1,1,149,114,3.3884432,"\int \left(a+b \text{csch}^2(c+d x)\right)^4 \, dx","Integrate[(a + b*Csch[c + d*x]^2)^4,x]","\frac{16 \sinh ^8(c+d x) \left(a+b \text{csch}^2(c+d x)\right)^4 \left(105 a^4 (c+d x)-b \coth (c+d x) \left(420 a^3+2 b \left(105 a^2-56 a b+12 b^2\right) \text{csch}^2(c+d x)-420 a^2 b+6 b^2 (14 a-3 b) \text{csch}^4(c+d x)+224 a b^2+15 b^3 \text{csch}^6(c+d x)-48 b^3\right)\right)}{105 d (a (-\cosh (2 (c+d x)))+a-2 b)^4}","a^4 x-\frac{b^2 \left(6 a^2-8 a b+3 b^2\right) \coth ^3(c+d x)}{3 d}-\frac{b (2 a-b) \left(2 a^2-2 a b+b^2\right) \coth (c+d x)}{d}-\frac{b^3 (4 a-3 b) \coth ^5(c+d x)}{5 d}-\frac{b^4 \coth ^7(c+d x)}{7 d}",1,"(16*(a + b*Csch[c + d*x]^2)^4*(105*a^4*(c + d*x) - b*Coth[c + d*x]*(420*a^3 - 420*a^2*b + 224*a*b^2 - 48*b^3 + 2*b*(105*a^2 - 56*a*b + 12*b^2)*Csch[c + d*x]^2 + 6*(14*a - 3*b)*b^2*Csch[c + d*x]^4 + 15*b^3*Csch[c + d*x]^6))*Sinh[c + d*x]^8)/(105*d*(a - 2*b - a*Cosh[2*(c + d*x)])^4)","A",1
2,1,113,74,3.5978883,"\int \left(a+b \text{csch}^2(c+d x)\right)^3 \, dx","Integrate[(a + b*Csch[c + d*x]^2)^3,x]","\frac{8 \sinh ^6(c+d x) \left(a+b \text{csch}^2(c+d x)\right)^3 \left(15 a^3 (c+d x)-b \coth (c+d x) \left(45 a^2+b (15 a-4 b) \text{csch}^2(c+d x)-30 a b+3 b^2 \text{csch}^4(c+d x)+8 b^2\right)\right)}{15 d (a \cosh (2 (c+d x))-a+2 b)^3}","a^3 x-\frac{b \left(3 a^2-3 a b+b^2\right) \coth (c+d x)}{d}-\frac{b^2 (3 a-2 b) \coth ^3(c+d x)}{3 d}-\frac{b^3 \coth ^5(c+d x)}{5 d}",1,"(8*(a + b*Csch[c + d*x]^2)^3*(15*a^3*(c + d*x) - b*Coth[c + d*x]*(45*a^2 - 30*a*b + 8*b^2 + (15*a - 4*b)*b*Csch[c + d*x]^2 + 3*b^2*Csch[c + d*x]^4))*Sinh[c + d*x]^6)/(15*d*(-a + 2*b + a*Cosh[2*(c + d*x)])^3)","A",1
3,1,84,43,0.644276,"\int \left(a+b \text{csch}^2(c+d x)\right)^2 \, dx","Integrate[(a + b*Csch[c + d*x]^2)^2,x]","\frac{4 \sinh ^4(c+d x) \left(a+b \text{csch}^2(c+d x)\right)^2 \left(3 a^2 (c+d x)-b \coth (c+d x) \left(6 a+b \text{csch}^2(c+d x)-2 b\right)\right)}{3 d (a (-\cosh (2 (c+d x)))+a-2 b)^2}","a^2 x-\frac{b (2 a-b) \coth (c+d x)}{d}-\frac{b^2 \coth ^3(c+d x)}{3 d}",1,"(4*(a + b*Csch[c + d*x]^2)^2*(3*a^2*(c + d*x) - b*Coth[c + d*x]*(6*a - 2*b + b*Csch[c + d*x]^2))*Sinh[c + d*x]^4)/(3*d*(a - 2*b - a*Cosh[2*(c + d*x)])^2)","A",1
4,1,16,16,0.0141206,"\int \left(a+b \text{csch}^2(c+d x)\right) \, dx","Integrate[a + b*Csch[c + d*x]^2,x]","a x-\frac{b \coth (c+d x)}{d}","a x-\frac{b \coth (c+d x)}{d}",1,"a*x - (b*Coth[c + d*x])/d","A",1
