1,1,183,0,0.1533738,"\int (d+e x)^3 \cosh ^{-1}(c x) \, dx","Int[(d + e*x)^3*ArcCosh[c*x],x]","-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(e x \left(26 c^2 d^2+9 e^2\right)+4 d \left(19 c^2 d^2+16 e^2\right)\right)}{96 c^3}-\frac{\left(24 c^2 d^2 e^2+8 c^4 d^4+3 e^4\right) \cosh ^{-1}(c x)}{32 c^4 e}-\frac{\sqrt{c x-1} \sqrt{c x+1} (d+e x)^3}{16 c}-\frac{7 d \sqrt{c x-1} \sqrt{c x+1} (d+e x)^2}{48 c}+\frac{\cosh ^{-1}(c x) (d+e x)^4}{4 e}","-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(e x \left(26 c^2 d^2+9 e^2\right)+4 d \left(19 c^2 d^2+16 e^2\right)\right)}{96 c^3}-\frac{\left(24 c^2 d^2 e^2+8 c^4 d^4+3 e^4\right) \cosh ^{-1}(c x)}{32 c^4 e}-\frac{\sqrt{c x-1} \sqrt{c x+1} (d+e x)^3}{16 c}-\frac{7 d \sqrt{c x-1} \sqrt{c x+1} (d+e x)^2}{48 c}+\frac{\cosh ^{-1}(c x) (d+e x)^4}{4 e}",1,"(-7*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(d + e*x)^2)/(48*c) - (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(d + e*x)^3)/(16*c) - (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(4*d*(19*c^2*d^2 + 16*e^2) + e*(26*c^2*d^2 + 9*e^2)*x))/(96*c^3) - ((8*c^4*d^4 + 24*c^2*d^2*e^2 + 3*e^4)*ArcCosh[c*x])/(32*c^4*e) + ((d + e*x)^4*ArcCosh[c*x])/(4*e)","A",5,5,12,0.4167,1,"{5802, 100, 153, 147, 52}"
2,1,123,0,0.1030746,"\int (d+e x)^2 \cosh ^{-1}(c x) \, dx","Int[(d + e*x)^2*ArcCosh[c*x],x]","-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(4 \left(4 c^2 d^2+e^2\right)+5 c^2 d e x\right)}{18 c^3}-\frac{1}{6} d \left(\frac{3 e}{c^2}+\frac{2 d^2}{e}\right) \cosh ^{-1}(c x)-\frac{\sqrt{c x-1} \sqrt{c x+1} (d+e x)^2}{9 c}+\frac{\cosh ^{-1}(c x) (d+e x)^3}{3 e}","-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(4 \left(4 c^2 d^2+e^2\right)+5 c^2 d e x\right)}{18 c^3}-\frac{1}{6} d \left(\frac{3 e}{c^2}+\frac{2 d^2}{e}\right) \cosh ^{-1}(c x)-\frac{\sqrt{c x-1} \sqrt{c x+1} (d+e x)^2}{9 c}+\frac{\cosh ^{-1}(c x) (d+e x)^3}{3 e}",1,"-(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(d + e*x)^2)/(9*c) - (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(4*(4*c^2*d^2 + e^2) + 5*c^2*d*e*x))/(18*c^3) - (d*((2*d^2)/e + (3*e)/c^2)*ArcCosh[c*x])/6 + ((d + e*x)^3*ArcCosh[c*x])/(3*e)","A",4,4,12,0.3333,1,"{5802, 100, 147, 52}"
3,1,97,0,0.0417405,"\int (d+e x) \cosh ^{-1}(c x) \, dx","Int[(d + e*x)*ArcCosh[c*x],x]","-\frac{1}{4} \left(\frac{e}{c^2}+\frac{2 d^2}{e}\right) \cosh ^{-1}(c x)-\frac{\sqrt{c x-1} \sqrt{c x+1} (d+e x)}{4 c}+\frac{\cosh ^{-1}(c x) (d+e x)^2}{2 e}-\frac{3 d \sqrt{c x-1} \sqrt{c x+1}}{4 c}","-\frac{1}{4} \left(\frac{e}{c^2}+\frac{2 d^2}{e}\right) \cosh ^{-1}(c x)-\frac{\sqrt{c x-1} \sqrt{c x+1} (d+e x)}{4 c}+\frac{\cosh ^{-1}(c x) (d+e x)^2}{2 e}-\frac{3 d \sqrt{c x-1} \sqrt{c x+1}}{4 c}",1,"(-3*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*c) - (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(d + e*x))/(4*c) - (((2*d^2)/e + e/c^2)*ArcCosh[c*x])/4 + ((d + e*x)^2*ArcCosh[c*x])/(2*e)","A",4,4,10,0.4000,1,"{5802, 90, 80, 52}"
4,1,178,0,0.2714441,"\int \frac{\cosh ^{-1}(c x)}{d+e x} \, dx","Int[ArcCosh[c*x]/(d + e*x),x]","\frac{\text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{\text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}+\frac{\cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e}+\frac{\cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e}-\frac{\cosh ^{-1}(c x)^2}{2 e}","\frac{\text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{\text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}+\frac{\cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e}+\frac{\cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e}-\frac{\cosh ^{-1}(c x)^2}{2 e}",1,"-ArcCosh[c*x]^2/(2*e) + (ArcCosh[c*x]*Log[1 + (e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2])])/e + (ArcCosh[c*x]*Log[1 + (e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2])])/e + PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2]))]/e + PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2]))]/e","A",8,5,12,0.4167,1,"{5800, 5562, 2190, 2279, 2391}"
5,1,83,0,0.0877095,"\int \frac{\cosh ^{-1}(c x)}{(d+e x)^2} \, dx","Int[ArcCosh[c*x]/(d + e*x)^2,x]","\frac{2 c \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{e \sqrt{c d-e} \sqrt{c d+e}}-\frac{\cosh ^{-1}(c x)}{e (d+e x)}","\frac{2 c \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{e \sqrt{c d-e} \sqrt{c d+e}}-\frac{\cosh ^{-1}(c x)}{e (d+e x)}",1,"-(ArcCosh[c*x]/(e*(d + e*x))) + (2*c*ArcTanh[(Sqrt[c*d + e]*Sqrt[1 + c*x])/(Sqrt[c*d - e]*Sqrt[-1 + c*x])])/(Sqrt[c*d - e]*e*Sqrt[c*d + e])","A",3,3,12,0.2500,1,"{5802, 93, 208}"
6,1,132,0,0.1348985,"\int \frac{\cosh ^{-1}(c x)}{(d+e x)^3} \, dx","Int[ArcCosh[c*x]/(d + e*x)^3,x]","-\frac{c \sqrt{c x-1} \sqrt{c x+1}}{2 \left(c^2 d^2-e^2\right) (d+e x)}+\frac{c^3 d \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{e (c d-e)^{3/2} (c d+e)^{3/2}}-\frac{\cosh ^{-1}(c x)}{2 e (d+e x)^2}","-\frac{c \sqrt{c x-1} \sqrt{c x+1}}{2 \left(c^2 d^2-e^2\right) (d+e x)}+\frac{c^3 d \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{e (c d-e)^{3/2} (c d+e)^{3/2}}-\frac{\cosh ^{-1}(c x)}{2 e (d+e x)^2}",1,"-(c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*(c^2*d^2 - e^2)*(d + e*x)) - ArcCosh[c*x]/(2*e*(d + e*x)^2) + (c^3*d*ArcTanh[(Sqrt[c*d + e]*Sqrt[1 + c*x])/(Sqrt[c*d - e]*Sqrt[-1 + c*x])])/((c*d - e)^(3/2)*e*(c*d + e)^(3/2))","A",4,4,12,0.3333,1,"{5802, 96, 93, 208}"
7,1,195,0,0.2372322,"\int \frac{\cosh ^{-1}(c x)}{(d+e x)^4} \, dx","Int[ArcCosh[c*x]/(d + e*x)^4,x]","-\frac{c \sqrt{c x-1} \sqrt{c x+1}}{6 \left(c^2 d^2-e^2\right) (d+e x)^2}+\frac{c^3 \left(2 c^2 d^2+e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{3 e (c d-e)^{5/2} (c d+e)^{5/2}}-\frac{c^3 d \sqrt{c x-1} \sqrt{c x+1}}{2 (c d-e)^2 (c d+e)^2 (d+e x)}-\frac{\cosh ^{-1}(c x)}{3 e (d+e x)^3}","-\frac{c \sqrt{c x-1} \sqrt{c x+1}}{6 \left(c^2 d^2-e^2\right) (d+e x)^2}+\frac{c^3 \left(2 c^2 d^2+e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{3 e (c d-e)^{5/2} (c d+e)^{5/2}}-\frac{c^3 d \sqrt{c x-1} \sqrt{c x+1}}{2 (c d-e)^2 (c d+e)^2 (d+e x)}-\frac{\cosh ^{-1}(c x)}{3 e (d+e x)^3}",1,"-(c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*(c^2*d^2 - e^2)*(d + e*x)^2) - (c^3*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*(c*d - e)^2*(c*d + e)^2*(d + e*x)) - ArcCosh[c*x]/(3*e*(d + e*x)^3) + (c^3*(2*c^2*d^2 + e^2)*ArcTanh[(Sqrt[c*d + e]*Sqrt[1 + c*x])/(Sqrt[c*d - e]*Sqrt[-1 + c*x])])/(3*(c*d - e)^(5/2)*e*(c*d + e)^(5/2))","A",6,6,12,0.5000,1,"{5802, 103, 151, 12, 93, 208}"
8,1,334,0,1.4635392,"\int (d+e x)^3 \cosh ^{-1}(c x)^2 \, dx","Int[(d + e*x)^3*ArcCosh[c*x]^2,x]","-\frac{3 d^2 e \cosh ^{-1}(c x)^2}{4 c^2}+\frac{4 d e^2 x}{3 c^2}-\frac{4 d e^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{3 c^3}+\frac{3 e^3 x^2}{32 c^2}-\frac{3 e^3 \cosh ^{-1}(c x)^2}{32 c^4}-\frac{3 e^3 x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{16 c^3}-\frac{d^4 \cosh ^{-1}(c x)^2}{4 e}-\frac{3 d^2 e x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{2 c}-\frac{2 d^3 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c}-\frac{2 d e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{3 c}+\frac{\cosh ^{-1}(c x)^2 (d+e x)^4}{4 e}-\frac{e^3 x^3 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{8 c}+\frac{3}{4} d^2 e x^2+2 d^3 x+\frac{2}{9} d e^2 x^3+\frac{e^3 x^4}{32}","-\frac{3 d^2 e \cosh ^{-1}(c x)^2}{4 c^2}+\frac{4 d e^2 x}{3 c^2}-\frac{4 d e^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{3 c^3}+\frac{3 e^3 x^2}{32 c^2}-\frac{3 e^3 \cosh ^{-1}(c x)^2}{32 c^4}-\frac{3 e^3 x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{16 c^3}-\frac{d^4 \cosh ^{-1}(c x)^2}{4 e}-\frac{3 d^2 e x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{2 c}-\frac{2 d^3 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c}-\frac{2 d e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{3 c}+\frac{\cosh ^{-1}(c x)^2 (d+e x)^4}{4 e}-\frac{e^3 x^3 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{8 c}+\frac{3}{4} d^2 e x^2+2 d^3 x+\frac{2}{9} d e^2 x^3+\frac{e^3 x^4}{32}",1,"2*d^3*x + (4*d*e^2*x)/(3*c^2) + (3*d^2*e*x^2)/4 + (3*e^3*x^2)/(32*c^2) + (2*d*e^2*x^3)/9 + (e^3*x^4)/32 - (2*d^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/c - (4*d*e^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(3*c^3) - (3*d^2*e*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(2*c) - (3*e^3*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(16*c^3) - (2*d*e^2*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(3*c) - (e^3*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(8*c) - (d^4*ArcCosh[c*x]^2)/(4*e) - (3*d^2*e*ArcCosh[c*x]^2)/(4*c^2) - (3*e^3*ArcCosh[c*x]^2)/(32*c^4) + ((d + e*x)^4*ArcCosh[c*x]^2)/(4*e)","A",18,7,14,0.5000,1,"{5802, 5822, 5676, 5718, 8, 5759, 30}"
9,1,215,0,0.996076,"\int (d+e x)^2 \cosh ^{-1}(c x)^2 \, dx","Int[(d + e*x)^2*ArcCosh[c*x]^2,x]","-\frac{d e \cosh ^{-1}(c x)^2}{2 c^2}+\frac{4 e^2 x}{9 c^2}-\frac{4 e^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{9 c^3}-\frac{d^3 \cosh ^{-1}(c x)^2}{3 e}-\frac{2 d^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c}-\frac{d e x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c}+\frac{\cosh ^{-1}(c x)^2 (d+e x)^3}{3 e}-\frac{2 e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{9 c}+2 d^2 x+\frac{1}{2} d e x^2+\frac{2 e^2 x^3}{27}","-\frac{d e \cosh ^{-1}(c x)^2}{2 c^2}+\frac{4 e^2 x}{9 c^2}-\frac{4 e^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{9 c^3}-\frac{d^3 \cosh ^{-1}(c x)^2}{3 e}-\frac{2 d^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c}-\frac{d e x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c}+\frac{\cosh ^{-1}(c x)^2 (d+e x)^3}{3 e}-\frac{2 e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{9 c}+2 d^2 x+\frac{1}{2} d e x^2+\frac{2 e^2 x^3}{27}",1,"2*d^2*x + (4*e^2*x)/(9*c^2) + (d*e*x^2)/2 + (2*e^2*x^3)/27 - (2*d^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/c - (4*e^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(9*c^3) - (d*e*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/c - (2*e^2*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(9*c) - (d^3*ArcCosh[c*x]^2)/(3*e) - (d*e*ArcCosh[c*x]^2)/(2*c^2) + ((d + e*x)^3*ArcCosh[c*x]^2)/(3*e)","A",13,7,14,0.5000,1,"{5802, 5822, 5676, 5718, 8, 5759, 30}"
10,1,122,0,0.6508729,"\int (d+e x) \cosh ^{-1}(c x)^2 \, dx","Int[(d + e*x)*ArcCosh[c*x]^2,x]","-\frac{e \cosh ^{-1}(c x)^2}{4 c^2}-\frac{d^2 \cosh ^{-1}(c x)^2}{2 e}+\frac{\cosh ^{-1}(c x)^2 (d+e x)^2}{2 e}-\frac{2 d \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c}-\frac{e x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{2 c}+2 d x+\frac{e x^2}{4}","-\frac{e \cosh ^{-1}(c x)^2}{4 c^2}-\frac{d^2 \cosh ^{-1}(c x)^2}{2 e}+\frac{\cosh ^{-1}(c x)^2 (d+e x)^2}{2 e}-\frac{2 d \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c}-\frac{e x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{2 c}+2 d x+\frac{e x^2}{4}",1,"2*d*x + (e*x^2)/4 - (2*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/c - (e*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(2*c) - (d^2*ArcCosh[c*x]^2)/(2*e) - (e*ArcCosh[c*x]^2)/(4*c^2) + ((d + e*x)^2*ArcCosh[c*x]^2)/(2*e)","A",9,7,12,0.5833,1,"{5802, 5822, 5676, 5718, 8, 5759, 30}"
11,1,272,0,0.4259401,"\int \frac{\cosh ^{-1}(c x)^2}{d+e x} \, dx","Int[ArcCosh[c*x]^2/(d + e*x),x]","\frac{2 \cosh ^{-1}(c x) \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{2 \cosh ^{-1}(c x) \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}-\frac{2 \text{PolyLog}\left(3,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}-\frac{2 \text{PolyLog}\left(3,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}+\frac{\cosh ^{-1}(c x)^2 \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e}+\frac{\cosh ^{-1}(c x)^2 \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e}-\frac{\cosh ^{-1}(c x)^3}{3 e}","\frac{2 \cosh ^{-1}(c x) \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{2 \cosh ^{-1}(c x) \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}-\frac{2 \text{PolyLog}\left(3,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}-\frac{2 \text{PolyLog}\left(3,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}+\frac{\cosh ^{-1}(c x)^2 \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e}+\frac{\cosh ^{-1}(c x)^2 \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e}-\frac{\cosh ^{-1}(c x)^3}{3 e}",1,"-ArcCosh[c*x]^3/(3*e) + (ArcCosh[c*x]^2*Log[1 + (e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2])])/e + (ArcCosh[c*x]^2*Log[1 + (e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2])])/e + (2*ArcCosh[c*x]*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2]))])/e + (2*ArcCosh[c*x]*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2]))])/e - (2*PolyLog[3, -((e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2]))])/e - (2*PolyLog[3, -((e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2]))])/e","A",10,6,14,0.4286,1,"{5800, 5562, 2190, 2531, 2282, 6589}"
12,1,259,0,0.5816501,"\int \frac{\cosh ^{-1}(c x)^2}{(d+e x)^2} \, dx","Int[ArcCosh[c*x]^2/(d + e*x)^2,x]","\frac{2 c \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{2 c \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e \sqrt{c^2 d^2-e^2}}+\frac{2 c \cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{2 c \cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{\cosh ^{-1}(c x)^2}{e (d+e x)}","\frac{2 c \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{2 c \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e \sqrt{c^2 d^2-e^2}}+\frac{2 c \cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{2 c \cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{\cosh ^{-1}(c x)^2}{e (d+e x)}",1,"-(ArcCosh[c*x]^2/(e*(d + e*x))) + (2*c*ArcCosh[c*x]*Log[1 + (e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2])])/(e*Sqrt[c^2*d^2 - e^2]) - (2*c*ArcCosh[c*x]*Log[1 + (e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2])])/(e*Sqrt[c^2*d^2 - e^2]) + (2*c*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2]))])/(e*Sqrt[c^2*d^2 - e^2]) - (2*c*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2]))])/(e*Sqrt[c^2*d^2 - e^2])","A",10,7,14,0.5000,1,"{5802, 5832, 3320, 2264, 2190, 2279, 2391}"
13,1,352,0,0.6943625,"\int \frac{\cosh ^{-1}(c x)^2}{(d+e x)^3} \, dx","Int[ArcCosh[c*x]^2/(d + e*x)^3,x]","\frac{c^3 d \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{c^3 d \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}+\frac{c^2 \log (d+e x)}{e \left(c^2 d^2-e^2\right)}-\frac{c \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \cosh ^{-1}(c x)}{\left(c^2 d^2-e^2\right) (d+e x)}+\frac{c^3 d \cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{c^3 d \cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{\cosh ^{-1}(c x)^2}{2 e (d+e x)^2}","\frac{c^3 d \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{c^3 d \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}+\frac{c^2 \log (d+e x)}{e \left(c^2 d^2-e^2\right)}-\frac{c \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \cosh ^{-1}(c x)}{\left(c^2 d^2-e^2\right) (d+e x)}+\frac{c^3 d \cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{c^3 d \cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{\cosh ^{-1}(c x)^2}{2 e (d+e x)^2}",1,"-((c*Sqrt[-((1 - c*x)/(1 + c*x))]*(1 + c*x)*ArcCosh[c*x])/((c^2*d^2 - e^2)*(d + e*x))) - ArcCosh[c*x]^2/(2*e*(d + e*x)^2) + (c^3*d*ArcCosh[c*x]*Log[1 + (e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2])])/(e*(c^2*d^2 - e^2)^(3/2)) - (c^3*d*ArcCosh[c*x]*Log[1 + (e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2])])/(e*(c^2*d^2 - e^2)^(3/2)) + (c^2*Log[d + e*x])/(e*(c^2*d^2 - e^2)) + (c^3*d*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2]))])/(e*(c^2*d^2 - e^2)^(3/2)) - (c^3*d*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2]))])/(e*(c^2*d^2 - e^2)^(3/2))","A",13,10,14,0.7143,1,"{5802, 5832, 3324, 3320, 2264, 2190, 2279, 2391, 2668, 31}"
14,1,191,0,0.1445223,"\int (d+e x)^3 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(d + e*x)^3*(a + b*ArcCosh[c*x]),x]","\frac{(d+e x)^4 \left(a+b \cosh ^{-1}(c x)\right)}{4 e}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \left(e x \left(26 c^2 d^2+9 e^2\right)+4 d \left(19 c^2 d^2+16 e^2\right)\right)}{96 c^3}-\frac{b \left(24 c^2 d^2 e^2+8 c^4 d^4+3 e^4\right) \cosh ^{-1}(c x)}{32 c^4 e}-\frac{b \sqrt{c x-1} \sqrt{c x+1} (d+e x)^3}{16 c}-\frac{7 b d \sqrt{c x-1} \sqrt{c x+1} (d+e x)^2}{48 c}","\frac{(d+e x)^4 \left(a+b \cosh ^{-1}(c x)\right)}{4 e}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \left(e x \left(26 c^2 d^2+9 e^2\right)+4 d \left(19 c^2 d^2+16 e^2\right)\right)}{96 c^3}-\frac{b \left(24 c^2 d^2 e^2+8 c^4 d^4+3 e^4\right) \cosh ^{-1}(c x)}{32 c^4 e}-\frac{b \sqrt{c x-1} \sqrt{c x+1} (d+e x)^3}{16 c}-\frac{7 b d \sqrt{c x-1} \sqrt{c x+1} (d+e x)^2}{48 c}",1,"(-7*b*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(d + e*x)^2)/(48*c) - (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(d + e*x)^3)/(16*c) - (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(4*d*(19*c^2*d^2 + 16*e^2) + e*(26*c^2*d^2 + 9*e^2)*x))/(96*c^3) - (b*(8*c^4*d^4 + 24*c^2*d^2*e^2 + 3*e^4)*ArcCosh[c*x])/(32*c^4*e) + ((d + e*x)^4*(a + b*ArcCosh[c*x]))/(4*e)","A",5,5,16,0.3125,1,"{5802, 100, 153, 147, 52}"
15,1,132,0,0.1045949,"\int (d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(d + e*x)^2*(a + b*ArcCosh[c*x]),x]","\frac{(d+e x)^3 \left(a+b \cosh ^{-1}(c x)\right)}{3 e}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \left(4 \left(4 c^2 d^2+e^2\right)+5 c^2 d e x\right)}{18 c^3}-\frac{b d \left(\frac{3 e^2}{c^2}+2 d^2\right) \cosh ^{-1}(c x)}{6 e}-\frac{b \sqrt{c x-1} \sqrt{c x+1} (d+e x)^2}{9 c}","\frac{(d+e x)^3 \left(a+b \cosh ^{-1}(c x)\right)}{3 e}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \left(4 \left(4 c^2 d^2+e^2\right)+5 c^2 d e x\right)}{18 c^3}-\frac{b d \left(\frac{3 e^2}{c^2}+2 d^2\right) \cosh ^{-1}(c x)}{6 e}-\frac{b \sqrt{c x-1} \sqrt{c x+1} (d+e x)^2}{9 c}",1,"-(b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(d + e*x)^2)/(9*c) - (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(4*(4*c^2*d^2 + e^2) + 5*c^2*d*e*x))/(18*c^3) - (b*d*(2*d^2 + (3*e^2)/c^2)*ArcCosh[c*x])/(6*e) + ((d + e*x)^3*(a + b*ArcCosh[c*x]))/(3*e)","A",4,4,16,0.2500,1,"{5802, 100, 147, 52}"
16,1,106,0,0.0444908,"\int (d+e x) \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(d + e*x)*(a + b*ArcCosh[c*x]),x]","\frac{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 e}-\frac{b \left(\frac{e^2}{c^2}+2 d^2\right) \cosh ^{-1}(c x)}{4 e}-\frac{b \sqrt{c x-1} \sqrt{c x+1} (d+e x)}{4 c}-\frac{3 b d \sqrt{c x-1} \sqrt{c x+1}}{4 c}","\frac{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 e}-\frac{b \left(\frac{e^2}{c^2}+2 d^2\right) \cosh ^{-1}(c x)}{4 e}-\frac{b \sqrt{c x-1} \sqrt{c x+1} (d+e x)}{4 c}-\frac{3 b d \sqrt{c x-1} \sqrt{c x+1}}{4 c}",1,"(-3*b*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*c) - (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(d + e*x))/(4*c) - (b*(2*d^2 + e^2/c^2)*ArcCosh[c*x])/(4*e) + ((d + e*x)^2*(a + b*ArcCosh[c*x]))/(2*e)","A",4,4,14,0.2857,1,"{5802, 90, 80, 52}"
17,1,195,0,0.2643151,"\int \frac{a+b \cosh ^{-1}(c x)}{d+e x} \, dx","Int[(a + b*ArcCosh[c*x])/(d + e*x),x]","\frac{b \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{b \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 b e}","\frac{b \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{b \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 b e}",1,"-(a + b*ArcCosh[c*x])^2/(2*b*e) + ((a + b*ArcCosh[c*x])*Log[1 + (e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2])])/e + ((a + b*ArcCosh[c*x])*Log[1 + (e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2])])/e + (b*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2]))])/e + (b*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2]))])/e","A",8,5,16,0.3125,1,"{5800, 5562, 2190, 2279, 2391}"
18,1,88,0,0.0564455,"\int \frac{a+b \cosh ^{-1}(c x)}{(d+e x)^2} \, dx","Int[(a + b*ArcCosh[c*x])/(d + e*x)^2,x]","\frac{2 b c \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{e \sqrt{c d-e} \sqrt{c d+e}}-\frac{a+b \cosh ^{-1}(c x)}{e (d+e x)}","\frac{2 b c \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{e \sqrt{c d-e} \sqrt{c d+e}}-\frac{a+b \cosh ^{-1}(c x)}{e (d+e x)}",1,"-((a + b*ArcCosh[c*x])/(e*(d + e*x))) + (2*b*c*ArcTanh[(Sqrt[c*d + e]*Sqrt[1 + c*x])/(Sqrt[c*d - e]*Sqrt[-1 + c*x])])/(Sqrt[c*d - e]*e*Sqrt[c*d + e])","A",3,3,16,0.1875,1,"{5802, 93, 208}"
19,1,138,0,0.1019198,"\int \frac{a+b \cosh ^{-1}(c x)}{(d+e x)^3} \, dx","Int[(a + b*ArcCosh[c*x])/(d + e*x)^3,x]","-\frac{a+b \cosh ^{-1}(c x)}{2 e (d+e x)^2}-\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 \left(c^2 d^2-e^2\right) (d+e x)}+\frac{b c^3 d \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{e (c d-e)^{3/2} (c d+e)^{3/2}}","-\frac{a+b \cosh ^{-1}(c x)}{2 e (d+e x)^2}-\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 \left(c^2 d^2-e^2\right) (d+e x)}+\frac{b c^3 d \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{e (c d-e)^{3/2} (c d+e)^{3/2}}",1,"-(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*(c^2*d^2 - e^2)*(d + e*x)) - (a + b*ArcCosh[c*x])/(2*e*(d + e*x)^2) + (b*c^3*d*ArcTanh[(Sqrt[c*d + e]*Sqrt[1 + c*x])/(Sqrt[c*d - e]*Sqrt[-1 + c*x])])/((c*d - e)^(3/2)*e*(c*d + e)^(3/2))","A",4,4,16,0.2500,1,"{5802, 96, 93, 208}"
20,1,202,0,0.1641905,"\int \frac{a+b \cosh ^{-1}(c x)}{(d+e x)^4} \, dx","Int[(a + b*ArcCosh[c*x])/(d + e*x)^4,x]","-\frac{a+b \cosh ^{-1}(c x)}{3 e (d+e x)^3}-\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{6 \left(c^2 d^2-e^2\right) (d+e x)^2}+\frac{b c^3 \left(2 c^2 d^2+e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{3 e (c d-e)^{5/2} (c d+e)^{5/2}}-\frac{b c^3 d \sqrt{c x-1} \sqrt{c x+1}}{2 (c d-e)^2 (c d+e)^2 (d+e x)}","-\frac{a+b \cosh ^{-1}(c x)}{3 e (d+e x)^3}-\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{6 \left(c^2 d^2-e^2\right) (d+e x)^2}+\frac{b c^3 \left(2 c^2 d^2+e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{3 e (c d-e)^{5/2} (c d+e)^{5/2}}-\frac{b c^3 d \sqrt{c x-1} \sqrt{c x+1}}{2 (c d-e)^2 (c d+e)^2 (d+e x)}",1,"-(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*(c^2*d^2 - e^2)*(d + e*x)^2) - (b*c^3*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*(c*d - e)^2*(c*d + e)^2*(d + e*x)) - (a + b*ArcCosh[c*x])/(3*e*(d + e*x)^3) + (b*c^3*(2*c^2*d^2 + e^2)*ArcTanh[(Sqrt[c*d + e]*Sqrt[1 + c*x])/(Sqrt[c*d - e]*Sqrt[-1 + c*x])])/(3*(c*d - e)^(5/2)*e*(c*d + e)^(5/2))","A",6,6,16,0.3750,1,"{5802, 103, 151, 12, 93, 208}"
21,1,398,0,1.6890633,"\int (d+e x)^3 \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)^3*(a + b*ArcCosh[c*x])^2,x]","-\frac{3 d^2 e \left(a+b \cosh ^{-1}(c x)\right)^2}{4 c^2}-\frac{4 b d e^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^3}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{32 c^4}-\frac{3 b e^3 x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{16 c^3}-\frac{d^4 \left(a+b \cosh ^{-1}(c x)\right)^2}{4 e}-\frac{3 b d^2 e x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{2 c}-\frac{2 b d^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}-\frac{2 b d e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c}+\frac{(d+e x)^4 \left(a+b \cosh ^{-1}(c x)\right)^2}{4 e}-\frac{b e^3 x^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{8 c}+\frac{4 b^2 d e^2 x}{3 c^2}+\frac{3 b^2 e^3 x^2}{32 c^2}+\frac{3}{4} b^2 d^2 e x^2+2 b^2 d^3 x+\frac{2}{9} b^2 d e^2 x^3+\frac{1}{32} b^2 e^3 x^4","-\frac{3 d^2 e \left(a+b \cosh ^{-1}(c x)\right)^2}{4 c^2}-\frac{4 b d e^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^3}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{32 c^4}-\frac{3 b e^3 x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{16 c^3}-\frac{d^4 \left(a+b \cosh ^{-1}(c x)\right)^2}{4 e}-\frac{3 b d^2 e x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{2 c}-\frac{2 b d^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}-\frac{2 b d e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c}+\frac{(d+e x)^4 \left(a+b \cosh ^{-1}(c x)\right)^2}{4 e}-\frac{b e^3 x^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{8 c}+\frac{4 b^2 d e^2 x}{3 c^2}+\frac{3 b^2 e^3 x^2}{32 c^2}+\frac{3}{4} b^2 d^2 e x^2+2 b^2 d^3 x+\frac{2}{9} b^2 d e^2 x^3+\frac{1}{32} b^2 e^3 x^4",1,"2*b^2*d^3*x + (4*b^2*d*e^2*x)/(3*c^2) + (3*b^2*d^2*e*x^2)/4 + (3*b^2*e^3*x^2)/(32*c^2) + (2*b^2*d*e^2*x^3)/9 + (b^2*e^3*x^4)/32 - (2*b*d^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/c - (4*b*d*e^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*c^3) - (3*b*d^2*e*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(2*c) - (3*b*e^3*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(16*c^3) - (2*b*d*e^2*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*c) - (b*e^3*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(8*c) - (d^4*(a + b*ArcCosh[c*x])^2)/(4*e) - (3*d^2*e*(a + b*ArcCosh[c*x])^2)/(4*c^2) - (3*e^3*(a + b*ArcCosh[c*x])^2)/(32*c^4) + ((d + e*x)^4*(a + b*ArcCosh[c*x])^2)/(4*e)","A",18,7,18,0.3889,1,"{5802, 5822, 5676, 5718, 8, 5759, 30}"
22,1,259,0,1.1483811,"\int (d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)^2*(a + b*ArcCosh[c*x])^2,x]","-\frac{d e \left(a+b \cosh ^{-1}(c x)\right)^2}{2 c^2}-\frac{4 b e^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{9 c^3}-\frac{d^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 e}-\frac{2 b d^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}-\frac{b d e x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}+\frac{(d+e x)^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 e}-\frac{2 b e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{9 c}+\frac{4 b^2 e^2 x}{9 c^2}+2 b^2 d^2 x+\frac{1}{2} b^2 d e x^2+\frac{2}{27} b^2 e^2 x^3","-\frac{d e \left(a+b \cosh ^{-1}(c x)\right)^2}{2 c^2}-\frac{4 b e^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{9 c^3}-\frac{d^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 e}-\frac{2 b d^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}-\frac{b d e x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}+\frac{(d+e x)^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 e}-\frac{2 b e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{9 c}+\frac{4 b^2 e^2 x}{9 c^2}+2 b^2 d^2 x+\frac{1}{2} b^2 d e x^2+\frac{2}{27} b^2 e^2 x^3",1,"2*b^2*d^2*x + (4*b^2*e^2*x)/(9*c^2) + (b^2*d*e*x^2)/2 + (2*b^2*e^2*x^3)/27 - (2*b*d^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/c - (4*b*e^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(9*c^3) - (b*d*e*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/c - (2*b*e^2*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(9*c) - (d^3*(a + b*ArcCosh[c*x])^2)/(3*e) - (d*e*(a + b*ArcCosh[c*x])^2)/(2*c^2) + ((d + e*x)^3*(a + b*ArcCosh[c*x])^2)/(3*e)","A",13,7,18,0.3889,1,"{5802, 5822, 5676, 5718, 8, 5759, 30}"
23,1,150,0,0.7562424,"\int (d+e x) \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)*(a + b*ArcCosh[c*x])^2,x]","-\frac{e \left(a+b \cosh ^{-1}(c x)\right)^2}{4 c^2}-\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{2 e}+\frac{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{2 e}-\frac{2 b d \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}-\frac{b e x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{2 c}+2 b^2 d x+\frac{1}{4} b^2 e x^2","-\frac{e \left(a+b \cosh ^{-1}(c x)\right)^2}{4 c^2}-\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{2 e}+\frac{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{2 e}-\frac{2 b d \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}-\frac{b e x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{2 c}+2 b^2 d x+\frac{1}{4} b^2 e x^2",1,"2*b^2*d*x + (b^2*e*x^2)/4 - (2*b*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/c - (b*e*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(2*c) - (d^2*(a + b*ArcCosh[c*x])^2)/(2*e) - (e*(a + b*ArcCosh[c*x])^2)/(4*c^2) + ((d + e*x)^2*(a + b*ArcCosh[c*x])^2)/(2*e)","A",9,7,16,0.4375,1,"{5802, 5822, 5676, 5718, 8, 5759, 30}"
24,1,303,0,0.4563475,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{d+e x} \, dx","Int[(a + b*ArcCosh[c*x])^2/(d + e*x),x]","\frac{2 b \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{2 b \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}-\frac{2 b^2 \text{PolyLog}\left(3,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}-\frac{2 b^2 \text{PolyLog}\left(3,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^3}{3 b e}","\frac{2 b \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{2 b \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}-\frac{2 b^2 \text{PolyLog}\left(3,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}-\frac{2 b^2 \text{PolyLog}\left(3,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^3}{3 b e}",1,"-(a + b*ArcCosh[c*x])^3/(3*b*e) + ((a + b*ArcCosh[c*x])^2*Log[1 + (e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2])])/e + ((a + b*ArcCosh[c*x])^2*Log[1 + (e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2])])/e + (2*b*(a + b*ArcCosh[c*x])*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2]))])/e + (2*b*(a + b*ArcCosh[c*x])*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2]))])/e - (2*b^2*PolyLog[3, -((e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2]))])/e - (2*b^2*PolyLog[3, -((e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2]))])/e","A",10,6,18,0.3333,1,"{5800, 5562, 2190, 2531, 2282, 6589}"
25,1,279,0,0.6101228,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{(d+e x)^2} \, dx","Int[(a + b*ArcCosh[c*x])^2/(d + e*x)^2,x]","\frac{2 b^2 c \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{2 b^2 c \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e \sqrt{c^2 d^2-e^2}}+\frac{2 b c \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{2 b c \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{e (d+e x)}","\frac{2 b^2 c \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{2 b^2 c \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e \sqrt{c^2 d^2-e^2}}+\frac{2 b c \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{2 b c \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{e (d+e x)}",1,"-((a + b*ArcCosh[c*x])^2/(e*(d + e*x))) + (2*b*c*(a + b*ArcCosh[c*x])*Log[1 + (e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2])])/(e*Sqrt[c^2*d^2 - e^2]) - (2*b*c*(a + b*ArcCosh[c*x])*Log[1 + (e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2])])/(e*Sqrt[c^2*d^2 - e^2]) + (2*b^2*c*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2]))])/(e*Sqrt[c^2*d^2 - e^2]) - (2*b^2*c*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2]))])/(e*Sqrt[c^2*d^2 - e^2])","A",10,7,18,0.3889,1,"{5802, 5832, 3320, 2264, 2190, 2279, 2391}"
26,1,380,0,0.7466475,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{(d+e x)^3} \, dx","Int[(a + b*ArcCosh[c*x])^2/(d + e*x)^3,x]","\frac{b^2 c^3 d \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b^2 c^3 d \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b c \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{\left(c^2 d^2-e^2\right) (d+e x)}+\frac{b c^3 d \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b c^3 d \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 e (d+e x)^2}+\frac{b^2 c^2 \log (d+e x)}{e \left(c^2 d^2-e^2\right)}","\frac{b^2 c^3 d \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b^2 c^3 d \text{PolyLog}\left(2,-\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b c \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{\left(c^2 d^2-e^2\right) (d+e x)}+\frac{b c^3 d \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b c^3 d \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 e (d+e x)^2}+\frac{b^2 c^2 \log (d+e x)}{e \left(c^2 d^2-e^2\right)}",1,"-((b*c*Sqrt[-((1 - c*x)/(1 + c*x))]*(1 + c*x)*(a + b*ArcCosh[c*x]))/((c^2*d^2 - e^2)*(d + e*x))) - (a + b*ArcCosh[c*x])^2/(2*e*(d + e*x)^2) + (b*c^3*d*(a + b*ArcCosh[c*x])*Log[1 + (e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2])])/(e*(c^2*d^2 - e^2)^(3/2)) - (b*c^3*d*(a + b*ArcCosh[c*x])*Log[1 + (e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2])])/(e*(c^2*d^2 - e^2)^(3/2)) + (b^2*c^2*Log[d + e*x])/(e*(c^2*d^2 - e^2)) + (b^2*c^3*d*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2]))])/(e*(c^2*d^2 - e^2)^(3/2)) - (b^2*c^3*d*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2]))])/(e*(c^2*d^2 - e^2)^(3/2))","A",13,10,18,0.5556,1,"{5802, 5832, 3324, 3320, 2264, 2190, 2279, 2391, 2668, 31}"
27,1,394,0,1.1702515,"\int \frac{(d+e x)^3}{a+b \cosh ^{-1}(c x)} \, dx","Int[(d + e*x)^3/(a + b*ArcCosh[c*x]),x]","-\frac{3 d^2 e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c^2}-\frac{3 d e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^3}-\frac{3 d e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b c^3}-\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{4 b c^4}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{8 b c^4}+\frac{3 d^2 e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c^2}+\frac{3 d e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^3}+\frac{3 d e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b c^3}+\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{4 b c^4}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{8 b c^4}-\frac{d^3 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}+\frac{d^3 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}","-\frac{3 d^2 e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c^2}-\frac{3 d e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^3}-\frac{3 d e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b c^3}-\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{4 b c^4}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{8 b c^4}+\frac{3 d^2 e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c^2}+\frac{3 d e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^3}+\frac{3 d e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b c^3}+\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{4 b c^4}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{8 b c^4}-\frac{d^3 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}+\frac{d^3 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}",1,"-((d^3*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b])/(b*c)) - (3*d*e^2*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b])/(4*b*c^3) - (3*d^2*e*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]]*Sinh[(2*a)/b])/(2*b*c^2) - (e^3*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]]*Sinh[(2*a)/b])/(4*b*c^4) - (3*d*e^2*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]]*Sinh[(3*a)/b])/(4*b*c^3) - (e^3*CoshIntegral[(4*a)/b + 4*ArcCosh[c*x]]*Sinh[(4*a)/b])/(8*b*c^4) + (d^3*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(b*c) + (3*d*e^2*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(4*b*c^3) + (3*d^2*e*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(2*b*c^2) + (e^3*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(4*b*c^4) + (3*d*e^2*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(4*b*c^3) + (e^3*Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(8*b*c^4)","A",27,7,18,0.3889,1,"{5806, 6742, 3303, 3298, 3301, 5448, 12}"
28,1,245,0,0.7042728,"\int \frac{(d+e x)^2}{a+b \cosh ^{-1}(c x)} \, dx","Int[(d + e*x)^2/(a + b*ArcCosh[c*x]),x]","-\frac{d e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b c^2}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^3}-\frac{e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b c^3}+\frac{d e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b c^2}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^3}+\frac{e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b c^3}-\frac{d^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}+\frac{d^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}","-\frac{d e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b c^2}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^3}-\frac{e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b c^3}+\frac{d e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b c^2}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^3}+\frac{e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b c^3}-\frac{d^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}+\frac{d^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}",1,"-((d^2*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b])/(b*c)) - (e^2*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b])/(4*b*c^3) - (d*e*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]]*Sinh[(2*a)/b])/(b*c^2) - (e^2*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]]*Sinh[(3*a)/b])/(4*b*c^3) + (d^2*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(b*c) + (e^2*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(4*b*c^3) + (d*e*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(b*c^2) + (e^2*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(4*b*c^3)","A",17,6,18,0.3333,1,"{5806, 6742, 3303, 3298, 3301, 5448}"
29,1,116,0,0.3375147,"\int \frac{d+e x}{a+b \cosh ^{-1}(c x)} \, dx","Int[(d + e*x)/(a + b*ArcCosh[c*x]),x]","-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c^2}+\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c^2}-\frac{d \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}+\frac{d \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}","-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c^2}+\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c^2}-\frac{d \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}+\frac{d \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}",1,"-((d*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b])/(b*c)) - (e*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]]*Sinh[(2*a)/b])/(2*b*c^2) + (d*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(b*c) + (e*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(2*b*c^2)","A",11,7,16,0.4375,1,"{5806, 6742, 3303, 3298, 3301, 5448, 12}"
30,0,0,0,0.0336285,"\int \frac{1}{(d+e x) \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x)*(a + b*ArcCosh[c*x])),x]","\int \frac{1}{(d+e x) \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{(d+e x) \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d + e*x)*(a + b*ArcCosh[c*x])), x]","A",0,0,0,0,-1,"{}"
31,0,0,0,0.031335,"\int \frac{1}{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x)^2*(a + b*ArcCosh[c*x])),x]","\int \frac{1}{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d + e*x)^2*(a + b*ArcCosh[c*x])), x]","A",0,0,0,0,-1,"{}"
32,1,366,0,0.7508568,"\int \frac{(d+e x)^2}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(d + e*x)^2/(a + b*ArcCosh[c*x])^2,x]","\frac{2 d e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b^2 c^2}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b^2 c^3}+\frac{3 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b^2 c^3}-\frac{2 d e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b^2 c^2}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b^2 c^3}-\frac{3 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b^2 c^3}+\frac{d^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b^2 c}-\frac{d^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b^2 c}-\frac{d^2 \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}-\frac{2 d e x \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}-\frac{e^2 x^2 \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}","\frac{2 d e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b^2 c^2}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b^2 c^3}+\frac{3 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^3}-\frac{2 d e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b^2 c^2}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b^2 c^3}-\frac{3 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^3}+\frac{d^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{d^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{d^2 \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}-\frac{2 d e x \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}-\frac{e^2 x^2 \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}",1,"-((d^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*(a + b*ArcCosh[c*x]))) - (2*d*e*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*(a + b*ArcCosh[c*x])) - (e^2*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*(a + b*ArcCosh[c*x])) + (d^2*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(b^2*c) + (e^2*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(4*b^2*c^3) + (2*d*e*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(b^2*c^2) + (3*e^2*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(4*b^2*c^3) - (d^2*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(b^2*c) - (e^2*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(4*b^2*c^3) - (2*d*e*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(b^2*c^2) - (3*e^2*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(4*b^2*c^3)","A",19,7,18,0.3889,1,"{5804, 5656, 5781, 3303, 3298, 3301, 5666}"
33,1,186,0,0.4745962,"\int \frac{d+e x}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(d + e*x)/(a + b*ArcCosh[c*x])^2,x]","\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b^2 c^2}-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b^2 c^2}+\frac{d \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b^2 c}-\frac{d \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b^2 c}-\frac{d \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}-\frac{e x \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}","\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b^2 c^2}-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b^2 c^2}+\frac{d \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{d \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{d \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}-\frac{e x \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}",1,"-((d*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*(a + b*ArcCosh[c*x]))) - (e*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*(a + b*ArcCosh[c*x])) + (d*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(b^2*c) + (e*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(b^2*c^2) - (d*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(b^2*c) - (e*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(b^2*c^2)","A",11,7,16,0.4375,1,"{5804, 5656, 5781, 3303, 3298, 3301, 5666}"
34,0,0,0,0.0314219,"\int \frac{1}{(d+e x) \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[1/((d + e*x)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{1}{(d+e x) \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{(d+e x) \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/((d + e*x)*(a + b*ArcCosh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
35,0,0,0,0.0315763,"\int \frac{1}{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[1/((d + e*x)^2*(a + b*ArcCosh[c*x])^2),x]","\int \frac{1}{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/((d + e*x)^2*(a + b*ArcCosh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
36,0,0,0,0.3834437,"\int (d+e x)^m \left(a+b \cosh ^{-1}(c x)\right)^3 \, dx","Int[(d + e*x)^m*(a + b*ArcCosh[c*x])^3,x]","\int (d+e x)^m \left(a+b \cosh ^{-1}(c x)\right)^3 \, dx","\frac{(d+e x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{e (m+1)}-\frac{3 b c \text{Int}\left(\frac{(d+e x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{c x-1} \sqrt{c x+1}},x\right)}{e (m+1)}",0,"((d + e*x)^(1 + m)*(a + b*ArcCosh[c*x])^3)/(e*(1 + m)) - (3*b*c*Defer[Int][((d + e*x)^(1 + m)*(a + b*ArcCosh[c*x])^2)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/(e*(1 + m))","A",0,0,0,0,-1,"{}"
37,0,0,0,0.3217077,"\int (d+e x)^m \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)^m*(a + b*ArcCosh[c*x])^2,x]","\int (d+e x)^m \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","\frac{(d+e x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{e (m+1)}-\frac{2 b c \text{Int}\left(\frac{(d+e x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}},x\right)}{e (m+1)}",0,"((d + e*x)^(1 + m)*(a + b*ArcCosh[c*x])^2)/(e*(1 + m)) - (2*b*c*Defer[Int][((d + e*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/(e*(1 + m))","A",0,0,0,0,-1,"{}"
38,1,125,0,0.0811056,"\int (d+e x)^m \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(d + e*x)^m*(a + b*ArcCosh[c*x]),x]","\frac{(d+e x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{e (m+1)}-\frac{\sqrt{2} b \sqrt{c x-1} (c d+e) (d+e x)^m \left(\frac{c (d+e x)}{c d+e}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m-1;\frac{3}{2};\frac{1}{2} (1-c x),\frac{e (1-c x)}{c d+e}\right)}{c e (m+1)}","\frac{(d+e x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{e (m+1)}-\frac{\sqrt{2} b \sqrt{c x-1} (c d+e) (d+e x)^m \left(\frac{c (d+e x)}{c d+e}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m-1;\frac{3}{2};\frac{1}{2} (1-c x),\frac{e (1-c x)}{c d+e}\right)}{c e (m+1)}",1,"-((Sqrt[2]*b*(c*d + e)*Sqrt[-1 + c*x]*(d + e*x)^m*AppellF1[1/2, 1/2, -1 - m, 3/2, (1 - c*x)/2, (e*(1 - c*x))/(c*d + e)])/(c*e*(1 + m)*((c*(d + e*x))/(c*d + e))^m)) + ((d + e*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(e*(1 + m))","A",3,3,16,0.1875,1,"{5802, 139, 138}"
39,0,0,0,0.0300302,"\int \frac{(d+e x)^m}{a+b \cosh ^{-1}(c x)} \, dx","Int[(d + e*x)^m/(a + b*ArcCosh[c*x]),x]","\int \frac{(d+e x)^m}{a+b \cosh ^{-1}(c x)} \, dx","\text{Int}\left(\frac{(d+e x)^m}{a+b \cosh ^{-1}(c x)},x\right)",0,"Defer[Int][(d + e*x)^m/(a + b*ArcCosh[c*x]), x]","A",0,0,0,0,-1,"{}"
40,0,0,0,0.0286618,"\int \frac{(d+e x)^m}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(d + e*x)^m/(a + b*ArcCosh[c*x])^2,x]","\int \frac{(d+e x)^m}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{(d+e x)^m}{\left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(d + e*x)^m/(a + b*ArcCosh[c*x])^2, x]","A",0,0,0,0,-1,"{}"
