14}"
195,1,92,0,0.0837145,"\int \text{csch}^7(c+d x) \left(a+b \sinh ^4(c+d x)\right) \, dx","Int[Csch[c + d*x]^7*(a + b*Sinh[c + d*x]^4),x]","\frac{(5 a+8 b) \tanh ^{-1}(\cosh (c+d x))}{16 d}-\frac{(5 a+8 b) \coth (c+d x) \text{csch}(c+d x)}{16 d}-\frac{a \coth (c+d x) \text{csch}^5(c+d x)}{6 d}+\frac{5 a \coth (c+d x) \text{csch}^3(c+d x)}{24 d}","\frac{(5 a+8 b) \tanh ^{-1}(\cosh (c+d x))}{16 d}-\frac{(5 a+8 b) \coth (c+d x) \text{csch}(c+d x)}{16 d}-\frac{a \coth (c+d x) \text{csch}^5(c+d x)}{6 d}+\frac{5 a \coth (c+d x) \text{csch}^3(c+d x)}{24 d}",1,"((5*a + 8*b)*ArcTanh[Cosh[c + d*x]])/(16*d) - ((5*a + 8*b)*Coth[c + d*x]*Csch[c + d*x])/(16*d) + (5*a*Coth[c + d*x]*Csch[c + d*x]^3)/(24*d) - (a*Coth[c + d*x]*Csch[c + d*x]^5)/(6*d)","A",5,5,21,0.2381,1,"{3215, 1157, 385, 199, 206}"
196,1,120,0,0.1294506,"\int \sinh ^3(c+d x) \left(a+b \sinh ^4(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]^3*(a + b*Sinh[c + d*x]^4)^2,x]","\frac{2 b (a+5 b) \cosh ^7(c+d x)}{7 d}-\frac{2 b (3 a+5 b) \cosh ^5(c+d x)}{5 d}+\frac{(a+b) (a+5 b) \cosh ^3(c+d x)}{3 d}-\frac{(a+b)^2 \cosh (c+d x)}{d}+\frac{b^2 \cosh ^{11}(c+d x)}{11 d}-\frac{5 b^2 \cosh ^9(c+d x)}{9 d}","\frac{2 b (a+5 b) \cosh ^7(c+d x)}{7 d}-\frac{2 b (3 a+5 b) \cosh ^5(c+d x)}{5 d}+\frac{(a+b) (a+5 b) \cosh ^3(c+d x)}{3 d}-\frac{(a+b)^2 \cosh (c+d x)}{d}+\frac{b^2 \cosh ^{11}(c+d x)}{11 d}-\frac{5 b^2 \cosh ^9(c+d x)}{9 d}",1,"-(((a + b)^2*Cosh[c + d*x])/d) + ((a + b)*(a + 5*b)*Cosh[c + d*x]^3)/(3*d) - (2*b*(3*a + 5*b)*Cosh[c + d*x]^5)/(5*d) + (2*b*(a + 5*b)*Cosh[c + d*x]^7)/(7*d) - (5*b^2*Cosh[c + d*x]^9)/(9*d) + (b^2*Cosh[c + d*x]^11)/(11*d)","A",3,2,23,0.08696,1,"{3215, 1153}"
197,1,161,0,0.2809848,"\int \sinh ^2(c+d x) \left(a+b \sinh ^4(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]^2*(a + b*Sinh[c + d*x]^4)^2,x]","\frac{\left(128 a^2+352 a b+193 b^2\right) \sinh (c+d x) \cosh (c+d x)}{256 d}-\frac{1}{256} x \left(128 a^2+160 a b+63 b^2\right)+\frac{b (160 a+513 b) \sinh (c+d x) \cosh ^5(c+d x)}{480 d}-\frac{b (416 a+447 b) \sinh (c+d x) \cosh ^3(c+d x)}{384 d}+\frac{b^2 \sinh (c+d x) \cosh ^9(c+d x)}{10 d}-\frac{41 b^2 \sinh (c+d x) \cosh ^7(c+d x)}{80 d}","\frac{\left(128 a^2+352 a b+193 b^2\right) \sinh (c+d x) \cosh (c+d x)}{256 d}-\frac{1}{256} x \left(128 a^2+160 a b+63 b^2\right)+\frac{b (160 a+513 b) \sinh (c+d x) \cosh ^5(c+d x)}{480 d}-\frac{b (416 a+447 b) \sinh (c+d x) \cosh ^3(c+d x)}{384 d}+\frac{b^2 \sinh (c+d x) \cosh ^9(c+d x)}{10 d}-\frac{41 b^2 \sinh (c+d x) \cosh ^7(c+d x)}{80 d}",1,"-((128*a^2 + 160*a*b + 63*b^2)*x)/256 + ((128*a^2 + 352*a*b + 193*b^2)*Cosh[c + d*x]*Sinh[c + d*x])/(256*d) - (b*(416*a + 447*b)*Cosh[c + d*x]^3*Sinh[c + d*x])/(384*d) + (b*(160*a + 513*b)*Cosh[c + d*x]^5*Sinh[c + d*x])/(480*d) - (41*b^2*Cosh[c + d*x]^7*Sinh[c + d*x])/(80*d) + (b^2*Cosh[c + d*x]^9*Sinh[c + d*x])/(10*d)","A",7,6,23,0.2609,1,"{3217, 1257, 1814, 1157, 385, 206}"
198,1,92,0,0.0860677,"\int \sinh (c+d x) \left(a+b \sinh ^4(c+d x)\right)^2 \, dx","Int[Sinh[c + d*x]*(a + b*Sinh[c + d*x]^4)^2,x]","\frac{2 b (a+3 b) \cosh ^5(c+d x)}{5 d}-\frac{4 b (a+b) \cosh ^3(c+d x)}{3 d}+\frac{(a+b)^2 \cosh (c+d x)}{d}+\frac{b^2 \cosh ^9(c+d x)}{9 d}-\frac{4 b^2 \cosh ^7(c+d x)}{7 d}","\frac{2 b (a+3 b) \cosh ^5(c+d x)}{5 d}-\frac{4 b (a+b) \cosh ^3(c+d x)}{3 d}+\frac{(a+b)^2 \cosh (c+d x)}{d}+\frac{b^2 \cosh ^9(c+d x)}{9 d}-\frac{4 b^2 \cosh ^7(c+d x)}{7 d}",1,"((a + b)^2*Cosh[c + d*x])/d - (4*b*(a + b)*Cosh[c + d*x]^3)/(3*d) + (2*b*(a + 3*b)*Cosh[c + d*x]^5)/(5*d) - (4*b^2*Cosh[c + d*x]^7)/(7*d) + (b^2*Cosh[c + d*x]^9)/(9*d)","A",3,2,21,0.09524,1,"{3215, 1090}"
199,1,125,0,0.1619428,"\int \left(a+b \sinh ^4(c+d x)\right)^2 \, dx","Int[(a + b*Sinh[c + d*x]^4)^2,x]","\frac{1}{128} x \left(128 a^2+96 a b+35 b^2\right)+\frac{b (96 a+163 b) \sinh (c+d x) \cosh ^3(c+d x)}{192 d}-\frac{b (160 a+93 b) \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{b^2 \sinh (c+d x) \cosh ^7(c+d x)}{8 d}-\frac{25 b^2 \sinh (c+d x) \cosh ^5(c+d x)}{48 d}","\frac{1}{128} x \left(128 a^2+96 a b+35 b^2\right)+\frac{b (96 a+163 b) \sinh (c+d x) \cosh ^3(c+d x)}{192 d}-\frac{b (160 a+93 b) \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{b^2 \sinh (c+d x) \cosh ^7(c+d x)}{8 d}-\frac{25 b^2 \sinh (c+d x) \cosh ^5(c+d x)}{48 d}",1,"((128*a^2 + 96*a*b + 35*b^2)*x)/128 - (b*(160*a + 93*b)*Cosh[c + d*x]*Sinh[c + d*x])/(128*d) + (b*(96*a + 163*b)*Cosh[c + d*x]^3*Sinh[c + d*x])/(192*d) - (25*b^2*Cosh[c + d*x]^5*Sinh[c + d*x])/(48*d) + (b^2*Cosh[c + d*x]^7*Sinh[c + d*x])/(8*d)","A",6,5,14,0.3571,1,"{3209, 1157, 1814, 385, 206}"
200,1,92,0,0.092699,"\int \text{csch}(c+d x) \left(a+b \sinh ^4(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]*(a + b*Sinh[c + d*x]^4)^2,x]","-\frac{a^2 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b (2 a+3 b) \cosh ^3(c+d x)}{3 d}-\frac{b (2 a+b) \cosh (c+d x)}{d}+\frac{b^2 \cosh ^7(c+d x)}{7 d}-\frac{3 b^2 \cosh ^5(c+d x)}{5 d}","-\frac{a^2 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b (2 a+3 b) \cosh ^3(c+d x)}{3 d}-\frac{b (2 a+b) \cosh (c+d x)}{d}+\frac{b^2 \cosh ^7(c+d x)}{7 d}-\frac{3 b^2 \cosh ^5(c+d x)}{5 d}",1,"-((a^2*ArcTanh[Cosh[c + d*x]])/d) - (b*(2*a + b)*Cosh[c + d*x])/d + (b*(2*a + 3*b)*Cosh[c + d*x]^3)/(3*d) - (3*b^2*Cosh[c + d*x]^5)/(5*d) + (b^2*Cosh[c + d*x]^7)/(7*d)","A",4,3,21,0.1429,1,"{3215, 1153, 206}"
201,1,103,0,0.1944661,"\int \text{csch}^2(c+d x) \left(a+b \sinh ^4(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^2*(a + b*Sinh[c + d*x]^4)^2,x]","-\frac{a^2 \coth (c+d x)}{d}+\frac{b (16 a+11 b) \sinh (c+d x) \cosh (c+d x)}{16 d}-\frac{1}{16} b x (16 a+5 b)+\frac{b^2 \sinh (c+d x) \cosh ^5(c+d x)}{6 d}-\frac{13 b^2 \sinh (c+d x) \cosh ^3(c+d x)}{24 d}","-\frac{a^2 \coth (c+d x)}{d}+\frac{b (16 a+11 b) \sinh (c+d x) \cosh (c+d x)}{16 d}-\frac{1}{16} b x (16 a+5 b)+\frac{b^2 \sinh (c+d x) \cosh ^5(c+d x)}{6 d}-\frac{13 b^2 \sinh (c+d x) \cosh ^3(c+d x)}{24 d}",1,"-(b*(16*a + 5*b)*x)/16 - (a^2*Coth[c + d*x])/d + (b*(16*a + 11*b)*Cosh[c + d*x]*Sinh[c + d*x])/(16*d) - (13*b^2*Cosh[c + d*x]^3*Sinh[c + d*x])/(24*d) + (b^2*Cosh[c + d*x]^5*Sinh[c + d*x])/(6*d)","A",6,5,23,0.2174,1,"{3217, 1259, 1805, 453, 206}"
202,1,92,0,0.1348618,"\int \text{csch}^3(c+d x) \left(a+b \sinh ^4(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^3*(a + b*Sinh[c + d*x]^4)^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{b (2 a+b) \cosh (c+d x)}{d}+\frac{b^2 \cosh ^5(c+d x)}{5 d}-\frac{2 b^2 \cosh ^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{b (2 a+b) \cosh (c+d x)}{d}+\frac{b^2 \cosh ^5(c+d x)}{5 d}-\frac{2 b^2 \cosh ^3(c+d x)}{3 d}",1,"(a^2*ArcTanh[Cosh[c + d*x]])/(2*d) + (b*(2*a + b)*Cosh[c + d*x])/d - (2*b^2*Cosh[c + d*x]^3)/(3*d) + (b^2*Cosh[c + d*x]^5)/(5*d) - (a^2*Coth[c + d*x]*Csch[c + d*x])/(2*d)","A",5,4,23,0.1739,1,"{3215, 1157, 1810, 206}"
203,1,91,0,0.1646251,"\int \text{csch}^4(c+d x) \left(a+b \sinh ^4(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^4*(a + b*Sinh[c + d*x]^4)^2,x]","-\frac{a^2 \coth ^3(c+d x)}{3 d}+\frac{a^2 \coth (c+d x)}{d}+\frac{1}{8} b x (16 a+3 b)+\frac{b^2 \sinh (c+d x) \cosh ^3(c+d x)}{4 d}-\frac{5 b^2 \sinh (c+d x) \cosh (c+d x)}{8 d}","-\frac{a^2 \coth ^3(c+d x)}{3 d}+\frac{a^2 \coth (c+d x)}{d}+\frac{1}{8} b x (16 a+3 b)+\frac{b^2 \sinh (c+d x) \cosh ^3(c+d x)}{4 d}-\frac{5 b^2 \sinh (c+d x) \cosh (c+d x)}{8 d}",1,"(b*(16*a + 3*b)*x)/8 + (a^2*Coth[c + d*x])/d - (a^2*Coth[c + d*x]^3)/(3*d) - (5*b^2*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (b^2*Cosh[c + d*x]^3*Sinh[c + d*x])/(4*d)","A",6,5,23,0.2174,1,"{3217, 1259, 1805, 1261, 207}"
204,1,101,0,0.1512086,"\int \text{csch}^5(c+d x) \left(a+b \sinh ^4(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^5*(a + b*Sinh[c + d*x]^4)^2,x]","-\frac{a^2 \coth (c+d x) \text{csch}^3(c+d x)}{4 d}+\frac{3 a^2 \coth (c+d x) \text{csch}(c+d x)}{8 d}-\frac{a (3 a+16 b) \tanh ^{-1}(\cosh (c+d x))}{8 d}+\frac{b^2 \cosh ^3(c+d x)}{3 d}-\frac{b^2 \cosh (c+d x)}{d}","-\frac{a^2 \coth (c+d x) \text{csch}^3(c+d x)}{4 d}+\frac{3 a^2 \coth (c+d x) \text{csch}(c+d x)}{8 d}-\frac{a (3 a+16 b) \tanh ^{-1}(\cosh (c+d x))}{8 d}+\frac{b^2 \cosh ^3(c+d x)}{3 d}-\frac{b^2 \cosh (c+d x)}{d}",1,"-(a*(3*a + 16*b)*ArcTanh[Cosh[c + d*x]])/(8*d) - (b^2*Cosh[c + d*x])/d + (b^2*Cosh[c + d*x]^3)/(3*d) + (3*a^2*Coth[c + d*x]*Csch[c + d*x])/(8*d) - (a^2*Coth[c + d*x]*Csch[c + d*x]^3)/(4*d)","A",6,5,23,0.2174,1,"{3215, 1157, 1814, 1153, 206}"
205,1,84,0,0.1457364,"\int \text{csch}^6(c+d x) \left(a+b \sinh ^4(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^6*(a + b*Sinh[c + d*x]^4)^2,x]","-\frac{a^2 \coth ^5(c+d x)}{5 d}+\frac{2 a^2 \coth ^3(c+d x)}{3 d}-\frac{a (a+2 b) \coth (c+d x)}{d}+\frac{b^2 \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{b^2 x}{2}","-\frac{a^2 \coth ^5(c+d x)}{5 d}+\frac{2 a^2 \coth ^3(c+d x)}{3 d}-\frac{a (a+2 b) \coth (c+d x)}{d}+\frac{b^2 \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{b^2 x}{2}",1,"-(b^2*x)/2 - (a*(a + 2*b)*Coth[c + d*x])/d + (2*a^2*Coth[c + d*x]^3)/(3*d) - (a^2*Coth[c + d*x]^5)/(5*d) + (b^2*Cosh[c + d*x]*Sinh[c + d*x])/(2*d)","A",5,4,23,0.1739,1,"{3217, 1259, 1802, 207}"
206,1,111,0,0.1741231,"\int \text{csch}^7(c+d x) \left(a+b \sinh ^4(c+d x)\right)^2 \, dx","Int[Csch[c + d*x]^7*(a + b*Sinh[c + d*x]^4)^2,x]","-\frac{a^2 \coth (c+d x) \text{csch}^5(c+d x)}{6 d}+\frac{5 a^2 \coth (c+d x) \text{csch}^3(c+d x)}{24 d}+\frac{a (5 a+16 b) \tanh ^{-1}(\cosh (c+d x))}{16 d}-\frac{a (5 a+16 b) \coth (c+d x) \text{csch}(c+d x)}{16 d}+\frac{b^2 \cosh (c+d x)}{d}","-\frac{a^2 \coth (c+d x) \text{csch}^5(c+d x)}{6 d}+\frac{5 a^2 \coth (c+d x) \text{csch}^3(c+d x)}{24 d}+\frac{a (5 a+16 b) \tanh ^{-1}(\cosh (c+d x))}{16 d}-\frac{a (5 a+16 b) \coth (c+d x) \text{csch}(c+d x)}{16 d}+\frac{b^2 \cosh (c+d x)}{d}",1,"(a*(5*a + 16*b)*ArcTanh[Cosh[c + d*x]])/(16*d) + (b^2*Cosh[c + d*x])/d - (a*(5*a + 16*b)*Coth[c + d*x]*Csch[c + d*x])/(16*d) + (5*a^2*Coth[c + d*x]*Csch[c + d*x]^3)/(24*d) - (a^2*Coth[c + d*x]*Csch[c + d*x]^5)/(6*d)","A",6,5,23,0.2174,1,"{3215, 1157, 1814, 388, 206}"
207,1,220,0,0.2180722,"\int \sinh ^5(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]^5*(a + b*Sinh[c + d*x]^4)^3,x]","\frac{b \left(3 a^2+45 a b+70 b^2\right) \cosh ^9(c+d x)}{9 d}-\frac{4 b \left(3 a^2+15 a b+14 b^2\right) \cosh ^7(c+d x)}{7 d}+\frac{(a+b) \left(a^2+17 a b+28 b^2\right) \cosh ^5(c+d x)}{5 d}+\frac{b^2 (3 a+28 b) \cosh ^{13}(c+d x)}{13 d}-\frac{2 b^2 (9 a+28 b) \cosh ^{11}(c+d x)}{11 d}-\frac{2 (a+b)^2 (a+4 b) \cosh ^3(c+d x)}{3 d}+\frac{(a+b)^3 \cosh (c+d x)}{d}+\frac{b^3 \cosh ^{17}(c+d x)}{17 d}-\frac{8 b^3 \cosh ^{15}(c+d x)}{15 d}","\frac{b \left(3 a^2+45 a b+70 b^2\right) \cosh ^9(c+d x)}{9 d}-\frac{4 b \left(3 a^2+15 a b+14 b^2\right) \cosh ^7(c+d x)}{7 d}+\frac{(a+b) \left(a^2+17 a b+28 b^2\right) \cosh ^5(c+d x)}{5 d}+\frac{b^2 (3 a+28 b) \cosh ^{13}(c+d x)}{13 d}-\frac{2 b^2 (9 a+28 b) \cosh ^{11}(c+d x)}{11 d}-\frac{2 (a+b)^2 (a+4 b) \cosh ^3(c+d x)}{3 d}+\frac{(a+b)^3 \cosh (c+d x)}{d}+\frac{b^3 \cosh ^{17}(c+d x)}{17 d}-\frac{8 b^3 \cosh ^{15}(c+d x)}{15 d}",1,"((a + b)^3*Cosh[c + d*x])/d - (2*(a + b)^2*(a + 4*b)*Cosh[c + d*x]^3)/(3*d) + ((a + b)*(a^2 + 17*a*b + 28*b^2)*Cosh[c + d*x]^5)/(5*d) - (4*b*(3*a^2 + 15*a*b + 14*b^2)*Cosh[c + d*x]^7)/(7*d) + (b*(3*a^2 + 45*a*b + 70*b^2)*Cosh[c + d*x]^9)/(9*d) - (2*b^2*(9*a + 28*b)*Cosh[c + d*x]^11)/(11*d) + (b^2*(3*a + 28*b)*Cosh[c + d*x]^13)/(13*d) - (8*b^3*Cosh[c + d*x]^15)/(15*d) + (b^3*Cosh[c + d*x]^17)/(17*d)","A",3,2,23,0.08696,1,"{3215, 1153}"
208,1,183,0,0.1751034,"\int \sinh ^3(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]^3*(a + b*Sinh[c + d*x]^4)^3,x]","\frac{b \left(3 a^2+30 a b+35 b^2\right) \cosh ^7(c+d x)}{7 d}+\frac{3 b^2 (a+7 b) \cosh ^{11}(c+d x)}{11 d}-\frac{5 b^2 (3 a+7 b) \cosh ^9(c+d x)}{9 d}-\frac{3 b (a+b) (3 a+7 b) \cosh ^5(c+d x)}{5 d}+\frac{(a+b)^2 (a+7 b) \cosh ^3(c+d x)}{3 d}-\frac{(a+b)^3 \cosh (c+d x)}{d}+\frac{b^3 \cosh ^{15}(c+d x)}{15 d}-\frac{7 b^3 \cosh ^{13}(c+d x)}{13 d}","\frac{b \left(3 a^2+30 a b+35 b^2\right) \cosh ^7(c+d x)}{7 d}+\frac{3 b^2 (a+7 b) \cosh ^{11}(c+d x)}{11 d}-\frac{5 b^2 (3 a+7 b) \cosh ^9(c+d x)}{9 d}-\frac{3 b (a+b) (3 a+7 b) \cosh ^5(c+d x)}{5 d}+\frac{(a+b)^2 (a+7 b) \cosh ^3(c+d x)}{3 d}-\frac{(a+b)^3 \cosh (c+d x)}{d}+\frac{b^3 \cosh ^{15}(c+d x)}{15 d}-\frac{7 b^3 \cosh ^{13}(c+d x)}{13 d}",1,"-(((a + b)^3*Cosh[c + d*x])/d) + ((a + b)^2*(a + 7*b)*Cosh[c + d*x]^3)/(3*d) - (3*b*(a + b)*(3*a + 7*b)*Cosh[c + d*x]^5)/(5*d) + (b*(3*a^2 + 30*a*b + 35*b^2)*Cosh[c + d*x]^7)/(7*d) - (5*b^2*(3*a + 7*b)*Cosh[c + d*x]^9)/(9*d) + (3*b^2*(a + 7*b)*Cosh[c + d*x]^11)/(11*d) - (7*b^3*Cosh[c + d*x]^13)/(13*d) + (b^3*Cosh[c + d*x]^15)/(15*d)","A",3,2,23,0.08696,1,"{3215, 1153}"
209,1,143,0,0.15744,"\int \sinh (c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]*(a + b*Sinh[c + d*x]^4)^3,x]","\frac{b^2 (a+5 b) \cosh ^9(c+d x)}{3 d}-\frac{4 b^2 (3 a+5 b) \cosh ^7(c+d x)}{7 d}+\frac{3 b (a+b) (a+5 b) \cosh ^5(c+d x)}{5 d}-\frac{2 b (a+b)^2 \cosh ^3(c+d x)}{d}+\frac{(a+b)^3 \cosh (c+d x)}{d}+\frac{b^3 \cosh ^{13}(c+d x)}{13 d}-\frac{6 b^3 \cosh ^{11}(c+d x)}{11 d}","\frac{b^2 (a+5 b) \cosh ^9(c+d x)}{3 d}-\frac{4 b^2 (3 a+5 b) \cosh ^7(c+d x)}{7 d}+\frac{3 b (a+b) (a+5 b) \cosh ^5(c+d x)}{5 d}-\frac{2 b (a+b)^2 \cosh ^3(c+d x)}{d}+\frac{(a+b)^3 \cosh (c+d x)}{d}+\frac{b^3 \cosh ^{13}(c+d x)}{13 d}-\frac{6 b^3 \cosh ^{11}(c+d x)}{11 d}",1,"((a + b)^3*Cosh[c + d*x])/d - (2*b*(a + b)^2*Cosh[c + d*x]^3)/d + (3*b*(a + b)*(a + 5*b)*Cosh[c + d*x]^5)/(5*d) - (4*b^2*(3*a + 5*b)*Cosh[c + d*x]^7)/(7*d) + (b^2*(a + 5*b)*Cosh[c + d*x]^9)/(3*d) - (6*b^3*Cosh[c + d*x]^11)/(11*d) + (b^3*Cosh[c + d*x]^13)/(13*d)","A",3,2,21,0.09524,1,"{3215, 1090}"
210,1,158,0,0.1354365,"\int \text{csch}(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]*(a + b*Sinh[c + d*x]^4)^3,x]","\frac{b \left(3 a^2+9 a b+5 b^2\right) \cosh ^3(c+d x)}{3 d}-\frac{b \left(3 a^2+3 a b+b^2\right) \cosh (c+d x)}{d}-\frac{a^3 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b^2 (3 a+10 b) \cosh ^7(c+d x)}{7 d}-\frac{b^2 (9 a+10 b) \cosh ^5(c+d x)}{5 d}+\frac{b^3 \cosh ^{11}(c+d x)}{11 d}-\frac{5 b^3 \cosh ^9(c+d x)}{9 d}","\frac{b \left(3 a^2+9 a b+5 b^2\right) \cosh ^3(c+d x)}{3 d}-\frac{b \left(3 a^2+3 a b+b^2\right) \cosh (c+d x)}{d}-\frac{a^3 \tanh ^{-1}(\cosh (c+d x))}{d}+\frac{b^2 (3 a+10 b) \cosh ^7(c+d x)}{7 d}-\frac{b^2 (9 a+10 b) \cosh ^5(c+d x)}{5 d}+\frac{b^3 \cosh ^{11}(c+d x)}{11 d}-\frac{5 b^3 \cosh ^9(c+d x)}{9 d}",1,"-((a^3*ArcTanh[Cosh[c + d*x]])/d) - (b*(3*a^2 + 3*a*b + b^2)*Cosh[c + d*x])/d + (b*(3*a^2 + 9*a*b + 5*b^2)*Cosh[c + d*x]^3)/(3*d) - (b^2*(9*a + 10*b)*Cosh[c + d*x]^5)/(5*d) + (b^2*(3*a + 10*b)*Cosh[c + d*x]^7)/(7*d) - (5*b^3*Cosh[c + d*x]^9)/(9*d) + (b^3*Cosh[c + d*x]^11)/(11*d)","A",4,3,21,0.1429,1,"{3215, 1153, 206}"
211,1,148,0,0.2093649,"\int \text{csch}^3(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^3*(a + b*Sinh[c + d*x]^4)^3,x]","\frac{b \left(3 a^2+3 a b+b^2\right) \cosh (c+d x)}{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 b^2 (a+2 b) \cosh ^5(c+d x)}{5 d}-\frac{2 b^2 (3 a+2 b) \cosh ^3(c+d x)}{3 d}+\frac{b^3 \cosh ^9(c+d x)}{9 d}-\frac{4 b^3 \cosh ^7(c+d x)}{7 d}","\frac{b \left(3 a^2+3 a b+b^2\right) \cosh (c+d x)}{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 b^2 (a+2 b) \cosh ^5(c+d x)}{5 d}-\frac{2 b^2 (3 a+2 b) \cosh ^3(c+d x)}{3 d}+\frac{b^3 \cosh ^9(c+d x)}{9 d}-\frac{4 b^3 \cosh ^7(c+d x)}{7 d}",1,"(a^3*ArcTanh[Cosh[c + d*x]])/(2*d) + (b*(3*a^2 + 3*a*b + b^2)*Cosh[c + d*x])/d - (2*b^2*(3*a + 2*b)*Cosh[c + d*x]^3)/(3*d) + (3*b^2*(a + 2*b)*Cosh[c + d*x]^5)/(5*d) - (4*b^3*Cosh[c + d*x]^7)/(7*d) + (b^3*Cosh[c + d*x]^9)/(9*d) - (a^3*Coth[c + d*x]*Csch[c + d*x])/(2*d)","A",5,4,23,0.1739,1,"{3215, 1157, 1810, 206}"
212,1,142,0,0.2727455,"\int \text{csch}^5(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^5*(a + b*Sinh[c + d*x]^4)^3,x]","-\frac{3 a^2 (a+8 b) \tanh ^{-1}(\cosh (c+d x))}{8 d}-\frac{a^3 \coth (c+d x) \text{csch}^3(c+d x)}{4 d}+\frac{3 a^3 \coth (c+d x) \text{csch}(c+d x)}{8 d}+\frac{b^2 (a+b) \cosh ^3(c+d x)}{d}-\frac{b^2 (3 a+b) \cosh (c+d x)}{d}+\frac{b^3 \cosh ^7(c+d x)}{7 d}-\frac{3 b^3 \cosh ^5(c+d x)}{5 d}","-\frac{3 a^2 (a+8 b) \tanh ^{-1}(\cosh (c+d x))}{8 d}-\frac{a^3 \coth (c+d x) \text{csch}^3(c+d x)}{4 d}+\frac{3 a^3 \coth (c+d x) \text{csch}(c+d x)}{8 d}+\frac{b^2 (a+b) \cosh ^3(c+d x)}{d}-\frac{b^2 (3 a+b) \cosh (c+d x)}{d}+\frac{b^3 \cosh ^7(c+d x)}{7 d}-\frac{3 b^3 \cosh ^5(c+d x)}{5 d}",1,"(-3*a^2*(a + 8*b)*ArcTanh[Cosh[c + d*x]])/(8*d) - (b^2*(3*a + b)*Cosh[c + d*x])/d + (b^2*(a + b)*Cosh[c + d*x]^3)/d - (3*b^3*Cosh[c + d*x]^5)/(5*d) + (b^3*Cosh[c + d*x]^7)/(7*d) + (3*a^3*Coth[c + d*x]*Csch[c + d*x])/(8*d) - (a^3*Coth[c + d*x]*Csch[c + d*x]^3)/(4*d)","A",6,5,23,0.2174,1,"{3215, 1157, 1814, 1810, 206}"
213,1,156,0,0.3044545,"\int \text{csch}^7(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^7*(a + b*Sinh[c + d*x]^4)^3,x]","\frac{a^2 (5 a+24 b) \tanh ^{-1}(\cosh (c+d x))}{16 d}-\frac{a^2 (5 a+24 b) \coth (c+d x) \text{csch}(c+d x)}{16 d}-\frac{a^3 \coth (c+d x) \text{csch}^5(c+d x)}{6 d}+\frac{5 a^3 \coth (c+d x) \text{csch}^3(c+d x)}{24 d}+\frac{b^2 (3 a+b) \cosh (c+d x)}{d}+\frac{b^3 \cosh ^5(c+d x)}{5 d}-\frac{2 b^3 \cosh ^3(c+d x)}{3 d}","\frac{a^2 (5 a+24 b) \tanh ^{-1}(\cosh (c+d x))}{16 d}-\frac{a^2 (5 a+24 b) \coth (c+d x) \text{csch}(c+d x)}{16 d}-\frac{a^3 \coth (c+d x) \text{csch}^5(c+d x)}{6 d}+\frac{5 a^3 \coth (c+d x) \text{csch}^3(c+d x)}{24 d}+\frac{b^2 (3 a+b) \cosh (c+d x)}{d}+\frac{b^3 \cosh ^5(c+d x)}{5 d}-\frac{2 b^3 \cosh ^3(c+d x)}{3 d}",1,"(a^2*(5*a + 24*b)*ArcTanh[Cosh[c + d*x]])/(16*d) + (b^2*(3*a + b)*Cosh[c + d*x])/d - (2*b^3*Cosh[c + d*x]^3)/(3*d) + (b^3*Cosh[c + d*x]^5)/(5*d) - (a^2*(5*a + 24*b)*Coth[c + d*x]*Csch[c + d*x])/(16*d) + (5*a^3*Coth[c + d*x]*Csch[c + d*x]^3)/(24*d) - (a^3*Coth[c + d*x]*Csch[c + d*x]^5)/(6*d)","A",7,5,23,0.2174,1,"{3215, 1157, 1814, 1810, 206}"
214,1,171,0,0.3318562,"\int \text{csch}^9(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^9*(a + b*Sinh[c + d*x]^4)^3,x]","-\frac{a \left(35 a^2+144 a b+384 b^2\right) \tanh ^{-1}(\cosh (c+d x))}{128 d}-\frac{a^2 (35 a+144 b) \coth (c+d x) \text{csch}^3(c+d x)}{192 d}+\frac{a^2 (35 a+144 b) \coth (c+d x) \text{csch}(c+d x)}{128 d}-\frac{a^3 \coth (c+d x) \text{csch}^7(c+d x)}{8 d}+\frac{7 a^3 \coth (c+d x) \text{csch}^5(c+d x)}{48 d}+\frac{b^3 \cosh ^3(c+d x)}{3 d}-\frac{b^3 \cosh (c+d x)}{d}","-\frac{a \left(35 a^2+144 a b+384 b^2\right) \tanh ^{-1}(\cosh (c+d x))}{128 d}-\frac{a^2 (35 a+144 b) \coth (c+d x) \text{csch}^3(c+d x)}{192 d}+\frac{a^2 (35 a+144 b) \coth (c+d x) \text{csch}(c+d x)}{128 d}-\frac{a^3 \coth (c+d x) \text{csch}^7(c+d x)}{8 d}+\frac{7 a^3 \coth (c+d x) \text{csch}^5(c+d x)}{48 d}+\frac{b^3 \cosh ^3(c+d x)}{3 d}-\frac{b^3 \cosh (c+d x)}{d}",1,"-(a*(35*a^2 + 144*a*b + 384*b^2)*ArcTanh[Cosh[c + d*x]])/(128*d) - (b^3*Cosh[c + d*x])/d + (b^3*Cosh[c + d*x]^3)/(3*d) + (a^2*(35*a + 144*b)*Coth[c + d*x]*Csch[c + d*x])/(128*d) - (a^2*(35*a + 144*b)*Coth[c + d*x]*Csch[c + d*x]^3)/(192*d) + (7*a^3*Coth[c + d*x]*Csch[c + d*x]^5)/(48*d) - (a^3*Coth[c + d*x]*Csch[c + d*x]^7)/(8*d)","A",8,5,23,0.2174,1,"{3215, 1157, 1814, 1153, 206}"
215,1,189,0,0.3690435,"\int \text{csch}^{11}(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^11*(a + b*Sinh[c + d*x]^4)^3,x]","\frac{3 a \left(21 a^2+80 a b+128 b^2\right) \tanh ^{-1}(\cosh (c+d x))}{256 d}-\frac{3 a \left(21 a^2+80 a b+128 b^2\right) \coth (c+d x) \text{csch}(c+d x)}{256 d}-\frac{a^2 (21 a+80 b) \coth (c+d x) \text{csch}^5(c+d x)}{160 d}+\frac{a^2 (21 a+80 b) \coth (c+d x) \text{csch}^3(c+d x)}{128 d}-\frac{a^3 \coth (c+d x) \text{csch}^9(c+d x)}{10 d}+\frac{9 a^3 \coth (c+d x) \text{csch}^7(c+d x)}{80 d}+\frac{b^3 \cosh (c+d x)}{d}","\frac{3 a \left(21 a^2+80 a b+128 b^2\right) \tanh ^{-1}(\cosh (c+d x))}{256 d}-\frac{3 a \left(21 a^2+80 a b+128 b^2\right) \coth (c+d x) \text{csch}(c+d x)}{256 d}-\frac{a^2 (21 a+80 b) \coth (c+d x) \text{csch}^5(c+d x)}{160 d}+\frac{a^2 (21 a+80 b) \coth (c+d x) \text{csch}^3(c+d x)}{128 d}-\frac{a^3 \coth (c+d x) \text{csch}^9(c+d x)}{10 d}+\frac{9 a^3 \coth (c+d x) \text{csch}^7(c+d x)}{80 d}+\frac{b^3 \cosh (c+d x)}{d}",1,"(3*a*(21*a^2 + 80*a*b + 128*b^2)*ArcTanh[Cosh[c + d*x]])/(256*d) + (b^3*Cosh[c + d*x])/d - (3*a*(21*a^2 + 80*a*b + 128*b^2)*Coth[c + d*x]*Csch[c + d*x])/(256*d) + (a^2*(21*a + 80*b)*Coth[c + d*x]*Csch[c + d*x]^3)/(128*d) - (a^2*(21*a + 80*b)*Coth[c + d*x]*Csch[c + d*x]^5)/(160*d) + (9*a^3*Coth[c + d*x]*Csch[c + d*x]^7)/(80*d) - (a^3*Coth[c + d*x]*Csch[c + d*x]^9)/(10*d)","A",8,5,23,0.2174,1,"{3215, 1157, 1814, 388, 206}"
216,1,220,0,0.3975894,"\int \text{csch}^{13}(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^13*(a + b*Sinh[c + d*x]^4)^3,x]","-\frac{\left(840 a^2 b+231 a^3+1152 a b^2+1024 b^3\right) \tanh ^{-1}(\cosh (c+d x))}{1024 d}-\frac{a \left(77 a^2+280 a b+384 b^2\right) \coth (c+d x) \text{csch}^3(c+d x)}{512 d}+\frac{3 a \left(77 a^2+280 a b+384 b^2\right) \coth (c+d x) \text{csch}(c+d x)}{1024 d}-\frac{3 a^2 (11 a+40 b) \coth (c+d x) \text{csch}^7(c+d x)}{320 d}+\frac{7 a^2 (11 a+40 b) \coth (c+d x) \text{csch}^5(c+d x)}{640 d}-\frac{a^3 \coth (c+d x) \text{csch}^{11}(c+d x)}{12 d}+\frac{11 a^3 \coth (c+d x) \text{csch}^9(c+d x)}{120 d}","-\frac{\left(840 a^2 b+231 a^3+1152 a b^2+1024 b^3\right) \tanh ^{-1}(\cosh (c+d x))}{1024 d}-\frac{a \left(77 a^2+280 a b+384 b^2\right) \coth (c+d x) \text{csch}^3(c+d x)}{512 d}+\frac{3 a \left(77 a^2+280 a b+384 b^2\right) \coth (c+d x) \text{csch}(c+d x)}{1024 d}-\frac{3 a^2 (11 a+40 b) \coth (c+d x) \text{csch}^7(c+d x)}{320 d}+\frac{7 a^2 (11 a+40 b) \coth (c+d x) \text{csch}^5(c+d x)}{640 d}-\frac{a^3 \coth (c+d x) \text{csch}^{11}(c+d x)}{12 d}+\frac{11 a^3 \coth (c+d x) \text{csch}^9(c+d x)}{120 d}",1,"-((231*a^3 + 840*a^2*b + 1152*a*b^2 + 1024*b^3)*ArcTanh[Cosh[c + d*x]])/(1024*d) + (3*a*(77*a^2 + 280*a*b + 384*b^2)*Coth[c + d*x]*Csch[c + d*x])/(1024*d) - (a*(77*a^2 + 280*a*b + 384*b^2)*Coth[c + d*x]*Csch[c + d*x]^3)/(512*d) + (7*a^2*(11*a + 40*b)*Coth[c + d*x]*Csch[c + d*x]^5)/(640*d) - (3*a^2*(11*a + 40*b)*Coth[c + d*x]*Csch[c + d*x]^7)/(320*d) + (11*a^3*Coth[c + d*x]*Csch[c + d*x]^9)/(120*d) - (a^3*Coth[c + d*x]*Csch[c + d*x]^11)/(12*d)","A",8,5,23,0.2174,1,"{3215, 1157, 1814, 385, 206}"
217,1,255,0,0.5570868,"\int \sinh ^2(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Sinh[c + d*x]^2*(a + b*Sinh[c + d*x]^4)^3,x]","\frac{b \left(1920 a^2+12312 a b+10579 b^2\right) \sinh (c+d x) \cosh ^5(c+d x)}{3840 d}-\frac{b \left(4992 a^2+10728 a b+5549 b^2\right) \sinh (c+d x) \cosh ^3(c+d x)}{3072 d}+\frac{\left(4224 a^2 b+1024 a^3+4632 a b^2+1619 b^3\right) \sinh (c+d x) \cosh (c+d x)}{2048 d}-\frac{x \left(1920 a^2 b+1024 a^3+1512 a b^2+429 b^3\right)}{2048}+\frac{b^2 (504 a+2593 b) \sinh (c+d x) \cosh ^9(c+d x)}{1680 d}-\frac{b^2 (6888 a+11821 b) \sinh (c+d x) \cosh ^7(c+d x)}{4480 d}+\frac{b^3 \sinh (c+d x) \cosh ^{13}(c+d x)}{14 d}-\frac{85 b^3 \sinh (c+d x) \cosh ^{11}(c+d x)}{168 d}","\frac{b \left(1920 a^2+12312 a b+10579 b^2\right) \sinh (c+d x) \cosh ^5(c+d x)}{3840 d}-\frac{b \left(4992 a^2+10728 a b+5549 b^2\right) \sinh (c+d x) \cosh ^3(c+d x)}{3072 d}+\frac{\left(4224 a^2 b+1024 a^3+4632 a b^2+1619 b^3\right) \sinh (c+d x) \cosh (c+d x)}{2048 d}-\frac{x \left(1920 a^2 b+1024 a^3+1512 a b^2+429 b^3\right)}{2048}+\frac{b^2 (504 a+2593 b) \sinh (c+d x) \cosh ^9(c+d x)}{1680 d}-\frac{b^2 (6888 a+11821 b) \sinh (c+d x) \cosh ^7(c+d x)}{4480 d}+\frac{b^3 \sinh (c+d x) \cosh ^{13}(c+d x)}{14 d}-\frac{85 b^3 \sinh (c+d x) \cosh ^{11}(c+d x)}{168 d}",1,"-((1024*a^3 + 1920*a^2*b + 1512*a*b^2 + 429*b^3)*x)/2048 + ((1024*a^3 + 4224*a^2*b + 4632*a*b^2 + 1619*b^3)*Cosh[c + d*x]*Sinh[c + d*x])/(2048*d) - (b*(4992*a^2 + 10728*a*b + 5549*b^2)*Cosh[c + d*x]^3*Sinh[c + d*x])/(3072*d) + (b*(1920*a^2 + 12312*a*b + 10579*b^2)*Cosh[c + d*x]^5*Sinh[c + d*x])/(3840*d) - (b^2*(6888*a + 11821*b)*Cosh[c + d*x]^7*Sinh[c + d*x])/(4480*d) + (b^2*(504*a + 2593*b)*Cosh[c + d*x]^9*Sinh[c + d*x])/(1680*d) - (85*b^3*Cosh[c + d*x]^11*Sinh[c + d*x])/(168*d) + (b^3*Cosh[c + d*x]^13*Sinh[c + d*x])/(14*d)","A",9,6,23,0.2609,1,"{3217, 1257, 1814, 1157, 385, 206}"
218,1,211,0,0.3868441,"\int \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[(a + b*Sinh[c + d*x]^4)^3,x]","\frac{b \left(1152 a^2+3912 a b+2279 b^2\right) \sinh (c+d x) \cosh ^3(c+d x)}{1536 d}-\frac{b \left(1920 a^2+2232 a b+793 b^2\right) \sinh (c+d x) \cosh (c+d x)}{1024 d}+\frac{x \left(1152 a^2 b+1024 a^3+840 a b^2+231 b^3\right)}{1024}+\frac{3 b^2 (40 a+139 b) \sinh (c+d x) \cosh ^7(c+d x)}{320 d}-\frac{b^2 (3000 a+3481 b) \sinh (c+d x) \cosh ^5(c+d x)}{1920 d}+\frac{b^3 \sinh (c+d x) \cosh ^{11}(c+d x)}{12 d}-\frac{61 b^3 \sinh (c+d x) \cosh ^9(c+d x)}{120 d}","\frac{b \left(1152 a^2+3912 a b+2279 b^2\right) \sinh (c+d x) \cosh ^3(c+d x)}{1536 d}-\frac{b \left(1920 a^2+2232 a b+793 b^2\right) \sinh (c+d x) \cosh (c+d x)}{1024 d}+\frac{x \left(1152 a^2 b+1024 a^3+840 a b^2+231 b^3\right)}{1024}+\frac{3 b^2 (40 a+139 b) \sinh (c+d x) \cosh ^7(c+d x)}{320 d}-\frac{b^2 (3000 a+3481 b) \sinh (c+d x) \cosh ^5(c+d x)}{1920 d}+\frac{b^3 \sinh (c+d x) \cosh ^{11}(c+d x)}{12 d}-\frac{61 b^3 \sinh (c+d x) \cosh ^9(c+d x)}{120 d}",1,"((1024*a^3 + 1152*a^2*b + 840*a*b^2 + 231*b^3)*x)/1024 - (b*(1920*a^2 + 2232*a*b + 793*b^2)*Cosh[c + d*x]*Sinh[c + d*x])/(1024*d) + (b*(1152*a^2 + 3912*a*b + 2279*b^2)*Cosh[c + d*x]^3*Sinh[c + d*x])/(1536*d) - (b^2*(3000*a + 3481*b)*Cosh[c + d*x]^5*Sinh[c + d*x])/(1920*d) + (3*b^2*(40*a + 139*b)*Cosh[c + d*x]^7*Sinh[c + d*x])/(320*d) - (61*b^3*Cosh[c + d*x]^9*Sinh[c + d*x])/(120*d) + (b^3*Cosh[c + d*x]^11*Sinh[c + d*x])/(12*d)","A",8,5,14,0.3571,1,"{3209, 1157, 1814, 385, 206}"
219,1,181,0,0.4381908,"\int \text{csch}^2(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^2*(a + b*Sinh[c + d*x]^4)^3,x]","\frac{b \left(384 a^2+528 a b+193 b^2\right) \sinh (c+d x) \cosh (c+d x)}{256 d}-\frac{3}{256} b x \left(128 a^2+80 a b+21 b^2\right)-\frac{a^3 \coth (c+d x)}{d}+\frac{b^2 (80 a+171 b) \sinh (c+d x) \cosh ^5(c+d x)}{160 d}-\frac{b^2 (208 a+149 b) \sinh (c+d x) \cosh ^3(c+d x)}{128 d}+\frac{b^3 \sinh (c+d x) \cosh ^9(c+d x)}{10 d}-\frac{41 b^3 \sinh (c+d x) \cosh ^7(c+d x)}{80 d}","\frac{b \left(384 a^2+528 a b+193 b^2\right) \sinh (c+d x) \cosh (c+d x)}{256 d}-\frac{3}{256} b x \left(128 a^2+80 a b+21 b^2\right)-\frac{a^3 \coth (c+d x)}{d}+\frac{b^2 (80 a+171 b) \sinh (c+d x) \cosh ^5(c+d x)}{160 d}-\frac{b^2 (208 a+149 b) \sinh (c+d x) \cosh ^3(c+d x)}{128 d}+\frac{b^3 \sinh (c+d x) \cosh ^9(c+d x)}{10 d}-\frac{41 b^3 \sinh (c+d x) \cosh ^7(c+d x)}{80 d}",1,"(-3*b*(128*a^2 + 80*a*b + 21*b^2)*x)/256 - (a^3*Coth[c + d*x])/d + (b*(384*a^2 + 528*a*b + 193*b^2)*Cosh[c + d*x]*Sinh[c + d*x])/(256*d) - (b^2*(208*a + 149*b)*Cosh[c + d*x]^3*Sinh[c + d*x])/(128*d) + (b^2*(80*a + 171*b)*Cosh[c + d*x]^5*Sinh[c + d*x])/(160*d) - (41*b^3*Cosh[c + d*x]^7*Sinh[c + d*x])/(80*d) + (b^3*Cosh[c + d*x]^9*Sinh[c + d*x])/(10*d)","A",8,5,23,0.2174,1,"{3217, 1259, 1805, 453, 206}"
220,1,161,0,0.3842837,"\int \text{csch}^4(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^4*(a + b*Sinh[c + d*x]^4)^3,x]","\frac{1}{128} b x \left(384 a^2+144 a b+35 b^2\right)-\frac{a^3 \coth ^3(c+d x)}{3 d}+\frac{a^3 \coth (c+d x)}{d}+\frac{b^2 (144 a+163 b) \sinh (c+d x) \cosh ^3(c+d x)}{192 d}-\frac{3 b^2 (80 a+31 b) \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{b^3 \sinh (c+d x) \cosh ^7(c+d x)}{8 d}-\frac{25 b^3 \sinh (c+d x) \cosh ^5(c+d x)}{48 d}","\frac{1}{128} b x \left(384 a^2+144 a b+35 b^2\right)-\frac{a^3 \coth ^3(c+d x)}{3 d}+\frac{a^3 \coth (c+d x)}{d}+\frac{b^2 (144 a+163 b) \sinh (c+d x) \cosh ^3(c+d x)}{192 d}-\frac{3 b^2 (80 a+31 b) \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{b^3 \sinh (c+d x) \cosh ^7(c+d x)}{8 d}-\frac{25 b^3 \sinh (c+d x) \cosh ^5(c+d x)}{48 d}",1,"(b*(384*a^2 + 144*a*b + 35*b^2)*x)/128 + (a^3*Coth[c + d*x])/d - (a^3*Coth[c + d*x]^3)/(3*d) - (3*b^2*(80*a + 31*b)*Cosh[c + d*x]*Sinh[c + d*x])/(128*d) + (b^2*(144*a + 163*b)*Cosh[c + d*x]^3*Sinh[c + d*x])/(192*d) - (25*b^3*Cosh[c + d*x]^5*Sinh[c + d*x])/(48*d) + (b^3*Cosh[c + d*x]^7*Sinh[c + d*x])/(8*d)","A",8,5,23,0.2174,1,"{3217, 1259, 1805, 1261, 207}"
221,1,148,0,0.3552555,"\int \text{csch}^6(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^6*(a + b*Sinh[c + d*x]^4)^3,x]","-\frac{a^2 (a+3 b) \coth (c+d x)}{d}-\frac{a^3 \coth ^5(c+d x)}{5 d}+\frac{2 a^3 \coth ^3(c+d x)}{3 d}+\frac{b^2 (24 a+11 b) \sinh (c+d x) \cosh (c+d x)}{16 d}-\frac{1}{16} b^2 x (24 a+5 b)+\frac{b^3 \sinh (c+d x) \cosh ^5(c+d x)}{6 d}-\frac{13 b^3 \sinh (c+d x) \cosh ^3(c+d x)}{24 d}","-\frac{a^2 (a+3 b) \coth (c+d x)}{d}-\frac{a^3 \coth ^5(c+d x)}{5 d}+\frac{2 a^3 \coth ^3(c+d x)}{3 d}+\frac{b^2 (24 a+11 b) \sinh (c+d x) \cosh (c+d x)}{16 d}-\frac{1}{16} b^2 x (24 a+5 b)+\frac{b^3 \sinh (c+d x) \cosh ^5(c+d x)}{6 d}-\frac{13 b^3 \sinh (c+d x) \cosh ^3(c+d x)}{24 d}",1,"-(b^2*(24*a + 5*b)*x)/16 - (a^2*(a + 3*b)*Coth[c + d*x])/d + (2*a^3*Coth[c + d*x]^3)/(3*d) - (a^3*Coth[c + d*x]^5)/(5*d) + (b^2*(24*a + 11*b)*Cosh[c + d*x]*Sinh[c + d*x])/(16*d) - (13*b^3*Cosh[c + d*x]^3*Sinh[c + d*x])/(24*d) + (b^3*Cosh[c + d*x]^5*Sinh[c + d*x])/(6*d)","A",7,5,23,0.2174,1,"{3217, 1259, 1805, 1802, 207}"
222,1,133,0,0.2888911,"\int \text{csch}^8(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^8*(a + b*Sinh[c + d*x]^4)^3,x]","-\frac{a^2 (a+b) \coth ^3(c+d x)}{d}+\frac{a^2 (a+3 b) \coth (c+d x)}{d}-\frac{a^3 \coth ^7(c+d x)}{7 d}+\frac{3 a^3 \coth ^5(c+d x)}{5 d}+\frac{3}{8} b^2 x (8 a+b)+\frac{b^3 \sinh (c+d x) \cosh ^3(c+d x)}{4 d}-\frac{5 b^3 \sinh (c+d x) \cosh (c+d x)}{8 d}","-\frac{a^2 (a+b) \coth ^3(c+d x)}{d}+\frac{a^2 (a+3 b) \coth (c+d x)}{d}-\frac{a^3 \coth ^7(c+d x)}{7 d}+\frac{3 a^3 \coth ^5(c+d x)}{5 d}+\frac{3}{8} b^2 x (8 a+b)+\frac{b^3 \sinh (c+d x) \cosh ^3(c+d x)}{4 d}-\frac{5 b^3 \sinh (c+d x) \cosh (c+d x)}{8 d}",1,"(3*b^2*(8*a + b)*x)/8 + (a^2*(a + 3*b)*Coth[c + d*x])/d - (a^2*(a + b)*Coth[c + d*x]^3)/d + (3*a^3*Coth[c + d*x]^5)/(5*d) - (a^3*Coth[c + d*x]^7)/(7*d) - (5*b^3*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (b^3*Cosh[c + d*x]^3*Sinh[c + d*x])/(4*d)","A",6,5,23,0.2174,1,"{3217, 1259, 1805, 1802, 207}"
223,1,140,0,0.2226522,"\int \text{csch}^{10}(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^10*(a + b*Sinh[c + d*x]^4)^3,x]","-\frac{a \left(a^2+3 a b+3 b^2\right) \coth (c+d x)}{d}-\frac{3 a^2 (2 a+b) \coth ^5(c+d x)}{5 d}+\frac{2 a^2 (2 a+3 b) \coth ^3(c+d x)}{3 d}-\frac{a^3 \coth ^9(c+d x)}{9 d}+\frac{4 a^3 \coth ^7(c+d x)}{7 d}+\frac{b^3 \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{b^3 x}{2}","-\frac{a \left(a^2+3 a b+3 b^2\right) \coth (c+d x)}{d}-\frac{3 a^2 (2 a+b) \coth ^5(c+d x)}{5 d}+\frac{2 a^2 (2 a+3 b) \coth ^3(c+d x)}{3 d}-\frac{a^3 \coth ^9(c+d x)}{9 d}+\frac{4 a^3 \coth ^7(c+d x)}{7 d}+\frac{b^3 \sinh (c+d x) \cosh (c+d x)}{2 d}-\frac{b^3 x}{2}",1,"-(b^3*x)/2 - (a*(a^2 + 3*a*b + 3*b^2)*Coth[c + d*x])/d + (2*a^2*(2*a + 3*b)*Coth[c + d*x]^3)/(3*d) - (3*a^2*(2*a + b)*Coth[c + d*x]^5)/(5*d) + (4*a^3*Coth[c + d*x]^7)/(7*d) - (a^3*Coth[c + d*x]^9)/(9*d) + (b^3*Cosh[c + d*x]*Sinh[c + d*x])/(2*d)","A",5,4,23,0.1739,1,"{3217, 1259, 1802, 207}"
224,1,147,0,0.1490971,"\int \text{csch}^{12}(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^12*(a + b*Sinh[c + d*x]^4)^3,x]","-\frac{a \left(5 a^2+9 a b+3 b^2\right) \coth ^3(c+d x)}{3 d}+\frac{a \left(a^2+3 a b+3 b^2\right) \coth (c+d x)}{d}-\frac{a^2 (10 a+3 b) \coth ^7(c+d x)}{7 d}+\frac{a^2 (10 a+9 b) \coth ^5(c+d x)}{5 d}-\frac{a^3 \coth ^{11}(c+d x)}{11 d}+\frac{5 a^3 \coth ^9(c+d x)}{9 d}+b^3 x","-\frac{a \left(5 a^2+9 a b+3 b^2\right) \coth ^3(c+d x)}{3 d}+\frac{a \left(a^2+3 a b+3 b^2\right) \coth (c+d x)}{d}-\frac{a^2 (10 a+3 b) \coth ^7(c+d x)}{7 d}+\frac{a^2 (10 a+9 b) \coth ^5(c+d x)}{5 d}-\frac{a^3 \coth ^{11}(c+d x)}{11 d}+\frac{5 a^3 \coth ^9(c+d x)}{9 d}+b^3 x",1,"b^3*x + (a*(a^2 + 3*a*b + 3*b^2)*Coth[c + d*x])/d - (a*(5*a^2 + 9*a*b + 3*b^2)*Coth[c + d*x]^3)/(3*d) + (a^2*(10*a + 9*b)*Coth[c + d*x]^5)/(5*d) - (a^2*(10*a + 3*b)*Coth[c + d*x]^7)/(7*d) + (5*a^3*Coth[c + d*x]^9)/(9*d) - (a^3*Coth[c + d*x]^11)/(11*d)","A",4,3,23,0.1304,1,"{3217, 1261, 207}"
225,1,144,0,0.1307759,"\int \text{csch}^{14}(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^14*(a + b*Sinh[c + d*x]^4)^3,x]","-\frac{a^2 (5 a+b) \coth ^9(c+d x)}{3 d}+\frac{4 a^2 (5 a+3 b) \coth ^7(c+d x)}{7 d}-\frac{a^3 \coth ^{13}(c+d x)}{13 d}+\frac{6 a^3 \coth ^{11}(c+d x)}{11 d}-\frac{3 a (a+b) (5 a+b) \coth ^5(c+d x)}{5 d}+\frac{2 a (a+b)^2 \coth ^3(c+d x)}{d}-\frac{(a+b)^3 \coth (c+d x)}{d}","-\frac{a^2 (5 a+b) \coth ^9(c+d x)}{3 d}+\frac{4 a^2 (5 a+3 b) \coth ^7(c+d x)}{7 d}-\frac{a^3 \coth ^{13}(c+d x)}{13 d}+\frac{6 a^3 \coth ^{11}(c+d x)}{11 d}-\frac{3 a (a+b) (5 a+b) \coth ^5(c+d x)}{5 d}+\frac{2 a (a+b)^2 \coth ^3(c+d x)}{d}-\frac{(a+b)^3 \coth (c+d x)}{d}",1,"-(((a + b)^3*Coth[c + d*x])/d) + (2*a*(a + b)^2*Coth[c + d*x]^3)/d - (3*a*(a + b)*(5*a + b)*Coth[c + d*x]^5)/(5*d) + (4*a^2*(5*a + 3*b)*Coth[c + d*x]^7)/(7*d) - (a^2*(5*a + b)*Coth[c + d*x]^9)/(3*d) + (6*a^3*Coth[c + d*x]^11)/(11*d) - (a^3*Coth[c + d*x]^13)/(13*d)","A",3,2,23,0.08696,1,"{3217, 1108}"
226,1,182,0,0.1588211,"\int \text{csch}^{16}(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^16*(a + b*Sinh[c + d*x]^4)^3,x]","-\frac{a \left(35 a^2+30 a b+3 b^2\right) \coth ^7(c+d x)}{7 d}-\frac{3 a^2 (7 a+b) \coth ^{11}(c+d x)}{11 d}+\frac{5 a^2 (7 a+3 b) \coth ^9(c+d x)}{9 d}-\frac{a^3 \coth ^{15}(c+d x)}{15 d}+\frac{7 a^3 \coth ^{13}(c+d x)}{13 d}+\frac{3 a (a+b) (7 a+3 b) \coth ^5(c+d x)}{5 d}-\frac{(a+b)^2 (7 a+b) \coth ^3(c+d x)}{3 d}+\frac{(a+b)^3 \coth (c+d x)}{d}","-\frac{a \left(35 a^2+30 a b+3 b^2\right) \coth ^7(c+d x)}{7 d}-\frac{3 a^2 (7 a+b) \coth ^{11}(c+d x)}{11 d}+\frac{5 a^2 (7 a+3 b) \coth ^9(c+d x)}{9 d}-\frac{a^3 \coth ^{15}(c+d x)}{15 d}+\frac{7 a^3 \coth ^{13}(c+d x)}{13 d}+\frac{3 a (a+b) (7 a+3 b) \coth ^5(c+d x)}{5 d}-\frac{(a+b)^2 (7 a+b) \coth ^3(c+d x)}{3 d}+\frac{(a+b)^3 \coth (c+d x)}{d}",1,"((a + b)^3*Coth[c + d*x])/d - ((a + b)^2*(7*a + b)*Coth[c + d*x]^3)/(3*d) + (3*a*(a + b)*(7*a + 3*b)*Coth[c + d*x]^5)/(5*d) - (a*(35*a^2 + 30*a*b + 3*b^2)*Coth[c + d*x]^7)/(7*d) + (5*a^2*(7*a + 3*b)*Coth[c + d*x]^9)/(9*d) - (3*a^2*(7*a + b)*Coth[c + d*x]^11)/(11*d) + (7*a^3*Coth[c + d*x]^13)/(13*d) - (a^3*Coth[c + d*x]^15)/(15*d)","A",3,2,23,0.08696,1,"{3217, 1261}"
227,1,221,0,0.1918169,"\int \text{csch}^{18}(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^18*(a + b*Sinh[c + d*x]^4)^3,x]","-\frac{a \left(70 a^2+45 a b+3 b^2\right) \coth ^9(c+d x)}{9 d}+\frac{4 a \left(14 a^2+15 a b+3 b^2\right) \coth ^7(c+d x)}{7 d}-\frac{(a+b) \left(28 a^2+17 a b+b^2\right) \coth ^5(c+d x)}{5 d}-\frac{a^2 (28 a+3 b) \coth ^{13}(c+d x)}{13 d}+\frac{2 a^2 (28 a+9 b) \coth ^{11}(c+d x)}{11 d}-\frac{a^3 \coth ^{17}(c+d x)}{17 d}+\frac{8 a^3 \coth ^{15}(c+d x)}{15 d}+\frac{2 (a+b)^2 (4 a+b) \coth ^3(c+d x)}{3 d}-\frac{(a+b)^3 \coth (c+d x)}{d}","-\frac{a \left(70 a^2+45 a b+3 b^2\right) \coth ^9(c+d x)}{9 d}+\frac{4 a \left(14 a^2+15 a b+3 b^2\right) \coth ^7(c+d x)}{7 d}-\frac{(a+b) \left(28 a^2+17 a b+b^2\right) \coth ^5(c+d x)}{5 d}-\frac{a^2 (28 a+3 b) \coth ^{13}(c+d x)}{13 d}+\frac{2 a^2 (28 a+9 b) \coth ^{11}(c+d x)}{11 d}-\frac{a^3 \coth ^{17}(c+d x)}{17 d}+\frac{8 a^3 \coth ^{15}(c+d x)}{15 d}+\frac{2 (a+b)^2 (4 a+b) \coth ^3(c+d x)}{3 d}-\frac{(a+b)^3 \coth (c+d x)}{d}",1,"-(((a + b)^3*Coth[c + d*x])/d) + (2*(a + b)^2*(4*a + b)*Coth[c + d*x]^3)/(3*d) - ((a + b)*(28*a^2 + 17*a*b + b^2)*Coth[c + d*x]^5)/(5*d) + (4*a*(14*a^2 + 15*a*b + 3*b^2)*Coth[c + d*x]^7)/(7*d) - (a*(70*a^2 + 45*a*b + 3*b^2)*Coth[c + d*x]^9)/(9*d) + (2*a^2*(28*a + 9*b)*Coth[c + d*x]^11)/(11*d) - (a^2*(28*a + 3*b)*Coth[c + d*x]^13)/(13*d) + (8*a^3*Coth[c + d*x]^15)/(15*d) - (a^3*Coth[c + d*x]^17)/(17*d)","A",3,2,23,0.08696,1,"{3217, 1261}"
228,1,248,0,0.2225218,"\int \text{csch}^{20}(c+d x) \left(a+b \sinh ^4(c+d x)\right)^3 \, dx","Int[Csch[c + d*x]^20*(a + b*Sinh[c + d*x]^4)^3,x]","-\frac{3 a \left(42 a^2+21 a b+b^2\right) \coth ^{11}(c+d x)}{11 d}+\frac{a \left(42 a^2+35 a b+5 b^2\right) \coth ^9(c+d x)}{3 d}-\frac{\left(105 a^2 b+84 a^3+30 a b^2+b^3\right) \coth ^7(c+d x)}{7 d}+\frac{3 (a+b) \left(12 a^2+9 a b+b^2\right) \coth ^5(c+d x)}{5 d}-\frac{a^2 (12 a+b) \coth ^{15}(c+d x)}{5 d}+\frac{21 a^2 (4 a+b) \coth ^{13}(c+d x)}{13 d}-\frac{a^3 \coth ^{19}(c+d x)}{19 d}+\frac{9 a^3 \coth ^{17}(c+d x)}{17 d}-\frac{(a+b)^2 (3 a+b) \coth ^3(c+d x)}{d}+\frac{(a+b)^3 \coth (c+d x)}{d}","-\frac{3 a \left(42 a^2+21 a b+b^2\right) \coth ^{11}(c+d x)}{11 d}+\frac{a \left(42 a^2+35 a b+5 b^2\right) \coth ^9(c+d x)}{3 d}-\frac{\left(105 a^2 b+84 a^3+30 a b^2+b^3\right) \coth ^7(c+d x)}{7 d}+\frac{3 (a+b) \left(12 a^2+9 a b+b^2\right) \coth ^5(c+d x)}{5 d}-\frac{a^2 (12 a+b) \coth ^{15}(c+d x)}{5 d}+\frac{21 a^2 (4 a+b) \coth ^{13}(c+d x)}{13 d}-\frac{a^3 \coth ^{19}(c+d x)}{19 d}+\frac{9 a^3 \coth ^{17}(c+d x)}{17 d}-\frac{(a+b)^2 (3 a+b) \coth ^3(c+d x)}{d}+\frac{(a+b)^3 \coth (c+d x)}{d}",1,"((a + b)^3*Coth[c + d*x])/d - ((a + b)^2*(3*a + b)*Coth[c + d*x]^3)/d + (3*(a + b)*(12*a^2 + 9*a*b + b^2)*Coth[c + d*x]^5)/(5*d) - ((84*a^3 + 105*a^2*b + 30*a*b^2 + b^3)*Coth[c + d*x]^7)/(7*d) + (a*(42*a^2 + 35*a*b + 5*b^2)*Coth[c + d*x]^9)/(3*d) - (3*a*(42*a^2 + 21*a*b + b^2)*Coth[c + d*x]^11)/(11*d) + (21*a^2*(4*a + b)*Coth[c + d*x]^13)/(13*d) - (a^2*(12*a + b)*Coth[c + d*x]^15)/(5*d) + (9*a^3*Coth[c + d*x]^17)/(17*d) - (a^3*Coth[c + d*x]^19)/(19*d)","A",3,2,23,0.08696,1,"{3217, 1261}"
229,1,148,0,0.2540649,"\int \frac{\sinh ^7(c+d x)}{a-b \sinh ^4(c+d x)} \, dx","Int[Sinh[c + d*x]^7/(a - b*Sinh[c + d*x]^4),x]","-\frac{a \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 b^{7/4} d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{a \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 b^{7/4} d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{\cosh ^3(c+d x)}{3 b d}+\frac{\cosh (c+d x)}{b d}","-\frac{a \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 b^{7/4} d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{a \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 b^{7/4} d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{\cosh ^3(c+d x)}{3 b d}+\frac{\cosh (c+d x)}{b d}",1,"-(a*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(2*Sqrt[Sqrt[a] - Sqrt[b]]*b^(7/4)*d) + (a*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(2*Sqrt[Sqrt[a] + Sqrt[b]]*b^(7/4)*d) + Cosh[c + d*x]/(b*d) - Cosh[c + d*x]^3/(3*b*d)","A",6,5,24,0.2083,1,"{3215, 1170, 1166, 205, 208}"
230,1,139,0,0.1975991,"\int \frac{\sinh ^5(c+d x)}{a-b \sinh ^4(c+d x)} \, dx","Int[Sinh[c + d*x]^5/(a - b*Sinh[c + d*x]^4),x]","\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 b^{5/4} d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 b^{5/4} d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{\cosh (c+d x)}{b d}","\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 b^{5/4} d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 b^{5/4} d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{\cosh (c+d x)}{b d}",1,"(Sqrt[a]*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(2*Sqrt[Sqrt[a] - Sqrt[b]]*b^(5/4)*d) + (Sqrt[a]*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(2*Sqrt[Sqrt[a] + Sqrt[b]]*b^(5/4)*d) - Cosh[c + d*x]/(b*d)","A",6,5,24,0.2083,1,"{3215, 1170, 1093, 205, 208}"