5,1,52,50,0.202733,"\int \frac{1}{a+b \text{csch}^2(c+d x)} \, dx","Integrate[(a + b*Csch[c + d*x]^2)^(-1),x]","\frac{-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{b}}\right)}{d \sqrt{a-b}}+\frac{c}{d}+x}{a}","\frac{x}{a}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{b}}\right)}{a d \sqrt{a-b}}",1,"(c/d + x - (Sqrt[b]*ArcTan[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[b]])/(Sqrt[a - b]*d))/a","A",1
6,1,199,100,0.7124913,"\int \frac{1}{\left(a+b \text{csch}^2(c+d x)\right)^2} \, dx","Integrate[(a + b*Csch[c + d*x]^2)^(-2),x]","\frac{\text{csch}^4(c+d x) (a \cosh (2 (c+d x))-a+2 b) \left(a b \sqrt{a-b} \sinh (2 (c+d x))+(a-2 b) \left(\sqrt{b} (3 a-2 b) \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{b}}\right)-2 (a-b)^{3/2} (c+d x)\right)+a \cosh (2 (c+d x)) \left(2 (a-b)^{3/2} (c+d x)+\sqrt{b} (2 b-3 a) \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{b}}\right)\right)\right)}{8 a^2 d (a-b)^{3/2} \left(a+b \text{csch}^2(c+d x)\right)^2}","-\frac{\sqrt{b} (3 a-2 b) \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{b}}\right)}{2 a^2 d (a-b)^{3/2}}+\frac{x}{a^2}+\frac{b \coth (c+d x)}{2 a d (a-b) \left(a+b \coth ^2(c+d x)-b\right)}",1,"((-a + 2*b + a*Cosh[2*(c + d*x)])*Csch[c + d*x]^4*((a - 2*b)*(-2*(a - b)^(3/2)*(c + d*x) + (3*a - 2*b)*Sqrt[b]*ArcTan[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[b]]) + a*(2*(a - b)^(3/2)*(c + d*x) + Sqrt[b]*(-3*a + 2*b)*ArcTan[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[b]])*Cosh[2*(c + d*x)] + a*Sqrt[a - b]*b*Sinh[2*(c + d*x)]))/(8*a^2*(a - b)^(3/2)*d*(a + b*Csch[c + d*x]^2)^2)","A",1
7,1,210,156,1.5662694,"\int \frac{1}{\left(a+b \text{csch}^2(c+d x)\right)^3} \, dx","Integrate[(a + b*Csch[c + d*x]^2)^(-3),x]","\frac{\text{csch}^6(c+d x) (a \cosh (2 (c+d x))-a+2 b) \left(-\frac{\sqrt{b} \left(15 a^2-20 a b+8 b^2\right) (a (-\cosh (2 (c+d x)))+a-2 b)^2 \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{b}}\right)}{(a-b)^{5/2}}-\frac{4 a b^2 \sinh (2 (c+d x))}{a-b}+8 (c+d x) (a (-\cosh (2 (c+d x)))+a-2 b)^2+\frac{3 a b (3 a-2 b) \sinh (2 (c+d x)) (a \cosh (2 (c+d x))-a+2 b)}{(a-b)^2}\right)}{64 a^3 d \left(a+b \text{csch}^2(c+d x)\right)^3}","\frac{x}{a^3}+\frac{b (7 a-4 b) \coth (c+d x)}{8 a^2 d (a-b)^2 \left(a+b \coth ^2(c+d x)-b\right)}-\frac{\sqrt{b} \left(15 a^2-20 a b+8 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{b}}\right)}{8 a^3 d (a-b)^{5/2}}+\frac{b \coth (c+d x)}{4 a d (a-b) \left(a+b \coth ^2(c+d x)-b\right)^2}",1,"((-a + 2*b + a*Cosh[2*(c + d*x)])*Csch[c + d*x]^6*(8*(c + d*x)*(a - 2*b - a*Cosh[2*(c + d*x)])^2 - (Sqrt[b]*(15*a^2 - 20*a*b + 8*b^2)*ArcTan[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[b]]*(a - 2*b - a*Cosh[2*(c + d*x)])^2)/(a - b)^(5/2) - (4*a*b^2*Sinh[2*(c + d*x)])/(a - b) + (3*a*(3*a - 2*b)*b*(-a + 2*b + a*Cosh[2*(c + d*x)])*Sinh[2*(c + d*x)])/(a - b)^2))/(64*a^3*d*(a + b*Csch[c + d*x]^2)^3)","A",1
