1,1,151,0,0.1504278,"\int x^4 \left(d-c^2 d x^2\right) \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^4*(d - c^2*d*x^2)*(a + b*ArcCosh[c*x]),x]","-\frac{1}{7} c^2 d x^7 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{5} d x^5 \left(a+b \cosh ^{-1}(c x)\right)-\frac{76 b d x^2 \sqrt{c x-1} \sqrt{c x+1}}{3675 c^3}-\frac{152 b d \sqrt{c x-1} \sqrt{c x+1}}{3675 c^5}+\frac{1}{49} b c d x^6 \sqrt{c x-1} \sqrt{c x+1}-\frac{19 b d x^4 \sqrt{c x-1} \sqrt{c x+1}}{1225 c}","-\frac{1}{7} c^2 d x^7 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{5} d x^5 \left(a+b \cosh ^{-1}(c x)\right)-\frac{76 b d x^2 \sqrt{c x-1} \sqrt{c x+1}}{3675 c^3}-\frac{152 b d \sqrt{c x-1} \sqrt{c x+1}}{3675 c^5}+\frac{1}{49} b c d x^6 \sqrt{c x-1} \sqrt{c x+1}-\frac{19 b d x^4 \sqrt{c x-1} \sqrt{c x+1}}{1225 c}",1,"(-152*b*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3675*c^5) - (76*b*d*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3675*c^3) - (19*b*d*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(1225*c) + (b*c*d*x^6*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/49 + (d*x^5*(a + b*ArcCosh[c*x]))/5 - (c^2*d*x^7*(a + b*ArcCosh[c*x]))/7","A",8,6,23,0.2609,1,"{14, 5731, 12, 460, 100, 74}"
2,1,135,0,0.1391089,"\int x^3 \left(d-c^2 d x^2\right) \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^3*(d - c^2*d*x^2)*(a + b*ArcCosh[c*x]),x]","-\frac{1}{6} c^2 d x^6 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} d x^4 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b d x \sqrt{c x-1} \sqrt{c x+1}}{24 c^3}-\frac{b d \cosh ^{-1}(c x)}{24 c^4}+\frac{1}{36} b c d x^5 \sqrt{c x-1} \sqrt{c x+1}-\frac{b d x^3 \sqrt{c x-1} \sqrt{c x+1}}{36 c}","-\frac{1}{6} c^2 d x^6 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} d x^4 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b d x \sqrt{c x-1} \sqrt{c x+1}}{24 c^3}-\frac{b d \cosh ^{-1}(c x)}{24 c^4}+\frac{1}{36} b c d x^5 \sqrt{c x-1} \sqrt{c x+1}-\frac{b d x^3 \sqrt{c x-1} \sqrt{c x+1}}{36 c}",1,"-(b*d*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(24*c^3) - (b*d*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(36*c) + (b*c*d*x^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/36 - (b*d*ArcCosh[c*x])/(24*c^4) + (d*x^4*(a + b*ArcCosh[c*x]))/4 - (c^2*d*x^6*(a + b*ArcCosh[c*x]))/6","A",7,7,23,0.3043,1,"{14, 5731, 12, 460, 100, 90, 52}"
3,1,121,0,0.1328754,"\int x^2 \left(d-c^2 d x^2\right) \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^2*(d - c^2*d*x^2)*(a + b*ArcCosh[c*x]),x]","-\frac{1}{5} c^2 d x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} d x^3 \left(a+b \cosh ^{-1}(c x)\right)-\frac{26 b d \sqrt{c x-1} \sqrt{c x+1}}{225 c^3}+\frac{1}{25} b c d x^4 \sqrt{c x-1} \sqrt{c x+1}-\frac{13 b d x^2 \sqrt{c x-1} \sqrt{c x+1}}{225 c}","-\frac{1}{5} c^2 d x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} d x^3 \left(a+b \cosh ^{-1}(c x)\right)-\frac{26 b d \sqrt{c x-1} \sqrt{c x+1}}{225 c^3}+\frac{1}{25} b c d x^4 \sqrt{c x-1} \sqrt{c x+1}-\frac{13 b d x^2 \sqrt{c x-1} \sqrt{c x+1}}{225 c}",1,"(-26*b*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(225*c^3) - (13*b*d*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(225*c) + (b*c*d*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/25 + (d*x^3*(a + b*ArcCosh[c*x]))/3 - (c^2*d*x^5*(a + b*ArcCosh[c*x]))/5","A",6,6,23,0.2609,1,"{14, 5731, 12, 460, 100, 74}"
4,1,98,0,0.0416606,"\int x \left(d-c^2 d x^2\right) \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x*(d - c^2*d*x^2)*(a + b*ArcCosh[c*x]),x]","-\frac{d \left(1-c^2 x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)}{4 c^2}+\frac{3 b d \cosh ^{-1}(c x)}{32 c^2}+\frac{b d x (c x-1)^{3/2} (c x+1)^{3/2}}{16 c}-\frac{3 b d x \sqrt{c x-1} \sqrt{c x+1}}{32 c}","-\frac{d \left(1-c^2 x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)}{4 c^2}+\frac{3 b d \cosh ^{-1}(c x)}{32 c^2}+\frac{b d x (c x-1)^{3/2} (c x+1)^{3/2}}{16 c}-\frac{3 b d x \sqrt{c x-1} \sqrt{c x+1}}{32 c}",1,"(-3*b*d*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(32*c) + (b*d*x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(16*c) + (3*b*d*ArcCosh[c*x])/(32*c^2) - (d*(1 - c^2*x^2)^2*(a + b*ArcCosh[c*x]))/(4*c^2)","A",4,3,21,0.1429,1,"{5716, 38, 52}"
5,1,86,0,0.074217,"\int \left(d-c^2 d x^2\right) \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(d - c^2*d*x^2)*(a + b*ArcCosh[c*x]),x]","-\frac{1}{3} c^2 d x^3 \left(a+b \cosh ^{-1}(c x)\right)+d x \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{9} b c d x^2 \sqrt{c x-1} \sqrt{c x+1}-\frac{7 b d \sqrt{c x-1} \sqrt{c x+1}}{9 c}","-\frac{1}{3} c^2 d x^3 \left(a+b \cosh ^{-1}(c x)\right)+d x \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{9} b c d x^2 \sqrt{c x-1} \sqrt{c x+1}-\frac{7 b d \sqrt{c x-1} \sqrt{c x+1}}{9 c}",1,"(-7*b*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(9*c) + (b*c*d*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/9 + d*x*(a + b*ArcCosh[c*x]) - (c^2*d*x^3*(a + b*ArcCosh[c*x]))/3","A",4,4,20,0.2000,1,"{5680, 12, 460, 74}"
6,1,117,0,0.1159412,"\int \frac{\left(d-c^2 d x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{x} \, dx","Int[((d - c^2*d*x^2)*(a + b*ArcCosh[c*x]))/x,x]","\frac{1}{2} b d \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)+\frac{1}{2} d \left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)-\frac{d \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b}+d \log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} b c d x \sqrt{c x-1} \sqrt{c x+1}-\frac{1}{4} b d \cosh ^{-1}(c x)","-\frac{1}{2} b d \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)+\frac{1}{2} d \left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)+\frac{d \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b}+d \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} b c d x \sqrt{c x-1} \sqrt{c x+1}-\frac{1}{4} b d \cosh ^{-1}(c x)",1,"(b*c*d*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/4 - (b*d*ArcCosh[c*x])/4 + (d*(1 - c^2*x^2)*(a + b*ArcCosh[c*x]))/2 - (d*(a + b*ArcCosh[c*x])^2)/(2*b) + d*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])] + (b*d*PolyLog[2, -E^(2*ArcCosh[c*x])])/2","A",8,8,23,0.3478,0,"{5727, 5660, 3718, 2190, 2279, 2391, 38, 52}"
7,1,76,0,0.1193746,"\int \frac{\left(d-c^2 d x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d - c^2*d*x^2)*(a + b*ArcCosh[c*x]))/x^2,x]","c^2 (-d) x \left(a+b \cosh ^{-1}(c x)\right)-\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{x}+b c d \sqrt{c x-1} \sqrt{c x+1}+b c d \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)","c^2 (-d) x \left(a+b \cosh ^{-1}(c x)\right)-\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{x}+b c d \sqrt{c x-1} \sqrt{c x+1}+b c d \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)",1,"b*c*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x] - (d*(a + b*ArcCosh[c*x]))/x - c^2*d*x*(a + b*ArcCosh[c*x]) + b*c*d*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]]","A",5,6,23,0.2609,1,"{14, 5731, 12, 460, 92, 205}"
8,1,135,0,0.1289908,"\int \frac{\left(d-c^2 d x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d - c^2*d*x^2)*(a + b*ArcCosh[c*x]))/x^3,x]","-\frac{1}{2} b c^2 d \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)-\frac{d \left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}+\frac{c^2 d \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b}-c^2 d \log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)-\frac{1}{2} b c^2 d \cosh ^{-1}(c x)+\frac{b c d \sqrt{c x-1} \sqrt{c x+1}}{2 x}","\frac{1}{2} b c^2 d \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)-\frac{d \left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}-\frac{c^2 d \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b}-c^2 d \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)-\frac{1}{2} b c^2 d \cosh ^{-1}(c x)+\frac{b c d \sqrt{c x-1} \sqrt{c x+1}}{2 x}",1,"(b*c*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*x) - (b*c^2*d*ArcCosh[c*x])/2 - (d*(1 - c^2*x^2)*(a + b*ArcCosh[c*x]))/(2*x^2) + (c^2*d*(a + b*ArcCosh[c*x])^2)/(2*b) - c^2*d*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])] - (b*c^2*d*PolyLog[2, -E^(2*ArcCosh[c*x])])/2","A",9,9,23,0.3913,0,"{5729, 97, 12, 52, 5660, 3718, 2190, 2279, 2391}"
9,1,90,0,0.1253072,"\int \frac{\left(d-c^2 d x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d - c^2*d*x^2)*(a + b*ArcCosh[c*x]))/x^4,x]","\frac{c^2 d \left(a+b \cosh ^{-1}(c x)\right)}{x}-\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}-\frac{5}{6} b c^3 d \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)+\frac{b c d \sqrt{c x-1} \sqrt{c x+1}}{6 x^2}","\frac{c^2 d \left(a+b \cosh ^{-1}(c x)\right)}{x}-\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}-\frac{5}{6} b c^3 d \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)+\frac{b c d \sqrt{c x-1} \sqrt{c x+1}}{6 x^2}",1,"(b*c*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*x^2) - (d*(a + b*ArcCosh[c*x]))/(3*x^3) + (c^2*d*(a + b*ArcCosh[c*x]))/x - (5*b*c^3*d*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/6","A",5,6,23,0.2609,1,"{14, 5731, 12, 454, 92, 205}"
10,1,264,0,0.2933864,"\int x^4 \left(d-c^2 d x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^4*(d - c^2*d*x^2)^2*(a + b*ArcCosh[c*x]),x]","\frac{1}{9} c^4 d^2 x^9 \left(a+b \cosh ^{-1}(c x)\right)-\frac{2}{7} c^2 d^2 x^7 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{5} d^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b d^2 \left(1-c^2 x^2\right)^5}{81 c^5 \sqrt{c x-1} \sqrt{c x+1}}-\frac{10 b d^2 \left(1-c^2 x^2\right)^4}{441 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 \left(1-c^2 x^2\right)^3}{525 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{4 b d^2 \left(1-c^2 x^2\right)^2}{945 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b d^2 \left(1-c^2 x^2\right)}{315 c^5 \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{9} c^4 d^2 x^9 \left(a+b \cosh ^{-1}(c x)\right)-\frac{2}{7} c^2 d^2 x^7 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{5} d^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b d^2 (c x-1)^{9/2} (c x+1)^{9/2}}{81 c^5}-\frac{10 b d^2 (c x-1)^{7/2} (c x+1)^{7/2}}{441 c^5}-\frac{b d^2 (c x-1)^{5/2} (c x+1)^{5/2}}{525 c^5}+\frac{4 b d^2 (c x-1)^{3/2} (c x+1)^{3/2}}{945 c^5}-\frac{8 b d^2 \sqrt{c x-1} \sqrt{c x+1}}{315 c^5}",1,"(8*b*d^2*(1 - c^2*x^2))/(315*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (4*b*d^2*(1 - c^2*x^2)^2)/(945*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^2*(1 - c^2*x^2)^3)/(525*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (10*b*d^2*(1 - c^2*x^2)^4)/(441*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^2*(1 - c^2*x^2)^5)/(81*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (d^2*x^5*(a + b*ArcCosh[c*x]))/5 - (2*c^2*d^2*x^7*(a + b*ArcCosh[c*x]))/7 + (c^4*d^2*x^9*(a + b*ArcCosh[c*x]))/9","A",7,7,25,0.2800,1,"{270, 5731, 12, 520, 1251, 897, 1153}"
11,1,284,0,0.2769142,"\int x^3 \left(d-c^2 d x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^3*(d - c^2*d*x^2)^2*(a + b*ArcCosh[c*x]),x]","\frac{1}{8} c^4 d^2 x^8 \left(a+b \cosh ^{-1}(c x)\right)-\frac{1}{3} c^2 d^2 x^6 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} d^2 x^4 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b c^3 d^2 x^7 \left(1-c^2 x^2\right)}{64 \sqrt{c x-1} \sqrt{c x+1}}-\frac{43 b c d^2 x^5 \left(1-c^2 x^2\right)}{1152 \sqrt{c x-1} \sqrt{c x+1}}+\frac{73 b d^2 x^3 \left(1-c^2 x^2\right)}{4608 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{73 b d^2 x \left(1-c^2 x^2\right)}{3072 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{73 b d^2 \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{3072 c^4 \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{8} c^4 d^2 x^8 \left(a+b \cosh ^{-1}(c x)\right)-\frac{1}{3} c^2 d^2 x^6 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} d^2 x^4 \left(a+b \cosh ^{-1}(c x)\right)-\frac{1}{64} b c^3 d^2 x^7 \sqrt{c x-1} \sqrt{c x+1}-\frac{73 b d^2 x \sqrt{c x-1} \sqrt{c x+1}}{3072 c^3}-\frac{73 b d^2 \cosh ^{-1}(c x)}{3072 c^4}+\frac{43 b c d^2 x^5 \sqrt{c x-1} \sqrt{c x+1}}{1152}-\frac{73 b d^2 x^3 \sqrt{c x-1} \sqrt{c x+1}}{4608 c}",1,"(73*b*d^2*x*(1 - c^2*x^2))/(3072*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (73*b*d^2*x^3*(1 - c^2*x^2))/(4608*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (43*b*c*d^2*x^5*(1 - c^2*x^2))/(1152*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d^2*x^7*(1 - c^2*x^2))/(64*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (d^2*x^4*(a + b*ArcCosh[c*x]))/4 - (c^2*d^2*x^6*(a + b*ArcCosh[c*x]))/3 + (c^4*d^2*x^8*(a + b*ArcCosh[c*x]))/8 - (73*b*d^2*Sqrt[-1 + c^2*x^2]*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/(3072*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",9,10,25,0.4000,1,"{266, 43, 5731, 12, 520, 1267, 459, 321, 217, 206}"
12,1,223,0,0.2484981,"\int x^2 \left(d-c^2 d x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^2*(d - c^2*d*x^2)^2*(a + b*ArcCosh[c*x]),x]","\frac{1}{7} c^4 d^2 x^7 \left(a+b \cosh ^{-1}(c x)\right)-\frac{2}{5} c^2 d^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} d^2 x^3 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b d^2 \left(1-c^2 x^2\right)^4}{49 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 \left(1-c^2 x^2\right)^3}{175 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{4 b d^2 \left(1-c^2 x^2\right)^2}{315 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b d^2 \left(1-c^2 x^2\right)}{105 c^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{7} c^4 d^2 x^7 \left(a+b \cosh ^{-1}(c x)\right)-\frac{2}{5} c^2 d^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} d^2 x^3 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b d^2 (c x-1)^{7/2} (c x+1)^{7/2}}{49 c^3}-\frac{b d^2 (c x-1)^{5/2} (c x+1)^{5/2}}{175 c^3}+\frac{4 b d^2 (c x-1)^{3/2} (c x+1)^{3/2}}{315 c^3}-\frac{8 b d^2 \sqrt{c x-1} \sqrt{c x+1}}{105 c^3}",1,"(8*b*d^2*(1 - c^2*x^2))/(105*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (4*b*d^2*(1 - c^2*x^2)^2)/(315*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^2*(1 - c^2*x^2)^3)/(175*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*d^2*(1 - c^2*x^2)^4)/(49*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (d^2*x^3*(a + b*ArcCosh[c*x]))/3 - (2*c^2*d^2*x^5*(a + b*ArcCosh[c*x]))/5 + (c^4*d^2*x^7*(a + b*ArcCosh[c*x]))/7","A",6,6,25,0.2400,1,"{270, 5731, 12, 520, 1251, 771}"
13,1,136,0,0.0673495,"\int x \left(d-c^2 d x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x*(d - c^2*d*x^2)^2*(a + b*ArcCosh[c*x]),x]","-\frac{d^2 \left(1-c^2 x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)}{6 c^2}+\frac{5 b d^2 \cosh ^{-1}(c x)}{96 c^2}-\frac{b d^2 x (c x-1)^{5/2} (c x+1)^{5/2}}{36 c}+\frac{5 b d^2 x (c x-1)^{3/2} (c x+1)^{3/2}}{144 c}-\frac{5 b d^2 x \sqrt{c x-1} \sqrt{c x+1}}{96 c}","-\frac{d^2 \left(1-c^2 x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)}{6 c^2}+\frac{5 b d^2 \cosh ^{-1}(c x)}{96 c^2}-\frac{b d^2 x (c x-1)^{5/2} (c x+1)^{5/2}}{36 c}+\frac{5 b d^2 x (c x-1)^{3/2} (c x+1)^{3/2}}{144 c}-\frac{5 b d^2 x \sqrt{c x-1} \sqrt{c x+1}}{96 c}",1,"(-5*b*d^2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(96*c) + (5*b*d^2*x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(144*c) - (b*d^2*x*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(36*c) + (5*b*d^2*ArcCosh[c*x])/(96*c^2) - (d^2*(1 - c^2*x^2)^3*(a + b*ArcCosh[c*x]))/(6*c^2)","A",5,3,23,0.1304,1,"{5716, 38, 52}"
14,1,177,0,0.1519036,"\int \left(d-c^2 d x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(d - c^2*d*x^2)^2*(a + b*ArcCosh[c*x]),x]","\frac{1}{5} c^4 d^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)-\frac{2}{3} c^2 d^2 x^3 \left(a+b \cosh ^{-1}(c x)\right)+d^2 x \left(a+b \cosh ^{-1}(c x)\right)+\frac{b d^2 \left(1-c^2 x^2\right)^3}{25 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{4 b d^2 \left(1-c^2 x^2\right)^2}{45 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b d^2 \left(1-c^2 x^2\right)}{15 c \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{5} c^4 d^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)-\frac{2}{3} c^2 d^2 x^3 \left(a+b \cosh ^{-1}(c x)\right)+d^2 x \left(a+b \cosh ^{-1}(c x)\right)-\frac{b d^2 (c x-1)^{5/2} (c x+1)^{5/2}}{25 c}+\frac{4 b d^2 (c x-1)^{3/2} (c x+1)^{3/2}}{45 c}-\frac{8 b d^2 \sqrt{c x-1} \sqrt{c x+1}}{15 c}",1,"(8*b*d^2*(1 - c^2*x^2))/(15*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (4*b*d^2*(1 - c^2*x^2)^2)/(45*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^2*(1 - c^2*x^2)^3)/(25*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + d^2*x*(a + b*ArcCosh[c*x]) - (2*c^2*d^2*x^3*(a + b*ArcCosh[c*x]))/3 + (c^4*d^2*x^5*(a + b*ArcCosh[c*x]))/5","A",6,6,22,0.2727,1,"{194, 5680, 12, 520, 1247, 698}"
15,1,184,0,0.2042026,"\int \frac{\left(d-c^2 d x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)}{x} \, dx","Int[((d - c^2*d*x^2)^2*(a + b*ArcCosh[c*x]))/x,x]","\frac{1}{2} b d^2 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)+\frac{1}{4} d^2 \left(1-c^2 x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{2} d^2 \left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)-\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b}+d^2 \log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)-\frac{1}{16} b c d^2 x (c x-1)^{3/2} (c x+1)^{3/2}+\frac{11}{32} b c d^2 x \sqrt{c x-1} \sqrt{c x+1}-\frac{11}{32} b d^2 \cosh ^{-1}(c x)","-\frac{1}{2} b d^2 \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)+\frac{1}{4} d^2 \left(1-c^2 x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{2} d^2 \left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)+\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b}+d^2 \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)-\frac{1}{16} b c d^2 x (c x-1)^{3/2} (c x+1)^{3/2}+\frac{11}{32} b c d^2 x \sqrt{c x-1} \sqrt{c x+1}-\frac{11}{32} b d^2 \cosh ^{-1}(c x)",1,"(11*b*c*d^2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/32 - (b*c*d^2*x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/16 - (11*b*d^2*ArcCosh[c*x])/32 + (d^2*(1 - c^2*x^2)*(a + b*ArcCosh[c*x]))/2 + (d^2*(1 - c^2*x^2)^2*(a + b*ArcCosh[c*x]))/4 - (d^2*(a + b*ArcCosh[c*x])^2)/(2*b) + d^2*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])] + (b*d^2*PolyLog[2, -E^(2*ArcCosh[c*x])])/2","A",12,8,25,0.3200,0,"{5727, 5660, 3718, 2190, 2279, 2391, 38, 52}"
16,1,182,0,0.229905,"\int \frac{\left(d-c^2 d x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d - c^2*d*x^2)^2*(a + b*ArcCosh[c*x]))/x^2,x]","\frac{1}{3} c^4 d^2 x^3 \left(a+b \cosh ^{-1}(c x)\right)-2 c^2 d^2 x \left(a+b \cosh ^{-1}(c x)\right)-\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)}{x}-\frac{b c d^2 \left(1-c^2 x^2\right)^2}{9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b c d^2 \left(1-c^2 x^2\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d^2 \sqrt{c^2 x^2-1} \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{\sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{3} c^4 d^2 x^3 \left(a+b \cosh ^{-1}(c x)\right)-2 c^2 d^2 x \left(a+b \cosh ^{-1}(c x)\right)-\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)}{x}-\frac{1}{9} b c d^2 (c x-1)^{3/2} (c x+1)^{3/2}+\frac{5}{3} b c d^2 \sqrt{c x-1} \sqrt{c x+1}+b c d^2 \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)",1,"(-5*b*c*d^2*(1 - c^2*x^2))/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d^2*(1 - c^2*x^2)^2)/(9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d^2*(a + b*ArcCosh[c*x]))/x - 2*c^2*d^2*x*(a + b*ArcCosh[c*x]) + (c^4*d^2*x^3*(a + b*ArcCosh[c*x]))/3 + (b*c*d^2*Sqrt[-1 + c^2*x^2]*ArcTan[Sqrt[-1 + c^2*x^2]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",8,8,25,0.3200,1,"{270, 5731, 12, 520, 1251, 897, 1153, 205}"
17,1,200,0,0.2175913,"\int \frac{\left(d-c^2 d x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d - c^2*d*x^2)^2*(a + b*ArcCosh[c*x]))/x^3,x]","-b c^2 d^2 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)-c^2 d^2 \left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)-\frac{d^2 \left(1-c^2 x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}+\frac{c^2 d^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{b}-2 c^2 d^2 \log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} b c^3 d^2 x \sqrt{c x-1} \sqrt{c x+1}-\frac{1}{4} b c^2 d^2 \cosh ^{-1}(c x)-\frac{b c d^2 (c x-1)^{3/2} (c x+1)^{3/2}}{2 x}","b c^2 d^2 \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)-c^2 d^2 \left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)-\frac{d^2 \left(1-c^2 x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}-\frac{c^2 d^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{b}-2 c^2 d^2 \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} b c^3 d^2 x \sqrt{c x-1} \sqrt{c x+1}-\frac{1}{4} b c^2 d^2 \cosh ^{-1}(c x)-\frac{b c d^2 (c x-1)^{3/2} (c x+1)^{3/2}}{2 x}",1,"(b*c^3*d^2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/4 - (b*c*d^2*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(2*x) - (b*c^2*d^2*ArcCosh[c*x])/4 - c^2*d^2*(1 - c^2*x^2)*(a + b*ArcCosh[c*x]) - (d^2*(1 - c^2*x^2)^2*(a + b*ArcCosh[c*x]))/(2*x^2) + (c^2*d^2*(a + b*ArcCosh[c*x])^2)/b - 2*c^2*d^2*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])] - b*c^2*d^2*PolyLog[2, -E^(2*ArcCosh[c*x])]","A",13,11,25,0.4400,0,"{5729, 97, 12, 38, 52, 5727, 5660, 3718, 2190, 2279, 2391}"
18,1,186,0,0.234374,"\int \frac{\left(d-c^2 d x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d - c^2*d*x^2)^2*(a + b*ArcCosh[c*x]))/x^4,x]","c^4 d^2 x \left(a+b \cosh ^{-1}(c x)\right)+\frac{2 c^2 d^2 \left(a+b \cosh ^{-1}(c x)\right)}{x}-\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}+\frac{b c^3 d^2 \left(1-c^2 x^2\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \left(1-c^2 x^2\right)}{6 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{11 b c^3 d^2 \sqrt{c^2 x^2-1} \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{6 \sqrt{c x-1} \sqrt{c x+1}}","c^4 d^2 x \left(a+b \cosh ^{-1}(c x)\right)+\frac{2 c^2 d^2 \left(a+b \cosh ^{-1}(c x)\right)}{x}-\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}-b c^3 d^2 \sqrt{c x-1} \sqrt{c x+1}-\frac{11}{6} b c^3 d^2 \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)+\frac{b c d^2 \sqrt{c x-1} \sqrt{c x+1}}{6 x^2}",1,"(b*c^3*d^2*(1 - c^2*x^2))/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d^2*(1 - c^2*x^2))/(6*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d^2*(a + b*ArcCosh[c*x]))/(3*x^3) + (2*c^2*d^2*(a + b*ArcCosh[c*x]))/x + c^4*d^2*x*(a + b*ArcCosh[c*x]) - (11*b*c^3*d^2*Sqrt[-1 + c^2*x^2]*ArcTan[Sqrt[-1 + c^2*x^2]])/(6*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",8,9,25,0.3600,1,"{270, 5731, 12, 520, 1251, 897, 1157, 388, 205}"
19,1,326,0,0.4386536,"\int x^4 \left(d-c^2 d x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^4*(d - c^2*d*x^2)^3*(a + b*ArcCosh[c*x]),x]","-\frac{1}{11} c^6 d^3 x^{11} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} c^4 d^3 x^9 \left(a+b \cosh ^{-1}(c x)\right)-\frac{3}{7} c^2 d^3 x^7 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{5} d^3 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b d^3 \left(1-c^2 x^2\right)^6}{121 c^5 \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 b d^3 \left(1-c^2 x^2\right)^5}{297 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^3 \left(1-c^2 x^2\right)^4}{1617 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d^3 \left(1-c^2 x^2\right)^3}{1925 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b d^3 \left(1-c^2 x^2\right)^2}{3465 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{16 b d^3 \left(1-c^2 x^2\right)}{1155 c^5 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{1}{11} c^6 d^3 x^{11} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} c^4 d^3 x^9 \left(a+b \cosh ^{-1}(c x)\right)-\frac{3}{7} c^2 d^3 x^7 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{5} d^3 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b d^3 (c x-1)^{11/2} (c x+1)^{11/2}}{121 c^5}+\frac{4 b d^3 (c x-1)^{9/2} (c x+1)^{9/2}}{297 c^5}+\frac{b d^3 (c x-1)^{7/2} (c x+1)^{7/2}}{1617 c^5}-\frac{2 b d^3 (c x-1)^{5/2} (c x+1)^{5/2}}{1925 c^5}+\frac{8 b d^3 (c x-1)^{3/2} (c x+1)^{3/2}}{3465 c^5}-\frac{16 b d^3 \sqrt{c x-1} \sqrt{c x+1}}{1155 c^5}",1,"(16*b*d^3*(1 - c^2*x^2))/(1155*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (8*b*d^3*(1 - c^2*x^2)^2)/(3465*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*d^3*(1 - c^2*x^2)^3)/(1925*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^3*(1 - c^2*x^2)^4)/(1617*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (4*b*d^3*(1 - c^2*x^2)^5)/(297*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^3*(1 - c^2*x^2)^6)/(121*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (d^3*x^5*(a + b*ArcCosh[c*x]))/5 - (3*c^2*d^3*x^7*(a + b*ArcCosh[c*x]))/7 + (c^4*d^3*x^9*(a + b*ArcCosh[c*x]))/3 - (c^6*d^3*x^11*(a + b*ArcCosh[c*x]))/11","A",6,6,25,0.2400,1,"{270, 5731, 12, 1610, 1799, 1620}"
20,1,328,0,0.2811955,"\int x^3 \left(d-c^2 d x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^3*(d - c^2*d*x^2)^3*(a + b*ArcCosh[c*x]),x]","\frac{d^3 \left(1-c^2 x^2\right)^5 \left(a+b \cosh ^{-1}(c x)\right)}{10 c^4}-\frac{d^3 \left(1-c^2 x^2\right)^4 \left(a+b \cosh ^{-1}(c x)\right)}{8 c^4}-\frac{b d^3 x \left(1-c^2 x^2\right)^5}{100 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{7 b d^3 x \left(1-c^2 x^2\right)^4}{1600 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{49 b d^3 x \left(1-c^2 x^2\right)^3}{9600 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{49 b d^3 x \left(1-c^2 x^2\right)^2}{7680 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{49 b d^3 x \left(1-c^2 x^2\right)}{5120 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{49 b d^3 \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{5120 c^4 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{d^3 (c x-1)^5 (c x+1)^5 \left(a+b \cosh ^{-1}(c x)\right)}{10 c^4}-\frac{d^3 (c x-1)^4 (c x+1)^4 \left(a+b \cosh ^{-1}(c x)\right)}{8 c^4}+\frac{b d^3 x (c x-1)^{9/2} (c x+1)^{9/2}}{100 c^3}+\frac{7 b d^3 x (c x-1)^{7/2} (c x+1)^{7/2}}{1600 c^3}-\frac{49 b d^3 x (c x-1)^{5/2} (c x+1)^{5/2}}{9600 c^3}+\frac{49 b d^3 x (c x-1)^{3/2} (c x+1)^{3/2}}{7680 c^3}-\frac{49 b d^3 x \sqrt{c x-1} \sqrt{c x+1}}{5120 c^3}+\frac{49 b d^3 \cosh ^{-1}(c x)}{5120 c^4}",1,"(49*b*d^3*x*(1 - c^2*x^2))/(5120*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (49*b*d^3*x*(1 - c^2*x^2)^2)/(7680*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (49*b*d^3*x*(1 - c^2*x^2)^3)/(9600*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (7*b*d^3*x*(1 - c^2*x^2)^4)/(1600*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*d^3*x*(1 - c^2*x^2)^5)/(100*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d^3*(1 - c^2*x^2)^4*(a + b*ArcCosh[c*x]))/(8*c^4) + (d^3*(1 - c^2*x^2)^5*(a + b*ArcCosh[c*x]))/(10*c^4) + (49*b*d^3*Sqrt[-1 + c^2*x^2]*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/(5120*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",11,10,25,0.4000,1,"{266, 43, 5731, 12, 566, 21, 388, 195, 217, 206}"
21,1,285,0,0.3959127,"\int x^2 \left(d-c^2 d x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^2*(d - c^2*d*x^2)^3*(a + b*ArcCosh[c*x]),x]","-\frac{1}{9} c^6 d^3 x^9 \left(a+b \cosh ^{-1}(c x)\right)+\frac{3}{7} c^4 d^3 x^7 \left(a+b \cosh ^{-1}(c x)\right)-\frac{3}{5} c^2 d^3 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} d^3 x^3 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b d^3 \left(1-c^2 x^2\right)^5}{81 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^3 \left(1-c^2 x^2\right)^4}{441 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d^3 \left(1-c^2 x^2\right)^3}{525 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b d^3 \left(1-c^2 x^2\right)^2}{945 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{16 b d^3 \left(1-c^2 x^2\right)}{315 c^3 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{1}{9} c^6 d^3 x^9 \left(a+b \cosh ^{-1}(c x)\right)+\frac{3}{7} c^4 d^3 x^7 \left(a+b \cosh ^{-1}(c x)\right)-\frac{3}{5} c^2 d^3 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} d^3 x^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b d^3 (c x-1)^{9/2} (c x+1)^{9/2}}{81 c^3}+\frac{b d^3 (c x-1)^{7/2} (c x+1)^{7/2}}{441 c^3}-\frac{2 b d^3 (c x-1)^{5/2} (c x+1)^{5/2}}{525 c^3}+\frac{8 b d^3 (c x-1)^{3/2} (c x+1)^{3/2}}{945 c^3}-\frac{16 b d^3 \sqrt{c x-1} \sqrt{c x+1}}{315 c^3}",1,"(16*b*d^3*(1 - c^2*x^2))/(315*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (8*b*d^3*(1 - c^2*x^2)^2)/(945*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*d^3*(1 - c^2*x^2)^3)/(525*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^3*(1 - c^2*x^2)^4)/(441*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*d^3*(1 - c^2*x^2)^5)/(81*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (d^3*x^3*(a + b*ArcCosh[c*x]))/3 - (3*c^2*d^3*x^5*(a + b*ArcCosh[c*x]))/5 + (3*c^4*d^3*x^7*(a + b*ArcCosh[c*x]))/7 - (c^6*d^3*x^9*(a + b*ArcCosh[c*x]))/9","A",6,6,25,0.2400,1,"{270, 5731, 12, 1610, 1799, 1620}"
22,1,166,0,0.0787097,"\int x \left(d-c^2 d x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x*(d - c^2*d*x^2)^3*(a + b*ArcCosh[c*x]),x]","-\frac{d^3 \left(1-c^2 x^2\right)^4 \left(a+b \cosh ^{-1}(c x)\right)}{8 c^2}+\frac{35 b d^3 \cosh ^{-1}(c x)}{1024 c^2}+\frac{b d^3 x (c x-1)^{7/2} (c x+1)^{7/2}}{64 c}-\frac{7 b d^3 x (c x-1)^{5/2} (c x+1)^{5/2}}{384 c}+\frac{35 b d^3 x (c x-1)^{3/2} (c x+1)^{3/2}}{1536 c}-\frac{35 b d^3 x \sqrt{c x-1} \sqrt{c x+1}}{1024 c}","-\frac{d^3 \left(1-c^2 x^2\right)^4 \left(a+b \cosh ^{-1}(c x)\right)}{8 c^2}+\frac{35 b d^3 \cosh ^{-1}(c x)}{1024 c^2}+\frac{b d^3 x (c x-1)^{7/2} (c x+1)^{7/2}}{64 c}-\frac{7 b d^3 x (c x-1)^{5/2} (c x+1)^{5/2}}{384 c}+\frac{35 b d^3 x (c x-1)^{3/2} (c x+1)^{3/2}}{1536 c}-\frac{35 b d^3 x \sqrt{c x-1} \sqrt{c x+1}}{1024 c}",1,"(-35*b*d^3*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(1024*c) + (35*b*d^3*x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(1536*c) - (7*b*d^3*x*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(384*c) + (b*d^3*x*(-1 + c*x)^(7/2)*(1 + c*x)^(7/2))/(64*c) + (35*b*d^3*ArcCosh[c*x])/(1024*c^2) - (d^3*(1 - c^2*x^2)^4*(a + b*ArcCosh[c*x]))/(8*c^2)","A",6,3,23,0.1304,1,"{5716, 38, 52}"
23,1,237,0,0.2620196,"\int \left(d-c^2 d x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(d - c^2*d*x^2)^3*(a + b*ArcCosh[c*x]),x]","-\frac{1}{7} c^6 d^3 x^7 \left(a+b \cosh ^{-1}(c x)\right)+\frac{3}{5} c^4 d^3 x^5 \left(a+b \cosh ^{-1}(c x)\right)-c^2 d^3 x^3 \left(a+b \cosh ^{-1}(c x)\right)+d^3 x \left(a+b \cosh ^{-1}(c x)\right)+\frac{b d^3 \left(1-c^2 x^2\right)^4}{49 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{6 b d^3 \left(1-c^2 x^2\right)^3}{175 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b d^3 \left(1-c^2 x^2\right)^2}{105 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{16 b d^3 \left(1-c^2 x^2\right)}{35 c \sqrt{c x-1} \sqrt{c x+1}}","-\frac{1}{7} c^6 d^3 x^7 \left(a+b \cosh ^{-1}(c x)\right)+\frac{3}{5} c^4 d^3 x^5 \left(a+b \cosh ^{-1}(c x)\right)-c^2 d^3 x^3 \left(a+b \cosh ^{-1}(c x)\right)+d^3 x \left(a+b \cosh ^{-1}(c x)\right)+\frac{b d^3 (c x-1)^{7/2} (c x+1)^{7/2}}{49 c}-\frac{6 b d^3 (c x-1)^{5/2} (c x+1)^{5/2}}{175 c}+\frac{8 b d^3 (c x-1)^{3/2} (c x+1)^{3/2}}{105 c}-\frac{16 b d^3 \sqrt{c x-1} \sqrt{c x+1}}{35 c}",1,"(16*b*d^3*(1 - c^2*x^2))/(35*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (8*b*d^3*(1 - c^2*x^2)^2)/(105*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (6*b*d^3*(1 - c^2*x^2)^3)/(175*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^3*(1 - c^2*x^2)^4)/(49*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + d^3*x*(a + b*ArcCosh[c*x]) - c^2*d^3*x^3*(a + b*ArcCosh[c*x]) + (3*c^4*d^3*x^5*(a + b*ArcCosh[c*x]))/5 - (c^6*d^3*x^7*(a + b*ArcCosh[c*x]))/7","A",6,6,22,0.2727,1,"{194, 5680, 12, 1610, 1799, 1850}"
24,1,239,0,0.3003584,"\int \frac{\left(d-c^2 d x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)}{x} \, dx","Int[((d - c^2*d*x^2)^3*(a + b*ArcCosh[c*x]))/x,x]","\frac{1}{2} b d^3 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)+\frac{1}{6} d^3 \left(1-c^2 x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} d^3 \left(1-c^2 x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{2} d^3 \left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)-\frac{d^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b}+d^3 \log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{36} b c d^3 x (c x-1)^{5/2} (c x+1)^{5/2}-\frac{7}{72} b c d^3 x (c x-1)^{3/2} (c x+1)^{3/2}+\frac{19}{48} b c d^3 x \sqrt{c x-1} \sqrt{c x+1}-\frac{19}{48} b d^3 \cosh ^{-1}(c x)","-\frac{1}{2} b d^3 \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)+\frac{1}{6} d^3 \left(1-c^2 x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} d^3 \left(1-c^2 x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{2} d^3 \left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)+\frac{d^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b}+d^3 \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{36} b c d^3 x (c x-1)^{5/2} (c x+1)^{5/2}-\frac{7}{72} b c d^3 x (c x-1)^{3/2} (c x+1)^{3/2}+\frac{19}{48} b c d^3 x \sqrt{c x-1} \sqrt{c x+1}-\frac{19}{48} b d^3 \cosh ^{-1}(c x)",1,"(19*b*c*d^3*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/48 - (7*b*c*d^3*x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/72 + (b*c*d^3*x*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/36 - (19*b*d^3*ArcCosh[c*x])/48 + (d^3*(1 - c^2*x^2)*(a + b*ArcCosh[c*x]))/2 + (d^3*(1 - c^2*x^2)^2*(a + b*ArcCosh[c*x]))/4 + (d^3*(1 - c^2*x^2)^3*(a + b*ArcCosh[c*x]))/6 - (d^3*(a + b*ArcCosh[c*x])^2)/(2*b) + d^3*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])] + (b*d^3*PolyLog[2, -E^(2*ArcCosh[c*x])])/2","A",17,8,25,0.3200,0,"{5727, 5660, 3718, 2190, 2279, 2391, 38, 52}"
25,1,239,0,0.3609772,"\int \frac{\left(d-c^2 d x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d - c^2*d*x^2)^3*(a + b*ArcCosh[c*x]))/x^2,x]","-\frac{1}{5} c^6 d^3 x^5 \left(a+b \cosh ^{-1}(c x)\right)+c^4 d^3 x^3 \left(a+b \cosh ^{-1}(c x)\right)-3 c^2 d^3 x \left(a+b \cosh ^{-1}(c x)\right)-\frac{d^3 \left(a+b \cosh ^{-1}(c x)\right)}{x}-\frac{b c d^3 \left(1-c^2 x^2\right)^3}{25 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^3 \left(1-c^2 x^2\right)^2}{5 \sqrt{c x-1} \sqrt{c x+1}}-\frac{11 b c d^3 \left(1-c^2 x^2\right)}{5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d^3 \sqrt{c^2 x^2-1} \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{\sqrt{c x-1} \sqrt{c x+1}}","-\frac{1}{5} c^6 d^3 x^5 \left(a+b \cosh ^{-1}(c x)\right)+c^4 d^3 x^3 \left(a+b \cosh ^{-1}(c x)\right)-3 c^2 d^3 x \left(a+b \cosh ^{-1}(c x)\right)-\frac{d^3 \left(a+b \cosh ^{-1}(c x)\right)}{x}+\frac{1}{25} b c d^3 (c x-1)^{5/2} (c x+1)^{5/2}-\frac{1}{5} b c d^3 (c x-1)^{3/2} (c x+1)^{3/2}+\frac{11}{5} b c d^3 \sqrt{c x-1} \sqrt{c x+1}+b c d^3 \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)",1,"(-11*b*c*d^3*(1 - c^2*x^2))/(5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d^3*(1 - c^2*x^2)^2)/(5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d^3*(1 - c^2*x^2)^3)/(25*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d^3*(a + b*ArcCosh[c*x]))/x - 3*c^2*d^3*x*(a + b*ArcCosh[c*x]) + c^4*d^3*x^3*(a + b*ArcCosh[c*x]) - (c^6*d^3*x^5*(a + b*ArcCosh[c*x]))/5 + (b*c*d^3*Sqrt[-1 + c^2*x^2]*ArcTan[Sqrt[-1 + c^2*x^2]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",8,8,25,0.3200,1,"{270, 5731, 12, 1610, 1799, 1620, 63, 205}"
26,1,267,0,0.3178034,"\int \frac{\left(d-c^2 d x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d - c^2*d*x^2)^3*(a + b*ArcCosh[c*x]))/x^3,x]","-\frac{3}{2} b c^2 d^3 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)-\frac{d^3 \left(1-c^2 x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}-\frac{3}{4} c^2 d^3 \left(1-c^2 x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)-\frac{3}{2} c^2 d^3 \left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)+\frac{3 c^2 d^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b}-3 c^2 d^3 \log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)-\frac{7}{16} b c^3 d^3 x (c x-1)^{3/2} (c x+1)^{3/2}-\frac{3}{32} b c^3 d^3 x \sqrt{c x-1} \sqrt{c x+1}+\frac{3}{32} b c^2 d^3 \cosh ^{-1}(c x)+\frac{b c d^3 (c x-1)^{5/2} (c x+1)^{5/2}}{2 x}","\frac{3}{2} b c^2 d^3 \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)-\frac{d^3 \left(1-c^2 x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}-\frac{3}{4} c^2 d^3 \left(1-c^2 x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)-\frac{3}{2} c^2 d^3 \left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)-\frac{3 c^2 d^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b}-3 c^2 d^3 \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)-\frac{7}{16} b c^3 d^3 x (c x-1)^{3/2} (c x+1)^{3/2}-\frac{3}{32} b c^3 d^3 x \sqrt{c x-1} \sqrt{c x+1}+\frac{3}{32} b c^2 d^3 \cosh ^{-1}(c x)+\frac{b c d^3 (c x-1)^{5/2} (c x+1)^{5/2}}{2 x}",1,"(-3*b*c^3*d^3*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/32 - (7*b*c^3*d^3*x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/16 + (b*c*d^3*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(2*x) + (3*b*c^2*d^3*ArcCosh[c*x])/32 - (3*c^2*d^3*(1 - c^2*x^2)*(a + b*ArcCosh[c*x]))/2 - (3*c^2*d^3*(1 - c^2*x^2)^2*(a + b*ArcCosh[c*x]))/4 - (d^3*(1 - c^2*x^2)^3*(a + b*ArcCosh[c*x]))/(2*x^2) + (3*c^2*d^3*(a + b*ArcCosh[c*x])^2)/(2*b) - 3*c^2*d^3*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])] - (3*b*c^2*d^3*PolyLog[2, -E^(2*ArcCosh[c*x])])/2","A",18,11,25,0.4400,0,"{5729, 97, 12, 38, 52, 5727, 5660, 3718, 2190, 2279, 2391}"
27,1,252,0,0.3897491,"\int \frac{\left(d-c^2 d x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d - c^2*d*x^2)^3*(a + b*ArcCosh[c*x]))/x^4,x]","-\frac{1}{3} c^6 d^3 x^3 \left(a+b \cosh ^{-1}(c x)\right)+3 c^4 d^3 x \left(a+b \cosh ^{-1}(c x)\right)+\frac{3 c^2 d^3 \left(a+b \cosh ^{-1}(c x)\right)}{x}-\frac{d^3 \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}+\frac{b c^3 d^3 \left(1-c^2 x^2\right)^2}{9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b c^3 d^3 \left(1-c^2 x^2\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^3 \left(1-c^2 x^2\right)}{6 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{17 b c^3 d^3 \sqrt{c^2 x^2-1} \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{6 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{1}{3} c^6 d^3 x^3 \left(a+b \cosh ^{-1}(c x)\right)+3 c^4 d^3 x \left(a+b \cosh ^{-1}(c x)\right)+\frac{3 c^2 d^3 \left(a+b \cosh ^{-1}(c x)\right)}{x}-\frac{d^3 \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}+\frac{1}{9} b c^3 d^3 (c x-1)^{3/2} (c x+1)^{3/2}-\frac{8}{3} b c^3 d^3 \sqrt{c x-1} \sqrt{c x+1}-\frac{17}{6} b c^3 d^3 \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)+\frac{b c d^3 \sqrt{c x-1} \sqrt{c x+1}}{6 x^2}",1,"(8*b*c^3*d^3*(1 - c^2*x^2))/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d^3*(1 - c^2*x^2))/(6*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d^3*(1 - c^2*x^2)^2)/(9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d^3*(a + b*ArcCosh[c*x]))/(3*x^3) + (3*c^2*d^3*(a + b*ArcCosh[c*x]))/x + 3*c^4*d^3*x*(a + b*ArcCosh[c*x]) - (c^6*d^3*x^3*(a + b*ArcCosh[c*x]))/3 - (17*b*c^3*d^3*Sqrt[-1 + c^2*x^2]*ArcTan[Sqrt[-1 + c^2*x^2]])/(6*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",9,9,25,0.3600,1,"{270, 5731, 12, 1610, 1799, 1621, 897, 1153, 205}"
28,1,158,0,0.2321908,"\int \frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)}{d-c^2 d x^2} \, dx","Int[(x^4*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2),x]","\frac{b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{c^5 d}-\frac{b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{c^5 d}-\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2 d}-\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{c^4 d}+\frac{2 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^5 d}+\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1}}{9 c^3 d}+\frac{11 b \sqrt{c x-1} \sqrt{c x+1}}{9 c^5 d}","\frac{b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{c^5 d}-\frac{b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{c^5 d}-\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2 d}-\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{c^4 d}+\frac{2 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^5 d}+\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1}}{9 c^3 d}+\frac{11 b \sqrt{c x-1} \sqrt{c x+1}}{9 c^5 d}",1,"(11*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(9*c^5*d) + (b*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(9*c^3*d) - (x*(a + b*ArcCosh[c*x]))/(c^4*d) - (x^3*(a + b*ArcCosh[c*x]))/(3*c^2*d) + (2*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(c^5*d) + (b*PolyLog[2, -E^ArcCosh[c*x]])/(c^5*d) - (b*PolyLog[2, E^ArcCosh[c*x]])/(c^5*d)","A",12,8,25,0.3200,1,"{5766, 100, 12, 74, 5694, 4182, 2279, 2391}"
29,1,140,0,0.1978751,"\int \frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{d-c^2 d x^2} \, dx","Int[(x^3*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2),x]","-\frac{b \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{2 c^4 d}-\frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^2 d}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c^4 d}-\frac{\log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^4 d}+\frac{b x \sqrt{c x-1} \sqrt{c x+1}}{4 c^3 d}+\frac{b \cosh ^{-1}(c x)}{4 c^4 d}","-\frac{b \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{2 c^4 d}-\frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^2 d}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c^4 d}-\frac{\log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^4 d}+\frac{b x \sqrt{c x-1} \sqrt{c x+1}}{4 c^3 d}+\frac{b \cosh ^{-1}(c x)}{4 c^4 d}",1,"(b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*c^3*d) + (b*ArcCosh[c*x])/(4*c^4*d) - (x^2*(a + b*ArcCosh[c*x]))/(2*c^2*d) + (a + b*ArcCosh[c*x])^2/(2*b*c^4*d) - ((a + b*ArcCosh[c*x])*Log[1 - E^(2*ArcCosh[c*x])])/(c^4*d) - (b*PolyLog[2, E^(2*ArcCosh[c*x])])/(2*c^4*d)","A",8,8,25,0.3200,1,"{5766, 90, 52, 5715, 3716, 2190, 2279, 2391}"
30,1,102,0,0.1377698,"\int \frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)}{d-c^2 d x^2} \, dx","Int[(x^2*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2),x]","\frac{b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{c^3 d}-\frac{b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{c^3 d}-\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{c^2 d}+\frac{2 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^3 d}+\frac{b \sqrt{c x-1} \sqrt{c x+1}}{c^3 d}","\frac{b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{c^3 d}-\frac{b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{c^3 d}-\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{c^2 d}+\frac{2 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^3 d}+\frac{b \sqrt{c x-1} \sqrt{c x+1}}{c^3 d}",1,"(b*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(c^3*d) - (x*(a + b*ArcCosh[c*x]))/(c^2*d) + (2*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(c^3*d) + (b*PolyLog[2, -E^ArcCosh[c*x]])/(c^3*d) - (b*PolyLog[2, E^ArcCosh[c*x]])/(c^3*d)","A",8,6,25,0.2400,1,"{5766, 74, 5694, 4182, 2279, 2391}"
31,1,74,0,0.1162869,"\int \frac{x \left(a+b \cosh ^{-1}(c x)\right)}{d-c^2 d x^2} \, dx","Int[(x*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2),x]","-\frac{b \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{2 c^2 d}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c^2 d}-\frac{\log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 d}","-\frac{b \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{2 c^2 d}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c^2 d}-\frac{\log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 d}",1,"(a + b*ArcCosh[c*x])^2/(2*b*c^2*d) - ((a + b*ArcCosh[c*x])*Log[1 - E^(2*ArcCosh[c*x])])/(c^2*d) - (b*PolyLog[2, E^(2*ArcCosh[c*x])])/(2*c^2*d)","A",5,5,23,0.2174,1,"{5715, 3716, 2190, 2279, 2391}"
32,1,59,0,0.0653781,"\int \frac{a+b \cosh ^{-1}(c x)}{d-c^2 d x^2} \, dx","Int[(a + b*ArcCosh[c*x])/(d - c^2*d*x^2),x]","\frac{b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{c d}-\frac{b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{c d}+\frac{2 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c d}","\frac{b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{c d}-\frac{b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{c d}+\frac{2 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c d}",1,"(2*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(c*d) + (b*PolyLog[2, -E^ArcCosh[c*x]])/(c*d) - (b*PolyLog[2, E^ArcCosh[c*x]])/(c*d)","A",6,4,22,0.1818,1,"{5694, 4182, 2279, 2391}"
33,1,61,0,0.1266029,"\int \frac{a+b \cosh ^{-1}(c x)}{x \left(d-c^2 d x^2\right)} \, dx","Int[(a + b*ArcCosh[c*x])/(x*(d - c^2*d*x^2)),x]","\frac{b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{2 d}+\frac{2 \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d}","\frac{b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{2 d}+\frac{2 \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d}",1,"(2*(a + b*ArcCosh[c*x])*ArcTanh[E^(2*ArcCosh[c*x])])/d + (b*PolyLog[2, -E^(2*ArcCosh[c*x])])/(2*d) - (b*PolyLog[2, E^(2*ArcCosh[c*x])])/(2*d)","A",7,5,25,0.2000,1,"{5721, 5461, 4182, 2279, 2391}"
34,1,95,0,0.1398018,"\int \frac{a+b \cosh ^{-1}(c x)}{x^2 \left(d-c^2 d x^2\right)} \, dx","Int[(a + b*ArcCosh[c*x])/(x^2*(d - c^2*d*x^2)),x]","\frac{b c \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{d}-\frac{b c \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{d}-\frac{a+b \cosh ^{-1}(c x)}{d x}+\frac{2 c \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d}+\frac{b c \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{d}","\frac{b c \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{d}-\frac{b c \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{d}-\frac{a+b \cosh ^{-1}(c x)}{d x}+\frac{2 c \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d}+\frac{b c \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{d}",1,"-((a + b*ArcCosh[c*x])/(d*x)) + (b*c*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/d + (2*c*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/d + (b*c*PolyLog[2, -E^ArcCosh[c*x]])/d - (b*c*PolyLog[2, E^ArcCosh[c*x]])/d","A",9,7,25,0.2800,1,"{5746, 92, 205, 5694, 4182, 2279, 2391}"
35,1,118,0,0.1972703,"\int \frac{a+b \cosh ^{-1}(c x)}{x^3 \left(d-c^2 d x^2\right)} \, dx","Int[(a + b*ArcCosh[c*x])/(x^3*(d - c^2*d*x^2)),x]","\frac{b c^2 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{2 d}-\frac{b c^2 \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{2 d}+\frac{2 c^2 \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d}-\frac{a+b \cosh ^{-1}(c x)}{2 d x^2}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 d x}","\frac{b c^2 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{2 d}-\frac{b c^2 \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{2 d}+\frac{2 c^2 \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d}-\frac{a+b \cosh ^{-1}(c x)}{2 d x^2}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 d x}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*d*x) - (a + b*ArcCosh[c*x])/(2*d*x^2) + (2*c^2*(a + b*ArcCosh[c*x])*ArcTanh[E^(2*ArcCosh[c*x])])/d + (b*c^2*PolyLog[2, -E^(2*ArcCosh[c*x])])/(2*d) - (b*c^2*PolyLog[2, E^(2*ArcCosh[c*x])])/(2*d)","A",9,7,25,0.2800,1,"{5746, 95, 5721, 5461, 4182, 2279, 2391}"
36,1,157,0,0.2344056,"\int \frac{a+b \cosh ^{-1}(c x)}{x^4 \left(d-c^2 d x^2\right)} \, dx","Int[(a + b*ArcCosh[c*x])/(x^4*(d - c^2*d*x^2)),x]","\frac{b c^3 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{d}-\frac{b c^3 \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{d}-\frac{c^2 \left(a+b \cosh ^{-1}(c x)\right)}{d x}+\frac{2 c^3 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d}-\frac{a+b \cosh ^{-1}(c x)}{3 d x^3}+\frac{7 b c^3 \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{6 d}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{6 d x^2}","\frac{b c^3 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{d}-\frac{b c^3 \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{d}-\frac{c^2 \left(a+b \cosh ^{-1}(c x)\right)}{d x}+\frac{2 c^3 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d}-\frac{a+b \cosh ^{-1}(c x)}{3 d x^3}+\frac{7 b c^3 \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{6 d}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{6 d x^2}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*d*x^2) - (a + b*ArcCosh[c*x])/(3*d*x^3) - (c^2*(a + b*ArcCosh[c*x]))/(d*x) + (7*b*c^3*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/(6*d) + (2*c^3*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/d + (b*c^3*PolyLog[2, -E^ArcCosh[c*x]])/d - (b*c^3*PolyLog[2, E^ArcCosh[c*x]])/d","A",14,9,25,0.3600,1,"{5746, 103, 12, 92, 205, 5694, 4182, 2279, 2391}"
37,1,177,0,0.2253767,"\int \frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(x^4*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^2,x]","-\frac{3 b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{2 c^5 d^2}+\frac{3 b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{2 c^5 d^2}+\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^2 d^2 \left(1-c^2 x^2\right)}+\frac{3 x \left(a+b \cosh ^{-1}(c x)\right)}{2 c^4 d^2}-\frac{3 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^5 d^2}-\frac{b x^2}{2 c^3 d^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{c x-1} \sqrt{c x+1}}{2 c^5 d^2}","-\frac{3 b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{2 c^5 d^2}+\frac{3 b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{2 c^5 d^2}+\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^2 d^2 \left(1-c^2 x^2\right)}+\frac{3 x \left(a+b \cosh ^{-1}(c x)\right)}{2 c^4 d^2}-\frac{3 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^5 d^2}-\frac{b x^2}{2 c^3 d^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{c x-1} \sqrt{c x+1}}{2 c^5 d^2}",1,"-(b*x^2)/(2*c^3*d^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*c^5*d^2) + (3*x*(a + b*ArcCosh[c*x]))/(2*c^4*d^2) + (x^3*(a + b*ArcCosh[c*x]))/(2*c^2*d^2*(1 - c^2*x^2)) - (3*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(c^5*d^2) - (3*b*PolyLog[2, -E^ArcCosh[c*x]])/(2*c^5*d^2) + (3*b*PolyLog[2, E^ArcCosh[c*x]])/(2*c^5*d^2)","A",12,9,25,0.3600,1,"{5750, 98, 21, 74, 5766, 5694, 4182, 2279, 2391}"
38,1,179,0,0.2042984,"\int \frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(x^3*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^2,x]","\frac{b \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{2 c^4 d^2}+\frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^2 d^2 \left(1-c^2 x^2\right)}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c^4 d^2}+\frac{\log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^4 d^2}-\frac{b \sqrt{c x-1}}{2 c^4 d^2 \sqrt{c x+1}}-\frac{b}{2 c^4 d^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \cosh ^{-1}(c x)}{2 c^4 d^2}","\frac{b \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{2 c^4 d^2}+\frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^2 d^2 \left(1-c^2 x^2\right)}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c^4 d^2}+\frac{\log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^4 d^2}-\frac{b \sqrt{c x-1}}{2 c^4 d^2 \sqrt{c x+1}}-\frac{b}{2 c^4 d^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \cosh ^{-1}(c x)}{2 c^4 d^2}",1,"-b/(2*c^4*d^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*Sqrt[-1 + c*x])/(2*c^4*d^2*Sqrt[1 + c*x]) + (b*ArcCosh[c*x])/(2*c^4*d^2) + (x^2*(a + b*ArcCosh[c*x]))/(2*c^2*d^2*(1 - c^2*x^2)) - (a + b*ArcCosh[c*x])^2/(2*b*c^4*d^2) + ((a + b*ArcCosh[c*x])*Log[1 - E^(2*ArcCosh[c*x])])/(c^4*d^2) + (b*PolyLog[2, E^(2*ArcCosh[c*x])])/(2*c^4*d^2)","A",10,10,25,0.4000,1,"{5750, 89, 12, 78, 52, 5715, 3716, 2190, 2279, 2391}"
39,1,124,0,0.1353973,"\int \frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(x^2*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^2,x]","-\frac{b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{2 c^3 d^2}+\frac{b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{2 c^3 d^2}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{2 c^2 d^2 \left(1-c^2 x^2\right)}-\frac{\tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^3 d^2}-\frac{b}{2 c^3 d^2 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{2 c^3 d^2}+\frac{b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{2 c^3 d^2}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{2 c^2 d^2 \left(1-c^2 x^2\right)}-\frac{\tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^3 d^2}-\frac{b}{2 c^3 d^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"-b/(2*c^3*d^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (x*(a + b*ArcCosh[c*x]))/(2*c^2*d^2*(1 - c^2*x^2)) - ((a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(c^3*d^2) - (b*PolyLog[2, -E^ArcCosh[c*x]])/(2*c^3*d^2) + (b*PolyLog[2, E^ArcCosh[c*x]])/(2*c^3*d^2)","A",8,6,25,0.2400,1,"{5750, 74, 5694, 4182, 2279, 2391}"
40,1,61,0,0.0521277,"\int \frac{x \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(x*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^2,x]","\frac{a+b \cosh ^{-1}(c x)}{2 c^2 d^2 \left(1-c^2 x^2\right)}-\frac{b x}{2 c d^2 \sqrt{c x-1} \sqrt{c x+1}}","\frac{a+b \cosh ^{-1}(c x)}{2 c^2 d^2 \left(1-c^2 x^2\right)}-\frac{b x}{2 c d^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*x)/(2*c*d^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (a + b*ArcCosh[c*x])/(2*c^2*d^2*(1 - c^2*x^2))","A",2,2,23,0.08696,1,"{5716, 39}"
41,1,120,0,0.0946673,"\int \frac{a+b \cosh ^{-1}(c x)}{\left(d-c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcCosh[c*x])/(d - c^2*d*x^2)^2,x]","\frac{b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{2 c d^2}-\frac{b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{2 c d^2}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{2 d^2 \left(1-c^2 x^2\right)}+\frac{\tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c d^2}-\frac{b}{2 c d^2 \sqrt{c x-1} \sqrt{c x+1}}","\frac{b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{2 c d^2}-\frac{b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{2 c d^2}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{2 d^2 \left(1-c^2 x^2\right)}+\frac{\tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c d^2}-\frac{b}{2 c d^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"-b/(2*c*d^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (x*(a + b*ArcCosh[c*x]))/(2*d^2*(1 - c^2*x^2)) + ((a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(c*d^2) + (b*PolyLog[2, -E^ArcCosh[c*x]])/(2*c*d^2) - (b*PolyLog[2, E^ArcCosh[c*x]])/(2*c*d^2)","A",8,6,22,0.2727,1,"{5689, 74, 5694, 4182, 2279, 2391}"
42,1,116,0,0.1795955,"\int \frac{a+b \cosh ^{-1}(c x)}{x \left(d-c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcCosh[c*x])/(x*(d - c^2*d*x^2)^2),x]","\frac{b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{2 d^2}+\frac{a+b \cosh ^{-1}(c x)}{2 d^2 \left(1-c^2 x^2\right)}+\frac{2 \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2}-\frac{b c x}{2 d^2 \sqrt{c x-1} \sqrt{c x+1}}","\frac{b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{2 d^2}+\frac{a+b \cosh ^{-1}(c x)}{2 d^2 \left(1-c^2 x^2\right)}+\frac{2 \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2}-\frac{b c x}{2 d^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*x)/(2*d^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (a + b*ArcCosh[c*x])/(2*d^2*(1 - c^2*x^2)) + (2*(a + b*ArcCosh[c*x])*ArcTanh[E^(2*ArcCosh[c*x])])/d^2 + (b*PolyLog[2, -E^(2*ArcCosh[c*x])])/(2*d^2) - (b*PolyLog[2, E^(2*ArcCosh[c*x])])/(2*d^2)","A",9,7,25,0.2800,1,"{5754, 5721, 5461, 4182, 2279, 2391, 39}"
43,1,170,0,0.1840925,"\int \frac{a+b \cosh ^{-1}(c x)}{x^2 \left(d-c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcCosh[c*x])/(x^2*(d - c^2*d*x^2)^2),x]","\frac{3 b c \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{2 d^2}-\frac{3 b c \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{2 d^2}+\frac{3 c^2 x \left(a+b \cosh ^{-1}(c x)\right)}{2 d^2 \left(1-c^2 x^2\right)}-\frac{a+b \cosh ^{-1}(c x)}{d^2 x \left(1-c^2 x^2\right)}+\frac{3 c \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2}-\frac{b c}{2 d^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{d^2}","\frac{3 b c \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{2 d^2}-\frac{3 b c \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{2 d^2}+\frac{3 c^2 x \left(a+b \cosh ^{-1}(c x)\right)}{2 d^2 \left(1-c^2 x^2\right)}-\frac{a+b \cosh ^{-1}(c x)}{d^2 x \left(1-c^2 x^2\right)}+\frac{3 c \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2}-\frac{b c}{2 d^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{d^2}",1,"-(b*c)/(2*d^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (a + b*ArcCosh[c*x])/(d^2*x*(1 - c^2*x^2)) + (3*c^2*x*(a + b*ArcCosh[c*x]))/(2*d^2*(1 - c^2*x^2)) + (b*c*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/d^2 + (3*c*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/d^2 + (3*b*c*PolyLog[2, -E^ArcCosh[c*x]])/(2*d^2) - (3*b*c*PolyLog[2, E^ArcCosh[c*x]])/(2*d^2)","A",13,11,25,0.4400,1,"{5746, 104, 21, 92, 205, 5689, 74, 5694, 4182, 2279, 2391}"
44,1,152,0,0.2616217,"\int \frac{a+b \cosh ^{-1}(c x)}{x^3 \left(d-c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcCosh[c*x])/(x^3*(d - c^2*d*x^2)^2),x]","\frac{b c^2 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{d^2}-\frac{b c^2 \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{d^2}+\frac{c^2 \left(a+b \cosh ^{-1}(c x)\right)}{d^2 \left(1-c^2 x^2\right)}-\frac{a+b \cosh ^{-1}(c x)}{2 d^2 x^2 \left(1-c^2 x^2\right)}+\frac{4 c^2 \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2}-\frac{b c}{2 d^2 x \sqrt{c x-1} \sqrt{c x+1}}","\frac{b c^2 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{d^2}-\frac{b c^2 \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{d^2}+\frac{c^2 \left(a+b \cosh ^{-1}(c x)\right)}{d^2 \left(1-c^2 x^2\right)}-\frac{a+b \cosh ^{-1}(c x)}{2 d^2 x^2 \left(1-c^2 x^2\right)}+\frac{4 c^2 \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2}-\frac{b c}{2 d^2 x \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c)/(2*d^2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (c^2*(a + b*ArcCosh[c*x]))/(d^2*(1 - c^2*x^2)) - (a + b*ArcCosh[c*x])/(2*d^2*x^2*(1 - c^2*x^2)) + (4*c^2*(a + b*ArcCosh[c*x])*ArcTanh[E^(2*ArcCosh[c*x])])/d^2 + (b*c^2*PolyLog[2, -E^(2*ArcCosh[c*x])])/d^2 - (b*c^2*PolyLog[2, E^(2*ArcCosh[c*x])])/d^2","A",13,10,25,0.4000,1,"{5746, 103, 12, 39, 5754, 5721, 5461, 4182, 2279, 2391}"
45,1,248,0,0.2908072,"\int \frac{a+b \cosh ^{-1}(c x)}{x^4 \left(d-c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcCosh[c*x])/(x^4*(d - c^2*d*x^2)^2),x]","\frac{5 b c^3 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{2 d^2}-\frac{5 b c^3 \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{2 d^2}+\frac{5 c^4 x \left(a+b \cosh ^{-1}(c x)\right)}{2 d^2 \left(1-c^2 x^2\right)}-\frac{5 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 x \left(1-c^2 x^2\right)}-\frac{a+b \cosh ^{-1}(c x)}{3 d^2 x^3 \left(1-c^2 x^2\right)}+\frac{5 c^3 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2}-\frac{b c^3}{3 d^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{13 b c^3 \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{6 d^2}-\frac{b c}{6 d^2 x^2 \sqrt{c x-1} \sqrt{c x+1}}","\frac{5 b c^3 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{2 d^2}-\frac{5 b c^3 \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{2 d^2}+\frac{5 c^4 x \left(a+b \cosh ^{-1}(c x)\right)}{2 d^2 \left(1-c^2 x^2\right)}-\frac{5 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 x \left(1-c^2 x^2\right)}-\frac{a+b \cosh ^{-1}(c x)}{3 d^2 x^3 \left(1-c^2 x^2\right)}+\frac{5 c^3 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2}-\frac{b c^3}{3 d^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{13 b c^3 \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{6 d^2}-\frac{b c}{6 d^2 x^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c^3)/(3*d^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c)/(6*d^2*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (a + b*ArcCosh[c*x])/(3*d^2*x^3*(1 - c^2*x^2)) - (5*c^2*(a + b*ArcCosh[c*x]))/(3*d^2*x*(1 - c^2*x^2)) + (5*c^4*x*(a + b*ArcCosh[c*x]))/(2*d^2*(1 - c^2*x^2)) + (13*b*c^3*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/(6*d^2) + (5*c^3*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/d^2 + (5*b*c^3*PolyLog[2, -E^ArcCosh[c*x]])/(2*d^2) - (5*b*c^3*PolyLog[2, E^ArcCosh[c*x]])/(2*d^2)","A",20,13,25,0.5200,1,"{5746, 103, 12, 104, 21, 92, 205, 5689, 74, 5694, 4182, 2279, 2391}"
46,1,249,0,0.2392204,"\int \frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(x^4*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^3,x]","\frac{3 b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{8 c^5 d^3}-\frac{3 b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{8 c^5 d^3}+\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}-\frac{3 x \left(a+b \cosh ^{-1}(c x)\right)}{8 c^4 d^3 \left(1-c^2 x^2\right)}+\frac{3 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 c^5 d^3}+\frac{b x^3}{12 c^2 d^3 (c x-1)^{3/2} (c x+1)^{3/2}}+\frac{3 b}{8 c^5 d^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b (c x-1)^{3/2}}{12 c^5 d^3 (c x+1)^{3/2}}+\frac{b}{4 c^5 d^3 \sqrt{c x-1} (c x+1)^{3/2}}","\frac{3 b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{8 c^5 d^3}-\frac{3 b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{8 c^5 d^3}+\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}-\frac{3 x \left(a+b \cosh ^{-1}(c x)\right)}{8 c^4 d^3 \left(1-c^2 x^2\right)}+\frac{3 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 c^5 d^3}+\frac{b x^3}{12 c^2 d^3 (c x-1)^{3/2} (c x+1)^{3/2}}+\frac{3 b}{8 c^5 d^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b (c x-1)^{3/2}}{12 c^5 d^3 (c x+1)^{3/2}}+\frac{b}{4 c^5 d^3 \sqrt{c x-1} (c x+1)^{3/2}}",1,"(b*x^3)/(12*c^2*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) + b/(4*c^5*d^3*Sqrt[-1 + c*x]*(1 + c*x)^(3/2)) - (b*(-1 + c*x)^(3/2))/(12*c^5*d^3*(1 + c*x)^(3/2)) + (3*b)/(8*c^5*d^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (x^3*(a + b*ArcCosh[c*x]))/(4*c^2*d^3*(1 - c^2*x^2)^2) - (3*x*(a + b*ArcCosh[c*x]))/(8*c^4*d^3*(1 - c^2*x^2)) + (3*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(4*c^5*d^3) + (3*b*PolyLog[2, -E^ArcCosh[c*x]])/(8*c^5*d^3) - (3*b*PolyLog[2, E^ArcCosh[c*x]])/(8*c^5*d^3)","A",13,10,25,0.4000,1,"{5750, 94, 89, 21, 37, 74, 5694, 4182, 2279, 2391}"
47,1,136,0,0.1049135,"\int \frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(x^3*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^3,x]","\frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}+\frac{b \sqrt{c x-1}}{4 c^4 d^3 \sqrt{c x+1}}+\frac{b}{4 c^4 d^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \cosh ^{-1}(c x)}{4 c^4 d^3}+\frac{b x^3}{12 c d^3 (c x-1)^{3/2} (c x+1)^{3/2}}","\frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}+\frac{b \sqrt{c x-1}}{4 c^4 d^3 \sqrt{c x+1}}+\frac{b}{4 c^4 d^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \cosh ^{-1}(c x)}{4 c^4 d^3}+\frac{b x^3}{12 c d^3 (c x-1)^{3/2} (c x+1)^{3/2}}",1,"(b*x^3)/(12*c*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) + b/(4*c^4*d^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*Sqrt[-1 + c*x])/(4*c^4*d^3*Sqrt[1 + c*x]) - (b*ArcCosh[c*x])/(4*c^4*d^3) + (x^4*(a + b*ArcCosh[c*x]))/(4*d^3*(1 - c^2*x^2)^2)","A",7,7,25,0.2800,1,"{5722, 98, 21, 89, 12, 78, 52}"
48,1,186,0,0.1793576,"\int \frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(x^2*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^3,x]","-\frac{b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{8 c^3 d^3}+\frac{b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{8 c^3 d^3}-\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{8 c^2 d^3 \left(1-c^2 x^2\right)}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}-\frac{\tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 c^3 d^3}+\frac{b}{8 c^3 d^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b}{12 c^3 d^3 (c x-1)^{3/2} (c x+1)^{3/2}}","-\frac{b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{8 c^3 d^3}+\frac{b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{8 c^3 d^3}-\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{8 c^2 d^3 \left(1-c^2 x^2\right)}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}-\frac{\tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 c^3 d^3}+\frac{b}{8 c^3 d^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b}{12 c^3 d^3 (c x-1)^{3/2} (c x+1)^{3/2}}",1,"b/(12*c^3*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) + b/(8*c^3*d^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (x*(a + b*ArcCosh[c*x]))/(4*c^2*d^3*(1 - c^2*x^2)^2) - (x*(a + b*ArcCosh[c*x]))/(8*c^2*d^3*(1 - c^2*x^2)) - ((a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(4*c^3*d^3) - (b*PolyLog[2, -E^ArcCosh[c*x]])/(8*c^3*d^3) + (b*PolyLog[2, E^ArcCosh[c*x]])/(8*c^3*d^3)","A",10,7,25,0.2800,1,"{5750, 74, 5689, 5694, 4182, 2279, 2391}"
49,1,91,0,0.0582914,"\int \frac{x \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(x*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^3,x]","\frac{a+b \cosh ^{-1}(c x)}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}-\frac{b x}{6 c d^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x}{12 c d^3 (c x-1)^{3/2} (c x+1)^{3/2}}","\frac{a+b \cosh ^{-1}(c x)}{4 c^2 d^3 \left(1-c^2 x^2\right)^2}-\frac{b x}{6 c d^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x}{12 c d^3 (c x-1)^{3/2} (c x+1)^{3/2}}",1,"(b*x)/(12*c*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) - (b*x)/(6*c*d^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (a + b*ArcCosh[c*x])/(4*c^2*d^3*(1 - c^2*x^2)^2)","A",3,3,23,0.1304,1,"{5716, 40, 39}"
50,1,180,0,0.134077,"\int \frac{a+b \cosh ^{-1}(c x)}{\left(d-c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcCosh[c*x])/(d - c^2*d*x^2)^3,x]","\frac{3 b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{8 c d^3}-\frac{3 b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{8 c d^3}+\frac{3 x \left(a+b \cosh ^{-1}(c x)\right)}{8 d^3 \left(1-c^2 x^2\right)}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}+\frac{3 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 c d^3}-\frac{3 b}{8 c d^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b}{12 c d^3 (c x-1)^{3/2} (c x+1)^{3/2}}","\frac{3 b \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{8 c d^3}-\frac{3 b \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{8 c d^3}+\frac{3 x \left(a+b \cosh ^{-1}(c x)\right)}{8 d^3 \left(1-c^2 x^2\right)}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}+\frac{3 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 c d^3}-\frac{3 b}{8 c d^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b}{12 c d^3 (c x-1)^{3/2} (c x+1)^{3/2}}",1,"b/(12*c*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) - (3*b)/(8*c*d^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (x*(a + b*ArcCosh[c*x]))/(4*d^3*(1 - c^2*x^2)^2) + (3*x*(a + b*ArcCosh[c*x]))/(8*d^3*(1 - c^2*x^2)) + (3*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(4*c*d^3) + (3*b*PolyLog[2, -E^ArcCosh[c*x]])/(8*c*d^3) - (3*b*PolyLog[2, E^ArcCosh[c*x]])/(8*c*d^3)","A",10,6,22,0.2727,1,"{5689, 74, 5694, 4182, 2279, 2391}"
51,1,171,0,0.2607959,"\int \frac{a+b \cosh ^{-1}(c x)}{x \left(d-c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcCosh[c*x])/(x*(d - c^2*d*x^2)^3),x]","\frac{b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{2 d^3}+\frac{a+b \cosh ^{-1}(c x)}{2 d^3 \left(1-c^2 x^2\right)}+\frac{a+b \cosh ^{-1}(c x)}{4 d^3 \left(1-c^2 x^2\right)^2}+\frac{2 \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^3}-\frac{2 b c x}{3 d^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c x}{12 d^3 (c x-1)^{3/2} (c x+1)^{3/2}}","\frac{b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{2 d^3}+\frac{a+b \cosh ^{-1}(c x)}{2 d^3 \left(1-c^2 x^2\right)}+\frac{a+b \cosh ^{-1}(c x)}{4 d^3 \left(1-c^2 x^2\right)^2}+\frac{2 \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^3}-\frac{2 b c x}{3 d^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c x}{12 d^3 (c x-1)^{3/2} (c x+1)^{3/2}}",1,"(b*c*x)/(12*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) - (2*b*c*x)/(3*d^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (a + b*ArcCosh[c*x])/(4*d^3*(1 - c^2*x^2)^2) + (a + b*ArcCosh[c*x])/(2*d^3*(1 - c^2*x^2)) + (2*(a + b*ArcCosh[c*x])*ArcTanh[E^(2*ArcCosh[c*x])])/d^3 + (b*PolyLog[2, -E^(2*ArcCosh[c*x])])/(2*d^3) - (b*PolyLog[2, E^(2*ArcCosh[c*x])])/(2*d^3)","A",12,8,25,0.3200,1,"{5754, 5721, 5461, 4182, 2279, 2391, 39, 40}"
52,1,230,0,0.2444663,"\int \frac{a+b \cosh ^{-1}(c x)}{x^2 \left(d-c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcCosh[c*x])/(x^2*(d - c^2*d*x^2)^3),x]","\frac{15 b c \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{8 d^3}-\frac{15 b c \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{8 d^3}+\frac{15 c^2 x \left(a+b \cosh ^{-1}(c x)\right)}{8 d^3 \left(1-c^2 x^2\right)}+\frac{5 c^2 x \left(a+b \cosh ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{a+b \cosh ^{-1}(c x)}{d^3 x \left(1-c^2 x^2\right)^2}+\frac{15 c \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 d^3}-\frac{7 b c}{8 d^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c}{12 d^3 (c x-1)^{3/2} (c x+1)^{3/2}}+\frac{b c \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{d^3}","\frac{15 b c \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{8 d^3}-\frac{15 b c \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{8 d^3}+\frac{15 c^2 x \left(a+b \cosh ^{-1}(c x)\right)}{8 d^3 \left(1-c^2 x^2\right)}+\frac{5 c^2 x \left(a+b \cosh ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{a+b \cosh ^{-1}(c x)}{d^3 x \left(1-c^2 x^2\right)^2}+\frac{15 c \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 d^3}-\frac{7 b c}{8 d^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c}{12 d^3 (c x-1)^{3/2} (c x+1)^{3/2}}+\frac{b c \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{d^3}",1,"(b*c)/(12*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) - (7*b*c)/(8*d^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (a + b*ArcCosh[c*x])/(d^3*x*(1 - c^2*x^2)^2) + (5*c^2*x*(a + b*ArcCosh[c*x]))/(4*d^3*(1 - c^2*x^2)^2) + (15*c^2*x*(a + b*ArcCosh[c*x]))/(8*d^3*(1 - c^2*x^2)) + (b*c*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/d^3 + (15*c*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(4*d^3) + (15*b*c*PolyLog[2, -E^ArcCosh[c*x]])/(8*d^3) - (15*b*c*PolyLog[2, E^ArcCosh[c*x]])/(8*d^3)","A",17,11,25,0.4400,1,"{5746, 104, 21, 92, 205, 5689, 74, 5694, 4182, 2279, 2391}"
53,1,250,0,0.3668516,"\int \frac{a+b \cosh ^{-1}(c x)}{x^3 \left(d-c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcCosh[c*x])/(x^3*(d - c^2*d*x^2)^3),x]","\frac{3 b c^2 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{2 d^3}-\frac{3 b c^2 \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{2 d^3}+\frac{3 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 d^3 \left(1-c^2 x^2\right)}+\frac{3 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{a+b \cosh ^{-1}(c x)}{2 d^3 x^2 \left(1-c^2 x^2\right)^2}+\frac{6 c^2 \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^3}-\frac{2 b c^3 x}{3 d^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b c^3 x}{12 d^3 (c x-1)^{3/2} (c x+1)^{3/2}}+\frac{b c}{2 d^3 x (c x-1)^{3/2} (c x+1)^{3/2}}","\frac{3 b c^2 \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{2 d^3}-\frac{3 b c^2 \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{2 d^3}+\frac{3 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 d^3 \left(1-c^2 x^2\right)}+\frac{3 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{4 d^3 \left(1-c^2 x^2\right)^2}-\frac{a+b \cosh ^{-1}(c x)}{2 d^3 x^2 \left(1-c^2 x^2\right)^2}+\frac{6 c^2 \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^3}-\frac{2 b c^3 x}{3 d^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b c^3 x}{12 d^3 (c x-1)^{3/2} (c x+1)^{3/2}}+\frac{b c}{2 d^3 x (c x-1)^{3/2} (c x+1)^{3/2}}",1,"(b*c)/(2*d^3*x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) - (5*b*c^3*x)/(12*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) - (2*b*c^3*x)/(3*d^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*c^2*(a + b*ArcCosh[c*x]))/(4*d^3*(1 - c^2*x^2)^2) - (a + b*ArcCosh[c*x])/(2*d^3*x^2*(1 - c^2*x^2)^2) + (3*c^2*(a + b*ArcCosh[c*x]))/(2*d^3*(1 - c^2*x^2)) + (6*c^2*(a + b*ArcCosh[c*x])*ArcTanh[E^(2*ArcCosh[c*x])])/d^3 + (3*b*c^2*PolyLog[2, -E^(2*ArcCosh[c*x])])/(2*d^3) - (3*b*c^2*PolyLog[2, E^(2*ArcCosh[c*x])])/(2*d^3)","A",17,11,25,0.4400,1,"{5746, 103, 12, 40, 39, 5754, 5721, 5461, 4182, 2279, 2391}"
54,1,310,0,0.3870416,"\int \frac{a+b \cosh ^{-1}(c x)}{x^4 \left(d-c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcCosh[c*x])/(x^4*(d - c^2*d*x^2)^3),x]","\frac{35 b c^3 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{8 d^3}-\frac{35 b c^3 \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{8 d^3}+\frac{35 c^4 x \left(a+b \cosh ^{-1}(c x)\right)}{8 d^3 \left(1-c^2 x^2\right)}+\frac{35 c^4 x \left(a+b \cosh ^{-1}(c x)\right)}{12 d^3 \left(1-c^2 x^2\right)^2}-\frac{7 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{3 d^3 x \left(1-c^2 x^2\right)^2}-\frac{a+b \cosh ^{-1}(c x)}{3 d^3 x^3 \left(1-c^2 x^2\right)^2}+\frac{35 c^3 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 d^3}-\frac{29 b c^3}{24 d^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^3}{12 d^3 (c x-1)^{3/2} (c x+1)^{3/2}}+\frac{19 b c^3 \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{6 d^3}+\frac{b c}{6 d^3 x^2 (c x-1)^{3/2} (c x+1)^{3/2}}","\frac{35 b c^3 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{8 d^3}-\frac{35 b c^3 \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{8 d^3}+\frac{35 c^4 x \left(a+b \cosh ^{-1}(c x)\right)}{8 d^3 \left(1-c^2 x^2\right)}+\frac{35 c^4 x \left(a+b \cosh ^{-1}(c x)\right)}{12 d^3 \left(1-c^2 x^2\right)^2}-\frac{7 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{3 d^3 x \left(1-c^2 x^2\right)^2}-\frac{a+b \cosh ^{-1}(c x)}{3 d^3 x^3 \left(1-c^2 x^2\right)^2}+\frac{35 c^3 \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 d^3}-\frac{29 b c^3}{24 d^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^3}{12 d^3 (c x-1)^{3/2} (c x+1)^{3/2}}+\frac{19 b c^3 \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{6 d^3}+\frac{b c}{6 d^3 x^2 (c x-1)^{3/2} (c x+1)^{3/2}}",1,"-(b*c^3)/(12*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) + (b*c)/(6*d^3*x^2*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) - (29*b*c^3)/(24*d^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (a + b*ArcCosh[c*x])/(3*d^3*x^3*(1 - c^2*x^2)^2) - (7*c^2*(a + b*ArcCosh[c*x]))/(3*d^3*x*(1 - c^2*x^2)^2) + (35*c^4*x*(a + b*ArcCosh[c*x]))/(12*d^3*(1 - c^2*x^2)^2) + (35*c^4*x*(a + b*ArcCosh[c*x]))/(8*d^3*(1 - c^2*x^2)) + (19*b*c^3*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/(6*d^3) + (35*c^3*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(4*d^3) + (35*b*c^3*PolyLog[2, -E^ArcCosh[c*x]])/(8*d^3) - (35*b*c^3*PolyLog[2, E^ArcCosh[c*x]])/(8*d^3)","A",26,13,25,0.5200,1,"{5746, 103, 12, 104, 21, 92, 205, 5689, 74, 5694, 4182, 2279, 2391}"
55,1,53,0,0.0519342,"\int \frac{\cosh ^{-1}(a x)}{c-a^2 c x^2} \, dx","Int[ArcCosh[a*x]/(c - a^2*c*x^2),x]","\frac{\text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{a c}-\frac{\text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{a c}+\frac{2 \cosh ^{-1}(a x) \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{a c}","\frac{\text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{a c}-\frac{\text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{a c}+\frac{2 \cosh ^{-1}(a x) \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{a c}",1,"(2*ArcCosh[a*x]*ArcTanh[E^ArcCosh[a*x]])/(a*c) + PolyLog[2, -E^ArcCosh[a*x]]/(a*c) - PolyLog[2, E^ArcCosh[a*x]]/(a*c)","A",6,4,18,0.2222,1,"{5694, 4182, 2279, 2391}"
56,1,109,0,0.0804365,"\int \frac{\cosh ^{-1}(a x)}{\left(c-a^2 c x^2\right)^2} \, dx","Int[ArcCosh[a*x]/(c - a^2*c*x^2)^2,x]","\frac{\text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{2 a c^2}-\frac{\text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{2 a c^2}+\frac{x \cosh ^{-1}(a x)}{2 c^2 \left(1-a^2 x^2\right)}-\frac{1}{2 a c^2 \sqrt{a x-1} \sqrt{a x+1}}+\frac{\cosh ^{-1}(a x) \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{a c^2}","\frac{\text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{2 a c^2}-\frac{\text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{2 a c^2}+\frac{x \cosh ^{-1}(a x)}{2 c^2 \left(1-a^2 x^2\right)}-\frac{1}{2 a c^2 \sqrt{a x-1} \sqrt{a x+1}}+\frac{\cosh ^{-1}(a x) \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{a c^2}",1,"-1/(2*a*c^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (x*ArcCosh[a*x])/(2*c^2*(1 - a^2*x^2)) + (ArcCosh[a*x]*ArcTanh[E^ArcCosh[a*x]])/(a*c^2) + PolyLog[2, -E^ArcCosh[a*x]]/(2*a*c^2) - PolyLog[2, E^ArcCosh[a*x]]/(2*a*c^2)","A",8,6,18,0.3333,1,"{5689, 74, 5694, 4182, 2279, 2391}"
57,1,164,0,0.1128876,"\int \frac{\cosh ^{-1}(a x)}{\left(c-a^2 c x^2\right)^3} \, dx","Int[ArcCosh[a*x]/(c - a^2*c*x^2)^3,x]","\frac{3 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{8 a c^3}-\frac{3 \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{8 a c^3}+\frac{3 x \cosh ^{-1}(a x)}{8 c^3 \left(1-a^2 x^2\right)}+\frac{x \cosh ^{-1}(a x)}{4 c^3 \left(1-a^2 x^2\right)^2}-\frac{3}{8 a c^3 \sqrt{a x-1} \sqrt{a x+1}}+\frac{1}{12 a c^3 (a x-1)^{3/2} (a x+1)^{3/2}}+\frac{3 \cosh ^{-1}(a x) \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}","\frac{3 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{8 a c^3}-\frac{3 \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{8 a c^3}+\frac{3 x \cosh ^{-1}(a x)}{8 c^3 \left(1-a^2 x^2\right)}+\frac{x \cosh ^{-1}(a x)}{4 c^3 \left(1-a^2 x^2\right)^2}-\frac{3}{8 a c^3 \sqrt{a x-1} \sqrt{a x+1}}+\frac{1}{12 a c^3 (a x-1)^{3/2} (a x+1)^{3/2}}+\frac{3 \cosh ^{-1}(a x) \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}",1,"1/(12*a*c^3*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)) - 3/(8*a*c^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (x*ArcCosh[a*x])/(4*c^3*(1 - a^2*x^2)^2) + (3*x*ArcCosh[a*x])/(8*c^3*(1 - a^2*x^2)) + (3*ArcCosh[a*x]*ArcTanh[E^ArcCosh[a*x]])/(4*a*c^3) + (3*PolyLog[2, -E^ArcCosh[a*x]])/(8*a*c^3) - (3*PolyLog[2, E^ArcCosh[a*x]])/(8*a*c^3)","A",10,6,18,0.3333,1,"{5689, 74, 5694, 4182, 2279, 2391}"
58,1,278,0,0.7823052,"\int x^4 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]),x]","\frac{1}{6} x^5 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{24 c^2}-\frac{x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{16 c^4}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c^5 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c x^6 \sqrt{d-c^2 d x^2}}{36 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x^4 \sqrt{d-c^2 d x^2}}{96 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x^2 \sqrt{d-c^2 d x^2}}{32 c^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{6} x^5 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{24 c^2}-\frac{x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{16 c^4}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c^5 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c x^6 \sqrt{d-c^2 d x^2}}{36 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x^4 \sqrt{d-c^2 d x^2}}{96 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x^2 \sqrt{d-c^2 d x^2}}{32 c^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*x^2*Sqrt[d - c^2*d*x^2])/(32*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*x^4*Sqrt[d - c^2*d*x^2])/(96*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*x^6*Sqrt[d - c^2*d*x^2])/(36*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(16*c^4) - (x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(24*c^2) + (x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/6 - (Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(32*b*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",8,5,27,0.1852,1,"{5798, 5743, 5759, 5676, 30}"
59,1,201,0,0.5789399,"\int x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]),x]","\frac{1}{4} x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 c^2}-\frac{\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 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{4} x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 c^2}-\frac{\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 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*x^2*Sqrt[d - c^2*d*x^2])/(16*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(8*c^2) + (x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/4 - (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",6,5,27,0.1852,1,"{5798, 5743, 5759, 5676, 30}"
60,1,124,0,0.2041539,"\int \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]),x]","\frac{1}{2} x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{\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{b c x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{2} x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{\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{b c x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*x^2*Sqrt[d - c^2*d*x^2])/(4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/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])","A",4,4,24,0.1667,1,"{5713, 5683, 5676, 30}"
61,1,118,0,0.367616,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x^2} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/x^2,x]","\frac{c \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}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x}+\frac{b c \log (x) \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}","\frac{c \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}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x}+\frac{b c \log (x) \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}",1,"-((Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/x) + (c*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c*Sqrt[d - c^2*d*x^2]*Log[x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",4,4,27,0.1481,1,"{5798, 5738, 29, 5676}"
62,1,127,0,0.2854782,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x^4} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/x^4,x]","-\frac{(1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}-\frac{b c \sqrt{d-c^2 d x^2}}{6 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^3 \log (x) \sqrt{d-c^2 d x^2}}{3 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{3 d x^3}-\frac{b c \sqrt{d-c^2 d x^2}}{6 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^3 \log (x) \sqrt{d-c^2 d x^2}}{3 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*Sqrt[d - c^2*d*x^2])/(6*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3*x^3) - (b*c^3*Sqrt[d - c^2*d*x^2]*Log[x])/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",4,3,27,0.1111,1,"{5798, 5724, 14}"
63,1,226,0,0.3456287,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x^6} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/x^6,x]","\frac{2 c^4 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{15 x}+\frac{c^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{15 x^3}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 x^5}+\frac{b c^3 \sqrt{d-c^2 d x^2}}{30 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \sqrt{d-c^2 d x^2}}{20 x^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c^5 \log (x) \sqrt{d-c^2 d x^2}}{15 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{2 c^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{15 d x^3}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{5 d x^5}+\frac{b c^3 \sqrt{d-c^2 d x^2}}{30 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \sqrt{d-c^2 d x^2}}{20 x^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c^5 \log (x) \sqrt{d-c^2 d x^2}}{15 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*Sqrt[d - c^2*d*x^2])/(20*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*Sqrt[d - c^2*d*x^2])/(30*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(5*x^5) + (c^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(15*x^3) + (2*c^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(15*x) - (2*b*c^5*Sqrt[d - c^2*d*x^2]*Log[x])/(15*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",5,7,27,0.2593,1,"{5798, 97, 12, 103, 95, 5733, 14}"
64,1,303,0,0.3775528,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x^8} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/x^8,x]","\frac{8 c^6 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{105 x}+\frac{4 c^4 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{105 x^3}+\frac{c^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{35 x^5}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 x^7}+\frac{2 b c^5 \sqrt{d-c^2 d x^2}}{105 x^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 \sqrt{d-c^2 d x^2}}{140 x^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \sqrt{d-c^2 d x^2}}{42 x^6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{8 b c^7 \log (x) \sqrt{d-c^2 d x^2}}{105 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{8 c^4 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{105 d x^3}-\frac{4 c^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{35 d x^5}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{7 d x^7}+\frac{2 b c^5 \sqrt{d-c^2 d x^2}}{105 x^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 \sqrt{d-c^2 d x^2}}{140 x^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \sqrt{d-c^2 d x^2}}{42 x^6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{8 b c^7 \log (x) \sqrt{d-c^2 d x^2}}{105 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*Sqrt[d - c^2*d*x^2])/(42*x^6*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*Sqrt[d - c^2*d*x^2])/(140*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*c^5*Sqrt[d - c^2*d*x^2])/(105*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(7*x^7) + (c^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(35*x^5) + (4*c^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(105*x^3) + (8*c^6*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(105*x) - (8*b*c^7*Sqrt[d - c^2*d*x^2]*Log[x])/(105*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",5,7,27,0.2593,1,"{5798, 97, 12, 103, 95, 5733, 14}"