231,1,115,0,0.1146158,"\int \frac{\sinh ^3(c+d x)}{a-b \sinh ^4(c+d x)} \, dx","Int[Sinh[c + d*x]^3/(a - b*Sinh[c + d*x]^4),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 b^{3/4} d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 b^{3/4} d \sqrt{\sqrt{a}-\sqrt{b}}}","\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 b^{3/4} d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 b^{3/4} d \sqrt{\sqrt{a}-\sqrt{b}}}",1,"-ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]]/(2*Sqrt[Sqrt[a] - Sqrt[b]]*b^(3/4)*d) + ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]]/(2*Sqrt[Sqrt[a] + Sqrt[b]]*b^(3/4)*d)","A",4,4,24,0.1667,1,"{3215, 1166, 205, 208}"
232,1,125,0,0.1035331,"\int \frac{\sinh (c+d x)}{a-b \sinh ^4(c+d x)} \, dx","Int[Sinh[c + d*x]/(a - b*Sinh[c + d*x]^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 \sqrt{a} \sqrt[4]{b} d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 \sqrt{a} \sqrt[4]{b} d \sqrt{\sqrt{a}+\sqrt{b}}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 \sqrt{a} \sqrt[4]{b} d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 \sqrt{a} \sqrt[4]{b} d \sqrt{\sqrt{a}+\sqrt{b}}}",1,"ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]]/(2*Sqrt[a]*Sqrt[Sqrt[a] - Sqrt[b]]*b^(1/4)*d) + ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]]/(2*Sqrt[a]*Sqrt[Sqrt[a] + Sqrt[b]]*b^(1/4)*d)","A",4,4,22,0.1818,1,"{3215, 1093, 205, 208}"
233,1,136,0,0.1630841,"\int \frac{\text{csch}(c+d x)}{a-b \sinh ^4(c+d x)} \, dx","Int[Csch[c + d*x]/(a - b*Sinh[c + d*x]^4),x]","-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 a d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{\sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 a d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a d}","-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 a d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{\sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 a d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a d}",1,"-(b^(1/4)*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(2*a*Sqrt[Sqrt[a] - Sqrt[b]]*d) - ArcTanh[Cosh[c + d*x]]/(a*d) + (b^(1/4)*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(2*a*Sqrt[Sqrt[a] + Sqrt[b]]*d)","A",7,6,22,0.2727,1,"{3215, 1170, 207, 1166, 205, 208}"
234,1,184,0,0.2007354,"\int \frac{\text{csch}^3(c+d x)}{a-b \sinh ^4(c+d x)} \, dx","Int[Csch[c + d*x]^3/(a - b*Sinh[c + d*x]^4),x]","\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 a^{3/2} d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 a^{3/2} d \sqrt{\sqrt{a}+\sqrt{b}}}+\frac{1}{4 a d (1-\cosh (c+d x))}-\frac{1}{4 a d (\cosh (c+d x)+1)}+\frac{\tanh ^{-1}(\cosh (c+d x))}{2 a d}","\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 a^{3/2} d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{b^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 a^{3/2} d \sqrt{\sqrt{a}+\sqrt{b}}}+\frac{1}{4 a d (1-\cosh (c+d x))}-\frac{1}{4 a d (\cosh (c+d x)+1)}+\frac{\tanh ^{-1}(\cosh (c+d x))}{2 a d}",1,"(b^(3/4)*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(2*a^(3/2)*Sqrt[Sqrt[a] - Sqrt[b]]*d) + ArcTanh[Cosh[c + d*x]]/(2*a*d) + (b^(3/4)*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(2*a^(3/2)*Sqrt[Sqrt[a] + Sqrt[b]]*d) + 1/(4*a*d*(1 - Cosh[c + d*x])) - 1/(4*a*d*(1 + Cosh[c + d*x]))","A",7,6,24,0.2500,1,"{3215, 1170, 207, 1093, 205, 208}"
235,1,175,0,0.2580262,"\int \frac{\sinh ^6(c+d x)}{a-b \sinh ^4(c+d x)} \, dx","Int[Sinh[c + d*x]^6/(a - b*Sinh[c + d*x]^4),x]","-\frac{a^{3/4} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 b^{3/2} d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{a^{3/4} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 b^{3/2} d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{1}{4 b d (1-\tanh (c+d x))}+\frac{1}{4 b d (\tanh (c+d x)+1)}+\frac{x}{2 b}","-\frac{a^{3/4} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 b^{3/2} d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{a^{3/4} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 b^{3/2} d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{1}{4 b d (1-\tanh (c+d x))}+\frac{1}{4 b d (\tanh (c+d x)+1)}+\frac{x}{2 b}",1,"x/(2*b) - (a^(3/4)*ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(2*Sqrt[Sqrt[a] - Sqrt[b]]*b^(3/2)*d) + (a^(3/4)*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(2*Sqrt[Sqrt[a] + Sqrt[b]]*b^(3/2)*d) - 1/(4*b*d*(1 - Tanh[c + d*x])) + 1/(4*b*d*(1 + Tanh[c + d*x]))","A",7,5,24,0.2083,1,"{3217, 1287, 207, 1130, 208}"
236,1,127,0,0.2063368,"\int \frac{\sinh ^4(c+d x)}{a-b \sinh ^4(c+d x)} \, dx","Int[Sinh[c + d*x]^4/(a - b*Sinh[c + d*x]^4),x]","\frac{\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 b d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 b d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{x}{b}","\frac{\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 b d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 b d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{x}{b}",1,"-(x/b) + (a^(1/4)*ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(2*Sqrt[Sqrt[a] - Sqrt[b]]*b*d) + (a^(1/4)*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(2*Sqrt[Sqrt[a] + Sqrt[b]]*b*d)","A",7,5,24,0.2083,1,"{3217, 1287, 207, 1166, 208}"
237,1,125,0,0.1206259,"\int \frac{\sinh ^2(c+d x)}{a-b \sinh ^4(c+d x)} \, dx","Int[Sinh[c + d*x]^2/(a - b*Sinh[c + d*x]^4),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt[4]{a} \sqrt{b} d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt[4]{a} \sqrt{b} d \sqrt{\sqrt{a}-\sqrt{b}}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt[4]{a} \sqrt{b} d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 \sqrt[4]{a} \sqrt{b} d \sqrt{\sqrt{a}-\sqrt{b}}}",1,"-ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)]/(2*a^(1/4)*Sqrt[Sqrt[a] - Sqrt[b]]*Sqrt[b]*d) + ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)]/(2*a^(1/4)*Sqrt[Sqrt[a] + Sqrt[b]]*Sqrt[b]*d)","A",4,3,24,0.1250,1,"{3217, 1130, 208}"
238,1,115,0,0.0976941,"\int \frac{1}{a-b \sinh ^4(c+d x)} \, dx","Int[(a - b*Sinh[c + d*x]^4)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 a^{3/4} d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 a^{3/4} d \sqrt{\sqrt{a}+\sqrt{b}}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 a^{3/4} d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 a^{3/4} d \sqrt{\sqrt{a}+\sqrt{b}}}",1,"ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)]/(2*a^(3/4)*Sqrt[Sqrt[a] - Sqrt[b]]*d) + ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)]/(2*a^(3/4)*Sqrt[Sqrt[a] + Sqrt[b]]*d)","A",4,3,15,0.2000,1,"{3209, 1166, 208}"
239,1,139,0,0.1813583,"\int \frac{\text{csch}^2(c+d x)}{a-b \sinh ^4(c+d x)} \, dx","Int[Csch[c + d*x]^2/(a - b*Sinh[c + d*x]^4),x]","-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 a^{5/4} d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 a^{5/4} d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{\coth (c+d x)}{a d}","-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 a^{5/4} d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 a^{5/4} d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{\coth (c+d x)}{a d}",1,"-(Sqrt[b]*ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(2*a^(5/4)*Sqrt[Sqrt[a] - Sqrt[b]]*d) + (Sqrt[b]*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(2*a^(5/4)*Sqrt[Sqrt[a] + Sqrt[b]]*d) - Coth[c + d*x]/(a*d)","A",6,4,24,0.1667,1,"{3217, 1287, 1130, 208}"
240,1,148,0,0.2112681,"\int \frac{\text{csch}^4(c+d x)}{a-b \sinh ^4(c+d x)} \, dx","Int[Csch[c + d*x]^4/(a - b*Sinh[c + d*x]^4),x]","\frac{b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 a^{7/4} d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 a^{7/4} d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{\coth ^3(c+d x)}{3 a d}+\frac{\coth (c+d x)}{a d}","\frac{b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 a^{7/4} d \sqrt{\sqrt{a}-\sqrt{b}}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 a^{7/4} d \sqrt{\sqrt{a}+\sqrt{b}}}-\frac{\coth ^3(c+d x)}{3 a d}+\frac{\coth (c+d x)}{a d}",1,"(b*ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(2*a^(7/4)*Sqrt[Sqrt[a] - Sqrt[b]]*d) + (b*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(2*a^(7/4)*Sqrt[Sqrt[a] + Sqrt[b]]*d) + Coth[c + d*x]/(a*d) - Coth[c + d*x]^3/(3*a*d)","A",6,4,24,0.1667,1,"{3217, 1287, 1166, 208}"
241,1,235,0,0.4858678,"\int \frac{\sinh ^9(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^9/(a - b*Sinh[c + d*x]^4)^2,x]","\frac{a \cosh (c+d x) \left(a-b \cosh ^2(c+d x)+b\right)}{4 b^2 d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}-\frac{\sqrt{a} \left(5 \sqrt{a}-6 \sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{8 b^{9/4} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}-\frac{\sqrt{a} \left(5 \sqrt{a}+6 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{8 b^{9/4} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}+\frac{\cosh (c+d x)}{b^2 d}","\frac{a \cosh (c+d x) \left(a-b \cosh ^2(c+d x)+b\right)}{4 b^2 d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}-\frac{\sqrt{a} \left(5 \sqrt{a}-6 \sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{8 b^{9/4} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}-\frac{\sqrt{a} \left(5 \sqrt{a}+6 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{8 b^{9/4} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}+\frac{\cosh (c+d x)}{b^2 d}",1,"-(Sqrt[a]*(5*Sqrt[a] - 6*Sqrt[b])*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(8*(Sqrt[a] - Sqrt[b])^(3/2)*b^(9/4)*d) - (Sqrt[a]*(5*Sqrt[a] + 6*Sqrt[b])*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(8*(Sqrt[a] + Sqrt[b])^(3/2)*b^(9/4)*d) + Cosh[c + d*x]/(b^2*d) + (a*Cosh[c + d*x]*(a + b - b*Cosh[c + d*x]^2))/(4*(a - b)*b^2*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4))","A",7,6,24,0.2500,1,"{3215, 1205, 1676, 1166, 205, 208}"
242,1,210,0,0.3704623,"\int \frac{\sinh ^7(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^7/(a - b*Sinh[c + d*x]^4)^2,x]","\frac{\left(3 \sqrt{a}-4 \sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{8 b^{7/4} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}-\frac{\left(3 \sqrt{a}+4 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{8 b^{7/4} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}-\frac{a \cosh (c+d x) \left(2-\cosh ^2(c+d x)\right)}{4 b d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}","\frac{\left(3 \sqrt{a}-4 \sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{8 b^{7/4} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}-\frac{\left(3 \sqrt{a}+4 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{8 b^{7/4} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}-\frac{a \cosh (c+d x) \left(2-\cosh ^2(c+d x)\right)}{4 b d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}",1,"((3*Sqrt[a] - 4*Sqrt[b])*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(8*(Sqrt[a] - Sqrt[b])^(3/2)*b^(7/4)*d) - ((3*Sqrt[a] + 4*Sqrt[b])*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(8*(Sqrt[a] + Sqrt[b])^(3/2)*b^(7/4)*d) - (a*Cosh[c + d*x]*(2 - Cosh[c + d*x]^2))/(4*(a - b)*b*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4))","A",5,5,24,0.2083,1,"{3215, 1205, 1166, 205, 208}"
243,1,217,0,0.2943867,"\int \frac{\sinh ^5(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^5/(a - b*Sinh[c + d*x]^4)^2,x]","-\frac{\left(\sqrt{a}-2 \sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{8 \sqrt{a} b^{5/4} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}-\frac{\left(\sqrt{a}+2 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{8 \sqrt{a} b^{5/4} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}+\frac{\cosh (c+d x) \left(a-b \cosh ^2(c+d x)+b\right)}{4 b d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}","-\frac{\left(\sqrt{a}-2 \sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{8 \sqrt{a} b^{5/4} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}-\frac{\left(\sqrt{a}+2 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{8 \sqrt{a} b^{5/4} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}+\frac{\cosh (c+d x) \left(a-b \cosh ^2(c+d x)+b\right)}{4 b d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}",1,"-((Sqrt[a] - 2*Sqrt[b])*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(8*Sqrt[a]*(Sqrt[a] - Sqrt[b])^(3/2)*b^(5/4)*d) - ((Sqrt[a] + 2*Sqrt[b])*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(8*Sqrt[a]*(Sqrt[a] + Sqrt[b])^(3/2)*b^(5/4)*d) + (Cosh[c + d*x]*(a + b - b*Cosh[c + d*x]^2))/(4*(a - b)*b*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4))","A",5,5,24,0.2083,1,"{3215, 1205, 1166, 205, 208}"
244,1,186,0,0.2052109,"\int \frac{\sinh ^3(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^3/(a - b*Sinh[c + d*x]^4)^2,x]","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{8 \sqrt{a} b^{3/4} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{8 \sqrt{a} b^{3/4} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}-\frac{\cosh (c+d x) \left(2-\cosh ^2(c+d x)\right)}{4 d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}","-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{8 \sqrt{a} b^{3/4} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{8 \sqrt{a} b^{3/4} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}-\frac{\cosh (c+d x) \left(2-\cosh ^2(c+d x)\right)}{4 d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}",1,"-ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]]/(8*Sqrt[a]*(Sqrt[a] - Sqrt[b])^(3/2)*b^(3/4)*d) + ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]]/(8*Sqrt[a]*(Sqrt[a] + Sqrt[b])^(3/2)*b^(3/4)*d) - (Cosh[c + d*x]*(2 - Cosh[c + d*x]^2))/(4*(a - b)*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4))","A",5,5,24,0.2083,1,"{3215, 1178, 1166, 205, 208}"
245,1,221,0,0.298505,"\int \frac{\sinh (c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]/(a - b*Sinh[c + d*x]^4)^2,x]","\frac{\left(3 \sqrt{a}-2 \sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{8 a^{3/2} \sqrt[4]{b} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}+\frac{\left(3 \sqrt{a}+2 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{8 a^{3/2} \sqrt[4]{b} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}+\frac{\cosh (c+d x) \left(a-b \cosh ^2(c+d x)+b\right)}{4 a d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}","\frac{\left(3 \sqrt{a}-2 \sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{8 a^{3/2} \sqrt[4]{b} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}+\frac{\left(3 \sqrt{a}+2 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{8 a^{3/2} \sqrt[4]{b} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}+\frac{\cosh (c+d x) \left(a-b \cosh ^2(c+d x)+b\right)}{4 a d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}",1,"((3*Sqrt[a] - 2*Sqrt[b])*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(8*a^(3/2)*(Sqrt[a] - Sqrt[b])^(3/2)*b^(1/4)*d) + ((3*Sqrt[a] + 2*Sqrt[b])*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(8*a^(3/2)*(Sqrt[a] + Sqrt[b])^(3/2)*b^(1/4)*d) + (Cosh[c + d*x]*(a + b - b*Cosh[c + d*x]^2))/(4*a*(a - b)*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4))","A",5,5,22,0.2273,1,"{3215, 1092, 1166, 205, 208}"
246,1,325,0,0.3614047,"\int \frac{\text{csch}(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^2} \, dx","Int[Csch[c + d*x]/(a - b*Sinh[c + d*x]^4)^2,x]","-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 a^2 d \sqrt{\sqrt{a}-\sqrt{b}}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{8 a^{3/2} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}+\frac{\sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 a^2 d \sqrt{\sqrt{a}+\sqrt{b}}}+\frac{\sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{8 a^{3/2} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a^2 d}-\frac{b \cosh (c+d x) \left(2-\cosh ^2(c+d x)\right)}{4 a d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}","-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 a^2 d \sqrt{\sqrt{a}-\sqrt{b}}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{8 a^{3/2} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}+\frac{\sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 a^2 d \sqrt{\sqrt{a}+\sqrt{b}}}+\frac{\sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{8 a^{3/2} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a^2 d}-\frac{b \cosh (c+d x) \left(2-\cosh ^2(c+d x)\right)}{4 a d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}",1,"-(b^(1/4)*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(8*a^(3/2)*(Sqrt[a] - Sqrt[b])^(3/2)*d) - (b^(1/4)*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(2*a^2*Sqrt[Sqrt[a] - Sqrt[b]]*d) - ArcTanh[Cosh[c + d*x]]/(a^2*d) + (b^(1/4)*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(8*a^(3/2)*(Sqrt[a] + Sqrt[b])^(3/2)*d) + (b^(1/4)*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(2*a^2*Sqrt[Sqrt[a] + Sqrt[b]]*d) - (b*Cosh[c + d*x]*(2 - Cosh[c + d*x]^2))/(4*a*(a - b)*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4))","A",11,7,22,0.3182,1,"{3215, 1238, 207, 1178, 1166, 205, 208}"
247,1,320,0,0.4611756,"\int \frac{\sinh ^8(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^8/(a - b*Sinh[c + d*x]^4)^2,x]","\frac{\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 b^{3/2} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}-\frac{\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 b^2 d \sqrt{\sqrt{a}-\sqrt{b}}}-\frac{\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 b^{3/2} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}-\frac{\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 b^2 d \sqrt{\sqrt{a}+\sqrt{b}}}+\frac{\tanh ^5(c+d x)}{4 b d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}-\frac{\tanh (c+d x)}{4 b d (a-b)}+\frac{x}{b^2}","\frac{\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 b^{3/2} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}-\frac{\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 b^2 d \sqrt{\sqrt{a}-\sqrt{b}}}-\frac{\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 b^{3/2} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}-\frac{\sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{2 b^2 d \sqrt{\sqrt{a}+\sqrt{b}}}+\frac{\tanh ^5(c+d x)}{4 b d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}-\frac{\tanh (c+d x)}{4 b d (a-b)}+\frac{x}{b^2}",1,"x/b^2 - (a^(1/4)*ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(2*Sqrt[Sqrt[a] - Sqrt[b]]*b^2*d) + (a^(1/4)*ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(8*(Sqrt[a] - Sqrt[b])^(3/2)*b^(3/2)*d) - (a^(1/4)*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(2*Sqrt[Sqrt[a] + Sqrt[b]]*b^2*d) - (a^(1/4)*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(8*(Sqrt[a] + Sqrt[b])^(3/2)*b^(3/2)*d) - Tanh[c + d*x]/(4*(a - b)*b*d) + Tanh[c + d*x]^5/(4*b*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4))","A",14,9,24,0.3750,1,"{3217, 1313, 1275, 12, 1122, 1166, 208, 1287, 207}"
248,1,233,0,0.3377976,"\int \frac{\sinh ^6(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^6/(a - b*Sinh[c + d*x]^4)^2,x]","\frac{\left(2 \sqrt{a}-3 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 \sqrt[4]{a} b^{3/2} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}-\frac{\left(2 \sqrt{a}+3 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 \sqrt[4]{a} b^{3/2} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}+\frac{\tanh (c+d x)}{4 b d (a-b)}+\frac{\tanh ^3(c+d x) \text{sech}^2(c+d x)}{4 b d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}","\frac{\left(2 \sqrt{a}-3 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 \sqrt[4]{a} b^{3/2} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}-\frac{\left(2 \sqrt{a}+3 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 \sqrt[4]{a} b^{3/2} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}+\frac{\tanh (c+d x)}{4 b d (a-b)}+\frac{\tanh ^3(c+d x) \text{sech}^2(c+d x)}{4 b d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}",1,"((2*Sqrt[a] - 3*Sqrt[b])*ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(8*a^(1/4)*(Sqrt[a] - Sqrt[b])^(3/2)*b^(3/2)*d) - ((2*Sqrt[a] + 3*Sqrt[b])*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(8*a^(1/4)*(Sqrt[a] + Sqrt[b])^(3/2)*b^(3/2)*d) + Tanh[c + d*x]/(4*(a - b)*b*d) + (Sech[c + d*x]^2*Tanh[c + d*x]^3)/(4*b*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4))","A",6,5,24,0.2083,1,"{3217, 1120, 1279, 1166, 208}"
249,1,195,0,0.2485144,"\int \frac{\sinh ^4(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^4/(a - b*Sinh[c + d*x]^4)^2,x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 a^{3/4} \sqrt{b} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 a^{3/4} \sqrt{b} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}+\frac{\tanh ^5(c+d x)}{4 a d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}-\frac{\tanh (c+d x)}{4 a d (a-b)}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 a^{3/4} \sqrt{b} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 a^{3/4} \sqrt{b} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}+\frac{\tanh ^5(c+d x)}{4 a d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}-\frac{\tanh (c+d x)}{4 a d (a-b)}",1,"ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)]/(8*a^(3/4)*(Sqrt[a] - Sqrt[b])^(3/2)*Sqrt[b]*d) - ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)]/(8*a^(3/4)*(Sqrt[a] + Sqrt[b])^(3/2)*Sqrt[b]*d) - Tanh[c + d*x]/(4*a*(a - b)*d) + Tanh[c + d*x]^5/(4*a*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4))","A",7,6,24,0.2500,1,"{3217, 1275, 12, 1122, 1166, 208}"
250,1,220,0,0.2976209,"\int \frac{\sinh ^2(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^2} \, dx","Int[Sinh[c + d*x]^2/(a - b*Sinh[c + d*x]^4)^2,x]","-\frac{\left(2 \sqrt{a}-\sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 a^{5/4} \sqrt{b} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}+\frac{\left(2 \sqrt{a}+\sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 a^{5/4} \sqrt{b} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}+\frac{\tanh (c+d x) \left(a-(a+b) \tanh ^2(c+d x)\right)}{4 a d (a-b) \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}","-\frac{\left(2 \sqrt{a}-\sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 a^{5/4} \sqrt{b} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}+\frac{\left(2 \sqrt{a}+\sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 a^{5/4} \sqrt{b} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}+\frac{\tanh (c+d x) \left(a-(a+b) \tanh ^2(c+d x)\right)}{4 a d (a-b) \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}",1,"-((2*Sqrt[a] - Sqrt[b])*ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(8*a^(5/4)*(Sqrt[a] - Sqrt[b])^(3/2)*Sqrt[b]*d) + ((2*Sqrt[a] + Sqrt[b])*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(8*a^(5/4)*(Sqrt[a] + Sqrt[b])^(3/2)*Sqrt[b]*d) + (Tanh[c + d*x]*(a - (a + b)*Tanh[c + d*x]^2))/(4*a*(a - b)*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4))","A",5,4,24,0.1667,1,"{3217, 1333, 1166, 208}"
251,1,210,0,0.2460259,"\int \frac{1}{\left(a-b \sinh ^4(c+d x)\right)^2} \, dx","Int[(a - b*Sinh[c + d*x]^4)^(-2),x]","\frac{\left(4 \sqrt{a}-3 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 a^{7/4} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}+\frac{\left(4 \sqrt{a}+3 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 a^{7/4} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}-\frac{b \tanh (c+d x) \left(1-2 \tanh ^2(c+d x)\right)}{4 a d (a-b) \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}","\frac{\left(4 \sqrt{a}-3 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 a^{7/4} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}+\frac{\left(4 \sqrt{a}+3 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 a^{7/4} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}-\frac{b \tanh (c+d x) \left(1-2 \tanh ^2(c+d x)\right)}{4 a d (a-b) \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}",1,"((4*Sqrt[a] - 3*Sqrt[b])*ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(8*a^(7/4)*(Sqrt[a] - Sqrt[b])^(3/2)*d) + ((4*Sqrt[a] + 3*Sqrt[b])*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(8*a^(7/4)*(Sqrt[a] + Sqrt[b])^(3/2)*d) - (b*Tanh[c + d*x]*(1 - 2*Tanh[c + d*x]^2))/(4*a*(a - b)*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4))","A",5,4,15,0.2667,1,"{3209, 1205, 1166, 208}"
252,1,237,0,0.533692,"\int \frac{\text{csch}^2(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^2} \, dx","Int[Csch[c + d*x]^2/(a - b*Sinh[c + d*x]^4)^2,x]","-\frac{\sqrt{b} \left(6 \sqrt{a}-5 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 a^{9/4} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}+\frac{\sqrt{b} \left(6 \sqrt{a}+5 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 a^{9/4} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}+\frac{b \tanh (c+d x) \left(a-(a+b) \tanh ^2(c+d x)\right)}{4 a^2 d (a-b) \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}-\frac{\coth (c+d x)}{a^2 d}","-\frac{\sqrt{b} \left(6 \sqrt{a}-5 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 a^{9/4} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}+\frac{\sqrt{b} \left(6 \sqrt{a}+5 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{8 a^{9/4} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}+\frac{b \tanh (c+d x) \left(a-(a+b) \tanh ^2(c+d x)\right)}{4 a^2 d (a-b) \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}-\frac{\coth (c+d x)}{a^2 d}",1,"-((6*Sqrt[a] - 5*Sqrt[b])*Sqrt[b]*ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(8*a^(9/4)*(Sqrt[a] - Sqrt[b])^(3/2)*d) + ((6*Sqrt[a] + 5*Sqrt[b])*Sqrt[b]*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(8*a^(9/4)*(Sqrt[a] + Sqrt[b])^(3/2)*d) - Coth[c + d*x]/(a^2*d) + (b*Tanh[c + d*x]*(a - (a + b)*Tanh[c + d*x]^2))/(4*a^2*(a - b)*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4))","A",7,5,24,0.2083,1,"{3217, 1334, 1664, 1166, 208}"
253,1,315,0,0.5773577,"\int \frac{\sinh ^9(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^9/(a - b*Sinh[c + d*x]^4)^3,x]","-\frac{\cosh (c+d x) \left(9 a^2-2 b (2 a-5 b) \cosh ^2(c+d x)-11 a b-10 b^2\right)}{32 b^2 d (a-b)^2 \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}+\frac{a \cosh (c+d x) \left(a-b \cosh ^2(c+d x)+b\right)}{8 b^2 d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)^2}+\frac{\left(-14 \sqrt{a} \sqrt{b}+5 a+12 b\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{64 \sqrt{a} b^{9/4} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}+\frac{\left(14 \sqrt{a} \sqrt{b}+5 a+12 b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{64 \sqrt{a} b^{9/4} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}","-\frac{\cosh (c+d x) \left(9 a^2-2 b (2 a-5 b) \cosh ^2(c+d x)-11 a b-10 b^2\right)}{32 b^2 d (a-b)^2 \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}+\frac{a \cosh (c+d x) \left(a-b \cosh ^2(c+d x)+b\right)}{8 b^2 d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)^2}+\frac{\left(-14 \sqrt{a} \sqrt{b}+5 a+12 b\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{64 \sqrt{a} b^{9/4} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}+\frac{\left(14 \sqrt{a} \sqrt{b}+5 a+12 b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{64 \sqrt{a} b^{9/4} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}",1,"((5*a - 14*Sqrt[a]*Sqrt[b] + 12*b)*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(64*Sqrt[a]*(Sqrt[a] - Sqrt[b])^(5/2)*b^(9/4)*d) + ((5*a + 14*Sqrt[a]*Sqrt[b] + 12*b)*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(64*Sqrt[a]*(Sqrt[a] + Sqrt[b])^(5/2)*b^(9/4)*d) + (a*Cosh[c + d*x]*(a + b - b*Cosh[c + d*x]^2))/(8*(a - b)*b^2*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4)^2) - (Cosh[c + d*x]*(9*a^2 - 11*a*b - 10*b^2 - 2*(2*a - 5*b)*b*Cosh[c + d*x]^2))/(32*(a - b)^2*b^2*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4))","A",6,6,24,0.2500,1,"{3215, 1205, 1678, 1166, 205, 208}"
254,1,290,0,0.4671146,"\int \frac{\sinh ^7(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^7/(a - b*Sinh[c + d*x]^4)^3,x]","\frac{3 \left(\sqrt{a}-2 \sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{64 \sqrt{a} b^{7/4} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}-\frac{3 \left(\sqrt{a}+2 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{64 \sqrt{a} b^{7/4} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}+\frac{\cosh (c+d x) \left(-3 (a-3 b) \cosh ^2(c+d x)+5 a-17 b\right)}{32 b d (a-b)^2 \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}-\frac{a \cosh (c+d x) \left(2-\cosh ^2(c+d x)\right)}{8 b d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)^2}","\frac{3 \left(\sqrt{a}-2 \sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{64 \sqrt{a} b^{7/4} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}-\frac{3 \left(\sqrt{a}+2 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{64 \sqrt{a} b^{7/4} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}+\frac{\cosh (c+d x) \left(-3 (a-3 b) \cosh ^2(c+d x)+5 a-17 b\right)}{32 b d (a-b)^2 \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}-\frac{a \cosh (c+d x) \left(2-\cosh ^2(c+d x)\right)}{8 b d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)^2}",1,"(3*(Sqrt[a] - 2*Sqrt[b])*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(64*Sqrt[a]*(Sqrt[a] - Sqrt[b])^(5/2)*b^(7/4)*d) - (3*(Sqrt[a] + 2*Sqrt[b])*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(64*Sqrt[a]*(Sqrt[a] + Sqrt[b])^(5/2)*b^(7/4)*d) - (a*Cosh[c + d*x]*(2 - Cosh[c + d*x]^2))/(8*(a - b)*b*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4)^2) + (Cosh[c + d*x]*(5*a - 17*b - 3*(a - 3*b)*Cosh[c + d*x]^2))/(32*(a - b)^2*b*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4))","A",6,6,24,0.2500,1,"{3215, 1205, 1178, 1166, 205, 208}"
255,1,313,0,0.4984318,"\int \frac{\sinh ^5(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^5/(a - b*Sinh[c + d*x]^4)^3,x]","-\frac{\cosh (c+d x) \left(a^2+2 b (2 a+b) \cosh ^2(c+d x)-11 a b-2 b^2\right)}{32 a b d (a-b)^2 \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}-\frac{\left(-10 \sqrt{a} \sqrt{b}+3 a+4 b\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{64 a^{3/2} b^{5/4} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}-\frac{\left(10 \sqrt{a} \sqrt{b}+3 a+4 b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{64 a^{3/2} b^{5/4} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}+\frac{\cosh (c+d x) \left(a-b \cosh ^2(c+d x)+b\right)}{8 b d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)^2}","-\frac{\cosh (c+d x) \left(a^2+2 b (2 a+b) \cosh ^2(c+d x)-11 a b-2 b^2\right)}{32 a b d (a-b)^2 \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}-\frac{\left(-10 \sqrt{a} \sqrt{b}+3 a+4 b\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{64 a^{3/2} b^{5/4} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}-\frac{\left(10 \sqrt{a} \sqrt{b}+3 a+4 b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{64 a^{3/2} b^{5/4} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}+\frac{\cosh (c+d x) \left(a-b \cosh ^2(c+d x)+b\right)}{8 b d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)^2}",1,"-((3*a - 10*Sqrt[a]*Sqrt[b] + 4*b)*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(64*a^(3/2)*(Sqrt[a] - Sqrt[b])^(5/2)*b^(5/4)*d) - ((3*a + 10*Sqrt[a]*Sqrt[b] + 4*b)*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(64*a^(3/2)*(Sqrt[a] + Sqrt[b])^(5/2)*b^(5/4)*d) + (Cosh[c + d*x]*(a + b - b*Cosh[c + d*x]^2))/(8*(a - b)*b*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4)^2) - (Cosh[c + d*x]*(a^2 - 11*a*b - 2*b^2 + 2*b*(2*a + b)*Cosh[c + d*x]^2))/(32*a*(a - b)^2*b*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4))","A",6,6,24,0.2500,1,"{3215, 1205, 1178, 1166, 205, 208}"
256,1,288,0,0.518835,"\int \frac{\sinh ^3(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^3/(a - b*Sinh[c + d*x]^4)^3,x]","-\frac{\left(5 \sqrt{a}-2 \sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{64 a^{3/2} b^{3/4} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}+\frac{\left(5 \sqrt{a}+2 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{64 a^{3/2} b^{3/4} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}-\frac{\cosh (c+d x) \left(-(5 a+b) \cosh ^2(c+d x)+11 a+b\right)}{32 a d (a-b)^2 \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}-\frac{\cosh (c+d x) \left(2-\cosh ^2(c+d x)\right)}{8 d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)^2}","-\frac{\left(5 \sqrt{a}-2 \sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{64 a^{3/2} b^{3/4} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}+\frac{\left(5 \sqrt{a}+2 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{64 a^{3/2} b^{3/4} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}-\frac{\cosh (c+d x) \left(-(5 a+b) \cosh ^2(c+d x)+11 a+b\right)}{32 a d (a-b)^2 \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}-\frac{\cosh (c+d x) \left(2-\cosh ^2(c+d x)\right)}{8 d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)^2}",1,"-((5*Sqrt[a] - 2*Sqrt[b])*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(64*a^(3/2)*(Sqrt[a] - Sqrt[b])^(5/2)*b^(3/4)*d) + ((5*Sqrt[a] + 2*Sqrt[b])*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(64*a^(3/2)*(Sqrt[a] + Sqrt[b])^(5/2)*b^(3/4)*d) - (Cosh[c + d*x]*(2 - Cosh[c + d*x]^2))/(8*(a - b)*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4)^2) - (Cosh[c + d*x]*(11*a + b - (5*a + b)*Cosh[c + d*x]^2))/(32*a*(a - b)^2*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4))","A",6,5,24,0.2083,1,"{3215, 1178, 1166, 205, 208}"
257,1,313,0,0.4631762,"\int \frac{\sinh (c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]/(a - b*Sinh[c + d*x]^4)^3,x]","\frac{\cosh (c+d x) \left((7 a-3 b) (a+2 b)-6 b (2 a-b) \cosh ^2(c+d x)\right)}{32 a^2 d (a-b)^2 \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}+\frac{3 \left(-10 \sqrt{a} \sqrt{b}+7 a+4 b\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{64 a^{5/2} \sqrt[4]{b} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}+\frac{3 \left(10 \sqrt{a} \sqrt{b}+7 a+4 b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{64 a^{5/2} \sqrt[4]{b} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}+\frac{\cosh (c+d x) \left(a-b \cosh ^2(c+d x)+b\right)}{8 a d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)^2}","\frac{\cosh (c+d x) \left((7 a-3 b) (a+2 b)-6 b (2 a-b) \cosh ^2(c+d x)\right)}{32 a^2 d (a-b)^2 \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}+\frac{3 \left(-10 \sqrt{a} \sqrt{b}+7 a+4 b\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{64 a^{5/2} \sqrt[4]{b} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}+\frac{3 \left(10 \sqrt{a} \sqrt{b}+7 a+4 b\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{64 a^{5/2} \sqrt[4]{b} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}+\frac{\cosh (c+d x) \left(a-b \cosh ^2(c+d x)+b\right)}{8 a d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)^2}",1,"(3*(7*a - 10*Sqrt[a]*Sqrt[b] + 4*b)*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(64*a^(5/2)*(Sqrt[a] - Sqrt[b])^(5/2)*b^(1/4)*d) + (3*(7*a + 10*Sqrt[a]*Sqrt[b] + 4*b)*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(64*a^(5/2)*(Sqrt[a] + Sqrt[b])^(5/2)*b^(1/4)*d) + (Cosh[c + d*x]*(a + b - b*Cosh[c + d*x]^2))/(8*a*(a - b)*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4)^2) + (Cosh[c + d*x]*((7*a - 3*b)*(a + 2*b) - 6*(2*a - b)*b*Cosh[c + d*x]^2))/(32*a^2*(a - b)^2*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4))","A",6,6,22,0.2727,1,"{3215, 1092, 1178, 1166, 205, 208}"
258,1,617,0,0.8185499,"\int \frac{\text{csch}(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^3} \, dx","Int[Csch[c + d*x]/(a - b*Sinh[c + d*x]^4)^3,x]","-\frac{b \cosh (c+d x) \left(2-\cosh ^2(c+d x)\right)}{4 a^2 d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}-\frac{b \cosh (c+d x) \left(-(5 a+b) \cosh ^2(c+d x)+11 a+b\right)}{32 a^2 d (a-b)^2 \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 a^3 d \sqrt{\sqrt{a}-\sqrt{b}}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{8 a^{5/2} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}-\frac{\sqrt[4]{b} \left(5 \sqrt{a}-2 \sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{64 a^{5/2} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}+\frac{\sqrt[4]{b} \left(5 \sqrt{a}+2 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{64 a^{5/2} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}+\frac{\sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 a^3 d \sqrt{\sqrt{a}+\sqrt{b}}}+\frac{\sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{8 a^{5/2} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a^3 d}-\frac{b \cosh (c+d x) \left(2-\cosh ^2(c+d x)\right)}{8 a d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)^2}","-\frac{b \cosh (c+d x) \left(2-\cosh ^2(c+d x)\right)}{4 a^2 d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}-\frac{b \cosh (c+d x) \left(-(5 a+b) \cosh ^2(c+d x)+11 a+b\right)}{32 a^2 d (a-b)^2 \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{2 a^3 d \sqrt{\sqrt{a}-\sqrt{b}}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{8 a^{5/2} d \left(\sqrt{a}-\sqrt{b}\right)^{3/2}}-\frac{\sqrt[4]{b} \left(5 \sqrt{a}-2 \sqrt{b}\right) \tan ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}-\sqrt{b}}}\right)}{64 a^{5/2} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}+\frac{\sqrt[4]{b} \left(5 \sqrt{a}+2 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{64 a^{5/2} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}+\frac{\sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{2 a^3 d \sqrt{\sqrt{a}+\sqrt{b}}}+\frac{\sqrt[4]{b} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \cosh (c+d x)}{\sqrt{\sqrt{a}+\sqrt{b}}}\right)}{8 a^{5/2} d \left(\sqrt{a}+\sqrt{b}\right)^{3/2}}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a^3 d}-\frac{b \cosh (c+d x) \left(2-\cosh ^2(c+d x)\right)}{8 a d (a-b) \left(a-b \cosh ^4(c+d x)+2 b \cosh ^2(c+d x)-b\right)^2}",1,"-((5*Sqrt[a] - 2*Sqrt[b])*b^(1/4)*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(64*a^(5/2)*(Sqrt[a] - Sqrt[b])^(5/2)*d) - (b^(1/4)*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(8*a^(5/2)*(Sqrt[a] - Sqrt[b])^(3/2)*d) - (b^(1/4)*ArcTan[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] - Sqrt[b]]])/(2*a^3*Sqrt[Sqrt[a] - Sqrt[b]]*d) - ArcTanh[Cosh[c + d*x]]/(a^3*d) + (b^(1/4)*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(8*a^(5/2)*(Sqrt[a] + Sqrt[b])^(3/2)*d) + (b^(1/4)*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(2*a^3*Sqrt[Sqrt[a] + Sqrt[b]]*d) + ((5*Sqrt[a] + 2*Sqrt[b])*b^(1/4)*ArcTanh[(b^(1/4)*Cosh[c + d*x])/Sqrt[Sqrt[a] + Sqrt[b]]])/(64*a^(5/2)*(Sqrt[a] + Sqrt[b])^(5/2)*d) - (b*Cosh[c + d*x]*(2 - Cosh[c + d*x]^2))/(8*a*(a - b)*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4)^2) - (b*Cosh[c + d*x]*(2 - Cosh[c + d*x]^2))/(4*a^2*(a - b)*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4)) - (b*Cosh[c + d*x]*(11*a + b - (5*a + b)*Cosh[c + d*x]^2))/(32*a^2*(a - b)^2*d*(a - b + 2*b*Cosh[c + d*x]^2 - b*Cosh[c + d*x]^4))","A",16,7,22,0.3182,1,"{3215, 1238, 207, 1178, 1166, 205, 208}"