41,1,370,0,0.4592958,"\int \left(c+d x^2\right)^4 \cosh ^{-1}(a x) \, dx","Int[(c + d*x^2)^4*ArcCosh[a*x],x]","\frac{2 d^2 \left(1-a^2 x^2\right)^3 \left(63 a^4 c^2+90 a^2 c d+35 d^2\right)}{525 a^9 \sqrt{a x-1} \sqrt{a x+1}}-\frac{4 d \left(1-a^2 x^2\right)^2 \left(189 a^4 c^2 d+105 a^6 c^3+135 a^2 c d^2+35 d^3\right)}{945 a^9 \sqrt{a x-1} \sqrt{a x+1}}+\frac{\left(1-a^2 x^2\right) \left(378 a^4 c^2 d^2+420 a^6 c^3 d+315 a^8 c^4+180 a^2 c d^3+35 d^4\right)}{315 a^9 \sqrt{a x-1} \sqrt{a x+1}}-\frac{4 d^3 \left(1-a^2 x^2\right)^4 \left(9 a^2 c+7 d\right)}{441 a^9 \sqrt{a x-1} \sqrt{a x+1}}+\frac{d^4 \left(1-a^2 x^2\right)^5}{81 a^9 \sqrt{a x-1} \sqrt{a x+1}}+\frac{6}{5} c^2 d^2 x^5 \cosh ^{-1}(a x)+\frac{4}{3} c^3 d x^3 \cosh ^{-1}(a x)+c^4 x \cosh ^{-1}(a x)+\frac{4}{7} c d^3 x^7 \cosh ^{-1}(a x)+\frac{1}{9} d^4 x^9 \cosh ^{-1}(a x)","\frac{2 d^2 \left(1-a^2 x^2\right)^3 \left(63 a^4 c^2+90 a^2 c d+35 d^2\right)}{525 a^9 \sqrt{a x-1} \sqrt{a x+1}}-\frac{4 d \left(1-a^2 x^2\right)^2 \left(189 a^4 c^2 d+105 a^6 c^3+135 a^2 c d^2+35 d^3\right)}{945 a^9 \sqrt{a x-1} \sqrt{a x+1}}+\frac{\left(1-a^2 x^2\right) \left(378 a^4 c^2 d^2+420 a^6 c^3 d+315 a^8 c^4+180 a^2 c d^3+35 d^4\right)}{315 a^9 \sqrt{a x-1} \sqrt{a x+1}}-\frac{4 d^3 \left(1-a^2 x^2\right)^4 \left(9 a^2 c+7 d\right)}{441 a^9 \sqrt{a x-1} \sqrt{a x+1}}+\frac{d^4 \left(1-a^2 x^2\right)^5}{81 a^9 \sqrt{a x-1} \sqrt{a x+1}}+\frac{6}{5} c^2 d^2 x^5 \cosh ^{-1}(a x)+\frac{4}{3} c^3 d x^3 \cosh ^{-1}(a x)+c^4 x \cosh ^{-1}(a x)+\frac{4}{7} c d^3 x^7 \cosh ^{-1}(a x)+\frac{1}{9} d^4 x^9 \cosh ^{-1}(a x)",1,"((315*a^8*c^4 + 420*a^6*c^3*d + 378*a^4*c^2*d^2 + 180*a^2*c*d^3 + 35*d^4)*(1 - a^2*x^2))/(315*a^9*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (4*d*(105*a^6*c^3 + 189*a^4*c^2*d + 135*a^2*c*d^2 + 35*d^3)*(1 - a^2*x^2)^2)/(945*a^9*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (2*d^2*(63*a^4*c^2 + 90*a^2*c*d + 35*d^2)*(1 - a^2*x^2)^3)/(525*a^9*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (4*d^3*(9*a^2*c + 7*d)*(1 - a^2*x^2)^4)/(441*a^9*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (d^4*(1 - a^2*x^2)^5)/(81*a^9*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + c^4*x*ArcCosh[a*x] + (4*c^3*d*x^3*ArcCosh[a*x])/3 + (6*c^2*d^2*x^5*ArcCosh[a*x])/5 + (4*c*d^3*x^7*ArcCosh[a*x])/7 + (d^4*x^9*ArcCosh[a*x])/9","A",6,6,14,0.4286,1,"{194, 5705, 12, 1610, 1799, 1850}"
42,1,267,0,0.3501821,"\int \left(c+d x^2\right)^3 \cosh ^{-1}(a x) \, dx","Int[(c + d*x^2)^3*ArcCosh[a*x],x]","-\frac{d \left(1-a^2 x^2\right)^2 \left(35 a^4 c^2+42 a^2 c d+15 d^2\right)}{105 a^7 \sqrt{a x-1} \sqrt{a x+1}}+\frac{\left(1-a^2 x^2\right) \left(35 a^4 c^2 d+35 a^6 c^3+21 a^2 c d^2+5 d^3\right)}{35 a^7 \sqrt{a x-1} \sqrt{a x+1}}+\frac{3 d^2 \left(1-a^2 x^2\right)^3 \left(7 a^2 c+5 d\right)}{175 a^7 \sqrt{a x-1} \sqrt{a x+1}}-\frac{d^3 \left(1-a^2 x^2\right)^4}{49 a^7 \sqrt{a x-1} \sqrt{a x+1}}+c^2 d x^3 \cosh ^{-1}(a x)+c^3 x \cosh ^{-1}(a x)+\frac{3}{5} c d^2 x^5 \cosh ^{-1}(a x)+\frac{1}{7} d^3 x^7 \cosh ^{-1}(a x)","-\frac{d \left(1-a^2 x^2\right)^2 \left(35 a^4 c^2+42 a^2 c d+15 d^2\right)}{105 a^7 \sqrt{a x-1} \sqrt{a x+1}}+\frac{\left(1-a^2 x^2\right) \left(35 a^4 c^2 d+35 a^6 c^3+21 a^2 c d^2+5 d^3\right)}{35 a^7 \sqrt{a x-1} \sqrt{a x+1}}+\frac{3 d^2 \left(1-a^2 x^2\right)^3 \left(7 a^2 c+5 d\right)}{175 a^7 \sqrt{a x-1} \sqrt{a x+1}}-\frac{d^3 \left(1-a^2 x^2\right)^4}{49 a^7 \sqrt{a x-1} \sqrt{a x+1}}+c^2 d x^3 \cosh ^{-1}(a x)+c^3 x \cosh ^{-1}(a x)+\frac{3}{5} c d^2 x^5 \cosh ^{-1}(a x)+\frac{1}{7} d^3 x^7 \cosh ^{-1}(a x)",1,"((35*a^6*c^3 + 35*a^4*c^2*d + 21*a^2*c*d^2 + 5*d^3)*(1 - a^2*x^2))/(35*a^7*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (d*(35*a^4*c^2 + 42*a^2*c*d + 15*d^2)*(1 - a^2*x^2)^2)/(105*a^7*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (3*d^2*(7*a^2*c + 5*d)*(1 - a^2*x^2)^3)/(175*a^7*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (d^3*(1 - a^2*x^2)^4)/(49*a^7*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + c^3*x*ArcCosh[a*x] + c^2*d*x^3*ArcCosh[a*x] + (3*c*d^2*x^5*ArcCosh[a*x])/5 + (d^3*x^7*ArcCosh[a*x])/7","A",6,6,14,0.4286,1,"{194, 5705, 12, 1610, 1799, 1850}"
43,1,181,0,0.1886723,"\int \left(c+d x^2\right)^2 \cosh ^{-1}(a x) \, dx","Int[(c + d*x^2)^2*ArcCosh[a*x],x]","\frac{\left(1-a^2 x^2\right) \left(15 a^4 c^2+10 a^2 c d+3 d^2\right)}{15 a^5 \sqrt{a x-1} \sqrt{a x+1}}-\frac{2 d \left(1-a^2 x^2\right)^2 \left(5 a^2 c+3 d\right)}{45 a^5 \sqrt{a x-1} \sqrt{a x+1}}+\frac{d^2 \left(1-a^2 x^2\right)^3}{25 a^5 \sqrt{a x-1} \sqrt{a x+1}}+c^2 x \cosh ^{-1}(a x)+\frac{2}{3} c d x^3 \cosh ^{-1}(a x)+\frac{1}{5} d^2 x^5 \cosh ^{-1}(a x)","\frac{\left(1-a^2 x^2\right) \left(15 a^4 c^2+10 a^2 c d+3 d^2\right)}{15 a^5 \sqrt{a x-1} \sqrt{a x+1}}-\frac{2 d \left(1-a^2 x^2\right)^2 \left(5 a^2 c+3 d\right)}{45 a^5 \sqrt{a x-1} \sqrt{a x+1}}+\frac{d^2 \left(1-a^2 x^2\right)^3}{25 a^5 \sqrt{a x-1} \sqrt{a x+1}}+c^2 x \cosh ^{-1}(a x)+\frac{2}{3} c d x^3 \cosh ^{-1}(a x)+\frac{1}{5} d^2 x^5 \cosh ^{-1}(a x)",1,"((15*a^4*c^2 + 10*a^2*c*d + 3*d^2)*(1 - a^2*x^2))/(15*a^5*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (2*d*(5*a^2*c + 3*d)*(1 - a^2*x^2)^2)/(45*a^5*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (d^2*(1 - a^2*x^2)^3)/(25*a^5*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + c^2*x*ArcCosh[a*x] + (2*c*d*x^3*ArcCosh[a*x])/3 + (d^2*x^5*ArcCosh[a*x])/5","A",6,6,14,0.4286,1,"{194, 5705, 12, 520, 1247, 698}"
44,1,84,0,0.0710306,"\int \left(c+d x^2\right) \cosh ^{-1}(a x) \, dx","Int[(c + d*x^2)*ArcCosh[a*x],x]","-\frac{\sqrt{a x-1} \sqrt{a x+1} \left(9 a^2 c+2 d\right)}{9 a^3}+c x \cosh ^{-1}(a x)-\frac{d x^2 \sqrt{a x-1} \sqrt{a x+1}}{9 a}+\frac{1}{3} d x^3 \cosh ^{-1}(a x)","-\frac{\sqrt{a x-1} \sqrt{a x+1} \left(9 a^2 c+2 d\right)}{9 a^3}+c x \cosh ^{-1}(a x)-\frac{d x^2 \sqrt{a x-1} \sqrt{a x+1}}{9 a}+\frac{1}{3} d x^3 \cosh ^{-1}(a x)",1,"-((9*a^2*c + 2*d)*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(9*a^3) - (d*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(9*a) + c*x*ArcCosh[a*x] + (d*x^3*ArcCosh[a*x])/3","A",3,3,12,0.2500,1,"{5705, 460, 74}"
45,1,481,0,0.7576932,"\int \frac{\cosh ^{-1}(a x)}{c+d x^2} \, dx","Int[ArcCosh[a*x]/(c + d*x^2),x]","-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}\right)}{2 \sqrt{-c} \sqrt{d}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}\right)}{2 \sqrt{-c} \sqrt{d}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}\right)}{2 \sqrt{-c} \sqrt{d}}+\frac{\cosh ^{-1}(a x) \log \left(1-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\cosh ^{-1}(a x) \log \left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}+1\right)}{2 \sqrt{-c} \sqrt{d}}+\frac{\cosh ^{-1}(a x) \log \left(1-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\cosh ^{-1}(a x) \log \left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}+1\right)}{2 \sqrt{-c} \sqrt{d}}","-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}\right)}{2 \sqrt{-c} \sqrt{d}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}\right)}{2 \sqrt{-c} \sqrt{d}}+\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}\right)}{2 \sqrt{-c} \sqrt{d}}+\frac{\cosh ^{-1}(a x) \log \left(1-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\cosh ^{-1}(a x) \log \left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}+1\right)}{2 \sqrt{-c} \sqrt{d}}+\frac{\cosh ^{-1}(a x) \log \left(1-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\cosh ^{-1}(a x) \log \left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}+1\right)}{2 \sqrt{-c} \sqrt{d}}",1,"(ArcCosh[a*x]*Log[1 - (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] - Sqrt[-(a^2*c) - d])])/(2*Sqrt[-c]*Sqrt[d]) - (ArcCosh[a*x]*Log[1 + (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] - Sqrt[-(a^2*c) - d])])/(2*Sqrt[-c]*Sqrt[d]) + (ArcCosh[a*x]*Log[1 - (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] + Sqrt[-(a^2*c) - d])])/(2*Sqrt[-c]*Sqrt[d]) - (ArcCosh[a*x]*Log[1 + (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] + Sqrt[-(a^2*c) - d])])/(2*Sqrt[-c]*Sqrt[d]) - PolyLog[2, -((Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] - Sqrt[-(a^2*c) - d]))]/(2*Sqrt[-c]*Sqrt[d]) + PolyLog[2, (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] - Sqrt[-(a^2*c) - d])]/(2*Sqrt[-c]*Sqrt[d]) - PolyLog[2, -((Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] + Sqrt[-(a^2*c) - d]))]/(2*Sqrt[-c]*Sqrt[d]) + PolyLog[2, (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] + Sqrt[-(a^2*c) - d])]/(2*Sqrt[-c]*Sqrt[d])","A",18,6,14,0.4286,1,"{5707, 5800, 5562, 2190, 2279, 2391}"
46,1,774,0,1.1014022,"\int \frac{\cosh ^{-1}(a x)}{\left(c+d x^2\right)^2} \, dx","Int[ArcCosh[a*x]/(c + d*x^2)^2,x]","\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}\right)}{4 (-c)^{3/2} \sqrt{d}}-\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}\right)}{4 (-c)^{3/2} \sqrt{d}}+\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}\right)}{4 (-c)^{3/2} \sqrt{d}}-\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}\right)}{4 (-c)^{3/2} \sqrt{d}}-\frac{\cosh ^{-1}(a x) \log \left(1-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}\right)}{4 (-c)^{3/2} \sqrt{d}}+\frac{\cosh ^{-1}(a x) \log \left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}+1\right)}{4 (-c)^{3/2} \sqrt{d}}-\frac{\cosh ^{-1}(a x) \log \left(1-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}\right)}{4 (-c)^{3/2} \sqrt{d}}+\frac{\cosh ^{-1}(a x) \log \left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}+1\right)}{4 (-c)^{3/2} \sqrt{d}}-\frac{\cosh ^{-1}(a x)}{4 c \sqrt{d} \left(\sqrt{-c}-\sqrt{d} x\right)}+\frac{\cosh ^{-1}(a x)}{4 c \sqrt{d} \left(\sqrt{-c}+\sqrt{d} x\right)}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{a x+1} \sqrt{a \sqrt{-c}-\sqrt{d}}}{\sqrt{a x-1} \sqrt{a \sqrt{-c}+\sqrt{d}}}\right)}{2 c \sqrt{d} \sqrt{a \sqrt{-c}-\sqrt{d}} \sqrt{a \sqrt{-c}+\sqrt{d}}}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{a x+1} \sqrt{a \sqrt{-c}+\sqrt{d}}}{\sqrt{a x-1} \sqrt{a \sqrt{-c}-\sqrt{d}}}\right)}{2 c \sqrt{d} \sqrt{a \sqrt{-c}-\sqrt{d}} \sqrt{a \sqrt{-c}+\sqrt{d}}}","\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}\right)}{4 (-c)^{3/2} \sqrt{d}}-\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}\right)}{4 (-c)^{3/2} \sqrt{d}}+\frac{\text{PolyLog}\left(2,-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}\right)}{4 (-c)^{3/2} \sqrt{d}}-\frac{\text{PolyLog}\left(2,\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}\right)}{4 (-c)^{3/2} \sqrt{d}}-\frac{\cosh ^{-1}(a x) \log \left(1-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}\right)}{4 (-c)^{3/2} \sqrt{d}}+\frac{\cosh ^{-1}(a x) \log \left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}+1\right)}{4 (-c)^{3/2} \sqrt{d}}-\frac{\cosh ^{-1}(a x) \log \left(1-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}\right)}{4 (-c)^{3/2} \sqrt{d}}+\frac{\cosh ^{-1}(a x) \log \left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}+1\right)}{4 (-c)^{3/2} \sqrt{d}}-\frac{\cosh ^{-1}(a x)}{4 c \sqrt{d} \left(\sqrt{-c}-\sqrt{d} x\right)}+\frac{\cosh ^{-1}(a x)}{4 c \sqrt{d} \left(\sqrt{-c}+\sqrt{d} x\right)}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{a x+1} \sqrt{a \sqrt{-c}-\sqrt{d}}}{\sqrt{a x-1} \sqrt{a \sqrt{-c}+\sqrt{d}}}\right)}{2 c \sqrt{d} \sqrt{a \sqrt{-c}-\sqrt{d}} \sqrt{a \sqrt{-c}+\sqrt{d}}}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{a x+1} \sqrt{a \sqrt{-c}+\sqrt{d}}}{\sqrt{a x-1} \sqrt{a \sqrt{-c}-\sqrt{d}}}\right)}{2 c \sqrt{d} \sqrt{a \sqrt{-c}-\sqrt{d}} \sqrt{a \sqrt{-c}+\sqrt{d}}}",1,"-ArcCosh[a*x]/(4*c*Sqrt[d]*(Sqrt[-c] - Sqrt[d]*x)) + ArcCosh[a*x]/(4*c*Sqrt[d]*(Sqrt[-c] + Sqrt[d]*x)) + (a*ArcTanh[(Sqrt[a*Sqrt[-c] - Sqrt[d]]*Sqrt[1 + a*x])/(Sqrt[a*Sqrt[-c] + Sqrt[d]]*Sqrt[-1 + a*x])])/(2*c*Sqrt[a*Sqrt[-c] - Sqrt[d]]*Sqrt[a*Sqrt[-c] + Sqrt[d]]*Sqrt[d]) - (a*ArcTanh[(Sqrt[a*Sqrt[-c] + Sqrt[d]]*Sqrt[1 + a*x])/(Sqrt[a*Sqrt[-c] - Sqrt[d]]*Sqrt[-1 + a*x])])/(2*c*Sqrt[a*Sqrt[-c] - Sqrt[d]]*Sqrt[a*Sqrt[-c] + Sqrt[d]]*Sqrt[d]) - (ArcCosh[a*x]*Log[1 - (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] - Sqrt[-(a^2*c) - d])])/(4*(-c)^(3/2)*Sqrt[d]) + (ArcCosh[a*x]*Log[1 + (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] - Sqrt[-(a^2*c) - d])])/(4*(-c)^(3/2)*Sqrt[d]) - (ArcCosh[a*x]*Log[1 - (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] + Sqrt[-(a^2*c) - d])])/(4*(-c)^(3/2)*Sqrt[d]) + (ArcCosh[a*x]*Log[1 + (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] + Sqrt[-(a^2*c) - d])])/(4*(-c)^(3/2)*Sqrt[d]) + PolyLog[2, -((Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] - Sqrt[-(a^2*c) - d]))]/(4*(-c)^(3/2)*Sqrt[d]) - PolyLog[2, (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] - Sqrt[-(a^2*c) - d])]/(4*(-c)^(3/2)*Sqrt[d]) + PolyLog[2, -((Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] + Sqrt[-(a^2*c) - d]))]/(4*(-c)^(3/2)*Sqrt[d]) - PolyLog[2, (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] + Sqrt[-(a^2*c) - d])]/(4*(-c)^(3/2)*Sqrt[d])","A",26,9,14,0.6429,1,"{5707, 5802, 93, 208, 5800, 5562, 2190, 2279, 2391}"
47,0,0,0,0.0313553,"\int \sqrt{c+d x^2} \cosh ^{-1}(a x) \, dx","Int[Sqrt[c + d*x^2]*ArcCosh[a*x],x]","\int \sqrt{c+d x^2} \cosh ^{-1}(a x) \, dx","\text{Int}\left(\cosh ^{-1}(a x) \sqrt{c+d x^2},x\right)",0,"Defer[Int][Sqrt[c + d*x^2]*ArcCosh[a*x], x]","A",0,0,0,0,-1,"{}"
48,0,0,0,0.0266791,"\int \frac{\cosh ^{-1}(a x)}{\sqrt{c+d x^2}} \, dx","Int[ArcCosh[a*x]/Sqrt[c + d*x^2],x]","\int \frac{\cosh ^{-1}(a x)}{\sqrt{c+d x^2}} \, dx","\text{Int}\left(\frac{\cosh ^{-1}(a x)}{\sqrt{c+d x^2}},x\right)",0,"Defer[Int][ArcCosh[a*x]/Sqrt[c + d*x^2], x]","A",0,0,0,0,-1,"{}"
49,1,96,0,0.193077,"\int \frac{\cosh ^{-1}(a x)}{\left(c+d x^2\right)^{3/2}} \, dx","Int[ArcCosh[a*x]/(c + d*x^2)^(3/2),x]","\frac{x \cosh ^{-1}(a x)}{c \sqrt{c+d x^2}}-\frac{\sqrt{a^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a^2 x^2-1}}{a \sqrt{c+d x^2}}\right)}{c \sqrt{d} \sqrt{a x-1} \sqrt{a x+1}}","\frac{x \cosh ^{-1}(a x)}{c \sqrt{c+d x^2}}-\frac{\sqrt{a^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a^2 x^2-1}}{a \sqrt{c+d x^2}}\right)}{c \sqrt{d} \sqrt{a x-1} \sqrt{a x+1}}",1,"(x*ArcCosh[a*x])/(c*Sqrt[c + d*x^2]) - (Sqrt[-1 + a^2*x^2]*ArcTanh[(Sqrt[d]*Sqrt[-1 + a^2*x^2])/(a*Sqrt[c + d*x^2])])/(c*Sqrt[d]*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",7,8,16,0.5000,1,"{191, 5705, 12, 519, 444, 63, 217, 206}"
50,1,180,0,0.175823,"\int \frac{\cosh ^{-1}(a x)}{\left(c+d x^2\right)^{5/2}} \, dx","Int[ArcCosh[a*x]/(c + d*x^2)^(5/2),x]","-\frac{2 \sqrt{a^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a^2 x^2-1}}{a \sqrt{c+d x^2}}\right)}{3 c^2 \sqrt{d} \sqrt{a x-1} \sqrt{a x+1}}+\frac{a \left(1-a^2 x^2\right)}{3 c \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right) \sqrt{c+d x^2}}+\frac{2 x \cosh ^{-1}(a x)}{3 c^2 \sqrt{c+d x^2}}+\frac{x \cosh ^{-1}(a x)}{3 c \left(c+d x^2\right)^{3/2}}","-\frac{2 \sqrt{a^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a^2 x^2-1}}{a \sqrt{c+d x^2}}\right)}{3 c^2 \sqrt{d} \sqrt{a x-1} \sqrt{a x+1}}+\frac{a \left(1-a^2 x^2\right)}{3 c \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right) \sqrt{c+d x^2}}+\frac{2 x \cosh ^{-1}(a x)}{3 c^2 \sqrt{c+d x^2}}+\frac{x \cosh ^{-1}(a x)}{3 c \left(c+d x^2\right)^{3/2}}",1,"(a*(1 - a^2*x^2))/(3*c*(a^2*c + d)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Sqrt[c + d*x^2]) + (x*ArcCosh[a*x])/(3*c*(c + d*x^2)^(3/2)) + (2*x*ArcCosh[a*x])/(3*c^2*Sqrt[c + d*x^2]) - (2*Sqrt[-1 + a^2*x^2]*ArcTanh[(Sqrt[d]*Sqrt[-1 + a^2*x^2])/(a*Sqrt[c + d*x^2])])/(3*c^2*Sqrt[d]*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",8,10,16,0.6250,1,"{192, 191, 5705, 12, 519, 571, 78, 63, 217, 206}"
51,1,269,0,0.8053973,"\int \frac{\cosh ^{-1}(a x)}{\left(c+d x^2\right)^{7/2}} \, dx","Int[ArcCosh[a*x]/(c + d*x^2)^(7/2),x]","\frac{2 a \left(1-a^2 x^2\right) \left(3 a^2 c+2 d\right)}{15 c^2 \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right)^2 \sqrt{c+d x^2}}-\frac{8 \sqrt{a^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a^2 x^2-1}}{a \sqrt{c+d x^2}}\right)}{15 c^3 \sqrt{d} \sqrt{a x-1} \sqrt{a x+1}}+\frac{a \left(1-a^2 x^2\right)}{15 c \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right) \left(c+d x^2\right)^{3/2}}+\frac{8 x \cosh ^{-1}(a x)}{15 c^3 \sqrt{c+d x^2}}+\frac{4 x \cosh ^{-1}(a x)}{15 c^2 \left(c+d x^2\right)^{3/2}}+\frac{x \cosh ^{-1}(a x)}{5 c \left(c+d x^2\right)^{5/2}}","\frac{2 a \left(1-a^2 x^2\right) \left(3 a^2 c+2 d\right)}{15 c^2 \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right)^2 \sqrt{c+d x^2}}-\frac{8 \sqrt{a^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a^2 x^2-1}}{a \sqrt{c+d x^2}}\right)}{15 c^3 \sqrt{d} \sqrt{a x-1} \sqrt{a x+1}}+\frac{a \left(1-a^2 x^2\right)}{15 c \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right) \left(c+d x^2\right)^{3/2}}+\frac{8 x \cosh ^{-1}(a x)}{15 c^3 \sqrt{c+d x^2}}+\frac{4 x \cosh ^{-1}(a x)}{15 c^2 \left(c+d x^2\right)^{3/2}}+\frac{x \cosh ^{-1}(a x)}{5 c \left(c+d x^2\right)^{5/2}}",1,"(a*(1 - a^2*x^2))/(15*c*(a^2*c + d)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(c + d*x^2)^(3/2)) + (2*a*(3*a^2*c + 2*d)*(1 - a^2*x^2))/(15*c^2*(a^2*c + d)^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Sqrt[c + d*x^2]) + (x*ArcCosh[a*x])/(5*c*(c + d*x^2)^(5/2)) + (4*x*ArcCosh[a*x])/(15*c^2*(c + d*x^2)^(3/2)) + (8*x*ArcCosh[a*x])/(15*c^3*Sqrt[c + d*x^2]) - (8*Sqrt[-1 + a^2*x^2]*ArcTanh[(Sqrt[d]*Sqrt[-1 + a^2*x^2])/(a*Sqrt[c + d*x^2])])/(15*c^3*Sqrt[d]*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",9,11,16,0.6875,1,"{192, 191, 5705, 12, 519, 6715, 949, 78, 63, 217, 206}"
52,1,369,0,1.0138168,"\int \frac{\cosh ^{-1}(a x)}{\left(c+d x^2\right)^{9/2}} \, dx","Int[ArcCosh[a*x]/(c + d*x^2)^(9/2),x]","\frac{4 a \left(1-a^2 x^2\right) \left(11 a^4 c^2+15 a^2 c d+6 d^2\right)}{105 c^3 \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right)^3 \sqrt{c+d x^2}}+\frac{2 a \left(1-a^2 x^2\right) \left(5 a^2 c+3 d\right)}{105 c^2 \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right)^2 \left(c+d x^2\right)^{3/2}}-\frac{16 \sqrt{a^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a^2 x^2-1}}{a \sqrt{c+d x^2}}\right)}{35 c^4 \sqrt{d} \sqrt{a x-1} \sqrt{a x+1}}+\frac{a \left(1-a^2 x^2\right)}{35 c \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right) \left(c+d x^2\right)^{5/2}}+\frac{16 x \cosh ^{-1}(a x)}{35 c^4 \sqrt{c+d x^2}}+\frac{8 x \cosh ^{-1}(a x)}{35 c^3 \left(c+d x^2\right)^{3/2}}+\frac{6 x \cosh ^{-1}(a x)}{35 c^2 \left(c+d x^2\right)^{5/2}}+\frac{x \cosh ^{-1}(a x)}{7 c \left(c+d x^2\right)^{7/2}}","\frac{4 a \left(1-a^2 x^2\right) \left(11 a^4 c^2+15 a^2 c d+6 d^2\right)}{105 c^3 \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right)^3 \sqrt{c+d x^2}}+\frac{2 a \left(1-a^2 x^2\right) \left(5 a^2 c+3 d\right)}{105 c^2 \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right)^2 \left(c+d x^2\right)^{3/2}}-\frac{16 \sqrt{a^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a^2 x^2-1}}{a \sqrt{c+d x^2}}\right)}{35 c^4 \sqrt{d} \sqrt{a x-1} \sqrt{a x+1}}+\frac{a \left(1-a^2 x^2\right)}{35 c \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right) \left(c+d x^2\right)^{5/2}}+\frac{16 x \cosh ^{-1}(a x)}{35 c^4 \sqrt{c+d x^2}}+\frac{8 x \cosh ^{-1}(a x)}{35 c^3 \left(c+d x^2\right)^{3/2}}+\frac{6 x \cosh ^{-1}(a x)}{35 c^2 \left(c+d x^2\right)^{5/2}}+\frac{x \cosh ^{-1}(a x)}{7 c \left(c+d x^2\right)^{7/2}}",1,"(a*(1 - a^2*x^2))/(35*c*(a^2*c + d)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(c + d*x^2)^(5/2)) + (2*a*(5*a^2*c + 3*d)*(1 - a^2*x^2))/(105*c^2*(a^2*c + d)^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(c + d*x^2)^(3/2)) + (4*a*(11*a^4*c^2 + 15*a^2*c*d + 6*d^2)*(1 - a^2*x^2))/(105*c^3*(a^2*c + d)^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Sqrt[c + d*x^2]) + (x*ArcCosh[a*x])/(7*c*(c + d*x^2)^(7/2)) + (6*x*ArcCosh[a*x])/(35*c^2*(c + d*x^2)^(5/2)) + (8*x*ArcCosh[a*x])/(35*c^3*(c + d*x^2)^(3/2)) + (16*x*ArcCosh[a*x])/(35*c^4*Sqrt[c + d*x^2]) - (16*Sqrt[-1 + a^2*x^2]*ArcTanh[(Sqrt[d]*Sqrt[-1 + a^2*x^2])/(a*Sqrt[c + d*x^2])])/(35*c^4*Sqrt[d]*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",10,12,16,0.7500,1,"{192, 191, 5705, 12, 519, 6715, 1622, 949, 78, 63, 217, 206}"
53,1,713,0,1.4838553,"\int (f+g x)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f + g*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]),x]","-\frac{f^2 g (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{c^2}+\frac{1}{2} f^3 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{f^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c \sqrt{c x-1} \sqrt{c x+1}}+\frac{3}{4} f g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{3 f g^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 c^2}-\frac{3 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{g^3 x^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^2}-\frac{2 g^3 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{15 c^4}-\frac{b c f^2 g x^3 \sqrt{d-c^2 d x^2}}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b f^2 g x \sqrt{d-c^2 d x^2}}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c f^3 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c f g^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b f g^2 x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c g^3 x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b g^3 x^3 \sqrt{d-c^2 d x^2}}{45 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b g^3 x \sqrt{d-c^2 d x^2}}{15 c^3 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{f^2 g (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{c^2}+\frac{1}{2} f^3 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{f^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c \sqrt{c x-1} \sqrt{c x+1}}+\frac{3}{4} f g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{3 f g^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 c^2}-\frac{3 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{g^3 x^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^2}-\frac{2 g^3 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{15 c^4}-\frac{b c f^2 g x^3 \sqrt{d-c^2 d x^2}}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b f^2 g x \sqrt{d-c^2 d x^2}}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c f^3 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c f g^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b f g^2 x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c g^3 x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b g^3 x^3 \sqrt{d-c^2 d x^2}}{45 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b g^3 x \sqrt{d-c^2 d x^2}}{15 c^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*f^2*g*x*Sqrt[d - c^2*d*x^2])/(c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*g^3*x*Sqrt[d - c^2*d*x^2])/(15*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*f^3*x^2*Sqrt[d - c^2*d*x^2])/(4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*b*f*g^2*x^2*Sqrt[d - c^2*d*x^2])/(16*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*f^2*g*x^3*Sqrt[d - c^2*d*x^2])/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*g^3*x^3*Sqrt[d - c^2*d*x^2])/(45*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*b*c*f*g^2*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*g^3*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (f^3*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/2 - (3*f*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(8*c^2) + (3*f*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/4 - (f^2*g*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/c^2 - (2*g^3*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(15*c^4) - (g^3*x^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(5*c^2) - (f^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(4*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*f*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(16*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",16,12,31,0.3871,1,"{5836, 5822, 5683, 5676, 30, 5718, 5743, 5759, 100, 12, 74, 5733}"
54,1,479,0,1.1757863,"\int (f+g x)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f + g*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]),x]","\frac{1}{2} f^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{f^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 f g (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2}+\frac{1}{4} g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{g^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 c^2}-\frac{g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c f^2 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c f g x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b f g x \sqrt{d-c^2 d x^2}}{3 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c g^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b g^2 x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{2} f^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{f^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 f g (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2}+\frac{1}{4} g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{g^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 c^2}-\frac{g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c f^2 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c f g x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b f g x \sqrt{d-c^2 d x^2}}{3 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c g^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b g^2 x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(2*b*f*g*x*Sqrt[d - c^2*d*x^2])/(3*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*f^2*x^2*Sqrt[d - c^2*d*x^2])/(4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*g^2*x^2*Sqrt[d - c^2*d*x^2])/(16*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*c*f*g*x^3*Sqrt[d - c^2*d*x^2])/(9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*g^2*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (f^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/2 - (g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(8*c^2) + (g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/4 - (2*f*g*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3*c^2) - (f^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(4*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(16*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",13,8,31,0.2581,1,"{5836, 5822, 5683, 5676, 30, 5718, 5743, 5759}"
55,1,255,0,0.5456691,"\int (f+g x) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f + g*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]),x]","\frac{1}{2} f x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{f \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{g (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2}-\frac{b c f x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c g x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b g x \sqrt{d-c^2 d x^2}}{3 c \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{2} f x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{f \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{g (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2}-\frac{b c f x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c g x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b g x \sqrt{d-c^2 d x^2}}{3 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*g*x*Sqrt[d - c^2*d*x^2])/(3*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*f*x^2*Sqrt[d - c^2*d*x^2])/(4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*g*x^3*Sqrt[d - c^2*d*x^2])/(9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/2 - (g*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3*c^2) - (f*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(4*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",8,6,29,0.2069,1,"{5836, 5822, 5683, 5676, 30, 5718}"
56,1,785,0,3.3788375,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{f+g x} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(f + g*x),x]","\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{g^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{d-c^2 d x^2} \left(1-\frac{c^2 f^2}{g^2}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c \sqrt{c x-1} \sqrt{c x+1} (f+g x)}-\frac{\left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c \sqrt{c x-1} \sqrt{c x+1} (f+g x)}-\frac{c x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b g \sqrt{c x-1} \sqrt{c x+1}}-\frac{a \sqrt{c^2 x^2-1} \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \tanh ^{-1}\left(\frac{c^2 f x+g}{\sqrt{c^2 x^2-1} \sqrt{c^2 f^2-g^2}}\right)}{g^2 (1-c x) (c x+1)}+\frac{a \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{g (1-c x) (c x+1)}+\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \cosh ^{-1}(c x) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \cosh ^{-1}(c x) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c x \sqrt{d-c^2 d x^2}}{g \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{g}","\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{g^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{d-c^2 d x^2} \left(1-\frac{c^2 f^2}{g^2}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c \sqrt{c x-1} \sqrt{c x+1} (f+g x)}-\frac{\left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c \sqrt{c x-1} \sqrt{c x+1} (f+g x)}-\frac{c x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b g \sqrt{c x-1} \sqrt{c x+1}}-\frac{a \sqrt{c^2 x^2-1} \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \tanh ^{-1}\left(\frac{c^2 f x+g}{\sqrt{c^2 x^2-1} \sqrt{c^2 f^2-g^2}}\right)}{g^2 (1-c x) (c x+1)}+\frac{a \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{g (1-c x) (c x+1)}+\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \cosh ^{-1}(c x) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \cosh ^{-1}(c x) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c x \sqrt{d-c^2 d x^2}}{g \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{g}",1,"-((b*c*x*Sqrt[d - c^2*d*x^2])/(g*Sqrt[-1 + c*x]*Sqrt[1 + c*x])) + (a*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(g*(1 - c*x)*(1 + c*x)) + (b*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/g - (c*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*b*g*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((1 - (c^2*f^2)/g^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(f + g*x)) - ((1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(f + g*x)) - (a*Sqrt[c^2*f^2 - g^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d - c^2*d*x^2]*ArcTanh[(g + c^2*f*x)/(Sqrt[c^2*f^2 - g^2]*Sqrt[-1 + c^2*x^2])])/(g^2*(1 - c*x)*(1 + c*x)) + (b*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x]*Log[1 + (E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x]*Log[1 + (E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/(g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/(g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",23,22,31,0.7097,1,"{5836, 5824, 683, 5816, 6742, 93, 208, 1610, 1654, 12, 725, 206, 5860, 5858, 5718, 8, 5832, 3320, 2264, 2190, 2279, 2391}"
57,1,918,0,3.5610762,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{(f+g x)^2} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(f + g*x)^2,x]","\frac{b f^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)^2 c^3}{2 g^2 \left(c^2 f^2-g^2\right) \sqrt{c x-1} \sqrt{c x+1}}+\frac{a f^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) c^3}{g^2 \left(c^2 f^2-g^2\right) \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 a f \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(\frac{\sqrt{c f+g} \sqrt{c x+1}}{\sqrt{c f-g} \sqrt{c x-1}}\right) c^2}{\sqrt{c f-g} g^2 \sqrt{c f+g} \sqrt{c x-1} \sqrt{c x+1}}-\frac{b f \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) \log \left(\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}+1\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b f \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) \log \left(\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}+1\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{c x-1} \sqrt{c x+1}}-\frac{b f \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b f \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \sqrt{d-c^2 d x^2} \log (f+g x) c}{g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{-\frac{1-c x}{c x+1}} \sqrt{c x+1} \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{g \sqrt{c x-1} (f+g x)}-\frac{a \sqrt{d-c^2 d x^2}}{g (f+g x)}-\frac{\left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b \sqrt{c x-1} \sqrt{c x+1} (f+g x)^2 c}-\frac{\left(f x c^2+g\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b \left(c^2 f^2-g^2\right) \sqrt{c x-1} \sqrt{c x+1} (f+g x)^2 c}","\frac{b f^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)^2 c^3}{2 g^2 \left(c^2 f^2-g^2\right) \sqrt{c x-1} \sqrt{c x+1}}+\frac{a f^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) c^3}{g^2 \left(c^2 f^2-g^2\right) \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 a f \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(\frac{\sqrt{c f+g} \sqrt{c x+1}}{\sqrt{c f-g} \sqrt{c x-1}}\right) c^2}{\sqrt{c f-g} g^2 \sqrt{c f+g} \sqrt{c x-1} \sqrt{c x+1}}-\frac{b f \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) \log \left(\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}+1\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b f \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) \log \left(\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}+1\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{c x-1} \sqrt{c x+1}}-\frac{b f \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b f \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \sqrt{d-c^2 d x^2} \log (f+g x) c}{g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{-\frac{1-c x}{c x+1}} \sqrt{c x+1} \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{g \sqrt{c x-1} (f+g x)}-\frac{a \sqrt{d-c^2 d x^2}}{g (f+g x)}-\frac{\left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b \sqrt{c x-1} \sqrt{c x+1} (f+g x)^2 c}-\frac{\left(f x c^2+g\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b \left(c^2 f^2-g^2\right) \sqrt{c x-1} \sqrt{c x+1} (f+g x)^2 c}",1,"-((a*Sqrt[d - c^2*d*x^2])/(g*(f + g*x))) + (a*c^3*f^2*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(g^2*(c^2*f^2 - g^2)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*Sqrt[-((1 - c*x)/(1 + c*x))]*Sqrt[1 + c*x]*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(g*Sqrt[-1 + c*x]*(f + g*x)) + (b*c^3*f^2*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x]^2)/(2*g^2*(c^2*f^2 - g^2)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((g + c^2*f*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*b*c*(c^2*f^2 - g^2)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(f + g*x)^2) - ((1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(f + g*x)^2) - (2*a*c^2*f*Sqrt[d - c^2*d*x^2]*ArcTanh[(Sqrt[c*f + g]*Sqrt[1 + c*x])/(Sqrt[c*f - g]*Sqrt[-1 + c*x])])/(Sqrt[c*f - g]*g^2*Sqrt[c*f + g]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^2*f*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x]*Log[1 + (E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[c^2*f^2 - g^2]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^2*f*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x]*Log[1 + (E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^2*Sqrt[c^2*f^2 - g^2]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c*Sqrt[d - c^2*d*x^2]*Log[f + g*x])/(g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^2*f*Sqrt[d - c^2*d*x^2]*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/(g^2*Sqrt[c^2*f^2 - g^2]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^2*f*Sqrt[d - c^2*d*x^2]*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/(g^2*Sqrt[c^2*f^2 - g^2]*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",38,22,31,0.7097,1,"{5836, 5824, 37, 5814, 12, 180, 52, 96, 93, 208, 5860, 5858, 5676, 5832, 3324, 3320, 2264, 2190, 2279, 2391, 2668, 31}"
58,1,1029,0,2.0570492,"\int (f+g x)^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f + g*x)^3*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]),x]","\frac{b c^3 d g^3 \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d f g^2 \sqrt{d-c^2 d x^2} x^6}{12 \sqrt{c x-1} \sqrt{c x+1}}-\frac{8 b c d g^3 \sqrt{d-c^2 d x^2} x^5}{175 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b c^3 d f^2 g \sqrt{d-c^2 d x^2} x^5}{25 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d f^3 \sqrt{d-c^2 d x^2} x^4}{16 \sqrt{c x-1} \sqrt{c x+1}}-\frac{7 b c d f g^2 \sqrt{d-c^2 d x^2} x^4}{32 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3}{8} d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{1}{2} d f g^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{b d g^3 \sqrt{d-c^2 d x^2} x^3}{105 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c d f^2 g \sqrt{d-c^2 d x^2} x^3}{5 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d g^3 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^2}{7 c^2}-\frac{5 b c d f^3 \sqrt{d-c^2 d x^2} x^2}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b d f g^2 \sqrt{d-c^2 d x^2} x^2}{32 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{3}{8} d f^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x-\frac{3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x}{16 c^2}+\frac{1}{4} d f^3 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x+\frac{2 b d g^3 \sqrt{d-c^2 d x^2} x}{35 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b d f^2 g \sqrt{d-c^2 d x^2} x}{5 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 d f^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 d g^3 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{35 c^4}-\frac{3 d f^2 g (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^2}","\frac{b c^3 d g^3 \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d f g^2 \sqrt{d-c^2 d x^2} x^6}{12 \sqrt{c x-1} \sqrt{c x+1}}-\frac{8 b c d g^3 \sqrt{d-c^2 d x^2} x^5}{175 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b c^3 d f^2 g \sqrt{d-c^2 d x^2} x^5}{25 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d f^3 \sqrt{d-c^2 d x^2} x^4}{16 \sqrt{c x-1} \sqrt{c x+1}}-\frac{7 b c d f g^2 \sqrt{d-c^2 d x^2} x^4}{32 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3}{8} d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{1}{2} d f g^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{b d g^3 \sqrt{d-c^2 d x^2} x^3}{105 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c d f^2 g \sqrt{d-c^2 d x^2} x^3}{5 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d g^3 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^2}{7 c^2}-\frac{5 b c d f^3 \sqrt{d-c^2 d x^2} x^2}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b d f g^2 \sqrt{d-c^2 d x^2} x^2}{32 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{3}{8} d f^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x-\frac{3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x}{16 c^2}+\frac{1}{4} d f^3 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x+\frac{2 b d g^3 \sqrt{d-c^2 d x^2} x}{35 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b d f^2 g \sqrt{d-c^2 d x^2} x}{5 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 d f^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 d g^3 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{35 c^4}-\frac{3 d f^2 g (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^2}",1,"(3*b*d*f^2*g*x*Sqrt[d - c^2*d*x^2])/(5*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*d*g^3*x*Sqrt[d - c^2*d*x^2])/(35*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*b*c*d*f^3*x^2*Sqrt[d - c^2*d*x^2])/(16*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*b*d*f*g^2*x^2*Sqrt[d - c^2*d*x^2])/(32*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*c*d*f^2*g*x^3*Sqrt[d - c^2*d*x^2])/(5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d*g^3*x^3*Sqrt[d - c^2*d*x^2])/(105*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*f^3*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (7*b*c*d*f*g^2*x^4*Sqrt[d - c^2*d*x^2])/(32*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*b*c^3*d*f^2*g*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (8*b*c*d*g^3*x^5*Sqrt[d - c^2*d*x^2])/(175*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*f*g^2*x^6*Sqrt[d - c^2*d*x^2])/(12*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*g^3*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*d*f^3*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/8 - (3*d*f*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(16*c^2) + (3*d*f*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/8 + (d*f^3*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/4 + (d*f*g^2*x^3*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/2 - (3*d*f^2*g*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(5*c^2) - (2*d*g^3*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(35*c^4) - (d*g^3*x^2*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(7*c^2) - (3*d*f^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(16*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*d*f*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(32*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",24,17,31,0.5484,1,"{5836, 5822, 5685, 5683, 5676, 30, 14, 5718, 194, 5745, 5743, 5759, 100, 12, 74, 5733, 373}"
59,1,725,0,1.6929027,"\int (f+g x)^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f + g*x)^2*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]),x]","\frac{3}{8} d f^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} d f^2 x (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{3 d f^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 d f g (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^2}+\frac{1}{8} d g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{6} d g^2 x^3 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{d g^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{16 c^2}-\frac{d g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d f^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b c d f^2 x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c^3 d f g x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 b c d f g x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d f g x \sqrt{d-c^2 d x^2}}{5 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d g^2 x^6 \sqrt{d-c^2 d x^2}}{36 \sqrt{c x-1} \sqrt{c x+1}}-\frac{7 b c d g^2 x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d g^2 x^2 \sqrt{d-c^2 d x^2}}{32 c \sqrt{c x-1} \sqrt{c x+1}}","\frac{3}{8} d f^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} d f^2 x (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{3 d f^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 d f g (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^2}+\frac{1}{8} d g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{6} d g^2 x^3 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{d g^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{16 c^2}-\frac{d g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d f^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b c d f^2 x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c^3 d f g x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 b c d f g x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d f g x \sqrt{d-c^2 d x^2}}{5 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d g^2 x^6 \sqrt{d-c^2 d x^2}}{36 \sqrt{c x-1} \sqrt{c x+1}}-\frac{7 b c d g^2 x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d g^2 x^2 \sqrt{d-c^2 d x^2}}{32 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(2*b*d*f*g*x*Sqrt[d - c^2*d*x^2])/(5*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*b*c*d*f^2*x^2*Sqrt[d - c^2*d*x^2])/(16*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d*g^2*x^2*Sqrt[d - c^2*d*x^2])/(32*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (4*b*c*d*f*g*x^3*Sqrt[d - c^2*d*x^2])/(15*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*f^2*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (7*b*c*d*g^2*x^4*Sqrt[d - c^2*d*x^2])/(96*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*c^3*d*f*g*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*g^2*x^6*Sqrt[d - c^2*d*x^2])/(36*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*d*f^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/8 - (d*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(16*c^2) + (d*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/8 + (d*f^2*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/4 + (d*g^2*x^3*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/6 - (2*d*f*g*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(5*c^2) - (3*d*f^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(16*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(32*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",20,12,31,0.3871,1,"{5836, 5822, 5685, 5683, 5676, 30, 14, 5718, 194, 5745, 5743, 5759}"
60,1,398,0,0.7568263,"\int (f+g x) \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f + g*x)*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]),x]","\frac{3}{8} d f x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} d f x (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{3 d f \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d g (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^2}+\frac{b c^3 d f x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b c d f x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d g x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c d g x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d g x \sqrt{d-c^2 d x^2}}{5 c \sqrt{c x-1} \sqrt{c x+1}}","\frac{3}{8} d f x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} d f x (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{3 d f \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d g (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^2}+\frac{b c^3 d f x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b c d f x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d g x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c d g x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d g x \sqrt{d-c^2 d x^2}}{5 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*d*g*x*Sqrt[d - c^2*d*x^2])/(5*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*b*c*d*f*x^2*Sqrt[d - c^2*d*x^2])/(16*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*c*d*g*x^3*Sqrt[d - c^2*d*x^2])/(15*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*f*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*g*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*d*f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/8 + (d*f*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/4 - (d*g*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(5*c^2) - (3*d*f*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(16*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",12,9,29,0.3103,1,"{5836, 5822, 5685, 5683, 5676, 30, 14, 5718, 194}"