65,1,302,0,0.3523604,"\int x^5 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]),x]","-\frac{x^4 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^2}-\frac{4 x^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{35 c^4}-\frac{8 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{105 c^6}-\frac{b c x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x^5 \sqrt{d-c^2 d x^2}}{175 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{4 b x^3 \sqrt{d-c^2 d x^2}}{315 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b x \sqrt{d-c^2 d x^2}}{105 c^5 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^6 d^3}+\frac{2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^6 d^2}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^6 d}-\frac{b c x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x^5 \sqrt{d-c^2 d x^2}}{175 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{4 b x^3 \sqrt{d-c^2 d x^2}}{315 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b x \sqrt{d-c^2 d x^2}}{105 c^5 \sqrt{c x-1} \sqrt{c x+1}}",1,"(8*b*x*Sqrt[d - c^2*d*x^2])/(105*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (4*b*x^3*Sqrt[d - c^2*d*x^2])/(315*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*x^5*Sqrt[d - c^2*d*x^2])/(175*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (8*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(105*c^6) - (4*x^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(35*c^4) - (x^4*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(7*c^2)","A",4,5,27,0.1852,1,"{5798, 100, 12, 74, 5733}"
66,1,214,0,0.3231373,"\int x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]),x]","-\frac{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 (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 x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x^3 \sqrt{d-c^2 d x^2}}{45 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b x \sqrt{d-c^2 d x^2}}{15 c^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^4 d^2}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^4 d}-\frac{b c x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x^3 \sqrt{d-c^2 d x^2}}{45 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b x \sqrt{d-c^2 d x^2}}{15 c^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(2*b*x*Sqrt[d - c^2*d*x^2])/(15*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*x^3*Sqrt[d - c^2*d*x^2])/(45*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(15*c^4) - (x^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(5*c^2)","A",4,5,27,0.1852,1,"{5798, 100, 12, 74, 5733}"
67,1,126,0,0.2119422,"\int x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]),x]","-\frac{(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 x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x \sqrt{d-c^2 d x^2}}{3 c \sqrt{c x-1} \sqrt{c x+1}}","-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2 d}-\frac{b c x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x \sqrt{d-c^2 d x^2}}{3 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*x*Sqrt[d - c^2*d*x^2])/(3*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*x^3*Sqrt[d - c^2*d*x^2])/(9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3*c^2)","A",3,2,25,0.08000,1,"{5798, 5718}"
68,1,213,0,0.5244526,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/x,x]","\frac{i b \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{i b \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c x \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}","\frac{i b \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{i b \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c x \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}",1,"-((b*c*x*Sqrt[d - c^2*d*x^2])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])) + Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]) - (2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*ArcTan[E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (I*b*Sqrt[d - c^2*d*x^2]*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (I*b*Sqrt[d - c^2*d*x^2]*PolyLog[2, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",9,7,27,0.2593,1,"{5798, 5743, 5761, 4180, 2279, 2391, 8}"
69,1,235,0,0.5201095,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x^3} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/x^3,x]","-\frac{i b c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{i b c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}+\frac{c^2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \sqrt{d-c^2 d x^2}}{2 x \sqrt{c x-1} \sqrt{c x+1}}","-\frac{i b c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{i b c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}+\frac{c^2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \sqrt{d-c^2 d x^2}}{2 x \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*Sqrt[d - c^2*d*x^2])/(2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(2*x^2) + (c^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*ArcTan[E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((I/2)*b*c^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((I/2)*b*c^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",9,7,27,0.2593,1,"{5798, 5738, 30, 5761, 4180, 2279, 2391}"
70,1,315,0,0.743373,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x^5} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/x^5,x]","-\frac{i b c^4 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{i b c^4 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{c^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 x^2}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{4 x^4}+\frac{c^4 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 \sqrt{d-c^2 d x^2}}{8 x \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \sqrt{d-c^2 d x^2}}{12 x^3 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{i b c^4 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{i b c^4 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{c^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 x^2}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{4 x^4}+\frac{c^4 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 \sqrt{d-c^2 d x^2}}{8 x \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \sqrt{d-c^2 d x^2}}{12 x^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*Sqrt[d - c^2*d*x^2])/(12*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*Sqrt[d - c^2*d*x^2])/(8*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(4*x^4) + (c^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(8*x^2) + (c^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*ArcTan[E^ArcCosh[c*x]])/(4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((I/8)*b*c^4*Sqrt[d - c^2*d*x^2]*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((I/8)*b*c^4*Sqrt[d - c^2*d*x^2]*PolyLog[2, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",11,8,27,0.2963,1,"{5798, 5738, 30, 5748, 5761, 4180, 2279, 2391}"
71,1,372,0,1.0642526,"\int x^4 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^4*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]),x]","\frac{1}{16} d x^5 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{8} d x^5 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{d x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{64 c^2}-\frac{3 d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{128 c^4}-\frac{3 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{256 b c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d x^8 \sqrt{d-c^2 d x^2}}{64 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d x^6 \sqrt{d-c^2 d x^2}}{32 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d x^4 \sqrt{d-c^2 d x^2}}{256 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b d x^2 \sqrt{d-c^2 d x^2}}{256 c^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{8} x^5 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{16} d x^5 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{d x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{64 c^2}-\frac{3 d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{128 c^4}-\frac{3 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{256 b c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d x^8 \sqrt{d-c^2 d x^2}}{64 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d x^6 \sqrt{d-c^2 d x^2}}{32 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d x^4 \sqrt{d-c^2 d x^2}}{256 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b d x^2 \sqrt{d-c^2 d x^2}}{256 c^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(3*b*d*x^2*Sqrt[d - c^2*d*x^2])/(256*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d*x^4*Sqrt[d - c^2*d*x^2])/(256*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d*x^6*Sqrt[d - c^2*d*x^2])/(32*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*x^8*Sqrt[d - c^2*d*x^2])/(64*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(128*c^4) - (d*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(64*c^2) + (d*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/16 + (d*x^5*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/8 - (3*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(256*b*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",11,7,27,0.2593,1,"{5798, 5745, 5743, 5759, 5676, 30, 14}"
72,1,293,0,0.8407161,"\int x^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^2*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]),x]","\frac{1}{8} d x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{6} d 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 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{16 c^2}-\frac{d \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 x^6 \sqrt{d-c^2 d x^2}}{36 \sqrt{c x-1} \sqrt{c x+1}}-\frac{7 b c d x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d x^2 \sqrt{d-c^2 d x^2}}{32 c \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{6} x^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{8} d x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{16 c^2}-\frac{d \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 x^6 \sqrt{d-c^2 d x^2}}{36 \sqrt{c x-1} \sqrt{c x+1}}-\frac{7 b c d x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d x^2 \sqrt{d-c^2 d x^2}}{32 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*d*x^2*Sqrt[d - c^2*d*x^2])/(32*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (7*b*c*d*x^4*Sqrt[d - c^2*d*x^2])/(96*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*x^6*Sqrt[d - c^2*d*x^2])/(36*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(16*c^2) + (d*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/8 + (d*x^3*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/6 - (d*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",9,7,27,0.2593,1,"{5798, 5745, 5743, 5759, 5676, 30, 14}"
73,1,212,0,0.3212913,"\int \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]),x]","\frac{3}{8} d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} d 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 \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{b c^3 d x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b c d x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{4} x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{3}{8} d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{3 d \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{b c^3 d x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b c d x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}",1,"(-5*b*c*d*x^2*Sqrt[d - c^2*d*x^2])/(16*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/8 + (d*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/4 - (3*d*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",7,6,24,0.2500,1,"{5713, 5685, 5683, 5676, 30, 14}"
74,1,209,0,0.5361155,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]))/x^2,x]","-\frac{3}{2} c^2 d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{3 c d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b \sqrt{c x-1} \sqrt{c x+1}}-\frac{d (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x}+\frac{b c^3 d x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d \log (x) \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}","-\frac{3}{2} c^2 d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{3 c d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b \sqrt{c x-1} \sqrt{c x+1}}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{x}+\frac{b c^3 d x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d \log (x) \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}",1,"(b*c^3*d*x^2*Sqrt[d - c^2*d*x^2])/(4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*c^2*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/2 - (d*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/x + (3*c*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(4*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c*d*Sqrt[d - c^2*d*x^2]*Log[x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",7,6,27,0.2222,1,"{5798, 5740, 5683, 5676, 30, 14}"
75,1,215,0,0.6336825,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]))/x^4,x]","-\frac{c^3 d \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}}+\frac{c^2 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x}-\frac{d (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}-\frac{b c d \sqrt{d-c^2 d x^2}}{6 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 b c^3 d \log (x) \sqrt{d-c^2 d x^2}}{3 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{c^3 d \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}}+\frac{c^2 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}-\frac{b c d \sqrt{d-c^2 d x^2}}{6 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 b c^3 d \log (x) \sqrt{d-c^2 d x^2}}{3 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*d*Sqrt[d - c^2*d*x^2])/(6*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/x - (d*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3*x^3) - (c^3*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (4*b*c^3*d*Sqrt[d - c^2*d*x^2]*Log[x])/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",7,6,27,0.2222,1,"{5798, 5740, 5738, 29, 5676, 14}"
76,1,179,0,0.3544731,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{x^6} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]))/x^6,x]","-\frac{d (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 x^5}+\frac{b c^3 d \sqrt{d-c^2 d x^2}}{5 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d \sqrt{d-c^2 d x^2}}{20 x^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^5 d \log (x) \sqrt{d-c^2 d x^2}}{5 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{5 d x^5}+\frac{b c^3 d \sqrt{d-c^2 d x^2}}{5 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d \sqrt{d-c^2 d x^2}}{20 x^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^5 d \log (x) \sqrt{d-c^2 d x^2}}{5 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*d*Sqrt[d - c^2*d*x^2])/(20*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*Sqrt[d - c^2*d*x^2])/(5*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(5*x^5) + (b*c^5*d*Sqrt[d - c^2*d*x^2]*Log[x])/(5*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",5,4,27,0.1481,1,"{5798, 5724, 266, 43}"
77,1,322,0,0.4452786,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{x^8} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]))/x^8,x]","-\frac{2 c^6 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{35 x}-\frac{c^4 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{35 x^3}+\frac{3 c^2 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{35 x^5}-\frac{d (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 x^7}-\frac{b c^5 d \sqrt{d-c^2 d x^2}}{70 x^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c^3 d \sqrt{d-c^2 d x^2}}{35 x^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d \sqrt{d-c^2 d x^2}}{42 x^6 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c^7 d \log (x) \sqrt{d-c^2 d x^2}}{35 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{2 c^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{35 d x^5}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{7 d x^7}-\frac{b c^5 d \sqrt{d-c^2 d x^2}}{70 x^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c^3 d \sqrt{d-c^2 d x^2}}{35 x^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d \sqrt{d-c^2 d x^2}}{42 x^6 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c^7 d \log (x) \sqrt{d-c^2 d x^2}}{35 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*d*Sqrt[d - c^2*d*x^2])/(42*x^6*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*c^3*d*Sqrt[d - c^2*d*x^2])/(35*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d*Sqrt[d - c^2*d*x^2])/(70*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(35*x^5) - (c^4*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(35*x^3) - (2*c^6*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(35*x) - (d*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(7*x^7) + (2*b*c^7*d*Sqrt[d - c^2*d*x^2]*Log[x])/(35*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",6,8,27,0.2963,1,"{5798, 97, 12, 103, 95, 5733, 446, 76}"
78,1,401,0,0.5128095,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{x^{10}} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]))/x^10,x]","-\frac{8 c^8 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{315 x}-\frac{4 c^6 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{315 x^3}-\frac{c^4 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{105 x^5}+\frac{c^2 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{21 x^7}-\frac{d (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{9 x^9}-\frac{2 b c^7 d \sqrt{d-c^2 d x^2}}{315 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 d \sqrt{d-c^2 d x^2}}{420 x^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c^3 d \sqrt{d-c^2 d x^2}}{189 x^6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d \sqrt{d-c^2 d x^2}}{72 x^8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b c^9 d \log (x) \sqrt{d-c^2 d x^2}}{315 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{8 c^4 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{315 d x^5}-\frac{4 c^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{63 d x^7}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{9 d x^9}-\frac{2 b c^7 d \sqrt{d-c^2 d x^2}}{315 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 d \sqrt{d-c^2 d x^2}}{420 x^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c^3 d \sqrt{d-c^2 d x^2}}{189 x^6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d \sqrt{d-c^2 d x^2}}{72 x^8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b c^9 d \log (x) \sqrt{d-c^2 d x^2}}{315 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*d*Sqrt[d - c^2*d*x^2])/(72*x^8*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*b*c^3*d*Sqrt[d - c^2*d*x^2])/(189*x^6*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d*Sqrt[d - c^2*d*x^2])/(420*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*c^7*d*Sqrt[d - c^2*d*x^2])/(315*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(21*x^7) - (c^4*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(105*x^5) - (4*c^6*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(315*x^3) - (8*c^8*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(315*x) - (d*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(9*x^9) + (8*b*c^9*d*Sqrt[d - c^2*d*x^2]*Log[x])/(315*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",6,8,27,0.2963,1,"{5798, 97, 12, 103, 95, 5733, 1251, 893}"
79,1,480,0,0.6064181,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{x^{12}} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]))/x^12,x]","-\frac{16 c^{10} d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{1155 x}-\frac{8 c^8 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{1155 x^3}-\frac{2 c^6 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{385 x^5}-\frac{c^4 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{231 x^7}+\frac{c^2 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{33 x^9}-\frac{d (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{11 x^{11}}-\frac{4 b c^9 d \sqrt{d-c^2 d x^2}}{1155 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^7 d \sqrt{d-c^2 d x^2}}{770 x^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 d \sqrt{d-c^2 d x^2}}{1386 x^6 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d \sqrt{d-c^2 d x^2}}{66 x^8 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d \sqrt{d-c^2 d x^2}}{110 x^{10} \sqrt{c x-1} \sqrt{c x+1}}+\frac{16 b c^{11} d \log (x) \sqrt{d-c^2 d x^2}}{1155 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{16 c^6 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{1155 d x^5}-\frac{8 c^4 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{231 d x^7}-\frac{2 c^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{33 d x^9}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{11 d x^{11}}-\frac{4 b c^9 d \sqrt{d-c^2 d x^2}}{1155 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^7 d \sqrt{d-c^2 d x^2}}{770 x^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 d \sqrt{d-c^2 d x^2}}{1386 x^6 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d \sqrt{d-c^2 d x^2}}{66 x^8 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d \sqrt{d-c^2 d x^2}}{110 x^{10} \sqrt{c x-1} \sqrt{c x+1}}+\frac{16 b c^{11} d \log (x) \sqrt{d-c^2 d x^2}}{1155 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*d*Sqrt[d - c^2*d*x^2])/(110*x^10*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*Sqrt[d - c^2*d*x^2])/(66*x^8*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d*Sqrt[d - c^2*d*x^2])/(1386*x^6*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^7*d*Sqrt[d - c^2*d*x^2])/(770*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (4*b*c^9*d*Sqrt[d - c^2*d*x^2])/(1155*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(33*x^9) - (c^4*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(231*x^7) - (2*c^6*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(385*x^5) - (8*c^8*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(1155*x^3) - (16*c^10*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(1155*x) - (d*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(11*x^11) + (16*b*c^11*d*Sqrt[d - c^2*d*x^2]*Log[x])/(1155*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",6,8,27,0.2963,1,"{5798, 97, 12, 103, 95, 5733, 1799, 1620}"
80,1,460,0,0.4959634,"\int x^7 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^7*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]),x]","-\frac{d x^6 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{11 c^2}-\frac{2 d x^4 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{33 c^4}-\frac{8 d x^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{231 c^6}-\frac{16 d (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{1155 c^8}+\frac{b c^3 d x^{11} \sqrt{d-c^2 d x^2}}{121 \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 b c d x^9 \sqrt{d-c^2 d x^2}}{297 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d x^7 \sqrt{d-c^2 d x^2}}{1617 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d x^5 \sqrt{d-c^2 d x^2}}{1925 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b d x^3 \sqrt{d-c^2 d x^2}}{3465 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{16 b d x \sqrt{d-c^2 d x^2}}{1155 c^7 \sqrt{c x-1} \sqrt{c x+1}}","\frac{\left(d-c^2 d x^2\right)^{11/2} \left(a+b \cosh ^{-1}(c x)\right)}{11 c^8 d^4}-\frac{\left(d-c^2 d x^2\right)^{9/2} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^8 d^3}+\frac{3 \left(d-c^2 d x^2\right)^{7/2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^8 d^2}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^8 d}+\frac{b c^3 d x^{11} \sqrt{d-c^2 d x^2}}{121 \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 b c d x^9 \sqrt{d-c^2 d x^2}}{297 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d x^7 \sqrt{d-c^2 d x^2}}{1617 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d x^5 \sqrt{d-c^2 d x^2}}{1925 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b d x^3 \sqrt{d-c^2 d x^2}}{3465 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{16 b d x \sqrt{d-c^2 d x^2}}{1155 c^7 \sqrt{c x-1} \sqrt{c x+1}}",1,"(16*b*d*x*Sqrt[d - c^2*d*x^2])/(1155*c^7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (8*b*d*x^3*Sqrt[d - c^2*d*x^2])/(3465*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*d*x^5*Sqrt[d - c^2*d*x^2])/(1925*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d*x^7*Sqrt[d - c^2*d*x^2])/(1617*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (4*b*c*d*x^9*Sqrt[d - c^2*d*x^2])/(297*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*x^11*Sqrt[d - c^2*d*x^2])/(121*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (16*d*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(1155*c^8) - (8*d*x^2*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(231*c^6) - (2*d*x^4*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(33*c^4) - (d*x^6*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(11*c^2)","A",5,6,27,0.2222,1,"{5798, 100, 12, 74, 5733, 1810}"
81,1,366,0,0.4372725,"\int x^5 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^5*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]),x]","-\frac{d x^4 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{9 c^2}-\frac{4 d x^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{63 c^4}-\frac{8 d (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{315 c^6}+\frac{b c^3 d x^9 \sqrt{d-c^2 d x^2}}{81 \sqrt{c x-1} \sqrt{c x+1}}-\frac{10 b c d x^7 \sqrt{d-c^2 d x^2}}{441 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d x^5 \sqrt{d-c^2 d x^2}}{525 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{4 b d x^3 \sqrt{d-c^2 d x^2}}{945 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b d x \sqrt{d-c^2 d x^2}}{315 c^5 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{\left(d-c^2 d x^2\right)^{9/2} \left(a+b \cosh ^{-1}(c x)\right)}{9 c^6 d^3}+\frac{2 \left(d-c^2 d x^2\right)^{7/2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^6 d^2}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^6 d}+\frac{b c^3 d x^9 \sqrt{d-c^2 d x^2}}{81 \sqrt{c x-1} \sqrt{c x+1}}-\frac{10 b c d x^7 \sqrt{d-c^2 d x^2}}{441 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d x^5 \sqrt{d-c^2 d x^2}}{525 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{4 b d x^3 \sqrt{d-c^2 d x^2}}{945 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b d x \sqrt{d-c^2 d x^2}}{315 c^5 \sqrt{c x-1} \sqrt{c x+1}}",1,"(8*b*d*x*Sqrt[d - c^2*d*x^2])/(315*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (4*b*d*x^3*Sqrt[d - c^2*d*x^2])/(945*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d*x^5*Sqrt[d - c^2*d*x^2])/(525*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (10*b*c*d*x^7*Sqrt[d - c^2*d*x^2])/(441*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*x^9*Sqrt[d - c^2*d*x^2])/(81*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (8*d*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(315*c^6) - (4*d*x^2*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(63*c^4) - (d*x^4*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(9*c^2)","A",5,6,27,0.2222,1,"{5798, 100, 12, 74, 5733, 1153}"
82,1,272,0,0.4119728,"\int x^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^3*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]),x]","-\frac{d x^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^2}-\frac{2 d (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{b c^3 d x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{c x-1} \sqrt{c x+1}}-\frac{8 b c d x^5 \sqrt{d-c^2 d x^2}}{175 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d x^3 \sqrt{d-c^2 d x^2}}{105 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d x \sqrt{d-c^2 d x^2}}{35 c^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^4 d^2}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^4 d}+\frac{b c^3 d x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{c x-1} \sqrt{c x+1}}-\frac{8 b c d x^5 \sqrt{d-c^2 d x^2}}{175 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d x^3 \sqrt{d-c^2 d x^2}}{105 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d x \sqrt{d-c^2 d x^2}}{35 c^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(2*b*d*x*Sqrt[d - c^2*d*x^2])/(35*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d*x^3*Sqrt[d - c^2*d*x^2])/(105*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (8*b*c*d*x^5*Sqrt[d - c^2*d*x^2])/(175*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*d*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(35*c^4) - (d*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)","A",5,6,27,0.2222,1,"{5798, 100, 12, 74, 5733, 373}"
83,1,178,0,0.2653242,"\int x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]),x]","-\frac{d (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 x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c d x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d x \sqrt{d-c^2 d x^2}}{5 c \sqrt{c x-1} \sqrt{c x+1}}","-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^2 d}+\frac{b c^3 d x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c d x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d x \sqrt{d-c^2 d x^2}}{5 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*d*x*Sqrt[d - c^2*d*x^2])/(5*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*c*d*x^3*Sqrt[d - c^2*d*x^2])/(15*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(5*c^2)","A",4,3,25,0.1200,1,"{5798, 5718, 194}"
84,1,304,0,0.7893032,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{x} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]))/x,x]","\frac{i b d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{i b d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} d (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{2 d \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 b c d x \sqrt{d-c^2 d x^2}}{3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{i b d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{i b d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{3} \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)+d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{2 d \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 b c d x \sqrt{d-c^2 d x^2}}{3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(-4*b*c*d*x*Sqrt[d - c^2*d*x^2])/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*x^3*Sqrt[d - c^2*d*x^2])/(9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]) + (d*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/3 - (2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*ArcTan[E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (I*b*d*Sqrt[d - c^2*d*x^2]*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (I*b*d*Sqrt[d - c^2*d*x^2]*PolyLog[2, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",11,8,27,0.2963,1,"{5798, 5745, 5743, 5761, 4180, 2279, 2391, 8}"
85,1,323,0,0.800931,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]))/x^3,x]","-\frac{3 i b c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 i b c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3}{2} c^2 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{d (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}+\frac{3 c^2 d \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d x \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d \sqrt{d-c^2 d x^2}}{2 x \sqrt{c x-1} \sqrt{c x+1}}","-\frac{3 i b c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 i b c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3}{2} c^2 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}+\frac{3 c^2 d \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d x \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d \sqrt{d-c^2 d x^2}}{2 x \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*d*Sqrt[d - c^2*d*x^2])/(2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*x*Sqrt[d - c^2*d*x^2])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/2 - (d*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(2*x^2) + (3*c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*ArcTan[E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (((3*I)/2)*b*c^2*d*Sqrt[d - c^2*d*x^2]*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (((3*I)/2)*b*c^2*d*Sqrt[d - c^2*d*x^2]*PolyLog[2, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",12,9,27,0.3333,1,"{5798, 5740, 5743, 5761, 4180, 2279, 2391, 8, 14}"
86,1,333,0,0.8366205,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{x^5} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]))/x^5,x]","\frac{3 i b c^4 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 i b c^4 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 c^2 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 x^2}-\frac{d (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{4 x^4}-\frac{3 c^4 d \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c^3 d \sqrt{d-c^2 d x^2}}{8 x \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d \sqrt{d-c^2 d x^2}}{12 x^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{3 i b c^4 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 i b c^4 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 c^2 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 x^2}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{4 x^4}-\frac{3 c^4 d \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c^3 d \sqrt{d-c^2 d x^2}}{8 x \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d \sqrt{d-c^2 d x^2}}{12 x^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*d*Sqrt[d - c^2*d*x^2])/(12*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*b*c^3*d*Sqrt[d - c^2*d*x^2])/(8*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(8*x^2) - (d*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(4*x^4) - (3*c^4*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*ArcTan[E^ArcCosh[c*x]])/(4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (((3*I)/8)*b*c^4*d*Sqrt[d - c^2*d*x^2]*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (((3*I)/8)*b*c^4*d*Sqrt[d - c^2*d*x^2]*PolyLog[2, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",12,9,27,0.3333,1,"{5798, 5740, 5738, 30, 5761, 4180, 2279, 2391, 14}"
87,1,485,0,1.3848059,"\int x^4 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^4*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]),x]","\frac{1}{32} d^2 x^5 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{10} d^2 x^5 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{16} d^2 x^5 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{128 c^2}-\frac{3 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{256 c^4}-\frac{3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{512 b c^5 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 d^2 x^{10} \sqrt{d-c^2 d x^2}}{100 \sqrt{c x-1} \sqrt{c x+1}}+\frac{21 b c^3 d^2 x^8 \sqrt{d-c^2 d x^2}}{640 \sqrt{c x-1} \sqrt{c x+1}}-\frac{31 b c d^2 x^6 \sqrt{d-c^2 d x^2}}{960 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 x^4 \sqrt{d-c^2 d x^2}}{512 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b d^2 x^2 \sqrt{d-c^2 d x^2}}{512 c^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{32} d^2 x^5 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{128 c^2}-\frac{3 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{256 c^4}-\frac{3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{512 b c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{10} x^5 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{16} d x^5 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{b c^5 d^2 x^{10} \sqrt{d-c^2 d x^2}}{100 \sqrt{c x-1} \sqrt{c x+1}}+\frac{21 b c^3 d^2 x^8 \sqrt{d-c^2 d x^2}}{640 \sqrt{c x-1} \sqrt{c x+1}}-\frac{31 b c d^2 x^6 \sqrt{d-c^2 d x^2}}{960 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 x^4 \sqrt{d-c^2 d x^2}}{512 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b d^2 x^2 \sqrt{d-c^2 d x^2}}{512 c^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(3*b*d^2*x^2*Sqrt[d - c^2*d*x^2])/(512*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^2*x^4*Sqrt[d - c^2*d*x^2])/(512*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (31*b*c*d^2*x^6*Sqrt[d - c^2*d*x^2])/(960*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (21*b*c^3*d^2*x^8*Sqrt[d - c^2*d*x^2])/(640*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*x^10*Sqrt[d - c^2*d*x^2])/(100*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(256*c^4) - (d^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(128*c^2) + (d^2*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/32 + (d^2*x^5*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/16 + (d^2*x^5*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/10 - (3*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(512*b*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",15,9,27,0.3333,1,"{5798, 5745, 5743, 5759, 5676, 30, 14, 266, 43}"
88,1,402,0,1.1706732,"\int x^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^2*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]),x]","\frac{5}{64} d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{8} d^2 x^3 (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}{48} d^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{5 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{128 c^2}-\frac{5 d^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{b c^5 d^2 x^8 \sqrt{d-c^2 d x^2}}{64 \sqrt{c x-1} \sqrt{c x+1}}+\frac{17 b c^3 d^2 x^6 \sqrt{d-c^2 d x^2}}{288 \sqrt{c x-1} \sqrt{c x+1}}-\frac{59 b c d^2 x^4 \sqrt{d-c^2 d x^2}}{768 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b d^2 x^2 \sqrt{d-c^2 d x^2}}{256 c \sqrt{c x-1} \sqrt{c x+1}}","\frac{5}{64} d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{5 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{128 c^2}-\frac{5 d^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{1}{8} x^3 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{5}{48} d x^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{b c^5 d^2 x^8 \sqrt{d-c^2 d x^2}}{64 \sqrt{c x-1} \sqrt{c x+1}}+\frac{17 b c^3 d^2 x^6 \sqrt{d-c^2 d x^2}}{288 \sqrt{c x-1} \sqrt{c x+1}}-\frac{59 b c d^2 x^4 \sqrt{d-c^2 d x^2}}{768 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b d^2 x^2 \sqrt{d-c^2 d x^2}}{256 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(5*b*d^2*x^2*Sqrt[d - c^2*d*x^2])/(256*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (59*b*c*d^2*x^4*Sqrt[d - c^2*d*x^2])/(768*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (17*b*c^3*d^2*x^6*Sqrt[d - c^2*d*x^2])/(288*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*x^8*Sqrt[d - c^2*d*x^2])/(64*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(128*c^2) + (5*d^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/64 + (5*d^2*x^3*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/48 + (d^2*x^3*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/8 - (5*d^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",13,9,27,0.3333,1,"{5798, 5745, 5743, 5759, 5676, 30, 14, 266, 43}"
89,1,324,0,0.5429579,"\int \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]),x]","\frac{5}{16} d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{6} d^2 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}{24} d^2 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 \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 b c^3 d^2 x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{c x-1} \sqrt{c x+1}}-\frac{25 b c d^2 x^2 \sqrt{d-c^2 d x^2}}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^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{5}{16} d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{5 d^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{1}{6} x \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{5}{24} d x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{5 b c^3 d^2 x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{c x-1} \sqrt{c x+1}}-\frac{25 b c d^2 x^2 \sqrt{d-c^2 d x^2}}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^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,"(-25*b*c*d^2*x^2*Sqrt[d - c^2*d*x^2])/(96*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*b*c^3*d^2*x^4*Sqrt[d - c^2*d*x^2])/(96*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^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*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/16 + (5*d^2*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/24 + (d^2*x*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/6 - (5*d^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])","A",9,7,24,0.2917,1,"{5713, 5685, 5683, 5676, 30, 14, 261}"
90,1,315,0,0.6782385,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]))/x^2,x]","-\frac{15}{8} c^2 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{5}{4} c^2 d^2 x (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{15 c d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^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{b c^5 d^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{9 b c^3 d^2 x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d^2 \log (x) \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}","-\frac{15}{8} c^2 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{15 c d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b \sqrt{c x-1} \sqrt{c x+1}}-\frac{5}{4} c^2 d x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{x}-\frac{b c^5 d^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{9 b c^3 d^2 x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d^2 \log (x) \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}",1,"(9*b*c^3*d^2*x^2*Sqrt[d - c^2*d*x^2])/(16*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*x^4*Sqrt[d - c^2*d*x^2])/(16*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (15*c^2*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/8 - (5*c^2*d^2*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/4 - (d^2*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/x + (15*c*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(16*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c*d^2*Sqrt[d - c^2*d*x^2]*Log[x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",11,9,27,0.3333,1,"{5798, 5740, 5685, 5683, 5676, 30, 14, 266, 43}"
91,1,324,0,0.8604699,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]))/x^4,x]","\frac{5}{2} c^4 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{5 c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 c^2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 x}-\frac{d^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}-\frac{b c^5 d^2 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{6 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{7 b c^3 d^2 \log (x) \sqrt{d-c^2 d x^2}}{3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{5}{2} c^4 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{5 c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{3 x}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}-\frac{b c^5 d^2 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{6 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{7 b c^3 d^2 \log (x) \sqrt{d-c^2 d x^2}}{3 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*d^2*Sqrt[d - c^2*d*x^2])/(6*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*x^2*Sqrt[d - c^2*d*x^2])/(4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*c^4*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/2 + (5*c^2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3*x) - (d^2*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3*x^3) - (5*c^3*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(4*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (7*b*c^3*d^2*Sqrt[d - c^2*d*x^2]*Log[x])/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",11,8,27,0.2963,1,"{5798, 5740, 5683, 5676, 30, 14, 266, 43}"
92,1,324,0,0.9472573,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{x^6} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]))/x^6,x]","\frac{c^5 d^2 \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}}-\frac{c^4 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x}+\frac{c^2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}-\frac{d^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 x^5}+\frac{11 b c^3 d^2 \sqrt{d-c^2 d x^2}}{30 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{20 x^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{23 b c^5 d^2 \log (x) \sqrt{d-c^2 d x^2}}{15 \sqrt{c x-1} \sqrt{c x+1}}","\frac{c^5 d^2 \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}}-\frac{c^4 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x}+\frac{c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{5 x^5}+\frac{11 b c^3 d^2 \sqrt{d-c^2 d x^2}}{30 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{20 x^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{23 b c^5 d^2 \log (x) \sqrt{d-c^2 d x^2}}{15 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*d^2*Sqrt[d - c^2*d*x^2])/(20*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (11*b*c^3*d^2*Sqrt[d - c^2*d*x^2])/(30*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (c^4*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/x + (c^2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3*x^3) - (d^2*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(5*x^5) + (c^5*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (23*b*c^5*d^2*Sqrt[d - c^2*d*x^2]*Log[x])/(15*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",11,8,27,0.2963,1,"{5798, 5740, 5738, 29, 5676, 14, 266, 43}"
93,1,234,0,0.3786471,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{x^8} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]))/x^8,x]","-\frac{d^2 (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 x^7}-\frac{3 b c^5 d^2 \sqrt{d-c^2 d x^2}}{14 x^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b c^3 d^2 \sqrt{d-c^2 d x^2}}{28 x^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{42 x^6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^7 d^2 \log (x) \sqrt{d-c^2 d x^2}}{7 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \cosh ^{-1}(c x)\right)}{7 d x^7}-\frac{3 b c^5 d^2 \sqrt{d-c^2 d x^2}}{14 x^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b c^3 d^2 \sqrt{d-c^2 d x^2}}{28 x^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{42 x^6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^7 d^2 \log (x) \sqrt{d-c^2 d x^2}}{7 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*d^2*Sqrt[d - c^2*d*x^2])/(42*x^6*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*b*c^3*d^2*Sqrt[d - c^2*d*x^2])/(28*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*b*c^5*d^2*Sqrt[d - c^2*d*x^2])/(14*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d^2*(1 - c*x)^3*(1 + c*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(7*x^7) - (b*c^7*d^2*Sqrt[d - c^2*d*x^2]*Log[x])/(7*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",5,4,27,0.1481,1,"{5798, 5724, 266, 43}"
94,1,448,0,0.5257985,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{x^{10}} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]))/x^10,x]","\frac{2 c^8 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{63 x}+\frac{c^6 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{63 x^3}-\frac{c^4 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{21 x^5}+\frac{5 c^2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{63 x^7}-\frac{d^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{9 x^9}-\frac{b c^7 d^2 \sqrt{d-c^2 d x^2}}{21 x^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^5 d^2 \sqrt{d-c^2 d x^2}}{42 x^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^3 d^2 \sqrt{d-c^2 d x^2}}{189 x^6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \left(1-c^2 x^2\right)^4 \sqrt{d-c^2 d x^2}}{72 x^8 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c^9 d^2 \log (x) \sqrt{d-c^2 d x^2}}{63 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{2 c^2 \left(d-c^2 d x^2\right)^{7/2} \left(a+b \cosh ^{-1}(c x)\right)}{63 d x^7}-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \cosh ^{-1}(c x)\right)}{9 d x^9}-\frac{b c^7 d^2 \sqrt{d-c^2 d x^2}}{21 x^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^5 d^2 \sqrt{d-c^2 d x^2}}{42 x^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^3 d^2 \sqrt{d-c^2 d x^2}}{189 x^6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \left(1-c^2 x^2\right)^4 \sqrt{d-c^2 d x^2}}{72 x^8 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c^9 d^2 \log (x) \sqrt{d-c^2 d x^2}}{63 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c^3*d^2*Sqrt[d - c^2*d*x^2])/(189*x^6*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^5*d^2*Sqrt[d - c^2*d*x^2])/(42*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^7*d^2*Sqrt[d - c^2*d*x^2])/(21*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d^2*(1 - c^2*x^2)^4*Sqrt[d - c^2*d*x^2])/(72*x^8*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (c^4*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(21*x^5) + (c^6*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(63*x^3) + (2*c^8*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(63*x) + (5*c^2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(63*x^7) - (d^2*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(9*x^9) - (2*b*c^9*d^2*Sqrt[d - c^2*d*x^2]*Log[x])/(63*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",7,9,27,0.3333,1,"{5798, 97, 12, 103, 95, 5733, 446, 78, 43}"
95,1,519,0,0.578848,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{x^{12}} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]))/x^12,x]","\frac{8 c^{10} d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{693 x}+\frac{4 c^8 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{693 x^3}+\frac{c^6 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{231 x^5}-\frac{5 c^4 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{231 x^7}+\frac{5 c^2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{99 x^9}-\frac{d^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{11 x^{11}}+\frac{2 b c^9 d^2 \sqrt{d-c^2 d x^2}}{693 x^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^7 d^2 \sqrt{d-c^2 d x^2}}{924 x^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{113 b c^5 d^2 \sqrt{d-c^2 d x^2}}{4158 x^6 \sqrt{c x-1} \sqrt{c x+1}}+\frac{23 b c^3 d^2 \sqrt{d-c^2 d x^2}}{792 x^8 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{110 x^{10} \sqrt{c x-1} \sqrt{c x+1}}-\frac{8 b c^{11} d^2 \log (x) \sqrt{d-c^2 d x^2}}{693 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{8 c^4 \left(d-c^2 d x^2\right)^{7/2} \left(a+b \cosh ^{-1}(c x)\right)}{693 d x^7}-\frac{4 c^2 \left(d-c^2 d x^2\right)^{7/2} \left(a+b \cosh ^{-1}(c x)\right)}{99 d x^9}-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \cosh ^{-1}(c x)\right)}{11 d x^{11}}+\frac{2 b c^9 d^2 \sqrt{d-c^2 d x^2}}{693 x^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^7 d^2 \sqrt{d-c^2 d x^2}}{924 x^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{113 b c^5 d^2 \sqrt{d-c^2 d x^2}}{4158 x^6 \sqrt{c x-1} \sqrt{c x+1}}+\frac{23 b c^3 d^2 \sqrt{d-c^2 d x^2}}{792 x^8 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{110 x^{10} \sqrt{c x-1} \sqrt{c x+1}}-\frac{8 b c^{11} d^2 \log (x) \sqrt{d-c^2 d x^2}}{693 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*d^2*Sqrt[d - c^2*d*x^2])/(110*x^10*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (23*b*c^3*d^2*Sqrt[d - c^2*d*x^2])/(792*x^8*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (113*b*c^5*d^2*Sqrt[d - c^2*d*x^2])/(4158*x^6*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^7*d^2*Sqrt[d - c^2*d*x^2])/(924*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*c^9*d^2*Sqrt[d - c^2*d*x^2])/(693*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*c^4*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(231*x^7) + (c^6*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(231*x^5) + (4*c^8*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(693*x^3) + (8*c^10*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(693*x) + (5*c^2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(99*x^9) - (d^2*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(11*x^11) - (8*b*c^11*d^2*Sqrt[d - c^2*d*x^2]*Log[x])/(693*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",6,8,27,0.2963,1,"{5798, 97, 12, 103, 95, 5733, 1251, 893}"
96,1,527,0,0.5156501,"\int x^7 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^7*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]),x]","-\frac{d^2 x^6 (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{13 c^2}-\frac{6 d^2 x^4 (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{143 c^4}-\frac{8 d^2 x^2 (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{429 c^6}-\frac{16 d^2 (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3003 c^8}-\frac{b c^5 d^2 x^{13} \sqrt{d-c^2 d x^2}}{169 \sqrt{c x-1} \sqrt{c x+1}}+\frac{27 b c^3 d^2 x^{11} \sqrt{d-c^2 d x^2}}{1573 \sqrt{c x-1} \sqrt{c x+1}}-\frac{53 b c d^2 x^9 \sqrt{d-c^2 d x^2}}{3861 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b d^2 x^7 \sqrt{d-c^2 d x^2}}{21021 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d^2 x^5 \sqrt{d-c^2 d x^2}}{5005 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b d^2 x^3 \sqrt{d-c^2 d x^2}}{9009 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{16 b d^2 x \sqrt{d-c^2 d x^2}}{3003 c^7 \sqrt{c x-1} \sqrt{c x+1}}","\frac{\left(d-c^2 d x^2\right)^{13/2} \left(a+b \cosh ^{-1}(c x)\right)}{13 c^8 d^4}-\frac{3 \left(d-c^2 d x^2\right)^{11/2} \left(a+b \cosh ^{-1}(c x)\right)}{11 c^8 d^3}+\frac{\left(d-c^2 d x^2\right)^{9/2} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^8 d^2}-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^8 d}-\frac{b c^5 d^2 x^{13} \sqrt{d-c^2 d x^2}}{169 \sqrt{c x-1} \sqrt{c x+1}}+\frac{27 b c^3 d^2 x^{11} \sqrt{d-c^2 d x^2}}{1573 \sqrt{c x-1} \sqrt{c x+1}}-\frac{53 b c d^2 x^9 \sqrt{d-c^2 d x^2}}{3861 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b d^2 x^7 \sqrt{d-c^2 d x^2}}{21021 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d^2 x^5 \sqrt{d-c^2 d x^2}}{5005 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b d^2 x^3 \sqrt{d-c^2 d x^2}}{9009 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{16 b d^2 x \sqrt{d-c^2 d x^2}}{3003 c^7 \sqrt{c x-1} \sqrt{c x+1}}",1,"(16*b*d^2*x*Sqrt[d - c^2*d*x^2])/(3003*c^7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (8*b*d^2*x^3*Sqrt[d - c^2*d*x^2])/(9009*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*d^2*x^5*Sqrt[d - c^2*d*x^2])/(5005*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*b*d^2*x^7*Sqrt[d - c^2*d*x^2])/(21021*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (53*b*c*d^2*x^9*Sqrt[d - c^2*d*x^2])/(3861*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (27*b*c^3*d^2*x^11*Sqrt[d - c^2*d*x^2])/(1573*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*x^13*Sqrt[d - c^2*d*x^2])/(169*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (16*d^2*(1 - c*x)^3*(1 + c*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3003*c^8) - (8*d^2*x^2*(1 - c*x)^3*(1 + c*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(429*c^6) - (6*d^2*x^4*(1 - c*x)^3*(1 + c*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(143*c^4) - (d^2*x^6*(1 - c*x)^3*(1 + c*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(13*c^2)","A",5,6,27,0.2222,1,"{5798, 100, 12, 74, 5733, 1810}"
97,1,429,0,0.4682813,"\int x^5 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^5*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]),x]","-\frac{d^2 x^4 (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{11 c^2}-\frac{4 d^2 x^2 (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{99 c^4}-\frac{8 d^2 (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{693 c^6}-\frac{b c^5 d^2 x^{11} \sqrt{d-c^2 d x^2}}{121 \sqrt{c x-1} \sqrt{c x+1}}+\frac{23 b c^3 d^2 x^9 \sqrt{d-c^2 d x^2}}{891 \sqrt{c x-1} \sqrt{c x+1}}-\frac{113 b c d^2 x^7 \sqrt{d-c^2 d x^2}}{4851 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 x^5 \sqrt{d-c^2 d x^2}}{1155 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{4 b d^2 x^3 \sqrt{d-c^2 d x^2}}{2079 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b d^2 x \sqrt{d-c^2 d x^2}}{693 c^5 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{\left(d-c^2 d x^2\right)^{11/2} \left(a+b \cosh ^{-1}(c x)\right)}{11 c^6 d^3}+\frac{2 \left(d-c^2 d x^2\right)^{9/2} \left(a+b \cosh ^{-1}(c x)\right)}{9 c^6 d^2}-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^6 d}-\frac{b c^5 d^2 x^{11} \sqrt{d-c^2 d x^2}}{121 \sqrt{c x-1} \sqrt{c x+1}}+\frac{23 b c^3 d^2 x^9 \sqrt{d-c^2 d x^2}}{891 \sqrt{c x-1} \sqrt{c x+1}}-\frac{113 b c d^2 x^7 \sqrt{d-c^2 d x^2}}{4851 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 x^5 \sqrt{d-c^2 d x^2}}{1155 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{4 b d^2 x^3 \sqrt{d-c^2 d x^2}}{2079 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b d^2 x \sqrt{d-c^2 d x^2}}{693 c^5 \sqrt{c x-1} \sqrt{c x+1}}",1,"(8*b*d^2*x*Sqrt[d - c^2*d*x^2])/(693*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (4*b*d^2*x^3*Sqrt[d - c^2*d*x^2])/(2079*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^2*x^5*Sqrt[d - c^2*d*x^2])/(1155*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (113*b*c*d^2*x^7*Sqrt[d - c^2*d*x^2])/(4851*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (23*b*c^3*d^2*x^9*Sqrt[d - c^2*d*x^2])/(891*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*x^11*Sqrt[d - c^2*d*x^2])/(121*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (8*d^2*(1 - c*x)^3*(1 + c*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(693*c^6) - (4*d^2*x^2*(1 - c*x)^3*(1 + c*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(99*c^4) - (d^2*x^4*(1 - c*x)^3*(1 + c*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(11*c^2)","A",5,6,27,0.2222,1,"{5798, 100, 12, 74, 5733, 1153}"
98,1,331,0,0.4237445,"\int x^3 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^3*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]),x]","-\frac{d^2 x^2 (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{9 c^2}-\frac{2 d^2 (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{b c^5 d^2 x^9 \sqrt{d-c^2 d x^2}}{81 \sqrt{c x-1} \sqrt{c x+1}}+\frac{19 b c^3 d^2 x^7 \sqrt{d-c^2 d x^2}}{441 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 x^5 \sqrt{d-c^2 d x^2}}{21 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 x^3 \sqrt{d-c^2 d x^2}}{189 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d^2 x \sqrt{d-c^2 d x^2}}{63 c^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{\left(d-c^2 d x^2\right)^{9/2} \left(a+b \cosh ^{-1}(c x)\right)}{9 c^4 d^2}-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^4 d}-\frac{b c^5 d^2 x^9 \sqrt{d-c^2 d x^2}}{81 \sqrt{c x-1} \sqrt{c x+1}}+\frac{19 b c^3 d^2 x^7 \sqrt{d-c^2 d x^2}}{441 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 x^5 \sqrt{d-c^2 d x^2}}{21 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 x^3 \sqrt{d-c^2 d x^2}}{189 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d^2 x \sqrt{d-c^2 d x^2}}{63 c^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(2*b*d^2*x*Sqrt[d - c^2*d*x^2])/(63*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^2*x^3*Sqrt[d - c^2*d*x^2])/(189*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d^2*x^5*Sqrt[d - c^2*d*x^2])/(21*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (19*b*c^3*d^2*x^7*Sqrt[d - c^2*d*x^2])/(441*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*x^9*Sqrt[d - c^2*d*x^2])/(81*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*d^2*(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*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)","A",5,6,27,0.2222,1,"{5798, 100, 12, 74, 5733, 373}"
99,1,233,0,0.2815779,"\int x \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]),x]","-\frac{d^2 (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 c^5 d^2 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 x^5 \sqrt{d-c^2 d x^2}}{35 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 x^3 \sqrt{d-c^2 d x^2}}{7 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 x \sqrt{d-c^2 d x^2}}{7 c \sqrt{c x-1} \sqrt{c x+1}}","-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^2 d}-\frac{b c^5 d^2 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 x^5 \sqrt{d-c^2 d x^2}}{35 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 x^3 \sqrt{d-c^2 d x^2}}{7 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 x \sqrt{d-c^2 d x^2}}{7 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*d^2*x*Sqrt[d - c^2*d*x^2])/(7*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d^2*x^3*Sqrt[d - c^2*d*x^2])/(7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*b*c^3*d^2*x^5*Sqrt[d - c^2*d*x^2])/(35*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*x^7*Sqrt[d - c^2*d*x^2])/(49*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d^2*(1 - c*x)^3*(1 + c*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(7*c^2)","A",4,3,25,0.1200,1,"{5798, 5718, 194}"
100,1,410,0,1.0588961,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{x} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]))/x,x]","\frac{i b d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{i b d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{5} d^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{2 d^2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 d^2 x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{c x-1} \sqrt{c x+1}}+\frac{11 b c^3 d^2 x^3 \sqrt{d-c^2 d x^2}}{45 \sqrt{c x-1} \sqrt{c x+1}}-\frac{23 b c d^2 x \sqrt{d-c^2 d x^2}}{15 \sqrt{c x-1} \sqrt{c x+1}}","\frac{i b d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{i b d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{2 d^2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{5} \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{b c^5 d^2 x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{c x-1} \sqrt{c x+1}}+\frac{11 b c^3 d^2 x^3 \sqrt{d-c^2 d x^2}}{45 \sqrt{c x-1} \sqrt{c x+1}}-\frac{23 b c d^2 x \sqrt{d-c^2 d x^2}}{15 \sqrt{c x-1} \sqrt{c x+1}}",1,"(-23*b*c*d^2*x*Sqrt[d - c^2*d*x^2])/(15*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (11*b*c^3*d^2*x^3*Sqrt[d - c^2*d*x^2])/(45*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*x^5*Sqrt[d - c^2*d*x^2])/(25*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]) + (d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/3 + (d^2*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/5 - (2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*ArcTan[E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (I*b*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (I*b*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",14,9,27,0.3333,1,"{5798, 5745, 5743, 5761, 4180, 2279, 2391, 8, 194}"
101,1,435,0,1.0637537,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]))/x^3,x]","-\frac{5 i b c^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 i b c^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5}{2} c^2 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{5}{6} c^2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{d^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}+\frac{5 c^2 d^2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 d^2 x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{7 b c^3 d^2 x \sqrt{d-c^2 d x^2}}{3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{2 x \sqrt{c x-1} \sqrt{c x+1}}","-\frac{5 i b c^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 i b c^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5}{2} c^2 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{5 c^2 d^2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{5}{6} c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}-\frac{b c^5 d^2 x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{7 b c^3 d^2 x \sqrt{d-c^2 d x^2}}{3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{2 x \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*d^2*Sqrt[d - c^2*d*x^2])/(2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (7*b*c^3*d^2*x*Sqrt[d - c^2*d*x^2])/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*x^3*Sqrt[d - c^2*d*x^2])/(9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*c^2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/2 - (5*c^2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/6 - (d^2*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(2*x^2) + (5*c^2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*ArcTan[E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (((5*I)/2)*b*c^2*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (((5*I)/2)*b*c^2*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",14,10,27,0.3704,1,"{5798, 5740, 5745, 5743, 5761, 4180, 2279, 2391, 8, 270}"
102,1,438,0,1.0826759,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{x^5} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]))/x^5,x]","\frac{15 i b c^4 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}-\frac{15 i b c^4 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{15}{8} c^4 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{5 c^2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 x^2}-\frac{d^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{4 x^4}-\frac{15 c^4 d^2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 d^2 x \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{9 b c^3 d^2 \sqrt{d-c^2 d x^2}}{8 x \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{12 x^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{15 i b c^4 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}-\frac{15 i b c^4 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{15}{8} c^4 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{15 c^4 d^2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{8 x^2}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{4 x^4}-\frac{b c^5 d^2 x \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{9 b c^3 d^2 \sqrt{d-c^2 d x^2}}{8 x \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \sqrt{d-c^2 d x^2}}{12 x^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*d^2*Sqrt[d - c^2*d*x^2])/(12*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (9*b*c^3*d^2*Sqrt[d - c^2*d*x^2])/(8*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*x*Sqrt[d - c^2*d*x^2])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (15*c^4*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/8 + (5*c^2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(8*x^2) - (d^2*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(4*x^4) - (15*c^4*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*ArcTan[E^ArcCosh[c*x]])/(4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (((15*I)/8)*b*c^4*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (((15*I)/8)*b*c^4*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",15,10,27,0.3704,1,"{5798, 5740, 5743, 5761, 4180, 2279, 2391, 8, 14, 270}"
103,1,84,0,0.104011,"\int \sqrt{1-x^2} \cosh ^{-1}(x) \, dx","Int[Sqrt[1 - x^2]*ArcCosh[x],x]","-\frac{\sqrt{1-x^2} x^2}{4 \sqrt{x-1} \sqrt{x+1}}+\frac{1}{2} \sqrt{1-x^2} x \cosh ^{-1}(x)-\frac{\sqrt{1-x^2} \cosh ^{-1}(x)^2}{4 \sqrt{x-1} \sqrt{x+1}}","-\frac{\sqrt{1-x} x^2}{4 \sqrt{x-1}}+\frac{1}{2} \sqrt{1-x^2} x \cosh ^{-1}(x)-\frac{\sqrt{1-x} \cosh ^{-1}(x)^2}{4 \sqrt{x-1}}",1,"-(x^2*Sqrt[1 - x^2])/(4*Sqrt[-1 + x]*Sqrt[1 + x]) + (x*Sqrt[1 - x^2]*ArcCosh[x])/2 - (Sqrt[1 - x^2]*ArcCosh[x]^2)/(4*Sqrt[-1 + x]*Sqrt[1 + x])","A",4,4,14,0.2857,1,"{5713, 5683, 5676, 30}"
104,1,260,0,0.708788,"\int \frac{x^5 \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^5*(a + b*ArcCosh[c*x]))/Sqrt[d - c^2*d*x^2],x]","-\frac{x^4 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{5 c^2 \sqrt{d-c^2 d x^2}}-\frac{4 x^2 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{15 c^4 \sqrt{d-c^2 d x^2}}-\frac{8 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{15 c^6 \sqrt{d-c^2 d x^2}}-\frac{b x^5 \sqrt{c x-1} \sqrt{c x+1}}{25 c \sqrt{d-c^2 d x^2}}-\frac{4 b x^3 \sqrt{c x-1} \sqrt{c x+1}}{45 c^3 \sqrt{d-c^2 d x^2}}-\frac{8 b x \sqrt{c x-1} \sqrt{c x+1}}{15 c^5 \sqrt{d-c^2 d x^2}}","-\frac{x^4 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^2 d}-\frac{4 x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{15 c^4 d}-\frac{8 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{15 c^6 d}-\frac{b x^5 \sqrt{c x-1} \sqrt{c x+1}}{25 c \sqrt{d-c^2 d x^2}}-\frac{4 b x^3 \sqrt{c x-1} \sqrt{c x+1}}{45 c^3 \sqrt{d-c^2 d x^2}}-\frac{8 b x \sqrt{c x-1} \sqrt{c x+1}}{15 c^5 \sqrt{d-c^2 d x^2}}",1,"(-8*b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(15*c^5*Sqrt[d - c^2*d*x^2]) - (4*b*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(45*c^3*Sqrt[d - c^2*d*x^2]) - (b*x^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(25*c*Sqrt[d - c^2*d*x^2]) - (8*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(15*c^6*Sqrt[d - c^2*d*x^2]) - (4*x^2*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(15*c^4*Sqrt[d - c^2*d*x^2]) - (x^4*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(5*c^2*Sqrt[d - c^2*d*x^2])","A",7,5,27,0.1852,1,"{5798, 5759, 5718, 8, 30}"
105,1,228,0,0.6476551,"\int \frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^4*(a + b*ArcCosh[c*x]))/Sqrt[d - c^2*d*x^2],x]","-\frac{x^3 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{4 c^2 \sqrt{d-c^2 d x^2}}-\frac{3 x (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{8 c^4 \sqrt{d-c^2 d x^2}}+\frac{3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c^5 \sqrt{d-c^2 d x^2}}-\frac{b x^4 \sqrt{c x-1} \sqrt{c x+1}}{16 c \sqrt{d-c^2 d x^2}}-\frac{3 b x^2 \sqrt{c x-1} \sqrt{c x+1}}{16 c^3 \sqrt{d-c^2 d x^2}}","-\frac{x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{4 c^2 d}-\frac{3 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 c^4 d}+\frac{3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c^5 \sqrt{d-c^2 d x^2}}-\frac{b x^4 \sqrt{c x-1} \sqrt{c x+1}}{16 c \sqrt{d-c^2 d x^2}}-\frac{3 b x^2 \sqrt{c x-1} \sqrt{c x+1}}{16 c^3 \sqrt{d-c^2 d x^2}}",1,"(-3*b*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(16*c^3*Sqrt[d - c^2*d*x^2]) - (b*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(16*c*Sqrt[d - c^2*d*x^2]) - (3*x*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(8*c^4*Sqrt[d - c^2*d*x^2]) - (x^3*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(4*c^2*Sqrt[d - c^2*d*x^2]) + (3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(16*b*c^5*Sqrt[d - c^2*d*x^2])","A",6,4,27,0.1481,1,"{5798, 5759, 5676, 30}"
106,1,172,0,0.4964496,"\int \frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^3*(a + b*ArcCosh[c*x]))/Sqrt[d - c^2*d*x^2],x]","-\frac{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{2 (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{b x^3 \sqrt{c x-1} \sqrt{c x+1}}{9 c \sqrt{d-c^2 d x^2}}-\frac{2 b x \sqrt{c x-1} \sqrt{c x+1}}{3 c^3 \sqrt{d-c^2 d x^2}}","-\frac{x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2 d}-\frac{2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^4 d}-\frac{b x^3 \sqrt{c x-1} \sqrt{c x+1}}{9 c \sqrt{d-c^2 d x^2}}-\frac{2 b x \sqrt{c x-1} \sqrt{c x+1}}{3 c^3 \sqrt{d-c^2 d x^2}}",1,"(-2*b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3*c^3*Sqrt[d - c^2*d*x^2]) - (b*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(9*c*Sqrt[d - c^2*d*x^2]) - (2*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(3*c^4*Sqrt[d - c^2*d*x^2]) - (x^2*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(3*c^2*Sqrt[d - c^2*d*x^2])","A",5,5,27,0.1852,1,"{5798, 5759, 5718, 8, 30}"
107,1,140,0,0.3982363,"\int \frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^2*(a + b*ArcCosh[c*x]))/Sqrt[d - c^2*d*x^2],x]","-\frac{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{\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{b x^2 \sqrt{c x-1} \sqrt{c x+1}}{4 c \sqrt{d-c^2 d x^2}}","-\frac{x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{2 c^2 d}+\frac{\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{b x^2 \sqrt{c x-1} \sqrt{c x+1}}{4 c \sqrt{d-c^2 d x^2}}",1,"-(b*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*c*Sqrt[d - c^2*d*x^2]) - (x*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(2*c^2*Sqrt[d - c^2*d*x^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",4,4,27,0.1481,1,"{5798, 5759, 5676, 30}"
108,1,80,0,0.2100741,"\int \frac{x \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x*(a + b*ArcCosh[c*x]))/Sqrt[d - c^2*d*x^2],x]","-\frac{(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 x \sqrt{c x-1} \sqrt{c x+1}}{c \sqrt{d-c^2 d x^2}}","-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{c^2 d}-\frac{b x \sqrt{c x-1} \sqrt{c x+1}}{c \sqrt{d-c^2 d x^2}}",1,"-((b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(c*Sqrt[d - c^2*d*x^2])) - ((1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(c^2*Sqrt[d - c^2*d*x^2])","A",3,3,25,0.1200,1,"{5798, 5718, 8}"
109,1,53,0,0.1214051,"\int \frac{a+b \cosh ^{-1}(c x)}{\sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCosh[c*x])/Sqrt[d - c^2*d*x^2],x]","\frac{\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{\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}}",1,"(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",2,2,24,0.08333,1,"{5713, 5676}"
110,1,151,0,0.3333077,"\int \frac{a+b \cosh ^{-1}(c x)}{x \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCosh[c*x])/(x*Sqrt[d - c^2*d*x^2]),x]","-\frac{i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}+\frac{i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}","-\frac{i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}+\frac{i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}",1,"(2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTan[E^ArcCosh[c*x]])/Sqrt[d - c^2*d*x^2] - (I*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, (-I)*E^ArcCosh[c*x]])/Sqrt[d - c^2*d*x^2] + (I*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, I*E^ArcCosh[c*x]])/Sqrt[d - c^2*d*x^2]","A",7,5,27,0.1852,1,"{5798, 5761, 4180, 2279, 2391}"
111,1,79,0,0.3025307,"\int \frac{a+b \cosh ^{-1}(c x)}{x^2 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCosh[c*x])/(x^2*Sqrt[d - c^2*d*x^2]),x]","-\frac{(1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{x \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{c x-1} \sqrt{c x+1} \log (x)}{\sqrt{d-c^2 d x^2}}","-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{d x}-\frac{b c \sqrt{c x-1} \sqrt{c x+1} \log (x)}{\sqrt{d-c^2 d x^2}}",1,"-(((1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(x*Sqrt[d - c^2*d*x^2])) - (b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[x])/Sqrt[d - c^2*d*x^2]","A",3,3,27,0.1111,1,"{5798, 5724, 29}"
112,1,246,0,0.5410377,"\int \frac{a+b \cosh ^{-1}(c x)}{x^3 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCosh[c*x])/(x^3*Sqrt[d - c^2*d*x^2]),x]","-\frac{i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{2 \sqrt{d-c^2 d x^2}}+\frac{i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{2 \sqrt{d-c^2 d x^2}}-\frac{(1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2 \sqrt{d-c^2 d x^2}}+\frac{c^2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 x \sqrt{d-c^2 d x^2}}","-\frac{i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{2 \sqrt{d-c^2 d x^2}}+\frac{i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{2 \sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{2 d x^2}+\frac{c^2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 x \sqrt{d-c^2 d x^2}}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*x*Sqrt[d - c^2*d*x^2]) - ((1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(2*x^2*Sqrt[d - c^2*d*x^2]) + (c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTan[E^ArcCosh[c*x]])/Sqrt[d - c^2*d*x^2] - ((I/2)*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, (-I)*E^ArcCosh[c*x]])/Sqrt[d - c^2*d*x^2] + ((I/2)*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, I*E^ArcCosh[c*x]])/Sqrt[d - c^2*d*x^2]","A",9,7,27,0.2593,1,"{5798, 5748, 5761, 4180, 2279, 2391, 30}"
113,1,171,0,0.5056761,"\int \frac{a+b \cosh ^{-1}(c x)}{x^4 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCosh[c*x])/(x^4*Sqrt[d - c^2*d*x^2]),x]","-\frac{2 c^2 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{3 x \sqrt{d-c^2 d x^2}}-\frac{(1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3 \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{6 x^2 \sqrt{d-c^2 d x^2}}-\frac{2 b c^3 \sqrt{c x-1} \sqrt{c x+1} \log (x)}{3 \sqrt{d-c^2 d x^2}}","-\frac{2 c^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 d x}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 d x^3}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{6 x^2 \sqrt{d-c^2 d x^2}}-\frac{2 b c^3 \sqrt{c x-1} \sqrt{c x+1} \log (x)}{3 \sqrt{d-c^2 d x^2}}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*x^2*Sqrt[d - c^2*d*x^2]) - ((1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(3*x^3*Sqrt[d - c^2*d*x^2]) - (2*c^2*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(3*x*Sqrt[d - c^2*d*x^2]) - (2*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[x])/(3*Sqrt[d - c^2*d*x^2])","A",5,5,27,0.1852,1,"{5798, 5748, 5724, 29, 30}"
114,1,262,0,0.434414,"\int \frac{x^5 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^5*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(3/2),x]","\frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{4 x^2 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^4 d \sqrt{d-c^2 d x^2}}+\frac{8 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^6 d \sqrt{d-c^2 d x^2}}+\frac{b x^3 \sqrt{c x-1} \sqrt{c x+1}}{9 c^3 d \sqrt{d-c^2 d x^2}}+\frac{5 b x \sqrt{c x-1} \sqrt{c x+1}}{3 c^5 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}(c x)}{c^6 d \sqrt{d-c^2 d x^2}}","-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^6 d^3}+\frac{2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{c^6 d^2}+\frac{a+b \cosh ^{-1}(c x)}{c^6 d \sqrt{d-c^2 d x^2}}-\frac{b x^3 \sqrt{d-c^2 d x^2}}{9 c^3 d^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b x \sqrt{d-c^2 d x^2}}{3 c^5 d^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{d-c^2 d x^2} \tanh ^{-1}(c x)}{c^6 d^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"(5*b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3*c^5*d*Sqrt[d - c^2*d*x^2]) + (b*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(9*c^3*d*Sqrt[d - c^2*d*x^2]) + (x^4*(a + b*ArcCosh[c*x]))/(c^2*d*Sqrt[d - c^2*d*x^2]) + (8*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(3*c^6*d*Sqrt[d - c^2*d*x^2]) + (4*x^2*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(3*c^4*d*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcTanh[c*x])/(c^6*d*Sqrt[d - c^2*d*x^2])","A",5,9,27,0.3333,1,"{5798, 98, 21, 100, 12, 74, 5733, 1153, 208}"
115,1,237,0,0.6809183,"\int \frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^4*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(3/2),x]","\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{3 x (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{2 c^4 d \sqrt{d-c^2 d x^2}}-\frac{3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c^5 d \sqrt{d-c^2 d x^2}}+\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1}}{4 c^3 d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-c^2 x^2\right)}{2 c^5 d \sqrt{d-c^2 d x^2}}","\frac{3 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{2 c^4 d^2}+\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c^5 d \sqrt{d-c^2 d x^2}}+\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1}}{4 c^3 d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-c^2 x^2\right)}{2 c^5 d \sqrt{d-c^2 d x^2}}",1,"(b*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*c^3*d*Sqrt[d - c^2*d*x^2]) + (x^3*(a + b*ArcCosh[c*x]))/(c^2*d*Sqrt[d - c^2*d*x^2]) + (3*x*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(2*c^4*d*Sqrt[d - c^2*d*x^2]) - (3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(4*b*c^5*d*Sqrt[d - c^2*d*x^2]) - (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[1 - c^2*x^2])/(2*c^5*d*Sqrt[d - c^2*d*x^2])","A",8,7,27,0.2593,1,"{5798, 5752, 5759, 5676, 30, 266, 43}"
116,1,163,0,0.3850167,"\int \frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^3*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(3/2),x]","\frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{2 (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 x \sqrt{c x-1} \sqrt{c x+1}}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}(c x)}{c^4 d \sqrt{d-c^2 d x^2}}","\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{c^4 d^2}+\frac{a+b \cosh ^{-1}(c x)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{b x \sqrt{d-c^2 d x^2}}{c^3 d^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{d-c^2 d x^2} \tanh ^{-1}(c x)}{c^4 d^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(c^3*d*Sqrt[d - c^2*d*x^2]) + (x^2*(a + b*ArcCosh[c*x]))/(c^2*d*Sqrt[d - c^2*d*x^2]) + (2*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(c^4*d*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcTanh[c*x])/(c^4*d*Sqrt[d - c^2*d*x^2])","A",4,7,27,0.2593,1,"{5798, 98, 21, 74, 5733, 388, 208}"
117,1,143,0,0.4538949,"\int \frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^2*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(3/2),x]","-\frac{\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{x \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} \log \left(1-c^2 x^2\right)}{2 c^3 d \sqrt{d-c^2 d x^2}}","-\frac{\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{x \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} \log \left(1-c^2 x^2\right)}{2 c^3 d \sqrt{d-c^2 d x^2}}",1,"(x*(a + b*ArcCosh[c*x]))/(c^2*d*Sqrt[d - c^2*d*x^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*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[1 - c^2*x^2])/(2*c^3*d*Sqrt[d - c^2*d*x^2])","A",4,4,27,0.1481,1,"{5798, 5752, 5676, 260}"
118,1,76,0,0.2483231,"\int \frac{x \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(3/2),x]","\frac{a+b \cosh ^{-1}(c x)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}(c x)}{c^2 d \sqrt{d-c^2 d x^2}}","\frac{a+b \cosh ^{-1}(c x)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}(c x)}{c^2 d \sqrt{d-c^2 d x^2}}",1,"(a + b*ArcCosh[c*x])/(c^2*d*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcTanh[c*x])/(c^2*d*Sqrt[d - c^2*d*x^2])","A",3,3,25,0.1200,1,"{5798, 5718, 207}"
119,1,84,0,0.1440781,"\int \frac{a+b \cosh ^{-1}(c x)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])/(d - c^2*d*x^2)^(3/2),x]","\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-c^2 x^2\right)}{2 c d \sqrt{d-c^2 d x^2}}","\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-c^2 x^2\right)}{2 c d \sqrt{d-c^2 d x^2}}",1,"(x*(a + b*ArcCosh[c*x]))/(d*Sqrt[d - c^2*d*x^2]) - (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[1 - c^2*x^2])/(2*c*d*Sqrt[d - c^2*d*x^2])","A",3,3,24,0.1250,1,"{5713, 5688, 260}"
120,1,229,0,0.5906001,"\int \frac{a+b \cosh ^{-1}(c x)}{x \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])/(x*(d - c^2*d*x^2)^(3/2)),x]","-\frac{i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{a+b \cosh ^{-1}(c x)}{d \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}(c x)}{d \sqrt{d-c^2 d x^2}}","-\frac{i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{a+b \cosh ^{-1}(c x)}{d \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}(c x)}{d \sqrt{d-c^2 d x^2}}",1,"(a + b*ArcCosh[c*x])/(d*Sqrt[d - c^2*d*x^2]) + (2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTan[E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcTanh[c*x])/(d*Sqrt[d - c^2*d*x^2]) - (I*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) + (I*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, I*E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2])","A",9,7,27,0.2593,1,"{5798, 5756, 5761, 4180, 2279, 2391, 207}"
121,1,159,0,0.3969385,"\int \frac{a+b \cosh ^{-1}(c x)}{x^2 \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])/(x^2*(d - c^2*d*x^2)^(3/2)),x]","\frac{2 c^2 x \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{a+b \cosh ^{-1}(c x)}{d x \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{c x-1} \sqrt{c x+1} \log (x)}{d \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{c x-1} \sqrt{c x+1} \log \left(1-c^2 x^2\right)}{2 d \sqrt{d-c^2 d x^2}}","\frac{2 c^2 x \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{a+b \cosh ^{-1}(c x)}{d x \sqrt{d-c^2 d x^2}}+\frac{b c \log (x) \sqrt{d-c^2 d x^2}}{d^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c \sqrt{d-c^2 d x^2} \log \left(1-c^2 x^2\right)}{2 d^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"-((a + b*ArcCosh[c*x])/(d*x*Sqrt[d - c^2*d*x^2])) + (2*c^2*x*(a + b*ArcCosh[c*x]))/(d*Sqrt[d - c^2*d*x^2]) - (b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[x])/(d*Sqrt[d - c^2*d*x^2]) - (b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[1 - c^2*x^2])/(2*d*Sqrt[d - c^2*d*x^2])","A",5,7,27,0.2593,1,"{5798, 103, 12, 39, 5733, 446, 72}"
122,1,329,0,0.8624785,"\int \frac{a+b \cosh ^{-1}(c x)}{x^3 \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])/(x^3*(d - c^2*d*x^2)^(3/2)),x]","-\frac{3 i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{2 d \sqrt{d-c^2 d x^2}}+\frac{3 i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{2 d \sqrt{d-c^2 d x^2}}+\frac{3 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 d \sqrt{d-c^2 d x^2}}-\frac{a+b \cosh ^{-1}(c x)}{2 d x^2 \sqrt{d-c^2 d x^2}}+\frac{3 c^2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 d x \sqrt{d-c^2 d x^2}}+\frac{b c^2 \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}(c x)}{d \sqrt{d-c^2 d x^2}}","-\frac{3 i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{2 d \sqrt{d-c^2 d x^2}}+\frac{3 i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{2 d \sqrt{d-c^2 d x^2}}+\frac{3 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 d \sqrt{d-c^2 d x^2}}-\frac{a+b \cosh ^{-1}(c x)}{2 d x^2 \sqrt{d-c^2 d x^2}}+\frac{3 c^2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 d x \sqrt{d-c^2 d x^2}}+\frac{b c^2 \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}(c x)}{d \sqrt{d-c^2 d x^2}}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*d*x*Sqrt[d - c^2*d*x^2]) + (3*c^2*(a + b*ArcCosh[c*x]))/(2*d*Sqrt[d - c^2*d*x^2]) - (a + b*ArcCosh[c*x])/(2*d*x^2*Sqrt[d - c^2*d*x^2]) + (3*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTan[E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) + (b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcTanh[c*x])/(d*Sqrt[d - c^2*d*x^2]) - (((3*I)/2)*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) + (((3*I)/2)*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, I*E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2])","A",12,9,27,0.3333,1,"{5798, 5748, 5756, 5761, 4180, 2279, 2391, 207, 325}"