259,1,319,0,0.4852599,"\int \frac{\sinh ^8(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^8/(a - b*Sinh[c + d*x]^4)^3,x]","-\frac{\left(2 \sqrt{a}-5 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{3/4} b^{3/2} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}+\frac{\left(2 \sqrt{a}+5 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{3/4} b^{3/2} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}+\frac{\tanh ^9(c+d x)}{8 a d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)^2}-\frac{\tanh ^3(c+d x)}{32 a b d (a-b)}-\frac{(a+5 b) \tanh (c+d x)}{32 a b d (a-b)^2}-\frac{\tanh ^5(c+d x) \text{sech}^2(c+d x)}{32 a b d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}","-\frac{\left(2 \sqrt{a}-5 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{3/4} b^{3/2} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}+\frac{\left(2 \sqrt{a}+5 \sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{3/4} b^{3/2} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}+\frac{\tanh ^9(c+d x)}{8 a d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)^2}-\frac{\tanh ^3(c+d x)}{32 a b d (a-b)}-\frac{(a+5 b) \tanh (c+d x)}{32 a b d (a-b)^2}-\frac{\tanh ^5(c+d x) \text{sech}^2(c+d x)}{32 a b d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}",1,"-((2*Sqrt[a] - 5*Sqrt[b])*ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(64*a^(3/4)*(Sqrt[a] - Sqrt[b])^(5/2)*b^(3/2)*d) + ((2*Sqrt[a] + 5*Sqrt[b])*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(64*a^(3/4)*(Sqrt[a] + Sqrt[b])^(5/2)*b^(3/2)*d) - ((a + 5*b)*Tanh[c + d*x])/(32*a*(a - b)^2*b*d) - Tanh[c + d*x]^3/(32*a*(a - b)*b*d) + Tanh[c + d*x]^9/(8*a*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4)^2) - (Sech[c + d*x]^2*Tanh[c + d*x]^5)/(32*a*b*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4))","A",9,7,24,0.2917,1,"{3217, 1275, 12, 1120, 1279, 1166, 208}"
260,1,345,0,0.7325519,"\int \frac{\sinh ^6(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^6/(a - b*Sinh[c + d*x]^4)^3,x]","\frac{\left(-10 \sqrt{a} \sqrt{b}+4 a+3 b\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{5/4} b^{3/2} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}-\frac{\left(10 \sqrt{a} \sqrt{b}+4 a+3 b\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{5/4} b^{3/2} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}+\frac{\tanh (c+d x) \left(\frac{2 a \left(a^2-a b-8 b^2\right)}{(a-b)^3}-\frac{\left(2 a^2+15 a b+3 b^2\right) \tanh ^2(c+d x)}{(a-b)^2}\right)}{32 a b d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}+\frac{\tanh (c+d x) \left(a (a+3 b)-\left(a^2+6 a b+b^2\right) \tanh ^2(c+d x)\right)}{8 d (a-b)^3 \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)^2}","\frac{\left(-10 \sqrt{a} \sqrt{b}+4 a+3 b\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{5/4} b^{3/2} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}-\frac{\left(10 \sqrt{a} \sqrt{b}+4 a+3 b\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{5/4} b^{3/2} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}+\frac{\tanh (c+d x) \left(\frac{2 a \left(a^2-a b-8 b^2\right)}{(a-b)^3}-\frac{\left(2 a^2+15 a b+3 b^2\right) \tanh ^2(c+d x)}{(a-b)^2}\right)}{32 a b d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}+\frac{\tanh (c+d x) \left(a (a+3 b)-\left(a^2+6 a b+b^2\right) \tanh ^2(c+d x)\right)}{8 d (a-b)^3 \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)^2}",1,"((4*a - 10*Sqrt[a]*Sqrt[b] + 3*b)*ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(64*a^(5/4)*(Sqrt[a] - Sqrt[b])^(5/2)*b^(3/2)*d) - ((4*a + 10*Sqrt[a]*Sqrt[b] + 3*b)*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(64*a^(5/4)*(Sqrt[a] + Sqrt[b])^(5/2)*b^(3/2)*d) + (Tanh[c + d*x]*(a*(a + 3*b) - (a^2 + 6*a*b + b^2)*Tanh[c + d*x]^2))/(8*(a - b)^3*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4)^2) + (Tanh[c + d*x]*((2*a*(a^2 - a*b - 8*b^2))/(a - b)^3 - ((2*a^2 + 15*a*b + 3*b^2)*Tanh[c + d*x]^2)/(a - b)^2))/(32*a*b*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4))","A",6,5,24,0.2083,1,"{3217, 1333, 1678, 1166, 208}"
261,1,314,0,0.6484696,"\int \frac{\sinh ^4(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^4/(a - b*Sinh[c + d*x]^4)^3,x]","-\frac{\tanh (c+d x) \left(\frac{9 a^2-24 a b-b^2}{(a-b)^3}-\frac{(17 a+3 b) \tanh ^2(c+d x)}{(a-b)^2}\right)}{32 a d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}+\frac{3 \left(2 \sqrt{a}-\sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{7/4} \sqrt{b} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}-\frac{3 \left(2 \sqrt{a}+\sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{7/4} \sqrt{b} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}-\frac{b \tanh (c+d x) \left(-4 (a+b) \tanh ^2(c+d x)+3 a+b\right)}{8 d (a-b)^3 \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)^2}","-\frac{\tanh (c+d x) \left(\frac{9 a^2-24 a b-b^2}{(a-b)^3}-\frac{(17 a+3 b) \tanh ^2(c+d x)}{(a-b)^2}\right)}{32 a d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}+\frac{3 \left(2 \sqrt{a}-\sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{7/4} \sqrt{b} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}-\frac{3 \left(2 \sqrt{a}+\sqrt{b}\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{7/4} \sqrt{b} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}-\frac{b \tanh (c+d x) \left(-4 (a+b) \tanh ^2(c+d x)+3 a+b\right)}{8 d (a-b)^3 \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)^2}",1,"(3*(2*Sqrt[a] - Sqrt[b])*ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(64*a^(7/4)*(Sqrt[a] - Sqrt[b])^(5/2)*Sqrt[b]*d) - (3*(2*Sqrt[a] + Sqrt[b])*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(64*a^(7/4)*(Sqrt[a] + Sqrt[b])^(5/2)*Sqrt[b]*d) - (b*Tanh[c + d*x]*(3*a + b - 4*(a + b)*Tanh[c + d*x]^2))/(8*(a - b)^3*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4)^2) - (Tanh[c + d*x]*((9*a^2 - 24*a*b - b^2)/(a - b)^3 - ((17*a + 3*b)*Tanh[c + d*x]^2)/(a - b)^2))/(32*a*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4))","A",6,5,24,0.2083,1,"{3217, 1333, 1678, 1166, 208}"
262,1,348,0,0.6643544,"\int \frac{\sinh ^2(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^3} \, dx","Int[Sinh[c + d*x]^2/(a - b*Sinh[c + d*x]^4)^3,x]","\frac{\tanh (c+d x) \left(\frac{2 a \left(5 a^2-9 a b-4 b^2\right)}{(a-b)^3}-\frac{5 \left(2 a^2+3 a b-b^2\right) \tanh ^2(c+d x)}{(a-b)^2}\right)}{32 a^2 d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}+\frac{b \tanh (c+d x) \left(a (a+3 b)-\left(a^2+6 a b+b^2\right) \tanh ^2(c+d x)\right)}{8 a d (a-b)^3 \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)^2}-\frac{\left(-14 \sqrt{a} \sqrt{b}+12 a+5 b\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{9/4} \sqrt{b} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}+\frac{\left(14 \sqrt{a} \sqrt{b}+12 a+5 b\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{9/4} \sqrt{b} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}","\frac{\tanh (c+d x) \left(\frac{2 a \left(5 a^2-9 a b-4 b^2\right)}{(a-b)^3}-\frac{5 \left(2 a^2+3 a b-b^2\right) \tanh ^2(c+d x)}{(a-b)^2}\right)}{32 a^2 d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}+\frac{b \tanh (c+d x) \left(a (a+3 b)-\left(a^2+6 a b+b^2\right) \tanh ^2(c+d x)\right)}{8 a d (a-b)^3 \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)^2}-\frac{\left(-14 \sqrt{a} \sqrt{b}+12 a+5 b\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{9/4} \sqrt{b} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}+\frac{\left(14 \sqrt{a} \sqrt{b}+12 a+5 b\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{9/4} \sqrt{b} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}",1,"-((12*a - 14*Sqrt[a]*Sqrt[b] + 5*b)*ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(64*a^(9/4)*(Sqrt[a] - Sqrt[b])^(5/2)*Sqrt[b]*d) + ((12*a + 14*Sqrt[a]*Sqrt[b] + 5*b)*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(64*a^(9/4)*(Sqrt[a] + Sqrt[b])^(5/2)*Sqrt[b]*d) + (b*Tanh[c + d*x]*(a*(a + 3*b) - (a^2 + 6*a*b + b^2)*Tanh[c + d*x]^2))/(8*a*(a - b)^3*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4)^2) + (Tanh[c + d*x]*((2*a*(5*a^2 - 9*a*b - 4*b^2))/(a - b)^3 - (5*(2*a^2 + 3*a*b - b^2)*Tanh[c + d*x]^2)/(a - b)^2))/(32*a^2*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4))","A",6,5,24,0.2083,1,"{3217, 1333, 1678, 1166, 208}"
263,1,320,0,0.6087704,"\int \frac{1}{\left(a-b \sinh ^4(c+d x)\right)^3} \, dx","Int[(a - b*Sinh[c + d*x]^4)^(-3),x]","-\frac{b \tanh (c+d x) \left(\frac{17 a^2-40 a b+7 b^2}{(a-b)^3}-\frac{(33 a-13 b) \tanh ^2(c+d x)}{(a-b)^2}\right)}{32 a^2 d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}+\frac{\left(-50 \sqrt{a} \sqrt{b}+32 a+21 b\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{11/4} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}+\frac{\left(50 \sqrt{a} \sqrt{b}+32 a+21 b\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{11/4} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}-\frac{b^2 \tanh (c+d x) \left(-4 (a+b) \tanh ^2(c+d x)+3 a+b\right)}{8 a d (a-b)^3 \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)^2}","-\frac{b \tanh (c+d x) \left(\frac{17 a^2-40 a b+7 b^2}{(a-b)^3}-\frac{(33 a-13 b) \tanh ^2(c+d x)}{(a-b)^2}\right)}{32 a^2 d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}+\frac{\left(-50 \sqrt{a} \sqrt{b}+32 a+21 b\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{11/4} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}+\frac{\left(50 \sqrt{a} \sqrt{b}+32 a+21 b\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{11/4} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}-\frac{b^2 \tanh (c+d x) \left(-4 (a+b) \tanh ^2(c+d x)+3 a+b\right)}{8 a d (a-b)^3 \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)^2}",1,"((32*a - 50*Sqrt[a]*Sqrt[b] + 21*b)*ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(64*a^(11/4)*(Sqrt[a] - Sqrt[b])^(5/2)*d) + ((32*a + 50*Sqrt[a]*Sqrt[b] + 21*b)*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(64*a^(11/4)*(Sqrt[a] + Sqrt[b])^(5/2)*d) - (b^2*Tanh[c + d*x]*(3*a + b - 4*(a + b)*Tanh[c + d*x]^2))/(8*a*(a - b)^3*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4)^2) - (b*Tanh[c + d*x]*((17*a^2 - 40*a*b + 7*b^2)/(a - b)^3 - ((33*a - 13*b)*Tanh[c + d*x]^2)/(a - b)^2))/(32*a^2*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4))","A",6,5,15,0.3333,1,"{3209, 1205, 1678, 1166, 208}"
264,1,359,0,1.1576969,"\int \frac{\text{csch}^2(c+d x)}{\left(a-b \sinh ^4(c+d x)\right)^3} \, dx","Int[Csch[c + d*x]^2/(a - b*Sinh[c + d*x]^4)^3,x]","\frac{b^2 \tanh (c+d x) \left(a (a+3 b)-\left(a^2+6 a b+b^2\right) \tanh ^2(c+d x)\right)}{8 a^2 d (a-b)^3 \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)^2}+\frac{b \tanh (c+d x) \left(\frac{2 a^2 (9 a-17 b)}{(a-b)^3}-\frac{\left(18 a^2+15 a b-13 b^2\right) \tanh ^2(c+d x)}{(a-b)^2}\right)}{32 a^3 d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}-\frac{3 \sqrt{b} \left(-34 \sqrt{a} \sqrt{b}+20 a+15 b\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{13/4} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}+\frac{3 \sqrt{b} \left(34 \sqrt{a} \sqrt{b}+20 a+15 b\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{13/4} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}-\frac{\coth (c+d x)}{a^3 d}","\frac{b^2 \tanh (c+d x) \left(a (a+3 b)-\left(a^2+6 a b+b^2\right) \tanh ^2(c+d x)\right)}{8 a^2 d (a-b)^3 \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)^2}+\frac{b \tanh (c+d x) \left(\frac{2 a^2 (9 a-17 b)}{(a-b)^3}-\frac{\left(18 a^2+15 a b-13 b^2\right) \tanh ^2(c+d x)}{(a-b)^2}\right)}{32 a^3 d \left((a-b) \tanh ^4(c+d x)-2 a \tanh ^2(c+d x)+a\right)}-\frac{3 \sqrt{b} \left(-34 \sqrt{a} \sqrt{b}+20 a+15 b\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{13/4} d \left(\sqrt{a}-\sqrt{b}\right)^{5/2}}+\frac{3 \sqrt{b} \left(34 \sqrt{a} \sqrt{b}+20 a+15 b\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \tanh (c+d x)}{\sqrt[4]{a}}\right)}{64 a^{13/4} d \left(\sqrt{a}+\sqrt{b}\right)^{5/2}}-\frac{\coth (c+d x)}{a^3 d}",1,"(-3*Sqrt[b]*(20*a - 34*Sqrt[a]*Sqrt[b] + 15*b)*ArcTanh[(Sqrt[Sqrt[a] - Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(64*a^(13/4)*(Sqrt[a] - Sqrt[b])^(5/2)*d) + (3*Sqrt[b]*(20*a + 34*Sqrt[a]*Sqrt[b] + 15*b)*ArcTanh[(Sqrt[Sqrt[a] + Sqrt[b]]*Tanh[c + d*x])/a^(1/4)])/(64*a^(13/4)*(Sqrt[a] + Sqrt[b])^(5/2)*d) - Coth[c + d*x]/(a^3*d) + (b^2*Tanh[c + d*x]*(a*(a + 3*b) - (a^2 + 6*a*b + b^2)*Tanh[c + d*x]^2))/(8*a^2*(a - b)^3*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4)^2) + (b*Tanh[c + d*x]*((2*a^2*(9*a - 17*b))/(a - b)^3 - ((18*a^2 + 15*a*b - 13*b^2)*Tanh[c + d*x]^2)/(a - b)^2))/(32*a^3*d*(a - 2*a*Tanh[c + d*x]^2 + (a - b)*Tanh[c + d*x]^4))","A",8,6,24,0.2500,1,"{3217, 1334, 1669, 1664, 1166, 208}"
265,1,25,0,0.018092,"\int \frac{1}{1-\sinh ^4(x)} \, dx","Int[(1 - Sinh[x]^4)^(-1),x]","\frac{\tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{2 \sqrt{2}}+\frac{\tanh (x)}{2}","\frac{\tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{2 \sqrt{2}}+\frac{\tanh (x)}{2}",1,"ArcTanh[Sqrt[2]*Tanh[x]]/(2*Sqrt[2]) + Tanh[x]/2","A",3,3,10,0.3000,1,"{3209, 388, 206}"
266,1,176,0,0.159089,"\int \frac{1}{1+\sinh ^4(x)} \, dx","Int[(1 + Sinh[x]^4)^(-1),x]","-\frac{1}{8} \sqrt{1+\sqrt{2}} \log \left(2 \tanh ^2(x)-2 \sqrt{1+\sqrt{2}} \tanh (x)+\sqrt{2}\right)+\frac{1}{8} \sqrt{1+\sqrt{2}} \log \left(\sqrt{2} \tanh ^2(x)+\sqrt{2 \left(1+\sqrt{2}\right)} \tanh (x)+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{1+\sqrt{2}}-2 \tanh (x)}{\sqrt{\sqrt{2}-1}}\right)}{4 \sqrt{1+\sqrt{2}}}+\frac{\tan ^{-1}\left(\frac{2 \tanh (x)+\sqrt{1+\sqrt{2}}}{\sqrt{\sqrt{2}-1}}\right)}{4 \sqrt{1+\sqrt{2}}}","-\frac{1}{8} \sqrt{1+\sqrt{2}} \log \left(2 \tanh ^2(x)-2 \sqrt{1+\sqrt{2}} \tanh (x)+\sqrt{2}\right)+\frac{1}{8} \sqrt{1+\sqrt{2}} \log \left(\sqrt{2} \tanh ^2(x)+\sqrt{2 \left(1+\sqrt{2}\right)} \tanh (x)+1\right)-\frac{\tan ^{-1}\left(\frac{\sqrt{1+\sqrt{2}}-2 \tanh (x)}{\sqrt{\sqrt{2}-1}}\right)}{4 \sqrt{1+\sqrt{2}}}+\frac{\tan ^{-1}\left(\frac{2 \tanh (x)+\sqrt{1+\sqrt{2}}}{\sqrt{\sqrt{2}-1}}\right)}{4 \sqrt{1+\sqrt{2}}}",1,"-ArcTan[(Sqrt[1 + Sqrt[2]] - 2*Tanh[x])/Sqrt[-1 + Sqrt[2]]]/(4*Sqrt[1 + Sqrt[2]]) + ArcTan[(Sqrt[1 + Sqrt[2]] + 2*Tanh[x])/Sqrt[-1 + Sqrt[2]]]/(4*Sqrt[1 + Sqrt[2]]) - (Sqrt[1 + Sqrt[2]]*Log[Sqrt[2] - 2*Sqrt[1 + Sqrt[2]]*Tanh[x] + 2*Tanh[x]^2])/8 + (Sqrt[1 + Sqrt[2]]*Log[1 + Sqrt[2*(1 + Sqrt[2])]*Tanh[x] + Sqrt[2]*Tanh[x]^2])/8","A",10,6,8,0.7500,1,"{3209, 1169, 634, 618, 204, 628}"
267,1,435,0,0.9746958,"\int \frac{1}{a+b \sinh ^5(x)} \, dx","Int[(a + b*Sinh[x]^5)^(-1),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[5]{b}-\sqrt[5]{a} \tanh \left(\frac{x}{2}\right)}{\sqrt{a^{2/5}+b^{2/5}}}\right)}{5 a^{4/5} \sqrt{a^{2/5}+b^{2/5}}}+\frac{2 (-1)^{9/10} \tanh ^{-1}\left(\frac{(-1)^{9/10} \left(\sqrt[5]{a} \tanh \left(\frac{x}{2}\right)+\sqrt[5]{-1} \sqrt[5]{b}\right)}{\sqrt{\sqrt[5]{-1} b^{2/5}-(-1)^{4/5} a^{2/5}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{-1} b^{2/5}-(-1)^{4/5} a^{2/5}}}+\frac{2 \sqrt[5]{-1} \tanh ^{-1}\left(\frac{\sqrt[5]{-1} \sqrt[5]{a} \tanh \left(\frac{x}{2}\right)+\sqrt[5]{b}}{\sqrt{(-1)^{2/5} a^{2/5}+b^{2/5}}}\right)}{5 a^{4/5} \sqrt{(-1)^{2/5} a^{2/5}+b^{2/5}}}+\frac{2 (-1)^{9/10} \tanh ^{-1}\left(\frac{(-1)^{3/10} \left((-1)^{3/5} \sqrt[5]{a} \tanh \left(\frac{x}{2}\right)+\sqrt[5]{b}\right)}{\sqrt{(-1)^{3/5} b^{2/5}-(-1)^{4/5} a^{2/5}}}\right)}{5 a^{4/5} \sqrt{(-1)^{3/5} b^{2/5}-(-1)^{4/5} a^{2/5}}}-\frac{2 (-1)^{9/10} \tanh ^{-1}\left(\frac{-(-1)^{9/10} \sqrt[5]{a} \tanh \left(\frac{x}{2}\right)+i \sqrt[5]{b}}{\sqrt{-(-1)^{4/5} a^{2/5}-b^{2/5}}}\right)}{5 a^{4/5} \sqrt{-(-1)^{4/5} a^{2/5}-b^{2/5}}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt[5]{b}-\sqrt[5]{a} \tanh \left(\frac{x}{2}\right)}{\sqrt{a^{2/5}+b^{2/5}}}\right)}{5 a^{4/5} \sqrt{a^{2/5}+b^{2/5}}}+\frac{2 (-1)^{9/10} \tanh ^{-1}\left(\frac{(-1)^{9/10} \left(\sqrt[5]{a} \tanh \left(\frac{x}{2}\right)+\sqrt[5]{-1} \sqrt[5]{b}\right)}{\sqrt{\sqrt[5]{-1} b^{2/5}-(-1)^{4/5} a^{2/5}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{-1} b^{2/5}-(-1)^{4/5} a^{2/5}}}+\frac{2 \sqrt[5]{-1} \tanh ^{-1}\left(\frac{\sqrt[5]{-1} \sqrt[5]{a} \tanh \left(\frac{x}{2}\right)+\sqrt[5]{b}}{\sqrt{(-1)^{2/5} a^{2/5}+b^{2/5}}}\right)}{5 a^{4/5} \sqrt{(-1)^{2/5} a^{2/5}+b^{2/5}}}+\frac{2 (-1)^{9/10} \tanh ^{-1}\left(\frac{(-1)^{3/10} \left((-1)^{3/5} \sqrt[5]{a} \tanh \left(\frac{x}{2}\right)+\sqrt[5]{b}\right)}{\sqrt{(-1)^{3/5} b^{2/5}-(-1)^{4/5} a^{2/5}}}\right)}{5 a^{4/5} \sqrt{(-1)^{3/5} b^{2/5}-(-1)^{4/5} a^{2/5}}}-\frac{2 (-1)^{9/10} \tanh ^{-1}\left(\frac{-(-1)^{9/10} \sqrt[5]{a} \tanh \left(\frac{x}{2}\right)+i \sqrt[5]{b}}{\sqrt{-(-1)^{4/5} a^{2/5}-b^{2/5}}}\right)}{5 a^{4/5} \sqrt{-(-1)^{4/5} a^{2/5}-b^{2/5}}}",1,"(-2*ArcTanh[(b^(1/5) - a^(1/5)*Tanh[x/2])/Sqrt[a^(2/5) + b^(2/5)]])/(5*a^(4/5)*Sqrt[a^(2/5) + b^(2/5)]) + (2*(-1)^(9/10)*ArcTanh[((-1)^(9/10)*((-1)^(1/5)*b^(1/5) + a^(1/5)*Tanh[x/2]))/Sqrt[-((-1)^(4/5)*a^(2/5)) + (-1)^(1/5)*b^(2/5)]])/(5*a^(4/5)*Sqrt[-((-1)^(4/5)*a^(2/5)) + (-1)^(1/5)*b^(2/5)]) + (2*(-1)^(1/5)*ArcTanh[(b^(1/5) + (-1)^(1/5)*a^(1/5)*Tanh[x/2])/Sqrt[(-1)^(2/5)*a^(2/5) + b^(2/5)]])/(5*a^(4/5)*Sqrt[(-1)^(2/5)*a^(2/5) + b^(2/5)]) + (2*(-1)^(9/10)*ArcTanh[((-1)^(3/10)*(b^(1/5) + (-1)^(3/5)*a^(1/5)*Tanh[x/2]))/Sqrt[-((-1)^(4/5)*a^(2/5)) + (-1)^(3/5)*b^(2/5)]])/(5*a^(4/5)*Sqrt[-((-1)^(4/5)*a^(2/5)) + (-1)^(3/5)*b^(2/5)]) - (2*(-1)^(9/10)*ArcTanh[(I*b^(1/5) - (-1)^(9/10)*a^(1/5)*Tanh[x/2])/Sqrt[-((-1)^(4/5)*a^(2/5)) - b^(2/5)]])/(5*a^(4/5)*Sqrt[-((-1)^(4/5)*a^(2/5)) - b^(2/5)])","A",17,5,10,0.5000,1,"{3213, 2660, 618, 206, 204}"
268,1,175,0,0.2793263,"\int \frac{1}{a+b \sinh ^6(x)} \, dx","Int[(a + b*Sinh[x]^6)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-\sqrt[3]{b}} \tanh (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-\sqrt[3]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}} \tanh (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}} \tanh (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-\sqrt[3]{b}} \tanh (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-\sqrt[3]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}} \tanh (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}} \tanh (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}}}",1,"ArcTanh[(Sqrt[a^(1/3) - b^(1/3)]*Tanh[x])/a^(1/6)]/(3*a^(5/6)*Sqrt[a^(1/3) - b^(1/3)]) + ArcTanh[(Sqrt[a^(1/3) + (-1)^(1/3)*b^(1/3)]*Tanh[x])/a^(1/6)]/(3*a^(5/6)*Sqrt[a^(1/3) + (-1)^(1/3)*b^(1/3)]) + ArcTanh[(Sqrt[a^(1/3) - (-1)^(2/3)*b^(1/3)]*Tanh[x])/a^(1/6)]/(3*a^(5/6)*Sqrt[a^(1/3) - (-1)^(2/3)*b^(1/3)])","A",7,3,10,0.3000,1,"{3211, 3181, 206}"
269,1,245,0,0.5168226,"\int \frac{1}{a+b \sinh ^8(x)} \, dx","Int[(a + b*Sinh[x]^8)^(-1),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt[4]{-a}-i \sqrt[4]{b}} \tanh (x)}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}-i \sqrt[4]{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt[4]{-a}+i \sqrt[4]{b}} \tanh (x)}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}+i \sqrt[4]{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt[4]{-a}+\sqrt[4]{b}} \tanh (x)}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a \sqrt[4]{b}+(-a)^{5/4}} \tanh (x)}{(-a)^{5/8}}\right)}{4 (-a)^{3/8} \sqrt{a \sqrt[4]{b}+(-a)^{5/4}}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt[4]{-a}-\sqrt[4]{b}} \tanh (x)}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt[4]{-a}-i \sqrt[4]{b}} \tanh (x)}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}-i \sqrt[4]{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt[4]{-a}+i \sqrt[4]{b}} \tanh (x)}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}+i \sqrt[4]{b}}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\sqrt[4]{-a}+\sqrt[4]{b}} \tanh (x)}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}",1,"-ArcTanh[(Sqrt[(-a)^(1/4) - I*b^(1/4)]*Tanh[x])/(-a)^(1/8)]/(4*(-a)^(7/8)*Sqrt[(-a)^(1/4) - I*b^(1/4)]) - ArcTanh[(Sqrt[(-a)^(1/4) + I*b^(1/4)]*Tanh[x])/(-a)^(1/8)]/(4*(-a)^(7/8)*Sqrt[(-a)^(1/4) + I*b^(1/4)]) - ArcTanh[(Sqrt[(-a)^(1/4) + b^(1/4)]*Tanh[x])/(-a)^(1/8)]/(4*(-a)^(7/8)*Sqrt[(-a)^(1/4) + b^(1/4)]) - ArcTanh[(Sqrt[(-a)^(5/4) + a*b^(1/4)]*Tanh[x])/(-a)^(5/8)]/(4*(-a)^(3/8)*Sqrt[(-a)^(5/4) + a*b^(1/4)])","A",9,3,10,0.3000,1,"{3211, 3181, 206}"
270,1,242,0,0.5184995,"\int \frac{1}{1+\sinh ^5(x)} \, dx","Int[(1 + Sinh[x]^5)^(-1),x]","-\frac{1}{5} \sqrt{2} \tanh ^{-1}\left(\frac{1-\tanh \left(\frac{x}{2}\right)}{\sqrt{2}}\right)+\frac{2 (-1)^{9/10} \tanh ^{-1}\left(\frac{(-1)^{7/10} \left(\sqrt[5]{-1} \tanh \left(\frac{x}{2}\right)+1\right)}{\sqrt{-(-1)^{2/5} \left(1+(-1)^{2/5}\right)}}\right)}{5 \sqrt{-(-1)^{2/5} \left(1+(-1)^{2/5}\right)}}-\frac{2 (-1)^{4/5} \tanh ^{-1}\left(\frac{1-(-1)^{4/5} \tanh \left(\frac{x}{2}\right)}{\sqrt{1-(-1)^{3/5}}}\right)}{5 \sqrt{1-(-1)^{3/5}}}-\frac{2 (-1)^{3/5} \tan ^{-1}\left(\frac{(-1)^{3/5} \tanh \left(\frac{x}{2}\right)+1}{\sqrt{\sqrt[5]{-1}-1}}\right)}{5 \sqrt{\sqrt[5]{-1}-1}}+\frac{2 (-1)^{9/10} \tan ^{-1}\left(\frac{-(-1)^{9/10} \tanh \left(\frac{x}{2}\right)+i}{\sqrt{1+(-1)^{4/5}}}\right)}{5 \sqrt{1+(-1)^{4/5}}}","-\frac{1}{5} \sqrt{2} \tanh ^{-1}\left(\frac{1-\tanh \left(\frac{x}{2}\right)}{\sqrt{2}}\right)+\frac{2 (-1)^{9/10} \tanh ^{-1}\left(\frac{(-1)^{7/10} \left(\sqrt[5]{-1} \tanh \left(\frac{x}{2}\right)+1\right)}{\sqrt{-(-1)^{2/5} \left(1+(-1)^{2/5}\right)}}\right)}{5 \sqrt{-(-1)^{2/5} \left(1+(-1)^{2/5}\right)}}-\frac{2 (-1)^{4/5} \tanh ^{-1}\left(\frac{1-(-1)^{4/5} \tanh \left(\frac{x}{2}\right)}{\sqrt{1-(-1)^{3/5}}}\right)}{5 \sqrt{1-(-1)^{3/5}}}-\frac{2 (-1)^{3/5} \tan ^{-1}\left(\frac{(-1)^{3/5} \tanh \left(\frac{x}{2}\right)+1}{\sqrt{\sqrt[5]{-1}-1}}\right)}{5 \sqrt{\sqrt[5]{-1}-1}}+\frac{2 (-1)^{9/10} \tan ^{-1}\left(\frac{-(-1)^{9/10} \tanh \left(\frac{x}{2}\right)+i}{\sqrt{1+(-1)^{4/5}}}\right)}{5 \sqrt{1+(-1)^{4/5}}}",1,"(-2*(-1)^(3/5)*ArcTan[(1 + (-1)^(3/5)*Tanh[x/2])/Sqrt[-1 + (-1)^(1/5)]])/(5*Sqrt[-1 + (-1)^(1/5)]) + (2*(-1)^(9/10)*ArcTan[(I - (-1)^(9/10)*Tanh[x/2])/Sqrt[1 + (-1)^(4/5)]])/(5*Sqrt[1 + (-1)^(4/5)]) - (Sqrt[2]*ArcTanh[(1 - Tanh[x/2])/Sqrt[2]])/5 + (2*(-1)^(9/10)*ArcTanh[((-1)^(7/10)*(1 + (-1)^(1/5)*Tanh[x/2]))/Sqrt[-((-1)^(2/5)*(1 + (-1)^(2/5)))]])/(5*Sqrt[-((-1)^(2/5)*(1 + (-1)^(2/5)))]) - (2*(-1)^(4/5)*ArcTanh[(1 - (-1)^(4/5)*Tanh[x/2])/Sqrt[1 - (-1)^(3/5)]])/(5*Sqrt[1 - (-1)^(3/5)])","A",17,6,8,0.7500,1,"{3213, 2660, 618, 204, 206, 617}"
271,1,71,0,0.137859,"\int \frac{1}{1+\sinh ^6(x)} \, dx","Int[(1 + Sinh[x]^6)^(-1),x]","\frac{\tanh ^{-1}\left(\sqrt{1+\sqrt[3]{-1}} \tanh (x)\right)}{3 \sqrt{1+\sqrt[3]{-1}}}+\frac{\tanh ^{-1}\left(\sqrt{1-(-1)^{2/3}} \tanh (x)\right)}{3 \sqrt{1-(-1)^{2/3}}}+\frac{\tanh (x)}{3}","\frac{\tanh ^{-1}\left(\sqrt{1+\sqrt[3]{-1}} \tanh (x)\right)}{3 \sqrt{1+\sqrt[3]{-1}}}+\frac{\tanh ^{-1}\left(\sqrt{1-(-1)^{2/3}} \tanh (x)\right)}{3 \sqrt{1-(-1)^{2/3}}}+\frac{\tanh (x)}{3}",1,"ArcTanh[Sqrt[1 + (-1)^(1/3)]*Tanh[x]]/(3*Sqrt[1 + (-1)^(1/3)]) + ArcTanh[Sqrt[1 - (-1)^(2/3)]*Tanh[x]]/(3*Sqrt[1 - (-1)^(2/3)]) + Tanh[x]/3","A",8,6,8,0.7500,1,"{3211, 3181, 206, 3175, 3767, 8}"
272,1,129,0,0.1977783,"\int \frac{1}{1+\sinh ^8(x)} \, dx","Int[(1 + Sinh[x]^8)^(-1),x]","\frac{\tanh ^{-1}\left(\sqrt{1-\sqrt[4]{-1}} \tanh (x)\right)}{4 \sqrt{1-\sqrt[4]{-1}}}+\frac{\tanh ^{-1}\left(\sqrt{1+\sqrt[4]{-1}} \tanh (x)\right)}{4 \sqrt{1+\sqrt[4]{-1}}}+\frac{\tanh ^{-1}\left(\sqrt{1-(-1)^{3/4}} \tanh (x)\right)}{4 \sqrt{1-(-1)^{3/4}}}+\frac{\tanh ^{-1}\left(\sqrt{1+(-1)^{3/4}} \tanh (x)\right)}{4 \sqrt{1+(-1)^{3/4}}}","\frac{\tanh ^{-1}\left(\sqrt{1-\sqrt[4]{-1}} \tanh (x)\right)}{4 \sqrt{1-\sqrt[4]{-1}}}+\frac{\tanh ^{-1}\left(\sqrt{1+\sqrt[4]{-1}} \tanh (x)\right)}{4 \sqrt{1+\sqrt[4]{-1}}}+\frac{\tanh ^{-1}\left(\sqrt{1-(-1)^{3/4}} \tanh (x)\right)}{4 \sqrt{1-(-1)^{3/4}}}+\frac{\tanh ^{-1}\left(\sqrt{1+(-1)^{3/4}} \tanh (x)\right)}{4 \sqrt{1+(-1)^{3/4}}}",1,"ArcTanh[Sqrt[1 - (-1)^(1/4)]*Tanh[x]]/(4*Sqrt[1 - (-1)^(1/4)]) + ArcTanh[Sqrt[1 + (-1)^(1/4)]*Tanh[x]]/(4*Sqrt[1 + (-1)^(1/4)]) + ArcTanh[Sqrt[1 - (-1)^(3/4)]*Tanh[x]]/(4*Sqrt[1 - (-1)^(3/4)]) + ArcTanh[Sqrt[1 + (-1)^(3/4)]*Tanh[x]]/(4*Sqrt[1 + (-1)^(3/4)])","A",9,3,8,0.3750,1,"{3211, 3181, 206}"
273,1,228,0,0.4170436,"\int \frac{1}{1-\sinh ^5(x)} \, dx","Int[(1 - Sinh[x]^5)^(-1),x]","-\frac{2 \tanh ^{-1}\left(\frac{(-1)^{3/5}-\tanh \left(\frac{x}{2}\right)}{\sqrt{1-\sqrt[5]{-1}}}\right)}{5 \sqrt{1-\sqrt[5]{-1}}}+\frac{1}{5} \sqrt{2} \tanh ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right)+1}{\sqrt{2}}\right)+\frac{2 \tanh ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right)+(-1)^{4/5}}{\sqrt{1-(-1)^{3/5}}}\right)}{5 \sqrt{1-(-1)^{3/5}}}-\frac{2 \sqrt[10]{-1} \tanh ^{-1}\left(\frac{(-1)^{3/10} \left((-1)^{4/5} \tanh \left(\frac{x}{2}\right)+1\right)}{\sqrt{\sqrt[5]{-1}+(-1)^{3/5}}}\right)}{5 \sqrt{\sqrt[5]{-1}+(-1)^{3/5}}}-\frac{2 \sqrt[10]{-1} \tan ^{-1}\left(\frac{\sqrt[10]{-1} \tanh \left(\frac{x}{2}\right)+i}{\sqrt{1-\sqrt[5]{-1}}}\right)}{5 \sqrt{1-\sqrt[5]{-1}}}","-\frac{2 \tanh ^{-1}\left(\frac{(-1)^{3/5}-\tanh \left(\frac{x}{2}\right)}{\sqrt{1-\sqrt[5]{-1}}}\right)}{5 \sqrt{1-\sqrt[5]{-1}}}+\frac{1}{5} \sqrt{2} \tanh ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right)+1}{\sqrt{2}}\right)+\frac{2 \tanh ^{-1}\left(\frac{\tanh \left(\frac{x}{2}\right)+(-1)^{4/5}}{\sqrt{1-(-1)^{3/5}}}\right)}{5 \sqrt{1-(-1)^{3/5}}}-\frac{2 \sqrt[10]{-1} \tanh ^{-1}\left(\frac{(-1)^{3/10} \left((-1)^{4/5} \tanh \left(\frac{x}{2}\right)+1\right)}{\sqrt{\sqrt[5]{-1}+(-1)^{3/5}}}\right)}{5 \sqrt{\sqrt[5]{-1}+(-1)^{3/5}}}-\frac{2 \sqrt[10]{-1} \tan ^{-1}\left(\frac{\sqrt[10]{-1} \tanh \left(\frac{x}{2}\right)+i}{\sqrt{1-\sqrt[5]{-1}}}\right)}{5 \sqrt{1-\sqrt[5]{-1}}}",1,"(-2*(-1)^(1/10)*ArcTan[(I + (-1)^(1/10)*Tanh[x/2])/Sqrt[1 - (-1)^(1/5)]])/(5*Sqrt[1 - (-1)^(1/5)]) - (2*ArcTanh[((-1)^(3/5) - Tanh[x/2])/Sqrt[1 - (-1)^(1/5)]])/(5*Sqrt[1 - (-1)^(1/5)]) + (Sqrt[2]*ArcTanh[(1 + Tanh[x/2])/Sqrt[2]])/5 + (2*ArcTanh[((-1)^(4/5) + Tanh[x/2])/Sqrt[1 - (-1)^(3/5)]])/(5*Sqrt[1 - (-1)^(3/5)]) - (2*(-1)^(1/10)*ArcTanh[((-1)^(3/10)*(1 + (-1)^(4/5)*Tanh[x/2]))/Sqrt[(-1)^(1/5) + (-1)^(3/5)]])/(5*Sqrt[(-1)^(1/5) + (-1)^(3/5)])","A",17,6,10,0.6000,1,"{3213, 2660, 618, 204, 617, 206}"
274,1,83,0,0.0998656,"\int \frac{1}{1-\sinh ^6(x)} \, dx","Int[(1 - Sinh[x]^6)^(-1),x]","\frac{\tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{3 \sqrt{2}}+\frac{\tanh ^{-1}\left(\sqrt{1-\sqrt[3]{-1}} \tanh (x)\right)}{3 \sqrt{1-\sqrt[3]{-1}}}+\frac{\tanh ^{-1}\left(\sqrt{1+(-1)^{2/3}} \tanh (x)\right)}{3 \sqrt{1+(-1)^{2/3}}}","\frac{\tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{3 \sqrt{2}}+\frac{\tanh ^{-1}\left(\sqrt{1-\sqrt[3]{-1}} \tanh (x)\right)}{3 \sqrt{1-\sqrt[3]{-1}}}+\frac{\tanh ^{-1}\left(\sqrt{1+(-1)^{2/3}} \tanh (x)\right)}{3 \sqrt{1+(-1)^{2/3}}}",1,"ArcTanh[Sqrt[2]*Tanh[x]]/(3*Sqrt[2]) + ArcTanh[Sqrt[1 - (-1)^(1/3)]*Tanh[x]]/(3*Sqrt[1 - (-1)^(1/3)]) + ArcTanh[Sqrt[1 + (-1)^(2/3)]*Tanh[x]]/(3*Sqrt[1 + (-1)^(2/3)])","A",7,3,10,0.3000,1,"{3211, 3181, 206}"
275,1,69,0,0.0772041,"\int \frac{1}{1-\sinh ^8(x)} \, dx","Int[(1 - Sinh[x]^8)^(-1),x]","\frac{\tanh ^{-1}\left(\sqrt{1-i} \tanh (x)\right)}{4 \sqrt{1-i}}+\frac{\tanh ^{-1}\left(\sqrt{1+i} \tanh (x)\right)}{4 \sqrt{1+i}}+\frac{\tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{4 \sqrt{2}}+\frac{\tanh (x)}{4}","\frac{\tanh ^{-1}\left(\sqrt{1-i} \tanh (x)\right)}{4 \sqrt{1-i}}+\frac{\tanh ^{-1}\left(\sqrt{1+i} \tanh (x)\right)}{4 \sqrt{1+i}}+\frac{\tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)}{4 \sqrt{2}}+\frac{\tanh (x)}{4}",1,"ArcTanh[Sqrt[1 - I]*Tanh[x]]/(4*Sqrt[1 - I]) + ArcTanh[Sqrt[1 + I]*Tanh[x]]/(4*Sqrt[1 + I]) + ArcTanh[Sqrt[2]*Tanh[x]]/(4*Sqrt[2]) + Tanh[x]/4","A",10,6,10,0.6000,1,"{3211, 3181, 206, 3175, 3767, 8}"
276,1,18,0,0.0516122,"\int \frac{\cosh ^5(x)}{a+a \sinh ^2(x)} \, dx","Int[Cosh[x]^5/(a + a*Sinh[x]^2),x]","\frac{\sinh ^3(x)}{3 a}+\frac{\sinh (x)}{a}","\frac{\sinh ^3(x)}{3 a}+\frac{\sinh (x)}{a}",1,"Sinh[x]/a + Sinh[x]^3/(3*a)","A",3,2,15,0.1333,1,"{3175, 2633}"
277,1,20,0,0.0501591,"\int \frac{\cosh ^4(x)}{a+a \sinh ^2(x)} \, dx","Int[Cosh[x]^4/(a + a*Sinh[x]^2),x]","\frac{x}{2 a}+\frac{\sinh (x) \cosh (x)}{2 a}","\frac{x}{2 a}+\frac{\sinh (x) \cosh (x)}{2 a}",1,"x/(2*a) + (Cosh[x]*Sinh[x])/(2*a)","A",3,3,15,0.2000,1,"{3175, 2635, 8}"
278,1,6,0,0.0439533,"\int \frac{\cosh ^3(x)}{a+a \sinh ^2(x)} \, dx","Int[Cosh[x]^3/(a + a*Sinh[x]^2),x]","\frac{\sinh (x)}{a}","\frac{\sinh (x)}{a}",1,"Sinh[x]/a","A",2,2,15,0.1333,1,"{3175, 2637}"
279,1,5,0,0.0415225,"\int \frac{\cosh ^2(x)}{a+a \sinh ^2(x)} \, dx","Int[Cosh[x]^2/(a + a*Sinh[x]^2),x]","\frac{x}{a}","\frac{x}{a}",1,"x/a","A",2,2,15,0.1333,1,"{3175, 8}"
280,1,7,0,0.0276392,"\int \frac{\cosh (x)}{a+a \sinh ^2(x)} \, dx","Int[Cosh[x]/(a + a*Sinh[x]^2),x]","\frac{\tan ^{-1}(\sinh (x))}{a}","\frac{\tan ^{-1}(\sinh (x))}{a}",1,"ArcTan[Sinh[x]]/a","A",2,2,13,0.1538,1,"{3175, 3770}"
281,1,22,0,0.0454984,"\int \frac{\text{sech}(x)}{a+a \sinh ^2(x)} \, dx","Int[Sech[x]/(a + a*Sinh[x]^2),x]","\frac{\tan ^{-1}(\sinh (x))}{2 a}+\frac{\tanh (x) \text{sech}(x)}{2 a}","\frac{\tan ^{-1}(\sinh (x))}{2 a}+\frac{\tanh (x) \text{sech}(x)}{2 a}",1,"ArcTan[Sinh[x]]/(2*a) + (Sech[x]*Tanh[x])/(2*a)","A",3,3,13,0.2308,1,"{3175, 3768, 3770}"
282,1,35,0,0.0598158,"\int \frac{\text{sech}^3(x)}{a+a \sinh ^2(x)} \, dx","Int[Sech[x]^3/(a + a*Sinh[x]^2),x]","\frac{3 \tan ^{-1}(\sinh (x))}{8 a}+\frac{\tanh (x) \text{sech}^3(x)}{4 a}+\frac{3 \tanh (x) \text{sech}(x)}{8 a}","\frac{3 \tan ^{-1}(\sinh (x))}{8 a}+\frac{\tanh (x) \text{sech}^3(x)}{4 a}+\frac{3 \tanh (x) \text{sech}(x)}{8 a}",1,"(3*ArcTan[Sinh[x]])/(8*a) + (3*Sech[x]*Tanh[x])/(8*a) + (Sech[x]^3*Tanh[x])/(4*a)","A",4,3,15,0.2000,1,"{3175, 3768, 3770}"
283,1,89,0,0.0571499,"\int \cosh ^4(c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Cosh[c + d*x]^4*(a + b*Sinh[c + d*x]^2),x]","\frac{(6 a-b) \sinh (c+d x) \cosh ^3(c+d x)}{24 d}+\frac{(6 a-b) \sinh (c+d x) \cosh (c+d x)}{16 d}+\frac{1}{16} x (6 a-b)+\frac{b \sinh (c+d x) \cosh ^5(c+d x)}{6 d}","\frac{(6 a-b) \sinh (c+d x) \cosh ^3(c+d x)}{24 d}+\frac{(6 a-b) \sinh (c+d x) \cosh (c+d x)}{16 d}+\frac{1}{16} x (6 a-b)+\frac{b \sinh (c+d x) \cosh ^5(c+d x)}{6 d}",1,"((6*a - b)*x)/16 + ((6*a - b)*Cosh[c + d*x]*Sinh[c + d*x])/(16*d) + ((6*a - b)*Cosh[c + d*x]^3*Sinh[c + d*x])/(24*d) + (b*Cosh[c + d*x]^5*Sinh[c + d*x])/(6*d)","A",5,4,21,0.1905,1,"{3191, 385, 199, 206}"
284,1,46,0,0.0416845,"\int \cosh ^3(c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Cosh[c + d*x]^3*(a + b*Sinh[c + d*x]^2),x]","\frac{(a+b) \sinh ^3(c+d x)}{3 d}+\frac{a \sinh (c+d x)}{d}+\frac{b \sinh ^5(c+d x)}{5 d}","\frac{(a+b) \sinh ^3(c+d x)}{3 d}+\frac{a \sinh (c+d x)}{d}+\frac{b \sinh ^5(c+d x)}{5 d}",1,"(a*Sinh[c + d*x])/d + ((a + b)*Sinh[c + d*x]^3)/(3*d) + (b*Sinh[c + d*x]^5)/(5*d)","A",3,2,21,0.09524,1,"{3190, 373}"
285,1,61,0,0.0488858,"\int \cosh ^2(c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Cosh[c + d*x]^2*(a + b*Sinh[c + d*x]^2),x]","\frac{(4 a-b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{1}{8} x (4 a-b)+\frac{b \sinh (c+d x) \cosh ^3(c+d x)}{4 d}","\frac{(4 a-b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{1}{8} x (4 a-b)+\frac{b \sinh (c+d x) \cosh ^3(c+d x)}{4 d}",1,"((4*a - b)*x)/8 + ((4*a - b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (b*Cosh[c + d*x]^3*Sinh[c + d*x])/(4*d)","A",4,4,21,0.1905,1,"{3191, 385, 199, 206}"
286,1,28,0,0.0216874,"\int \cosh (c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Cosh[c + d*x]*(a + b*Sinh[c + d*x]^2),x]","\frac{a \sinh (c+d x)}{d}+\frac{b \sinh ^3(c+d x)}{3 d}","\frac{a \sinh (c+d x)}{d}+\frac{b \sinh ^3(c+d x)}{3 d}",1,"(a*Sinh[c + d*x])/d + (b*Sinh[c + d*x]^3)/(3*d)","A",2,1,19,0.05263,1,"{3190}"
287,1,28,0,0.0319274,"\int \text{sech}(c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Sech[c + d*x]*(a + b*Sinh[c + d*x]^2),x]","\frac{(a-b) \tan ^{-1}(\sinh (c+d x))}{d}+\frac{b \sinh (c+d x)}{d}","\frac{(a-b) \tan ^{-1}(\sinh (c+d x))}{d}+\frac{b \sinh (c+d x)}{d}",1,"((a - b)*ArcTan[Sinh[c + d*x]])/d + (b*Sinh[c + d*x])/d","A",3,3,19,0.1579,1,"{3190, 388, 203}"
288,1,19,0,0.0340843,"\int \text{sech}^2(c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Sech[c + d*x]^2*(a + b*Sinh[c + d*x]^2),x]","\frac{(a-b) \tanh (c+d x)}{d}+b x","\frac{(a-b) \tanh (c+d x)}{d}+b x",1,"b*x + ((a - b)*Tanh[c + d*x])/d","A",3,3,21,0.1429,1,"{3191, 388, 206}"
289,1,42,0,0.0395048,"\int \text{sech}^3(c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Sech[c + d*x]^3*(a + b*Sinh[c + d*x]^2),x]","\frac{(a+b) \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{(a-b) \tanh (c+d x) \text{sech}(c+d x)}{2 d}","\frac{(a+b) \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{(a-b) \tanh (c+d x) \text{sech}(c+d x)}{2 d}",1,"((a + b)*ArcTan[Sinh[c + d*x]])/(2*d) + ((a - b)*Sech[c + d*x]*Tanh[c + d*x])/(2*d)","A",3,3,21,0.1429,1,"{3190, 385, 203}"
290,1,32,0,0.0337702,"\int \text{sech}^4(c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Sech[c + d*x]^4*(a + b*Sinh[c + d*x]^2),x]","\frac{a \tanh (c+d x)}{d}-\frac{(a-b) \tanh ^3(c+d x)}{3 d}","\frac{a \tanh (c+d x)}{d}-\frac{(a-b) \tanh ^3(c+d x)}{3 d}",1,"(a*Tanh[c + d*x])/d - ((a - b)*Tanh[c + d*x]^3)/(3*d)","A",2,1,21,0.04762,1,"{3191}"
291,1,70,0,0.0470149,"\int \text{sech}^5(c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Sech[c + d*x]^5*(a + b*Sinh[c + d*x]^2),x]","\frac{(3 a+b) \tan ^{-1}(\sinh (c+d x))}{8 d}+\frac{(a-b) \tanh (c+d x) \text{sech}^3(c+d x)}{4 d}+\frac{(3 a+b) \tanh (c+d x) \text{sech}(c+d x)}{8 d}","\frac{(3 a+b) \tan ^{-1}(\sinh (c+d x))}{8 d}+\frac{(a-b) \tanh (c+d x) \text{sech}^3(c+d x)}{4 d}+\frac{(3 a+b) \tanh (c+d x) \text{sech}(c+d x)}{8 d}",1,"((3*a + b)*ArcTan[Sinh[c + d*x]])/(8*d) + ((3*a + b)*Sech[c + d*x]*Tanh[c + d*x])/(8*d) + ((a - b)*Sech[c + d*x]^3*Tanh[c + d*x])/(4*d)","A",4,4,21,0.1905,1,"{3190, 385, 199, 203}"
292,1,54,0,0.0474164,"\int \text{sech}^6(c+d x) \left(a+b \sinh ^2(c+d x)\right) \, dx","Int[Sech[c + d*x]^6*(a + b*Sinh[c + d*x]^2),x]","\frac{(a-b) \tanh ^5(c+d x)}{5 d}-\frac{(2 a-b) \tanh ^3(c+d x)}{3 d}+\frac{a \tanh (c+d x)}{d}","\frac{(a-b) \tanh ^5(c+d x)}{5 d}-\frac{(2 a-b) \tanh ^3(c+d x)}{3 d}+\frac{a \tanh (c+d x)}{d}",1,"(a*Tanh[c + d*x])/d - ((2*a - b)*Tanh[c + d*x]^3)/(3*d) + ((a - b)*Tanh[c + d*x]^5)/(5*d)","A",3,2,21,0.09524,1,"{3191, 373}"
293,1,159,0,0.1740467,"\int \cosh ^4(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Cosh[c + d*x]^4*(a + b*Sinh[c + d*x]^2)^2,x]","\frac{\left(48 a^2-16 a b+3 b^2\right) \sinh (c+d x) \cosh ^3(c+d x)}{192 d}+\frac{\left(48 a^2-16 a b+3 b^2\right) \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{1}{128} x \left(48 a^2-16 a b+3 b^2\right)+\frac{b (10 a-3 b) \sinh (c+d x) \cosh ^5(c+d x)}{48 d}+\frac{b \sinh (c+d x) \cosh ^7(c+d x) \left(a-(a-b) \tanh ^2(c+d x)\right)}{8 d}","\frac{\left(48 a^2-16 a b+3 b^2\right) \sinh (c+d x) \cosh ^3(c+d x)}{192 d}+\frac{\left(48 a^2-16 a b+3 b^2\right) \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{1}{128} x \left(48 a^2-16 a b+3 b^2\right)+\frac{b (10 a-3 b) \sinh (c+d x) \cosh ^5(c+d x)}{48 d}+\frac{b \sinh (c+d x) \cosh ^7(c+d x) \left(a-(a-b) \tanh ^2(c+d x)\right)}{8 d}",1,"((48*a^2 - 16*a*b + 3*b^2)*x)/128 + ((48*a^2 - 16*a*b + 3*b^2)*Cosh[c + d*x]*Sinh[c + d*x])/(128*d) + ((48*a^2 - 16*a*b + 3*b^2)*Cosh[c + d*x]^3*Sinh[c + d*x])/(192*d) + ((10*a - 3*b)*b*Cosh[c + d*x]^5*Sinh[c + d*x])/(48*d) + (b*Cosh[c + d*x]^7*Sinh[c + d*x]*(a - (a - b)*Tanh[c + d*x]^2))/(8*d)","A",6,5,23,0.2174,1,"{3191, 413, 385, 199, 206}"
294,1,74,0,0.0723943,"\int \cosh ^3(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Cosh[c + d*x]^3*(a + b*Sinh[c + d*x]^2)^2,x]","\frac{a^2 \sinh (c+d x)}{d}+\frac{b (2 a+b) \sinh ^5(c+d x)}{5 d}+\frac{a (a+2 b) \sinh ^3(c+d x)}{3 d}+\frac{b^2 \sinh ^7(c+d x)}{7 d}","\frac{a^2 \sinh (c+d x)}{d}+\frac{b (2 a+b) \sinh ^5(c+d x)}{5 d}+\frac{a (a+2 b) \sinh ^3(c+d x)}{3 d}+\frac{b^2 \sinh ^7(c+d x)}{7 d}",1,"(a^2*Sinh[c + d*x])/d + (a*(a + 2*b)*Sinh[c + d*x]^3)/(3*d) + (b*(2*a + b)*Sinh[c + d*x]^5)/(5*d) + (b^2*Sinh[c + d*x]^7)/(7*d)","A",3,2,23,0.08696,1,"{3190, 373}"
295,1,119,0,0.1427095,"\int \cosh ^2(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Cosh[c + d*x]^2*(a + b*Sinh[c + d*x]^2)^2,x]","\frac{\left(8 a^2-4 a b+b^2\right) \sinh (c+d x) \cosh (c+d x)}{16 d}+\frac{1}{16} x \left(8 a^2-4 a b+b^2\right)+\frac{b (8 a-3 b) \sinh (c+d x) \cosh ^3(c+d x)}{24 d}+\frac{b \sinh (c+d x) \cosh ^5(c+d x) \left(a-(a-b) \tanh ^2(c+d x)\right)}{6 d}","\frac{\left(8 a^2-4 a b+b^2\right) \sinh (c+d x) \cosh (c+d x)}{16 d}+\frac{1}{16} x \left(8 a^2-4 a b+b^2\right)+\frac{b (8 a-3 b) \sinh (c+d x) \cosh ^3(c+d x)}{24 d}+\frac{b \sinh (c+d x) \cosh ^5(c+d x) \left(a-(a-b) \tanh ^2(c+d x)\right)}{6 d}",1,"((8*a^2 - 4*a*b + b^2)*x)/16 + ((8*a^2 - 4*a*b + b^2)*Cosh[c + d*x]*Sinh[c + d*x])/(16*d) + ((8*a - 3*b)*b*Cosh[c + d*x]^3*Sinh[c + d*x])/(24*d) + (b*Cosh[c + d*x]^5*Sinh[c + d*x]*(a - (a - b)*Tanh[c + d*x]^2))/(6*d)","A",5,5,23,0.2174,1,"{3191, 413, 385, 199, 206}"
296,1,49,0,0.0370079,"\int \cosh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Cosh[c + d*x]*(a + b*Sinh[c + d*x]^2)^2,x]","\frac{a^2 \sinh (c+d x)}{d}+\frac{2 a b \sinh ^3(c+d x)}{3 d}+\frac{b^2 \sinh ^5(c+d x)}{5 d}","\frac{a^2 \sinh (c+d x)}{d}+\frac{2 a b \sinh ^3(c+d x)}{3 d}+\frac{b^2 \sinh ^5(c+d x)}{5 d}",1,"(a^2*Sinh[c + d*x])/d + (2*a*b*Sinh[c + d*x]^3)/(3*d) + (b^2*Sinh[c + d*x]^5)/(5*d)","A",3,2,21,0.09524,1,"{3190, 194}"
297,1,55,0,0.0577477,"\int \text{sech}(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Sech[c + d*x]*(a + b*Sinh[c + d*x]^2)^2,x]","\frac{b (2 a-b) \sinh (c+d x)}{d}+\frac{(a-b)^2 \tan ^{-1}(\sinh (c+d x))}{d}+\frac{b^2 \sinh ^3(c+d x)}{3 d}","\frac{b (2 a-b) \sinh (c+d x)}{d}+\frac{(a-b)^2 \tan ^{-1}(\sinh (c+d x))}{d}+\frac{b^2 \sinh ^3(c+d x)}{3 d}",1,"((a - b)^2*ArcTan[Sinh[c + d*x]])/d + ((2*a - b)*b*Sinh[c + d*x])/d + (b^2*Sinh[c + d*x]^3)/(3*d)","A",4,3,21,0.1429,1,"{3190, 390, 203}"
298,1,53,0,0.0949116,"\int \text{sech}^2(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Sech[c + d*x]^2*(a + b*Sinh[c + d*x]^2)^2,x]","\frac{(a-b)^2 \tanh (c+d x)}{d}+\frac{1}{2} b x (4 a-3 b)+\frac{b^2 \sinh (c+d x) \cosh (c+d x)}{2 d}","\frac{(a-b)^2 \tanh (c+d x)}{d}+\frac{1}{2} b x (4 a-3 b)+\frac{b^2 \sinh (c+d x) \cosh (c+d x)}{2 d}",1,"((4*a - 3*b)*b*x)/2 + (b^2*Cosh[c + d*x]*Sinh[c + d*x])/(2*d) + ((a - b)^2*Tanh[c + d*x])/d","A",5,4,23,0.1739,1,"{3191, 390, 385, 206}"
299,1,64,0,0.079862,"\int \text{sech}^3(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Sech[c + d*x]^3*(a + b*Sinh[c + d*x]^2)^2,x]","\frac{(a+3 b) (a-b) \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{(a-b)^2 \tanh (c+d x) \text{sech}(c+d x)}{2 d}+\frac{b^2 \sinh (c+d x)}{d}","\frac{(a+3 b) (a-b) \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{(a-b)^2 \tanh (c+d x) \text{sech}(c+d x)}{2 d}+\frac{b^2 \sinh (c+d x)}{d}",1,"((a - b)*(a + 3*b)*ArcTan[Sinh[c + d*x]])/(2*d) + (b^2*Sinh[c + d*x])/d + ((a - b)^2*Sech[c + d*x]*Tanh[c + d*x])/(2*d)","A",5,4,23,0.1739,1,"{3190, 390, 385, 203}"
300,1,47,0,0.062746,"\int \text{sech}^4(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Sech[c + d*x]^4*(a + b*Sinh[c + d*x]^2)^2,x]","\frac{\left(a^2-b^2\right) \tanh (c+d x)}{d}-\frac{(a-b)^2 \tanh ^3(c+d x)}{3 d}+b^2 x","\frac{\left(a^2-b^2\right) \tanh (c+d x)}{d}-\frac{(a-b)^2 \tanh ^3(c+d x)}{3 d}+b^2 x",1,"b^2*x + ((a^2 - b^2)*Tanh[c + d*x])/d - ((a - b)^2*Tanh[c + d*x]^3)/(3*d)","A",4,3,23,0.1304,1,"{3191, 390, 206}"