61,0,0,0,3.8532961,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{f+g x} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]))/(f + g*x),x]","\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{f+g x} \, dx","-\frac{b c^2 d (c f-g) \sqrt{d-c^2 d x^2} x^2}{4 g^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{c d (c f-g) (c f+g) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 x}{2 b g^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{c d (c f-g) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x}{2 g^2}+\frac{b c d \left(4 c^2 x^2-9 c x-12\right) \sqrt{d-c^2 d x^2} x}{36 g \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d (c f-g) (c f+g) \sqrt{d-c^2 d x^2} x}{g^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)^2}{4 g \sqrt{c x-1} \sqrt{c x+1}}+\frac{d (c f-g) (c f+g) \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c g^2 \sqrt{c x-1} \sqrt{c x+1} (f+g x)}-\frac{d (c f-g) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b g^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d (c f-g)^2 (c f+g)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c g^4 \sqrt{c x-1} \sqrt{c x+1} (f+g x)}-\frac{b d (c f-g) (c f+g) \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{g^3}+\frac{b d \left(-2 c^2 x^2+3 c x+2\right) \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{6 g}-\frac{a d \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{2 g \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 a d (c f-g)^{3/2} (c f+g)^{3/2} \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(\frac{\sqrt{c f+g} \sqrt{c x+1}}{\sqrt{c f-g} \sqrt{c x-1}}\right)}{g^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d (c f-g) (c f+g) \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) \log \left(\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{g^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d (c f-g) (c f+g) \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) \log \left(\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}+1\right)}{g^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d (c f-g) (c f+g) \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d (c f-g) (c f+g) \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{a d (c f-g) (c f+g) \sqrt{d-c^2 d x^2}}{g^3}+\frac{a d \left(-2 c^2 x^2+3 c x+2\right) \sqrt{d-c^2 d x^2}}{6 g}",1,"(b*c*d*(c*f - g)*(c*f + g)*x*Sqrt[d - c^2*d*x^2])/(g^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^2*d*(c*f - g)*x^2*Sqrt[d - c^2*d*x^2])/(4*g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (a*d*(c*f - g)*(c*f + g)*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(g^3*(1 - c*x)*(1 + c*x)) - (b*d*(c*f - g)*(c*f + g)*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/g^3 + (c*d*(c*f - g)*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(2*g^2) - (d*(c*f - g)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(4*b*g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (c*d*(c*f - g)*(c*f + g)*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*b*g^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (d*(c*f - g)^2*(c*f + g)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*b*c*g^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(f + g*x)) + (d*(c*f - g)*(c*f + g)*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*b*c*g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(f + g*x)) + (a*d*(c*f - g)*(c*f + g)*Sqrt[c^2*f^2 - g^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d - c^2*d*x^2]*ArcTanh[(g + c^2*f*x)/(Sqrt[c^2*f^2 - g^2]*Sqrt[-1 + c^2*x^2])])/(g^4*(1 - c*x)*(1 + c*x)) - (b*d*(c*f - g)*(c*f + g)*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x]*Log[1 + (E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d*(c*f - g)*(c*f + g)*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x]*Log[1 + (E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*d*(c*f - g)*(c*f + g)*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/(g^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d*(c*f - g)*(c*f + g)*Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/(g^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (c*d*Sqrt[d - c^2*d*x^2]*Defer[Int][(-1 + c*x)^(3/2)*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]), x])/(g*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","F",0,0,0,0,-1,"{}"
62,1,1385,0,2.5178974,"\int (f+g x)^3 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f + g*x)^3*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]),x]","-\frac{b c^5 d^2 g^3 \sqrt{d-c^2 d x^2} x^9}{81 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c^5 d^2 f g^2 \sqrt{d-c^2 d x^2} x^8}{64 \sqrt{c x-1} \sqrt{c x+1}}+\frac{19 b c^3 d^2 g^3 \sqrt{d-c^2 d x^2} x^7}{441 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c^5 d^2 f^2 g \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{c x-1} \sqrt{c x+1}}+\frac{17 b c^3 d^2 f g^2 \sqrt{d-c^2 d x^2} x^6}{96 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 g^3 \sqrt{d-c^2 d x^2} x^5}{21 \sqrt{c x-1} \sqrt{c x+1}}+\frac{9 b c^3 d^2 f^2 g \sqrt{d-c^2 d x^2} x^5}{35 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c^3 d^2 f^3 \sqrt{d-c^2 d x^2} x^4}{96 \sqrt{c x-1} \sqrt{c x+1}}-\frac{59 b c d^2 f g^2 \sqrt{d-c^2 d x^2} x^4}{256 \sqrt{c x-1} \sqrt{c x+1}}+\frac{15}{64} d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{3}{8} d^2 f g^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{5}{16} d^2 f g^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{b d^2 g^3 \sqrt{d-c^2 d x^2} x^3}{189 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c d^2 f^2 g \sqrt{d-c^2 d x^2} x^3}{7 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 g^3 (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^2}{9 c^2}-\frac{25 b c d^2 f^3 \sqrt{d-c^2 d x^2} x^2}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{15 b d^2 f g^2 \sqrt{d-c^2 d x^2} x^2}{256 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{5}{16} d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x-\frac{15 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^3 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^3 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x+\frac{2 b d^2 g^3 \sqrt{d-c^2 d x^2} x}{63 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b d^2 f^2 g \sqrt{d-c^2 d x^2} x}{7 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{15 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 d^2 g^3 (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{63 c^4}-\frac{3 d^2 f^2 g (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^2}+\frac{b d^2 f^3 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{36 c \sqrt{c x-1} \sqrt{c x+1}}","-\frac{b c^5 d^2 g^3 \sqrt{d-c^2 d x^2} x^9}{81 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c^5 d^2 f g^2 \sqrt{d-c^2 d x^2} x^8}{64 \sqrt{c x-1} \sqrt{c x+1}}+\frac{19 b c^3 d^2 g^3 \sqrt{d-c^2 d x^2} x^7}{441 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c^5 d^2 f^2 g \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{c x-1} \sqrt{c x+1}}+\frac{17 b c^3 d^2 f g^2 \sqrt{d-c^2 d x^2} x^6}{96 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 g^3 \sqrt{d-c^2 d x^2} x^5}{21 \sqrt{c x-1} \sqrt{c x+1}}+\frac{9 b c^3 d^2 f^2 g \sqrt{d-c^2 d x^2} x^5}{35 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c^3 d^2 f^3 \sqrt{d-c^2 d x^2} x^4}{96 \sqrt{c x-1} \sqrt{c x+1}}-\frac{59 b c d^2 f g^2 \sqrt{d-c^2 d x^2} x^4}{256 \sqrt{c x-1} \sqrt{c x+1}}+\frac{15}{64} d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{3}{8} d^2 f g^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{5}{16} d^2 f g^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{b d^2 g^3 \sqrt{d-c^2 d x^2} x^3}{189 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c d^2 f^2 g \sqrt{d-c^2 d x^2} x^3}{7 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 g^3 (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^2}{9 c^2}-\frac{25 b c d^2 f^3 \sqrt{d-c^2 d x^2} x^2}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{15 b d^2 f g^2 \sqrt{d-c^2 d x^2} x^2}{256 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{5}{16} d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x-\frac{15 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^3 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^3 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x+\frac{2 b d^2 g^3 \sqrt{d-c^2 d x^2} x}{63 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b d^2 f^2 g \sqrt{d-c^2 d x^2} x}{7 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{15 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 d^2 g^3 (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{63 c^4}-\frac{3 d^2 f^2 g (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^2}+\frac{b d^2 f^3 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{36 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(3*b*d^2*f^2*g*x*Sqrt[d - c^2*d*x^2])/(7*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*d^2*g^3*x*Sqrt[d - c^2*d*x^2])/(63*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (25*b*c*d^2*f^3*x^2*Sqrt[d - c^2*d*x^2])/(96*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (15*b*d^2*f*g^2*x^2*Sqrt[d - c^2*d*x^2])/(256*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*b*c*d^2*f^2*g*x^3*Sqrt[d - c^2*d*x^2])/(7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^2*g^3*x^3*Sqrt[d - c^2*d*x^2])/(189*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*b*c^3*d^2*f^3*x^4*Sqrt[d - c^2*d*x^2])/(96*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (59*b*c*d^2*f*g^2*x^4*Sqrt[d - c^2*d*x^2])/(256*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (9*b*c^3*d^2*f^2*g*x^5*Sqrt[d - c^2*d*x^2])/(35*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d^2*g^3*x^5*Sqrt[d - c^2*d*x^2])/(21*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (17*b*c^3*d^2*f*g^2*x^6*Sqrt[d - c^2*d*x^2])/(96*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*b*c^5*d^2*f^2*g*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (19*b*c^3*d^2*g^3*x^7*Sqrt[d - c^2*d*x^2])/(441*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*b*c^5*d^2*f*g^2*x^8*Sqrt[d - c^2*d*x^2])/(64*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*g^3*x^9*Sqrt[d - c^2*d*x^2])/(81*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^2*f^3*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2])/(36*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*d^2*f^3*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/16 - (15*d^2*f*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(128*c^2) + (15*d^2*f*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/64 + (5*d^2*f^3*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/24 + (5*d^2*f*g^2*x^3*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/16 + (d^2*f^3*x*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/6 + (3*d^2*f*g^2*x^3*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/8 - (3*d^2*f^2*g*(1 - c*x)^3*(1 + c*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(7*c^2) - (2*d^2*g^3*(1 - c*x)^3*(1 + c*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(63*c^4) - (d^2*g^3*x^2*(1 - c*x)^3*(1 + c*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(9*c^2) - (5*d^2*f^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(32*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (15*d^2*f*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(256*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",30,20,31,0.6452,1,"{5836, 5822, 5685, 5683, 5676, 30, 14, 261, 5718, 194, 5745, 5743, 5759, 266, 43, 100, 12, 74, 5733, 373}"
63,1,1015,0,2.1058324,"\int (f+g x)^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f + g*x)^2*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]),x]","-\frac{b c^5 d^2 g^2 \sqrt{d-c^2 d x^2} x^8}{64 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c^5 d^2 f g \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{c x-1} \sqrt{c x+1}}+\frac{17 b c^3 d^2 g^2 \sqrt{d-c^2 d x^2} x^6}{288 \sqrt{c x-1} \sqrt{c x+1}}+\frac{6 b c^3 d^2 f g \sqrt{d-c^2 d x^2} x^5}{35 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c^3 d^2 f^2 \sqrt{d-c^2 d x^2} x^4}{96 \sqrt{c x-1} \sqrt{c x+1}}-\frac{59 b c d^2 g^2 \sqrt{d-c^2 d x^2} x^4}{768 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5}{64} d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{1}{8} d^2 g^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{5}{48} d^2 g^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3-\frac{2 b c d^2 f g \sqrt{d-c^2 d x^2} x^3}{7 \sqrt{c x-1} \sqrt{c x+1}}-\frac{25 b c d^2 f^2 \sqrt{d-c^2 d x^2} x^2}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b d^2 g^2 \sqrt{d-c^2 d x^2} x^2}{256 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{5}{16} d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x-\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x+\frac{2 b d^2 f g \sqrt{d-c^2 d x^2} x}{7 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 d^2 f g (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^2}+\frac{b d^2 f^2 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{36 c \sqrt{c x-1} \sqrt{c x+1}}","-\frac{b c^5 d^2 g^2 \sqrt{d-c^2 d x^2} x^8}{64 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c^5 d^2 f g \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{c x-1} \sqrt{c x+1}}+\frac{17 b c^3 d^2 g^2 \sqrt{d-c^2 d x^2} x^6}{288 \sqrt{c x-1} \sqrt{c x+1}}+\frac{6 b c^3 d^2 f g \sqrt{d-c^2 d x^2} x^5}{35 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c^3 d^2 f^2 \sqrt{d-c^2 d x^2} x^4}{96 \sqrt{c x-1} \sqrt{c x+1}}-\frac{59 b c d^2 g^2 \sqrt{d-c^2 d x^2} x^4}{768 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5}{64} d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{1}{8} d^2 g^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{5}{48} d^2 g^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3-\frac{2 b c d^2 f g \sqrt{d-c^2 d x^2} x^3}{7 \sqrt{c x-1} \sqrt{c x+1}}-\frac{25 b c d^2 f^2 \sqrt{d-c^2 d x^2} x^2}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b d^2 g^2 \sqrt{d-c^2 d x^2} x^2}{256 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{5}{16} d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x-\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x+\frac{2 b d^2 f g \sqrt{d-c^2 d x^2} x}{7 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 d^2 f g (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^2}+\frac{b d^2 f^2 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{36 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(2*b*d^2*f*g*x*Sqrt[d - c^2*d*x^2])/(7*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (25*b*c*d^2*f^2*x^2*Sqrt[d - c^2*d*x^2])/(96*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*b*d^2*g^2*x^2*Sqrt[d - c^2*d*x^2])/(256*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*c*d^2*f*g*x^3*Sqrt[d - c^2*d*x^2])/(7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*b*c^3*d^2*f^2*x^4*Sqrt[d - c^2*d*x^2])/(96*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (59*b*c*d^2*g^2*x^4*Sqrt[d - c^2*d*x^2])/(768*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (6*b*c^3*d^2*f*g*x^5*Sqrt[d - c^2*d*x^2])/(35*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (17*b*c^3*d^2*g^2*x^6*Sqrt[d - c^2*d*x^2])/(288*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*c^5*d^2*f*g*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*g^2*x^8*Sqrt[d - c^2*d*x^2])/(64*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^2*f^2*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2])/(36*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*d^2*f^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/16 - (5*d^2*g^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(128*c^2) + (5*d^2*g^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/64 + (5*d^2*f^2*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/24 + (5*d^2*g^2*x^3*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/48 + (d^2*f^2*x*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/6 + (d^2*g^2*x^3*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/8 - (2*d^2*f*g*(1 - c*x)^3*(1 + c*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(7*c^2) - (5*d^2*f^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(32*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*d^2*g^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(256*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",26,15,31,0.4839,1,"{5836, 5822, 5685, 5683, 5676, 30, 14, 261, 5718, 194, 5745, 5743, 5759, 266, 43}"
64,1,568,0,0.904908,"\int (f+g x) \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f + g*x)*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]),x]","\frac{1}{6} d^2 f x (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{5}{16} d^2 f x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{5}{24} d^2 f x (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{5 d^2 f \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 g (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^2}+\frac{5 b c^3 d^2 f x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{c x-1} \sqrt{c x+1}}-\frac{25 b c d^2 f x^2 \sqrt{d-c^2 d x^2}}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 f \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{36 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 d^2 g x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b c^3 d^2 g x^5 \sqrt{d-c^2 d x^2}}{35 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 g x^3 \sqrt{d-c^2 d x^2}}{7 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 g x \sqrt{d-c^2 d x^2}}{7 c \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{6} d^2 f x (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{5}{16} d^2 f x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{5}{24} d^2 f x (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{5 d^2 f \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 g (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^2}+\frac{5 b c^3 d^2 f x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{c x-1} \sqrt{c x+1}}-\frac{25 b c d^2 f x^2 \sqrt{d-c^2 d x^2}}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 f \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{36 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 d^2 g x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b c^3 d^2 g x^5 \sqrt{d-c^2 d x^2}}{35 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 g x^3 \sqrt{d-c^2 d x^2}}{7 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 g x \sqrt{d-c^2 d x^2}}{7 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*d^2*g*x*Sqrt[d - c^2*d*x^2])/(7*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (25*b*c*d^2*f*x^2*Sqrt[d - c^2*d*x^2])/(96*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d^2*g*x^3*Sqrt[d - c^2*d*x^2])/(7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*b*c^3*d^2*f*x^4*Sqrt[d - c^2*d*x^2])/(96*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*b*c^3*d^2*g*x^5*Sqrt[d - c^2*d*x^2])/(35*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*g*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^2*f*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2])/(36*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*d^2*f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/16 + (5*d^2*f*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/24 + (d^2*f*x*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/6 - (d^2*g*(1 - c*x)^3*(1 + c*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(7*c^2) - (5*d^2*f*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(32*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",14,10,29,0.3448,1,"{5836, 5822, 5685, 5683, 5676, 30, 14, 261, 5718, 194}"
65,1,1744,0,4.779262,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{f+g x} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]))/(f + g*x),x]","-\frac{b d^2 x^5 \sqrt{d-c^2 d x^2} c^5}{25 g \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 f x^4 \sqrt{d-c^2 d x^2} c^5}{16 g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 f x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c^4}{4 g^2}-\frac{b d^2 \left(c^2 f^2-2 g^2\right) x^3 \sqrt{d-c^2 d x^2} c^3}{9 g^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 x^3 \sqrt{d-c^2 d x^2} c^3}{45 g \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 f \left(c^2 f^2-2 g^2\right) x^2 \sqrt{d-c^2 d x^2} c^3}{4 g^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^2 f x^2 \sqrt{d-c^2 d x^2} c^3}{16 g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 f \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c^2}{2 g^4}+\frac{d^2 f x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c^2}{8 g^2}-\frac{d^2 x^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c^2}{5 g}+\frac{d^2 f \left(c^2 f^2-2 g^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 c}{4 b g^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 c}{2 b g^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d^2 f \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 c}{16 b g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} c}{g^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} c}{3 g^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d^2 x \sqrt{d-c^2 d x^2} c}{15 g \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{g^5}-\frac{d^2 \left(c^2 f^2-2 g^2\right) (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 g^3}-\frac{2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{15 g}-\frac{a d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{c^2 x^2-1} \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{c^2 x^2-1}}\right)}{g^6 (1-c x) (c x+1)}+\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) \log \left(\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{g^6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) \log \left(\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}+1\right)}{g^6 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{c x-1} \sqrt{c x+1}}+\frac{a d^2 \left(c^2 f^2-g^2\right)^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{g^5 (1-c x) (c x+1)}-\frac{d^2 \left(c^2 f^2-g^2\right)^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b g^4 \sqrt{c x-1} \sqrt{c x+1} (f+g x) c}-\frac{d^2 \left(c^2 f^2-g^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b g^6 \sqrt{c x-1} \sqrt{c x+1} (f+g x) c}","-\frac{b d^2 x^5 \sqrt{d-c^2 d x^2} c^5}{25 g \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 f x^4 \sqrt{d-c^2 d x^2} c^5}{16 g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 f x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c^4}{4 g^2}-\frac{b d^2 \left(c^2 f^2-2 g^2\right) x^3 \sqrt{d-c^2 d x^2} c^3}{9 g^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 x^3 \sqrt{d-c^2 d x^2} c^3}{45 g \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 f \left(c^2 f^2-2 g^2\right) x^2 \sqrt{d-c^2 d x^2} c^3}{4 g^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^2 f x^2 \sqrt{d-c^2 d x^2} c^3}{16 g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 f \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c^2}{2 g^4}+\frac{d^2 f x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c^2}{8 g^2}-\frac{d^2 x^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c^2}{5 g}+\frac{d^2 f \left(c^2 f^2-2 g^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 c}{4 b g^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 c}{2 b g^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d^2 f \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 c}{16 b g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} c}{g^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} c}{3 g^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d^2 x \sqrt{d-c^2 d x^2} c}{15 g \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{g^5}-\frac{d^2 \left(c^2 f^2-2 g^2\right) (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 g^3}-\frac{2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{15 g}-\frac{a d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{c^2 x^2-1} \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{c^2 x^2-1}}\right)}{g^6 (1-c x) (c x+1)}+\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) \log \left(\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{g^6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) \log \left(\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}+1\right)}{g^6 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{c x-1} \sqrt{c x+1}}+\frac{a d^2 \left(c^2 f^2-g^2\right)^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{g^5 (1-c x) (c x+1)}-\frac{d^2 \left(c^2 f^2-g^2\right)^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b g^4 \sqrt{c x-1} \sqrt{c x+1} (f+g x) c}-\frac{d^2 \left(c^2 f^2-g^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b g^6 \sqrt{c x-1} \sqrt{c x+1} (f+g x) c}",1,"(2*b*c*d^2*x*Sqrt[d - c^2*d*x^2])/(15*g*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c*d^2*(c^2*f^2 - 2*g^2)*x*Sqrt[d - c^2*d*x^2])/(3*g^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d^2*(c^2*f^2 - g^2)^2*x*Sqrt[d - c^2*d*x^2])/(g^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^3*d^2*f*x^2*Sqrt[d - c^2*d*x^2])/(16*g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d^2*f*(c^2*f^2 - 2*g^2)*x^2*Sqrt[d - c^2*d*x^2])/(4*g^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d^2*x^3*Sqrt[d - c^2*d*x^2])/(45*g*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^3*d^2*(c^2*f^2 - 2*g^2)*x^3*Sqrt[d - c^2*d*x^2])/(9*g^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^5*d^2*f*x^4*Sqrt[d - c^2*d*x^2])/(16*g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*x^5*Sqrt[d - c^2*d*x^2])/(25*g*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (a*d^2*(c^2*f^2 - g^2)^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(g^5*(1 - c*x)*(1 + c*x)) + (b*d^2*(c^2*f^2 - g^2)^2*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/g^5 + (c^2*d^2*f*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(8*g^2) - (c^2*d^2*f*(c^2*f^2 - 2*g^2)*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(2*g^4) - (c^4*d^2*f*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(4*g^2) - (2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(15*g) - (d^2*(c^2*f^2 - 2*g^2)*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3*g^3) - (c^2*d^2*x^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(5*g) + (c*d^2*f*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(16*b*g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (c*d^2*f*(c^2*f^2 - 2*g^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(4*b*g^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (c*d^2*(c^2*f^2 - g^2)^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*b*g^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d^2*(c^2*f^2 - g^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*b*c*g^6*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(f + g*x)) - (d^2*(c^2*f^2 - g^2)^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*b*c*g^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(f + g*x)) - (a*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[-1 + c^2*x^2]*Sqrt[d - c^2*d*x^2]*ArcTanh[(g + c^2*f*x)/(Sqrt[c^2*f^2 - g^2]*Sqrt[-1 + c^2*x^2])])/(g^6*(1 - c*x)*(1 + c*x)) + (b*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x]*Log[1 + (E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x]*Log[1 + (E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(g^6*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/(g^6*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*d^2*(c^2*f^2 - g^2)^(5/2)*Sqrt[d - c^2*d*x^2]*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/(g^6*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",38,31,31,1.000,1,"{5836, 5826, 5683, 5676, 30, 5718, 5743, 5759, 100, 12, 74, 5733, 5824, 683, 5816, 6742, 93, 208, 1610, 1654, 725, 206, 5860, 5858, 8, 5832, 3320, 2264, 2190, 2279, 2391}"
66,1,478,0,1.2882989,"\int \frac{(f+g x)^3 \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f + g*x)^3*(a + b*ArcCosh[c*x]))/Sqrt[d - c^2*d*x^2],x]","-\frac{3 f^2 g (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{f^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}+\frac{3 f g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c^3 \sqrt{d-c^2 d x^2}}-\frac{3 f g^2 x (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{2 c^2 \sqrt{d-c^2 d x^2}}-\frac{2 g^3 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^4 \sqrt{d-c^2 d x^2}}-\frac{g^3 x^2 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2 \sqrt{d-c^2 d x^2}}-\frac{3 b f^2 g x \sqrt{c x-1} \sqrt{c x+1}}{c \sqrt{d-c^2 d x^2}}-\frac{3 b f g^2 x^2 \sqrt{c x-1} \sqrt{c x+1}}{4 c \sqrt{d-c^2 d x^2}}-\frac{b g^3 x^3 \sqrt{c x-1} \sqrt{c x+1}}{9 c \sqrt{d-c^2 d x^2}}-\frac{2 b g^3 x \sqrt{c x-1} \sqrt{c x+1}}{3 c^3 \sqrt{d-c^2 d x^2}}","-\frac{3 f^2 g (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{f^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}+\frac{3 f g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c^3 \sqrt{d-c^2 d x^2}}-\frac{3 f g^2 x (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{2 c^2 \sqrt{d-c^2 d x^2}}-\frac{2 g^3 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^4 \sqrt{d-c^2 d x^2}}-\frac{g^3 x^2 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2 \sqrt{d-c^2 d x^2}}-\frac{3 b f^2 g x \sqrt{c x-1} \sqrt{c x+1}}{c \sqrt{d-c^2 d x^2}}-\frac{3 b f g^2 x^2 \sqrt{c x-1} \sqrt{c x+1}}{4 c \sqrt{d-c^2 d x^2}}-\frac{b g^3 x^3 \sqrt{c x-1} \sqrt{c x+1}}{9 c \sqrt{d-c^2 d x^2}}-\frac{2 b g^3 x \sqrt{c x-1} \sqrt{c x+1}}{3 c^3 \sqrt{d-c^2 d x^2}}",1,"(-3*b*f^2*g*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(c*Sqrt[d - c^2*d*x^2]) - (2*b*g^3*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3*c^3*Sqrt[d - c^2*d*x^2]) - (3*b*f*g^2*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*c*Sqrt[d - c^2*d*x^2]) - (b*g^3*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(9*c*Sqrt[d - c^2*d*x^2]) - (3*f^2*g*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(c^2*Sqrt[d - c^2*d*x^2]) - (2*g^3*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(3*c^4*Sqrt[d - c^2*d*x^2]) - (3*f*g^2*x*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(2*c^2*Sqrt[d - c^2*d*x^2]) - (g^3*x^2*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(3*c^2*Sqrt[d - c^2*d*x^2]) + (f^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(2*b*c*Sqrt[d - c^2*d*x^2]) + (3*f*g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(4*b*c^3*Sqrt[d - c^2*d*x^2])","A",13,7,31,0.2258,1,"{5836, 5822, 5676, 5718, 8, 5759, 30}"
67,1,288,0,0.9142417,"\int \frac{(f+g x)^2 \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f + g*x)^2*(a + b*ArcCosh[c*x]))/Sqrt[d - c^2*d*x^2],x]","\frac{f^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{2 f g (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c^3 \sqrt{d-c^2 d x^2}}-\frac{g^2 x (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{2 c^2 \sqrt{d-c^2 d x^2}}-\frac{2 b f g x \sqrt{c x-1} \sqrt{c x+1}}{c \sqrt{d-c^2 d x^2}}-\frac{b g^2 x^2 \sqrt{c x-1} \sqrt{c x+1}}{4 c \sqrt{d-c^2 d x^2}}","\frac{f^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{2 f g (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}+\frac{g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c^3 \sqrt{d-c^2 d x^2}}-\frac{g^2 x (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{2 c^2 \sqrt{d-c^2 d x^2}}-\frac{2 b f g x \sqrt{c x-1} \sqrt{c x+1}}{c \sqrt{d-c^2 d x^2}}-\frac{b g^2 x^2 \sqrt{c x-1} \sqrt{c x+1}}{4 c \sqrt{d-c^2 d x^2}}",1,"(-2*b*f*g*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(c*Sqrt[d - c^2*d*x^2]) - (b*g^2*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*c*Sqrt[d - c^2*d*x^2]) - (2*f*g*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(c^2*Sqrt[d - c^2*d*x^2]) - (g^2*x*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(2*c^2*Sqrt[d - c^2*d*x^2]) + (f^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(2*b*c*Sqrt[d - c^2*d*x^2]) + (g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(4*b*c^3*Sqrt[d - c^2*d*x^2])","A",9,7,31,0.2258,1,"{5836, 5822, 5676, 5718, 8, 5759, 30}"
68,1,136,0,0.4720784,"\int \frac{(f+g x) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f + g*x)*(a + b*ArcCosh[c*x]))/Sqrt[d - c^2*d*x^2],x]","\frac{f \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{g (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}-\frac{b g x \sqrt{c x-1} \sqrt{c x+1}}{c \sqrt{d-c^2 d x^2}}","\frac{f \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{g (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}-\frac{b g x \sqrt{c x-1} \sqrt{c x+1}}{c \sqrt{d-c^2 d x^2}}",1,"-((b*g*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(c*Sqrt[d - c^2*d*x^2])) - (g*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(c^2*Sqrt[d - c^2*d*x^2]) + (f*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(2*b*c*Sqrt[d - c^2*d*x^2])","A",6,5,29,0.1724,1,"{5836, 5822, 5676, 5718, 8}"
69,1,365,0,0.7029934,"\int \frac{a+b \cosh ^{-1}(c x)}{(f+g x) \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCosh[c*x])/((f + g*x)*Sqrt[d - c^2*d*x^2]),x]","\frac{b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}","\frac{b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}",1,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 + (E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) - (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 + (E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2]) - (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/(Sqrt[c^2*f^2 - g^2]*Sqrt[d - c^2*d*x^2])","A",10,7,31,0.2258,1,"{5836, 5832, 3320, 2264, 2190, 2279, 2391}"
70,1,523,0,0.8363346,"\int \frac{a+b \cosh ^{-1}(c x)}{(f+g x)^2 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCosh[c*x])/((f + g*x)^2*Sqrt[d - c^2*d*x^2]),x]","\frac{b c^2 f \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{b c^2 f \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{g \sqrt{c x-1} \sqrt{-\frac{1-c x}{c x+1}} (c x+1)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right) (f+g x)}+\frac{c^2 f \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{c^2 f \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} \log (f+g x)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)}","\frac{b c^2 f \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{b c^2 f \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{g \sqrt{c x-1} \sqrt{-\frac{1-c x}{c x+1}} (c x+1)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right) (f+g x)}+\frac{c^2 f \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{c^2 f \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} \log (f+g x)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)}",1,"-((g*Sqrt[-1 + c*x]*Sqrt[-((1 - c*x)/(1 + c*x))]*(1 + c*x)^(3/2)*(a + b*ArcCosh[c*x]))/((c^2*f^2 - g^2)*(f + g*x)*Sqrt[d - c^2*d*x^2])) + (c^2*f*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 + (E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) - (c^2*f*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 + (E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) + (b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[f + g*x])/((c^2*f^2 - g^2)*Sqrt[d - c^2*d*x^2]) + (b*c^2*f*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) - (b*c^2*f*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/((c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2])","A",13,10,31,0.3226,1,"{5836, 5832, 3324, 3320, 2264, 2190, 2279, 2391, 2668, 31}"
71,1,549,0,1.5994943,"\int \frac{(f+g x)^3 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[((f + g*x)^3*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(3/2),x]","-\frac{3 f g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c^3 d \sqrt{d-c^2 d x^2}}-\frac{(1-c x) (c f-g)^3 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^4 d \sqrt{d-c^2 d x^2}}+\frac{(c x+1) (c f+g)^3 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^4 d \sqrt{d-c^2 d x^2}}+\frac{g^3 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f-g)^3 \log \left(\frac{2}{c x+1}\right)}{2 c^4 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f+g)^3 \log \left(\sqrt{-\frac{1-c x}{c x+1}}\right)}{c^4 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f+g)^3 \log \left(\frac{2}{c x+1}\right)}{2 c^4 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b g^3 x \sqrt{c x-1} \sqrt{c x+1}}{c^3 d \sqrt{d-c^2 d x^2}}","-\frac{3 f g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c^3 d \sqrt{d-c^2 d x^2}}-\frac{(1-c x) (c f-g)^3 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^4 d \sqrt{d-c^2 d x^2}}+\frac{(c x+1) (c f+g)^3 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^4 d \sqrt{d-c^2 d x^2}}+\frac{g^3 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f-g)^3 \log \left(\frac{2}{c x+1}\right)}{2 c^4 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f+g)^3 \log \left(\sqrt{-\frac{1-c x}{c x+1}}\right)}{c^4 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f+g)^3 \log \left(\frac{2}{c x+1}\right)}{2 c^4 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b g^3 x \sqrt{c x-1} \sqrt{c x+1}}{c^3 d \sqrt{d-c^2 d x^2}}",1,"(b*g^3*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(c^3*d*Sqrt[d - c^2*d*x^2]) - ((c*f - g)^3*(1 - c*x)*(a + b*ArcCosh[c*x]))/(2*c^4*d*Sqrt[d - c^2*d*x^2]) + ((c*f + g)^3*(1 + c*x)*(a + b*ArcCosh[c*x]))/(2*c^4*d*Sqrt[d - c^2*d*x^2]) + (g^3*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(c^4*d*Sqrt[d - c^2*d*x^2]) - (3*f*g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(2*b*c^3*d*Sqrt[d - c^2*d*x^2]) + (b*(c*f + g)^3*Sqrt[(1 - c*x)*(1 + c*x)]*Sqrt[1 - c^2*x^2]*Log[Sqrt[-((1 - c*x)/(1 + c*x))]])/(c^4*d*Sqrt[-((1 - c*x)/(1 + c*x))]*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (b*(c*f - g)^3*Sqrt[(1 - c*x)*(1 + c*x)]*Sqrt[1 - c^2*x^2]*Log[2/(1 + c*x)])/(2*c^4*d*Sqrt[-((1 - c*x)/(1 + c*x))]*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (b*(c*f + g)^3*Sqrt[(1 - c*x)*(1 + c*x)]*Sqrt[1 - c^2*x^2]*Log[2/(1 + c*x)])/(2*c^4*d*Sqrt[-((1 - c*x)/(1 + c*x))]*(1 + c*x)*Sqrt[d - c^2*d*x^2])","A",19,14,31,0.4516,1,"{5836, 5834, 37, 5848, 12, 6719, 260, 266, 36, 31, 29, 5676, 5718, 8}"
72,1,459,0,1.2666384,"\int \frac{(f+g x)^2 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[((f + g*x)^2*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(3/2),x]","-\frac{(1-c x) (c f-g)^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^3 d \sqrt{d-c^2 d x^2}}+\frac{(c x+1) (c f+g)^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^3 d \sqrt{d-c^2 d x^2}}-\frac{g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c^3 d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f-g)^2 \log \left(\frac{2}{c x+1}\right)}{2 c^3 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f+g)^2 \log \left(\sqrt{-\frac{1-c x}{c x+1}}\right)}{c^3 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f+g)^2 \log \left(\frac{2}{c x+1}\right)}{2 c^3 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}","-\frac{(1-c x) (c f-g)^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^3 d \sqrt{d-c^2 d x^2}}+\frac{(c x+1) (c f+g)^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^3 d \sqrt{d-c^2 d x^2}}-\frac{g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c^3 d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f-g)^2 \log \left(\frac{2}{c x+1}\right)}{2 c^3 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f+g)^2 \log \left(\sqrt{-\frac{1-c x}{c x+1}}\right)}{c^3 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f+g)^2 \log \left(\frac{2}{c x+1}\right)}{2 c^3 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}",1,"-((c*f - g)^2*(1 - c*x)*(a + b*ArcCosh[c*x]))/(2*c^3*d*Sqrt[d - c^2*d*x^2]) + ((c*f + g)^2*(1 + c*x)*(a + b*ArcCosh[c*x]))/(2*c^3*d*Sqrt[d - c^2*d*x^2]) - (g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(2*b*c^3*d*Sqrt[d - c^2*d*x^2]) + (b*(c*f + g)^2*Sqrt[(1 - c*x)*(1 + c*x)]*Sqrt[1 - c^2*x^2]*Log[Sqrt[-((1 - c*x)/(1 + c*x))]])/(c^3*d*Sqrt[-((1 - c*x)/(1 + c*x))]*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (b*(c*f - g)^2*Sqrt[(1 - c*x)*(1 + c*x)]*Sqrt[1 - c^2*x^2]*Log[2/(1 + c*x)])/(2*c^3*d*Sqrt[-((1 - c*x)/(1 + c*x))]*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (b*(c*f + g)^2*Sqrt[(1 - c*x)*(1 + c*x)]*Sqrt[1 - c^2*x^2]*Log[2/(1 + c*x)])/(2*c^3*d*Sqrt[-((1 - c*x)/(1 + c*x))]*(1 + c*x)*Sqrt[d - c^2*d*x^2])","A",17,12,31,0.3871,1,"{5836, 5834, 37, 5848, 12, 6719, 260, 266, 36, 31, 29, 5676}"
73,1,178,0,0.3065863,"\int \frac{(f+g x) \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[((f + g*x)*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(3/2),x]","-\frac{(c f-g) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{f (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{c d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{c x-1} \sqrt{c x+1} (c f-g) \tanh ^{-1}(c x)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{b f \sqrt{c x-1} \sqrt{c x+1} \log (1-c x)}{c d \sqrt{d-c^2 d x^2}}","\frac{\left(c^2 f x+g\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{c x-1} \sqrt{c x+1} (c f-g) \tanh ^{-1}(c x)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{b f \sqrt{c x-1} \sqrt{c x+1} \log (1-c x)}{c d \sqrt{d-c^2 d x^2}}",1,"-(((c*f - g)*(a + b*ArcCosh[c*x]))/(c^2*d*Sqrt[d - c^2*d*x^2])) + (f*(1 + c*x)*(a + b*ArcCosh[c*x]))/(c*d*Sqrt[d - c^2*d*x^2]) - (b*(c*f - g)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcTanh[c*x])/(c^2*d*Sqrt[d - c^2*d*x^2]) - (b*f*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[1 - c*x])/(c*d*Sqrt[d - c^2*d*x^2])","A",5,6,29,0.2069,1,"{5836, 78, 37, 5820, 35, 206}"
74,1,773,0,1.8573348,"\int \frac{a+b \cosh ^{-1}(c x)}{(f+g x) \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])/((f + g*x)*(d - c^2*d*x^2)^(3/2)),x]","-\frac{b g^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{b g^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{(1-c x) \left(a+b \cosh ^{-1}(c x)\right)}{2 d \sqrt{d-c^2 d x^2} (c f-g)}+\frac{(c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{2 d \sqrt{d-c^2 d x^2} (c f+g)}+\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} \log \left(\sqrt{-\frac{1-c x}{c x+1}}\right)}{d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2} (c f+g)}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} \log \left(\frac{2}{c x+1}\right)}{2 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2} (c f-g)}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} \log \left(\frac{2}{c x+1}\right)}{2 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2} (c f+g)}","-\frac{b g^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{b g^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{(1-c x) \left(a+b \cosh ^{-1}(c x)\right)}{2 d \sqrt{d-c^2 d x^2} (c f-g)}+\frac{(c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{2 d \sqrt{d-c^2 d x^2} (c f+g)}+\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} \log \left(\sqrt{-\frac{1-c x}{c x+1}}\right)}{d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2} (c f+g)}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} \log \left(\frac{2}{c x+1}\right)}{2 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2} (c f-g)}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} \log \left(\frac{2}{c x+1}\right)}{2 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2} (c f+g)}",1,"-((1 - c*x)*(a + b*ArcCosh[c*x]))/(2*d*(c*f - g)*Sqrt[d - c^2*d*x^2]) + ((1 + c*x)*(a + b*ArcCosh[c*x]))/(2*d*(c*f + g)*Sqrt[d - c^2*d*x^2]) - (g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 + (E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) + (g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 + (E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[(1 - c*x)*(1 + c*x)]*Sqrt[1 - c^2*x^2]*Log[Sqrt[-((1 - c*x)/(1 + c*x))]])/(d*(c*f + g)*Sqrt[-((1 - c*x)/(1 + c*x))]*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (b*Sqrt[(1 - c*x)*(1 + c*x)]*Sqrt[1 - c^2*x^2]*Log[2/(1 + c*x)])/(2*d*(c*f - g)*Sqrt[-((1 - c*x)/(1 + c*x))]*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (b*Sqrt[(1 - c*x)*(1 + c*x)]*Sqrt[1 - c^2*x^2]*Log[2/(1 + c*x)])/(2*d*(c*f + g)*Sqrt[-((1 - c*x)/(1 + c*x))]*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (b*g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/(d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2]) + (b*g^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/(d*(c^2*f^2 - g^2)^(3/2)*Sqrt[d - c^2*d*x^2])","A",25,17,31,0.5484,1,"{5836, 5834, 37, 5848, 12, 6719, 260, 266, 36, 31, 29, 5832, 3320, 2264, 2190, 2279, 2391}"
75,1,239,0,0.470914,"\int \frac{(f+g x) \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{1-c^2 x^2}} \, dx","Int[((f + g*x)*(a + b*ArcCosh[c*x])^n)/Sqrt[1 - c^2*x^2],x]","\frac{g e^{-\frac{a}{b}} \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^n \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{1-c^2 x^2}}-\frac{g e^{a/b} \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^n \left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{1-c^2 x^2}}+\frac{f \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{b c (n+1) \sqrt{1-c^2 x^2}}","\frac{g e^{-\frac{a}{b}} \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^n \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{1-c^2 x^2}}-\frac{g e^{a/b} \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^n \left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{1-c^2 x^2}}+\frac{f \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{b c (n+1) \sqrt{1-c^2 x^2}}",1,"(f*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^(1 + n))/(b*c*(1 + n)*Sqrt[1 - c^2*x^2]) + (g*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, -((a + b*ArcCosh[c*x])/b)])/(2*c^2*E^(a/b)*Sqrt[1 - c^2*x^2]*(-((a + b*ArcCosh[c*x])/b))^n) - (E^(a/b)*g*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (a + b*ArcCosh[c*x])/b])/(2*c^2*Sqrt[1 - c^2*x^2]*((a + b*ArcCosh[c*x])/b)^n)","A",7,5,30,0.1667,1,"{5836, 5832, 3317, 3307, 2181}"
76,1,242,0,0.6253531,"\int \frac{(f+g x) \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{1-c x} \sqrt{1+c x}} \, dx","Int[((f + g*x)*(a + b*ArcCosh[c*x])^n)/(Sqrt[1 - c*x]*Sqrt[1 + c*x]),x]","\frac{g e^{-\frac{a}{b}} \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{1-c x} \sqrt{c x+1}}-\frac{g e^{a/b} \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{1-c x} \sqrt{c x+1}}+\frac{f \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{b c (n+1) \sqrt{1-c x} \sqrt{c x+1}}","\frac{g e^{-\frac{a}{b}} \sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)^n \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{1-c x}}-\frac{g e^{a/b} \sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)^n \left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{1-c x}}+\frac{f \sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{b c (n+1) \sqrt{1-c x}}",1,"(f*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])^(1 + n))/(b*c*(1 + n)*Sqrt[1 - c*x]*Sqrt[1 + c*x]) + (g*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, -((a + b*ArcCosh[c*x])/b)])/(2*c^2*E^(a/b)*Sqrt[1 - c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (E^(a/b)*g*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (a + b*ArcCosh[c*x])/b])/(2*c^2*Sqrt[1 - c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n)","A",7,5,35,0.1429,0,"{5837, 5832, 3317, 3307, 2181}"