123,1,250,0,0.4583352,"\int \frac{a+b \cosh ^{-1}(c x)}{x^4 \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])/(x^4*(d - c^2*d*x^2)^(3/2)),x]","\frac{8 c^4 x \left(a+b \cosh ^{-1}(c x)\right)}{3 d \sqrt{d-c^2 d x^2}}-\frac{4 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{3 d x \sqrt{d-c^2 d x^2}}-\frac{a+b \cosh ^{-1}(c x)}{3 d x^3 \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{6 d x^2 \sqrt{d-c^2 d x^2}}-\frac{5 b c^3 \sqrt{c x-1} \sqrt{c x+1} \log (x)}{3 d \sqrt{d-c^2 d x^2}}-\frac{b c^3 \sqrt{c x-1} \sqrt{c x+1} \log \left(1-c^2 x^2\right)}{2 d \sqrt{d-c^2 d x^2}}","\frac{8 c^4 x \left(a+b \cosh ^{-1}(c x)\right)}{3 d \sqrt{d-c^2 d x^2}}-\frac{4 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{3 d x \sqrt{d-c^2 d x^2}}-\frac{a+b \cosh ^{-1}(c x)}{3 d x^3 \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{d-c^2 d x^2}}{6 d^2 x^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c^3 \log (x) \sqrt{d-c^2 d x^2}}{3 d^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 \sqrt{d-c^2 d x^2} \log \left(1-c^2 x^2\right)}{2 d^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*d*x^2*Sqrt[d - c^2*d*x^2]) - (a + b*ArcCosh[c*x])/(3*d*x^3*Sqrt[d - c^2*d*x^2]) - (4*c^2*(a + b*ArcCosh[c*x]))/(3*d*x*Sqrt[d - c^2*d*x^2]) + (8*c^4*x*(a + b*ArcCosh[c*x]))/(3*d*Sqrt[d - c^2*d*x^2]) - (5*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[x])/(3*d*Sqrt[d - c^2*d*x^2]) - (b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[1 - c^2*x^2])/(2*d*Sqrt[d - c^2*d*x^2])","A",6,7,27,0.2593,1,"{5798, 103, 12, 39, 5733, 1251, 893}"
124,1,280,0,0.4426933,"\int \frac{x^5 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^5*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(5/2),x]","\frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}-\frac{4 x^2 \left(a+b \cosh ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{8 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^6 d^2 \sqrt{d-c^2 d x^2}}-\frac{b x \sqrt{c x-1} \sqrt{c x+1}}{c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{b x \sqrt{c x-1} \sqrt{c x+1}}{6 c^5 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{11 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}(c x)}{6 c^6 d^2 \sqrt{d-c^2 d x^2}}","-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{c^6 d^3}-\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{c^6 d^2 \sqrt{d-c^2 d x^2}}+\frac{a+b \cosh ^{-1}(c x)}{3 c^6 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b x \sqrt{d-c^2 d x^2}}{c^5 d^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b x \sqrt{d-c^2 d x^2}}{6 c^5 d^3 \sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)}+\frac{11 b \sqrt{d-c^2 d x^2} \tanh ^{-1}(c x)}{6 c^6 d^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"-((b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(c^5*d^2*Sqrt[d - c^2*d*x^2])) + (b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*c^5*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) - (4*x^2*(a + b*ArcCosh[c*x]))/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) + (x^4*(a + b*ArcCosh[c*x]))/(3*c^2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (8*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x]))/(3*c^6*d^2*Sqrt[d - c^2*d*x^2]) - (11*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcTanh[c*x])/(6*c^6*d^2*Sqrt[d - c^2*d*x^2])","A",6,9,27,0.3333,1,"{5798, 98, 21, 74, 5733, 12, 1157, 388, 206}"
125,1,251,0,0.7571943,"\int \frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^4*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(5/2),x]","\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}-\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1}}{6 c^5 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{2 b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-c^2 x^2\right)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}","-\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{2 b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-c^2 x^2\right)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1}}{6 c^5 d \left(d-c^2 d x^2\right)^{3/2}}",1,"(b*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*c^5*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) - (x*(a + b*ArcCosh[c*x]))/(c^4*d^2*Sqrt[d - c^2*d*x^2]) + (x^3*(a + b*ArcCosh[c*x]))/(3*c^2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(2*b*c^5*d^2*Sqrt[d - c^2*d*x^2]) + (2*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[1 - c^2*x^2])/(3*c^5*d^2*Sqrt[d - c^2*d*x^2])","A",8,6,27,0.2222,1,"{5798, 5752, 5676, 260, 266, 43}"
126,1,243,0,0.4476812,"\int \frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^3*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(5/2),x]","\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{3 c d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{(1-c x)^2 \left(a+b \cosh ^{-1}(c x)\right)}{3 c^4 d^2 (c x+1) \sqrt{d-c^2 d x^2}}-\frac{a+b \cosh ^{-1}(c x)}{c^4 d^2 (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b x \sqrt{c x-1} \sqrt{c x+1}}{6 c^3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{5 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}(c x)}{6 c^4 d^2 \sqrt{d-c^2 d x^2}}","-\frac{a+b \cosh ^{-1}(c x)}{c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{a+b \cosh ^{-1}(c x)}{3 c^4 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b x \sqrt{d-c^2 d x^2}}{6 c^3 d^3 (c x-1)^{3/2} (c x+1)^{3/2}}+\frac{5 b \sqrt{d-c^2 d x^2} \tanh ^{-1}(c x)}{6 c^4 d^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*c^3*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) - (a + b*ArcCosh[c*x])/(c^4*d^2*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + (x^3*(a + b*ArcCosh[c*x]))/(3*c*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + ((1 - c*x)^2*(a + b*ArcCosh[c*x]))/(3*c^4*d^2*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (5*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcTanh[c*x])/(6*c^4*d^2*Sqrt[d - c^2*d*x^2])","A",5,9,27,0.3333,1,"{5798, 94, 89, 21, 37, 5733, 12, 385, 206}"
127,1,160,0,0.4048689,"\int \frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^2*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(5/2),x]","\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1}}{6 c^3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-c^2 x^2\right)}{6 c^3 d^2 \sqrt{d-c^2 d x^2}}","\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{3 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-c^2 x^2\right)}{6 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1}}{6 c^3 d \left(d-c^2 d x^2\right)^{3/2}}",1,"(b*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*c^3*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (x^3*(a + b*ArcCosh[c*x]))/(3*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[1 - c^2*x^2])/(6*c^3*d^2*Sqrt[d - c^2*d*x^2])","A",5,4,27,0.1481,1,"{5798, 5724, 266, 43}"
128,1,154,0,0.2758236,"\int \frac{x \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(5/2),x]","\frac{a+b \cosh ^{-1}(c x)}{3 c^2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b x \sqrt{c x-1} \sqrt{c x+1}}{6 c d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}(c x)}{6 c^2 d^2 \sqrt{d-c^2 d x^2}}","\frac{a+b \cosh ^{-1}(c x)}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}(c x)}{6 c^2 d^2 \sqrt{d-c^2 d x^2}}+\frac{b x \sqrt{c x-1} \sqrt{c x+1}}{6 c d \left(d-c^2 d x^2\right)^{3/2}}",1,"(b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*c*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (a + b*ArcCosh[c*x])/(3*c^2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcTanh[c*x])/(6*c^2*d^2*Sqrt[d - c^2*d*x^2])","A",4,4,25,0.1600,1,"{5798, 5718, 199, 207}"
129,1,189,0,0.2681823,"\int \frac{a+b \cosh ^{-1}(c x)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCosh[c*x])/(d - c^2*d*x^2)^(5/2),x]","\frac{2 x \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1}}{6 c d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-c^2 x^2\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}","\frac{2 x \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-c^2 x^2\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1}}{6 c d \left(d-c^2 d x^2\right)^{3/2}}",1,"(b*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*c*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (2*x*(a + b*ArcCosh[c*x]))/(3*d^2*Sqrt[d - c^2*d*x^2]) + (x*(a + b*ArcCosh[c*x]))/(3*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[1 - c^2*x^2])/(3*c*d^2*Sqrt[d - c^2*d*x^2])","A",5,5,24,0.2083,1,"{5713, 5691, 5688, 260, 261}"
130,1,332,0,0.8316963,"\int \frac{a+b \cosh ^{-1}(c x)}{x \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCosh[c*x])/(x*(d - c^2*d*x^2)^(5/2)),x]","-\frac{i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{a+b \cosh ^{-1}(c x)}{3 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{a+b \cosh ^{-1}(c x)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{b c x \sqrt{c x-1} \sqrt{c x+1}}{6 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{7 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}(c x)}{6 d^2 \sqrt{d-c^2 d x^2}}","-\frac{i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{a+b \cosh ^{-1}(c x)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{a+b \cosh ^{-1}(c x)}{3 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b c x \sqrt{c x-1} \sqrt{c x+1}}{6 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{7 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}(c x)}{6 d^2 \sqrt{d-c^2 d x^2}}",1,"(b*c*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (a + b*ArcCosh[c*x])/(d^2*Sqrt[d - c^2*d*x^2]) + (a + b*ArcCosh[c*x])/(3*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + (2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTan[E^ArcCosh[c*x]])/(d^2*Sqrt[d - c^2*d*x^2]) + (7*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcTanh[c*x])/(6*d^2*Sqrt[d - c^2*d*x^2]) - (I*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(d^2*Sqrt[d - c^2*d*x^2]) + (I*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, I*E^ArcCosh[c*x]])/(d^2*Sqrt[d - c^2*d*x^2])","A",12,8,27,0.2963,1,"{5798, 5756, 5761, 4180, 2279, 2391, 207, 199}"
131,1,279,0,0.4419498,"\int \frac{a+b \cosh ^{-1}(c x)}{x^2 \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCosh[c*x])/(x^2*(d - c^2*d*x^2)^(5/2)),x]","\frac{8 c^2 x \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{4 c^2 x \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}-\frac{a+b \cosh ^{-1}(c x)}{d^2 x (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{6 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{c x-1} \sqrt{c x+1} \log (x)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{5 b c \sqrt{c x-1} \sqrt{c x+1} \log \left(1-c^2 x^2\right)}{6 d^2 \sqrt{d-c^2 d x^2}}","\frac{8 c^2 x \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{4 c^2 x \left(a+b \cosh ^{-1}(c x)\right)}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{a+b \cosh ^{-1}(c x)}{d x \left(d-c^2 d x^2\right)^{3/2}}-\frac{b c \sqrt{d-c^2 d x^2}}{6 d^3 \sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)}+\frac{b c \log (x) \sqrt{d-c^2 d x^2}}{d^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c \sqrt{d-c^2 d x^2} \log \left(1-c^2 x^2\right)}{6 d^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (8*c^2*x*(a + b*ArcCosh[c*x]))/(3*d^2*Sqrt[d - c^2*d*x^2]) - (a + b*ArcCosh[c*x])/(d^2*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + (4*c^2*x*(a + b*ArcCosh[c*x]))/(3*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[x])/(d^2*Sqrt[d - c^2*d*x^2]) - (5*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[1 - c^2*x^2])/(6*d^2*Sqrt[d - c^2*d*x^2])","A",6,8,27,0.2963,1,"{5798, 103, 12, 40, 39, 5733, 1251, 893}"
132,1,509,0,1.1427858,"\int \frac{a+b \cosh ^{-1}(c x)}{x^3 \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCosh[c*x])/(x^3*(d - c^2*d*x^2)^(5/2)),x]","-\frac{5 i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{2 d^2 \sqrt{d-c^2 d x^2}}+\frac{5 i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{2 d^2 \sqrt{d-c^2 d x^2}}+\frac{5 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{6 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{5 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 d^2 \sqrt{d-c^2 d x^2}}-\frac{a+b \cosh ^{-1}(c x)}{2 d^2 x^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{5 c^2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{5 b c^3 x \sqrt{c x-1} \sqrt{c x+1}}{12 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{3 b c \sqrt{c x-1} \sqrt{c x+1}}{4 d^2 x \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{4 d^2 x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{13 b c^2 \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}(c x)}{6 d^2 \sqrt{d-c^2 d x^2}}","-\frac{5 i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{2 d^2 \sqrt{d-c^2 d x^2}}+\frac{5 i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{2 d^2 \sqrt{d-c^2 d x^2}}+\frac{5 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 d^2 \sqrt{d-c^2 d x^2}}+\frac{5 c^2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{5 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{6 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{a+b \cosh ^{-1}(c x)}{2 d x^2 \left(d-c^2 d x^2\right)^{3/2}}+\frac{5 b c^3 x \sqrt{c x-1} \sqrt{c x+1}}{12 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{3 b c \sqrt{c x-1} \sqrt{c x+1}}{4 d^2 x \sqrt{d-c^2 d x^2}}-\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{4 d^2 x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{13 b c^2 \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}(c x)}{6 d^2 \sqrt{d-c^2 d x^2}}",1,"(3*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*d^2*x*Sqrt[d - c^2*d*x^2]) - (b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*d^2*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (5*b*c^3*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(12*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (5*c^2*(a + b*ArcCosh[c*x]))/(2*d^2*Sqrt[d - c^2*d*x^2]) + (5*c^2*(a + b*ArcCosh[c*x]))/(6*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (a + b*ArcCosh[c*x])/(2*d^2*x^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + (5*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTan[E^ArcCosh[c*x]])/(d^2*Sqrt[d - c^2*d*x^2]) + (13*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcTanh[c*x])/(6*d^2*Sqrt[d - c^2*d*x^2]) - (((5*I)/2)*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(d^2*Sqrt[d - c^2*d*x^2]) + (((5*I)/2)*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, I*E^ArcCosh[c*x]])/(d^2*Sqrt[d - c^2*d*x^2])","A",16,11,27,0.4074,1,"{5798, 5748, 5756, 5761, 4180, 2279, 2391, 207, 199, 290, 325}"
133,1,383,0,0.5413762,"\int \frac{a+b \cosh ^{-1}(c x)}{x^4 \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCosh[c*x])/(x^4*(d - c^2*d*x^2)^(5/2)),x]","\frac{16 c^4 x \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{8 c^4 x \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}-\frac{2 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{d^2 x (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}-\frac{a+b \cosh ^{-1}(c x)}{3 d^2 x^3 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b c^3 \sqrt{c x-1} \sqrt{c x+1}}{6 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{6 d^2 x^2 \sqrt{d-c^2 d x^2}}-\frac{8 b c^3 \sqrt{c x-1} \sqrt{c x+1} \log (x)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{4 b c^3 \sqrt{c x-1} \sqrt{c x+1} \log \left(1-c^2 x^2\right)}{3 d^2 \sqrt{d-c^2 d x^2}}","\frac{16 c^4 x \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{8 c^4 x \left(a+b \cosh ^{-1}(c x)\right)}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{2 c^2 \left(a+b \cosh ^{-1}(c x)\right)}{d x \left(d-c^2 d x^2\right)^{3/2}}-\frac{a+b \cosh ^{-1}(c x)}{3 d x^3 \left(d-c^2 d x^2\right)^{3/2}}-\frac{b c^3 \sqrt{d-c^2 d x^2}}{6 d^3 \sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)}-\frac{b c \sqrt{d-c^2 d x^2}}{6 d^3 x^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{8 b c^3 \log (x) \sqrt{d-c^2 d x^2}}{3 d^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{4 b c^3 \sqrt{d-c^2 d x^2} \log \left(1-c^2 x^2\right)}{3 d^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*d^2*x^2*Sqrt[d - c^2*d*x^2]) + (b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (16*c^4*x*(a + b*ArcCosh[c*x]))/(3*d^2*Sqrt[d - c^2*d*x^2]) - (a + b*ArcCosh[c*x])/(3*d^2*x^3*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (2*c^2*(a + b*ArcCosh[c*x]))/(d^2*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + (8*c^4*x*(a + b*ArcCosh[c*x]))/(3*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (8*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[x])/(3*d^2*Sqrt[d - c^2*d*x^2]) - (4*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[1 - c^2*x^2])/(3*d^2*Sqrt[d - c^2*d*x^2])","A",6,8,27,0.2963,1,"{5798, 103, 12, 40, 39, 5733, 1799, 1620}"
134,1,276,0,0.3391777,"\int \frac{\cosh ^{-1}(a x)}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[ArcCosh[a*x]/(c - a^2*c*x^2)^(7/2),x]","\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{15 a c^3 \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1}}{20 a c^3 \left(1-a^2 x^2\right)^2 \sqrt{c-a^2 c x^2}}-\frac{4 \sqrt{a x-1} \sqrt{a x+1} \log \left(1-a^2 x^2\right)}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{8 x \cosh ^{-1}(a x)}{15 c^3 \sqrt{c-a^2 c x^2}}+\frac{4 x \cosh ^{-1}(a x)}{15 c^3 (1-a x) (a x+1) \sqrt{c-a^2 c x^2}}+\frac{x \cosh ^{-1}(a x)}{5 c^3 (1-a x)^2 (a x+1)^2 \sqrt{c-a^2 c x^2}}","\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{15 a c^3 \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1}}{20 a c^3 \left(1-a^2 x^2\right)^2 \sqrt{c-a^2 c x^2}}-\frac{4 \sqrt{a x-1} \sqrt{a x+1} \log \left(1-a^2 x^2\right)}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{8 x \cosh ^{-1}(a x)}{15 c^3 \sqrt{c-a^2 c x^2}}+\frac{4 x \cosh ^{-1}(a x)}{15 c^2 \left(c-a^2 c x^2\right)^{3/2}}+\frac{x \cosh ^{-1}(a x)}{5 c \left(c-a^2 c x^2\right)^{5/2}}",1,"(Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(20*a*c^3*(1 - a^2*x^2)^2*Sqrt[c - a^2*c*x^2]) + (2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(15*a*c^3*(1 - a^2*x^2)*Sqrt[c - a^2*c*x^2]) + (8*x*ArcCosh[a*x])/(15*c^3*Sqrt[c - a^2*c*x^2]) + (x*ArcCosh[a*x])/(5*c^3*(1 - a*x)^2*(1 + a*x)^2*Sqrt[c - a^2*c*x^2]) + (4*x*ArcCosh[a*x])/(15*c^3*(1 - a*x)*(1 + a*x)*Sqrt[c - a^2*c*x^2]) - (4*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Log[1 - a^2*x^2])/(15*a*c^3*Sqrt[c - a^2*c*x^2])","A",7,5,20,0.2500,1,"{5713, 5691, 5688, 260, 261}"
135,1,206,0,0.5008432,"\int \frac{x^4 \cosh ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^4*ArcCosh[a*x])/Sqrt[1 - a^2*x^2],x]","-\frac{x^4 \sqrt{a x-1} \sqrt{a x+1}}{16 a \sqrt{1-a^2 x^2}}-\frac{3 x^2 \sqrt{a x-1} \sqrt{a x+1}}{16 a^3 \sqrt{1-a^2 x^2}}-\frac{x^3 (1-a x) (a x+1) \cosh ^{-1}(a x)}{4 a^2 \sqrt{1-a^2 x^2}}-\frac{3 x (1-a x) (a x+1) \cosh ^{-1}(a x)}{8 a^4 \sqrt{1-a^2 x^2}}+\frac{3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{16 a^5 \sqrt{1-a^2 x^2}}","-\frac{3 x^2 \sqrt{a x-1}}{16 a^3 \sqrt{1-a x}}-\frac{x^3 \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)}{4 a^2}-\frac{3 x \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)}{8 a^4}+\frac{3 \sqrt{a x-1} \cosh ^{-1}(a x)^2}{16 a^5 \sqrt{1-a x}}-\frac{x^4 \sqrt{a x-1}}{16 a \sqrt{1-a x}}",1,"(-3*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(16*a^3*Sqrt[1 - a^2*x^2]) - (x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(16*a*Sqrt[1 - a^2*x^2]) - (3*x*(1 - a*x)*(1 + a*x)*ArcCosh[a*x])/(8*a^4*Sqrt[1 - a^2*x^2]) - (x^3*(1 - a*x)*(1 + a*x)*ArcCosh[a*x])/(4*a^2*Sqrt[1 - a^2*x^2]) + (3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(16*a^5*Sqrt[1 - a^2*x^2])","A",6,4,22,0.1818,1,"{5798, 5759, 5676, 30}"
136,1,158,0,0.3922736,"\int \frac{x^3 \cosh ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^3*ArcCosh[a*x])/Sqrt[1 - a^2*x^2],x]","-\frac{x^3 \sqrt{a x-1} \sqrt{a x+1}}{9 a \sqrt{1-a^2 x^2}}-\frac{2 x \sqrt{a x-1} \sqrt{a x+1}}{3 a^3 \sqrt{1-a^2 x^2}}-\frac{x^2 (1-a x) (a x+1) \cosh ^{-1}(a x)}{3 a^2 \sqrt{1-a^2 x^2}}-\frac{2 (1-a x) (a x+1) \cosh ^{-1}(a x)}{3 a^4 \sqrt{1-a^2 x^2}}","-\frac{x^2 \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)}{3 a^2}-\frac{2 \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)}{3 a^4}-\frac{2 x \sqrt{a x-1}}{3 a^3 \sqrt{1-a x}}-\frac{x^3 \sqrt{a x-1}}{9 a \sqrt{1-a x}}",1,"(-2*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(3*a^3*Sqrt[1 - a^2*x^2]) - (x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(9*a*Sqrt[1 - a^2*x^2]) - (2*(1 - a*x)*(1 + a*x)*ArcCosh[a*x])/(3*a^4*Sqrt[1 - a^2*x^2]) - (x^2*(1 - a*x)*(1 + a*x)*ArcCosh[a*x])/(3*a^2*Sqrt[1 - a^2*x^2])","A",5,5,22,0.2273,1,"{5798, 5759, 5718, 8, 30}"
137,1,125,0,0.3243359,"\int \frac{x^2 \cosh ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^2*ArcCosh[a*x])/Sqrt[1 - a^2*x^2],x]","-\frac{x^2 \sqrt{a x-1} \sqrt{a x+1}}{4 a \sqrt{1-a^2 x^2}}-\frac{x (1-a x) (a x+1) \cosh ^{-1}(a x)}{2 a^2 \sqrt{1-a^2 x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{4 a^3 \sqrt{1-a^2 x^2}}","-\frac{x \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)}{2 a^2}+\frac{\sqrt{a x-1} \cosh ^{-1}(a x)^2}{4 a^3 \sqrt{1-a x}}-\frac{x^2 \sqrt{a x-1}}{4 a \sqrt{1-a x}}",1,"-(x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(4*a*Sqrt[1 - a^2*x^2]) - (x*(1 - a*x)*(1 + a*x)*ArcCosh[a*x])/(2*a^2*Sqrt[1 - a^2*x^2]) + (Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(4*a^3*Sqrt[1 - a^2*x^2])","A",4,4,22,0.1818,1,"{5798, 5759, 5676, 30}"
138,1,73,0,0.1768848,"\int \frac{x \cosh ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[(x*ArcCosh[a*x])/Sqrt[1 - a^2*x^2],x]","-\frac{x \sqrt{a x-1} \sqrt{a x+1}}{a \sqrt{1-a^2 x^2}}-\frac{(1-a x) (a x+1) \cosh ^{-1}(a x)}{a^2 \sqrt{1-a^2 x^2}}","-\frac{\sqrt{1-a^2 x^2} \cosh ^{-1}(a x)}{a^2}-\frac{x \sqrt{a x-1}}{a \sqrt{1-a x}}",1,"-((x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a*Sqrt[1 - a^2*x^2])) - ((1 - a*x)*(1 + a*x)*ArcCosh[a*x])/(a^2*Sqrt[1 - a^2*x^2])","A",3,3,20,0.1500,1,"{5798, 5718, 8}"
139,1,45,0,0.098098,"\int \frac{\cosh ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[ArcCosh[a*x]/Sqrt[1 - a^2*x^2],x]","\frac{\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{2 a \sqrt{1-a^2 x^2}}","\frac{\sqrt{a x-1} \cosh ^{-1}(a x)^2}{2 a \sqrt{1-a x}}",1,"(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(2*a*Sqrt[1 - a^2*x^2])","A",2,2,19,0.1053,1,"{5713, 5676}"
140,1,142,0,0.2760473,"\int \frac{\cosh ^{-1}(a x)}{x \sqrt{1-a^2 x^2}} \, dx","Int[ArcCosh[a*x]/(x*Sqrt[1 - a^2*x^2]),x]","-\frac{i \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}+\frac{i \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}+\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}","-\frac{i \sqrt{a x-1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{i \sqrt{a x-1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{2 \sqrt{a x-1} \cosh ^{-1}(a x) \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}",1,"(2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*ArcTan[E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] - (I*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[2, (-I)*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] + (I*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[2, I*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2]","A",7,5,22,0.2273,1,"{5798, 5761, 4180, 2279, 2391}"
141,1,72,0,0.2541046,"\int \frac{\cosh ^{-1}(a x)}{x^2 \sqrt{1-a^2 x^2}} \, dx","Int[ArcCosh[a*x]/(x^2*Sqrt[1 - a^2*x^2]),x]","-\frac{a \sqrt{a x-1} \sqrt{a x+1} \log (x)}{\sqrt{1-a^2 x^2}}-\frac{(1-a x) (a x+1) \cosh ^{-1}(a x)}{x \sqrt{1-a^2 x^2}}","-\frac{\sqrt{1-a^2 x^2} \cosh ^{-1}(a x)}{x}-\frac{a \sqrt{a x-1} \log (x)}{\sqrt{1-a x}}",1,"-(((1 - a*x)*(1 + a*x)*ArcCosh[a*x])/(x*Sqrt[1 - a^2*x^2])) - (a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Log[x])/Sqrt[1 - a^2*x^2]","A",3,3,22,0.1364,1,"{5798, 5724, 29}"
142,1,230,0,0.4712886,"\int \frac{\cosh ^{-1}(a x)}{x^3 \sqrt{1-a^2 x^2}} \, dx","Int[ArcCosh[a*x]/(x^3*Sqrt[1 - a^2*x^2]),x]","-\frac{i a^2 \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)}{2 \sqrt{1-a^2 x^2}}+\frac{i a^2 \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)}{2 \sqrt{1-a^2 x^2}}+\frac{a \sqrt{a x-1} \sqrt{a x+1}}{2 x \sqrt{1-a^2 x^2}}-\frac{(1-a x) (a x+1) \cosh ^{-1}(a x)}{2 x^2 \sqrt{1-a^2 x^2}}+\frac{a^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}","-\frac{i a^2 \sqrt{a x-1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)}{2 \sqrt{1-a x}}+\frac{i a^2 \sqrt{a x-1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)}{2 \sqrt{1-a x}}-\frac{\sqrt{1-a^2 x^2} \cosh ^{-1}(a x)}{2 x^2}+\frac{a^2 \sqrt{a x-1} \cosh ^{-1}(a x) \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{a \sqrt{a x-1}}{2 x \sqrt{1-a x}}",1,"(a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(2*x*Sqrt[1 - a^2*x^2]) - ((1 - a*x)*(1 + a*x)*ArcCosh[a*x])/(2*x^2*Sqrt[1 - a^2*x^2]) + (a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*ArcTan[E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] - ((I/2)*a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[2, (-I)*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] + ((I/2)*a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[2, I*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2]","A",9,7,22,0.3182,1,"{5798, 5748, 5761, 4180, 2279, 2391, 30}"
143,1,111,0,0.3577044,"\int \frac{(f x)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{1-c^2 x^2}} \, dx","Int[((f*x)^(3/2)*(a + b*ArcCosh[c*x]))/Sqrt[1 - c^2*x^2],x]","\frac{4 b c \sqrt{c x-1} \sqrt{c x+1} (f x)^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};c^2 x^2\right)}{35 f^2 \sqrt{1-c^2 x^2}}+\frac{2 (f x)^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{5 f}","\frac{4 b c \sqrt{c x-1} (f x)^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};c^2 x^2\right)}{35 f^2 \sqrt{1-c x}}+\frac{2 (f x)^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{5 f}",1,"(2*(f*x)^(5/2)*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, 5/4, 9/4, c^2*x^2])/(5*f) + (4*b*c*(f*x)^(7/2)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*HypergeometricPFQ[{1, 7/4, 7/4}, {9/4, 11/4}, c^2*x^2])/(35*f^2*Sqrt[1 - c^2*x^2])","A",2,2,30,0.06667,1,"{5798, 5763}"
144,1,141,0,0.3825494,"\int \frac{(f x)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f*x)^(3/2)*(a + b*ArcCosh[c*x]))/Sqrt[d - c^2*d*x^2],x]","\frac{4 b c \sqrt{c x-1} \sqrt{c x+1} (f x)^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};c^2 x^2\right)}{35 f^2 \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{1-c^2 x^2} (f x)^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{5 f \sqrt{d-c^2 d x^2}}","\frac{4 b c \sqrt{c x-1} \sqrt{c x+1} (f x)^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};c^2 x^2\right)}{35 f^2 \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{1-c^2 x^2} (f x)^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{5 f \sqrt{d-c^2 d x^2}}",1,"(2*(f*x)^(5/2)*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, 5/4, 9/4, c^2*x^2])/(5*f*Sqrt[d - c^2*d*x^2]) + (4*b*c*(f*x)^(7/2)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*HypergeometricPFQ[{1, 7/4, 7/4}, {9/4, 11/4}, c^2*x^2])/(35*f^2*Sqrt[d - c^2*d*x^2])","A",2,2,31,0.06452,1,"{5798, 5763}"
145,1,429,0,2.7550457,"\int (f x)^m \left(d-c^2 d x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d - c^2*d*x^2)^3*(a + b*ArcCosh[c*x]),x]","-\frac{3 c^2 d^3 (f x)^{m+3} \left(a+b \cosh ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{3 c^4 d^3 (f x)^{m+5} \left(a+b \cosh ^{-1}(c x)\right)}{f^5 (m+5)}-\frac{c^6 d^3 (f x)^{m+7} \left(a+b \cosh ^{-1}(c x)\right)}{f^7 (m+7)}+\frac{d^3 (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+1)}-\frac{3 b c d^3 \left(35 m^3+455 m^2+1813 m+2161\right) \sqrt{1-c^2 x^2} (f x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{f^2 (m+1) (m+2) (m+3)^2 (m+5)^2 (m+7)^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^3 \left(m^4+27 m^3+284 m^2+1329 m+2271\right) \left(1-c^2 x^2\right) (f x)^{m+2}}{f^2 (m+3)^2 (m+5)^2 (m+7)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d^3 (m+9) (2 m+13) \left(1-c^2 x^2\right) (f x)^{m+4}}{f^4 (m+5)^2 (m+7)^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 d^3 \left(1-c^2 x^2\right) (f x)^{m+6}}{f^6 (m+7)^2 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{3 c^2 d^3 (f x)^{m+3} \left(a+b \cosh ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{3 c^4 d^3 (f x)^{m+5} \left(a+b \cosh ^{-1}(c x)\right)}{f^5 (m+5)}-\frac{c^6 d^3 (f x)^{m+7} \left(a+b \cosh ^{-1}(c x)\right)}{f^7 (m+7)}+\frac{d^3 (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+1)}-\frac{3 b c d^3 \left(35 m^3+455 m^2+1813 m+2161\right) \sqrt{1-c^2 x^2} (f x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{f^2 (m+1) (m+2) (m+3)^2 (m+5)^2 (m+7)^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^3 \left(m^4+27 m^3+284 m^2+1329 m+2271\right) \left(1-c^2 x^2\right) (f x)^{m+2}}{f^2 (m+3)^2 (m+5)^2 (m+7)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d^3 (m+9) (2 m+13) \left(1-c^2 x^2\right) (f x)^{m+4}}{f^4 (m+5)^2 (m+7)^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 d^3 \left(1-c^2 x^2\right) (f x)^{m+6}}{f^6 (m+7)^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"-((b*c*d^3*(2271 + 1329*m + 284*m^2 + 27*m^3 + m^4)*(f*x)^(2 + m)*(1 - c^2*x^2))/(f^2*(3 + m)^2*(5 + m)^2*(7 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])) + (b*c^3*d^3*(9 + m)*(13 + 2*m)*(f*x)^(4 + m)*(1 - c^2*x^2))/(f^4*(5 + m)^2*(7 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^3*(f*x)^(6 + m)*(1 - c^2*x^2))/(f^6*(7 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (d^3*(f*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(f*(1 + m)) - (3*c^2*d^3*(f*x)^(3 + m)*(a + b*ArcCosh[c*x]))/(f^3*(3 + m)) + (3*c^4*d^3*(f*x)^(5 + m)*(a + b*ArcCosh[c*x]))/(f^5*(5 + m)) - (c^6*d^3*(f*x)^(7 + m)*(a + b*ArcCosh[c*x]))/(f^7*(7 + m)) - (3*b*c*d^3*(2161 + 1813*m + 455*m^2 + 35*m^3)*(f*x)^(2 + m)*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(f^2*(1 + m)*(2 + m)*(3 + m)^2*(5 + m)^2*(7 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",8,9,27,0.3333,1,"{270, 5731, 12, 1610, 1809, 1267, 459, 365, 364}"
146,1,307,0,0.5009948,"\int (f x)^m \left(d-c^2 d x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d - c^2*d*x^2)^2*(a + b*ArcCosh[c*x]),x]","-\frac{2 c^2 d^2 (f x)^{m+3} \left(a+b \cosh ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{c^4 d^2 (f x)^{m+5} \left(a+b \cosh ^{-1}(c x)\right)}{f^5 (m+5)}+\frac{d^2 (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+1)}-\frac{b c d^2 \left(15 m^2+100 m+149\right) \sqrt{1-c^2 x^2} (f x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{f^2 (m+1) (m+2) (m+3)^2 (m+5)^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \left(m^2+13 m+38\right) \left(1-c^2 x^2\right) (f x)^{m+2}}{f^2 (m+3)^2 (m+5)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d^2 \left(1-c^2 x^2\right) (f x)^{m+4}}{f^4 (m+5)^2 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{2 c^2 d^2 (f x)^{m+3} \left(a+b \cosh ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{c^4 d^2 (f x)^{m+5} \left(a+b \cosh ^{-1}(c x)\right)}{f^5 (m+5)}+\frac{d^2 (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+1)}-\frac{b c d^2 \left(15 m^2+100 m+149\right) \sqrt{1-c^2 x^2} (f x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{f^2 (m+1) (m+2) (m+3)^2 (m+5)^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \left(m^2+13 m+38\right) \left(1-c^2 x^2\right) (f x)^{m+2}}{f^2 (m+3)^2 (m+5)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d^2 \left(1-c^2 x^2\right) (f x)^{m+4}}{f^4 (m+5)^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"-((b*c*d^2*(38 + 13*m + m^2)*(f*x)^(2 + m)*(1 - c^2*x^2))/(f^2*(3 + m)^2*(5 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])) + (b*c^3*d^2*(f*x)^(4 + m)*(1 - c^2*x^2))/(f^4*(5 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (d^2*(f*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(f*(1 + m)) - (2*c^2*d^2*(f*x)^(3 + m)*(a + b*ArcCosh[c*x]))/(f^3*(3 + m)) + (c^4*d^2*(f*x)^(5 + m)*(a + b*ArcCosh[c*x]))/(f^5*(5 + m)) - (b*c*d^2*(149 + 100*m + 15*m^2)*(f*x)^(2 + m)*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(f^2*(1 + m)*(2 + m)*(3 + m)^2*(5 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",7,8,27,0.2963,1,"{270, 5731, 12, 520, 1267, 459, 365, 364}"
147,1,184,0,0.2582239,"\int (f x)^m \left(d-c^2 d x^2\right) \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d - c^2*d*x^2)*(a + b*ArcCosh[c*x]),x]","-\frac{c^2 d (f x)^{m+3} \left(a+b \cosh ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{d (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+1)}-\frac{b c d (3 m+7) \sqrt{1-c^2 x^2} (f x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{f^2 (m+1) (m+2) (m+3)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2}}{f^2 (m+3)^2}","-\frac{c^2 d (f x)^{m+3} \left(a+b \cosh ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{d (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+1)}-\frac{b c d (3 m+7) \sqrt{1-c^2 x^2} (f x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{f^2 (m+1) (m+2) (m+3)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2}}{f^2 (m+3)^2}",1,"(b*c*d*(f*x)^(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(f^2*(3 + m)^2) + (d*(f*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(f*(1 + m)) - (c^2*d*(f*x)^(3 + m)*(a + b*ArcCosh[c*x]))/(f^3*(3 + m)) - (b*c*d*(7 + 3*m)*(f*x)^(2 + m)*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(f^2*(1 + m)*(2 + m)*(3 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",6,7,25,0.2800,1,"{14, 5731, 12, 460, 126, 365, 364}"
148,0,0,0,0.0720581,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{d-c^2 d x^2} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2),x]","\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{d-c^2 d x^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{d-c^2 d x^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2), x]","A",0,0,0,0,-1,"{}"
149,0,0,0,0.2074917,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^2} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^2,x]","\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^2} \, dx","\frac{(1-m) \text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{d-c^2 d x^2},x\right)}{2 d}+\frac{(f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{2 d^2 f \left(1-c^2 x^2\right)}-\frac{b c \sqrt{1-c^2 x^2} (f x)^{m+2} \, _2F_1\left(\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{2 d^2 f^2 (m+2) \sqrt{c x-1} \sqrt{c x+1}}",0,"((f*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(2*d^2*f*(1 - c^2*x^2)) - (b*c*(f*x)^(2 + m)*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[3/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(2*d^2*f^2*(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((1 - m)*Defer[Int][((f*x)^m*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2), x])/(2*d)","A",0,0,0,0,-1,"{}"
150,0,0,0,0.3354634,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^3} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^3,x]","\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^3} \, dx","\frac{(1-m) (3-m) \text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{d-c^2 d x^2},x\right)}{8 d^2}+\frac{(3-m) (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{8 d^3 f \left(1-c^2 x^2\right)}+\frac{(f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{4 d^3 f \left(1-c^2 x^2\right)^2}-\frac{b c (3-m) \sqrt{1-c^2 x^2} (f x)^{m+2} \, _2F_1\left(\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{8 d^3 f^2 (m+2) \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \sqrt{1-c^2 x^2} (f x)^{m+2} \, _2F_1\left(\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{4 d^3 f^2 (m+2) \sqrt{c x-1} \sqrt{c x+1}}",0,"((f*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(4*d^3*f*(1 - c^2*x^2)^2) + ((3 - m)*(f*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(8*d^3*f*(1 - c^2*x^2)) - (b*c*(3 - m)*(f*x)^(2 + m)*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[3/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(8*d^3*f^2*(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*(f*x)^(2 + m)*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[5/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(4*d^3*f^2*(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((1 - m)*(3 - m)*Defer[Int][((f*x)^m*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2), x])/(8*d^2)","A",0,0,0,0,-1,"{}"
151,1,764,0,1.3882744,"\int (f x)^m \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]),x]","-\frac{15 b c d^2 \sqrt{d-c^2 d x^2} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{f^2 (m+1) (m+2)^2 (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}+\frac{15 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{f (m+4) (m+6) \left(m^2+3 m+2\right) (1-c x) (c x+1)}+\frac{15 d^2 \sqrt{d-c^2 d x^2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+6) \left(m^2+6 m+8\right)}+\frac{d^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+6)}+\frac{5 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+4) (m+6)}-\frac{b c d^2 \sqrt{d-c^2 d x^2} (f x)^{m+2}}{f^2 (m+2) (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b c d^2 \sqrt{d-c^2 d x^2} (f x)^{m+2}}{f^2 (m+2) (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{15 b c d^2 \sqrt{d-c^2 d x^2} (f x)^{m+2}}{f^2 (m+2)^2 (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c^3 d^2 \sqrt{d-c^2 d x^2} (f x)^{m+4}}{f^4 (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c^3 d^2 \sqrt{d-c^2 d x^2} (f x)^{m+4}}{f^4 (m+4)^2 (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 d^2 \sqrt{d-c^2 d x^2} (f x)^{m+6}}{f^6 (m+6)^2 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{15 b c d^2 \sqrt{d-c^2 d x^2} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{f^2 (m+1) (m+2)^2 (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}+\frac{15 d^2 \sqrt{d-c^2 d x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{f (m+4) (m+6) \left(m^2+3 m+2\right) \sqrt{1-c x} \sqrt{c x+1}}+\frac{15 d^2 \sqrt{d-c^2 d x^2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+6) \left(m^2+6 m+8\right)}+\frac{\left(d-c^2 d x^2\right)^{5/2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+6)}+\frac{5 d \left(d-c^2 d x^2\right)^{3/2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+4) (m+6)}-\frac{b c d^2 \sqrt{d-c^2 d x^2} (f x)^{m+2}}{f^2 (m+2) (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b c d^2 \sqrt{d-c^2 d x^2} (f x)^{m+2}}{f^2 (m+2) (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{15 b c d^2 \sqrt{d-c^2 d x^2} (f x)^{m+2}}{f^2 (m+2)^2 (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c^3 d^2 \sqrt{d-c^2 d x^2} (f x)^{m+4}}{f^4 (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c^3 d^2 \sqrt{d-c^2 d x^2} (f x)^{m+4}}{f^4 (m+4)^2 (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 d^2 \sqrt{d-c^2 d x^2} (f x)^{m+6}}{f^6 (m+6)^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"-((b*c*d^2*(f*x)^(2 + m)*Sqrt[d - c^2*d*x^2])/(f^2*(2 + m)*(6 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])) - (15*b*c*d^2*(f*x)^(2 + m)*Sqrt[d - c^2*d*x^2])/(f^2*(2 + m)^2*(4 + m)*(6 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*b*c*d^2*(f*x)^(2 + m)*Sqrt[d - c^2*d*x^2])/(f^2*(2 + m)*(4 + m)*(6 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*b*c^3*d^2*(f*x)^(4 + m)*Sqrt[d - c^2*d*x^2])/(f^4*(4 + m)^2*(6 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*c^3*d^2*(f*x)^(4 + m)*Sqrt[d - c^2*d*x^2])/(f^4*(4 + m)*(6 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*(f*x)^(6 + m)*Sqrt[d - c^2*d*x^2])/(f^6*(6 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (15*d^2*(f*x)^(1 + m)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(f*(6 + m)*(8 + 6*m + m^2)) + (5*d^2*(f*x)^(1 + m)*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(f*(4 + m)*(6 + m)) + (d^2*(f*x)^(1 + m)*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(f*(6 + m)) + (15*d^2*(f*x)^(1 + m)*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(f*(4 + m)*(6 + m)*(2 + 3*m + m^2)*(1 - c*x)*(1 + c*x)) - (15*b*c*d^2*(f*x)^(2 + m)*Sqrt[d - c^2*d*x^2]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/(f^2*(1 + m)*(2 + m)^2*(4 + m)*(6 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",10,7,29,0.2414,1,"{5798, 5745, 5743, 5763, 32, 14, 270}"
152,1,477,0,0.9041623,"\int (f x)^m \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]),x]","-\frac{3 b c d \sqrt{d-c^2 d x^2} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{f^2 (m+1) (m+2)^2 (m+4) \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 d \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{f (m+4) \left(m^2+3 m+2\right) (1-c x) (c x+1)}+\frac{3 d \sqrt{d-c^2 d x^2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f \left(m^2+6 m+8\right)}+\frac{d (1-c x) (c x+1) \sqrt{d-c^2 d x^2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+4)}-\frac{b c d \sqrt{d-c^2 d x^2} (f x)^{m+2}}{f^2 (m+2) (m+4) \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c d \sqrt{d-c^2 d x^2} (f x)^{m+2}}{f^2 (m+2)^2 (m+4) \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d \sqrt{d-c^2 d x^2} (f x)^{m+4}}{f^4 (m+4)^2 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{3 b c d \sqrt{d-c^2 d x^2} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{f^2 (m+1) (m+2)^2 (m+4) \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 d \sqrt{d-c^2 d x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{f (m+4) \left(m^2+3 m+2\right) \sqrt{1-c x} \sqrt{c x+1}}+\frac{3 d \sqrt{d-c^2 d x^2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f \left(m^2+6 m+8\right)}+\frac{\left(d-c^2 d x^2\right)^{3/2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+4)}-\frac{b c d \sqrt{d-c^2 d x^2} (f x)^{m+2}}{f^2 (m+2) (m+4) \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c d \sqrt{d-c^2 d x^2} (f x)^{m+2}}{f^2 (m+2)^2 (m+4) \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d \sqrt{d-c^2 d x^2} (f x)^{m+4}}{f^4 (m+4)^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"(-3*b*c*d*(f*x)^(2 + m)*Sqrt[d - c^2*d*x^2])/(f^2*(2 + m)^2*(4 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d*(f*x)^(2 + m)*Sqrt[d - c^2*d*x^2])/(f^2*(2 + m)*(4 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*(f*x)^(4 + m)*Sqrt[d - c^2*d*x^2])/(f^4*(4 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*d*(f*x)^(1 + m)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(f*(8 + 6*m + m^2)) + (d*(f*x)^(1 + m)*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(f*(4 + m)) + (3*d*(f*x)^(1 + m)*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(f*(4 + m)*(2 + 3*m + m^2)*(1 - c*x)*(1 + c*x)) - (3*b*c*d*(f*x)^(2 + m)*Sqrt[d - c^2*d*x^2]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/(f^2*(1 + m)*(2 + m)^2*(4 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",7,6,29,0.2069,1,"{5798, 5745, 5743, 5763, 32, 14}"
153,1,288,0,0.5765078,"\int (f x)^m \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f*x)^m*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]),x]","-\frac{b c \sqrt{d-c^2 d x^2} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{f^2 (m+1) (m+2)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{f \left(m^2+3 m+2\right) (1-c x) (c x+1)}+\frac{\sqrt{d-c^2 d x^2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+2)}-\frac{b c \sqrt{d-c^2 d x^2} (f x)^{m+2}}{f^2 (m+2)^2 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{b c \sqrt{d-c^2 d x^2} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{f^2 (m+1) (m+2)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{d-c^2 d x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{f \left(m^2+3 m+2\right) \sqrt{1-c x} \sqrt{c x+1}}+\frac{\sqrt{d-c^2 d x^2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+2)}-\frac{b c \sqrt{d-c^2 d x^2} (f x)^{m+2}}{f^2 (m+2)^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"-((b*c*(f*x)^(2 + m)*Sqrt[d - c^2*d*x^2])/(f^2*(2 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])) + ((f*x)^(1 + m)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(f*(2 + m)) + ((f*x)^(1 + m)*Sqrt[1 - c^2*x^2]*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(f*(2 + 3*m + m^2)*(1 - c*x)*(1 + c*x)) - (b*c*(f*x)^(2 + m)*Sqrt[d - c^2*d*x^2]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/(f^2*(1 + m)*(2 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",4,4,29,0.1379,1,"{5798, 5743, 5763, 32}"
154,1,176,0,0.3523832,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x]))/Sqrt[d - c^2*d*x^2],x]","\frac{b c \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{f^2 (m+1) (m+2) \sqrt{d-c^2 d x^2}}+\frac{\sqrt{1-c^2 x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{f (m+1) \sqrt{d-c^2 d x^2}}","\frac{b c \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{f^2 (m+1) (m+2) \sqrt{d-c^2 d x^2}}+\frac{\sqrt{1-c^2 x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{f (m+1) \sqrt{d-c^2 d x^2}}",1,"((f*x)^(1 + m)*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(f*(1 + m)*Sqrt[d - c^2*d*x^2]) + (b*c*(f*x)^(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/(f^2*(1 + m)*(2 + m)*Sqrt[d - c^2*d*x^2])","A",2,2,29,0.06897,1,"{5798, 5763}"
155,1,300,0,0.6600308,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(3/2),x]","-\frac{b c m \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{d f^2 (m+1) (m+2) \sqrt{d-c^2 d x^2}}-\frac{m \sqrt{1-c^2 x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{d f (m+1) \sqrt{d-c^2 d x^2}}+\frac{(f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{d f \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{d f^2 (m+2) \sqrt{d-c^2 d x^2}}","-\frac{b c m \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{d f^2 (m+1) (m+2) \sqrt{d-c^2 d x^2}}-\frac{m \sqrt{1-c^2 x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{d f (m+1) \sqrt{d-c^2 d x^2}}+\frac{(f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{d f \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{d f^2 (m+2) \sqrt{d-c^2 d x^2}}",1,"((f*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(d*f*Sqrt[d - c^2*d*x^2]) - (m*(f*x)^(1 + m)*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(d*f*(1 + m)*Sqrt[d - c^2*d*x^2]) + (b*c*(f*x)^(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, c^2*x^2])/(d*f^2*(2 + m)*Sqrt[d - c^2*d*x^2]) - (b*c*m*(f*x)^(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/(d*f^2*(1 + m)*(2 + m)*Sqrt[d - c^2*d*x^2])","A",4,4,29,0.1379,1,"{5798, 5756, 5763, 364}"
156,1,465,0,0.9930076,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(5/2),x]","-\frac{b c (2-m) m \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{3 d^2 f^2 (m+1) (m+2) \sqrt{d-c^2 d x^2}}-\frac{(2-m) m \sqrt{1-c^2 x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 f (m+1) \sqrt{d-c^2 d x^2}}+\frac{(2-m) (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 f \sqrt{d-c^2 d x^2}}+\frac{(f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 f (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b c (2-m) \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{3 d^2 f^2 (m+2) \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{3 d^2 f^2 (m+2) \sqrt{d-c^2 d x^2}}","-\frac{b c (2-m) m \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{3 d^2 f^2 (m+1) (m+2) \sqrt{d-c^2 d x^2}}-\frac{(2-m) m \sqrt{1-c^2 x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 f (m+1) \sqrt{d-c^2 d x^2}}+\frac{(2-m) (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 f \sqrt{d-c^2 d x^2}}+\frac{(f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 d f \left(d-c^2 d x^2\right)^{3/2}}+\frac{b c (2-m) \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{3 d^2 f^2 (m+2) \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{3 d^2 f^2 (m+2) \sqrt{d-c^2 d x^2}}",1,"((2 - m)*(f*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(3*d^2*f*Sqrt[d - c^2*d*x^2]) + ((f*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(3*d^2*f*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - ((2 - m)*m*(f*x)^(1 + m)*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(3*d^2*f*(1 + m)*Sqrt[d - c^2*d*x^2]) + (b*c*(2 - m)*(f*x)^(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, c^2*x^2])/(3*d^2*f^2*(2 + m)*Sqrt[d - c^2*d*x^2]) + (b*c*(f*x)^(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Hypergeometric2F1[2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(3*d^2*f^2*(2 + m)*Sqrt[d - c^2*d*x^2]) - (b*c*(2 - m)*m*(f*x)^(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/(3*d^2*f^2*(1 + m)*(2 + m)*Sqrt[d - c^2*d*x^2])","A",6,4,29,0.1379,1,"{5798, 5756, 5763, 364}"
157,1,827,0,1.5798241,"\int (f x)^m (\text{d1}+c \text{d1} x)^{5/2} (\text{d2}-c \text{d2} x)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d1 + c*d1*x)^(5/2)*(d2 - c*d2*x)^(5/2)*(a + b*ArcCosh[c*x]),x]","\frac{(c x \text{d1}+\text{d1})^{5/2} (\text{d2}-c \text{d2} x)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) (f x)^{m+1}}{f (m+6)}+\frac{5 \text{d1} \text{d2} (c x \text{d1}+\text{d1})^{3/2} (\text{d2}-c \text{d2} x)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) (f x)^{m+1}}{f (m+4) (m+6)}+\frac{15 \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} \left(a+b \cosh ^{-1}(c x)\right) (f x)^{m+1}}{f (m+6) \left(m^2+6 m+8\right)}+\frac{15 \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) (f x)^{m+1}}{f (m+4) (m+6) \left(m^2+3 m+2\right) (1-c x) (c x+1)}-\frac{15 b c \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right) (f x)^{m+2}}{f^2 (m+1) (m+2)^2 (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+2}}{f^2 (m+2) (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b c \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+2}}{f^2 (m+2) (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{15 b c \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+2}}{f^2 (m+2)^2 (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c^3 \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+4}}{f^4 (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c^3 \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+4}}{f^4 (m+4)^2 (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+6}}{f^6 (m+6)^2 \sqrt{c x-1} \sqrt{c x+1}}","\frac{(c x \text{d1}+\text{d1})^{5/2} (\text{d2}-c \text{d2} x)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) (f x)^{m+1}}{f (m+6)}+\frac{5 \text{d1} \text{d2} (c x \text{d1}+\text{d1})^{3/2} (\text{d2}-c \text{d2} x)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) (f x)^{m+1}}{f (m+4) (m+6)}+\frac{15 \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} \left(a+b \cosh ^{-1}(c x)\right) (f x)^{m+1}}{f (m+6) \left(m^2+6 m+8\right)}+\frac{15 \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} \left(a+b \cosh ^{-1}(c x)\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) (f x)^{m+1}}{f (m+4) (m+6) \left(m^2+3 m+2\right) \sqrt{1-c x} \sqrt{c x+1}}-\frac{15 b c \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right) (f x)^{m+2}}{f^2 (m+1) (m+2)^2 (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+2}}{f^2 (m+2) (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b c \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+2}}{f^2 (m+2) (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{15 b c \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+2}}{f^2 (m+2)^2 (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c^3 \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+4}}{f^4 (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c^3 \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+4}}{f^4 (m+4)^2 (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 \text{d1}^2 \text{d2}^2 \sqrt{c x \text{d1}+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+6}}{f^6 (m+6)^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"-((b*c*d1^2*d2^2*(f*x)^(2 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x])/(f^2*(2 + m)*(6 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])) - (15*b*c*d1^2*d2^2*(f*x)^(2 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x])/(f^2*(2 + m)^2*(4 + m)*(6 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*b*c*d1^2*d2^2*(f*x)^(2 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x])/(f^2*(2 + m)*(4 + m)*(6 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*b*c^3*d1^2*d2^2*(f*x)^(4 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x])/(f^4*(4 + m)^2*(6 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*c^3*d1^2*d2^2*(f*x)^(4 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x])/(f^4*(4 + m)*(6 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d1^2*d2^2*(f*x)^(6 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x])/(f^6*(6 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (15*d1^2*d2^2*(f*x)^(1 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]*(a + b*ArcCosh[c*x]))/(f*(6 + m)*(8 + 6*m + m^2)) + (5*d1*d2*(f*x)^(1 + m)*(d1 + c*d1*x)^(3/2)*(d2 - c*d2*x)^(3/2)*(a + b*ArcCosh[c*x]))/(f*(4 + m)*(6 + m)) + ((f*x)^(1 + m)*(d1 + c*d1*x)^(5/2)*(d2 - c*d2*x)^(5/2)*(a + b*ArcCosh[c*x]))/(f*(6 + m)) + (15*d1^2*d2^2*(f*x)^(1 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(f*(4 + m)*(6 + m)*(2 + 3*m + m^2)*(1 - c*x)*(1 + c*x)) - (15*b*c*d1^2*d2^2*(f*x)^(2 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/(f^2*(1 + m)*(2 + m)^2*(4 + m)*(6 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",9,6,35,0.1714,1,"{5745, 5743, 5763, 32, 14, 270}"
158,1,513,0,0.9909237,"\int (f x)^m (\text{d1}+c \text{d1} x)^{3/2} (\text{d2}-c \text{d2} x)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d1 + c*d1*x)^(3/2)*(d2 - c*d2*x)^(3/2)*(a + b*ArcCosh[c*x]),x]","-\frac{3 b c \text{d1} \text{d2} \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{f^2 (m+1) (m+2)^2 (m+4) \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 \text{d1} \text{d2} \sqrt{1-c^2 x^2} \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{f (m+4) \left(m^2+3 m+2\right) (1-c x) (c x+1)}+\frac{3 \text{d1} \text{d2} \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f \left(m^2+6 m+8\right)}+\frac{(c \text{d1} x+\text{d1})^{3/2} (\text{d2}-c \text{d2} x)^{3/2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+4)}+\frac{b c^3 \text{d1} \text{d2} \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+4}}{f^4 (m+4)^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \text{d1} \text{d2} \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+2}}{f^2 (m+2) (m+4) \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c \text{d1} \text{d2} \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+2}}{f^2 (m+2)^2 (m+4) \sqrt{c x-1} \sqrt{c x+1}}","-\frac{3 b c \text{d1} \text{d2} \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{f^2 (m+1) (m+2)^2 (m+4) \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 \text{d1} \text{d2} \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{f (m+4) \left(m^2+3 m+2\right) \sqrt{1-c x} \sqrt{c x+1}}+\frac{3 \text{d1} \text{d2} \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f \left(m^2+6 m+8\right)}+\frac{(c \text{d1} x+\text{d1})^{3/2} (\text{d2}-c \text{d2} x)^{3/2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+4)}+\frac{b c^3 \text{d1} \text{d2} \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+4}}{f^4 (m+4)^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \text{d1} \text{d2} \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+2}}{f^2 (m+2) (m+4) \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c \text{d1} \text{d2} \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+2}}{f^2 (m+2)^2 (m+4) \sqrt{c x-1} \sqrt{c x+1}}",1,"(-3*b*c*d1*d2*(f*x)^(2 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x])/(f^2*(2 + m)^2*(4 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d1*d2*(f*x)^(2 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x])/(f^2*(2 + m)*(4 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d1*d2*(f*x)^(4 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x])/(f^4*(4 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*d1*d2*(f*x)^(1 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]*(a + b*ArcCosh[c*x]))/(f*(8 + 6*m + m^2)) + ((f*x)^(1 + m)*(d1 + c*d1*x)^(3/2)*(d2 - c*d2*x)^(3/2)*(a + b*ArcCosh[c*x]))/(f*(4 + m)) + (3*d1*d2*(f*x)^(1 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(f*(4 + m)*(2 + 3*m + m^2)*(1 - c*x)*(1 + c*x)) - (3*b*c*d1*d2*(f*x)^(2 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/(f^2*(1 + m)*(2 + m)^2*(4 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",6,5,35,0.1429,1,"{5745, 5743, 5763, 32, 14}"
159,1,312,0,0.5571335,"\int (f x)^m \sqrt{\text{d1}+c \text{d1} x} \sqrt{\text{d2}-c \text{d2} x} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f*x)^m*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]*(a + b*ArcCosh[c*x]),x]","-\frac{b c \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{f^2 (m+1) (m+2)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{f \left(m^2+3 m+2\right) (1-c x) (c x+1)}+\frac{\sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+2)}-\frac{b c \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+2}}{f^2 (m+2)^2 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{b c \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{f^2 (m+1) (m+2)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{f \left(m^2+3 m+2\right) \sqrt{1-c x} \sqrt{c x+1}}+\frac{\sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+2)}-\frac{b c \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} (f x)^{m+2}}{f^2 (m+2)^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"-((b*c*(f*x)^(2 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x])/(f^2*(2 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])) + ((f*x)^(1 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]*(a + b*ArcCosh[c*x]))/(f*(2 + m)) + ((f*x)^(1 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(f*(2 + 3*m + m^2)*(1 - c*x)*(1 + c*x)) - (b*c*(f*x)^(2 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/(f^2*(1 + m)*(2 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",3,3,35,0.08571,1,"{5743, 5763, 32}"
160,1,188,0,0.5589317,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{\text{d1}+c \text{d1} x} \sqrt{\text{d2}-c \text{d2} x}} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x]))/(Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]),x]","\frac{b c \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{f^2 (m+1) (m+2) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}+\frac{\sqrt{1-c^2 x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{f (m+1) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}","\frac{b c \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{f^2 (m+1) (m+2) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}+\frac{\sqrt{1-c^2 x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{f (m+1) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}",1,"((f*x)^(1 + m)*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(f*(1 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]) + (b*c*(f*x)^(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/(f^2*(1 + m)*(2 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x])","A",2,2,35,0.05714,1,"{5765, 5763}"
161,1,336,0,0.9434764,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{(\text{d1}+c \text{d1} x)^{3/2} (\text{d2}-c \text{d2} x)^{3/2}} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x]))/((d1 + c*d1*x)^(3/2)*(d2 - c*d2*x)^(3/2)),x]","-\frac{b c m \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{\text{d1} \text{d2} f^2 (m+1) (m+2) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}-\frac{m \sqrt{1-c^2 x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{\text{d1} \text{d2} f (m+1) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}+\frac{(f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{\text{d1} \text{d2} f \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{\text{d1} \text{d2} f^2 (m+2) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}","-\frac{b c m \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{\text{d1} \text{d2} f^2 (m+1) (m+2) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}-\frac{m \sqrt{1-c^2 x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{\text{d1} \text{d2} f (m+1) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}+\frac{(f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{\text{d1} \text{d2} f \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{\text{d1} \text{d2} f^2 (m+2) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}",1,"((f*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(d1*d2*f*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]) - (m*(f*x)^(1 + m)*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(d1*d2*f*(1 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]) + (b*c*(f*x)^(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, c^2*x^2])/(d1*d2*f^2*(2 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]) - (b*c*m*(f*x)^(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/(d1*d2*f^2*(1 + m)*(2 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x])","A",4,4,35,0.1143,1,"{5756, 5765, 5763, 364}"
162,1,504,0,1.4519259,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{(\text{d1}+c \text{d1} x)^{5/2} (\text{d2}-c \text{d2} x)^{5/2}} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x]))/((d1 + c*d1*x)^(5/2)*(d2 - c*d2*x)^(5/2)),x]","-\frac{b c (2-m) m \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{3 \text{d1}^2 \text{d2}^2 f^2 (m+1) (m+2) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}-\frac{(2-m) m \sqrt{1-c^2 x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 \text{d1}^2 \text{d2}^2 f (m+1) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}+\frac{(2-m) (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 \text{d1}^2 \text{d2}^2 f \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}+\frac{(f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 \text{d1} \text{d2} f (c \text{d1} x+\text{d1})^{3/2} (\text{d2}-c \text{d2} x)^{3/2}}+\frac{b c (2-m) \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{3 \text{d1}^2 \text{d2}^2 f^2 (m+2) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{3 \text{d1}^2 \text{d2}^2 f^2 (m+2) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}","-\frac{b c (2-m) m \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;c^2 x^2\right)}{3 \text{d1}^2 \text{d2}^2 f^2 (m+1) (m+2) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}-\frac{(2-m) m \sqrt{1-c^2 x^2} (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 \text{d1}^2 \text{d2}^2 f (m+1) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}+\frac{(2-m) (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 \text{d1}^2 \text{d2}^2 f \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}+\frac{(f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 \text{d1} \text{d2} f (c \text{d1} x+\text{d1})^{3/2} (\text{d2}-c \text{d2} x)^{3/2}}+\frac{b c (2-m) \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{3 \text{d1}^2 \text{d2}^2 f^2 (m+2) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{3 \text{d1}^2 \text{d2}^2 f^2 (m+2) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}",1,"((f*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(3*d1*d2*f*(d1 + c*d1*x)^(3/2)*(d2 - c*d2*x)^(3/2)) + ((2 - m)*(f*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(3*d1^2*d2^2*f*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]) - ((2 - m)*m*(f*x)^(1 + m)*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(3*d1^2*d2^2*f*(1 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]) + (b*c*(2 - m)*(f*x)^(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, c^2*x^2])/(3*d1^2*d2^2*f^2*(2 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]) + (b*c*(f*x)^(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Hypergeometric2F1[2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(3*d1^2*d2^2*f^2*(2 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]) - (b*c*(2 - m)*m*(f*x)^(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, c^2*x^2])/(3*d1^2*d2^2*f^2*(1 + m)*(2 + m)*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x])","A",6,4,35,0.1143,1,"{5756, 5765, 5763, 364}"
163,1,141,0,0.2867758,"\int \frac{(f x)^m \cosh ^{-1}(a x)}{\sqrt{1-a^2 x^2}} \, dx","Int[((f*x)^m*ArcCosh[a*x])/Sqrt[1 - a^2*x^2],x]","\frac{a \sqrt{a x-1} \sqrt{a x+1} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;a^2 x^2\right)}{f^2 (m+1) (m+2) \sqrt{1-a^2 x^2}}+\frac{\cosh ^{-1}(a x) (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{f (m+1)}","\frac{a \sqrt{a x-1} (f x)^{m+2} \, _3F_2\left(1,\frac{m}{2}+1,\frac{m}{2}+1;\frac{m}{2}+\frac{3}{2},\frac{m}{2}+2;a^2 x^2\right)}{f^2 (m+1) (m+2) \sqrt{1-a x}}+\frac{\cosh ^{-1}(a x) (f x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{f (m+1)}",1,"((f*x)^(1 + m)*ArcCosh[a*x]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, a^2*x^2])/(f*(1 + m)) + (a*(f*x)^(2 + m)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, a^2*x^2])/(f^2*(1 + m)*(2 + m)*Sqrt[1 - a^2*x^2])","A",2,2,24,0.08333,1,"{5798, 5763}"
164,1,266,0,0.6762785,"\int \left(c-a^2 c x^2\right)^3 \cosh ^{-1}(a x)^2 \, dx","Int[(c - a^2*c*x^2)^3*ArcCosh[a*x]^2,x]","-\frac{2}{343} a^6 c^3 x^7+\frac{234 a^4 c^3 x^5}{6125}-\frac{1514 a^2 c^3 x^3}{11025}+\frac{1}{7} c^3 x \left(1-a^2 x^2\right)^3 \cosh ^{-1}(a x)^2+\frac{6}{35} c^3 x \left(1-a^2 x^2\right)^2 \cosh ^{-1}(a x)^2+\frac{8}{35} c^3 x \left(1-a^2 x^2\right) \cosh ^{-1}(a x)^2+\frac{16}{35} c^3 x \cosh ^{-1}(a x)^2+\frac{2 c^3 (a x-1)^{7/2} (a x+1)^{7/2} \cosh ^{-1}(a x)}{49 a}-\frac{12 c^3 (a x-1)^{5/2} (a x+1)^{5/2} \cosh ^{-1}(a x)}{175 a}+\frac{16 c^3 (a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)}{105 a}-\frac{32 c^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{35 a}+\frac{4322 c^3 x}{3675}","-\frac{2}{343} a^6 c^3 x^7+\frac{234 a^4 c^3 x^5}{6125}-\frac{1514 a^2 c^3 x^3}{11025}+\frac{1}{7} c^3 x \left(1-a^2 x^2\right)^3 \cosh ^{-1}(a x)^2+\frac{6}{35} c^3 x \left(1-a^2 x^2\right)^2 \cosh ^{-1}(a x)^2+\frac{8}{35} c^3 x \left(1-a^2 x^2\right) \cosh ^{-1}(a x)^2+\frac{16}{35} c^3 x \cosh ^{-1}(a x)^2+\frac{2 c^3 (a x-1)^{7/2} (a x+1)^{7/2} \cosh ^{-1}(a x)}{49 a}-\frac{12 c^3 (a x-1)^{5/2} (a x+1)^{5/2} \cosh ^{-1}(a x)}{175 a}+\frac{16 c^3 (a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)}{105 a}-\frac{32 c^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{35 a}+\frac{4322 c^3 x}{3675}",1,"(4322*c^3*x)/3675 - (1514*a^2*c^3*x^3)/11025 + (234*a^4*c^3*x^5)/6125 - (2*a^6*c^3*x^7)/343 - (32*c^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(35*a) + (16*c^3*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*ArcCosh[a*x])/(105*a) - (12*c^3*(-1 + a*x)^(5/2)*(1 + a*x)^(5/2)*ArcCosh[a*x])/(175*a) + (2*c^3*(-1 + a*x)^(7/2)*(1 + a*x)^(7/2)*ArcCosh[a*x])/(49*a) + (16*c^3*x*ArcCosh[a*x]^2)/35 + (8*c^3*x*(1 - a^2*x^2)*ArcCosh[a*x]^2)/35 + (6*c^3*x*(1 - a^2*x^2)^2*ArcCosh[a*x]^2)/35 + (c^3*x*(1 - a^2*x^2)^3*ArcCosh[a*x]^2)/7","A",14,5,20,0.2500,1,"{5681, 5718, 194, 5654, 8}"
165,1,195,0,0.4616899,"\int \left(c-a^2 c x^2\right)^2 \cosh ^{-1}(a x)^2 \, dx","Int[(c - a^2*c*x^2)^2*ArcCosh[a*x]^2,x]","\frac{2}{125} a^4 c^2 x^5-\frac{76}{675} a^2 c^2 x^3+\frac{1}{5} c^2 x \left(1-a^2 x^2\right)^2 \cosh ^{-1}(a x)^2+\frac{4}{15} c^2 x \left(1-a^2 x^2\right) \cosh ^{-1}(a x)^2+\frac{8}{15} c^2 x \cosh ^{-1}(a x)^2-\frac{2 c^2 (a x-1)^{5/2} (a x+1)^{5/2} \cosh ^{-1}(a x)}{25 a}+\frac{8 c^2 (a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)}{45 a}-\frac{16 c^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{15 a}+\frac{298 c^2 x}{225}","\frac{2}{125} a^4 c^2 x^5-\frac{76}{675} a^2 c^2 x^3+\frac{1}{5} c^2 x \left(1-a^2 x^2\right)^2 \cosh ^{-1}(a x)^2+\frac{4}{15} c^2 x \left(1-a^2 x^2\right) \cosh ^{-1}(a x)^2+\frac{8}{15} c^2 x \cosh ^{-1}(a x)^2-\frac{2 c^2 (a x-1)^{5/2} (a x+1)^{5/2} \cosh ^{-1}(a x)}{25 a}+\frac{8 c^2 (a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)}{45 a}-\frac{16 c^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{15 a}+\frac{298 c^2 x}{225}",1,"(298*c^2*x)/225 - (76*a^2*c^2*x^3)/675 + (2*a^4*c^2*x^5)/125 - (16*c^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(15*a) + (8*c^2*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*ArcCosh[a*x])/(45*a) - (2*c^2*(-1 + a*x)^(5/2)*(1 + a*x)^(5/2)*ArcCosh[a*x])/(25*a) + (8*c^2*x*ArcCosh[a*x]^2)/15 + (4*c^2*x*(1 - a^2*x^2)*ArcCosh[a*x]^2)/15 + (c^2*x*(1 - a^2*x^2)^2*ArcCosh[a*x]^2)/5","A",10,5,20,0.2500,1,"{5681, 5718, 194, 5654, 8}"
166,1,112,0,0.2630922,"\int \left(c-a^2 c x^2\right) \cosh ^{-1}(a x)^2 \, dx","Int[(c - a^2*c*x^2)*ArcCosh[a*x]^2,x]","-\frac{2}{27} a^2 c x^3+\frac{1}{3} c x \left(1-a^2 x^2\right) \cosh ^{-1}(a x)^2+\frac{2}{3} c x \cosh ^{-1}(a x)^2+\frac{2 c (a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)}{9 a}-\frac{4 c \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{3 a}+\frac{14 c x}{9}","-\frac{2}{27} a^2 c x^3+\frac{1}{3} c x \left(1-a^2 x^2\right) \cosh ^{-1}(a x)^2+\frac{2}{3} c x \cosh ^{-1}(a x)^2+\frac{2 c (a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)}{9 a}-\frac{4 c \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{3 a}+\frac{14 c x}{9}",1,"(14*c*x)/9 - (2*a^2*c*x^3)/27 - (4*c*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(3*a) + (2*c*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*ArcCosh[a*x])/(9*a) + (2*c*x*ArcCosh[a*x]^2)/3 + (c*x*(1 - a^2*x^2)*ArcCosh[a*x]^2)/3","A",6,4,18,0.2222,1,"{5681, 5718, 5654, 8}"
167,1,98,0,0.0978093,"\int \frac{\cosh ^{-1}(a x)^2}{c-a^2 c x^2} \, dx","Int[ArcCosh[a*x]^2/(c - a^2*c*x^2),x]","\frac{2 \cosh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{a c}-\frac{2 \cosh ^{-1}(a x) \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{a c}-\frac{2 \text{PolyLog}\left(3,-e^{\cosh ^{-1}(a x)}\right)}{a c}+\frac{2 \text{PolyLog}\left(3,e^{\cosh ^{-1}(a x)}\right)}{a c}+\frac{2 \cosh ^{-1}(a x)^2 \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{a c}","\frac{2 \cosh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{a c}-\frac{2 \cosh ^{-1}(a x) \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{a c}-\frac{2 \text{PolyLog}\left(3,-e^{\cosh ^{-1}(a x)}\right)}{a c}+\frac{2 \text{PolyLog}\left(3,e^{\cosh ^{-1}(a x)}\right)}{a c}+\frac{2 \cosh ^{-1}(a x)^2 \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{a c}",1,"(2*ArcCosh[a*x]^2*ArcTanh[E^ArcCosh[a*x]])/(a*c) + (2*ArcCosh[a*x]*PolyLog[2, -E^ArcCosh[a*x]])/(a*c) - (2*ArcCosh[a*x]*PolyLog[2, E^ArcCosh[a*x]])/(a*c) - (2*PolyLog[3, -E^ArcCosh[a*x]])/(a*c) + (2*PolyLog[3, E^ArcCosh[a*x]])/(a*c)","A",8,5,20,0.2500,1,"{5694, 4182, 2531, 2282, 6589}"
168,1,163,0,0.2871994,"\int \frac{\cosh ^{-1}(a x)^2}{\left(c-a^2 c x^2\right)^2} \, dx","Int[ArcCosh[a*x]^2/(c - a^2*c*x^2)^2,x]","\frac{\cosh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{a c^2}-\frac{\cosh ^{-1}(a x) \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{a c^2}-\frac{\text{PolyLog}\left(3,-e^{\cosh ^{-1}(a x)}\right)}{a c^2}+\frac{\text{PolyLog}\left(3,e^{\cosh ^{-1}(a x)}\right)}{a c^2}+\frac{x \cosh ^{-1}(a x)^2}{2 c^2 \left(1-a^2 x^2\right)}-\frac{\cosh ^{-1}(a x)}{a c^2 \sqrt{a x-1} \sqrt{a x+1}}-\frac{\tanh ^{-1}(a x)}{a c^2}+\frac{\cosh ^{-1}(a x)^2 \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{a c^2}","\frac{\cosh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{a c^2}-\frac{\cosh ^{-1}(a x) \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{a c^2}-\frac{\text{PolyLog}\left(3,-e^{\cosh ^{-1}(a x)}\right)}{a c^2}+\frac{\text{PolyLog}\left(3,e^{\cosh ^{-1}(a x)}\right)}{a c^2}+\frac{x \cosh ^{-1}(a x)^2}{2 c^2 \left(1-a^2 x^2\right)}-\frac{\cosh ^{-1}(a x)}{a c^2 \sqrt{a x-1} \sqrt{a x+1}}-\frac{\tanh ^{-1}(a x)}{a c^2}+\frac{\cosh ^{-1}(a x)^2 \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{a c^2}",1,"-(ArcCosh[a*x]/(a*c^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])) + (x*ArcCosh[a*x]^2)/(2*c^2*(1 - a^2*x^2)) + (ArcCosh[a*x]^2*ArcTanh[E^ArcCosh[a*x]])/(a*c^2) - ArcTanh[a*x]/(a*c^2) + (ArcCosh[a*x]*PolyLog[2, -E^ArcCosh[a*x]])/(a*c^2) - (ArcCosh[a*x]*PolyLog[2, E^ArcCosh[a*x]])/(a*c^2) - PolyLog[3, -E^ArcCosh[a*x]]/(a*c^2) + PolyLog[3, E^ArcCosh[a*x]]/(a*c^2)","A",11,8,20,0.4000,1,"{5689, 5718, 207, 5694, 4182, 2531, 2282, 6589}"
169,1,258,0,0.4926503,"\int \frac{\cosh ^{-1}(a x)^2}{\left(c-a^2 c x^2\right)^3} \, dx","Int[ArcCosh[a*x]^2/(c - a^2*c*x^2)^3,x]","\frac{3 \cosh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}-\frac{3 \cosh ^{-1}(a x) \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}-\frac{3 \text{PolyLog}\left(3,-e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}+\frac{3 \text{PolyLog}\left(3,e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}-\frac{x}{12 c^3 \left(1-a^2 x^2\right)}+\frac{3 x \cosh ^{-1}(a x)^2}{8 c^3 \left(1-a^2 x^2\right)}+\frac{x \cosh ^{-1}(a x)^2}{4 c^3 \left(1-a^2 x^2\right)^2}-\frac{3 \cosh ^{-1}(a x)}{4 a c^3 \sqrt{a x-1} \sqrt{a x+1}}+\frac{\cosh ^{-1}(a x)}{6 a c^3 (a x-1)^{3/2} (a x+1)^{3/2}}-\frac{5 \tanh ^{-1}(a x)}{6 a c^3}+\frac{3 \cosh ^{-1}(a x)^2 \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}","\frac{3 \cosh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}-\frac{3 \cosh ^{-1}(a x) \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}-\frac{3 \text{PolyLog}\left(3,-e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}+\frac{3 \text{PolyLog}\left(3,e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}-\frac{x}{12 c^3 \left(1-a^2 x^2\right)}+\frac{3 x \cosh ^{-1}(a x)^2}{8 c^3 \left(1-a^2 x^2\right)}+\frac{x \cosh ^{-1}(a x)^2}{4 c^3 \left(1-a^2 x^2\right)^2}-\frac{3 \cosh ^{-1}(a x)}{4 a c^3 \sqrt{a x-1} \sqrt{a x+1}}+\frac{\cosh ^{-1}(a x)}{6 a c^3 (a x-1)^{3/2} (a x+1)^{3/2}}-\frac{5 \tanh ^{-1}(a x)}{6 a c^3}+\frac{3 \cosh ^{-1}(a x)^2 \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}",1,"-x/(12*c^3*(1 - a^2*x^2)) + ArcCosh[a*x]/(6*a*c^3*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)) - (3*ArcCosh[a*x])/(4*a*c^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (x*ArcCosh[a*x]^2)/(4*c^3*(1 - a^2*x^2)^2) + (3*x*ArcCosh[a*x]^2)/(8*c^3*(1 - a^2*x^2)) + (3*ArcCosh[a*x]^2*ArcTanh[E^ArcCosh[a*x]])/(4*a*c^3) - (5*ArcTanh[a*x])/(6*a*c^3) + (3*ArcCosh[a*x]*PolyLog[2, -E^ArcCosh[a*x]])/(4*a*c^3) - (3*ArcCosh[a*x]*PolyLog[2, E^ArcCosh[a*x]])/(4*a*c^3) - (3*PolyLog[3, -E^ArcCosh[a*x]])/(4*a*c^3) + (3*PolyLog[3, E^ArcCosh[a*x]])/(4*a*c^3)","A",15,9,20,0.4500,1,"{5689, 5718, 199, 207, 5694, 4182, 2531, 2282, 6589}"
170,1,371,0,1.05567,"\int x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2,x]","\frac{4 a b x \sqrt{d-c^2 d x^2}}{15 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c x^5 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{25 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{5} x^4 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{2 b x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{45 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{15 c^2}-\frac{2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{15 c^4}+\frac{2}{125} b^2 x^4 \sqrt{d-c^2 d x^2}+\frac{22 b^2 x^2 \sqrt{d-c^2 d x^2}}{3375 c^2}-\frac{856 b^2 \sqrt{d-c^2 d x^2}}{3375 c^4}+\frac{4 b^2 x \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{15 c^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{4 a b x \sqrt{d-c^2 d x^2}}{15 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c x^5 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{25 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{5} x^4 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{2 b x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{45 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{15 c^2}-\frac{2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{15 c^4}+\frac{2}{125} b^2 x^4 \sqrt{d-c^2 d x^2}+\frac{22 b^2 x^2 \sqrt{d-c^2 d x^2}}{3375 c^2}-\frac{856 b^2 \sqrt{d-c^2 d x^2}}{3375 c^4}+\frac{4 b^2 x \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{15 c^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(-856*b^2*Sqrt[d - c^2*d*x^2])/(3375*c^4) + (22*b^2*x^2*Sqrt[d - c^2*d*x^2])/(3375*c^2) + (2*b^2*x^4*Sqrt[d - c^2*d*x^2])/125 + (4*a*b*x*Sqrt[d - c^2*d*x^2])/(15*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (4*b^2*x*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(15*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(45*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*c*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(25*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(15*c^4) - (x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(15*c^2) + (x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/5","A",17,9,29,0.3103,1,"{5798, 5743, 5759, 5718, 5654, 74, 5662, 100, 12}"
171,1,319,0,0.9303895,"\int x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2,x]","-\frac{b c x^4 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{4} x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{b x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{8 c^2}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{24 b c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{32} b^2 x^3 \sqrt{d-c^2 d x^2}-\frac{b^2 x \sqrt{d-c^2 d x^2}}{64 c^2}-\frac{b^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{64 c^3 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{b c x^4 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{4} x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{b x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{8 c^2}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{24 b c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{32} b^2 x^3 \sqrt{d-c^2 d x^2}-\frac{b^2 x \sqrt{d-c^2 d x^2}}{64 c^2}-\frac{b^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{64 c^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b^2*x*Sqrt[d - c^2*d*x^2])/(64*c^2) + (b^2*x^3*Sqrt[d - c^2*d*x^2])/32 - (b^2*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(64*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(8*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(8*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(8*c^2) + (x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/4 - (Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^3)/(24*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",12,9,29,0.3103,1,"{5798, 5743, 5759, 5676, 5662, 90, 52, 100, 12}"
172,1,194,0,0.3702479,"\int x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2,x]","-\frac{2 b c x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{(1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^2}+\frac{2}{27} b^2 x^2 \sqrt{d-c^2 d x^2}-\frac{14 b^2 \sqrt{d-c^2 d x^2}}{27 c^2}","-\frac{2 b c x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^2 d}+\frac{2}{27} b^2 x^2 \sqrt{d-c^2 d x^2}-\frac{14 b^2 \sqrt{d-c^2 d x^2}}{27 c^2}",1,"(-14*b^2*Sqrt[d - c^2*d*x^2])/(27*c^2) + (2*b^2*x^2*Sqrt[d - c^2*d*x^2])/27 + (2*b*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*c*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(3*c^2)","A",6,6,27,0.2222,1,"{5798, 5718, 5680, 12, 460, 74}"
173,1,204,0,0.3486358,"\int \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2,x]","-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{6 b c \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{2} x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{b c x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{4} b^2 x \sqrt{d-c^2 d x^2}+\frac{b^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{4 c \sqrt{c x-1} \sqrt{c x+1}}","-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{6 b c \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{2} x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{b c x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{4} b^2 x \sqrt{d-c^2 d x^2}+\frac{b^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{4 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(b^2*x*Sqrt[d - c^2*d*x^2])/4 + (b^2*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(4*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/2 - (Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^3)/(6*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",6,6,26,0.2308,1,"{5713, 5683, 5676, 5662, 90, 52}"
174,1,402,0,0.7861365,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/x,x]","\frac{2 i b \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 i b \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 i b^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{2 i b^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 a b c x \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}+\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{c x-1} \sqrt{c x+1}}+2 b^2 \sqrt{d-c^2 d x^2}-\frac{2 b^2 c x \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}","\frac{2 i b \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 i b \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 i b^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{2 i b^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 a b c x \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}+\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{c x-1} \sqrt{c x+1}}+2 b^2 \sqrt{d-c^2 d x^2}-\frac{2 b^2 c x \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}",1,"2*b^2*Sqrt[d - c^2*d*x^2] - (2*a*b*c*x*Sqrt[d - c^2*d*x^2])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b^2*c*x*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2 - (2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2*ArcTan[E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((2*I)*b*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((2*I)*b*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*PolyLog[2, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((2*I)*b^2*Sqrt[d - c^2*d*x^2]*PolyLog[3, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((2*I)*b^2*Sqrt[d - c^2*d*x^2]*PolyLog[3, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",13,9,29,0.3103,1,"{5798, 5743, 5761, 4180, 2531, 2282, 6589, 5654, 74}"
175,1,234,0,0.6314331,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x^2} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/x^2,x]","\frac{b^2 c \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{c \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{3 b \sqrt{c x-1} \sqrt{c x+1}}-\frac{c \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x}+\frac{2 b c \sqrt{d-c^2 d x^2} \log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}","-\frac{b^2 c \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{c \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{3 b \sqrt{c x-1} \sqrt{c x+1}}+\frac{c \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x}+\frac{2 b c \sqrt{d-c^2 d x^2} \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}",1,"-((Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/x) - (c*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (c*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^3)/(3*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*c*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b^2*c*Sqrt[d - c^2*d*x^2]*PolyLog[2, -E^(2*ArcCosh[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",8,8,29,0.2759,0,"{5798, 5738, 5660, 3718, 2190, 2279, 2391, 5676}"
176,1,427,0,0.8766321,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x^3} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/x^3,x]","-\frac{i b c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{i b c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{i b^2 c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{i b^2 c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 x^2}+\frac{c^2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{b^2 c^2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{\sqrt{c x-1} \sqrt{c x+1}}","-\frac{i b c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{i b c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{i b^2 c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{i b^2 c^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 x^2}+\frac{c^2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{b^2 c^2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{\sqrt{c x-1} \sqrt{c x+1}}",1,"-((b*c*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])) - (Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*x^2) + (c^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2*ArcTan[E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b^2*c^2*Sqrt[d - c^2*d*x^2]*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (I*b*c^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (I*b*c^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*PolyLog[2, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (I*b^2*c^2*Sqrt[d - c^2*d*x^2]*PolyLog[3, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (I*b^2*c^2*Sqrt[d - c^2*d*x^2]*PolyLog[3, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",13,10,29,0.3448,1,"{5798, 5738, 5662, 92, 205, 5761, 4180, 2531, 2282, 6589}"
177,1,344,0,0.5827521,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x^4} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/x^4,x]","-\frac{b^2 c^3 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{c^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{(1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 x^3}-\frac{2 b c^3 \sqrt{d-c^2 d x^2} \log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b^2 c^2 \sqrt{d-c^2 d x^2}}{3 x}-\frac{b^2 c^3 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{b^2 c^3 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{c^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d x^3}-\frac{2 b c^3 \sqrt{d-c^2 d x^2} \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b^2 c^2 \sqrt{d-c^2 d x^2}}{3 x}-\frac{b^2 c^3 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b^2*c^2*Sqrt[d - c^2*d*x^2])/(3*x) - (b^2*c^3*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (c^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(3*x^3) - (2*b*c^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])])/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b^2*c^3*Sqrt[d - c^2*d*x^2]*PolyLog[2, -E^(2*ArcCosh[c*x])])/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",11,11,29,0.3793,0,"{5798, 5724, 5729, 97, 12, 52, 5660, 3718, 2190, 2279, 2391}"