301,1,96,0,0.0927501,"\int \text{sech}^5(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Sech[c + d*x]^5*(a + b*Sinh[c + d*x]^2)^2,x]","\frac{\left(3 a^2+2 a b+3 b^2\right) \tan ^{-1}(\sinh (c+d x))}{8 d}+\frac{3 \left(a^2-b^2\right) \tanh (c+d x) \text{sech}(c+d x)}{8 d}+\frac{(a-b) \tanh (c+d x) \text{sech}^3(c+d x) \left(a+b \sinh ^2(c+d x)\right)}{4 d}","\frac{\left(3 a^2+2 a b+3 b^2\right) \tan ^{-1}(\sinh (c+d x))}{8 d}+\frac{3 \left(a^2-b^2\right) \tanh (c+d x) \text{sech}(c+d x)}{8 d}+\frac{(a-b) \tanh (c+d x) \text{sech}^3(c+d x) \left(a+b \sinh ^2(c+d x)\right)}{4 d}",1,"((3*a^2 + 2*a*b + 3*b^2)*ArcTan[Sinh[c + d*x]])/(8*d) + (3*(a^2 - b^2)*Sech[c + d*x]*Tanh[c + d*x])/(8*d) + ((a - b)*Sech[c + d*x]^3*(a + b*Sinh[c + d*x]^2)*Tanh[c + d*x])/(4*d)","A",4,4,23,0.1739,1,"{3190, 413, 385, 203}"
302,1,57,0,0.0601492,"\int \text{sech}^6(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Sech[c + d*x]^6*(a + b*Sinh[c + d*x]^2)^2,x]","\frac{a^2 \tanh (c+d x)}{d}+\frac{(a-b)^2 \tanh ^5(c+d x)}{5 d}-\frac{2 a (a-b) \tanh ^3(c+d x)}{3 d}","\frac{a^2 \tanh (c+d x)}{d}+\frac{(a-b)^2 \tanh ^5(c+d x)}{5 d}-\frac{2 a (a-b) \tanh ^3(c+d x)}{3 d}",1,"(a^2*Tanh[c + d*x])/d - (2*a*(a - b)*Tanh[c + d*x]^3)/(3*d) + ((a - b)^2*Tanh[c + d*x]^5)/(5*d)","A",3,2,23,0.08696,1,"{3191, 194}"
303,1,131,0,0.1325925,"\int \text{sech}^7(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2 \, dx","Int[Sech[c + d*x]^7*(a + b*Sinh[c + d*x]^2)^2,x]","\frac{\left(5 a^2+2 a b+b^2\right) \tan ^{-1}(\sinh (c+d x))}{16 d}+\frac{\left(5 a^2+2 a b+b^2\right) \tanh (c+d x) \text{sech}(c+d x)}{16 d}+\frac{(a-b) (5 a+3 b) \tanh (c+d x) \text{sech}^3(c+d x)}{24 d}+\frac{(a-b) \tanh (c+d x) \text{sech}^5(c+d x) \left(a+b \sinh ^2(c+d x)\right)}{6 d}","\frac{\left(5 a^2+2 a b+b^2\right) \tan ^{-1}(\sinh (c+d x))}{16 d}+\frac{\left(5 a^2+2 a b+b^2\right) \tanh (c+d x) \text{sech}(c+d x)}{16 d}+\frac{(a-b) (5 a+3 b) \tanh (c+d x) \text{sech}^3(c+d x)}{24 d}+\frac{(a-b) \tanh (c+d x) \text{sech}^5(c+d x) \left(a+b \sinh ^2(c+d x)\right)}{6 d}",1,"((5*a^2 + 2*a*b + b^2)*ArcTan[Sinh[c + d*x]])/(16*d) + ((5*a^2 + 2*a*b + b^2)*Sech[c + d*x]*Tanh[c + d*x])/(16*d) + ((a - b)*(5*a + 3*b)*Sech[c + d*x]^3*Tanh[c + d*x])/(24*d) + ((a - b)*Sech[c + d*x]^5*(a + b*Sinh[c + d*x]^2)*Tanh[c + d*x])/(6*d)","A",5,5,23,0.2174,1,"{3190, 413, 385, 199, 203}"
304,1,238,0,0.3317565,"\int \cosh ^4(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Cosh[c + d*x]^4*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{b \left(44 a^2-28 a b+5 b^2\right) \sinh (c+d x) \cosh ^5(c+d x)}{160 d}+\frac{(4 a-b) \left(8 a^2-2 a b+b^2\right) \sinh (c+d x) \cosh ^3(c+d x)}{128 d}+\frac{3 (4 a-b) \left(8 a^2-2 a b+b^2\right) \sinh (c+d x) \cosh (c+d x)}{256 d}+\frac{3}{256} x (4 a-b) \left(8 a^2-2 a b+b^2\right)+\frac{b \sinh (c+d x) \cosh ^9(c+d x) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}{10 d}+\frac{b \sinh (c+d x) \cosh ^7(c+d x) \left(a (10 a-b)-5 (a-b) (2 a-b) \tanh ^2(c+d x)\right)}{80 d}","\frac{b \left(44 a^2-28 a b+5 b^2\right) \sinh (c+d x) \cosh ^5(c+d x)}{160 d}+\frac{(4 a-b) \left(8 a^2-2 a b+b^2\right) \sinh (c+d x) \cosh ^3(c+d x)}{128 d}+\frac{3 (4 a-b) \left(8 a^2-2 a b+b^2\right) \sinh (c+d x) \cosh (c+d x)}{256 d}+\frac{3}{256} x (4 a-b) \left(8 a^2-2 a b+b^2\right)+\frac{b \sinh (c+d x) \cosh ^9(c+d x) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}{10 d}+\frac{b \sinh (c+d x) \cosh ^7(c+d x) \left(a (10 a-b)-5 (a-b) (2 a-b) \tanh ^2(c+d x)\right)}{80 d}",1,"(3*(4*a - b)*(8*a^2 - 2*a*b + b^2)*x)/256 + (3*(4*a - b)*(8*a^2 - 2*a*b + b^2)*Cosh[c + d*x]*Sinh[c + d*x])/(256*d) + ((4*a - b)*(8*a^2 - 2*a*b + b^2)*Cosh[c + d*x]^3*Sinh[c + d*x])/(128*d) + (b*(44*a^2 - 28*a*b + 5*b^2)*Cosh[c + d*x]^5*Sinh[c + d*x])/(160*d) + (b*Cosh[c + d*x]^9*Sinh[c + d*x]*(a - (a - b)*Tanh[c + d*x]^2)^2)/(10*d) + (b*Cosh[c + d*x]^7*Sinh[c + d*x]*(a*(10*a - b) - 5*(a - b)*(2*a - b)*Tanh[c + d*x]^2))/(80*d)","A",7,6,23,0.2609,1,"{3191, 413, 526, 385, 199, 206}"
305,1,98,0,0.0902005,"\int \cosh ^3(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Cosh[c + d*x]^3*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{a^2 (a+3 b) \sinh ^3(c+d x)}{3 d}+\frac{a^3 \sinh (c+d x)}{d}+\frac{b^2 (3 a+b) \sinh ^7(c+d x)}{7 d}+\frac{3 a b (a+b) \sinh ^5(c+d x)}{5 d}+\frac{b^3 \sinh ^9(c+d x)}{9 d}","\frac{a^2 (a+3 b) \sinh ^3(c+d x)}{3 d}+\frac{a^3 \sinh (c+d x)}{d}+\frac{b^2 (3 a+b) \sinh ^7(c+d x)}{7 d}+\frac{3 a b (a+b) \sinh ^5(c+d x)}{5 d}+\frac{b^3 \sinh ^9(c+d x)}{9 d}",1,"(a^3*Sinh[c + d*x])/d + (a^2*(a + 3*b)*Sinh[c + d*x]^3)/(3*d) + (3*a*b*(a + b)*Sinh[c + d*x]^5)/(5*d) + (b^2*(3*a + b)*Sinh[c + d*x]^7)/(7*d) + (b^3*Sinh[c + d*x]^9)/(9*d)","A",3,2,23,0.08696,1,"{3190, 373}"
306,1,203,0,0.2680318,"\int \cosh ^2(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Cosh[c + d*x]^2*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{b \left(88 a^2-68 a b+15 b^2\right) \sinh (c+d x) \cosh ^3(c+d x)}{192 d}+\frac{\left(-48 a^2 b+64 a^3+24 a b^2-5 b^3\right) \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{1}{128} x \left(-48 a^2 b+64 a^3+24 a b^2-5 b^3\right)+\frac{b \sinh (c+d x) \cosh ^7(c+d x) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}{8 d}+\frac{b \sinh (c+d x) \cosh ^5(c+d x) \left(a (8 a-b)-(8 a-5 b) (a-b) \tanh ^2(c+d x)\right)}{48 d}","\frac{b \left(88 a^2-68 a b+15 b^2\right) \sinh (c+d x) \cosh ^3(c+d x)}{192 d}+\frac{\left(-48 a^2 b+64 a^3+24 a b^2-5 b^3\right) \sinh (c+d x) \cosh (c+d x)}{128 d}+\frac{1}{128} x \left(-48 a^2 b+64 a^3+24 a b^2-5 b^3\right)+\frac{b \sinh (c+d x) \cosh ^7(c+d x) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}{8 d}+\frac{b \sinh (c+d x) \cosh ^5(c+d x) \left(a (8 a-b)-(8 a-5 b) (a-b) \tanh ^2(c+d x)\right)}{48 d}",1,"((64*a^3 - 48*a^2*b + 24*a*b^2 - 5*b^3)*x)/128 + ((64*a^3 - 48*a^2*b + 24*a*b^2 - 5*b^3)*Cosh[c + d*x]*Sinh[c + d*x])/(128*d) + (b*(88*a^2 - 68*a*b + 15*b^2)*Cosh[c + d*x]^3*Sinh[c + d*x])/(192*d) + (b*Cosh[c + d*x]^7*Sinh[c + d*x]*(a - (a - b)*Tanh[c + d*x]^2)^2)/(8*d) + (b*Cosh[c + d*x]^5*Sinh[c + d*x]*(a*(8*a - b) - (8*a - 5*b)*(a - b)*Tanh[c + d*x]^2))/(48*d)","A",6,6,23,0.2609,1,"{3191, 413, 526, 385, 199, 206}"
307,1,67,0,0.0454635,"\int \cosh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Cosh[c + d*x]*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{a^2 b \sinh ^3(c+d x)}{d}+\frac{a^3 \sinh (c+d x)}{d}+\frac{3 a b^2 \sinh ^5(c+d x)}{5 d}+\frac{b^3 \sinh ^7(c+d x)}{7 d}","\frac{a^2 b \sinh ^3(c+d x)}{d}+\frac{a^3 \sinh (c+d x)}{d}+\frac{3 a b^2 \sinh ^5(c+d x)}{5 d}+\frac{b^3 \sinh ^7(c+d x)}{7 d}",1,"(a^3*Sinh[c + d*x])/d + (a^2*b*Sinh[c + d*x]^3)/d + (3*a*b^2*Sinh[c + d*x]^5)/(5*d) + (b^3*Sinh[c + d*x]^7)/(7*d)","A",3,2,21,0.09524,1,"{3190, 194}"
308,1,86,0,0.0755837,"\int \text{sech}(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Sech[c + d*x]*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{b \left(3 a^2-3 a b+b^2\right) \sinh (c+d x)}{d}+\frac{b^2 (3 a-b) \sinh ^3(c+d x)}{3 d}+\frac{(a-b)^3 \tan ^{-1}(\sinh (c+d x))}{d}+\frac{b^3 \sinh ^5(c+d x)}{5 d}","\frac{b \left(3 a^2-3 a b+b^2\right) \sinh (c+d x)}{d}+\frac{b^2 (3 a-b) \sinh ^3(c+d x)}{3 d}+\frac{(a-b)^3 \tan ^{-1}(\sinh (c+d x))}{d}+\frac{b^3 \sinh ^5(c+d x)}{5 d}",1,"((a - b)^3*ArcTan[Sinh[c + d*x]])/d + (b*(3*a^2 - 3*a*b + b^2)*Sinh[c + d*x])/d + ((3*a - b)*b^2*Sinh[c + d*x]^3)/(3*d) + (b^3*Sinh[c + d*x]^5)/(5*d)","A",4,3,21,0.1429,1,"{3190, 390, 203}"
309,1,92,0,0.1290996,"\int \text{sech}^2(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Sech[c + d*x]^2*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{3}{8} b x \left(8 a^2-12 a b+5 b^2\right)+\frac{3 b^2 (4 a-3 b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{(a-b)^3 \tanh (c+d x)}{d}+\frac{b^3 \sinh (c+d x) \cosh ^3(c+d x)}{4 d}","\frac{3}{8} b x \left(8 a^2-12 a b+5 b^2\right)+\frac{3 b^2 (4 a-3 b) \sinh (c+d x) \cosh (c+d x)}{8 d}+\frac{(a-b)^3 \tanh (c+d x)}{d}+\frac{b^3 \sinh (c+d x) \cosh ^3(c+d x)}{4 d}",1,"(3*b*(8*a^2 - 12*a*b + 5*b^2)*x)/8 + (3*(4*a - 3*b)*b^2*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (b^3*Cosh[c + d*x]^3*Sinh[c + d*x])/(4*d) + ((a - b)^3*Tanh[c + d*x])/d","A",6,5,23,0.2174,1,"{3191, 390, 1157, 385, 206}"
310,1,91,0,0.0957924,"\int \text{sech}^3(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Sech[c + d*x]^3*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{b^2 (3 a-2 b) \sinh (c+d x)}{d}+\frac{(a+5 b) (a-b)^2 \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{(a-b)^3 \tanh (c+d x) \text{sech}(c+d x)}{2 d}+\frac{b^3 \sinh ^3(c+d x)}{3 d}","\frac{b^2 (3 a-2 b) \sinh (c+d x)}{d}+\frac{(a+5 b) (a-b)^2 \tan ^{-1}(\sinh (c+d x))}{2 d}+\frac{(a-b)^3 \tanh (c+d x) \text{sech}(c+d x)}{2 d}+\frac{b^3 \sinh ^3(c+d x)}{3 d}",1,"((a - b)^2*(a + 5*b)*ArcTan[Sinh[c + d*x]])/(2*d) + ((3*a - 2*b)*b^2*Sinh[c + d*x])/d + (b^3*Sinh[c + d*x]^3)/(3*d) + ((a - b)^3*Sech[c + d*x]*Tanh[c + d*x])/(2*d)","A",5,4,23,0.1739,1,"{3190, 390, 385, 203}"
311,1,82,0,0.1084888,"\int \text{sech}^4(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Sech[c + d*x]^4*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{1}{2} b^2 x (6 a-5 b)-\frac{(a-b)^3 \tanh ^3(c+d x)}{3 d}+\frac{(a-b)^2 (a+2 b) \tanh (c+d x)}{d}+\frac{b^3 \sinh (c+d x) \cosh (c+d x)}{2 d}","\frac{1}{2} b^2 x (6 a-5 b)-\frac{(a-b)^3 \tanh ^3(c+d x)}{3 d}+\frac{(a-b)^2 (a+2 b) \tanh (c+d x)}{d}+\frac{b^3 \sinh (c+d x) \cosh (c+d x)}{2 d}",1,"((6*a - 5*b)*b^2*x)/2 + (b^3*Cosh[c + d*x]*Sinh[c + d*x])/(2*d) + ((a - b)^2*(a + 2*b)*Tanh[c + d*x])/d - ((a - b)^3*Tanh[c + d*x]^3)/(3*d)","A",5,4,23,0.1739,1,"{3191, 390, 385, 206}"
312,1,103,0,0.1320086,"\int \text{sech}^5(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Sech[c + d*x]^5*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{3 (a-b) \left((a+b)^2+4 b^2\right) \tan ^{-1}(\sinh (c+d x))}{8 d}+\frac{(a-b)^3 \tanh (c+d x) \text{sech}^3(c+d x)}{4 d}+\frac{3 (a-b)^2 (a+3 b) \tanh (c+d x) \text{sech}(c+d x)}{8 d}+\frac{b^3 \sinh (c+d x)}{d}","\frac{3 (a-b) \left((a+b)^2+4 b^2\right) \tan ^{-1}(\sinh (c+d x))}{8 d}+\frac{(a-b)^3 \tanh (c+d x) \text{sech}^3(c+d x)}{4 d}+\frac{3 (a-b)^2 (a+3 b) \tanh (c+d x) \text{sech}(c+d x)}{8 d}+\frac{b^3 \sinh (c+d x)}{d}",1,"(3*(a - b)*(4*b^2 + (a + b)^2)*ArcTan[Sinh[c + d*x]])/(8*d) + (b^3*Sinh[c + d*x])/d + (3*(a - b)^2*(a + 3*b)*Sech[c + d*x]*Tanh[c + d*x])/(8*d) + ((a - b)^3*Sech[c + d*x]^3*Tanh[c + d*x])/(4*d)","A",6,5,23,0.2174,1,"{3190, 390, 1157, 385, 203}"
313,1,74,0,0.0798852,"\int \text{sech}^6(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Sech[c + d*x]^6*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{\left(a^3-b^3\right) \tanh (c+d x)}{d}+\frac{(a-b)^3 \tanh ^5(c+d x)}{5 d}-\frac{(a-b)^2 (2 a+b) \tanh ^3(c+d x)}{3 d}+b^3 x","\frac{\left(a^3-b^3\right) \tanh (c+d x)}{d}+\frac{(a-b)^3 \tanh ^5(c+d x)}{5 d}-\frac{(a-b)^2 (2 a+b) \tanh ^3(c+d x)}{3 d}+b^3 x",1,"b^3*x + ((a^3 - b^3)*Tanh[c + d*x])/d - ((a - b)^2*(2*a + b)*Tanh[c + d*x]^3)/(3*d) + ((a - b)^3*Tanh[c + d*x]^5)/(5*d)","A",4,3,23,0.1304,1,"{3191, 390, 206}"
314,1,154,0,0.1529183,"\int \text{sech}^7(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Sech[c + d*x]^7*(a + b*Sinh[c + d*x]^2)^3,x]","\frac{(a+b) \left(5 a^2-2 a b+5 b^2\right) \tan ^{-1}(\sinh (c+d x))}{16 d}+\frac{(a-b) \left(15 a^2+14 a b+15 b^2\right) \tanh (c+d x) \text{sech}(c+d x)}{48 d}+\frac{5 \left(a^2-b^2\right) \tanh (c+d x) \text{sech}^3(c+d x) \left(a+b \sinh ^2(c+d x)\right)}{24 d}+\frac{(a-b) \tanh (c+d x) \text{sech}^5(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2}{6 d}","\frac{(a+b) \left(5 a^2-2 a b+5 b^2\right) \tan ^{-1}(\sinh (c+d x))}{16 d}+\frac{(a-b) \left(15 a^2+14 a b+15 b^2\right) \tanh (c+d x) \text{sech}(c+d x)}{48 d}+\frac{5 \left(a^2-b^2\right) \tanh (c+d x) \text{sech}^3(c+d x) \left(a+b \sinh ^2(c+d x)\right)}{24 d}+\frac{(a-b) \tanh (c+d x) \text{sech}^5(c+d x) \left(a+b \sinh ^2(c+d x)\right)^2}{6 d}",1,"((a + b)*(5*a^2 - 2*a*b + 5*b^2)*ArcTan[Sinh[c + d*x]])/(16*d) + ((a - b)*(15*a^2 + 14*a*b + 15*b^2)*Sech[c + d*x]*Tanh[c + d*x])/(48*d) + (5*(a^2 - b^2)*Sech[c + d*x]^3*(a + b*Sinh[c + d*x]^2)*Tanh[c + d*x])/(24*d) + ((a - b)*Sech[c + d*x]^5*(a + b*Sinh[c + d*x]^2)^2*Tanh[c + d*x])/(6*d)","A",5,5,23,0.2174,1,"{3190, 413, 526, 385, 203}"
315,1,80,0,0.0738987,"\int \text{sech}^8(c+d x) \left(a+b \sinh ^2(c+d x)\right)^3 \, dx","Int[Sech[c + d*x]^8*(a + b*Sinh[c + d*x]^2)^3,x]","-\frac{a^2 (a-b) \tanh ^3(c+d x)}{d}+\frac{a^3 \tanh (c+d x)}{d}-\frac{(a-b)^3 \tanh ^7(c+d x)}{7 d}+\frac{3 a (a-b)^2 \tanh ^5(c+d x)}{5 d}","-\frac{a^2 (a-b) \tanh ^3(c+d x)}{d}+\frac{a^3 \tanh (c+d x)}{d}-\frac{(a-b)^3 \tanh ^7(c+d x)}{7 d}+\frac{3 a (a-b)^2 \tanh ^5(c+d x)}{5 d}",1,"(a^3*Tanh[c + d*x])/d - (a^2*(a - b)*Tanh[c + d*x]^3)/d + (3*a*(a - b)^2*Tanh[c + d*x]^5)/(5*d) - ((a - b)^3*Tanh[c + d*x]^7)/(7*d)","A",3,2,23,0.08696,1,"{3191, 194}"
316,1,108,0,0.1129277,"\int \frac{\cosh ^7(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Cosh[c + d*x]^7/(a + b*Sinh[c + d*x]^2),x]","\frac{\left(a^2-3 a b+3 b^2\right) \sinh (c+d x)}{b^3 d}-\frac{(a-3 b) \sinh ^3(c+d x)}{3 b^2 d}-\frac{(a-b)^3 \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b^{7/2} d}+\frac{\sinh ^5(c+d x)}{5 b d}","\frac{\left(a^2-3 a b+3 b^2\right) \sinh (c+d x)}{b^3 d}-\frac{(a-3 b) \sinh ^3(c+d x)}{3 b^2 d}-\frac{(a-b)^3 \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b^{7/2} d}+\frac{\sinh ^5(c+d x)}{5 b d}",1,"-(((a - b)^3*ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]])/(Sqrt[a]*b^(7/2)*d)) + ((a^2 - 3*a*b + 3*b^2)*Sinh[c + d*x])/(b^3*d) - ((a - 3*b)*Sinh[c + d*x]^3)/(3*b^2*d) + Sinh[c + d*x]^5/(5*b*d)","A",4,3,23,0.1304,1,"{3190, 390, 205}"
317,1,121,0,0.2205122,"\int \frac{\cosh ^6(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Cosh[c + d*x]^6/(a + b*Sinh[c + d*x]^2),x]","\frac{x \left(8 a^2-20 a b+15 b^2\right)}{8 b^3}-\frac{(a-b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b^3 d}-\frac{(4 a-7 b) \sinh (c+d x) \cosh (c+d x)}{8 b^2 d}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 b d}","\frac{x \left(8 a^2-20 a b+15 b^2\right)}{8 b^3}-\frac{(a-b)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b^3 d}-\frac{(4 a-7 b) \sinh (c+d x) \cosh (c+d x)}{8 b^2 d}+\frac{\sinh (c+d x) \cosh ^3(c+d x)}{4 b d}",1,"((8*a^2 - 20*a*b + 15*b^2)*x)/(8*b^3) - ((a - b)^(5/2)*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(Sqrt[a]*b^3*d) - ((4*a - 7*b)*Cosh[c + d*x]*Sinh[c + d*x])/(8*b^2*d) + (Cosh[c + d*x]^3*Sinh[c + d*x])/(4*b*d)","A",6,6,23,0.2609,1,"{3191, 414, 527, 522, 206, 208}"
318,1,77,0,0.0933289,"\int \frac{\cosh ^5(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Cosh[c + d*x]^5/(a + b*Sinh[c + d*x]^2),x]","-\frac{(a-2 b) \sinh (c+d x)}{b^2 d}+\frac{(a-b)^2 \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b^{5/2} d}+\frac{\sinh ^3(c+d x)}{3 b d}","-\frac{(a-2 b) \sinh (c+d x)}{b^2 d}+\frac{(a-b)^2 \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b^{5/2} d}+\frac{\sinh ^3(c+d x)}{3 b d}",1,"((a - b)^2*ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]])/(Sqrt[a]*b^(5/2)*d) - ((a - 2*b)*Sinh[c + d*x])/(b^2*d) + Sinh[c + d*x]^3/(3*b*d)","A",4,3,23,0.1304,1,"{3190, 390, 205}"
319,1,81,0,0.1329274,"\int \frac{\cosh ^4(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Cosh[c + d*x]^4/(a + b*Sinh[c + d*x]^2),x]","\frac{(a-b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b^2 d}-\frac{x (2 a-3 b)}{2 b^2}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 b d}","\frac{(a-b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b^2 d}-\frac{x (2 a-3 b)}{2 b^2}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 b d}",1,"-((2*a - 3*b)*x)/(2*b^2) + ((a - b)^(3/2)*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(Sqrt[a]*b^2*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*b*d)","A",5,5,23,0.2174,1,"{3191, 414, 522, 206, 208}"
320,1,52,0,0.0704174,"\int \frac{\cosh ^3(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Cosh[c + d*x]^3/(a + b*Sinh[c + d*x]^2),x]","\frac{\sinh (c+d x)}{b d}-\frac{(a-b) \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2} d}","\frac{\sinh (c+d x)}{b d}-\frac{(a-b) \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2} d}",1,"-(((a - b)*ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]])/(Sqrt[a]*b^(3/2)*d)) + Sinh[c + d*x]/(b*d)","A",3,3,23,0.1304,1,"{3190, 388, 205}"
321,1,50,0,0.0817953,"\int \frac{\cosh ^2(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Cosh[c + d*x]^2/(a + b*Sinh[c + d*x]^2),x]","\frac{x}{b}-\frac{\sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b d}","\frac{x}{b}-\frac{\sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} b d}",1,"x/b - (Sqrt[a - b]*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(Sqrt[a]*b*d)","A",4,4,23,0.1739,1,"{3191, 391, 206, 208}"
322,1,32,0,0.0365203,"\int \frac{\cosh (c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Cosh[c + d*x]/(a + b*Sinh[c + d*x]^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} d}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} d}",1,"ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]]/(Sqrt[a]*Sqrt[b]*d)","A",2,2,21,0.09524,1,"{3190, 205}"
323,1,59,0,0.0667097,"\int \frac{\text{sech}(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Sech[c + d*x]/(a + b*Sinh[c + d*x]^2),x]","\frac{\tan ^{-1}(\sinh (c+d x))}{d (a-b)}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a-b)}","\frac{\tan ^{-1}(\sinh (c+d x))}{d (a-b)}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a-b)}",1,"ArcTan[Sinh[c + d*x]]/((a - b)*d) - (Sqrt[b]*ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]])/(Sqrt[a]*(a - b)*d)","A",4,4,21,0.1905,1,"{3190, 391, 203, 205}"
324,1,60,0,0.0788262,"\int \frac{\text{sech}^2(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Sech[c + d*x]^2/(a + b*Sinh[c + d*x]^2),x]","\frac{\tanh (c+d x)}{d (a-b)}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a-b)^{3/2}}","\frac{\tanh (c+d x)}{d (a-b)}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a-b)^{3/2}}",1,"-((b*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(Sqrt[a]*(a - b)^(3/2)*d)) + Tanh[c + d*x]/((a - b)*d)","A",3,3,23,0.1304,1,"{3191, 388, 208}"
325,1,92,0,0.1054295,"\int \frac{\text{sech}^3(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Sech[c + d*x]^3/(a + b*Sinh[c + d*x]^2),x]","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a-b)^2}+\frac{(a-3 b) \tan ^{-1}(\sinh (c+d x))}{2 d (a-b)^2}+\frac{\tanh (c+d x) \text{sech}(c+d x)}{2 d (a-b)}","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a-b)^2}+\frac{(a-3 b) \tan ^{-1}(\sinh (c+d x))}{2 d (a-b)^2}+\frac{\tanh (c+d x) \text{sech}(c+d x)}{2 d (a-b)}",1,"((a - 3*b)*ArcTan[Sinh[c + d*x]])/(2*(a - b)^2*d) + (b^(3/2)*ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]])/(Sqrt[a]*(a - b)^2*d) + (Sech[c + d*x]*Tanh[c + d*x])/(2*(a - b)*d)","A",5,5,23,0.2174,1,"{3190, 414, 522, 203, 205}"
326,1,88,0,0.1053801,"\int \frac{\text{sech}^4(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Sech[c + d*x]^4/(a + b*Sinh[c + d*x]^2),x]","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a-b)^{5/2}}-\frac{\tanh ^3(c+d x)}{3 d (a-b)}+\frac{(a-2 b) \tanh (c+d x)}{d (a-b)^2}","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a-b)^{5/2}}-\frac{\tanh ^3(c+d x)}{3 d (a-b)}+\frac{(a-2 b) \tanh (c+d x)}{d (a-b)^2}",1,"(b^2*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(Sqrt[a]*(a - b)^(5/2)*d) + ((a - 2*b)*Tanh[c + d*x])/((a - b)^2*d) - Tanh[c + d*x]^3/(3*(a - b)*d)","A",4,3,23,0.1304,1,"{3191, 390, 208}"
327,1,138,0,0.1618517,"\int \frac{\text{sech}^5(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Sech[c + d*x]^5/(a + b*Sinh[c + d*x]^2),x]","\frac{\left(3 a^2-10 a b+15 b^2\right) \tan ^{-1}(\sinh (c+d x))}{8 d (a-b)^3}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a-b)^3}+\frac{\tanh (c+d x) \text{sech}^3(c+d x)}{4 d (a-b)}+\frac{(3 a-7 b) \tanh (c+d x) \text{sech}(c+d x)}{8 d (a-b)^2}","\frac{\left(3 a^2-10 a b+15 b^2\right) \tan ^{-1}(\sinh (c+d x))}{8 d (a-b)^3}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a-b)^3}+\frac{\tanh (c+d x) \text{sech}^3(c+d x)}{4 d (a-b)}+\frac{(3 a-7 b) \tanh (c+d x) \text{sech}(c+d x)}{8 d (a-b)^2}",1,"((3*a^2 - 10*a*b + 15*b^2)*ArcTan[Sinh[c + d*x]])/(8*(a - b)^3*d) - (b^(5/2)*ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]])/(Sqrt[a]*(a - b)^3*d) + ((3*a - 7*b)*Sech[c + d*x]*Tanh[c + d*x])/(8*(a - b)^2*d) + (Sech[c + d*x]^3*Tanh[c + d*x])/(4*(a - b)*d)","A",6,6,23,0.2609,1,"{3190, 414, 527, 522, 203, 205}"
328,1,126,0,0.147213,"\int \frac{\text{sech}^6(c+d x)}{a+b \sinh ^2(c+d x)} \, dx","Int[Sech[c + d*x]^6/(a + b*Sinh[c + d*x]^2),x]","\frac{\left(a^2-3 a b+3 b^2\right) \tanh (c+d x)}{d (a-b)^3}-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a-b)^{7/2}}+\frac{\tanh ^5(c+d x)}{5 d (a-b)}-\frac{(2 a-3 b) \tanh ^3(c+d x)}{3 d (a-b)^2}","\frac{\left(a^2-3 a b+3 b^2\right) \tanh (c+d x)}{d (a-b)^3}-\frac{b^3 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{\sqrt{a} d (a-b)^{7/2}}+\frac{\tanh ^5(c+d x)}{5 d (a-b)}-\frac{(2 a-3 b) \tanh ^3(c+d x)}{3 d (a-b)^2}",1,"-((b^3*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(Sqrt[a]*(a - b)^(7/2)*d)) + ((a^2 - 3*a*b + 3*b^2)*Tanh[c + d*x])/((a - b)^3*d) - ((2*a - 3*b)*Tanh[c + d*x]^3)/(3*(a - b)^2*d) + Tanh[c + d*x]^5/(5*(a - b)*d)","A",4,3,23,0.1304,1,"{3191, 390, 208}"
329,1,158,0,0.2578498,"\int \frac{\cosh ^6(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Cosh[c + d*x]^6/(a + b*Sinh[c + d*x]^2)^2,x]","\frac{(4 a+b) (a-b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} b^3 d}+\frac{(2 a-b) (a-b) \tanh (c+d x)}{2 a b^2 d \left(a-(a-b) \tanh ^2(c+d x)\right)}-\frac{x (4 a-5 b)}{2 b^3}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 b d \left(a-(a-b) \tanh ^2(c+d x)\right)}","\frac{(4 a+b) (a-b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} b^3 d}+\frac{(2 a-b) (a-b) \tanh (c+d x)}{2 a b^2 d \left(a-(a-b) \tanh ^2(c+d x)\right)}-\frac{x (4 a-5 b)}{2 b^3}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 b d \left(a-(a-b) \tanh ^2(c+d x)\right)}",1,"-((4*a - 5*b)*x)/(2*b^3) + ((a - b)^(3/2)*(4*a + b)*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*b^3*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*b*d*(a - (a - b)*Tanh[c + d*x]^2)) + ((a - b)*(2*a - b)*Tanh[c + d*x])/(2*a*b^2*d*(a - (a - b)*Tanh[c + d*x]^2))","A",6,6,23,0.2609,1,"{3191, 414, 527, 522, 206, 208}"
330,1,104,0,0.138491,"\int \frac{\cosh ^5(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Cosh[c + d*x]^5/(a + b*Sinh[c + d*x]^2)^2,x]","-\frac{\left(3 a^2-2 a b-b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} b^{5/2} d}+\frac{(a-b)^2 \sinh (c+d x)}{2 a b^2 d \left(a+b \sinh ^2(c+d x)\right)}+\frac{\sinh (c+d x)}{b^2 d}","-\frac{\left(3 a^2-2 a b-b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} b^{5/2} d}+\frac{(a-b)^2 \sinh (c+d x)}{2 a b^2 d \left(a+b \sinh ^2(c+d x)\right)}+\frac{\sinh (c+d x)}{b^2 d}",1,"-((3*a^2 - 2*a*b - b^2)*ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*b^(5/2)*d) + Sinh[c + d*x]/(b^2*d) + ((a - b)^2*Sinh[c + d*x])/(2*a*b^2*d*(a + b*Sinh[c + d*x]^2))","A",5,4,23,0.1739,1,"{3190, 390, 385, 205}"
331,1,100,0,0.1383997,"\int \frac{\cosh ^4(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Cosh[c + d*x]^4/(a + b*Sinh[c + d*x]^2)^2,x]","-\frac{\sqrt{a-b} (2 a+b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} b^2 d}-\frac{(a-b) \tanh (c+d x)}{2 a b d \left(a-(a-b) \tanh ^2(c+d x)\right)}+\frac{x}{b^2}","-\frac{\sqrt{a-b} (2 a+b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} b^2 d}-\frac{(a-b) \tanh (c+d x)}{2 a b d \left(a-(a-b) \tanh ^2(c+d x)\right)}+\frac{x}{b^2}",1,"x/b^2 - (Sqrt[a - b]*(2*a + b)*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*b^2*d) - ((a - b)*Tanh[c + d*x])/(2*a*b*d*(a - (a - b)*Tanh[c + d*x]^2))","A",5,5,23,0.2174,1,"{3191, 414, 522, 206, 208}"
332,1,77,0,0.0781891,"\int \frac{\cosh ^3(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Cosh[c + d*x]^3/(a + b*Sinh[c + d*x]^2)^2,x]","\frac{(a+b) \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} b^{3/2} d}-\frac{(a-b) \sinh (c+d x)}{2 a b d \left(a+b \sinh ^2(c+d x)\right)}","\frac{(a+b) \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} b^{3/2} d}-\frac{(a-b) \sinh (c+d x)}{2 a b d \left(a+b \sinh ^2(c+d x)\right)}",1,"((a + b)*ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*b^(3/2)*d) - ((a - b)*Sinh[c + d*x])/(2*a*b*d*(a + b*Sinh[c + d*x]^2))","A",3,3,23,0.1304,1,"{3190, 385, 205}"
333,1,79,0,0.0768361,"\int \frac{\cosh ^2(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Cosh[c + d*x]^2/(a + b*Sinh[c + d*x]^2)^2,x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d \sqrt{a-b}}+\frac{\tanh (c+d x)}{2 a d \left(a-(a-b) \tanh ^2(c+d x)\right)}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d \sqrt{a-b}}+\frac{\tanh (c+d x)}{2 a d \left(a-(a-b) \tanh ^2(c+d x)\right)}",1,"ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]]/(2*a^(3/2)*Sqrt[a - b]*d) + Tanh[c + d*x]/(2*a*d*(a - (a - b)*Tanh[c + d*x]^2))","A",3,3,23,0.1304,1,"{3191, 199, 208}"
334,1,66,0,0.0466733,"\int \frac{\cosh (c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Cosh[c + d*x]/(a + b*Sinh[c + d*x]^2)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} d}+\frac{\sinh (c+d x)}{2 a d \left(a+b \sinh ^2(c+d x)\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} d}+\frac{\sinh (c+d x)}{2 a d \left(a+b \sinh ^2(c+d x)\right)}",1,"ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]]/(2*a^(3/2)*Sqrt[b]*d) + Sinh[c + d*x]/(2*a*d*(a + b*Sinh[c + d*x]^2))","A",3,3,21,0.1429,1,"{3190, 199, 205}"
335,1,106,0,0.1079072,"\int \frac{\text{sech}(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]/(a + b*Sinh[c + d*x]^2)^2,x]","-\frac{\sqrt{b} (3 a-b) \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a-b)^2}-\frac{b \sinh (c+d x)}{2 a d (a-b) \left(a+b \sinh ^2(c+d x)\right)}+\frac{\tan ^{-1}(\sinh (c+d x))}{d (a-b)^2}","-\frac{\sqrt{b} (3 a-b) \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a-b)^2}-\frac{b \sinh (c+d x)}{2 a d (a-b) \left(a+b \sinh ^2(c+d x)\right)}+\frac{\tan ^{-1}(\sinh (c+d x))}{d (a-b)^2}",1,"ArcTan[Sinh[c + d*x]]/((a - b)^2*d) - ((3*a - b)*Sqrt[b]*ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*(a - b)^2*d) - (b*Sinh[c + d*x])/(2*a*(a - b)*d*(a + b*Sinh[c + d*x]^2))","A",5,5,21,0.2381,1,"{3190, 414, 522, 203, 205}"
336,1,114,0,0.1793529,"\int \frac{\text{sech}^2(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]^2/(a + b*Sinh[c + d*x]^2)^2,x]","-\frac{b (4 a-b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a-b)^{5/2}}+\frac{b^2 \tanh (c+d x)}{2 a d (a-b)^2 \left(a-(a-b) \tanh ^2(c+d x)\right)}+\frac{\tanh (c+d x)}{d (a-b)^2}","-\frac{b (4 a-b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a-b)^{5/2}}+\frac{b^2 \tanh (c+d x)}{2 a d (a-b)^2 \left(a-(a-b) \tanh ^2(c+d x)\right)}+\frac{\tanh (c+d x)}{d (a-b)^2}",1,"-((4*a - b)*b*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*(a - b)^(5/2)*d) + Tanh[c + d*x]/((a - b)^2*d) + (b^2*Tanh[c + d*x])/(2*a*(a - b)^2*d*(a - (a - b)*Tanh[c + d*x]^2))","A",5,4,23,0.1739,1,"{3191, 390, 385, 208}"
337,1,157,0,0.1927904,"\int \frac{\text{sech}^3(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]^3/(a + b*Sinh[c + d*x]^2)^2,x]","\frac{b^{3/2} (5 a-b) \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a-b)^3}+\frac{b (a+b) \sinh (c+d x)}{2 a d (a-b)^2 \left(a+b \sinh ^2(c+d x)\right)}+\frac{(a-5 b) \tan ^{-1}(\sinh (c+d x))}{2 d (a-b)^3}+\frac{\tanh (c+d x) \text{sech}(c+d x)}{2 d (a-b) \left(a+b \sinh ^2(c+d x)\right)}","\frac{b^{3/2} (5 a-b) \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a-b)^3}+\frac{b (a+b) \sinh (c+d x)}{2 a d (a-b)^2 \left(a+b \sinh ^2(c+d x)\right)}+\frac{(a-5 b) \tan ^{-1}(\sinh (c+d x))}{2 d (a-b)^3}+\frac{\tanh (c+d x) \text{sech}(c+d x)}{2 d (a-b) \left(a+b \sinh ^2(c+d x)\right)}",1,"((a - 5*b)*ArcTan[Sinh[c + d*x]])/(2*(a - b)^3*d) + ((5*a - b)*b^(3/2)*ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*(a - b)^3*d) + (b*(a + b)*Sinh[c + d*x])/(2*a*(a - b)^2*d*(a + b*Sinh[c + d*x]^2)) + (Sech[c + d*x]*Tanh[c + d*x])/(2*(a - b)*d*(a + b*Sinh[c + d*x]^2))","A",6,6,23,0.2609,1,"{3190, 414, 527, 522, 203, 205}"
338,1,143,0,0.2070409,"\int \frac{\text{sech}^4(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^2} \, dx","Int[Sech[c + d*x]^4/(a + b*Sinh[c + d*x]^2)^2,x]","\frac{b^2 (6 a-b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a-b)^{7/2}}-\frac{b^3 \tanh (c+d x)}{2 a d (a-b)^3 \left(a-(a-b) \tanh ^2(c+d x)\right)}-\frac{\tanh ^3(c+d x)}{3 d (a-b)^2}+\frac{(a-3 b) \tanh (c+d x)}{d (a-b)^3}","\frac{b^2 (6 a-b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{2 a^{3/2} d (a-b)^{7/2}}-\frac{b^3 \tanh (c+d x)}{2 a d (a-b)^3 \left(a-(a-b) \tanh ^2(c+d x)\right)}-\frac{\tanh ^3(c+d x)}{3 d (a-b)^2}+\frac{(a-3 b) \tanh (c+d x)}{d (a-b)^3}",1,"((6*a - b)*b^2*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(2*a^(3/2)*(a - b)^(7/2)*d) + ((a - 3*b)*Tanh[c + d*x])/((a - b)^3*d) - Tanh[c + d*x]^3/(3*(a - b)^2*d) - (b^3*Tanh[c + d*x])/(2*a*(a - b)^3*d*(a - (a - b)*Tanh[c + d*x]^2))","A",5,4,23,0.1739,1,"{3191, 390, 385, 208}"
339,1,160,0,0.2364038,"\int \frac{\cosh ^6(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Cosh[c + d*x]^6/(a + b*Sinh[c + d*x]^2)^3,x]","-\frac{\sqrt{a-b} \left(8 a^2+4 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} b^3 d}-\frac{(a-b) (4 a+3 b) \tanh (c+d x)}{8 a^2 b^2 d \left(a-(a-b) \tanh ^2(c+d x)\right)}-\frac{(a-b) \tanh (c+d x)}{4 a b d \left(a-(a-b) \tanh ^2(c+d x)\right)^2}+\frac{x}{b^3}","-\frac{\sqrt{a-b} \left(8 a^2+4 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} b^3 d}-\frac{(a-b) (4 a+3 b) \tanh (c+d x)}{8 a^2 b^2 d \left(a-(a-b) \tanh ^2(c+d x)\right)}-\frac{(a-b) \tanh (c+d x)}{4 a b d \left(a-(a-b) \tanh ^2(c+d x)\right)^2}+\frac{x}{b^3}",1,"x/b^3 - (Sqrt[a - b]*(8*a^2 + 4*a*b + 3*b^2)*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*b^3*d) - ((a - b)*Tanh[c + d*x])/(4*a*b*d*(a - (a - b)*Tanh[c + d*x]^2)^2) - ((a - b)*(4*a + 3*b)*Tanh[c + d*x])/(8*a^2*b^2*d*(a - (a - b)*Tanh[c + d*x]^2))","A",6,6,23,0.2609,1,"{3191, 414, 527, 522, 206, 208}"
340,1,133,0,0.1245374,"\int \frac{\cosh ^5(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Cosh[c + d*x]^5/(a + b*Sinh[c + d*x]^2)^3,x]","\frac{3 \left(\frac{1}{a^2}-\frac{1}{b^2}\right) \sinh (c+d x)}{8 d \left(a+b \sinh ^2(c+d x)\right)}+\frac{\left(3 a^2+2 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} b^{5/2} d}-\frac{(a-b) \sinh (c+d x) \cosh ^2(c+d x)}{4 a b d \left(a+b \sinh ^2(c+d x)\right)^2}","\frac{3 \left(\frac{1}{a^2}-\frac{1}{b^2}\right) \sinh (c+d x)}{8 d \left(a+b \sinh ^2(c+d x)\right)}+\frac{\left(3 a^2+2 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} b^{5/2} d}-\frac{(a-b) \sinh (c+d x) \cosh ^2(c+d x)}{4 a b d \left(a+b \sinh ^2(c+d x)\right)^2}",1,"((3*a^2 + 2*a*b + 3*b^2)*ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*b^(5/2)*d) - ((a - b)*Cosh[c + d*x]^2*Sinh[c + d*x])/(4*a*b*d*(a + b*Sinh[c + d*x]^2)^2) + (3*(a^(-2) - b^(-2))*Sinh[c + d*x])/(8*d*(a + b*Sinh[c + d*x]^2))","A",4,4,23,0.1739,1,"{3190, 413, 385, 205}"
341,1,114,0,0.0954025,"\int \frac{\cosh ^4(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Cosh[c + d*x]^4/(a + b*Sinh[c + d*x]^2)^3,x]","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d \sqrt{a-b}}+\frac{3 \tanh (c+d x)}{8 a^2 d \left(a-(a-b) \tanh ^2(c+d x)\right)}+\frac{\tanh (c+d x)}{4 a d \left(a-(a-b) \tanh ^2(c+d x)\right)^2}","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d \sqrt{a-b}}+\frac{3 \tanh (c+d x)}{8 a^2 d \left(a-(a-b) \tanh ^2(c+d x)\right)}+\frac{\tanh (c+d x)}{4 a d \left(a-(a-b) \tanh ^2(c+d x)\right)^2}",1,"(3*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*Sqrt[a - b]*d) + Tanh[c + d*x]/(4*a*d*(a - (a - b)*Tanh[c + d*x]^2)^2) + (3*Tanh[c + d*x])/(8*a^2*d*(a - (a - b)*Tanh[c + d*x]^2))","A",4,3,23,0.1304,1,"{3191, 199, 208}"
342,1,117,0,0.0925692,"\int \frac{\cosh ^3(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Cosh[c + d*x]^3/(a + b*Sinh[c + d*x]^2)^3,x]","\frac{(a+3 b) \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} b^{3/2} d}+\frac{(a+3 b) \sinh (c+d x)}{8 a^2 b d \left(a+b \sinh ^2(c+d x)\right)}-\frac{(a-b) \sinh (c+d x)}{4 a b d \left(a+b \sinh ^2(c+d x)\right)^2}","\frac{(a+3 b) \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} b^{3/2} d}+\frac{(a+3 b) \sinh (c+d x)}{8 a^2 b d \left(a+b \sinh ^2(c+d x)\right)}-\frac{(a-b) \sinh (c+d x)}{4 a b d \left(a+b \sinh ^2(c+d x)\right)^2}",1,"((a + 3*b)*ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*b^(3/2)*d) - ((a - b)*Sinh[c + d*x])/(4*a*b*d*(a + b*Sinh[c + d*x]^2)^2) + ((a + 3*b)*Sinh[c + d*x])/(8*a^2*b*d*(a + b*Sinh[c + d*x]^2))","A",4,4,23,0.1739,1,"{3190, 385, 199, 205}"
343,1,143,0,0.1255225,"\int \frac{\cosh ^2(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Cosh[c + d*x]^2/(a + b*Sinh[c + d*x]^2)^3,x]","\frac{(4 a-3 b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a-b)^{3/2}}+\frac{(4 a-3 b) \tanh (c+d x)}{8 a^2 d (a-b) \left(a-(a-b) \tanh ^2(c+d x)\right)}-\frac{b \tanh (c+d x)}{4 a d (a-b) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}","\frac{(4 a-3 b) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a-b)^{3/2}}+\frac{(4 a-3 b) \tanh (c+d x)}{8 a^2 d (a-b) \left(a-(a-b) \tanh ^2(c+d x)\right)}-\frac{b \tanh (c+d x)}{4 a d (a-b) \left(a-(a-b) \tanh ^2(c+d x)\right)^2}",1,"((4*a - 3*b)*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*(a - b)^(3/2)*d) - (b*Tanh[c + d*x])/(4*a*(a - b)*d*(a - (a - b)*Tanh[c + d*x]^2)^2) + ((4*a - 3*b)*Tanh[c + d*x])/(8*a^2*(a - b)*d*(a - (a - b)*Tanh[c + d*x]^2))","A",4,4,23,0.1739,1,"{3191, 385, 199, 208}"
344,1,96,0,0.0571966,"\int \frac{\cosh (c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Cosh[c + d*x]/(a + b*Sinh[c + d*x]^2)^3,x]","\frac{3 \sinh (c+d x)}{8 a^2 d \left(a+b \sinh ^2(c+d x)\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} d}+\frac{\sinh (c+d x)}{4 a d \left(a+b \sinh ^2(c+d x)\right)^2}","\frac{3 \sinh (c+d x)}{8 a^2 d \left(a+b \sinh ^2(c+d x)\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} d}+\frac{\sinh (c+d x)}{4 a d \left(a+b \sinh ^2(c+d x)\right)^2}",1,"(3*ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*Sqrt[b]*d) + Sinh[c + d*x]/(4*a*d*(a + b*Sinh[c + d*x]^2)^2) + (3*Sinh[c + d*x])/(8*a^2*d*(a + b*Sinh[c + d*x]^2))","A",4,3,21,0.1429,1,"{3190, 199, 205}"
345,1,159,0,0.1803835,"\int \frac{\text{sech}(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]/(a + b*Sinh[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} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a-b)^3}-\frac{b (7 a-3 b) \sinh (c+d x)}{8 a^2 d (a-b)^2 \left(a+b \sinh ^2(c+d x)\right)}-\frac{b \sinh (c+d x)}{4 a d (a-b) \left(a+b \sinh ^2(c+d x)\right)^2}+\frac{\tan ^{-1}(\sinh (c+d x))}{d (a-b)^3}","-\frac{\sqrt{b} \left(15 a^2-10 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a-b)^3}-\frac{b (7 a-3 b) \sinh (c+d x)}{8 a^2 d (a-b)^2 \left(a+b \sinh ^2(c+d x)\right)}-\frac{b \sinh (c+d x)}{4 a d (a-b) \left(a+b \sinh ^2(c+d x)\right)^2}+\frac{\tan ^{-1}(\sinh (c+d x))}{d (a-b)^3}",1,"ArcTan[Sinh[c + d*x]]/((a - b)^3*d) - (Sqrt[b]*(15*a^2 - 10*a*b + 3*b^2)*ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*(a - b)^3*d) - (b*Sinh[c + d*x])/(4*a*(a - b)*d*(a + b*Sinh[c + d*x]^2)^2) - ((7*a - 3*b)*b*Sinh[c + d*x])/(8*a^2*(a - b)^2*d*(a + b*Sinh[c + d*x]^2))","A",6,6,21,0.2857,1,"{3190, 414, 527, 522, 203, 205}"
346,1,172,0,0.2645943,"\int \frac{\text{sech}^2(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]^2/(a + b*Sinh[c + d*x]^2)^3,x]","\frac{3 b^2 (4 a-b) \tanh (c+d x)}{8 a^2 d (a-b)^3 \left(a-(a-b) \tanh ^2(c+d x)\right)}-\frac{3 b \left(8 a^2-4 a b+b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a-b)^{7/2}}-\frac{b^3 \tanh (c+d x)}{4 a d (a-b)^3 \left(a-(a-b) \tanh ^2(c+d x)\right)^2}+\frac{\tanh (c+d x)}{d (a-b)^3}","\frac{3 b^2 (4 a-b) \tanh (c+d x)}{8 a^2 d (a-b)^3 \left(a-(a-b) \tanh ^2(c+d x)\right)}-\frac{3 b \left(8 a^2-4 a b+b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a-b)^{7/2}}-\frac{b^3 \tanh (c+d x)}{4 a d (a-b)^3 \left(a-(a-b) \tanh ^2(c+d x)\right)^2}+\frac{\tanh (c+d x)}{d (a-b)^3}",1,"(-3*b*(8*a^2 - 4*a*b + b^2)*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*(a - b)^(7/2)*d) + Tanh[c + d*x]/((a - b)^3*d) - (b^3*Tanh[c + d*x])/(4*a*(a - b)^3*d*(a - (a - b)*Tanh[c + d*x]^2)^2) + (3*(4*a - b)*b^2*Tanh[c + d*x])/(8*a^2*(a - b)^3*d*(a - (a - b)*Tanh[c + d*x]^2))","A",6,5,23,0.2174,1,"{3191, 390, 1157, 385, 208}"
347,1,217,0,0.3034914,"\int \frac{\text{sech}^3(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]^3/(a + b*Sinh[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} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a-b)^4}+\frac{b (4 a-b) (a+3 b) \sinh (c+d x)}{8 a^2 d (a-b)^3 \left(a+b \sinh ^2(c+d x)\right)}+\frac{b (2 a+b) \sinh (c+d x)}{4 a d (a-b)^2 \left(a+b \sinh ^2(c+d x)\right)^2}+\frac{(a-7 b) \tan ^{-1}(\sinh (c+d x))}{2 d (a-b)^4}+\frac{\tanh (c+d x) \text{sech}(c+d x)}{2 d (a-b) \left(a+b \sinh ^2(c+d x)\right)^2}","\frac{b^{3/2} \left(35 a^2-14 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{b} \sinh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a-b)^4}+\frac{b (4 a-b) (a+3 b) \sinh (c+d x)}{8 a^2 d (a-b)^3 \left(a+b \sinh ^2(c+d x)\right)}+\frac{b (2 a+b) \sinh (c+d x)}{4 a d (a-b)^2 \left(a+b \sinh ^2(c+d x)\right)^2}+\frac{(a-7 b) \tan ^{-1}(\sinh (c+d x))}{2 d (a-b)^4}+\frac{\tanh (c+d x) \text{sech}(c+d x)}{2 d (a-b) \left(a+b \sinh ^2(c+d x)\right)^2}",1,"((a - 7*b)*ArcTan[Sinh[c + d*x]])/(2*(a - b)^4*d) + (b^(3/2)*(35*a^2 - 14*a*b + 3*b^2)*ArcTan[(Sqrt[b]*Sinh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*(a - b)^4*d) + (b*(2*a + b)*Sinh[c + d*x])/(4*a*(a - b)^2*d*(a + b*Sinh[c + d*x]^2)^2) + ((4*a - b)*b*(a + 3*b)*Sinh[c + d*x])/(8*a^2*(a - b)^3*d*(a + b*Sinh[c + d*x]^2)) + (Sech[c + d*x]*Tanh[c + d*x])/(2*(a - b)*d*(a + b*Sinh[c + d*x]^2)^2)","A",7,6,23,0.2609,1,"{3190, 414, 527, 522, 203, 205}"
348,1,203,0,0.3408807,"\int \frac{\text{sech}^4(c+d x)}{\left(a+b \sinh ^2(c+d x)\right)^3} \, dx","Int[Sech[c + d*x]^4/(a + b*Sinh[c + d*x]^2)^3,x]","-\frac{b^3 (16 a-3 b) \tanh (c+d x)}{8 a^2 d (a-b)^4 \left(a-(a-b) \tanh ^2(c+d x)\right)}+\frac{b^2 \left(48 a^2-16 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a-b)^{9/2}}+\frac{b^4 \tanh (c+d x)}{4 a d (a-b)^4 \left(a-(a-b) \tanh ^2(c+d x)\right)^2}-\frac{\tanh ^3(c+d x)}{3 d (a-b)^3}+\frac{(a-4 b) \tanh (c+d x)}{d (a-b)^4}","-\frac{b^3 (16 a-3 b) \tanh (c+d x)}{8 a^2 d (a-b)^4 \left(a-(a-b) \tanh ^2(c+d x)\right)}+\frac{b^2 \left(48 a^2-16 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{a}}\right)}{8 a^{5/2} d (a-b)^{9/2}}+\frac{b^4 \tanh (c+d x)}{4 a d (a-b)^4 \left(a-(a-b) \tanh ^2(c+d x)\right)^2}-\frac{\tanh ^3(c+d x)}{3 d (a-b)^3}+\frac{(a-4 b) \tanh (c+d x)}{d (a-b)^4}",1,"(b^2*(48*a^2 - 16*a*b + 3*b^2)*ArcTanh[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[a]])/(8*a^(5/2)*(a - b)^(9/2)*d) + ((a - 4*b)*Tanh[c + d*x])/((a - b)^4*d) - Tanh[c + d*x]^3/(3*(a - b)^3*d) + (b^4*Tanh[c + d*x])/(4*a*(a - b)^4*d*(a - (a - b)*Tanh[c + d*x]^2)^2) - ((16*a - 3*b)*b^3*Tanh[c + d*x])/(8*a^2*(a - b)^4*d*(a - (a - b)*Tanh[c + d*x]^2))","A",6,5,23,0.2174,1,"{3191, 390, 1157, 385, 208}"
349,1,19,0,0.0450643,"\int \frac{\cosh ^2(x)}{1-\sinh ^2(x)} \, dx","Int[Cosh[x]^2/(1 - Sinh[x]^2),x]","\sqrt{2} \tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)-x","\sqrt{2} \tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)-x",1,"-x + Sqrt[2]*ArcTanh[Sqrt[2]*Tanh[x]]","A",4,3,15,0.2000,1,"{3191, 391, 206}"