77,1,248,0,0.694553,"\int \frac{(f+g x) \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{\text{d1}+c \text{d1} x} \sqrt{\text{d2}-c \text{d2} x}} \, dx","Int[((f + g*x)*(a + b*ArcCosh[c*x])^n)/(Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]),x]","\frac{g e^{-\frac{a}{b}} \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}-\frac{g e^{a/b} \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}+\frac{f \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{b c (n+1) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}","\frac{g e^{-\frac{a}{b}} \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^n \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}-\frac{g e^{a/b} \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^n \left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}+\frac{f \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{b c (n+1) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}",1,"(f*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])^(1 + n))/(b*c*(1 + n)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]) + (g*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, -((a + b*ArcCosh[c*x])/b)])/(2*c^2*E^(a/b)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (E^(a/b)*g*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (a + b*ArcCosh[c*x])/b])/(2*c^2*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]*((a + b*ArcCosh[c*x])/b)^n)","A",7,5,37,0.1351,0,"{5837, 5832, 3317, 3307, 2181}"
78,0,0,0,0.9554793,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Int[((a + b*ArcCosh[c*x])^n*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2],x]","\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","\frac{\sqrt{c x-1} \sqrt{c x+1} \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^n \log \left(h (f+g x)^m\right)}{\sqrt{c x-1} \sqrt{c x+1}},x\right)}{\sqrt{1-c^2 x^2}}",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][((a + b*ArcCosh[c*x])^n*Log[h*(f + g*x)^m])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/Sqrt[1 - c^2*x^2]","A",0,0,0,0,-1,"{}"
79,1,774,0,1.5987473,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Int[((a + b*ArcCosh[c*x])^2*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2],x]","-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c \sqrt{1-c^2 x^2}}+\frac{2 b m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(3,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}+\frac{2 b m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(3,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c \sqrt{1-c^2 x^2}}-\frac{2 b^2 m \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(4,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}-\frac{2 b^2 m \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(4,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c \sqrt{1-c^2 x^2}}+\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^4}{12 b^2 c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3 \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{3 b c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3 \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{3 b c \sqrt{1-c^2 x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3 \log \left(h (f+g x)^m\right)}{3 b c \sqrt{1-c^2 x^2}}","-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c \sqrt{1-c^2 x^2}}+\frac{2 b m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(3,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}+\frac{2 b m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(3,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c \sqrt{1-c^2 x^2}}-\frac{2 b^2 m \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(4,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}-\frac{2 b^2 m \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(4,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c \sqrt{1-c^2 x^2}}+\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^4}{12 b^2 c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3 \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{3 b c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3 \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{3 b c \sqrt{1-c^2 x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3 \log \left(h (f+g x)^m\right)}{3 b c \sqrt{1-c^2 x^2}}",1,"(m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^4)/(12*b^2*c*Sqrt[1 - c^2*x^2]) - (m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^3*Log[1 + (E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(3*b*c*Sqrt[1 - c^2*x^2]) - (m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^3*Log[1 + (E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(3*b*c*Sqrt[1 - c^2*x^2]) + (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^3*Log[h*(f + g*x)^m])/(3*b*c*Sqrt[1 - c^2*x^2]) - (m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/(c*Sqrt[1 - c^2*x^2]) - (m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/(c*Sqrt[1 - c^2*x^2]) + (2*b*m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*PolyLog[3, -((E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/(c*Sqrt[1 - c^2*x^2]) + (2*b*m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*PolyLog[3, -((E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/(c*Sqrt[1 - c^2*x^2]) - (2*b^2*m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[4, -((E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/(c*Sqrt[1 - c^2*x^2]) - (2*b^2*m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[4, -((E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/(c*Sqrt[1 - c^2*x^2])","A",14,11,35,0.3143,1,"{5713, 5676, 5841, 5839, 5800, 5562, 2190, 2531, 6609, 2282, 6589}"
80,1,600,0,1.1292659,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Int[((a + b*ArcCosh[c*x])*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2],x]","-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c \sqrt{1-c^2 x^2}}+\frac{b m \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}+\frac{b m \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c \sqrt{1-c^2 x^2}}+\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{6 b^2 c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{2 b c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{2 b c \sqrt{1-c^2 x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(h (f+g x)^m\right)}{2 b c \sqrt{1-c^2 x^2}}","-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c \sqrt{1-c^2 x^2}}+\frac{b m \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,-\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}+\frac{b m \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,-\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c \sqrt{1-c^2 x^2}}+\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{6 b^2 c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{2 b c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{2 b c \sqrt{1-c^2 x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(h (f+g x)^m\right)}{2 b c \sqrt{1-c^2 x^2}}",1,"(m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^3)/(6*b^2*c*Sqrt[1 - c^2*x^2]) - (m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2*Log[1 + (E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/(2*b*c*Sqrt[1 - c^2*x^2]) - (m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2*Log[1 + (E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/(2*b*c*Sqrt[1 - c^2*x^2]) + (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2*Log[h*(f + g*x)^m])/(2*b*c*Sqrt[1 - c^2*x^2]) - (m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/(c*Sqrt[1 - c^2*x^2]) - (m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*PolyLog[2, -((E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/(c*Sqrt[1 - c^2*x^2]) + (b*m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[3, -((E^ArcCosh[c*x]*g)/(c*f - Sqrt[c^2*f^2 - g^2]))])/(c*Sqrt[1 - c^2*x^2]) + (b*m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[3, -((E^ArcCosh[c*x]*g)/(c*f + Sqrt[c^2*f^2 - g^2]))])/(c*Sqrt[1 - c^2*x^2])","A",12,10,33,0.3030,1,"{5713, 5676, 5841, 5839, 5800, 5562, 2190, 2531, 2282, 6589}"
81,1,237,0,0.3456121,"\int \frac{\log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Int[Log[h*(f + g*x)^m]/Sqrt[1 - c^2*x^2],x]","\frac{i m \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{i m \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{m \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{m \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{\sin ^{-1}(c x) \log \left(h (f+g x)^m\right)}{c}+\frac{i m \sin ^{-1}(c x)^2}{2 c}","\frac{i m \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{i m \text{PolyLog}\left(2,\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}-\frac{m \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{m \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{\sin ^{-1}(c x) \log \left(h (f+g x)^m\right)}{c}+\frac{i m \sin ^{-1}(c x)^2}{2 c}",1,"((I/2)*m*ArcSin[c*x]^2)/c - (m*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/c - (m*ArcSin[c*x]*Log[1 - (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/c + (ArcSin[c*x]*Log[h*(f + g*x)^m])/c + (I*m*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/c + (I*m*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/c","A",9,7,25,0.2800,1,"{216, 2404, 4741, 4519, 2190, 2279, 2391}"
82,0,0,0,1.0626735,"\int \frac{\log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[Log[h*(f + g*x)^m]/(Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])),x]","\int \frac{\log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\frac{\sqrt{c x-1} \sqrt{c x+1} \text{Int}\left(\frac{\log \left(h (f+g x)^m\right)}{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{\sqrt{1-c^2 x^2}}",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][Log[h*(f + g*x)^m]/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])), x])/Sqrt[1 - c^2*x^2]","A",0,0,0,0,-1,"{}"
83,1,152,0,0.1866383,"\int x^3 \cosh ^{-1}(a+b x) \, dx","Int[x^3*ArcCosh[a + b*x],x]","\frac{\sqrt{a+b x-1} \sqrt{a+b x+1} \left(4 a \left(19 a^2+16\right)-\left(26 a^2+9\right) (a+b x)\right)}{96 b^4}-\frac{\left(8 a^4+24 a^2+3\right) \cosh ^{-1}(a+b x)}{32 b^4}+\frac{7 a x^2 \sqrt{a+b x-1} \sqrt{a+b x+1}}{48 b^2}-\frac{x^3 \sqrt{a+b x-1} \sqrt{a+b x+1}}{16 b}+\frac{1}{4} x^4 \cosh ^{-1}(a+b x)","\frac{\sqrt{a+b x-1} \sqrt{a+b x+1} \left(4 a \left(19 a^2+16\right)-\left(26 a^2+9\right) (a+b x)\right)}{96 b^4}-\frac{\left(8 a^4+24 a^2+3\right) \cosh ^{-1}(a+b x)}{32 b^4}+\frac{7 a x^2 \sqrt{a+b x-1} \sqrt{a+b x+1}}{48 b^2}-\frac{x^3 \sqrt{a+b x-1} \sqrt{a+b x+1}}{16 b}+\frac{1}{4} x^4 \cosh ^{-1}(a+b x)",1,"(7*a*x^2*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/(48*b^2) - (x^3*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/(16*b) + (Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]*(4*a*(16 + 19*a^2) - (9 + 26*a^2)*(a + b*x)))/(96*b^4) - ((3 + 24*a^2 + 8*a^4)*ArcCosh[a + b*x])/(32*b^4) + (x^4*ArcCosh[a + b*x])/4","A",6,6,10,0.6000,1,"{5866, 5802, 100, 153, 147, 52}"
84,1,104,0,0.1190969,"\int x^2 \cosh ^{-1}(a+b x) \, dx","Int[x^2*ArcCosh[a + b*x],x]","-\frac{\sqrt{a+b x-1} \sqrt{a+b x+1} \left(11 a^2-5 a b x+4\right)}{18 b^3}+\frac{a \left(2 a^2+3\right) \cosh ^{-1}(a+b x)}{6 b^3}-\frac{x^2 \sqrt{a+b x-1} \sqrt{a+b x+1}}{9 b}+\frac{1}{3} x^3 \cosh ^{-1}(a+b x)","-\frac{\sqrt{a+b x-1} \sqrt{a+b x+1} \left(11 a^2-5 a b x+4\right)}{18 b^3}+\frac{a \left(2 a^2+3\right) \cosh ^{-1}(a+b x)}{6 b^3}-\frac{x^2 \sqrt{a+b x-1} \sqrt{a+b x+1}}{9 b}+\frac{1}{3} x^3 \cosh ^{-1}(a+b x)",1,"-(x^2*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/(9*b) - (Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]*(4 + 11*a^2 - 5*a*b*x))/(18*b^3) + (a*(3 + 2*a^2)*ArcCosh[a + b*x])/(6*b^3) + (x^3*ArcCosh[a + b*x])/3","A",5,5,10,0.5000,1,"{5866, 5802, 100, 147, 52}"
85,1,90,0,0.0638357,"\int x \cosh ^{-1}(a+b x) \, dx","Int[x*ArcCosh[a + b*x],x]","-\frac{\left(2 a^2+1\right) \cosh ^{-1}(a+b x)}{4 b^2}+\frac{3 a \sqrt{a+b x-1} \sqrt{a+b x+1}}{4 b^2}+\frac{1}{2} x^2 \cosh ^{-1}(a+b x)-\frac{x \sqrt{a+b x-1} \sqrt{a+b x+1}}{4 b}","-\frac{\left(2 a^2+1\right) \cosh ^{-1}(a+b x)}{4 b^2}+\frac{3 a \sqrt{a+b x-1} \sqrt{a+b x+1}}{4 b^2}+\frac{1}{2} x^2 \cosh ^{-1}(a+b x)-\frac{x \sqrt{a+b x-1} \sqrt{a+b x+1}}{4 b}",1,"(3*a*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/(4*b^2) - (x*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/(4*b) - ((1 + 2*a^2)*ArcCosh[a + b*x])/(4*b^2) + (x^2*ArcCosh[a + b*x])/2","A",5,5,8,0.6250,1,"{5866, 5802, 90, 80, 52}"
86,1,41,0,0.0158476,"\int \cosh ^{-1}(a+b x) \, dx","Int[ArcCosh[a + b*x],x]","\frac{(a+b x) \cosh ^{-1}(a+b x)}{b}-\frac{\sqrt{a+b x-1} \sqrt{a+b x+1}}{b}","\frac{(a+b x) \cosh ^{-1}(a+b x)}{b}-\frac{\sqrt{a+b x-1} \sqrt{a+b x+1}}{b}",1,"-((Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/b) + ((a + b*x)*ArcCosh[a + b*x])/b","A",3,3,6,0.5000,1,"{5864, 5654, 74}"
87,1,131,0,0.2491891,"\int \frac{\cosh ^{-1}(a+b x)}{x} \, dx","Int[ArcCosh[a + b*x]/x,x]","\text{PolyLog}\left(2,\frac{e^{\cosh ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)+\text{PolyLog}\left(2,\frac{e^{\cosh ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)+\cosh ^{-1}(a+b x) \log \left(1-\frac{e^{\cosh ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)+\cosh ^{-1}(a+b x) \log \left(1-\frac{e^{\cosh ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)-\frac{1}{2} \cosh ^{-1}(a+b x)^2","\text{PolyLog}\left(2,\frac{e^{\cosh ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)+\text{PolyLog}\left(2,\frac{e^{\cosh ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)+\cosh ^{-1}(a+b x) \log \left(1-\frac{e^{\cosh ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)+\cosh ^{-1}(a+b x) \log \left(1-\frac{e^{\cosh ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)-\frac{1}{2} \cosh ^{-1}(a+b x)^2",1,"-ArcCosh[a + b*x]^2/2 + ArcCosh[a + b*x]*Log[1 - E^ArcCosh[a + b*x]/(a - Sqrt[-1 + a^2])] + ArcCosh[a + b*x]*Log[1 - E^ArcCosh[a + b*x]/(a + Sqrt[-1 + a^2])] + PolyLog[2, E^ArcCosh[a + b*x]/(a - Sqrt[-1 + a^2])] + PolyLog[2, E^ArcCosh[a + b*x]/(a + Sqrt[-1 + a^2])]","A",9,6,10,0.6000,1,"{5866, 5800, 5562, 2190, 2279, 2391}"
88,1,64,0,0.0828594,"\int \frac{\cosh ^{-1}(a+b x)}{x^2} \, dx","Int[ArcCosh[a + b*x]/x^2,x]","-\frac{2 b \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{\sqrt{1-a^2}}-\frac{\cosh ^{-1}(a+b x)}{x}","-\frac{2 b \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{\sqrt{1-a^2}}-\frac{\cosh ^{-1}(a+b x)}{x}",1,"-(ArcCosh[a + b*x]/x) - (2*b*ArcTan[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[-1 + a + b*x])])/Sqrt[1 - a^2]","A",4,4,10,0.4000,1,"{5866, 5802, 93, 205}"
89,1,106,0,0.1020586,"\int \frac{\cosh ^{-1}(a+b x)}{x^3} \, dx","Int[ArcCosh[a + b*x]/x^3,x]","-\frac{a b^2 \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{\left(1-a^2\right)^{3/2}}+\frac{b \sqrt{a+b x-1} \sqrt{a+b x+1}}{2 \left(1-a^2\right) x}-\frac{\cosh ^{-1}(a+b x)}{2 x^2}","-\frac{a b^2 \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{\left(1-a^2\right)^{3/2}}+\frac{b \sqrt{a+b x-1} \sqrt{a+b x+1}}{2 \left(1-a^2\right) x}-\frac{\cosh ^{-1}(a+b x)}{2 x^2}",1,"(b*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/(2*(1 - a^2)*x) - ArcCosh[a + b*x]/(2*x^2) - (a*b^2*ArcTan[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[-1 + a + b*x])])/(1 - a^2)^(3/2)","A",5,5,10,0.5000,1,"{5866, 5802, 96, 93, 205}"
90,1,154,0,0.1718418,"\int \frac{\cosh ^{-1}(a+b x)}{x^4} \, dx","Int[ArcCosh[a + b*x]/x^4,x]","\frac{a b^2 \sqrt{a+b x-1} \sqrt{a+b x+1}}{2 \left(1-a^2\right)^2 x}-\frac{\left(2 a^2+1\right) b^3 \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{3 \left(1-a^2\right)^{5/2}}+\frac{b \sqrt{a+b x-1} \sqrt{a+b x+1}}{6 \left(1-a^2\right) x^2}-\frac{\cosh ^{-1}(a+b x)}{3 x^3}","\frac{a b^2 \sqrt{a+b x-1} \sqrt{a+b x+1}}{2 \left(1-a^2\right)^2 x}-\frac{\left(2 a^2+1\right) b^3 \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{3 \left(1-a^2\right)^{5/2}}+\frac{b \sqrt{a+b x-1} \sqrt{a+b x+1}}{6 \left(1-a^2\right) x^2}-\frac{\cosh ^{-1}(a+b x)}{3 x^3}",1,"(b*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/(6*(1 - a^2)*x^2) + (a*b^2*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/(2*(1 - a^2)^2*x) - ArcCosh[a + b*x]/(3*x^3) - ((1 + 2*a^2)*b^3*ArcTan[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[-1 + a + b*x])])/(3*(1 - a^2)^(5/2))","A",7,7,10,0.7000,1,"{5866, 5802, 103, 151, 12, 93, 205}"
91,1,92,0,0.135609,"\int \frac{1}{\sqrt{a+b \cosh ^{-1}(c+d x)}} \, dx","Int[1/Sqrt[a + b*ArcCosh[c + d*x]],x]","\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}","\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}",1,"-(E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(2*Sqrt[b]*d) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(2*Sqrt[b]*d*E^(a/b))","A",7,6,14,0.4286,1,"{5864, 5658, 3308, 2180, 2205, 2204}"
92,1,94,0,0.1286338,"\int \frac{1}{\sqrt{a-b \cosh ^{-1}(c+d x)}} \, dx","Int[1/Sqrt[a - b*ArcCosh[c + d*x]],x]","\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a-b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a-b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}","\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a-b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a-b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}",1,"-(E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a - b*ArcCosh[c + d*x]]/Sqrt[b]])/(2*Sqrt[b]*d) + (Sqrt[Pi]*Erfi[Sqrt[a - b*ArcCosh[c + d*x]]/Sqrt[b]])/(2*Sqrt[b]*d*E^(a/b))","A",7,6,15,0.4000,1,"{5864, 5658, 3308, 2180, 2205, 2204}"
93,1,135,0,0.0855618,"\int (c e+d e x)^4 \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^4*(a + b*ArcCosh[c + d*x]),x]","\frac{e^4 (c+d x)^5 \left(a+b \cosh ^{-1}(c+d x)\right)}{5 d}-\frac{b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{25 d}-\frac{4 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{75 d}-\frac{8 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1}}{75 d}","\frac{e^4 (c+d x)^5 \left(a+b \cosh ^{-1}(c+d x)\right)}{5 d}-\frac{b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{25 d}-\frac{4 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{75 d}-\frac{8 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1}}{75 d}",1,"(-8*b*e^4*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(75*d) - (4*b*e^4*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])/(75*d) - (b*e^4*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x])/(25*d) + (e^4*(c + d*x)^5*(a + b*ArcCosh[c + d*x]))/(5*d)","A",8,5,21,0.2381,1,"{5866, 12, 5662, 100, 74}"
94,1,119,0,0.0705448,"\int (c e+d e x)^3 \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcCosh[c + d*x]),x]","\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)}{4 d}-\frac{b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{16 d}-\frac{3 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{32 d}-\frac{3 b e^3 \cosh ^{-1}(c+d x)}{32 d}","\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)}{4 d}-\frac{b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{16 d}-\frac{3 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{32 d}-\frac{3 b e^3 \cosh ^{-1}(c+d x)}{32 d}",1,"(-3*b*e^3*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(32*d) - (b*e^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x])/(16*d) - (3*b*e^3*ArcCosh[c + d*x])/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcCosh[c + d*x]))/(4*d)","A",7,6,21,0.2857,1,"{5866, 12, 5662, 100, 90, 52}"
95,1,97,0,0.0630765,"\int (c e+d e x)^2 \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcCosh[c + d*x]),x]","\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d}-\frac{b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{9 d}-\frac{2 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{9 d}","\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d}-\frac{b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{9 d}-\frac{2 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{9 d}",1,"(-2*b*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(9*d) - (b*e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])/(9*d) + (e^2*(c + d*x)^3*(a + b*ArcCosh[c + d*x]))/(3*d)","A",6,5,21,0.2381,1,"{5866, 12, 5662, 100, 74}"
96,1,75,0,0.0389998,"\int (c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)*(a + b*ArcCosh[c + d*x]),x]","\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{2 d}-\frac{b e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{4 d}-\frac{b e \cosh ^{-1}(c+d x)}{4 d}","\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{2 d}-\frac{b e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{4 d}-\frac{b e \cosh ^{-1}(c+d x)}{4 d}",1,"-(b*e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(4*d) - (b*e*ArcCosh[c + d*x])/(4*d) + (e*(c + d*x)^2*(a + b*ArcCosh[c + d*x]))/(2*d)","A",5,5,19,0.2632,1,"{5866, 12, 5662, 90, 52}"
97,1,46,0,0.0235829,"\int \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Int[a + b*ArcCosh[c + d*x],x]","a x-\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{d}+\frac{b (c+d x) \cosh ^{-1}(c+d x)}{d}","a x-\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{d}+\frac{b (c+d x) \cosh ^{-1}(c+d x)}{d}",1,"a*x - (b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/d + (b*(c + d*x)*ArcCosh[c + d*x])/d","A",4,3,10,0.3000,1,"{5864, 5654, 74}"
98,1,81,0,0.1070322,"\int \frac{a+b \cosh ^{-1}(c+d x)}{c e+d e x} \, dx","Int[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x),x]","\frac{b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c+d x)}\right)}{2 d e}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 b d e}+\frac{\log \left(e^{2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e}","-\frac{b \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c+d x)}\right)}{2 d e}+\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 b d e}+\frac{\log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e}",1,"-(a + b*ArcCosh[c + d*x])^2/(2*b*d*e) + ((a + b*ArcCosh[c + d*x])*Log[1 + E^(2*ArcCosh[c + d*x])])/(d*e) + (b*PolyLog[2, -E^(2*ArcCosh[c + d*x])])/(2*d*e)","A",7,7,21,0.3333,0,"{5866, 12, 5660, 3718, 2190, 2279, 2391}"
99,1,56,0,0.0516872,"\int \frac{a+b \cosh ^{-1}(c+d x)}{(c e+d e x)^2} \, dx","Int[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x)^2,x]","\frac{b \tan ^{-1}\left(\sqrt{c+d x-1} \sqrt{c+d x+1}\right)}{d e^2}-\frac{a+b \cosh ^{-1}(c+d x)}{d e^2 (c+d x)}","\frac{b \tan ^{-1}\left(\sqrt{c+d x-1} \sqrt{c+d x+1}\right)}{d e^2}-\frac{a+b \cosh ^{-1}(c+d x)}{d e^2 (c+d x)}",1,"-((a + b*ArcCosh[c + d*x])/(d*e^2*(c + d*x))) + (b*ArcTan[Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]])/(d*e^2)","A",5,5,21,0.2381,1,"{5866, 12, 5662, 92, 203}"
100,1,66,0,0.0542246,"\int \frac{a+b \cosh ^{-1}(c+d x)}{(c e+d e x)^3} \, dx","Int[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x)^3,x]","\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{2 d e^3 (c+d x)}-\frac{a+b \cosh ^{-1}(c+d x)}{2 d e^3 (c+d x)^2}","\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{2 d e^3 (c+d x)}-\frac{a+b \cosh ^{-1}(c+d x)}{2 d e^3 (c+d x)^2}",1,"(b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(2*d*e^3*(c + d*x)) - (a + b*ArcCosh[c + d*x])/(2*d*e^3*(c + d*x)^2)","A",4,4,21,0.1905,1,"{5866, 12, 5662, 95}"
101,1,99,0,0.0650914,"\int \frac{a+b \cosh ^{-1}(c+d x)}{(c e+d e x)^4} \, dx","Int[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x)^4,x]","-\frac{a+b \cosh ^{-1}(c+d x)}{3 d e^4 (c+d x)^3}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{6 d e^4 (c+d x)^2}+\frac{b \tan ^{-1}\left(\sqrt{c+d x-1} \sqrt{c+d x+1}\right)}{6 d e^4}","-\frac{a+b \cosh ^{-1}(c+d x)}{3 d e^4 (c+d x)^3}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{6 d e^4 (c+d x)^2}+\frac{b \tan ^{-1}\left(\sqrt{c+d x-1} \sqrt{c+d x+1}\right)}{6 d e^4}",1,"(b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(6*d*e^4*(c + d*x)^2) - (a + b*ArcCosh[c + d*x])/(3*d*e^4*(c + d*x)^3) + (b*ArcTan[Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]])/(6*d*e^4)","A",6,6,21,0.2857,1,"{5866, 12, 5662, 103, 92, 203}"
102,1,104,0,0.0694655,"\int \frac{a+b \cosh ^{-1}(c+d x)}{(c e+d e x)^5} \, dx","Int[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x)^5,x]","-\frac{a+b \cosh ^{-1}(c+d x)}{4 d e^5 (c+d x)^4}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{6 d e^5 (c+d x)}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{12 d e^5 (c+d x)^3}","-\frac{a+b \cosh ^{-1}(c+d x)}{4 d e^5 (c+d x)^4}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{6 d e^5 (c+d x)}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{12 d e^5 (c+d x)^3}",1,"(b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(12*d*e^5*(c + d*x)^3) + (b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(6*d*e^5*(c + d*x)) - (a + b*ArcCosh[c + d*x])/(4*d*e^5*(c + d*x)^4)","A",6,5,21,0.2381,1,"{5866, 12, 5662, 103, 95}"
103,1,137,0,0.0866639,"\int \frac{a+b \cosh ^{-1}(c+d x)}{(c e+d e x)^6} \, dx","Int[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x)^6,x]","-\frac{a+b \cosh ^{-1}(c+d x)}{5 d e^6 (c+d x)^5}+\frac{3 b \sqrt{c+d x-1} \sqrt{c+d x+1}}{40 d e^6 (c+d x)^2}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{20 d e^6 (c+d x)^4}+\frac{3 b \tan ^{-1}\left(\sqrt{c+d x-1} \sqrt{c+d x+1}\right)}{40 d e^6}","-\frac{a+b \cosh ^{-1}(c+d x)}{5 d e^6 (c+d x)^5}+\frac{3 b \sqrt{c+d x-1} \sqrt{c+d x+1}}{40 d e^6 (c+d x)^2}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{20 d e^6 (c+d x)^4}+\frac{3 b \tan ^{-1}\left(\sqrt{c+d x-1} \sqrt{c+d x+1}\right)}{40 d e^6}",1,"(b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(20*d*e^6*(c + d*x)^4) + (3*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(40*d*e^6*(c + d*x)^2) - (a + b*ArcCosh[c + d*x])/(5*d*e^6*(c + d*x)^5) + (3*b*ArcTan[Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]])/(40*d*e^6)","A",8,6,21,0.2857,1,"{5866, 12, 5662, 103, 92, 203}"
104,1,218,0,0.4851177,"\int (c e+d e x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^4*(a + b*ArcCosh[c + d*x])^2,x]","\frac{e^4 (c+d x)^5 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{5 d}-\frac{2 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)}{25 d}-\frac{8 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{75 d}-\frac{16 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{75 d}+\frac{2 b^2 e^4 (c+d x)^5}{125 d}+\frac{8 b^2 e^4 (c+d x)^3}{225 d}+\frac{16}{75} b^2 e^4 x","\frac{e^4 (c+d x)^5 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{5 d}-\frac{2 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)}{25 d}-\frac{8 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{75 d}-\frac{16 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{75 d}+\frac{2 b^2 e^4 (c+d x)^5}{125 d}+\frac{8 b^2 e^4 (c+d x)^3}{225 d}+\frac{16}{75} b^2 e^4 x",1,"(16*b^2*e^4*x)/75 + (8*b^2*e^4*(c + d*x)^3)/(225*d) + (2*b^2*e^4*(c + d*x)^5)/(125*d) - (16*b*e^4*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/(75*d) - (8*b*e^4*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/(75*d) - (2*b*e^4*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/(25*d) + (e^4*(c + d*x)^5*(a + b*ArcCosh[c + d*x])^2)/(5*d)","A",9,7,23,0.3043,1,"{5866, 12, 5662, 5759, 5718, 8, 30}"
105,1,186,0,0.4358379,"\int (c e+d e x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcCosh[c + d*x])^2,x]","\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{4 d}-\frac{b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)}{8 d}-\frac{3 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)}{16 d}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{32 d}+\frac{b^2 e^3 (c+d x)^4}{32 d}+\frac{3 b^2 e^3 (c+d x)^2}{32 d}","\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{4 d}-\frac{b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)}{8 d}-\frac{3 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)}{16 d}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{32 d}+\frac{b^2 e^3 (c+d x)^4}{32 d}+\frac{3 b^2 e^3 (c+d x)^2}{32 d}",1,"(3*b^2*e^3*(c + d*x)^2)/(32*d) + (b^2*e^3*(c + d*x)^4)/(32*d) - (3*b*e^3*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/(16*d) - (b*e^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/(8*d) - (3*e^3*(a + b*ArcCosh[c + d*x])^2)/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcCosh[c + d*x])^2)/(4*d)","A",8,6,23,0.2609,1,"{5866, 12, 5662, 5759, 5676, 30}"
106,1,150,0,0.323398,"\int (c e+d e x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcCosh[c + d*x])^2,x]","\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d}-\frac{2 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{9 d}-\frac{4 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{9 d}+\frac{2 b^2 e^2 (c+d x)^3}{27 d}+\frac{4}{9} b^2 e^2 x","\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d}-\frac{2 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{9 d}-\frac{4 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{9 d}+\frac{2 b^2 e^2 (c+d x)^3}{27 d}+\frac{4}{9} b^2 e^2 x",1,"(4*b^2*e^2*x)/9 + (2*b^2*e^2*(c + d*x)^3)/(27*d) - (4*b*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/(9*d) - (2*b*e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/(9*d) + (e^2*(c + d*x)^3*(a + b*ArcCosh[c + d*x])^2)/(3*d)","A",7,7,23,0.3043,1,"{5866, 12, 5662, 5759, 5718, 8, 30}"
107,1,110,0,0.2507055,"\int (c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^2,x]","\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d}-\frac{b e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)}{2 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^2}{4 d}+\frac{b^2 e (c+d x)^2}{4 d}","\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d}-\frac{b e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)}{2 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^2}{4 d}+\frac{b^2 e (c+d x)^2}{4 d}",1,"(b^2*e*(c + d*x)^2)/(4*d) - (b*e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/(2*d) - (e*(a + b*ArcCosh[c + d*x])^2)/(4*d) + (e*(c + d*x)^2*(a + b*ArcCosh[c + d*x])^2)/(2*d)","A",6,6,21,0.2857,1,"{5866, 12, 5662, 5759, 5676, 30}"
108,1,64,0,0.1246947,"\int \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Int[(a + b*ArcCosh[c + d*x])^2,x]","-\frac{2 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d}+2 b^2 x","-\frac{2 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d}+2 b^2 x",1,"2*b^2*x - (2*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/d + ((c + d*x)*(a + b*ArcCosh[c + d*x])^2)/d","A",4,4,12,0.3333,1,"{5864, 5654, 5718, 8}"
109,1,117,0,0.1900746,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{c e+d e x} \, dx","Int[(a + b*ArcCosh[c + d*x])^2/(c*e + d*e*x),x]","\frac{b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 \cosh ^{-1}(c+d x)}\right)}{2 d e}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 b d e}+\frac{\log \left(e^{2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e}","-\frac{b \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e}-\frac{b^2 \text{PolyLog}\left(3,-e^{-2 \cosh ^{-1}(c+d x)}\right)}{2 d e}+\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 b d e}+\frac{\log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e}",1,"-(a + b*ArcCosh[c + d*x])^3/(3*b*d*e) + ((a + b*ArcCosh[c + d*x])^2*Log[1 + E^(2*ArcCosh[c + d*x])])/(d*e) + (b*(a + b*ArcCosh[c + d*x])*PolyLog[2, -E^(2*ArcCosh[c + d*x])])/(d*e) - (b^2*PolyLog[3, -E^(2*ArcCosh[c + d*x])])/(2*d*e)","A",8,8,23,0.3478,0,"{5866, 12, 5660, 3718, 2190, 2531, 2282, 6589}"
110,1,110,0,0.2429456,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{(c e+d e x)^2} \, dx","Int[(a + b*ArcCosh[c + d*x])^2/(c*e + d*e*x)^2,x]","-\frac{2 i b^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}+\frac{2 i b^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^2 (c+d x)}+\frac{4 b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2}","-\frac{2 i b^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}+\frac{2 i b^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^2 (c+d x)}+\frac{4 b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2}",1,"-((a + b*ArcCosh[c + d*x])^2/(d*e^2*(c + d*x))) + (4*b*(a + b*ArcCosh[c + d*x])*ArcTan[E^ArcCosh[c + d*x]])/(d*e^2) - ((2*I)*b^2*PolyLog[2, (-I)*E^ArcCosh[c + d*x]])/(d*e^2) + ((2*I)*b^2*PolyLog[2, I*E^ArcCosh[c + d*x]])/(d*e^2)","A",9,7,23,0.3043,1,"{5866, 12, 5662, 5761, 4180, 2279, 2391}"
111,1,92,0,0.2139521,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{(c e+d e x)^3} \, dx","Int[(a + b*ArcCosh[c + d*x])^2/(c*e + d*e*x)^3,x]","\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^3 (c+d x)}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)^2}-\frac{b^2 \log (c+d x)}{d e^3}","\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^3 (c+d x)}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)^2}-\frac{b^2 \log (c+d x)}{d e^3}",1,"(b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/(d*e^3*(c + d*x)) - (a + b*ArcCosh[c + d*x])^2/(2*d*e^3*(c + d*x)^2) - (b^2*Log[c + d*x])/(d*e^3)","A",5,5,23,0.2174,1,"{5866, 12, 5662, 5724, 29}"
112,1,186,0,0.3868171,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{(c e+d e x)^4} \, dx","Int[(a + b*ArcCosh[c + d*x])^2/(c*e + d*e*x)^4,x]","-\frac{i b^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c+d x)}\right)}{3 d e^4}+\frac{i b^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c+d x)}\right)}{3 d e^4}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d e^4 (c+d x)^3}+\frac{2 b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e^4}+\frac{b^2}{3 d e^4 (c+d x)}","-\frac{i b^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c+d x)}\right)}{3 d e^4}+\frac{i b^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c+d x)}\right)}{3 d e^4}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d e^4 (c+d x)^3}+\frac{2 b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e^4}+\frac{b^2}{3 d e^4 (c+d x)}",1,"b^2/(3*d*e^4*(c + d*x)) + (b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/(3*d*e^4*(c + d*x)^2) - (a + b*ArcCosh[c + d*x])^2/(3*d*e^4*(c + d*x)^3) + (2*b*(a + b*ArcCosh[c + d*x])*ArcTan[E^ArcCosh[c + d*x]])/(3*d*e^4) - ((I/3)*b^2*PolyLog[2, (-I)*E^ArcCosh[c + d*x]])/(d*e^4) + ((I/3)*b^2*PolyLog[2, I*E^ArcCosh[c + d*x]])/(d*e^4)","A",11,9,23,0.3913,1,"{5866, 12, 5662, 5748, 5761, 4180, 2279, 2391, 30}"
113,1,382,0,0.7231726,"\int (c e+d e x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^4*(a + b*ArcCosh[c + d*x])^3,x]","\frac{6 b^2 e^4 (c+d x)^5 \left(a+b \cosh ^{-1}(c+d x)\right)}{125 d}+\frac{8 b^2 e^4 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)}{75 d}+\frac{16}{25} a b^2 e^4 x+\frac{e^4 (c+d x)^5 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{5 d}-\frac{3 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{25 d}-\frac{4 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{25 d}-\frac{8 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{25 d}-\frac{6 b^3 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{625 d}-\frac{272 b^3 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{5625 d}-\frac{4144 b^3 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1}}{5625 d}+\frac{16 b^3 e^4 (c+d x) \cosh ^{-1}(c+d x)}{25 d}","\frac{6 b^2 e^4 (c+d x)^5 \left(a+b \cosh ^{-1}(c+d x)\right)}{125 d}+\frac{8 b^2 e^4 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)}{75 d}+\frac{16}{25} a b^2 e^4 x+\frac{e^4 (c+d x)^5 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{5 d}-\frac{3 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{25 d}-\frac{4 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{25 d}-\frac{8 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{25 d}-\frac{6 b^3 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{625 d}-\frac{272 b^3 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{5625 d}-\frac{4144 b^3 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1}}{5625 d}+\frac{16 b^3 e^4 (c+d x) \cosh ^{-1}(c+d x)}{25 d}",1,"(16*a*b^2*e^4*x)/25 - (4144*b^3*e^4*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(5625*d) - (272*b^3*e^4*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])/(5625*d) - (6*b^3*e^4*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x])/(625*d) + (16*b^3*e^4*(c + d*x)*ArcCosh[c + d*x])/(25*d) + (8*b^2*e^4*(c + d*x)^3*(a + b*ArcCosh[c + d*x]))/(75*d) + (6*b^2*e^4*(c + d*x)^5*(a + b*ArcCosh[c + d*x]))/(125*d) - (8*b*e^4*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^2)/(25*d) - (4*b*e^4*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^2)/(25*d) - (3*b*e^4*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^2)/(25*d) + (e^4*(c + d*x)^5*(a + b*ArcCosh[c + d*x])^3)/(5*d)","A",19,8,23,0.3478,1,"{5866, 12, 5662, 5759, 5718, 5654, 74, 100}"
114,1,307,0,0.6245997,"\int (c e+d e x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcCosh[c + d*x])^3,x]","\frac{3 b^2 e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)}{32 d}+\frac{9 b^2 e^3 (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{32 d}+\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{4 d}-\frac{3 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{16 d}-\frac{9 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{32 d}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{32 d}-\frac{3 b^3 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{128 d}-\frac{45 b^3 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{256 d}-\frac{45 b^3 e^3 \cosh ^{-1}(c+d x)}{256 d}","\frac{3 b^2 e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)}{32 d}+\frac{9 b^2 e^3 (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{32 d}+\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{4 d}-\frac{3 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{16 d}-\frac{9 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{32 d}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{32 d}-\frac{3 b^3 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{128 d}-\frac{45 b^3 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{256 d}-\frac{45 b^3 e^3 \cosh ^{-1}(c+d x)}{256 d}",1,"(-45*b^3*e^3*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(256*d) - (3*b^3*e^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x])/(128*d) - (45*b^3*e^3*ArcCosh[c + d*x])/(256*d) + (9*b^2*e^3*(c + d*x)^2*(a + b*ArcCosh[c + d*x]))/(32*d) + (3*b^2*e^3*(c + d*x)^4*(a + b*ArcCosh[c + d*x]))/(32*d) - (9*b*e^3*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^2)/(32*d) - (3*b*e^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^2)/(16*d) - (3*e^3*(a + b*ArcCosh[c + d*x])^3)/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcCosh[c + d*x])^3)/(4*d)","A",14,8,23,0.3478,1,"{5866, 12, 5662, 5759, 5676, 90, 52, 100}"
115,1,262,0,0.4722061,"\int (c e+d e x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcCosh[c + d*x])^3,x]","\frac{2 b^2 e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)}{9 d}+\frac{4}{3} a b^2 e^2 x-\frac{b e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d}-\frac{2 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d}+\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 d}-\frac{2 b^3 e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1}}{27 d}-\frac{40 b^3 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{27 d}+\frac{4 b^3 e^2 (c+d x) \cosh ^{-1}(c+d x)}{3 d}","\frac{2 b^2 e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)}{9 d}+\frac{4}{3} a b^2 e^2 x-\frac{b e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d}-\frac{2 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d}+\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 d}-\frac{2 b^3 e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1}}{27 d}-\frac{40 b^3 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{27 d}+\frac{4 b^3 e^2 (c+d x) \cosh ^{-1}(c+d x)}{3 d}",1,"(4*a*b^2*e^2*x)/3 - (40*b^3*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(27*d) - (2*b^3*e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])/(27*d) + (4*b^3*e^2*(c + d*x)*ArcCosh[c + d*x])/(3*d) + (2*b^2*e^2*(c + d*x)^3*(a + b*ArcCosh[c + d*x]))/(9*d) - (2*b*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^2)/(3*d) - (b*e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^2)/(3*d) + (e^2*(c + d*x)^3*(a + b*ArcCosh[c + d*x])^3)/(3*d)","A",12,8,23,0.3478,1,"{5866, 12, 5662, 5759, 5718, 5654, 74, 100}"
116,1,175,0,0.3586652,"\int (c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^3,x]","\frac{3 b^2 e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{4 d}-\frac{3 b e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{4 d}+\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{2 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^3}{4 d}-\frac{3 b^3 e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1}}{8 d}-\frac{3 b^3 e \cosh ^{-1}(c+d x)}{8 d}","\frac{3 b^2 e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{4 d}-\frac{3 b e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{4 d}+\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{2 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^3}{4 d}-\frac{3 b^3 e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1}}{8 d}-\frac{3 b^3 e \cosh ^{-1}(c+d x)}{8 d}",1,"(-3*b^3*e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(8*d) - (3*b^3*e*ArcCosh[c + d*x])/(8*d) + (3*b^2*e*(c + d*x)^2*(a + b*ArcCosh[c + d*x]))/(4*d) - (3*b*e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^2)/(4*d) - (e*(a + b*ArcCosh[c + d*x])^3)/(4*d) + (e*(c + d*x)^2*(a + b*ArcCosh[c + d*x])^3)/(2*d)","A",8,7,21,0.3333,1,"{5866, 12, 5662, 5759, 5676, 90, 52}"
117,1,114,0,0.184149,"\int \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","Int[(a + b*ArcCosh[c + d*x])^3,x]","6 a b^2 x-\frac{3 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d}-\frac{6 b^3 \sqrt{c+d x-1} \sqrt{c+d x+1}}{d}+\frac{6 b^3 (c+d x) \cosh ^{-1}(c+d x)}{d}","6 a b^2 x-\frac{3 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d}-\frac{6 b^3 \sqrt{c+d x-1} \sqrt{c+d x+1}}{d}+\frac{6 b^3 (c+d x) \cosh ^{-1}(c+d x)}{d}",1,"6*a*b^2*x - (6*b^3*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/d + (6*b^3*(c + d*x)*ArcCosh[c + d*x])/d - (3*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^2)/d + ((c + d*x)*(a + b*ArcCosh[c + d*x])^3)/d","A",6,4,12,0.3333,1,"{5864, 5654, 5718, 74}"
118,1,159,0,0.2160491,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{c e+d e x} \, dx","Int[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x),x]","-\frac{3 b^2 \text{PolyLog}\left(3,-e^{2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{2 d e}+\frac{3 b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d e}+\frac{3 b^3 \text{PolyLog}\left(4,-e^{2 \cosh ^{-1}(c+d x)}\right)}{4 d e}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{4 b d e}+\frac{\log \left(e^{2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e}","-\frac{3 b^2 \text{PolyLog}\left(3,-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{2 d e}-\frac{3 b \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d e}-\frac{3 b^3 \text{PolyLog}\left(4,-e^{-2 \cosh ^{-1}(c+d x)}\right)}{4 d e}+\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{4 b d e}+\frac{\log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e}",1,"-(a + b*ArcCosh[c + d*x])^4/(4*b*d*e) + ((a + b*ArcCosh[c + d*x])^3*Log[1 + E^(2*ArcCosh[c + d*x])])/(d*e) + (3*b*(a + b*ArcCosh[c + d*x])^2*PolyLog[2, -E^(2*ArcCosh[c + d*x])])/(2*d*e) - (3*b^2*(a + b*ArcCosh[c + d*x])*PolyLog[3, -E^(2*ArcCosh[c + d*x])])/(2*d*e) + (3*b^3*PolyLog[4, -E^(2*ArcCosh[c + d*x])])/(4*d*e)","A",9,9,23,0.3913,0,"{5866, 12, 5660, 3718, 2190, 2531, 6609, 2282, 6589}"
119,1,186,0,0.3620096,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^2} \, dx","Int[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x)^2,x]","-\frac{6 i b^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2}+\frac{6 i b^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2}+\frac{6 i b^3 \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}-\frac{6 i b^3 \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e^2 (c+d x)}+\frac{6 b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^2}","-\frac{6 i b^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2}+\frac{6 i b^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2}+\frac{6 i b^3 \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}-\frac{6 i b^3 \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e^2 (c+d x)}+\frac{6 b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^2}",1,"-((a + b*ArcCosh[c + d*x])^3/(d*e^2*(c + d*x))) + (6*b*(a + b*ArcCosh[c + d*x])^2*ArcTan[E^ArcCosh[c + d*x]])/(d*e^2) - ((6*I)*b^2*(a + b*ArcCosh[c + d*x])*PolyLog[2, (-I)*E^ArcCosh[c + d*x]])/(d*e^2) + ((6*I)*b^2*(a + b*ArcCosh[c + d*x])*PolyLog[2, I*E^ArcCosh[c + d*x]])/(d*e^2) + ((6*I)*b^3*PolyLog[3, (-I)*E^ArcCosh[c + d*x]])/(d*e^2) - ((6*I)*b^3*PolyLog[3, I*E^ArcCosh[c + d*x]])/(d*e^2)","A",11,8,23,0.3478,1,"{5866, 12, 5662, 5761, 4180, 2531, 2282, 6589}"
120,1,164,0,0.3692109,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^3} \, dx","Int[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x)^3,x]","-\frac{3 b^3 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c+d x)}\right)}{2 d e^3}-\frac{3 b^2 \log \left(e^{2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^3}+\frac{3 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)}+\frac{3 b \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d e^3}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{2 d e^3 (c+d x)^2}","\frac{3 b^3 \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c+d x)}\right)}{2 d e^3}-\frac{3 b^2 \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^3}+\frac{3 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)}-\frac{3 b \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d e^3}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{2 d e^3 (c+d x)^2}",1,"(3*b*(a + b*ArcCosh[c + d*x])^2)/(2*d*e^3) + (3*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^2)/(2*d*e^3*(c + d*x)) - (a + b*ArcCosh[c + d*x])^3/(2*d*e^3*(c + d*x)^2) - (3*b^2*(a + b*ArcCosh[c + d*x])*Log[1 + E^(2*ArcCosh[c + d*x])])/(d*e^3) - (3*b^3*PolyLog[2, -E^(2*ArcCosh[c + d*x])])/(2*d*e^3)","A",9,9,23,0.3913,0,"{5866, 12, 5662, 5724, 5660, 3718, 2190, 2279, 2391}"
121,1,297,0,0.5938792,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^4} \, dx","Int[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x)^4,x]","-\frac{i b^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4}+\frac{i b^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4}+\frac{i b^3 \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}-\frac{i b^3 \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}+\frac{b^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4 (c+d x)}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d e^4 (c+d x)^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^3}+\frac{b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^4}-\frac{b^3 \tan ^{-1}\left(\sqrt{c+d x-1} \sqrt{c+d x+1}\right)}{d e^4}","-\frac{i b^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4}+\frac{i b^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4}+\frac{i b^3 \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}-\frac{i b^3 \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}+\frac{b^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4 (c+d x)}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d e^4 (c+d x)^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^3}+\frac{b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^4}-\frac{b^3 \tan ^{-1}\left(\sqrt{c+d x-1} \sqrt{c+d x+1}\right)}{d e^4}",1,"(b^2*(a + b*ArcCosh[c + d*x]))/(d*e^4*(c + d*x)) + (b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^2)/(2*d*e^4*(c + d*x)^2) - (a + b*ArcCosh[c + d*x])^3/(3*d*e^4*(c + d*x)^3) + (b*(a + b*ArcCosh[c + d*x])^2*ArcTan[E^ArcCosh[c + d*x]])/(d*e^4) - (b^3*ArcTan[Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]])/(d*e^4) - (I*b^2*(a + b*ArcCosh[c + d*x])*PolyLog[2, (-I)*E^ArcCosh[c + d*x]])/(d*e^4) + (I*b^2*(a + b*ArcCosh[c + d*x])*PolyLog[2, I*E^ArcCosh[c + d*x]])/(d*e^4) + (I*b^3*PolyLog[3, (-I)*E^ArcCosh[c + d*x]])/(d*e^4) - (I*b^3*PolyLog[3, I*E^ArcCosh[c + d*x]])/(d*e^4)","A",15,11,23,0.4783,1,"{5866, 12, 5662, 5748, 5761, 4180, 2531, 2282, 6589, 92, 203}"