178,1,507,0,1.6737417,"\int x^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[x^3*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2,x]","\frac{4 a b d x \sqrt{d-c^2 d x^2}}{35 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c^3 d x^7 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{49 \sqrt{c x-1} \sqrt{c x+1}}-\frac{16 b c d x^5 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{175 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3}{35} d x^4 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{1}{7} d x^4 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{2 b d x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{105 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{35 c^2}-\frac{2 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{35 c^4}-\frac{2}{343} b^2 c^2 d x^6 \sqrt{d-c^2 d x^2}+\frac{484 b^2 d x^4 \sqrt{d-c^2 d x^2}}{42875}+\frac{3358 b^2 d x^2 \sqrt{d-c^2 d x^2}}{385875 c^2}-\frac{37384 b^2 d \sqrt{d-c^2 d x^2}}{385875 c^4}+\frac{4 b^2 d x \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{35 c^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{4 a b d x \sqrt{d-c^2 d x^2}}{35 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c^3 d x^7 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{49 \sqrt{c x-1} \sqrt{c x+1}}-\frac{16 b c d x^5 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{175 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{7} x^4 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{3}{35} d x^4 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{2 b d x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{105 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{35 c^2}-\frac{2 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{35 c^4}-\frac{2}{343} b^2 c^2 d x^6 \sqrt{d-c^2 d x^2}+\frac{484 b^2 d x^4 \sqrt{d-c^2 d x^2}}{42875}+\frac{3358 b^2 d x^2 \sqrt{d-c^2 d x^2}}{385875 c^2}-\frac{37384 b^2 d \sqrt{d-c^2 d x^2}}{385875 c^4}+\frac{4 b^2 d x \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{35 c^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(-37384*b^2*d*Sqrt[d - c^2*d*x^2])/(385875*c^4) + (3358*b^2*d*x^2*Sqrt[d - c^2*d*x^2])/(385875*c^2) + (484*b^2*d*x^4*Sqrt[d - c^2*d*x^2])/42875 - (2*b^2*c^2*d*x^6*Sqrt[d - c^2*d*x^2])/343 + (4*a*b*d*x*Sqrt[d - c^2*d*x^2])/(35*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (4*b^2*d*x*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(35*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*d*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(105*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (16*b*c*d*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(175*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*c^3*d*x^7*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(49*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(35*c^4) - (d*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(35*c^2) + (3*d*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/35 + (d*x^4*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/7","A",26,13,29,0.4483,1,"{5798, 5745, 5743, 5759, 5718, 5654, 74, 5662, 100, 12, 14, 5731, 460}"
179,1,453,0,1.4774041,"\int x^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[x^2*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2,x]","\frac{b c^3 d x^6 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{18 \sqrt{c x-1} \sqrt{c x+1}}-\frac{7 b c d x^4 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{48 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{8} d x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{1}{6} d x^3 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{b d x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{16 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 c^2}-\frac{d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{48 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{1}{108} b^2 c^2 d x^5 \sqrt{d-c^2 d x^2}+\frac{43 b^2 d x^3 \sqrt{d-c^2 d x^2}}{1728}+\frac{7 b^2 d x \sqrt{d-c^2 d x^2}}{1152 c^2}+\frac{7 b^2 d \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{1152 c^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{b c^3 d x^6 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{18 \sqrt{c x-1} \sqrt{c x+1}}-\frac{7 b c d x^4 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{48 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{6} x^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{1}{8} d x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{b d x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{16 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 c^2}-\frac{d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{48 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{1}{108} b^2 c^2 d x^5 \sqrt{d-c^2 d x^2}+\frac{43 b^2 d x^3 \sqrt{d-c^2 d x^2}}{1728}+\frac{7 b^2 d x \sqrt{d-c^2 d x^2}}{1152 c^2}+\frac{7 b^2 d \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{1152 c^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(7*b^2*d*x*Sqrt[d - c^2*d*x^2])/(1152*c^2) + (43*b^2*d*x^3*Sqrt[d - c^2*d*x^2])/1728 - (b^2*c^2*d*x^5*Sqrt[d - c^2*d*x^2])/108 + (7*b^2*d*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(1152*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(16*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (7*b*c*d*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(48*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c^3*d*x^6*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(18*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(16*c^2) + (d*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/8 + (d*x^3*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/6 - (d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^3)/(48*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",20,13,29,0.4483,1,"{5798, 5745, 5743, 5759, 5676, 5662, 90, 52, 100, 12, 14, 5731, 460}"
180,1,361,0,0.5541611,"\int x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[x*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2,x]","\frac{2 b c^3 d x^5 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{25 \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 b c d x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{15 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{5 c^2}-\frac{2 b^2 d \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{125 c^2 (1-c x) (c x+1)}-\frac{8 b^2 d \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{225 c^2 (1-c x) (c x+1)}-\frac{16 b^2 d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{75 c^2 (1-c x) (c x+1)}","\frac{2 b c^3 d x^5 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{25 \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 b c d x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{15 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{5 c^2 d}-\frac{2 b^2 d \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{125 c^2 (1-c x) (c x+1)}-\frac{8 b^2 d \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{225 c^2 (1-c x) (c x+1)}-\frac{16 b^2 d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{75 c^2 (1-c x) (c x+1)}",1,"(-16*b^2*d*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(75*c^2*(1 - c*x)*(1 + c*x)) - (8*b^2*d*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(225*c^2*(1 - c*x)*(1 + c*x)) - (2*b^2*d*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2])/(125*c^2*(1 - c*x)*(1 + c*x)) + (2*b*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(5*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (4*b*c*d*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(15*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*c^3*d*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(25*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(5*c^2)","A",8,8,27,0.2963,1,"{5798, 5718, 194, 5680, 12, 520, 1247, 698}"
181,1,348,0,0.6089322,"\int \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2,x]","-\frac{d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{8 b c \sqrt{c x-1} \sqrt{c x+1}}+\frac{3}{8} d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{1}{4} d x (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{b d \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c d x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{15}{64} b^2 d x \sqrt{d-c^2 d x^2}+\frac{1}{32} b^2 d x (1-c x) (c x+1) \sqrt{d-c^2 d x^2}+\frac{9 b^2 d \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{64 c \sqrt{c x-1} \sqrt{c x+1}}","-\frac{d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{8 b c \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{4} x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{3}{8} d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{b d \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c d x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{15}{64} b^2 d x \sqrt{d-c^2 d x^2}+\frac{1}{32} b^2 d x (1-c x) (c x+1) \sqrt{d-c^2 d x^2}+\frac{9 b^2 d \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{64 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(15*b^2*d*x*Sqrt[d - c^2*d*x^2])/64 + (b^2*d*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2])/32 + (9*b^2*d*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(64*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*b*c*d*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(8*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(8*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/8 + (d*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/4 - (d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^3)/(8*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",11,9,26,0.3462,1,"{5713, 5685, 5683, 5676, 5662, 90, 52, 5716, 38}"
182,1,585,0,1.2549014,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2)/x,x]","\frac{2 i b d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 i b d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 i b^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{2 i b^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 a b c d x \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c^3 d x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}+d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{1}{3} d (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 d \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2}{27} b^2 c^2 d x^2 \sqrt{d-c^2 d x^2}+\frac{68}{27} b^2 d \sqrt{d-c^2 d x^2}-\frac{2 b^2 c d x \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}","\frac{2 i b d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 i b d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 i b^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{2 i b^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 a b c d x \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c^3 d x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{3} \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2+d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 d \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2}{27} b^2 c^2 d x^2 \sqrt{d-c^2 d x^2}+\frac{68}{27} b^2 d \sqrt{d-c^2 d x^2}-\frac{2 b^2 c d x \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}",1,"(68*b^2*d*Sqrt[d - c^2*d*x^2])/27 - (2*b^2*c^2*d*x^2*Sqrt[d - c^2*d*x^2])/27 - (2*a*b*c*d*x*Sqrt[d - c^2*d*x^2])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b^2*c*d*x*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*c*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*c^3*d*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2 + (d*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/3 - (2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2*ArcTan[E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((2*I)*b*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((2*I)*b*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*PolyLog[2, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((2*I)*b^2*d*Sqrt[d - c^2*d*x^2]*PolyLog[3, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((2*I)*b^2*d*Sqrt[d - c^2*d*x^2]*PolyLog[3, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",18,13,29,0.4483,1,"{5798, 5745, 5743, 5761, 4180, 2531, 2282, 6589, 5654, 74, 5680, 12, 460}"
183,1,465,0,0.9659131,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x^2} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2)/x^2,x]","\frac{b^2 c d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b c^3 d x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3}{2} c^2 d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{c d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{2 b \sqrt{c x-1} \sqrt{c x+1}}-\frac{c d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{d (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x}+\frac{2 b c d \sqrt{d-c^2 d x^2} \log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{1}{4} b^2 c^2 d x \sqrt{d-c^2 d x^2}-\frac{5 b^2 c d \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{4 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{b^2 c d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b c^3 d x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3}{2} c^2 d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{c d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{2 b \sqrt{c x-1} \sqrt{c x+1}}+\frac{c d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x}+\frac{2 b c d \sqrt{d-c^2 d x^2} \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{1}{4} b^2 c^2 d x \sqrt{d-c^2 d x^2}-\frac{5 b^2 c d \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{4 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b^2*c^2*d*x*Sqrt[d - c^2*d*x^2])/4 - (5*b^2*c*d*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*b*c^3*d*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c*d*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*c^2*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/2 - (c*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/x + (c*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^3)/(2*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*c*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b^2*c*d*Sqrt[d - c^2*d*x^2]*PolyLog[2, -E^(2*ArcCosh[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",15,14,29,0.4828,0,"{5798, 5740, 5683, 5676, 5662, 90, 52, 5727, 5660, 3718, 2190, 2279, 2391, 38}"
184,1,642,0,1.3741313,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x^3} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2)/x^3,x]","-\frac{3 i b c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{3 i b c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{3 i b^2 c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{3 i b^2 c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{3 a b c^3 d x \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^3 d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{3}{2} c^2 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{b c d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x \sqrt{c x-1} \sqrt{c x+1}}-\frac{d (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 x^2}+\frac{3 c^2 d \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{c x-1} \sqrt{c x+1}}-2 b^2 c^2 d \sqrt{d-c^2 d x^2}+\frac{b^2 c^2 d \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b^2 c^3 d x \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}","-\frac{3 i b c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{3 i b c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{3 i b^2 c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{3 i b^2 c^2 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{3 a b c^3 d x \sqrt{d-c^2 d x^2}}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^3 d x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{3}{2} c^2 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{b c d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{x \sqrt{c x-1} \sqrt{c x+1}}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 x^2}+\frac{3 c^2 d \sqrt{d-c^2 d x^2} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{c x-1} \sqrt{c x+1}}-2 b^2 c^2 d \sqrt{d-c^2 d x^2}+\frac{b^2 c^2 d \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b^2 c^3 d x \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}",1,"-2*b^2*c^2*d*Sqrt[d - c^2*d*x^2] + (3*a*b*c^3*d*x*Sqrt[d - c^2*d*x^2])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*b^2*c^3*d*x*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^3*d*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/2 - (d*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*x^2) + (3*c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2*ArcTan[E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b^2*c^2*d*Sqrt[d - c^2*d*x^2]*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((3*I)*b*c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((3*I)*b*c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*PolyLog[2, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((3*I)*b^2*c^2*d*Sqrt[d - c^2*d*x^2]*PolyLog[3, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((3*I)*b^2*c^2*d*Sqrt[d - c^2*d*x^2]*PolyLog[3, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",18,15,29,0.5172,1,"{5798, 5740, 5743, 5761, 4180, 2531, 2282, 6589, 5654, 74, 14, 5731, 460, 92, 205}"
185,1,438,0,1.1669723,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x^4} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2)/x^4,x]","-\frac{4 b^2 c^3 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{c^3 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{3 b \sqrt{c x-1} \sqrt{c x+1}}+\frac{4 c^3 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{c^2 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x}-\frac{b c d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 x^3}-\frac{8 b c^3 d \sqrt{d-c^2 d x^2} \log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b^2 c^2 d \sqrt{d-c^2 d x^2}}{3 x}-\frac{b^2 c^3 d \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{4 b^2 c^3 d \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{c^3 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{3 b \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 c^3 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{c^2 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x}-\frac{b c d \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 x^3}-\frac{8 b c^3 d \sqrt{d-c^2 d x^2} \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b^2 c^2 d \sqrt{d-c^2 d x^2}}{3 x}-\frac{b^2 c^3 d \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b^2*c^2*d*Sqrt[d - c^2*d*x^2])/(3*x) - (b^2*c^3*d*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (c^2*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/x + (4*c^3*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(3*x^3) - (c^3*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^3)/(3*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (8*b*c^3*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])])/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (4*b^2*c^3*d*Sqrt[d - c^2*d*x^2]*PolyLog[2, -E^(2*ArcCosh[c*x])])/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",18,13,29,0.4483,0,"{5798, 5740, 5738, 5660, 3718, 2190, 2279, 2391, 5676, 5729, 97, 12, 52}"
186,1,911,0,2.3446778,"\int x^3 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[x^3*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2,x]","-\frac{2 b c^5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^9}{81 \sqrt{c x-1} \sqrt{c x+1}}+\frac{38 b c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^7}{441 \sqrt{c x-1} \sqrt{c x+1}}-\frac{10 b^2 c^2 d^2 \sqrt{d-c^2 d x^2} x^6}{3087}-\frac{2 b c d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^5}{21 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{21} d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 x^4+\frac{1}{9} d^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 x^4+\frac{5}{63} d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 x^4+\frac{484 b^2 d^2 \sqrt{d-c^2 d x^2} x^4}{77175}+\frac{2 b d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3}{189 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 x^2}{63 c^2}+\frac{3358 b^2 d^2 \sqrt{d-c^2 d x^2} x^2}{694575 c^2}+\frac{4 b^2 d^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) x}{63 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{4 a b d^2 \sqrt{d-c^2 d x^2} x}{63 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{63 c^4}+\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^5 \sqrt{d-c^2 d x^2}}{729 c^4 (1-c x) (c x+1)}-\frac{20 b^2 d^2 \left(1-c^2 x^2\right)^4 \sqrt{d-c^2 d x^2}}{3969 c^4 (1-c x) (c x+1)}+\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{4725 c^4 (1-c x) (c x+1)}-\frac{37384 b^2 d^2 \sqrt{d-c^2 d x^2}}{694575 c^4}+\frac{8 b^2 d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{8505 c^4 (1-c x) (c x+1)}+\frac{16 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{2835 c^4 (1-c x) (c x+1)}","-\frac{2 b c^5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^9}{81 \sqrt{c x-1} \sqrt{c x+1}}+\frac{38 b c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^7}{441 \sqrt{c x-1} \sqrt{c x+1}}-\frac{10 b^2 c^2 d^2 \sqrt{d-c^2 d x^2} x^6}{3087}-\frac{2 b c d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^5}{21 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{9} \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2 x^4+\frac{5}{63} d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2 x^4+\frac{1}{21} d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 x^4+\frac{484 b^2 d^2 \sqrt{d-c^2 d x^2} x^4}{77175}+\frac{2 b d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3}{189 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 x^2}{63 c^2}+\frac{3358 b^2 d^2 \sqrt{d-c^2 d x^2} x^2}{694575 c^2}+\frac{4 b^2 d^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) x}{63 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{4 a b d^2 \sqrt{d-c^2 d x^2} x}{63 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{63 c^4}+\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^5 \sqrt{d-c^2 d x^2}}{729 c^4 (1-c x) (c x+1)}-\frac{20 b^2 d^2 \left(1-c^2 x^2\right)^4 \sqrt{d-c^2 d x^2}}{3969 c^4 (1-c x) (c x+1)}+\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{4725 c^4 (1-c x) (c x+1)}-\frac{37384 b^2 d^2 \sqrt{d-c^2 d x^2}}{694575 c^4}+\frac{8 b^2 d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{8505 c^4 (1-c x) (c x+1)}+\frac{16 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{2835 c^4 (1-c x) (c x+1)}",1,"(-37384*b^2*d^2*Sqrt[d - c^2*d*x^2])/(694575*c^4) + (3358*b^2*d^2*x^2*Sqrt[d - c^2*d*x^2])/(694575*c^2) + (484*b^2*d^2*x^4*Sqrt[d - c^2*d*x^2])/77175 - (10*b^2*c^2*d^2*x^6*Sqrt[d - c^2*d*x^2])/3087 + (4*a*b*d^2*x*Sqrt[d - c^2*d*x^2])/(63*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (16*b^2*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(2835*c^4*(1 - c*x)*(1 + c*x)) + (8*b^2*d^2*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(8505*c^4*(1 - c*x)*(1 + c*x)) + (2*b^2*d^2*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2])/(4725*c^4*(1 - c*x)*(1 + c*x)) - (20*b^2*d^2*(1 - c^2*x^2)^4*Sqrt[d - c^2*d*x^2])/(3969*c^4*(1 - c*x)*(1 + c*x)) + (2*b^2*d^2*(1 - c^2*x^2)^5*Sqrt[d - c^2*d*x^2])/(729*c^4*(1 - c*x)*(1 + c*x)) + (4*b^2*d^2*x*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(63*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*d^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(189*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*c*d^2*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(21*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (38*b*c^3*d^2*x^7*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(441*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*c^5*d^2*x^9*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(81*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(63*c^4) - (d^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(63*c^2) + (d^2*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/21 + (5*d^2*x^4*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/63 + (d^2*x^4*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/9","A",34,18,29,0.6207,1,"{5798, 5745, 5743, 5759, 5718, 5654, 74, 5662, 100, 12, 14, 5731, 460, 270, 520, 1251, 897, 1153}"
187,1,872,0,2.1238773,"\int x^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[x^2*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2,x]","-\frac{b c^5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^8}{32 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b^2 c^4 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x^7}{256 (1-c x) (c x+1)}+\frac{17 b c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^6}{144 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5}{864} b^2 c^2 d^2 \sqrt{d-c^2 d x^2} x^5-\frac{43 b^2 c^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x^5}{4608 (1-c x) (c x+1)}-\frac{59 b c d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^4}{384 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5}{64} d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 x^3+\frac{1}{8} d^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 x^3+\frac{5}{48} d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 x^3+\frac{215 b^2 d^2 \sqrt{d-c^2 d x^2} x^3}{13824}+\frac{73 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x^3}{18432 (1-c x) (c x+1)}+\frac{5 b d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^2}{128 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 x}{128 c^2}+\frac{35 b^2 d^2 \sqrt{d-c^2 d x^2} x}{9216 c^2}+\frac{73 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x}{12288 c^2 (1-c x) (c x+1)}-\frac{5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{384 b c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{35 b^2 d^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{9216 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{73 b^2 d^2 \sqrt{c^2 x^2-1} \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{12288 c^3 (1-c x) (c x+1)}","-\frac{b c^5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^8}{32 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b^2 c^4 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x^7}{256 (1-c x) (c x+1)}+\frac{17 b c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^6}{144 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5}{864} b^2 c^2 d^2 \sqrt{d-c^2 d x^2} x^5-\frac{43 b^2 c^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x^5}{4608 (1-c x) (c x+1)}-\frac{59 b c d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^4}{384 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{8} \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2 x^3+\frac{5}{48} d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2 x^3+\frac{5}{64} d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 x^3+\frac{215 b^2 d^2 \sqrt{d-c^2 d x^2} x^3}{13824}+\frac{73 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x^3}{18432 (1-c x) (c x+1)}+\frac{5 b d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^2}{128 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 x}{128 c^2}+\frac{35 b^2 d^2 \sqrt{d-c^2 d x^2} x}{9216 c^2}+\frac{73 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} x}{12288 c^2 (1-c x) (c x+1)}-\frac{5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{384 b c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{35 b^2 d^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{9216 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{73 b^2 d^2 \sqrt{c^2 x^2-1} \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{12288 c^3 (1-c x) (c x+1)}",1,"(35*b^2*d^2*x*Sqrt[d - c^2*d*x^2])/(9216*c^2) + (215*b^2*d^2*x^3*Sqrt[d - c^2*d*x^2])/13824 - (5*b^2*c^2*d^2*x^5*Sqrt[d - c^2*d*x^2])/864 + (73*b^2*d^2*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(12288*c^2*(1 - c*x)*(1 + c*x)) + (73*b^2*d^2*x^3*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(18432*(1 - c*x)*(1 + c*x)) - (43*b^2*c^2*d^2*x^5*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(4608*(1 - c*x)*(1 + c*x)) + (b^2*c^4*d^2*x^7*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(256*(1 - c*x)*(1 + c*x)) + (35*b^2*d^2*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(9216*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*b*d^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(128*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (59*b*c*d^2*x^4*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(384*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (17*b*c^3*d^2*x^6*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(144*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^5*d^2*x^8*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(32*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(128*c^2) + (5*d^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/64 + (5*d^2*x^3*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/48 + (d^2*x^3*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/8 - (5*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^3)/(384*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (73*b^2*d^2*Sqrt[-1 + c^2*x^2]*Sqrt[d - c^2*d*x^2]*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/(12288*c^3*(1 - c*x)*(1 + c*x))","A",30,21,29,0.7241,1,"{5798, 5745, 5743, 5759, 5676, 5662, 90, 52, 100, 12, 14, 5731, 460, 266, 43, 520, 1267, 459, 321, 217, 206}"
188,1,485,0,0.6802305,"\int x \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[x*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2,x]","-\frac{2 b c^5 d^2 x^7 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{49 \sqrt{c x-1} \sqrt{c x+1}}+\frac{6 b c^3 d^2 x^5 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{35 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{7 c^2}-\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^4 \sqrt{d-c^2 d x^2}}{343 c^2 (1-c x) (c x+1)}-\frac{12 b^2 d^2 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{1225 c^2 (1-c x) (c x+1)}-\frac{16 b^2 d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{735 c^2 (1-c x) (c x+1)}-\frac{32 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{245 c^2 (1-c x) (c x+1)}","-\frac{2 b c^5 d^2 x^7 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{49 \sqrt{c x-1} \sqrt{c x+1}}+\frac{6 b c^3 d^2 x^5 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{35 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{\left(d-c^2 d x^2\right)^{7/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{7 c^2 d}-\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^4 \sqrt{d-c^2 d x^2}}{343 c^2 (1-c x) (c x+1)}-\frac{12 b^2 d^2 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{1225 c^2 (1-c x) (c x+1)}-\frac{16 b^2 d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{735 c^2 (1-c x) (c x+1)}-\frac{32 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{245 c^2 (1-c x) (c x+1)}",1,"(-32*b^2*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(245*c^2*(1 - c*x)*(1 + c*x)) - (16*b^2*d^2*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(735*c^2*(1 - c*x)*(1 + c*x)) - (12*b^2*d^2*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2])/(1225*c^2*(1 - c*x)*(1 + c*x)) - (2*b^2*d^2*(1 - c^2*x^2)^4*Sqrt[d - c^2*d*x^2])/(343*c^2*(1 - c*x)*(1 + c*x)) + (2*b*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(7*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*c*d^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (6*b*c^3*d^2*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(35*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*c^5*d^2*x^7*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(49*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d^2*(1 - c*x)^3*(1 + c*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(7*c^2)","A",8,8,27,0.2963,1,"{5798, 5718, 194, 5680, 12, 1610, 1799, 1850}"
189,1,517,0,0.8676421,"\int \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2,x]","\frac{b d^2 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{18 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{48 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{48 b c \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{6} d^2 x (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{5}{16} d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{5}{24} d^2 x (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{5 b c d^2 x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{108} b^2 d^2 x (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2}+\frac{245 b^2 d^2 x \sqrt{d-c^2 d x^2}}{1152}+\frac{65 b^2 d^2 x (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}{1728}+\frac{115 b^2 d^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{1152 c \sqrt{c x-1} \sqrt{c x+1}}","\frac{b d^2 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{18 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{48 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{48 b c \sqrt{c x-1} \sqrt{c x+1}}+\frac{5}{16} d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{5 b c d^2 x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{6} x \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{5}{24} d x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{1}{108} b^2 d^2 x (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2}+\frac{245 b^2 d^2 x \sqrt{d-c^2 d x^2}}{1152}+\frac{65 b^2 d^2 x (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}{1728}+\frac{115 b^2 d^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{1152 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(245*b^2*d^2*x*Sqrt[d - c^2*d*x^2])/1152 + (65*b^2*d^2*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2])/1728 + (b^2*d^2*x*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2])/108 + (115*b^2*d^2*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(1152*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*b*c*d^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(16*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*b*d^2*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(48*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^2*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(18*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/16 + (5*d^2*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/24 + (d^2*x*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/6 - (5*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^3)/(48*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",17,9,26,0.3462,1,"{5713, 5685, 5683, 5676, 5662, 90, 52, 5716, 38}"
190,1,867,0,1.7756654,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2)/x,x]","-\frac{2 b c^5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^5}{25 \sqrt{c x-1} \sqrt{c x+1}}+\frac{22 b c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3}{45 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2}{27} b^2 c^2 d^2 \sqrt{d-c^2 d x^2} x^2-\frac{2 b^2 c d^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) x}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{16 b c d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x}{15 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 a b c d^2 \sqrt{d-c^2 d x^2} x}{\sqrt{c x-1} \sqrt{c x+1}}+d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{1}{5} d^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{1}{3} d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{2 i b d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 i b d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 i b^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{2 i b^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{125 (1-c x) (c x+1)}+\frac{68}{27} b^2 d^2 \sqrt{d-c^2 d x^2}+\frac{8 b^2 d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{225 (1-c x) (c x+1)}+\frac{16 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{75 (1-c x) (c x+1)}","-\frac{2 b c^5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^5}{25 \sqrt{c x-1} \sqrt{c x+1}}+\frac{22 b c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3}{45 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2}{27} b^2 c^2 d^2 \sqrt{d-c^2 d x^2} x^2-\frac{2 b^2 c d^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) x}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{16 b c d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x}{15 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 a b c d^2 \sqrt{d-c^2 d x^2} x}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{1}{5} \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{1}{3} d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2+d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{2 i b d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 i b d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 i b^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{2 i b^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b^2 d^2 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{125 (1-c x) (c x+1)}+\frac{68}{27} b^2 d^2 \sqrt{d-c^2 d x^2}+\frac{8 b^2 d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2}}{225 (1-c x) (c x+1)}+\frac{16 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{75 (1-c x) (c x+1)}",1,"(68*b^2*d^2*Sqrt[d - c^2*d*x^2])/27 - (2*b^2*c^2*d^2*x^2*Sqrt[d - c^2*d*x^2])/27 - (2*a*b*c*d^2*x*Sqrt[d - c^2*d*x^2])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (16*b^2*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(75*(1 - c*x)*(1 + c*x)) + (8*b^2*d^2*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(225*(1 - c*x)*(1 + c*x)) + (2*b^2*d^2*(1 - c^2*x^2)^3*Sqrt[d - c^2*d*x^2])/(125*(1 - c*x)*(1 + c*x)) - (2*b^2*c*d^2*x*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (16*b*c*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(15*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (22*b*c^3*d^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(45*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*c^5*d^2*x^5*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(25*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2 + (d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/3 + (d^2*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/5 - (2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2*ArcTan[E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((2*I)*b*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((2*I)*b*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*PolyLog[2, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((2*I)*b^2*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[3, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((2*I)*b^2*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[3, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",25,17,29,0.5862,1,"{5798, 5745, 5743, 5761, 4180, 2531, 2282, 6589, 5654, 74, 5680, 12, 460, 194, 520, 1247, 698}"
191,1,638,0,1.2900132,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x^2} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2)/x^2,x]","\frac{b^2 c d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{15 b c^3 d^2 x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}-\frac{15}{8} c^2 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{5}{4} c^2 d^2 x (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{5 c d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{8 b \sqrt{c x-1} \sqrt{c x+1}}-\frac{c d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x}+\frac{2 b c d^2 \sqrt{d-c^2 d x^2} \log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{31}{64} b^2 c^2 d^2 x \sqrt{d-c^2 d x^2}-\frac{1}{32} b^2 c^2 d^2 x (1-c x) (c x+1) \sqrt{d-c^2 d x^2}-\frac{89 b^2 c d^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{64 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{b^2 c d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{15 b c^3 d^2 x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}-\frac{15}{8} c^2 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2+\frac{5 c d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{8 b \sqrt{c x-1} \sqrt{c x+1}}+\frac{c d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c d^2 \sqrt{d-c^2 d x^2} \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{5}{4} c^2 d x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x}-\frac{31}{64} b^2 c^2 d^2 x \sqrt{d-c^2 d x^2}-\frac{1}{32} b^2 c^2 d^2 x (1-c x) (c x+1) \sqrt{d-c^2 d x^2}-\frac{89 b^2 c d^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{64 \sqrt{c x-1} \sqrt{c x+1}}",1,"(-31*b^2*c^2*d^2*x*Sqrt[d - c^2*d*x^2])/64 - (b^2*c^2*d^2*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2])/32 - (89*b^2*c*d^2*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(64*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (15*b*c^3*d^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(8*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d^2*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(8*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (15*c^2*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/8 - (c*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*c^2*d^2*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/4 - (d^2*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/x + (5*c*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^3)/(8*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*c*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b^2*c*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, -E^(2*ArcCosh[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",24,16,29,0.5517,0,"{5798, 5740, 5685, 5683, 5676, 5662, 90, 52, 5716, 38, 5727, 5660, 3718, 2190, 2279, 2391}"
192,1,921,0,1.9853759,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x^3} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2)/x^3,x]","-\frac{2 b d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c^5}{9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5}{27} b^2 d^2 x^2 \sqrt{d-c^2 d x^2} c^4+\frac{5 b^2 d^2 x \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) c^3}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c^3}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 a b d^2 x \sqrt{d-c^2 d x^2} c^3}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{5}{2} d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 c^2-\frac{5}{6} d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 c^2+\frac{5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) c^2}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b^2 d^2 \sqrt{c^2 x^2-1} \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right) c^2}{(1-c x) (c x+1)}-\frac{5 i b d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) c^2}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{5 i b d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) c^2}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{5 i b^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right) c^2}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{5 i b^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right) c^2}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{170}{27} b^2 d^2 \sqrt{d-c^2 d x^2} c^2+\frac{b^2 d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} c^2}{9 (1-c x) (c x+1)}+\frac{5 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} c^2}{3 (1-c x) (c x+1)}-\frac{b d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c}{x \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 x^2}","-\frac{2 b d^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c^5}{9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5}{27} b^2 d^2 x^2 \sqrt{d-c^2 d x^2} c^4+\frac{5 b^2 d^2 x \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) c^3}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c^3}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 a b d^2 x \sqrt{d-c^2 d x^2} c^3}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{5}{6} d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2 c^2-\frac{5}{2} d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 c^2+\frac{5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) c^2}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b^2 d^2 \sqrt{c^2 x^2-1} \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right) c^2}{(1-c x) (c x+1)}-\frac{5 i b d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) c^2}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{5 i b d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) c^2}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{5 i b^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right) c^2}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{5 i b^2 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right) c^2}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{170}{27} b^2 d^2 \sqrt{d-c^2 d x^2} c^2+\frac{b^2 d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} c^2}{9 (1-c x) (c x+1)}+\frac{5 b^2 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} c^2}{3 (1-c x) (c x+1)}-\frac{b d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c}{x \sqrt{c x-1} \sqrt{c x+1}}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 x^2}",1,"(-170*b^2*c^2*d^2*Sqrt[d - c^2*d*x^2])/27 + (5*b^2*c^4*d^2*x^2*Sqrt[d - c^2*d*x^2])/27 + (5*a*b*c^3*d^2*x*Sqrt[d - c^2*d*x^2])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*b^2*c^2*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2])/(3*(1 - c*x)*(1 + c*x)) + (b^2*c^2*d^2*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2])/(9*(1 - c*x)*(1 + c*x)) + (5*b^2*c^3*d^2*x*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c^3*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*c^5*d^2*x^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*c^2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/2 - (5*c^2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/6 - (d^2*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(2*x^2) + (5*c^2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2*ArcTan[E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b^2*c^2*d^2*Sqrt[-1 + c^2*x^2]*Sqrt[d - c^2*d*x^2]*ArcTan[Sqrt[-1 + c^2*x^2]])/((1 - c*x)*(1 + c*x)) - ((5*I)*b*c^2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((5*I)*b*c^2*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*PolyLog[2, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((5*I)*b^2*c^2*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[3, (-I)*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((5*I)*b^2*c^2*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[3, I*E^ArcCosh[c*x]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",27,21,29,0.7241,1,"{5798, 5740, 5745, 5743, 5761, 4180, 2531, 2282, 6589, 5654, 74, 5680, 12, 460, 270, 5731, 520, 1251, 897, 1153, 205}"
193,1,669,0,1.6153298,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{x^4} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2)/x^4,x]","-\frac{7 b^2 c^3 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b c^5 d^2 x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5}{2} c^4 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{5 c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{6 b \sqrt{c x-1} \sqrt{c x+1}}+\frac{7 c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{7 b c^3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 c^2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 x}-\frac{b c d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 x^3}-\frac{14 b c^3 d^2 \sqrt{d-c^2 d x^2} \log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{7}{12} b^2 c^4 d^2 x \sqrt{d-c^2 d x^2}+\frac{b^2 c^2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}{3 x}+\frac{23 b^2 c^3 d^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{12 \sqrt{c x-1} \sqrt{c x+1}}","\frac{7 b^2 c^3 d^2 \sqrt{d-c^2 d x^2} \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b c^5 d^2 x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5}{2} c^4 d^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{5 c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^3}{6 b \sqrt{c x-1} \sqrt{c x+1}}-\frac{7 c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{7 b c^3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 \left(1-c^2 x^2\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 x^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{14 b c^3 d^2 \sqrt{d-c^2 d x^2} \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 c^2 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 x}-\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 x^3}+\frac{7}{12} b^2 c^4 d^2 x \sqrt{d-c^2 d x^2}+\frac{b^2 c^2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}{3 x}+\frac{23 b^2 c^3 d^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{12 \sqrt{c x-1} \sqrt{c x+1}}",1,"(7*b^2*c^4*d^2*x*Sqrt[d - c^2*d*x^2])/12 + (b^2*c^2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2])/(3*x) + (23*b^2*c^3*d^2*Sqrt[d - c^2*d*x^2]*ArcCosh[c*x])/(12*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*b*c^5*d^2*x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (7*b*c^3*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d^2*(1 - c^2*x^2)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(3*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*c^4*d^2*x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/2 + (7*c^3*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*c^2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(3*x) - (d^2*(1 - c*x)^2*(1 + c*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2)/(3*x^3) - (5*c^3*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^3)/(6*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (14*b*c^3*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])])/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (7*b^2*c^3*d^2*Sqrt[d - c^2*d*x^2]*PolyLog[2, -E^(2*ArcCosh[c*x])])/(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",29,17,29,0.5862,0,"{5798, 5740, 5683, 5676, 5662, 90, 52, 5727, 5660, 3718, 2190, 2279, 2391, 38, 5729, 97, 12}"
194,1,445,0,1.1313474,"\int \frac{x^5 \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^5*(a + b*ArcCosh[c*x])^2)/Sqrt[d - c^2*d*x^2],x]","-\frac{16 a b x \sqrt{c x-1} \sqrt{c x+1}}{15 c^5 \sqrt{d-c^2 d x^2}}-\frac{2 b x^5 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{25 c \sqrt{d-c^2 d x^2}}-\frac{x^4 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{5 c^2 \sqrt{d-c^2 d x^2}}-\frac{8 b x^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{45 c^3 \sqrt{d-c^2 d x^2}}-\frac{4 x^2 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{15 c^4 \sqrt{d-c^2 d x^2}}-\frac{8 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{15 c^6 \sqrt{d-c^2 d x^2}}-\frac{2 b^2 x^4 (1-c x) (c x+1)}{125 c^2 \sqrt{d-c^2 d x^2}}-\frac{272 b^2 x^2 (1-c x) (c x+1)}{3375 c^4 \sqrt{d-c^2 d x^2}}-\frac{4144 b^2 (1-c x) (c x+1)}{3375 c^6 \sqrt{d-c^2 d x^2}}-\frac{16 b^2 x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{15 c^5 \sqrt{d-c^2 d x^2}}","-\frac{16 a b x \sqrt{c x-1} \sqrt{c x+1}}{15 c^5 \sqrt{d-c^2 d x^2}}-\frac{2 b x^5 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{25 c \sqrt{d-c^2 d x^2}}-\frac{x^4 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{5 c^2 d}-\frac{8 b x^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{45 c^3 \sqrt{d-c^2 d x^2}}-\frac{4 x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{15 c^4 d}-\frac{8 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{15 c^6 d}-\frac{2 b^2 x^4 (1-c x) (c x+1)}{125 c^2 \sqrt{d-c^2 d x^2}}-\frac{272 b^2 x^2 (1-c x) (c x+1)}{3375 c^4 \sqrt{d-c^2 d x^2}}-\frac{4144 b^2 (1-c x) (c x+1)}{3375 c^6 \sqrt{d-c^2 d x^2}}-\frac{16 b^2 x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{15 c^5 \sqrt{d-c^2 d x^2}}",1,"(-16*a*b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(15*c^5*Sqrt[d - c^2*d*x^2]) - (4144*b^2*(1 - c*x)*(1 + c*x))/(3375*c^6*Sqrt[d - c^2*d*x^2]) - (272*b^2*x^2*(1 - c*x)*(1 + c*x))/(3375*c^4*Sqrt[d - c^2*d*x^2]) - (2*b^2*x^4*(1 - c*x)*(1 + c*x))/(125*c^2*Sqrt[d - c^2*d*x^2]) - (16*b^2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(15*c^5*Sqrt[d - c^2*d*x^2]) - (8*b*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(45*c^3*Sqrt[d - c^2*d*x^2]) - (2*b*x^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(25*c*Sqrt[d - c^2*d*x^2]) - (8*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(15*c^6*Sqrt[d - c^2*d*x^2]) - (4*x^2*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(15*c^4*Sqrt[d - c^2*d*x^2]) - (x^4*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(5*c^2*Sqrt[d - c^2*d*x^2])","A",17,8,29,0.2759,1,"{5798, 5759, 5718, 5654, 74, 5662, 100, 12}"
195,1,371,0,1.0244312,"\int \frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^4*(a + b*ArcCosh[c*x])^2)/Sqrt[d - c^2*d*x^2],x]","-\frac{b x^4 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{8 c \sqrt{d-c^2 d x^2}}-\frac{x^3 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{4 c^2 \sqrt{d-c^2 d x^2}}-\frac{3 b x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{8 c^3 \sqrt{d-c^2 d x^2}}-\frac{3 x (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{8 c^4 \sqrt{d-c^2 d x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{8 b c^5 \sqrt{d-c^2 d x^2}}-\frac{b^2 x^3 (1-c x) (c x+1)}{32 c^2 \sqrt{d-c^2 d x^2}}-\frac{15 b^2 x (1-c x) (c x+1)}{64 c^4 \sqrt{d-c^2 d x^2}}+\frac{15 b^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{64 c^5 \sqrt{d-c^2 d x^2}}","-\frac{b x^4 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{8 c \sqrt{d-c^2 d x^2}}-\frac{x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 c^2 d}-\frac{3 b x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{8 c^3 \sqrt{d-c^2 d x^2}}-\frac{3 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{8 c^4 d}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{8 b c^5 \sqrt{d-c^2 d x^2}}-\frac{b^2 x^3 (1-c x) (c x+1)}{32 c^2 \sqrt{d-c^2 d x^2}}-\frac{15 b^2 x (1-c x) (c x+1)}{64 c^4 \sqrt{d-c^2 d x^2}}+\frac{15 b^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{64 c^5 \sqrt{d-c^2 d x^2}}",1,"(-15*b^2*x*(1 - c*x)*(1 + c*x))/(64*c^4*Sqrt[d - c^2*d*x^2]) - (b^2*x^3*(1 - c*x)*(1 + c*x))/(32*c^2*Sqrt[d - c^2*d*x^2]) + (15*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(64*c^5*Sqrt[d - c^2*d*x^2]) - (3*b*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(8*c^3*Sqrt[d - c^2*d*x^2]) - (b*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(8*c*Sqrt[d - c^2*d*x^2]) - (3*x*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(8*c^4*Sqrt[d - c^2*d*x^2]) - (x^3*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(4*c^2*Sqrt[d - c^2*d*x^2]) + (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^3)/(8*b*c^5*Sqrt[d - c^2*d*x^2])","A",12,8,29,0.2759,1,"{5798, 5759, 5676, 5662, 90, 52, 100, 12}"
196,1,308,0,0.7694461,"\int \frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^3*(a + b*ArcCosh[c*x])^2)/Sqrt[d - c^2*d*x^2],x]","-\frac{4 a b x \sqrt{c x-1} \sqrt{c x+1}}{3 c^3 \sqrt{d-c^2 d x^2}}-\frac{2 b x^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{9 c \sqrt{d-c^2 d x^2}}-\frac{x^2 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^2 \sqrt{d-c^2 d x^2}}-\frac{2 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^4 \sqrt{d-c^2 d x^2}}-\frac{2 b^2 x^2 (1-c x) (c x+1)}{27 c^2 \sqrt{d-c^2 d x^2}}-\frac{40 b^2 (1-c x) (c x+1)}{27 c^4 \sqrt{d-c^2 d x^2}}-\frac{4 b^2 x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{3 c^3 \sqrt{d-c^2 d x^2}}","-\frac{4 a b x \sqrt{c x-1} \sqrt{c x+1}}{3 c^3 \sqrt{d-c^2 d x^2}}-\frac{2 b x^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{9 c \sqrt{d-c^2 d x^2}}-\frac{x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^2 d}-\frac{2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^4 d}-\frac{2 b^2 x^2 (1-c x) (c x+1)}{27 c^2 \sqrt{d-c^2 d x^2}}-\frac{40 b^2 (1-c x) (c x+1)}{27 c^4 \sqrt{d-c^2 d x^2}}-\frac{4 b^2 x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{3 c^3 \sqrt{d-c^2 d x^2}}",1,"(-4*a*b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3*c^3*Sqrt[d - c^2*d*x^2]) - (40*b^2*(1 - c*x)*(1 + c*x))/(27*c^4*Sqrt[d - c^2*d*x^2]) - (2*b^2*x^2*(1 - c*x)*(1 + c*x))/(27*c^2*Sqrt[d - c^2*d*x^2]) - (4*b^2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(3*c^3*Sqrt[d - c^2*d*x^2]) - (2*b*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(9*c*Sqrt[d - c^2*d*x^2]) - (2*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(3*c^4*Sqrt[d - c^2*d*x^2]) - (x^2*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(3*c^2*Sqrt[d - c^2*d*x^2])","A",10,8,29,0.2759,1,"{5798, 5759, 5718, 5654, 74, 5662, 100, 12}"
197,1,234,0,0.626361,"\int \frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^2*(a + b*ArcCosh[c*x])^2)/Sqrt[d - c^2*d*x^2],x]","\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{6 b c^3 \sqrt{d-c^2 d x^2}}-\frac{x (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{2 c^2 \sqrt{d-c^2 d x^2}}-\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{2 c \sqrt{d-c^2 d x^2}}-\frac{b^2 x (1-c x) (c x+1)}{4 c^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{4 c^3 \sqrt{d-c^2 d x^2}}","\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{6 b c^3 \sqrt{d-c^2 d x^2}}-\frac{x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 c^2 d}-\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{2 c \sqrt{d-c^2 d x^2}}-\frac{b^2 x (1-c x) (c x+1)}{4 c^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{4 c^3 \sqrt{d-c^2 d x^2}}",1,"-(b^2*x*(1 - c*x)*(1 + c*x))/(4*c^2*Sqrt[d - c^2*d*x^2]) + (b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(4*c^3*Sqrt[d - c^2*d*x^2]) - (b*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(2*c*Sqrt[d - c^2*d*x^2]) - (x*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(2*c^2*Sqrt[d - c^2*d*x^2]) + (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^3)/(6*b*c^3*Sqrt[d - c^2*d*x^2])","A",6,6,29,0.2069,1,"{5798, 5759, 5676, 5662, 90, 52}"
198,1,163,0,0.341503,"\int \frac{x \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x*(a + b*ArcCosh[c*x])^2)/Sqrt[d - c^2*d*x^2],x]","-\frac{2 a b x \sqrt{c x-1} \sqrt{c x+1}}{c \sqrt{d-c^2 d x^2}}-\frac{(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^2 (1-c x) (c x+1)}{c^2 \sqrt{d-c^2 d x^2}}-\frac{2 b^2 x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c \sqrt{d-c^2 d x^2}}","-\frac{2 a b x \sqrt{c x-1} \sqrt{c x+1}}{c \sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{c^2 d}-\frac{2 b^2 (1-c x) (c x+1)}{c^2 \sqrt{d-c^2 d x^2}}-\frac{2 b^2 x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c \sqrt{d-c^2 d x^2}}",1,"(-2*a*b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(c*Sqrt[d - c^2*d*x^2]) - (2*b^2*(1 - c*x)*(1 + c*x))/(c^2*Sqrt[d - c^2*d*x^2]) - (2*b^2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(c*Sqrt[d - c^2*d*x^2]) - ((1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(c^2*Sqrt[d - c^2*d*x^2])","A",5,4,27,0.1481,1,"{5798, 5718, 5654, 74}"
199,1,53,0,0.1954406,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/Sqrt[d - c^2*d*x^2],x]","\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{3 b c \sqrt{d-c^2 d x^2}}","\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{3 b c \sqrt{d-c^2 d x^2}}",1,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^3)/(3*b*c*Sqrt[d - c^2*d*x^2])","A",2,2,26,0.07692,1,"{5713, 5676}"
200,1,273,0,0.5212595,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{x \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/(x*Sqrt[d - c^2*d*x^2]),x]","-\frac{2 i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}+\frac{2 i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}+\frac{2 i b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}-\frac{2 i b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}}","-\frac{2 i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}+\frac{2 i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}+\frac{2 i b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}-\frac{2 i b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}}",1,"(2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2*ArcTan[E^ArcCosh[c*x]])/Sqrt[d - c^2*d*x^2] - ((2*I)*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*PolyLog[2, (-I)*E^ArcCosh[c*x]])/Sqrt[d - c^2*d*x^2] + ((2*I)*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*PolyLog[2, I*E^ArcCosh[c*x]])/Sqrt[d - c^2*d*x^2] + ((2*I)*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[3, (-I)*E^ArcCosh[c*x]])/Sqrt[d - c^2*d*x^2] - ((2*I)*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[3, I*E^ArcCosh[c*x]])/Sqrt[d - c^2*d*x^2]","A",9,6,29,0.2069,1,"{5798, 5761, 4180, 2531, 2282, 6589}"
201,1,194,0,0.518662,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{x^2 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/(x^2*Sqrt[d - c^2*d*x^2]),x]","-\frac{b^2 c \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}-\frac{(1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{x \sqrt{d-c^2 d x^2}}+\frac{c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}}-\frac{2 b c \sqrt{c x-1} \sqrt{c x+1} \log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}","\frac{b^2 c \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{d x}-\frac{c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}}-\frac{2 b c \sqrt{c x-1} \sqrt{c x+1} \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}",1,"(c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/Sqrt[d - c^2*d*x^2] - ((1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(x*Sqrt[d - c^2*d*x^2]) - (2*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])])/Sqrt[d - c^2*d*x^2] - (b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -E^(2*ArcCosh[c*x])])/Sqrt[d - c^2*d*x^2]","A",7,7,29,0.2414,0,"{5798, 5724, 5660, 3718, 2190, 2279, 2391}"
202,1,438,0,0.8806439,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{x^3 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/(x^3*Sqrt[d - c^2*d*x^2]),x]","-\frac{i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}+\frac{i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}+\frac{i b^2 c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}-\frac{i b^2 c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{x \sqrt{d-c^2 d x^2}}-\frac{(1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{2 x^2 \sqrt{d-c^2 d x^2}}+\frac{c^2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{\sqrt{d-c^2 d x^2}}","-\frac{i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}+\frac{i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}}+\frac{i b^2 c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}-\frac{i b^2 c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{\sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{x \sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 d x^2}+\frac{c^2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{\sqrt{d-c^2 d x^2}}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(x*Sqrt[d - c^2*d*x^2]) - ((1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(2*x^2*Sqrt[d - c^2*d*x^2]) + (c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2*ArcTan[E^ArcCosh[c*x]])/Sqrt[d - c^2*d*x^2] - (b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/Sqrt[d - c^2*d*x^2] - (I*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*PolyLog[2, (-I)*E^ArcCosh[c*x]])/Sqrt[d - c^2*d*x^2] + (I*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*PolyLog[2, I*E^ArcCosh[c*x]])/Sqrt[d - c^2*d*x^2] + (I*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[3, (-I)*E^ArcCosh[c*x]])/Sqrt[d - c^2*d*x^2] - (I*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[3, I*E^ArcCosh[c*x]])/Sqrt[d - c^2*d*x^2]","A",13,10,29,0.3448,1,"{5798, 5748, 5761, 4180, 2531, 2282, 6589, 5662, 92, 205}"
203,1,344,0,0.8689043,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{x^4 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/(x^4*Sqrt[d - c^2*d*x^2]),x]","-\frac{2 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{3 \sqrt{d-c^2 d x^2}}+\frac{2 c^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 \sqrt{d-c^2 d x^2}}-\frac{2 c^2 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{3 x \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 x^2 \sqrt{d-c^2 d x^2}}-\frac{(1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{3 x^3 \sqrt{d-c^2 d x^2}}-\frac{4 b c^3 \sqrt{c x-1} \sqrt{c x+1} \log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 \sqrt{d-c^2 d x^2}}+\frac{b^2 c^2 (1-c x) (c x+1)}{3 x \sqrt{d-c^2 d x^2}}","\frac{2 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)}{3 \sqrt{d-c^2 d x^2}}-\frac{2 c^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 \sqrt{d-c^2 d x^2}}-\frac{2 c^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d x}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 x^2 \sqrt{d-c^2 d x^2}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d x^3}-\frac{4 b c^3 \sqrt{c x-1} \sqrt{c x+1} \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 \sqrt{d-c^2 d x^2}}+\frac{b^2 c^2 (1-c x) (c x+1)}{3 x \sqrt{d-c^2 d x^2}}",1,"(b^2*c^2*(1 - c*x)*(1 + c*x))/(3*x*Sqrt[d - c^2*d*x^2]) + (b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*x^2*Sqrt[d - c^2*d*x^2]) + (2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(3*Sqrt[d - c^2*d*x^2]) - ((1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(3*x^3*Sqrt[d - c^2*d*x^2]) - (2*c^2*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(3*x*Sqrt[d - c^2*d*x^2]) - (4*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])])/(3*Sqrt[d - c^2*d*x^2]) - (2*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -E^(2*ArcCosh[c*x])])/(3*Sqrt[d - c^2*d*x^2])","A",10,10,29,0.3448,0,"{5798, 5748, 5724, 5660, 3718, 2190, 2279, 2391, 5662, 95}"
204,1,578,0,1.3670336,"\int \frac{x^5 \left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^5*(a + b*ArcCosh[c*x])^2)/(d - c^2*d*x^2)^(3/2),x]","\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{c^6 d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{c^6 d \sqrt{d-c^2 d x^2}}+\frac{16 a b x \sqrt{c x-1} \sqrt{c x+1}}{3 c^5 d \sqrt{d-c^2 d x^2}}+\frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{2 b x^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{9 c^3 d \sqrt{d-c^2 d x^2}}+\frac{4 x^2 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^4 d \sqrt{d-c^2 d x^2}}-\frac{2 b x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c^5 d \sqrt{d-c^2 d x^2}}+\frac{8 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^6 d \sqrt{d-c^2 d x^2}}+\frac{4 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^6 d \sqrt{d-c^2 d x^2}}+\frac{2 b^2 x^2 (1-c x) (c x+1)}{27 c^4 d \sqrt{d-c^2 d x^2}}+\frac{94 b^2 (1-c x) (c x+1)}{27 c^6 d \sqrt{d-c^2 d x^2}}+\frac{16 b^2 x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{3 c^5 d \sqrt{d-c^2 d x^2}}","\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{c^6 d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{c^6 d \sqrt{d-c^2 d x^2}}+\frac{4 x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^4 d^2}+\frac{8 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^6 d^2}+\frac{16 a b x \sqrt{c x-1} \sqrt{c x+1}}{3 c^5 d \sqrt{d-c^2 d x^2}}+\frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{2 b x^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{9 c^3 d \sqrt{d-c^2 d x^2}}-\frac{2 b x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c^5 d \sqrt{d-c^2 d x^2}}+\frac{4 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^6 d \sqrt{d-c^2 d x^2}}+\frac{2 b^2 x^2 (1-c x) (c x+1)}{27 c^4 d \sqrt{d-c^2 d x^2}}+\frac{94 b^2 (1-c x) (c x+1)}{27 c^6 d \sqrt{d-c^2 d x^2}}+\frac{16 b^2 x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{3 c^5 d \sqrt{d-c^2 d x^2}}",1,"(16*a*b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3*c^5*d*Sqrt[d - c^2*d*x^2]) + (94*b^2*(1 - c*x)*(1 + c*x))/(27*c^6*d*Sqrt[d - c^2*d*x^2]) + (2*b^2*x^2*(1 - c*x)*(1 + c*x))/(27*c^4*d*Sqrt[d - c^2*d*x^2]) + (16*b^2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(3*c^5*d*Sqrt[d - c^2*d*x^2]) - (2*b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(c^5*d*Sqrt[d - c^2*d*x^2]) + (2*b*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(9*c^3*d*Sqrt[d - c^2*d*x^2]) + (x^4*(a + b*ArcCosh[c*x])^2)/(c^2*d*Sqrt[d - c^2*d*x^2]) + (8*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(3*c^6*d*Sqrt[d - c^2*d*x^2]) + (4*x^2*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(3*c^4*d*Sqrt[d - c^2*d*x^2]) + (4*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(c^6*d*Sqrt[d - c^2*d*x^2]) + (2*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -E^ArcCosh[c*x]])/(c^6*d*Sqrt[d - c^2*d*x^2]) - (2*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^ArcCosh[c*x]])/(c^6*d*Sqrt[d - c^2*d*x^2])","A",23,14,29,0.4828,1,"{5798, 5752, 5759, 5718, 5654, 74, 5662, 100, 12, 5766, 5694, 4182, 2279, 2391}"
205,1,451,0,1.20541,"\int \frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^4*(a + b*ArcCosh[c*x])^2)/(d - c^2*d*x^2)^(3/2),x]","-\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{c^5 d \sqrt{d-c^2 d x^2}}+\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{2 c^3 d \sqrt{d-c^2 d x^2}}+\frac{3 x (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{2 c^4 d \sqrt{d-c^2 d x^2}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{2 b c^5 d \sqrt{d-c^2 d x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{c^5 d \sqrt{d-c^2 d x^2}}-\frac{2 b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^5 d \sqrt{d-c^2 d x^2}}+\frac{b^2 x (1-c x) (c x+1)}{4 c^4 d \sqrt{d-c^2 d x^2}}-\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{4 c^5 d \sqrt{d-c^2 d x^2}}","-\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{c^5 d \sqrt{d-c^2 d x^2}}+\frac{3 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 c^4 d^2}+\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{2 c^3 d \sqrt{d-c^2 d x^2}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{2 b c^5 d \sqrt{d-c^2 d x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{c^5 d \sqrt{d-c^2 d x^2}}-\frac{2 b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^5 d \sqrt{d-c^2 d x^2}}+\frac{b^2 x (1-c x) (c x+1)}{4 c^4 d \sqrt{d-c^2 d x^2}}-\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{4 c^5 d \sqrt{d-c^2 d x^2}}",1,"(b^2*x*(1 - c*x)*(1 + c*x))/(4*c^4*d*Sqrt[d - c^2*d*x^2]) - (b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(4*c^5*d*Sqrt[d - c^2*d*x^2]) + (b*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(2*c^3*d*Sqrt[d - c^2*d*x^2]) + (x^3*(a + b*ArcCosh[c*x])^2)/(c^2*d*Sqrt[d - c^2*d*x^2]) + (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(c^5*d*Sqrt[d - c^2*d*x^2]) + (3*x*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(2*c^4*d*Sqrt[d - c^2*d*x^2]) - (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^3)/(2*b*c^5*d*Sqrt[d - c^2*d*x^2]) - (2*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 - E^(2*ArcCosh[c*x])])/(c^5*d*Sqrt[d - c^2*d*x^2]) - (b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^(2*ArcCosh[c*x])])/(c^5*d*Sqrt[d - c^2*d*x^2])","A",15,13,29,0.4483,1,"{5798, 5752, 5759, 5676, 5662, 90, 52, 5766, 5715, 3716, 2190, 2279, 2391}"
206,1,424,0,0.9210472,"\int \frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^3*(a + b*ArcCosh[c*x])^2)/(d - c^2*d*x^2)^(3/2),x]","\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{c^4 d \sqrt{d-c^2 d x^2}}+\frac{4 a b x \sqrt{c x-1} \sqrt{c x+1}}{c^3 d \sqrt{d-c^2 d x^2}}-\frac{2 b x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{2 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{c^4 d \sqrt{d-c^2 d x^2}}+\frac{4 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^4 d \sqrt{d-c^2 d x^2}}+\frac{2 b^2 (1-c x) (c x+1)}{c^4 d \sqrt{d-c^2 d x^2}}+\frac{4 b^2 x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c^3 d \sqrt{d-c^2 d x^2}}","\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{c^4 d \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{c^4 d^2}+\frac{4 a b x \sqrt{c x-1} \sqrt{c x+1}}{c^3 d \sqrt{d-c^2 d x^2}}-\frac{2 b x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c^3 d \sqrt{d-c^2 d x^2}}+\frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{4 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^4 d \sqrt{d-c^2 d x^2}}+\frac{2 b^2 (1-c x) (c x+1)}{c^4 d \sqrt{d-c^2 d x^2}}+\frac{4 b^2 x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c^3 d \sqrt{d-c^2 d x^2}}",1,"(4*a*b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(c^3*d*Sqrt[d - c^2*d*x^2]) + (2*b^2*(1 - c*x)*(1 + c*x))/(c^4*d*Sqrt[d - c^2*d*x^2]) + (4*b^2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(c^3*d*Sqrt[d - c^2*d*x^2]) - (2*b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(c^3*d*Sqrt[d - c^2*d*x^2]) + (x^2*(a + b*ArcCosh[c*x])^2)/(c^2*d*Sqrt[d - c^2*d*x^2]) + (2*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(c^4*d*Sqrt[d - c^2*d*x^2]) + (4*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(c^4*d*Sqrt[d - c^2*d*x^2]) + (2*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -E^ArcCosh[c*x]])/(c^4*d*Sqrt[d - c^2*d*x^2]) - (2*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^ArcCosh[c*x]])/(c^4*d*Sqrt[d - c^2*d*x^2])","A",14,10,29,0.3448,1,"{5798, 5752, 5718, 5654, 74, 5766, 5694, 4182, 2279, 2391}"
207,1,257,0,0.7952873,"\int \frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^2*(a + b*ArcCosh[c*x])^2)/(d - c^2*d*x^2)^(3/2),x]","-\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{c^3 d \sqrt{d-c^2 d x^2}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{3 b c^3 d \sqrt{d-c^2 d x^2}}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{c^3 d \sqrt{d-c^2 d x^2}}-\frac{2 b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^3 d \sqrt{d-c^2 d x^2}}","-\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{c^3 d \sqrt{d-c^2 d x^2}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{3 b c^3 d \sqrt{d-c^2 d x^2}}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{c^3 d \sqrt{d-c^2 d x^2}}-\frac{2 b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^3 d \sqrt{d-c^2 d x^2}}",1,"(x*(a + b*ArcCosh[c*x])^2)/(c^2*d*Sqrt[d - c^2*d*x^2]) + (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(c^3*d*Sqrt[d - c^2*d*x^2]) - (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^3)/(3*b*c^3*d*Sqrt[d - c^2*d*x^2]) - (2*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 - E^(2*ArcCosh[c*x])])/(c^3*d*Sqrt[d - c^2*d*x^2]) - (b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^(2*ArcCosh[c*x])])/(c^3*d*Sqrt[d - c^2*d*x^2])","A",8,8,29,0.2759,1,"{5798, 5752, 5676, 5715, 3716, 2190, 2279, 2391}"
208,1,196,0,0.4453515,"\int \frac{x \left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x*(a + b*ArcCosh[c*x])^2)/(d - c^2*d*x^2)^(3/2),x]","\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{4 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}","\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{c^2 d \sqrt{d-c^2 d x^2}}+\frac{4 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}",1,"(a + b*ArcCosh[c*x])^2/(c^2*d*Sqrt[d - c^2*d*x^2]) + (4*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(c^2*d*Sqrt[d - c^2*d*x^2]) + (2*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -E^ArcCosh[c*x]])/(c^2*d*Sqrt[d - c^2*d*x^2]) - (2*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^ArcCosh[c*x]])/(c^2*d*Sqrt[d - c^2*d*x^2])","A",8,6,27,0.2222,1,"{5798, 5718, 5694, 4182, 2279, 2391}"
209,1,198,0,0.3511885,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/(d - c^2*d*x^2)^(3/2),x]","-\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{c d \sqrt{d-c^2 d x^2}}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{c d \sqrt{d-c^2 d x^2}}-\frac{2 b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c d \sqrt{d-c^2 d x^2}}","-\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{c d \sqrt{d-c^2 d x^2}}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{c d \sqrt{d-c^2 d x^2}}-\frac{2 b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{c d \sqrt{d-c^2 d x^2}}",1,"(x*(a + b*ArcCosh[c*x])^2)/(d*Sqrt[d - c^2*d*x^2]) + (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(c*d*Sqrt[d - c^2*d*x^2]) - (2*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 - E^(2*ArcCosh[c*x])])/(c*d*Sqrt[d - c^2*d*x^2]) - (b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^(2*ArcCosh[c*x])])/(c*d*Sqrt[d - c^2*d*x^2])","A",7,7,26,0.2692,1,"{5713, 5688, 5715, 3716, 2190, 2279, 2391}"
210,1,471,0,0.9635028,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{x \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/(x*(d - c^2*d*x^2)^(3/2)),x]","-\frac{2 i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 i b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{2 i b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}+\frac{4 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}","-\frac{2 i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 i b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{2 i b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}+\frac{4 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}",1,"(a + b*ArcCosh[c*x])^2/(d*Sqrt[d - c^2*d*x^2]) + (2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2*ArcTan[E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) + (4*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) + (2*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) - ((2*I)*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) + ((2*I)*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*PolyLog[2, I*E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) - (2*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) + ((2*I)*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[3, (-I)*E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) - ((2*I)*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[3, I*E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2])","A",16,11,29,0.3793,1,"{5798, 5756, 5761, 4180, 2531, 2282, 6589, 5694, 4182, 2279, 2391}"
211,1,341,0,0.9363625,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{x^2 \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/(x^2*(d - c^2*d*x^2)^(3/2)),x]","-\frac{b^2 c \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{b^2 c \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 c^2 x \left(a+b \cosh ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}+\frac{2 c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{d x \sqrt{d-c^2 d x^2}}-\frac{4 b c \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{4 b c \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}","-\frac{b^2 c \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{b^2 c \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 c^2 x \left(a+b \cosh ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}+\frac{2 c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{d x \sqrt{d-c^2 d x^2}}-\frac{4 b c \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{4 b c \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}",1,"-((a + b*ArcCosh[c*x])^2/(d*x*Sqrt[d - c^2*d*x^2])) + (2*c^2*x*(a + b*ArcCosh[c*x])^2)/(d*Sqrt[d - c^2*d*x^2]) + (2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(d*Sqrt[d - c^2*d*x^2]) - (4*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTanh[E^(2*ArcCosh[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - (4*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 - E^(2*ArcCosh[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - (b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -E^(2*ArcCosh[c*x])])/(d*Sqrt[d - c^2*d*x^2]) - (b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^(2*ArcCosh[c*x])])/(d*Sqrt[d - c^2*d*x^2])","A",15,11,29,0.3793,1,"{5798, 5748, 5688, 5715, 3716, 2190, 2279, 2391, 5721, 5461, 4182}"
212,1,650,0,1.4864934,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{x^3 \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/(x^3*(d - c^2*d*x^2)^(3/2)),x]","-\frac{3 i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}+\frac{3 i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{3 i b^2 c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{3 i b^2 c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{3 c^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{2 d \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{d x \sqrt{d-c^2 d x^2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 d x^2 \sqrt{d-c^2 d x^2}}+\frac{3 c^2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}+\frac{4 b c^2 \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{d \sqrt{d-c^2 d x^2}}","-\frac{3 i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}+\frac{3 i b c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}+\frac{2 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{2 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{3 i b^2 c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}-\frac{3 i b^2 c^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{3 c^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{2 d \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{d x \sqrt{d-c^2 d x^2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 d x^2 \sqrt{d-c^2 d x^2}}+\frac{3 c^2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{d \sqrt{d-c^2 d x^2}}+\frac{4 b c^2 \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{d \sqrt{d-c^2 d x^2}}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(d*x*Sqrt[d - c^2*d*x^2]) + (3*c^2*(a + b*ArcCosh[c*x])^2)/(2*d*Sqrt[d - c^2*d*x^2]) - (a + b*ArcCosh[c*x])^2/(2*d*x^2*Sqrt[d - c^2*d*x^2]) + (3*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2*ArcTan[E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) - (b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/(d*Sqrt[d - c^2*d*x^2]) + (4*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) + (2*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) - ((3*I)*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) + ((3*I)*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*PolyLog[2, I*E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) - (2*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) + ((3*I)*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[3, (-I)*E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2]) - ((3*I)*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[3, I*E^ArcCosh[c*x]])/(d*Sqrt[d - c^2*d*x^2])","A",26,15,29,0.5172,1,"{5798, 5748, 5756, 5761, 4180, 2531, 2282, 6589, 5694, 4182, 2279, 2391, 5746, 92, 205}"
213,1,496,0,1.4613619,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{x^4 \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/(x^4*(d - c^2*d*x^2)^(3/2)),x]","-\frac{5 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{3 d \sqrt{d-c^2 d x^2}}-\frac{b^2 c^3 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{8 c^4 x \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d \sqrt{d-c^2 d x^2}}+\frac{8 c^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d \sqrt{d-c^2 d x^2}}-\frac{4 c^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d x \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 d x^2 \sqrt{d-c^2 d x^2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{3 d x^3 \sqrt{d-c^2 d x^2}}-\frac{16 b c^3 \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 d \sqrt{d-c^2 d x^2}}-\frac{20 b c^3 \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 d \sqrt{d-c^2 d x^2}}+\frac{b^2 c^2 (1-c x) (c x+1)}{3 d x \sqrt{d-c^2 d x^2}}","-\frac{5 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{3 d \sqrt{d-c^2 d x^2}}-\frac{b^2 c^3 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{d \sqrt{d-c^2 d x^2}}+\frac{8 c^4 x \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d \sqrt{d-c^2 d x^2}}+\frac{8 c^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d \sqrt{d-c^2 d x^2}}-\frac{4 c^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d x \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 d x^2 \sqrt{d-c^2 d x^2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{3 d x^3 \sqrt{d-c^2 d x^2}}-\frac{16 b c^3 \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 d \sqrt{d-c^2 d x^2}}-\frac{20 b c^3 \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 d \sqrt{d-c^2 d x^2}}+\frac{b^2 c^2 (1-c x) (c x+1)}{3 d x \sqrt{d-c^2 d x^2}}",1,"(b^2*c^2*(1 - c*x)*(1 + c*x))/(3*d*x*Sqrt[d - c^2*d*x^2]) + (b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*d*x^2*Sqrt[d - c^2*d*x^2]) - (a + b*ArcCosh[c*x])^2/(3*d*x^3*Sqrt[d - c^2*d*x^2]) - (4*c^2*(a + b*ArcCosh[c*x])^2)/(3*d*x*Sqrt[d - c^2*d*x^2]) + (8*c^4*x*(a + b*ArcCosh[c*x])^2)/(3*d*Sqrt[d - c^2*d*x^2]) + (8*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(3*d*Sqrt[d - c^2*d*x^2]) - (20*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTanh[E^(2*ArcCosh[c*x])])/(3*d*Sqrt[d - c^2*d*x^2]) - (16*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 - E^(2*ArcCosh[c*x])])/(3*d*Sqrt[d - c^2*d*x^2]) - (5*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -E^(2*ArcCosh[c*x])])/(3*d*Sqrt[d - c^2*d*x^2]) - (b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^(2*ArcCosh[c*x])])/(d*Sqrt[d - c^2*d*x^2])","A",25,13,29,0.4483,1,"{5798, 5748, 5688, 5715, 3716, 2190, 2279, 2391, 5721, 5461, 4182, 5746, 95}"
214,1,594,0,1.4762252,"\int \frac{x^5 \left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^5*(a + b*ArcCosh[c*x])^2)/(d - c^2*d*x^2)^(5/2),x]","-\frac{11 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{3 c^6 d^2 \sqrt{d-c^2 d x^2}}+\frac{11 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{3 c^6 d^2 \sqrt{d-c^2 d x^2}}-\frac{16 a b x \sqrt{c x-1} \sqrt{c x+1}}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b x^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{4 x^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{11 b x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{8 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^6 d^2 \sqrt{d-c^2 d x^2}}-\frac{22 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^6 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 x^2}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{7 b^2 (1-c x) (c x+1)}{3 c^6 d^2 \sqrt{d-c^2 d x^2}}-\frac{16 b^2 x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}","-\frac{11 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{3 c^6 d^2 \sqrt{d-c^2 d x^2}}+\frac{11 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{3 c^6 d^2 \sqrt{d-c^2 d x^2}}-\frac{16 a b x \sqrt{c x-1} \sqrt{c x+1}}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{b x^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{4 x^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{11 b x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{8 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^6 d^3}-\frac{22 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^6 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b^2 x^2}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{7 b^2 (1-c x) (c x+1)}{3 c^6 d^2 \sqrt{d-c^2 d x^2}}-\frac{16 b^2 x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}",1,"-(b^2*x^2)/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) - (16*a*b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3*c^5*d^2*Sqrt[d - c^2*d*x^2]) - (7*b^2*(1 - c*x)*(1 + c*x))/(3*c^6*d^2*Sqrt[d - c^2*d*x^2]) - (16*b^2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(3*c^5*d^2*Sqrt[d - c^2*d*x^2]) + (11*b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*c^5*d^2*Sqrt[d - c^2*d*x^2]) + (b*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*c^3*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) - (4*x^2*(a + b*ArcCosh[c*x])^2)/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) + (x^4*(a + b*ArcCosh[c*x])^2)/(3*c^2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (8*(1 - c*x)*(1 + c*x)*(a + b*ArcCosh[c*x])^2)/(3*c^6*d^2*Sqrt[d - c^2*d*x^2]) - (22*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(3*c^6*d^2*Sqrt[d - c^2*d*x^2]) - (11*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -E^ArcCosh[c*x]])/(3*c^6*d^2*Sqrt[d - c^2*d*x^2]) + (11*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^ArcCosh[c*x]])/(3*c^6*d^2*Sqrt[d - c^2*d*x^2])","A",27,13,29,0.4483,1,"{5798, 5752, 5718, 5654, 74, 5766, 5694, 4182, 2279, 2391, 5750, 98, 21}"