350,1,10,0,0.0389517,"\int \frac{\cosh ^3(x)}{1-\sinh ^2(x)} \, dx","Int[Cosh[x]^3/(1 - Sinh[x]^2),x]","2 \tanh ^{-1}(\sinh (x))-\sinh (x)","2 \tanh ^{-1}(\sinh (x))-\sinh (x)",1,"2*ArcTanh[Sinh[x]] - Sinh[x]","A",3,3,15,0.2000,1,"{3190, 388, 206}"
351,1,30,0,0.0589306,"\int \frac{\cosh ^4(x)}{1-\sinh ^2(x)} \, dx","Int[Cosh[x]^4/(1 - Sinh[x]^2),x]","-\frac{5 x}{2}+2 \sqrt{2} \tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)-\frac{1}{2} \sinh (x) \cosh (x)","-\frac{5 x}{2}+2 \sqrt{2} \tanh ^{-1}\left(\sqrt{2} \tanh (x)\right)-\frac{1}{2} \sinh (x) \cosh (x)",1,"(-5*x)/2 + 2*Sqrt[2]*ArcTanh[Sqrt[2]*Tanh[x]] - (Cosh[x]*Sinh[x])/2","A",5,4,15,0.2667,1,"{3191, 414, 522, 206}"
352,1,117,0,0.1135066,"\int \cosh ^3(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Cosh[e + f*x]^3*Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{a (a-4 b) \tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{8 b^{3/2} f}+\frac{\sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{4 b f}-\frac{(a-4 b) \sinh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{8 b f}","-\frac{a (a-4 b) \tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{8 b^{3/2} f}+\frac{\sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{4 b f}-\frac{(a-4 b) \sinh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{8 b f}",1,"-(a*(a - 4*b)*ArcTanh[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/(8*b^(3/2)*f) - ((a - 4*b)*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(8*b*f) + (Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^(3/2))/(4*b*f)","A",5,5,25,0.2000,1,"{3190, 388, 195, 217, 206}"
353,1,72,0,0.0555239,"\int \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Cosh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\sinh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{2 f}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{2 \sqrt{b} f}","\frac{\sinh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{2 f}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{2 \sqrt{b} f}",1,"(a*ArcTanh[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/(2*Sqrt[b]*f) + (Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(2*f)","A",4,4,23,0.1739,1,"{3190, 195, 217, 206}"
354,1,85,0,0.0920647,"\int \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\sqrt{a-b} \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{f}+\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{f}","\frac{\sqrt{a-b} \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{f}+\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{f}",1,"(Sqrt[a - b]*ArcTan[(Sqrt[a - b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/f + (Sqrt[b]*ArcTanh[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/f","A",6,6,23,0.2609,1,"{3190, 402, 217, 206, 377, 203}"
355,1,86,0,0.0964859,"\int \text{sech}^3(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Sech[e + f*x]^3*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{a \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{2 f \sqrt{a-b}}+\frac{\tanh (e+f x) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{2 f}","\frac{a \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{2 f \sqrt{a-b}}+\frac{\tanh (e+f x) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{2 f}",1,"(a*ArcTan[(Sqrt[a - b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/(2*Sqrt[a - b]*f) + (Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(2*f)","A",4,4,25,0.1600,1,"{3190, 378, 377, 203}"
356,1,151,0,0.1434617,"\int \text{sech}^5(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Sech[e + f*x]^5*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{a (3 a-4 b) \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{8 f (a-b)^{3/2}}+\frac{\tanh (e+f x) \text{sech}^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{4 f (a-b)}+\frac{(3 a-4 b) \tanh (e+f x) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{8 f (a-b)}","\frac{a (3 a-4 b) \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{8 f (a-b)^{3/2}}+\frac{\tanh (e+f x) \text{sech}^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{4 f (a-b)}+\frac{(3 a-4 b) \tanh (e+f x) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{8 f (a-b)}",1,"(a*(3*a - 4*b)*ArcTan[(Sqrt[a - b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/(8*(a - b)^(3/2)*f) + ((3*a - 4*b)*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(8*(a - b)*f) + (Sech[e + f*x]^3*(a + b*Sinh[e + f*x]^2)^(3/2)*Tanh[e + f*x])/(4*(a - b)*f)","A",5,5,25,0.2000,1,"{3190, 382, 378, 377, 203}"
357,1,301,0,0.2975748,"\int \cosh ^4(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Cosh[e + f*x]^4*Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{\left(2 a^2-7 a b-3 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{15 b^2 f}+\frac{\left(2 a^2-7 a b-3 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{15 b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{\sinh (e+f x) \cosh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{5 b f}-\frac{2 (a-3 b) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{15 b f}-\frac{(a-9 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{15 b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","-\frac{\left(2 a^2-7 a b-3 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{15 b^2 f}+\frac{\left(2 a^2-7 a b-3 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{15 b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{\sinh (e+f x) \cosh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{5 b f}-\frac{2 (a-3 b) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{15 b f}-\frac{(a-9 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{15 b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(-2*(a - 3*b)*Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(15*b*f) + (Cosh[e + f*x]*Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^(3/2))/(5*b*f) + ((2*a^2 - 7*a*b - 3*b^2)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(15*b^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - ((a - 9*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(15*b*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - ((2*a^2 - 7*a*b - 3*b^2)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(15*b^2*f)","A",7,7,25,0.2800,1,"{3192, 416, 528, 531, 418, 492, 411}"
358,1,223,0,0.2033408,"\int \cosh ^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Cosh[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{(a+b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 b f}+\frac{\sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{2 \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{(a+b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 b f}+\frac{\sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{2 \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f) - ((a + b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*b*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (2*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((a + b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*b*f)","A",6,6,25,0.2400,1,"{3192, 417, 531, 418, 492, 411}"
359,1,60,0,0.036322,"\int \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{i \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}","-\frac{i \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}",1,"((-I)*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/(f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])","A",2,2,16,0.1250,1,"{3178, 3177}"
360,1,70,0,0.0844919,"\int \text{sech}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Sech[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a])","A",2,2,25,0.08000,1,"{3192, 411}"
361,1,206,0,0.1669381,"\int \text{sech}^4(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Sech[e + f*x]^4*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\tanh (e+f x) \text{sech}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{(2 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{\tanh (e+f x) \text{sech}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{(2 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"((2*a - b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*(a - b)*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (b*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*(a - b)*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (Sech[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*f)","A",5,5,25,0.2000,1,"{3192, 412, 525, 418, 411}"
362,1,157,0,0.1288955,"\int \cosh ^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Cosh[e + f*x]^3*(a + b*Sinh[e + f*x]^2)^(3/2),x]","-\frac{a^2 (a-6 b) \tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{16 b^{3/2} f}+\frac{\sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{5/2}}{6 b f}-\frac{(a-6 b) \sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{24 b f}-\frac{a (a-6 b) \sinh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{16 b f}","-\frac{a^2 (a-6 b) \tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{16 b^{3/2} f}+\frac{\sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{5/2}}{6 b f}-\frac{(a-6 b) \sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{24 b f}-\frac{a (a-6 b) \sinh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{16 b f}",1,"-(a^2*(a - 6*b)*ArcTanh[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/(16*b^(3/2)*f) - (a*(a - 6*b)*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(16*b*f) - ((a - 6*b)*Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^(3/2))/(24*b*f) + (Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^(5/2))/(6*b*f)","A",6,5,25,0.2000,1,"{3190, 388, 195, 217, 206}"
363,1,104,0,0.0687584,"\int \cosh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Cosh[e + f*x]*(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{8 \sqrt{b} f}+\frac{3 a \sinh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{8 f}+\frac{\sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{4 f}","\frac{3 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{8 \sqrt{b} f}+\frac{3 a \sinh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{8 f}+\frac{\sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{4 f}",1,"(3*a^2*ArcTanh[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/(8*Sqrt[b]*f) + (3*a*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(8*f) + (Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^(3/2))/(4*f)","A",5,4,23,0.1739,1,"{3190, 195, 217, 206}"
364,1,125,0,0.138583,"\int \text{sech}(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Sech[e + f*x]*(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{b \sinh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{2 f}+\frac{(a-b)^{3/2} \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{f}+\frac{\sqrt{b} (3 a-2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{2 f}","\frac{b \sinh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{2 f}+\frac{(a-b)^{3/2} \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{f}+\frac{\sqrt{b} (3 a-2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{2 f}",1,"((a - b)^(3/2)*ArcTan[(Sqrt[a - b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/f + ((3*a - 2*b)*Sqrt[b]*ArcTanh[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/(2*f) + (b*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(2*f)","A",7,7,23,0.3043,1,"{3190, 416, 523, 217, 206, 377, 203}"
365,1,133,0,0.1461025,"\int \text{sech}^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Sech[e + f*x]^3*(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{f}+\frac{\sqrt{a-b} (a+2 b) \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{2 f}+\frac{(a-b) \tanh (e+f x) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{2 f}","\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{f}+\frac{\sqrt{a-b} (a+2 b) \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{2 f}+\frac{(a-b) \tanh (e+f x) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{2 f}",1,"(Sqrt[a - b]*(a + 2*b)*ArcTan[(Sqrt[a - b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/(2*f) + (b^(3/2)*ArcTanh[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/f + ((a - b)*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(2*f)","A",7,7,25,0.2800,1,"{3190, 413, 523, 217, 206, 377, 203}"
366,1,126,0,0.1208554,"\int \text{sech}^5(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Sech[e + f*x]^5*(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{3 a^2 \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{8 f \sqrt{a-b}}+\frac{\tanh (e+f x) \text{sech}^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{4 f}+\frac{3 a \tanh (e+f x) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{8 f}","\frac{3 a^2 \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{8 f \sqrt{a-b}}+\frac{\tanh (e+f x) \text{sech}^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{4 f}+\frac{3 a \tanh (e+f x) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{8 f}",1,"(3*a^2*ArcTan[(Sqrt[a - b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/(8*Sqrt[a - b]*f) + (3*a*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(8*f) + (Sech[e + f*x]^3*(a + b*Sinh[e + f*x]^2)^(3/2)*Tanh[e + f*x])/(4*f)","A",5,4,25,0.1600,1,"{3190, 378, 377, 203}"
367,1,205,0,0.1722939,"\int \text{sech}^7(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Sech[e + f*x]^7*(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{a^2 (5 a-6 b) \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{16 f (a-b)^{3/2}}+\frac{\tanh (e+f x) \text{sech}^5(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{5/2}}{6 f (a-b)}+\frac{(5 a-6 b) \tanh (e+f x) \text{sech}^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{24 f (a-b)}+\frac{a (5 a-6 b) \tanh (e+f x) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{16 f (a-b)}","\frac{a^2 (5 a-6 b) \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{16 f (a-b)^{3/2}}+\frac{\tanh (e+f x) \text{sech}^5(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{5/2}}{6 f (a-b)}+\frac{(5 a-6 b) \tanh (e+f x) \text{sech}^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{24 f (a-b)}+\frac{a (5 a-6 b) \tanh (e+f x) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{16 f (a-b)}",1,"(a^2*(5*a - 6*b)*ArcTan[(Sqrt[a - b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/(16*(a - b)^(3/2)*f) + (a*(5*a - 6*b)*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(16*(a - b)*f) + ((5*a - 6*b)*Sech[e + f*x]^3*(a + b*Sinh[e + f*x]^2)^(3/2)*Tanh[e + f*x])/(24*(a - b)*f) + (Sech[e + f*x]^5*(a + b*Sinh[e + f*x]^2)^(5/2)*Tanh[e + f*x])/(6*(a - b)*f)","A",6,5,25,0.2000,1,"{3190, 382, 378, 377, 203}"
368,1,357,0,0.3929573,"\int \cosh ^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Cosh[e + f*x]^4*(a + b*Sinh[e + f*x]^2)^(3/2),x]","-\frac{2 (a+b) \left(a^2-6 a b+b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{35 b^2 f}+\frac{\left(a^2+9 a b-2 b^2\right) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{35 b f}-\frac{\left(a^2-18 a b+b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{35 b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{2 (a+b) \left(a^2-6 a b+b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{35 b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{b \sinh (e+f x) \cosh ^5(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{7 f}+\frac{2 (4 a-b) \sinh (e+f x) \cosh ^3(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{35 f}","-\frac{2 (a+b) \left(a^2-6 a b+b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{35 b^2 f}+\frac{\left(a^2+9 a b-2 b^2\right) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{35 b f}-\frac{\left(a^2-18 a b+b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{35 b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{2 (a+b) \left(a^2-6 a b+b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{35 b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{b \sinh (e+f x) \cosh ^5(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{7 f}+\frac{2 (4 a-b) \sinh (e+f x) \cosh ^3(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{35 f}",1,"((a^2 + 9*a*b - 2*b^2)*Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(35*b*f) + (2*(4*a - b)*Cosh[e + f*x]^3*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(35*f) + (b*Cosh[e + f*x]^5*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(7*f) + (2*(a + b)*(a^2 - 6*a*b + b^2)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(35*b^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - ((a^2 - 18*a*b + b^2)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(35*b*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (2*(a + b)*(a^2 - 6*a*b + b^2)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(35*b^2*f)","A",8,7,25,0.2800,1,"{3192, 416, 528, 531, 418, 492, 411}"
369,1,299,0,0.2908542,"\int \cosh ^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Cosh[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{\left(3 a^2+7 a b-2 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{15 b f}-\frac{\left(3 a^2+7 a b-2 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{15 b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{b \sinh (e+f x) \cosh ^3(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{5 f}+\frac{2 (3 a-b) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{15 f}+\frac{(9 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{15 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{\left(3 a^2+7 a b-2 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{15 b f}-\frac{\left(3 a^2+7 a b-2 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{15 b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{b \sinh (e+f x) \cosh ^3(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{5 f}+\frac{2 (3 a-b) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{15 f}+\frac{(9 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{15 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(2*(3*a - b)*Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(15*f) + (b*Cosh[e + f*x]^3*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(5*f) - ((3*a^2 + 7*a*b - 2*b^2)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(15*b*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((9*a - b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(15*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((3*a^2 + 7*a*b - 2*b^2)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(15*b*f)","A",7,7,25,0.2800,1,"{3192, 416, 528, 531, 418, 492, 411}"
370,1,174,0,0.1895292,"\int \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{b \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{i a (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{2 i (2 a-b) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}","\frac{b \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{i a (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{2 i (2 a-b) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}",1,"(b*Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f) - (((2*I)/3)*(2*a - b)*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/(f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a]) + ((I/3)*a*(a - b)*EllipticF[I*e + I*f*x, b/a]*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])/(f*Sqrt[a + b*Sinh[e + f*x]^2])","A",6,6,16,0.3750,1,"{3180, 3172, 3178, 3177, 3183, 3182}"
371,1,210,0,0.2012493,"\int \text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^(3/2),x]","-\frac{(a-2 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{(a-b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{(a-2 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","-\frac{(a-2 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{(a-b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{(a-2 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"((a - 2*b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (b*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - ((a - 2*b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/f + ((a - b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/f","A",6,6,25,0.2400,1,"{3192, 413, 531, 418, 492, 411}"
372,1,193,0,0.187938,"\int \text{sech}^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Sech[e + f*x]^4*(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{(a-b) \tanh (e+f x) \text{sech}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{2 (a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{(a-b) \tanh (e+f x) \text{sech}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{2 (a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(2*(a + b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (b*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((a - b)*Sech[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*f)","A",5,5,25,0.2000,1,"{3192, 413, 525, 418, 411}"
373,1,79,0,0.0897847,"\int \frac{\cosh ^3(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Cosh[e + f*x]^3/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\sinh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{2 b f}-\frac{(a-2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{2 b^{3/2} f}","\frac{\sinh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{2 b f}-\frac{(a-2 b) \tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{2 b^{3/2} f}",1,"-((a - 2*b)*ArcTanh[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/(2*b^(3/2)*f) + (Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(2*b*f)","A",4,4,25,0.1600,1,"{3190, 388, 217, 206}"
374,1,38,0,0.0465059,"\int \frac{\cosh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Cosh[e + f*x]/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{\sqrt{b} f}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{\sqrt{b} f}",1,"ArcTanh[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]]/(Sqrt[b]*f)","A",3,3,23,0.1304,1,"{3190, 217, 206}"
375,1,46,0,0.0688678,"\int \frac{\text{sech}(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Sech[e + f*x]/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{f \sqrt{a-b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{f \sqrt{a-b}}",1,"ArcTan[(Sqrt[a - b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]]/(Sqrt[a - b]*f)","A",3,3,23,0.1304,1,"{3190, 377, 203}"
376,1,97,0,0.1072276,"\int \frac{\text{sech}^3(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Sech[e + f*x]^3/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{(a-2 b) \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{2 f (a-b)^{3/2}}+\frac{\tanh (e+f x) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{2 f (a-b)}","\frac{(a-2 b) \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{2 f (a-b)^{3/2}}+\frac{\tanh (e+f x) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{2 f (a-b)}",1,"((a - 2*b)*ArcTan[(Sqrt[a - b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/(2*(a - b)^(3/2)*f) + (Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(2*(a - b)*f)","A",4,4,25,0.1600,1,"{3190, 382, 377, 203}"
377,1,241,0,0.2185487,"\int \frac{\cosh ^4(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Cosh[e + f*x]^4/Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{2 (a-2 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 b^2 f}+\frac{2 (a-2 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{\sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 b f}-\frac{(a-3 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","-\frac{2 (a-2 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 b^2 f}+\frac{2 (a-2 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{\sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 b f}-\frac{(a-3 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*b*f) + (2*(a - 2*b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*b^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - ((a - 3*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*b*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (2*(a - 2*b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*b^2*f)","A",6,6,25,0.2400,1,"{3192, 416, 531, 418, 492, 411}"
378,1,177,0,0.1480904,"\int \frac{\cosh ^2(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Cosh[e + f*x]^2/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{b f}+\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{\tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{b f}+\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"-((EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(b*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a])) + (EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(b*f)","A",5,5,25,0.2000,1,"{3192, 422, 418, 492, 411}"
379,1,60,0,0.0383432,"\int \frac{1}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[1/Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{i \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{f \sqrt{a+b \sinh ^2(e+f x)}}","-\frac{i \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{f \sqrt{a+b \sinh ^2(e+f x)}}",1,"((-I)*EllipticF[I*e + I*f*x, b/a]*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])/(f*Sqrt[a + b*Sinh[e + f*x]^2])","A",2,2,16,0.1250,1,"{3183, 3182}"
380,1,160,0,0.1805253,"\int \frac{\text{sech}^2(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Sech[e + f*x]^2/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/((a - b)*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (b*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*(a - b)*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a])","A",7,7,25,0.2800,1,"{3192, 414, 21, 422, 418, 492, 411}"
381,1,219,0,0.1949289,"\int \frac{\text{sech}^4(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Sech[e + f*x]^4/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\tanh (e+f x) \text{sech}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f (a-b)}-\frac{b (a-3 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{2 (a-2 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{\tanh (e+f x) \text{sech}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f (a-b)}-\frac{b (a-3 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{2 (a-2 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(2*(a - 2*b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*(a - b)^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - ((a - 3*b)*b*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*(a - b)^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (Sech[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*(a - b)*f)","A",5,5,25,0.2000,1,"{3192, 414, 525, 418, 411}"
382,1,77,0,0.0985304,"\int \frac{\cosh ^3(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Cosh[e + f*x]^3/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{b^{3/2} f}-\frac{(a-b) \sinh (e+f x)}{a b f \sqrt{a+b \sinh ^2(e+f x)}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{b^{3/2} f}-\frac{(a-b) \sinh (e+f x)}{a b f \sqrt{a+b \sinh ^2(e+f x)}}",1,"ArcTanh[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]]/(b^(3/2)*f) - ((a - b)*Sinh[e + f*x])/(a*b*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",4,4,25,0.1600,1,"{3190, 385, 217, 206}"
383,1,29,0,0.0442715,"\int \frac{\cosh (e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Cosh[e + f*x]/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{\sinh (e+f x)}{a f \sqrt{a+b \sinh ^2(e+f x)}}","\frac{\sinh (e+f x)}{a f \sqrt{a+b \sinh ^2(e+f x)}}",1,"Sinh[e + f*x]/(a*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",2,2,23,0.08696,1,"{3190, 191}"
384,1,85,0,0.0965584,"\int \frac{\text{sech}(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Sech[e + f*x]/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{f (a-b)^{3/2}}-\frac{b \sinh (e+f x)}{a f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}","\frac{\tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{f (a-b)^{3/2}}-\frac{b \sinh (e+f x)}{a f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}",1,"ArcTan[(Sqrt[a - b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]]/((a - b)^(3/2)*f) - (b*Sinh[e + f*x])/(a*(a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",4,4,23,0.1739,1,"{3190, 382, 377, 203}"
385,1,142,0,0.1649145,"\int \frac{\text{sech}^3(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Sech[e + f*x]^3/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{b (a+2 b) \sinh (e+f x)}{2 a f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}+\frac{(a-4 b) \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{2 f (a-b)^{5/2}}+\frac{\tanh (e+f x) \text{sech}(e+f x)}{2 f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}","\frac{b (a+2 b) \sinh (e+f x)}{2 a f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}+\frac{(a-4 b) \tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{2 f (a-b)^{5/2}}+\frac{\tanh (e+f x) \text{sech}(e+f x)}{2 f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}",1,"((a - 4*b)*ArcTan[(Sqrt[a - b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]])/(2*(a - b)^(5/2)*f) + (b*(a + 2*b)*Sinh[e + f*x])/(2*a*(a - b)^2*f*Sqrt[a + b*Sinh[e + f*x]^2]) + (Sech[e + f*x]*Tanh[e + f*x])/(2*(a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",6,6,25,0.2400,1,"{3190, 414, 527, 12, 377, 203}"
386,1,325,0,0.3007373,"\int \frac{\cosh ^6(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Cosh[e + f*x]^6/(a + b*Sinh[e + f*x]^2)^(3/2),x]","-\frac{\left(8 a^2-13 a b+3 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a b^3 f}+\frac{\left(8 a^2-13 a b+3 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a b^3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{(4 a-3 b) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a b^2 f}-\frac{2 (2 a-3 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a-b) \sinh (e+f x) \cosh ^3(e+f x)}{a b f \sqrt{a+b \sinh ^2(e+f x)}}","-\frac{\left(8 a^2-13 a b+3 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a b^3 f}+\frac{\left(8 a^2-13 a b+3 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a b^3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{(4 a-3 b) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a b^2 f}-\frac{2 (2 a-3 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a-b) \sinh (e+f x) \cosh ^3(e+f x)}{a b f \sqrt{a+b \sinh ^2(e+f x)}}",1,"-(((a - b)*Cosh[e + f*x]^3*Sinh[e + f*x])/(a*b*f*Sqrt[a + b*Sinh[e + f*x]^2])) + ((4*a - 3*b)*Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*b^2*f) + ((8*a^2 - 13*a*b + 3*b^2)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*b^3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (2*(2*a - 3*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*b^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - ((8*a^2 - 13*a*b + 3*b^2)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*a*b^3*f)","A",7,7,25,0.2800,1,"{3192, 413, 528, 531, 418, 492, 411}"
387,1,244,0,0.2180616,"\int \frac{\cosh ^4(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Cosh[e + f*x]^4/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{(2 a-b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a b^2 f}-\frac{(2 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a-b) \sinh (e+f x) \cosh (e+f x)}{a b f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{(2 a-b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a b^2 f}-\frac{(2 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a-b) \sinh (e+f x) \cosh (e+f x)}{a b f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"-(((a - b)*Cosh[e + f*x]*Sinh[e + f*x])/(a*b*f*Sqrt[a + b*Sinh[e + f*x]^2])) - ((2*a - b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*b^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*b*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((2*a - b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(a*b^2*f)","A",6,6,25,0.2400,1,"{3192, 413, 531, 418, 492, 411}"
388,1,91,0,0.1012004,"\int \frac{\cosh ^2(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Cosh[e + f*x]^2/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{\cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{\sqrt{a} \sqrt{b} f \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}","\frac{\cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{\sqrt{a} \sqrt{b} f \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}",1,"(Cosh[e + f*x]*EllipticE[ArcTan[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a]], 1 - a/b])/(Sqrt[a]*Sqrt[b]*f*Sqrt[(a*Cosh[e + f*x]^2)/(a + b*Sinh[e + f*x]^2)]*Sqrt[a + b*Sinh[e + f*x]^2])","A",2,2,25,0.08000,1,"{3192, 411}"
389,1,115,0,0.0611369,"\int \frac{1}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[(a + b*Sinh[e + f*x]^2)^(-3/2),x]","-\frac{b \sinh (e+f x) \cosh (e+f x)}{a f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}-\frac{i \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{a f (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}","-\frac{b \sinh (e+f x) \cosh (e+f x)}{a f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}-\frac{i \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{a f (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}",1,"-((b*Cosh[e + f*x]*Sinh[e + f*x])/(a*(a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2])) - (I*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*(a - b)*f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])","A",4,4,16,0.2500,1,"{3184, 21, 3178, 3177}"
390,1,217,0,0.2025352,"\int \frac{\text{sech}^2(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Sech[e + f*x]^2/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{\tanh (e+f x)}{f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}+\frac{\sqrt{b} (a+b) \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{\sqrt{a} f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}-\frac{2 b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{\tanh (e+f x)}{f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}+\frac{\sqrt{b} (a+b) \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{\sqrt{a} f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}-\frac{2 b \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(Sqrt[b]*(a + b)*Cosh[e + f*x]*EllipticE[ArcTan[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a]], 1 - a/b])/(Sqrt[a]*(a - b)^2*f*Sqrt[(a*Cosh[e + f*x]^2)/(a + b*Sinh[e + f*x]^2)]*Sqrt[a + b*Sinh[e + f*x]^2]) - (2*b*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*(a - b)^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + Tanh[e + f*x]/((a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",5,5,25,0.2000,1,"{3192, 414, 525, 418, 411}"
391,1,134,0,0.1414915,"\int \frac{\cosh ^5(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Cosh[e + f*x]^5/(a + b*Sinh[e + f*x]^2)^(5/2),x]","-\frac{(a-b) (3 a+2 b) \sinh (e+f x)}{3 a^2 b^2 f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{b^{5/2} f}-\frac{(a-b) \sinh (e+f x) \cosh ^2(e+f x)}{3 a b f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}","-\frac{(a-b) (3 a+2 b) \sinh (e+f x)}{3 a^2 b^2 f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{b^{5/2} f}-\frac{(a-b) \sinh (e+f x) \cosh ^2(e+f x)}{3 a b f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}",1,"ArcTanh[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]]/(b^(5/2)*f) - ((a - b)*Cosh[e + f*x]^2*Sinh[e + f*x])/(3*a*b*f*(a + b*Sinh[e + f*x]^2)^(3/2)) - ((a - b)*(3*a + 2*b)*Sinh[e + f*x])/(3*a^2*b^2*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",5,5,25,0.2000,1,"{3190, 413, 385, 217, 206}"
392,1,73,0,0.0929841,"\int \frac{\cosh ^3(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Cosh[e + f*x]^3/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{2 \sinh (e+f x)}{3 a^2 f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{\sinh (e+f x) \cosh ^2(e+f x)}{3 a f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}","\frac{2 \sinh (e+f x)}{3 a^2 f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{\sinh (e+f x) \cosh ^2(e+f x)}{3 a f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}",1,"(Cosh[e + f*x]^2*Sinh[e + f*x])/(3*a*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + (2*Sinh[e + f*x])/(3*a^2*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",3,3,25,0.1200,1,"{3190, 378, 191}"
393,1,65,0,0.0579766,"\int \frac{\cosh (e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Cosh[e + f*x]/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{2 \sinh (e+f x)}{3 a^2 f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{\sinh (e+f x)}{3 a f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}","\frac{2 \sinh (e+f x)}{3 a^2 f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{\sinh (e+f x)}{3 a f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}",1,"Sinh[e + f*x]/(3*a*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + (2*Sinh[e + f*x])/(3*a^2*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",3,3,23,0.1304,1,"{3190, 192, 191}"
394,1,134,0,0.1489092,"\int \frac{\text{sech}(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Sech[e + f*x]/(a + b*Sinh[e + f*x]^2)^(5/2),x]","-\frac{b (5 a-2 b) \sinh (e+f x)}{3 a^2 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}-\frac{b \sinh (e+f x)}{3 a f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{f (a-b)^{5/2}}","-\frac{b (5 a-2 b) \sinh (e+f x)}{3 a^2 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}-\frac{b \sinh (e+f x)}{3 a f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{a-b} \sinh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}}\right)}{f (a-b)^{5/2}}",1,"ArcTan[(Sqrt[a - b]*Sinh[e + f*x])/Sqrt[a + b*Sinh[e + f*x]^2]]/((a - b)^(5/2)*f) - (b*Sinh[e + f*x])/(3*a*(a - b)*f*(a + b*Sinh[e + f*x]^2)^(3/2)) - ((5*a - 2*b)*b*Sinh[e + f*x])/(3*a^2*(a - b)^2*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",6,6,23,0.2609,1,"{3190, 414, 527, 12, 377, 203}"
395,1,330,0,0.3314673,"\int \frac{\cosh ^6(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Cosh[e + f*x]^6/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{\left(8 a^2-3 a b-2 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^2 b^3 f}-\frac{2 (a-b) (2 a+b) \sinh (e+f x) \cosh (e+f x)}{3 a^2 b^2 f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{(4 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{\left(8 a^2-3 a b-2 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 b^3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a-b) \sinh (e+f x) \cosh ^3(e+f x)}{3 a b f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}","\frac{\left(8 a^2-3 a b-2 b^2\right) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^2 b^3 f}-\frac{2 (a-b) (2 a+b) \sinh (e+f x) \cosh (e+f x)}{3 a^2 b^2 f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{(4 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 b^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{\left(8 a^2-3 a b-2 b^2\right) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 b^3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a-b) \sinh (e+f x) \cosh ^3(e+f x)}{3 a b f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}",1,"-((a - b)*Cosh[e + f*x]^3*Sinh[e + f*x])/(3*a*b*f*(a + b*Sinh[e + f*x]^2)^(3/2)) - (2*(a - b)*(2*a + b)*Cosh[e + f*x]*Sinh[e + f*x])/(3*a^2*b^2*f*Sqrt[a + b*Sinh[e + f*x]^2]) - ((8*a^2 - 3*a*b - 2*b^2)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^2*b^3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((4*a - b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^2*b^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((8*a^2 - 3*a*b - 2*b^2)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*a^2*b^3*f)","A",7,7,25,0.2800,1,"{3192, 413, 526, 531, 418, 492, 411}"