8,1,273,220,3.6598641,"\int \frac{1}{\left(a+b \text{csch}^2(c+d x)\right)^4} \, dx","Integrate[(a + b*Csch[c + d*x]^2)^(-4),x]","\frac{\text{csch}^8(c+d x) (a \cosh (2 (c+d x))-a+2 b) \left(\frac{a b \left(87 a^2-116 a b+44 b^2\right) \sinh (2 (c+d x)) (a (-\cosh (2 (c+d x)))+a-2 b)^2}{(a-b)^3}+\frac{3 \sqrt{b} \left(-35 a^3+70 a^2 b-56 a b^2+16 b^3\right) (a \cosh (2 (c+d x))-a+2 b)^3 \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{b}}\right)}{(a-b)^{7/2}}+\frac{32 a b^3 \sinh (2 (c+d x))}{a-b}-\frac{4 a b^2 (19 a-14 b) \sinh (2 (c+d x)) (a \cosh (2 (c+d x))-a+2 b)}{(a-b)^2}+48 (c+d x) (a \cosh (2 (c+d x))-a+2 b)^3\right)}{768 a^4 d \left(a+b \text{csch}^2(c+d x)\right)^4}","\frac{x}{a^4}+\frac{b (11 a-6 b) \coth (c+d x)}{24 a^2 d (a-b)^2 \left(a+b \coth ^2(c+d x)-b\right)^2}+\frac{b \left(19 a^2-22 a b+8 b^2\right) \coth (c+d x)}{16 a^3 d (a-b)^3 \left(a+b \coth ^2(c+d x)-b\right)}-\frac{\sqrt{b} \left(35 a^3-70 a^2 b+56 a b^2-16 b^3\right) \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh (c+d x)}{\sqrt{b}}\right)}{16 a^4 d (a-b)^{7/2}}+\frac{b \coth (c+d x)}{6 a d (a-b) \left(a+b \coth ^2(c+d x)-b\right)^3}",1,"((-a + 2*b + a*Cosh[2*(c + d*x)])*Csch[c + d*x]^8*(48*(c + d*x)*(-a + 2*b + a*Cosh[2*(c + d*x)])^3 + (3*Sqrt[b]*(-35*a^3 + 70*a^2*b - 56*a*b^2 + 16*b^3)*ArcTan[(Sqrt[a - b]*Tanh[c + d*x])/Sqrt[b]]*(-a + 2*b + a*Cosh[2*(c + d*x)])^3)/(a - b)^(7/2) + (32*a*b^3*Sinh[2*(c + d*x)])/(a - b) + (a*b*(87*a^2 - 116*a*b + 44*b^2)*(a - 2*b - a*Cosh[2*(c + d*x)])^2*Sinh[2*(c + d*x)])/(a - b)^3 - (4*a*(19*a - 14*b)*b^2*(-a + 2*b + a*Cosh[2*(c + d*x)])*Sinh[2*(c + d*x)])/(a - b)^2))/(768*a^4*d*(a + b*Csch[c + d*x]^2)^4)","A",1
9,1,231,174,4.8993098,"\int \left(a+b \text{csch}^2(c+d x)\right)^{5/2} \, dx","Integrate[(a + b*Csch[c + d*x]^2)^(5/2),x]","\frac{\sinh ^5(c+d x) \left(a+b \text{csch}^2(c+d x)\right)^{5/2} \left(16 \sqrt{2} a^{5/2} \log \left(\sqrt{a \cosh (2 (c+d x))-a+2 b}+\sqrt{2} \sqrt{a} \cosh (c+d x)\right)-2 \sqrt{2} \sqrt{b} \left(15 a^2-10 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \cosh (c+d x)}{\sqrt{a \cosh (2 (c+d x))-a+2 b}}\right)+b \coth (c+d x) \text{csch}^3(c+d x) \sqrt{a \cosh (2 (c+d x))-a+2 b} ((3 b-9 a) \cosh (2 (c+d x))+9 a-7 b)\right)}{4 d (a \cosh (2 (c+d x))-a+2 b)^{5/2}}","\frac{a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{a+b \coth ^2(c+d x)-b}}\right)}{d}-\frac{\sqrt{b} \left(15 a^2-10 a b+3 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{b} \coth (c+d x)}{\sqrt{a+b \coth ^2(c+d x)-b}}\right)}{8 d}-\frac{b \coth (c+d x) \left(a+b \coth ^2(c+d x)-b\right)^{3/2}}{4 d}-\frac{b (7 a-3 b) \coth (c+d x) \sqrt{a+b \coth ^2(c+d x)-b}}{8 d}",1,"((a + b*Csch[c + d*x]^2)^(5/2)*(-2*Sqrt[2]*Sqrt[b]*(15*a^2 - 10*a*b + 3*b^2)*ArcTanh[(Sqrt[2]*Sqrt[b]*Cosh[c + d*x])/Sqrt[-a + 2*b + a*Cosh[2*(c + d*x)]]] + b*Sqrt[-a + 2*b + a*Cosh[2*(c + d*x)]]*(9*a - 7*b + (-9*a + 3*b)*Cosh[2*(c + d*x)])*Coth[c + d*x]*Csch[c + d*x]^3 + 16*Sqrt[2]*a^(5/2)*Log[Sqrt[2]*Sqrt[a]*Cosh[c + d*x] + Sqrt[-a + 2*b + a*Cosh[2*(c + d*x)]]])*Sinh[c + d*x]^5)/(4*d*(-a + 2*b + a*Cosh[2*(c + d*x)])^(5/2))","A",1
10,1,193,126,0.8252955,"\int \left(a+b \text{csch}^2(c+d x)\right)^{3/2} \, dx","Integrate[(a + b*Csch[c + d*x]^2)^(3/2),x]","\frac{\sinh ^3(c+d x) \left(a+b \text{csch}^2(c+d x)\right)^{3/2} \left(2 \sqrt{2} a^{3/2} \log \left(\sqrt{a \cosh (2 (c+d x))-a+2 b}+\sqrt{2} \sqrt{a} \cosh (c+d x)\right)+\sqrt{2} \sqrt{b} (b-3 a) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \cosh (c+d x)}{\sqrt{a \cosh (2 (c+d x))-a+2 b}}\right)-b \coth (c+d x) \text{csch}(c+d x) \sqrt{a \cosh (2 (c+d x))-a+2 b}\right)}{d (a \cosh (2 (c+d x))-a+2 b)^{3/2}}","\frac{a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{a+b \coth ^2(c+d x)-b}}\right)}{d}-\frac{b \coth (c+d x) \sqrt{a+b \coth ^2(c+d x)-b}}{2 d}-\frac{\sqrt{b} (3 a-b) \tanh ^{-1}\left(\frac{\sqrt{b} \coth (c+d x)}{\sqrt{a+b \coth ^2(c+d x)-b}}\right)}{2 d}",1,"((a + b*Csch[c + d*x]^2)^(3/2)*(Sqrt[2]*Sqrt[b]*(-3*a + b)*ArcTanh[(Sqrt[2]*Sqrt[b]*Cosh[c + d*x])/Sqrt[-a + 2*b + a*Cosh[2*(c + d*x)]]] - b*Sqrt[-a + 2*b + a*Cosh[2*(c + d*x)]]*Coth[c + d*x]*Csch[c + d*x] + 2*Sqrt[2]*a^(3/2)*Log[Sqrt[2]*Sqrt[a]*Cosh[c + d*x] + Sqrt[-a + 2*b + a*Cosh[2*(c + d*x)]]])*Sinh[c + d*x]^3)/(d*(-a + 2*b + a*Cosh[2*(c + d*x)])^(3/2))","A",1