215,1,497,0,1.3330718,"\int \frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^4*(a + b*ArcCosh[c*x])^2)/(d - c^2*d*x^2)^(5/2),x]","\frac{4 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{x \left(a+b \cosh ^{-1}(c x)\right)^2}{c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{3 b c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{4 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{8 b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 (1-c x)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}","\frac{4 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{x \left(a+b \cosh ^{-1}(c x)\right)^2}{c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{3 b c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{4 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{8 b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2 (1-c x)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{3 c^5 d^2 \sqrt{d-c^2 d x^2}}",1,"-b^2/(3*c^5*d^2*Sqrt[d - c^2*d*x^2]) + (b^2*(1 - c*x))/(3*c^5*d^2*Sqrt[d - c^2*d*x^2]) + (b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(3*c^5*d^2*Sqrt[d - c^2*d*x^2]) + (b*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*c^3*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) - (x*(a + b*ArcCosh[c*x])^2)/(c^4*d^2*Sqrt[d - c^2*d*x^2]) + (x^3*(a + b*ArcCosh[c*x])^2)/(3*c^2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(3*c^5*d^2*Sqrt[d - c^2*d*x^2]) + (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^3)/(3*b*c^5*d^2*Sqrt[d - c^2*d*x^2]) + (8*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 - E^(2*ArcCosh[c*x])])/(3*c^5*d^2*Sqrt[d - c^2*d*x^2]) + (4*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^(2*ArcCosh[c*x])])/(3*c^5*d^2*Sqrt[d - c^2*d*x^2])","A",19,13,29,0.4483,1,"{5798, 5752, 5676, 5715, 3716, 2190, 2279, 2391, 5750, 89, 12, 78, 52}"
216,1,351,0,0.9686662,"\int \frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^3*(a + b*ArcCosh[c*x])^2)/(d - c^2*d*x^2)^(5/2),x]","-\frac{5 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{5 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{b x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}-\frac{2 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{10 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}","-\frac{5 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{5 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{b x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{2 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}-\frac{10 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b^2}{3 c^4 d^2 \sqrt{d-c^2 d x^2}}",1,"-b^2/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) + (b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*c^3*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) - (2*(a + b*ArcCosh[c*x])^2)/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) + (x^2*(a + b*ArcCosh[c*x])^2)/(3*c^2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (10*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) - (5*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -E^ArcCosh[c*x]])/(3*c^4*d^2*Sqrt[d - c^2*d*x^2]) + (5*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^ArcCosh[c*x]])/(3*c^4*d^2*Sqrt[d - c^2*d*x^2])","A",17,9,29,0.3103,1,"{5798, 5752, 5718, 5694, 4182, 2279, 2391, 5750, 74}"
217,1,404,0,0.7308083,"\int \frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x^2*(a + b*ArcCosh[c*x])^2)/(d - c^2*d*x^2)^(5/2),x]","\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{2 b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 (1-c x)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}","\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{2 b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{b^2 (1-c x)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{3 c^3 d^2 \sqrt{d-c^2 d x^2}}",1,"-b^2/(3*c^3*d^2*Sqrt[d - c^2*d*x^2]) + (b^2*(1 - c*x))/(3*c^3*d^2*Sqrt[d - c^2*d*x^2]) + (b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(3*c^3*d^2*Sqrt[d - c^2*d*x^2]) + (b*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*c*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (x^3*(a + b*ArcCosh[c*x])^2)/(3*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(3*c^3*d^2*Sqrt[d - c^2*d*x^2]) + (2*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 - E^(2*ArcCosh[c*x])])/(3*c^3*d^2*Sqrt[d - c^2*d*x^2]) + (b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^(2*ArcCosh[c*x])])/(3*c^3*d^2*Sqrt[d - c^2*d*x^2])","A",12,12,29,0.4138,1,"{5798, 5724, 5750, 89, 12, 78, 52, 5715, 3716, 2190, 2279, 2391}"
218,1,313,0,0.4731912,"\int \frac{x \left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(x*(a + b*ArcCosh[c*x])^2)/(d - c^2*d*x^2)^(5/2),x]","\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}+\frac{b x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{2 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}","\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}+\frac{b x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{2 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{3 c^2 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b^2}{3 c^2 d^2 \sqrt{d-c^2 d x^2}}",1,"-b^2/(3*c^2*d^2*Sqrt[d - c^2*d*x^2]) + (b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*c*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (a + b*ArcCosh[c*x])^2/(3*c^2*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + (2*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(3*c^2*d^2*Sqrt[d - c^2*d*x^2]) + (b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -E^ArcCosh[c*x]])/(3*c^2*d^2*Sqrt[d - c^2*d*x^2]) - (b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^ArcCosh[c*x]])/(3*c^2*d^2*Sqrt[d - c^2*d*x^2])","A",10,8,27,0.2963,1,"{5798, 5718, 5689, 74, 5694, 4182, 2279, 2391}"
219,1,346,0,0.5604097,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/(d - c^2*d*x^2)^(5/2),x]","-\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{2 x \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c d^2 \sqrt{d-c^2 d x^2}}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}-\frac{4 b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 x}{3 d^2 \sqrt{d-c^2 d x^2}}","-\frac{2 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{2 x \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 c d^2 \sqrt{d-c^2 d x^2}}-\frac{4 b \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 c d^2 \sqrt{d-c^2 d x^2}}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b^2 x}{3 d^2 \sqrt{d-c^2 d x^2}}",1,"-(b^2*x)/(3*d^2*Sqrt[d - c^2*d*x^2]) + (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*c*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (2*x*(a + b*ArcCosh[c*x])^2)/(3*d^2*Sqrt[d - c^2*d*x^2]) + (x*(a + b*ArcCosh[c*x])^2)/(3*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + (2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(3*c*d^2*Sqrt[d - c^2*d*x^2]) - (4*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 - E^(2*ArcCosh[c*x])])/(3*c*d^2*Sqrt[d - c^2*d*x^2]) - (2*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^(2*ArcCosh[c*x])])/(3*c*d^2*Sqrt[d - c^2*d*x^2])","A",10,10,26,0.3846,1,"{5713, 5691, 5688, 5715, 3716, 2190, 2279, 2391, 5716, 39}"
220,1,612,0,1.3300371,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{x \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/(x*(d - c^2*d*x^2)^(5/2)),x]","-\frac{2 i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{2 i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{7 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{7 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{2 i b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{2 i b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{b c x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{3 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{d^2 \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{d^2 \sqrt{d-c^2 d x^2}}+\frac{14 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2}{3 d^2 \sqrt{d-c^2 d x^2}}","-\frac{2 i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{2 i b \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{7 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{7 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{2 i b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{2 i b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{b c x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{d^2 \sqrt{d-c^2 d x^2}}+\frac{2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{d^2 \sqrt{d-c^2 d x^2}}+\frac{14 b \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{b^2}{3 d^2 \sqrt{d-c^2 d x^2}}",1,"-b^2/(3*d^2*Sqrt[d - c^2*d*x^2]) + (b*c*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (a + b*ArcCosh[c*x])^2/(d^2*Sqrt[d - c^2*d*x^2]) + (a + b*ArcCosh[c*x])^2/(3*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + (2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2*ArcTan[E^ArcCosh[c*x]])/(d^2*Sqrt[d - c^2*d*x^2]) + (14*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(3*d^2*Sqrt[d - c^2*d*x^2]) + (7*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -E^ArcCosh[c*x]])/(3*d^2*Sqrt[d - c^2*d*x^2]) - ((2*I)*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(d^2*Sqrt[d - c^2*d*x^2]) + ((2*I)*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*PolyLog[2, I*E^ArcCosh[c*x]])/(d^2*Sqrt[d - c^2*d*x^2]) - (7*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^ArcCosh[c*x]])/(3*d^2*Sqrt[d - c^2*d*x^2]) + ((2*I)*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[3, (-I)*E^ArcCosh[c*x]])/(d^2*Sqrt[d - c^2*d*x^2]) - ((2*I)*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[3, I*E^ArcCosh[c*x]])/(d^2*Sqrt[d - c^2*d*x^2])","A",25,13,29,0.4483,1,"{5798, 5756, 5761, 4180, 2531, 2282, 6589, 5694, 4182, 2279, 2391, 5689, 74}"
221,1,506,0,1.1914266,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{x^2 \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/(x^2*(d - c^2*d*x^2)^(5/2)),x]","-\frac{b^2 c \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{5 b^2 c \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{8 c^2 x \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{8 c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{4 c^2 x \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{d^2 x (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}-\frac{16 b c \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{4 b c \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 c^2 x}{3 d^2 \sqrt{d-c^2 d x^2}}","-\frac{b^2 c \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{d^2 \sqrt{d-c^2 d x^2}}-\frac{5 b^2 c \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{8 c^2 x \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{8 c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{16 b c \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{4 b c \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2 \sqrt{d-c^2 d x^2}}+\frac{4 c^2 x \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{d x \left(d-c^2 d x^2\right)^{3/2}}-\frac{b^2 c^2 x}{3 d^2 \sqrt{d-c^2 d x^2}}",1,"-(b^2*c^2*x)/(3*d^2*Sqrt[d - c^2*d*x^2]) + (b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (8*c^2*x*(a + b*ArcCosh[c*x])^2)/(3*d^2*Sqrt[d - c^2*d*x^2]) - (a + b*ArcCosh[c*x])^2/(d^2*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + (4*c^2*x*(a + b*ArcCosh[c*x])^2)/(3*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + (8*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(3*d^2*Sqrt[d - c^2*d*x^2]) - (4*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTanh[E^(2*ArcCosh[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - (16*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 - E^(2*ArcCosh[c*x])])/(3*d^2*Sqrt[d - c^2*d*x^2]) - (b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -E^(2*ArcCosh[c*x])])/(d^2*Sqrt[d - c^2*d*x^2]) - (5*b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^(2*ArcCosh[c*x])])/(3*d^2*Sqrt[d - c^2*d*x^2])","A",20,15,29,0.5172,1,"{5798, 5748, 5691, 5688, 5715, 3716, 2190, 2279, 2391, 5716, 39, 5754, 5721, 5461, 4182}"
222,1,826,0,1.9381166,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{x^3 \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/(x^3*(d - c^2*d*x^2)^(5/2)),x]","-\frac{2 b x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) c^3}{3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{5 \left(a+b \cosh ^{-1}(c x)\right)^2 c^2}{6 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{5 \left(a+b \cosh ^{-1}(c x)\right)^2 c^2}{2 d^2 \sqrt{d-c^2 d x^2}}+\frac{5 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) c^2}{d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right) c^2}{d^2 \sqrt{d-c^2 d x^2}}+\frac{26 b \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) c^2}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{13 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right) c^2}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{5 i b \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) c^2}{d^2 \sqrt{d-c^2 d x^2}}+\frac{5 i b \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) c^2}{d^2 \sqrt{d-c^2 d x^2}}-\frac{13 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right) c^2}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{5 i b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right) c^2}{d^2 \sqrt{d-c^2 d x^2}}-\frac{5 i b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right) c^2}{d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 c^2}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) c}{d^2 x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 d^2 x^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}","-\frac{2 b x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) c^3}{3 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}+\frac{5 \left(a+b \cosh ^{-1}(c x)\right)^2 c^2}{2 d^2 \sqrt{d-c^2 d x^2}}+\frac{5 \left(a+b \cosh ^{-1}(c x)\right)^2 c^2}{6 d \left(d-c^2 d x^2\right)^{3/2}}+\frac{5 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \tan ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) c^2}{d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 \sqrt{c x-1} \sqrt{c x+1} \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right) c^2}{d^2 \sqrt{d-c^2 d x^2}}+\frac{26 b \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \tanh ^{-1}\left(e^{\cosh ^{-1}(c x)}\right) c^2}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{13 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{\cosh ^{-1}(c x)}\right) c^2}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{5 i b \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(c x)}\right) c^2}{d^2 \sqrt{d-c^2 d x^2}}+\frac{5 i b \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,i e^{\cosh ^{-1}(c x)}\right) c^2}{d^2 \sqrt{d-c^2 d x^2}}-\frac{13 b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{\cosh ^{-1}(c x)}\right) c^2}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{5 i b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(c x)}\right) c^2}{d^2 \sqrt{d-c^2 d x^2}}-\frac{5 i b^2 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(c x)}\right) c^2}{d^2 \sqrt{d-c^2 d x^2}}-\frac{b^2 c^2}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) c}{d^2 x \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 d x^2 \left(d-c^2 d x^2\right)^{3/2}}",1,"-(b^2*c^2)/(3*d^2*Sqrt[d - c^2*d*x^2]) + (b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(d^2*x*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) - (2*b*c^3*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*d^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (5*c^2*(a + b*ArcCosh[c*x])^2)/(2*d^2*Sqrt[d - c^2*d*x^2]) + (5*c^2*(a + b*ArcCosh[c*x])^2)/(6*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (a + b*ArcCosh[c*x])^2/(2*d^2*x^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + (5*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2*ArcTan[E^ArcCosh[c*x]])/(d^2*Sqrt[d - c^2*d*x^2]) - (b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/(d^2*Sqrt[d - c^2*d*x^2]) + (26*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTanh[E^ArcCosh[c*x]])/(3*d^2*Sqrt[d - c^2*d*x^2]) + (13*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -E^ArcCosh[c*x]])/(3*d^2*Sqrt[d - c^2*d*x^2]) - ((5*I)*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*PolyLog[2, (-I)*E^ArcCosh[c*x]])/(d^2*Sqrt[d - c^2*d*x^2]) + ((5*I)*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*PolyLog[2, I*E^ArcCosh[c*x]])/(d^2*Sqrt[d - c^2*d*x^2]) - (13*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^ArcCosh[c*x]])/(3*d^2*Sqrt[d - c^2*d*x^2]) + ((5*I)*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[3, (-I)*E^ArcCosh[c*x]])/(d^2*Sqrt[d - c^2*d*x^2]) - ((5*I)*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[3, I*E^ArcCosh[c*x]])/(d^2*Sqrt[d - c^2*d*x^2])","A",39,19,29,0.6552,1,"{5798, 5748, 5756, 5761, 4180, 2531, 2282, 6589, 5694, 4182, 2279, 2391, 5689, 74, 5746, 104, 21, 92, 205}"
223,1,607,0,1.8213884,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{x^4 \left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/(x^4*(d - c^2*d*x^2)^(5/2)),x]","-\frac{8 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{8 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{16 c^4 x \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{8 c^4 x \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{16 c^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{2 c^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{d^2 x (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 x^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{3 d^2 x^3 (1-c x) (c x+1) \sqrt{d-c^2 d x^2}}-\frac{32 b c^3 \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{32 b c^3 \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{2 b^2 c^4 x}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 c^2}{3 d^2 x \sqrt{d-c^2 d x^2}}","-\frac{8 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{8 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(c x)}\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{16 c^4 x \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{16 c^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 x^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}-\frac{32 b c^3 \sqrt{c x-1} \sqrt{c x+1} \log \left(1-e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}-\frac{32 b c^3 \sqrt{c x-1} \sqrt{c x+1} \tanh ^{-1}\left(e^{2 \cosh ^{-1}(c x)}\right) \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{8 c^4 x \left(a+b \cosh ^{-1}(c x)\right)^2}{3 d \left(d-c^2 d x^2\right)^{3/2}}-\frac{2 c^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{d x \left(d-c^2 d x^2\right)^{3/2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{3 d x^3 \left(d-c^2 d x^2\right)^{3/2}}-\frac{2 b^2 c^4 x}{3 d^2 \sqrt{d-c^2 d x^2}}+\frac{b^2 c^2}{3 d^2 x \sqrt{d-c^2 d x^2}}",1,"(b^2*c^2)/(3*d^2*x*Sqrt[d - c^2*d*x^2]) - (2*b^2*c^4*x)/(3*d^2*Sqrt[d - c^2*d*x^2]) + (b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*d^2*x^2*(1 - c^2*x^2)*Sqrt[d - c^2*d*x^2]) + (16*c^4*x*(a + b*ArcCosh[c*x])^2)/(3*d^2*Sqrt[d - c^2*d*x^2]) - (a + b*ArcCosh[c*x])^2/(3*d^2*x^3*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) - (2*c^2*(a + b*ArcCosh[c*x])^2)/(d^2*x*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + (8*c^4*x*(a + b*ArcCosh[c*x])^2)/(3*d^2*(1 - c*x)*(1 + c*x)*Sqrt[d - c^2*d*x^2]) + (16*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2)/(3*d^2*Sqrt[d - c^2*d*x^2]) - (32*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*ArcTanh[E^(2*ArcCosh[c*x])])/(3*d^2*Sqrt[d - c^2*d*x^2]) - (32*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])*Log[1 - E^(2*ArcCosh[c*x])])/(3*d^2*Sqrt[d - c^2*d*x^2]) - (8*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, -E^(2*ArcCosh[c*x])])/(3*d^2*Sqrt[d - c^2*d*x^2]) - (8*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*PolyLog[2, E^(2*ArcCosh[c*x])])/(3*d^2*Sqrt[d - c^2*d*x^2])","A",34,18,29,0.6207,1,"{5798, 5748, 5691, 5688, 5715, 3716, 2190, 2279, 2391, 5716, 39, 5754, 5721, 5461, 4182, 5746, 103, 12}"
224,1,459,0,0.6715823,"\int \frac{\cosh ^{-1}(a x)^2}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[ArcCosh[a*x]^2/(c - a^2*c*x^2)^(7/2),x]","-\frac{8 \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(a x)}\right)}{15 a c^3 \sqrt{c-a^2 c x^2}}-\frac{x}{3 c^3 \sqrt{c-a^2 c x^2}}-\frac{x}{30 c^3 (1-a x) (a x+1) \sqrt{c-a^2 c x^2}}+\frac{8 x \cosh ^{-1}(a x)^2}{15 c^3 \sqrt{c-a^2 c x^2}}+\frac{8 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{4 x \cosh ^{-1}(a x)^2}{15 c^3 (1-a x) (a x+1) \sqrt{c-a^2 c x^2}}+\frac{x \cosh ^{-1}(a x)^2}{5 c^3 (1-a x)^2 (a x+1)^2 \sqrt{c-a^2 c x^2}}+\frac{4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{15 a c^3 \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{10 a c^3 \left(1-a^2 x^2\right)^2 \sqrt{c-a^2 c x^2}}-\frac{16 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \log \left(1-e^{2 \cosh ^{-1}(a x)}\right)}{15 a c^3 \sqrt{c-a^2 c x^2}}","-\frac{8 \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(a x)}\right)}{15 a c^3 \sqrt{c-a^2 c x^2}}-\frac{x}{3 c^3 \sqrt{c-a^2 c x^2}}-\frac{x}{30 c^3 (1-a x) (a x+1) \sqrt{c-a^2 c x^2}}+\frac{8 x \cosh ^{-1}(a x)^2}{15 c^3 \sqrt{c-a^2 c x^2}}+\frac{8 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{4 x \cosh ^{-1}(a x)^2}{15 c^2 \left(c-a^2 c x^2\right)^{3/2}}+\frac{4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{15 a c^3 \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{10 a c^3 \left(1-a^2 x^2\right)^2 \sqrt{c-a^2 c x^2}}-\frac{16 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \log \left(1-e^{2 \cosh ^{-1}(a x)}\right)}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{x \cosh ^{-1}(a x)^2}{5 c \left(c-a^2 c x^2\right)^{5/2}}",1,"-x/(3*c^3*Sqrt[c - a^2*c*x^2]) - x/(30*c^3*(1 - a*x)*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(10*a*c^3*(1 - a^2*x^2)^2*Sqrt[c - a^2*c*x^2]) + (4*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(15*a*c^3*(1 - a^2*x^2)*Sqrt[c - a^2*c*x^2]) + (8*x*ArcCosh[a*x]^2)/(15*c^3*Sqrt[c - a^2*c*x^2]) + (x*ArcCosh[a*x]^2)/(5*c^3*(1 - a*x)^2*(1 + a*x)^2*Sqrt[c - a^2*c*x^2]) + (4*x*ArcCosh[a*x]^2)/(15*c^3*(1 - a*x)*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (8*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(15*a*c^3*Sqrt[c - a^2*c*x^2]) - (16*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*Log[1 - E^(2*ArcCosh[a*x])])/(15*a*c^3*Sqrt[c - a^2*c*x^2]) - (8*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[2, E^(2*ArcCosh[a*x])])/(15*a*c^3*Sqrt[c - a^2*c*x^2])","A",14,11,22,0.5000,1,"{5713, 5691, 5688, 5715, 3716, 2190, 2279, 2391, 5716, 39, 40}"
225,1,329,0,0.7928079,"\int \frac{x^4 \cosh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^4*ArcCosh[a*x]^2)/Sqrt[1 - a^2*x^2],x]","-\frac{x^3 (1-a x) (a x+1)}{32 a^2 \sqrt{1-a^2 x^2}}-\frac{15 x (1-a x) (a x+1)}{64 a^4 \sqrt{1-a^2 x^2}}-\frac{x^4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{8 a \sqrt{1-a^2 x^2}}-\frac{x^3 (1-a x) (a x+1) \cosh ^{-1}(a x)^2}{4 a^2 \sqrt{1-a^2 x^2}}-\frac{3 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{8 a^3 \sqrt{1-a^2 x^2}}-\frac{3 x (1-a x) (a x+1) \cosh ^{-1}(a x)^2}{8 a^4 \sqrt{1-a^2 x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{8 a^5 \sqrt{1-a^2 x^2}}+\frac{15 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{64 a^5 \sqrt{1-a^2 x^2}}","-\frac{x^3 \sqrt{1-a x} \sqrt{a x+1}}{32 a^2}-\frac{x^3 \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^2}{4 a^2}-\frac{3 x^2 \sqrt{a x-1} \cosh ^{-1}(a x)}{8 a^3 \sqrt{1-a x}}-\frac{3 x \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^2}{8 a^4}-\frac{15 x \sqrt{1-a x} \sqrt{a x+1}}{64 a^4}+\frac{\sqrt{a x-1} \cosh ^{-1}(a x)^3}{8 a^5 \sqrt{1-a x}}+\frac{15 \sqrt{a x-1} \cosh ^{-1}(a x)}{64 a^5 \sqrt{1-a x}}-\frac{x^4 \sqrt{a x-1} \cosh ^{-1}(a x)}{8 a \sqrt{1-a x}}",1,"(-15*x*(1 - a*x)*(1 + a*x))/(64*a^4*Sqrt[1 - a^2*x^2]) - (x^3*(1 - a*x)*(1 + a*x))/(32*a^2*Sqrt[1 - a^2*x^2]) + (15*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(64*a^5*Sqrt[1 - a^2*x^2]) - (3*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(8*a^3*Sqrt[1 - a^2*x^2]) - (x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(8*a*Sqrt[1 - a^2*x^2]) - (3*x*(1 - a*x)*(1 + a*x)*ArcCosh[a*x]^2)/(8*a^4*Sqrt[1 - a^2*x^2]) - (x^3*(1 - a*x)*(1 + a*x)*ArcCosh[a*x]^2)/(4*a^2*Sqrt[1 - a^2*x^2]) + (Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(8*a^5*Sqrt[1 - a^2*x^2])","A",12,8,24,0.3333,1,"{5798, 5759, 5676, 5662, 90, 52, 100, 12}"
226,1,237,0,0.5918626,"\int \frac{x^3 \cosh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^3*ArcCosh[a*x]^2)/Sqrt[1 - a^2*x^2],x]","-\frac{2 x^2 (1-a x) (a x+1)}{27 a^2 \sqrt{1-a^2 x^2}}-\frac{40 (1-a x) (a x+1)}{27 a^4 \sqrt{1-a^2 x^2}}-\frac{2 x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{9 a \sqrt{1-a^2 x^2}}-\frac{x^2 (1-a x) (a x+1) \cosh ^{-1}(a x)^2}{3 a^2 \sqrt{1-a^2 x^2}}-\frac{4 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{3 a^3 \sqrt{1-a^2 x^2}}-\frac{2 (1-a x) (a x+1) \cosh ^{-1}(a x)^2}{3 a^4 \sqrt{1-a^2 x^2}}","-\frac{2 x^2 \sqrt{1-a x} \sqrt{a x+1}}{27 a^2}-\frac{x^2 \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^2}{3 a^2}-\frac{2 \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^2}{3 a^4}-\frac{40 \sqrt{1-a x} \sqrt{a x+1}}{27 a^4}-\frac{4 x \sqrt{a x-1} \cosh ^{-1}(a x)}{3 a^3 \sqrt{1-a x}}-\frac{2 x^3 \sqrt{a x-1} \cosh ^{-1}(a x)}{9 a \sqrt{1-a x}}",1,"(-40*(1 - a*x)*(1 + a*x))/(27*a^4*Sqrt[1 - a^2*x^2]) - (2*x^2*(1 - a*x)*(1 + a*x))/(27*a^2*Sqrt[1 - a^2*x^2]) - (4*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(3*a^3*Sqrt[1 - a^2*x^2]) - (2*x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(9*a*Sqrt[1 - a^2*x^2]) - (2*(1 - a*x)*(1 + a*x)*ArcCosh[a*x]^2)/(3*a^4*Sqrt[1 - a^2*x^2]) - (x^2*(1 - a*x)*(1 + a*x)*ArcCosh[a*x]^2)/(3*a^2*Sqrt[1 - a^2*x^2])","A",9,8,24,0.3333,1,"{5798, 5759, 5718, 5654, 74, 5662, 100, 12}"
227,1,207,0,0.5103419,"\int \frac{x^2 \cosh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^2*ArcCosh[a*x]^2)/Sqrt[1 - a^2*x^2],x]","-\frac{x (1-a x) (a x+1)}{4 a^2 \sqrt{1-a^2 x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{6 a^3 \sqrt{1-a^2 x^2}}-\frac{x (1-a x) (a x+1) \cosh ^{-1}(a x)^2}{2 a^2 \sqrt{1-a^2 x^2}}-\frac{x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{2 a \sqrt{1-a^2 x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{4 a^3 \sqrt{1-a^2 x^2}}","-\frac{x \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^2}{2 a^2}-\frac{x \sqrt{1-a x} \sqrt{a x+1}}{4 a^2}+\frac{\sqrt{a x-1} \cosh ^{-1}(a x)^3}{6 a^3 \sqrt{1-a x}}+\frac{\sqrt{a x-1} \cosh ^{-1}(a x)}{4 a^3 \sqrt{1-a x}}-\frac{x^2 \sqrt{a x-1} \cosh ^{-1}(a x)}{2 a \sqrt{1-a x}}",1,"-(x*(1 - a*x)*(1 + a*x))/(4*a^2*Sqrt[1 - a^2*x^2]) + (Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(4*a^3*Sqrt[1 - a^2*x^2]) - (x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(2*a*Sqrt[1 - a^2*x^2]) - (x*(1 - a*x)*(1 + a*x)*ArcCosh[a*x]^2)/(2*a^2*Sqrt[1 - a^2*x^2]) + (Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(6*a^3*Sqrt[1 - a^2*x^2])","A",6,6,24,0.2500,1,"{5798, 5759, 5676, 5662, 90, 52}"
228,1,109,0,0.2717087,"\int \frac{x \cosh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx","Int[(x*ArcCosh[a*x]^2)/Sqrt[1 - a^2*x^2],x]","-\frac{2 (1-a x) (a x+1)}{a^2 \sqrt{1-a^2 x^2}}-\frac{(1-a x) (a x+1) \cosh ^{-1}(a x)^2}{a^2 \sqrt{1-a^2 x^2}}-\frac{2 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{a \sqrt{1-a^2 x^2}}","-\frac{\sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^2}{a^2}-\frac{2 \sqrt{1-a x} \sqrt{a x+1}}{a^2}-\frac{2 x \sqrt{a x-1} \cosh ^{-1}(a x)}{a \sqrt{1-a x}}",1,"(-2*(1 - a*x)*(1 + a*x))/(a^2*Sqrt[1 - a^2*x^2]) - (2*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(a*Sqrt[1 - a^2*x^2]) - ((1 - a*x)*(1 + a*x)*ArcCosh[a*x]^2)/(a^2*Sqrt[1 - a^2*x^2])","A",4,4,22,0.1818,1,"{5798, 5718, 5654, 74}"
229,1,45,0,0.1499316,"\int \frac{\cosh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}} \, dx","Int[ArcCosh[a*x]^2/Sqrt[1 - a^2*x^2],x]","\frac{\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{3 a \sqrt{1-a^2 x^2}}","\frac{\sqrt{a x-1} \cosh ^{-1}(a x)^3}{3 a \sqrt{1-a x}}",1,"(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(3*a*Sqrt[1 - a^2*x^2])","A",2,2,21,0.09524,1,"{5713, 5676}"
230,1,248,0,0.4203953,"\int \frac{\cosh ^{-1}(a x)^2}{x \sqrt{1-a^2 x^2}} \, dx","Int[ArcCosh[a*x]^2/(x*Sqrt[1 - a^2*x^2]),x]","-\frac{2 i \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}+\frac{2 i \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}+\frac{2 i \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}-\frac{2 i \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}+\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}","-\frac{2 i \sqrt{a x-1} \cosh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{2 i \sqrt{a x-1} \cosh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{2 i \sqrt{a x-1} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}-\frac{2 i \sqrt{a x-1} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{2 \sqrt{a x-1} \cosh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}",1,"(2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2*ArcTan[E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] - ((2*I)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*PolyLog[2, (-I)*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] + ((2*I)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*PolyLog[2, I*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] + ((2*I)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[3, (-I)*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] - ((2*I)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[3, I*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2]","A",9,6,24,0.2500,1,"{5798, 5761, 4180, 2531, 2282, 6589}"
231,1,174,0,0.4444927,"\int \frac{\cosh ^{-1}(a x)^2}{x^2 \sqrt{1-a^2 x^2}} \, dx","Int[ArcCosh[a*x]^2/(x^2*Sqrt[1 - a^2*x^2]),x]","-\frac{a \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}-\frac{(1-a x) (a x+1) \cosh ^{-1}(a x)^2}{x \sqrt{1-a^2 x^2}}+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{\sqrt{1-a^2 x^2}}-\frac{2 a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)}{\sqrt{1-a^2 x^2}}","-\frac{a \sqrt{a x-1} \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}-\frac{\sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^2}{x}+\frac{a \sqrt{a x-1} \cosh ^{-1}(a x)^2}{\sqrt{1-a x}}-\frac{2 a \sqrt{a x-1} \cosh ^{-1}(a x) \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)}{\sqrt{1-a x}}",1,"(a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/Sqrt[1 - a^2*x^2] - ((1 - a*x)*(1 + a*x)*ArcCosh[a*x]^2)/(x*Sqrt[1 - a^2*x^2]) - (2*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*Log[1 + E^(2*ArcCosh[a*x])])/Sqrt[1 - a^2*x^2] - (a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[2, -E^(2*ArcCosh[a*x])])/Sqrt[1 - a^2*x^2]","A",7,7,24,0.2917,1,"{5798, 5724, 5660, 3718, 2190, 2279, 2391}"
232,1,398,0,0.7228174,"\int \frac{\cosh ^{-1}(a x)^2}{x^3 \sqrt{1-a^2 x^2}} \, dx","Int[ArcCosh[a*x]^2/(x^3*Sqrt[1 - a^2*x^2]),x]","-\frac{i a^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}+\frac{i a^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}+\frac{i a^2 \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}-\frac{i a^2 \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}-\frac{a^2 \sqrt{a x-1} \sqrt{a x+1} \tan ^{-1}\left(\sqrt{a x-1} \sqrt{a x+1}\right)}{\sqrt{1-a^2 x^2}}+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{x \sqrt{1-a^2 x^2}}-\frac{(1-a x) (a x+1) \cosh ^{-1}(a x)^2}{2 x^2 \sqrt{1-a^2 x^2}}+\frac{a^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}","-\frac{i a^2 \sqrt{a x-1} \cosh ^{-1}(a x) \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{i a^2 \sqrt{a x-1} \cosh ^{-1}(a x) \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{i a^2 \sqrt{a x-1} \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}-\frac{i a^2 \sqrt{a x-1} \text{PolyLog}\left(3,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}-\frac{\sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^2}{2 x^2}-\frac{a^2 \sqrt{a x-1} \tan ^{-1}\left(\sqrt{a x-1} \sqrt{a x+1}\right)}{\sqrt{1-a x}}+\frac{a^2 \sqrt{a x-1} \cosh ^{-1}(a x)^2 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{a \sqrt{a x-1} \cosh ^{-1}(a x)}{x \sqrt{1-a x}}",1,"(a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(x*Sqrt[1 - a^2*x^2]) - ((1 - a*x)*(1 + a*x)*ArcCosh[a*x]^2)/(2*x^2*Sqrt[1 - a^2*x^2]) + (a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2*ArcTan[E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] - (a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcTan[Sqrt[-1 + a*x]*Sqrt[1 + a*x]])/Sqrt[1 - a^2*x^2] - (I*a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*PolyLog[2, (-I)*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] + (I*a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*PolyLog[2, I*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] + (I*a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[3, (-I)*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] - (I*a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[3, I*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2]","A",13,10,24,0.4167,1,"{5798, 5748, 5761, 4180, 2531, 2282, 6589, 5662, 92, 205}"
233,0,0,0,0.5448336,"\int (f x)^m \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[(f*x)^m*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2,x]","\int (f x)^m \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","\frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2 (f x)^{m+1}}{f (m+6)}+\frac{5 d \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2 (f x)^{m+1}}{f (m+4) (m+6)}+\frac{15 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 (f x)^{m+1}}{f (m+6) \left(m^2+6 m+8\right)}-\frac{2 b c d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) (f x)^{m+2}}{f^2 (m+2) (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{10 b c d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) (f x)^{m+2}}{f^2 (m+2) (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{30 b c d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) (f x)^{m+2}}{f^2 (m+2)^2 (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}-\frac{10 b^2 c^2 d^2 (3 m+10) \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};c^2 x^2\right) (f x)^{m+3}}{f^3 (m+2) (m+3) (m+4)^3 (m+6) (1-c x) (c x+1)}-\frac{2 b^2 c^2 d^2 \left(15 m^2+130 m+264\right) \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};c^2 x^2\right) (f x)^{m+3}}{f^3 (m+2) (m+3) (m+4)^2 (m+6)^3 (1-c x) (c x+1)}-\frac{30 b^2 c^2 d^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};c^2 x^2\right) (f x)^{m+3}}{f^3 (m+2)^2 (m+3) (m+4) (m+6) (1-c x) (c x+1)}-\frac{2 b^2 c^2 d^2 \left(m^2+15 m+52\right) \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} (f x)^{m+3}}{f^3 (m+4)^2 (m+6)^3 (1-c x) (c x+1)}-\frac{10 b^2 c^2 d^2 \sqrt{d-c^2 d x^2} (f x)^{m+3}}{f^3 (m+4)^3 (m+6)}+\frac{4 b c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) (f x)^{m+4}}{f^4 (m+4) (m+6) \sqrt{c x-1} \sqrt{c x+1}}+\frac{10 b c^3 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) (f x)^{m+4}}{f^4 (m+4)^2 (m+6) \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b^2 c^4 d^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} (f x)^{m+5}}{f^5 (m+6)^3 (1-c x) (c x+1)}-\frac{2 b c^5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) (f x)^{m+6}}{f^6 (m+6)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{15 d^3 \text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}},x\right)}{(m+6) \left(m^2+6 m+8\right)}",0,"(d^2*Sqrt[d - c^2*d*x^2]*Defer[Int][(f*x)^m*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2)*(a + b*ArcCosh[c*x])^2, x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
234,0,0,0,0.5231171,"\int (f x)^m \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[(f*x)^m*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2,x]","\int (f x)^m \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","\frac{3 d^2 \text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}},x\right)}{m^2+6 m+8}-\frac{2 b c d \sqrt{d-c^2 d x^2} (f x)^{m+2} \left(a+b \cosh ^{-1}(c x)\right)}{f^2 (m+2) (m+4) \sqrt{c x-1} \sqrt{c x+1}}-\frac{6 b c d \sqrt{d-c^2 d x^2} (f x)^{m+2} \left(a+b \cosh ^{-1}(c x)\right)}{f^2 (m+2)^2 (m+4) \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c^3 d \sqrt{d-c^2 d x^2} (f x)^{m+4} \left(a+b \cosh ^{-1}(c x)\right)}{f^4 (m+4)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 d \sqrt{d-c^2 d x^2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{f \left(m^2+6 m+8\right)}+\frac{\left(d-c^2 d x^2\right)^{3/2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{f (m+4)}-\frac{2 b^2 c^2 d (3 m+10) \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} (f x)^{m+3} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};c^2 x^2\right)}{f^3 (m+2) (m+3) (m+4)^3 (1-c x) (c x+1)}-\frac{6 b^2 c^2 d \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} (f x)^{m+3} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};c^2 x^2\right)}{f^3 (m+2)^2 (m+3) (m+4) (1-c x) (c x+1)}-\frac{2 b^2 c^2 d \sqrt{d-c^2 d x^2} (f x)^{m+3}}{f^3 (m+4)^3}",0,"-((d*Sqrt[d - c^2*d*x^2]*Defer[Int][(f*x)^m*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)*(a + b*ArcCosh[c*x])^2, x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]))","A",0,0,0,0,-1,"{}"
235,0,0,0,0.4481438,"\int (f x)^m \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[(f*x)^m*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^2,x]","\int (f x)^m \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","\frac{d \text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}},x\right)}{m+2}-\frac{2 b c \sqrt{d-c^2 d x^2} (f x)^{m+2} \left(a+b \cosh ^{-1}(c x)\right)}{f^2 (m+2)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{d-c^2 d x^2} (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{f (m+2)}-\frac{2 b^2 c^2 \sqrt{1-c^2 x^2} \sqrt{d-c^2 d x^2} (f x)^{m+3} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};c^2 x^2\right)}{f^3 (m+2)^2 (m+3) (1-c x) (c x+1)}",0,"(Sqrt[d - c^2*d*x^2]*Defer[Int][(f*x)^m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^2, x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
236,0,0,0,0.4743112,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x])^2)/Sqrt[d - c^2*d*x^2],x]","\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d-c^2 d x^2}},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][((f*x)^m*(a + b*ArcCosh[c*x])^2)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/Sqrt[d - c^2*d*x^2]","A",0,0,0,0,-1,"{}"
237,0,0,0,0.5612444,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x])^2)/(d - c^2*d*x^2)^(3/2),x]","\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{3/2}},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][((f*x)^m*(a + b*ArcCosh[c*x])^2)/((-1 + c*x)^(3/2)*(1 + c*x)^(3/2)), x])/(d*Sqrt[d - c^2*d*x^2]))","A",0,0,0,0,-1,"{}"
238,0,0,0,0.5566314,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x])^2)/(d - c^2*d*x^2)^(5/2),x]","\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d-c^2 d x^2\right)^{5/2}},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][((f*x)^m*(a + b*ArcCosh[c*x])^2)/((-1 + c*x)^(5/2)*(1 + c*x)^(5/2)), x])/(d^2*Sqrt[d - c^2*d*x^2])","A",0,0,0,0,-1,"{}"
239,0,0,0,0.3699149,"\int \frac{(f x)^m \cosh ^{-1}(c x)^2}{\sqrt{1-c^2 x^2}} \, dx","Int[((f*x)^m*ArcCosh[c*x]^2)/Sqrt[1 - c^2*x^2],x]","\int \frac{(f x)^m \cosh ^{-1}(c x)^2}{\sqrt{1-c^2 x^2}} \, dx","\text{Int}\left(\frac{\cosh ^{-1}(c x)^2 (f x)^m}{\sqrt{1-c^2 x^2}},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][((f*x)^m*ArcCosh[c*x]^2)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/Sqrt[1 - c^2*x^2]","A",0,0,0,0,-1,"{}"
240,1,505,0,1.408183,"\int \left(c-a^2 c x^2\right)^3 \cosh ^{-1}(a x)^3 \, dx","Int[(c - a^2*c*x^2)^3*ArcCosh[a*x]^3,x]","\frac{6 c^3 \left(1-a^2 x^2\right)^4}{2401 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{2664 c^3 \left(1-a^2 x^2\right)^3}{214375 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{1184 c^3 \left(1-a^2 x^2\right)^2}{42875 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{7104 c^3 \left(1-a^2 x^2\right)}{42875 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{6}{343} a^6 c^3 x^7 \cosh ^{-1}(a x)+\frac{702 a^4 c^3 x^5 \cosh ^{-1}(a x)}{6125}-\frac{1514 a^2 c^3 x^3 \cosh ^{-1}(a x)}{3675}+\frac{1}{7} c^3 x \left(1-a^2 x^2\right)^3 \cosh ^{-1}(a x)^3+\frac{6}{35} c^3 x \left(1-a^2 x^2\right)^2 \cosh ^{-1}(a x)^3+\frac{8}{35} c^3 x \left(1-a^2 x^2\right) \cosh ^{-1}(a x)^3+\frac{16}{315} a c^3 x^2 \sqrt{a x-1} \sqrt{a x+1}-\frac{976 c^3 \sqrt{a x-1} \sqrt{a x+1}}{315 a}+\frac{16}{35} c^3 x \cosh ^{-1}(a x)^3+\frac{4322 c^3 x \cosh ^{-1}(a x)}{1225}+\frac{3 c^3 (a x-1)^{7/2} (a x+1)^{7/2} \cosh ^{-1}(a x)^2}{49 a}-\frac{18 c^3 (a x-1)^{5/2} (a x+1)^{5/2} \cosh ^{-1}(a x)^2}{175 a}+\frac{8 c^3 (a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)^2}{35 a}-\frac{48 c^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{35 a}","\frac{6 c^3 \left(1-a^2 x^2\right)^4}{2401 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{2664 c^3 \left(1-a^2 x^2\right)^3}{214375 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{1184 c^3 \left(1-a^2 x^2\right)^2}{42875 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{7104 c^3 \left(1-a^2 x^2\right)}{42875 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{6}{343} a^6 c^3 x^7 \cosh ^{-1}(a x)+\frac{702 a^4 c^3 x^5 \cosh ^{-1}(a x)}{6125}-\frac{1514 a^2 c^3 x^3 \cosh ^{-1}(a x)}{3675}+\frac{1}{7} c^3 x \left(1-a^2 x^2\right)^3 \cosh ^{-1}(a x)^3+\frac{6}{35} c^3 x \left(1-a^2 x^2\right)^2 \cosh ^{-1}(a x)^3+\frac{8}{35} c^3 x \left(1-a^2 x^2\right) \cosh ^{-1}(a x)^3+\frac{16}{315} a c^3 x^2 \sqrt{a x-1} \sqrt{a x+1}-\frac{976 c^3 \sqrt{a x-1} \sqrt{a x+1}}{315 a}+\frac{16}{35} c^3 x \cosh ^{-1}(a x)^3+\frac{4322 c^3 x \cosh ^{-1}(a x)}{1225}+\frac{3 c^3 (a x-1)^{7/2} (a x+1)^{7/2} \cosh ^{-1}(a x)^2}{49 a}-\frac{18 c^3 (a x-1)^{5/2} (a x+1)^{5/2} \cosh ^{-1}(a x)^2}{175 a}+\frac{8 c^3 (a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)^2}{35 a}-\frac{48 c^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{35 a}",1,"(-976*c^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(315*a) + (16*a*c^3*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/315 + (7104*c^3*(1 - a^2*x^2))/(42875*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (1184*c^3*(1 - a^2*x^2)^2)/(42875*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (2664*c^3*(1 - a^2*x^2)^3)/(214375*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (6*c^3*(1 - a^2*x^2)^4)/(2401*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (4322*c^3*x*ArcCosh[a*x])/1225 - (1514*a^2*c^3*x^3*ArcCosh[a*x])/3675 + (702*a^4*c^3*x^5*ArcCosh[a*x])/6125 - (6*a^6*c^3*x^7*ArcCosh[a*x])/343 - (48*c^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(35*a) + (8*c^3*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*ArcCosh[a*x]^2)/(35*a) - (18*c^3*(-1 + a*x)^(5/2)*(1 + a*x)^(5/2)*ArcCosh[a*x]^2)/(175*a) + (3*c^3*(-1 + a*x)^(7/2)*(1 + a*x)^(7/2)*ArcCosh[a*x]^2)/(49*a) + (16*c^3*x*ArcCosh[a*x]^3)/35 + (8*c^3*x*(1 - a^2*x^2)*ArcCosh[a*x]^3)/35 + (6*c^3*x*(1 - a^2*x^2)^2*ArcCosh[a*x]^3)/35 + (c^3*x*(1 - a^2*x^2)^3*ArcCosh[a*x]^3)/7","A",26,14,20,0.7000,1,"{5681, 5718, 194, 5680, 12, 1610, 1799, 1850, 520, 1247, 698, 460, 74, 5654}"
241,1,388,0,0.8440149,"\int \left(c-a^2 c x^2\right)^2 \cosh ^{-1}(a x)^3 \, dx","Int[(c - a^2*c*x^2)^2*ArcCosh[a*x]^3,x]","\frac{6 c^2 \left(1-a^2 x^2\right)^3}{625 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{8 c^2 \left(1-a^2 x^2\right)^2}{375 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{16 c^2 \left(1-a^2 x^2\right)}{125 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{6}{125} a^4 c^2 x^5 \cosh ^{-1}(a x)-\frac{76}{225} a^2 c^2 x^3 \cosh ^{-1}(a x)+\frac{1}{5} c^2 x \left(1-a^2 x^2\right)^2 \cosh ^{-1}(a x)^3+\frac{4}{15} c^2 x \left(1-a^2 x^2\right) \cosh ^{-1}(a x)^3+\frac{8}{135} a c^2 x^2 \sqrt{a x-1} \sqrt{a x+1}-\frac{488 c^2 \sqrt{a x-1} \sqrt{a x+1}}{135 a}+\frac{8}{15} c^2 x \cosh ^{-1}(a x)^3+\frac{298}{75} c^2 x \cosh ^{-1}(a x)-\frac{3 c^2 (a x-1)^{5/2} (a x+1)^{5/2} \cosh ^{-1}(a x)^2}{25 a}+\frac{4 c^2 (a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)^2}{15 a}-\frac{8 c^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{5 a}","\frac{6 c^2 \left(1-a^2 x^2\right)^3}{625 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{8 c^2 \left(1-a^2 x^2\right)^2}{375 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{16 c^2 \left(1-a^2 x^2\right)}{125 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{6}{125} a^4 c^2 x^5 \cosh ^{-1}(a x)-\frac{76}{225} a^2 c^2 x^3 \cosh ^{-1}(a x)+\frac{1}{5} c^2 x \left(1-a^2 x^2\right)^2 \cosh ^{-1}(a x)^3+\frac{4}{15} c^2 x \left(1-a^2 x^2\right) \cosh ^{-1}(a x)^3+\frac{8}{135} a c^2 x^2 \sqrt{a x-1} \sqrt{a x+1}-\frac{488 c^2 \sqrt{a x-1} \sqrt{a x+1}}{135 a}+\frac{8}{15} c^2 x \cosh ^{-1}(a x)^3+\frac{298}{75} c^2 x \cosh ^{-1}(a x)-\frac{3 c^2 (a x-1)^{5/2} (a x+1)^{5/2} \cosh ^{-1}(a x)^2}{25 a}+\frac{4 c^2 (a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)^2}{15 a}-\frac{8 c^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{5 a}",1,"(-488*c^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(135*a) + (8*a*c^2*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/135 + (16*c^2*(1 - a^2*x^2))/(125*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (8*c^2*(1 - a^2*x^2)^2)/(375*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (6*c^2*(1 - a^2*x^2)^3)/(625*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (298*c^2*x*ArcCosh[a*x])/75 - (76*a^2*c^2*x^3*ArcCosh[a*x])/225 + (6*a^4*c^2*x^5*ArcCosh[a*x])/125 - (8*c^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(5*a) + (4*c^2*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*ArcCosh[a*x]^2)/(15*a) - (3*c^2*(-1 + a*x)^(5/2)*(1 + a*x)^(5/2)*ArcCosh[a*x]^2)/(25*a) + (8*c^2*x*ArcCosh[a*x]^3)/15 + (4*c^2*x*(1 - a^2*x^2)*ArcCosh[a*x]^3)/15 + (c^2*x*(1 - a^2*x^2)^2*ArcCosh[a*x]^3)/5","A",18,11,20,0.5500,1,"{5681, 5718, 194, 5680, 12, 520, 1247, 698, 460, 74, 5654}"
242,1,175,0,0.4774692,"\int \left(c-a^2 c x^2\right) \cosh ^{-1}(a x)^3 \, dx","Int[(c - a^2*c*x^2)*ArcCosh[a*x]^3,x]","-\frac{2}{9} a^2 c x^3 \cosh ^{-1}(a x)+\frac{1}{3} c x \left(1-a^2 x^2\right) \cosh ^{-1}(a x)^3+\frac{2}{27} a c x^2 \sqrt{a x-1} \sqrt{a x+1}-\frac{122 c \sqrt{a x-1} \sqrt{a x+1}}{27 a}+\frac{2}{3} c x \cosh ^{-1}(a x)^3+\frac{14}{3} c x \cosh ^{-1}(a x)+\frac{c (a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)^2}{3 a}-\frac{2 c \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{a}","-\frac{2}{9} a^2 c x^3 \cosh ^{-1}(a x)+\frac{1}{3} c x \left(1-a^2 x^2\right) \cosh ^{-1}(a x)^3+\frac{2}{27} a c x^2 \sqrt{a x-1} \sqrt{a x+1}-\frac{122 c \sqrt{a x-1} \sqrt{a x+1}}{27 a}+\frac{2}{3} c x \cosh ^{-1}(a x)^3+\frac{14}{3} c x \cosh ^{-1}(a x)+\frac{c (a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)^2}{3 a}-\frac{2 c \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{a}",1,"(-122*c*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(27*a) + (2*a*c*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/27 + (14*c*x*ArcCosh[a*x])/3 - (2*a^2*c*x^3*ArcCosh[a*x])/9 - (2*c*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/a + (c*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*ArcCosh[a*x]^2)/(3*a) + (2*c*x*ArcCosh[a*x]^3)/3 + (c*x*(1 - a^2*x^2)*ArcCosh[a*x]^3)/3","A",10,7,18,0.3889,1,"{5681, 5718, 5680, 12, 460, 74, 5654}"
243,1,144,0,0.1291495,"\int \frac{\cosh ^{-1}(a x)^3}{c-a^2 c x^2} \, dx","Int[ArcCosh[a*x]^3/(c - a^2*c*x^2),x]","\frac{3 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{a c}-\frac{3 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{a c}-\frac{6 \cosh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\cosh ^{-1}(a x)}\right)}{a c}+\frac{6 \cosh ^{-1}(a x) \text{PolyLog}\left(3,e^{\cosh ^{-1}(a x)}\right)}{a c}+\frac{6 \text{PolyLog}\left(4,-e^{\cosh ^{-1}(a x)}\right)}{a c}-\frac{6 \text{PolyLog}\left(4,e^{\cosh ^{-1}(a x)}\right)}{a c}+\frac{2 \cosh ^{-1}(a x)^3 \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{a c}","\frac{3 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{a c}-\frac{3 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{a c}-\frac{6 \cosh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\cosh ^{-1}(a x)}\right)}{a c}+\frac{6 \cosh ^{-1}(a x) \text{PolyLog}\left(3,e^{\cosh ^{-1}(a x)}\right)}{a c}+\frac{6 \text{PolyLog}\left(4,-e^{\cosh ^{-1}(a x)}\right)}{a c}-\frac{6 \text{PolyLog}\left(4,e^{\cosh ^{-1}(a x)}\right)}{a c}+\frac{2 \cosh ^{-1}(a x)^3 \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{a c}",1,"(2*ArcCosh[a*x]^3*ArcTanh[E^ArcCosh[a*x]])/(a*c) + (3*ArcCosh[a*x]^2*PolyLog[2, -E^ArcCosh[a*x]])/(a*c) - (3*ArcCosh[a*x]^2*PolyLog[2, E^ArcCosh[a*x]])/(a*c) - (6*ArcCosh[a*x]*PolyLog[3, -E^ArcCosh[a*x]])/(a*c) + (6*ArcCosh[a*x]*PolyLog[3, E^ArcCosh[a*x]])/(a*c) + (6*PolyLog[4, -E^ArcCosh[a*x]])/(a*c) - (6*PolyLog[4, E^ArcCosh[a*x]])/(a*c)","A",10,6,20,0.3000,1,"{5694, 4182, 2531, 6609, 2282, 6589}"
244,1,260,0,0.4415879,"\int \frac{\cosh ^{-1}(a x)^3}{\left(c-a^2 c x^2\right)^2} \, dx","Int[ArcCosh[a*x]^3/(c - a^2*c*x^2)^2,x]","\frac{3 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{2 a c^2}-\frac{3 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{2 a c^2}-\frac{3 \cosh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\cosh ^{-1}(a x)}\right)}{a c^2}+\frac{3 \cosh ^{-1}(a x) \text{PolyLog}\left(3,e^{\cosh ^{-1}(a x)}\right)}{a c^2}-\frac{3 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{a c^2}+\frac{3 \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{a c^2}+\frac{3 \text{PolyLog}\left(4,-e^{\cosh ^{-1}(a x)}\right)}{a c^2}-\frac{3 \text{PolyLog}\left(4,e^{\cosh ^{-1}(a x)}\right)}{a c^2}+\frac{x \cosh ^{-1}(a x)^3}{2 c^2 \left(1-a^2 x^2\right)}-\frac{3 \cosh ^{-1}(a x)^2}{2 a c^2 \sqrt{a x-1} \sqrt{a x+1}}+\frac{\cosh ^{-1}(a x)^3 \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{a c^2}-\frac{6 \cosh ^{-1}(a x) \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{a c^2}","\frac{3 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{2 a c^2}-\frac{3 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{2 a c^2}-\frac{3 \cosh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\cosh ^{-1}(a x)}\right)}{a c^2}+\frac{3 \cosh ^{-1}(a x) \text{PolyLog}\left(3,e^{\cosh ^{-1}(a x)}\right)}{a c^2}-\frac{3 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{a c^2}+\frac{3 \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{a c^2}+\frac{3 \text{PolyLog}\left(4,-e^{\cosh ^{-1}(a x)}\right)}{a c^2}-\frac{3 \text{PolyLog}\left(4,e^{\cosh ^{-1}(a x)}\right)}{a c^2}+\frac{x \cosh ^{-1}(a x)^3}{2 c^2 \left(1-a^2 x^2\right)}-\frac{3 \cosh ^{-1}(a x)^2}{2 a c^2 \sqrt{a x-1} \sqrt{a x+1}}+\frac{\cosh ^{-1}(a x)^3 \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{a c^2}-\frac{6 \cosh ^{-1}(a x) \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{a c^2}",1,"(-3*ArcCosh[a*x]^2)/(2*a*c^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (x*ArcCosh[a*x]^3)/(2*c^2*(1 - a^2*x^2)) - (6*ArcCosh[a*x]*ArcTanh[E^ArcCosh[a*x]])/(a*c^2) + (ArcCosh[a*x]^3*ArcTanh[E^ArcCosh[a*x]])/(a*c^2) - (3*PolyLog[2, -E^ArcCosh[a*x]])/(a*c^2) + (3*ArcCosh[a*x]^2*PolyLog[2, -E^ArcCosh[a*x]])/(2*a*c^2) + (3*PolyLog[2, E^ArcCosh[a*x]])/(a*c^2) - (3*ArcCosh[a*x]^2*PolyLog[2, E^ArcCosh[a*x]])/(2*a*c^2) - (3*ArcCosh[a*x]*PolyLog[3, -E^ArcCosh[a*x]])/(a*c^2) + (3*ArcCosh[a*x]*PolyLog[3, E^ArcCosh[a*x]])/(a*c^2) + (3*PolyLog[4, -E^ArcCosh[a*x]])/(a*c^2) - (3*PolyLog[4, E^ArcCosh[a*x]])/(a*c^2)","A",18,10,20,0.5000,1,"{5689, 5718, 5694, 4182, 2279, 2391, 2531, 6609, 2282, 6589}"
245,1,387,0,0.8142258,"\int \frac{\cosh ^{-1}(a x)^3}{\left(c-a^2 c x^2\right)^3} \, dx","Int[ArcCosh[a*x]^3/(c - a^2*c*x^2)^3,x]","\frac{9 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{8 a c^3}-\frac{9 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{8 a c^3}-\frac{9 \cosh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}+\frac{9 \cosh ^{-1}(a x) \text{PolyLog}\left(3,e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}-\frac{5 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{2 a c^3}+\frac{5 \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{2 a c^3}+\frac{9 \text{PolyLog}\left(4,-e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}-\frac{9 \text{PolyLog}\left(4,e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}+\frac{3 x \cosh ^{-1}(a x)^3}{8 c^3 \left(1-a^2 x^2\right)}+\frac{x \cosh ^{-1}(a x)^3}{4 c^3 \left(1-a^2 x^2\right)^2}-\frac{x \cosh ^{-1}(a x)}{4 c^3 \left(1-a^2 x^2\right)}+\frac{1}{4 a c^3 \sqrt{a x-1} \sqrt{a x+1}}-\frac{9 \cosh ^{-1}(a x)^2}{8 a c^3 \sqrt{a x-1} \sqrt{a x+1}}+\frac{\cosh ^{-1}(a x)^2}{4 a c^3 (a x-1)^{3/2} (a x+1)^{3/2}}+\frac{3 \cosh ^{-1}(a x)^3 \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}-\frac{5 \cosh ^{-1}(a x) \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{a c^3}","\frac{9 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{8 a c^3}-\frac{9 \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{8 a c^3}-\frac{9 \cosh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}+\frac{9 \cosh ^{-1}(a x) \text{PolyLog}\left(3,e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}-\frac{5 \text{PolyLog}\left(2,-e^{\cosh ^{-1}(a x)}\right)}{2 a c^3}+\frac{5 \text{PolyLog}\left(2,e^{\cosh ^{-1}(a x)}\right)}{2 a c^3}+\frac{9 \text{PolyLog}\left(4,-e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}-\frac{9 \text{PolyLog}\left(4,e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}+\frac{3 x \cosh ^{-1}(a x)^3}{8 c^3 \left(1-a^2 x^2\right)}+\frac{x \cosh ^{-1}(a x)^3}{4 c^3 \left(1-a^2 x^2\right)^2}-\frac{x \cosh ^{-1}(a x)}{4 c^3 \left(1-a^2 x^2\right)}+\frac{1}{4 a c^3 \sqrt{a x-1} \sqrt{a x+1}}-\frac{9 \cosh ^{-1}(a x)^2}{8 a c^3 \sqrt{a x-1} \sqrt{a x+1}}+\frac{\cosh ^{-1}(a x)^2}{4 a c^3 (a x-1)^{3/2} (a x+1)^{3/2}}+\frac{3 \cosh ^{-1}(a x)^3 \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{4 a c^3}-\frac{5 \cosh ^{-1}(a x) \tanh ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{a c^3}",1,"1/(4*a*c^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (x*ArcCosh[a*x])/(4*c^3*(1 - a^2*x^2)) + ArcCosh[a*x]^2/(4*a*c^3*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)) - (9*ArcCosh[a*x]^2)/(8*a*c^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (x*ArcCosh[a*x]^3)/(4*c^3*(1 - a^2*x^2)^2) + (3*x*ArcCosh[a*x]^3)/(8*c^3*(1 - a^2*x^2)) - (5*ArcCosh[a*x]*ArcTanh[E^ArcCosh[a*x]])/(a*c^3) + (3*ArcCosh[a*x]^3*ArcTanh[E^ArcCosh[a*x]])/(4*a*c^3) - (5*PolyLog[2, -E^ArcCosh[a*x]])/(2*a*c^3) + (9*ArcCosh[a*x]^2*PolyLog[2, -E^ArcCosh[a*x]])/(8*a*c^3) + (5*PolyLog[2, E^ArcCosh[a*x]])/(2*a*c^3) - (9*ArcCosh[a*x]^2*PolyLog[2, E^ArcCosh[a*x]])/(8*a*c^3) - (9*ArcCosh[a*x]*PolyLog[3, -E^ArcCosh[a*x]])/(4*a*c^3) + (9*ArcCosh[a*x]*PolyLog[3, E^ArcCosh[a*x]])/(4*a*c^3) + (9*PolyLog[4, -E^ArcCosh[a*x]])/(4*a*c^3) - (9*PolyLog[4, E^ArcCosh[a*x]])/(4*a*c^3)","A",28,11,20,0.5500,1,"{5689, 5718, 74, 5694, 4182, 2279, 2391, 2531, 6609, 2282, 6589}"
246,1,636,0,1.4966664,"\int \left(c-a^2 c x^2\right)^{5/2} \cosh ^{-1}(a x)^3 \, dx","Int[(c - a^2*c*x^2)^(5/2)*ArcCosh[a*x]^3,x]","\frac{65 a^3 c^2 x^4 \sqrt{c-a^2 c x^2}}{2304 \sqrt{a x-1} \sqrt{a x+1}}-\frac{865 a c^2 x^2 \sqrt{c-a^2 c x^2}}{2304 \sqrt{a x-1} \sqrt{a x+1}}+\frac{c^2 \left(1-a^2 x^2\right)^3 \sqrt{c-a^2 c x^2}}{216 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{15 a c^2 x^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{32 \sqrt{a x-1} \sqrt{a x+1}}+\frac{5}{16} c^2 x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^3+\frac{1}{6} c^2 x (1-a x)^2 (a x+1)^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^3+\frac{5}{24} c^2 x (1-a x) (a x+1) \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^3+\frac{245}{384} c^2 x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)+\frac{1}{36} c^2 x (1-a x)^2 (a x+1)^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)+\frac{65}{576} c^2 x (1-a x) (a x+1) \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)-\frac{5 c^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^4}{64 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{c^2 \left(1-a^2 x^2\right)^3 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{12 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{5 c^2 \left(1-a^2 x^2\right)^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{32 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{115 c^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{768 a \sqrt{a x-1} \sqrt{a x+1}}","\frac{65 a^3 c^2 x^4 \sqrt{c-a^2 c x^2}}{2304 \sqrt{a x-1} \sqrt{a x+1}}-\frac{865 a c^2 x^2 \sqrt{c-a^2 c x^2}}{2304 \sqrt{a x-1} \sqrt{a x+1}}+\frac{c^2 \left(1-a^2 x^2\right)^3 \sqrt{c-a^2 c x^2}}{216 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{15 a c^2 x^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{32 \sqrt{a x-1} \sqrt{a x+1}}+\frac{5}{16} c^2 x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^3+\frac{245}{384} c^2 x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)+\frac{1}{36} c^2 x (1-a x)^2 (a x+1)^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)+\frac{65}{576} c^2 x (1-a x) (a x+1) \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)-\frac{5 c^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^4}{64 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{c^2 \left(1-a^2 x^2\right)^3 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{12 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{5 c^2 \left(1-a^2 x^2\right)^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{32 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{115 c^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{768 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{1}{6} x \left(c-a^2 c x^2\right)^{5/2} \cosh ^{-1}(a x)^3+\frac{5}{24} c x \left(c-a^2 c x^2\right)^{3/2} \cosh ^{-1}(a x)^3",1,"(-865*a*c^2*x^2*Sqrt[c - a^2*c*x^2])/(2304*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (65*a^3*c^2*x^4*Sqrt[c - a^2*c*x^2])/(2304*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (c^2*(1 - a^2*x^2)^3*Sqrt[c - a^2*c*x^2])/(216*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (245*c^2*x*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x])/384 + (65*c^2*x*(1 - a*x)*(1 + a*x)*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x])/576 + (c^2*x*(1 - a*x)^2*(1 + a*x)^2*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x])/36 + (115*c^2*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^2)/(768*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (15*a*c^2*x^2*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^2)/(32*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (5*c^2*(1 - a^2*x^2)^2*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^2)/(32*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (c^2*(1 - a^2*x^2)^3*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^2)/(12*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (5*c^2*x*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^3)/16 + (5*c^2*x*(1 - a*x)*(1 + a*x)*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^3)/24 + (c^2*x*(1 - a*x)^2*(1 + a*x)^2*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^3)/6 - (5*c^2*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^4)/(64*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",25,10,22,0.4545,1,"{5713, 5685, 5683, 5676, 5662, 5759, 30, 5716, 14, 261}"
247,1,414,0,0.945539,"\int \left(c-a^2 c x^2\right)^{3/2} \cosh ^{-1}(a x)^3 \, dx","Int[(c - a^2*c*x^2)^(3/2)*ArcCosh[a*x]^3,x]","\frac{3 a^3 c x^4 \sqrt{c-a^2 c x^2}}{128 \sqrt{a x-1} \sqrt{a x+1}}-\frac{51 a c x^2 \sqrt{c-a^2 c x^2}}{128 \sqrt{a x-1} \sqrt{a x+1}}-\frac{9 a c x^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{16 \sqrt{a x-1} \sqrt{a x+1}}+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^3+\frac{1}{4} c x (1-a x) (a x+1) \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^3+\frac{45}{64} c x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)+\frac{3}{32} c x (1-a x) (a x+1) \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)-\frac{3 c \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^4}{32 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{3 c \left(1-a^2 x^2\right)^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{16 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{27 c \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{128 a \sqrt{a x-1} \sqrt{a x+1}}","\frac{3 a^3 c x^4 \sqrt{c-a^2 c x^2}}{128 \sqrt{a x-1} \sqrt{a x+1}}-\frac{51 a c x^2 \sqrt{c-a^2 c x^2}}{128 \sqrt{a x-1} \sqrt{a x+1}}-\frac{9 a c x^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{16 \sqrt{a x-1} \sqrt{a x+1}}+\frac{1}{4} x \left(c-a^2 c x^2\right)^{3/2} \cosh ^{-1}(a x)^3+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^3+\frac{45}{64} c x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)+\frac{3}{32} c x (1-a x) (a x+1) \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)-\frac{3 c \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^4}{32 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{3 c \left(1-a^2 x^2\right)^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{16 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{27 c \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{128 a \sqrt{a x-1} \sqrt{a x+1}}",1,"(-51*a*c*x^2*Sqrt[c - a^2*c*x^2])/(128*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (3*a^3*c*x^4*Sqrt[c - a^2*c*x^2])/(128*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (45*c*x*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x])/64 + (3*c*x*(1 - a*x)*(1 + a*x)*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x])/32 + (27*c*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^2)/(128*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (9*a*c*x^2*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^2)/(16*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (3*c*(1 - a^2*x^2)^2*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^2)/(16*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (3*c*x*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^3)/8 + (c*x*(1 - a*x)*(1 + a*x)*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^3)/4 - (3*c*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^4)/(32*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",15,9,22,0.4091,1,"{5713, 5685, 5683, 5676, 5662, 5759, 30, 5716, 14}"
248,1,231,0,0.5368327,"\int \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^3 \, dx","Int[Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^3,x]","-\frac{3 a x^2 \sqrt{c-a^2 c x^2}}{8 \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^4}{8 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^3-\frac{3 a x^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{4 \sqrt{a x-1} \sqrt{a x+1}}+\frac{3 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{8 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{3}{4} x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)","-\frac{3 a x^2 \sqrt{c-a^2 c x^2}}{8 \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^4}{8 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^3-\frac{3 a x^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{4 \sqrt{a x-1} \sqrt{a x+1}}+\frac{3 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^2}{8 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{3}{4} x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)",1,"(-3*a*x^2*Sqrt[c - a^2*c*x^2])/(8*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (3*x*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x])/4 + (3*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^2)/(8*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (3*a*x^2*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^2)/(4*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (x*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^3)/2 - (Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^4)/(8*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",7,6,22,0.2727,1,"{5713, 5683, 5676, 5662, 5759, 30}"
249,1,46,0,0.1561547,"\int \frac{\cosh ^{-1}(a x)^3}{\sqrt{c-a^2 c x^2}} \, dx","Int[ArcCosh[a*x]^3/Sqrt[c - a^2*c*x^2],x]","\frac{\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^4}{4 a \sqrt{c-a^2 c x^2}}","\frac{\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^4}{4 a \sqrt{c-a^2 c x^2}}",1,"(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^4)/(4*a*Sqrt[c - a^2*c*x^2])","A",2,2,22,0.09091,1,"{5713, 5676}"
250,1,241,0,0.3489379,"\int \frac{\cosh ^{-1}(a x)^3}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[ArcCosh[a*x]^3/(c - a^2*c*x^2)^(3/2),x]","-\frac{3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(a x)}\right)}{a c \sqrt{c-a^2 c x^2}}+\frac{3 \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(3,e^{2 \cosh ^{-1}(a x)}\right)}{2 a c \sqrt{c-a^2 c x^2}}+\frac{x \cosh ^{-1}(a x)^3}{c \sqrt{c-a^2 c x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{a c \sqrt{c-a^2 c x^2}}-\frac{3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2 \log \left(1-e^{2 \cosh ^{-1}(a x)}\right)}{a c \sqrt{c-a^2 c x^2}}","-\frac{3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(a x)}\right)}{a c \sqrt{c-a^2 c x^2}}+\frac{3 \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(3,e^{2 \cosh ^{-1}(a x)}\right)}{2 a c \sqrt{c-a^2 c x^2}}+\frac{x \cosh ^{-1}(a x)^3}{c \sqrt{c-a^2 c x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{a c \sqrt{c-a^2 c x^2}}-\frac{3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2 \log \left(1-e^{2 \cosh ^{-1}(a x)}\right)}{a c \sqrt{c-a^2 c x^2}}",1,"(x*ArcCosh[a*x]^3)/(c*Sqrt[c - a^2*c*x^2]) + (Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(a*c*Sqrt[c - a^2*c*x^2]) - (3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2*Log[1 - E^(2*ArcCosh[a*x])])/(a*c*Sqrt[c - a^2*c*x^2]) - (3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*PolyLog[2, E^(2*ArcCosh[a*x])])/(a*c*Sqrt[c - a^2*c*x^2]) + (3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[3, E^(2*ArcCosh[a*x])])/(2*a*c*Sqrt[c - a^2*c*x^2])","A",8,8,22,0.3636,1,"{5713, 5688, 5715, 3716, 2190, 2531, 2282, 6589}"
251,1,428,0,0.6378234,"\int \frac{\cosh ^{-1}(a x)^3}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[ArcCosh[a*x]^3/(c - a^2*c*x^2)^(5/2),x]","-\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(a x)}\right)}{a c^2 \sqrt{c-a^2 c x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(3,e^{2 \cosh ^{-1}(a x)}\right)}{a c^2 \sqrt{c-a^2 c x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \log \left(1-a^2 x^2\right)}{2 a c^2 \sqrt{c-a^2 c x^2}}+\frac{2 x \cosh ^{-1}(a x)^3}{3 c^2 \sqrt{c-a^2 c x^2}}+\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{3 a c^2 \sqrt{c-a^2 c x^2}}+\frac{x \cosh ^{-1}(a x)^3}{3 c^2 (1-a x) (a x+1) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{2 a c^2 \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}-\frac{x \cosh ^{-1}(a x)}{c^2 \sqrt{c-a^2 c x^2}}-\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2 \log \left(1-e^{2 \cosh ^{-1}(a x)}\right)}{a c^2 \sqrt{c-a^2 c x^2}}","-\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(a x)}\right)}{a c^2 \sqrt{c-a^2 c x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(3,e^{2 \cosh ^{-1}(a x)}\right)}{a c^2 \sqrt{c-a^2 c x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \log \left(1-a^2 x^2\right)}{2 a c^2 \sqrt{c-a^2 c x^2}}+\frac{2 x \cosh ^{-1}(a x)^3}{3 c^2 \sqrt{c-a^2 c x^2}}+\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{3 a c^2 \sqrt{c-a^2 c x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{2 a c^2 \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}-\frac{x \cosh ^{-1}(a x)}{c^2 \sqrt{c-a^2 c x^2}}-\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2 \log \left(1-e^{2 \cosh ^{-1}(a x)}\right)}{a c^2 \sqrt{c-a^2 c x^2}}+\frac{x \cosh ^{-1}(a x)^3}{3 c \left(c-a^2 c x^2\right)^{3/2}}",1,"-((x*ArcCosh[a*x])/(c^2*Sqrt[c - a^2*c*x^2])) + (Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(2*a*c^2*(1 - a^2*x^2)*Sqrt[c - a^2*c*x^2]) + (2*x*ArcCosh[a*x]^3)/(3*c^2*Sqrt[c - a^2*c*x^2]) + (x*ArcCosh[a*x]^3)/(3*c^2*(1 - a*x)*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(3*a*c^2*Sqrt[c - a^2*c*x^2]) - (2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2*Log[1 - E^(2*ArcCosh[a*x])])/(a*c^2*Sqrt[c - a^2*c*x^2]) + (Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Log[1 - a^2*x^2])/(2*a*c^2*Sqrt[c - a^2*c*x^2]) - (2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*PolyLog[2, E^(2*ArcCosh[a*x])])/(a*c^2*Sqrt[c - a^2*c*x^2]) + (Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[3, E^(2*ArcCosh[a*x])])/(a*c^2*Sqrt[c - a^2*c*x^2])","A",12,11,22,0.5000,1,"{5713, 5691, 5688, 5715, 3716, 2190, 2531, 2282, 6589, 5716, 260}"
252,1,637,0,1.0768935,"\int \frac{\cosh ^{-1}(a x)^3}{\left(c-a^2 c x^2\right)^{7/2}} \, dx","Int[ArcCosh[a*x]^3/(c - a^2*c*x^2)^(7/2),x]","-\frac{8 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(a x)}\right)}{5 a c^3 \sqrt{c-a^2 c x^2}}+\frac{4 \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(3,e^{2 \cosh ^{-1}(a x)}\right)}{5 a c^3 \sqrt{c-a^2 c x^2}}-\frac{\sqrt{a x-1} \sqrt{a x+1}}{20 a c^3 \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \log \left(1-a^2 x^2\right)}{2 a c^3 \sqrt{c-a^2 c x^2}}+\frac{8 x \cosh ^{-1}(a x)^3}{15 c^3 \sqrt{c-a^2 c x^2}}+\frac{8 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{4 x \cosh ^{-1}(a x)^3}{15 c^3 (1-a x) (a x+1) \sqrt{c-a^2 c x^2}}+\frac{x \cosh ^{-1}(a x)^3}{5 c^3 (1-a x)^2 (a x+1)^2 \sqrt{c-a^2 c x^2}}+\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{5 a c^3 \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}+\frac{3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{20 a c^3 \left(1-a^2 x^2\right)^2 \sqrt{c-a^2 c x^2}}-\frac{x \cosh ^{-1}(a x)}{c^3 \sqrt{c-a^2 c x^2}}-\frac{x \cosh ^{-1}(a x)}{10 c^3 (1-a x) (a x+1) \sqrt{c-a^2 c x^2}}-\frac{8 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2 \log \left(1-e^{2 \cosh ^{-1}(a x)}\right)}{5 a c^3 \sqrt{c-a^2 c x^2}}","-\frac{8 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \text{PolyLog}\left(2,e^{2 \cosh ^{-1}(a x)}\right)}{5 a c^3 \sqrt{c-a^2 c x^2}}+\frac{4 \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(3,e^{2 \cosh ^{-1}(a x)}\right)}{5 a c^3 \sqrt{c-a^2 c x^2}}-\frac{\sqrt{a x-1} \sqrt{a x+1}}{20 a c^3 \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \log \left(1-a^2 x^2\right)}{2 a c^3 \sqrt{c-a^2 c x^2}}+\frac{8 x \cosh ^{-1}(a x)^3}{15 c^3 \sqrt{c-a^2 c x^2}}+\frac{8 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{15 a c^3 \sqrt{c-a^2 c x^2}}+\frac{4 x \cosh ^{-1}(a x)^3}{15 c^2 \left(c-a^2 c x^2\right)^{3/2}}+\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{5 a c^3 \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}+\frac{3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{20 a c^3 \left(1-a^2 x^2\right)^2 \sqrt{c-a^2 c x^2}}-\frac{x \cosh ^{-1}(a x)}{c^3 \sqrt{c-a^2 c x^2}}-\frac{x \cosh ^{-1}(a x)}{10 c^3 (1-a x) (a x+1) \sqrt{c-a^2 c x^2}}-\frac{8 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2 \log \left(1-e^{2 \cosh ^{-1}(a x)}\right)}{5 a c^3 \sqrt{c-a^2 c x^2}}+\frac{x \cosh ^{-1}(a x)^3}{5 c \left(c-a^2 c x^2\right)^{5/2}}",1,"-(Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(20*a*c^3*(1 - a^2*x^2)*Sqrt[c - a^2*c*x^2]) - (x*ArcCosh[a*x])/(c^3*Sqrt[c - a^2*c*x^2]) - (x*ArcCosh[a*x])/(10*c^3*(1 - a*x)*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(20*a*c^3*(1 - a^2*x^2)^2*Sqrt[c - a^2*c*x^2]) + (2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(5*a*c^3*(1 - a^2*x^2)*Sqrt[c - a^2*c*x^2]) + (8*x*ArcCosh[a*x]^3)/(15*c^3*Sqrt[c - a^2*c*x^2]) + (x*ArcCosh[a*x]^3)/(5*c^3*(1 - a*x)^2*(1 + a*x)^2*Sqrt[c - a^2*c*x^2]) + (4*x*ArcCosh[a*x]^3)/(15*c^3*(1 - a*x)*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (8*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/(15*a*c^3*Sqrt[c - a^2*c*x^2]) - (8*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2*Log[1 - E^(2*ArcCosh[a*x])])/(5*a*c^3*Sqrt[c - a^2*c*x^2]) + (Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Log[1 - a^2*x^2])/(2*a*c^3*Sqrt[c - a^2*c*x^2]) - (8*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*PolyLog[2, E^(2*ArcCosh[a*x])])/(5*a*c^3*Sqrt[c - a^2*c*x^2]) + (4*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[3, E^(2*ArcCosh[a*x])])/(5*a*c^3*Sqrt[c - a^2*c*x^2])","A",18,12,22,0.5455,1,"{5713, 5691, 5688, 5715, 3716, 2190, 2531, 2282, 6589, 5716, 260, 261}"
253,1,427,0,1.4416346,"\int \frac{x^4 \cosh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^4*ArcCosh[a*x]^3)/Sqrt[1 - a^2*x^2],x]","-\frac{3 x^4 \sqrt{a x-1} \sqrt{a x+1}}{128 a \sqrt{1-a^2 x^2}}-\frac{45 x^2 \sqrt{a x-1} \sqrt{a x+1}}{128 a^3 \sqrt{1-a^2 x^2}}-\frac{3 x^4 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{16 a \sqrt{1-a^2 x^2}}-\frac{x^3 (1-a x) (a x+1) \cosh ^{-1}(a x)^3}{4 a^2 \sqrt{1-a^2 x^2}}-\frac{3 x^3 (1-a x) (a x+1) \cosh ^{-1}(a x)}{32 a^2 \sqrt{1-a^2 x^2}}-\frac{9 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{16 a^3 \sqrt{1-a^2 x^2}}-\frac{3 x (1-a x) (a x+1) \cosh ^{-1}(a x)^3}{8 a^4 \sqrt{1-a^2 x^2}}-\frac{45 x (1-a x) (a x+1) \cosh ^{-1}(a x)}{64 a^4 \sqrt{1-a^2 x^2}}+\frac{3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^4}{32 a^5 \sqrt{1-a^2 x^2}}+\frac{45 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{128 a^5 \sqrt{1-a^2 x^2}}","-\frac{45 x^2 \sqrt{a x-1}}{128 a^3 \sqrt{1-a x}}-\frac{x^3 \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^3}{4 a^2}-\frac{3 x^3 \sqrt{1-a x} \sqrt{a x+1} \cosh ^{-1}(a x)}{32 a^2}-\frac{9 x^2 \sqrt{a x-1} \cosh ^{-1}(a x)^2}{16 a^3 \sqrt{1-a x}}-\frac{3 x \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^3}{8 a^4}-\frac{45 x \sqrt{1-a x} \sqrt{a x+1} \cosh ^{-1}(a x)}{64 a^4}+\frac{3 \sqrt{a x-1} \cosh ^{-1}(a x)^4}{32 a^5 \sqrt{1-a x}}+\frac{45 \sqrt{a x-1} \cosh ^{-1}(a x)^2}{128 a^5 \sqrt{1-a x}}-\frac{3 x^4 \sqrt{a x-1}}{128 a \sqrt{1-a x}}-\frac{3 x^4 \sqrt{a x-1} \cosh ^{-1}(a x)^2}{16 a \sqrt{1-a x}}",1,"(-45*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(128*a^3*Sqrt[1 - a^2*x^2]) - (3*x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(128*a*Sqrt[1 - a^2*x^2]) - (45*x*(1 - a*x)*(1 + a*x)*ArcCosh[a*x])/(64*a^4*Sqrt[1 - a^2*x^2]) - (3*x^3*(1 - a*x)*(1 + a*x)*ArcCosh[a*x])/(32*a^2*Sqrt[1 - a^2*x^2]) + (45*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(128*a^5*Sqrt[1 - a^2*x^2]) - (9*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(16*a^3*Sqrt[1 - a^2*x^2]) - (3*x^4*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(16*a*Sqrt[1 - a^2*x^2]) - (3*x*(1 - a*x)*(1 + a*x)*ArcCosh[a*x]^3)/(8*a^4*Sqrt[1 - a^2*x^2]) - (x^3*(1 - a*x)*(1 + a*x)*ArcCosh[a*x]^3)/(4*a^2*Sqrt[1 - a^2*x^2]) + (3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^4)/(32*a^5*Sqrt[1 - a^2*x^2])","A",14,5,24,0.2083,1,"{5798, 5759, 5676, 5662, 30}"
254,1,329,0,1.0262554,"\int \frac{x^3 \cosh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^3*ArcCosh[a*x]^3)/Sqrt[1 - a^2*x^2],x]","-\frac{2 x^3 \sqrt{a x-1} \sqrt{a x+1}}{27 a \sqrt{1-a^2 x^2}}-\frac{40 x \sqrt{a x-1} \sqrt{a x+1}}{9 a^3 \sqrt{1-a^2 x^2}}-\frac{x^3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{3 a \sqrt{1-a^2 x^2}}-\frac{x^2 (1-a x) (a x+1) \cosh ^{-1}(a x)^3}{3 a^2 \sqrt{1-a^2 x^2}}-\frac{2 x^2 (1-a x) (a x+1) \cosh ^{-1}(a x)}{9 a^2 \sqrt{1-a^2 x^2}}-\frac{2 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{a^3 \sqrt{1-a^2 x^2}}-\frac{2 (1-a x) (a x+1) \cosh ^{-1}(a x)^3}{3 a^4 \sqrt{1-a^2 x^2}}-\frac{40 (1-a x) (a x+1) \cosh ^{-1}(a x)}{9 a^4 \sqrt{1-a^2 x^2}}","-\frac{x^2 \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^3}{3 a^2}-\frac{2 x^2 \sqrt{1-a x} \sqrt{a x+1} \cosh ^{-1}(a x)}{9 a^2}-\frac{2 \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^3}{3 a^4}-\frac{40 x \sqrt{a x-1}}{9 a^3 \sqrt{1-a x}}-\frac{2 x \sqrt{a x-1} \cosh ^{-1}(a x)^2}{a^3 \sqrt{1-a x}}-\frac{40 \sqrt{1-a x} \sqrt{a x+1} \cosh ^{-1}(a x)}{9 a^4}-\frac{2 x^3 \sqrt{a x-1}}{27 a \sqrt{1-a x}}-\frac{x^3 \sqrt{a x-1} \cosh ^{-1}(a x)^2}{3 a \sqrt{1-a x}}",1,"(-40*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(9*a^3*Sqrt[1 - a^2*x^2]) - (2*x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(27*a*Sqrt[1 - a^2*x^2]) - (40*(1 - a*x)*(1 + a*x)*ArcCosh[a*x])/(9*a^4*Sqrt[1 - a^2*x^2]) - (2*x^2*(1 - a*x)*(1 + a*x)*ArcCosh[a*x])/(9*a^2*Sqrt[1 - a^2*x^2]) - (2*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(a^3*Sqrt[1 - a^2*x^2]) - (x^3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(3*a*Sqrt[1 - a^2*x^2]) - (2*(1 - a*x)*(1 + a*x)*ArcCosh[a*x]^3)/(3*a^4*Sqrt[1 - a^2*x^2]) - (x^2*(1 - a*x)*(1 + a*x)*ArcCosh[a*x]^3)/(3*a^2*Sqrt[1 - a^2*x^2])","A",11,7,24,0.2917,1,"{5798, 5759, 5718, 5654, 8, 5662, 30}"
255,1,257,0,0.7653041,"\int \frac{x^2 \cosh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx","Int[(x^2*ArcCosh[a*x]^3)/Sqrt[1 - a^2*x^2],x]","-\frac{3 x^2 \sqrt{a x-1} \sqrt{a x+1}}{8 a \sqrt{1-a^2 x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^4}{8 a^3 \sqrt{1-a^2 x^2}}-\frac{x (1-a x) (a x+1) \cosh ^{-1}(a x)^3}{2 a^2 \sqrt{1-a^2 x^2}}-\frac{3 x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{4 a \sqrt{1-a^2 x^2}}+\frac{3 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{8 a^3 \sqrt{1-a^2 x^2}}-\frac{3 x (1-a x) (a x+1) \cosh ^{-1}(a x)}{4 a^2 \sqrt{1-a^2 x^2}}","-\frac{x \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^3}{2 a^2}+\frac{\sqrt{a x-1} \cosh ^{-1}(a x)^4}{8 a^3 \sqrt{1-a x}}+\frac{3 \sqrt{a x-1} \cosh ^{-1}(a x)^2}{8 a^3 \sqrt{1-a x}}-\frac{3 x \sqrt{1-a x} \sqrt{a x+1} \cosh ^{-1}(a x)}{4 a^2}-\frac{3 x^2 \sqrt{a x-1}}{8 a \sqrt{1-a x}}-\frac{3 x^2 \sqrt{a x-1} \cosh ^{-1}(a x)^2}{4 a \sqrt{1-a x}}",1,"(-3*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(8*a*Sqrt[1 - a^2*x^2]) - (3*x*(1 - a*x)*(1 + a*x)*ArcCosh[a*x])/(4*a^2*Sqrt[1 - a^2*x^2]) + (3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(8*a^3*Sqrt[1 - a^2*x^2]) - (3*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(4*a*Sqrt[1 - a^2*x^2]) - (x*(1 - a*x)*(1 + a*x)*ArcCosh[a*x]^3)/(2*a^2*Sqrt[1 - a^2*x^2]) + (Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^4)/(8*a^3*Sqrt[1 - a^2*x^2])","A",7,5,24,0.2083,1,"{5798, 5759, 5676, 5662, 30}"
256,1,153,0,0.3925368,"\int \frac{x \cosh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx","Int[(x*ArcCosh[a*x]^3)/Sqrt[1 - a^2*x^2],x]","-\frac{6 x \sqrt{a x-1} \sqrt{a x+1}}{a \sqrt{1-a^2 x^2}}-\frac{(1-a x) (a x+1) \cosh ^{-1}(a x)^3}{a^2 \sqrt{1-a^2 x^2}}-\frac{3 x \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{a \sqrt{1-a^2 x^2}}-\frac{6 (1-a x) (a x+1) \cosh ^{-1}(a x)}{a^2 \sqrt{1-a^2 x^2}}","-\frac{\sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^3}{a^2}-\frac{6 \sqrt{1-a x} \sqrt{a x+1} \cosh ^{-1}(a x)}{a^2}-\frac{6 x \sqrt{a x-1}}{a \sqrt{1-a x}}-\frac{3 x \sqrt{a x-1} \cosh ^{-1}(a x)^2}{a \sqrt{1-a x}}",1,"(-6*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a*Sqrt[1 - a^2*x^2]) - (6*(1 - a*x)*(1 + a*x)*ArcCosh[a*x])/(a^2*Sqrt[1 - a^2*x^2]) - (3*x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(a*Sqrt[1 - a^2*x^2]) - ((1 - a*x)*(1 + a*x)*ArcCosh[a*x]^3)/(a^2*Sqrt[1 - a^2*x^2])","A",5,4,22,0.1818,1,"{5798, 5718, 5654, 8}"
257,1,45,0,0.1614066,"\int \frac{\cosh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}} \, dx","Int[ArcCosh[a*x]^3/Sqrt[1 - a^2*x^2],x]","\frac{\sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^4}{4 a \sqrt{1-a^2 x^2}}","\frac{\sqrt{a x-1} \cosh ^{-1}(a x)^4}{4 a \sqrt{1-a x}}",1,"(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^4)/(4*a*Sqrt[1 - a^2*x^2])","A",2,2,21,0.09524,1,"{5713, 5676}"
258,1,356,0,0.4787426,"\int \frac{\cosh ^{-1}(a x)^3}{x \sqrt{1-a^2 x^2}} \, dx","Int[ArcCosh[a*x]^3/(x*Sqrt[1 - a^2*x^2]),x]","-\frac{3 i \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}+\frac{3 i \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}+\frac{6 i \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}-\frac{6 i \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}-\frac{6 i \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(4,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}+\frac{6 i \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(4,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}+\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}","-\frac{3 i \sqrt{a x-1} \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{3 i \sqrt{a x-1} \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{6 i \sqrt{a x-1} \cosh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}-\frac{6 i \sqrt{a x-1} \cosh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}-\frac{6 i \sqrt{a x-1} \text{PolyLog}\left(4,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{6 i \sqrt{a x-1} \text{PolyLog}\left(4,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{2 \sqrt{a x-1} \cosh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}",1,"(2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3*ArcTan[E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] - ((3*I)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2*PolyLog[2, (-I)*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] + ((3*I)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2*PolyLog[2, I*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] + ((6*I)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*PolyLog[3, (-I)*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] - ((6*I)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*PolyLog[3, I*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] - ((6*I)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[4, (-I)*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] + ((6*I)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[4, I*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2]","A",11,7,24,0.2917,1,"{5798, 5761, 4180, 2531, 6609, 2282, 6589}"
259,1,229,0,0.4920105,"\int \frac{\cosh ^{-1}(a x)^3}{x^2 \sqrt{1-a^2 x^2}} \, dx","Int[ArcCosh[a*x]^3/(x^2*Sqrt[1 - a^2*x^2]),x]","-\frac{3 a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}+\frac{3 a \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(3,-e^{2 \cosh ^{-1}(a x)}\right)}{2 \sqrt{1-a^2 x^2}}-\frac{(1-a x) (a x+1) \cosh ^{-1}(a x)^3}{x \sqrt{1-a^2 x^2}}+\frac{a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3}{\sqrt{1-a^2 x^2}}-\frac{3 a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2 \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)}{\sqrt{1-a^2 x^2}}","-\frac{3 a \sqrt{a x-1} \cosh ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{3 a \sqrt{a x-1} \text{PolyLog}\left(3,-e^{2 \cosh ^{-1}(a x)}\right)}{2 \sqrt{1-a x}}-\frac{\sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^3}{x}+\frac{a \sqrt{a x-1} \cosh ^{-1}(a x)^3}{\sqrt{1-a x}}-\frac{3 a \sqrt{a x-1} \cosh ^{-1}(a x)^2 \log \left(e^{2 \cosh ^{-1}(a x)}+1\right)}{\sqrt{1-a x}}",1,"(a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3)/Sqrt[1 - a^2*x^2] - ((1 - a*x)*(1 + a*x)*ArcCosh[a*x]^3)/(x*Sqrt[1 - a^2*x^2]) - (3*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2*Log[1 + E^(2*ArcCosh[a*x])])/Sqrt[1 - a^2*x^2] - (3*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*PolyLog[2, -E^(2*ArcCosh[a*x])])/Sqrt[1 - a^2*x^2] + (3*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[3, -E^(2*ArcCosh[a*x])])/(2*Sqrt[1 - a^2*x^2])","A",8,8,24,0.3333,1,"{5798, 5724, 5660, 3718, 2190, 2531, 2282, 6589}"
260,1,614,0,1.0133703,"\int \frac{\cosh ^{-1}(a x)^3}{x^3 \sqrt{1-a^2 x^2}} \, dx","Int[ArcCosh[a*x]^3/(x^3*Sqrt[1 - a^2*x^2]),x]","-\frac{3 i a^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)}{2 \sqrt{1-a^2 x^2}}+\frac{3 i a^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)}{2 \sqrt{1-a^2 x^2}}+\frac{3 i a^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}-\frac{3 i a^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}+\frac{3 i a^2 \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}-\frac{3 i a^2 \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}-\frac{3 i a^2 \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(4,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}+\frac{3 i a^2 \sqrt{a x-1} \sqrt{a x+1} \text{PolyLog}\left(4,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}-\frac{(1-a x) (a x+1) \cosh ^{-1}(a x)^3}{2 x^2 \sqrt{1-a^2 x^2}}+\frac{3 a \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^2}{2 x \sqrt{1-a^2 x^2}}+\frac{a^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}-\frac{6 a^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a^2 x^2}}","-\frac{3 i a^2 \sqrt{a x-1} \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)}{2 \sqrt{1-a x}}+\frac{3 i a^2 \sqrt{a x-1} \cosh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)}{2 \sqrt{1-a x}}+\frac{3 i a^2 \sqrt{a x-1} \cosh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}-\frac{3 i a^2 \sqrt{a x-1} \cosh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{3 i a^2 \sqrt{a x-1} \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}-\frac{3 i a^2 \sqrt{a x-1} \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}-\frac{3 i a^2 \sqrt{a x-1} \text{PolyLog}\left(4,-i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{3 i a^2 \sqrt{a x-1} \text{PolyLog}\left(4,i e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}-\frac{\sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^3}{2 x^2}+\frac{a^2 \sqrt{a x-1} \cosh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}-\frac{6 a^2 \sqrt{a x-1} \cosh ^{-1}(a x) \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{\sqrt{1-a x}}+\frac{3 a \sqrt{a x-1} \cosh ^{-1}(a x)^2}{2 x \sqrt{1-a x}}",1,"(3*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2)/(2*x*Sqrt[1 - a^2*x^2]) - ((1 - a*x)*(1 + a*x)*ArcCosh[a*x]^3)/(2*x^2*Sqrt[1 - a^2*x^2]) - (6*a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*ArcTan[E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] + (a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^3*ArcTan[E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] + ((3*I)*a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[2, (-I)*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] - (((3*I)/2)*a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2*PolyLog[2, (-I)*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] - ((3*I)*a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[2, I*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] + (((3*I)/2)*a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^2*PolyLog[2, I*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] + ((3*I)*a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*PolyLog[3, (-I)*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] - ((3*I)*a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*PolyLog[3, I*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] - ((3*I)*a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[4, (-I)*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2] + ((3*I)*a^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*PolyLog[4, I*E^ArcCosh[a*x]])/Sqrt[1 - a^2*x^2]","A",19,11,24,0.4583,1,"{5798, 5748, 5761, 4180, 2531, 6609, 2282, 6589, 5662, 2279, 2391}"