396,1,223,0,0.2106485,"\int \frac{\cosh ^4(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Cosh[e + f*x]^4/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{2 (a+b) \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{3 a^{3/2} b^{3/2} f \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}-\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a-b) \sinh (e+f x) \cosh (e+f x)}{3 a b f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}","\frac{2 (a+b) \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{3 a^{3/2} b^{3/2} f \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}-\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 b f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a-b) \sinh (e+f x) \cosh (e+f x)}{3 a b f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}",1,"-((a - b)*Cosh[e + f*x]*Sinh[e + f*x])/(3*a*b*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + (2*(a + b)*Cosh[e + f*x]*EllipticE[ArcTan[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a]], 1 - a/b])/(3*a^(3/2)*b^(3/2)*f*Sqrt[(a*Cosh[e + f*x]^2)/(a + b*Sinh[e + f*x]^2)]*Sqrt[a + b*Sinh[e + f*x]^2]) - (EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^2*b*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a])","A",5,5,25,0.2000,1,"{3192, 413, 525, 418, 411}"
397,1,228,0,0.2042901,"\int \frac{\cosh ^2(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Cosh[e + f*x]^2/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{(a-2 b) \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{3 a^{3/2} \sqrt{b} f (a-b) \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}+\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{\sinh (e+f x) \cosh (e+f x)}{3 a f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}","\frac{(a-2 b) \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{3 a^{3/2} \sqrt{b} f (a-b) \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}+\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{\sinh (e+f x) \cosh (e+f x)}{3 a f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}",1,"(Cosh[e + f*x]*Sinh[e + f*x])/(3*a*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + ((a - 2*b)*Cosh[e + f*x]*EllipticE[ArcTan[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a]], 1 - a/b])/(3*a^(3/2)*(a - b)*Sqrt[b]*f*Sqrt[(a*Cosh[e + f*x]^2)/(a + b*Sinh[e + f*x]^2)]*Sqrt[a + b*Sinh[e + f*x]^2]) + (EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^2*(a - b)*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a])","A",5,5,25,0.2000,1,"{3192, 412, 525, 418, 411}"
398,1,251,0,0.2806014,"\int \frac{1}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[(a + b*Sinh[e + f*x]^2)^(-5/2),x]","-\frac{2 b (2 a-b) \sinh (e+f x) \cosh (e+f x)}{3 a^2 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}-\frac{2 i (2 a-b) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 a^2 f (a-b)^2 \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}-\frac{b \sinh (e+f x) \cosh (e+f x)}{3 a f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}+\frac{i \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 a f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}","-\frac{2 b (2 a-b) \sinh (e+f x) \cosh (e+f x)}{3 a^2 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}-\frac{2 i (2 a-b) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 a^2 f (a-b)^2 \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}-\frac{b \sinh (e+f x) \cosh (e+f x)}{3 a f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}+\frac{i \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 a f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}",1,"-(b*Cosh[e + f*x]*Sinh[e + f*x])/(3*a*(a - b)*f*(a + b*Sinh[e + f*x]^2)^(3/2)) - (2*(2*a - b)*b*Cosh[e + f*x]*Sinh[e + f*x])/(3*a^2*(a - b)^2*f*Sqrt[a + b*Sinh[e + f*x]^2]) - (((2*I)/3)*(2*a - b)*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/(a^2*(a - b)^2*f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a]) + ((I/3)*EllipticF[I*e + I*f*x, b/a]*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])/(a*(a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",7,7,16,0.4375,1,"{3184, 3173, 3172, 3178, 3177, 3183, 3182}"
399,1,292,0,0.3137248,"\int \frac{\text{sech}^2(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Sech[e + f*x]^2/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{\sqrt{b} \left(3 a^2+7 a b-2 b^2\right) \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{3 a^{3/2} f (a-b)^3 \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}-\frac{b (9 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 f (a-b)^3 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{\tanh (e+f x)}{f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}+\frac{b (3 a+b) \sinh (e+f x) \cosh (e+f x)}{3 a f (a-b)^2 \left(a+b \sinh ^2(e+f x)\right)^{3/2}}","\frac{\sqrt{b} \left(3 a^2+7 a b-2 b^2\right) \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{3 a^{3/2} f (a-b)^3 \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}-\frac{b (9 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 f (a-b)^3 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{\tanh (e+f x)}{f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}+\frac{b (3 a+b) \sinh (e+f x) \cosh (e+f x)}{3 a f (a-b)^2 \left(a+b \sinh ^2(e+f x)\right)^{3/2}}",1,"(b*(3*a + b)*Cosh[e + f*x]*Sinh[e + f*x])/(3*a*(a - b)^2*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + (Sqrt[b]*(3*a^2 + 7*a*b - 2*b^2)*Cosh[e + f*x]*EllipticE[ArcTan[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a]], 1 - a/b])/(3*a^(3/2)*(a - b)^3*f*Sqrt[(a*Cosh[e + f*x]^2)/(a + b*Sinh[e + f*x]^2)]*Sqrt[a + b*Sinh[e + f*x]^2]) - ((9*a - b)*b*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^2*(a - b)^3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + Tanh[e + f*x]/((a - b)*f*(a + b*Sinh[e + f*x]^2)^(3/2))","A",6,6,25,0.2400,1,"{3192, 414, 527, 525, 418, 411}"
400,1,117,0,0.1107781,"\int (d \cosh (e+f x))^m \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[(d*Cosh[e + f*x])^m*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{d \sinh (e+f x) \cosh ^2(e+f x)^{\frac{1-m}{2}} (d \cosh (e+f x))^{m-1} \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{1}{2};\frac{1-m}{2},-p;\frac{3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}","\frac{d \sinh (e+f x) \cosh ^2(e+f x)^{\frac{1-m}{2}} (d \cosh (e+f x))^{m-1} \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{1}{2};\frac{1-m}{2},-p;\frac{3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}",1,"(d*AppellF1[1/2, (1 - m)/2, -p, 3/2, -Sinh[e + f*x]^2, -((b*Sinh[e + f*x]^2)/a)]*(d*Cosh[e + f*x])^(-1 + m)*(Cosh[e + f*x]^2)^((1 - m)/2)*Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^p)/(f*(1 + (b*Sinh[e + f*x]^2)/a)^p)","A",3,3,25,0.1200,1,"{3193, 430, 429}"
401,1,214,0,0.2044902,"\int \cosh ^5(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Cosh[e + f*x]^5*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{\left(3 a^2-2 a b (2 p+5)+b^2 \left(4 p^2+16 p+15\right)\right) \sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b \sinh ^2(e+f x)}{a}\right)}{b^2 f (2 p+3) (2 p+5)}-\frac{(3 a-b (2 p+7)) \sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{p+1}}{b^2 f (2 p+3) (2 p+5)}+\frac{\sinh (e+f x) \cosh ^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{p+1}}{b f (2 p+5)}","\frac{\left(3 a^2-2 a b (2 p+5)+b^2 \left(4 p^2+16 p+15\right)\right) \sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b \sinh ^2(e+f x)}{a}\right)}{b^2 f (2 p+3) (2 p+5)}-\frac{(3 a-b (2 p+7)) \sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{p+1}}{b^2 f (2 p+3) (2 p+5)}+\frac{\sinh (e+f x) \cosh ^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{p+1}}{b f (2 p+5)}",1,"-(((3*a - b*(7 + 2*p))*Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^(1 + p))/(b^2*f*(3 + 2*p)*(5 + 2*p))) + (Cosh[e + f*x]^2*Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^(1 + p))/(b*f*(5 + 2*p)) + ((3*a^2 - 2*a*b*(5 + 2*p) + b^2*(15 + 16*p + 4*p^2))*Hypergeometric2F1[1/2, -p, 3/2, -((b*Sinh[e + f*x]^2)/a)]*Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^p)/(b^2*f*(3 + 2*p)*(5 + 2*p)*(1 + (b*Sinh[e + f*x]^2)/a)^p)","A",5,5,23,0.2174,1,"{3190, 416, 388, 246, 245}"
402,1,119,0,0.1024175,"\int \cosh ^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Cosh[e + f*x]^3*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{\left(1-\frac{a}{2 b p+3 b}\right) \sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}+\frac{\sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{p+1}}{b f (2 p+3)}","\frac{\sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{p+1}}{b f (2 p+3)}-\frac{(a-b (2 p+3)) \sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b \sinh ^2(e+f x)}{a}\right)}{b f (2 p+3)}",1,"(Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^(1 + p))/(b*f*(3 + 2*p)) + ((1 - a/(3*b + 2*b*p))*Hypergeometric2F1[1/2, -p, 3/2, -((b*Sinh[e + f*x]^2)/a)]*Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^p)/(f*(1 + (b*Sinh[e + f*x]^2)/a)^p)","A",4,4,23,0.1739,1,"{3190, 388, 246, 245}"
403,1,67,0,0.0462517,"\int \cosh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Cosh[e + f*x]*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{\sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}","\frac{\sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}",1,"(Hypergeometric2F1[1/2, -p, 3/2, -((b*Sinh[e + f*x]^2)/a)]*Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^p)/(f*(1 + (b*Sinh[e + f*x]^2)/a)^p)","A",3,3,21,0.1429,1,"{3190, 246, 245}"
404,1,78,0,0.0757751,"\int \text{sech}(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Sech[e + f*x]*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{\sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{1}{2};1,-p;\frac{3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}","\frac{\sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{1}{2};1,-p;\frac{3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}",1,"(AppellF1[1/2, 1, -p, 3/2, -Sinh[e + f*x]^2, -((b*Sinh[e + f*x]^2)/a)]*Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^p)/(f*(1 + (b*Sinh[e + f*x]^2)/a)^p)","A",3,3,21,0.1429,1,"{3190, 430, 429}"
405,1,78,0,0.0819552,"\int \text{sech}^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Sech[e + f*x]^3*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{\sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{1}{2};2,-p;\frac{3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}","\frac{\sinh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{1}{2};2,-p;\frac{3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}",1,"(AppellF1[1/2, 2, -p, 3/2, -Sinh[e + f*x]^2, -((b*Sinh[e + f*x]^2)/a)]*Sinh[e + f*x]*(a + b*Sinh[e + f*x]^2)^p)/(f*(1 + (b*Sinh[e + f*x]^2)/a)^p)","A",3,3,23,0.1304,1,"{3190, 430, 429}"
406,1,92,0,0.0856548,"\int \cosh ^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Cosh[e + f*x]^4*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{\sqrt{\cosh ^2(e+f x)} \tanh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-\frac{3}{2},-p;\frac{3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}","\frac{\sqrt{\cosh ^2(e+f x)} \tanh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-\frac{3}{2},-p;\frac{3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}",1,"(AppellF1[1/2, -3/2, -p, 3/2, -Sinh[e + f*x]^2, -((b*Sinh[e + f*x]^2)/a)]*Sqrt[Cosh[e + f*x]^2]*(a + b*Sinh[e + f*x]^2)^p*Tanh[e + f*x])/(f*(1 + (b*Sinh[e + f*x]^2)/a)^p)","A",3,3,23,0.1304,1,"{3192, 430, 429}"
407,1,92,0,0.0822861,"\int \cosh ^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Cosh[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{\sqrt{\cosh ^2(e+f x)} \tanh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-\frac{1}{2},-p;\frac{3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}","\frac{\sqrt{\cosh ^2(e+f x)} \tanh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{1}{2};-\frac{1}{2},-p;\frac{3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}",1,"(AppellF1[1/2, -1/2, -p, 3/2, -Sinh[e + f*x]^2, -((b*Sinh[e + f*x]^2)/a)]*Sqrt[Cosh[e + f*x]^2]*(a + b*Sinh[e + f*x]^2)^p*Tanh[e + f*x])/(f*(1 + (b*Sinh[e + f*x]^2)/a)^p)","A",3,3,23,0.1304,1,"{3192, 430, 429}"
408,1,92,0,0.0515143,"\int \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[(a + b*Sinh[e + f*x]^2)^p,x]","\frac{\sqrt{\cosh ^2(e+f x)} \tanh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{1}{2};\frac{1}{2},-p;\frac{3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}","\frac{\sqrt{\cosh ^2(e+f x)} \tanh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{1}{2};\frac{1}{2},-p;\frac{3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}",1,"(AppellF1[1/2, 1/2, -p, 3/2, -Sinh[e + f*x]^2, -((b*Sinh[e + f*x]^2)/a)]*Sqrt[Cosh[e + f*x]^2]*(a + b*Sinh[e + f*x]^2)^p*Tanh[e + f*x])/(f*(1 + (b*Sinh[e + f*x]^2)/a)^p)","A",3,3,14,0.2143,1,"{3185, 430, 429}"
409,1,92,0,0.0828345,"\int \text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{\sqrt{\cosh ^2(e+f x)} \tanh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{1}{2};\frac{3}{2},-p;\frac{3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}","\frac{\sqrt{\cosh ^2(e+f x)} \tanh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{1}{2};\frac{3}{2},-p;\frac{3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}",1,"(AppellF1[1/2, 3/2, -p, 3/2, -Sinh[e + f*x]^2, -((b*Sinh[e + f*x]^2)/a)]*Sqrt[Cosh[e + f*x]^2]*(a + b*Sinh[e + f*x]^2)^p*Tanh[e + f*x])/(f*(1 + (b*Sinh[e + f*x]^2)/a)^p)","A",3,3,23,0.1304,1,"{3192, 430, 429}"
410,1,92,0,0.0818326,"\int \text{sech}^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \, dx","Int[Sech[e + f*x]^4*(a + b*Sinh[e + f*x]^2)^p,x]","\frac{\sqrt{\cosh ^2(e+f x)} \tanh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{1}{2};\frac{5}{2},-p;\frac{3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}","\frac{\sqrt{\cosh ^2(e+f x)} \tanh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{1}{2};\frac{5}{2},-p;\frac{3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{f}",1,"(AppellF1[1/2, 5/2, -p, 3/2, -Sinh[e + f*x]^2, -((b*Sinh[e + f*x]^2)/a)]*Sqrt[Cosh[e + f*x]^2]*(a + b*Sinh[e + f*x]^2)^p*Tanh[e + f*x])/(f*(1 + (b*Sinh[e + f*x]^2)/a)^p)","A",3,3,23,0.1304,1,"{3192, 430, 429}"
411,1,259,0,0.2963162,"\int \frac{\cosh ^5(c+d x)}{a+b \sqrt{\sinh (c+d x)}} \, dx","Int[Cosh[c + d*x]^5/(a + b*Sqrt[Sinh[c + d*x]]),x]","\frac{2 a^2 \sinh ^{\frac{7}{2}}(c+d x)}{7 b^3 d}-\frac{a^3 \sinh ^3(c+d x)}{3 b^4 d}+\frac{2 \left(a^4+2 b^4\right) \sinh ^{\frac{5}{2}}(c+d x)}{5 b^5 d}-\frac{a \left(a^4+2 b^4\right) \sinh ^2(c+d x)}{2 b^6 d}+\frac{2 a^2 \left(a^4+2 b^4\right) \sinh ^{\frac{3}{2}}(c+d x)}{3 b^7 d}-\frac{a^3 \left(a^4+2 b^4\right) \sinh (c+d x)}{b^8 d}+\frac{2 \left(a^4+b^4\right)^2 \sqrt{\sinh (c+d x)}}{b^9 d}-\frac{2 a \left(a^4+b^4\right)^2 \log \left(a+b \sqrt{\sinh (c+d x)}\right)}{b^{10} d}-\frac{a \sinh ^4(c+d x)}{4 b^2 d}+\frac{2 \sinh ^{\frac{9}{2}}(c+d x)}{9 b d}","\frac{2 a^2 \sinh ^{\frac{7}{2}}(c+d x)}{7 b^3 d}-\frac{a^3 \sinh ^3(c+d x)}{3 b^4 d}+\frac{2 \left(a^4+2 b^4\right) \sinh ^{\frac{5}{2}}(c+d x)}{5 b^5 d}-\frac{a \left(a^4+2 b^4\right) \sinh ^2(c+d x)}{2 b^6 d}+\frac{2 a^2 \left(a^4+2 b^4\right) \sinh ^{\frac{3}{2}}(c+d x)}{3 b^7 d}-\frac{a^3 \left(a^4+2 b^4\right) \sinh (c+d x)}{b^8 d}+\frac{2 \left(a^4+b^4\right)^2 \sqrt{\sinh (c+d x)}}{b^9 d}-\frac{2 a \left(a^4+b^4\right)^2 \log \left(a+b \sqrt{\sinh (c+d x)}\right)}{b^{10} d}-\frac{a \sinh ^4(c+d x)}{4 b^2 d}+\frac{2 \sinh ^{\frac{9}{2}}(c+d x)}{9 b d}",1,"(-2*a*(a^4 + b^4)^2*Log[a + b*Sqrt[Sinh[c + d*x]]])/(b^10*d) + (2*(a^4 + b^4)^2*Sqrt[Sinh[c + d*x]])/(b^9*d) - (a^3*(a^4 + 2*b^4)*Sinh[c + d*x])/(b^8*d) + (2*a^2*(a^4 + 2*b^4)*Sinh[c + d*x]^(3/2))/(3*b^7*d) - (a*(a^4 + 2*b^4)*Sinh[c + d*x]^2)/(2*b^6*d) + (2*(a^4 + 2*b^4)*Sinh[c + d*x]^(5/2))/(5*b^5*d) - (a^3*Sinh[c + d*x]^3)/(3*b^4*d) + (2*a^2*Sinh[c + d*x]^(7/2))/(7*b^3*d) - (a*Sinh[c + d*x]^4)/(4*b^2*d) + (2*Sinh[c + d*x]^(9/2))/(9*b*d)","A",4,3,25,0.1200,1,"{3223, 1890, 1620}"
412,1,136,0,0.1567008,"\int \frac{\cosh ^3(c+d x)}{a+b \sqrt{\sinh (c+d x)}} \, dx","Int[Cosh[c + d*x]^3/(a + b*Sqrt[Sinh[c + d*x]]),x]","\frac{2 a^2 \sinh ^{\frac{3}{2}}(c+d x)}{3 b^3 d}-\frac{a^3 \sinh (c+d x)}{b^4 d}+\frac{2 \left(a^4+b^4\right) \sqrt{\sinh (c+d x)}}{b^5 d}-\frac{2 a \left(a^4+b^4\right) \log \left(a+b \sqrt{\sinh (c+d x)}\right)}{b^6 d}-\frac{a \sinh ^2(c+d x)}{2 b^2 d}+\frac{2 \sinh ^{\frac{5}{2}}(c+d x)}{5 b d}","\frac{2 a^2 \sinh ^{\frac{3}{2}}(c+d x)}{3 b^3 d}-\frac{a^3 \sinh (c+d x)}{b^4 d}+\frac{2 \left(a^4+b^4\right) \sqrt{\sinh (c+d x)}}{b^5 d}-\frac{2 a \left(a^4+b^4\right) \log \left(a+b \sqrt{\sinh (c+d x)}\right)}{b^6 d}-\frac{a \sinh ^2(c+d x)}{2 b^2 d}+\frac{2 \sinh ^{\frac{5}{2}}(c+d x)}{5 b d}",1,"(-2*a*(a^4 + b^4)*Log[a + b*Sqrt[Sinh[c + d*x]]])/(b^6*d) + (2*(a^4 + b^4)*Sqrt[Sinh[c + d*x]])/(b^5*d) - (a^3*Sinh[c + d*x])/(b^4*d) + (2*a^2*Sinh[c + d*x]^(3/2))/(3*b^3*d) - (a*Sinh[c + d*x]^2)/(2*b^2*d) + (2*Sinh[c + d*x]^(5/2))/(5*b*d)","A",4,3,25,0.1200,1,"{3223, 1890, 1620}"
413,1,43,0,0.050232,"\int \frac{\cosh (c+d x)}{a+b \sqrt{\sinh (c+d x)}} \, dx","Int[Cosh[c + d*x]/(a + b*Sqrt[Sinh[c + d*x]]),x]","\frac{2 \sqrt{\sinh (c+d x)}}{b d}-\frac{2 a \log \left(a+b \sqrt{\sinh (c+d x)}\right)}{b^2 d}","\frac{2 \sqrt{\sinh (c+d x)}}{b d}-\frac{2 a \log \left(a+b \sqrt{\sinh (c+d x)}\right)}{b^2 d}",1,"(-2*a*Log[a + b*Sqrt[Sinh[c + d*x]]])/(b^2*d) + (2*Sqrt[Sinh[c + d*x]])/(b*d)","A",4,3,23,0.1304,1,"{3223, 190, 43}"
414,1,286,0,0.4824661,"\int \frac{\text{sech}(c+d x)}{a+b \sqrt{\sinh (c+d x)}} \, dx","Int[Sech[c + d*x]/(a + b*Sqrt[Sinh[c + d*x]]),x]","-\frac{2 a b^2 \log \left(a+b \sqrt{\sinh (c+d x)}\right)}{d \left(a^4+b^4\right)}-\frac{b \left(a^2+b^2\right) \log \left(\sinh (c+d x)-\sqrt{2} \sqrt{\sinh (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^4+b^4\right)}+\frac{b \left(a^2+b^2\right) \log \left(\sinh (c+d x)+\sqrt{2} \sqrt{\sinh (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^4+b^4\right)}+\frac{a^3 \tan ^{-1}(\sinh (c+d x))}{d \left(a^4+b^4\right)}+\frac{b \left(a^2-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\sinh (c+d x)}\right)}{\sqrt{2} d \left(a^4+b^4\right)}-\frac{b \left(a^2-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\sinh (c+d x)}+1\right)}{\sqrt{2} d \left(a^4+b^4\right)}+\frac{a b^2 \log (\cosh (c+d x))}{d \left(a^4+b^4\right)}","-\frac{2 a b^2 \log \left(a+b \sqrt{\sinh (c+d x)}\right)}{d \left(a^4+b^4\right)}-\frac{b \left(a^2+b^2\right) \log \left(\sinh (c+d x)-\sqrt{2} \sqrt{\sinh (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^4+b^4\right)}+\frac{b \left(a^2+b^2\right) \log \left(\sinh (c+d x)+\sqrt{2} \sqrt{\sinh (c+d x)}+1\right)}{2 \sqrt{2} d \left(a^4+b^4\right)}+\frac{a^3 \tan ^{-1}(\sinh (c+d x))}{d \left(a^4+b^4\right)}+\frac{b \left(a^2-b^2\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\sinh (c+d x)}\right)}{\sqrt{2} d \left(a^4+b^4\right)}-\frac{b \left(a^2-b^2\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\sinh (c+d x)}+1\right)}{\sqrt{2} d \left(a^4+b^4\right)}+\frac{a b^2 \log (\cosh (c+d x))}{d \left(a^4+b^4\right)}",1,"(b*(a^2 - b^2)*ArcTan[1 - Sqrt[2]*Sqrt[Sinh[c + d*x]]])/(Sqrt[2]*(a^4 + b^4)*d) - (b*(a^2 - b^2)*ArcTan[1 + Sqrt[2]*Sqrt[Sinh[c + d*x]]])/(Sqrt[2]*(a^4 + b^4)*d) + (a^3*ArcTan[Sinh[c + d*x]])/((a^4 + b^4)*d) + (a*b^2*Log[Cosh[c + d*x]])/((a^4 + b^4)*d) - (2*a*b^2*Log[a + b*Sqrt[Sinh[c + d*x]]])/((a^4 + b^4)*d) - (b*(a^2 + b^2)*Log[1 - Sqrt[2]*Sqrt[Sinh[c + d*x]] + Sinh[c + d*x]])/(2*Sqrt[2]*(a^4 + b^4)*d) + (b*(a^2 + b^2)*Log[1 + Sqrt[2]*Sqrt[Sinh[c + d*x]] + Sinh[c + d*x]])/(2*Sqrt[2]*(a^4 + b^4)*d)","A",19,13,23,0.5652,1,"{3223, 6725, 1876, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 203, 260}"
415,1,270,0,0.3230826,"\int \frac{\cosh ^5(c+d x)}{\left(a+b \sqrt{\sinh (c+d x)}\right)^2} \, dx","Int[Cosh[c + d*x]^5/(a + b*Sqrt[Sinh[c + d*x]])^2,x]","\frac{a^2 \sinh ^3(c+d x)}{b^4 d}-\frac{8 a^3 \sinh ^{\frac{5}{2}}(c+d x)}{5 b^5 d}+\frac{\left(5 a^4+2 b^4\right) \sinh ^2(c+d x)}{2 b^6 d}-\frac{4 a \left(3 a^4+2 b^4\right) \sinh ^{\frac{3}{2}}(c+d x)}{3 b^7 d}+\frac{a^2 \left(7 a^4+6 b^4\right) \sinh (c+d x)}{b^8 d}-\frac{16 a^3 \left(a^4+b^4\right) \sqrt{\sinh (c+d x)}}{b^9 d}+\frac{2 a \left(a^4+b^4\right)^2}{b^{10} d \left(a+b \sqrt{\sinh (c+d x)}\right)}+\frac{2 \left(a^4+b^4\right) \left(9 a^4+b^4\right) \log \left(a+b \sqrt{\sinh (c+d x)}\right)}{b^{10} d}-\frac{4 a \sinh ^{\frac{7}{2}}(c+d x)}{7 b^3 d}+\frac{\sinh ^4(c+d x)}{4 b^2 d}","\frac{a^2 \sinh ^3(c+d x)}{b^4 d}-\frac{8 a^3 \sinh ^{\frac{5}{2}}(c+d x)}{5 b^5 d}+\frac{\left(5 a^4+2 b^4\right) \sinh ^2(c+d x)}{2 b^6 d}-\frac{4 a \left(3 a^4+2 b^4\right) \sinh ^{\frac{3}{2}}(c+d x)}{3 b^7 d}+\frac{a^2 \left(7 a^4+6 b^4\right) \sinh (c+d x)}{b^8 d}-\frac{16 a^3 \left(a^4+b^4\right) \sqrt{\sinh (c+d x)}}{b^9 d}+\frac{2 a \left(a^4+b^4\right)^2}{b^{10} d \left(a+b \sqrt{\sinh (c+d x)}\right)}+\frac{2 \left(a^4+b^4\right) \left(9 a^4+b^4\right) \log \left(a+b \sqrt{\sinh (c+d x)}\right)}{b^{10} d}-\frac{4 a \sinh ^{\frac{7}{2}}(c+d x)}{7 b^3 d}+\frac{\sinh ^4(c+d x)}{4 b^2 d}",1,"(2*(a^4 + b^4)*(9*a^4 + b^4)*Log[a + b*Sqrt[Sinh[c + d*x]]])/(b^10*d) + (2*a*(a^4 + b^4)^2)/(b^10*d*(a + b*Sqrt[Sinh[c + d*x]])) - (16*a^3*(a^4 + b^4)*Sqrt[Sinh[c + d*x]])/(b^9*d) + (a^2*(7*a^4 + 6*b^4)*Sinh[c + d*x])/(b^8*d) - (4*a*(3*a^4 + 2*b^4)*Sinh[c + d*x]^(3/2))/(3*b^7*d) + ((5*a^4 + 2*b^4)*Sinh[c + d*x]^2)/(2*b^6*d) - (8*a^3*Sinh[c + d*x]^(5/2))/(5*b^5*d) + (a^2*Sinh[c + d*x]^3)/(b^4*d) - (4*a*Sinh[c + d*x]^(7/2))/(7*b^3*d) + Sinh[c + d*x]^4/(4*b^2*d)","A",4,3,25,0.1200,1,"{3223, 1890, 1620}"
416,1,142,0,0.1636055,"\int \frac{\cosh ^3(c+d x)}{\left(a+b \sqrt{\sinh (c+d x)}\right)^2} \, dx","Int[Cosh[c + d*x]^3/(a + b*Sqrt[Sinh[c + d*x]])^2,x]","-\frac{8 a^3 \sqrt{\sinh (c+d x)}}{b^5 d}+\frac{3 a^2 \sinh (c+d x)}{b^4 d}+\frac{2 a \left(a^4+b^4\right)}{b^6 d \left(a+b \sqrt{\sinh (c+d x)}\right)}+\frac{2 \left(5 a^4+b^4\right) \log \left(a+b \sqrt{\sinh (c+d x)}\right)}{b^6 d}-\frac{4 a \sinh ^{\frac{3}{2}}(c+d x)}{3 b^3 d}+\frac{\sinh ^2(c+d x)}{2 b^2 d}","-\frac{8 a^3 \sqrt{\sinh (c+d x)}}{b^5 d}+\frac{3 a^2 \sinh (c+d x)}{b^4 d}+\frac{2 a \left(a^4+b^4\right)}{b^6 d \left(a+b \sqrt{\sinh (c+d x)}\right)}+\frac{2 \left(5 a^4+b^4\right) \log \left(a+b \sqrt{\sinh (c+d x)}\right)}{b^6 d}-\frac{4 a \sinh ^{\frac{3}{2}}(c+d x)}{3 b^3 d}+\frac{\sinh ^2(c+d x)}{2 b^2 d}",1,"(2*(5*a^4 + b^4)*Log[a + b*Sqrt[Sinh[c + d*x]]])/(b^6*d) + (2*a*(a^4 + b^4))/(b^6*d*(a + b*Sqrt[Sinh[c + d*x]])) - (8*a^3*Sqrt[Sinh[c + d*x]])/(b^5*d) + (3*a^2*Sinh[c + d*x])/(b^4*d) - (4*a*Sinh[c + d*x]^(3/2))/(3*b^3*d) + Sinh[c + d*x]^2/(2*b^2*d)","A",4,3,25,0.1200,1,"{3223, 1890, 1620}"
417,1,49,0,0.0545739,"\int \frac{\cosh (c+d x)}{\left(a+b \sqrt{\sinh (c+d x)}\right)^2} \, dx","Int[Cosh[c + d*x]/(a + b*Sqrt[Sinh[c + d*x]])^2,x]","\frac{2 a}{b^2 d \left(a+b \sqrt{\sinh (c+d x)}\right)}+\frac{2 \log \left(a+b \sqrt{\sinh (c+d x)}\right)}{b^2 d}","\frac{2 a}{b^2 d \left(a+b \sqrt{\sinh (c+d x)}\right)}+\frac{2 \log \left(a+b \sqrt{\sinh (c+d x)}\right)}{b^2 d}",1,"(2*Log[a + b*Sqrt[Sinh[c + d*x]]])/(b^2*d) + (2*a)/(b^2*d*(a + b*Sqrt[Sinh[c + d*x]]))","A",4,3,23,0.1304,1,"{3223, 190, 43}"
418,1,384,0,0.6307773,"\int \frac{\text{sech}(c+d x)}{\left(a+b \sqrt{\sinh (c+d x)}\right)^2} \, dx","Int[Sech[c + d*x]/(a + b*Sqrt[Sinh[c + d*x]])^2,x]","\frac{2 a b^2}{d \left(a^4+b^4\right) \left(a+b \sqrt{\sinh (c+d x)}\right)}-\frac{a b \left(2 a^2 b^2+a^4-b^4\right) \log \left(\sinh (c+d x)-\sqrt{2} \sqrt{\sinh (c+d x)}+1\right)}{\sqrt{2} d \left(a^4+b^4\right)^2}+\frac{a b \left(2 a^2 b^2+a^4-b^4\right) \log \left(\sinh (c+d x)+\sqrt{2} \sqrt{\sinh (c+d x)}+1\right)}{\sqrt{2} d \left(a^4+b^4\right)^2}-\frac{2 b^2 \left(3 a^4-b^4\right) \log \left(a+b \sqrt{\sinh (c+d x)}\right)}{d \left(a^4+b^4\right)^2}+\frac{a^2 \left(a^4-3 b^4\right) \tan ^{-1}(\sinh (c+d x))}{d \left(a^4+b^4\right)^2}+\frac{\sqrt{2} a b \left(-2 a^2 b^2+a^4-b^4\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\sinh (c+d x)}\right)}{d \left(a^4+b^4\right)^2}-\frac{\sqrt{2} a b \left(-2 a^2 b^2+a^4-b^4\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\sinh (c+d x)}+1\right)}{d \left(a^4+b^4\right)^2}+\frac{b^2 \left(3 a^4-b^4\right) \log (\cosh (c+d x))}{d \left(a^4+b^4\right)^2}","\frac{2 a b^2}{d \left(a^4+b^4\right) \left(a+b \sqrt{\sinh (c+d x)}\right)}-\frac{a b \left(2 a^2 b^2+a^4-b^4\right) \log \left(\sinh (c+d x)-\sqrt{2} \sqrt{\sinh (c+d x)}+1\right)}{\sqrt{2} d \left(a^4+b^4\right)^2}+\frac{a b \left(2 a^2 b^2+a^4-b^4\right) \log \left(\sinh (c+d x)+\sqrt{2} \sqrt{\sinh (c+d x)}+1\right)}{\sqrt{2} d \left(a^4+b^4\right)^2}-\frac{2 b^2 \left(3 a^4-b^4\right) \log \left(a+b \sqrt{\sinh (c+d x)}\right)}{d \left(a^4+b^4\right)^2}+\frac{a^2 \left(a^4-3 b^4\right) \tan ^{-1}(\sinh (c+d x))}{d \left(a^4+b^4\right)^2}+\frac{\sqrt{2} a b \left(-2 a^2 b^2+a^4-b^4\right) \tan ^{-1}\left(1-\sqrt{2} \sqrt{\sinh (c+d x)}\right)}{d \left(a^4+b^4\right)^2}-\frac{\sqrt{2} a b \left(-2 a^2 b^2+a^4-b^4\right) \tan ^{-1}\left(\sqrt{2} \sqrt{\sinh (c+d x)}+1\right)}{d \left(a^4+b^4\right)^2}+\frac{b^2 \left(3 a^4-b^4\right) \log (\cosh (c+d x))}{d \left(a^4+b^4\right)^2}",1,"(Sqrt[2]*a*b*(a^4 - 2*a^2*b^2 - b^4)*ArcTan[1 - Sqrt[2]*Sqrt[Sinh[c + d*x]]])/((a^4 + b^4)^2*d) - (Sqrt[2]*a*b*(a^4 - 2*a^2*b^2 - b^4)*ArcTan[1 + Sqrt[2]*Sqrt[Sinh[c + d*x]]])/((a^4 + b^4)^2*d) + (a^2*(a^4 - 3*b^4)*ArcTan[Sinh[c + d*x]])/((a^4 + b^4)^2*d) + (b^2*(3*a^4 - b^4)*Log[Cosh[c + d*x]])/((a^4 + b^4)^2*d) - (2*b^2*(3*a^4 - b^4)*Log[a + b*Sqrt[Sinh[c + d*x]]])/((a^4 + b^4)^2*d) - (a*b*(a^4 + 2*a^2*b^2 - b^4)*Log[1 - Sqrt[2]*Sqrt[Sinh[c + d*x]] + Sinh[c + d*x]])/(Sqrt[2]*(a^4 + b^4)^2*d) + (a*b*(a^4 + 2*a^2*b^2 - b^4)*Log[1 + Sqrt[2]*Sqrt[Sinh[c + d*x]] + Sinh[c + d*x]])/(Sqrt[2]*(a^4 + b^4)^2*d) + (2*a*b^2)/((a^4 + b^4)*d*(a + b*Sqrt[Sinh[c + d*x]]))","A",19,13,23,0.5652,1,"{3223, 6725, 1876, 1168, 1162, 617, 204, 1165, 628, 1248, 635, 203, 260}"
419,1,130,0,0.1404006,"\int \frac{\cosh ^5(c+d x)}{a+b \sinh ^n(c+d x)} \, dx","Int[Cosh[c + d*x]^5/(a + b*Sinh[c + d*x]^n),x]","\frac{\sinh ^5(c+d x) \, _2F_1\left(1,\frac{5}{n};\frac{n+5}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{5 a d}+\frac{2 \sinh ^3(c+d x) \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{3 a d}+\frac{\sinh (c+d x) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{a d}","\frac{\sinh ^5(c+d x) \, _2F_1\left(1,\frac{5}{n};\frac{n+5}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{5 a d}+\frac{2 \sinh ^3(c+d x) \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{3 a d}+\frac{\sinh (c+d x) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{a d}",1,"(Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*Sinh[c + d*x]^n)/a)]*Sinh[c + d*x])/(a*d) + (2*Hypergeometric2F1[1, 3/n, (3 + n)/n, -((b*Sinh[c + d*x]^n)/a)]*Sinh[c + d*x]^3)/(3*a*d) + (Hypergeometric2F1[1, 5/n, (5 + n)/n, -((b*Sinh[c + d*x]^n)/a)]*Sinh[c + d*x]^5)/(5*a*d)","A",6,4,23,0.1739,1,"{3223, 1893, 245, 364}"
420,1,84,0,0.103662,"\int \frac{\cosh ^3(c+d x)}{a+b \sinh ^n(c+d x)} \, dx","Int[Cosh[c + d*x]^3/(a + b*Sinh[c + d*x]^n),x]","\frac{\sinh ^3(c+d x) \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{3 a d}+\frac{\sinh (c+d x) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{a d}","\frac{\sinh ^3(c+d x) \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{3 a d}+\frac{\sinh (c+d x) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{a d}",1,"(Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*Sinh[c + d*x]^n)/a)]*Sinh[c + d*x])/(a*d) + (Hypergeometric2F1[1, 3/n, (3 + n)/n, -((b*Sinh[c + d*x]^n)/a)]*Sinh[c + d*x]^3)/(3*a*d)","A",5,4,23,0.1739,1,"{3223, 1893, 245, 364}"
421,1,37,0,0.0434645,"\int \frac{\cosh (c+d x)}{a+b \sinh ^n(c+d x)} \, dx","Int[Cosh[c + d*x]/(a + b*Sinh[c + d*x]^n),x]","\frac{\sinh (c+d x) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{a d}","\frac{\sinh (c+d x) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{a d}",1,"(Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*Sinh[c + d*x]^n)/a)]*Sinh[c + d*x])/(a*d)","A",2,2,21,0.09524,1,"{3223, 245}"
422,1,130,0,0.1332396,"\int \frac{\cosh ^5(c+d x)}{\left(a+b \sinh ^n(c+d x)\right)^2} \, dx","Int[Cosh[c + d*x]^5/(a + b*Sinh[c + d*x]^n)^2,x]","\frac{\sinh ^5(c+d x) \, _2F_1\left(2,\frac{5}{n};\frac{n+5}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{5 a^2 d}+\frac{2 \sinh ^3(c+d x) \, _2F_1\left(2,\frac{3}{n};\frac{n+3}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{3 a^2 d}+\frac{\sinh (c+d x) \, _2F_1\left(2,\frac{1}{n};1+\frac{1}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{a^2 d}","\frac{\sinh ^5(c+d x) \, _2F_1\left(2,\frac{5}{n};\frac{n+5}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{5 a^2 d}+\frac{2 \sinh ^3(c+d x) \, _2F_1\left(2,\frac{3}{n};\frac{n+3}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{3 a^2 d}+\frac{\sinh (c+d x) \, _2F_1\left(2,\frac{1}{n};1+\frac{1}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{a^2 d}",1,"(Hypergeometric2F1[2, n^(-1), 1 + n^(-1), -((b*Sinh[c + d*x]^n)/a)]*Sinh[c + d*x])/(a^2*d) + (2*Hypergeometric2F1[2, 3/n, (3 + n)/n, -((b*Sinh[c + d*x]^n)/a)]*Sinh[c + d*x]^3)/(3*a^2*d) + (Hypergeometric2F1[2, 5/n, (5 + n)/n, -((b*Sinh[c + d*x]^n)/a)]*Sinh[c + d*x]^5)/(5*a^2*d)","A",6,4,23,0.1739,1,"{3223, 1893, 245, 364}"
423,1,84,0,0.1022416,"\int \frac{\cosh ^3(c+d x)}{\left(a+b \sinh ^n(c+d x)\right)^2} \, dx","Int[Cosh[c + d*x]^3/(a + b*Sinh[c + d*x]^n)^2,x]","\frac{\sinh ^3(c+d x) \, _2F_1\left(2,\frac{3}{n};\frac{n+3}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{3 a^2 d}+\frac{\sinh (c+d x) \, _2F_1\left(2,\frac{1}{n};1+\frac{1}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{a^2 d}","\frac{\sinh ^3(c+d x) \, _2F_1\left(2,\frac{3}{n};\frac{n+3}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{3 a^2 d}+\frac{\sinh (c+d x) \, _2F_1\left(2,\frac{1}{n};1+\frac{1}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{a^2 d}",1,"(Hypergeometric2F1[2, n^(-1), 1 + n^(-1), -((b*Sinh[c + d*x]^n)/a)]*Sinh[c + d*x])/(a^2*d) + (Hypergeometric2F1[2, 3/n, (3 + n)/n, -((b*Sinh[c + d*x]^n)/a)]*Sinh[c + d*x]^3)/(3*a^2*d)","A",5,4,23,0.1739,1,"{3223, 1893, 245, 364}"
424,1,37,0,0.0439955,"\int \frac{\cosh (c+d x)}{\left(a+b \sinh ^n(c+d x)\right)^2} \, dx","Int[Cosh[c + d*x]/(a + b*Sinh[c + d*x]^n)^2,x]","\frac{\sinh (c+d x) \, _2F_1\left(2,\frac{1}{n};1+\frac{1}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{a^2 d}","\frac{\sinh (c+d x) \, _2F_1\left(2,\frac{1}{n};1+\frac{1}{n};-\frac{b \sinh ^n(c+d x)}{a}\right)}{a^2 d}",1,"(Hypergeometric2F1[2, n^(-1), 1 + n^(-1), -((b*Sinh[c + d*x]^n)/a)]*Sinh[c + d*x])/(a^2*d)","A",2,2,21,0.09524,1,"{3223, 245}"
425,1,17,0,0.0324463,"\int \frac{\coth (x)}{1-\sinh ^2(x)} \, dx","Int[Coth[x]/(1 - Sinh[x]^2),x]","\log (\sinh (x))-\frac{1}{2} \log \left(1-\sinh ^2(x)\right)","\log (\sinh (x))-\frac{1}{2} \log \left(1-\sinh ^2(x)\right)",1,"Log[Sinh[x]] - Log[1 - Sinh[x]^2]/2","A",4,4,13,0.3077,1,"{3194, 36, 31, 29}"
426,1,63,0,0.1280253,"\int \sqrt{a+a \sinh ^2(e+f x)} \tanh ^5(e+f x) \, dx","Int[Sqrt[a + a*Sinh[e + f*x]^2]*Tanh[e + f*x]^5,x]","-\frac{a^2}{3 f \left(a \cosh ^2(e+f x)\right)^{3/2}}+\frac{2 a}{f \sqrt{a \cosh ^2(e+f x)}}+\frac{\sqrt{a \cosh ^2(e+f x)}}{f}","-\frac{a^2}{3 f \left(a \cosh ^2(e+f x)\right)^{3/2}}+\frac{2 a}{f \sqrt{a \cosh ^2(e+f x)}}+\frac{\sqrt{a \cosh ^2(e+f x)}}{f}",1,"-a^2/(3*f*(a*Cosh[e + f*x]^2)^(3/2)) + (2*a)/(f*Sqrt[a*Cosh[e + f*x]^2]) + Sqrt[a*Cosh[e + f*x]^2]/f","A",5,4,25,0.1600,1,"{3176, 3205, 16, 43}"
427,1,38,0,0.1132875,"\int \sqrt{a+a \sinh ^2(e+f x)} \tanh ^3(e+f x) \, dx","Int[Sqrt[a + a*Sinh[e + f*x]^2]*Tanh[e + f*x]^3,x]","\frac{a}{f \sqrt{a \cosh ^2(e+f x)}}+\frac{\sqrt{a \cosh ^2(e+f x)}}{f}","\frac{a}{f \sqrt{a \cosh ^2(e+f x)}}+\frac{\sqrt{a \cosh ^2(e+f x)}}{f}",1,"a/(f*Sqrt[a*Cosh[e + f*x]^2]) + Sqrt[a*Cosh[e + f*x]^2]/f","A",5,4,25,0.1600,1,"{3176, 3205, 16, 43}"
428,1,18,0,0.0693726,"\int \sqrt{a+a \sinh ^2(e+f x)} \tanh (e+f x) \, dx","Int[Sqrt[a + a*Sinh[e + f*x]^2]*Tanh[e + f*x],x]","\frac{\sqrt{a \cosh ^2(e+f x)}}{f}","\frac{\sqrt{a \cosh ^2(e+f x)}}{f}",1,"Sqrt[a*Cosh[e + f*x]^2]/f","A",4,4,23,0.1739,1,"{3176, 3205, 16, 32}"
429,1,50,0,0.0977005,"\int \coth (e+f x) \sqrt{a+a \sinh ^2(e+f x)} \, dx","Int[Coth[e + f*x]*Sqrt[a + a*Sinh[e + f*x]^2],x]","\frac{\sqrt{a \cosh ^2(e+f x)}}{f}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a \cosh ^2(e+f x)}}{\sqrt{a}}\right)}{f}","\frac{\sqrt{a \cosh ^2(e+f x)}}{f}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a \cosh ^2(e+f x)}}{\sqrt{a}}\right)}{f}",1,"-((Sqrt[a]*ArcTanh[Sqrt[a*Cosh[e + f*x]^2]/Sqrt[a]])/f) + Sqrt[a*Cosh[e + f*x]^2]/f","A",5,5,23,0.2174,1,"{3176, 3205, 50, 63, 206}"
430,1,87,0,0.1421482,"\int \coth ^3(e+f x) \sqrt{a+a \sinh ^2(e+f x)} \, dx","Int[Coth[e + f*x]^3*Sqrt[a + a*Sinh[e + f*x]^2],x]","\frac{3 \sqrt{a \cosh ^2(e+f x)}}{2 f}-\frac{3 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a \cosh ^2(e+f x)}}{\sqrt{a}}\right)}{2 f}-\frac{\text{csch}^2(e+f x) \left(a \cosh ^2(e+f x)\right)^{3/2}}{2 a f}","\frac{3 \sqrt{a \cosh ^2(e+f x)}}{2 f}-\frac{3 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a \cosh ^2(e+f x)}}{\sqrt{a}}\right)}{2 f}-\frac{\text{csch}^2(e+f x) \left(a \cosh ^2(e+f x)\right)^{3/2}}{2 a f}",1,"(-3*Sqrt[a]*ArcTanh[Sqrt[a*Cosh[e + f*x]^2]/Sqrt[a]])/(2*f) + (3*Sqrt[a*Cosh[e + f*x]^2])/(2*f) - ((a*Cosh[e + f*x]^2)^(3/2)*Csch[e + f*x]^2)/(2*a*f)","A",7,7,25,0.2800,1,"{3176, 3205, 16, 47, 50, 63, 206}"
431,1,120,0,0.129995,"\int \sqrt{a+a \sinh ^2(e+f x)} \tanh ^6(e+f x) \, dx","Int[Sqrt[a + a*Sinh[e + f*x]^2]*Tanh[e + f*x]^6,x]","-\frac{\tanh ^5(e+f x) \sqrt{a \cosh ^2(e+f x)}}{4 f}-\frac{5 \tanh ^3(e+f x) \sqrt{a \cosh ^2(e+f x)}}{8 f}+\frac{15 \tanh (e+f x) \sqrt{a \cosh ^2(e+f x)}}{8 f}-\frac{15 \text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)} \tan ^{-1}(\sinh (e+f x))}{8 f}","-\frac{\tanh ^5(e+f x) \sqrt{a \cosh ^2(e+f x)}}{4 f}-\frac{5 \tanh ^3(e+f x) \sqrt{a \cosh ^2(e+f x)}}{8 f}+\frac{15 \tanh (e+f x) \sqrt{a \cosh ^2(e+f x)}}{8 f}-\frac{15 \text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)} \tan ^{-1}(\sinh (e+f x))}{8 f}",1,"(-15*ArcTan[Sinh[e + f*x]]*Sqrt[a*Cosh[e + f*x]^2]*Sech[e + f*x])/(8*f) + (15*Sqrt[a*Cosh[e + f*x]^2]*Tanh[e + f*x])/(8*f) - (5*Sqrt[a*Cosh[e + f*x]^2]*Tanh[e + f*x]^3)/(8*f) - (Sqrt[a*Cosh[e + f*x]^2]*Tanh[e + f*x]^5)/(4*f)","A",7,6,25,0.2400,1,"{3176, 3207, 2592, 288, 321, 203}"
432,1,91,0,0.1245768,"\int \sqrt{a+a \sinh ^2(e+f x)} \tanh ^4(e+f x) \, dx","Int[Sqrt[a + a*Sinh[e + f*x]^2]*Tanh[e + f*x]^4,x]","-\frac{\tanh ^3(e+f x) \sqrt{a \cosh ^2(e+f x)}}{2 f}+\frac{3 \tanh (e+f x) \sqrt{a \cosh ^2(e+f x)}}{2 f}-\frac{3 \text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)} \tan ^{-1}(\sinh (e+f x))}{2 f}","-\frac{\tanh ^3(e+f x) \sqrt{a \cosh ^2(e+f x)}}{2 f}+\frac{3 \tanh (e+f x) \sqrt{a \cosh ^2(e+f x)}}{2 f}-\frac{3 \text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)} \tan ^{-1}(\sinh (e+f x))}{2 f}",1,"(-3*ArcTan[Sinh[e + f*x]]*Sqrt[a*Cosh[e + f*x]^2]*Sech[e + f*x])/(2*f) + (3*Sqrt[a*Cosh[e + f*x]^2]*Tanh[e + f*x])/(2*f) - (Sqrt[a*Cosh[e + f*x]^2]*Tanh[e + f*x]^3)/(2*f)","A",6,6,25,0.2400,1,"{3176, 3207, 2592, 288, 321, 203}"
433,1,57,0,0.1085512,"\int \sqrt{a+a \sinh ^2(e+f x)} \tanh ^2(e+f x) \, dx","Int[Sqrt[a + a*Sinh[e + f*x]^2]*Tanh[e + f*x]^2,x]","\frac{\tanh (e+f x) \sqrt{a \cosh ^2(e+f x)}}{f}-\frac{\text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)} \tan ^{-1}(\sinh (e+f x))}{f}","\frac{\tanh (e+f x) \sqrt{a \cosh ^2(e+f x)}}{f}-\frac{\text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)} \tan ^{-1}(\sinh (e+f x))}{f}",1,"-((ArcTan[Sinh[e + f*x]]*Sqrt[a*Cosh[e + f*x]^2]*Sech[e + f*x])/f) + (Sqrt[a*Cosh[e + f*x]^2]*Tanh[e + f*x])/f","A",5,5,25,0.2000,1,"{3176, 3207, 2592, 321, 203}"
434,1,56,0,0.1136879,"\int \coth ^2(e+f x) \sqrt{a+a \sinh ^2(e+f x)} \, dx","Int[Coth[e + f*x]^2*Sqrt[a + a*Sinh[e + f*x]^2],x]","\frac{\tanh (e+f x) \sqrt{a \cosh ^2(e+f x)}}{f}-\frac{\text{csch}(e+f x) \text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)}}{f}","\frac{\tanh (e+f x) \sqrt{a \cosh ^2(e+f x)}}{f}-\frac{\text{csch}(e+f x) \text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)}}{f}",1,"-((Sqrt[a*Cosh[e + f*x]^2]*Csch[e + f*x]*Sech[e + f*x])/f) + (Sqrt[a*Cosh[e + f*x]^2]*Tanh[e + f*x])/f","A",5,4,25,0.1600,1,"{3176, 3207, 2590, 14}"
435,1,91,0,0.1216941,"\int \coth ^4(e+f x) \sqrt{a+a \sinh ^2(e+f x)} \, dx","Int[Coth[e + f*x]^4*Sqrt[a + a*Sinh[e + f*x]^2],x]","\frac{\tanh (e+f x) \sqrt{a \cosh ^2(e+f x)}}{f}-\frac{\text{csch}^3(e+f x) \text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)}}{3 f}-\frac{2 \text{csch}(e+f x) \text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)}}{f}","\frac{\tanh (e+f x) \sqrt{a \cosh ^2(e+f x)}}{f}-\frac{\text{csch}^3(e+f x) \text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)}}{3 f}-\frac{2 \text{csch}(e+f x) \text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)}}{f}",1,"(-2*Sqrt[a*Cosh[e + f*x]^2]*Csch[e + f*x]*Sech[e + f*x])/f - (Sqrt[a*Cosh[e + f*x]^2]*Csch[e + f*x]^3*Sech[e + f*x])/(3*f) + (Sqrt[a*Cosh[e + f*x]^2]*Tanh[e + f*x])/f","A",5,4,25,0.1600,1,"{3176, 3207, 2590, 270}"
436,1,124,0,0.124526,"\int \coth ^6(e+f x) \sqrt{a+a \sinh ^2(e+f x)} \, dx","Int[Coth[e + f*x]^6*Sqrt[a + a*Sinh[e + f*x]^2],x]","\frac{\tanh (e+f x) \sqrt{a \cosh ^2(e+f x)}}{f}-\frac{\text{csch}^5(e+f x) \text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)}}{5 f}-\frac{\text{csch}^3(e+f x) \text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)}}{f}-\frac{3 \text{csch}(e+f x) \text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)}}{f}","\frac{\tanh (e+f x) \sqrt{a \cosh ^2(e+f x)}}{f}-\frac{\text{csch}^5(e+f x) \text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)}}{5 f}-\frac{\text{csch}^3(e+f x) \text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)}}{f}-\frac{3 \text{csch}(e+f x) \text{sech}(e+f x) \sqrt{a \cosh ^2(e+f x)}}{f}",1,"(-3*Sqrt[a*Cosh[e + f*x]^2]*Csch[e + f*x]*Sech[e + f*x])/f - (Sqrt[a*Cosh[e + f*x]^2]*Csch[e + f*x]^3*Sech[e + f*x])/f - (Sqrt[a*Cosh[e + f*x]^2]*Csch[e + f*x]^5*Sech[e + f*x])/(5*f) + (Sqrt[a*Cosh[e + f*x]^2]*Tanh[e + f*x])/f","A",5,4,25,0.1600,1,"{3176, 3207, 2590, 270}"
437,1,66,0,0.1290551,"\int \frac{\tanh ^5(e+f x)}{\sqrt{a+a \sinh ^2(e+f x)}} \, dx","Int[Tanh[e + f*x]^5/Sqrt[a + a*Sinh[e + f*x]^2],x]","-\frac{a^2}{5 f \left(a \cosh ^2(e+f x)\right)^{5/2}}+\frac{2 a}{3 f \left(a \cosh ^2(e+f x)\right)^{3/2}}-\frac{1}{f \sqrt{a \cosh ^2(e+f x)}}","-\frac{a^2}{5 f \left(a \cosh ^2(e+f x)\right)^{5/2}}+\frac{2 a}{3 f \left(a \cosh ^2(e+f x)\right)^{3/2}}-\frac{1}{f \sqrt{a \cosh ^2(e+f x)}}",1,"-a^2/(5*f*(a*Cosh[e + f*x]^2)^(5/2)) + (2*a)/(3*f*(a*Cosh[e + f*x]^2)^(3/2)) - 1/(f*Sqrt[a*Cosh[e + f*x]^2])","A",5,4,25,0.1600,1,"{3176, 3205, 16, 43}"
438,1,42,0,0.1176409,"\int \frac{\tanh ^3(e+f x)}{\sqrt{a+a \sinh ^2(e+f x)}} \, dx","Int[Tanh[e + f*x]^3/Sqrt[a + a*Sinh[e + f*x]^2],x]","\frac{a}{3 f \left(a \cosh ^2(e+f x)\right)^{3/2}}-\frac{1}{f \sqrt{a \cosh ^2(e+f x)}}","\frac{a}{3 f \left(a \cosh ^2(e+f x)\right)^{3/2}}-\frac{1}{f \sqrt{a \cosh ^2(e+f x)}}",1,"a/(3*f*(a*Cosh[e + f*x]^2)^(3/2)) - 1/(f*Sqrt[a*Cosh[e + f*x]^2])","A",5,4,25,0.1600,1,"{3176, 3205, 16, 43}"
439,1,19,0,0.0696189,"\int \frac{\tanh (e+f x)}{\sqrt{a+a \sinh ^2(e+f x)}} \, dx","Int[Tanh[e + f*x]/Sqrt[a + a*Sinh[e + f*x]^2],x]","-\frac{1}{f \sqrt{a \cosh ^2(e+f x)}}","-\frac{1}{f \sqrt{a \cosh ^2(e+f x)}}",1,"-(1/(f*Sqrt[a*Cosh[e + f*x]^2]))","A",4,4,23,0.1739,1,"{3176, 3205, 16, 32}"