122,1,377,0,1.1744934,"\int (c e+d e x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcCosh[c + d*x])^4,x]","-\frac{3 b^3 e^3 \sqrt{c+d x-1} (c+d x)^3 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{32 d}-\frac{45 b^3 e^3 \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{64 d}+\frac{3 b^2 e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{16 d}-\frac{45 b^2 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{128 d}+\frac{9 b^2 e^3 (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{16 d}-\frac{b e^3 \sqrt{c+d x-1} (c+d x)^3 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{4 d}-\frac{3 b e^3 \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{8 d}+\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{4 d}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{32 d}+\frac{3 b^4 e^3 (c+d x)^4}{128 d}+\frac{45 b^4 e^3 (c+d x)^2}{128 d}","-\frac{3 b^3 e^3 \sqrt{c+d x-1} (c+d x)^3 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{32 d}-\frac{45 b^3 e^3 \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{64 d}+\frac{3 b^2 e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{16 d}-\frac{45 b^2 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{128 d}+\frac{9 b^2 e^3 (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{16 d}-\frac{b e^3 \sqrt{c+d x-1} (c+d x)^3 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{4 d}-\frac{3 b e^3 \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{8 d}+\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{4 d}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{32 d}+\frac{3 b^4 e^3 (c+d x)^4}{128 d}+\frac{45 b^4 e^3 (c+d x)^2}{128 d}",1,"(45*b^4*e^3*(c + d*x)^2)/(128*d) + (3*b^4*e^3*(c + d*x)^4)/(128*d) - (45*b^3*e^3*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/(64*d) - (3*b^3*e^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/(32*d) - (45*b^2*e^3*(a + b*ArcCosh[c + d*x])^2)/(128*d) + (9*b^2*e^3*(c + d*x)^2*(a + b*ArcCosh[c + d*x])^2)/(16*d) + (3*b^2*e^3*(c + d*x)^4*(a + b*ArcCosh[c + d*x])^2)/(16*d) - (3*b*e^3*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^3)/(8*d) - (b*e^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^3)/(4*d) - (3*e^3*(a + b*ArcCosh[c + d*x])^4)/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcCosh[c + d*x])^4)/(4*d)","A",16,6,23,0.2609,1,"{5866, 12, 5662, 5759, 5676, 30}"
123,1,309,0,0.8351343,"\int (c e+d e x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcCosh[c + d*x])^4,x]","-\frac{8 b^3 e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{27 d}-\frac{160 b^3 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{27 d}+\frac{4 b^2 e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{9 d}+\frac{8 b^2 e^2 (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d}-\frac{4 b e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{9 d}-\frac{8 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{9 d}+\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{3 d}+\frac{8 b^4 e^2 (c+d x)^3}{81 d}+\frac{160}{27} b^4 e^2 x","-\frac{8 b^3 e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{27 d}-\frac{160 b^3 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{27 d}+\frac{4 b^2 e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{9 d}+\frac{8 b^2 e^2 (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d}-\frac{4 b e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{9 d}-\frac{8 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{9 d}+\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{3 d}+\frac{8 b^4 e^2 (c+d x)^3}{81 d}+\frac{160}{27} b^4 e^2 x",1,"(160*b^4*e^2*x)/27 + (8*b^4*e^2*(c + d*x)^3)/(81*d) - (160*b^3*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/(27*d) - (8*b^3*e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/(27*d) + (8*b^2*e^2*(c + d*x)*(a + b*ArcCosh[c + d*x])^2)/(3*d) + (4*b^2*e^2*(c + d*x)^3*(a + b*ArcCosh[c + d*x])^2)/(9*d) - (8*b*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^3)/(9*d) - (4*b*e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^3)/(9*d) + (e^2*(c + d*x)^3*(a + b*ArcCosh[c + d*x])^4)/(3*d)","A",13,8,23,0.3478,1,"{5866, 12, 5662, 5759, 5718, 5654, 8, 30}"
124,1,209,0,0.5620421,"\int (c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","Int[(c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^4,x]","-\frac{3 b^3 e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{2 d}+\frac{3 b^2 e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d}-\frac{3 b^2 e \left(a+b \cosh ^{-1}(c+d x)\right)^2}{4 d}-\frac{b e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d}+\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{2 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^4}{4 d}+\frac{3 b^4 e (c+d x)^2}{4 d}","-\frac{3 b^3 e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{2 d}+\frac{3 b^2 e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d}-\frac{3 b^2 e \left(a+b \cosh ^{-1}(c+d x)\right)^2}{4 d}-\frac{b e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d}+\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{2 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^4}{4 d}+\frac{3 b^4 e (c+d x)^2}{4 d}",1,"(3*b^4*e*(c + d*x)^2)/(4*d) - (3*b^3*e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/(2*d) - (3*b^2*e*(a + b*ArcCosh[c + d*x])^2)/(4*d) + (3*b^2*e*(c + d*x)^2*(a + b*ArcCosh[c + d*x])^2)/(2*d) - (b*e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^3)/d - (e*(a + b*ArcCosh[c + d*x])^4)/(4*d) + (e*(c + d*x)^2*(a + b*ArcCosh[c + d*x])^4)/(2*d)","A",9,6,21,0.2857,1,"{5866, 12, 5662, 5759, 5676, 30}"
125,1,129,0,0.2840798,"\int \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","Int[(a + b*ArcCosh[c + d*x])^4,x]","-\frac{24 b^3 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{d}+\frac{12 b^2 (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d}-\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^4}{d}+24 b^4 x","-\frac{24 b^3 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{d}+\frac{12 b^2 (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d}-\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^4}{d}+24 b^4 x",1,"24*b^4*x - (24*b^3*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/d + (12*b^2*(c + d*x)*(a + b*ArcCosh[c + d*x])^2)/d - (4*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^3)/d + ((c + d*x)*(a + b*ArcCosh[c + d*x])^4)/d","A",6,4,12,0.3333,1,"{5864, 5654, 5718, 8}"
126,1,192,0,0.2659439,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{c e+d e x} \, dx","Int[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x),x]","-\frac{3 b^2 \text{PolyLog}\left(3,-e^{2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e}+\frac{3 b^3 \text{PolyLog}\left(4,-e^{2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e}+\frac{2 b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e}-\frac{3 b^4 \text{PolyLog}\left(5,-e^{2 \cosh ^{-1}(c+d x)}\right)}{2 d e}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^5}{5 b d e}+\frac{\log \left(e^{2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)^4}{d e}","-\frac{3 b^2 \text{PolyLog}\left(3,-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e}-\frac{3 b^3 \text{PolyLog}\left(4,-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e}-\frac{2 b \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e}-\frac{3 b^4 \text{PolyLog}\left(5,-e^{-2 \cosh ^{-1}(c+d x)}\right)}{2 d e}+\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^5}{5 b d e}+\frac{\log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)^4}{d e}",1,"-(a + b*ArcCosh[c + d*x])^5/(5*b*d*e) + ((a + b*ArcCosh[c + d*x])^4*Log[1 + E^(2*ArcCosh[c + d*x])])/(d*e) + (2*b*(a + b*ArcCosh[c + d*x])^3*PolyLog[2, -E^(2*ArcCosh[c + d*x])])/(d*e) - (3*b^2*(a + b*ArcCosh[c + d*x])^2*PolyLog[3, -E^(2*ArcCosh[c + d*x])])/(d*e) + (3*b^3*(a + b*ArcCosh[c + d*x])*PolyLog[4, -E^(2*ArcCosh[c + d*x])])/(d*e) - (3*b^4*PolyLog[5, -E^(2*ArcCosh[c + d*x])])/(2*d*e)","A",10,9,23,0.3913,0,"{5866, 12, 5660, 3718, 2190, 2531, 6609, 2282, 6589}"
127,1,264,0,0.4125143,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^2} \, dx","Int[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x)^2,x]","\frac{24 i b^3 \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2}-\frac{24 i b^3 \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2}-\frac{12 i b^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^2}+\frac{12 i b^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^2}-\frac{24 i b^4 \text{PolyLog}\left(4,-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}+\frac{24 i b^4 \text{PolyLog}\left(4,i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{d e^2 (c+d x)}+\frac{8 b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e^2}","\frac{24 i b^3 \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2}-\frac{24 i b^3 \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2}-\frac{12 i b^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^2}+\frac{12 i b^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^2}-\frac{24 i b^4 \text{PolyLog}\left(4,-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}+\frac{24 i b^4 \text{PolyLog}\left(4,i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{d e^2 (c+d x)}+\frac{8 b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e^2}",1,"-((a + b*ArcCosh[c + d*x])^4/(d*e^2*(c + d*x))) + (8*b*(a + b*ArcCosh[c + d*x])^3*ArcTan[E^ArcCosh[c + d*x]])/(d*e^2) - ((12*I)*b^2*(a + b*ArcCosh[c + d*x])^2*PolyLog[2, (-I)*E^ArcCosh[c + d*x]])/(d*e^2) + ((12*I)*b^2*(a + b*ArcCosh[c + d*x])^2*PolyLog[2, I*E^ArcCosh[c + d*x]])/(d*e^2) + ((24*I)*b^3*(a + b*ArcCosh[c + d*x])*PolyLog[3, (-I)*E^ArcCosh[c + d*x]])/(d*e^2) - ((24*I)*b^3*(a + b*ArcCosh[c + d*x])*PolyLog[3, I*E^ArcCosh[c + d*x]])/(d*e^2) - ((24*I)*b^4*PolyLog[4, (-I)*E^ArcCosh[c + d*x]])/(d*e^2) + ((24*I)*b^4*PolyLog[4, I*E^ArcCosh[c + d*x]])/(d*e^2)","A",13,9,23,0.3913,1,"{5866, 12, 5662, 5761, 4180, 2531, 6609, 2282, 6589}"
128,1,195,0,0.4263615,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^3} \, dx","Int[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x)^3,x]","-\frac{6 b^3 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^3}+\frac{3 b^4 \text{PolyLog}\left(3,-e^{2 \cosh ^{-1}(c+d x)}\right)}{d e^3}-\frac{6 b^2 \log \left(e^{2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^3}+\frac{2 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e^3 (c+d x)}+\frac{2 b \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e^3}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{2 d e^3 (c+d x)^2}","\frac{6 b^3 \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^3}+\frac{3 b^4 \text{PolyLog}\left(3,-e^{-2 \cosh ^{-1}(c+d x)}\right)}{d e^3}-\frac{6 b^2 \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^3}+\frac{2 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e^3 (c+d x)}-\frac{2 b \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e^3}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{2 d e^3 (c+d x)^2}",1,"(2*b*(a + b*ArcCosh[c + d*x])^3)/(d*e^3) + (2*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^3)/(d*e^3*(c + d*x)) - (a + b*ArcCosh[c + d*x])^4/(2*d*e^3*(c + d*x)^2) - (6*b^2*(a + b*ArcCosh[c + d*x])^2*Log[1 + E^(2*ArcCosh[c + d*x])])/(d*e^3) - (6*b^3*(a + b*ArcCosh[c + d*x])*PolyLog[2, -E^(2*ArcCosh[c + d*x])])/(d*e^3) + (3*b^4*PolyLog[3, -E^(2*ArcCosh[c + d*x])])/(d*e^3)","A",10,10,23,0.4348,0,"{5866, 12, 5662, 5724, 5660, 3718, 2190, 2531, 2282, 6589}"
129,1,432,0,0.8417572,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^4} \, dx","Int[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x)^4,x]","\frac{4 i b^3 \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4}-\frac{4 i b^3 \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4}-\frac{2 i b^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^4}+\frac{2 i b^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^4}+\frac{4 i b^4 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}-\frac{4 i b^4 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}-\frac{4 i b^4 \text{PolyLog}\left(4,-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}+\frac{4 i b^4 \text{PolyLog}\left(4,i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}+\frac{2 b^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^4 (c+d x)}-\frac{8 b^3 \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4}+\frac{2 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{3 d e^4 (c+d x)^3}+\frac{4 b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 d e^4}","\frac{4 i b^3 \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4}-\frac{4 i b^3 \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4}-\frac{2 i b^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^4}+\frac{2 i b^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^4}+\frac{4 i b^4 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}-\frac{4 i b^4 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}-\frac{4 i b^4 \text{PolyLog}\left(4,-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}+\frac{4 i b^4 \text{PolyLog}\left(4,i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}+\frac{2 b^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^4 (c+d x)}-\frac{8 b^3 \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4}+\frac{2 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{3 d e^4 (c+d x)^3}+\frac{4 b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 d e^4}",1,"(2*b^2*(a + b*ArcCosh[c + d*x])^2)/(d*e^4*(c + d*x)) + (2*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^3)/(3*d*e^4*(c + d*x)^2) - (a + b*ArcCosh[c + d*x])^4/(3*d*e^4*(c + d*x)^3) - (8*b^3*(a + b*ArcCosh[c + d*x])*ArcTan[E^ArcCosh[c + d*x]])/(d*e^4) + (4*b*(a + b*ArcCosh[c + d*x])^3*ArcTan[E^ArcCosh[c + d*x]])/(3*d*e^4) + ((4*I)*b^4*PolyLog[2, (-I)*E^ArcCosh[c + d*x]])/(d*e^4) - ((2*I)*b^2*(a + b*ArcCosh[c + d*x])^2*PolyLog[2, (-I)*E^ArcCosh[c + d*x]])/(d*e^4) - ((4*I)*b^4*PolyLog[2, I*E^ArcCosh[c + d*x]])/(d*e^4) + ((2*I)*b^2*(a + b*ArcCosh[c + d*x])^2*PolyLog[2, I*E^ArcCosh[c + d*x]])/(d*e^4) + ((4*I)*b^3*(a + b*ArcCosh[c + d*x])*PolyLog[3, (-I)*E^ArcCosh[c + d*x]])/(d*e^4) - ((4*I)*b^3*(a + b*ArcCosh[c + d*x])*PolyLog[3, I*E^ArcCosh[c + d*x]])/(d*e^4) - ((4*I)*b^4*PolyLog[4, (-I)*E^ArcCosh[c + d*x]])/(d*e^4) + ((4*I)*b^4*PolyLog[4, I*E^ArcCosh[c + d*x]])/(d*e^4)","A",21,12,23,0.5217,1,"{5866, 12, 5662, 5748, 5761, 4180, 2531, 6609, 2282, 6589, 2279, 2391}"
130,1,209,0,0.4285664,"\int \frac{(c e+d e x)^4}{a+b \cosh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcCosh[c + d*x]),x]","-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{8 b d}-\frac{3 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c+d x)\right)}{16 b d}-\frac{e^4 \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c+d x)\right)}{16 b d}+\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{8 b d}+\frac{3 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c+d x)\right)}{16 b d}+\frac{e^4 \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c+d x)\right)}{16 b d}","-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{8 b d}-\frac{3 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{16 b d}-\frac{e^4 \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{16 b d}+\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{8 b d}+\frac{3 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{16 b d}+\frac{e^4 \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{16 b d}",1,"-(e^4*CoshIntegral[a/b + ArcCosh[c + d*x]]*Sinh[a/b])/(8*b*d) - (3*e^4*CoshIntegral[(3*a)/b + 3*ArcCosh[c + d*x]]*Sinh[(3*a)/b])/(16*b*d) - (e^4*CoshIntegral[(5*a)/b + 5*ArcCosh[c + d*x]]*Sinh[(5*a)/b])/(16*b*d) + (e^4*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]])/(8*b*d) + (3*e^4*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c + d*x]])/(16*b*d) + (e^4*Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcCosh[c + d*x]])/(16*b*d)","A",14,7,23,0.3043,1,"{5866, 12, 5670, 5448, 3303, 3298, 3301}"
131,1,145,0,0.3344974,"\int \frac{(c e+d e x)^3}{a+b \cosh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcCosh[c + d*x]),x]","-\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)}{4 b d}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c+d x)\right)}{8 b d}+\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)}{4 b d}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c+d x)\right)}{8 b d}","-\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{4 b d}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{8 b d}+\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{4 b d}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{8 b d}",1,"-(e^3*CoshIntegral[(2*a)/b + 2*ArcCosh[c + d*x]]*Sinh[(2*a)/b])/(4*b*d) - (e^3*CoshIntegral[(4*a)/b + 4*ArcCosh[c + d*x]]*Sinh[(4*a)/b])/(8*b*d) + (e^3*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c + d*x]])/(4*b*d) + (e^3*Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c + d*x]])/(8*b*d)","A",11,7,23,0.3043,1,"{5866, 12, 5670, 5448, 3303, 3298, 3301}"
132,1,137,0,0.2983167,"\int \frac{(c e+d e x)^2}{a+b \cosh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcCosh[c + d*x]),x]","-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{4 b d}-\frac{e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c+d x)\right)}{4 b d}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{4 b d}+\frac{e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c+d x)\right)}{4 b d}","-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{4 b d}-\frac{e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{4 b d}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{4 b d}+\frac{e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{4 b d}",1,"-(e^2*CoshIntegral[a/b + ArcCosh[c + d*x]]*Sinh[a/b])/(4*b*d) - (e^2*CoshIntegral[(3*a)/b + 3*ArcCosh[c + d*x]]*Sinh[(3*a)/b])/(4*b*d) + (e^2*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]])/(4*b*d) + (e^2*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c + d*x]])/(4*b*d)","A",11,7,23,0.3043,1,"{5866, 12, 5670, 5448, 3303, 3298, 3301}"
133,1,69,0,0.1596922,"\int \frac{c e+d e x}{a+b \cosh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)/(a + b*ArcCosh[c + d*x]),x]","\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)}{2 b d}-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)}{2 b d}","\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{2 b d}-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{2 b d}",1,"-(e*CoshIntegral[(2*a)/b + 2*ArcCosh[c + d*x]]*Sinh[(2*a)/b])/(2*b*d) + (e*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c + d*x]])/(2*b*d)","A",8,7,21,0.3333,1,"{5866, 12, 5670, 5448, 3303, 3298, 3301}"
134,1,58,0,0.0901135,"\int \frac{1}{a+b \cosh ^{-1}(c+d x)} \, dx","Int[(a + b*ArcCosh[c + d*x])^(-1),x]","\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{b d}-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{b d}","\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{b d}-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{b d}",1,"-((CoshIntegral[(a + b*ArcCosh[c + d*x])/b]*Sinh[a/b])/(b*d)) + (Cosh[a/b]*SinhIntegral[(a + b*ArcCosh[c + d*x])/b])/(b*d)","A",5,5,12,0.4167,1,"{5864, 5658, 3303, 3298, 3301}"
135,0,0,0,0.0641847,"\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])),x]","\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcCosh[x])), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
136,1,259,0,0.3936987,"\int \frac{(c e+d e x)^4}{\left(a+b \cosh ^{-1}(c+d x)\right)^2} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcCosh[c + d*x])^2,x]","\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{8 b^2 d}+\frac{9 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c+d x)\right)}{16 b^2 d}+\frac{5 e^4 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c+d x)\right)}{16 b^2 d}-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{8 b^2 d}-\frac{9 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c+d x)\right)}{16 b^2 d}-\frac{5 e^4 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c+d x)\right)}{16 b^2 d}-\frac{e^4 \sqrt{c+d x-1} (c+d x)^4 \sqrt{c+d x+1}}{b d \left(a+b \cosh ^{-1}(c+d x)\right)}","\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{8 b^2 d}+\frac{9 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{16 b^2 d}+\frac{5 e^4 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{16 b^2 d}-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{8 b^2 d}-\frac{9 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{16 b^2 d}-\frac{5 e^4 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{16 b^2 d}-\frac{e^4 \sqrt{c+d x-1} (c+d x)^4 \sqrt{c+d x+1}}{b d \left(a+b \cosh ^{-1}(c+d x)\right)}",1,"-((e^4*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x])/(b*d*(a + b*ArcCosh[c + d*x]))) + (e^4*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c + d*x]])/(8*b^2*d) + (9*e^4*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c + d*x]])/(16*b^2*d) + (5*e^4*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcCosh[c + d*x]])/(16*b^2*d) - (e^4*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]])/(8*b^2*d) - (9*e^4*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c + d*x]])/(16*b^2*d) - (5*e^4*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcCosh[c + d*x]])/(16*b^2*d)","A",13,6,23,0.2609,1,"{5866, 12, 5666, 3303, 3298, 3301}"
137,1,195,0,0.2984002,"\int \frac{(c e+d e x)^3}{\left(a+b \cosh ^{-1}(c+d x)\right)^2} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcCosh[c + d*x])^2,x]","\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)}{2 b^2 d}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c+d x)\right)}{2 b^2 d}-\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)}{2 b^2 d}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c+d x)\right)}{2 b^2 d}-\frac{e^3 \sqrt{c+d x-1} (c+d x)^3 \sqrt{c+d x+1}}{b d \left(a+b \cosh ^{-1}(c+d x)\right)}","\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{2 b^2 d}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{2 b^2 d}-\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{2 b^2 d}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{2 b^2 d}-\frac{e^3 \sqrt{c+d x-1} (c+d x)^3 \sqrt{c+d x+1}}{b d \left(a+b \cosh ^{-1}(c+d x)\right)}",1,"-((e^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x])/(b*d*(a + b*ArcCosh[c + d*x]))) + (e^3*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcCosh[c + d*x]])/(2*b^2*d) + (e^3*Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcCosh[c + d*x]])/(2*b^2*d) - (e^3*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c + d*x]])/(2*b^2*d) - (e^3*Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c + d*x]])/(2*b^2*d)","A",10,6,23,0.2609,1,"{5866, 12, 5666, 3303, 3298, 3301}"
138,1,187,0,0.2759114,"\int \frac{(c e+d e x)^2}{\left(a+b \cosh ^{-1}(c+d x)\right)^2} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcCosh[c + d*x])^2,x]","\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{4 b^2 d}+\frac{3 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c+d x)\right)}{4 b^2 d}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{4 b^2 d}-\frac{3 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c+d x)\right)}{4 b^2 d}-\frac{e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1}}{b d \left(a+b \cosh ^{-1}(c+d x)\right)}","\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{4 b^2 d}+\frac{3 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{4 b^2 d}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{4 b^2 d}-\frac{3 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{4 b^2 d}-\frac{e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1}}{b d \left(a+b \cosh ^{-1}(c+d x)\right)}",1,"-((e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])/(b*d*(a + b*ArcCosh[c + d*x]))) + (e^2*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c + d*x]])/(4*b^2*d) + (3*e^2*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c + d*x]])/(4*b^2*d) - (e^2*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]])/(4*b^2*d) - (3*e^2*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c + d*x]])/(4*b^2*d)","A",10,6,23,0.2609,1,"{5866, 12, 5666, 3303, 3298, 3301}"
139,1,110,0,0.1480756,"\int \frac{c e+d e x}{\left(a+b \cosh ^{-1}(c+d x)\right)^2} \, dx","Int[(c*e + d*e*x)/(a + b*ArcCosh[c + d*x])^2,x]","\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)}{b^2 d}-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)}{b^2 d}-\frac{e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{b d \left(a+b \cosh ^{-1}(c+d x)\right)}","\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{b^2 d}-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{b^2 d}-\frac{e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{b d \left(a+b \cosh ^{-1}(c+d x)\right)}",1,"-((e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(b*d*(a + b*ArcCosh[c + d*x]))) + (e*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcCosh[c + d*x]])/(b^2*d) - (e*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c + d*x]])/(b^2*d)","A",6,6,21,0.2857,1,"{5866, 12, 5666, 3303, 3298, 3301}"
140,1,94,0,0.2520034,"\int \frac{1}{\left(a+b \cosh ^{-1}(c+d x)\right)^2} \, dx","Int[(a + b*ArcCosh[c + d*x])^(-2),x]","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{b^2 d}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{b^2 d}-\frac{\sqrt{c+d x-1} \sqrt{c+d x+1}}{b d \left(a+b \cosh ^{-1}(c+d x)\right)}","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{b^2 d}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{b^2 d}-\frac{\sqrt{c+d x-1} \sqrt{c+d x+1}}{b d \left(a+b \cosh ^{-1}(c+d x)\right)}",1,"-((Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(b*d*(a + b*ArcCosh[c + d*x]))) + (Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c + d*x]])/(b^2*d) - (Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]])/(b^2*d)","A",6,6,12,0.5000,1,"{5864, 5656, 5781, 3303, 3298, 3301}"
141,0,0,0,0.0617535,"\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^2} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^2),x]","\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^2} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^2},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcCosh[x])^2), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
142,1,323,0,1.1106281,"\int \frac{(c e+d e x)^4}{\left(a+b \cosh ^{-1}(c+d x)\right)^3} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcCosh[c + d*x])^3,x]","-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{16 b^3 d}-\frac{27 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c+d x)\right)}{32 b^3 d}-\frac{25 e^4 \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c+d x)\right)}{32 b^3 d}+\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{16 b^3 d}+\frac{27 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c+d x)\right)}{32 b^3 d}+\frac{25 e^4 \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c+d x)\right)}{32 b^3 d}-\frac{5 e^4 (c+d x)^5}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{2 e^4 (c+d x)^3}{b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{2 b d \left(a+b \cosh ^{-1}(c+d x)\right)^2}","-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{16 b^3 d}-\frac{27 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{32 b^3 d}-\frac{25 e^4 \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{32 b^3 d}+\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{16 b^3 d}+\frac{27 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{32 b^3 d}+\frac{25 e^4 \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{32 b^3 d}-\frac{5 e^4 (c+d x)^5}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{2 e^4 (c+d x)^3}{b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{2 b d \left(a+b \cosh ^{-1}(c+d x)\right)^2}",1,"-(e^4*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x])/(2*b*d*(a + b*ArcCosh[c + d*x])^2) + (2*e^4*(c + d*x)^3)/(b^2*d*(a + b*ArcCosh[c + d*x])) - (5*e^4*(c + d*x)^5)/(2*b^2*d*(a + b*ArcCosh[c + d*x])) - (e^4*CoshIntegral[a/b + ArcCosh[c + d*x]]*Sinh[a/b])/(16*b^3*d) - (27*e^4*CoshIntegral[(3*a)/b + 3*ArcCosh[c + d*x]]*Sinh[(3*a)/b])/(32*b^3*d) - (25*e^4*CoshIntegral[(5*a)/b + 5*ArcCosh[c + d*x]]*Sinh[(5*a)/b])/(32*b^3*d) + (e^4*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]])/(16*b^3*d) + (27*e^4*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c + d*x]])/(32*b^3*d) + (25*e^4*Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcCosh[c + d*x]])/(32*b^3*d)","A",26,9,23,0.3913,1,"{5866, 12, 5668, 5775, 5670, 5448, 3303, 3298, 3301}"
143,1,254,0,0.8986269,"\int \frac{(c e+d e x)^3}{\left(a+b \cosh ^{-1}(c+d x)\right)^3} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcCosh[c + d*x])^3,x]","-\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)}{2 b^3 d}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c+d x)\right)}{b^3 d}+\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)}{2 b^3 d}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c+d x)\right)}{b^3 d}-\frac{2 e^3 (c+d x)^4}{b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{3 e^3 (c+d x)^2}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{2 b d \left(a+b \cosh ^{-1}(c+d x)\right)^2}","-\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{2 b^3 d}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{b^3 d}+\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{2 b^3 d}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{b^3 d}-\frac{2 e^3 (c+d x)^4}{b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{3 e^3 (c+d x)^2}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{2 b d \left(a+b \cosh ^{-1}(c+d x)\right)^2}",1,"-(e^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x])/(2*b*d*(a + b*ArcCosh[c + d*x])^2) + (3*e^3*(c + d*x)^2)/(2*b^2*d*(a + b*ArcCosh[c + d*x])) - (2*e^3*(c + d*x)^4)/(b^2*d*(a + b*ArcCosh[c + d*x])) - (e^3*CoshIntegral[(2*a)/b + 2*ArcCosh[c + d*x]]*Sinh[(2*a)/b])/(2*b^3*d) - (e^3*CoshIntegral[(4*a)/b + 4*ArcCosh[c + d*x]]*Sinh[(4*a)/b])/(b^3*d) + (e^3*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c + d*x]])/(2*b^3*d) + (e^3*Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c + d*x]])/(b^3*d)","A",20,9,23,0.3913,1,"{5866, 12, 5668, 5775, 5670, 5448, 3303, 3298, 3301}"
144,1,311,0,0.7992176,"\int \frac{(c e+d e x)^2}{\left(a+b \cosh ^{-1}(c+d x)\right)^3} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcCosh[c + d*x])^3,x]","-\frac{9 e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{8 b^3 d}+\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{b^3 d}-\frac{9 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c+d x)\right)}{8 b^3 d}+\frac{9 e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{8 b^3 d}+\frac{9 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c+d x)\right)}{8 b^3 d}-\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{b^3 d}-\frac{3 e^2 (c+d x)^3}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{e^2 (c+d x)}{b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{2 b d \left(a+b \cosh ^{-1}(c+d x)\right)^2}","-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{8 b^3 d}-\frac{9 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{8 b^3 d}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{8 b^3 d}+\frac{9 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{8 b^3 d}-\frac{3 e^2 (c+d x)^3}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{e^2 (c+d x)}{b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{2 b d \left(a+b \cosh ^{-1}(c+d x)\right)^2}",1,"-(e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])/(2*b*d*(a + b*ArcCosh[c + d*x])^2) + (e^2*(c + d*x))/(b^2*d*(a + b*ArcCosh[c + d*x])) - (3*e^2*(c + d*x)^3)/(2*b^2*d*(a + b*ArcCosh[c + d*x])) - (9*e^2*CoshIntegral[a/b + ArcCosh[c + d*x]]*Sinh[a/b])/(8*b^3*d) + (e^2*CoshIntegral[(a + b*ArcCosh[c + d*x])/b]*Sinh[a/b])/(b^3*d) - (9*e^2*CoshIntegral[(3*a)/b + 3*ArcCosh[c + d*x]]*Sinh[(3*a)/b])/(8*b^3*d) + (9*e^2*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]])/(8*b^3*d) + (9*e^2*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c + d*x]])/(8*b^3*d) - (e^2*Cosh[a/b]*SinhIntegral[(a + b*ArcCosh[c + d*x])/b])/(b^3*d)","A",18,10,23,0.4348,1,"{5866, 12, 5668, 5775, 5670, 5448, 3303, 3298, 3301, 5658}"
145,1,163,0,0.5085204,"\int \frac{c e+d e x}{\left(a+b \cosh ^{-1}(c+d x)\right)^3} \, dx","Int[(c*e + d*e*x)/(a + b*ArcCosh[c + d*x])^3,x]","-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)}{b^3 d}+\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)}{b^3 d}-\frac{e (c+d x)^2}{b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{e}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{2 b d \left(a+b \cosh ^{-1}(c+d x)\right)^2}","-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{b^3 d}+\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{b^3 d}-\frac{e (c+d x)^2}{b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{e}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{2 b d \left(a+b \cosh ^{-1}(c+d x)\right)^2}",1,"-(e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(2*b*d*(a + b*ArcCosh[c + d*x])^2) + e/(2*b^2*d*(a + b*ArcCosh[c + d*x])) - (e*(c + d*x)^2)/(b^2*d*(a + b*ArcCosh[c + d*x])) - (e*CoshIntegral[(2*a)/b + 2*ArcCosh[c + d*x]]*Sinh[(2*a)/b])/(b^3*d) + (e*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c + d*x]])/(b^3*d)","A",11,10,21,0.4762,1,"{5866, 12, 5668, 5775, 5670, 5448, 3303, 3298, 3301, 5676}"
146,1,132,0,0.2597144,"\int \frac{1}{\left(a+b \cosh ^{-1}(c+d x)\right)^3} \, dx","Int[(a + b*ArcCosh[c + d*x])^(-3),x]","-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{2 b^3 d}+\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{2 b^3 d}-\frac{c+d x}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{\sqrt{c+d x-1} \sqrt{c+d x+1}}{2 b d \left(a+b \cosh ^{-1}(c+d x)\right)^2}","-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{2 b^3 d}+\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{2 b^3 d}-\frac{c+d x}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{\sqrt{c+d x-1} \sqrt{c+d x+1}}{2 b d \left(a+b \cosh ^{-1}(c+d x)\right)^2}",1,"-(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(2*b*d*(a + b*ArcCosh[c + d*x])^2) - (c + d*x)/(2*b^2*d*(a + b*ArcCosh[c + d*x])) - (CoshIntegral[(a + b*ArcCosh[c + d*x])/b]*Sinh[a/b])/(2*b^3*d) + (Cosh[a/b]*SinhIntegral[(a + b*ArcCosh[c + d*x])/b])/(2*b^3*d)","A",7,7,12,0.5833,1,"{5864, 5656, 5775, 5658, 3303, 3298, 3301}"
147,0,0,0,0.0635637,"\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^3} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^3),x]","\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^3} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^3},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcCosh[x])^3), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
148,1,427,0,1.1039949,"\int \frac{(c e+d e x)^4}{\left(a+b \cosh ^{-1}(c+d x)\right)^4} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcCosh[c + d*x])^4,x]","\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{48 b^4 d}+\frac{27 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c+d x)\right)}{32 b^4 d}+\frac{125 e^4 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c+d x)\right)}{96 b^4 d}-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{48 b^4 d}-\frac{27 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c+d x)\right)}{32 b^4 d}-\frac{125 e^4 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c+d x)\right)}{96 b^4 d}-\frac{5 e^4 (c+d x)^5}{6 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{25 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{6 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{2 e^4 (c+d x)^3}{3 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}+\frac{2 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^3}","\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{48 b^4 d}+\frac{27 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{32 b^4 d}+\frac{125 e^4 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{96 b^4 d}-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{48 b^4 d}-\frac{27 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{32 b^4 d}-\frac{125 e^4 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{96 b^4 d}-\frac{5 e^4 (c+d x)^5}{6 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{25 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{6 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{2 e^4 (c+d x)^3}{3 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}+\frac{2 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^3}",1,"-(e^4*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x])/(3*b*d*(a + b*ArcCosh[c + d*x])^3) + (2*e^4*(c + d*x)^3)/(3*b^2*d*(a + b*ArcCosh[c + d*x])^2) - (5*e^4*(c + d*x)^5)/(6*b^2*d*(a + b*ArcCosh[c + d*x])^2) + (2*e^4*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])/(b^3*d*(a + b*ArcCosh[c + d*x])) - (25*e^4*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x])/(6*b^3*d*(a + b*ArcCosh[c + d*x])) + (e^4*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c + d*x]])/(48*b^4*d) + (27*e^4*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c + d*x]])/(32*b^4*d) + (125*e^4*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcCosh[c + d*x]])/(96*b^4*d) - (e^4*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]])/(48*b^4*d) - (27*e^4*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c + d*x]])/(32*b^4*d) - (125*e^4*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcCosh[c + d*x]])/(96*b^4*d)","A",24,8,23,0.3478,1,"{5866, 12, 5668, 5775, 5666, 3303, 3298, 3301}"
149,1,360,0,0.8872191,"\int \frac{(c e+d e x)^3}{\left(a+b \cosh ^{-1}(c+d x)\right)^4} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcCosh[c + d*x])^4,x]","\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)}{3 b^4 d}+\frac{4 e^3 \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c+d x)\right)}{3 b^4 d}-\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)}{3 b^4 d}-\frac{4 e^3 \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c+d x)\right)}{3 b^4 d}-\frac{2 e^3 (c+d x)^4}{3 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{8 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{3 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{e^3 (c+d x)^2}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}+\frac{e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^3}","\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}+\frac{4 e^3 \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}-\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}-\frac{4 e^3 \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}-\frac{2 e^3 (c+d x)^4}{3 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{8 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{3 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{e^3 (c+d x)^2}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}+\frac{e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^3}",1,"-(e^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x])/(3*b*d*(a + b*ArcCosh[c + d*x])^3) + (e^3*(c + d*x)^2)/(2*b^2*d*(a + b*ArcCosh[c + d*x])^2) - (2*e^3*(c + d*x)^4)/(3*b^2*d*(a + b*ArcCosh[c + d*x])^2) + (e^3*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(b^3*d*(a + b*ArcCosh[c + d*x])) - (8*e^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x])/(3*b^3*d*(a + b*ArcCosh[c + d*x])) + (e^3*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcCosh[c + d*x]])/(3*b^4*d) + (4*e^3*Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcCosh[c + d*x]])/(3*b^4*d) - (e^3*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c + d*x]])/(3*b^4*d) - (4*e^3*Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c + d*x]])/(3*b^4*d)","A",17,8,23,0.3478,1,"{5866, 12, 5668, 5775, 5666, 3303, 3298, 3301}"
150,1,348,0,0.9648158,"\int \frac{(c e+d e x)^2}{\left(a+b \cosh ^{-1}(c+d x)\right)^4} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcCosh[c + d*x])^4,x]","\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{24 b^4 d}+\frac{9 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c+d x)\right)}{8 b^4 d}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{24 b^4 d}-\frac{9 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c+d x)\right)}{8 b^4 d}-\frac{e^2 (c+d x)^3}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{3 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{2 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{e^2 (c+d x)}{3 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}+\frac{e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{3 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^3}","\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{24 b^4 d}+\frac{9 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{8 b^4 d}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{24 b^4 d}-\frac{9 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{8 b^4 d}-\frac{e^2 (c+d x)^3}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{3 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{2 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{e^2 (c+d x)}{3 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}+\frac{e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{3 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^3}",1,"-(e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])/(3*b*d*(a + b*ArcCosh[c + d*x])^3) + (e^2*(c + d*x))/(3*b^2*d*(a + b*ArcCosh[c + d*x])^2) - (e^2*(c + d*x)^3)/(2*b^2*d*(a + b*ArcCosh[c + d*x])^2) + (e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(3*b^3*d*(a + b*ArcCosh[c + d*x])) - (3*e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])/(2*b^3*d*(a + b*ArcCosh[c + d*x])) + (e^2*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c + d*x]])/(24*b^4*d) + (9*e^2*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c + d*x]])/(8*b^4*d) - (e^2*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]])/(24*b^4*d) - (9*e^2*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c + d*x]])/(8*b^4*d)","A",18,10,23,0.4348,1,"{5866, 12, 5668, 5775, 5666, 3303, 3298, 3301, 5656, 5781}"
151,1,218,0,0.5106866,"\int \frac{c e+d e x}{\left(a+b \cosh ^{-1}(c+d x)\right)^4} \, dx","Int[(c*e + d*e*x)/(a + b*ArcCosh[c + d*x])^4,x]","\frac{2 e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)}{3 b^4 d}-\frac{2 e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)}{3 b^4 d}-\frac{e (c+d x)^2}{3 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{2 e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{3 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{e}{6 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^3}","\frac{2 e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}-\frac{2 e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}-\frac{e (c+d x)^2}{3 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{2 e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{3 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{e}{6 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^3}",1,"-(e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(3*b*d*(a + b*ArcCosh[c + d*x])^3) + e/(6*b^2*d*(a + b*ArcCosh[c + d*x])^2) - (e*(c + d*x)^2)/(3*b^2*d*(a + b*ArcCosh[c + d*x])^2) - (2*e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(3*b^3*d*(a + b*ArcCosh[c + d*x])) + (2*e*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcCosh[c + d*x]])/(3*b^4*d) - (2*e*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c + d*x]])/(3*b^4*d)","A",9,9,21,0.4286,1,"{5866, 12, 5668, 5775, 5666, 3303, 3298, 3301, 5676}"
152,1,170,0,0.445229,"\int \frac{1}{\left(a+b \cosh ^{-1}(c+d x)\right)^4} \, dx","Int[(a + b*ArcCosh[c + d*x])^(-4),x]","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{6 b^4 d}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{6 b^4 d}-\frac{c+d x}{6 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{\sqrt{c+d x-1} \sqrt{c+d x+1}}{6 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{\sqrt{c+d x-1} \sqrt{c+d x+1}}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^3}","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{6 b^4 d}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{6 b^4 d}-\frac{c+d x}{6 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{\sqrt{c+d x-1} \sqrt{c+d x+1}}{6 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{\sqrt{c+d x-1} \sqrt{c+d x+1}}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^3}",1,"-(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(3*b*d*(a + b*ArcCosh[c + d*x])^3) - (c + d*x)/(6*b^2*d*(a + b*ArcCosh[c + d*x])^2) - (Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(6*b^3*d*(a + b*ArcCosh[c + d*x])) + (Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c + d*x]])/(6*b^4*d) - (Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]])/(6*b^4*d)","A",8,7,12,0.5833,1,"{5864, 5656, 5775, 5781, 3303, 3298, 3301}"
153,0,0,0,0.061085,"\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^4} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^4),x]","\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^4} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^4},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcCosh[x])^4), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
154,1,361,0,0.9511334,"\int (c e+d e x)^4 \sqrt{a+b \cosh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^4*Sqrt[a + b*ArcCosh[c + d*x]],x]","-\frac{\sqrt{\pi } \sqrt{b} e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{\sqrt{\frac{\pi }{5}} \sqrt{b} e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{320 d}-\frac{\sqrt{\pi } \sqrt{b} e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{\sqrt{\frac{\pi }{5}} \sqrt{b} e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{320 d}+\frac{e^4 (c+d x)^5 \sqrt{a+b \cosh ^{-1}(c+d x)}}{5 d}","-\frac{\sqrt{\pi } \sqrt{b} e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{\sqrt{\frac{\pi }{5}} \sqrt{b} e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{320 d}-\frac{\sqrt{\pi } \sqrt{b} e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{\sqrt{\frac{\pi }{5}} \sqrt{b} e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{320 d}+\frac{e^4 (c+d x)^5 \sqrt{a+b \cosh ^{-1}(c+d x)}}{5 d}",1,"(e^4*(c + d*x)^5*Sqrt[a + b*ArcCosh[c + d*x]])/(5*d) - (Sqrt[b]*e^4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(32*d) - (Sqrt[b]*e^4*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(64*d) - (Sqrt[b]*e^4*E^((5*a)/b)*Sqrt[Pi/5]*Erf[(Sqrt[5]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(320*d) - (Sqrt[b]*e^4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(32*d*E^(a/b)) - (Sqrt[b]*e^4*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(64*d*E^((3*a)/b)) - (Sqrt[b]*e^4*Sqrt[Pi/5]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(320*d*E^((5*a)/b))","A",21,9,25,0.3600,1,"{5866, 12, 5664, 5781, 3312, 3307, 2180, 2204, 2205}"