261,0,0,0,0.4584366,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^3}{\sqrt{1-c^2 x^2}} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x])^3)/Sqrt[1 - c^2*x^2],x]","\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^3}{\sqrt{1-c^2 x^2}} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^3}{\sqrt{1-c^2 x^2}},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][((f*x)^m*(a + b*ArcCosh[c*x])^3)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/Sqrt[1 - c^2*x^2]","A",0,0,0,0,-1,"{}"
262,1,67,0,0.1400963,"\int \frac{\left(c-a^2 c x^2\right)^3}{\cosh ^{-1}(a x)} \, dx","Int[(c - a^2*c*x^2)^3/ArcCosh[a*x],x]","\frac{35 c^3 \text{Shi}\left(\cosh ^{-1}(a x)\right)}{64 a}-\frac{21 c^3 \text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{64 a}+\frac{7 c^3 \text{Shi}\left(5 \cosh ^{-1}(a x)\right)}{64 a}-\frac{c^3 \text{Shi}\left(7 \cosh ^{-1}(a x)\right)}{64 a}","\frac{35 c^3 \text{Shi}\left(\cosh ^{-1}(a x)\right)}{64 a}-\frac{21 c^3 \text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{64 a}+\frac{7 c^3 \text{Shi}\left(5 \cosh ^{-1}(a x)\right)}{64 a}-\frac{c^3 \text{Shi}\left(7 \cosh ^{-1}(a x)\right)}{64 a}",1,"(35*c^3*SinhIntegral[ArcCosh[a*x]])/(64*a) - (21*c^3*SinhIntegral[3*ArcCosh[a*x]])/(64*a) + (7*c^3*SinhIntegral[5*ArcCosh[a*x]])/(64*a) - (c^3*SinhIntegral[7*ArcCosh[a*x]])/(64*a)","A",7,3,20,0.1500,1,"{5700, 3312, 3298}"
263,1,50,0,0.1133277,"\int \frac{\left(c-a^2 c x^2\right)^2}{\cosh ^{-1}(a x)} \, dx","Int[(c - a^2*c*x^2)^2/ArcCosh[a*x],x]","\frac{5 c^2 \text{Shi}\left(\cosh ^{-1}(a x)\right)}{8 a}-\frac{5 c^2 \text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{16 a}+\frac{c^2 \text{Shi}\left(5 \cosh ^{-1}(a x)\right)}{16 a}","\frac{5 c^2 \text{Shi}\left(\cosh ^{-1}(a x)\right)}{8 a}-\frac{5 c^2 \text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{16 a}+\frac{c^2 \text{Shi}\left(5 \cosh ^{-1}(a x)\right)}{16 a}",1,"(5*c^2*SinhIntegral[ArcCosh[a*x]])/(8*a) - (5*c^2*SinhIntegral[3*ArcCosh[a*x]])/(16*a) + (c^2*SinhIntegral[5*ArcCosh[a*x]])/(16*a)","A",6,3,20,0.1500,1,"{5700, 3312, 3298}"
264,1,29,0,0.080804,"\int \frac{c-a^2 c x^2}{\cosh ^{-1}(a x)} \, dx","Int[(c - a^2*c*x^2)/ArcCosh[a*x],x]","\frac{3 c \text{Shi}\left(\cosh ^{-1}(a x)\right)}{4 a}-\frac{c \text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{4 a}","\frac{3 c \text{Shi}\left(\cosh ^{-1}(a x)\right)}{4 a}-\frac{c \text{Shi}\left(3 \cosh ^{-1}(a x)\right)}{4 a}",1,"(3*c*SinhIntegral[ArcCosh[a*x]])/(4*a) - (c*SinhIntegral[3*ArcCosh[a*x]])/(4*a)","A",5,3,18,0.1667,1,"{5700, 3312, 3298}"
265,0,0,0,0.0332269,"\int \frac{1}{\left(c-a^2 c x^2\right) \cosh ^{-1}(a x)} \, dx","Int[1/((c - a^2*c*x^2)*ArcCosh[a*x]),x]","\int \frac{1}{\left(c-a^2 c x^2\right) \cosh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{\left(c-a^2 c x^2\right) \cosh ^{-1}(a x)},x\right)",0,"Defer[Int][1/((c - a^2*c*x^2)*ArcCosh[a*x]), x]","A",0,0,0,0,-1,"{}"
266,0,0,0,0.0316224,"\int \frac{1}{\left(c-a^2 c x^2\right)^2 \cosh ^{-1}(a x)} \, dx","Int[1/((c - a^2*c*x^2)^2*ArcCosh[a*x]),x]","\int \frac{1}{\left(c-a^2 c x^2\right)^2 \cosh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{\left(c-a^2 c x^2\right)^2 \cosh ^{-1}(a x)},x\right)",0,"Defer[Int][1/((c - a^2*c*x^2)^2*ArcCosh[a*x]), x]","A",0,0,0,0,-1,"{}"
267,1,430,0,0.8794196,"\int \frac{x^4 \sqrt{1-c^2 x^2}}{a+b \cosh ^{-1}(c x)} \, dx","Int[(x^4*Sqrt[1 - c^2*x^2])/(a + b*ArcCosh[c*x]),x]","-\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{32 b c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{16 b c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 a}{b}+6 \cosh ^{-1}(c x)\right)}{32 b c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{32 b c^5 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{16 b c^5 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 a}{b}+6 \cosh ^{-1}(c x)\right)}{32 b c^5 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \log \left(a+b \cosh ^{-1}(c x)\right)}{16 b c^5 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{\sqrt{1-c x} \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c^5 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c^5 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c^5 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c^5 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c^5 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c^5 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \log \left(a+b \cosh ^{-1}(c x)\right)}{16 b c^5 \sqrt{c x-1}}",1,"-(Sqrt[1 - c^2*x^2]*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(32*b*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(16*b*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(6*a)/b]*CoshIntegral[(6*a)/b + 6*ArcCosh[c*x]])/(32*b*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Log[a + b*ArcCosh[c*x]])/(16*b*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(32*b*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(16*b*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(6*a)/b]*SinhIntegral[(6*a)/b + 6*ArcCosh[c*x]])/(32*b*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",13,6,28,0.2143,1,"{5798, 5781, 5448, 3303, 3298, 3301}"
268,1,371,0,0.8609354,"\int \frac{x^3 \sqrt{1-c^2 x^2}}{a+b \cosh ^{-1}(c x)} \, dx","Int[(x^3*Sqrt[1 - c^2*x^2])/(a + b*ArcCosh[c*x]),x]","-\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{8 b c^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{16 b c^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{16 b c^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{8 b c^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{16 b c^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{16 b c^4 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{\sqrt{1-c x} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b c^4 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c^4 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c^4 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b c^4 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c^4 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c^4 \sqrt{c x-1}}",1,"-(Sqrt[1 - c^2*x^2]*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(8*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(16*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(16*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(8*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(16*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(16*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",13,6,28,0.2143,1,"{5798, 5781, 5448, 3303, 3298, 3301}"
269,1,178,0,0.6716735,"\int \frac{x^2 \sqrt{1-c^2 x^2}}{a+b \cosh ^{-1}(c x)} \, dx","Int[(x^2*Sqrt[1 - c^2*x^2])/(a + b*ArcCosh[c*x]),x]","\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{8 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{8 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \log \left(a+b \cosh ^{-1}(c x)\right)}{8 b c^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{\sqrt{1-c x} \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 b c^3 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 b c^3 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \log \left(a+b \cosh ^{-1}(c x)\right)}{8 b c^3 \sqrt{c x-1}}",1,"(Sqrt[1 - c^2*x^2]*Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(8*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Log[a + b*ArcCosh[c*x]])/(8*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(8*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",7,6,28,0.2143,1,"{5798, 5781, 5448, 3303, 3298, 3301}"
270,1,245,0,0.5716374,"\int \frac{x \sqrt{1-c^2 x^2}}{a+b \cosh ^{-1}(c x)} \, dx","Int[(x*Sqrt[1 - c^2*x^2])/(a + b*ArcCosh[c*x]),x]","-\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b c^2 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{\sqrt{1-c x} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b c^2 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b c^2 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b c^2 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b c^2 \sqrt{c x-1}}",1,"-(Sqrt[1 - c^2*x^2]*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(4*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(4*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(4*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(4*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",10,6,26,0.2308,1,"{5798, 5781, 5448, 3303, 3298, 3301}"
271,1,178,0,0.3433713,"\int \frac{\sqrt{1-c^2 x^2}}{a+b \cosh ^{-1}(c x)} \, dx","Int[Sqrt[1 - c^2*x^2]/(a + b*ArcCosh[c*x]),x]","\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \log \left(a+b \cosh ^{-1}(c x)\right)}{2 b c \sqrt{c x-1} \sqrt{c x+1}}","\frac{\sqrt{1-c x} \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b c \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b c \sqrt{c x-1}}-\frac{\sqrt{1-c x} \log \left(a+b \cosh ^{-1}(c x)\right)}{2 b c \sqrt{c x-1}}",1,"(Sqrt[1 - c^2*x^2]*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(2*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Log[a + b*ArcCosh[c*x]])/(2*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(2*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",7,6,25,0.2400,1,"{5713, 5701, 3312, 3303, 3298, 3301}"
272,0,0,0,1.0770319,"\int \frac{\sqrt{1-c^2 x^2}}{x \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[Sqrt[1 - c^2*x^2]/(x*(a + b*ArcCosh[c*x])),x]","\int \frac{\sqrt{1-c^2 x^2}}{x \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)-\frac{\sqrt{c x-1} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b \sqrt{1-c x}}+\frac{\sqrt{c x-1} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b \sqrt{1-c x}}",0,"(Sqrt[1 - c^2*x^2]*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Defer[Int][1/(x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
273,0,0,0,0.9305625,"\int \frac{\sqrt{1-c^2 x^2}}{x^2 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[Sqrt[1 - c^2*x^2]/(x^2*(a + b*ArcCosh[c*x])),x]","\int \frac{\sqrt{1-c^2 x^2}}{x^2 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)-\frac{c \sqrt{c x-1} \log \left(a+b \cosh ^{-1}(c x)\right)}{b \sqrt{1-c x}}",0,"(c*Sqrt[1 - c^2*x^2]*Log[a + b*ArcCosh[c*x]])/(b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Defer[Int][1/(x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
274,0,0,0,0.4473234,"\int \frac{\sqrt{1-c^2 x^2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[Sqrt[1 - c^2*x^2]/(x^3*(a + b*ArcCosh[c*x])),x]","\int \frac{\sqrt{1-c^2 x^2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\sqrt{1-c^2 x^2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"(Sqrt[1 - c^2*x^2]*Defer[Int][(Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(x^3*(a + b*ArcCosh[c*x])), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
275,0,0,0,0.4379651,"\int \frac{\sqrt{1-c^2 x^2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[Sqrt[1 - c^2*x^2]/(x^4*(a + b*ArcCosh[c*x])),x]","\int \frac{\sqrt{1-c^2 x^2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\sqrt{1-c^2 x^2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"(Sqrt[1 - c^2*x^2]*Defer[Int][(Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(x^4*(a + b*ArcCosh[c*x])), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
276,1,497,0,0.945604,"\int \frac{x^3 \left(1-c^2 x^2\right)^{3/2}}{a+b \cosh ^{-1}(c x)} \, dx","Int[(x^3*(1 - c^2*x^2)^(3/2))/(a + b*ArcCosh[c*x]),x]","-\frac{3 \sqrt{1-c^2 x^2} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{64 b c^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 \sqrt{1-c^2 x^2} \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{64 b c^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{64 b c^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 a}{b}+7 \cosh ^{-1}(c x)\right)}{64 b c^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 \sqrt{1-c^2 x^2} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{64 b c^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 \sqrt{1-c^2 x^2} \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{64 b c^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{64 b c^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 a}{b}+7 \cosh ^{-1}(c x)\right)}{64 b c^4 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{3 \sqrt{1-c x} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{64 b c^4 \sqrt{c x-1}}+\frac{3 \sqrt{1-c x} \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b c^4 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b c^4 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \cosh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b c^4 \sqrt{c x-1}}+\frac{3 \sqrt{1-c x} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{64 b c^4 \sqrt{c x-1}}-\frac{3 \sqrt{1-c x} \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b c^4 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b c^4 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \sinh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b c^4 \sqrt{c x-1}}",1,"(-3*Sqrt[1 - c^2*x^2]*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(64*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*Sqrt[1 - c^2*x^2]*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(64*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(64*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Cosh[(7*a)/b]*CoshIntegral[(7*a)/b + 7*ArcCosh[c*x]])/(64*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*Sqrt[1 - c^2*x^2]*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(64*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*Sqrt[1 - c^2*x^2]*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(64*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(64*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Sinh[(7*a)/b]*SinhIntegral[(7*a)/b + 7*ArcCosh[c*x]])/(64*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",16,6,28,0.2143,1,"{5798, 5781, 5448, 3303, 3298, 3301}"
277,1,430,0,0.8813941,"\int \frac{x^2 \left(1-c^2 x^2\right)^{3/2}}{a+b \cosh ^{-1}(c x)} \, dx","Int[(x^2*(1 - c^2*x^2)^(3/2))/(a + b*ArcCosh[c*x]),x]","\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{32 b c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{16 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 a}{b}+6 \cosh ^{-1}(c x)\right)}{32 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{32 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{16 b c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 a}{b}+6 \cosh ^{-1}(c x)\right)}{32 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \log \left(a+b \cosh ^{-1}(c x)\right)}{16 b c^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{\sqrt{1-c x} \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c^3 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c^3 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \cosh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c^3 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c^3 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c^3 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \sinh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c^3 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \log \left(a+b \cosh ^{-1}(c x)\right)}{16 b c^3 \sqrt{c x-1}}",1,"(Sqrt[1 - c^2*x^2]*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(32*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(16*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Cosh[(6*a)/b]*CoshIntegral[(6*a)/b + 6*ArcCosh[c*x]])/(32*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Log[a + b*ArcCosh[c*x]])/(16*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(32*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(16*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Sinh[(6*a)/b]*SinhIntegral[(6*a)/b + 6*ArcCosh[c*x]])/(32*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",13,6,28,0.2143,1,"{5798, 5781, 5448, 3303, 3298, 3301}"
278,1,371,0,0.6753415,"\int \frac{x \left(1-c^2 x^2\right)^{3/2}}{a+b \cosh ^{-1}(c x)} \, dx","Int[(x*(1 - c^2*x^2)^(3/2))/(a + b*ArcCosh[c*x]),x]","-\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{8 b c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 \sqrt{1-c^2 x^2} \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{16 b c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{16 b c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{8 b c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 \sqrt{1-c^2 x^2} \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{16 b c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{16 b c^2 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{\sqrt{1-c x} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b c^2 \sqrt{c x-1}}+\frac{3 \sqrt{1-c x} \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c^2 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c^2 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b c^2 \sqrt{c x-1}}-\frac{3 \sqrt{1-c x} \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c^2 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c^2 \sqrt{c x-1}}",1,"-(Sqrt[1 - c^2*x^2]*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(8*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*Sqrt[1 - c^2*x^2]*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(16*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(16*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(8*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*Sqrt[1 - c^2*x^2]*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(16*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(16*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",13,6,26,0.2308,1,"{5798, 5781, 5448, 3303, 3298, 3301}"
279,1,304,0,0.458781,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{a+b \cosh ^{-1}(c x)} \, dx","Int[(1 - c^2*x^2)^(3/2)/(a + b*ArcCosh[c*x]),x]","\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{8 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{8 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 \sqrt{1-c^2 x^2} \log \left(a+b \cosh ^{-1}(c x)\right)}{8 b c \sqrt{c x-1} \sqrt{c x+1}}","\frac{\sqrt{1-c x} \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b c \sqrt{c x-1}}-\frac{\sqrt{1-c x} \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 b c \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b c \sqrt{c x-1}}+\frac{\sqrt{1-c x} \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 b c \sqrt{c x-1}}-\frac{3 \sqrt{1-c x} \log \left(a+b \cosh ^{-1}(c x)\right)}{8 b c \sqrt{c x-1}}",1,"(Sqrt[1 - c^2*x^2]*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(2*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(8*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*Sqrt[1 - c^2*x^2]*Log[a + b*ArcCosh[c*x]])/(8*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(2*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(8*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",10,6,25,0.2400,1,"{5713, 5701, 3312, 3303, 3298, 3301}"
280,0,0,0,1.7516687,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[(1 - c^2*x^2)^(3/2)/(x*(a + b*ArcCosh[c*x])),x]","\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)-\frac{5 \sqrt{c x-1} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b \sqrt{1-c x}}+\frac{\sqrt{c x-1} \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b \sqrt{1-c x}}+\frac{5 \sqrt{c x-1} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b \sqrt{1-c x}}-\frac{\sqrt{c x-1} \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b \sqrt{1-c x}}",0,"(5*Sqrt[1 - c^2*x^2]*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(4*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(4*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*Sqrt[1 - c^2*x^2]*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(4*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(4*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Defer[Int][1/(x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
281,0,0,0,1.5250499,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^2 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[(1 - c^2*x^2)^(3/2)/(x^2*(a + b*ArcCosh[c*x])),x]","\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^2 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)+\frac{c \sqrt{c x-1} \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b \sqrt{1-c x}}-\frac{c \sqrt{c x-1} \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b \sqrt{1-c x}}-\frac{3 c \sqrt{c x-1} \log \left(a+b \cosh ^{-1}(c x)\right)}{2 b \sqrt{1-c x}}",0,"-(c*Sqrt[1 - c^2*x^2]*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(2*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*c*Sqrt[1 - c^2*x^2]*Log[a + b*ArcCosh[c*x]])/(2*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (c*Sqrt[1 - c^2*x^2]*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(2*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Defer[Int][1/(x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
282,0,0,0,0.5253982,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[(1 - c^2*x^2)^(3/2)/(x^3*(a + b*ArcCosh[c*x])),x]","\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{3/2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"-((Sqrt[1 - c^2*x^2]*Defer[Int][((-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(x^3*(a + b*ArcCosh[c*x])), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]))","A",0,0,0,0,-1,"{}"
283,0,0,0,0.5393998,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[(1 - c^2*x^2)^(3/2)/(x^4*(a + b*ArcCosh[c*x])),x]","\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{3/2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"-((Sqrt[1 - c^2*x^2]*Defer[Int][((-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(x^4*(a + b*ArcCosh[c*x])), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]))","A",0,0,0,0,-1,"{}"
284,1,497,0,0.9968481,"\int \frac{x^3 \left(1-c^2 x^2\right)^{5/2}}{a+b \cosh ^{-1}(c x)} \, dx","Int[(x^3*(1 - c^2*x^2)^(5/2))/(a + b*ArcCosh[c*x]),x]","-\frac{3 \sqrt{1-c^2 x^2} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{128 b c^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{32 b c^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 \sqrt{1-c^2 x^2} \cosh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 a}{b}+7 \cosh ^{-1}(c x)\right)}{256 b c^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{9 a}{b}\right) \text{Chi}\left(\frac{9 a}{b}+9 \cosh ^{-1}(c x)\right)}{256 b c^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 \sqrt{1-c^2 x^2} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{128 b c^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{32 b c^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 \sqrt{1-c^2 x^2} \sinh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 a}{b}+7 \cosh ^{-1}(c x)\right)}{256 b c^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{9 a}{b}\right) \text{Shi}\left(\frac{9 a}{b}+9 \cosh ^{-1}(c x)\right)}{256 b c^4 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{3 \sqrt{1-c x} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{128 b c^4 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c^4 \sqrt{c x-1}}-\frac{3 \sqrt{1-c x} \cosh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{256 b c^4 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{9 a}{b}\right) \text{Chi}\left(\frac{9 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{256 b c^4 \sqrt{c x-1}}+\frac{3 \sqrt{1-c x} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{128 b c^4 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c^4 \sqrt{c x-1}}+\frac{3 \sqrt{1-c x} \sinh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{256 b c^4 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{9 a}{b}\right) \text{Shi}\left(\frac{9 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{256 b c^4 \sqrt{c x-1}}",1,"(-3*Sqrt[1 - c^2*x^2]*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(128*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(32*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*Sqrt[1 - c^2*x^2]*Cosh[(7*a)/b]*CoshIntegral[(7*a)/b + 7*ArcCosh[c*x]])/(256*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(9*a)/b]*CoshIntegral[(9*a)/b + 9*ArcCosh[c*x]])/(256*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*Sqrt[1 - c^2*x^2]*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(128*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(32*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*Sqrt[1 - c^2*x^2]*Sinh[(7*a)/b]*SinhIntegral[(7*a)/b + 7*ArcCosh[c*x]])/(256*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(9*a)/b]*SinhIntegral[(9*a)/b + 9*ArcCosh[c*x]])/(256*b*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",16,6,28,0.2143,1,"{5798, 5781, 5448, 3303, 3298, 3301}"
285,1,556,0,0.9790513,"\int \frac{x^2 \left(1-c^2 x^2\right)^{5/2}}{a+b \cosh ^{-1}(c x)} \, dx","Int[(x^2*(1 - c^2*x^2)^(5/2))/(a + b*ArcCosh[c*x]),x]","\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{32 b c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{32 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 a}{b}+6 \cosh ^{-1}(c x)\right)}{32 b c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{8 a}{b}\right) \text{Chi}\left(\frac{8 a}{b}+8 \cosh ^{-1}(c x)\right)}{128 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{32 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{32 b c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 a}{b}+6 \cosh ^{-1}(c x)\right)}{32 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{8 a}{b}\right) \text{Shi}\left(\frac{8 a}{b}+8 \cosh ^{-1}(c x)\right)}{128 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 \sqrt{1-c^2 x^2} \log \left(a+b \cosh ^{-1}(c x)\right)}{128 b c^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{\sqrt{1-c x} \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c^3 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c^3 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \cosh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c^3 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{8 a}{b}\right) \text{Chi}\left(\frac{8 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{128 b c^3 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c^3 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c^3 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \sinh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c^3 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{8 a}{b}\right) \text{Shi}\left(\frac{8 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{128 b c^3 \sqrt{c x-1}}-\frac{5 \sqrt{1-c x} \log \left(a+b \cosh ^{-1}(c x)\right)}{128 b c^3 \sqrt{c x-1}}",1,"(Sqrt[1 - c^2*x^2]*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(32*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(32*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Cosh[(6*a)/b]*CoshIntegral[(6*a)/b + 6*ArcCosh[c*x]])/(32*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(8*a)/b]*CoshIntegral[(8*a)/b + 8*ArcCosh[c*x]])/(128*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*Sqrt[1 - c^2*x^2]*Log[a + b*ArcCosh[c*x]])/(128*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(32*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(32*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Sinh[(6*a)/b]*SinhIntegral[(6*a)/b + 6*ArcCosh[c*x]])/(32*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(8*a)/b]*SinhIntegral[(8*a)/b + 8*ArcCosh[c*x]])/(128*b*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",16,6,28,0.2143,1,"{5798, 5781, 5448, 3303, 3298, 3301}"
286,1,497,0,0.7910209,"\int \frac{x \left(1-c^2 x^2\right)^{5/2}}{a+b \cosh ^{-1}(c x)} \, dx","Int[(x*(1 - c^2*x^2)^(5/2))/(a + b*ArcCosh[c*x]),x]","-\frac{5 \sqrt{1-c^2 x^2} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{64 b c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{9 \sqrt{1-c^2 x^2} \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{64 b c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 \sqrt{1-c^2 x^2} \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{64 b c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 a}{b}+7 \cosh ^{-1}(c x)\right)}{64 b c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 \sqrt{1-c^2 x^2} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{64 b c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{9 \sqrt{1-c^2 x^2} \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{64 b c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 \sqrt{1-c^2 x^2} \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{64 b c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 a}{b}+7 \cosh ^{-1}(c x)\right)}{64 b c^2 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{5 \sqrt{1-c x} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{64 b c^2 \sqrt{c x-1}}+\frac{9 \sqrt{1-c x} \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b c^2 \sqrt{c x-1}}-\frac{5 \sqrt{1-c x} \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b c^2 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b c^2 \sqrt{c x-1}}+\frac{5 \sqrt{1-c x} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{64 b c^2 \sqrt{c x-1}}-\frac{9 \sqrt{1-c x} \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b c^2 \sqrt{c x-1}}+\frac{5 \sqrt{1-c x} \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b c^2 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b c^2 \sqrt{c x-1}}",1,"(-5*Sqrt[1 - c^2*x^2]*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(64*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (9*Sqrt[1 - c^2*x^2]*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(64*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*Sqrt[1 - c^2*x^2]*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(64*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(7*a)/b]*CoshIntegral[(7*a)/b + 7*ArcCosh[c*x]])/(64*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*Sqrt[1 - c^2*x^2]*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(64*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (9*Sqrt[1 - c^2*x^2]*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(64*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*Sqrt[1 - c^2*x^2]*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(64*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(7*a)/b]*SinhIntegral[(7*a)/b + 7*ArcCosh[c*x]])/(64*b*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",16,6,26,0.2308,1,"{5798, 5781, 5448, 3303, 3298, 3301}"
287,1,430,0,0.568075,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{a+b \cosh ^{-1}(c x)} \, dx","Int[(1 - c^2*x^2)^(5/2)/(a + b*ArcCosh[c*x]),x]","\frac{15 \sqrt{1-c^2 x^2} \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{32 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 \sqrt{1-c^2 x^2} \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{16 b c \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 a}{b}+6 \cosh ^{-1}(c x)\right)}{32 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{15 \sqrt{1-c^2 x^2} \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{32 b c \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 \sqrt{1-c^2 x^2} \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{16 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 a}{b}+6 \cosh ^{-1}(c x)\right)}{32 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 \sqrt{1-c^2 x^2} \log \left(a+b \cosh ^{-1}(c x)\right)}{16 b c \sqrt{c x-1} \sqrt{c x+1}}","\frac{15 \sqrt{1-c x} \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c \sqrt{c x-1}}-\frac{3 \sqrt{1-c x} \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c \sqrt{c x-1}}-\frac{15 \sqrt{1-c x} \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c \sqrt{c x-1}}+\frac{3 \sqrt{1-c x} \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 b c \sqrt{c x-1}}-\frac{5 \sqrt{1-c x} \log \left(a+b \cosh ^{-1}(c x)\right)}{16 b c \sqrt{c x-1}}",1,"(15*Sqrt[1 - c^2*x^2]*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(32*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*Sqrt[1 - c^2*x^2]*Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(16*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(6*a)/b]*CoshIntegral[(6*a)/b + 6*ArcCosh[c*x]])/(32*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*Sqrt[1 - c^2*x^2]*Log[a + b*ArcCosh[c*x]])/(16*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (15*Sqrt[1 - c^2*x^2]*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(32*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*Sqrt[1 - c^2*x^2]*Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(16*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(6*a)/b]*SinhIntegral[(6*a)/b + 6*ArcCosh[c*x]])/(32*b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",13,6,25,0.2400,1,"{5713, 5701, 3312, 3303, 3298, 3301}"
288,0,0,0,2.3761364,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[(1 - c^2*x^2)^(5/2)/(x*(a + b*ArcCosh[c*x])),x]","\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)-\frac{11 \sqrt{c x-1} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b \sqrt{1-c x}}+\frac{7 \sqrt{c x-1} \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b \sqrt{1-c x}}-\frac{\sqrt{c x-1} \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b \sqrt{1-c x}}+\frac{11 \sqrt{c x-1} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b \sqrt{1-c x}}-\frac{7 \sqrt{c x-1} \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b \sqrt{1-c x}}+\frac{\sqrt{c x-1} \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b \sqrt{1-c x}}",0,"(11*Sqrt[1 - c^2*x^2]*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(8*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (7*Sqrt[1 - c^2*x^2]*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(16*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(16*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (11*Sqrt[1 - c^2*x^2]*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(8*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (7*Sqrt[1 - c^2*x^2]*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(16*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(16*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Defer[Int][1/(x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
289,0,0,0,2.0930265,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^2 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[(1 - c^2*x^2)^(5/2)/(x^2*(a + b*ArcCosh[c*x])),x]","\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^2 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)+\frac{c \sqrt{c x-1} \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b \sqrt{1-c x}}-\frac{c \sqrt{c x-1} \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 b \sqrt{1-c x}}-\frac{c \sqrt{c x-1} \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b \sqrt{1-c x}}+\frac{c \sqrt{c x-1} \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 b \sqrt{1-c x}}-\frac{15 c \sqrt{c x-1} \log \left(a+b \cosh ^{-1}(c x)\right)}{8 b \sqrt{1-c x}}",0,"-((c*Sqrt[1 - c^2*x^2]*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(b*Sqrt[-1 + c*x]*Sqrt[1 + c*x])) + (c*Sqrt[1 - c^2*x^2]*Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(8*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (15*c*Sqrt[1 - c^2*x^2]*Log[a + b*ArcCosh[c*x]])/(8*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (c*Sqrt[1 - c^2*x^2]*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (c*Sqrt[1 - c^2*x^2]*Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(8*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Defer[Int][1/(x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
290,0,0,0,0.5461646,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[(1 - c^2*x^2)^(5/2)/(x^3*(a + b*ArcCosh[c*x])),x]","\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{5/2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"(Sqrt[1 - c^2*x^2]*Defer[Int][((-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(x^3*(a + b*ArcCosh[c*x])), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
291,0,0,0,0.551468,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[(1 - c^2*x^2)^(5/2)/(x^4*(a + b*ArcCosh[c*x])),x]","\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{5/2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"(Sqrt[1 - c^2*x^2]*Defer[Int][((-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(x^4*(a + b*ArcCosh[c*x])), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
292,1,137,0,0.4658726,"\int \frac{x^4}{\sqrt{1-a^2 x^2} \cosh ^{-1}(a x)} \, dx","Int[x^4/(Sqrt[1 - a^2*x^2]*ArcCosh[a*x]),x]","\frac{\sqrt{a x-1} \sqrt{a x+1} \text{Chi}\left(2 \cosh ^{-1}(a x)\right)}{2 a^5 \sqrt{1-a^2 x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \text{Chi}\left(4 \cosh ^{-1}(a x)\right)}{8 a^5 \sqrt{1-a^2 x^2}}+\frac{3 \sqrt{a x-1} \sqrt{a x+1} \log \left(\cosh ^{-1}(a x)\right)}{8 a^5 \sqrt{1-a^2 x^2}}","\frac{\sqrt{a x-1} \text{Chi}\left(2 \cosh ^{-1}(a x)\right)}{2 a^5 \sqrt{1-a x}}+\frac{\sqrt{a x-1} \text{Chi}\left(4 \cosh ^{-1}(a x)\right)}{8 a^5 \sqrt{1-a x}}+\frac{3 \sqrt{a x-1} \log \left(\cosh ^{-1}(a x)\right)}{8 a^5 \sqrt{1-a x}}",1,"(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*CoshIntegral[2*ArcCosh[a*x]])/(2*a^5*Sqrt[1 - a^2*x^2]) + (Sqrt[-1 + a*x]*Sqrt[1 + a*x]*CoshIntegral[4*ArcCosh[a*x]])/(8*a^5*Sqrt[1 - a^2*x^2]) + (3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Log[ArcCosh[a*x]])/(8*a^5*Sqrt[1 - a^2*x^2])","A",6,4,24,0.1667,1,"{5798, 5781, 3312, 3301}"
293,1,91,0,0.4504742,"\int \frac{x^3}{\sqrt{1-a^2 x^2} \cosh ^{-1}(a x)} \, dx","Int[x^3/(Sqrt[1 - a^2*x^2]*ArcCosh[a*x]),x]","\frac{3 \sqrt{a x-1} \sqrt{a x+1} \text{Chi}\left(\cosh ^{-1}(a x)\right)}{4 a^4 \sqrt{1-a^2 x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{4 a^4 \sqrt{1-a^2 x^2}}","\frac{3 \sqrt{a x-1} \text{Chi}\left(\cosh ^{-1}(a x)\right)}{4 a^4 \sqrt{1-a x}}+\frac{\sqrt{a x-1} \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{4 a^4 \sqrt{1-a x}}",1,"(3*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*CoshIntegral[ArcCosh[a*x]])/(4*a^4*Sqrt[1 - a^2*x^2]) + (Sqrt[-1 + a*x]*Sqrt[1 + a*x]*CoshIntegral[3*ArcCosh[a*x]])/(4*a^4*Sqrt[1 - a^2*x^2])","A",6,4,24,0.1667,1,"{5798, 5781, 3312, 3301}"
294,1,91,0,0.4339892,"\int \frac{x^2}{\sqrt{1-a^2 x^2} \cosh ^{-1}(a x)} \, dx","Int[x^2/(Sqrt[1 - a^2*x^2]*ArcCosh[a*x]),x]","\frac{\sqrt{a x-1} \sqrt{a x+1} \text{Chi}\left(2 \cosh ^{-1}(a x)\right)}{2 a^3 \sqrt{1-a^2 x^2}}+\frac{\sqrt{a x-1} \sqrt{a x+1} \log \left(\cosh ^{-1}(a x)\right)}{2 a^3 \sqrt{1-a^2 x^2}}","\frac{\sqrt{a x-1} \text{Chi}\left(2 \cosh ^{-1}(a x)\right)}{2 a^3 \sqrt{1-a x}}+\frac{\sqrt{a x-1} \log \left(\cosh ^{-1}(a x)\right)}{2 a^3 \sqrt{1-a x}}",1,"(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*CoshIntegral[2*ArcCosh[a*x]])/(2*a^3*Sqrt[1 - a^2*x^2]) + (Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Log[ArcCosh[a*x]])/(2*a^3*Sqrt[1 - a^2*x^2])","A",5,4,24,0.1667,1,"{5798, 5781, 3312, 3301}"
295,1,41,0,0.3005947,"\int \frac{x}{\sqrt{1-a^2 x^2} \cosh ^{-1}(a x)} \, dx","Int[x/(Sqrt[1 - a^2*x^2]*ArcCosh[a*x]),x]","\frac{\sqrt{a x-1} \sqrt{a x+1} \text{Chi}\left(\cosh ^{-1}(a x)\right)}{a^2 \sqrt{1-a^2 x^2}}","\frac{\sqrt{a x-1} \text{Chi}\left(\cosh ^{-1}(a x)\right)}{a^2 \sqrt{1-a x}}",1,"(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*CoshIntegral[ArcCosh[a*x]])/(a^2*Sqrt[1 - a^2*x^2])","A",3,3,22,0.1364,1,"{5798, 5781, 3301}"
296,1,41,0,0.1624253,"\int \frac{1}{\sqrt{1-a^2 x^2} \cosh ^{-1}(a x)} \, dx","Int[1/(Sqrt[1 - a^2*x^2]*ArcCosh[a*x]),x]","\frac{\sqrt{a x-1} \sqrt{a x+1} \log \left(\cosh ^{-1}(a x)\right)}{a \sqrt{1-a^2 x^2}}","\frac{\sqrt{a x-1} \log \left(\cosh ^{-1}(a x)\right)}{a \sqrt{1-a x}}",1,"(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Log[ArcCosh[a*x]])/(a*Sqrt[1 - a^2*x^2])","A",2,2,21,0.09524,1,"{5713, 5674}"
297,0,0,0,0.3781797,"\int \frac{1}{x \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)} \, dx","Int[1/(x*Sqrt[1 - a^2*x^2]*ArcCosh[a*x]),x]","\int \frac{1}{x \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)},x\right)",0,"(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Defer[Int][1/(x*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]), x])/Sqrt[1 - a^2*x^2]","A",0,0,0,0,-1,"{}"
298,0,0,0,0.3770711,"\int \frac{1}{x^2 \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)} \, dx","Int[1/(x^2*Sqrt[1 - a^2*x^2]*ArcCosh[a*x]),x]","\int \frac{1}{x^2 \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)},x\right)",0,"(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Defer[Int][1/(x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]), x])/Sqrt[1 - a^2*x^2]","A",0,0,0,0,-1,"{}"
299,1,245,0,0.6899443,"\int \frac{x^3}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[x^3/(Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])),x]","\frac{3 \sqrt{c x-1} \sqrt{c x+1} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^4 \sqrt{1-c^2 x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b c^4 \sqrt{1-c^2 x^2}}-\frac{3 \sqrt{c x-1} \sqrt{c x+1} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^4 \sqrt{1-c^2 x^2}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b c^4 \sqrt{1-c^2 x^2}}","\frac{3 \sqrt{c x-1} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b c^4 \sqrt{1-c x}}+\frac{\sqrt{c x-1} \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b c^4 \sqrt{1-c x}}-\frac{3 \sqrt{c x-1} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b c^4 \sqrt{1-c x}}-\frac{\sqrt{c x-1} \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b c^4 \sqrt{1-c x}}",1,"(3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(4*b*c^4*Sqrt[1 - c^2*x^2]) + (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(4*b*c^4*Sqrt[1 - c^2*x^2]) - (3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(4*b*c^4*Sqrt[1 - c^2*x^2]) - (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(4*b*c^4*Sqrt[1 - c^2*x^2])","A",10,6,28,0.2143,1,"{5798, 5781, 3312, 3303, 3298, 3301}"
300,1,178,0,0.6318255,"\int \frac{x^2}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[x^2/(Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])),x]","\frac{\sqrt{c x-1} \sqrt{c x+1} \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c^3 \sqrt{1-c^2 x^2}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c^3 \sqrt{1-c^2 x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \log \left(a+b \cosh ^{-1}(c x)\right)}{2 b c^3 \sqrt{1-c^2 x^2}}","\frac{\sqrt{c x-1} \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b c^3 \sqrt{1-c x}}-\frac{\sqrt{c x-1} \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b c^3 \sqrt{1-c x}}+\frac{\sqrt{c x-1} \log \left(a+b \cosh ^{-1}(c x)\right)}{2 b c^3 \sqrt{1-c x}}",1,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(2*b*c^3*Sqrt[1 - c^2*x^2]) + (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[a + b*ArcCosh[c*x]])/(2*b*c^3*Sqrt[1 - c^2*x^2]) - (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(2*b*c^3*Sqrt[1 - c^2*x^2])","A",7,6,28,0.2143,1,"{5798, 5781, 3312, 3303, 3298, 3301}"
301,1,114,0,0.4259268,"\int \frac{x}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[x/(Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])),x]","\frac{\sqrt{c x-1} \sqrt{c x+1} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c^2 \sqrt{1-c^2 x^2}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c^2 \sqrt{1-c^2 x^2}}","\frac{\sqrt{c x-1} \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b c^2 \sqrt{1-c x}}-\frac{\sqrt{c x-1} \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b c^2 \sqrt{1-c x}}",1,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(b*c^2*Sqrt[1 - c^2*x^2]) - (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(b*c^2*Sqrt[1 - c^2*x^2])","A",5,5,26,0.1923,1,"{5798, 5781, 3303, 3298, 3301}"
302,1,48,0,0.2205791,"\int \frac{1}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[1/(Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])),x]","\frac{\sqrt{c x-1} \sqrt{c x+1} \log \left(a+b \cosh ^{-1}(c x)\right)}{b c \sqrt{1-c^2 x^2}}","\frac{\sqrt{c x-1} \log \left(a+b \cosh ^{-1}(c x)\right)}{b c \sqrt{1-c x}}",1,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Log[a + b*ArcCosh[c*x]])/(b*c*Sqrt[1 - c^2*x^2])","A",2,2,25,0.08000,1,"{5713, 5674}"
303,0,0,0,0.49831,"\int \frac{1}{x \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[1/(x*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])),x]","\int \frac{1}{x \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][1/(x*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,"{}"
304,0,0,0,0.5073938,"\int \frac{1}{x^2 \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[1/(x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])),x]","\int \frac{1}{x^2 \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][1/(x^2*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,"{}"
305,0,0,0,0.5753803,"\int \frac{x^2}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[x^2/((1 - c^2*x^2)^(3/2)*(a + b*ArcCosh[c*x])),x]","\int \frac{x^2}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{x^2}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][x^2/((-1 + c*x)^(3/2)*(1 + c*x)^(3/2)*(a + b*ArcCosh[c*x])), x])/Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
306,0,0,0,0.4014723,"\int \frac{x}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[x/((1 - c^2*x^2)^(3/2)*(a + b*ArcCosh[c*x])),x]","\int \frac{x}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{x}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][x/((-1 + c*x)^(3/2)*(1 + c*x)^(3/2)*(a + b*ArcCosh[c*x])), x])/Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
307,0,0,0,0.249598,"\int \frac{1}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[1/((1 - c^2*x^2)^(3/2)*(a + b*ArcCosh[c*x])),x]","\int \frac{1}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][1/((-1 + c*x)^(3/2)*(1 + c*x)^(3/2)*(a + b*ArcCosh[c*x])), x])/Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
308,0,0,0,0.5675044,"\int \frac{1}{x \left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[1/(x*(1 - c^2*x^2)^(3/2)*(a + b*ArcCosh[c*x])),x]","\int \frac{1}{x \left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][1/(x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)*(a + b*ArcCosh[c*x])), x])/Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
309,0,0,0,0.5767666,"\int \frac{1}{x^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[1/(x^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcCosh[c*x])),x]","\int \frac{1}{x^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][1/(x^2*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)*(a + b*ArcCosh[c*x])), x])/Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
310,0,0,0,0.5399409,"\int \frac{x^m \left(1-c^2 x^2\right)^{3/2}}{a+b \cosh ^{-1}(c x)} \, dx","Int[(x^m*(1 - c^2*x^2)^(3/2))/(a + b*ArcCosh[c*x]),x]","\int \frac{x^m \left(1-c^2 x^2\right)^{3/2}}{a+b \cosh ^{-1}(c x)} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{3/2} x^m}{a+b \cosh ^{-1}(c x)},x\right)",0,"-((Sqrt[1 - c^2*x^2]*Defer[Int][(x^m*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(a + b*ArcCosh[c*x]), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]))","A",0,0,0,0,-1,"{}"
311,0,0,0,0.4509332,"\int \frac{x^m \sqrt{1-c^2 x^2}}{a+b \cosh ^{-1}(c x)} \, dx","Int[(x^m*Sqrt[1 - c^2*x^2])/(a + b*ArcCosh[c*x]),x]","\int \frac{x^m \sqrt{1-c^2 x^2}}{a+b \cosh ^{-1}(c x)} \, dx","\text{Int}\left(\frac{\sqrt{1-c^2 x^2} x^m}{a+b \cosh ^{-1}(c x)},x\right)",0,"(Sqrt[1 - c^2*x^2]*Defer[Int][(x^m*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(a + b*ArcCosh[c*x]), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
312,0,0,0,0.4827969,"\int \frac{x^m}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[x^m/(Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])),x]","\int \frac{x^m}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{x^m}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][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,"{}"
313,0,0,0,0.5654055,"\int \frac{x^m}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[x^m/((1 - c^2*x^2)^(3/2)*(a + b*ArcCosh[c*x])),x]","\int \frac{x^m}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{x^m}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][x^m/((-1 + c*x)^(3/2)*(1 + c*x)^(3/2)*(a + b*ArcCosh[c*x])), x])/Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
314,0,0,0,0.5799294,"\int \frac{x^m}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[x^m/((1 - c^2*x^2)^(5/2)*(a + b*ArcCosh[c*x])),x]","\int \frac{x^m}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{x^m}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][x^m/((-1 + c*x)^(5/2)*(1 + c*x)^(5/2)*(a + b*ArcCosh[c*x])), x])/Sqrt[1 - c^2*x^2]","A",0,0,0,0,-1,"{}"
315,1,98,0,0.3250857,"\int \frac{\left(c-a^2 c x^2\right)^3}{\cosh ^{-1}(a x)^2} \, dx","Int[(c - a^2*c*x^2)^3/ArcCosh[a*x]^2,x]","\frac{35 c^3 \text{Chi}\left(\cosh ^{-1}(a x)\right)}{64 a}-\frac{63 c^3 \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{64 a}+\frac{35 c^3 \text{Chi}\left(5 \cosh ^{-1}(a x)\right)}{64 a}-\frac{7 c^3 \text{Chi}\left(7 \cosh ^{-1}(a x)\right)}{64 a}+\frac{c^3 (a x-1)^{7/2} (a x+1)^{7/2}}{a \cosh ^{-1}(a x)}","\frac{35 c^3 \text{Chi}\left(\cosh ^{-1}(a x)\right)}{64 a}-\frac{63 c^3 \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{64 a}+\frac{35 c^3 \text{Chi}\left(5 \cosh ^{-1}(a x)\right)}{64 a}-\frac{7 c^3 \text{Chi}\left(7 \cosh ^{-1}(a x)\right)}{64 a}+\frac{c^3 (a x-1)^{7/2} (a x+1)^{7/2}}{a \cosh ^{-1}(a x)}",1,"(c^3*(-1 + a*x)^(7/2)*(1 + a*x)^(7/2))/(a*ArcCosh[a*x]) + (35*c^3*CoshIntegral[ArcCosh[a*x]])/(64*a) - (63*c^3*CoshIntegral[3*ArcCosh[a*x]])/(64*a) + (35*c^3*CoshIntegral[5*ArcCosh[a*x]])/(64*a) - (7*c^3*CoshIntegral[7*ArcCosh[a*x]])/(64*a)","A",8,4,20,0.2000,1,"{5695, 5781, 5448, 3301}"
316,1,82,0,0.3050469,"\int \frac{\left(c-a^2 c x^2\right)^2}{\cosh ^{-1}(a x)^2} \, dx","Int[(c - a^2*c*x^2)^2/ArcCosh[a*x]^2,x]","\frac{5 c^2 \text{Chi}\left(\cosh ^{-1}(a x)\right)}{8 a}-\frac{15 c^2 \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{16 a}+\frac{5 c^2 \text{Chi}\left(5 \cosh ^{-1}(a x)\right)}{16 a}-\frac{c^2 (a x-1)^{5/2} (a x+1)^{5/2}}{a \cosh ^{-1}(a x)}","\frac{5 c^2 \text{Chi}\left(\cosh ^{-1}(a x)\right)}{8 a}-\frac{15 c^2 \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{16 a}+\frac{5 c^2 \text{Chi}\left(5 \cosh ^{-1}(a x)\right)}{16 a}-\frac{c^2 (a x-1)^{5/2} (a x+1)^{5/2}}{a \cosh ^{-1}(a x)}",1,"-((c^2*(-1 + a*x)^(5/2)*(1 + a*x)^(5/2))/(a*ArcCosh[a*x])) + (5*c^2*CoshIntegral[ArcCosh[a*x]])/(8*a) - (15*c^2*CoshIntegral[3*ArcCosh[a*x]])/(16*a) + (5*c^2*CoshIntegral[5*ArcCosh[a*x]])/(16*a)","A",7,4,20,0.2000,1,"{5695, 5781, 5448, 3301}"
317,1,58,0,0.2352042,"\int \frac{c-a^2 c x^2}{\cosh ^{-1}(a x)^2} \, dx","Int[(c - a^2*c*x^2)/ArcCosh[a*x]^2,x]","\frac{3 c \text{Chi}\left(\cosh ^{-1}(a x)\right)}{4 a}-\frac{3 c \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{4 a}+\frac{c (a x-1)^{3/2} (a x+1)^{3/2}}{a \cosh ^{-1}(a x)}","\frac{3 c \text{Chi}\left(\cosh ^{-1}(a x)\right)}{4 a}-\frac{3 c \text{Chi}\left(3 \cosh ^{-1}(a x)\right)}{4 a}+\frac{c (a x-1)^{3/2} (a x+1)^{3/2}}{a \cosh ^{-1}(a x)}",1,"(c*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2))/(a*ArcCosh[a*x]) + (3*c*CoshIntegral[ArcCosh[a*x]])/(4*a) - (3*c*CoshIntegral[3*ArcCosh[a*x]])/(4*a)","A",6,4,18,0.2222,1,"{5695, 5781, 5448, 3301}"
318,0,0,0,0.2458978,"\int \frac{1}{\left(c-a^2 c x^2\right) \cosh ^{-1}(a x)^2} \, dx","Int[1/((c - a^2*c*x^2)*ArcCosh[a*x]^2),x]","\int \frac{1}{\left(c-a^2 c x^2\right) \cosh ^{-1}(a x)^2} \, dx","\frac{a \text{Int}\left(\frac{x}{(a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)},x\right)}{c}+\frac{1}{a c \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}",0,"1/(a*c*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]) + (a*Defer[Int][x/((-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*ArcCosh[a*x]), x])/c","A",0,0,0,0,-1,"{}"
319,0,0,0,0.2538279,"\int \frac{1}{\left(c-a^2 c x^2\right)^2 \cosh ^{-1}(a x)^2} \, dx","Int[1/((c - a^2*c*x^2)^2*ArcCosh[a*x]^2),x]","\int \frac{1}{\left(c-a^2 c x^2\right)^2 \cosh ^{-1}(a x)^2} \, dx","-\frac{3 a \text{Int}\left(\frac{x}{(a x-1)^{5/2} (a x+1)^{5/2} \cosh ^{-1}(a x)},x\right)}{c^2}-\frac{1}{a c^2 (a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)}",0,"-(1/(a*c^2*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*ArcCosh[a*x])) - (3*a*Defer[Int][x/((-1 + a*x)^(5/2)*(1 + a*x)^(5/2)*ArcCosh[a*x]), x])/c^2","A",0,0,0,0,-1,"{}"
320,1,429,0,1.0849329,"\int \frac{x^3 \sqrt{1-c^2 x^2}}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(x^3*Sqrt[1 - c^2*x^2])/(a + b*ArcCosh[c*x])^2,x]","\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{8 b^2 c^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 \sqrt{1-c^2 x^2} \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{16 b^2 c^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 \sqrt{1-c^2 x^2} \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{16 b^2 c^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{8 b^2 c^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 \sqrt{1-c^2 x^2} \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{16 b^2 c^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 \sqrt{1-c^2 x^2} \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{16 b^2 c^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{x^3 (1-c x) \sqrt{c x+1} \sqrt{1-c^2 x^2}}{b c \sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)}","\frac{\sqrt{1-c x} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b^2 c^4 \sqrt{c x-1}}-\frac{3 \sqrt{1-c x} \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^4 \sqrt{c x-1}}-\frac{5 \sqrt{1-c x} \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^4 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b^2 c^4 \sqrt{c x-1}}+\frac{3 \sqrt{1-c x} \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^4 \sqrt{c x-1}}+\frac{5 \sqrt{1-c x} \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^4 \sqrt{c x-1}}-\frac{x^3 \sqrt{c x-1} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{b c \left(a+b \cosh ^{-1}(c x)\right)}",1,"(x^3*(1 - c*x)*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) + (Sqrt[1 - c^2*x^2]*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b])/(8*b^2*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*Sqrt[1 - c^2*x^2]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]]*Sinh[(3*a)/b])/(16*b^2*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*Sqrt[1 - c^2*x^2]*CoshIntegral[(5*a)/b + 5*ArcCosh[c*x]]*Sinh[(5*a)/b])/(16*b^2*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(8*b^2*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*Sqrt[1 - c^2*x^2]*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(16*b^2*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*Sqrt[1 - c^2*x^2]*Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(16*b^2*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",23,7,28,0.2500,1,"{5798, 5778, 5670, 5448, 3303, 3298, 3301}"
321,1,185,0,0.878566,"\int \frac{x^2 \sqrt{1-c^2 x^2}}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(x^2*Sqrt[1 - c^2*x^2])/(a + b*ArcCosh[c*x])^2,x]","-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{2 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{2 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{x^2 (1-c x) \sqrt{c x+1} \sqrt{1-c^2 x^2}}{b c \sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)}","-\frac{\sqrt{1-c x} \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^3 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^3 \sqrt{c x-1}}-\frac{x^2 \sqrt{c x-1} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{b c \left(a+b \cosh ^{-1}(c x)\right)}",1,"(x^2*(1 - c*x)*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) - (Sqrt[1 - c^2*x^2]*CoshIntegral[(4*a)/b + 4*ArcCosh[c*x]]*Sinh[(4*a)/b])/(2*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(2*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",17,8,28,0.2857,1,"{5798, 5778, 5670, 5448, 12, 3303, 3298, 3301}"
322,1,418,0,0.6887785,"\int \frac{x \sqrt{1-c^2 x^2}}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(x*Sqrt[1 - c^2*x^2])/(a + b*ArcCosh[c*x])^2,x]","-\frac{3 \sqrt{1-c^2 x^2} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 \sqrt{1-c^2 x^2} \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 \sqrt{1-c^2 x^2} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 \sqrt{1-c^2 x^2} \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{x \sqrt{c x+1} \sqrt{1-c^2 x^2} (1-c x)}{b c \sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)}","\frac{\sqrt{1-c x} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b^2 c^2 \sqrt{c x-1}}-\frac{3 \sqrt{1-c x} \sinh \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^2 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b^2 c^2 \sqrt{c x-1}}+\frac{3 \sqrt{1-c x} \cosh \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^2 \sqrt{c x-1}}-\frac{x \sqrt{c x-1} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{b c \left(a+b \cosh ^{-1}(c x)\right)}",1,"(x*(1 - c*x)*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) - (3*Sqrt[1 - c^2*x^2]*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b])/(4*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*CoshIntegral[(a + b*ArcCosh[c*x])/b]*Sinh[a/b])/(b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*Sqrt[1 - c^2*x^2]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]]*Sinh[(3*a)/b])/(4*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*Sqrt[1 - c^2*x^2]*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(4*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*Sqrt[1 - c^2*x^2]*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(4*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Cosh[a/b]*SinhIntegral[(a + b*ArcCosh[c*x])/b])/(b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",15,8,26,0.3077,1,"{5798, 5778, 5658, 3303, 3298, 3301, 5670, 5448}"
323,1,177,0,0.3351758,"\int \frac{\sqrt{1-c^2 x^2}}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[1 - c^2*x^2]/(a + b*ArcCosh[c*x])^2,x]","-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b^2 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b^2 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{c x+1} \sqrt{1-c^2 x^2} (1-c x)}{b c \sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)}","-\frac{\sqrt{1-c x} \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b^2 c \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b^2 c \sqrt{c x-1}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{b c \left(a+b \cosh ^{-1}(c x)\right)}",1,"((1 - c*x)*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) - (Sqrt[1 - c^2*x^2]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]]*Sinh[(2*a)/b])/(b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",8,8,25,0.3200,1,"{5713, 5697, 5670, 5448, 12, 3303, 3298, 3301}"
324,0,0,0,0.5703318,"\int \frac{\sqrt{1-c^2 x^2}}{x \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[1 - c^2*x^2]/(x*(a + b*ArcCosh[c*x])^2),x]","\int \frac{\sqrt{1-c^2 x^2}}{x \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\frac{\sqrt{1-c x} \text{Int}\left(\frac{1}{x^2 \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{b c \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 \sqrt{c x-1}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{b c x \left(a+b \cosh ^{-1}(c x)\right)}",0,"((1 - c*x)*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(b*c*x*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) - (Sqrt[1 - c^2*x^2]*CoshIntegral[(a + b*ArcCosh[c*x])/b]*Sinh[a/b])/(b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[a/b]*SinhIntegral[(a + b*ArcCosh[c*x])/b])/(b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Defer[Int][1/(x^2*(a + b*ArcCosh[c*x])), x])/(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
325,0,0,0,0.4934881,"\int \frac{\sqrt{1-c^2 x^2}}{x^2 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[1 - c^2*x^2]/(x^2*(a + b*ArcCosh[c*x])^2),x]","\int \frac{\sqrt{1-c^2 x^2}}{x^2 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\frac{2 \sqrt{1-c x} \text{Int}\left(\frac{1}{x^3 \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{b c \sqrt{c x-1}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \sqrt{1-c^2 x^2}}{b c x^2 \left(a+b \cosh ^{-1}(c x)\right)}",0,"((1 - c*x)*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2])/(b*c*x^2*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) + (2*Sqrt[1 - c^2*x^2]*Defer[Int][1/(x^3*(a + b*ArcCosh[c*x])), x])/(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
326,0,0,0,0.4607936,"\int \frac{\sqrt{1-c^2 x^2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[1 - c^2*x^2]/(x^3*(a + b*ArcCosh[c*x])^2),x]","\int \frac{\sqrt{1-c^2 x^2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{1-c^2 x^2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"(Sqrt[1 - c^2*x^2]*Defer[Int][(Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(x^3*(a + b*ArcCosh[c*x])^2), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
327,0,0,0,0.4560949,"\int \frac{\sqrt{1-c^2 x^2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[1 - c^2*x^2]/(x^4*(a + b*ArcCosh[c*x])^2),x]","\int \frac{\sqrt{1-c^2 x^2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{1-c^2 x^2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"(Sqrt[1 - c^2*x^2]*Defer[Int][(Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(x^4*(a + b*ArcCosh[c*x])^2), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
328,1,439,0,1.135408,"\int \frac{x^2 \left(1-c^2 x^2\right)^{3/2}}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(x^2*(1 - c^2*x^2)^(3/2))/(a + b*ArcCosh[c*x])^2,x]","-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{16 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{4 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 \sqrt{1-c^2 x^2} \sinh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 a}{b}+6 \cosh ^{-1}(c x)\right)}{16 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{16 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{4 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 \sqrt{1-c^2 x^2} \cosh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 a}{b}+6 \cosh ^{-1}(c x)\right)}{16 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{x^2 (c x+1)^{3/2} \sqrt{1-c^2 x^2} (1-c x)^2}{b c \sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)}","-\frac{\sqrt{1-c x} \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^3 \sqrt{c x-1}}+\frac{3 \sqrt{1-c x} \sinh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^3 \sqrt{c x-1}}-\frac{3 \sqrt{1-c x} \cosh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3 \sqrt{c x-1}}-\frac{x^2 \sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)^{3/2}}{b c \left(a+b \cosh ^{-1}(c x)\right)}",1,"(x^2*(1 - c*x)^2*(1 + c*x)^(3/2)*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) - (Sqrt[1 - c^2*x^2]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]]*Sinh[(2*a)/b])/(16*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*CoshIntegral[(4*a)/b + 4*ArcCosh[c*x]]*Sinh[(4*a)/b])/(4*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*Sqrt[1 - c^2*x^2]*CoshIntegral[(6*a)/b + 6*ArcCosh[c*x]]*Sinh[(6*a)/b])/(16*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(16*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(4*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*Sqrt[1 - c^2*x^2]*Cosh[(6*a)/b]*SinhIntegral[(6*a)/b + 6*ArcCosh[c*x]])/(16*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",20,7,28,0.2500,1,"{5798, 5778, 5780, 5448, 3303, 3298, 3301}"
329,1,429,0,1.0555393,"\int \frac{x \left(1-c^2 x^2\right)^{3/2}}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(x*(1 - c^2*x^2)^(3/2))/(a + b*ArcCosh[c*x])^2,x]","\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{8 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{9 \sqrt{1-c^2 x^2} \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{16 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 \sqrt{1-c^2 x^2} \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{16 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{8 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{9 \sqrt{1-c^2 x^2} \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{16 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 \sqrt{1-c^2 x^2} \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{16 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{x (c x+1)^{3/2} \sqrt{1-c^2 x^2} (1-c x)^2}{b c \sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)}","\frac{\sqrt{1-c x} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b^2 c^2 \sqrt{c x-1}}-\frac{9 \sqrt{1-c x} \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^2 \sqrt{c x-1}}+\frac{5 \sqrt{1-c x} \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^2 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b^2 c^2 \sqrt{c x-1}}+\frac{9 \sqrt{1-c x} \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^2 \sqrt{c x-1}}-\frac{5 \sqrt{1-c x} \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^2 \sqrt{c x-1}}-\frac{x \sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)^{3/2}}{b c \left(a+b \cosh ^{-1}(c x)\right)}",1,"(x*(1 - c*x)^2*(1 + c*x)^(3/2)*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) + (Sqrt[1 - c^2*x^2]*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b])/(8*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (9*Sqrt[1 - c^2*x^2]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]]*Sinh[(3*a)/b])/(16*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*Sqrt[1 - c^2*x^2]*CoshIntegral[(5*a)/b + 5*ArcCosh[c*x]]*Sinh[(5*a)/b])/(16*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(8*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (9*Sqrt[1 - c^2*x^2]*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(16*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*Sqrt[1 - c^2*x^2]*Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(16*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",23,9,26,0.3462,1,"{5798, 5778, 5700, 3312, 3303, 3298, 3301, 5780, 5448}"
330,1,305,0,0.5238205,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(3/2)/(a + b*ArcCosh[c*x])^2,x]","-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b^2 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{2 b^2 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b^2 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{2 b^2 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{(c x+1)^{3/2} \sqrt{1-c^2 x^2} (1-c x)^2}{b c \sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)}","-\frac{\sqrt{1-c x} \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b^2 c \sqrt{c x-1}}+\frac{\sqrt{1-c x} \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b^2 c \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b^2 c \sqrt{c x-1}}-\frac{\sqrt{1-c x} \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b^2 c \sqrt{c x-1}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)^{3/2}}{b c \left(a+b \cosh ^{-1}(c x)\right)}",1,"((1 - c*x)^2*(1 + c*x)^(3/2)*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) - (Sqrt[1 - c^2*x^2]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]]*Sinh[(2*a)/b])/(b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*CoshIntegral[(4*a)/b + 4*ArcCosh[c*x]]*Sinh[(4*a)/b])/(2*b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(2*b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",11,7,25,0.2800,1,"{5713, 5697, 5780, 5448, 3303, 3298, 3301}"
331,0,0,0,0.8718801,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(3/2)/(x*(a + b*ArcCosh[c*x])^2),x]","\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","-\frac{\sqrt{1-c x} \text{Int}\left(\frac{c^2 x^2-1}{x^2 \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{b c \sqrt{c x-1}}-\frac{9 \sqrt{1-c x} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b^2 \sqrt{c x-1}}+\frac{3 \sqrt{1-c x} \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b^2 \sqrt{c x-1}}+\frac{9 \sqrt{1-c x} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b^2 \sqrt{c x-1}}-\frac{3 \sqrt{1-c x} \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b^2 \sqrt{c x-1}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)^{3/2}}{b c x \left(a+b \cosh ^{-1}(c x)\right)}",0,"((1 - c*x)^2*(1 + c*x)^(3/2)*Sqrt[1 - c^2*x^2])/(b*c*x*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) - (9*Sqrt[1 - c^2*x^2]*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b])/(4*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*Sqrt[1 - c^2*x^2]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]]*Sinh[(3*a)/b])/(4*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (9*Sqrt[1 - c^2*x^2]*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(4*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*Sqrt[1 - c^2*x^2]*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(4*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*Defer[Int][(-1 + c^2*x^2)/(x^2*(a + b*ArcCosh[c*x])), x])/(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
332,0,0,0,0.6618316,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^2 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(3/2)/(x^2*(a + b*ArcCosh[c*x])^2),x]","\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^2 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","-\frac{2 \sqrt{1-c x} \text{Int}\left(\frac{c^2 x^2-1}{x^3 \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{b c \sqrt{c x-1}}-\frac{2 c \sqrt{1-c x} \text{Int}\left(\frac{c^2 x^2-1}{x \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{b \sqrt{c x-1}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)^{3/2}}{b c x^2 \left(a+b \cosh ^{-1}(c x)\right)}",0,"((1 - c*x)^2*(1 + c*x)^(3/2)*Sqrt[1 - c^2*x^2])/(b*c*x^2*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) - (2*Sqrt[1 - c^2*x^2]*Defer[Int][(-1 + c^2*x^2)/(x^3*(a + b*ArcCosh[c*x])), x])/(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*c*Sqrt[1 - c^2*x^2]*Defer[Int][(-1 + c^2*x^2)/(x*(a + b*ArcCosh[c*x])), x])/(b*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
333,0,0,0,0.5418502,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(3/2)/(x^3*(a + b*ArcCosh[c*x])^2),x]","\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{3/2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"-((Sqrt[1 - c^2*x^2]*Defer[Int][((-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(x^3*(a + b*ArcCosh[c*x])^2), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]))","A",0,0,0,0,-1,"{}"
334,0,0,0,0.6117478,"\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(3/2)/(x^4*(a + b*ArcCosh[c*x])^2),x]","\int \frac{\left(1-c^2 x^2\right)^{3/2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","-\frac{4 \sqrt{1-c x} \text{Int}\left(\frac{c^2 x^2-1}{x^5 \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{b c \sqrt{c x-1}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)^{3/2}}{b c x^4 \left(a+b \cosh ^{-1}(c x)\right)}",0,"((1 - c*x)^2*(1 + c*x)^(3/2)*Sqrt[1 - c^2*x^2])/(b*c*x^4*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) - (4*Sqrt[1 - c^2*x^2]*Defer[Int][(-1 + c^2*x^2)/(x^5*(a + b*ArcCosh[c*x])), x])/(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
335,1,565,0,1.5146629,"\int \frac{x^2 \left(1-c^2 x^2\right)^{5/2}}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(x^2*(1 - c^2*x^2)^(5/2))/(a + b*ArcCosh[c*x])^2,x]","-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{16 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{8 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 \sqrt{1-c^2 x^2} \sinh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 a}{b}+6 \cosh ^{-1}(c x)\right)}{16 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{1-c^2 x^2} \sinh \left(\frac{8 a}{b}\right) \text{Chi}\left(\frac{8 a}{b}+8 \cosh ^{-1}(c x)\right)}{16 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{16 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{8 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 \sqrt{1-c^2 x^2} \cosh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 a}{b}+6 \cosh ^{-1}(c x)\right)}{16 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{\sqrt{1-c^2 x^2} \cosh \left(\frac{8 a}{b}\right) \text{Shi}\left(\frac{8 a}{b}+8 \cosh ^{-1}(c x)\right)}{16 b^2 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{x^2 (c x+1)^{5/2} \sqrt{1-c^2 x^2} (1-c x)^3}{b c \sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)}","-\frac{\sqrt{1-c x} \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 b^2 c^3 \sqrt{c x-1}}+\frac{3 \sqrt{1-c x} \sinh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3 \sqrt{c x-1}}-\frac{\sqrt{1-c x} \sinh \left(\frac{8 a}{b}\right) \text{Chi}\left(\frac{8 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 b^2 c^3 \sqrt{c x-1}}-\frac{3 \sqrt{1-c x} \cosh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3 \sqrt{c x-1}}+\frac{\sqrt{1-c x} \cosh \left(\frac{8 a}{b}\right) \text{Shi}\left(\frac{8 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3 \sqrt{c x-1}}-\frac{x^2 \sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)^{5/2}}{b c \left(a+b \cosh ^{-1}(c x)\right)}",1,"(x^2*(1 - c*x)^3*(1 + c*x)^(5/2)*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) - (Sqrt[1 - c^2*x^2]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]]*Sinh[(2*a)/b])/(16*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*CoshIntegral[(4*a)/b + 4*ArcCosh[c*x]]*Sinh[(4*a)/b])/(8*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*Sqrt[1 - c^2*x^2]*CoshIntegral[(6*a)/b + 6*ArcCosh[c*x]]*Sinh[(6*a)/b])/(16*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[1 - c^2*x^2]*CoshIntegral[(8*a)/b + 8*ArcCosh[c*x]]*Sinh[(8*a)/b])/(16*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(16*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(8*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*Sqrt[1 - c^2*x^2]*Cosh[(6*a)/b]*SinhIntegral[(6*a)/b + 6*ArcCosh[c*x]])/(16*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Cosh[(8*a)/b]*SinhIntegral[(8*a)/b + 8*ArcCosh[c*x]])/(16*b^2*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",29,7,28,0.2500,1,"{5798, 5778, 5780, 5448, 3303, 3298, 3301}"
336,1,555,0,1.3307122,"\int \frac{x \left(1-c^2 x^2\right)^{5/2}}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(x*(1 - c^2*x^2)^(5/2))/(a + b*ArcCosh[c*x])^2,x]","\frac{5 \sqrt{1-c^2 x^2} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{64 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{27 \sqrt{1-c^2 x^2} \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{64 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{25 \sqrt{1-c^2 x^2} \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{64 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{7 \sqrt{1-c^2 x^2} \sinh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 a}{b}+7 \cosh ^{-1}(c x)\right)}{64 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 \sqrt{1-c^2 x^2} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{64 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{27 \sqrt{1-c^2 x^2} \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{64 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{25 \sqrt{1-c^2 x^2} \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{64 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{7 \sqrt{1-c^2 x^2} \cosh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 a}{b}+7 \cosh ^{-1}(c x)\right)}{64 b^2 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{x (c x+1)^{5/2} \sqrt{1-c^2 x^2} (1-c x)^3}{b c \sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)}","\frac{5 \sqrt{1-c x} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{64 b^2 c^2 \sqrt{c x-1}}-\frac{27 \sqrt{1-c x} \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2 \sqrt{c x-1}}+\frac{25 \sqrt{1-c x} \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2 \sqrt{c x-1}}-\frac{7 \sqrt{1-c x} \sinh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2 \sqrt{c x-1}}-\frac{5 \sqrt{1-c x} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{64 b^2 c^2 \sqrt{c x-1}}+\frac{27 \sqrt{1-c x} \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2 \sqrt{c x-1}}-\frac{25 \sqrt{1-c x} \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2 \sqrt{c x-1}}+\frac{7 \sqrt{1-c x} \cosh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2 \sqrt{c x-1}}-\frac{x \sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)^{5/2}}{b c \left(a+b \cosh ^{-1}(c x)\right)}",1,"(x*(1 - c*x)^3*(1 + c*x)^(5/2)*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) + (5*Sqrt[1 - c^2*x^2]*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b])/(64*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (27*Sqrt[1 - c^2*x^2]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]]*Sinh[(3*a)/b])/(64*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (25*Sqrt[1 - c^2*x^2]*CoshIntegral[(5*a)/b + 5*ArcCosh[c*x]]*Sinh[(5*a)/b])/(64*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (7*Sqrt[1 - c^2*x^2]*CoshIntegral[(7*a)/b + 7*ArcCosh[c*x]]*Sinh[(7*a)/b])/(64*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*Sqrt[1 - c^2*x^2]*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(64*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (27*Sqrt[1 - c^2*x^2]*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(64*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (25*Sqrt[1 - c^2*x^2]*Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(64*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (7*Sqrt[1 - c^2*x^2]*Cosh[(7*a)/b]*SinhIntegral[(7*a)/b + 7*ArcCosh[c*x]])/(64*b^2*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",29,9,26,0.3462,1,"{5798, 5778, 5700, 3312, 3303, 3298, 3301, 5780, 5448}"
337,1,436,0,0.6518289,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(5/2)/(a + b*ArcCosh[c*x])^2,x]","-\frac{15 \sqrt{1-c^2 x^2} \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{16 b^2 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 \sqrt{1-c^2 x^2} \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{4 b^2 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 \sqrt{1-c^2 x^2} \sinh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 a}{b}+6 \cosh ^{-1}(c x)\right)}{16 b^2 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{15 \sqrt{1-c^2 x^2} \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{16 b^2 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 \sqrt{1-c^2 x^2} \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{4 b^2 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 \sqrt{1-c^2 x^2} \cosh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 a}{b}+6 \cosh ^{-1}(c x)\right)}{16 b^2 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{(c x+1)^{5/2} \sqrt{1-c^2 x^2} (1-c x)^3}{b c \sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)}","-\frac{15 \sqrt{1-c x} \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c \sqrt{c x-1}}+\frac{3 \sqrt{1-c x} \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c \sqrt{c x-1}}-\frac{3 \sqrt{1-c x} \sinh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c \sqrt{c x-1}}+\frac{15 \sqrt{1-c x} \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c \sqrt{c x-1}}-\frac{3 \sqrt{1-c x} \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c \sqrt{c x-1}}+\frac{3 \sqrt{1-c x} \cosh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c \sqrt{c x-1}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)^{5/2}}{b c \left(a+b \cosh ^{-1}(c x)\right)}",1,"((1 - c*x)^3*(1 + c*x)^(5/2)*Sqrt[1 - c^2*x^2])/(b*c*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) - (15*Sqrt[1 - c^2*x^2]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]]*Sinh[(2*a)/b])/(16*b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*Sqrt[1 - c^2*x^2]*CoshIntegral[(4*a)/b + 4*ArcCosh[c*x]]*Sinh[(4*a)/b])/(4*b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*Sqrt[1 - c^2*x^2]*CoshIntegral[(6*a)/b + 6*ArcCosh[c*x]]*Sinh[(6*a)/b])/(16*b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (15*Sqrt[1 - c^2*x^2]*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(16*b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*Sqrt[1 - c^2*x^2]*Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(4*b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*Sqrt[1 - c^2*x^2]*Cosh[(6*a)/b]*SinhIntegral[(6*a)/b + 6*ArcCosh[c*x]])/(16*b^2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",14,7,25,0.2800,1,"{5713, 5697, 5780, 5448, 3303, 3298, 3301}"
338,0,0,0,0.9849969,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(5/2)/(x*(a + b*ArcCosh[c*x])^2),x]","\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\frac{\sqrt{1-c x} \text{Int}\left(\frac{\left(c^2 x^2-1\right)^2}{x^2 \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{b c \sqrt{c x-1}}-\frac{25 \sqrt{1-c x} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b^2 \sqrt{c x-1}}+\frac{25 \sqrt{1-c x} \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 \sqrt{c x-1}}-\frac{5 \sqrt{1-c x} \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 \sqrt{c x-1}}+\frac{25 \sqrt{1-c x} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b^2 \sqrt{c x-1}}-\frac{25 \sqrt{1-c x} \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 \sqrt{c x-1}}+\frac{5 \sqrt{1-c x} \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 \sqrt{c x-1}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)^{5/2}}{b c x \left(a+b \cosh ^{-1}(c x)\right)}",0,"((1 - c*x)^3*(1 + c*x)^(5/2)*Sqrt[1 - c^2*x^2])/(b*c*x*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) - (25*Sqrt[1 - c^2*x^2]*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b])/(8*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (25*Sqrt[1 - c^2*x^2]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]]*Sinh[(3*a)/b])/(16*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (5*Sqrt[1 - c^2*x^2]*CoshIntegral[(5*a)/b + 5*ArcCosh[c*x]]*Sinh[(5*a)/b])/(16*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (25*Sqrt[1 - c^2*x^2]*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(8*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (25*Sqrt[1 - c^2*x^2]*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(16*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*Sqrt[1 - c^2*x^2]*Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(16*b^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[1 - c^2*x^2]*Defer[Int][(-1 + c^2*x^2)^2/(x^2*(a + b*ArcCosh[c*x])), x])/(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
339,0,0,0,0.7117715,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^2 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(5/2)/(x^2*(a + b*ArcCosh[c*x])^2),x]","\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^2 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\frac{2 \sqrt{1-c x} \text{Int}\left(\frac{\left(c^2 x^2-1\right)^2}{x^3 \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{b c \sqrt{c x-1}}+\frac{4 c \sqrt{1-c x} \text{Int}\left(\frac{\left(c^2 x^2-1\right)^2}{x \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{b \sqrt{c x-1}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)^{5/2}}{b c x^2 \left(a+b \cosh ^{-1}(c x)\right)}",0,"((1 - c*x)^3*(1 + c*x)^(5/2)*Sqrt[1 - c^2*x^2])/(b*c*x^2*Sqrt[-1 + c*x]*(a + b*ArcCosh[c*x])) + (2*Sqrt[1 - c^2*x^2]*Defer[Int][(-1 + c^2*x^2)^2/(x^3*(a + b*ArcCosh[c*x])), x])/(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (4*c*Sqrt[1 - c^2*x^2]*Defer[Int][(-1 + c^2*x^2)^2/(x*(a + b*ArcCosh[c*x])), x])/(b*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
340,0,0,0,0.529828,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(5/2)/(x^3*(a + b*ArcCosh[c*x])^2),x]","\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{5/2}}{x^3 \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"(Sqrt[1 - c^2*x^2]*Defer[Int][((-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(x^3*(a + b*ArcCosh[c*x])^2), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
341,0,0,0,0.5256278,"\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(1 - c^2*x^2)^(5/2)/(x^4*(a + b*ArcCosh[c*x])^2),x]","\int \frac{\left(1-c^2 x^2\right)^{5/2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{5/2}}{x^4 \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"(Sqrt[1 - c^2*x^2]*Defer[Int][((-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(x^4*(a + b*ArcCosh[c*x])^2), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
342,1,424,0,0.8603578,"\int \frac{x^5}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[x^5/(Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])^2),x]","-\frac{5 \sqrt{c x-1} \sqrt{c x+1} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{8 b^2 c^6 \sqrt{1-c^2 x^2}}-\frac{15 \sqrt{c x-1} \sqrt{c x+1} \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{16 b^2 c^6 \sqrt{1-c^2 x^2}}-\frac{5 \sqrt{c x-1} \sqrt{c x+1} \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{16 b^2 c^6 \sqrt{1-c^2 x^2}}+\frac{5 \sqrt{c x-1} \sqrt{c x+1} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{8 b^2 c^6 \sqrt{1-c^2 x^2}}+\frac{15 \sqrt{c x-1} \sqrt{c x+1} \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{16 b^2 c^6 \sqrt{1-c^2 x^2}}+\frac{5 \sqrt{c x-1} \sqrt{c x+1} \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{16 b^2 c^6 \sqrt{1-c^2 x^2}}-\frac{x^5 \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)}","-\frac{5 \sqrt{c x-1} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b^2 c^6 \sqrt{1-c x}}-\frac{15 \sqrt{c x-1} \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^6 \sqrt{1-c x}}-\frac{5 \sqrt{c x-1} \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^6 \sqrt{1-c x}}+\frac{5 \sqrt{c x-1} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b^2 c^6 \sqrt{1-c x}}+\frac{15 \sqrt{c x-1} \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^6 \sqrt{1-c x}}+\frac{5 \sqrt{c x-1} \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^6 \sqrt{1-c x}}-\frac{x^5 \sqrt{c x-1}}{b c \sqrt{1-c x} \left(a+b \cosh ^{-1}(c x)\right)}",1,"-((x^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x]))) - (5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b])/(8*b^2*c^6*Sqrt[1 - c^2*x^2]) - (15*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]]*Sinh[(3*a)/b])/(16*b^2*c^6*Sqrt[1 - c^2*x^2]) - (5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*CoshIntegral[(5*a)/b + 5*ArcCosh[c*x]]*Sinh[(5*a)/b])/(16*b^2*c^6*Sqrt[1 - c^2*x^2]) + (5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(8*b^2*c^6*Sqrt[1 - c^2*x^2]) + (15*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(16*b^2*c^6*Sqrt[1 - c^2*x^2]) + (5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(16*b^2*c^6*Sqrt[1 - c^2*x^2])","A",14,7,28,0.2500,1,"{5798, 5775, 5670, 5448, 3303, 3298, 3301}"