440,1,31,0,0.0856261,"\int \frac{\coth (e+f x)}{\sqrt{a+a \sinh ^2(e+f x)}} \, dx","Int[Coth[e + f*x]/Sqrt[a + a*Sinh[e + f*x]^2],x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a \cosh ^2(e+f x)}}{\sqrt{a}}\right)}{\sqrt{a} f}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a \cosh ^2(e+f x)}}{\sqrt{a}}\right)}{\sqrt{a} f}",1,"-(ArcTanh[Sqrt[a*Cosh[e + f*x]^2]/Sqrt[a]]/(Sqrt[a]*f))","A",4,4,23,0.1739,1,"{3176, 3205, 63, 206}"
441,1,66,0,0.1293946,"\int \frac{\coth ^3(e+f x)}{\sqrt{a+a \sinh ^2(e+f x)}} \, dx","Int[Coth[e + f*x]^3/Sqrt[a + a*Sinh[e + f*x]^2],x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a \cosh ^2(e+f x)}}{\sqrt{a}}\right)}{2 \sqrt{a} f}-\frac{\text{csch}^2(e+f x) \sqrt{a \cosh ^2(e+f x)}}{2 a f}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a \cosh ^2(e+f x)}}{\sqrt{a}}\right)}{2 \sqrt{a} f}-\frac{\text{csch}^2(e+f x) \sqrt{a \cosh ^2(e+f x)}}{2 a f}",1,"-ArcTanh[Sqrt[a*Cosh[e + f*x]^2]/Sqrt[a]]/(2*Sqrt[a]*f) - (Sqrt[a*Cosh[e + f*x]^2]*Csch[e + f*x]^2)/(2*a*f)","A",6,6,25,0.2400,1,"{3176, 3205, 16, 47, 63, 206}"
442,1,91,0,0.1442371,"\int \frac{\tanh ^4(e+f x)}{\sqrt{a+a \sinh ^2(e+f x)}} \, dx","Int[Tanh[e + f*x]^4/Sqrt[a + a*Sinh[e + f*x]^2],x]","-\frac{\tanh ^3(e+f x)}{4 f \sqrt{a \cosh ^2(e+f x)}}-\frac{3 \tanh (e+f x)}{8 f \sqrt{a \cosh ^2(e+f x)}}+\frac{3 \cosh (e+f x) \tan ^{-1}(\sinh (e+f x))}{8 f \sqrt{a \cosh ^2(e+f x)}}","-\frac{\tanh ^3(e+f x)}{4 f \sqrt{a \cosh ^2(e+f x)}}-\frac{3 \tanh (e+f x)}{8 f \sqrt{a \cosh ^2(e+f x)}}+\frac{3 \cosh (e+f x) \tan ^{-1}(\sinh (e+f x))}{8 f \sqrt{a \cosh ^2(e+f x)}}",1,"(3*ArcTan[Sinh[e + f*x]]*Cosh[e + f*x])/(8*f*Sqrt[a*Cosh[e + f*x]^2]) - (3*Tanh[e + f*x])/(8*f*Sqrt[a*Cosh[e + f*x]^2]) - Tanh[e + f*x]^3/(4*f*Sqrt[a*Cosh[e + f*x]^2])","A",5,4,25,0.1600,1,"{3176, 3207, 2611, 3770}"
443,1,62,0,0.1206515,"\int \frac{\tanh ^2(e+f x)}{\sqrt{a+a \sinh ^2(e+f x)}} \, dx","Int[Tanh[e + f*x]^2/Sqrt[a + a*Sinh[e + f*x]^2],x]","\frac{\cosh (e+f x) \tan ^{-1}(\sinh (e+f x))}{2 f \sqrt{a \cosh ^2(e+f x)}}-\frac{\tanh (e+f x)}{2 f \sqrt{a \cosh ^2(e+f x)}}","\frac{\cosh (e+f x) \tan ^{-1}(\sinh (e+f x))}{2 f \sqrt{a \cosh ^2(e+f x)}}-\frac{\tanh (e+f x)}{2 f \sqrt{a \cosh ^2(e+f x)}}",1,"(ArcTan[Sinh[e + f*x]]*Cosh[e + f*x])/(2*f*Sqrt[a*Cosh[e + f*x]^2]) - Tanh[e + f*x]/(2*f*Sqrt[a*Cosh[e + f*x]^2])","A",4,4,25,0.1600,1,"{3176, 3207, 2611, 3770}"
444,1,25,0,0.1044427,"\int \frac{\coth ^2(e+f x)}{\sqrt{a+a \sinh ^2(e+f x)}} \, dx","Int[Coth[e + f*x]^2/Sqrt[a + a*Sinh[e + f*x]^2],x]","-\frac{\coth (e+f x)}{f \sqrt{a \cosh ^2(e+f x)}}","-\frac{\coth (e+f x)}{f \sqrt{a \cosh ^2(e+f x)}}",1,"-(Coth[e + f*x]/(f*Sqrt[a*Cosh[e + f*x]^2]))","A",4,4,25,0.1600,1,"{3176, 3207, 2606, 8}"
445,1,61,0,0.1147106,"\int \frac{\coth ^4(e+f x)}{\sqrt{a+a \sinh ^2(e+f x)}} \, dx","Int[Coth[e + f*x]^4/Sqrt[a + a*Sinh[e + f*x]^2],x]","-\frac{\coth (e+f x)}{f \sqrt{a \cosh ^2(e+f x)}}-\frac{\coth (e+f x) \text{csch}^2(e+f x)}{3 f \sqrt{a \cosh ^2(e+f x)}}","-\frac{\coth (e+f x)}{f \sqrt{a \cosh ^2(e+f x)}}-\frac{\coth (e+f x) \text{csch}^2(e+f x)}{3 f \sqrt{a \cosh ^2(e+f x)}}",1,"-(Coth[e + f*x]/(f*Sqrt[a*Cosh[e + f*x]^2])) - (Coth[e + f*x]*Csch[e + f*x]^2)/(3*f*Sqrt[a*Cosh[e + f*x]^2])","A",4,3,25,0.1200,1,"{3176, 3207, 2606}"
446,1,96,0,0.1227237,"\int \frac{\coth ^6(e+f x)}{\sqrt{a+a \sinh ^2(e+f x)}} \, dx","Int[Coth[e + f*x]^6/Sqrt[a + a*Sinh[e + f*x]^2],x]","-\frac{\coth (e+f x)}{f \sqrt{a \cosh ^2(e+f x)}}-\frac{\coth (e+f x) \text{csch}^4(e+f x)}{5 f \sqrt{a \cosh ^2(e+f x)}}-\frac{2 \coth (e+f x) \text{csch}^2(e+f x)}{3 f \sqrt{a \cosh ^2(e+f x)}}","-\frac{\coth (e+f x)}{f \sqrt{a \cosh ^2(e+f x)}}-\frac{\coth (e+f x) \text{csch}^4(e+f x)}{5 f \sqrt{a \cosh ^2(e+f x)}}-\frac{2 \coth (e+f x) \text{csch}^2(e+f x)}{3 f \sqrt{a \cosh ^2(e+f x)}}",1,"-(Coth[e + f*x]/(f*Sqrt[a*Cosh[e + f*x]^2])) - (2*Coth[e + f*x]*Csch[e + f*x]^2)/(3*f*Sqrt[a*Cosh[e + f*x]^2]) - (Coth[e + f*x]*Csch[e + f*x]^4)/(5*f*Sqrt[a*Cosh[e + f*x]^2])","A",5,4,25,0.1600,1,"{3176, 3207, 2606, 194}"
447,1,68,0,0.1411467,"\int \frac{\tanh ^5(e+f x)}{\left(a+a \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Tanh[e + f*x]^5/(a + a*Sinh[e + f*x]^2)^(3/2),x]","-\frac{a^2}{7 f \left(a \cosh ^2(e+f x)\right)^{7/2}}+\frac{2 a}{5 f \left(a \cosh ^2(e+f x)\right)^{5/2}}-\frac{1}{3 f \left(a \cosh ^2(e+f x)\right)^{3/2}}","-\frac{a^2}{7 f \left(a \cosh ^2(e+f x)\right)^{7/2}}+\frac{2 a}{5 f \left(a \cosh ^2(e+f x)\right)^{5/2}}-\frac{1}{3 f \left(a \cosh ^2(e+f x)\right)^{3/2}}",1,"-a^2/(7*f*(a*Cosh[e + f*x]^2)^(7/2)) + (2*a)/(5*f*(a*Cosh[e + f*x]^2)^(5/2)) - 1/(3*f*(a*Cosh[e + f*x]^2)^(3/2))","A",5,4,25,0.1600,1,"{3176, 3205, 16, 43}"
448,1,44,0,0.1261335,"\int \frac{\tanh ^3(e+f x)}{\left(a+a \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Tanh[e + f*x]^3/(a + a*Sinh[e + f*x]^2)^(3/2),x]","\frac{a}{5 f \left(a \cosh ^2(e+f x)\right)^{5/2}}-\frac{1}{3 f \left(a \cosh ^2(e+f x)\right)^{3/2}}","\frac{a}{5 f \left(a \cosh ^2(e+f x)\right)^{5/2}}-\frac{1}{3 f \left(a \cosh ^2(e+f x)\right)^{3/2}}",1,"a/(5*f*(a*Cosh[e + f*x]^2)^(5/2)) - 1/(3*f*(a*Cosh[e + f*x]^2)^(3/2))","A",5,4,25,0.1600,1,"{3176, 3205, 16, 43}"
449,1,21,0,0.0774936,"\int \frac{\tanh (e+f x)}{\left(a+a \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Tanh[e + f*x]/(a + a*Sinh[e + f*x]^2)^(3/2),x]","-\frac{1}{3 f \left(a \cosh ^2(e+f x)\right)^{3/2}}","-\frac{1}{3 f \left(a \cosh ^2(e+f x)\right)^{3/2}}",1,"-1/(3*f*(a*Cosh[e + f*x]^2)^(3/2))","A",4,4,23,0.1739,1,"{3176, 3205, 16, 32}"
450,1,53,0,0.1076512,"\int \frac{\coth (e+f x)}{\left(a+a \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Coth[e + f*x]/(a + a*Sinh[e + f*x]^2)^(3/2),x]","\frac{1}{a f \sqrt{a \cosh ^2(e+f x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a \cosh ^2(e+f x)}}{\sqrt{a}}\right)}{a^{3/2} f}","\frac{1}{a f \sqrt{a \cosh ^2(e+f x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a \cosh ^2(e+f x)}}{\sqrt{a}}\right)}{a^{3/2} f}",1,"-(ArcTanh[Sqrt[a*Cosh[e + f*x]^2]/Sqrt[a]]/(a^(3/2)*f)) + 1/(a*f*Sqrt[a*Cosh[e + f*x]^2])","A",5,5,23,0.2174,1,"{3176, 3205, 51, 63, 206}"
451,1,66,0,0.1394671,"\int \frac{\coth ^3(e+f x)}{\left(a+a \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Coth[e + f*x]^3/(a + a*Sinh[e + f*x]^2)^(3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a \cosh ^2(e+f x)}}{\sqrt{a}}\right)}{2 a^{3/2} f}-\frac{\text{csch}^2(e+f x) \sqrt{a \cosh ^2(e+f x)}}{2 a^2 f}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a \cosh ^2(e+f x)}}{\sqrt{a}}\right)}{2 a^{3/2} f}-\frac{\text{csch}^2(e+f x) \sqrt{a \cosh ^2(e+f x)}}{2 a^2 f}",1,"ArcTanh[Sqrt[a*Cosh[e + f*x]^2]/Sqrt[a]]/(2*a^(3/2)*f) - (Sqrt[a*Cosh[e + f*x]^2]*Csch[e + f*x]^2)/(2*a^2*f)","A",6,6,25,0.2400,1,"{3176, 3205, 16, 51, 63, 206}"
452,1,106,0,0.1598194,"\int \frac{\tanh ^2(e+f x)}{\left(a+a \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Tanh[e + f*x]^2/(a + a*Sinh[e + f*x]^2)^(3/2),x]","\frac{\tanh (e+f x)}{8 a f \sqrt{a \cosh ^2(e+f x)}}+\frac{\cosh (e+f x) \tan ^{-1}(\sinh (e+f x))}{8 a f \sqrt{a \cosh ^2(e+f x)}}-\frac{\tanh (e+f x) \text{sech}^2(e+f x)}{4 a f \sqrt{a \cosh ^2(e+f x)}}","\frac{\tanh (e+f x)}{8 a f \sqrt{a \cosh ^2(e+f x)}}+\frac{\cosh (e+f x) \tan ^{-1}(\sinh (e+f x))}{8 a f \sqrt{a \cosh ^2(e+f x)}}-\frac{\tanh (e+f x) \text{sech}^2(e+f x)}{4 a f \sqrt{a \cosh ^2(e+f x)}}",1,"(ArcTan[Sinh[e + f*x]]*Cosh[e + f*x])/(8*a*f*Sqrt[a*Cosh[e + f*x]^2]) + Tanh[e + f*x]/(8*a*f*Sqrt[a*Cosh[e + f*x]^2]) - (Sech[e + f*x]^2*Tanh[e + f*x])/(4*a*f*Sqrt[a*Cosh[e + f*x]^2])","A",5,5,25,0.2000,1,"{3176, 3207, 2611, 3768, 3770}"
453,1,64,0,0.1317318,"\int \frac{\coth ^2(e+f x)}{\left(a+a \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Coth[e + f*x]^2/(a + a*Sinh[e + f*x]^2)^(3/2),x]","-\frac{\coth (e+f x)}{a f \sqrt{a \cosh ^2(e+f x)}}-\frac{\cosh (e+f x) \tan ^{-1}(\sinh (e+f x))}{a f \sqrt{a \cosh ^2(e+f x)}}","-\frac{\coth (e+f x)}{a f \sqrt{a \cosh ^2(e+f x)}}-\frac{\cosh (e+f x) \tan ^{-1}(\sinh (e+f x))}{a f \sqrt{a \cosh ^2(e+f x)}}",1,"-((ArcTan[Sinh[e + f*x]]*Cosh[e + f*x])/(a*f*Sqrt[a*Cosh[e + f*x]^2])) - Coth[e + f*x]/(a*f*Sqrt[a*Cosh[e + f*x]^2])","A",5,5,25,0.2000,1,"{3176, 3207, 2621, 321, 207}"
454,1,38,0,0.1262044,"\int \frac{\coth ^4(e+f x)}{\left(a+a \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Coth[e + f*x]^4/(a + a*Sinh[e + f*x]^2)^(3/2),x]","-\frac{\coth (e+f x) \text{csch}^2(e+f x)}{3 a f \sqrt{a \cosh ^2(e+f x)}}","-\frac{\coth (e+f x) \text{csch}^2(e+f x)}{3 a f \sqrt{a \cosh ^2(e+f x)}}",1,"-(Coth[e + f*x]*Csch[e + f*x]^2)/(3*a*f*Sqrt[a*Cosh[e + f*x]^2])","A",4,4,25,0.1600,1,"{3176, 3207, 2606, 30}"
455,1,77,0,0.1437454,"\int \frac{\coth ^6(e+f x)}{\left(a+a \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Coth[e + f*x]^6/(a + a*Sinh[e + f*x]^2)^(3/2),x]","-\frac{\coth (e+f x) \text{csch}^4(e+f x)}{5 a f \sqrt{a \cosh ^2(e+f x)}}-\frac{\coth (e+f x) \text{csch}^2(e+f x)}{3 a f \sqrt{a \cosh ^2(e+f x)}}","-\frac{\coth (e+f x) \text{csch}^4(e+f x)}{5 a f \sqrt{a \cosh ^2(e+f x)}}-\frac{\coth (e+f x) \text{csch}^2(e+f x)}{3 a f \sqrt{a \cosh ^2(e+f x)}}",1,"-(Coth[e + f*x]*Csch[e + f*x]^2)/(3*a*f*Sqrt[a*Cosh[e + f*x]^2]) - (Coth[e + f*x]*Csch[e + f*x]^4)/(5*a*f*Sqrt[a*Cosh[e + f*x]^2])","A",5,4,25,0.1600,1,"{3176, 3207, 2606, 14}"
456,1,115,0,0.149823,"\int \frac{\coth ^8(e+f x)}{\left(a+a \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Coth[e + f*x]^8/(a + a*Sinh[e + f*x]^2)^(3/2),x]","-\frac{\coth (e+f x) \text{csch}^6(e+f x)}{7 a f \sqrt{a \cosh ^2(e+f x)}}-\frac{2 \coth (e+f x) \text{csch}^4(e+f x)}{5 a f \sqrt{a \cosh ^2(e+f x)}}-\frac{\coth (e+f x) \text{csch}^2(e+f x)}{3 a f \sqrt{a \cosh ^2(e+f x)}}","-\frac{\coth (e+f x) \text{csch}^6(e+f x)}{7 a f \sqrt{a \cosh ^2(e+f x)}}-\frac{2 \coth (e+f x) \text{csch}^4(e+f x)}{5 a f \sqrt{a \cosh ^2(e+f x)}}-\frac{\coth (e+f x) \text{csch}^2(e+f x)}{3 a f \sqrt{a \cosh ^2(e+f x)}}",1,"-(Coth[e + f*x]*Csch[e + f*x]^2)/(3*a*f*Sqrt[a*Cosh[e + f*x]^2]) - (2*Coth[e + f*x]*Csch[e + f*x]^4)/(5*a*f*Sqrt[a*Cosh[e + f*x]^2]) - (Coth[e + f*x]*Csch[e + f*x]^6)/(7*a*f*Sqrt[a*Cosh[e + f*x]^2])","A",5,4,25,0.1600,1,"{3176, 3207, 2606, 270}"
457,1,187,0,0.22461,"\int \sqrt{a+b \sinh ^2(e+f x)} \tanh ^5(e+f x) \, dx","Int[Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x]^5,x]","\frac{\left(8 a^2-24 a b+15 b^2\right) \sqrt{a+b \sinh ^2(e+f x)}}{8 f (a-b)^2}-\frac{\left(8 a^2-24 a b+15 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{8 f (a-b)^{3/2}}-\frac{\text{sech}^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{4 f (a-b)}+\frac{(8 a-7 b) \text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{8 f (a-b)^2}","\frac{\left(8 a^2-24 a b+15 b^2\right) \sqrt{a+b \sinh ^2(e+f x)}}{8 f (a-b)^2}-\frac{\left(8 a^2-24 a b+15 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{8 f (a-b)^{3/2}}-\frac{\text{sech}^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{4 f (a-b)}+\frac{(8 a-7 b) \text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{8 f (a-b)^2}",1,"-((8*a^2 - 24*a*b + 15*b^2)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a - b]])/(8*(a - b)^(3/2)*f) + ((8*a^2 - 24*a*b + 15*b^2)*Sqrt[a + b*Sinh[e + f*x]^2])/(8*(a - b)^2*f) + ((8*a - 7*b)*Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^(3/2))/(8*(a - b)^2*f) - (Sech[e + f*x]^4*(a + b*Sinh[e + f*x]^2)^(3/2))/(4*(a - b)*f)","A",6,6,25,0.2400,1,"{3194, 89, 78, 50, 63, 208}"
458,1,126,0,0.1252831,"\int \sqrt{a+b \sinh ^2(e+f x)} \tanh ^3(e+f x) \, dx","Int[Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x]^3,x]","\frac{(2 a-3 b) \sqrt{a+b \sinh ^2(e+f x)}}{2 f (a-b)}-\frac{(2 a-3 b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{2 f \sqrt{a-b}}+\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{2 f (a-b)}","\frac{(2 a-3 b) \sqrt{a+b \sinh ^2(e+f x)}}{2 f (a-b)}-\frac{(2 a-3 b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{2 f \sqrt{a-b}}+\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{2 f (a-b)}",1,"-((2*a - 3*b)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a - b]])/(2*Sqrt[a - b]*f) + ((2*a - 3*b)*Sqrt[a + b*Sinh[e + f*x]^2])/(2*(a - b)*f) + (Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^(3/2))/(2*(a - b)*f)","A",5,5,25,0.2000,1,"{3194, 78, 50, 63, 208}"
459,1,62,0,0.0635905,"\int \sqrt{a+b \sinh ^2(e+f x)} \tanh (e+f x) \, dx","Int[Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x],x]","\frac{\sqrt{a+b \sinh ^2(e+f x)}}{f}-\frac{\sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{f}","\frac{\sqrt{a+b \sinh ^2(e+f x)}}{f}-\frac{\sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{f}",1,"-((Sqrt[a - b]*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a - b]])/f) + Sqrt[a + b*Sinh[e + f*x]^2]/f","A",4,4,23,0.1739,1,"{3194, 50, 63, 208}"
460,1,54,0,0.0742229,"\int \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\sqrt{a+b \sinh ^2(e+f x)}}{f}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{f}","\frac{\sqrt{a+b \sinh ^2(e+f x)}}{f}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{f}",1,"-((Sqrt[a]*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a]])/f) + Sqrt[a + b*Sinh[e + f*x]^2]/f","A",4,4,23,0.1739,1,"{3194, 50, 63, 208}"
461,1,106,0,0.121803,"\int \coth ^3(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Coth[e + f*x]^3*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{(2 a+b) \sqrt{a+b \sinh ^2(e+f x)}}{2 a f}-\frac{(2 a+b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{2 \sqrt{a} f}-\frac{\text{csch}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{2 a f}","\frac{(2 a+b) \sqrt{a+b \sinh ^2(e+f x)}}{2 a f}-\frac{(2 a+b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{2 \sqrt{a} f}-\frac{\text{csch}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{2 a f}",1,"-((2*a + b)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a]])/(2*Sqrt[a]*f) + ((2*a + b)*Sqrt[a + b*Sinh[e + f*x]^2])/(2*a*f) - (Csch[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^(3/2))/(2*a*f)","A",5,5,25,0.2000,1,"{3194, 78, 50, 63, 208}"
462,1,167,0,0.1798315,"\int \coth ^5(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Coth[e + f*x]^5*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\left(8 a^2+8 a b-b^2\right) \sqrt{a+b \sinh ^2(e+f x)}}{8 a^2 f}-\frac{\left(8 a^2+8 a b-b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{8 a^{3/2} f}-\frac{(8 a-b) \text{csch}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{8 a^2 f}-\frac{\text{csch}^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{4 a f}","\frac{\left(8 a^2+8 a b-b^2\right) \sqrt{a+b \sinh ^2(e+f x)}}{8 a^2 f}-\frac{\left(8 a^2+8 a b-b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{8 a^{3/2} f}-\frac{(8 a-b) \text{csch}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{8 a^2 f}-\frac{\text{csch}^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{4 a f}",1,"-((8*a^2 + 8*a*b - b^2)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a]])/(8*a^(3/2)*f) + ((8*a^2 + 8*a*b - b^2)*Sqrt[a + b*Sinh[e + f*x]^2])/(8*a^2*f) - ((8*a - b)*Csch[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^(3/2))/(8*a^2*f) - (Csch[e + f*x]^4*(a + b*Sinh[e + f*x]^2)^(3/2))/(4*a*f)","A",6,6,25,0.2400,1,"{3194, 89, 78, 50, 63, 208}"
463,1,292,0,0.3064282,"\int \sqrt{a+b \sinh ^2(e+f x)} \tanh ^4(e+f x) \, dx","Int[Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x]^4,x]","-\frac{\tanh ^3(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{(7 a-8 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f (a-b)}-\frac{(3 a-4 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f (a-b)}+\frac{(3 a-4 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(7 a-8 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","-\frac{\tanh ^3(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{(7 a-8 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f (a-b)}-\frac{(3 a-4 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f (a-b)}+\frac{(3 a-4 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(7 a-8 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"-((7*a - 8*b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*(a - b)*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((3*a - 4*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*(a - b)*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((7*a - 8*b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*(a - b)*f) - ((3*a - 4*b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*(a - b)*f) - (Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x]^3)/(3*f)","A",7,7,25,0.2800,1,"{3196, 467, 578, 531, 418, 492, 411}"
464,1,168,0,0.1771732,"\int \sqrt{a+b \sinh ^2(e+f x)} \tanh ^2(e+f x) \, dx","Int[Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x]^2,x]","\frac{\tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{2 \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{\tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{2 \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(-2*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/f","A",6,6,25,0.2400,1,"{3196, 467, 531, 418, 492, 411}"
465,1,60,0,0.0380248,"\int \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{i \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}","-\frac{i \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}",1,"((-I)*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/(f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])","A",2,2,16,0.1250,1,"{3178, 3177}"
466,1,202,0,0.1988977,"\int \coth ^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Coth[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{2 \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}-\frac{\coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{(a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{2 \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{2 \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}-\frac{\coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{(a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{2 \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"-((Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/f) - (2*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((a + b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (2*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/f","A",6,6,25,0.2400,1,"{3196, 473, 531, 418, 492, 411}"
467,1,270,0,0.2957583,"\int \coth ^4(e+f x) \sqrt{a+b \sinh ^2(e+f x)} \, dx","Int[Coth[e + f*x]^4*Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{(7 a+b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a f}-\frac{\coth ^3(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{(3 a+b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a f}+\frac{(3 a+5 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(7 a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{(7 a+b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a f}-\frac{\coth ^3(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{(3 a+b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a f}+\frac{(3 a+5 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(7 a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"-((3*a + b)*Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*f) - (Coth[e + f*x]^3*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f) - ((7*a + b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((3*a + 5*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((7*a + b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*a*f)","A",7,7,25,0.2800,1,"{3196, 473, 580, 531, 418, 492, 411}"
468,1,232,0,0.2902545,"\int \left(a+b \sinh ^2(e+f x)\right)^{3/2} \tanh ^5(e+f x) \, dx","Int[(a + b*Sinh[e + f*x]^2)^(3/2)*Tanh[e + f*x]^5,x]","\frac{\left(8 a^2-40 a b+35 b^2\right) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{24 f (a-b)^2}+\frac{\left(8 a^2-40 a b+35 b^2\right) \sqrt{a+b \sinh ^2(e+f x)}}{8 f (a-b)}-\frac{\left(8 a^2-40 a b+35 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{8 f \sqrt{a-b}}-\frac{\text{sech}^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{5/2}}{4 f (a-b)}+\frac{(8 a-9 b) \text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{5/2}}{8 f (a-b)^2}","\frac{\left(8 a^2-40 a b+35 b^2\right) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{24 f (a-b)^2}+\frac{\left(8 a^2-40 a b+35 b^2\right) \sqrt{a+b \sinh ^2(e+f x)}}{8 f (a-b)}-\frac{\left(8 a^2-40 a b+35 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{8 f \sqrt{a-b}}-\frac{\text{sech}^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{5/2}}{4 f (a-b)}+\frac{(8 a-9 b) \text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{5/2}}{8 f (a-b)^2}",1,"-((8*a^2 - 40*a*b + 35*b^2)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a - b]])/(8*Sqrt[a - b]*f) + ((8*a^2 - 40*a*b + 35*b^2)*Sqrt[a + b*Sinh[e + f*x]^2])/(8*(a - b)*f) + ((8*a^2 - 40*a*b + 35*b^2)*(a + b*Sinh[e + f*x]^2)^(3/2))/(24*(a - b)^2*f) + ((8*a - 9*b)*Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^(5/2))/(8*(a - b)^2*f) - (Sech[e + f*x]^4*(a + b*Sinh[e + f*x]^2)^(5/2))/(4*(a - b)*f)","A",7,6,25,0.2400,1,"{3194, 89, 78, 50, 63, 208}"
469,1,156,0,0.1589174,"\int \left(a+b \sinh ^2(e+f x)\right)^{3/2} \tanh ^3(e+f x) \, dx","Int[(a + b*Sinh[e + f*x]^2)^(3/2)*Tanh[e + f*x]^3,x]","\frac{(2 a-5 b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{6 f (a-b)}+\frac{(2 a-5 b) \sqrt{a+b \sinh ^2(e+f x)}}{2 f}-\frac{(2 a-5 b) \sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{2 f}+\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{5/2}}{2 f (a-b)}","\frac{(2 a-5 b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{6 f (a-b)}+\frac{(2 a-5 b) \sqrt{a+b \sinh ^2(e+f x)}}{2 f}-\frac{(2 a-5 b) \sqrt{a-b} \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{2 f}+\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{5/2}}{2 f (a-b)}",1,"-((2*a - 5*b)*Sqrt[a - b]*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a - b]])/(2*f) + ((2*a - 5*b)*Sqrt[a + b*Sinh[e + f*x]^2])/(2*f) + ((2*a - 5*b)*(a + b*Sinh[e + f*x]^2)^(3/2))/(6*(a - b)*f) + (Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^(5/2))/(2*(a - b)*f)","A",6,5,25,0.2000,1,"{3194, 78, 50, 63, 208}"
470,1,90,0,0.090232,"\int \left(a+b \sinh ^2(e+f x)\right)^{3/2} \tanh (e+f x) \, dx","Int[(a + b*Sinh[e + f*x]^2)^(3/2)*Tanh[e + f*x],x]","\frac{(a-b) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{\left(a+b \sinh ^2(e+f x)\right)^{3/2}}{3 f}-\frac{(a-b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{f}","\frac{(a-b) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{\left(a+b \sinh ^2(e+f x)\right)^{3/2}}{3 f}-\frac{(a-b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{f}",1,"-(((a - b)^(3/2)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a - b]])/f) + ((a - b)*Sqrt[a + b*Sinh[e + f*x]^2])/f + (a + b*Sinh[e + f*x]^2)^(3/2)/(3*f)","A",5,4,23,0.1739,1,"{3194, 50, 63, 208}"
471,1,78,0,0.0924509,"\int \coth (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Coth[e + f*x]*(a + b*Sinh[e + f*x]^2)^(3/2),x]","-\frac{a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{f}+\frac{a \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{\left(a+b \sinh ^2(e+f x)\right)^{3/2}}{3 f}","-\frac{a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{f}+\frac{a \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{\left(a+b \sinh ^2(e+f x)\right)^{3/2}}{3 f}",1,"-((a^(3/2)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a]])/f) + (a*Sqrt[a + b*Sinh[e + f*x]^2])/f + (a + b*Sinh[e + f*x]^2)^(3/2)/(3*f)","A",5,4,23,0.1739,1,"{3194, 50, 63, 208}"
472,1,140,0,0.147753,"\int \coth ^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Coth[e + f*x]^3*(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{(2 a+3 b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{6 a f}+\frac{(2 a+3 b) \sqrt{a+b \sinh ^2(e+f x)}}{2 f}-\frac{\sqrt{a} (2 a+3 b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{2 f}-\frac{\text{csch}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{5/2}}{2 a f}","\frac{(2 a+3 b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{6 a f}+\frac{(2 a+3 b) \sqrt{a+b \sinh ^2(e+f x)}}{2 f}-\frac{\sqrt{a} (2 a+3 b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{2 f}-\frac{\text{csch}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{5/2}}{2 a f}",1,"-(Sqrt[a]*(2*a + 3*b)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a]])/(2*f) + ((2*a + 3*b)*Sqrt[a + b*Sinh[e + f*x]^2])/(2*f) + ((2*a + 3*b)*(a + b*Sinh[e + f*x]^2)^(3/2))/(6*a*f) - (Csch[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^(5/2))/(2*a*f)","A",6,5,25,0.2000,1,"{3194, 78, 50, 63, 208}"
473,1,199,0,0.2324802,"\int \coth ^5(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Coth[e + f*x]^5*(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{\left(\frac{3 b (8 a+b)}{a^2}+8\right) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{24 f}+\frac{\left(8 a^2+3 b (8 a+b)\right) \sqrt{a+b \sinh ^2(e+f x)}}{8 a f}-\frac{\left(8 a^2+3 b (8 a+b)\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{8 \sqrt{a} f}-\frac{(8 a+b) \text{csch}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{5/2}}{8 a^2 f}-\frac{\text{csch}^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{5/2}}{4 a f}","\frac{\left(8 a^2+3 b (8 a+b)\right) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{24 a^2 f}+\frac{\left(8 a^2+3 b (8 a+b)\right) \sqrt{a+b \sinh ^2(e+f x)}}{8 a f}-\frac{\left(8 a^2+3 b (8 a+b)\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{8 \sqrt{a} f}-\frac{(8 a+b) \text{csch}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{5/2}}{8 a^2 f}-\frac{\text{csch}^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{5/2}}{4 a f}",1,"-((8*a^2 + 3*b*(8*a + b))*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a]])/(8*Sqrt[a]*f) + ((8*a^2 + 3*b*(8*a + b))*Sqrt[a + b*Sinh[e + f*x]^2])/(8*a*f) + ((8 + (3*b*(8*a + b))/a^2)*(a + b*Sinh[e + f*x]^2)^(3/2))/(24*f) - ((8*a + b)*Csch[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^(5/2))/(8*a^2*f) - (Csch[e + f*x]^4*(a + b*Sinh[e + f*x]^2)^(5/2))/(4*a*f)","A",7,6,25,0.2400,1,"{3194, 89, 78, 50, 63, 208}"
474,1,305,0,0.3797039,"\int \left(a+b \sinh ^2(e+f x)\right)^{3/2} \tanh ^4(e+f x) \, dx","Int[(a + b*Sinh[e + f*x]^2)^(3/2)*Tanh[e + f*x]^4,x]","-\frac{\tanh ^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{3 f}+\frac{(a-2 b) \sinh ^2(e+f x) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{8 (a-2 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{(3 a-8 b) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{(3 a-8 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{8 (a-2 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","-\frac{\tanh ^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{3 f}+\frac{(a-2 b) \sinh ^2(e+f x) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{8 (a-2 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{(3 a-8 b) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{(3 a-8 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{8 (a-2 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"-((3*a - 8*b)*Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f) - (8*(a - 2*b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((3*a - 8*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (8*(a - 2*b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*f) + ((a - 2*b)*Sinh[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/f - ((a + b*Sinh[e + f*x]^2)^(3/2)*Tanh[e + f*x]^3)/(3*f)","A",8,8,25,0.3200,1,"{3196, 467, 577, 582, 531, 418, 492, 411}"
475,1,260,0,0.2453382,"\int \left(a+b \sinh ^2(e+f x)\right)^{3/2} \tanh ^2(e+f x) \, dx","Int[(a + b*Sinh[e + f*x]^2)^(3/2)*Tanh[e + f*x]^2,x]","-\frac{\tanh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{f}+\frac{(7 a-8 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{4 b \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{(3 a-4 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(7 a-8 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","-\frac{\tanh (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{f}+\frac{(7 a-8 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{4 b \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{(3 a-4 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(7 a-8 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(4*b*Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f) - ((7*a - 8*b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((3*a - 4*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((7*a - 8*b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*f) - ((a + b*Sinh[e + f*x]^2)^(3/2)*Tanh[e + f*x])/f","A",7,7,25,0.2800,1,"{3196, 467, 528, 531, 418, 492, 411}"
476,1,174,0,0.1823636,"\int \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{b \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{i a (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{2 i (2 a-b) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}","\frac{b \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{i a (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{2 i (2 a-b) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 f \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}",1,"(b*Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f) - (((2*I)/3)*(2*a - b)*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/(f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a]) + ((I/3)*a*(a - b)*EllipticF[I*e + I*f*x, b/a]*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])/(f*Sqrt[a + b*Sinh[e + f*x]^2])","A",6,6,16,0.3750,1,"{3180, 3172, 3178, 3177, 3183, 3182}"
477,1,256,0,0.2715292,"\int \coth ^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Coth[e + f*x]^2*(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{(7 a+b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{4 b \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{\coth (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{f}+\frac{(3 a+5 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(7 a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{(7 a+b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{4 b \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{\coth (e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{f}+\frac{(3 a+5 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(7 a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(4*b*Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f) - (Coth[e + f*x]*(a + b*Sinh[e + f*x]^2)^(3/2))/f - ((7*a + b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((3*a + 5*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((7*a + b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*f)","A",7,7,25,0.2800,1,"{3196, 473, 528, 531, 418, 492, 411}"
478,1,306,0,0.3588559,"\int \coth ^4(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2} \, dx","Int[Coth[e + f*x]^4*(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{8 (a+b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{(3 a+5 b) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{\coth ^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{3 f}-\frac{(a+b) \cosh ^2(e+f x) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{(3 a+b) (a+3 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{8 (a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{8 (a+b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}+\frac{(3 a+5 b) \sinh (e+f x) \cosh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f}-\frac{\coth ^3(e+f x) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}{3 f}-\frac{(a+b) \cosh ^2(e+f x) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{f}+\frac{(3 a+b) (a+3 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{8 (a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"-(((a + b)*Cosh[e + f*x]^2*Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/f) + ((3*a + 5*b)*Cosh[e + f*x]*Sinh[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f) - (Coth[e + f*x]^3*(a + b*Sinh[e + f*x]^2)^(3/2))/(3*f) - (8*(a + b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((3*a + b)*(a + 3*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (8*(a + b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*f)","A",8,8,25,0.3200,1,"{3196, 473, 580, 528, 531, 418, 492, 411}"
479,1,142,0,0.1933361,"\int \frac{\tanh ^5(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Tanh[e + f*x]^5/Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{\left(8 a^2-8 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{8 f (a-b)^{5/2}}-\frac{\text{sech}^4(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{4 f (a-b)}+\frac{(8 a-5 b) \text{sech}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{8 f (a-b)^2}","-\frac{\left(8 a^2-8 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{8 f (a-b)^{5/2}}-\frac{\text{sech}^4(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{4 f (a-b)}+\frac{(8 a-5 b) \text{sech}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{8 f (a-b)^2}",1,"-((8*a^2 - 8*a*b + 3*b^2)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a - b]])/(8*(a - b)^(5/2)*f) + ((8*a - 5*b)*Sech[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2])/(8*(a - b)^2*f) - (Sech[e + f*x]^4*Sqrt[a + b*Sinh[e + f*x]^2])/(4*(a - b)*f)","A",5,5,25,0.2000,1,"{3194, 89, 78, 63, 208}"
480,1,89,0,0.1122568,"\int \frac{\tanh ^3(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Tanh[e + f*x]^3/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\text{sech}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{2 f (a-b)}-\frac{(2 a-b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{2 f (a-b)^{3/2}}","\frac{\text{sech}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{2 f (a-b)}-\frac{(2 a-b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{2 f (a-b)^{3/2}}",1,"-((2*a - b)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a - b]])/(2*(a - b)^(3/2)*f) + (Sech[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2])/(2*(a - b)*f)","A",4,4,25,0.1600,1,"{3194, 78, 63, 208}"
481,1,41,0,0.0583869,"\int \frac{\tanh (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Tanh[e + f*x]/Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{f \sqrt{a-b}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{f \sqrt{a-b}}",1,"-(ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a - b]]/(Sqrt[a - b]*f))","A",3,3,23,0.1304,1,"{3194, 63, 208}"
482,1,33,0,0.070531,"\int \frac{\coth (e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Coth[e + f*x]/Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{\sqrt{a} f}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{\sqrt{a} f}",1,"-(ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a]]/(Sqrt[a]*f))","A",3,3,23,0.1304,1,"{3194, 63, 208}"
483,1,77,0,0.1021983,"\int \frac{\coth ^3(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Coth[e + f*x]^3/Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{(2 a-b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{2 a^{3/2} f}-\frac{\text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{2 a f}","-\frac{(2 a-b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{2 a^{3/2} f}-\frac{\text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{2 a f}",1,"-((2*a - b)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a]])/(2*a^(3/2)*f) - (Csch[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2])/(2*a*f)","A",4,4,25,0.1600,1,"{3194, 78, 63, 208}"
484,1,126,0,0.1472646,"\int \frac{\coth ^5(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Coth[e + f*x]^5/Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{\left(8 a^2-8 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{8 a^{5/2} f}-\frac{(8 a-3 b) \text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{8 a^2 f}-\frac{\text{csch}^4(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{4 a f}","-\frac{\left(8 a^2-8 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{8 a^{5/2} f}-\frac{(8 a-3 b) \text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{8 a^2 f}-\frac{\text{csch}^4(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{4 a f}",1,"-((8*a^2 - 8*a*b + 3*b^2)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a]])/(8*a^(5/2)*f) - ((8*a - 3*b)*Csch[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2])/(8*a^2*f) - (Csch[e + f*x]^4*Sqrt[a + b*Sinh[e + f*x]^2])/(4*a*f)","A",5,5,25,0.2000,1,"{3194, 89, 78, 63, 208}"
485,1,219,0,0.1962341,"\int \frac{\tanh ^4(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Tanh[e + f*x]^4/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\tanh (e+f x) \text{sech}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f (a-b)}+\frac{(3 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{2 (2 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{\tanh (e+f x) \text{sech}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 f (a-b)}+\frac{(3 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{2 (2 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(-2*(2*a - b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*(a - b)^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((3*a - b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*(a - b)^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (Sech[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*(a - b)*f)","A",5,5,25,0.2000,1,"{3196, 470, 525, 418, 411}"
486,1,156,0,0.1812551,"\int \frac{\tanh ^2(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Tanh[e + f*x]^2/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"-((EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/((a - b)*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a])) + (EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/((a - b)*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a])","A",6,6,25,0.2400,1,"{3196, 471, 422, 418, 492, 411}"
487,1,60,0,0.0365019,"\int \frac{1}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[1/Sqrt[a + b*Sinh[e + f*x]^2],x]","-\frac{i \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{f \sqrt{a+b \sinh ^2(e+f x)}}","-\frac{i \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{f \sqrt{a+b \sinh ^2(e+f x)}}",1,"((-I)*EllipticF[I*e + I*f*x, b/a]*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])/(f*Sqrt[a + b*Sinh[e + f*x]^2])","A",2,2,16,0.1250,1,"{3183, 3182}"
488,1,207,0,0.197208,"\int \frac{\coth ^2(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Coth[e + f*x]^2/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{\tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a f}-\frac{\coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a f}+\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","\frac{\tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a f}-\frac{\coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a f}+\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"-((Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*f)) - (EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(a*f)","A",6,6,25,0.2400,1,"{3196, 475, 422, 418, 492, 411}"