155,1,272,0,0.7931647,"\int (c e+d e x)^3 \sqrt{a+b \cosh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^3*Sqrt[a + b*ArcCosh[c + d*x]],x]","-\frac{\sqrt{\pi } \sqrt{b} e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{\sqrt{\pi } \sqrt{b} e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{e^3 (c+d x)^4 \sqrt{a+b \cosh ^{-1}(c+d x)}}{4 d}-\frac{3 e^3 \sqrt{a+b \cosh ^{-1}(c+d x)}}{32 d}","-\frac{\sqrt{\pi } \sqrt{b} e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{\sqrt{\pi } \sqrt{b} e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{e^3 (c+d x)^4 \sqrt{a+b \cosh ^{-1}(c+d x)}}{4 d}-\frac{3 e^3 \sqrt{a+b \cosh ^{-1}(c+d x)}}{32 d}",1,"(-3*e^3*Sqrt[a + b*ArcCosh[c + d*x]])/(32*d) + (e^3*(c + d*x)^4*Sqrt[a + b*ArcCosh[c + d*x]])/(4*d) - (Sqrt[b]*e^3*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(256*d) - (Sqrt[b]*e^3*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(32*d) - (Sqrt[b]*e^3*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(256*d*E^((4*a)/b)) - (Sqrt[b]*e^3*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(32*d*E^((2*a)/b))","A",16,9,25,0.3600,1,"{5866, 12, 5664, 5781, 3312, 3307, 2180, 2204, 2205}"
156,1,245,0,0.759198,"\int (c e+d e x)^2 \sqrt{a+b \cosh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^2*Sqrt[a + b*ArcCosh[c + d*x]],x]","-\frac{\sqrt{\pi } \sqrt{b} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{48 d}-\frac{\sqrt{\pi } \sqrt{b} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{48 d}+\frac{e^2 (c+d x)^3 \sqrt{a+b \cosh ^{-1}(c+d x)}}{3 d}","-\frac{\sqrt{\pi } \sqrt{b} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{48 d}-\frac{\sqrt{\pi } \sqrt{b} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{48 d}+\frac{e^2 (c+d x)^3 \sqrt{a+b \cosh ^{-1}(c+d x)}}{3 d}",1,"(e^2*(c + d*x)^3*Sqrt[a + b*ArcCosh[c + d*x]])/(3*d) - (Sqrt[b]*e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(16*d) - (Sqrt[b]*e^2*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(48*d) - (Sqrt[b]*e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(16*d*E^(a/b)) - (Sqrt[b]*e^2*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(48*d*E^((3*a)/b))","A",16,9,25,0.3600,1,"{5866, 12, 5664, 5781, 3312, 3307, 2180, 2204, 2205}"
157,1,164,0,0.575408,"\int (c e+d e x) \sqrt{a+b \cosh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)*Sqrt[a + b*ArcCosh[c + d*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}+\frac{e (c+d x)^2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{2 d}-\frac{e \sqrt{a+b \cosh ^{-1}(c+d x)}}{4 d}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}+\frac{e (c+d x)^2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{2 d}-\frac{e \sqrt{a+b \cosh ^{-1}(c+d x)}}{4 d}",1,"-(e*Sqrt[a + b*ArcCosh[c + d*x]])/(4*d) + (e*(c + d*x)^2*Sqrt[a + b*ArcCosh[c + d*x]])/(2*d) - (Sqrt[b]*e*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(16*d) - (Sqrt[b]*e*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(16*d*E^((2*a)/b))","A",11,9,23,0.3913,1,"{5866, 12, 5664, 5781, 3312, 3307, 2180, 2204, 2205}"
158,1,115,0,0.3500213,"\int \sqrt{a+b \cosh ^{-1}(c+d x)} \, dx","Int[Sqrt[a + b*ArcCosh[c + d*x]],x]","-\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}-\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}+\frac{(c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}}{d}","-\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}-\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}+\frac{(c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}}{d}",1,"((c + d*x)*Sqrt[a + b*ArcCosh[c + d*x]])/d - (Sqrt[b]*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(4*d) - (Sqrt[b]*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(4*d*E^(a/b))","A",8,7,14,0.5000,1,"{5864, 5654, 5781, 3307, 2180, 2204, 2205}"
159,0,0,0,0.0870347,"\int \frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{c e+d e x} \, dx","Int[Sqrt[a + b*ArcCosh[c + d*x]]/(c*e + d*e*x),x]","\int \frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{c e+d e x} \, dx","\frac{\text{Int}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{c+d x},x\right)}{e}",0,"Defer[Subst][Defer[Int][Sqrt[a + b*ArcCosh[x]]/x, x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
160,1,374,0,1.4122542,"\int (c e+d e x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2} \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcCosh[c + d*x])^(3/2),x]","-\frac{3 \sqrt{\pi } b^{3/2} e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2048 d}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{3 \sqrt{\pi } b^{3/2} e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2048 d}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{4 d}-\frac{3 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3 \sqrt{a+b \cosh ^{-1}(c+d x)}}{32 d}-\frac{9 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}}{64 d}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{32 d}","-\frac{3 \sqrt{\pi } b^{3/2} e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2048 d}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{3 \sqrt{\pi } b^{3/2} e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2048 d}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{4 d}-\frac{3 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3 \sqrt{a+b \cosh ^{-1}(c+d x)}}{32 d}-\frac{9 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}}{64 d}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{32 d}",1,"(-9*b*e^3*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]])/(64*d) - (3*b*e^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]])/(32*d) - (3*e^3*(a + b*ArcCosh[c + d*x])^(3/2))/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcCosh[c + d*x])^(3/2))/(4*d) - (3*b^(3/2)*e^3*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(2048*d) - (3*b^(3/2)*e^3*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(128*d) + (3*b^(3/2)*e^3*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(2048*d*E^((4*a)/b)) + (3*b^(3/2)*e^3*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(128*d*E^((2*a)/b))","A",27,11,25,0.4400,1,"{5866, 12, 5664, 5759, 5676, 5670, 5448, 3308, 2180, 2204, 2205}"
161,1,342,0,1.1097347,"\int (c e+d e x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2} \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcCosh[c + d*x])^(3/2),x]","-\frac{3 \sqrt{\pi } b^{3/2} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{96 d}+\frac{3 \sqrt{\pi } b^{3/2} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{96 d}+\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{3 d}-\frac{b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{6 d}-\frac{b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{3 d}","-\frac{3 \sqrt{\pi } b^{3/2} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{96 d}+\frac{3 \sqrt{\pi } b^{3/2} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{96 d}+\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{3 d}-\frac{b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{6 d}-\frac{b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{3 d}",1,"-(b*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]])/(3*d) - (b*e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]])/(6*d) + (e^2*(c + d*x)^3*(a + b*ArcCosh[c + d*x])^(3/2))/(3*d) - (3*b^(3/2)*e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(32*d) - (b^(3/2)*e^2*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(96*d) + (3*b^(3/2)*e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(32*d*E^(a/b)) + (b^(3/2)*e^2*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(96*d*E^((3*a)/b))","A",24,12,25,0.4800,1,"{5866, 12, 5664, 5759, 5718, 5658, 3308, 2180, 2205, 2204, 5670, 5448}"
162,1,212,0,0.6873082,"\int (c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2} \, dx","Int[(c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{2 d}-\frac{3 b e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}}{8 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{4 d}","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{2 d}-\frac{3 b e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}}{8 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{4 d}",1,"(-3*b*e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]])/(8*d) - (e*(a + b*ArcCosh[c + d*x])^(3/2))/(4*d) + (e*(c + d*x)^2*(a + b*ArcCosh[c + d*x])^(3/2))/(2*d) - (3*b^(3/2)*e*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(64*d) + (3*b^(3/2)*e*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(64*d*E^((2*a)/b))","A",13,11,23,0.4783,1,"{5866, 12, 5664, 5759, 5676, 5670, 5448, 3308, 2180, 2204, 2205}"
163,1,157,0,0.3630212,"\int \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2} \, dx","Int[(a + b*ArcCosh[c + d*x])^(3/2),x]","-\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}+\frac{3 \sqrt{\pi } b^{3/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}-\frac{3 b \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{2 d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{d}","-\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}+\frac{3 \sqrt{\pi } b^{3/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}-\frac{3 b \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{2 d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{d}",1,"(-3*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]])/(2*d) + ((c + d*x)*(a + b*ArcCosh[c + d*x])^(3/2))/d - (3*b^(3/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(8*d) + (3*b^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(8*d*E^(a/b))","A",9,8,14,0.5714,1,"{5864, 5654, 5718, 5658, 3308, 2180, 2205, 2204}"
164,0,0,0,0.1018718,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{c e+d e x} \, dx","Int[(a + b*ArcCosh[c + d*x])^(3/2)/(c*e + d*e*x),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{c e+d e x} \, dx","\frac{\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{c+d x},x\right)}{e}",0,"Defer[Subst][Defer[Int][(a + b*ArcCosh[x])^(3/2)/x, x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
165,1,469,0,2.2387949,"\int (c e+d e x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2} \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcCosh[c + d*x])^(5/2),x]","-\frac{15 \sqrt{\pi } b^{5/2} e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16384 d}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{512 d}-\frac{15 \sqrt{\pi } b^{5/2} e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16384 d}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{512 d}+\frac{15 b^2 e^3 (c+d x)^4 \sqrt{a+b \cosh ^{-1}(c+d x)}}{256 d}+\frac{45 b^2 e^3 (c+d x)^2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{256 d}-\frac{225 b^2 e^3 \sqrt{a+b \cosh ^{-1}(c+d x)}}{2048 d}+\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{4 d}-\frac{5 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{32 d}-\frac{15 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{64 d}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{32 d}","-\frac{15 \sqrt{\pi } b^{5/2} e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16384 d}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{512 d}-\frac{15 \sqrt{\pi } b^{5/2} e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16384 d}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{512 d}+\frac{15 b^2 e^3 (c+d x)^4 \sqrt{a+b \cosh ^{-1}(c+d x)}}{256 d}+\frac{45 b^2 e^3 (c+d x)^2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{256 d}-\frac{225 b^2 e^3 \sqrt{a+b \cosh ^{-1}(c+d x)}}{2048 d}+\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{4 d}-\frac{5 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{32 d}-\frac{15 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{64 d}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{32 d}",1,"(-225*b^2*e^3*Sqrt[a + b*ArcCosh[c + d*x]])/(2048*d) + (45*b^2*e^3*(c + d*x)^2*Sqrt[a + b*ArcCosh[c + d*x]])/(256*d) + (15*b^2*e^3*(c + d*x)^4*Sqrt[a + b*ArcCosh[c + d*x]])/(256*d) - (15*b*e^3*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^(3/2))/(64*d) - (5*b*e^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^(3/2))/(32*d) - (3*e^3*(a + b*ArcCosh[c + d*x])^(5/2))/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcCosh[c + d*x])^(5/2))/(4*d) - (15*b^(5/2)*e^3*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(16384*d) - (15*b^(5/2)*e^3*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(512*d) - (15*b^(5/2)*e^3*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(16384*d*E^((4*a)/b)) - (15*b^(5/2)*e^3*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(512*d*E^((2*a)/b))","A",29,11,25,0.4400,1,"{5866, 12, 5664, 5759, 5676, 5781, 3312, 3307, 2180, 2204, 2205}"
166,1,408,0,1.7514216,"\int (c e+d e x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2} \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcCosh[c + d*x])^(5/2),x]","-\frac{15 \sqrt{\pi } b^{5/2} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{5 \sqrt{\frac{\pi }{3}} b^{5/2} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{576 d}-\frac{15 \sqrt{\pi } b^{5/2} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{5 \sqrt{\frac{\pi }{3}} b^{5/2} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{576 d}+\frac{5 b^2 e^2 (c+d x)^3 \sqrt{a+b \cosh ^{-1}(c+d x)}}{36 d}+\frac{5 b^2 e^2 (c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}}{6 d}+\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{3 d}-\frac{5 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{18 d}-\frac{5 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{9 d}","-\frac{15 \sqrt{\pi } b^{5/2} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{5 \sqrt{\frac{\pi }{3}} b^{5/2} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{576 d}-\frac{15 \sqrt{\pi } b^{5/2} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{5 \sqrt{\frac{\pi }{3}} b^{5/2} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{576 d}+\frac{5 b^2 e^2 (c+d x)^3 \sqrt{a+b \cosh ^{-1}(c+d x)}}{36 d}+\frac{5 b^2 e^2 (c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}}{6 d}+\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{3 d}-\frac{5 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{18 d}-\frac{5 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{9 d}",1,"(5*b^2*e^2*(c + d*x)*Sqrt[a + b*ArcCosh[c + d*x]])/(6*d) + (5*b^2*e^2*(c + d*x)^3*Sqrt[a + b*ArcCosh[c + d*x]])/(36*d) - (5*b*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^(3/2))/(9*d) - (5*b*e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^(3/2))/(18*d) + (e^2*(c + d*x)^3*(a + b*ArcCosh[c + d*x])^(5/2))/(3*d) - (15*b^(5/2)*e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(64*d) - (5*b^(5/2)*e^2*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(576*d) - (15*b^(5/2)*e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(64*d*E^(a/b)) - (5*b^(5/2)*e^2*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(576*d*E^((3*a)/b))","A",26,12,25,0.4800,1,"{5866, 12, 5664, 5759, 5718, 5654, 5781, 3307, 2180, 2204, 2205, 3312}"
167,1,269,0,1.1079633,"\int (c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2} \, dx","Int[(c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^(5/2),x]","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}+\frac{15 b^2 e (c+d x)^2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{32 d}-\frac{15 b^2 e \sqrt{a+b \cosh ^{-1}(c+d x)}}{64 d}-\frac{5 b e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{8 d}+\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{2 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{4 d}","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}+\frac{15 b^2 e (c+d x)^2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{32 d}-\frac{15 b^2 e \sqrt{a+b \cosh ^{-1}(c+d x)}}{64 d}-\frac{5 b e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{8 d}+\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{2 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{4 d}",1,"(-15*b^2*e*Sqrt[a + b*ArcCosh[c + d*x]])/(64*d) + (15*b^2*e*(c + d*x)^2*Sqrt[a + b*ArcCosh[c + d*x]])/(32*d) - (5*b*e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^(3/2))/(8*d) - (e*(a + b*ArcCosh[c + d*x])^(5/2))/(4*d) + (e*(c + d*x)^2*(a + b*ArcCosh[c + d*x])^(5/2))/(2*d) - (15*b^(5/2)*e*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(256*d) - (15*b^(5/2)*e*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(256*d*E^((2*a)/b))","A",14,11,23,0.4783,1,"{5866, 12, 5664, 5759, 5676, 5781, 3312, 3307, 2180, 2204, 2205}"
168,1,186,0,0.6091134,"\int \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2} \, dx","Int[(a + b*ArcCosh[c + d*x])^(5/2),x]","-\frac{15 \sqrt{\pi } b^{5/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{15 \sqrt{\pi } b^{5/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}+\frac{15 b^2 (c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}}{4 d}-\frac{5 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{2 d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{d}","-\frac{15 \sqrt{\pi } b^{5/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{15 \sqrt{\pi } b^{5/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}+\frac{15 b^2 (c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}}{4 d}-\frac{5 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{2 d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{d}",1,"(15*b^2*(c + d*x)*Sqrt[a + b*ArcCosh[c + d*x]])/(4*d) - (5*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^(3/2))/(2*d) + ((c + d*x)*(a + b*ArcCosh[c + d*x])^(5/2))/d - (15*b^(5/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(16*d) - (15*b^(5/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(16*d*E^(a/b))","A",10,8,14,0.5714,1,"{5864, 5654, 5718, 5781, 3307, 2180, 2204, 2205}"
169,0,0,0,0.1007522,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{c e+d e x} \, dx","Int[(a + b*ArcCosh[c + d*x])^(5/2)/(c*e + d*e*x),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{c e+d e x} \, dx","\frac{\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{c+d x},x\right)}{e}",0,"Defer[Subst][Defer[Int][(a + b*ArcCosh[x])^(5/2)/x, x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
170,1,509,0,2.1423826,"\int (c e+d e x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2} \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcCosh[c + d*x])^(7/2),x]","-\frac{105 \sqrt{\pi } b^{7/2} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}-\frac{35 \sqrt{\frac{\pi }{3}} b^{7/2} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3456 d}+\frac{105 \sqrt{\pi } b^{7/2} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{35 \sqrt{\frac{\pi }{3}} b^{7/2} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3456 d}-\frac{35 b^3 e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{216 d}-\frac{175 b^3 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{54 d}+\frac{35 b^2 e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{108 d}+\frac{35 b^2 e^2 (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{18 d}-\frac{7 b e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{18 d}-\frac{7 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{9 d}+\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{3 d}","-\frac{105 \sqrt{\pi } b^{7/2} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}-\frac{35 \sqrt{\frac{\pi }{3}} b^{7/2} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3456 d}+\frac{105 \sqrt{\pi } b^{7/2} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{35 \sqrt{\frac{\pi }{3}} b^{7/2} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3456 d}-\frac{35 b^3 e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{216 d}-\frac{175 b^3 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{54 d}+\frac{35 b^2 e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{108 d}+\frac{35 b^2 e^2 (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{18 d}-\frac{7 b e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{18 d}-\frac{7 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{9 d}+\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{3 d}",1,"(-175*b^3*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]])/(54*d) - (35*b^3*e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]])/(216*d) + (35*b^2*e^2*(c + d*x)*(a + b*ArcCosh[c + d*x])^(3/2))/(18*d) + (35*b^2*e^2*(c + d*x)^3*(a + b*ArcCosh[c + d*x])^(3/2))/(108*d) - (7*b*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^(5/2))/(9*d) - (7*b*e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^(5/2))/(18*d) + (e^2*(c + d*x)^3*(a + b*ArcCosh[c + d*x])^(7/2))/(3*d) - (105*b^(7/2)*e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(128*d) - (35*b^(7/2)*e^2*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(3456*d) + (105*b^(7/2)*e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(128*d*E^(a/b)) + (35*b^(7/2)*e^2*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(3456*d*E^((3*a)/b))","A",35,13,25,0.5200,1,"{5866, 12, 5664, 5759, 5718, 5654, 5658, 3308, 2180, 2205, 2204, 5670, 5448}"
171,1,319,0,1.2764756,"\int (c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2} \, dx","Int[(c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^(7/2),x]","-\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{1024 d}+\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{1024 d}-\frac{105 b^3 e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{128 d}+\frac{35 b^2 e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{32 d}-\frac{35 b^2 e \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{64 d}-\frac{7 b e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{8 d}+\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{2 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{4 d}","-\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{1024 d}+\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{1024 d}-\frac{105 b^3 e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{128 d}+\frac{35 b^2 e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{32 d}-\frac{35 b^2 e \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{64 d}-\frac{7 b e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{8 d}+\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{2 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{4 d}",1,"(-105*b^3*e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]])/(128*d) - (35*b^2*e*(a + b*ArcCosh[c + d*x])^(3/2))/(64*d) + (35*b^2*e*(c + d*x)^2*(a + b*ArcCosh[c + d*x])^(3/2))/(32*d) - (7*b*e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^(5/2))/(8*d) - (e*(a + b*ArcCosh[c + d*x])^(7/2))/(4*d) + (e*(c + d*x)^2*(a + b*ArcCosh[c + d*x])^(7/2))/(2*d) - (105*b^(7/2)*e*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(1024*d) + (105*b^(7/2)*e*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(1024*d*E^((2*a)/b))","A",16,11,23,0.4783,1,"{5866, 12, 5664, 5759, 5676, 5670, 5448, 3308, 2180, 2204, 2205}"
172,1,230,0,0.642199,"\int \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2} \, dx","Int[(a + b*ArcCosh[c + d*x])^(7/2),x]","-\frac{105 \sqrt{\pi } b^{7/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{105 \sqrt{\pi } b^{7/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{105 b^3 \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{8 d}+\frac{35 b^2 (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{4 d}-\frac{7 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{2 d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{d}","-\frac{105 \sqrt{\pi } b^{7/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{105 \sqrt{\pi } b^{7/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{105 b^3 \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{8 d}+\frac{35 b^2 (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{4 d}-\frac{7 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{2 d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{d}",1,"(-105*b^3*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]])/(8*d) + (35*b^2*(c + d*x)*(a + b*ArcCosh[c + d*x])^(3/2))/(4*d) - (7*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x])^(5/2))/(2*d) + ((c + d*x)*(a + b*ArcCosh[c + d*x])^(7/2))/d - (105*b^(7/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(32*d) + (105*b^(7/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(32*d*E^(a/b))","A",11,8,14,0.5714,1,"{5864, 5654, 5718, 5658, 3308, 2180, 2205, 2204}"
173,0,0,0,0.1007892,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{c e+d e x} \, dx","Int[(a + b*ArcCosh[c + d*x])^(7/2)/(c*e + d*e*x),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{c e+d e x} \, dx","\frac{\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{c+d x},x\right)}{e}",0,"Defer[Subst][Defer[Int][(a + b*ArcCosh[x])^(7/2)/x, x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
174,1,326,0,0.6224911,"\int \frac{(c e+d e x)^4}{\sqrt{a+b \cosh ^{-1}(c+d x)}} \, dx","Int[(c*e + d*e*x)^4/Sqrt[a + b*ArcCosh[c + d*x]],x]","-\frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 \sqrt{b} d}-\frac{\sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{5}} e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 \sqrt{b} d}+\frac{\sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{5}} e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}","-\frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 \sqrt{b} d}-\frac{\sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{5}} e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 \sqrt{b} d}+\frac{\sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{5}} e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}",1,"-(e^4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(16*Sqrt[b]*d) - (e^4*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(32*Sqrt[b]*d) - (e^4*E^((5*a)/b)*Sqrt[Pi/5]*Erf[(Sqrt[5]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(32*Sqrt[b]*d) + (e^4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(16*Sqrt[b]*d*E^(a/b)) + (e^4*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(32*Sqrt[b]*d*E^((3*a)/b)) + (e^4*Sqrt[Pi/5]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(32*Sqrt[b]*d*E^((5*a)/b))","A",20,8,25,0.3200,1,"{5866, 12, 5670, 5448, 3308, 2180, 2204, 2205}"
175,1,217,0,0.4562338,"\int \frac{(c e+d e x)^3}{\sqrt{a+b \cosh ^{-1}(c+d x)}} \, dx","Int[(c*e + d*e*x)^3/Sqrt[a + b*ArcCosh[c + d*x]],x]","-\frac{\sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{2}} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{2}} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}","-\frac{\sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{2}} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{2}} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}",1,"-(e^3*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(32*Sqrt[b]*d) - (e^3*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(8*Sqrt[b]*d) + (e^3*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(32*Sqrt[b]*d*E^((4*a)/b)) + (e^3*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(8*Sqrt[b]*d*E^((2*a)/b))","A",15,8,25,0.3200,1,"{5866, 12, 5670, 5448, 3308, 2180, 2204, 2205}"
176,1,214,0,0.4593933,"\int \frac{(c e+d e x)^2}{\sqrt{a+b \cosh ^{-1}(c+d x)}} \, dx","Int[(c*e + d*e*x)^2/Sqrt[a + b*ArcCosh[c + d*x]],x]","-\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{3}} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{3}} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}","-\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{3}} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{3}} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}",1,"-(e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(8*Sqrt[b]*d) - (e^2*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(8*Sqrt[b]*d) + (e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(8*Sqrt[b]*d*E^(a/b)) + (e^2*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(8*Sqrt[b]*d*E^((3*a)/b))","A",15,8,25,0.3200,1,"{5866, 12, 5670, 5448, 3308, 2180, 2204, 2205}"
177,1,113,0,0.2369563,"\int \frac{c e+d e x}{\sqrt{a+b \cosh ^{-1}(c+d x)}} \, dx","Int[(c*e + d*e*x)/Sqrt[a + b*ArcCosh[c + d*x]],x]","\frac{\sqrt{\frac{\pi }{2}} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{2}} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d}","\frac{\sqrt{\frac{\pi }{2}} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{2}} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d}",1,"-(e*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(4*Sqrt[b]*d) + (e*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(4*Sqrt[b]*d*E^((2*a)/b))","A",10,8,23,0.3478,1,"{5866, 12, 5670, 5448, 3308, 2180, 2204, 2205}"
178,1,92,0,0.1288263,"\int \frac{1}{\sqrt{a+b \cosh ^{-1}(c+d x)}} \, dx","Int[1/Sqrt[a + b*ArcCosh[c + d*x]],x]","\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}","\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}",1,"-(E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(2*Sqrt[b]*d) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(2*Sqrt[b]*d*E^(a/b))","A",7,6,14,0.4286,1,"{5864, 5658, 3308, 2180, 2205, 2204}"
179,0,0,0,0.0936042,"\int \frac{1}{(c e+d e x) \sqrt{a+b \cosh ^{-1}(c+d x)}} \, dx","Int[1/((c*e + d*e*x)*Sqrt[a + b*ArcCosh[c + d*x]]),x]","\int \frac{1}{(c e+d e x) \sqrt{a+b \cosh ^{-1}(c+d x)}} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*Sqrt[a + b*ArcCosh[x]]), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
180,1,374,0,0.6437511,"\int \frac{(c e+d e x)^4}{\left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcCosh[c + d*x])^(3/2),x]","\frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{3/2} d}+\frac{3 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}+\frac{\sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{3/2} d}+\frac{3 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}+\frac{\sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}-\frac{2 e^4 \sqrt{c+d x-1} (c+d x)^4 \sqrt{c+d x+1}}{b d \sqrt{a+b \cosh ^{-1}(c+d x)}}","\frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{3/2} d}+\frac{3 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}+\frac{\sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{3/2} d}+\frac{3 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}+\frac{\sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}-\frac{2 e^4 \sqrt{c+d x-1} (c+d x)^4 \sqrt{c+d x+1}}{b d \sqrt{a+b \cosh ^{-1}(c+d x)}}",1,"(-2*e^4*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x])/(b*d*Sqrt[a + b*ArcCosh[c + d*x]]) + (e^4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(8*b^(3/2)*d) + (3*e^4*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(16*b^(3/2)*d) + (e^4*E^((5*a)/b)*Sqrt[5*Pi]*Erf[(Sqrt[5]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(16*b^(3/2)*d) + (e^4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(8*b^(3/2)*d*E^(a/b)) + (3*e^4*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(16*b^(3/2)*d*E^((3*a)/b)) + (e^4*Sqrt[5*Pi]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(16*b^(3/2)*d*E^((5*a)/b))","A",19,7,25,0.2800,1,"{5866, 12, 5666, 3307, 2180, 2204, 2205}"
181,1,269,0,0.4494481,"\int \frac{(c e+d e x)^3}{\left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcCosh[c + d*x])^(3/2),x]","\frac{\sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{\frac{\pi }{2}} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{3/2} d}+\frac{\sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{\frac{\pi }{2}} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{3/2} d}-\frac{2 e^3 \sqrt{c+d x-1} (c+d x)^3 \sqrt{c+d x+1}}{b d \sqrt{a+b \cosh ^{-1}(c+d x)}}","\frac{\sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{\frac{\pi }{2}} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{3/2} d}+\frac{\sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{\frac{\pi }{2}} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{3/2} d}-\frac{2 e^3 \sqrt{c+d x-1} (c+d x)^3 \sqrt{c+d x+1}}{b d \sqrt{a+b \cosh ^{-1}(c+d x)}}",1,"(-2*e^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x])/(b*d*Sqrt[a + b*ArcCosh[c + d*x]]) + (e^3*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(4*b^(3/2)*d) + (e^3*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(2*b^(3/2)*d) + (e^3*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(4*b^(3/2)*d*E^((4*a)/b)) + (e^3*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(2*b^(3/2)*d*E^((2*a)/b))","A",14,7,25,0.2800,1,"{5866, 12, 5666, 3307, 2180, 2204, 2205}"
182,1,262,0,0.4495667,"\int \frac{(c e+d e x)^2}{\left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcCosh[c + d*x])^(3/2),x]","\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{2 e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1}}{b d \sqrt{a+b \cosh ^{-1}(c+d x)}}","\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{2 e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1}}{b d \sqrt{a+b \cosh ^{-1}(c+d x)}}",1,"(-2*e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])/(b*d*Sqrt[a + b*ArcCosh[c + d*x]]) + (e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(4*b^(3/2)*d) + (e^2*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(4*b^(3/2)*d) + (e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(4*b^(3/2)*d*E^(a/b)) + (e^2*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(4*b^(3/2)*d*E^((3*a)/b))","A",14,7,25,0.2800,1,"{5866, 12, 5666, 3307, 2180, 2204, 2205}"
183,1,155,0,0.2250431,"\int \frac{c e+d e x}{\left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(c*e + d*e*x)/(a + b*ArcCosh[c + d*x])^(3/2),x]","\frac{\sqrt{\frac{\pi }{2}} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\frac{\pi }{2}} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{b d \sqrt{a+b \cosh ^{-1}(c+d x)}}","\frac{\sqrt{\frac{\pi }{2}} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\frac{\pi }{2}} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{b d \sqrt{a+b \cosh ^{-1}(c+d x)}}",1,"(-2*e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(b*d*Sqrt[a + b*ArcCosh[c + d*x]]) + (e*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(b^(3/2)*d) + (e*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(b^(3/2)*d*E^((2*a)/b))","A",8,7,23,0.3043,1,"{5866, 12, 5666, 3307, 2180, 2204, 2205}"
184,1,128,0,0.3544127,"\int \frac{1}{\left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c + d*x])^(-3/2),x]","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{b d \sqrt{a+b \cosh ^{-1}(c+d x)}}","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{b d \sqrt{a+b \cosh ^{-1}(c+d x)}}",1,"(-2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(b*d*Sqrt[a + b*ArcCosh[c + d*x]]) + (E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(b^(3/2)*d) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(b^(3/2)*d*E^(a/b))","A",8,7,14,0.5000,1,"{5864, 5656, 5781, 3307, 2180, 2204, 2205}"
185,0,0,0,0.1044093,"\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^(3/2)),x]","\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcCosh[x])^(3/2)), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
186,1,444,0,1.7650109,"\int \frac{(c e+d e x)^4}{\left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcCosh[c + d*x])^(5/2),x]","-\frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{5/2} d}-\frac{3 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{5/2} d}-\frac{5 \sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{24 b^{5/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{5/2} d}+\frac{3 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{5/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{24 b^{5/2} d}-\frac{20 e^4 (c+d x)^5}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{16 e^4 (c+d x)^3}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}","-\frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{5/2} d}-\frac{3 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{5/2} d}-\frac{5 \sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{24 b^{5/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{5/2} d}+\frac{3 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{5/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{24 b^{5/2} d}-\frac{20 e^4 (c+d x)^5}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{16 e^4 (c+d x)^3}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}",1,"(-2*e^4*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x])/(3*b*d*(a + b*ArcCosh[c + d*x])^(3/2)) + (16*e^4*(c + d*x)^3)/(3*b^2*d*Sqrt[a + b*ArcCosh[c + d*x]]) - (20*e^4*(c + d*x)^5)/(3*b^2*d*Sqrt[a + b*ArcCosh[c + d*x]]) - (e^4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(12*b^(5/2)*d) - (3*e^4*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(8*b^(5/2)*d) - (5*e^4*E^((5*a)/b)*Sqrt[5*Pi]*Erf[(Sqrt[5]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(24*b^(5/2)*d) + (e^4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(12*b^(5/2)*d*E^(a/b)) + (3*e^4*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(8*b^(5/2)*d*E^((3*a)/b)) + (5*e^4*Sqrt[5*Pi]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(24*b^(5/2)*d*E^((5*a)/b))","A",36,10,25,0.4000,1,"{5866, 12, 5668, 5775, 5670, 5448, 3308, 2180, 2204, 2205}"
187,1,333,0,1.4411638,"\int \frac{(c e+d e x)^3}{\left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcCosh[c + d*x])^(5/2),x]","-\frac{2 \sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{\sqrt{2 \pi } e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{\sqrt{2 \pi } e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{16 e^3 (c+d x)^4}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{4 e^3 (c+d x)^2}{b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}","-\frac{2 \sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{\sqrt{2 \pi } e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{\sqrt{2 \pi } e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{16 e^3 (c+d x)^4}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{4 e^3 (c+d x)^2}{b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}",1,"(-2*e^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x])/(3*b*d*(a + b*ArcCosh[c + d*x])^(3/2)) + (4*e^3*(c + d*x)^2)/(b^2*d*Sqrt[a + b*ArcCosh[c + d*x]]) - (16*e^3*(c + d*x)^4)/(3*b^2*d*Sqrt[a + b*ArcCosh[c + d*x]]) - (2*e^3*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d) - (e^3*E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d) + (2*e^3*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d*E^((4*a)/b)) + (e^3*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d*E^((2*a)/b))","A",26,10,25,0.4000,1,"{5866, 12, 5668, 5775, 5670, 5448, 3308, 2180, 2204, 2205}"
188,1,328,0,1.2372807,"\int \frac{(c e+d e x)^2}{\left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcCosh[c + d*x])^(5/2),x]","-\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{6 b^{5/2} d}-\frac{\sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{5/2} d}+\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{6 b^{5/2} d}+\frac{\sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{5/2} d}-\frac{4 e^2 (c+d x)^3}{b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{8 e^2 (c+d x)}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}","-\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{6 b^{5/2} d}-\frac{\sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{5/2} d}+\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{6 b^{5/2} d}+\frac{\sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{5/2} d}-\frac{4 e^2 (c+d x)^3}{b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{8 e^2 (c+d x)}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}",1,"(-2*e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])/(3*b*d*(a + b*ArcCosh[c + d*x])^(3/2)) + (8*e^2*(c + d*x))/(3*b^2*d*Sqrt[a + b*ArcCosh[c + d*x]]) - (4*e^2*(c + d*x)^3)/(b^2*d*Sqrt[a + b*ArcCosh[c + d*x]]) - (e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(6*b^(5/2)*d) - (e^2*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(2*b^(5/2)*d) + (e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(6*b^(5/2)*d*E^(a/b)) + (e^2*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(2*b^(5/2)*d*E^((3*a)/b))","A",24,11,25,0.4400,1,"{5866, 12, 5668, 5775, 5670, 5448, 3308, 2180, 2204, 2205, 5658}"
189,1,216,0,0.7796369,"\int \frac{c e+d e x}{\left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[(c*e + d*e*x)/(a + b*ArcCosh[c + d*x])^(5/2),x]","-\frac{2 \sqrt{2 \pi } e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{2 \pi } e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{8 e (c+d x)^2}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{4 e}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}","-\frac{2 \sqrt{2 \pi } e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{2 \pi } e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{8 e (c+d x)^2}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{4 e}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}",1,"(-2*e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(3*b*d*(a + b*ArcCosh[c + d*x])^(3/2)) + (4*e)/(3*b^2*d*Sqrt[a + b*ArcCosh[c + d*x]]) - (8*e*(c + d*x)^2)/(3*b^2*d*Sqrt[a + b*ArcCosh[c + d*x]]) - (2*e*E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d) + (2*e*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d*E^((2*a)/b))","A",13,11,23,0.4783,1,"{5866, 12, 5668, 5775, 5670, 5448, 3308, 2180, 2204, 2205, 5676}"
190,1,165,0,0.4088767,"\int \frac{1}{\left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[(a + b*ArcCosh[c + d*x])^(-5/2),x]","-\frac{2 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{4 (c+d x)}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}","-\frac{2 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{4 (c+d x)}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}",1,"(-2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(3*b*d*(a + b*ArcCosh[c + d*x])^(3/2)) - (4*(c + d*x))/(3*b^2*d*Sqrt[a + b*ArcCosh[c + d*x]]) - (2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(3*b^(5/2)*d) + (2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(3*b^(5/2)*d*E^(a/b))","A",9,8,14,0.5714,1,"{5864, 5656, 5775, 5658, 3308, 2180, 2205, 2204}"
191,0,0,0,0.1075403,"\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^(5/2)),x]","\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcCosh[x])^(5/2)), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
192,1,552,0,1.7755783,"\int \frac{(c e+d e x)^4}{\left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcCosh[c + d*x])^(7/2),x]","\frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{30 b^{7/2} d}+\frac{9 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{20 b^{7/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{7/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{30 b^{7/2} d}+\frac{9 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{20 b^{7/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{7/2} d}-\frac{4 e^4 (c+d x)^5}{3 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{40 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{3 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{16 e^4 (c+d x)^3}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}+\frac{32 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{5 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{5 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}","\frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{30 b^{7/2} d}+\frac{9 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{20 b^{7/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{7/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{30 b^{7/2} d}+\frac{9 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{20 b^{7/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{7/2} d}-\frac{4 e^4 (c+d x)^5}{3 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{40 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{3 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{16 e^4 (c+d x)^3}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}+\frac{32 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{5 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{5 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}",1,"(-2*e^4*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x])/(5*b*d*(a + b*ArcCosh[c + d*x])^(5/2)) + (16*e^4*(c + d*x)^3)/(15*b^2*d*(a + b*ArcCosh[c + d*x])^(3/2)) - (4*e^4*(c + d*x)^5)/(3*b^2*d*(a + b*ArcCosh[c + d*x])^(3/2)) + (32*e^4*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])/(5*b^3*d*Sqrt[a + b*ArcCosh[c + d*x]]) - (40*e^4*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x])/(3*b^3*d*Sqrt[a + b*ArcCosh[c + d*x]]) + (e^4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(30*b^(7/2)*d) + (9*e^4*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(20*b^(7/2)*d) + (5*e^4*E^((5*a)/b)*Sqrt[5*Pi]*Erf[(Sqrt[5]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(12*b^(7/2)*d) + (e^4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(30*b^(7/2)*d*E^(a/b)) + (9*e^4*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(20*b^(7/2)*d*E^((3*a)/b)) + (5*e^4*Sqrt[5*Pi]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(12*b^(7/2)*d*E^((5*a)/b))","A",34,9,25,0.3600,1,"{5866, 12, 5668, 5775, 5666, 3307, 2180, 2204, 2205}"