343,1,301,0,0.7865369,"\int \frac{x^4}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[x^4/(Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])^2),x]","-\frac{\sqrt{c x-1} \sqrt{c x+1} \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b^2 c^5 \sqrt{1-c^2 x^2}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{2 b^2 c^5 \sqrt{1-c^2 x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b^2 c^5 \sqrt{1-c^2 x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{2 b^2 c^5 \sqrt{1-c^2 x^2}}-\frac{x^4 \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)}","-\frac{\sqrt{c x-1} \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b^2 c^5 \sqrt{1-c x}}-\frac{\sqrt{c x-1} \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^5 \sqrt{1-c x}}+\frac{\sqrt{c x-1} \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b^2 c^5 \sqrt{1-c x}}+\frac{\sqrt{c x-1} \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^5 \sqrt{1-c x}}-\frac{x^4 \sqrt{c x-1}}{b c \sqrt{1-c x} \left(a+b \cosh ^{-1}(c x)\right)}",1,"-((x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x]))) - (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]]*Sinh[(2*a)/b])/(b^2*c^5*Sqrt[1 - c^2*x^2]) - (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*CoshIntegral[(4*a)/b + 4*ArcCosh[c*x]]*Sinh[(4*a)/b])/(2*b^2*c^5*Sqrt[1 - c^2*x^2]) + (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(b^2*c^5*Sqrt[1 - c^2*x^2]) + (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcCosh[c*x]])/(2*b^2*c^5*Sqrt[1 - c^2*x^2])","A",11,7,28,0.2500,1,"{5798, 5775, 5670, 5448, 3303, 3298, 3301}"
344,1,298,0,0.7678863,"\int \frac{x^3}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[x^3/(Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])^2),x]","-\frac{3 \sqrt{c x-1} \sqrt{c x+1} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b^2 c^4 \sqrt{1-c^2 x^2}}-\frac{3 \sqrt{c x-1} \sqrt{c x+1} \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b^2 c^4 \sqrt{1-c^2 x^2}}+\frac{3 \sqrt{c x-1} \sqrt{c x+1} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b^2 c^4 \sqrt{1-c^2 x^2}}+\frac{3 \sqrt{c x-1} \sqrt{c x+1} \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b^2 c^4 \sqrt{1-c^2 x^2}}-\frac{x^3 \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)}","-\frac{3 \sqrt{c x-1} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b^2 c^4 \sqrt{1-c x}}-\frac{3 \sqrt{c x-1} \sinh \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^4 \sqrt{1-c x}}+\frac{3 \sqrt{c x-1} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b^2 c^4 \sqrt{1-c x}}+\frac{3 \sqrt{c x-1} \cosh \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^4 \sqrt{1-c x}}-\frac{x^3 \sqrt{c x-1}}{b c \sqrt{1-c x} \left(a+b \cosh ^{-1}(c x)\right)}",1,"-((x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x]))) - (3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b])/(4*b^2*c^4*Sqrt[1 - c^2*x^2]) - (3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]]*Sinh[(3*a)/b])/(4*b^2*c^4*Sqrt[1 - c^2*x^2]) + (3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(4*b^2*c^4*Sqrt[1 - c^2*x^2]) + (3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(4*b^2*c^4*Sqrt[1 - c^2*x^2])","A",11,7,28,0.2500,1,"{5798, 5775, 5670, 5448, 3303, 3298, 3301}"
345,1,175,0,0.6264403,"\int \frac{x^2}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[x^2/(Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])^2),x]","-\frac{\sqrt{c x-1} \sqrt{c x+1} \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b^2 c^3 \sqrt{1-c^2 x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b^2 c^3 \sqrt{1-c^2 x^2}}-\frac{x^2 \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)}","-\frac{\sqrt{c x-1} \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b^2 c^3 \sqrt{1-c x}}+\frac{\sqrt{c x-1} \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b^2 c^3 \sqrt{1-c x}}-\frac{x^2 \sqrt{c x-1}}{b c \sqrt{1-c x} \left(a+b \cosh ^{-1}(c x)\right)}",1,"-((x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x]))) - (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*CoshIntegral[(2*a)/b + 2*ArcCosh[c*x]]*Sinh[(2*a)/b])/(b^2*c^3*Sqrt[1 - c^2*x^2]) + (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c*x]])/(b^2*c^3*Sqrt[1 - c^2*x^2])","A",8,8,28,0.2857,1,"{5798, 5775, 5670, 5448, 12, 3303, 3298, 3301}"
346,1,169,0,0.4312795,"\int \frac{x}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[x/(Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])^2),x]","-\frac{\sqrt{c x-1} \sqrt{c x+1} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 c^2 \sqrt{1-c^2 x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 c^2 \sqrt{1-c^2 x^2}}-\frac{x \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)}","-\frac{\sqrt{c x-1} \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 c^2 \sqrt{1-c x}}+\frac{\sqrt{c x-1} \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 c^2 \sqrt{1-c x}}-\frac{x \sqrt{c x-1}}{b c \sqrt{1-c x} \left(a+b \cosh ^{-1}(c x)\right)}",1,"-((x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x]))) - (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*CoshIntegral[(a + b*ArcCosh[c*x])/b]*Sinh[a/b])/(b^2*c^2*Sqrt[1 - c^2*x^2]) + (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Cosh[a/b]*SinhIntegral[(a + b*ArcCosh[c*x])/b])/(b^2*c^2*Sqrt[1 - c^2*x^2])","A",6,6,26,0.2308,1,"{5798, 5775, 5658, 3303, 3298, 3301}"
347,1,50,0,0.2153329,"\int \frac{1}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[1/(Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])^2),x]","-\frac{\sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)}","-\frac{\sqrt{c x-1}}{b c \sqrt{1-c x} \left(a+b \cosh ^{-1}(c x)\right)}",1,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])))","A",2,2,25,0.08000,1,"{5713, 5676}"
348,0,0,0,0.5275553,"\int \frac{1}{x \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[1/(x*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])^2),x]","\int \frac{1}{x \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","-\frac{\sqrt{c x-1} \text{Int}\left(\frac{1}{x^2 \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{b c \sqrt{1-c x}}-\frac{\sqrt{c x-1}}{b c x \sqrt{1-c x} \left(a+b \cosh ^{-1}(c x)\right)}",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*x*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x]))) - (Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][1/(x^2*(a + b*ArcCosh[c*x])), x])/(b*c*Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
349,0,0,0,0.5424753,"\int \frac{1}{x^2 \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[1/(x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])^2),x]","\int \frac{1}{x^2 \sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","-\frac{2 \sqrt{c x-1} \text{Int}\left(\frac{1}{x^3 \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{b c \sqrt{1-c x}}-\frac{\sqrt{c x-1}}{b c x^2 \sqrt{1-c x} \left(a+b \cosh ^{-1}(c x)\right)}",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*x^2*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x]))) - (2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][1/(x^3*(a + b*ArcCosh[c*x])), x])/(b*c*Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
350,0,0,0,0.5680858,"\int \frac{x^3}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[x^3/((1 - c^2*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{x^3}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x^3}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][x^3/((-1 + c*x)^(3/2)*(1 + c*x)^(3/2)*(a + b*ArcCosh[c*x])^2), x])/Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
351,0,0,0,0.6455301,"\int \frac{x^2}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[x^2/((1 - c^2*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{x^2}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\frac{2 \sqrt{c x-1} \text{Int}\left(\frac{x}{\left(c^2 x^2-1\right)^2 \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{b c \sqrt{1-c x}}-\frac{x^2 \sqrt{c x-1} \sqrt{c x+1}}{b c \left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}",0,"-((x^2*Sqrt[-1 + c*x])/(b*c*(1 - c*x)*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x]))) + (2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][x/((-1 + c^2*x^2)^2*(a + b*ArcCosh[c*x])), x])/(b*c*Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
352,0,0,0,0.4028199,"\int \frac{x}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[x/((1 - c^2*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{x}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][x/((-1 + c*x)^(3/2)*(1 + c*x)^(3/2)*(a + b*ArcCosh[c*x])^2), x])/Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
353,0,0,0,0.3195954,"\int \frac{1}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[1/((1 - c^2*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{1}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\frac{2 c \sqrt{c x-1} \text{Int}\left(\frac{x}{\left(c^2 x^2-1\right)^2 \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{b \sqrt{1-c x}}-\frac{\sqrt{c x-1} \sqrt{c x+1}}{b c \left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}",0,"-(Sqrt[-1 + c*x]/(b*c*(1 - c*x)*Sqrt[1 + c*x]*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x]))) + (2*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][x/((-1 + c^2*x^2)^2*(a + b*ArcCosh[c*x])), x])/(b*Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
354,0,0,0,0.549333,"\int \frac{1}{x \left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[1/(x*(1 - c^2*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{1}{x \left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][1/(x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)*(a + b*ArcCosh[c*x])^2), x])/Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
355,0,0,0,0.560465,"\int \frac{1}{x^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[1/(x^2*(1 - c^2*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{1}{x^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][1/(x^2*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)*(a + b*ArcCosh[c*x])^2), x])/Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
356,0,0,0,0.6544273,"\int \frac{x^4}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[x^4/((1 - c^2*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{x^4}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","-\frac{4 \sqrt{c x-1} \text{Int}\left(\frac{x^3}{\left(c^2 x^2-1\right)^3 \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{b c \sqrt{1-c x}}-\frac{x^4 \sqrt{c x-1} \sqrt{c x+1}}{b c \left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}",0,"-((x^4*Sqrt[-1 + c*x])/(b*c*(1 - c*x)^2*(1 + c*x)^(3/2)*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x]))) - (4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][x^3/((-1 + c^2*x^2)^3*(a + b*ArcCosh[c*x])), x])/(b*c*Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
357,0,0,0,0.5568785,"\int \frac{x^3}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[x^3/((1 - c^2*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{x^3}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x^3}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][x^3/((-1 + c*x)^(5/2)*(1 + c*x)^(5/2)*(a + b*ArcCosh[c*x])^2), x])/Sqrt[1 - c^2*x^2]","A",0,0,0,0,-1,"{}"
358,0,0,0,0.5566861,"\int \frac{x^2}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[x^2/((1 - c^2*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{x^2}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x^2}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][x^2/((-1 + c*x)^(5/2)*(1 + c*x)^(5/2)*(a + b*ArcCosh[c*x])^2), x])/Sqrt[1 - c^2*x^2]","A",0,0,0,0,-1,"{}"
359,0,0,0,0.3911622,"\int \frac{x}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[x/((1 - c^2*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{x}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][x/((-1 + c*x)^(5/2)*(1 + c*x)^(5/2)*(a + b*ArcCosh[c*x])^2), x])/Sqrt[1 - c^2*x^2]","A",0,0,0,0,-1,"{}"
360,0,0,0,0.3048869,"\int \frac{1}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[1/((1 - c^2*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{1}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","-\frac{4 c \sqrt{c x-1} \text{Int}\left(\frac{x}{\left(c^2 x^2-1\right)^3 \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{b \sqrt{1-c x}}-\frac{\sqrt{c x-1} \sqrt{c x+1}}{b c \left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}",0,"-(Sqrt[-1 + c*x]/(b*c*(1 - c*x)^2*(1 + c*x)^(3/2)*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x]))) - (4*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][x/((-1 + c^2*x^2)^3*(a + b*ArcCosh[c*x])), x])/(b*Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
361,0,0,0,0.5431594,"\int \frac{1}{x \left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[1/(x*(1 - c^2*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{1}{x \left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][1/(x*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2)*(a + b*ArcCosh[c*x])^2), x])/Sqrt[1 - c^2*x^2]","A",0,0,0,0,-1,"{}"
362,0,0,0,0.5507563,"\int \frac{1}{x^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[1/(x^2*(1 - c^2*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{1}{x^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][1/(x^2*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2)*(a + b*ArcCosh[c*x])^2), x])/Sqrt[1 - c^2*x^2]","A",0,0,0,0,-1,"{}"
363,0,0,0,0.53223,"\int \frac{(f x)^m \left(1-c^2 x^2\right)^{3/2}}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[((f*x)^m*(1 - c^2*x^2)^(3/2))/(a + b*ArcCosh[c*x])^2,x]","\int \frac{(f x)^m \left(1-c^2 x^2\right)^{3/2}}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\left(1-c^2 x^2\right)^{3/2} (f x)^m}{\left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"-((Sqrt[1 - c^2*x^2]*Defer[Int][((f*x)^m*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(a + b*ArcCosh[c*x])^2, x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]))","A",0,0,0,0,-1,"{}"
364,0,0,0,0.4502381,"\int \frac{(f x)^m \sqrt{1-c^2 x^2}}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[((f*x)^m*Sqrt[1 - c^2*x^2])/(a + b*ArcCosh[c*x])^2,x]","\int \frac{(f x)^m \sqrt{1-c^2 x^2}}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{1-c^2 x^2} (f x)^m}{\left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"(Sqrt[1 - c^2*x^2]*Defer[Int][((f*x)^m*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(a + b*ArcCosh[c*x])^2, x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
365,0,0,0,0.5219803,"\int \frac{(f x)^m}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(f*x)^m/(Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])^2),x]","\int \frac{(f x)^m}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\frac{f m \sqrt{c x-1} \text{Int}\left(\frac{(f x)^{m-1}}{a+b \cosh ^{-1}(c x)},x\right)}{b c \sqrt{1-c x}}-\frac{\sqrt{c x-1} (f x)^m}{b c \sqrt{1-c x} \left(a+b \cosh ^{-1}(c x)\right)}",0,"-(((f*x)^m*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x]))) + (f*m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][(f*x)^(-1 + m)/(a + b*ArcCosh[c*x]), x])/(b*c*Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
366,0,0,0,0.55825,"\int \frac{(f x)^m}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(f*x)^m/((1 - c^2*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{(f x)^m}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{(f x)^m}{\left(1-c^2 x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][(f*x)^m/((-1 + c*x)^(3/2)*(1 + c*x)^(3/2)*(a + b*ArcCosh[c*x])^2), x])/Sqrt[1 - c^2*x^2])","A",0,0,0,0,-1,"{}"
367,0,0,0,0.5512105,"\int \frac{(f x)^m}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(f*x)^m/((1 - c^2*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{(f x)^m}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{(f x)^m}{\left(1-c^2 x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][(f*x)^m/((-1 + c*x)^(5/2)*(1 + c*x)^(5/2)*(a + b*ArcCosh[c*x])^2), x])/Sqrt[1 - c^2*x^2]","A",0,0,0,0,-1,"{}"
368,1,45,0,0.1480906,"\int \frac{1}{\sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^3} \, dx","Int[1/(Sqrt[1 - a^2*x^2]*ArcCosh[a*x]^3),x]","-\frac{\sqrt{a x-1} \sqrt{a x+1}}{2 a \sqrt{1-a^2 x^2} \cosh ^{-1}(a x)^2}","-\frac{\sqrt{a x-1}}{2 a \sqrt{1-a x} \cosh ^{-1}(a x)^2}",1,"-(Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(2*a*Sqrt[1 - a^2*x^2]*ArcCosh[a*x]^2)","A",2,2,21,0.09524,1,"{5713, 5676}"
369,1,269,0,1.7474949,"\int \frac{x^3 \left(d-c^2 d x^2\right)}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x^3*(d - c^2*d*x^2))/(a + b*ArcCosh[c*x])^(3/2),x]","\frac{3 \sqrt{\frac{\pi }{2}} d e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^4}-\frac{\sqrt{\frac{3 \pi }{2}} d e^{\frac{6 a}{b}} \text{Erf}\left(\frac{\sqrt{6} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^4}+\frac{3 \sqrt{\frac{\pi }{2}} d e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^4}-\frac{\sqrt{\frac{3 \pi }{2}} d e^{-\frac{6 a}{b}} \text{Erfi}\left(\frac{\sqrt{6} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^4}-\frac{2 d x^3 \sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)}{b c \sqrt{a+b \cosh ^{-1}(c x)}}","\frac{3 \sqrt{\frac{\pi }{2}} d e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^4}-\frac{\sqrt{\frac{3 \pi }{2}} d e^{\frac{6 a}{b}} \text{Erf}\left(\frac{\sqrt{6} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^4}+\frac{3 \sqrt{\frac{\pi }{2}} d e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^4}-\frac{\sqrt{\frac{3 \pi }{2}} d e^{-\frac{6 a}{b}} \text{Erfi}\left(\frac{\sqrt{6} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^4}+\frac{2 d x^3 (c x-1)^{3/2} (c x+1)^{3/2}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}",1,"(-2*d*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(1 - c^2*x^2))/(b*c*Sqrt[a + b*ArcCosh[c*x]]) + (3*d*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^4) - (d*E^((6*a)/b)*Sqrt[(3*Pi)/2]*Erf[(Sqrt[6]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^4) + (3*d*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^4*E^((2*a)/b)) - (d*Sqrt[(3*Pi)/2]*Erfi[(Sqrt[6]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^4*E^((6*a)/b))","A",27,7,27,0.2593,1,"{5776, 5781, 5448, 3307, 2180, 2204, 2205}"
370,1,350,0,1.7724774,"\int \frac{x^2 \left(d-c^2 d x^2\right)}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x^2*(d - c^2*d*x^2))/(a + b*ArcCosh[c*x])^(3/2),x]","\frac{\sqrt{\pi } d e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c^3}+\frac{\sqrt{3 \pi } d e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{\sqrt{5 \pi } d e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}+\frac{\sqrt{\pi } d e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c^3}+\frac{\sqrt{3 \pi } d e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{\sqrt{5 \pi } d e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{2 d x^2 \sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)}{b c \sqrt{a+b \cosh ^{-1}(c x)}}","\frac{\sqrt{\pi } d e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c^3}+\frac{\sqrt{3 \pi } d e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{\sqrt{5 \pi } d e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}+\frac{\sqrt{\pi } d e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c^3}+\frac{\sqrt{3 \pi } d e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{\sqrt{5 \pi } d e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}+\frac{2 d x^2 (c x-1)^{3/2} (c x+1)^{3/2}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}",1,"(-2*d*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(1 - c^2*x^2))/(b*c*Sqrt[a + b*ArcCosh[c*x]]) + (d*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(8*b^(3/2)*c^3) + (d*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^3) - (d*E^((5*a)/b)*Sqrt[5*Pi]*Erf[(Sqrt[5]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^3) + (d*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(8*b^(3/2)*c^3*E^(a/b)) + (d*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^3*E^((3*a)/b)) - (d*Sqrt[5*Pi]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^3*E^((5*a)/b))","A",32,7,27,0.2593,1,"{5776, 5781, 5448, 3307, 2180, 2204, 2205}"
371,1,251,0,1.1541154,"\int \frac{x \left(d-c^2 d x^2\right)}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x*(d - c^2*d*x^2))/(a + b*ArcCosh[c*x])^(3/2),x]","-\frac{\sqrt{\pi } d e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^2}+\frac{\sqrt{\frac{\pi }{2}} d e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2} c^2}-\frac{\sqrt{\pi } d e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^2}+\frac{\sqrt{\frac{\pi }{2}} d e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2} c^2}-\frac{2 d x \sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)}{b c \sqrt{a+b \cosh ^{-1}(c x)}}","-\frac{\sqrt{\pi } d e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^2}+\frac{\sqrt{\frac{\pi }{2}} d e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2} c^2}-\frac{\sqrt{\pi } d e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^2}+\frac{\sqrt{\frac{\pi }{2}} d e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2} c^2}+\frac{2 d x (c x-1)^{3/2} (c x+1)^{3/2}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}",1,"(-2*d*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(1 - c^2*x^2))/(b*c*Sqrt[a + b*ArcCosh[c*x]]) - (d*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c^2) + (d*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(2*b^(3/2)*c^2) - (d*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c^2*E^((4*a)/b)) + (d*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(2*b^(3/2)*c^2*E^((2*a)/b))","A",17,9,25,0.3600,1,"{5776, 5701, 3312, 3307, 2180, 2204, 2205, 5781, 5448}"
372,1,233,0,0.7224644,"\int \frac{d-c^2 d x^2}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(d - c^2*d*x^2)/(a + b*ArcCosh[c*x])^(3/2),x]","\frac{3 \sqrt{\pi } d e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}-\frac{\sqrt{3 \pi } d e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}+\frac{3 \sqrt{\pi } d e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}-\frac{\sqrt{3 \pi } d e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}+\frac{2 d (c x-1)^{3/2} (c x+1)^{3/2}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}","\frac{3 \sqrt{\pi } d e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}-\frac{\sqrt{3 \pi } d e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}+\frac{3 \sqrt{\pi } d e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}-\frac{\sqrt{3 \pi } d e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}+\frac{2 d (c x-1)^{3/2} (c x+1)^{3/2}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}",1,"(2*d*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(b*c*Sqrt[a + b*ArcCosh[c*x]]) + (3*d*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(4*b^(3/2)*c) - (d*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c) + (3*d*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(4*b^(3/2)*c*E^(a/b)) - (d*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c*E^((3*a)/b))","A",14,7,24,0.2917,1,"{5695, 5781, 5448, 3307, 2180, 2204, 2205}"
373,0,0,0,1.6619029,"\int \frac{d-c^2 d x^2}{x \left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(d - c^2*d*x^2)/(x*(a + b*ArcCosh[c*x])^(3/2)),x]","\int \frac{d-c^2 d x^2}{x \left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","\frac{2 d \text{Int}\left(\frac{1}{x^2 \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}},x\right)}{b c}-\frac{\sqrt{\frac{\pi }{2}} d e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} d e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2}}+\frac{2 d (c x-1)^{3/2} (c x+1)^{3/2}}{b c x \sqrt{a+b \cosh ^{-1}(c x)}}",0,"(-2*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(1 - c^2*x^2))/(b*c*x*Sqrt[a + b*ArcCosh[c*x]]) - (d*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/b^(3/2) - (d*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(b^(3/2)*E^((2*a)/b)) + (2*d*Defer[Int][1/(x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Sqrt[a + b*ArcCosh[c*x]]), x])/(b*c)","A",0,0,0,0,-1,"{}"
374,1,491,0,2.1326771,"\int \frac{x^3 \left(d-c^2 d x^2\right)^2}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x^3*(d - c^2*d*x^2)^2)/(a + b*ArcCosh[c*x])^(3/2),x]","-\frac{\sqrt{\pi } d^2 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}+\frac{3 \sqrt{\frac{\pi }{2}} d^2 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}+\frac{\sqrt{\frac{\pi }{2}} d^2 e^{\frac{8 a}{b}} \text{Erf}\left(\frac{2 \sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}-\frac{\sqrt{\frac{3 \pi }{2}} d^2 e^{\frac{6 a}{b}} \text{Erf}\left(\frac{\sqrt{6} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}-\frac{\sqrt{\pi } d^2 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}+\frac{3 \sqrt{\frac{\pi }{2}} d^2 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}+\frac{\sqrt{\frac{\pi }{2}} d^2 e^{-\frac{8 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}-\frac{\sqrt{\frac{3 \pi }{2}} d^2 e^{-\frac{6 a}{b}} \text{Erfi}\left(\frac{\sqrt{6} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}-\frac{2 d^2 x^3 \sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)^2}{b c \sqrt{a+b \cosh ^{-1}(c x)}}","-\frac{\sqrt{\pi } d^2 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}+\frac{3 \sqrt{\frac{\pi }{2}} d^2 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}+\frac{\sqrt{\frac{\pi }{2}} d^2 e^{\frac{8 a}{b}} \text{Erf}\left(\frac{2 \sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}-\frac{\sqrt{\frac{3 \pi }{2}} d^2 e^{\frac{6 a}{b}} \text{Erf}\left(\frac{\sqrt{6} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}-\frac{\sqrt{\pi } d^2 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}+\frac{3 \sqrt{\frac{\pi }{2}} d^2 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}+\frac{\sqrt{\frac{\pi }{2}} d^2 e^{-\frac{8 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}-\frac{\sqrt{\frac{3 \pi }{2}} d^2 e^{-\frac{6 a}{b}} \text{Erfi}\left(\frac{\sqrt{6} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}-\frac{2 d^2 x^3 (c x-1)^{5/2} (c x+1)^{5/2}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}",1,"(-2*d^2*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(1 - c^2*x^2)^2)/(b*c*Sqrt[a + b*ArcCosh[c*x]]) - (d^2*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(32*b^(3/2)*c^4) + (3*d^2*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(32*b^(3/2)*c^4) + (d^2*E^((8*a)/b)*Sqrt[Pi/2]*Erf[(2*Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(32*b^(3/2)*c^4) - (d^2*E^((6*a)/b)*Sqrt[(3*Pi)/2]*Erf[(Sqrt[6]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(32*b^(3/2)*c^4) - (d^2*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(32*b^(3/2)*c^4*E^((4*a)/b)) + (3*d^2*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(32*b^(3/2)*c^4*E^((2*a)/b)) + (d^2*Sqrt[Pi/2]*Erfi[(2*Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(32*b^(3/2)*c^4*E^((8*a)/b)) - (d^2*Sqrt[(3*Pi)/2]*Erfi[(Sqrt[6]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(32*b^(3/2)*c^4*E^((6*a)/b))","A",32,7,29,0.2414,1,"{5776, 5781, 5448, 3307, 2180, 2204, 2205}"
375,1,474,0,2.2665706,"\int \frac{x^2 \left(d-c^2 d x^2\right)^2}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x^2*(d - c^2*d*x^2)^2)/(a + b*ArcCosh[c*x])^(3/2),x]","\frac{5 \sqrt{\pi } d^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}+\frac{\sqrt{3 \pi } d^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}-\frac{3 \sqrt{5 \pi } d^2 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}+\frac{\sqrt{7 \pi } d^2 e^{\frac{7 a}{b}} \text{Erf}\left(\frac{\sqrt{7} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}+\frac{5 \sqrt{\pi } d^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}+\frac{\sqrt{3 \pi } d^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}-\frac{3 \sqrt{5 \pi } d^2 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}+\frac{\sqrt{7 \pi } d^2 e^{-\frac{7 a}{b}} \text{Erfi}\left(\frac{\sqrt{7} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}-\frac{2 d^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)^2}{b c \sqrt{a+b \cosh ^{-1}(c x)}}","\frac{5 \sqrt{\pi } d^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}+\frac{\sqrt{3 \pi } d^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}-\frac{3 \sqrt{5 \pi } d^2 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}+\frac{\sqrt{7 \pi } d^2 e^{\frac{7 a}{b}} \text{Erf}\left(\frac{\sqrt{7} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}+\frac{5 \sqrt{\pi } d^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}+\frac{\sqrt{3 \pi } d^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}-\frac{3 \sqrt{5 \pi } d^2 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}+\frac{\sqrt{7 \pi } d^2 e^{-\frac{7 a}{b}} \text{Erfi}\left(\frac{\sqrt{7} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}-\frac{2 d^2 x^2 (c x-1)^{5/2} (c x+1)^{5/2}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}",1,"(-2*d^2*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(1 - c^2*x^2)^2)/(b*c*Sqrt[a + b*ArcCosh[c*x]]) + (5*d^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(64*b^(3/2)*c^3) + (d^2*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(64*b^(3/2)*c^3) - (3*d^2*E^((5*a)/b)*Sqrt[5*Pi]*Erf[(Sqrt[5]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(64*b^(3/2)*c^3) + (d^2*E^((7*a)/b)*Sqrt[7*Pi]*Erf[(Sqrt[7]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(64*b^(3/2)*c^3) + (5*d^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(64*b^(3/2)*c^3*E^(a/b)) + (d^2*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(64*b^(3/2)*c^3*E^((3*a)/b)) - (3*d^2*Sqrt[5*Pi]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(64*b^(3/2)*c^3*E^((5*a)/b)) + (d^2*Sqrt[7*Pi]*Erfi[(Sqrt[7]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(64*b^(3/2)*c^3*E^((7*a)/b))","A",42,7,29,0.2414,1,"{5776, 5781, 5448, 3307, 2180, 2204, 2205}"
376,1,375,0,1.7754704,"\int \frac{x \left(d-c^2 d x^2\right)^2}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x*(d - c^2*d*x^2)^2)/(a + b*ArcCosh[c*x])^(3/2),x]","-\frac{\sqrt{\pi } d^2 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^2}+\frac{5 \sqrt{\frac{\pi }{2}} d^2 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^2}+\frac{\sqrt{\frac{3 \pi }{2}} d^2 e^{\frac{6 a}{b}} \text{Erf}\left(\frac{\sqrt{6} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^2}-\frac{\sqrt{\pi } d^2 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^2}+\frac{5 \sqrt{\frac{\pi }{2}} d^2 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^2}+\frac{\sqrt{\frac{3 \pi }{2}} d^2 e^{-\frac{6 a}{b}} \text{Erfi}\left(\frac{\sqrt{6} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^2}-\frac{2 d^2 x \sqrt{c x-1} \sqrt{c x+1} \left(1-c^2 x^2\right)^2}{b c \sqrt{a+b \cosh ^{-1}(c x)}}","-\frac{\sqrt{\pi } d^2 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^2}+\frac{5 \sqrt{\frac{\pi }{2}} d^2 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^2}+\frac{\sqrt{\frac{3 \pi }{2}} d^2 e^{\frac{6 a}{b}} \text{Erf}\left(\frac{\sqrt{6} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^2}-\frac{\sqrt{\pi } d^2 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^2}+\frac{5 \sqrt{\frac{\pi }{2}} d^2 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^2}+\frac{\sqrt{\frac{3 \pi }{2}} d^2 e^{-\frac{6 a}{b}} \text{Erfi}\left(\frac{\sqrt{6} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^2}-\frac{2 d^2 x (c x-1)^{5/2} (c x+1)^{5/2}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}",1,"(-2*d^2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(1 - c^2*x^2)^2)/(b*c*Sqrt[a + b*ArcCosh[c*x]]) - (d^2*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c^2) + (5*d^2*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^2) + (d^2*E^((6*a)/b)*Sqrt[(3*Pi)/2]*Erf[(Sqrt[6]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^2) - (d^2*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c^2*E^((4*a)/b)) + (5*d^2*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^2*E^((2*a)/b)) + (d^2*Sqrt[(3*Pi)/2]*Erfi[(Sqrt[6]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^2*E^((6*a)/b))","A",32,9,27,0.3333,1,"{5776, 5701, 3312, 3307, 2180, 2204, 2205, 5781, 5448}"
377,1,351,0,0.9243359,"\int \frac{\left(d-c^2 d x^2\right)^2}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(d - c^2*d*x^2)^2/(a + b*ArcCosh[c*x])^(3/2),x]","\frac{5 \sqrt{\pi } d^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c}-\frac{5 \sqrt{3 \pi } d^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c}+\frac{\sqrt{5 \pi } d^2 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c}+\frac{5 \sqrt{\pi } d^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c}-\frac{5 \sqrt{3 \pi } d^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c}+\frac{\sqrt{5 \pi } d^2 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c}-\frac{2 d^2 (c x-1)^{5/2} (c x+1)^{5/2}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}","\frac{5 \sqrt{\pi } d^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c}-\frac{5 \sqrt{3 \pi } d^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c}+\frac{\sqrt{5 \pi } d^2 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c}+\frac{5 \sqrt{\pi } d^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 b^{3/2} c}-\frac{5 \sqrt{3 \pi } d^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c}+\frac{\sqrt{5 \pi } d^2 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c}-\frac{2 d^2 (c x-1)^{5/2} (c x+1)^{5/2}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}",1,"(-2*d^2*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(b*c*Sqrt[a + b*ArcCosh[c*x]]) + (5*d^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(8*b^(3/2)*c) - (5*d^2*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c) + (d^2*E^((5*a)/b)*Sqrt[5*Pi]*Erf[(Sqrt[5]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c) + (5*d^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(8*b^(3/2)*c*E^(a/b)) - (5*d^2*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c*E^((3*a)/b)) + (d^2*Sqrt[5*Pi]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c*E^((5*a)/b))","A",19,7,26,0.2692,1,"{5695, 5781, 5448, 3307, 2180, 2204, 2205}"
378,0,0,0,2.4958942,"\int \frac{\left(d-c^2 d x^2\right)^2}{x \left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(d - c^2*d*x^2)^2/(x*(a + b*ArcCosh[c*x])^(3/2)),x]","\int \frac{\left(d-c^2 d x^2\right)^2}{x \left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","\frac{2 d^2 \text{Int}\left(\frac{1}{x^2 \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}},x\right)}{b c}+\frac{\sqrt{\pi } d^2 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2}}-\frac{3 \sqrt{\frac{\pi }{2}} d^2 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2}}+\frac{\sqrt{\pi } d^2 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2}}-\frac{3 \sqrt{\frac{\pi }{2}} d^2 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2}}-\frac{2 d^2 (c x-1)^{5/2} (c x+1)^{5/2}}{b c x \sqrt{a+b \cosh ^{-1}(c x)}}",0,"(-2*d^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(1 - c^2*x^2)^2)/(b*c*x*Sqrt[a + b*ArcCosh[c*x]]) + (d^2*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(4*b^(3/2)) + (d^2*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(2*b^(3/2)) - (d^2*E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/b^(3/2) + (d^2*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(4*b^(3/2)*E^((4*a)/b)) + (d^2*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(2*b^(3/2)*E^((2*a)/b)) - (d^2*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(b^(3/2)*E^((2*a)/b)) + (2*d^2*Defer[Int][1/(x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Sqrt[a + b*ArcCosh[c*x]]), x])/(b*c)","A",0,0,0,0,-1,"{}"
379,1,363,0,0.7230193,"\int \left(c-a^2 c x^2\right)^{3/2} \sqrt{\cosh ^{-1}(a x)} \, dx","Int[(c - a^2*c*x^2)^(3/2)*Sqrt[ArcCosh[a*x]],x]","-\frac{\sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{256 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{256 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{c \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}}{4 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}+\frac{1}{4} c x (1-a x) (a x+1) \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}","-\frac{\sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{256 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{256 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{1}{4} x \left(c-a^2 c x^2\right)^{3/2} \sqrt{\cosh ^{-1}(a x)}-\frac{c \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}}{4 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}",1,"(3*c*x*Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]])/8 + (c*x*(1 - a*x)*(1 + a*x)*Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]])/4 - (c*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(3/2))/(4*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*Erf[2*Sqrt[ArcCosh[a*x]]])/(256*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (c*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(16*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*Erfi[2*Sqrt[ArcCosh[a*x]]])/(256*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (c*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(16*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",25,12,24,0.5000,1,"{5713, 5685, 5683, 5676, 5670, 5448, 12, 3308, 2180, 2204, 2205, 5780}"
380,1,205,0,0.3745432,"\int \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)} \, dx","Int[Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}}{3 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}}{3 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}",1,"(x*Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]])/2 - (Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(3/2))/(3*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(16*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(16*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",11,10,24,0.4167,1,"{5713, 5683, 5676, 5670, 5448, 12, 3308, 2180, 2204, 2205}"
381,1,48,0,0.1639255,"\int \frac{\sqrt{\cosh ^{-1}(a x)}}{\sqrt{c-a^2 c x^2}} \, dx","Int[Sqrt[ArcCosh[a*x]]/Sqrt[c - a^2*c*x^2],x]","\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{3 a \sqrt{c-a^2 c x^2}}","\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{3/2}}{3 a \sqrt{c-a^2 c x^2}}",1,"(2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^(3/2))/(3*a*Sqrt[c - a^2*c*x^2])","A",2,2,24,0.08333,1,"{5713, 5676}"
382,0,0,0,0.2436863,"\int \frac{\sqrt{\cosh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[Sqrt[ArcCosh[a*x]]/(c - a^2*c*x^2)^(3/2),x]","\int \frac{\sqrt{\cosh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","\frac{a \sqrt{a x-1} \sqrt{a x+1} \text{Int}\left(\frac{x}{\left(1-a^2 x^2\right) \sqrt{\cosh ^{-1}(a x)}},x\right)}{2 c \sqrt{c-a^2 c x^2}}+\frac{x \sqrt{\cosh ^{-1}(a x)}}{c \sqrt{c-a^2 c x^2}}",0,"(x*Sqrt[ArcCosh[a*x]])/(c*Sqrt[c - a^2*c*x^2]) + (a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Defer[Int][x/((1 - a^2*x^2)*Sqrt[ArcCosh[a*x]]), x])/(2*c*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
383,0,0,0,0.4321645,"\int \frac{\sqrt{\cosh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","Int[Sqrt[ArcCosh[a*x]]/(c - a^2*c*x^2)^(5/2),x]","\int \frac{\sqrt{\cosh ^{-1}(a x)}}{\left(c-a^2 c x^2\right)^{5/2}} \, dx","\frac{a \sqrt{a x-1} \sqrt{a x+1} \text{Int}\left(\frac{x}{\left(1-a^2 x^2\right) \sqrt{\cosh ^{-1}(a x)}},x\right)}{3 c^2 \sqrt{c-a^2 c x^2}}+\frac{a \sqrt{a x-1} \sqrt{a x+1} \text{Int}\left(\frac{x}{\left(a^2 x^2-1\right)^2 \sqrt{\cosh ^{-1}(a x)}},x\right)}{6 c^2 \sqrt{c-a^2 c x^2}}+\frac{2 x \sqrt{\cosh ^{-1}(a x)}}{3 c^2 \sqrt{c-a^2 c x^2}}+\frac{x \sqrt{\cosh ^{-1}(a x)}}{3 c \left(c-a^2 c x^2\right)^{3/2}}",0,"(2*x*Sqrt[ArcCosh[a*x]])/(3*c^2*Sqrt[c - a^2*c*x^2]) + (x*Sqrt[ArcCosh[a*x]])/(3*c^2*(1 - a*x)*(1 + a*x)*Sqrt[c - a^2*c*x^2]) + (a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Defer[Int][x/((1 - a^2*x^2)*Sqrt[ArcCosh[a*x]]), x])/(3*c^2*Sqrt[c - a^2*c*x^2]) + (a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Defer[Int][x/((-1 + a^2*x^2)^2*Sqrt[ArcCosh[a*x]]), x])/(6*c^2*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
384,1,523,0,1.0975931,"\int \left(c-a^2 c x^2\right)^{3/2} \cosh ^{-1}(a x)^{3/2} \, dx","Int[(c - a^2*c*x^2)^(3/2)*ArcCosh[a*x]^(3/2),x]","-\frac{3 \sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{2048 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{3 \sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{3 \sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{2048 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{3 \sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{3 c \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{5/2}}{20 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}+\frac{1}{4} c x (1-a x) (a x+1) \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}+\frac{3 c \left(1-a^2 x^2\right)^2 \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}{32 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{9 a c x^2 \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}{32 \sqrt{a x-1} \sqrt{a x+1}}+\frac{27 c \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}{256 a \sqrt{a x-1} \sqrt{a x+1}}","-\frac{3 \sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{2048 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{3 \sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{3 \sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{2048 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{3 \sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{3 c \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{5/2}}{20 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{1}{4} x \left(c-a^2 c x^2\right)^{3/2} \cosh ^{-1}(a x)^{3/2}+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}+\frac{3 c \left(1-a^2 x^2\right)^2 \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}{32 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{9 a c x^2 \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}{32 \sqrt{a x-1} \sqrt{a x+1}}+\frac{27 c \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}{256 a \sqrt{a x-1} \sqrt{a x+1}}",1,"(27*c*Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]])/(256*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (9*a*c*x^2*Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]])/(32*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (3*c*(1 - a^2*x^2)^2*Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]])/(32*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (3*c*x*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(3/2))/8 + (c*x*(1 - a*x)*(1 + a*x)*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(3/2))/4 - (3*c*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(5/2))/(20*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (3*c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*Erf[2*Sqrt[ArcCosh[a*x]]])/(2048*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (3*c*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(64*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (3*c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*Erfi[2*Sqrt[ArcCosh[a*x]]])/(2048*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (3*c*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(64*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",27,13,24,0.5417,1,"{5713, 5685, 5683, 5676, 5664, 5781, 3312, 3307, 2180, 2204, 2205, 5716, 5701}"
385,1,302,0,0.61828,"\int \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2} \, dx","Int[Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(3/2),x]","\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{5/2}}{5 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}-\frac{3 a x^2 \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}{8 \sqrt{a x-1} \sqrt{a x+1}}+\frac{3 \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}{16 a \sqrt{a x-1} \sqrt{a x+1}}","\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{5/2}}{5 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}-\frac{3 a x^2 \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}{8 \sqrt{a x-1} \sqrt{a x+1}}+\frac{3 \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}{16 a \sqrt{a x-1} \sqrt{a x+1}}",1,"(3*Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]])/(16*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (3*a*x^2*Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]])/(8*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (x*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(3/2))/2 - (Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(5/2))/(5*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (3*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(64*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (3*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(64*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",12,10,24,0.4167,1,"{5713, 5683, 5676, 5664, 5781, 3312, 3307, 2180, 2204, 2205}"
386,1,48,0,0.1614808,"\int \frac{\cosh ^{-1}(a x)^{3/2}}{\sqrt{c-a^2 c x^2}} \, dx","Int[ArcCosh[a*x]^(3/2)/Sqrt[c - a^2*c*x^2],x]","\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{5/2}}{5 a \sqrt{c-a^2 c x^2}}","\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{5/2}}{5 a \sqrt{c-a^2 c x^2}}",1,"(2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^(5/2))/(5*a*Sqrt[c - a^2*c*x^2])","A",2,2,24,0.08333,1,"{5713, 5676}"
387,0,0,0,0.2317146,"\int \frac{\cosh ^{-1}(a x)^{3/2}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[ArcCosh[a*x]^(3/2)/(c - a^2*c*x^2)^(3/2),x]","\int \frac{\cosh ^{-1}(a x)^{3/2}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","\frac{3 a \sqrt{a x-1} \sqrt{a x+1} \text{Int}\left(\frac{x \sqrt{\cosh ^{-1}(a x)}}{1-a^2 x^2},x\right)}{2 c \sqrt{c-a^2 c x^2}}+\frac{x \cosh ^{-1}(a x)^{3/2}}{c \sqrt{c-a^2 c x^2}}",0,"(x*ArcCosh[a*x]^(3/2))/(c*Sqrt[c - a^2*c*x^2]) + (3*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Defer[Int][(x*Sqrt[ArcCosh[a*x]])/(1 - a^2*x^2), x])/(2*c*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
388,1,592,0,1.5260215,"\int \left(c-a^2 c x^2\right)^{3/2} \cosh ^{-1}(a x)^{5/2} \, dx","Int[(c - a^2*c*x^2)^(3/2)*ArcCosh[a*x]^(5/2),x]","-\frac{15 \sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{16384 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{15 \sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{256 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{15 \sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{16384 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{15 \sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{256 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{3 c \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{7/2}}{28 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{5/2}+\frac{1}{4} c x (1-a x) (a x+1) \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{5/2}+\frac{5 c \left(1-a^2 x^2\right)^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}}{32 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{15 a c x^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}}{32 \sqrt{a x-1} \sqrt{a x+1}}+\frac{45 c \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}}{256 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{225}{512} c x \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}+\frac{15}{256} c x (1-a x) (a x+1) \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}","-\frac{15 \sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{16384 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{15 \sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{256 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{15 \sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{16384 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{15 \sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{256 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{3 c \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{7/2}}{28 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{1}{4} x \left(c-a^2 c x^2\right)^{3/2} \cosh ^{-1}(a x)^{5/2}+\frac{3}{8} c x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{5/2}+\frac{5 c \left(1-a^2 x^2\right)^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}}{32 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{15 a c x^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}}{32 \sqrt{a x-1} \sqrt{a x+1}}+\frac{45 c \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}}{256 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{225}{512} c x \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}+\frac{15}{256} c x (1-a x) (a x+1) \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}",1,"(225*c*x*Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]])/512 + (15*c*x*(1 - a*x)*(1 + a*x)*Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]])/256 + (45*c*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(3/2))/(256*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (15*a*c*x^2*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(3/2))/(32*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (5*c*(1 - a^2*x^2)^2*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(3/2))/(32*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (3*c*x*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(5/2))/8 + (c*x*(1 - a*x)*(1 + a*x)*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(5/2))/4 - (3*c*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(7/2))/(28*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (15*c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*Erf[2*Sqrt[ArcCosh[a*x]]])/(16384*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (15*c*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(256*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (15*c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*Erfi[2*Sqrt[ArcCosh[a*x]]])/(16384*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (15*c*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(256*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",40,15,24,0.6250,1,"{5713, 5685, 5683, 5676, 5664, 5759, 5670, 5448, 12, 3308, 2180, 2204, 2205, 5716, 5780}"
389,1,330,0,0.7071156,"\int \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{5/2} \, dx","Int[Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(5/2),x]","\frac{15 \sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{256 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{15 \sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{256 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{7/2}}{7 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{5/2}-\frac{5 a x^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}}{8 \sqrt{a x-1} \sqrt{a x+1}}+\frac{5 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}}{16 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{15}{32} x \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}","\frac{15 \sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{256 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{15 \sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{256 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{7/2}}{7 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{1}{2} x \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{5/2}-\frac{5 a x^2 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}}{8 \sqrt{a x-1} \sqrt{a x+1}}+\frac{5 \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}}{16 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{15}{32} x \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}",1,"(15*x*Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]])/32 + (5*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(3/2))/(16*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (5*a*x^2*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(3/2))/(8*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (x*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(5/2))/2 - (Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(7/2))/(7*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (15*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(256*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (15*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(256*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",14,12,24,0.5000,1,"{5713, 5683, 5676, 5664, 5759, 5670, 5448, 12, 3308, 2180, 2204, 2205}"
390,1,48,0,0.1534818,"\int \frac{\cosh ^{-1}(a x)^{5/2}}{\sqrt{c-a^2 c x^2}} \, dx","Int[ArcCosh[a*x]^(5/2)/Sqrt[c - a^2*c*x^2],x]","\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{7/2}}{7 a \sqrt{c-a^2 c x^2}}","\frac{2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)^{7/2}}{7 a \sqrt{c-a^2 c x^2}}",1,"(2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]^(7/2))/(7*a*Sqrt[c - a^2*c*x^2])","A",2,2,24,0.08333,1,"{5713, 5676}"
391,0,0,0,0.2278441,"\int \frac{\cosh ^{-1}(a x)^{5/2}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","Int[ArcCosh[a*x]^(5/2)/(c - a^2*c*x^2)^(3/2),x]","\int \frac{\cosh ^{-1}(a x)^{5/2}}{\left(c-a^2 c x^2\right)^{3/2}} \, dx","\frac{5 a \sqrt{a x-1} \sqrt{a x+1} \text{Int}\left(\frac{x \cosh ^{-1}(a x)^{3/2}}{1-a^2 x^2},x\right)}{2 c \sqrt{c-a^2 c x^2}}+\frac{x \cosh ^{-1}(a x)^{5/2}}{c \sqrt{c-a^2 c x^2}}",0,"(x*ArcCosh[a*x]^(5/2))/(c*Sqrt[c - a^2*c*x^2]) + (5*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Defer[Int][(x*ArcCosh[a*x]^(3/2))/(1 - a^2*x^2), x])/(2*c*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
392,1,376,0,0.7787969,"\int \left(a^2-x^2\right)^{3/2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)} \, dx","Int[(a^2 - x^2)^(3/2)*Sqrt[ArcCosh[x/a]],x]","-\frac{\sqrt{\pi } a^3 \sqrt{a^2-x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{256 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{\sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2-x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{16 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{\sqrt{\pi } a^3 \sqrt{a^2-x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{256 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}-\frac{\sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2-x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{16 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}-\frac{a^3 \sqrt{a^2-x^2} \cosh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{4 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{3}{8} a^2 x \sqrt{a^2-x^2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}+\frac{1}{4} x (a-x) (a+x) \sqrt{a^2-x^2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}","-\frac{\sqrt{\pi } a^3 \sqrt{a^2-x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{256 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{\sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2-x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{16 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{\sqrt{\pi } a^3 \sqrt{a^2-x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{256 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}-\frac{\sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2-x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{16 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}-\frac{a^3 \sqrt{a^2-x^2} \cosh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{4 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{3}{8} a^2 x \sqrt{a^2-x^2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}+\frac{1}{4} x \left(a^2-x^2\right)^{3/2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}",1,"(3*a^2*x*Sqrt[a^2 - x^2]*Sqrt[ArcCosh[x/a]])/8 + ((a - x)*x*(a + x)*Sqrt[a^2 - x^2]*Sqrt[ArcCosh[x/a]])/4 - (a^3*Sqrt[a^2 - x^2]*ArcCosh[x/a]^(3/2))/(4*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) - (a^3*Sqrt[Pi]*Sqrt[a^2 - x^2]*Erf[2*Sqrt[ArcCosh[x/a]]])/(256*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) + (a^3*Sqrt[Pi/2]*Sqrt[a^2 - x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[x/a]]])/(16*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) + (a^3*Sqrt[Pi]*Sqrt[a^2 - x^2]*Erfi[2*Sqrt[ArcCosh[x/a]]])/(256*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) - (a^3*Sqrt[Pi/2]*Sqrt[a^2 - x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[x/a]]])/(16*Sqrt[-1 + x/a]*Sqrt[1 + x/a])","A",25,12,24,0.5000,1,"{5713, 5685, 5683, 5676, 5670, 5448, 12, 3308, 2180, 2204, 2205, 5780}"
393,1,211,0,0.3921674,"\int \sqrt{a^2-x^2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)} \, dx","Int[Sqrt[a^2 - x^2]*Sqrt[ArcCosh[x/a]],x]","\frac{\sqrt{\frac{\pi }{2}} a \sqrt{a^2-x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{16 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}-\frac{\sqrt{\frac{\pi }{2}} a \sqrt{a^2-x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{16 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}-\frac{a \sqrt{a^2-x^2} \cosh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{3 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{1}{2} x \sqrt{a^2-x^2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}","\frac{\sqrt{\frac{\pi }{2}} a \sqrt{a^2-x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{16 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}-\frac{\sqrt{\frac{\pi }{2}} a \sqrt{a^2-x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{16 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}-\frac{a \sqrt{a^2-x^2} \cosh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{3 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{1}{2} x \sqrt{a^2-x^2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}",1,"(x*Sqrt[a^2 - x^2]*Sqrt[ArcCosh[x/a]])/2 - (a*Sqrt[a^2 - x^2]*ArcCosh[x/a]^(3/2))/(3*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) + (a*Sqrt[Pi/2]*Sqrt[a^2 - x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[x/a]]])/(16*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) - (a*Sqrt[Pi/2]*Sqrt[a^2 - x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[x/a]]])/(16*Sqrt[-1 + x/a]*Sqrt[1 + x/a])","A",11,10,24,0.4167,1,"{5713, 5683, 5676, 5670, 5448, 12, 3308, 2180, 2204, 2205}"
394,1,50,0,0.1749256,"\int \frac{\sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{\sqrt{a^2-x^2}} \, dx","Int[Sqrt[ArcCosh[x/a]]/Sqrt[a^2 - x^2],x]","\frac{2 a \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1} \cosh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{3 \sqrt{a^2-x^2}}","\frac{2 a \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1} \cosh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{3 \sqrt{a^2-x^2}}",1,"(2*a*Sqrt[-1 + x/a]*Sqrt[1 + x/a]*ArcCosh[x/a]^(3/2))/(3*Sqrt[a^2 - x^2])","A",2,2,24,0.08333,1,"{5713, 5676}"
395,0,0,0,0.2576016,"\int \frac{\sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{\left(a^2-x^2\right)^{3/2}} \, dx","Int[Sqrt[ArcCosh[x/a]]/(a^2 - x^2)^(3/2),x]","\int \frac{\sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{\left(a^2-x^2\right)^{3/2}} \, dx","\frac{\sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1} \text{Int}\left(\frac{x}{\left(1-\frac{x^2}{a^2}\right) \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}},x\right)}{2 a^3 \sqrt{a^2-x^2}}+\frac{x \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{a^2 \sqrt{a^2-x^2}}",0,"(x*Sqrt[ArcCosh[x/a]])/(a^2*Sqrt[a^2 - x^2]) + (Sqrt[-1 + x/a]*Sqrt[1 + x/a]*Defer[Int][x/((1 - x^2/a^2)*Sqrt[ArcCosh[x/a]]), x])/(2*a^3*Sqrt[a^2 - x^2])","A",0,0,0,0,-1,"{}"
396,0,0,0,0.47886,"\int \frac{\sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{\left(a^2-x^2\right)^{5/2}} \, dx","Int[Sqrt[ArcCosh[x/a]]/(a^2 - x^2)^(5/2),x]","\int \frac{\sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{\left(a^2-x^2\right)^{5/2}} \, dx","\frac{\sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1} \text{Int}\left(\frac{x}{\left(1-\frac{x^2}{a^2}\right) \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}},x\right)}{3 a^5 \sqrt{a^2-x^2}}+\frac{\sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1} \text{Int}\left(\frac{x}{\left(\frac{x^2}{a^2}-1\right)^2 \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}},x\right)}{6 a^5 \sqrt{a^2-x^2}}+\frac{2 x \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{3 a^4 \sqrt{a^2-x^2}}+\frac{x \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{3 a^2 \left(a^2-x^2\right)^{3/2}}",0,"(2*x*Sqrt[ArcCosh[x/a]])/(3*a^4*Sqrt[a^2 - x^2]) + (x*Sqrt[ArcCosh[x/a]])/(3*a^2*(a - x)*(a + x)*Sqrt[a^2 - x^2]) + (Sqrt[-1 + x/a]*Sqrt[1 + x/a]*Defer[Int][x/((1 - x^2/a^2)*Sqrt[ArcCosh[x/a]]), x])/(3*a^5*Sqrt[a^2 - x^2]) + (Sqrt[-1 + x/a]*Sqrt[1 + x/a]*Defer[Int][x/((-1 + x^2/a^2)^2*Sqrt[ArcCosh[x/a]]), x])/(6*a^5*Sqrt[a^2 - x^2])","A",0,0,0,0,-1,"{}"
397,1,533,0,1.2820429,"\int \left(a^2-x^2\right)^{3/2} \cosh ^{-1}\left(\frac{x}{a}\right)^{3/2} \, dx","Int[(a^2 - x^2)^(3/2)*ArcCosh[x/a]^(3/2),x]","-\frac{3 \sqrt{\pi } a^3 \sqrt{a^2-x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{2048 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{3 \sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2-x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}-\frac{3 \sqrt{\pi } a^3 \sqrt{a^2-x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{2048 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{3 \sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2-x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}-\frac{3 a^3 \sqrt{a^2-x^2} \cosh ^{-1}\left(\frac{x}{a}\right)^{5/2}}{20 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{27 a^3 \sqrt{a^2-x^2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{256 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{3}{8} a^2 x \sqrt{a^2-x^2} \cosh ^{-1}\left(\frac{x}{a}\right)^{3/2}-\frac{9 a x^2 \sqrt{a^2-x^2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{32 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{1}{4} x (a-x) (a+x) \sqrt{a^2-x^2} \cosh ^{-1}\left(\frac{x}{a}\right)^{3/2}+\frac{3 \left(a^2-x^2\right)^{5/2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{32 a \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}","-\frac{3 \sqrt{\pi } a^3 \sqrt{a^2-x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{2048 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{3 \sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2-x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}-\frac{3 \sqrt{\pi } a^3 \sqrt{a^2-x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{2048 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{3 \sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2-x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}-\frac{3 a^3 \sqrt{a^2-x^2} \cosh ^{-1}\left(\frac{x}{a}\right)^{5/2}}{20 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{27 a^3 \sqrt{a^2-x^2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{256 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{3}{8} a^2 x \sqrt{a^2-x^2} \cosh ^{-1}\left(\frac{x}{a}\right)^{3/2}-\frac{9 a x^2 \sqrt{a^2-x^2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{32 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{1}{4} x \left(a^2-x^2\right)^{3/2} \cosh ^{-1}\left(\frac{x}{a}\right)^{3/2}+\frac{3 \left(a^2-x^2\right)^{5/2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{32 a \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}",1,"(27*a^3*Sqrt[a^2 - x^2]*Sqrt[ArcCosh[x/a]])/(256*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) - (9*a*x^2*Sqrt[a^2 - x^2]*Sqrt[ArcCosh[x/a]])/(32*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) + (3*(a^2 - x^2)^(5/2)*Sqrt[ArcCosh[x/a]])/(32*a*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) + (3*a^2*x*Sqrt[a^2 - x^2]*ArcCosh[x/a]^(3/2))/8 + ((a - x)*x*(a + x)*Sqrt[a^2 - x^2]*ArcCosh[x/a]^(3/2))/4 - (3*a^3*Sqrt[a^2 - x^2]*ArcCosh[x/a]^(5/2))/(20*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) - (3*a^3*Sqrt[Pi]*Sqrt[a^2 - x^2]*Erf[2*Sqrt[ArcCosh[x/a]]])/(2048*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) + (3*a^3*Sqrt[Pi/2]*Sqrt[a^2 - x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[x/a]]])/(64*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) - (3*a^3*Sqrt[Pi]*Sqrt[a^2 - x^2]*Erfi[2*Sqrt[ArcCosh[x/a]]])/(2048*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) + (3*a^3*Sqrt[Pi/2]*Sqrt[a^2 - x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[x/a]]])/(64*Sqrt[-1 + x/a]*Sqrt[1 + x/a])","A",27,13,24,0.5417,1,"{5713, 5685, 5683, 5676, 5664, 5781, 3312, 3307, 2180, 2204, 2205, 5716, 5701}"
398,1,316,0,0.7278193,"\int \sqrt{a^2-x^2} \cosh ^{-1}\left(\frac{x}{a}\right)^{3/2} \, dx","Int[Sqrt[a^2 - x^2]*ArcCosh[x/a]^(3/2),x]","\frac{3 \sqrt{\frac{\pi }{2}} a \sqrt{a^2-x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{3 \sqrt{\frac{\pi }{2}} a \sqrt{a^2-x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}-\frac{a \sqrt{a^2-x^2} \cosh ^{-1}\left(\frac{x}{a}\right)^{5/2}}{5 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{1}{2} x \sqrt{a^2-x^2} \cosh ^{-1}\left(\frac{x}{a}\right)^{3/2}-\frac{3 x^2 \sqrt{a^2-x^2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{8 a \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{3 a \sqrt{a^2-x^2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{16 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}","\frac{3 \sqrt{\frac{\pi }{2}} a \sqrt{a^2-x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{3 \sqrt{\frac{\pi }{2}} a \sqrt{a^2-x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}-\frac{a \sqrt{a^2-x^2} \cosh ^{-1}\left(\frac{x}{a}\right)^{5/2}}{5 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{1}{2} x \sqrt{a^2-x^2} \cosh ^{-1}\left(\frac{x}{a}\right)^{3/2}-\frac{3 x^2 \sqrt{a^2-x^2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{8 a \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}+\frac{3 a \sqrt{a^2-x^2} \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{16 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1}}",1,"(3*a*Sqrt[a^2 - x^2]*Sqrt[ArcCosh[x/a]])/(16*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) - (3*x^2*Sqrt[a^2 - x^2]*Sqrt[ArcCosh[x/a]])/(8*a*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) + (x*Sqrt[a^2 - x^2]*ArcCosh[x/a]^(3/2))/2 - (a*Sqrt[a^2 - x^2]*ArcCosh[x/a]^(5/2))/(5*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) + (3*a*Sqrt[Pi/2]*Sqrt[a^2 - x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[x/a]]])/(64*Sqrt[-1 + x/a]*Sqrt[1 + x/a]) + (3*a*Sqrt[Pi/2]*Sqrt[a^2 - x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[x/a]]])/(64*Sqrt[-1 + x/a]*Sqrt[1 + x/a])","A",12,10,24,0.4167,1,"{5713, 5683, 5676, 5664, 5781, 3312, 3307, 2180, 2204, 2205}"
399,1,50,0,0.167808,"\int \frac{\cosh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{\sqrt{a^2-x^2}} \, dx","Int[ArcCosh[x/a]^(3/2)/Sqrt[a^2 - x^2],x]","\frac{2 a \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1} \cosh ^{-1}\left(\frac{x}{a}\right)^{5/2}}{5 \sqrt{a^2-x^2}}","\frac{2 a \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1} \cosh ^{-1}\left(\frac{x}{a}\right)^{5/2}}{5 \sqrt{a^2-x^2}}",1,"(2*a*Sqrt[-1 + x/a]*Sqrt[1 + x/a]*ArcCosh[x/a]^(5/2))/(5*Sqrt[a^2 - x^2])","A",2,2,24,0.08333,1,"{5713, 5676}"
400,0,0,0,0.2481702,"\int \frac{\cosh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{\left(a^2-x^2\right)^{3/2}} \, dx","Int[ArcCosh[x/a]^(3/2)/(a^2 - x^2)^(3/2),x]","\int \frac{\cosh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{\left(a^2-x^2\right)^{3/2}} \, dx","\frac{3 \sqrt{\frac{x}{a}-1} \sqrt{\frac{x}{a}+1} \text{Int}\left(\frac{x \sqrt{\cosh ^{-1}\left(\frac{x}{a}\right)}}{1-\frac{x^2}{a^2}},x\right)}{2 a^3 \sqrt{a^2-x^2}}+\frac{x \cosh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{a^2 \sqrt{a^2-x^2}}",0,"(x*ArcCosh[x/a]^(3/2))/(a^2*Sqrt[a^2 - x^2]) + (3*Sqrt[-1 + x/a]*Sqrt[1 + x/a]*Defer[Int][(x*Sqrt[ArcCosh[x/a]])/(1 - x^2/a^2), x])/(2*a^3*Sqrt[a^2 - x^2])","A",0,0,0,0,-1,"{}"
401,1,83,0,0.1917036,"\int \frac{x}{\sqrt{1-x^2} \sqrt{\cosh ^{-1}(x)}} \, dx","Int[x/(Sqrt[1 - x^2]*Sqrt[ArcCosh[x]]),x]","\frac{\sqrt{\pi } \sqrt{x-1} \sqrt{x+1} \text{Erf}\left(\sqrt{\cosh ^{-1}(x)}\right)}{2 \sqrt{1-x^2}}+\frac{\sqrt{\pi } \sqrt{x-1} \sqrt{x+1} \text{Erfi}\left(\sqrt{\cosh ^{-1}(x)}\right)}{2 \sqrt{1-x^2}}","\frac{\sqrt{\pi } \sqrt{x-1} \text{Erf}\left(\sqrt{\cosh ^{-1}(x)}\right)}{2 \sqrt{1-x}}+\frac{\sqrt{\pi } \sqrt{x-1} \text{Erfi}\left(\sqrt{\cosh ^{-1}(x)}\right)}{2 \sqrt{1-x}}",1,"(Sqrt[Pi]*Sqrt[-1 + x]*Sqrt[1 + x]*Erf[Sqrt[ArcCosh[x]]])/(2*Sqrt[1 - x^2]) + (Sqrt[Pi]*Sqrt[-1 + x]*Sqrt[1 + x]*Erfi[Sqrt[ArcCosh[x]]])/(2*Sqrt[1 - x^2])","A",7,6,19,0.3158,1,"{5798, 5781, 3307, 2180, 2204, 2205}"
402,1,438,0,0.4448483,"\int \frac{\left(c-a^2 c x^2\right)^{5/2}}{\sqrt{\cosh ^{-1}(a x)}} \, dx","Int[(c - a^2*c*x^2)^(5/2)/Sqrt[ArcCosh[a*x]],x]","-\frac{3 \sqrt{\pi } c^2 \sqrt{c-a^2 c x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{15 \sqrt{\frac{\pi }{2}} c^2 \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{\pi }{6}} c^2 \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{6} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{3 \sqrt{\pi } c^2 \sqrt{c-a^2 c x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{15 \sqrt{\frac{\pi }{2}} c^2 \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{\pi }{6}} c^2 \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{6} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{5 c^2 \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}{8 a \sqrt{a x-1} \sqrt{a x+1}}","-\frac{3 \sqrt{\pi } c^2 \sqrt{c-a^2 c x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{15 \sqrt{\frac{\pi }{2}} c^2 \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{\pi }{6}} c^2 \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{6} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{3 \sqrt{\pi } c^2 \sqrt{c-a^2 c x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{15 \sqrt{\frac{\pi }{2}} c^2 \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{\pi }{6}} c^2 \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{6} \sqrt{\cosh ^{-1}(a x)}\right)}{64 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{5 c^2 \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}{8 a \sqrt{a x-1} \sqrt{a x+1}}",1,"(-5*c^2*Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]])/(8*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (3*c^2*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*Erf[2*Sqrt[ArcCosh[a*x]]])/(64*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (15*c^2*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(64*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (c^2*Sqrt[Pi/6]*Sqrt[c - a^2*c*x^2]*Erf[Sqrt[6]*Sqrt[ArcCosh[a*x]]])/(64*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (3*c^2*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*Erfi[2*Sqrt[ArcCosh[a*x]]])/(64*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (15*c^2*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(64*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (c^2*Sqrt[Pi/6]*Sqrt[c - a^2*c*x^2]*Erfi[Sqrt[6]*Sqrt[ArcCosh[a*x]]])/(64*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",19,7,24,0.2917,1,"{5713, 5701, 3312, 3307, 2180, 2204, 2205}"
403,1,294,0,0.3392925,"\int \frac{\left(c-a^2 c x^2\right)^{3/2}}{\sqrt{\cosh ^{-1}(a x)}} \, dx","Int[(c - a^2*c*x^2)^(3/2)/Sqrt[ArcCosh[a*x]],x]","-\frac{\sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{32 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{4 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{32 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{4 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{3 c \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}{4 a \sqrt{a x-1} \sqrt{a x+1}}","-\frac{\sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{32 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{4 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{32 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{4 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{3 c \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}{4 a \sqrt{a x-1} \sqrt{a x+1}}",1,"(-3*c*Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]])/(4*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*Erf[2*Sqrt[ArcCosh[a*x]]])/(32*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (c*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(4*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*Erfi[2*Sqrt[ArcCosh[a*x]]])/(32*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (c*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(4*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",14,7,24,0.2917,1,"{5713, 5701, 3312, 3307, 2180, 2204, 2205}"
404,1,175,0,0.2538085,"\int \frac{\sqrt{c-a^2 c x^2}}{\sqrt{\cosh ^{-1}(a x)}} \, dx","Int[Sqrt[c - a^2*c*x^2]/Sqrt[ArcCosh[a*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{4 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{4 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}{a \sqrt{a x-1} \sqrt{a x+1}}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{4 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{4 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}{a \sqrt{a x-1} \sqrt{a x+1}}",1,"-((Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]])/(a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])) + (Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(4*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(4*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",9,7,24,0.2917,1,"{5713, 5701, 3312, 3307, 2180, 2204, 2205}"
405,1,46,0,0.1596424,"\int \frac{1}{\sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}} \, dx","Int[1/(Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]]),x]","\frac{2 \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{a \sqrt{c-a^2 c x^2}}","\frac{2 \sqrt{a x-1} \sqrt{a x+1} \sqrt{\cosh ^{-1}(a x)}}{a \sqrt{c-a^2 c x^2}}",1,"(2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Sqrt[ArcCosh[a*x]])/(a*Sqrt[c - a^2*c*x^2])","A",2,2,24,0.08333,1,"{5713, 5676}"
406,0,0,0,0.198037,"\int \frac{1}{\left(c-a^2 c x^2\right)^{3/2} \sqrt{\cosh ^{-1}(a x)}} \, dx","Int[1/((c - a^2*c*x^2)^(3/2)*Sqrt[ArcCosh[a*x]]),x]","\int \frac{1}{\left(c-a^2 c x^2\right)^{3/2} \sqrt{\cosh ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{1}{\left(c-a^2 c x^2\right)^{3/2} \sqrt{\cosh ^{-1}(a x)}},x\right)",0,"-((Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Defer[Int][1/((-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*Sqrt[ArcCosh[a*x]]), x])/(c*Sqrt[c - a^2*c*x^2]))","A",0,0,0,0,-1,"{}"
407,0,0,0,0.2034317,"\int \frac{1}{\left(c-a^2 c x^2\right)^{5/2} \sqrt{\cosh ^{-1}(a x)}} \, dx","Int[1/((c - a^2*c*x^2)^(5/2)*Sqrt[ArcCosh[a*x]]),x]","\int \frac{1}{\left(c-a^2 c x^2\right)^{5/2} \sqrt{\cosh ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{1}{\left(c-a^2 c x^2\right)^{5/2} \sqrt{\cosh ^{-1}(a x)}},x\right)",0,"(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Defer[Int][1/((-1 + a*x)^(5/2)*(1 + a*x)^(5/2)*Sqrt[ArcCosh[a*x]]), x])/(c^2*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
408,1,444,0,0.4609333,"\int \frac{\left(c-a^2 c x^2\right)^{5/2}}{\cosh ^{-1}(a x)^{3/2}} \, dx","Int[(c - a^2*c*x^2)^(5/2)/ArcCosh[a*x]^(3/2),x]","\frac{3 \sqrt{\pi } c^2 \sqrt{c-a^2 c x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{8 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{15 \sqrt{\frac{\pi }{2}} c^2 \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{\frac{3 \pi }{2}} c^2 \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{6} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{3 \sqrt{\pi } c^2 \sqrt{c-a^2 c x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{8 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{15 \sqrt{\frac{\pi }{2}} c^2 \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{3 \pi }{2}} c^2 \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{6} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{2 c^2 (a x+1)^{5/2} (1-a x)^3 \sqrt{c-a^2 c x^2}}{a \sqrt{a x-1} \sqrt{\cosh ^{-1}(a x)}}","\frac{3 \sqrt{\pi } c^2 \sqrt{c-a^2 c x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{8 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{15 \sqrt{\frac{\pi }{2}} c^2 \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{\frac{3 \pi }{2}} c^2 \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{6} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{3 \sqrt{\pi } c^2 \sqrt{c-a^2 c x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{8 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{15 \sqrt{\frac{\pi }{2}} c^2 \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{3 \pi }{2}} c^2 \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{6} \sqrt{\cosh ^{-1}(a x)}\right)}{16 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{2 \sqrt{a x-1} \sqrt{a x+1} \left(c-a^2 c x^2\right)^{5/2}}{a \sqrt{\cosh ^{-1}(a x)}}",1,"(2*c^2*(1 - a*x)^3*(1 + a*x)^(5/2)*Sqrt[c - a^2*c*x^2])/(a*Sqrt[-1 + a*x]*Sqrt[ArcCosh[a*x]]) + (3*c^2*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*Erf[2*Sqrt[ArcCosh[a*x]]])/(8*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (15*c^2*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(16*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (c^2*Sqrt[(3*Pi)/2]*Sqrt[c - a^2*c*x^2]*Erf[Sqrt[6]*Sqrt[ArcCosh[a*x]]])/(16*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (3*c^2*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*Erfi[2*Sqrt[ArcCosh[a*x]]])/(8*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (15*c^2*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(16*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (c^2*Sqrt[(3*Pi)/2]*Sqrt[c - a^2*c*x^2]*Erfi[Sqrt[6]*Sqrt[ArcCosh[a*x]]])/(16*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",20,8,24,0.3333,1,"{5713, 5697, 5780, 5448, 3308, 2180, 2204, 2205}"
409,1,295,0,0.3488363,"\int \frac{\left(c-a^2 c x^2\right)^{3/2}}{\cosh ^{-1}(a x)^{3/2}} \, dx","Int[(c - a^2*c*x^2)^(3/2)/ArcCosh[a*x]^(3/2),x]","\frac{\sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{4 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{4 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{a \sqrt{a x-1} \sqrt{a x+1}}+\frac{2 c (a x+1)^{3/2} (1-a x)^2 \sqrt{c-a^2 c x^2}}{a \sqrt{a x-1} \sqrt{\cosh ^{-1}(a x)}}","\frac{\sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{4 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{a \sqrt{a x-1} \sqrt{a x+1}}-\frac{\sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{4 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{\pi }{2}} c \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{a \sqrt{a x-1} \sqrt{a x+1}}-\frac{2 \sqrt{a x-1} \sqrt{a x+1} \left(c-a^2 c x^2\right)^{3/2}}{a \sqrt{\cosh ^{-1}(a x)}}",1,"(2*c*(1 - a*x)^2*(1 + a*x)^(3/2)*Sqrt[c - a^2*c*x^2])/(a*Sqrt[-1 + a*x]*Sqrt[ArcCosh[a*x]]) + (c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*Erf[2*Sqrt[ArcCosh[a*x]]])/(4*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (c*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*Erfi[2*Sqrt[ArcCosh[a*x]]])/(4*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (c*Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",15,8,24,0.3333,1,"{5713, 5697, 5780, 5448, 3308, 2180, 2204, 2205}"
410,1,176,0,0.2387792,"\int \frac{\sqrt{c-a^2 c x^2}}{\cosh ^{-1}(a x)^{3/2}} \, dx","Int[Sqrt[c - a^2*c*x^2]/ArcCosh[a*x]^(3/2),x]","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{a \sqrt{a x-1} \sqrt{a x+1}}+\frac{2 \sqrt{a x+1} (1-a x) \sqrt{c-a^2 c x^2}}{a \sqrt{a x-1} \sqrt{\cosh ^{-1}(a x)}}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{a \sqrt{a x-1} \sqrt{a x+1}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{a \sqrt{a x-1} \sqrt{a x+1}}-\frac{2 \sqrt{a x-1} \sqrt{a x+1} \sqrt{c-a^2 c x^2}}{a \sqrt{\cosh ^{-1}(a x)}}",1,"(2*(1 - a*x)*Sqrt[1 + a*x]*Sqrt[c - a^2*c*x^2])/(a*Sqrt[-1 + a*x]*Sqrt[ArcCosh[a*x]]) - (Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (Sqrt[Pi/2]*Sqrt[c - a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",10,9,24,0.3750,1,"{5713, 5697, 5670, 5448, 12, 3308, 2180, 2204, 2205}"
411,1,46,0,0.1535497,"\int \frac{1}{\sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}} \, dx","Int[1/(Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(3/2)),x]","-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{a \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}","-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{a \sqrt{c-a^2 c x^2} \sqrt{\cosh ^{-1}(a x)}}",1,"(-2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(a*Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]])","A",2,2,24,0.08333,1,"{5713, 5676}"
412,0,0,0,0.2336065,"\int \frac{1}{\left(c-a^2 c x^2\right)^{3/2} \cosh ^{-1}(a x)^{3/2}} \, dx","Int[1/((c - a^2*c*x^2)^(3/2)*ArcCosh[a*x]^(3/2)),x]","\int \frac{1}{\left(c-a^2 c x^2\right)^{3/2} \cosh ^{-1}(a x)^{3/2}} \, dx","\frac{4 a \sqrt{a x-1} \sqrt{a x+1} \text{Int}\left(\frac{x}{\left(a^2 x^2-1\right)^2 \sqrt{\cosh ^{-1}(a x)}},x\right)}{c \sqrt{c-a^2 c x^2}}-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{a \left(c-a^2 c x^2\right)^{3/2} \sqrt{\cosh ^{-1}(a x)}}",0,"(-2*Sqrt[-1 + a*x])/(a*c*(1 - a*x)*Sqrt[1 + a*x]*Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]]) + (4*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Defer[Int][x/((-1 + a^2*x^2)^2*Sqrt[ArcCosh[a*x]]), x])/(c*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
413,0,0,0,0.2475128,"\int \frac{1}{\left(c-a^2 c x^2\right)^{5/2} \cosh ^{-1}(a x)^{3/2}} \, dx","Int[1/((c - a^2*c*x^2)^(5/2)*ArcCosh[a*x]^(3/2)),x]","\int \frac{1}{\left(c-a^2 c x^2\right)^{5/2} \cosh ^{-1}(a x)^{3/2}} \, dx","-\frac{8 a \sqrt{a x-1} \sqrt{a x+1} \text{Int}\left(\frac{x}{\left(a^2 x^2-1\right)^3 \sqrt{\cosh ^{-1}(a x)}},x\right)}{c^2 \sqrt{c-a^2 c x^2}}-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{a \left(c-a^2 c x^2\right)^{5/2} \sqrt{\cosh ^{-1}(a x)}}",0,"(-2*Sqrt[-1 + a*x])/(a*c^2*(1 - a*x)^2*(1 + a*x)^(3/2)*Sqrt[c - a^2*c*x^2]*Sqrt[ArcCosh[a*x]]) - (8*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Defer[Int][x/((-1 + a^2*x^2)^3*Sqrt[ArcCosh[a*x]]), x])/(c^2*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
414,1,337,0,0.7451051,"\int \frac{\left(c-a^2 c x^2\right)^{3/2}}{\cosh ^{-1}(a x)^{5/2}} \, dx","Int[(c - a^2*c*x^2)^(3/2)/ArcCosh[a*x]^(5/2),x]","-\frac{2 \sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{3 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{2 \sqrt{2 \pi } c \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{3 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{2 \sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{3 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{2 \sqrt{2 \pi } c \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{3 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{2 c (a x+1)^{3/2} (1-a x)^2 \sqrt{c-a^2 c x^2}}{3 a \sqrt{a x-1} \cosh ^{-1}(a x)^{3/2}}-\frac{16 c x \left(1-a^2 x^2\right) \sqrt{c-a^2 c x^2}}{3 \sqrt{\cosh ^{-1}(a x)}}","-\frac{2 \sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erf}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{3 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{2 \sqrt{2 \pi } c \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{3 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{2 \sqrt{\pi } c \sqrt{c-a^2 c x^2} \text{Erfi}\left(2 \sqrt{\cosh ^{-1}(a x)}\right)}{3 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{2 \sqrt{2 \pi } c \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{3 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{2 \sqrt{a x-1} \sqrt{a x+1} \left(c-a^2 c x^2\right)^{3/2}}{3 a \cosh ^{-1}(a x)^{3/2}}-\frac{16 c x (1-a x) (a x+1) \sqrt{c-a^2 c x^2}}{3 \sqrt{\cosh ^{-1}(a x)}}",1,"(2*c*(1 - a*x)^2*(1 + a*x)^(3/2)*Sqrt[c - a^2*c*x^2])/(3*a*Sqrt[-1 + a*x]*ArcCosh[a*x]^(3/2)) - (16*c*x*(1 - a^2*x^2)*Sqrt[c - a^2*c*x^2])/(3*Sqrt[ArcCosh[a*x]]) - (2*c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*Erf[2*Sqrt[ArcCosh[a*x]]])/(3*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (2*c*Sqrt[2*Pi]*Sqrt[c - a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(3*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) - (2*c*Sqrt[Pi]*Sqrt[c - a^2*c*x^2]*Erfi[2*Sqrt[ArcCosh[a*x]]])/(3*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (2*c*Sqrt[2*Pi]*Sqrt[c - a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(3*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",19,11,24,0.4583,1,"{5713, 5697, 5776, 5701, 3312, 3307, 2180, 2204, 2205, 5781, 5448}"
415,1,207,0,0.2233673,"\int \frac{\sqrt{c-a^2 c x^2}}{\cosh ^{-1}(a x)^{5/2}} \, dx","Int[Sqrt[c - a^2*c*x^2]/ArcCosh[a*x]^(5/2),x]","\frac{2 \sqrt{2 \pi } \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{3 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{2 \sqrt{2 \pi } \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{3 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{8 x \sqrt{c-a^2 c x^2}}{3 \sqrt{\cosh ^{-1}(a x)}}+\frac{2 (1-a x) \sqrt{a x+1} \sqrt{c-a^2 c x^2}}{3 a \sqrt{a x-1} \cosh ^{-1}(a x)^{3/2}}","\frac{2 \sqrt{2 \pi } \sqrt{c-a^2 c x^2} \text{Erf}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{3 a \sqrt{a x-1} \sqrt{a x+1}}+\frac{2 \sqrt{2 \pi } \sqrt{c-a^2 c x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\cosh ^{-1}(a x)}\right)}{3 a \sqrt{a x-1} \sqrt{a x+1}}-\frac{8 x \sqrt{c-a^2 c x^2}}{3 \sqrt{\cosh ^{-1}(a x)}}-\frac{2 \sqrt{a x-1} \sqrt{a x+1} \sqrt{c-a^2 c x^2}}{3 a \cosh ^{-1}(a x)^{3/2}}",1,"(2*(1 - a*x)*Sqrt[1 + a*x]*Sqrt[c - a^2*c*x^2])/(3*a*Sqrt[-1 + a*x]*ArcCosh[a*x]^(3/2)) - (8*x*Sqrt[c - a^2*c*x^2])/(3*Sqrt[ArcCosh[a*x]]) + (2*Sqrt[2*Pi]*Sqrt[c - a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(3*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]) + (2*Sqrt[2*Pi]*Sqrt[c - a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcCosh[a*x]]])/(3*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x])","A",8,7,24,0.2917,1,"{5713, 5697, 5666, 3307, 2180, 2204, 2205}"
416,1,48,0,0.1543371,"\int \frac{1}{\sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{5/2}} \, dx","Int[1/(Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(5/2)),x]","-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{3 a \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}}","-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{3 a \sqrt{c-a^2 c x^2} \cosh ^{-1}(a x)^{3/2}}",1,"(-2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(3*a*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(3/2))","A",2,2,24,0.08333,1,"{5713, 5676}"