11,1,143,84,0.2115818,"\int \sqrt{a+b \text{csch}^2(c+d x)} \, dx","Integrate[Sqrt[a + b*Csch[c + d*x]^2],x]","\frac{\sinh (c+d x) \sqrt{a+b \text{csch}^2(c+d x)} \left(\sqrt{a} \log \left(\sqrt{a \cosh (2 (c+d x))-a+2 b}+\sqrt{2} \sqrt{a} \cosh (c+d x)\right)-\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \cosh (c+d x)}{\sqrt{a \cosh (2 (c+d x))-a+2 b}}\right)\right)}{d \sqrt{\frac{1}{2} a \cosh (2 (c+d x))-\frac{a}{2}+b}}","\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{a+b \coth ^2(c+d x)-b}}\right)}{d}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \coth (c+d x)}{\sqrt{a+b \coth ^2(c+d x)-b}}\right)}{d}",1,"(Sqrt[a + b*Csch[c + d*x]^2]*(-(Sqrt[b]*ArcTanh[(Sqrt[2]*Sqrt[b]*Cosh[c + d*x])/Sqrt[-a + 2*b + a*Cosh[2*(c + d*x)]]]) + Sqrt[a]*Log[Sqrt[2]*Sqrt[a]*Cosh[c + d*x] + Sqrt[-a + 2*b + a*Cosh[2*(c + d*x)]]])*Sinh[c + d*x])/(d*Sqrt[-1/2*a + b + (a*Cosh[2*(c + d*x)])/2])","A",1
12,1,97,38,0.1445923,"\int \frac{1}{\sqrt{a+b \text{csch}^2(c+d x)}} \, dx","Integrate[1/Sqrt[a + b*Csch[c + d*x]^2],x]","\frac{\text{csch}(c+d x) \sqrt{a \cosh (2 (c+d x))-a+2 b} \log \left(\sqrt{a \cosh (2 (c+d x))-a+2 b}+\sqrt{2} \sqrt{a} \cosh (c+d x)\right)}{\sqrt{2} \sqrt{a} d \sqrt{a+b \text{csch}^2(c+d x)}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{a+b \text{csch}^2(c+d x)}}\right)}{\sqrt{a} d}",1,"(Sqrt[-a + 2*b + a*Cosh[2*(c + d*x)]]*Csch[c + d*x]*Log[Sqrt[2]*Sqrt[a]*Cosh[c + d*x] + Sqrt[-a + 2*b + a*Cosh[2*(c + d*x)]]])/(Sqrt[2]*Sqrt[a]*d*Sqrt[a + b*Csch[c + d*x]^2])","B",1
13,1,148,82,0.3535008,"\int \frac{1}{\left(a+b \text{csch}^2(c+d x)\right)^{3/2}} \, dx","Integrate[(a + b*Csch[c + d*x]^2)^(-3/2),x]","\frac{\text{csch}^2(c+d x) \left(\frac{2 \sqrt{a} b \coth (c+d x) (a \cosh (2 (c+d x))-a+2 b)}{a-b}+\sqrt{2} \text{csch}(c+d x) (a \cosh (2 (c+d x))-a+2 b)^{3/2} \log \left(\sqrt{a \cosh (2 (c+d x))-a+2 b}+\sqrt{2} \sqrt{a} \cosh (c+d x)\right)\right)}{4 a^{3/2} d \left(a+b \text{csch}^2(c+d x)\right)^{3/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{a+b \coth ^2(c+d x)-b}}\right)}{a^{3/2} d}+\frac{b \coth (c+d x)}{a d (a-b) \sqrt{a+b \coth ^2(c+d x)-b}}",1,"(Csch[c + d*x]^2*((2*Sqrt[a]*b*(-a + 2*b + a*Cosh[2*(c + d*x)])*Coth[c + d*x])/(a - b) + Sqrt[2]*(-a + 2*b + a*Cosh[2*(c + d*x)])^(3/2)*Csch[c + d*x]*Log[Sqrt[2]*Sqrt[a]*Cosh[c + d*x] + Sqrt[-a + 2*b + a*Cosh[2*(c + d*x)]]]))/(4*a^(3/2)*d*(a + b*Csch[c + d*x]^2)^(3/2))","A",1
14,1,174,135,1.7044056,"\int \frac{1}{\left(a+b \text{csch}^2(c+d x)\right)^{5/2}} \, dx","Integrate[(a + b*Csch[c + d*x]^2)^(-5/2),x]","\frac{\text{csch}^5(c+d x) \left(\frac{\sqrt{2} (a \cosh (2 (c+d x))-a+2 b)^{5/2} \log \left(\sqrt{a \cosh (2 (c+d x))-a+2 b}+\sqrt{2} \sqrt{a} \cosh (c+d x)\right)}{a^{5/2}}-\frac{4 b \cosh (c+d x) (a \cosh (2 (c+d x))-a+2 b) \left(3 a^2+a (2 b-3 a) \cosh (2 (c+d x))-7 a b+3 b^2\right)}{3 a^2 (a-b)^2}\right)}{8 