193,1,441,0,1.4061626,"\int \frac{(c e+d e x)^3}{\left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcCosh[c + d*x])^(7/2),x]","\frac{16 \sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 \sqrt{2 \pi } e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{16 \sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 \sqrt{2 \pi } e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{16 e^3 (c+d x)^4}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{128 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{15 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{4 e^3 (c+d x)^2}{5 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}+\frac{16 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{5 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{5 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}","\frac{16 \sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 \sqrt{2 \pi } e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{16 \sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 \sqrt{2 \pi } e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{16 e^3 (c+d x)^4}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{128 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{15 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{4 e^3 (c+d x)^2}{5 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}+\frac{16 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{5 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{5 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}",1,"(-2*e^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x])/(5*b*d*(a + b*ArcCosh[c + d*x])^(5/2)) + (4*e^3*(c + d*x)^2)/(5*b^2*d*(a + b*ArcCosh[c + d*x])^(3/2)) - (16*e^3*(c + d*x)^4)/(15*b^2*d*(a + b*ArcCosh[c + d*x])^(3/2)) + (16*e^3*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(5*b^3*d*Sqrt[a + b*ArcCosh[c + d*x]]) - (128*e^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x])/(15*b^3*d*Sqrt[a + b*ArcCosh[c + d*x]]) + (16*e^3*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d) + (4*e^3*E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d) + (16*e^3*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d*E^((4*a)/b)) + (4*e^3*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d*E^((2*a)/b))","A",23,9,25,0.3600,1,"{5866, 12, 5668, 5775, 5666, 3307, 2180, 2204, 2205}"
194,1,431,0,1.4749797,"\int \frac{(c e+d e x)^2}{\left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcCosh[c + d*x])^(7/2),x]","\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{3 \sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{5 b^{7/2} d}+\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{3 \sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{5 b^{7/2} d}-\frac{4 e^2 (c+d x)^3}{5 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{24 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{5 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{8 e^2 (c+d x)}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}+\frac{16 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{15 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{5 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}","\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{3 \sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{5 b^{7/2} d}+\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{3 \sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{5 b^{7/2} d}-\frac{4 e^2 (c+d x)^3}{5 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{24 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{5 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{8 e^2 (c+d x)}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}+\frac{16 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{15 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{5 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}",1,"(-2*e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])/(5*b*d*(a + b*ArcCosh[c + d*x])^(5/2)) + (8*e^2*(c + d*x))/(15*b^2*d*(a + b*ArcCosh[c + d*x])^(3/2)) - (4*e^2*(c + d*x)^3)/(5*b^2*d*(a + b*ArcCosh[c + d*x])^(3/2)) + (16*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(15*b^3*d*Sqrt[a + b*ArcCosh[c + d*x]]) - (24*e^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])/(5*b^3*d*Sqrt[a + b*ArcCosh[c + d*x]]) + (e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(15*b^(7/2)*d) + (3*e^2*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(5*b^(7/2)*d) + (e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(15*b^(7/2)*d*E^(a/b)) + (3*e^2*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(5*b^(7/2)*d*E^((3*a)/b))","A",24,11,25,0.4400,1,"{5866, 12, 5668, 5775, 5666, 3307, 2180, 2204, 2205, 5656, 5781}"
195,1,266,0,0.7843471,"\int \frac{c e+d e x}{\left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[(c*e + d*e*x)/(a + b*ArcCosh[c + d*x])^(7/2),x]","\frac{8 \sqrt{2 \pi } e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{8 \sqrt{2 \pi } e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{8 e (c+d x)^2}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{32 e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{15 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{4 e}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{2 e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{5 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}","\frac{8 \sqrt{2 \pi } e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{8 \sqrt{2 \pi } e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{8 e (c+d x)^2}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{32 e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{15 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{4 e}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{2 e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{5 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}",1,"(-2*e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(5*b*d*(a + b*ArcCosh[c + d*x])^(5/2)) + (4*e)/(15*b^2*d*(a + b*ArcCosh[c + d*x])^(3/2)) - (8*e*(c + d*x)^2)/(15*b^2*d*(a + b*ArcCosh[c + d*x])^(3/2)) - (32*e*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(15*b^3*d*Sqrt[a + b*ArcCosh[c + d*x]]) + (8*e*E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d) + (8*e*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d*E^((2*a)/b))","A",11,10,23,0.4348,1,"{5866, 12, 5668, 5775, 5666, 3307, 2180, 2204, 2205, 5676}"
196,1,209,0,0.6274653,"\int \frac{1}{\left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[(a + b*ArcCosh[c + d*x])^(-7/2),x]","\frac{4 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 \sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{4 (c+d x)}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{8 \sqrt{c+d x-1} \sqrt{c+d x+1}}{15 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{5 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}","\frac{4 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 \sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{4 (c+d x)}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{8 \sqrt{c+d x-1} \sqrt{c+d x+1}}{15 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{5 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}",1,"(-2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(5*b*d*(a + b*ArcCosh[c + d*x])^(5/2)) - (4*(c + d*x))/(15*b^2*d*(a + b*ArcCosh[c + d*x])^(3/2)) - (8*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(15*b^3*d*Sqrt[a + b*ArcCosh[c + d*x]]) + (4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(15*b^(7/2)*d) + (4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(15*b^(7/2)*d*E^(a/b))","A",10,8,14,0.5714,1,"{5864, 5656, 5775, 5781, 3307, 2180, 2204, 2205}"
197,0,0,0,0.1030438,"\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^(7/2)),x]","\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcCosh[x])^(7/2)), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
198,1,189,0,0.1437045,"\int (c e+d e x)^{7/2} \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^(7/2)*(a + b*ArcCosh[c + d*x]),x]","\frac{2 (e (c+d x))^{9/2} \left(a+b \cosh ^{-1}(c+d x)\right)}{9 d e}-\frac{28 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{3/2}}{405 d}-\frac{28 b e^3 \sqrt{-c-d x+1} \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c+d x+1}}{\sqrt{2}}\right)\right|2\right)}{135 d \sqrt{-c-d x} \sqrt{c+d x-1}}-\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{7/2}}{81 d}","\frac{2 (e (c+d x))^{9/2} \left(a+b \cosh ^{-1}(c+d x)\right)}{9 d e}-\frac{28 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{3/2}}{405 d}-\frac{28 b e^3 \sqrt{-c-d x+1} \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c+d x+1}}{\sqrt{2}}\right)\right|2\right)}{135 d \sqrt{-c-d x} \sqrt{c+d x-1}}-\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{7/2}}{81 d}",1,"(-28*b*e^2*Sqrt[-1 + c + d*x]*(e*(c + d*x))^(3/2)*Sqrt[1 + c + d*x])/(405*d) - (4*b*Sqrt[-1 + c + d*x]*(e*(c + d*x))^(7/2)*Sqrt[1 + c + d*x])/(81*d) + (2*(e*(c + d*x))^(9/2)*(a + b*ArcCosh[c + d*x]))/(9*d*e) - (28*b*e^3*Sqrt[1 - c - d*x]*Sqrt[e*(c + d*x)]*EllipticE[ArcSin[Sqrt[1 + c + d*x]/Sqrt[2]], 2])/(135*d*Sqrt[-c - d*x]*Sqrt[-1 + c + d*x])","A",8,6,23,0.2609,1,"{5866, 5662, 102, 12, 114, 113}"
199,1,169,0,0.133221,"\int (c e+d e x)^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^(5/2)*(a + b*ArcCosh[c + d*x]),x]","\frac{2 (e (c+d x))^{7/2} \left(a+b \cosh ^{-1}(c+d x)\right)}{7 d e}-\frac{20 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{e (c+d x)}}{147 d}-\frac{20 b e^{5/2} \sqrt{-c-d x+1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{147 d \sqrt{c+d x-1}}-\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{5/2}}{49 d}","\frac{2 (e (c+d x))^{7/2} \left(a+b \cosh ^{-1}(c+d x)\right)}{7 d e}-\frac{20 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{e (c+d x)}}{147 d}-\frac{20 b e^{5/2} \sqrt{-c-d x+1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{147 d \sqrt{c+d x-1}}-\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{5/2}}{49 d}",1,"(-20*b*e^2*Sqrt[-1 + c + d*x]*Sqrt[e*(c + d*x)]*Sqrt[1 + c + d*x])/(147*d) - (4*b*Sqrt[-1 + c + d*x]*(e*(c + d*x))^(5/2)*Sqrt[1 + c + d*x])/(49*d) + (2*(e*(c + d*x))^(7/2)*(a + b*ArcCosh[c + d*x]))/(7*d*e) - (20*b*e^(5/2)*Sqrt[1 - c - d*x]*EllipticF[ArcSin[Sqrt[e*(c + d*x)]/Sqrt[e]], -1])/(147*d*Sqrt[-1 + c + d*x])","A",8,6,23,0.2609,1,"{5866, 5662, 102, 12, 117, 116}"
200,1,145,0,0.111114,"\int (c e+d e x)^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^(3/2)*(a + b*ArcCosh[c + d*x]),x]","\frac{2 (e (c+d x))^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right)}{5 d e}-\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{3/2}}{25 d}-\frac{12 b e \sqrt{-c-d x+1} \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c+d x+1}}{\sqrt{2}}\right)\right|2\right)}{25 d \sqrt{-c-d x} \sqrt{c+d x-1}}","\frac{2 (e (c+d x))^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right)}{5 d e}-\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{3/2}}{25 d}-\frac{12 b e \sqrt{-c-d x+1} \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c+d x+1}}{\sqrt{2}}\right)\right|2\right)}{25 d \sqrt{-c-d x} \sqrt{c+d x-1}}",1,"(-4*b*Sqrt[-1 + c + d*x]*(e*(c + d*x))^(3/2)*Sqrt[1 + c + d*x])/(25*d) + (2*(e*(c + d*x))^(5/2)*(a + b*ArcCosh[c + d*x]))/(5*d*e) - (12*b*e*Sqrt[1 - c - d*x]*Sqrt[e*(c + d*x)]*EllipticE[ArcSin[Sqrt[1 + c + d*x]/Sqrt[2]], 2])/(25*d*Sqrt[-c - d*x]*Sqrt[-1 + c + d*x])","A",6,6,23,0.2609,1,"{5866, 5662, 102, 12, 114, 113}"
201,1,127,0,0.0971451,"\int \sqrt{c e+d e x} \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Int[Sqrt[c*e + d*e*x]*(a + b*ArcCosh[c + d*x]),x]","\frac{2 (e (c+d x))^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e}-\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{e (c+d x)}}{9 d}-\frac{4 b \sqrt{e} \sqrt{-c-d x+1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{9 d \sqrt{c+d x-1}}","\frac{2 (e (c+d x))^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e}-\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{e (c+d x)}}{9 d}-\frac{4 b \sqrt{e} \sqrt{-c-d x+1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{9 d \sqrt{c+d x-1}}",1,"(-4*b*Sqrt[-1 + c + d*x]*Sqrt[e*(c + d*x)]*Sqrt[1 + c + d*x])/(9*d) + (2*(e*(c + d*x))^(3/2)*(a + b*ArcCosh[c + d*x]))/(3*d*e) - (4*b*Sqrt[e]*Sqrt[1 - c - d*x]*EllipticF[ArcSin[Sqrt[e*(c + d*x)]/Sqrt[e]], -1])/(9*d*Sqrt[-1 + c + d*x])","A",6,6,23,0.2609,1,"{5866, 5662, 102, 12, 117, 116}"
202,1,104,0,0.0878043,"\int \frac{a+b \cosh ^{-1}(c+d x)}{\sqrt{c e+d e x}} \, dx","Int[(a + b*ArcCosh[c + d*x])/Sqrt[c*e + d*e*x],x]","\frac{2 \sqrt{e (c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right)}{d e}-\frac{4 b \sqrt{-c-d x+1} \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c+d x+1}}{\sqrt{2}}\right)\right|2\right)}{d e \sqrt{-c-d x} \sqrt{c+d x-1}}","\frac{2 \sqrt{e (c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right)}{d e}-\frac{4 b \sqrt{-c-d x+1} \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c+d x+1}}{\sqrt{2}}\right)\right|2\right)}{d e \sqrt{-c-d x} \sqrt{c+d x-1}}",1,"(2*Sqrt[e*(c + d*x)]*(a + b*ArcCosh[c + d*x]))/(d*e) - (4*b*Sqrt[1 - c - d*x]*Sqrt[e*(c + d*x)]*EllipticE[ArcSin[Sqrt[1 + c + d*x]/Sqrt[2]], 2])/(d*e*Sqrt[-c - d*x]*Sqrt[-1 + c + d*x])","A",4,4,23,0.1739,1,"{5866, 5662, 114, 113}"
203,1,84,0,0.0839204,"\int \frac{a+b \cosh ^{-1}(c+d x)}{(c e+d e x)^{3/2}} \, dx","Int[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x)^(3/2),x]","\frac{4 b \sqrt{-c-d x+1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{d e^{3/2} \sqrt{c+d x-1}}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{d e \sqrt{e (c+d x)}}","\frac{4 b \sqrt{-c-d x+1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{d e^{3/2} \sqrt{c+d x-1}}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{d e \sqrt{e (c+d x)}}",1,"(-2*(a + b*ArcCosh[c + d*x]))/(d*e*Sqrt[e*(c + d*x)]) + (4*b*Sqrt[1 - c - d*x]*EllipticF[ArcSin[Sqrt[e*(c + d*x)]/Sqrt[e]], -1])/(d*e^(3/2)*Sqrt[-1 + c + d*x])","A",4,4,23,0.1739,1,"{5866, 5662, 117, 116}"
204,1,150,0,0.1205693,"\int \frac{a+b \cosh ^{-1}(c+d x)}{(c e+d e x)^{5/2}} \, dx","Int[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x)^(5/2),x]","-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e (e (c+d x))^{3/2}}+\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1}}{3 d e^2 \sqrt{e (c+d x)}}-\frac{4 b \sqrt{-c-d x+1} \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c+d x+1}}{\sqrt{2}}\right)\right|2\right)}{3 d e^3 \sqrt{-c-d x} \sqrt{c+d x-1}}","-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e (e (c+d x))^{3/2}}+\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1}}{3 d e^2 \sqrt{e (c+d x)}}-\frac{4 b \sqrt{-c-d x+1} \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c+d x+1}}{\sqrt{2}}\right)\right|2\right)}{3 d e^3 \sqrt{-c-d x} \sqrt{c+d x-1}}",1,"(4*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(3*d*e^2*Sqrt[e*(c + d*x)]) - (2*(a + b*ArcCosh[c + d*x]))/(3*d*e*(e*(c + d*x))^(3/2)) - (4*b*Sqrt[1 - c - d*x]*Sqrt[e*(c + d*x)]*EllipticE[ArcSin[Sqrt[1 + c + d*x]/Sqrt[2]], 2])/(3*d*e^3*Sqrt[-c - d*x]*Sqrt[-1 + c + d*x])","A",7,7,23,0.3043,1,"{5866, 5662, 104, 12, 16, 114, 113}"
205,1,130,0,0.1111536,"\int \frac{a+b \cosh ^{-1}(c+d x)}{(c e+d e x)^{7/2}} \, dx","Int[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x)^(7/2),x]","-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{5 d e (e (c+d x))^{5/2}}+\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1}}{15 d e^2 (e (c+d x))^{3/2}}+\frac{4 b \sqrt{-c-d x+1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{15 d e^{7/2} \sqrt{c+d x-1}}","-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{5 d e (e (c+d x))^{5/2}}+\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1}}{15 d e^2 (e (c+d x))^{3/2}}+\frac{4 b \sqrt{-c-d x+1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{15 d e^{7/2} \sqrt{c+d x-1}}",1,"(4*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(15*d*e^2*(e*(c + d*x))^(3/2)) - (2*(a + b*ArcCosh[c + d*x]))/(5*d*e*(e*(c + d*x))^(5/2)) + (4*b*Sqrt[1 - c - d*x]*EllipticF[ArcSin[Sqrt[e*(c + d*x)]/Sqrt[e]], -1])/(15*d*e^(7/2)*Sqrt[-1 + c + d*x])","A",7,7,23,0.3043,1,"{5866, 5662, 104, 12, 16, 117, 116}"
206,1,165,0,0.3213796,"\int (c e+d e x)^{7/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^(7/2)*(a + b*ArcCosh[c + d*x])^2,x]","-\frac{16 b^2 (e (c+d x))^{13/2} \, _3F_2\left(1,\frac{13}{4},\frac{13}{4};\frac{15}{4},\frac{17}{4};(c+d x)^2\right)}{1287 d e^3}-\frac{8 b \sqrt{1-(c+d x)^2} (e (c+d x))^{11/2} \, _2F_1\left(\frac{1}{2},\frac{11}{4};\frac{15}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{99 d e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}+\frac{2 (e (c+d x))^{9/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{9 d e}","-\frac{16 b^2 (e (c+d x))^{13/2} \, _3F_2\left(1,\frac{13}{4},\frac{13}{4};\frac{15}{4},\frac{17}{4};(c+d x)^2\right)}{1287 d e^3}-\frac{8 b \sqrt{-c-d x+1} (e (c+d x))^{11/2} \, _2F_1\left(\frac{1}{2},\frac{11}{4};\frac{15}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{99 d e^2 \sqrt{c+d x-1}}+\frac{2 (e (c+d x))^{9/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{9 d e}",1,"(2*(e*(c + d*x))^(9/2)*(a + b*ArcCosh[c + d*x])^2)/(9*d*e) - (8*b*(e*(c + d*x))^(11/2)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[1/2, 11/4, 15/4, (c + d*x)^2])/(99*d*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]) - (16*b^2*(e*(c + d*x))^(13/2)*HypergeometricPFQ[{1, 13/4, 13/4}, {15/4, 17/4}, (c + d*x)^2])/(1287*d*e^3)","A",3,3,25,0.1200,1,"{5866, 5662, 5763}"
207,1,165,0,0.3276721,"\int (c e+d e x)^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^(5/2)*(a + b*ArcCosh[c + d*x])^2,x]","-\frac{16 b^2 (e (c+d x))^{11/2} \, _3F_2\left(1,\frac{11}{4},\frac{11}{4};\frac{13}{4},\frac{15}{4};(c+d x)^2\right)}{693 d e^3}-\frac{8 b \sqrt{1-(c+d x)^2} (e (c+d x))^{9/2} \, _2F_1\left(\frac{1}{2},\frac{9}{4};\frac{13}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{63 d e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}+\frac{2 (e (c+d x))^{7/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{7 d e}","-\frac{16 b^2 (e (c+d x))^{11/2} \, _3F_2\left(1,\frac{11}{4},\frac{11}{4};\frac{13}{4},\frac{15}{4};(c+d x)^2\right)}{693 d e^3}-\frac{8 b \sqrt{-c-d x+1} (e (c+d x))^{9/2} \, _2F_1\left(\frac{1}{2},\frac{9}{4};\frac{13}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{63 d e^2 \sqrt{c+d x-1}}+\frac{2 (e (c+d x))^{7/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{7 d e}",1,"(2*(e*(c + d*x))^(7/2)*(a + b*ArcCosh[c + d*x])^2)/(7*d*e) - (8*b*(e*(c + d*x))^(9/2)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[1/2, 9/4, 13/4, (c + d*x)^2])/(63*d*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]) - (16*b^2*(e*(c + d*x))^(11/2)*HypergeometricPFQ[{1, 11/4, 11/4}, {13/4, 15/4}, (c + d*x)^2])/(693*d*e^3)","A",3,3,25,0.1200,1,"{5866, 5662, 5763}"
208,1,165,0,0.3263409,"\int (c e+d e x)^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^(3/2)*(a + b*ArcCosh[c + d*x])^2,x]","-\frac{16 b^2 (e (c+d x))^{9/2} \, _3F_2\left(1,\frac{9}{4},\frac{9}{4};\frac{11}{4},\frac{13}{4};(c+d x)^2\right)}{315 d e^3}-\frac{8 b \sqrt{1-(c+d x)^2} (e (c+d x))^{7/2} \, _2F_1\left(\frac{1}{2},\frac{7}{4};\frac{11}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{35 d e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}+\frac{2 (e (c+d x))^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{5 d e}","-\frac{16 b^2 (e (c+d x))^{9/2} \, _3F_2\left(1,\frac{9}{4},\frac{9}{4};\frac{11}{4},\frac{13}{4};(c+d x)^2\right)}{315 d e^3}-\frac{8 b \sqrt{-c-d x+1} (e (c+d x))^{7/2} \, _2F_1\left(\frac{1}{2},\frac{7}{4};\frac{11}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{35 d e^2 \sqrt{c+d x-1}}+\frac{2 (e (c+d x))^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{5 d e}",1,"(2*(e*(c + d*x))^(5/2)*(a + b*ArcCosh[c + d*x])^2)/(5*d*e) - (8*b*(e*(c + d*x))^(7/2)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[1/2, 7/4, 11/4, (c + d*x)^2])/(35*d*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]) - (16*b^2*(e*(c + d*x))^(9/2)*HypergeometricPFQ[{1, 9/4, 9/4}, {11/4, 13/4}, (c + d*x)^2])/(315*d*e^3)","A",3,3,25,0.1200,1,"{5866, 5662, 5763}"
209,1,165,0,0.3157277,"\int \sqrt{c e+d e x} \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Int[Sqrt[c*e + d*e*x]*(a + b*ArcCosh[c + d*x])^2,x]","-\frac{16 b^2 (e (c+d x))^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};(c+d x)^2\right)}{105 d e^3}-\frac{8 b \sqrt{1-(c+d x)^2} (e (c+d x))^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{15 d e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}+\frac{2 (e (c+d x))^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d e}","-\frac{16 b^2 (e (c+d x))^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};(c+d x)^2\right)}{105 d e^3}-\frac{8 b \sqrt{-c-d x+1} (e (c+d x))^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{15 d e^2 \sqrt{c+d x-1}}+\frac{2 (e (c+d x))^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d e}",1,"(2*(e*(c + d*x))^(3/2)*(a + b*ArcCosh[c + d*x])^2)/(3*d*e) - (8*b*(e*(c + d*x))^(5/2)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[1/2, 5/4, 9/4, (c + d*x)^2])/(15*d*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]) - (16*b^2*(e*(c + d*x))^(7/2)*HypergeometricPFQ[{1, 7/4, 7/4}, {9/4, 11/4}, (c + d*x)^2])/(105*d*e^3)","A",3,3,25,0.1200,1,"{5866, 5662, 5763}"
210,1,163,0,0.2891525,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{\sqrt{c e+d e x}} \, dx","Int[(a + b*ArcCosh[c + d*x])^2/Sqrt[c*e + d*e*x],x]","-\frac{16 b^2 (e (c+d x))^{5/2} \, _3F_2\left(1,\frac{5}{4},\frac{5}{4};\frac{7}{4},\frac{9}{4};(c+d x)^2\right)}{15 d e^3}-\frac{8 b \sqrt{1-(c+d x)^2} (e (c+d x))^{3/2} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}+\frac{2 \sqrt{e (c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e}","-\frac{16 b^2 (e (c+d x))^{5/2} \, _3F_2\left(1,\frac{5}{4},\frac{5}{4};\frac{7}{4},\frac{9}{4};(c+d x)^2\right)}{15 d e^3}-\frac{8 b \sqrt{-c-d x+1} (e (c+d x))^{3/2} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e^2 \sqrt{c+d x-1}}+\frac{2 \sqrt{e (c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e}",1,"(2*Sqrt[e*(c + d*x)]*(a + b*ArcCosh[c + d*x])^2)/(d*e) - (8*b*(e*(c + d*x))^(3/2)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[1/2, 3/4, 7/4, (c + d*x)^2])/(3*d*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]) - (16*b^2*(e*(c + d*x))^(5/2)*HypergeometricPFQ[{1, 5/4, 5/4}, {7/4, 9/4}, (c + d*x)^2])/(15*d*e^3)","A",3,3,25,0.1200,1,"{5866, 5662, 5763}"
211,1,161,0,0.304253,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{(c e+d e x)^{3/2}} \, dx","Int[(a + b*ArcCosh[c + d*x])^2/(c*e + d*e*x)^(3/2),x]","\frac{16 b^2 (e (c+d x))^{3/2} \, _3F_2\left(\frac{3}{4},\frac{3}{4},1;\frac{5}{4},\frac{7}{4};(c+d x)^2\right)}{3 d e^3}+\frac{8 b \sqrt{1-(c+d x)^2} \sqrt{e (c+d x)} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e \sqrt{e (c+d x)}}","\frac{16 b^2 (e (c+d x))^{3/2} \, _3F_2\left(\frac{3}{4},\frac{3}{4},1;\frac{5}{4},\frac{7}{4};(c+d x)^2\right)}{3 d e^3}+\frac{8 b \sqrt{-c-d x+1} \sqrt{e (c+d x)} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2 \sqrt{c+d x-1}}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e \sqrt{e (c+d x)}}",1,"(-2*(a + b*ArcCosh[c + d*x])^2)/(d*e*Sqrt[e*(c + d*x)]) + (8*b*Sqrt[e*(c + d*x)]*Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[1/4, 1/2, 5/4, (c + d*x)^2])/(d*e^2*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]) + (16*b^2*(e*(c + d*x))^(3/2)*HypergeometricPFQ[{3/4, 3/4, 1}, {5/4, 7/4}, (c + d*x)^2])/(3*d*e^3)","A",3,3,25,0.1200,1,"{5866, 5662, 5763}"
212,1,165,0,0.3122312,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{(c e+d e x)^{5/2}} \, dx","Int[(a + b*ArcCosh[c + d*x])^2/(c*e + d*e*x)^(5/2),x]","-\frac{16 b^2 \sqrt{e (c+d x)} \, _3F_2\left(\frac{1}{4},\frac{1}{4},1;\frac{3}{4},\frac{5}{4};(c+d x)^2\right)}{3 d e^3}-\frac{8 b \sqrt{1-(c+d x)^2} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{e (c+d x)}}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d e (e (c+d x))^{3/2}}","-\frac{16 b^2 \sqrt{e (c+d x)} \, _3F_2\left(\frac{1}{4},\frac{1}{4},1;\frac{3}{4},\frac{5}{4};(c+d x)^2\right)}{3 d e^3}-\frac{8 b \sqrt{-c-d x+1} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e^2 \sqrt{c+d x-1} \sqrt{e (c+d x)}}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d e (e (c+d x))^{3/2}}",1,"(-2*(a + b*ArcCosh[c + d*x])^2)/(3*d*e*(e*(c + d*x))^(3/2)) - (8*b*Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[-1/4, 1/2, 3/4, (c + d*x)^2])/(3*d*e^2*Sqrt[-1 + c + d*x]*Sqrt[e*(c + d*x)]*Sqrt[1 + c + d*x]) - (16*b^2*Sqrt[e*(c + d*x)]*HypergeometricPFQ[{1/4, 1/4, 1}, {3/4, 5/4}, (c + d*x)^2])/(3*d*e^3)","A",3,3,25,0.1200,1,"{5866, 5662, 5763}"
213,1,165,0,0.3173032,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{(c e+d e x)^{7/2}} \, dx","Int[(a + b*ArcCosh[c + d*x])^2/(c*e + d*e*x)^(7/2),x]","\frac{16 b^2 \, _3F_2\left(-\frac{1}{4},-\frac{1}{4},1;\frac{1}{4},\frac{3}{4};(c+d x)^2\right)}{15 d e^3 \sqrt{e (c+d x)}}-\frac{8 b \sqrt{1-(c+d x)^2} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{15 d e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{3/2}}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{5 d e (e (c+d x))^{5/2}}","\frac{16 b^2 \, _3F_2\left(-\frac{1}{4},-\frac{1}{4},1;\frac{1}{4},\frac{3}{4};(c+d x)^2\right)}{15 d e^3 \sqrt{e (c+d x)}}-\frac{8 b \sqrt{-c-d x+1} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{15 d e^2 \sqrt{c+d x-1} (e (c+d x))^{3/2}}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{5 d e (e (c+d x))^{5/2}}",1,"(-2*(a + b*ArcCosh[c + d*x])^2)/(5*d*e*(e*(c + d*x))^(5/2)) - (8*b*Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[-3/4, 1/2, 1/4, (c + d*x)^2])/(15*d*e^2*Sqrt[-1 + c + d*x]*(e*(c + d*x))^(3/2)*Sqrt[1 + c + d*x]) + (16*b^2*HypergeometricPFQ[{-1/4, -1/4, 1}, {1/4, 3/4}, (c + d*x)^2])/(15*d*e^3*Sqrt[e*(c + d*x)])","A",3,3,25,0.1200,1,"{5866, 5662, 5763}"
214,0,0,0,0.3204827,"\int (c e+d e x)^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^(3/2)*(a + b*ArcCosh[c + d*x])^3,x]","\int (c e+d e x)^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","\frac{2 (e (c+d x))^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{5 d e}-\frac{6 b \text{Int}\left(\frac{(e (c+d x))^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{\sqrt{c+d x-1} \sqrt{c+d x+1}},x\right)}{5 e}",0,"(2*(e*(c + d*x))^(5/2)*(a + b*ArcCosh[c + d*x])^3)/(5*d*e) - (6*b*Defer[Subst][Defer[Int][((e*x)^(5/2)*(a + b*ArcCosh[x])^2)/(Sqrt[-1 + x]*Sqrt[1 + x]), x], x, c + d*x])/(5*d*e)","A",0,0,0,0,-1,"{}"
215,0,0,0,0.3108306,"\int \sqrt{c e+d e x} \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","Int[Sqrt[c*e + d*e*x]*(a + b*ArcCosh[c + d*x])^3,x]","\int \sqrt{c e+d e x} \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","\frac{2 (e (c+d x))^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 d e}-\frac{2 b \text{Int}\left(\frac{(e (c+d x))^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{\sqrt{c+d x-1} \sqrt{c+d x+1}},x\right)}{e}",0,"(2*(e*(c + d*x))^(3/2)*(a + b*ArcCosh[c + d*x])^3)/(3*d*e) - (2*b*Defer[Subst][Defer[Int][((e*x)^(3/2)*(a + b*ArcCosh[x])^2)/(Sqrt[-1 + x]*Sqrt[1 + x]), x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
216,0,0,0,0.2865925,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c e+d e x}} \, dx","Int[(a + b*ArcCosh[c + d*x])^3/Sqrt[c*e + d*e*x],x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c e+d e x}} \, dx","\frac{2 \sqrt{e (c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e}-\frac{6 b \text{Int}\left(\frac{\sqrt{e (c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{\sqrt{c+d x-1} \sqrt{c+d x+1}},x\right)}{e}",0,"(2*Sqrt[e*(c + d*x)]*(a + b*ArcCosh[c + d*x])^3)/(d*e) - (6*b*Defer[Subst][Defer[Int][(Sqrt[e*x]*(a + b*ArcCosh[x])^2)/(Sqrt[-1 + x]*Sqrt[1 + x]), x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
217,0,0,0,0.3029544,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{3/2}} \, dx","Int[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x)^(3/2),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{3/2}} \, dx","\frac{6 b \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{\sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{e (c+d x)}},x\right)}{e}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e \sqrt{e (c+d x)}}",0,"(-2*(a + b*ArcCosh[c + d*x])^3)/(d*e*Sqrt[e*(c + d*x)]) + (6*b*Defer[Subst][Defer[Int][(a + b*ArcCosh[x])^2/(Sqrt[-1 + x]*Sqrt[e*x]*Sqrt[1 + x]), x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
218,0,0,0,0.3216622,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{5/2}} \, dx","Int[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x)^(5/2),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{5/2}} \, dx","\frac{2 b \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{\sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{3/2}},x\right)}{e}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 d e (e (c+d x))^{3/2}}",0,"(-2*(a + b*ArcCosh[c + d*x])^3)/(3*d*e*(e*(c + d*x))^(3/2)) + (2*b*Defer[Subst][Defer[Int][(a + b*ArcCosh[x])^2/(Sqrt[-1 + x]*(e*x)^(3/2)*Sqrt[1 + x]), x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
219,0,0,0,0.3239434,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{7/2}} \, dx","Int[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x)^(7/2),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{7/2}} \, dx","\frac{6 b \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{\sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{5/2}},x\right)}{5 e}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{5 d e (e (c+d x))^{5/2}}",0,"(-2*(a + b*ArcCosh[c + d*x])^3)/(5*d*e*(e*(c + d*x))^(5/2)) + (6*b*Defer[Subst][Defer[Int][(a + b*ArcCosh[x])^2/(Sqrt[-1 + x]*(e*x)^(5/2)*Sqrt[1 + x]), x], x, c + d*x])/(5*d*e)","A",0,0,0,0,-1,"{}"
220,0,0,0,0.3152734,"\int (c e+d e x)^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","Int[(c*e + d*e*x)^(3/2)*(a + b*ArcCosh[c + d*x])^4,x]","\int (c e+d e x)^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","\frac{2 (e (c+d x))^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right)^4}{5 d e}-\frac{8 b \text{Int}\left(\frac{(e (c+d x))^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c+d x-1} \sqrt{c+d x+1}},x\right)}{5 e}",0,"(2*(e*(c + d*x))^(5/2)*(a + b*ArcCosh[c + d*x])^4)/(5*d*e) - (8*b*Defer[Subst][Defer[Int][((e*x)^(5/2)*(a + b*ArcCosh[x])^3)/(Sqrt[-1 + x]*Sqrt[1 + x]), x], x, c + d*x])/(5*d*e)","A",0,0,0,0,-1,"{}"
221,0,0,0,0.3086671,"\int \sqrt{c e+d e x} \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","Int[Sqrt[c*e + d*e*x]*(a + b*ArcCosh[c + d*x])^4,x]","\int \sqrt{c e+d e x} \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","\frac{2 (e (c+d x))^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^4}{3 d e}-\frac{8 b \text{Int}\left(\frac{(e (c+d x))^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c+d x-1} \sqrt{c+d x+1}},x\right)}{3 e}",0,"(2*(e*(c + d*x))^(3/2)*(a + b*ArcCosh[c + d*x])^4)/(3*d*e) - (8*b*Defer[Subst][Defer[Int][((e*x)^(3/2)*(a + b*ArcCosh[x])^3)/(Sqrt[-1 + x]*Sqrt[1 + x]), x], x, c + d*x])/(3*d*e)","A",0,0,0,0,-1,"{}"
222,0,0,0,0.280245,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{\sqrt{c e+d e x}} \, dx","Int[(a + b*ArcCosh[c + d*x])^4/Sqrt[c*e + d*e*x],x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{\sqrt{c e+d e x}} \, dx","\frac{2 \sqrt{e (c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right)^4}{d e}-\frac{8 b \text{Int}\left(\frac{\sqrt{e (c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c+d x-1} \sqrt{c+d x+1}},x\right)}{e}",0,"(2*Sqrt[e*(c + d*x)]*(a + b*ArcCosh[c + d*x])^4)/(d*e) - (8*b*Defer[Subst][Defer[Int][(Sqrt[e*x]*(a + b*ArcCosh[x])^3)/(Sqrt[-1 + x]*Sqrt[1 + x]), x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
223,0,0,0,0.2928285,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{3/2}} \, dx","Int[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x)^(3/2),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{3/2}} \, dx","\frac{8 b \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{e (c+d x)}},x\right)}{e}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{d e \sqrt{e (c+d x)}}",0,"(-2*(a + b*ArcCosh[c + d*x])^4)/(d*e*Sqrt[e*(c + d*x)]) + (8*b*Defer[Subst][Defer[Int][(a + b*ArcCosh[x])^3/(Sqrt[-1 + x]*Sqrt[e*x]*Sqrt[1 + x]), x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
224,0,0,0,0.3146414,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{5/2}} \, dx","Int[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x)^(5/2),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{5/2}} \, dx","\frac{8 b \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{3/2}},x\right)}{3 e}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{3 d e (e (c+d x))^{3/2}}",0,"(-2*(a + b*ArcCosh[c + d*x])^4)/(3*d*e*(e*(c + d*x))^(3/2)) + (8*b*Defer[Subst][Defer[Int][(a + b*ArcCosh[x])^3/(Sqrt[-1 + x]*(e*x)^(3/2)*Sqrt[1 + x]), x], x, c + d*x])/(3*d*e)","A",0,0,0,0,-1,"{}"
225,0,0,0,0.3139268,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{7/2}} \, dx","Int[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x)^(7/2),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{7/2}} \, dx","\frac{8 b \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{5/2}},x\right)}{5 e}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{5 d e (e (c+d x))^{5/2}}",0,"(-2*(a + b*ArcCosh[c + d*x])^4)/(5*d*e*(e*(c + d*x))^(5/2)) + (8*b*Defer[Subst][Defer[Int][(a + b*ArcCosh[x])^3/(Sqrt[-1 + x]*(e*x)^(5/2)*Sqrt[1 + x]), x], x, c + d*x])/(5*d*e)","A",0,0,0,0,-1,"{}"
226,0,0,0,0.2902634,"\int (c e+d e x)^m \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","Int[(c*e + d*e*x)^m*(a + b*ArcCosh[c + d*x])^4,x]","\int (c e+d e x)^m \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","\frac{(e (c+d x))^{m+1} \left(a+b \cosh ^{-1}(c+d x)\right)^4}{d e (m+1)}-\frac{4 b \text{Int}\left(\frac{(e (c+d x))^{m+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c+d x-1} \sqrt{c+d x+1}},x\right)}{e (m+1)}",0,"((e*(c + d*x))^(1 + m)*(a + b*ArcCosh[c + d*x])^4)/(d*e*(1 + m)) - (4*b*Defer[Subst][Defer[Int][((e*x)^(1 + m)*(a + b*ArcCosh[x])^3)/(Sqrt[-1 + x]*Sqrt[1 + x]), x], x, c + d*x])/(d*e*(1 + m))","A",0,0,0,0,-1,"{}"
227,0,0,0,0.293982,"\int (c e+d e x)^m \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^m*(a + b*ArcCosh[c + d*x])^3,x]","\int (c e+d e x)^m \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","\frac{(e (c+d x))^{m+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e (m+1)}-\frac{3 b \text{Int}\left(\frac{(e (c+d x))^{m+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{\sqrt{c+d x-1} \sqrt{c+d x+1}},x\right)}{e (m+1)}",0,"((e*(c + d*x))^(1 + m)*(a + b*ArcCosh[c + d*x])^3)/(d*e*(1 + m)) - (3*b*Defer[Subst][Defer[Int][((e*x)^(1 + m)*(a + b*ArcCosh[x])^2)/(Sqrt[-1 + x]*Sqrt[1 + x]), x], x, c + d*x])/(d*e*(1 + m))","A",0,0,0,0,-1,"{}"
228,1,218,0,0.3186613,"\int (c e+d e x)^m \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^m*(a + b*ArcCosh[c + d*x])^2,x]","-\frac{2 b^2 (e (c+d x))^{m+3} \, _3F_2\left(1,\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};\frac{m}{2}+2,\frac{m}{2}+\frac{5}{2};(c+d x)^2\right)}{d e^3 (m+1) (m+2) (m+3)}-\frac{2 b \sqrt{1-(c+d x)^2} (e (c+d x))^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2 (m+1) (m+2) \sqrt{c+d x-1} \sqrt{c+d x+1}}+\frac{(e (c+d x))^{m+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e (m+1)}","-\frac{2 b^2 (e (c+d x))^{m+3} \, _3F_2\left(1,\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};\frac{m}{2}+2,\frac{m}{2}+\frac{5}{2};(c+d x)^2\right)}{d e^3 (m+1) (m+2) (m+3)}-\frac{2 b \sqrt{-c-d x+1} (e (c+d x))^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2 (m+1) (m+2) \sqrt{c+d x-1}}+\frac{(e (c+d x))^{m+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e (m+1)}",1,"((e*(c + d*x))^(1 + m)*(a + b*ArcCosh[c + d*x])^2)/(d*e*(1 + m)) - (2*b*(e*(c + d*x))^(2 + m)*Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, (c + d*x)^2])/(d*e^2*(1 + m)*(2 + m)*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]) - (2*b^2*(e*(c + d*x))^(3 + m)*HypergeometricPFQ[{1, 3/2 + m/2, 3/2 + m/2}, {2 + m/2, 5/2 + m/2}, (c + d*x)^2])/(d*e^3*(1 + m)*(2 + m)*(3 + m))","A",3,3,23,0.1304,1,"{5866, 5662, 5763}"
229,1,124,0,0.0989388,"\int (c e+d e x)^m \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^m*(a + b*ArcCosh[c + d*x]),x]","\frac{(e (c+d x))^{m+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{d e (m+1)}-\frac{b \sqrt{1-(c+d x)^2} (e (c+d x))^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};(c+d x)^2\right)}{d e^2 (m+1) (m+2) \sqrt{c+d x-1} \sqrt{c+d x+1}}","\frac{(e (c+d x))^{m+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{d e (m+1)}-\frac{b \left(1-(c+d x)^2\right) (e (c+d x))^{m+2} \, _2F_1\left(1,\frac{m+3}{2};\frac{m+4}{2};(c+d x)^2\right)}{d e^2 (m+1) (m+2) \sqrt{c+d x-1} \sqrt{c+d x+1}}",1,"((e*(c + d*x))^(1 + m)*(a + b*ArcCosh[c + d*x]))/(d*e*(1 + m)) - (b*(e*(c + d*x))^(2 + m)*Sqrt[1 - (c + d*x)^2]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, (c + d*x)^2])/(d*e^2*(1 + m)*(2 + m)*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])","A",5,5,21,0.2381,1,"{5866, 5662, 126, 365, 364}"
230,0,0,0,0.0610087,"\int \frac{(c e+d e x)^m}{a+b \cosh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^m/(a + b*ArcCosh[c + d*x]),x]","\int \frac{(c e+d e x)^m}{a+b \cosh ^{-1}(c+d x)} \, dx","\text{Int}\left(\frac{(e (c+d x))^m}{a+b \cosh ^{-1}(c+d x)},x\right)",0,"Defer[Subst][Defer[Int][(e*x)^m/(a + b*ArcCosh[x]), x], x, c + d*x]/d","A",0,0,0,0,-1,"{}"
231,1,54,0,0.0668968,"\int \frac{\cosh ^{-1}\left(a x^5\right)}{x} \, dx","Int[ArcCosh[a*x^5]/x,x]","\frac{1}{10} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}\left(a x^5\right)}\right)-\frac{1}{10} \cosh ^{-1}\left(a x^5\right)^2+\frac{1}{5} \cosh ^{-1}\left(a x^5\right) \log \left(e^{2 \cosh ^{-1}\left(a x^5\right)}+1\right)","\frac{1}{10} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}\left(a x^5\right)}\right)-\frac{1}{10} \cosh ^{-1}\left(a x^5\right)^2+\frac{1}{5} \cosh ^{-1}\left(a x^5\right) \log \left(e^{2 \cosh ^{-1}\left(a x^5\right)}+1\right)",1,"-ArcCosh[a*x^5]^2/10 + (ArcCosh[a*x^5]*Log[1 + E^(2*ArcCosh[a*x^5])])/5 + PolyLog[2, -E^(2*ArcCosh[a*x^5])]/10","A",5,5,10,0.5000,1,"{5891, 3718, 2190, 2279, 2391}"
232,1,117,0,0.0704343,"\int x^2 \cosh ^{-1}\left(\sqrt{x}\right) \, dx","Int[x^2*ArcCosh[Sqrt[x]],x]","-\frac{1}{18} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{5/2}-\frac{5}{72} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{3/2}+\frac{1}{3} x^3 \cosh ^{-1}\left(\sqrt{x}\right)-\frac{5}{48} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}-\frac{5}{48} \cosh ^{-1}\left(\sqrt{x}\right)","-\frac{1}{18} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{5/2}-\frac{5}{72} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{3/2}+\frac{1}{3} x^3 \cosh ^{-1}\left(\sqrt{x}\right)-\frac{5}{48} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}-\frac{5}{48} \cosh ^{-1}\left(\sqrt{x}\right)",1,"(-5*Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x])/48 - (5*Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(3/2))/72 - (Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(5/2))/18 - (5*ArcCosh[Sqrt[x]])/48 + (x^3*ArcCosh[Sqrt[x]])/3","A",7,5,10,0.5000,1,"{5903, 12, 323, 330, 52}"
233,1,86,0,0.0503724,"\int x \cosh ^{-1}\left(\sqrt{x}\right) \, dx","Int[x*ArcCosh[Sqrt[x]],x]","-\frac{1}{8} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{3/2}+\frac{1}{2} x^2 \cosh ^{-1}\left(\sqrt{x}\right)-\frac{3}{16} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}-\frac{3}{16} \cosh ^{-1}\left(\sqrt{x}\right)","-\frac{1}{8} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{3/2}+\frac{1}{2} x^2 \cosh ^{-1}\left(\sqrt{x}\right)-\frac{3}{16} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}-\frac{3}{16} \cosh ^{-1}\left(\sqrt{x}\right)",1,"(-3*Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x])/16 - (Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(3/2))/8 - (3*ArcCosh[Sqrt[x]])/16 + (x^2*ArcCosh[Sqrt[x]])/2","A",6,5,8,0.6250,1,"{5903, 12, 323, 330, 52}"
234,1,50,0,0.0313341,"\int \cosh ^{-1}\left(\sqrt{x}\right) \, dx","Int[ArcCosh[Sqrt[x]],x]","-\frac{1}{2} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}+x \cosh ^{-1}\left(\sqrt{x}\right)-\frac{1}{2} \cosh ^{-1}\left(\sqrt{x}\right)","-\frac{1}{2} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}+x \cosh ^{-1}\left(\sqrt{x}\right)-\frac{1}{2} \cosh ^{-1}\left(\sqrt{x}\right)",1,"-(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x])/2 - ArcCosh[Sqrt[x]]/2 + x*ArcCosh[Sqrt[x]]","A",5,5,6,0.8333,1,"{5901, 12, 323, 330, 52}"
235,1,46,0,0.0638731,"\int \frac{\cosh ^{-1}\left(\sqrt{x}\right)}{x} \, dx","Int[ArcCosh[Sqrt[x]]/x,x]","\text{PolyLog}\left(2,-e^{2 \cosh ^{-1}\left(\sqrt{x}\right)}\right)-\cosh ^{-1}\left(\sqrt{x}\right)^2+2 \cosh ^{-1}\left(\sqrt{x}\right) \log \left(e^{2 \cosh ^{-1}\left(\sqrt{x}\right)}+1\right)","\text{PolyLog}\left(2,-e^{2 \cosh ^{-1}\left(\sqrt{x}\right)}\right)-\cosh ^{-1}\left(\sqrt{x}\right)^2+2 \cosh ^{-1}\left(\sqrt{x}\right) \log \left(e^{2 \cosh ^{-1}\left(\sqrt{x}\right)}+1\right)",1,"-ArcCosh[Sqrt[x]]^2 + 2*ArcCosh[Sqrt[x]]*Log[1 + E^(2*ArcCosh[Sqrt[x]])] + PolyLog[2, -E^(2*ArcCosh[Sqrt[x]])]","A",5,5,10,0.5000,1,"{5891, 3718, 2190, 2279, 2391}"
236,1,40,0,0.0256731,"\int \frac{\cosh ^{-1}\left(\sqrt{x}\right)}{x^2} \, dx","Int[ArcCosh[Sqrt[x]]/x^2,x]","\frac{\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{\sqrt{x}}-\frac{\cosh ^{-1}\left(\sqrt{x}\right)}{x}","\frac{\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{\sqrt{x}}-\frac{\cosh ^{-1}\left(\sqrt{x}\right)}{x}",1,"(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/Sqrt[x] - ArcCosh[Sqrt[x]]/x","A",3,3,10,0.3000,1,"{5903, 12, 265}"
237,1,76,0,0.0406338,"\int \frac{\cosh ^{-1}\left(\sqrt{x}\right)}{x^3} \, dx","Int[ArcCosh[Sqrt[x]]/x^3,x]","\frac{\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{6 x^{3/2}}-\frac{\cosh ^{-1}\left(\sqrt{x}\right)}{2 x^2}+\frac{\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{3 \sqrt{x}}","\frac{\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{6 x^{3/2}}-\frac{\cosh ^{-1}\left(\sqrt{x}\right)}{2 x^2}+\frac{\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{3 \sqrt{x}}",1,"(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/(6*x^(3/2)) + (Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/(3*Sqrt[x]) - ArcCosh[Sqrt[x]]/(2*x^2)","A",4,4,10,0.4000,1,"{5903, 12, 272, 265}"
238,1,24,0,0.008589,"\int \cosh ^{-1}\left(\frac{1}{x}\right) \, dx","Int[ArcCosh[x^(-1)],x]","\sqrt{\frac{1}{x+1}} \sqrt{x+1} \sin ^{-1}(x)+x \text{sech}^{-1}(x)","\sqrt{\frac{1}{x+1}} \sqrt{x+1} \sin ^{-1}(x)+x \text{sech}^{-1}(x)",1,"x*ArcSech[x] + Sqrt[(1 + x)^(-1)]*Sqrt[1 + x]*ArcSin[x]","A",3,3,4,0.7500,1,"{5893, 6277, 216}"
239,1,60,0,0.0654295,"\int \frac{\cosh ^{-1}\left(a x^n\right)}{x} \, dx","Int[ArcCosh[a*x^n]/x,x]","\frac{\text{PolyLog}\left(2,-e^{2 \cosh ^{-1}\left(a x^n\right)}\right)}{2 n}-\frac{\cosh ^{-1}\left(a x^n\right)^2}{2 n}+\frac{\cosh ^{-1}\left(a x^n\right) \log \left(e^{2 \cosh ^{-1}\left(a x^n\right)}+1\right)}{n}","\frac{\text{PolyLog}\left(2,-e^{2 \cosh ^{-1}\left(a x^n\right)}\right)}{2 n}-\frac{\cosh ^{-1}\left(a x^n\right)^2}{2 n}+\frac{\cosh ^{-1}\left(a x^n\right) \log \left(e^{2 \cosh ^{-1}\left(a x^n\right)}+1\right)}{n}",1,"-ArcCosh[a*x^n]^2/(2*n) + (ArcCosh[a*x^n]*Log[1 + E^(2*ArcCosh[a*x^n])])/n + PolyLog[2, -E^(2*ArcCosh[a*x^n])]/(2*n)","A",5,5,10,0.5000,1,"{5891, 3718, 2190, 2279, 2391}"
240,1,145,0,0.0360027,"\int \left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^4 \, dx","Int[(a + b*ArcCosh[1 + d*x^2])^4,x]","-\frac{192 b^3 \left(d x^4+2 x^2\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)}{x \sqrt{d x^2} \sqrt{d x^2+2}}+48 b^2 x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^2-\frac{8 b \left(d x^4+2 x^2\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^3}{x \sqrt{d x^2} \sqrt{d x^2+2}}+x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^4+384 b^4 x","-\frac{192 b^3 \left(d x^4+2 x^2\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)}{x \sqrt{d x^2} \sqrt{d x^2+2}}+48 b^2 x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^2-\frac{8 b \left(d x^4+2 x^2\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^3}{x \sqrt{d x^2} \sqrt{d x^2+2}}+x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^4+384 b^4 x",1,"384*b^4*x - (192*b^3*(2*x^2 + d*x^4)*(a + b*ArcCosh[1 + d*x^2]))/(x*Sqrt[d*x^2]*Sqrt[2 + d*x^2]) + 48*b^2*x*(a + b*ArcCosh[1 + d*x^2])^2 - (8*b*(2*x^2 + d*x^4)*(a + b*ArcCosh[1 + d*x^2])^3)/(x*Sqrt[d*x^2]*Sqrt[2 + d*x^2]) + x*(a + b*ArcCosh[1 + d*x^2])^4","A",3,2,14,0.1429,1,"{5880, 8}"
241,1,125,0,0.0625657,"\int \left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^3 \, dx","Int[(a + b*ArcCosh[1 + d*x^2])^3,x]","24 a b^2 x-\frac{6 b \left(d x^4+2 x^2\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^2}{x \sqrt{d x^2} \sqrt{d x^2+2}}+x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^3-\frac{48 b^3 \sqrt{\frac{d x^2}{d x^2+2}} \left(d x^2+2\right)}{d x}+24 b^3 x \cosh ^{-1}\left(d x^2+1\right)","24 a b^2 x-\frac{6 b \left(d x^4+2 x^2\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^2}{x \sqrt{d x^2} \sqrt{d x^2+2}}+x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^3-\frac{48 b^3 \sqrt{\frac{d x^2}{d x^2+2}} \left(d x^2+2\right)}{d x}+24 b^3 x \cosh ^{-1}\left(d x^2+1\right)",1,"24*a*b^2*x - (48*b^3*Sqrt[(d*x^2)/(2 + d*x^2)]*(2 + d*x^2))/(d*x) + 24*b^3*x*ArcCosh[1 + d*x^2] - (6*b*(2*x^2 + d*x^4)*(a + b*ArcCosh[1 + d*x^2])^2)/(x*Sqrt[d*x^2]*Sqrt[2 + d*x^2]) + x*(a + b*ArcCosh[1 + d*x^2])^3","A",6,5,14,0.3571,1,"{5880, 5901, 12, 6719, 261}"
242,1,72,0,0.0143908,"\int \left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^2 \, dx","Int[(a + b*ArcCosh[1 + d*x^2])^2,x]","-\frac{4 b \left(d x^4+2 x^2\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)}{x \sqrt{d x^2} \sqrt{d x^2+2}}+x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^2+8 b^2 x","-\frac{4 b \left(d x^4+2 x^2\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)}{x \sqrt{d x^2} \sqrt{d x^2+2}}+x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^2+8 b^2 x",1,"8*b^2*x - (4*b*(2*x^2 + d*x^4)*(a + b*ArcCosh[1 + d*x^2]))/(x*Sqrt[d*x^2]*Sqrt[2 + d*x^2]) + x*(a + b*ArcCosh[1 + d*x^2])^2","A",2,2,14,0.1429,1,"{5880, 8}"
243,1,49,0,0.0390155,"\int \left(a+b \cosh ^{-1}\left(1+d x^2\right)\right) \, dx","Int[a + b*ArcCosh[1 + d*x^2],x]","a x-\frac{2 b \sqrt{\frac{d x^2}{d x^2+2}} \left(d x^2+2\right)}{d x}+b x \cosh ^{-1}\left(d x^2+1\right)","a x-\frac{2 b \sqrt{\frac{d x^2}{d x^2+2}} \left(d x^2+2\right)}{d x}+b x \cosh ^{-1}\left(d x^2+1\right)",1,"a*x - (2*b*Sqrt[(d*x^2)/(2 + d*x^2)]*(2 + d*x^2))/(d*x) + b*x*ArcCosh[1 + d*x^2]","A",5,4,12,0.3333,1,"{5901, 12, 6719, 261}"
244,1,98,0,0.0318139,"\int \frac{1}{a+b \cosh ^{-1}\left(1+d x^2\right)} \, dx","Int[(a + b*ArcCosh[1 + d*x^2])^(-1),x]","\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{d x^2}}-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{d x^2}}","\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{d x^2}}-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{d x^2}}",1,"(x*Cosh[a/(2*b)]*CoshIntegral[(a + b*ArcCosh[1 + d*x^2])/(2*b)])/(Sqrt[2]*b*Sqrt[d*x^2]) - (x*Sinh[a/(2*b)]*SinhIntegral[(a + b*ArcCosh[1 + d*x^2])/(2*b)])/(Sqrt[2]*b*Sqrt[d*x^2])","A",1,1,14,0.07143,1,"{5881}"