489,1,285,0,0.3047444,"\int \frac{\coth ^4(e+f x)}{\sqrt{a+b \sinh ^2(e+f x)}} \, dx","Int[Coth[e + f*x]^4/Sqrt[a + b*Sinh[e + f*x]^2],x]","\frac{2 (2 a-b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^2 f}-\frac{2 (2 a-b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^2 f}+\frac{(3 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{2 (2 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{\coth (e+f x) \text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a f}","\frac{2 (2 a-b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^2 f}-\frac{2 (2 a-b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^2 f}+\frac{(3 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{2 (2 a-b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{\coth (e+f x) \text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a f}",1,"(-2*(2*a - b)*Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^2*f) - (Coth[e + f*x]*Csch[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*f) - (2*(2*a - b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((3*a - b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (2*(2*a - b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*a^2*f)","A",7,7,25,0.2800,1,"{3196, 474, 583, 531, 418, 492, 411}"
490,1,187,0,0.2513661,"\int \frac{\tanh ^5(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Tanh[e + f*x]^5/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{8 a^2+8 a b-b^2}{8 f (a-b)^3 \sqrt{a+b \sinh ^2(e+f x)}}-\frac{\left(8 a^2+8 a b-b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{8 f (a-b)^{7/2}}-\frac{\text{sech}^4(e+f x)}{4 f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}+\frac{(8 a-3 b) \text{sech}^2(e+f x)}{8 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}","\frac{8 a^2+8 a b-b^2}{8 f (a-b)^3 \sqrt{a+b \sinh ^2(e+f x)}}-\frac{\left(8 a^2+8 a b-b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{8 f (a-b)^{7/2}}-\frac{\text{sech}^4(e+f x)}{4 f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}+\frac{(8 a-3 b) \text{sech}^2(e+f x)}{8 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}",1,"-((8*a^2 + 8*a*b - b^2)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a - b]])/(8*(a - b)^(7/2)*f) + (8*a^2 + 8*a*b - b^2)/(8*(a - b)^3*f*Sqrt[a + b*Sinh[e + f*x]^2]) + ((8*a - 3*b)*Sech[e + f*x]^2)/(8*(a - b)^2*f*Sqrt[a + b*Sinh[e + f*x]^2]) - Sech[e + f*x]^4/(4*(a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",6,6,25,0.2400,1,"{3194, 89, 78, 51, 63, 208}"
491,1,122,0,0.1396278,"\int \frac{\tanh ^3(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Tanh[e + f*x]^3/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{2 a+b}{2 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}-\frac{(2 a+b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{2 f (a-b)^{5/2}}+\frac{\text{sech}^2(e+f x)}{2 f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}","\frac{2 a+b}{2 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}-\frac{(2 a+b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{2 f (a-b)^{5/2}}+\frac{\text{sech}^2(e+f x)}{2 f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}",1,"-((2*a + b)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a - b]])/(2*(a - b)^(5/2)*f) + (2*a + b)/(2*(a - b)^2*f*Sqrt[a + b*Sinh[e + f*x]^2]) + Sech[e + f*x]^2/(2*(a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",5,5,25,0.2000,1,"{3194, 78, 51, 63, 208}"
492,1,69,0,0.0738817,"\int \frac{\tanh (e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Tanh[e + f*x]/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{1}{f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{f (a-b)^{3/2}}","\frac{1}{f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{f (a-b)^{3/2}}",1,"-(ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a - b]]/((a - b)^(3/2)*f)) + 1/((a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",4,4,23,0.1739,1,"{3194, 51, 63, 208}"
493,1,57,0,0.0840825,"\int \frac{\coth (e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Coth[e + f*x]/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{1}{a f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{a^{3/2} f}","\frac{1}{a f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{a^{3/2} f}",1,"-(ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a]]/(a^(3/2)*f)) + 1/(a*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",4,4,23,0.1739,1,"{3194, 51, 63, 208}"
494,1,110,0,0.1359622,"\int \frac{\coth ^3(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Coth[e + f*x]^3/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{2 a-3 b}{2 a^2 f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{(2 a-3 b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{2 a^{5/2} f}-\frac{\text{csch}^2(e+f x)}{2 a f \sqrt{a+b \sinh ^2(e+f x)}}","\frac{2 a-3 b}{2 a^2 f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{(2 a-3 b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{2 a^{5/2} f}-\frac{\text{csch}^2(e+f x)}{2 a f \sqrt{a+b \sinh ^2(e+f x)}}",1,"-((2*a - 3*b)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a]])/(2*a^(5/2)*f) + (2*a - 3*b)/(2*a^2*f*Sqrt[a + b*Sinh[e + f*x]^2]) - Csch[e + f*x]^2/(2*a*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",5,5,25,0.2000,1,"{3194, 78, 51, 63, 208}"
495,1,167,0,0.201072,"\int \frac{\coth ^5(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Coth[e + f*x]^5/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{8 a^2-24 a b+15 b^2}{8 a^3 f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{\left(8 a^2-24 a b+15 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{8 a^{7/2} f}-\frac{(8 a-5 b) \text{csch}^2(e+f x)}{8 a^2 f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{\text{csch}^4(e+f x)}{4 a f \sqrt{a+b \sinh ^2(e+f x)}}","\frac{8 a^2-24 a b+15 b^2}{8 a^3 f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{\left(8 a^2-24 a b+15 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{8 a^{7/2} f}-\frac{(8 a-5 b) \text{csch}^2(e+f x)}{8 a^2 f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{\text{csch}^4(e+f x)}{4 a f \sqrt{a+b \sinh ^2(e+f x)}}",1,"-((8*a^2 - 24*a*b + 15*b^2)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a]])/(8*a^(7/2)*f) + (8*a^2 - 24*a*b + 15*b^2)/(8*a^3*f*Sqrt[a + b*Sinh[e + f*x]^2]) - ((8*a - 5*b)*Csch[e + f*x]^2)/(8*a^2*f*Sqrt[a + b*Sinh[e + f*x]^2]) - Csch[e + f*x]^4/(4*a*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",6,6,25,0.2400,1,"{3194, 89, 78, 51, 63, 208}"
496,1,275,0,0.2759379,"\int \frac{\tanh ^4(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Tanh[e + f*x]^4/(a + b*Sinh[e + f*x]^2)^(3/2),x]","-\frac{4 a \tanh (e+f x)}{3 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}+\frac{\tanh (e+f x) \text{sech}^2(e+f x)}{3 f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}-\frac{\sqrt{a} \sqrt{b} (7 a+b) \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{3 f (a-b)^3 \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}+\frac{(3 a+5 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f (a-b)^3 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","-\frac{4 a \tanh (e+f x)}{3 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}+\frac{\tanh (e+f x) \text{sech}^2(e+f x)}{3 f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}-\frac{\sqrt{a} \sqrt{b} (7 a+b) \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{3 f (a-b)^3 \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}+\frac{(3 a+5 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 f (a-b)^3 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"-(Sqrt[a]*Sqrt[b]*(7*a + b)*Cosh[e + f*x]*EllipticE[ArcTan[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a]], 1 - a/b])/(3*(a - b)^3*f*Sqrt[(a*Cosh[e + f*x]^2)/(a + b*Sinh[e + f*x]^2)]*Sqrt[a + b*Sinh[e + f*x]^2]) + ((3*a + 5*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*(a - b)^3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (4*a*Tanh[e + f*x])/(3*(a - b)^2*f*Sqrt[a + b*Sinh[e + f*x]^2]) + (Sech[e + f*x]^2*Tanh[e + f*x])/(3*(a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",6,6,25,0.2400,1,"{3196, 470, 527, 525, 418, 411}"
497,1,217,0,0.2128582,"\int \frac{\tanh ^2(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Tanh[e + f*x]^2/(a + b*Sinh[e + f*x]^2)^(3/2),x]","-\frac{\tanh (e+f x)}{f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}-\frac{2 \sqrt{a} \sqrt{b} \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}+\frac{(a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","-\frac{\tanh (e+f x)}{f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}-\frac{2 \sqrt{a} \sqrt{b} \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}+\frac{(a+b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a f (a-b)^2 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(-2*Sqrt[a]*Sqrt[b]*Cosh[e + f*x]*EllipticE[ArcTan[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a]], 1 - a/b])/((a - b)^2*f*Sqrt[(a*Cosh[e + f*x]^2)/(a + b*Sinh[e + f*x]^2)]*Sqrt[a + b*Sinh[e + f*x]^2]) + ((a + b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*(a - b)^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - Tanh[e + f*x]/((a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",5,5,25,0.2000,1,"{3196, 471, 525, 418, 411}"
498,1,115,0,0.067648,"\int \frac{1}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[(a + b*Sinh[e + f*x]^2)^(-3/2),x]","-\frac{b \sinh (e+f x) \cosh (e+f x)}{a f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}-\frac{i \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{a f (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}","-\frac{b \sinh (e+f x) \cosh (e+f x)}{a f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}-\frac{i \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{a f (a-b) \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}",1,"-((b*Cosh[e + f*x]*Sinh[e + f*x])/(a*(a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2])) - (I*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/(a*(a - b)*f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])","A",4,4,16,0.2500,1,"{3184, 21, 3178, 3177}"
499,1,237,0,0.2703227,"\int \frac{\coth ^2(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Coth[e + f*x]^2/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{2 \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a^2 f}-\frac{2 \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a^2 f}+\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{2 \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{\coth (e+f x)}{a f \sqrt{a+b \sinh ^2(e+f x)}}","\frac{2 \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a^2 f}-\frac{2 \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{a^2 f}+\frac{\text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{2 \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{a^2 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{\coth (e+f x)}{a f \sqrt{a+b \sinh ^2(e+f x)}}",1,"Coth[e + f*x]/(a*f*Sqrt[a + b*Sinh[e + f*x]^2]) - (2*Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a^2*f) - (2*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(a^2*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (2*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(a^2*f)","A",7,7,25,0.2800,1,"{3196, 469, 583, 531, 418, 492, 411}"
500,1,341,0,0.4083503,"\int \frac{\coth ^4(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{3/2}} \, dx","Int[Coth[e + f*x]^4/(a + b*Sinh[e + f*x]^2)^(3/2),x]","\frac{(7 a-8 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^3 f}-\frac{(7 a-8 b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^3 f}+\frac{(3 a-4 b) \coth (e+f x) \text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^2 b f}+\frac{(3 a-4 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(7 a-8 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a-b) \coth (e+f x) \text{csch}^2(e+f x)}{a b f \sqrt{a+b \sinh ^2(e+f x)}}","\frac{(7 a-8 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^3 f}-\frac{(7 a-8 b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^3 f}+\frac{(3 a-4 b) \coth (e+f x) \text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^2 b f}+\frac{(3 a-4 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(7 a-8 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^3 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a-b) \coth (e+f x) \text{csch}^2(e+f x)}{a b f \sqrt{a+b \sinh ^2(e+f x)}}",1,"-(((a - b)*Coth[e + f*x]*Csch[e + f*x]^2)/(a*b*f*Sqrt[a + b*Sinh[e + f*x]^2])) - ((7*a - 8*b)*Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^3*f) + ((3*a - 4*b)*Coth[e + f*x]*Csch[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^2*b*f) - ((7*a - 8*b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((3*a - 4*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((7*a - 8*b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*a^3*f)","A",8,7,25,0.2800,1,"{3196, 468, 583, 531, 418, 492, 411}"
501,1,232,0,0.3158455,"\int \frac{\tanh ^5(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Tanh[e + f*x]^5/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{8 a^2+24 a b+3 b^2}{8 f (a-b)^4 \sqrt{a+b \sinh ^2(e+f x)}}+\frac{8 a^2+24 a b+3 b^2}{24 f (a-b)^3 \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{\left(8 a^2+24 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{8 f (a-b)^{9/2}}-\frac{\text{sech}^4(e+f x)}{4 f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}+\frac{(8 a-b) \text{sech}^2(e+f x)}{8 f (a-b)^2 \left(a+b \sinh ^2(e+f x)\right)^{3/2}}","\frac{8 a^2+24 a b+3 b^2}{8 f (a-b)^4 \sqrt{a+b \sinh ^2(e+f x)}}+\frac{8 a^2+24 a b+3 b^2}{24 f (a-b)^3 \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{\left(8 a^2+24 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{8 f (a-b)^{9/2}}-\frac{\text{sech}^4(e+f x)}{4 f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}+\frac{(8 a-b) \text{sech}^2(e+f x)}{8 f (a-b)^2 \left(a+b \sinh ^2(e+f x)\right)^{3/2}}",1,"-((8*a^2 + 24*a*b + 3*b^2)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a - b]])/(8*(a - b)^(9/2)*f) + (8*a^2 + 24*a*b + 3*b^2)/(24*(a - b)^3*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + ((8*a - b)*Sech[e + f*x]^2)/(8*(a - b)^2*f*(a + b*Sinh[e + f*x]^2)^(3/2)) - Sech[e + f*x]^4/(4*(a - b)*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + (8*a^2 + 24*a*b + 3*b^2)/(8*(a - b)^4*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",7,6,25,0.2400,1,"{3194, 89, 78, 51, 63, 208}"
502,1,163,0,0.1657291,"\int \frac{\tanh ^3(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Tanh[e + f*x]^3/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{2 a+3 b}{2 f (a-b)^3 \sqrt{a+b \sinh ^2(e+f x)}}+\frac{2 a+3 b}{6 f (a-b)^2 \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{(2 a+3 b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{2 f (a-b)^{7/2}}+\frac{\text{sech}^2(e+f x)}{2 f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}","\frac{2 a+3 b}{2 f (a-b)^3 \sqrt{a+b \sinh ^2(e+f x)}}+\frac{2 a+3 b}{6 f (a-b)^2 \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{(2 a+3 b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{2 f (a-b)^{7/2}}+\frac{\text{sech}^2(e+f x)}{2 f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}",1,"-((2*a + 3*b)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a - b]])/(2*(a - b)^(7/2)*f) + (2*a + 3*b)/(6*(a - b)^2*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + Sech[e + f*x]^2/(2*(a - b)*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + (2*a + 3*b)/(2*(a - b)^3*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",6,5,25,0.2000,1,"{3194, 78, 51, 63, 208}"
503,1,99,0,0.0929154,"\int \frac{\tanh (e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Tanh[e + f*x]/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{1}{f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}+\frac{1}{3 f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{f (a-b)^{5/2}}","\frac{1}{f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}+\frac{1}{3 f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a-b}}\right)}{f (a-b)^{5/2}}",1,"-(ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a - b]]/((a - b)^(5/2)*f)) + 1/(3*(a - b)*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + 1/((a - b)^2*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",5,4,23,0.1739,1,"{3194, 51, 63, 208}"
504,1,83,0,0.0995702,"\int \frac{\coth (e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Coth[e + f*x]/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{1}{a^2 f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{a^{5/2} f}+\frac{1}{3 a f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}","\frac{1}{a^2 f \sqrt{a+b \sinh ^2(e+f x)}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{a^{5/2} f}+\frac{1}{3 a f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}",1,"-(ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a]]/(a^(5/2)*f)) + 1/(3*a*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + 1/(a^2*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",5,4,23,0.1739,1,"{3194, 51, 63, 208}"
505,1,143,0,0.1523581,"\int \frac{\coth ^3(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Coth[e + f*x]^3/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{2 a-5 b}{2 a^3 f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{2 a-5 b}{6 a^2 f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{(2 a-5 b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{2 a^{7/2} f}-\frac{\text{csch}^2(e+f x)}{2 a f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}","\frac{2 a-5 b}{2 a^3 f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{2 a-5 b}{6 a^2 f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{(2 a-5 b) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{2 a^{7/2} f}-\frac{\text{csch}^2(e+f x)}{2 a f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}",1,"-((2*a - 5*b)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a]])/(2*a^(7/2)*f) + (2*a - 5*b)/(6*a^2*f*(a + b*Sinh[e + f*x]^2)^(3/2)) - Csch[e + f*x]^2/(2*a*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + (2*a - 5*b)/(2*a^3*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",6,5,25,0.2000,1,"{3194, 78, 51, 63, 208}"
506,1,208,0,0.2249054,"\int \frac{\coth ^5(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Coth[e + f*x]^5/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{8 a^2-40 a b+35 b^2}{8 a^4 f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{8 a^2-40 a b+35 b^2}{24 a^3 f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{\left(8 a^2-40 a b+35 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{8 a^{9/2} f}-\frac{(8 a-7 b) \text{csch}^2(e+f x)}{8 a^2 f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{\text{csch}^4(e+f x)}{4 a f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}","\frac{8 a^2-40 a b+35 b^2}{8 a^4 f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{8 a^2-40 a b+35 b^2}{24 a^3 f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{\left(8 a^2-40 a b+35 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^2(e+f x)}}{\sqrt{a}}\right)}{8 a^{9/2} f}-\frac{(8 a-7 b) \text{csch}^2(e+f x)}{8 a^2 f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{\text{csch}^4(e+f x)}{4 a f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}",1,"-((8*a^2 - 40*a*b + 35*b^2)*ArcTanh[Sqrt[a + b*Sinh[e + f*x]^2]/Sqrt[a]])/(8*a^(9/2)*f) + (8*a^2 - 40*a*b + 35*b^2)/(24*a^3*f*(a + b*Sinh[e + f*x]^2)^(3/2)) - ((8*a - 7*b)*Csch[e + f*x]^2)/(8*a^2*f*(a + b*Sinh[e + f*x]^2)^(3/2)) - Csch[e + f*x]^4/(4*a*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + (8*a^2 - 40*a*b + 35*b^2)/(8*a^4*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",7,6,25,0.2400,1,"{3194, 89, 78, 51, 63, 208}"
507,1,333,0,0.3994764,"\int \frac{\tanh ^4(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Tanh[e + f*x]^4/(a + b*Sinh[e + f*x]^2)^(5/2),x]","-\frac{2 (2 a+b) \tanh (e+f x)}{3 f (a-b)^2 \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{b (5 a+3 b) \sinh (e+f x) \cosh (e+f x)}{3 f (a-b)^3 \left(a+b \sinh ^2(e+f x)\right)^{3/2}}+\frac{\tanh (e+f x) \text{sech}^2(e+f x)}{3 f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{8 \sqrt{a} \sqrt{b} (a+b) \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{3 f (a-b)^4 \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}+\frac{(3 a+b) (a+3 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f (a-b)^4 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","-\frac{2 (2 a+b) \tanh (e+f x)}{3 f (a-b)^2 \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{b (5 a+3 b) \sinh (e+f x) \cosh (e+f x)}{3 f (a-b)^3 \left(a+b \sinh ^2(e+f x)\right)^{3/2}}+\frac{\tanh (e+f x) \text{sech}^2(e+f x)}{3 f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{8 \sqrt{a} \sqrt{b} (a+b) \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{3 f (a-b)^4 \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}+\frac{(3 a+b) (a+3 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f (a-b)^4 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"-(b*(5*a + 3*b)*Cosh[e + f*x]*Sinh[e + f*x])/(3*(a - b)^3*f*(a + b*Sinh[e + f*x]^2)^(3/2)) - (8*Sqrt[a]*Sqrt[b]*(a + b)*Cosh[e + f*x]*EllipticE[ArcTan[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a]], 1 - a/b])/(3*(a - b)^4*f*Sqrt[(a*Cosh[e + f*x]^2)/(a + b*Sinh[e + f*x]^2)]*Sqrt[a + b*Sinh[e + f*x]^2]) + ((3*a + b)*(a + 3*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*(a - b)^4*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - (2*(2*a + b)*Tanh[e + f*x])/(3*(a - b)^2*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + (Sech[e + f*x]^2*Tanh[e + f*x])/(3*(a - b)*f*(a + b*Sinh[e + f*x]^2)^(3/2))","A",7,6,25,0.2400,1,"{3196, 470, 527, 525, 418, 411}"
508,1,274,0,0.2801795,"\int \frac{\tanh ^2(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Tanh[e + f*x]^2/(a + b*Sinh[e + f*x]^2)^(5/2),x]","-\frac{\tanh (e+f x)}{f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{4 b \sinh (e+f x) \cosh (e+f x)}{3 f (a-b)^2 \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{\sqrt{b} (7 a+b) \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{3 \sqrt{a} f (a-b)^3 \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}+\frac{(3 a+5 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f (a-b)^3 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}","-\frac{\tanh (e+f x)}{f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{4 b \sinh (e+f x) \cosh (e+f x)}{3 f (a-b)^2 \left(a+b \sinh ^2(e+f x)\right)^{3/2}}-\frac{\sqrt{b} (7 a+b) \cosh (e+f x) E\left(\tan ^{-1}\left(\frac{\sqrt{b} \sinh (e+f x)}{\sqrt{a}}\right)|1-\frac{a}{b}\right)}{3 \sqrt{a} f (a-b)^3 \sqrt{a+b \sinh ^2(e+f x)} \sqrt{\frac{a \cosh ^2(e+f x)}{a+b \sinh ^2(e+f x)}}}+\frac{(3 a+5 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a f (a-b)^3 \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}",1,"(-4*b*Cosh[e + f*x]*Sinh[e + f*x])/(3*(a - b)^2*f*(a + b*Sinh[e + f*x]^2)^(3/2)) - (Sqrt[b]*(7*a + b)*Cosh[e + f*x]*EllipticE[ArcTan[(Sqrt[b]*Sinh[e + f*x])/Sqrt[a]], 1 - a/b])/(3*Sqrt[a]*(a - b)^3*f*Sqrt[(a*Cosh[e + f*x]^2)/(a + b*Sinh[e + f*x]^2)]*Sqrt[a + b*Sinh[e + f*x]^2]) + ((3*a + 5*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a*(a - b)^3*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) - Tanh[e + f*x]/((a - b)*f*(a + b*Sinh[e + f*x]^2)^(3/2))","A",6,6,25,0.2400,1,"{3196, 471, 527, 525, 418, 411}"
509,1,251,0,0.2882622,"\int \frac{1}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[(a + b*Sinh[e + f*x]^2)^(-5/2),x]","-\frac{2 b (2 a-b) \sinh (e+f x) \cosh (e+f x)}{3 a^2 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}-\frac{2 i (2 a-b) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 a^2 f (a-b)^2 \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}-\frac{b \sinh (e+f x) \cosh (e+f x)}{3 a f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}+\frac{i \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 a f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}","-\frac{2 b (2 a-b) \sinh (e+f x) \cosh (e+f x)}{3 a^2 f (a-b)^2 \sqrt{a+b \sinh ^2(e+f x)}}-\frac{2 i (2 a-b) \sqrt{a+b \sinh ^2(e+f x)} E\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 a^2 f (a-b)^2 \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1}}-\frac{b \sinh (e+f x) \cosh (e+f x)}{3 a f (a-b) \left(a+b \sinh ^2(e+f x)\right)^{3/2}}+\frac{i \sqrt{\frac{b \sinh ^2(e+f x)}{a}+1} F\left(i e+i f x\left|\frac{b}{a}\right.\right)}{3 a f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}",1,"-(b*Cosh[e + f*x]*Sinh[e + f*x])/(3*a*(a - b)*f*(a + b*Sinh[e + f*x]^2)^(3/2)) - (2*(2*a - b)*b*Cosh[e + f*x]*Sinh[e + f*x])/(3*a^2*(a - b)^2*f*Sqrt[a + b*Sinh[e + f*x]^2]) - (((2*I)/3)*(2*a - b)*EllipticE[I*e + I*f*x, b/a]*Sqrt[a + b*Sinh[e + f*x]^2])/(a^2*(a - b)^2*f*Sqrt[1 + (b*Sinh[e + f*x]^2)/a]) + ((I/3)*EllipticF[I*e + I*f*x, b/a]*Sqrt[1 + (b*Sinh[e + f*x]^2)/a])/(a*(a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2])","A",7,7,16,0.4375,1,"{3184, 3173, 3172, 3178, 3177, 3183, 3182}"
510,1,351,0,0.4119002,"\int \frac{\coth ^2(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Coth[e + f*x]^2/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{(7 a-8 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^3 f (a-b)}-\frac{(7 a-8 b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^3 f (a-b)}+\frac{(3 a-4 b) \coth (e+f x)}{3 a^2 f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}+\frac{(3 a-4 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^3 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(7 a-8 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^3 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{\coth (e+f x)}{3 a f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}","\frac{(7 a-8 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^3 f (a-b)}-\frac{(7 a-8 b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^3 f (a-b)}+\frac{(3 a-4 b) \coth (e+f x)}{3 a^2 f (a-b) \sqrt{a+b \sinh ^2(e+f x)}}+\frac{(3 a-4 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^3 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(7 a-8 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^3 f (a-b) \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}+\frac{\coth (e+f x)}{3 a f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}",1,"Coth[e + f*x]/(3*a*f*(a + b*Sinh[e + f*x]^2)^(3/2)) + ((3*a - 4*b)*Coth[e + f*x])/(3*a^2*(a - b)*f*Sqrt[a + b*Sinh[e + f*x]^2]) - ((7*a - 8*b)*Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^3*(a - b)*f) - ((7*a - 8*b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^3*(a - b)*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((3*a - 4*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^3*(a - b)*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((7*a - 8*b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*a^3*(a - b)*f)","A",8,8,25,0.3200,1,"{3196, 469, 579, 583, 531, 418, 492, 411}"
511,1,385,0,0.5618055,"\int \frac{\coth ^4(e+f x)}{\left(a+b \sinh ^2(e+f x)\right)^{5/2}} \, dx","Int[Coth[e + f*x]^4/(a + b*Sinh[e + f*x]^2)^(5/2),x]","\frac{8 (a-2 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^4 f}-\frac{8 (a-2 b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^4 f}+\frac{(3 a-8 b) \coth (e+f x) \text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^3 b f}-\frac{2 (a-3 b) \coth (e+f x) \text{csch}^2(e+f x)}{3 a^2 b f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{(3 a-8 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^4 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{8 (a-2 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^4 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a-b) \coth (e+f x) \text{csch}^2(e+f x)}{3 a b f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}","\frac{8 (a-2 b) \tanh (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^4 f}-\frac{8 (a-2 b) \coth (e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^4 f}+\frac{(3 a-8 b) \coth (e+f x) \text{csch}^2(e+f x) \sqrt{a+b \sinh ^2(e+f x)}}{3 a^3 b f}-\frac{2 (a-3 b) \coth (e+f x) \text{csch}^2(e+f x)}{3 a^2 b f \sqrt{a+b \sinh ^2(e+f x)}}+\frac{(3 a-8 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} F\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^4 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{8 (a-2 b) \text{sech}(e+f x) \sqrt{a+b \sinh ^2(e+f x)} E\left(\tan ^{-1}(\sinh (e+f x))|1-\frac{b}{a}\right)}{3 a^4 f \sqrt{\frac{\text{sech}^2(e+f x) \left(a+b \sinh ^2(e+f x)\right)}{a}}}-\frac{(a-b) \coth (e+f x) \text{csch}^2(e+f x)}{3 a b f \left(a+b \sinh ^2(e+f x)\right)^{3/2}}",1,"-((a - b)*Coth[e + f*x]*Csch[e + f*x]^2)/(3*a*b*f*(a + b*Sinh[e + f*x]^2)^(3/2)) - (2*(a - 3*b)*Coth[e + f*x]*Csch[e + f*x]^2)/(3*a^2*b*f*Sqrt[a + b*Sinh[e + f*x]^2]) - (8*(a - 2*b)*Coth[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^4*f) + ((3*a - 8*b)*Coth[e + f*x]*Csch[e + f*x]^2*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^3*b*f) - (8*(a - 2*b)*EllipticE[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^4*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + ((3*a - 8*b)*EllipticF[ArcTan[Sinh[e + f*x]], 1 - b/a]*Sech[e + f*x]*Sqrt[a + b*Sinh[e + f*x]^2])/(3*a^4*f*Sqrt[(Sech[e + f*x]^2*(a + b*Sinh[e + f*x]^2))/a]) + (8*(a - 2*b)*Sqrt[a + b*Sinh[e + f*x]^2]*Tanh[e + f*x])/(3*a^4*f)","A",9,8,25,0.3200,1,"{3196, 468, 579, 583, 531, 418, 492, 411}"
512,1,122,0,0.1293489,"\int \left(a+b \sinh ^2(e+f x)\right)^p (d \tanh (e+f x))^m \, dx","Int[(a + b*Sinh[e + f*x]^2)^p*(d*Tanh[e + f*x])^m,x]","\frac{\cosh ^2(e+f x)^{\frac{m+1}{2}} (d \tanh (e+f x))^{m+1} \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{m+1}{2};\frac{m+1}{2},-p;\frac{m+3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{d f (m+1)}","\frac{\cosh ^2(e+f x)^{\frac{m+1}{2}} (d \tanh (e+f x))^{m+1} \left(a+b \sinh ^2(e+f x)\right)^p \left(\frac{b \sinh ^2(e+f x)}{a}+1\right)^{-p} F_1\left(\frac{m+1}{2};\frac{m+1}{2},-p;\frac{m+3}{2};-\sinh ^2(e+f x),-\frac{b \sinh ^2(e+f x)}{a}\right)}{d f (m+1)}",1,"(AppellF1[(1 + m)/2, (1 + m)/2, -p, (3 + m)/2, -Sinh[e + f*x]^2, -((b*Sinh[e + f*x]^2)/a)]*(Cosh[e + f*x]^2)^((1 + m)/2)*(a + b*Sinh[e + f*x]^2)^p*(d*Tanh[e + f*x])^(1 + m))/(d*f*(1 + m)*(1 + (b*Sinh[e + f*x]^2)/a)^p)","A",3,3,25,0.1200,1,"{3197, 511, 510}"
513,1,110,0,0.120445,"\int \left(a+b \sinh ^2(c+d x)\right)^p \tanh ^3(c+d x) \, dx","Int[(a + b*Sinh[c + d*x]^2)^p*Tanh[c + d*x]^3,x]","\frac{\text{sech}^2(c+d x) \left(a+b \sinh ^2(c+d x)\right)^{p+1}}{2 d (a-b)}-\frac{(a-b (p+1)) \left(a+b \sinh ^2(c+d x)\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b \sinh ^2(c+d x)+a}{a-b}\right)}{2 d (p+1) (a-b)^2}","\frac{\text{sech}^2(c+d x) \left(a+b \sinh ^2(c+d x)\right)^{p+1}}{2 d (a-b)}-\frac{(a-b (p+1)) \left(a+b \sinh ^2(c+d x)\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b \sinh ^2(c+d x)+a}{a-b}\right)}{2 d (p+1) (a-b)^2}",1,"-((a - b*(1 + p))*Hypergeometric2F1[1, 1 + p, 2 + p, (a + b*Sinh[c + d*x]^2)/(a - b)]*(a + b*Sinh[c + d*x]^2)^(1 + p))/(2*(a - b)^2*d*(1 + p)) + (Sech[c + d*x]^2*(a + b*Sinh[c + d*x]^2)^(1 + p))/(2*(a - b)*d)","A",3,3,23,0.1304,1,"{3194, 78, 68}"
514,1,63,0,0.0547016,"\int \left(a+b \sinh ^2(c+d x)\right)^p \tanh (c+d x) \, dx","Int[(a + b*Sinh[c + d*x]^2)^p*Tanh[c + d*x],x]","-\frac{\left(a+b \sinh ^2(c+d x)\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b \sinh ^2(c+d x)+a}{a-b}\right)}{2 d (p+1) (a-b)}","-\frac{\left(a+b \sinh ^2(c+d x)\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b \sinh ^2(c+d x)+a}{a-b}\right)}{2 d (p+1) (a-b)}",1,"-(Hypergeometric2F1[1, 1 + p, 2 + p, (a + b*Sinh[c + d*x]^2)/(a - b)]*(a + b*Sinh[c + d*x]^2)^(1 + p))/(2*(a - b)*d*(1 + p))","A",2,2,21,0.09524,1,"{3194, 68}"
515,1,54,0,0.0632654,"\int \coth (c+d x) \left(a+b \sinh ^2(c+d x)\right)^p \, dx","Int[Coth[c + d*x]*(a + b*Sinh[c + d*x]^2)^p,x]","-\frac{\left(a+b \sinh ^2(c+d x)\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b \sinh ^2(c+d x)}{a}+1\right)}{2 a d (p+1)}","-\frac{\left(a+b \sinh ^2(c+d x)\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b \sinh ^2(c+d x)}{a}+1\right)}{2 a d (p+1)}",1,"-(Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*Sinh[c + d*x]^2)/a]*(a + b*Sinh[c + d*x]^2)^(1 + p))/(2*a*d*(1 + p))","A",2,2,21,0.09524,1,"{3194, 65}"
516,1,94,0,0.0907626,"\int \coth ^3(c+d x) \left(a+b \sinh ^2(c+d x)\right)^p \, dx","Int[Coth[c + d*x]^3*(a + b*Sinh[c + d*x]^2)^p,x]","-\frac{(a+b p) \left(a+b \sinh ^2(c+d x)\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b \sinh ^2(c+d x)}{a}+1\right)}{2 a^2 d (p+1)}-\frac{\text{csch}^2(c+d x) \left(a+b \sinh ^2(c+d x)\right)^{p+1}}{2 a d}","-\frac{(a+b p) \left(a+b \sinh ^2(c+d x)\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{b \sinh ^2(c+d x)}{a}+1\right)}{2 a^2 d (p+1)}-\frac{\text{csch}^2(c+d x) \left(a+b \sinh ^2(c+d x)\right)^{p+1}}{2 a d}",1,"-(Csch[c + d*x]^2*(a + b*Sinh[c + d*x]^2)^(1 + p))/(2*a*d) - ((a + b*p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (b*Sinh[c + d*x]^2)/a]*(a + b*Sinh[c + d*x]^2)^(1 + p))/(2*a^2*d*(1 + p))","A",3,3,23,0.1304,1,"{3194, 78, 65}"
517,1,103,0,0.1208595,"\int \left(a+b \sinh ^2(c+d x)\right)^p \tanh ^4(c+d x) \, dx","Int[(a + b*Sinh[c + d*x]^2)^p*Tanh[c + d*x]^4,x]","\frac{\sinh ^4(c+d x) \sqrt{\cosh ^2(c+d x)} \tanh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^p \left(\frac{b \sinh ^2(c+d x)}{a}+1\right)^{-p} F_1\left(\frac{5}{2};\frac{5}{2},-p;\frac{7}{2};-\sinh ^2(c+d x),-\frac{b \sinh ^2(c+d x)}{a}\right)}{5 d}","\frac{\sinh ^4(c+d x) \sqrt{\cosh ^2(c+d x)} \tanh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^p \left(\frac{b \sinh ^2(c+d x)}{a}+1\right)^{-p} F_1\left(\frac{5}{2};\frac{5}{2},-p;\frac{7}{2};-\sinh ^2(c+d x),-\frac{b \sinh ^2(c+d x)}{a}\right)}{5 d}",1,"(AppellF1[5/2, 5/2, -p, 7/2, -Sinh[c + d*x]^2, -((b*Sinh[c + d*x]^2)/a)]*Sqrt[Cosh[c + d*x]^2]*Sinh[c + d*x]^4*(a + b*Sinh[c + d*x]^2)^p*Tanh[c + d*x])/(5*d*(1 + (b*Sinh[c + d*x]^2)/a)^p)","A",3,3,23,0.1304,1,"{3196, 511, 510}"
518,1,103,0,0.1072917,"\int \left(a+b \sinh ^2(c+d x)\right)^p \tanh ^2(c+d x) \, dx","Int[(a + b*Sinh[c + d*x]^2)^p*Tanh[c + d*x]^2,x]","\frac{\sinh ^2(c+d x) \sqrt{\cosh ^2(c+d x)} \tanh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^p \left(\frac{b \sinh ^2(c+d x)}{a}+1\right)^{-p} F_1\left(\frac{3}{2};\frac{3}{2},-p;\frac{5}{2};-\sinh ^2(c+d x),-\frac{b \sinh ^2(c+d x)}{a}\right)}{3 d}","\frac{\sinh ^2(c+d x) \sqrt{\cosh ^2(c+d x)} \tanh (c+d x) \left(a+b \sinh ^2(c+d x)\right)^p \left(\frac{b \sinh ^2(c+d x)}{a}+1\right)^{-p} F_1\left(\frac{3}{2};\frac{3}{2},-p;\frac{5}{2};-\sinh ^2(c+d x),-\frac{b \sinh ^2(c+d x)}{a}\right)}{3 d}",1,"(AppellF1[3/2, 3/2, -p, 5/2, -Sinh[c + d*x]^2, -((b*Sinh[c + d*x]^2)/a)]*Sqrt[Cosh[c + d*x]^2]*Sinh[c + d*x]^2*(a + b*Sinh[c + d*x]^2)^p*Tanh[c + d*x])/(3*d*(1 + (b*Sinh[c + d*x]^2)/a)^p)","A",3,3,23,0.1304,1,"{3196, 511, 510}"
519,1,99,0,0.1016769,"\int \coth ^2(c+d x) \left(a+b \sinh ^2(c+d x)\right)^p \, dx","Int[Coth[c + d*x]^2*(a + b*Sinh[c + d*x]^2)^p,x]","-\frac{\sqrt{\cosh ^2(c+d x)} \text{csch}(c+d x) \text{sech}(c+d x) \left(a+b \sinh ^2(c+d x)\right)^p \left(\frac{b \sinh ^2(c+d x)}{a}+1\right)^{-p} F_1\left(-\frac{1}{2};-\frac{1}{2},-p;\frac{1}{2};-\sinh ^2(c+d x),-\frac{b \sinh ^2(c+d x)}{a}\right)}{d}","-\frac{\sqrt{\cosh ^2(c+d x)} \text{csch}(c+d x) \text{sech}(c+d x) \left(a+b \sinh ^2(c+d x)\right)^p \left(\frac{b \sinh ^2(c+d x)}{a}+1\right)^{-p} F_1\left(-\frac{1}{2};-\frac{1}{2},-p;\frac{1}{2};-\sinh ^2(c+d x),-\frac{b \sinh ^2(c+d x)}{a}\right)}{d}",1,"-((AppellF1[-1/2, -1/2, -p, 1/2, -Sinh[c + d*x]^2, -((b*Sinh[c + d*x]^2)/a)]*Sqrt[Cosh[c + d*x]^2]*Csch[c + d*x]*Sech[c + d*x]*(a + b*Sinh[c + d*x]^2)^p)/(d*(1 + (b*Sinh[c + d*x]^2)/a)^p))","A",3,3,23,0.1304,1,"{3196, 511, 510}"
520,1,103,0,0.1019071,"\int \coth ^4(c+d x) \left(a+b \sinh ^2(c+d x)\right)^p \, dx","Int[Coth[c + d*x]^4*(a + b*Sinh[c + d*x]^2)^p,x]","-\frac{\sqrt{\cosh ^2(c+d x)} \text{csch}^3(c+d x) \text{sech}(c+d x) \left(a+b \sinh ^2(c+d x)\right)^p \left(\frac{b \sinh ^2(c+d x)}{a}+1\right)^{-p} F_1\left(-\frac{3}{2};-\frac{3}{2},-p;-\frac{1}{2};-\sinh ^2(c+d x),-\frac{b \sinh ^2(c+d x)}{a}\right)}{3 d}","-\frac{\sqrt{\cosh ^2(c+d x)} \text{csch}^3(c+d x) \text{sech}(c+d x) \left(a+b \sinh ^2(c+d x)\right)^p \left(\frac{b \sinh ^2(c+d x)}{a}+1\right)^{-p} F_1\left(-\frac{3}{2};-\frac{3}{2},-p;-\frac{1}{2};-\sinh ^2(c+d x),-\frac{b \sinh ^2(c+d x)}{a}\right)}{3 d}",1,"-(AppellF1[-3/2, -3/2, -p, -1/2, -Sinh[c + d*x]^2, -((b*Sinh[c + d*x]^2)/a)]*Sqrt[Cosh[c + d*x]^2]*Csch[c + d*x]^3*Sech[c + d*x]*(a + b*Sinh[c + d*x]^2)^p)/(3*d*(1 + (b*Sinh[c + d*x]^2)/a)^p)","A",3,3,23,0.1304,1,"{3196, 511, 510}"
521,1,152,0,0.2516574,"\int \frac{\coth ^3(x)}{a+b \sinh ^3(x)} \, dx","Int[Coth[x]^3/(a + b*Sinh[x]^3),x]","\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sinh (x)+b^{2/3} \sinh ^2(x)\right)}{6 a^{5/3}}-\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sinh (x)\right)}{3 a^{5/3}}+\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sinh (x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3}}-\frac{\log \left(a+b \sinh ^3(x)\right)}{3 a}-\frac{\text{csch}^2(x)}{2 a}+\frac{\log (\sinh (x))}{a}","\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \sinh (x)+b^{2/3} \sinh ^2(x)\right)}{6 a^{5/3}}-\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \sinh (x)\right)}{3 a^{5/3}}+\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \sinh (x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3}}-\frac{\log \left(a+b \sinh ^3(x)\right)}{3 a}-\frac{\text{csch}^2(x)}{2 a}+\frac{\log (\sinh (x))}{a}",1,"(b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*Sinh[x])/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)) - Csch[x]^2/(2*a) + Log[Sinh[x]]/a - (b^(2/3)*Log[a^(1/3) + b^(1/3)*Sinh[x]])/(3*a^(5/3)) + (b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*Sinh[x] + b^(2/3)*Sinh[x]^2])/(6*a^(5/3)) - Log[a + b*Sinh[x]^3]/(3*a)","A",12,11,15,0.7333,1,"{3230, 1834, 1871, 12, 200, 31, 634, 617, 204, 628, 260}"
522,1,28,0,0.0763304,"\int \frac{\coth (x)}{\sqrt{a+b \sinh ^3(x)}} \, dx","Int[Coth[x]/Sqrt[a + b*Sinh[x]^3],x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^3(x)}}{\sqrt{a}}\right)}{3 \sqrt{a}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^3(x)}}{\sqrt{a}}\right)}{3 \sqrt{a}}",1,"(-2*ArcTanh[Sqrt[a + b*Sinh[x]^3]/Sqrt[a]])/(3*Sqrt[a])","A",4,4,15,0.2667,1,"{3230, 266, 63, 208}"
523,1,45,0,0.0822686,"\int \coth (x) \sqrt{a+b \sinh ^3(x)} \, dx","Int[Coth[x]*Sqrt[a + b*Sinh[x]^3],x]","\frac{2}{3} \sqrt{a+b \sinh ^3(x)}-\frac{2}{3} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^3(x)}}{\sqrt{a}}\right)","\frac{2}{3} \sqrt{a+b \sinh ^3(x)}-\frac{2}{3} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^3(x)}}{\sqrt{a}}\right)",1,"(-2*Sqrt[a]*ArcTanh[Sqrt[a + b*Sinh[x]^3]/Sqrt[a]])/3 + (2*Sqrt[a + b*Sinh[x]^3])/3","A",5,5,15,0.3333,1,"{3230, 266, 50, 63, 208}"
524,1,29,0,0.0865435,"\int \frac{\coth (x)}{\sqrt{a+b \sinh ^n(x)}} \, dx","Int[Coth[x]/Sqrt[a + b*Sinh[x]^n],x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^n(x)}}{\sqrt{a}}\right)}{\sqrt{a} n}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^n(x)}}{\sqrt{a}}\right)}{\sqrt{a} n}",1,"(-2*ArcTanh[Sqrt[a + b*Sinh[x]^n]/Sqrt[a]])/(Sqrt[a]*n)","A",4,4,15,0.2667,1,"{3230, 266, 63, 208}"
525,1,47,0,0.0919908,"\int \coth (x) \sqrt{a+b \sinh ^n(x)} \, dx","Int[Coth[x]*Sqrt[a + b*Sinh[x]^n],x]","\frac{2 \sqrt{a+b \sinh ^n(x)}}{n}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^n(x)}}{\sqrt{a}}\right)}{n}","\frac{2 \sqrt{a+b \sinh ^n(x)}}{n}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh ^n(x)}}{\sqrt{a}}\right)}{n}",1,"(-2*Sqrt[a]*ArcTanh[Sqrt[a + b*Sinh[x]^n]/Sqrt[a]])/n + (2*Sqrt[a + b*Sinh[x]^n])/n","A",5,5,15,0.3333,1,"{3230, 266, 50, 63, 208}"