d \left(a+b \text{csch}^2(c+d x)\right)^{5/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{a+b \coth ^2(c+d x)-b}}\right)}{a^{5/2} d}+\frac{b (5 a-3 b) \coth (c+d x)}{3 a^2 d (a-b)^2 \sqrt{a+b \coth ^2(c+d x)-b}}+\frac{b \coth (c+d x)}{3 a d (a-b) \left(a+b \coth ^2(c+d x)-b\right)^{3/2}}",1,"(Csch[c + d*x]^5*((-4*b*Cosh[c + d*x]*(-a + 2*b + a*Cosh[2*(c + d*x)])*(3*a^2 - 7*a*b + 3*b^2 + a*(-3*a + 2*b)*Cosh[2*(c + d*x)]))/(3*a^2*(a - b)^2) + (Sqrt[2]*(-a + 2*b + a*Cosh[2*(c + d*x)])^(5/2)*Log[Sqrt[2]*Sqrt[a]*Cosh[c + d*x] + Sqrt[-a + 2*b + a*Cosh[2*(c + d*x)]]])/a^(5/2)))/(8*d*(a + b*Csch[c + d*x]^2)^(5/2))","A",1
15,1,234,193,1.4365849,"\int \frac{1}{\left(a+b \text{csch}^2(c+d x)\right)^{7/2}} \, dx","Integrate[(a + b*Csch[c + d*x]^2)^(-7/2),x]","\frac{\text{csch}^7(c+d x) \left(\frac{\sqrt{2} (a \cosh (2 (c+d x))-a+2 b)^{7/2} \log \left(\sqrt{a \cosh (2 (c+d x))-a+2 b}+\sqrt{2} \sqrt{a} \cosh (c+d x)\right)}{a^{7/2}}+\frac{b \cosh (c+d x) \left(135 a^4-480 a^3 b+a^2 \left(45 a^2-60 a b+23 b^2\right) \cosh (4 (c+d x))+709 a^2 b^2-4 a \left(45 a^3-135 a^2 b+117 a b^2-35 b^3\right) \cosh (2 (c+d x))-460 a b^3+120 b^4\right) (a \cosh (2 (c+d x))-a+2 b)}{15 a^3 (a-b)^3}\right)}{16 d \left(a+b \text{csch}^2(c+d x)\right)^{7/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \coth (c+d x)}{\sqrt{a+b \coth ^2(c+d x)-b}}\right)}{a^{7/2} d}+\frac{b (9 a-5 b) \coth (c+d x)}{15 a^2 d (a-b)^2 \left(a+b \coth ^2(c+d x)-b\right)^{3/2}}+\frac{b \left(33 a^2-40 a b+15 b^2\right) \coth (c+d x)}{15 a^3 d (a-b)^3 \sqrt{a+b \coth ^2(c+d x)-b}}+\frac{b \coth (c+d x)}{5 a d (a-b) \left(a+b \coth ^2(c+d x)-b\right)^{5/2}}",1,"(Csch[c + d*x]^7*((b*Cosh[c + d*x]*(-a + 2*b + a*Cosh[2*(c + d*x)])*(135*a^4 - 480*a^3*b + 709*a^2*b^2 - 460*a*b^3 + 120*b^4 - 4*a*(45*a^3 - 135*a^2*b + 117*a*b^2 - 35*b^3)*Cosh[2*(c + d*x)] + a^2*(45*a^2 - 60*a*b + 23*b^2)*Cosh[4*(c + d*x)]))/(15*a^3*(a - b)^3) + (Sqrt[2]*(-a + 2*b + a*Cosh[2*(c + d*x)])^(7/2)*Log[Sqrt[2]*Sqrt[a]*Cosh[c + d*x] + Sqrt[-a + 2*b + a*Cosh[2*(c + d*x)]]])/a^(7/2)))/(16*d*(a + b*Csch[c + d*x]^2)^(7/2))","A",1
16,1,24,29,0.0171417,"\int \left(1+\text{csch}^2(x)\right)^{3/2} \, dx","Integrate[(1 + Csch[x]^2)^(3/2),x]","-\frac{1}{2} \tanh (x) \sqrt{\coth ^2(x)} \left(\text{csch}^2(x)-2 \log (\sinh (x))\right)","\tanh (x) \sqrt{\coth ^2(x)} \log (\sinh (x))-\frac{1}{2} \tanh (x) \coth ^2(x)^{3/2}",1,"-1/2*(Sqrt[Coth[x]^2]*(Csch[x]^2 - 2*Log[Sinh[x]])*Tanh[x])","A",1