245,1,150,0,0.0216295,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^2} \, dx","Int[(a + b*ArcCosh[1 + d*x^2])^(-2),x]","-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{d x^2}}+\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{d x^2}}-\frac{\sqrt{d x^2} \sqrt{d x^2+2}}{2 b d x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)}","-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{d x^2}}+\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{d x^2}}-\frac{\sqrt{d x^2} \sqrt{d x^2+2}}{2 b d x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)}",1,"-(Sqrt[d*x^2]*Sqrt[2 + d*x^2])/(2*b*d*x*(a + b*ArcCosh[1 + d*x^2])) - (x*CoshIntegral[(a + b*ArcCosh[1 + d*x^2])/(2*b)]*Sinh[a/(2*b)])/(2*Sqrt[2]*b^2*Sqrt[d*x^2]) + (x*Cosh[a/(2*b)]*SinhIntegral[(a + b*ArcCosh[1 + d*x^2])/(2*b)])/(2*Sqrt[2]*b^2*Sqrt[d*x^2])","A",1,1,14,0.07143,1,"{5887}"
246,1,180,0,0.0380817,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^3} \, dx","Int[(a + b*ArcCosh[1 + d*x^2])^(-3),x]","\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{d x^2}}-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{d x^2}}-\frac{x}{8 b^2 \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)}-\frac{d x^4+2 x^2}{4 b x \sqrt{d x^2} \sqrt{d x^2+2} \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^2}","\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{d x^2}}-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{d x^2}}-\frac{x}{8 b^2 \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)}-\frac{d x^4+2 x^2}{4 b x \sqrt{d x^2} \sqrt{d x^2+2} \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^2}",1,"-(2*x^2 + d*x^4)/(4*b*x*Sqrt[d*x^2]*Sqrt[2 + d*x^2]*(a + b*ArcCosh[1 + d*x^2])^2) - x/(8*b^2*(a + b*ArcCosh[1 + d*x^2])) + (x*Cosh[a/(2*b)]*CoshIntegral[(a + b*ArcCosh[1 + d*x^2])/(2*b)])/(8*Sqrt[2]*b^3*Sqrt[d*x^2]) - (x*Sinh[a/(2*b)]*SinhIntegral[(a + b*ArcCosh[1 + d*x^2])/(2*b)])/(8*Sqrt[2]*b^3*Sqrt[d*x^2])","A",2,2,14,0.1429,1,"{5889, 5881}"
247,1,147,0,0.0337011,"\int \left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^4 \, dx","Int[(a + b*ArcCosh[-1 + d*x^2])^4,x]","\frac{192 b^3 \left(2 x^2-d x^4\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)}{x \sqrt{d x^2} \sqrt{d x^2-2}}+48 b^2 x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^2+\frac{8 b \left(2 x^2-d x^4\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^3}{x \sqrt{d x^2} \sqrt{d x^2-2}}+x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^4+384 b^4 x","\frac{192 b^3 \left(2 x^2-d x^4\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)}{x \sqrt{d x^2} \sqrt{d x^2-2}}+48 b^2 x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^2+\frac{8 b \left(2 x^2-d x^4\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^3}{x \sqrt{d x^2} \sqrt{d x^2-2}}+x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^4+384 b^4 x",1,"384*b^4*x + (192*b^3*(2*x^2 - d*x^4)*(a + b*ArcCosh[-1 + d*x^2]))/(x*Sqrt[d*x^2]*Sqrt[-2 + d*x^2]) + 48*b^2*x*(a + b*ArcCosh[-1 + d*x^2])^2 + (8*b*(2*x^2 - d*x^4)*(a + b*ArcCosh[-1 + d*x^2])^3)/(x*Sqrt[d*x^2]*Sqrt[-2 + d*x^2]) + x*(a + b*ArcCosh[-1 + d*x^2])^4","A",3,2,14,0.1429,1,"{5880, 8}"
248,1,110,0,0.0456404,"\int \left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^3 \, dx","Int[(a + b*ArcCosh[-1 + d*x^2])^3,x]","24 a b^2 x+\frac{6 b \left(2 x^2-d x^4\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^2}{x \sqrt{d x^2} \sqrt{d x^2-2}}+x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^3-48 b^3 x \sqrt{1-\frac{2}{d x^2}}+24 b^3 x \cosh ^{-1}\left(d x^2-1\right)","24 a b^2 x+\frac{6 b \left(2 x^2-d x^4\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^2}{x \sqrt{d x^2} \sqrt{d x^2-2}}+x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^3-48 b^3 x \sqrt{1-\frac{2}{d x^2}}+24 b^3 x \cosh ^{-1}\left(d x^2-1\right)",1,"24*a*b^2*x - 48*b^3*Sqrt[1 - 2/(d*x^2)]*x + 24*b^3*x*ArcCosh[-1 + d*x^2] + (6*b*(2*x^2 - d*x^4)*(a + b*ArcCosh[-1 + d*x^2])^2)/(x*Sqrt[d*x^2]*Sqrt[-2 + d*x^2]) + x*(a + b*ArcCosh[-1 + d*x^2])^3","A",5,4,14,0.2857,1,"{5880, 5901, 12, 191}"
249,1,73,0,0.0138888,"\int \left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^2 \, dx","Int[(a + b*ArcCosh[-1 + d*x^2])^2,x]","\frac{4 b \left(2 x^2-d x^4\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)}{x \sqrt{d x^2} \sqrt{d x^2-2}}+x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^2+8 b^2 x","\frac{4 b \left(2 x^2-d x^4\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)}{x \sqrt{d x^2} \sqrt{d x^2-2}}+x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^2+8 b^2 x",1,"8*b^2*x + (4*b*(2*x^2 - d*x^4)*(a + b*ArcCosh[-1 + d*x^2]))/(x*Sqrt[d*x^2]*Sqrt[-2 + d*x^2]) + x*(a + b*ArcCosh[-1 + d*x^2])^2","A",2,2,14,0.1429,1,"{5880, 8}"
250,1,33,0,0.0168854,"\int \left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right) \, dx","Int[a + b*ArcCosh[-1 + d*x^2],x]","a x-2 b x \sqrt{1-\frac{2}{d x^2}}+b x \cosh ^{-1}\left(d x^2-1\right)","a x-2 b x \sqrt{1-\frac{2}{d x^2}}+b x \cosh ^{-1}\left(d x^2-1\right)",1,"a*x - 2*b*Sqrt[1 - 2/(d*x^2)]*x + b*x*ArcCosh[-1 + d*x^2]","A",4,3,12,0.2500,1,"{5901, 12, 191}"
251,1,98,0,0.0153676,"\int \frac{1}{a+b \cosh ^{-1}\left(-1+d x^2\right)} \, dx","Int[(a + b*ArcCosh[-1 + d*x^2])^(-1),x]","\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{d x^2}}-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{d x^2}}","\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{d x^2}}-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{d x^2}}",1,"-((x*CoshIntegral[(a + b*ArcCosh[-1 + d*x^2])/(2*b)]*Sinh[a/(2*b)])/(Sqrt[2]*b*Sqrt[d*x^2])) + (x*Cosh[a/(2*b)]*SinhIntegral[(a + b*ArcCosh[-1 + d*x^2])/(2*b)])/(Sqrt[2]*b*Sqrt[d*x^2])","A",1,1,14,0.07143,1,"{5882}"
252,1,150,0,0.0192627,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^2} \, dx","Int[(a + b*ArcCosh[-1 + d*x^2])^(-2),x]","\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{d x^2}}-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{d x^2}}-\frac{\sqrt{d x^2} \sqrt{d x^2-2}}{2 b d x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)}","\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{d x^2}}-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{d x^2}}-\frac{\sqrt{d x^2} \sqrt{d x^2-2}}{2 b d x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)}",1,"-(Sqrt[d*x^2]*Sqrt[-2 + d*x^2])/(2*b*d*x*(a + b*ArcCosh[-1 + d*x^2])) + (x*Cosh[a/(2*b)]*CoshIntegral[(a + b*ArcCosh[-1 + d*x^2])/(2*b)])/(2*Sqrt[2]*b^2*Sqrt[d*x^2]) - (x*Sinh[a/(2*b)]*SinhIntegral[(a + b*ArcCosh[-1 + d*x^2])/(2*b)])/(2*Sqrt[2]*b^2*Sqrt[d*x^2])","A",1,1,14,0.07143,1,"{5888}"
253,1,181,0,0.0334418,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^3} \, dx","Int[(a + b*ArcCosh[-1 + d*x^2])^(-3),x]","-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{d x^2}}+\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{d x^2}}-\frac{x}{8 b^2 \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)}+\frac{2 x^2-d x^4}{4 b x \sqrt{d x^2} \sqrt{d x^2-2} \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^2}","-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{d x^2}}+\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{d x^2}}-\frac{x}{8 b^2 \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)}+\frac{2 x^2-d x^4}{4 b x \sqrt{d x^2} \sqrt{d x^2-2} \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^2}",1,"(2*x^2 - d*x^4)/(4*b*x*Sqrt[d*x^2]*Sqrt[-2 + d*x^2]*(a + b*ArcCosh[-1 + d*x^2])^2) - x/(8*b^2*(a + b*ArcCosh[-1 + d*x^2])) - (x*CoshIntegral[(a + b*ArcCosh[-1 + d*x^2])/(2*b)]*Sinh[a/(2*b)])/(8*Sqrt[2]*b^3*Sqrt[d*x^2]) + (x*Cosh[a/(2*b)]*SinhIntegral[(a + b*ArcCosh[-1 + d*x^2])/(2*b)])/(8*Sqrt[2]*b^3*Sqrt[d*x^2])","A",2,2,14,0.1429,1,"{5889, 5882}"
254,1,280,0,0.1089645,"\int \left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^{5/2} \, dx","Int[(a + b*ArcCosh[1 + d*x^2])^(5/2),x]","\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{30 b^2 \sinh ^2\left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{d x}-\frac{5 b \left(d x^4+2 x^2\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{3/2}}{x \sqrt{d x^2} \sqrt{d x^2+2}}+x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{5/2}","\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{30 b^2 \sinh ^2\left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{d x}-\frac{5 b \left(d x^4+2 x^2\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{3/2}}{x \sqrt{d x^2} \sqrt{d x^2+2}}+x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{5/2}",1,"(-5*b*(2*x^2 + d*x^4)*(a + b*ArcCosh[1 + d*x^2])^(3/2))/(x*Sqrt[d*x^2]*Sqrt[2 + d*x^2]) + x*(a + b*ArcCosh[1 + d*x^2])^(5/2) - (15*b^(5/2)*Sqrt[Pi/2]*Erfi[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)])*Sinh[ArcCosh[1 + d*x^2]/2])/(d*x) + (15*b^(5/2)*Sqrt[Pi/2]*Erf[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)])*Sinh[ArcCosh[1 + d*x^2]/2])/(d*x) + (30*b^2*Sqrt[a + b*ArcCosh[1 + d*x^2]]*Sinh[ArcCosh[1 + d*x^2]/2]^2)/(d*x)","A",2,2,16,0.1250,1,"{5880, 5878}"
255,1,238,0,0.0967674,"\int \left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^{3/2} \, dx","Int[(a + b*ArcCosh[1 + d*x^2])^(3/2),x]","\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}-\frac{3 b \left(d x^4+2 x^2\right) \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{x \sqrt{d x^2} \sqrt{d x^2+2}}+x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{3/2}","\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}-\frac{3 b \left(d x^4+2 x^2\right) \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{x \sqrt{d x^2} \sqrt{d x^2+2}}+x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{3/2}",1,"(-3*b*(2*x^2 + d*x^4)*Sqrt[a + b*ArcCosh[1 + d*x^2]])/(x*Sqrt[d*x^2]*Sqrt[2 + d*x^2]) + x*(a + b*ArcCosh[1 + d*x^2])^(3/2) + (3*b^(3/2)*Sqrt[Pi/2]*Erfi[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)])*Sinh[ArcCosh[1 + d*x^2]/2])/(d*x) + (3*b^(3/2)*Sqrt[Pi/2]*Erf[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)])*Sinh[ArcCosh[1 + d*x^2]/2])/(d*x)","A",2,2,16,0.1250,1,"{5880, 5883}"
256,1,205,0,0.0264593,"\int \sqrt{a+b \cosh ^{-1}\left(1+d x^2\right)} \, dx","Int[Sqrt[a + b*ArcCosh[1 + d*x^2]],x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{2 \sinh ^2\left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{d x}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{2 \sinh ^2\left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{d x}",1,"-((Sqrt[b]*Sqrt[Pi/2]*Erfi[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)])*Sinh[ArcCosh[1 + d*x^2]/2])/(d*x)) + (Sqrt[b]*Sqrt[Pi/2]*Erf[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)])*Sinh[ArcCosh[1 + d*x^2]/2])/(d*x) + (2*Sqrt[a + b*ArcCosh[1 + d*x^2]]*Sinh[ArcCosh[1 + d*x^2]/2]^2)/(d*x)","A",1,1,16,0.06250,1,"{5878}"
257,1,165,0,0.0245432,"\int \frac{1}{\sqrt{a+b \cosh ^{-1}\left(1+d x^2\right)}} \, dx","Int[1/Sqrt[a + b*ArcCosh[1 + d*x^2]],x]","\frac{\sqrt{\frac{\pi }{2}} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{b} d x}+\frac{\sqrt{\frac{\pi }{2}} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{b} d x}","\frac{\sqrt{\frac{\pi }{2}} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{b} d x}+\frac{\sqrt{\frac{\pi }{2}} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{b} d x}",1,"(Sqrt[Pi/2]*Erfi[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)])*Sinh[ArcCosh[1 + d*x^2]/2])/(Sqrt[b]*d*x) + (Sqrt[Pi/2]*Erf[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)])*Sinh[ArcCosh[1 + d*x^2]/2])/(Sqrt[b]*d*x)","A",1,1,16,0.06250,1,"{5883}"
258,1,213,0,0.0431451,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[1 + d*x^2])^(-3/2),x]","-\frac{\sqrt{\frac{\pi }{2}} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{b^{3/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{b^{3/2} d x}-\frac{\sqrt{d x^2} \sqrt{d x^2+2}}{b d x \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}","-\frac{\sqrt{\frac{\pi }{2}} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{b^{3/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{b^{3/2} d x}-\frac{\sqrt{d x^2} \sqrt{d x^2+2}}{b d x \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}",1,"-((Sqrt[d*x^2]*Sqrt[2 + d*x^2])/(b*d*x*Sqrt[a + b*ArcCosh[1 + d*x^2]])) + (Sqrt[Pi/2]*Erfi[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)])*Sinh[ArcCosh[1 + d*x^2]/2])/(b^(3/2)*d*x) - (Sqrt[Pi/2]*Erf[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)])*Sinh[ArcCosh[1 + d*x^2]/2])/(b^(3/2)*d*x)","A",1,1,16,0.06250,1,"{5885}"
259,1,252,0,0.0715158,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^{5/2}} \, dx","Int[(a + b*ArcCosh[1 + d*x^2])^(-5/2),x]","\frac{\sqrt{\frac{\pi }{2}} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{3 b^{5/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{3 b^{5/2} d x}-\frac{x}{3 b^2 \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}-\frac{d x^4+2 x^2}{3 b x \sqrt{d x^2} \sqrt{d x^2+2} \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{3/2}}","\frac{\sqrt{\frac{\pi }{2}} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{3 b^{5/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{3 b^{5/2} d x}-\frac{x}{3 b^2 \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}-\frac{d x^4+2 x^2}{3 b x \sqrt{d x^2} \sqrt{d x^2+2} \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{3/2}}",1,"-(2*x^2 + d*x^4)/(3*b*x*Sqrt[d*x^2]*Sqrt[2 + d*x^2]*(a + b*ArcCosh[1 + d*x^2])^(3/2)) - x/(3*b^2*Sqrt[a + b*ArcCosh[1 + d*x^2]]) + (Sqrt[Pi/2]*Erfi[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)])*Sinh[ArcCosh[1 + d*x^2]/2])/(3*b^(5/2)*d*x) + (Sqrt[Pi/2]*Erf[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)])*Sinh[ArcCosh[1 + d*x^2]/2])/(3*b^(5/2)*d*x)","A",2,2,16,0.1250,1,"{5889, 5883}"
260,1,301,0,0.0774556,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^{7/2}} \, dx","Int[(a + b*ArcCosh[1 + d*x^2])^(-7/2),x]","-\frac{\sqrt{\frac{\pi }{2}} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{15 b^{7/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{15 b^{7/2} d x}-\frac{x}{15 b^2 \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{3/2}}-\frac{\sqrt{d x^2} \sqrt{d x^2+2}}{15 b^3 d x \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}-\frac{d x^4+2 x^2}{5 b x \sqrt{d x^2} \sqrt{d x^2+2} \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{5/2}}","-\frac{\sqrt{\frac{\pi }{2}} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{15 b^{7/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{15 b^{7/2} d x}-\frac{x}{15 b^2 \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{3/2}}-\frac{\sqrt{d x^2} \sqrt{d x^2+2}}{15 b^3 d x \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}-\frac{d x^4+2 x^2}{5 b x \sqrt{d x^2} \sqrt{d x^2+2} \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{5/2}}",1,"-(2*x^2 + d*x^4)/(5*b*x*Sqrt[d*x^2]*Sqrt[2 + d*x^2]*(a + b*ArcCosh[1 + d*x^2])^(5/2)) - x/(15*b^2*(a + b*ArcCosh[1 + d*x^2])^(3/2)) - (Sqrt[d*x^2]*Sqrt[2 + d*x^2])/(15*b^3*d*x*Sqrt[a + b*ArcCosh[1 + d*x^2]]) + (Sqrt[Pi/2]*Erfi[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)])*Sinh[ArcCosh[1 + d*x^2]/2])/(15*b^(7/2)*d*x) - (Sqrt[Pi/2]*Erf[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)])*Sinh[ArcCosh[1 + d*x^2]/2])/(15*b^(7/2)*d*x)","A",2,2,16,0.1250,1,"{5889, 5885}"
261,1,281,0,0.0593825,"\int \left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^{5/2} \, dx","Int[(a + b*ArcCosh[-1 + d*x^2])^(5/2),x]","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{30 b^2 \cosh ^2\left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{d x}+\frac{5 b \left(2 x^2-d x^4\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{3/2}}{x \sqrt{d x^2} \sqrt{d x^2-2}}+x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{5/2}","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{30 b^2 \cosh ^2\left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{d x}+\frac{5 b \left(2 x^2-d x^4\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{3/2}}{x \sqrt{d x^2} \sqrt{d x^2-2}}+x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{5/2}",1,"(5*b*(2*x^2 - d*x^4)*(a + b*ArcCosh[-1 + d*x^2])^(3/2))/(x*Sqrt[d*x^2]*Sqrt[-2 + d*x^2]) + x*(a + b*ArcCosh[-1 + d*x^2])^(5/2) + (30*b^2*Sqrt[a + b*ArcCosh[-1 + d*x^2]]*Cosh[ArcCosh[-1 + d*x^2]/2]^2)/(d*x) - (15*b^(5/2)*Sqrt[Pi/2]*Cosh[ArcCosh[-1 + d*x^2]/2]*Erfi[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)]))/(d*x) - (15*b^(5/2)*Sqrt[Pi/2]*Cosh[ArcCosh[-1 + d*x^2]/2]*Erf[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]))/(d*x)","A",2,2,16,0.1250,1,"{5880, 5879}"
262,1,239,0,0.0542718,"\int \left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^{3/2} \, dx","Int[(a + b*ArcCosh[-1 + d*x^2])^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{3 b \left(2 x^2-d x^4\right) \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{x \sqrt{d x^2} \sqrt{d x^2-2}}+x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{3/2}","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{3 b \left(2 x^2-d x^4\right) \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{x \sqrt{d x^2} \sqrt{d x^2-2}}+x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{3/2}",1,"(3*b*(2*x^2 - d*x^4)*Sqrt[a + b*ArcCosh[-1 + d*x^2]])/(x*Sqrt[d*x^2]*Sqrt[-2 + d*x^2]) + x*(a + b*ArcCosh[-1 + d*x^2])^(3/2) + (3*b^(3/2)*Sqrt[Pi/2]*Cosh[ArcCosh[-1 + d*x^2]/2]*Erfi[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)]))/(d*x) - (3*b^(3/2)*Sqrt[Pi/2]*Cosh[ArcCosh[-1 + d*x^2]/2]*Erf[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]))/(d*x)","A",2,2,16,0.1250,1,"{5880, 5884}"
263,1,206,0,0.0263156,"\int \sqrt{a+b \cosh ^{-1}\left(-1+d x^2\right)} \, dx","Int[Sqrt[a + b*ArcCosh[-1 + d*x^2]],x]","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{2 \cosh ^2\left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{d x}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{2 \cosh ^2\left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{d x}",1,"(2*Sqrt[a + b*ArcCosh[-1 + d*x^2]]*Cosh[ArcCosh[-1 + d*x^2]/2]^2)/(d*x) - (Sqrt[b]*Sqrt[Pi/2]*Cosh[ArcCosh[-1 + d*x^2]/2]*Erfi[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)]))/(d*x) - (Sqrt[b]*Sqrt[Pi/2]*Cosh[ArcCosh[-1 + d*x^2]/2]*Erf[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]))/(d*x)","A",1,1,16,0.06250,1,"{5879}"
264,1,166,0,0.025722,"\int \frac{1}{\sqrt{a+b \cosh ^{-1}\left(-1+d x^2\right)}} \, dx","Int[1/Sqrt[a + b*ArcCosh[-1 + d*x^2]],x]","\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{b} d x}-\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{b} d x}","\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{b} d x}-\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{b} d x}",1,"(Sqrt[Pi/2]*Cosh[ArcCosh[-1 + d*x^2]/2]*Erfi[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)]))/(Sqrt[b]*d*x) - (Sqrt[Pi/2]*Cosh[ArcCosh[-1 + d*x^2]/2]*Erf[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]))/(Sqrt[b]*d*x)","A",1,1,16,0.06250,1,"{5884}"
265,1,212,0,0.0273975,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[-1 + d*x^2])^(-3/2),x]","\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{b^{3/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{b^{3/2} d x}-\frac{\sqrt{d x^2} \sqrt{d x^2-2}}{b d x \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}","\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{b^{3/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{b^{3/2} d x}-\frac{\sqrt{d x^2} \sqrt{d x^2-2}}{b d x \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}",1,"-((Sqrt[d*x^2]*Sqrt[-2 + d*x^2])/(b*d*x*Sqrt[a + b*ArcCosh[-1 + d*x^2]])) + (Sqrt[Pi/2]*Cosh[ArcCosh[-1 + d*x^2]/2]*Erfi[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)]))/(b^(3/2)*d*x) + (Sqrt[Pi/2]*Cosh[ArcCosh[-1 + d*x^2]/2]*Erf[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]))/(b^(3/2)*d*x)","A",1,1,16,0.06250,1,"{5886}"
266,1,253,0,0.055022,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^{5/2}} \, dx","Int[(a + b*ArcCosh[-1 + d*x^2])^(-5/2),x]","-\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{3 b^{5/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{3 b^{5/2} d x}-\frac{x}{3 b^2 \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}+\frac{2 x^2-d x^4}{3 b x \sqrt{d x^2} \sqrt{d x^2-2} \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{3/2}}","-\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{3 b^{5/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{3 b^{5/2} d x}-\frac{x}{3 b^2 \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}+\frac{2 x^2-d x^4}{3 b x \sqrt{d x^2} \sqrt{d x^2-2} \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{3/2}}",1,"(2*x^2 - d*x^4)/(3*b*x*Sqrt[d*x^2]*Sqrt[-2 + d*x^2]*(a + b*ArcCosh[-1 + d*x^2])^(3/2)) - x/(3*b^2*Sqrt[a + b*ArcCosh[-1 + d*x^2]]) + (Sqrt[Pi/2]*Cosh[ArcCosh[-1 + d*x^2]/2]*Erfi[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)]))/(3*b^(5/2)*d*x) - (Sqrt[Pi/2]*Cosh[ArcCosh[-1 + d*x^2]/2]*Erf[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]))/(3*b^(5/2)*d*x)","A",2,2,16,0.1250,1,"{5889, 5884}"
267,1,302,0,0.0601722,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^{7/2}} \, dx","Int[(a + b*ArcCosh[-1 + d*x^2])^(-7/2),x]","\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{15 b^{7/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{15 b^{7/2} d x}-\frac{x}{15 b^2 \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{3/2}}-\frac{\sqrt{d x^2} \sqrt{d x^2-2}}{15 b^3 d x \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}+\frac{2 x^2-d x^4}{5 b x \sqrt{d x^2} \sqrt{d x^2-2} \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{5/2}}","\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{15 b^{7/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{15 b^{7/2} d x}-\frac{x}{15 b^2 \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{3/2}}-\frac{\sqrt{d x^2} \sqrt{d x^2-2}}{15 b^3 d x \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}+\frac{2 x^2-d x^4}{5 b x \sqrt{d x^2} \sqrt{d x^2-2} \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{5/2}}",1,"(2*x^2 - d*x^4)/(5*b*x*Sqrt[d*x^2]*Sqrt[-2 + d*x^2]*(a + b*ArcCosh[-1 + d*x^2])^(5/2)) - x/(15*b^2*(a + b*ArcCosh[-1 + d*x^2])^(3/2)) - (Sqrt[d*x^2]*Sqrt[-2 + d*x^2])/(15*b^3*d*x*Sqrt[a + b*ArcCosh[-1 + d*x^2]]) + (Sqrt[Pi/2]*Cosh[ArcCosh[-1 + d*x^2]/2]*Erfi[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)]))/(15*b^(7/2)*d*x) + (Sqrt[Pi/2]*Cosh[ArcCosh[-1 + d*x^2]/2]*Erf[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]))/(15*b^(7/2)*d*x)","A",2,2,16,0.1250,1,"{5889, 5886}"
268,0,0,0,0.0513401,"\int \frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^n}{1-c^2 x^2} \, dx","Int[(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2),x]","\int \frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^n}{1-c^2 x^2} \, dx","\text{Int}\left(\frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^n}{1-c^2 x^2},x\right)",0,"Defer[Int][(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2), x]","A",0,0,0,0,-1,"{}"
269,1,265,0,0.2207621,"\int \frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^3}{1-c^2 x^2} \, dx","Int[(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3/(1 - c^2*x^2),x]","\frac{3 b^2 \text{PolyLog}\left(3,-e^{2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}-\frac{3 b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}-\frac{3 b^3 \text{PolyLog}\left(4,-e^{2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{4 c}+\frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^4}{4 b c}-\frac{\log \left(e^{2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}+1\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{c}","\frac{3 b^2 \text{PolyLog}\left(3,-e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}+\frac{3 b \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}+\frac{3 b^3 \text{PolyLog}\left(4,-e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{4 c}-\frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^4}{4 b c}-\frac{\log \left(e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}+1\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{c}",1,"(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^4/(4*b*c) - ((a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3*Log[1 + E^(2*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c - (3*b*(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*PolyLog[2, -E^(2*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/(2*c) + (3*b^2*(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[3, -E^(2*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/(2*c) - (3*b^3*PolyLog[4, -E^(2*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/(4*c)","A",8,8,40,0.2000,0,"{6681, 5660, 3718, 2190, 2531, 6609, 2282, 6589}"
270,1,197,0,0.1951453,"\int \frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2}{1-c^2 x^2} \, dx","Int[(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2/(1 - c^2*x^2),x]","-\frac{b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}+\frac{b^2 \text{PolyLog}\left(3,-e^{2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}+\frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{3 b c}-\frac{\log \left(e^{2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}+1\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{c}","\frac{b \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}+\frac{b^2 \text{PolyLog}\left(3,-e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}-\frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{3 b c}-\frac{\log \left(e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}+1\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{c}",1,"(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3/(3*b*c) - ((a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*Log[1 + E^(2*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c - (b*(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[2, -E^(2*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c + (b^2*PolyLog[3, -E^(2*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/(2*c)","A",7,7,40,0.1750,0,"{6681, 5660, 3718, 2190, 2531, 2282, 6589}"
271,1,133,0,0.1194647,"\int \frac{a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)}{1-c^2 x^2} \, dx","Int[(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])/(1 - c^2*x^2),x]","-\frac{b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}+\frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 b c}-\frac{\log \left(e^{2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}+1\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}","\frac{b \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}-\frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 b c}-\frac{\log \left(e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}+1\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}",1,"(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2/(2*b*c) - ((a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*Log[1 + E^(2*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c - (b*PolyLog[2, -E^(2*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/(2*c)","A",6,7,38,0.1842,0,"{206, 6681, 5660, 3718, 2190, 2279, 2391}"
272,0,0,0,0.0463448,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)} \, dx","Int[1/((1 - c^2*x^2)*(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])),x]","\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)} \, dx","\text{Int}\left(\frac{1}{\left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)},x\right)",0,"Defer[Int][1/((1 - c^2*x^2)*(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])), x]","A",0,0,0,0,-1,"{}"
273,0,0,0,0.0436054,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2} \, dx","Int[1/((1 - c^2*x^2)*(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2),x]","\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2},x\right)",0,"Defer[Int][1/((1 - c^2*x^2)*(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2), x]","A",0,0,0,0,-1,"{}"
274,1,76,0,0.073347,"\int \cosh ^{-1}\left(c e^{a+b x}\right) \, dx","Int[ArcCosh[c*E^(a + b*x)],x]","\frac{\text{PolyLog}\left(2,-e^{2 \cosh ^{-1}\left(c e^{a+b x}\right)}\right)}{2 b}-\frac{\cosh ^{-1}\left(c e^{a+b x}\right)^2}{2 b}+\frac{\cosh ^{-1}\left(c e^{a+b x}\right) \log \left(e^{2 \cosh ^{-1}\left(c e^{a+b x}\right)}+1\right)}{b}","\frac{\text{PolyLog}\left(2,-e^{2 \cosh ^{-1}\left(c e^{a+b x}\right)}\right)}{2 b}-\frac{\cosh ^{-1}\left(c e^{a+b x}\right)^2}{2 b}+\frac{\cosh ^{-1}\left(c e^{a+b x}\right) \log \left(e^{2 \cosh ^{-1}\left(c e^{a+b x}\right)}+1\right)}{b}",1,"-ArcCosh[c*E^(a + b*x)]^2/(2*b) + (ArcCosh[c*E^(a + b*x)]*Log[1 + E^(2*ArcCosh[c*E^(a + b*x)])])/b + PolyLog[2, -E^(2*ArcCosh[c*E^(a + b*x)])]/(2*b)","A",6,6,10,0.6000,1,"{2282, 5660, 3718, 2190, 2279, 2391}"
275,1,165,0,0.1609198,"\int e^{\cosh ^{-1}(a+b x)} x^3 \, dx","Int[E^ArcCosh[a + b*x]*x^3,x]","-\frac{\left(4 a^2+3\right) a e^{2 \cosh ^{-1}(a+b x)}}{16 b^4}+\frac{\left(4 a^2+3\right) a \cosh ^{-1}(a+b x)}{8 b^4}+\frac{\left(6 a^2+1\right) e^{-\cosh ^{-1}(a+b x)}}{8 b^4}+\frac{\left(6 a^2+1\right) e^{3 \cosh ^{-1}(a+b x)}}{24 b^4}-\frac{3 a e^{-2 \cosh ^{-1}(a+b x)}}{16 b^4}-\frac{3 a e^{4 \cosh ^{-1}(a+b x)}}{32 b^4}+\frac{e^{-3 \cosh ^{-1}(a+b x)}}{48 b^4}+\frac{e^{5 \cosh ^{-1}(a+b x)}}{80 b^4}","-\frac{\left(4 a^2+3\right) a e^{2 \cosh ^{-1}(a+b x)}}{16 b^4}+\frac{\left(4 a^2+3\right) a \cosh ^{-1}(a+b x)}{8 b^4}+\frac{\left(6 a^2+1\right) e^{-\cosh ^{-1}(a+b x)}}{8 b^4}+\frac{\left(6 a^2+1\right) e^{3 \cosh ^{-1}(a+b x)}}{24 b^4}-\frac{3 a e^{-2 \cosh ^{-1}(a+b x)}}{16 b^4}-\frac{3 a e^{4 \cosh ^{-1}(a+b x)}}{32 b^4}+\frac{e^{-3 \cosh ^{-1}(a+b x)}}{48 b^4}+\frac{e^{5 \cosh ^{-1}(a+b x)}}{80 b^4}",1,"1/(48*b^4*E^(3*ArcCosh[a + b*x])) - (3*a)/(16*b^4*E^(2*ArcCosh[a + b*x])) + (1 + 6*a^2)/(8*b^4*E^ArcCosh[a + b*x]) - (a*(3 + 4*a^2)*E^(2*ArcCosh[a + b*x]))/(16*b^4) + ((1 + 6*a^2)*E^(3*ArcCosh[a + b*x]))/(24*b^4) - (3*a*E^(4*ArcCosh[a + b*x]))/(32*b^4) + E^(5*ArcCosh[a + b*x])/(80*b^4) + (a*(3 + 4*a^2)*ArcCosh[a + b*x])/(8*b^4)","A",5,4,12,0.3333,1,"{5899, 2282, 12, 1628}"
276,1,115,0,0.12071,"\int e^{\cosh ^{-1}(a+b x)} x^2 \, dx","Int[E^ArcCosh[a + b*x]*x^2,x]","\frac{\left(4 a^2+1\right) e^{2 \cosh ^{-1}(a+b x)}}{16 b^3}-\frac{\left(4 a^2+1\right) \cosh ^{-1}(a+b x)}{8 b^3}-\frac{a e^{-\cosh ^{-1}(a+b x)}}{2 b^3}-\frac{a e^{3 \cosh ^{-1}(a+b x)}}{6 b^3}+\frac{e^{-2 \cosh ^{-1}(a+b x)}}{16 b^3}+\frac{e^{4 \cosh ^{-1}(a+b x)}}{32 b^3}","\frac{\left(4 a^2+1\right) e^{2 \cosh ^{-1}(a+b x)}}{16 b^3}-\frac{\left(4 a^2+1\right) \cosh ^{-1}(a+b x)}{8 b^3}-\frac{a e^{-\cosh ^{-1}(a+b x)}}{2 b^3}-\frac{a e^{3 \cosh ^{-1}(a+b x)}}{6 b^3}+\frac{e^{-2 \cosh ^{-1}(a+b x)}}{16 b^3}+\frac{e^{4 \cosh ^{-1}(a+b x)}}{32 b^3}",1,"1/(16*b^3*E^(2*ArcCosh[a + b*x])) - a/(2*b^3*E^ArcCosh[a + b*x]) + ((1 + 4*a^2)*E^(2*ArcCosh[a + b*x]))/(16*b^3) - (a*E^(3*ArcCosh[a + b*x]))/(6*b^3) + E^(4*ArcCosh[a + b*x])/(32*b^3) - ((1 + 4*a^2)*ArcCosh[a + b*x])/(8*b^3)","A",5,4,12,0.3333,1,"{5899, 2282, 12, 1628}"
277,1,67,0,0.0702901,"\int e^{\cosh ^{-1}(a+b x)} x \, dx","Int[E^ArcCosh[a + b*x]*x,x]","-\frac{a e^{2 \cosh ^{-1}(a+b x)}}{4 b^2}+\frac{a \cosh ^{-1}(a+b x)}{2 b^2}+\frac{e^{-\cosh ^{-1}(a+b x)}}{4 b^2}+\frac{e^{3 \cosh ^{-1}(a+b x)}}{12 b^2}","-\frac{a e^{2 \cosh ^{-1}(a+b x)}}{4 b^2}+\frac{a \cosh ^{-1}(a+b x)}{2 b^2}+\frac{e^{-\cosh ^{-1}(a+b x)}}{4 b^2}+\frac{e^{3 \cosh ^{-1}(a+b x)}}{12 b^2}",1,"1/(4*b^2*E^ArcCosh[a + b*x]) - (a*E^(2*ArcCosh[a + b*x]))/(4*b^2) + E^(3*ArcCosh[a + b*x])/(12*b^2) + (a*ArcCosh[a + b*x])/(2*b^2)","A",5,4,10,0.4000,1,"{5899, 2282, 12, 1628}"
278,1,31,0,0.0173356,"\int e^{\cosh ^{-1}(a+b x)} \, dx","Int[E^ArcCosh[a + b*x],x]","\frac{e^{2 \cosh ^{-1}(a+b x)}}{4 b}-\frac{\cosh ^{-1}(a+b x)}{2 b}","\frac{e^{2 \cosh ^{-1}(a+b x)}}{4 b}-\frac{\cosh ^{-1}(a+b x)}{2 b}",1,"E^(2*ArcCosh[a + b*x])/(4*b) - ArcCosh[a + b*x]/(2*b)","A",5,4,8,0.5000,1,"{5897, 2282, 12, 14}"
279,1,100,0,0.091578,"\int \frac{e^{\cosh ^{-1}(a+b x)}}{x} \, dx","Int[E^ArcCosh[a + b*x]/x,x]","2 \sqrt{1-a^2} \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)+\sqrt{a+b x-1} \sqrt{a+b x+1}+2 a \sinh ^{-1}\left(\frac{\sqrt{a+b x-1}}{\sqrt{2}}\right)+a \log (x)+b x","2 \sqrt{1-a^2} \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)+\sqrt{a+b x-1} \sqrt{a+b x+1}+2 a \sinh ^{-1}\left(\frac{\sqrt{a+b x-1}}{\sqrt{2}}\right)+a \log (x)+b x",1,"b*x + Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x] + 2*a*ArcSinh[Sqrt[-1 + a + b*x]/Sqrt[2]] + 2*Sqrt[1 - a^2]*ArcTan[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[-1 + a + b*x])] + a*Log[x]","A",9,8,12,0.6667,1,"{5909, 14, 101, 157, 63, 215, 93, 205}"
280,1,109,0,0.0737779,"\int \frac{e^{\cosh ^{-1}(a+b x)}}{x^2} \, dx","Int[E^ArcCosh[a + b*x]/x^2,x]","-\frac{2 a b \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{\sqrt{1-a^2}}-\frac{\sqrt{a+b x-1} \sqrt{a+b x+1}}{x}+2 b \sinh ^{-1}\left(\frac{\sqrt{a+b x-1}}{\sqrt{2}}\right)-\frac{a}{x}+b \log (x)","-\frac{2 a b \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{\sqrt{1-a^2}}-\frac{\sqrt{a+b x-1} \sqrt{a+b x+1}}{x}+2 b \sinh ^{-1}\left(\frac{\sqrt{a+b x-1}}{\sqrt{2}}\right)-\frac{a}{x}+b \log (x)",1,"-(a/x) - (Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/x + 2*b*ArcSinh[Sqrt[-1 + a + b*x]/Sqrt[2]] - (2*a*b*ArcTan[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[-1 + a + b*x])])/Sqrt[1 - a^2] + b*Log[x]","A",9,8,12,0.6667,1,"{5909, 14, 97, 157, 63, 215, 93, 205}"
281,1,138,0,0.1089848,"\int \frac{e^{\cosh ^{-1}(a+b x)}}{x^3} \, dx","Int[E^ArcCosh[a + b*x]/x^3,x]","-\frac{b^2 \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{\left(1-a^2\right)^{3/2}}+\frac{b \sqrt{a+b x-1} \sqrt{a+b x+1}}{2 \left(1-a^2\right) x}-\frac{\sqrt{a+b x-1} (a+b x+1)^{3/2}}{2 (a+1) x^2}-\frac{a}{2 x^2}-\frac{b}{x}","-\frac{b^2 \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{\left(1-a^2\right)^{3/2}}+\frac{b \sqrt{a+b x-1} \sqrt{a+b x+1}}{2 \left(1-a^2\right) x}-\frac{\sqrt{a+b x-1} (a+b x+1)^{3/2}}{2 (a+1) x^2}-\frac{a}{2 x^2}-\frac{b}{x}",1,"-a/(2*x^2) - b/x + (b*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/(2*(1 - a^2)*x) - (Sqrt[-1 + a + b*x]*(1 + a + b*x)^(3/2))/(2*(1 + a)*x^2) - (b^2*ArcTan[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[-1 + a + b*x])])/(1 - a^2)^(3/2)","A",7,5,12,0.4167,1,"{5909, 14, 94, 93, 205}"
282,1,189,0,0.1564065,"\int \frac{e^{\cosh ^{-1}(a+b x)}}{x^4} \, dx","Int[E^ArcCosh[a + b*x]/x^4,x]","\frac{a b^2 \sqrt{a+b x-1} \sqrt{a+b x+1}}{2 \left(1-a^2\right)^2 x}-\frac{a b^3 \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{\left(1-a^2\right)^{5/2}}+\frac{(a+b x-1)^{3/2} (a+b x+1)^{3/2}}{3 \left(1-a^2\right) x^3}-\frac{a b \sqrt{a+b x-1} (a+b x+1)^{3/2}}{2 (1-a) (a+1)^2 x^2}-\frac{a}{3 x^3}-\frac{b}{2 x^2}","\frac{a b^2 \sqrt{a+b x-1} \sqrt{a+b x+1}}{2 \left(1-a^2\right)^2 x}-\frac{a b^3 \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{\left(1-a^2\right)^{5/2}}+\frac{(a+b x-1)^{3/2} (a+b x+1)^{3/2}}{3 \left(1-a^2\right) x^3}-\frac{a b \sqrt{a+b x-1} (a+b x+1)^{3/2}}{2 (1-a) (a+1)^2 x^2}-\frac{a}{3 x^3}-\frac{b}{2 x^2}",1,"-a/(3*x^3) - b/(2*x^2) + (a*b^2*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/(2*(1 - a^2)^2*x) - (a*b*Sqrt[-1 + a + b*x]*(1 + a + b*x)^(3/2))/(2*(1 - a)*(1 + a)^2*x^2) + ((-1 + a + b*x)^(3/2)*(1 + a + b*x)^(3/2))/(3*(1 - a^2)*x^3) - (a*b^3*ArcTan[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[-1 + a + b*x])])/(1 - a^2)^(5/2)","A",8,6,12,0.5000,1,"{5909, 14, 96, 94, 93, 205}"
283,1,238,0,0.2013715,"\int \frac{e^{\cosh ^{-1}(a+b x)}}{x^5} \, dx","Int[E^ArcCosh[a + b*x]/x^5,x]","\frac{\left(2 a^2+3\right) b^2 \sqrt{a+b x-1} \sqrt{a+b x+1}}{24 \left(1-a^2\right)^2 x^2}+\frac{a \left(2 a^2+13\right) b^3 \sqrt{a+b x-1} \sqrt{a+b x+1}}{24 \left(1-a^2\right)^3 x}-\frac{\left(4 a^2+1\right) b^4 \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{4 \left(1-a^2\right)^{7/2}}+\frac{a b \sqrt{a+b x-1} \sqrt{a+b x+1}}{12 \left(1-a^2\right) x^3}-\frac{\sqrt{a+b x-1} \sqrt{a+b x+1}}{4 x^4}-\frac{a}{4 x^4}-\frac{b}{3 x^3}","\frac{\left(2 a^2+3\right) b^2 \sqrt{a+b x-1} \sqrt{a+b x+1}}{24 \left(1-a^2\right)^2 x^2}+\frac{a \left(2 a^2+13\right) b^3 \sqrt{a+b x-1} \sqrt{a+b x+1}}{24 \left(1-a^2\right)^3 x}-\frac{\left(4 a^2+1\right) b^4 \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{4 \left(1-a^2\right)^{7/2}}+\frac{a b \sqrt{a+b x-1} \sqrt{a+b x+1}}{12 \left(1-a^2\right) x^3}-\frac{\sqrt{a+b x-1} \sqrt{a+b x+1}}{4 x^4}-\frac{a}{4 x^4}-\frac{b}{3 x^3}",1,"-a/(4*x^4) - b/(3*x^3) - (Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/(4*x^4) + (a*b*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/(12*(1 - a^2)*x^3) + ((3 + 2*a^2)*b^2*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/(24*(1 - a^2)^2*x^2) + (a*(13 + 2*a^2)*b^3*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/(24*(1 - a^2)^3*x) - ((1 + 4*a^2)*b^4*ArcTan[(Sqrt[1 - a]*Sqrt[1 + a + b*x])/(Sqrt[1 + a]*Sqrt[-1 + a + b*x])])/(4*(1 - a^2)^(7/2))","A",10,7,12,0.5833,1,"{5909, 14, 97, 151, 12, 93, 205}"
284,1,359,0,0.7375648,"\int e^{\cosh ^{-1}(a+b x)^2} x^3 \, dx","Int[E^ArcCosh[a + b*x]^2*x^3,x]","\frac{\sqrt{\pi } a^3 \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b^4}-\frac{\sqrt{\pi } a^3 \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b^4}+\frac{3 \sqrt{\pi } a^2 \text{Erfi}\left(1-\cosh ^{-1}(a+b x)\right)}{8 e b^4}+\frac{3 \sqrt{\pi } a^2 \text{Erfi}\left(\cosh ^{-1}(a+b x)+1\right)}{8 e b^4}+\frac{3 \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-3\right)\right)}{16 e^{9/4} b^4}+\frac{3 \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{16 \sqrt[4]{e} b^4}-\frac{3 \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{16 \sqrt[4]{e} b^4}-\frac{3 \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+3\right)\right)}{16 e^{9/4} b^4}+\frac{\sqrt{\pi } \text{Erfi}\left(1-\cosh ^{-1}(a+b x)\right)}{16 e b^4}+\frac{\sqrt{\pi } \text{Erfi}\left(2-\cosh ^{-1}(a+b x)\right)}{32 e^4 b^4}+\frac{\sqrt{\pi } \text{Erfi}\left(\cosh ^{-1}(a+b x)+1\right)}{16 e b^4}+\frac{\sqrt{\pi } \text{Erfi}\left(\cosh ^{-1}(a+b x)+2\right)}{32 e^4 b^4}","\frac{\sqrt{\pi } a^3 \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b^4}-\frac{\sqrt{\pi } a^3 \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b^4}+\frac{3 \sqrt{\pi } a^2 \text{Erfi}\left(1-\cosh ^{-1}(a+b x)\right)}{8 e b^4}+\frac{3 \sqrt{\pi } a^2 \text{Erfi}\left(\cosh ^{-1}(a+b x)+1\right)}{8 e b^4}+\frac{3 \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-3\right)\right)}{16 e^{9/4} b^4}+\frac{3 \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{16 \sqrt[4]{e} b^4}-\frac{3 \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{16 \sqrt[4]{e} b^4}-\frac{3 \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+3\right)\right)}{16 e^{9/4} b^4}+\frac{\sqrt{\pi } \text{Erfi}\left(1-\cosh ^{-1}(a+b x)\right)}{16 e b^4}+\frac{\sqrt{\pi } \text{Erfi}\left(2-\cosh ^{-1}(a+b x)\right)}{32 e^4 b^4}+\frac{\sqrt{\pi } \text{Erfi}\left(\cosh ^{-1}(a+b x)+1\right)}{16 e b^4}+\frac{\sqrt{\pi } \text{Erfi}\left(\cosh ^{-1}(a+b x)+2\right)}{32 e^4 b^4}",1,"(Sqrt[Pi]*Erfi[1 - ArcCosh[a + b*x]])/(16*b^4*E) + (3*a^2*Sqrt[Pi]*Erfi[1 - ArcCosh[a + b*x]])/(8*b^4*E) + (Sqrt[Pi]*Erfi[2 - ArcCosh[a + b*x]])/(32*b^4*E^4) + (Sqrt[Pi]*Erfi[1 + ArcCosh[a + b*x]])/(16*b^4*E) + (3*a^2*Sqrt[Pi]*Erfi[1 + ArcCosh[a + b*x]])/(8*b^4*E) + (Sqrt[Pi]*Erfi[2 + ArcCosh[a + b*x]])/(32*b^4*E^4) + (3*a*Sqrt[Pi]*Erfi[(-3 + 2*ArcCosh[a + b*x])/2])/(16*b^4*E^(9/4)) + (3*a*Sqrt[Pi]*Erfi[(-1 + 2*ArcCosh[a + b*x])/2])/(16*b^4*E^(1/4)) + (a^3*Sqrt[Pi]*Erfi[(-1 + 2*ArcCosh[a + b*x])/2])/(4*b^4*E^(1/4)) - (3*a*Sqrt[Pi]*Erfi[(1 + 2*ArcCosh[a + b*x])/2])/(16*b^4*E^(1/4)) - (a^3*Sqrt[Pi]*Erfi[(1 + 2*ArcCosh[a + b*x])/2])/(4*b^4*E^(1/4)) - (3*a*Sqrt[Pi]*Erfi[(3 + 2*ArcCosh[a + b*x])/2])/(16*b^4*E^(9/4))","A",37,8,14,0.5714,1,"{5899, 6741, 12, 6742, 5512, 2234, 2204, 5514}"
285,1,251,0,0.4930698,"\int e^{\cosh ^{-1}(a+b x)^2} x^2 \, dx","Int[E^ArcCosh[a + b*x]^2*x^2,x]","-\frac{\sqrt{\pi } a^2 \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b^3}+\frac{\sqrt{\pi } a^2 \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b^3}-\frac{\sqrt{\pi } a \text{Erfi}\left(1-\cosh ^{-1}(a+b x)\right)}{4 e b^3}-\frac{\sqrt{\pi } a \text{Erfi}\left(\cosh ^{-1}(a+b x)+1\right)}{4 e b^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-3\right)\right)}{16 e^{9/4} b^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{16 \sqrt[4]{e} b^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{16 \sqrt[4]{e} b^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+3\right)\right)}{16 e^{9/4} b^3}","-\frac{\sqrt{\pi } a^2 \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b^3}+\frac{\sqrt{\pi } a^2 \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b^3}-\frac{\sqrt{\pi } a \text{Erfi}\left(1-\cosh ^{-1}(a+b x)\right)}{4 e b^3}-\frac{\sqrt{\pi } a \text{Erfi}\left(\cosh ^{-1}(a+b x)+1\right)}{4 e b^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-3\right)\right)}{16 e^{9/4} b^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{16 \sqrt[4]{e} b^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{16 \sqrt[4]{e} b^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+3\right)\right)}{16 e^{9/4} b^3}",1,"-(a*Sqrt[Pi]*Erfi[1 - ArcCosh[a + b*x]])/(4*b^3*E) - (a*Sqrt[Pi]*Erfi[1 + ArcCosh[a + b*x]])/(4*b^3*E) - (Sqrt[Pi]*Erfi[(-3 + 2*ArcCosh[a + b*x])/2])/(16*b^3*E^(9/4)) - (Sqrt[Pi]*Erfi[(-1 + 2*ArcCosh[a + b*x])/2])/(16*b^3*E^(1/4)) - (a^2*Sqrt[Pi]*Erfi[(-1 + 2*ArcCosh[a + b*x])/2])/(4*b^3*E^(1/4)) + (Sqrt[Pi]*Erfi[(1 + 2*ArcCosh[a + b*x])/2])/(16*b^3*E^(1/4)) + (a^2*Sqrt[Pi]*Erfi[(1 + 2*ArcCosh[a + b*x])/2])/(4*b^3*E^(1/4)) + (Sqrt[Pi]*Erfi[(3 + 2*ArcCosh[a + b*x])/2])/(16*b^3*E^(9/4))","A",27,8,14,0.5714,1,"{5899, 6741, 12, 6742, 5512, 2234, 2204, 5514}"
286,1,117,0,0.2784604,"\int e^{\cosh ^{-1}(a+b x)^2} x \, dx","Int[E^ArcCosh[a + b*x]^2*x,x]","\frac{\sqrt{\pi } \text{Erfi}\left(1-\cosh ^{-1}(a+b x)\right)}{8 e b^2}+\frac{\sqrt{\pi } \text{Erfi}\left(\cosh ^{-1}(a+b x)+1\right)}{8 e b^2}+\frac{\sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b^2}-\frac{\sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b^2}","\frac{\sqrt{\pi } \text{Erfi}\left(1-\cosh ^{-1}(a+b x)\right)}{8 e b^2}+\frac{\sqrt{\pi } \text{Erfi}\left(\cosh ^{-1}(a+b x)+1\right)}{8 e b^2}+\frac{\sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b^2}-\frac{\sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b^2}",1,"(Sqrt[Pi]*Erfi[1 - ArcCosh[a + b*x]])/(8*b^2*E) + (Sqrt[Pi]*Erfi[1 + ArcCosh[a + b*x]])/(8*b^2*E) + (a*Sqrt[Pi]*Erfi[(-1 + 2*ArcCosh[a + b*x])/2])/(4*b^2*E^(1/4)) - (a*Sqrt[Pi]*Erfi[(1 + 2*ArcCosh[a + b*x])/2])/(4*b^2*E^(1/4))","A",17,8,12,0.6667,1,"{5899, 6741, 12, 6742, 5512, 2234, 2204, 5514}"
287,1,65,0,0.054025,"\int e^{\cosh ^{-1}(a+b x)^2} \, dx","Int[E^ArcCosh[a + b*x]^2,x]","\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b}-\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b}","\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b}-\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b}",1,"-(Sqrt[Pi]*Erfi[(-1 + 2*ArcCosh[a + b*x])/2])/(4*b*E^(1/4)) + (Sqrt[Pi]*Erfi[(1 + 2*ArcCosh[a + b*x])/2])/(4*b*E^(1/4))","A",7,4,10,0.4000,1,"{5897, 5512, 2234, 2204}"
288,0,0,0,0.0402105,"\int \frac{e^{\cosh ^{-1}(a+b x)^2}}{x} \, dx","Int[E^ArcCosh[a + b*x]^2/x,x]","\int \frac{e^{\cosh ^{-1}(a+b x)^2}}{x} \, dx","\text{Int}\left(\frac{e^{\cosh ^{-1}(a+b x)^2}}{x},x\right)",0,"Defer[Int][E^ArcCosh[a + b*x]^2/x, x]","A",0,0,0,0,-1,"{}"
289,0,0,0,0.0388042,"\int \frac{e^{\cosh ^{-1}(a+b x)^2}}{x^2} \, dx","Int[E^ArcCosh[a + b*x]^2/x^2,x]","\int \frac{e^{\cosh ^{-1}(a+b x)^2}}{x^2} \, dx","\text{Int}\left(\frac{e^{\cosh ^{-1}(a+b x)^2}}{x^2},x\right)",0,"Defer[Int][E^ArcCosh[a + b*x]^2/x^2, x]","A",0,0,0,0,-1,"{}"
290,1,60,0,0.0898679,"\int \frac{\cosh ^{-1}(a+b x)}{\frac{a d}{b}+d x} \, dx","Int[ArcCosh[a + b*x]/((a*d)/b + d*x),x]","\frac{\text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a+b x)}\right)}{2 d}-\frac{\cosh ^{-1}(a+b x)^2}{2 d}+\frac{\cosh ^{-1}(a+b x) \log \left(e^{2 \cosh ^{-1}(a+b x)}+1\right)}{d}","\frac{\text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a+b x)}\right)}{2 d}-\frac{\cosh ^{-1}(a+b x)^2}{2 d}+\frac{\cosh ^{-1}(a+b x) \log \left(e^{2 \cosh ^{-1}(a+b x)}+1\right)}{d}",1,"-ArcCosh[a + b*x]^2/(2*d) + (ArcCosh[a + b*x]*Log[1 + E^(2*ArcCosh[a + b*x])])/d + PolyLog[2, -E^(2*ArcCosh[a + b*x])]/(2*d)","A",7,7,19,0.3684,1,"{5866, 12, 5660, 3718, 2190, 2279, 2391}"
291,1,3,0,0.1206129,"\int \frac{x}{\sqrt{-1+x} \sqrt{1+x} \cosh ^{-1}(x)} \, dx","Int[x/(Sqrt[-1 + x]*Sqrt[1 + x]*ArcCosh[x]),x]","\text{Chi}\left(\cosh ^{-1}(x)\right)","\text{Chi}\left(\cosh ^{-1}(x)\right)",1,"CoshIntegral[ArcCosh[x]]","A",2,2,20,0.1000,1,"{5781, 3301}"
292,1,54,0,0.0521281,"\int x^3 \cosh ^{-1}\left(a+b x^4\right) \, dx","Int[x^3*ArcCosh[a + b*x^4],x]","\frac{\left(a+b x^4\right) \cosh ^{-1}\left(a+b x^4\right)}{4 b}-\frac{\sqrt{a+b x^4-1} \sqrt{a+b x^4+1}}{4 b}","\frac{\left(a+b x^4\right) \cosh ^{-1}\left(a+b x^4\right)}{4 b}-\frac{\sqrt{a+b x^4-1} \sqrt{a+b x^4+1}}{4 b}",1,"-(Sqrt[-1 + a + b*x^4]*Sqrt[1 + a + b*x^4])/(4*b) + ((a + b*x^4)*ArcCosh[a + b*x^4])/(4*b)","A",4,4,12,0.3333,1,"{6715, 5864, 5654, 74}"
293,1,55,0,0.0544168,"\int x^{-1+n} \cosh ^{-1}\left(a+b x^n\right) \, dx","Int[x^(-1 + n)*ArcCosh[a + b*x^n],x]","\frac{\left(a+b x^n\right) \cosh ^{-1}\left(a+b x^n\right)}{b n}-\frac{\sqrt{a+b x^n-1} \sqrt{a+b x^n+1}}{b n}","\frac{\left(a+b x^n\right) \cosh ^{-1}\left(a+b x^n\right)}{b n}-\frac{\sqrt{a+b x^n-1} \sqrt{a+b x^n+1}}{b n}",1,"-((Sqrt[-1 + a + b*x^n]*Sqrt[1 + a + b*x^n])/(b*n)) + ((a + b*x^n)*ArcCosh[a + b*x^n])/(b*n)","A",4,4,14,0.2857,1,"{6715, 5864, 5654, 74}"
294,1,58,0,0.09298,"\int \cosh ^{-1}\left(\frac{c}{a+b x}\right) \, dx","Int[ArcCosh[c/(a + b*x)],x]","\frac{(a+b x) \text{sech}^{-1}\left(\frac{a}{c}+\frac{b x}{c}\right)}{b}-\frac{2 c \tan ^{-1}\left(\sqrt{\frac{c \left(1-\frac{a}{c}\right)-b x}{a+b x+c}}\right)}{b}","\frac{(a+b x) \text{sech}^{-1}\left(\frac{a}{c}+\frac{b x}{c}\right)}{b}-\frac{2 c \tan ^{-1}\left(\sqrt{\frac{c \left(1-\frac{a}{c}\right)-b x}{a+b x+c}}\right)}{b}",1,"((a + b*x)*ArcSech[a/c + (b*x)/c])/b - (2*c*ArcTan[Sqrt[((1 - a/c)*c - b*x)/(a + c + b*x)]])/b","A",5,5,10,0.5000,1,"{5893, 6313, 1961, 12, 203}"
295,1,62,0,0.1189076,"\int \frac{\cosh ^{-1}\left(\sqrt{1+b x^2}\right)^n}{\sqrt{1+b x^2}} \, dx","Int[ArcCosh[Sqrt[1 + b*x^2]]^n/Sqrt[1 + b*x^2],x]","\frac{\sqrt{\sqrt{b x^2+1}-1} \sqrt{\sqrt{b x^2+1}+1} \cosh ^{-1}\left(\sqrt{b x^2+1}\right)^{n+1}}{b (n+1) x}","\frac{\sqrt{\sqrt{b x^2+1}-1} \sqrt{\sqrt{b x^2+1}+1} \cosh ^{-1}\left(\sqrt{b x^2+1}\right)^{n+1}}{b (n+1) x}",1,"(Sqrt[-1 + Sqrt[1 + b*x^2]]*Sqrt[1 + Sqrt[1 + b*x^2]]*ArcCosh[Sqrt[1 + b*x^2]]^(1 + n))/(b*(1 + n)*x)","A",2,2,26,0.07692,1,"{5895, 5676}"
296,1,54,0,0.1086256,"\int \frac{1}{\sqrt{1+b x^2} \cosh ^{-1}\left(\sqrt{1+b x^2}\right)} \, dx","Int[1/(Sqrt[1 + b*x^2]*ArcCosh[Sqrt[1 + b*x^2]]),x]","\frac{\sqrt{\sqrt{b x^2+1}-1} \sqrt{\sqrt{b x^2+1}+1} \log \left(\cosh ^{-1}\left(\sqrt{b x^2+1}\right)\right)}{b x}","\frac{\sqrt{\sqrt{b x^2+1}-1} \sqrt{\sqrt{b x^2+1}+1} \log \left(\cosh ^{-1}\left(\sqrt{b x^2+1}\right)\right)}{b x}",1,"(Sqrt[-1 + Sqrt[1 + b*x^2]]*Sqrt[1 + Sqrt[1 + b*x^2]]*Log[ArcCosh[Sqrt[1 + b*x^2]]])/(b*x)","A",2,2,26,0.07692,1,"{5895, 5674}"