17,1,14,14,0.0061054,"\int \sqrt{1+\text{csch}^2(x)} \, dx","Integrate[Sqrt[1 + Csch[x]^2],x]","\tanh (x) \sqrt{\coth ^2(x)} \log (\sinh (x))","\tanh (x) \sqrt{\coth ^2(x)} \log (\sinh (x))",1,"Sqrt[Coth[x]^2]*Log[Sinh[x]]*Tanh[x]","A",1
18,1,14,14,0.0103849,"\int \frac{1}{\sqrt{1+\text{csch}^2(x)}} \, dx","Integrate[1/Sqrt[1 + Csch[x]^2],x]","\frac{\coth (x) \log (\cosh (x))}{\sqrt{\coth ^2(x)}}","\frac{\coth (x) \log (\cosh (x))}{\sqrt{\coth ^2(x)}}",1,"(Coth[x]*Log[Cosh[x]])/Sqrt[Coth[x]^2]","A",1
19,1,92,46,0.2177321,"\int \left(1-\text{csch}^2(x)\right)^{3/2} \, dx","Integrate[(1 - Csch[x]^2)^(3/2),x]","\frac{\sinh ^3(x) \left(1-\text{csch}^2(x)\right)^{3/2} \left(2 \sqrt{2} \left(\log \left(\sqrt{2} \cosh (x)+\sqrt{\cosh (2 x)-3}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} \cosh (x)}{\sqrt{\cosh (2 x)-3}}\right)\right)+\sqrt{\cosh (2 x)-3} \coth (x) \text{csch}(x)\right)}{(\cosh (2 x)-3)^{3/2}}","\frac{1}{2} \coth (x) \sqrt{2-\coth ^2(x)}+\tanh ^{-1}\left(\frac{\coth (x)}{\sqrt{2-\coth ^2(x)}}\right)+2 \sin ^{-1}\left(\frac{\coth (x)}{\sqrt{2}}\right)",1,"((1 - Csch[x]^2)^(3/2)*(Sqrt[-3 + Cosh[2*x]]*Coth[x]*Csch[x] + 2*Sqrt[2]*(2*ArcTan[(Sqrt[2]*Cosh[x])/Sqrt[-3 + Cosh[2*x]]] + Log[Sqrt[2]*Cosh[x] + Sqrt[-3 + Cosh[2*x]]]))*Sinh[x]^3)/(-3 + Cosh[2*x])^(3/2)","A",1
20,1,65,26,0.0681446,"\int \sqrt{1-\text{csch}^2(x)} \, dx","Integrate[Sqrt[1 - Csch[x]^2],x]","\frac{\sinh (x) \sqrt{2-2 \text{csch}^2(x)} \left(\log \left(\sqrt{2} \cosh (x)+\sqrt{\cosh (2 x)-3}\right)+\tan ^{-1}\left(\frac{\sqrt{2} \cosh (x)}{\sqrt{\cosh (2 x)-3}}\right)\right)}{\sqrt{\cosh (2 x)-3}}","\tanh ^{-1}\left(\frac{\coth (x)}{\sqrt{2-\coth ^2(x)}}\right)+\sin ^{-1}\left(\frac{\coth (x)}{\sqrt{2}}\right)",1,"(Sqrt[2 - 2*Csch[x]^2]*(ArcTan[(Sqrt[2]*Cosh[x])/Sqrt[-3 + Cosh[2*x]]] + Log[Sqrt[2]*Cosh[x] + Sqrt[-3 + Cosh[2*x]]])*Sinh[x])/Sqrt[-3 + Cosh[2*x]]","B",1
21,1,45,16,0.0548021,"\int \frac{1}{\sqrt{1-\text{csch}^2(x)}} \, dx","Integrate[1/Sqrt[1 - Csch[x]^2],x]","\frac{\sqrt{\cosh (2 x)-3} \text{csch}(x) \log \left(\sqrt{2} \cosh (x)+\sqrt{\cosh (2 x)-3}\right)}{\sqrt{2-2 \text{csch}^2(x)}}","\tanh ^{-1}\left(\frac{\coth (x)}{\sqrt{2-\coth ^2(x)}}\right)",1,"(Sqrt[-3 + Cosh[2*x]]*Csch[x]*Log[Sqrt[2]*Cosh[x] + Sqrt[-3 + Cosh[2*x]]])/Sqrt[2 - 2*Csch[x]^2]","B",1
22,1,90,47,0.0986874,"\int \left(-1+\text{csch}^2(x)\right)^{3/2} \, dx","Integrate[(-1 + Csch[x]^2)^(3/2),x]","\frac{\sinh ^3(x) \left(\text{csch}^2(x)-1\right)^{3/2} \left(2 \sqrt{2} \left(\log \left(\sqrt{2} \cosh (x)+\sqrt{\cosh (2 x)-3}\right)+2 \tan ^{-1}\left(\frac{\sqrt{2} \cosh (x)}{\sqrt{\cosh (2 x)-3}}\right)\right)+\sqrt{\cosh (2 x)-3} \coth (x) \text{csch}(x)\right)}{(\cosh (2 x)-3)^{3/2}}","-\frac{1}{2} \coth (x) \sqrt{\coth ^2(x)-2}+\tan ^{-1}\left(\frac{\coth (x)}{\sqrt{\coth ^2(x)-2}}\right)+2 \tanh ^{-1}\left(\frac{\coth (x)}{\sqrt{\coth ^2(x)-2}}\right)",1,"((-1 + Csch[x]^2)^(3/2)*(Sqrt[-3 + Cosh[2*x]]*Coth[x]*Csch[x] + 2*Sqrt[2]*(2*ArcTan[(Sqrt[2]*Cosh[x])/Sqrt[-3 + Cosh[2*x]]] + Log[Sqrt[2]*Cosh[x] + Sqrt[-3 + Cosh[2*x]]]))*Sinh[x]^3)/(-3 + Cosh[2*x])^(3/2)","A",1
23,1,68,33,0.039668,"\int \sqrt{-1+\text{csch}^2(x)} \, dx","Integrate[Sqrt[-1 + Csch[x]^2],x]","\frac{\sqrt{2} \sinh (x) \sqrt{\text{csch}^2(x)-1} \left(\log \left(\sqrt{2} \cosh (x)+\sqrt{\cosh (2 x)-3}\right)+\tan ^{-1}\left(\frac{\sqrt{2} \cosh (x)}{\sqrt{\cosh (2 x)-3}}\right)\right)}{\sqrt{\cosh (2 x)-3}}","-\tan ^{-1}\left(\frac{\coth (x)}{\sqrt{\coth ^2(x)-2}}\right)-\tanh ^{-1}\left(\frac{\coth (x)}{\sqrt{\coth ^2(x)-2}}\right)",1,"(Sqrt[2]*Sqrt[-1 + Csch[x]^2]*(ArcTan[(Sqrt[2]*Cosh[x])/Sqrt[-3 + Cosh[2*x]]] + Log[Sqrt[2]*Cosh[x] + Sqrt[-3 + Cosh[2*x]]])*Sinh[x])/Sqrt[-3 + Cosh[2*x]]","B",1
24,1,48,14,0.0308958,"\int \frac{1}{\sqrt{-1+\text{csch}^2(x)}} \, dx","Integrate[1/Sqrt[-1 + Csch[x]^2],x]","\frac{\sqrt{\cosh (2 x)-3} \text{csch}(x) \log \left(\sqrt{2} \cosh (x)+\sqrt{\cosh (2 x)-3}\right)}{\sqrt{2} \sqrt{\text{csch}^2(x)-1}}","\tan ^{-1}\left(\frac{\coth (x)}{\sqrt{\coth ^2(x)-2}}\right)",1,"(Sqrt[-3 + Cosh[2*x]]*Csch[x]*Log[Sqrt[2]*Cosh[x] + Sqrt[-3 + Cosh[2*x]]])/(Sqrt[2]*Sqrt[-1 + Csch[x]^2])","B",1
25,1,26,34,0.0154893,"\int \left(-1-\text{csch}^2(x)\right)^{3/2} \, dx","Integrate[(-1 - Csch[x]^2)^(3/2),x]","\frac{1}{2} \tanh (x) \sqrt{-\coth ^2(x)} \left(\text{csch}^2(x)-2 \log (\sinh (x))\right)","\frac{1}{2} \coth (x) \sqrt{-\coth ^2(x)}-\tanh (x) \sqrt{-\coth ^2(x)} \log (\sinh (x))",1,"(Sqrt[-Coth[x]^2]*(Csch[x]^2 - 2*Log[Sinh[x]])*Tanh[x])/2","A",1
26,1,16,16,0.0057772,"\int \sqrt{-1-\text{csch}^2(x)} \, dx","Integrate[Sqrt[-1 - Csch[x]^2],x]","\tanh (x) \sqrt{-\coth ^2(x)} \log (\sinh (x))","\tanh (x) \sqrt{-\coth ^2(x)} \log (\sinh (x))",1,"Sqrt[-Coth[x]^2]*Log[Sinh[x]]*Tanh[x]","A",1
27,1,16,16,0.0082634,"\int \frac{1}{\sqrt{-1-\text{csch}^2(x)}} \, dx","Integrate[1/Sqrt[-1 - Csch[x]^2],x]","\frac{\coth (x) \log (\cosh (x))}{\sqrt{-\coth ^2(x)}}","\frac{\coth (x) \log (\cosh (x))}{\sqrt{-\coth ^2(x)}}",1,"(Coth[x]*Log[Cosh[x]])/Sqrt[-Coth[x]^2]","A",1