417,0,0,0,0.2281312,"\int \frac{1}{\left(c-a^2 c x^2\right)^{3/2} \cosh ^{-1}(a x)^{5/2}} \, dx","Int[1/((c - a^2*c*x^2)^(3/2)*ArcCosh[a*x]^(5/2)),x]","\int \frac{1}{\left(c-a^2 c x^2\right)^{3/2} \cosh ^{-1}(a x)^{5/2}} \, dx","\frac{4 a \sqrt{a x-1} \sqrt{a x+1} \text{Int}\left(\frac{x}{\left(a^2 x^2-1\right)^2 \cosh ^{-1}(a x)^{3/2}},x\right)}{3 c \sqrt{c-a^2 c x^2}}-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{3 a \left(c-a^2 c x^2\right)^{3/2} \cosh ^{-1}(a x)^{3/2}}",0,"(-2*Sqrt[-1 + a*x])/(3*a*c*(1 - a*x)*Sqrt[1 + a*x]*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(3/2)) + (4*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Defer[Int][x/((-1 + a^2*x^2)^2*ArcCosh[a*x]^(3/2)), x])/(3*c*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
418,0,0,0,0.2255754,"\int \frac{1}{\left(c-a^2 c x^2\right)^{5/2} \cosh ^{-1}(a x)^{5/2}} \, dx","Int[1/((c - a^2*c*x^2)^(5/2)*ArcCosh[a*x]^(5/2)),x]","\int \frac{1}{\left(c-a^2 c x^2\right)^{5/2} \cosh ^{-1}(a x)^{5/2}} \, dx","-\frac{8 a \sqrt{a x-1} \sqrt{a x+1} \text{Int}\left(\frac{x}{\left(a^2 x^2-1\right)^3 \cosh ^{-1}(a x)^{3/2}},x\right)}{3 c^2 \sqrt{c-a^2 c x^2}}-\frac{2 \sqrt{a x-1} \sqrt{a x+1}}{3 a \left(c-a^2 c x^2\right)^{5/2} \cosh ^{-1}(a x)^{3/2}}",0,"(-2*Sqrt[-1 + a*x])/(3*a*c^2*(1 - a*x)^2*(1 + a*x)^(3/2)*Sqrt[c - a^2*c*x^2]*ArcCosh[a*x]^(3/2)) - (8*a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Defer[Int][x/((-1 + a^2*x^2)^3*ArcCosh[a*x]^(3/2)), x])/(3*c^2*Sqrt[c - a^2*c*x^2])","A",0,0,0,0,-1,"{}"
419,1,253,0,0.6204481,"\int x^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","Int[x^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n,x]","\frac{2^{-2 (n+3)} e^{-\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2^{-2 (n+3)} e^{\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{8 b c^3 (n+1) \sqrt{c x-1} \sqrt{c x+1}}","\frac{2^{-2 (n+3)} e^{-\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2^{-2 (n+3)} e^{\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{8 b c^3 (n+1) \sqrt{c x-1} \sqrt{c x+1}}",1,"-(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^(1 + n))/(8*b*c^3*(1 + n)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-4*(a + b*ArcCosh[c*x]))/b])/(2^(2*(3 + n))*c^3*E^((4*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (E^((4*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (4*(a + b*ArcCosh[c*x]))/b])/(2^(2*(3 + n))*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n)","A",7,5,29,0.1724,1,"{5798, 5781, 5448, 3307, 2181}"
420,1,379,0,0.6799727,"\int x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","Int[x*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n,x]","\frac{3^{-n-1} e^{-\frac{3 a}{b}} \sqrt{d-c^2 d 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{e^{-\frac{a}{b}} \sqrt{d-c^2 d 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)}{8 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{e^{a/b} \sqrt{d-c^2 d 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)}{8 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3^{-n-1} e^{\frac{3 a}{b}} \sqrt{d-c^2 d 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 c^2 \sqrt{c x-1} \sqrt{c x+1}}","\frac{3^{-n-1} e^{-\frac{3 a}{b}} \sqrt{d-c^2 d 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{e^{-\frac{a}{b}} \sqrt{d-c^2 d 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)}{8 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{e^{a/b} \sqrt{d-c^2 d 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)}{8 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3^{-n-1} e^{\frac{3 a}{b}} \sqrt{d-c^2 d 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 c^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"(3^(-1 - n)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-3*(a + b*ArcCosh[c*x]))/b])/(8*c^2*E^((3*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, -((a + b*ArcCosh[c*x])/b)])/(8*c^2*E^(a/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) + (E^(a/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (a + b*ArcCosh[c*x])/b])/(8*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) - (3^(-1 - n)*E^((3*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (3*(a + b*ArcCosh[c*x]))/b])/(8*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n)","A",10,5,27,0.1852,1,"{5798, 5781, 5448, 3307, 2181}"
421,1,253,0,0.3756732,"\int \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","Int[Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n,x]","\frac{2^{-n-3} e^{-\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{2^{-n-3} e^{\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{2 b c (n+1) \sqrt{c x-1} \sqrt{c x+1}}","\frac{2^{-n-3} e^{-\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{2^{-n-3} e^{\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{2 b c (n+1) \sqrt{c x-1} \sqrt{c x+1}}",1,"-(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^(1 + n))/(2*b*c*(1 + n)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2^(-3 - n)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-2*(a + b*ArcCosh[c*x]))/b])/(c*E^((2*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (2^(-3 - n)*E^((2*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (2*(a + b*ArcCosh[c*x]))/b])/(c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n)","A",7,5,26,0.1923,1,"{5713, 5701, 3312, 3307, 2181}"
422,0,0,0,1.0824971,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n}{x} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n)/x,x]","\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n}{x} \, dx","d \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x \sqrt{d-c^2 d x^2}},x\right)-\frac{d 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 \sqrt{d-c^2 d x^2}}+\frac{d 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 \sqrt{d-c^2 d x^2}}",0,"(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, -((a + b*ArcCosh[c*x])/b)])/(2*E^(a/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (E^(a/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (a + b*ArcCosh[c*x])/b])/(2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) - (Sqrt[d - c^2*d*x^2]*Defer[Int][(a + b*ArcCosh[c*x])^n/(x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
423,0,0,0,0.9016844,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n}{x^2} \, dx","Int[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n)/x^2,x]","\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n}{x^2} \, dx","d \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x^2 \sqrt{d-c^2 d x^2}},x\right)-\frac{c d \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{b (n+1) \sqrt{d-c^2 d x^2}}",0,"(c*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^(1 + n))/(b*(1 + n)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (Sqrt[d - c^2*d*x^2]*Defer[Int][(a + b*ArcCosh[c*x])^n/(x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
424,1,658,0,1.0516238,"\int x^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","Int[x^2*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])^n,x]","-\frac{d 2^{-n-7} 3^{-n-1} e^{-\frac{6 a}{b}} \sqrt{d-c^2 d 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{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d 2^{-2 n-7} e^{-\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d 2^{-n-7} e^{-\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d 2^{-n-7} e^{\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d 2^{-2 n-7} e^{\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d 2^{-n-7} 3^{-n-1} e^{\frac{6 a}{b}} \sqrt{d-c^2 d 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{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{16 b c^3 (n+1) \sqrt{c x-1} \sqrt{c x+1}}","-\frac{d 2^{-n-7} 3^{-n-1} e^{-\frac{6 a}{b}} \sqrt{d-c^2 d 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{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d 2^{-2 n-7} e^{-\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d 2^{-n-7} e^{-\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d 2^{-n-7} e^{\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d 2^{-2 n-7} e^{\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d 2^{-n-7} 3^{-n-1} e^{\frac{6 a}{b}} \sqrt{d-c^2 d 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{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{16 b c^3 (n+1) \sqrt{c x-1} \sqrt{c x+1}}",1,"-(d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^(1 + n))/(16*b*c^3*(1 + n)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2^(-7 - n)*3^(-1 - n)*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-6*(a + b*ArcCosh[c*x]))/b])/(c^3*E^((6*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) + (2^(-7 - 2*n)*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-4*(a + b*ArcCosh[c*x]))/b])/(c^3*E^((4*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) + (2^(-7 - n)*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-2*(a + b*ArcCosh[c*x]))/b])/(c^3*E^((2*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (2^(-7 - n)*d*E^((2*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (2*(a + b*ArcCosh[c*x]))/b])/(c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) - (2^(-7 - 2*n)*d*E^((4*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (4*(a + b*ArcCosh[c*x]))/b])/(c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) + (2^(-7 - n)*3^(-1 - n)*d*E^((6*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (6*(a + b*ArcCosh[c*x]))/b])/(c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n)","A",13,5,29,0.1724,1,"{5798, 5781, 5448, 3307, 2181}"
425,1,578,0,0.8253034,"\int x \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","Int[x*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])^n,x]","-\frac{d 5^{-n-1} e^{-\frac{5 a}{b}} \sqrt{d-c^2 d 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{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d 3^{-n} e^{-\frac{3 a}{b}} \sqrt{d-c^2 d 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d e^{-\frac{a}{b}} \sqrt{d-c^2 d 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)}{16 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d e^{a/b} \sqrt{d-c^2 d 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)}{16 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d 3^{-n} e^{\frac{3 a}{b}} \sqrt{d-c^2 d 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d 5^{-n-1} e^{\frac{5 a}{b}} \sqrt{d-c^2 d 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{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{d 5^{-n-1} e^{-\frac{5 a}{b}} \sqrt{d-c^2 d 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{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d 3^{-n} e^{-\frac{3 a}{b}} \sqrt{d-c^2 d 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d e^{-\frac{a}{b}} \sqrt{d-c^2 d 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)}{16 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d e^{a/b} \sqrt{d-c^2 d 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)}{16 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d 3^{-n} e^{\frac{3 a}{b}} \sqrt{d-c^2 d 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d 5^{-n-1} e^{\frac{5 a}{b}} \sqrt{d-c^2 d 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{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"-(5^(-1 - n)*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-5*(a + b*ArcCosh[c*x]))/b])/(32*c^2*E^((5*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) + (d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-3*(a + b*ArcCosh[c*x]))/b])/(32*3^n*c^2*E^((3*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, -((a + b*ArcCosh[c*x])/b)])/(16*c^2*E^(a/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) + (d*E^(a/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (a + b*ArcCosh[c*x])/b])/(16*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) - (d*E^((3*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (3*(a + b*ArcCosh[c*x]))/b])/(32*3^n*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) + (5^(-1 - n)*d*E^((5*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (5*(a + b*ArcCosh[c*x]))/b])/(32*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n)","A",13,5,27,0.1852,1,"{5798, 5781, 5448, 3307, 2181}"
426,1,450,0,0.5635485,"\int \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","Int[(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])^n,x]","-\frac{d 2^{-2 (n+3)} e^{-\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}+\frac{d 2^{-n-3} e^{-\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d 2^{-n-3} e^{\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}+\frac{d 2^{-2 (n+3)} e^{\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{8 b c (n+1) \sqrt{c x-1} \sqrt{c x+1}}","-\frac{d 2^{-2 (n+3)} e^{-\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}+\frac{d 2^{-n-3} e^{-\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d 2^{-n-3} e^{\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}+\frac{d 2^{-2 (n+3)} e^{\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 d \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{8 b c (n+1) \sqrt{c x-1} \sqrt{c x+1}}",1,"(-3*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^(1 + n))/(8*b*c*(1 + n)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-4*(a + b*ArcCosh[c*x]))/b])/(2^(2*(3 + n))*c*E^((4*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) + (2^(-3 - n)*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-2*(a + b*ArcCosh[c*x]))/b])/(c*E^((2*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (2^(-3 - n)*d*E^((2*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (2*(a + b*ArcCosh[c*x]))/b])/(c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) + (d*E^((4*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (4*(a + b*ArcCosh[c*x]))/b])/(2^(2*(3 + n))*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n)","A",10,5,26,0.1923,1,"{5713, 5701, 3312, 3307, 2181}"
427,0,0,0,1.8356393,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^n}{x} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])^n)/x,x]","\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^n}{x} \, dx","d^2 \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x \sqrt{d-c^2 d x^2}},x\right)+\frac{d^2 3^{-n-1} e^{-\frac{3 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 \sqrt{d-c^2 d x^2}}-\frac{5 d^2 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)}{8 \sqrt{d-c^2 d x^2}}+\frac{5 d^2 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)}{8 \sqrt{d-c^2 d x^2}}-\frac{d^2 3^{-n-1} e^{\frac{3 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 \sqrt{d-c^2 d x^2}}",0,"-(3^(-1 - n)*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-3*(a + b*ArcCosh[c*x]))/b])/(8*E^((3*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) + (5*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, -((a + b*ArcCosh[c*x])/b)])/(8*E^(a/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (5*d*E^(a/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (a + b*ArcCosh[c*x])/b])/(8*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) + (3^(-1 - n)*d*E^((3*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (3*(a + b*ArcCosh[c*x]))/b])/(8*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) - (d*Sqrt[d - c^2*d*x^2]*Defer[Int][(a + b*ArcCosh[c*x])^n/(x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
428,0,0,0,1.517457,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^n}{x^2} \, dx","Int[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])^n)/x^2,x]","\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^n}{x^2} \, dx","d^2 \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x^2 \sqrt{d-c^2 d x^2}},x\right)+\frac{c d^2 2^{-n-3} e^{-\frac{2 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{\sqrt{d-c^2 d x^2}}-\frac{c d^2 2^{-n-3} e^{\frac{2 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{\sqrt{d-c^2 d x^2}}-\frac{3 c d^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{2 b (n+1) \sqrt{d-c^2 d x^2}}",0,"(3*c*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^(1 + n))/(2*b*(1 + n)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2^(-3 - n)*c*d*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-2*(a + b*ArcCosh[c*x]))/b])/(E^((2*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) + (2^(-3 - n)*c*d*E^((2*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (2*(a + b*ArcCosh[c*x]))/b])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) - (d*Sqrt[d - c^2*d*x^2]*Defer[Int][(a + b*ArcCosh[c*x])^n/(x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
429,1,870,0,1.2415477,"\int x^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","Int[x^2*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x])^n,x]","\frac{2^{-3 n-11} d^2 e^{-\frac{8 a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{8 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n}}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2^{-n-7} 3^{-n-1} d^2 e^{-\frac{6 a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n}}{c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2^{-2 (n+4)} d^2 e^{-\frac{4 a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n}}{c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2^{-n-7} d^2 e^{-\frac{2 a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n}}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{128 b c^3 (n+1) \sqrt{c x-1} \sqrt{c x+1}}-\frac{2^{-n-7} d^2 e^{\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2^{-2 (n+4)} d^2 e^{\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2^{-n-7} 3^{-n-1} d^2 e^{\frac{6 a}{b}} \sqrt{d-c^2 d 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{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2^{-3 n-11} d^2 e^{\frac{8 a}{b}} \sqrt{d-c^2 d 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{8 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{2^{-3 n-11} d^2 e^{-\frac{8 a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{8 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n}}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2^{-n-7} 3^{-n-1} d^2 e^{-\frac{6 a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n}}{c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2^{-2 (n+4)} d^2 e^{-\frac{4 a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n}}{c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2^{-n-7} d^2 e^{-\frac{2 a}{b}} \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n}}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{128 b c^3 (n+1) \sqrt{c x-1} \sqrt{c x+1}}-\frac{2^{-n-7} d^2 e^{\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2^{-2 (n+4)} d^2 e^{\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2^{-n-7} 3^{-n-1} d^2 e^{\frac{6 a}{b}} \sqrt{d-c^2 d 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{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2^{-3 n-11} d^2 e^{\frac{8 a}{b}} \sqrt{d-c^2 d 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{8 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(-5*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^(1 + n))/(128*b*c^3*(1 + n)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2^(-11 - 3*n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-8*(a + b*ArcCosh[c*x]))/b])/(c^3*E^((8*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (2^(-7 - n)*3^(-1 - n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-6*(a + b*ArcCosh[c*x]))/b])/(c^3*E^((6*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) + (d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-4*(a + b*ArcCosh[c*x]))/b])/(2^(2*(4 + n))*c^3*E^((4*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) + (2^(-7 - n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-2*(a + b*ArcCosh[c*x]))/b])/(c^3*E^((2*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (2^(-7 - n)*d^2*E^((2*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (2*(a + b*ArcCosh[c*x]))/b])/(c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) - (d^2*E^((4*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (4*(a + b*ArcCosh[c*x]))/b])/(2^(2*(4 + n))*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) + (2^(-7 - n)*3^(-1 - n)*d^2*E^((6*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (6*(a + b*ArcCosh[c*x]))/b])/(c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) - (2^(-11 - 3*n)*d^2*E^((8*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (8*(a + b*ArcCosh[c*x]))/b])/(c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n)","A",16,5,29,0.1724,1,"{5798, 5781, 5448, 3307, 2181}"
430,1,793,0,1.0540185,"\int x \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","Int[x*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x])^n,x]","\frac{d^2 7^{-n-1} e^{-\frac{7 a}{b}} \sqrt{d-c^2 d 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{7 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 5^{-n} e^{-\frac{5 a}{b}} \sqrt{d-c^2 d 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{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d^2 3^{1-n} e^{-\frac{3 a}{b}} \sqrt{d-c^2 d 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 e^{-\frac{a}{b}} \sqrt{d-c^2 d 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)}{128 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 d^2 e^{a/b} \sqrt{d-c^2 d 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)}{128 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 3^{1-n} e^{\frac{3 a}{b}} \sqrt{d-c^2 d 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d^2 5^{-n} e^{\frac{5 a}{b}} \sqrt{d-c^2 d 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{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 7^{-n-1} e^{\frac{7 a}{b}} \sqrt{d-c^2 d 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{7 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c x-1} \sqrt{c x+1}}","\frac{d^2 7^{-n-1} e^{-\frac{7 a}{b}} \sqrt{d-c^2 d 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{7 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 5^{-n} e^{-\frac{5 a}{b}} \sqrt{d-c^2 d 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{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d^2 3^{1-n} e^{-\frac{3 a}{b}} \sqrt{d-c^2 d 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 e^{-\frac{a}{b}} \sqrt{d-c^2 d 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)}{128 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 d^2 e^{a/b} \sqrt{d-c^2 d 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)}{128 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 3^{1-n} e^{\frac{3 a}{b}} \sqrt{d-c^2 d 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d^2 5^{-n} e^{\frac{5 a}{b}} \sqrt{d-c^2 d 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{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 7^{-n-1} e^{\frac{7 a}{b}} \sqrt{d-c^2 d 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{7 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"(7^(-1 - n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-7*(a + b*ArcCosh[c*x]))/b])/(128*c^2*E^((7*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-5*(a + b*ArcCosh[c*x]))/b])/(128*5^n*c^2*E^((5*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) + (3^(1 - n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-3*(a + b*ArcCosh[c*x]))/b])/(128*c^2*E^((3*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (5*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, -((a + b*ArcCosh[c*x])/b)])/(128*c^2*E^(a/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) + (5*d^2*E^(a/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (a + b*ArcCosh[c*x])/b])/(128*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) - (3^(1 - n)*d^2*E^((3*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (3*(a + b*ArcCosh[c*x]))/b])/(128*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) + (d^2*E^((5*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (5*(a + b*ArcCosh[c*x]))/b])/(128*5^n*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) - (7^(-1 - n)*d^2*E^((7*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (7*(a + b*ArcCosh[c*x]))/b])/(128*c^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n)","A",16,5,27,0.1852,1,"{5798, 5781, 5448, 3307, 2181}"
431,1,674,0,0.7033047,"\int \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","Int[(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x])^n,x]","\frac{d^2 2^{-n-7} 3^{-n-1} e^{-\frac{6 a}{b}} \sqrt{d-c^2 d 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{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 d^2 2^{-2 n-7} e^{-\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}+\frac{15 d^2 2^{-n-7} e^{-\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{15 d^2 2^{-n-7} e^{\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 d^2 2^{-2 n-7} e^{\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 2^{-n-7} 3^{-n-1} e^{\frac{6 a}{b}} \sqrt{d-c^2 d 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{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{16 b c (n+1) \sqrt{c x-1} \sqrt{c x+1}}","\frac{d^2 2^{-n-7} 3^{-n-1} e^{-\frac{6 a}{b}} \sqrt{d-c^2 d 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{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 d^2 2^{-2 n-7} e^{-\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}+\frac{15 d^2 2^{-n-7} e^{-\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{15 d^2 2^{-n-7} e^{\frac{2 a}{b}} \sqrt{d-c^2 d 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 d^2 2^{-2 n-7} e^{\frac{4 a}{b}} \sqrt{d-c^2 d 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 2^{-n-7} 3^{-n-1} e^{\frac{6 a}{b}} \sqrt{d-c^2 d 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{6 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{16 b c (n+1) \sqrt{c x-1} \sqrt{c x+1}}",1,"(-5*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^(1 + n))/(16*b*c*(1 + n)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2^(-7 - n)*3^(-1 - n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-6*(a + b*ArcCosh[c*x]))/b])/(c*E^((6*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (3*2^(-7 - 2*n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-4*(a + b*ArcCosh[c*x]))/b])/(c*E^((4*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) + (15*2^(-7 - n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-2*(a + b*ArcCosh[c*x]))/b])/(c*E^((2*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (15*2^(-7 - n)*d^2*E^((2*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (2*(a + b*ArcCosh[c*x]))/b])/(c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) + (3*2^(-7 - 2*n)*d^2*E^((4*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (4*(a + b*ArcCosh[c*x]))/b])/(c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) - (2^(-7 - n)*3^(-1 - n)*d^2*E^((6*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (6*(a + b*ArcCosh[c*x]))/b])/(c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n)","A",13,5,26,0.1923,1,"{5713, 5701, 3312, 3307, 2181}"
432,0,0,0,2.5546986,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^n}{x} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x])^n)/x,x]","\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^n}{x} \, dx","-\frac{5^{-n-1} d^3 e^{-\frac{5 a}{b}} \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n}}{32 \sqrt{d-c^2 d x^2}}-\frac{5\ 3^{-n-1} d^3 e^{-\frac{3 a}{b}} \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n}}{32 \sqrt{d-c^2 d x^2}}+\frac{3^{-n} d^3 e^{-\frac{3 a}{b}} \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n}}{8 \sqrt{d-c^2 d x^2}}-\frac{11 d^3 e^{-\frac{a}{b}} \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{a+b \cosh ^{-1}(c x)}{b}\right) \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n}}{16 \sqrt{d-c^2 d x^2}}+\frac{11 d^3 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)}{16 \sqrt{d-c^2 d x^2}}+\frac{5\ 3^{-n-1} d^3 e^{\frac{3 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 \sqrt{d-c^2 d x^2}}-\frac{3^{-n} d^3 e^{\frac{3 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 \sqrt{d-c^2 d x^2}}+\frac{5^{-n-1} d^3 e^{\frac{5 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{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{32 \sqrt{d-c^2 d x^2}}+d^3 \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x \sqrt{d-c^2 d x^2}},x\right)",0,"(5^(-1 - n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-5*(a + b*ArcCosh[c*x]))/b])/(32*E^((5*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) + (5*3^(-1 - n)*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-3*(a + b*ArcCosh[c*x]))/b])/(32*E^((3*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-3*(a + b*ArcCosh[c*x]))/b])/(8*3^n*E^((3*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) + (11*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, -((a + b*ArcCosh[c*x])/b)])/(16*E^(a/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (11*d^2*E^(a/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (a + b*ArcCosh[c*x])/b])/(16*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) - (5*3^(-1 - n)*d^2*E^((3*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (3*(a + b*ArcCosh[c*x]))/b])/(32*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) + (d^2*E^((3*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (3*(a + b*ArcCosh[c*x]))/b])/(8*3^n*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) - (5^(-1 - n)*d^2*E^((5*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (5*(a + b*ArcCosh[c*x]))/b])/(32*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) - (d^2*Sqrt[d - c^2*d*x^2]*Defer[Int][(a + b*ArcCosh[c*x])^n/(x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
433,0,0,0,2.1881793,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^n}{x^2} \, dx","Int[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x])^n)/x^2,x]","\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^n}{x^2} \, dx","d^3 \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x^2 \sqrt{d-c^2 d x^2}},x\right)-\frac{c d^3 2^{-2 (n+3)} e^{-\frac{4 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{\sqrt{d-c^2 d x^2}}+\frac{c d^3 2^{-n-2} e^{-\frac{2 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{\sqrt{d-c^2 d x^2}}-\frac{c d^3 2^{-n-2} e^{\frac{2 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{\sqrt{d-c^2 d x^2}}+\frac{c d^3 2^{-2 (n+3)} e^{\frac{4 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{4 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{\sqrt{d-c^2 d x^2}}-\frac{15 c d^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{8 b (n+1) \sqrt{d-c^2 d x^2}}",0,"(15*c*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^(1 + n))/(8*b*(1 + n)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (c*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-4*(a + b*ArcCosh[c*x]))/b])/(2^(2*(3 + n))*E^((4*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) - (2^(-2 - n)*c*d^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-2*(a + b*ArcCosh[c*x]))/b])/(E^((2*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(-((a + b*ArcCosh[c*x])/b))^n) + (2^(-2 - n)*c*d^2*E^((2*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (2*(a + b*ArcCosh[c*x]))/b])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) - (c*d^2*E^((4*a)/b)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (4*(a + b*ArcCosh[c*x]))/b])/(2^(2*(3 + n))*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*((a + b*ArcCosh[c*x])/b)^n) - (d^2*Sqrt[d - c^2*d*x^2]*Defer[Int][(a + b*ArcCosh[c*x])^n/(x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
434,1,375,0,0.7320979,"\int \frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{1-c^2 x^2}} \, dx","Int[(x^3*(a + b*ArcCosh[c*x])^n)/Sqrt[1 - c^2*x^2],x]","\frac{3^{-n-1} e^{-\frac{3 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 c^4 \sqrt{1-c^2 x^2}}+\frac{3 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)}{8 c^4 \sqrt{1-c^2 x^2}}-\frac{3 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)}{8 c^4 \sqrt{1-c^2 x^2}}-\frac{3^{-n-1} e^{\frac{3 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 c^4 \sqrt{1-c^2 x^2}}","\frac{3^{-n-1} e^{-\frac{3 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 c^4 \sqrt{1-c x}}+\frac{3 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)}{8 c^4 \sqrt{1-c x}}-\frac{3 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)}{8 c^4 \sqrt{1-c x}}-\frac{3^{-n-1} e^{\frac{3 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 c^4 \sqrt{1-c x}}",1,"(3^(-1 - n)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-3*(a + b*ArcCosh[c*x]))/b])/(8*c^4*E^((3*a)/b)*Sqrt[1 - c^2*x^2]*(-((a + b*ArcCosh[c*x])/b))^n) + (3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, -((a + b*ArcCosh[c*x])/b)])/(8*c^4*E^(a/b)*Sqrt[1 - c^2*x^2]*(-((a + b*ArcCosh[c*x])/b))^n) - (3*E^(a/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (a + b*ArcCosh[c*x])/b])/(8*c^4*Sqrt[1 - c^2*x^2]*((a + b*ArcCosh[c*x])/b)^n) - (3^(-1 - n)*E^((3*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (3*(a + b*ArcCosh[c*x]))/b])/(8*c^4*Sqrt[1 - c^2*x^2]*((a + b*ArcCosh[c*x])/b)^n)","A",10,5,28,0.1786,1,"{5798, 5781, 3312, 3307, 2181}"
435,1,250,0,0.6157178,"\int \frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{1-c^2 x^2}} \, dx","Int[(x^2*(a + b*ArcCosh[c*x])^n)/Sqrt[1 - c^2*x^2],x]","\frac{2^{-n-3} e^{-\frac{2 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}-\frac{2^{-n-3} e^{\frac{2 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c^2 x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{2 b c^3 (n+1) \sqrt{1-c^2 x^2}}","\frac{2^{-n-3} e^{-\frac{2 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c x}}-\frac{2^{-n-3} e^{\frac{2 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{1-c x}}+\frac{\sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{2 b c^3 (n+1) \sqrt{1-c x}}",1,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^(1 + n))/(2*b*c^3*(1 + n)*Sqrt[1 - c^2*x^2]) + (2^(-3 - n)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-2*(a + b*ArcCosh[c*x]))/b])/(c^3*E^((2*a)/b)*Sqrt[1 - c^2*x^2]*(-((a + b*ArcCosh[c*x])/b))^n) - (2^(-3 - n)*E^((2*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (2*(a + b*ArcCosh[c*x]))/b])/(c^3*Sqrt[1 - c^2*x^2]*((a + b*ArcCosh[c*x])/b)^n)","A",7,5,28,0.1786,1,"{5798, 5781, 3312, 3307, 2181}"
436,1,180,0,0.4216909,"\int \frac{x \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{1-c^2 x^2}} \, dx","Int[(x*(a + b*ArcCosh[c*x])^n)/Sqrt[1 - c^2*x^2],x]","\frac{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{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{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{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}}",1,"(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)*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",5,4,26,0.1538,1,"{5798, 5781, 3307, 2181}"
437,1,56,0,0.2078318,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{1-c^2 x^2}} \, dx","Int[(a + b*ArcCosh[c*x])^n/Sqrt[1 - c^2*x^2],x]","\frac{\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{\sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{b c (n+1) \sqrt{1-c x}}",1,"(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])","A",2,2,25,0.08000,1,"{5713, 5676}"
438,0,0,0,0.4352391,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x \sqrt{1-c^2 x^2}} \, dx","Int[(a + b*ArcCosh[c*x])^n/(x*Sqrt[1 - c^2*x^2]),x]","\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x \sqrt{1-c^2 x^2}} \, dx","\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x \sqrt{1-c^2 x^2}},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][(a + b*ArcCosh[c*x])^n/(x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/Sqrt[1 - c^2*x^2]","A",0,0,0,0,-1,"{}"
439,0,0,0,0.445807,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x^2 \sqrt{1-c^2 x^2}} \, dx","Int[(a + b*ArcCosh[c*x])^n/(x^2*Sqrt[1 - c^2*x^2]),x]","\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x^2 \sqrt{1-c^2 x^2}} \, dx","\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x^2 \sqrt{1-c^2 x^2}},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][(a + b*ArcCosh[c*x])^n/(x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/Sqrt[1 - c^2*x^2]","A",0,0,0,0,-1,"{}"
440,1,379,0,0.8087105,"\int \frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^3*(a + b*ArcCosh[c*x])^n)/Sqrt[d - c^2*d*x^2],x]","\frac{3^{-n-1} e^{-\frac{3 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 c^4 \sqrt{d-c^2 d x^2}}+\frac{3 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)}{8 c^4 \sqrt{d-c^2 d x^2}}-\frac{3 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)}{8 c^4 \sqrt{d-c^2 d x^2}}-\frac{3^{-n-1} e^{\frac{3 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 c^4 \sqrt{d-c^2 d x^2}}","\frac{3^{-n-1} e^{-\frac{3 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 c^4 \sqrt{d-c^2 d x^2}}+\frac{3 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)}{8 c^4 \sqrt{d-c^2 d x^2}}-\frac{3 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)}{8 c^4 \sqrt{d-c^2 d x^2}}-\frac{3^{-n-1} e^{\frac{3 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{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{8 c^4 \sqrt{d-c^2 d x^2}}",1,"(3^(-1 - n)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-3*(a + b*ArcCosh[c*x]))/b])/(8*c^4*E^((3*a)/b)*Sqrt[d - c^2*d*x^2]*(-((a + b*ArcCosh[c*x])/b))^n) + (3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, -((a + b*ArcCosh[c*x])/b)])/(8*c^4*E^(a/b)*Sqrt[d - c^2*d*x^2]*(-((a + b*ArcCosh[c*x])/b))^n) - (3*E^(a/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (a + b*ArcCosh[c*x])/b])/(8*c^4*Sqrt[d - c^2*d*x^2]*((a + b*ArcCosh[c*x])/b)^n) - (3^(-1 - n)*E^((3*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (3*(a + b*ArcCosh[c*x]))/b])/(8*c^4*Sqrt[d - c^2*d*x^2]*((a + b*ArcCosh[c*x])/b)^n)","A",10,5,29,0.1724,1,"{5798, 5781, 3312, 3307, 2181}"
441,1,253,0,0.6399699,"\int \frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x^2*(a + b*ArcCosh[c*x])^n)/Sqrt[d - c^2*d*x^2],x]","\frac{2^{-n-3} e^{-\frac{2 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{d-c^2 d x^2}}-\frac{2^{-n-3} e^{\frac{2 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{d-c^2 d x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{2 b c^3 (n+1) \sqrt{d-c^2 d x^2}}","\frac{2^{-n-3} e^{-\frac{2 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{d-c^2 d x^2}}-\frac{2^{-n-3} e^{\frac{2 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{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{d-c^2 d x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{2 b c^3 (n+1) \sqrt{d-c^2 d x^2}}",1,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^(1 + n))/(2*b*c^3*(1 + n)*Sqrt[d - c^2*d*x^2]) + (2^(-3 - n)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (-2*(a + b*ArcCosh[c*x]))/b])/(c^3*E^((2*a)/b)*Sqrt[d - c^2*d*x^2]*(-((a + b*ArcCosh[c*x])/b))^n) - (2^(-3 - n)*E^((2*a)/b)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^n*Gamma[1 + n, (2*(a + b*ArcCosh[c*x]))/b])/(c^3*Sqrt[d - c^2*d*x^2]*((a + b*ArcCosh[c*x])/b)^n)","A",7,5,29,0.1724,1,"{5798, 5781, 3312, 3307, 2181}"
442,1,182,0,0.4194804,"\int \frac{x \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{d-c^2 d x^2}} \, dx","Int[(x*(a + b*ArcCosh[c*x])^n)/Sqrt[d - c^2*d*x^2],x]","\frac{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{d-c^2 d x^2}}-\frac{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{d-c^2 d x^2}}","\frac{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{d-c^2 d x^2}}-\frac{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{d-c^2 d x^2}}",1,"(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[d - c^2*d*x^2]*(-((a + b*ArcCosh[c*x])/b))^n) - (E^(a/b)*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[d - c^2*d*x^2]*((a + b*ArcCosh[c*x])/b)^n)","A",5,4,27,0.1481,1,"{5798, 5781, 3307, 2181}"
443,1,57,0,0.1937844,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCosh[c*x])^n/Sqrt[d - c^2*d*x^2],x]","\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{b c (n+1) \sqrt{d-c^2 d x^2}}","\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{b c (n+1) \sqrt{d-c^2 d x^2}}",1,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^(1 + n))/(b*c*(1 + n)*Sqrt[d - c^2*d*x^2])","A",2,2,26,0.07692,1,"{5713, 5676}"
444,0,0,0,0.442886,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCosh[c*x])^n/(x*Sqrt[d - c^2*d*x^2]),x]","\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x \sqrt{d-c^2 d x^2}} \, dx","\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x \sqrt{d-c^2 d x^2}},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][(a + b*ArcCosh[c*x])^n/(x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/Sqrt[d - c^2*d*x^2]","A",0,0,0,0,-1,"{}"
445,0,0,0,0.4647722,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x^2 \sqrt{d-c^2 d x^2}} \, dx","Int[(a + b*ArcCosh[c*x])^n/(x^2*Sqrt[d - c^2*d*x^2]),x]","\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x^2 \sqrt{d-c^2 d x^2}} \, dx","\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x^2 \sqrt{d-c^2 d x^2}},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][(a + b*ArcCosh[c*x])^n/(x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/Sqrt[d - c^2*d*x^2]","A",0,0,0,0,-1,"{}"
446,0,0,0,0.5253203,"\int \frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)^n}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x^2*(a + b*ArcCosh[c*x])^n)/(d - c^2*d*x^2)^(3/2),x]","\int \frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)^n}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)^n}{\left(d-c^2 d x^2\right)^{3/2}},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][(x^2*(a + b*ArcCosh[c*x])^n)/((-1 + c*x)^(3/2)*(1 + c*x)^(3/2)), x])/(d*Sqrt[d - c^2*d*x^2]))","A",0,0,0,0,-1,"{}"
447,0,0,0,0.3680617,"\int \frac{x \left(a+b \cosh ^{-1}(c x)\right)^n}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(x*(a + b*ArcCosh[c*x])^n)/(d - c^2*d*x^2)^(3/2),x]","\int \frac{x \left(a+b \cosh ^{-1}(c x)\right)^n}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{x \left(a+b \cosh ^{-1}(c x)\right)^n}{\left(d-c^2 d x^2\right)^{3/2}},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][(x*(a + b*ArcCosh[c*x])^n)/((-1 + c*x)^(3/2)*(1 + c*x)^(3/2)), x])/(d*Sqrt[d - c^2*d*x^2]))","A",0,0,0,0,-1,"{}"
448,0,0,0,0.2229322,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])^n/(d - c^2*d*x^2)^(3/2),x]","\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{\left(d-c^2 d x^2\right)^{3/2}},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][(a + b*ArcCosh[c*x])^n/((-1 + c*x)^(3/2)*(1 + c*x)^(3/2)), x])/(d*Sqrt[d - c^2*d*x^2]))","A",0,0,0,0,-1,"{}"
449,0,0,0,0.5208248,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])^n/(x*(d - c^2*d*x^2)^(3/2)),x]","\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x \left(d-c^2 d x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x \left(d-c^2 d x^2\right)^{3/2}},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][(a + b*ArcCosh[c*x])^n/(x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)), x])/(d*Sqrt[d - c^2*d*x^2]))","A",0,0,0,0,-1,"{}"
450,0,0,0,0.5249752,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x^2 \left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])^n/(x^2*(d - c^2*d*x^2)^(3/2)),x]","\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x^2 \left(d-c^2 d x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^n}{x^2 \left(d-c^2 d x^2\right)^{3/2}},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][(a + b*ArcCosh[c*x])^n/(x^2*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)), x])/(d*Sqrt[d - c^2*d*x^2]))","A",0,0,0,0,-1,"{}"
451,0,0,0,0.4167925,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{1-c^2 x^2}} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x])^n)/Sqrt[1 - c^2*x^2],x]","\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{1-c^2 x^2}} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{1-c^2 x^2}},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][((f*x)^m*(a + b*ArcCosh[c*x])^n)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/Sqrt[1 - c^2*x^2]","A",0,0,0,0,-1,"{}"
452,0,0,0,0.0900236,"\int (f x)^m \left(d-c^2 d x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","Int[(f*x)^m*(d - c^2*d*x^2)^2*(a + b*ArcCosh[c*x])^n,x]","\int (f x)^m \left(d-c^2 d x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","\text{Int}\left(\left(d-c^2 d x^2\right)^2 (f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n,x\right)",0,"Defer[Int][(f*x)^m*(d - c^2*d*x^2)^2*(a + b*ArcCosh[c*x])^n, x]","A",0,0,0,0,-1,"{}"
453,0,0,0,0.0572402,"\int (f x)^m \left(d-c^2 d x^2\right) \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","Int[(f*x)^m*(d - c^2*d*x^2)*(a + b*ArcCosh[c*x])^n,x]","\int (f x)^m \left(d-c^2 d x^2\right) \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","\text{Int}\left(\left(d-c^2 d x^2\right) (f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n,x\right)",0,"Defer[Int][(f*x)^m*(d - c^2*d*x^2)*(a + b*ArcCosh[c*x])^n, x]","A",0,0,0,0,-1,"{}"
454,0,0,0,0.0225902,"\int (f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","Int[(f*x)^m*(a + b*ArcCosh[c*x])^n,x]","\int (f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","\text{Int}\left((f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n,x\right)",0,"Defer[Int][(f*x)^m*(a + b*ArcCosh[c*x])^n, x]","A",0,0,0,0,-1,"{}"
455,0,0,0,0.1023929,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n}{d-c^2 d x^2} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x])^n)/(d - c^2*d*x^2),x]","\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n}{d-c^2 d x^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n}{d-c^2 d x^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcCosh[c*x])^n)/(d - c^2*d*x^2), x]","A",0,0,0,0,-1,"{}"
456,0,0,0,0.0992411,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n}{\left(d-c^2 d x^2\right)^2} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x])^n)/(d - c^2*d*x^2)^2,x]","\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n}{\left(d-c^2 d x^2\right)^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n}{\left(d-c^2 d x^2\right)^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcCosh[c*x])^n)/(d - c^2*d*x^2)^2, x]","A",0,0,0,0,-1,"{}"
457,0,0,0,0.4980896,"\int (f x)^m \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","Int[(f*x)^m*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])^n,x]","\int (f x)^m \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","\text{Int}\left(\left(d-c^2 d x^2\right)^{3/2} (f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n,x\right)",0,"-((d*Sqrt[d - c^2*d*x^2]*Defer[Int][(f*x)^m*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)*(a + b*ArcCosh[c*x])^n, x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]))","A",0,0,0,0,-1,"{}"
458,0,0,0,0.4011813,"\int (f x)^m \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","Int[(f*x)^m*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x])^n,x]","\int (f x)^m \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^n \, dx","\text{Int}\left(\sqrt{d-c^2 d x^2} (f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n,x\right)",0,"(Sqrt[d - c^2*d*x^2]*Defer[Int][(f*x)^m*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x])^n, x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",0,0,0,0,-1,"{}"
459,0,0,0,0.4362333,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{d-c^2 d x^2}} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x])^n)/Sqrt[d - c^2*d*x^2],x]","\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{d-c^2 d x^2}} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{d-c^2 d x^2}},x\right)",0,"(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][((f*x)^m*(a + b*ArcCosh[c*x])^n)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]), x])/Sqrt[d - c^2*d*x^2]","A",0,0,0,0,-1,"{}"
460,0,0,0,0.5029429,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x])^n)/(d - c^2*d*x^2)^(3/2),x]","\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)^n}{\left(d-c^2 d x^2\right)^{3/2}},x\right)",0,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Defer[Int][((f*x)^m*(a + b*ArcCosh[c*x])^n)/((-1 + c*x)^(3/2)*(1 + c*x)^(3/2)), x])/(d*Sqrt[d - c^2*d*x^2]))","A",0,0,0,0,-1,"{}"
461,1,177,0,0.1419173,"\int x^4 \left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^4*(d + e*x^2)*(a + b*ArcCosh[c*x]),x]","\frac{1}{5} d x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{7} e x^7 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b x^4 \sqrt{c x-1} \sqrt{c x+1} \left(49 c^2 d+30 e\right)}{1225 c^3}-\frac{4 b x^2 \sqrt{c x-1} \sqrt{c x+1} \left(49 c^2 d+30 e\right)}{3675 c^5}-\frac{8 b \sqrt{c x-1} \sqrt{c x+1} \left(49 c^2 d+30 e\right)}{3675 c^7}-\frac{b e x^6 \sqrt{c x-1} \sqrt{c x+1}}{49 c}","\frac{1}{5} d x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{7} e x^7 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b x^4 \sqrt{c x-1} \sqrt{c x+1} \left(49 c^2 d+30 e\right)}{1225 c^3}-\frac{4 b x^2 \sqrt{c x-1} \sqrt{c x+1} \left(49 c^2 d+30 e\right)}{3675 c^5}-\frac{8 b \sqrt{c x-1} \sqrt{c x+1} \left(49 c^2 d+30 e\right)}{3675 c^7}-\frac{b e x^6 \sqrt{c x-1} \sqrt{c x+1}}{49 c}",1,"(-8*b*(49*c^2*d + 30*e)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3675*c^7) - (4*b*(49*c^2*d + 30*e)*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(3675*c^5) - (b*(49*c^2*d + 30*e)*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(1225*c^3) - (b*e*x^6*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(49*c) + (d*x^5*(a + b*ArcCosh[c*x]))/5 + (e*x^7*(a + b*ArcCosh[c*x]))/7","A",7,5,19,0.2632,1,"{5786, 460, 100, 12, 74}"
462,1,161,0,0.1366144,"\int x^3 \left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)*(a + b*ArcCosh[c*x]),x]","\frac{1}{4} d x^4 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{6} e x^6 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b x^3 \sqrt{c x-1} \sqrt{c x+1} \left(9 c^2 d+5 e\right)}{144 c^3}-\frac{b x \sqrt{c x-1} \sqrt{c x+1} \left(9 c^2 d+5 e\right)}{96 c^5}-\frac{b \left(9 c^2 d+5 e\right) \cosh ^{-1}(c x)}{96 c^6}-\frac{b e x^5 \sqrt{c x-1} \sqrt{c x+1}}{36 c}","\frac{1}{4} d x^4 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{6} e x^6 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b x^3 \sqrt{c x-1} \sqrt{c x+1} \left(9 c^2 d+5 e\right)}{144 c^3}-\frac{b x \sqrt{c x-1} \sqrt{c x+1} \left(9 c^2 d+5 e\right)}{96 c^5}-\frac{b \left(9 c^2 d+5 e\right) \cosh ^{-1}(c x)}{96 c^6}-\frac{b e x^5 \sqrt{c x-1} \sqrt{c x+1}}{36 c}",1,"-(b*(9*c^2*d + 5*e)*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(96*c^5) - (b*(9*c^2*d + 5*e)*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(144*c^3) - (b*e*x^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(36*c) - (b*(9*c^2*d + 5*e)*ArcCosh[c*x])/(96*c^6) + (d*x^4*(a + b*ArcCosh[c*x]))/4 + (e*x^6*(a + b*ArcCosh[c*x]))/6","A",6,6,19,0.3158,1,"{5786, 460, 100, 12, 90, 52}"
463,1,138,0,0.1213128,"\int x^2 \left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)*(a + b*ArcCosh[c*x]),x]","\frac{1}{3} d x^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{5} e x^5 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1} \left(25 c^2 d+12 e\right)}{225 c^3}-\frac{2 b \sqrt{c x-1} \sqrt{c x+1} \left(25 c^2 d+12 e\right)}{225 c^5}-\frac{b e x^4 \sqrt{c x-1} \sqrt{c x+1}}{25 c}","\frac{1}{3} d x^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{5} e x^5 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1} \left(25 c^2 d+12 e\right)}{225 c^3}-\frac{2 b \sqrt{c x-1} \sqrt{c x+1} \left(25 c^2 d+12 e\right)}{225 c^5}-\frac{b e x^4 \sqrt{c x-1} \sqrt{c x+1}}{25 c}",1,"(-2*b*(25*c^2*d + 12*e)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(225*c^5) - (b*(25*c^2*d + 12*e)*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(225*c^3) - (b*e*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(25*c) + (d*x^3*(a + b*ArcCosh[c*x]))/3 + (e*x^5*(a + b*ArcCosh[c*x]))/5","A",5,5,19,0.2632,1,"{5786, 460, 100, 12, 74}"
464,1,122,0,0.1093577,"\int x \left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)*(a + b*ArcCosh[c*x]),x]","\frac{1}{2} d x^2 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} e x^4 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b x \sqrt{c x-1} \sqrt{c x+1} \left(8 c^2 d+3 e\right)}{32 c^3}-\frac{b \left(8 c^2 d+3 e\right) \cosh ^{-1}(c x)}{32 c^4}-\frac{b e x^3 \sqrt{c x-1} \sqrt{c x+1}}{16 c}","\frac{1}{2} d x^2 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} e x^4 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b x \sqrt{c x-1} \sqrt{c x+1} \left(8 c^2 d+3 e\right)}{32 c^3}-\frac{b \left(8 c^2 d+3 e\right) \cosh ^{-1}(c x)}{32 c^4}-\frac{b e x^3 \sqrt{c x-1} \sqrt{c x+1}}{16 c}",1,"-(b*(8*c^2*d + 3*e)*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(32*c^3) - (b*e*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(16*c) - (b*(8*c^2*d + 3*e)*ArcCosh[c*x])/(32*c^4) + (d*x^2*(a + b*ArcCosh[c*x]))/2 + (e*x^4*(a + b*ArcCosh[c*x]))/4","A",4,4,17,0.2353,1,"{5786, 460, 90, 52}"
465,1,94,0,0.0799358,"\int \left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)*(a + b*ArcCosh[c*x]),x]","d x \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} e x^3 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b \sqrt{c x-1} \sqrt{c x+1} \left(9 c^2 d+2 e\right)}{9 c^3}-\frac{b e x^2 \sqrt{c x-1} \sqrt{c x+1}}{9 c}","d x \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} e x^3 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b \sqrt{c x-1} \sqrt{c x+1} \left(9 c^2 d+2 e\right)}{9 c^3}-\frac{b e x^2 \sqrt{c x-1} \sqrt{c x+1}}{9 c}",1,"-(b*(9*c^2*d + 2*e)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(9*c^3) - (b*e*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(9*c) + d*x*(a + b*ArcCosh[c*x]) + (e*x^3*(a + b*ArcCosh[c*x]))/3","A",3,3,16,0.1875,1,"{5705, 460, 74}"
466,1,264,0,0.6757704,"\int \frac{\left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)*(a + b*ArcCosh[c*x]))/x,x]","-\frac{i b d \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+d \log (x) \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{2} e x^2 \left(a+b \cosh ^{-1}(c x)\right)-\frac{i b d \sqrt{1-c^2 x^2} \sin ^{-1}(c x)^2}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d \sqrt{1-c^2 x^2} \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b d \sqrt{1-c^2 x^2} \log (x) \sin ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b e \cosh ^{-1}(c x)}{4 c^2}-\frac{b e x \sqrt{c x-1} \sqrt{c x+1}}{4 c}","-\frac{i b d \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+d \log (x) \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{2} e x^2 \left(a+b \cosh ^{-1}(c x)\right)-\frac{i b d \sqrt{1-c^2 x^2} \sin ^{-1}(c x)^2}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d \sqrt{1-c^2 x^2} \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b d \sqrt{1-c^2 x^2} \log (x) \sin ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b e \cosh ^{-1}(c x)}{4 c^2}-\frac{b e x \sqrt{c x-1} \sqrt{c x+1}}{4 c}",1,"-(b*e*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*c) - (b*e*ArcCosh[c*x])/(4*c^2) + (e*x^2*(a + b*ArcCosh[c*x]))/2 - ((I/2)*b*d*Sqrt[1 - c^2*x^2]*ArcSin[c*x]^2)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d*Sqrt[1 - c^2*x^2]*ArcSin[c*x]*Log[1 - E^((2*I)*ArcSin[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + d*(a + b*ArcCosh[c*x])*Log[x] - (b*d*Sqrt[1 - c^2*x^2]*ArcSin[c*x]*Log[x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((I/2)*b*d*Sqrt[1 - c^2*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",13,13,19,0.6842,1,"{14, 5790, 12, 6742, 90, 52, 2328, 2326, 4625, 3717, 2190, 2279, 2391}"
467,1,75,0,0.0991049,"\int \frac{\left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)*(a + b*ArcCosh[c*x]))/x^2,x]","-\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{x}+e x \left(a+b \cosh ^{-1}(c x)\right)+b c d \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)-\frac{b e \sqrt{c x-1} \sqrt{c x+1}}{c}","-\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{x}+e x \left(a+b \cosh ^{-1}(c x)\right)+b c d \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)-\frac{b e \sqrt{c x-1} \sqrt{c x+1}}{c}",1,"-((b*e*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/c) - (d*(a + b*ArcCosh[c*x]))/x + e*x*(a + b*ArcCosh[c*x]) + b*c*d*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]]","A",4,4,19,0.2105,1,"{5786, 460, 92, 205}"
468,1,251,0,0.6114722,"\int \frac{\left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)*(a + b*ArcCosh[c*x]))/x^3,x]","-\frac{i b e \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}+e \log (x) \left(a+b \cosh ^{-1}(c x)\right)-\frac{i b e \sqrt{1-c^2 x^2} \sin ^{-1}(c x)^2}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e \sqrt{1-c^2 x^2} \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b e \sqrt{1-c^2 x^2} \log (x) \sin ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d \sqrt{c x-1} \sqrt{c x+1}}{2 x}","-\frac{i b e \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}+e \log (x) \left(a+b \cosh ^{-1}(c x)\right)-\frac{i b e \sqrt{1-c^2 x^2} \sin ^{-1}(c x)^2}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e \sqrt{1-c^2 x^2} \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b e \sqrt{1-c^2 x^2} \log (x) \sin ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d \sqrt{c x-1} \sqrt{c x+1}}{2 x}",1,"(b*c*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*x) - (d*(a + b*ArcCosh[c*x]))/(2*x^2) - ((I/2)*b*e*Sqrt[1 - c^2*x^2]*ArcSin[c*x]^2)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*e*Sqrt[1 - c^2*x^2]*ArcSin[c*x]*Log[1 - E^((2*I)*ArcSin[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + e*(a + b*ArcCosh[c*x])*Log[x] - (b*e*Sqrt[1 - c^2*x^2]*ArcSin[c*x]*Log[x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((I/2)*b*e*Sqrt[1 - c^2*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",11,11,19,0.5789,1,"{14, 5790, 6742, 95, 2328, 2326, 4625, 3717, 2190, 2279, 2391}"
469,1,94,0,0.1042772,"\int \frac{\left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)*(a + b*ArcCosh[c*x]))/x^4,x]","-\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}-\frac{e \left(a+b \cosh ^{-1}(c x)\right)}{x}+\frac{1}{6} b c \left(c^2 d+6 e\right) \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)+\frac{b c d \sqrt{c x-1} \sqrt{c x+1}}{6 x^2}","-\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}-\frac{e \left(a+b \cosh ^{-1}(c x)\right)}{x}+\frac{1}{6} b c \left(c^2 d+6 e\right) \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)+\frac{b c d \sqrt{c x-1} \sqrt{c x+1}}{6 x^2}",1,"(b*c*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*x^2) - (d*(a + b*ArcCosh[c*x]))/(3*x^3) - (e*(a + b*ArcCosh[c*x]))/x + (b*c*(c^2*d + 6*e)*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/6","A",4,4,19,0.2105,1,"{5786, 454, 92, 205}"
470,1,319,0,0.411012,"\int x^4 \left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^4*(d + e*x^2)^2*(a + b*ArcCosh[c*x]),x]","\frac{1}{5} d^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{2}{7} d e x^7 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{9} e^2 x^9 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b \left(1-c^2 x^2\right)^3 \left(21 c^4 d^2+90 c^2 d e+70 e^2\right)}{525 c^9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b \left(1-c^2 x^2\right)^2 \left(63 c^4 d^2+135 c^2 d e+70 e^2\right)}{945 c^9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \left(1-c^2 x^2\right) \left(63 c^4 d^2+90 c^2 d e+35 e^2\right)}{315 c^9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b e \left(1-c^2 x^2\right)^4 \left(9 c^2 d+14 e\right)}{441 c^9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^2 \left(1-c^2 x^2\right)^5}{81 c^9 \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{5} d^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{2}{7} d e x^7 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{9} e^2 x^9 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b \left(1-c^2 x^2\right)^3 \left(21 c^4 d^2+90 c^2 d e+70 e^2\right)}{525 c^9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b \left(1-c^2 x^2\right)^2 \left(63 c^4 d^2+135 c^2 d e+70 e^2\right)}{945 c^9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \left(1-c^2 x^2\right) \left(63 c^4 d^2+90 c^2 d e+35 e^2\right)}{315 c^9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b e \left(1-c^2 x^2\right)^4 \left(9 c^2 d+14 e\right)}{441 c^9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^2 \left(1-c^2 x^2\right)^5}{81 c^9 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*(63*c^4*d^2 + 90*c^2*d*e + 35*e^2)*(1 - c^2*x^2))/(315*c^9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*(63*c^4*d^2 + 135*c^2*d*e + 70*e^2)*(1 - c^2*x^2)^2)/(945*c^9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*(21*c^4*d^2 + 90*c^2*d*e + 70*e^2)*(1 - c^2*x^2)^3)/(525*c^9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*e*(9*c^2*d + 14*e)*(1 - c^2*x^2)^4)/(441*c^9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*e^2*(1 - c^2*x^2)^5)/(81*c^9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (d^2*x^5*(a + b*ArcCosh[c*x]))/5 + (2*d*e*x^7*(a + b*ArcCosh[c*x]))/7 + (e^2*x^9*(a + b*ArcCosh[c*x]))/9","A",7,7,21,0.3333,1,"{270, 5790, 12, 520, 1251, 897, 1153}"
471,1,341,0,0.3603076,"\int x^3 \left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)^2*(a + b*ArcCosh[c*x]),x]","\frac{1}{4} d^2 x^4 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} d e x^6 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{8} e^2 x^8 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b x^3 \left(1-c^2 x^2\right) \left(288 c^4 d^2+320 c^2 d e+105 e^2\right)}{4608 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x \left(1-c^2 x^2\right) \left(288 c^4 d^2+320 c^2 d e+105 e^2\right)}{3072 c^7 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{c^2 x^2-1} \left(288 c^4 d^2+320 c^2 d e+105 e^2\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{3072 c^8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e x^5 \left(1-c^2 x^2\right) \left(64 c^2 d+21 e\right)}{1152 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^2 x^7 \left(1-c^2 x^2\right)}{64 c \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{4} d^2 x^4 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} d e x^6 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{8} e^2 x^8 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b x^3 \left(1-c^2 x^2\right) \left(288 c^4 d^2+320 c^2 d e+105 e^2\right)}{4608 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x \left(1-c^2 x^2\right) \left(288 c^4 d^2+320 c^2 d e+105 e^2\right)}{3072 c^7 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{c^2 x^2-1} \left(288 c^4 d^2+320 c^2 d e+105 e^2\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{3072 c^8 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e x^5 \left(1-c^2 x^2\right) \left(64 c^2 d+21 e\right)}{1152 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^2 x^7 \left(1-c^2 x^2\right)}{64 c \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*(288*c^4*d^2 + 320*c^2*d*e + 105*e^2)*x*(1 - c^2*x^2))/(3072*c^7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*(288*c^4*d^2 + 320*c^2*d*e + 105*e^2)*x^3*(1 - c^2*x^2))/(4608*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*e*(64*c^2*d + 21*e)*x^5*(1 - c^2*x^2))/(1152*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*e^2*x^7*(1 - c^2*x^2))/(64*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (d^2*x^4*(a + b*ArcCosh[c*x]))/4 + (d*e*x^6*(a + b*ArcCosh[c*x]))/3 + (e^2*x^8*(a + b*ArcCosh[c*x]))/8 - (b*(288*c^4*d^2 + 320*c^2*d*e + 105*e^2)*Sqrt[-1 + c^2*x^2]*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/(3072*c^8*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",9,10,21,0.4762,1,"{266, 43, 5790, 12, 520, 1267, 459, 321, 217, 206}"
472,1,260,0,0.3184931,"\int x^2 \left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)^2*(a + b*ArcCosh[c*x]),x]","\frac{1}{3} d^2 x^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{2}{5} d e x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{7} e^2 x^7 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b \left(1-c^2 x^2\right)^2 \left(35 c^4 d^2+84 c^2 d e+45 e^2\right)}{315 c^7 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \left(1-c^2 x^2\right) \left(35 c^4 d^2+42 c^2 d e+15 e^2\right)}{105 c^7 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e \left(1-c^2 x^2\right)^3 \left(14 c^2 d+15 e\right)}{175 c^7 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b e^2 \left(1-c^2 x^2\right)^4}{49 c^7 \sqrt{c x-1} \sqrt{c x+1}}","\frac{1}{3} d^2 x^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{2}{5} d e x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{7} e^2 x^7 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b \left(1-c^2 x^2\right)^2 \left(35 c^4 d^2+84 c^2 d e+45 e^2\right)}{315 c^7 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \left(1-c^2 x^2\right) \left(35 c^4 d^2+42 c^2 d e+15 e^2\right)}{105 c^7 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e \left(1-c^2 x^2\right)^3 \left(14 c^2 d+15 e\right)}{175 c^7 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b e^2 \left(1-c^2 x^2\right)^4}{49 c^7 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*(35*c^4*d^2 + 42*c^2*d*e + 15*e^2)*(1 - c^2*x^2))/(105*c^7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*(35*c^4*d^2 + 84*c^2*d*e + 45*e^2)*(1 - c^2*x^2)^2)/(315*c^7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*e*(14*c^2*d + 15*e)*(1 - c^2*x^2)^3)/(175*c^7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*e^2*(1 - c^2*x^2)^4)/(49*c^7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (d^2*x^3*(a + b*ArcCosh[c*x]))/3 + (2*d*e*x^5*(a + b*ArcCosh[c*x]))/5 + (e^2*x^7*(a + b*ArcCosh[c*x]))/7","A",6,6,21,0.2857,1,"{270, 5790, 12, 520, 1251, 771}"
473,1,269,0,0.248621,"\int x \left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)^2*(a + b*ArcCosh[c*x]),x]","\frac{\left(d+e x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)}{6 e}+\frac{b x \left(1-c^2 x^2\right) \left(44 c^4 d^2+44 c^2 d e+15 e^2\right)}{288 c^5 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{c^2 x^2-1} \left(2 c^2 d+e\right) \left(8 c^4 d^2+8 c^2 d e+5 e^2\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{96 c^6 e \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x \left(1-c^2 x^2\right) \left(d+e x^2\right)^2}{36 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b x \left(1-c^2 x^2\right) \left(2 c^2 d+e\right) \left(d+e x^2\right)}{144 c^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{\left(d+e x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)}{6 e}+\frac{b x \left(1-c^2 x^2\right) \left(44 c^4 d^2+44 c^2 d e+15 e^2\right)}{288 c^5 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{c^2 x^2-1} \left(2 c^2 d+e\right) \left(8 c^4 d^2+8 c^2 d e+5 e^2\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{96 c^6 e \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x \left(1-c^2 x^2\right) \left(d+e x^2\right)^2}{36 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b x \left(1-c^2 x^2\right) \left(2 c^2 d+e\right) \left(d+e x^2\right)}{144 c^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*(44*c^4*d^2 + 44*c^2*d*e + 15*e^2)*x*(1 - c^2*x^2))/(288*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (5*b*(2*c^2*d + e)*x*(1 - c^2*x^2)*(d + e*x^2))/(144*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*x*(1 - c^2*x^2)*(d + e*x^2)^2)/(36*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((d + e*x^2)^3*(a + b*ArcCosh[c*x]))/(6*e) - (b*(2*c^2*d + e)*(8*c^4*d^2 + 8*c^2*d*e + 5*e^2)*Sqrt[-1 + c^2*x^2]*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/(96*c^6*e*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",7,7,19,0.3684,1,"{5788, 902, 416, 528, 388, 217, 206}"
474,1,196,0,0.2032846,"\int \left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^2*(a + b*ArcCosh[c*x]),x]","d^2 x \left(a+b \cosh ^{-1}(c x)\right)+\frac{2}{3} d e x^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{5} e^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b \left(1-c^2 x^2\right) \left(15 c^4 d^2+10 c^2 d e+3 e^2\right)}{15 c^5 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b e \left(1-c^2 x^2\right)^2 \left(5 c^2 d+3 e\right)}{45 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^2 \left(1-c^2 x^2\right)^3}{25 c^5 \sqrt{c x-1} \sqrt{c x+1}}","d^2 x \left(a+b \cosh ^{-1}(c x)\right)+\frac{2}{3} d e x^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{5} e^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b \left(1-c^2 x^2\right) \left(15 c^4 d^2+10 c^2 d e+3 e^2\right)}{15 c^5 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b e \left(1-c^2 x^2\right)^2 \left(5 c^2 d+3 e\right)}{45 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^2 \left(1-c^2 x^2\right)^3}{25 c^5 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*(15*c^4*d^2 + 10*c^2*d*e + 3*e^2)*(1 - c^2*x^2))/(15*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (2*b*e*(5*c^2*d + 3*e)*(1 - c^2*x^2)^2)/(45*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*e^2*(1 - c^2*x^2)^3)/(25*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + d^2*x*(a + b*ArcCosh[c*x]) + (2*d*e*x^3*(a + b*ArcCosh[c*x]))/3 + (e^2*x^5*(a + b*ArcCosh[c*x]))/5","A",6,6,18,0.3333,1,"{194, 5705, 12, 520, 1247, 698}"
475,1,369,0,0.7864138,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)^2*(a + b*ArcCosh[c*x]))/x,x]","-\frac{i b d^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+d^2 \log (x) \left(a+b \cosh ^{-1}(c x)\right)+d e x^2 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} e^2 x^4 \left(a+b \cosh ^{-1}(c x)\right)-\frac{i b d^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)^2}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^2 \sqrt{1-c^2 x^2} \log (x) \sin ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b d e \cosh ^{-1}(c x)}{2 c^2}-\frac{3 b e^2 x \sqrt{c x-1} \sqrt{c x+1}}{32 c^3}-\frac{3 b e^2 \cosh ^{-1}(c x)}{32 c^4}-\frac{b d e x \sqrt{c x-1} \sqrt{c x+1}}{2 c}-\frac{b e^2 x^3 \sqrt{c x-1} \sqrt{c x+1}}{16 c}","-\frac{i b d^2 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+d^2 \log (x) \left(a+b \cosh ^{-1}(c x)\right)+d e x^2 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} e^2 x^4 \left(a+b \cosh ^{-1}(c x)\right)-\frac{i b d^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)^2}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 \sqrt{1-c^2 x^2} \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^2 \sqrt{1-c^2 x^2} \log (x) \sin ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b e x \sqrt{c x-1} \sqrt{c x+1} \left(16 c^2 d+3 e\right)}{32 c^3}-\frac{b e \left(16 c^2 d+3 e\right) \cosh ^{-1}(c x)}{32 c^4}-\frac{b e^2 x^3 \sqrt{c x-1} \sqrt{c x+1}}{16 c}",1,"-(b*d*e*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*c) - (3*b*e^2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(32*c^3) - (b*e^2*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(16*c) - (b*d*e*ArcCosh[c*x])/(2*c^2) - (3*b*e^2*ArcCosh[c*x])/(32*c^4) + d*e*x^2*(a + b*ArcCosh[c*x]) + (e^2*x^4*(a + b*ArcCosh[c*x]))/4 - ((I/2)*b*d^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x]^2)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x]*Log[1 - E^((2*I)*ArcSin[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + d^2*(a + b*ArcCosh[c*x])*Log[x] - (b*d^2*Sqrt[1 - c^2*x^2]*ArcSin[c*x]*Log[x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((I/2)*b*d^2*Sqrt[1 - c^2*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",16,15,21,0.7143,1,"{266, 43, 5790, 6742, 90, 52, 100, 12, 2328, 2326, 4625, 3717, 2190, 2279, 2391}"
476,1,185,0,0.3022259,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)^2*(a + b*ArcCosh[c*x]))/x^2,x]","-\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)}{x}+2 d e x \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} e^2 x^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b c d^2 \sqrt{c^2 x^2-1} \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{b e \left(1-c^2 x^2\right) \left(6 c^2 d+e\right)}{3 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b e^2 \left(1-c^2 x^2\right)^2}{9 c^3 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)}{x}+2 d e x \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} e^2 x^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b e \left(1-c^2 x^2\right) \left(6 c^2 d+e\right)}{3 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b e^2 \left(1-c^2 x^2\right)^2}{9 c^3 \sqrt{c x-1} \sqrt{c x+1}}+b c d^2 \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)",1,"(b*e*(6*c^2*d + e)*(1 - c^2*x^2))/(3*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*e^2*(1 - c^2*x^2)^2)/(9*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d^2*(a + b*ArcCosh[c*x]))/x + 2*d*e*x*(a + b*ArcCosh[c*x]) + (e^2*x^3*(a + b*ArcCosh[c*x]))/3 + (b*c*d^2*Sqrt[-1 + c^2*x^2]*ArcTan[Sqrt[-1 + c^2*x^2]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",7,7,21,0.3333,1,"{270, 5790, 520, 1251, 897, 1153, 205}"
477,1,321,0,0.8142146,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)^2*(a + b*ArcCosh[c*x]))/x^3,x]","-\frac{i b d e \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}+2 d e \log (x) \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{2} e^2 x^2 \left(a+b \cosh ^{-1}(c x)\right)-\frac{i b d e \sqrt{1-c^2 x^2} \sin ^{-1}(c x)^2}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d e \sqrt{1-c^2 x^2} \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b d e \sqrt{1-c^2 x^2} \log (x) \sin ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b e^2 \cosh ^{-1}(c x)}{4 c^2}+\frac{b c d^2 \sqrt{c x-1} \sqrt{c x+1}}{2 x}-\frac{b e^2 x \sqrt{c x-1} \sqrt{c x+1}}{4 c}","-\frac{i b d e \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}+2 d e \log (x) \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{2} e^2 x^2 \left(a+b \cosh ^{-1}(c x)\right)-\frac{i b d e \sqrt{1-c^2 x^2} \sin ^{-1}(c x)^2}{\sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d e \sqrt{1-c^2 x^2} \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b d e \sqrt{1-c^2 x^2} \log (x) \sin ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b e^2 \cosh ^{-1}(c x)}{4 c^2}+\frac{b c d^2 \sqrt{c x-1} \sqrt{c x+1}}{2 x}-\frac{b e^2 x \sqrt{c x-1} \sqrt{c x+1}}{4 c}",1,"(b*c*d^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*x) - (b*e^2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*c) - (b*e^2*ArcCosh[c*x])/(4*c^2) - (d^2*(a + b*ArcCosh[c*x]))/(2*x^2) + (e^2*x^2*(a + b*ArcCosh[c*x]))/2 - (I*b*d*e*Sqrt[1 - c^2*x^2]*ArcSin[c*x]^2)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*d*e*Sqrt[1 - c^2*x^2]*ArcSin[c*x]*Log[1 - E^((2*I)*ArcSin[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + 2*d*e*(a + b*ArcCosh[c*x])*Log[x] - (2*b*d*e*Sqrt[1 - c^2*x^2]*ArcSin[c*x]*Log[x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (I*b*d*e*Sqrt[1 - c^2*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",14,15,21,0.7143,1,"{266, 43, 5790, 12, 6742, 95, 90, 52, 2328, 2326, 4625, 3717, 2190, 2279, 2391}"
478,1,184,0,0.2787894,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)^2*(a + b*ArcCosh[c*x]))/x^4,x]","-\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}-\frac{2 d e \left(a+b \cosh ^{-1}(c x)\right)}{x}+e^2 x \left(a+b \cosh ^{-1}(c x)\right)-\frac{b c d^2 \left(1-c^2 x^2\right)}{6 x^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d \sqrt{c^2 x^2-1} \left(c^2 d+12 e\right) \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{6 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^2 \left(1-c^2 x^2\right)}{c \sqrt{c x-1} \sqrt{c x+1}}","-\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}-\frac{2 d e \left(a+b \cosh ^{-1}(c x)\right)}{x}+e^2 x \left(a+b \cosh ^{-1}(c x)\right)-\frac{b c d^2 \left(1-c^2 x^2\right)}{6 x^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d \sqrt{c^2 x^2-1} \left(c^2 d+12 e\right) \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{6 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^2 \left(1-c^2 x^2\right)}{c \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*e^2*(1 - c^2*x^2))/(c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d^2*(1 - c^2*x^2))/(6*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d^2*(a + b*ArcCosh[c*x]))/(3*x^3) - (2*d*e*(a + b*ArcCosh[c*x]))/x + e^2*x*(a + b*ArcCosh[c*x]) + (b*c*d*(c^2*d + 12*e)*Sqrt[-1 + c^2*x^2]*ArcTan[Sqrt[-1 + c^2*x^2]])/(6*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",7,8,21,0.3810,1,"{270, 5790, 520, 1251, 897, 1157, 388, 205}"
479,1,435,0,0.6168259,"\int x^4 \left(d+e x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^4*(d + e*x^2)^3*(a + b*ArcCosh[c*x]),x]","\frac{3}{7} d^2 e x^7 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{5} d^3 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} d e^2 x^9 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{11} e^3 x^{11} \left(a+b \cosh ^{-1}(c x)\right)-\frac{b e \left(1-c^2 x^2\right)^4 \left(99 c^4 d^2+308 c^2 d e+210 e^2\right)}{1617 c^{11} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \left(1-c^2 x^2\right)^3 \left(495 c^4 d^2 e+77 c^6 d^3+770 c^2 d e^2+350 e^3\right)}{1925 c^{11} \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \left(1-c^2 x^2\right)^2 \left(1485 c^4 d^2 e+462 c^6 d^3+1540 c^2 d e^2+525 e^3\right)}{3465 c^{11} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \left(1-c^2 x^2\right) \left(495 c^4 d^2 e+231 c^6 d^3+385 c^2 d e^2+105 e^3\right)}{1155 c^{11} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^2 \left(1-c^2 x^2\right)^5 \left(11 c^2 d+15 e\right)}{297 c^{11} \sqrt{c x-1} \sqrt{c x+1}}-\frac{b e^3 \left(1-c^2 x^2\right)^6}{121 c^{11} \sqrt{c x-1} \sqrt{c x+1}}","\frac{3}{7} d^2 e x^7 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{5} d^3 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} d e^2 x^9 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{11} e^3 x^{11} \left(a+b \cosh ^{-1}(c x)\right)-\frac{b e \left(1-c^2 x^2\right)^4 \left(99 c^4 d^2+308 c^2 d e+210 e^2\right)}{1617 c^{11} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \left(1-c^2 x^2\right)^3 \left(495 c^4 d^2 e+77 c^6 d^3+770 c^2 d e^2+350 e^3\right)}{1925 c^{11} \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \left(1-c^2 x^2\right)^2 \left(1485 c^4 d^2 e+462 c^6 d^3+1540 c^2 d e^2+525 e^3\right)}{3465 c^{11} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \left(1-c^2 x^2\right) \left(495 c^4 d^2 e+231 c^6 d^3+385 c^2 d e^2+105 e^3\right)}{1155 c^{11} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^2 \left(1-c^2 x^2\right)^5 \left(11 c^2 d+15 e\right)}{297 c^{11} \sqrt{c x-1} \sqrt{c x+1}}-\frac{b e^3 \left(1-c^2 x^2\right)^6}{121 c^{11} \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*(231*c^6*d^3 + 495*c^4*d^2*e + 385*c^2*d*e^2 + 105*e^3)*(1 - c^2*x^2))/(1155*c^11*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*(462*c^6*d^3 + 1485*c^4*d^2*e + 1540*c^2*d*e^2 + 525*e^3)*(1 - c^2*x^2)^2)/(3465*c^11*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*(77*c^6*d^3 + 495*c^4*d^2*e + 770*c^2*d*e^2 + 350*e^3)*(1 - c^2*x^2)^3)/(1925*c^11*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*e*(99*c^4*d^2 + 308*c^2*d*e + 210*e^2)*(1 - c^2*x^2)^4)/(1617*c^11*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*e^2*(11*c^2*d + 15*e)*(1 - c^2*x^2)^5)/(297*c^11*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*e^3*(1 - c^2*x^2)^6)/(121*c^11*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (d^3*x^5*(a + b*ArcCosh[c*x]))/5 + (3*d^2*e*x^7*(a + b*ArcCosh[c*x]))/7 + (d*e^2*x^9*(a + b*ArcCosh[c*x]))/3 + (e^3*x^11*(a + b*ArcCosh[c*x]))/11","A",6,6,21,0.2857,1,"{270, 5790, 12, 1610, 1799, 1620}"
480,1,494,0,0.6479435,"\int x^3 \left(d+e x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)^3*(a + b*ArcCosh[c*x]),x]","\frac{\left(d+e x^2\right)^5 \left(a+b \cosh ^{-1}(c x)\right)}{10 e^2}-\frac{d \left(d+e x^2\right)^4 \left(a+b \cosh ^{-1}(c x)\right)}{8 e^2}+\frac{b x \left(1-c^2 x^2\right) \left(26 c^4 d^2+201 c^2 d e+126 e^2\right) \left(d+e x^2\right)^2}{9600 c^5 e \sqrt{c x-1} \sqrt{c x+1}}-\frac{b x \left(1-c^2 x^2\right) \left(-1096 c^4 d^2 e+136 c^6 d^3-1617 c^2 d e^2-630 e^3\right) \left(d+e x^2\right)}{38400 c^7 e \sqrt{c x-1} \sqrt{c x+1}}-\frac{b x \left(1-c^2 x^2\right) \left(-7758 c^4 d^2 e^2-2536 c^6 d^3 e+1232 c^8 d^4-6615 c^2 d e^3-1890 e^4\right)}{76800 c^9 e \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \sqrt{c^2 x^2-1} \left(-480 c^6 d^3 e^2-800 c^4 d^2 e^3+128 c^{10} d^5-525 c^2 d e^4-126 e^5\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{5120 c^{10} e^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x \left(1-c^2 x^2\right) \left(d+e x^2\right)^4}{100 c e \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x \left(1-c^2 x^2\right) \left(11 c^2 d+18 e\right) \left(d+e x^2\right)^3}{1600 c^3 e \sqrt{c x-1} \sqrt{c x+1}}","\frac{\left(d+e x^2\right)^5 \left(a+b \cosh ^{-1}(c x)\right)}{10 e^2}-\frac{d \left(d+e x^2\right)^4 \left(a+b \cosh ^{-1}(c x)\right)}{8 e^2}+\frac{b x \left(1-c^2 x^2\right) \left(26 c^4 d^2+201 c^2 d e+126 e^2\right) \left(d+e x^2\right)^2}{9600 c^5 e \sqrt{c x-1} \sqrt{c x+1}}-\frac{b x \left(1-c^2 x^2\right) \left(-1096 c^4 d^2 e+136 c^6 d^3-1617 c^2 d e^2-630 e^3\right) \left(d+e x^2\right)}{38400 c^7 e \sqrt{c x-1} \sqrt{c x+1}}-\frac{b x \left(1-c^2 x^2\right) \left(-7758 c^4 d^2 e^2-2536 c^6 d^3 e+1232 c^8 d^4-6615 c^2 d e^3-1890 e^4\right)}{76800 c^9 e \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \sqrt{c^2 x^2-1} \left(-480 c^6 d^3 e^2-800 c^4 d^2 e^3+128 c^{10} d^5-525 c^2 d e^4-126 e^5\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{5120 c^{10} e^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x \left(1-c^2 x^2\right) \left(d+e x^2\right)^4}{100 c e \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x \left(1-c^2 x^2\right) \left(11 c^2 d+18 e\right) \left(d+e x^2\right)^3}{1600 c^3 e \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*(1232*c^8*d^4 - 2536*c^6*d^3*e - 7758*c^4*d^2*e^2 - 6615*c^2*d*e^3 - 1890*e^4)*x*(1 - c^2*x^2))/(76800*c^9*e*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*(136*c^6*d^3 - 1096*c^4*d^2*e - 1617*c^2*d*e^2 - 630*e^3)*x*(1 - c^2*x^2)*(d + e*x^2))/(38400*c^7*e*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*(26*c^4*d^2 + 201*c^2*d*e + 126*e^2)*x*(1 - c^2*x^2)*(d + e*x^2)^2)/(9600*c^5*e*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*(11*c^2*d + 18*e)*x*(1 - c^2*x^2)*(d + e*x^2)^3)/(1600*c^3*e*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*x*(1 - c^2*x^2)*(d + e*x^2)^4)/(100*c*e*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d*(d + e*x^2)^4*(a + b*ArcCosh[c*x]))/(8*e^2) + ((d + e*x^2)^5*(a + b*ArcCosh[c*x]))/(10*e^2) + (b*(128*c^10*d^5 - 480*c^6*d^3*e^2 - 800*c^4*d^2*e^3 - 525*c^2*d*e^4 - 126*e^5)*Sqrt[-1 + c^2*x^2]*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/(5120*c^10*e^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",10,9,21,0.4286,1,"{266, 43, 5790, 12, 566, 528, 388, 217, 206}"
481,1,365,0,0.5412528,"\int x^2 \left(d+e x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)^3*(a + b*ArcCosh[c*x]),x]","\frac{3}{5} d^2 e x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} d^3 x^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{3}{7} d e^2 x^7 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{9} e^3 x^9 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b e \left(1-c^2 x^2\right)^3 \left(63 c^4 d^2+135 c^2 d e+70 e^2\right)}{525 c^9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \left(1-c^2 x^2\right)^2 \left(378 c^4 d^2 e+105 c^6 d^3+405 c^2 d e^2+140 e^3\right)}{945 c^9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \left(1-c^2 x^2\right) \left(189 c^4 d^2 e+105 c^6 d^3+135 c^2 d e^2+35 e^3\right)}{315 c^9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b e^2 \left(1-c^2 x^2\right)^4 \left(27 c^2 d+28 e\right)}{441 c^9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^3 \left(1-c^2 x^2\right)^5}{81 c^9 \sqrt{c x-1} \sqrt{c x+1}}","\frac{3}{5} d^2 e x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} d^3 x^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{3}{7} d e^2 x^7 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{9} e^3 x^9 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b e \left(1-c^2 x^2\right)^3 \left(63 c^4 d^2+135 c^2 d e+70 e^2\right)}{525 c^9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \left(1-c^2 x^2\right)^2 \left(378 c^4 d^2 e+105 c^6 d^3+405 c^2 d e^2+140 e^3\right)}{945 c^9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \left(1-c^2 x^2\right) \left(189 c^4 d^2 e+105 c^6 d^3+135 c^2 d e^2+35 e^3\right)}{315 c^9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b e^2 \left(1-c^2 x^2\right)^4 \left(27 c^2 d+28 e\right)}{441 c^9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^3 \left(1-c^2 x^2\right)^5}{81 c^9 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*(105*c^6*d^3 + 189*c^4*d^2*e + 135*c^2*d*e^2 + 35*e^3)*(1 - c^2*x^2))/(315*c^9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*(105*c^6*d^3 + 378*c^4*d^2*e + 405*c^2*d*e^2 + 140*e^3)*(1 - c^2*x^2)^2)/(945*c^9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*e*(63*c^4*d^2 + 135*c^2*d*e + 70*e^2)*(1 - c^2*x^2)^3)/(525*c^9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*e^2*(27*c^2*d + 28*e)*(1 - c^2*x^2)^4)/(441*c^9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*e^3*(1 - c^2*x^2)^5)/(81*c^9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (d^3*x^3*(a + b*ArcCosh[c*x]))/3 + (3*d^2*e*x^5*(a + b*ArcCosh[c*x]))/5 + (3*d*e^2*x^7*(a + b*ArcCosh[c*x]))/7 + (e^3*x^9*(a + b*ArcCosh[c*x]))/9","A",6,6,21,0.2857,1,"{270, 5790, 12, 1610, 1799, 1620}"
482,1,358,0,0.3643053,"\int x \left(d+e x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)^3*(a + b*ArcCosh[c*x]),x]","\frac{\left(d+e x^2\right)^4 \left(a+b \cosh ^{-1}(c x)\right)}{8 e}+\frac{b x \left(1-c^2 x^2\right) \left(104 c^4 d^2+104 c^2 d e+35 e^2\right) \left(d+e x^2\right)}{1536 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b x \left(1-c^2 x^2\right) \left(2 c^2 d+e\right) \left(40 c^4 d^2+40 c^2 d e+21 e^2\right)}{3072 c^7 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{c^2 x^2-1} \left(288 c^4 d^2 e^2+256 c^6 d^3 e+128 c^8 d^4+160 c^2 d e^3+35 e^4\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{1024 c^8 e \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x \left(1-c^2 x^2\right) \left(d+e x^2\right)^3}{64 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{7 b x \left(1-c^2 x^2\right) \left(2 c^2 d+e\right) \left(d+e x^2\right)^2}{384 c^3 \sqrt{c x-1} \sqrt{c x+1}}","\frac{\left(d+e x^2\right)^4 \left(a+b \cosh ^{-1}(c x)\right)}{8 e}+\frac{b x \left(1-c^2 x^2\right) \left(104 c^4 d^2+104 c^2 d e+35 e^2\right) \left(d+e x^2\right)}{1536 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b x \left(1-c^2 x^2\right) \left(2 c^2 d+e\right) \left(40 c^4 d^2+40 c^2 d e+21 e^2\right)}{3072 c^7 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{c^2 x^2-1} \left(288 c^4 d^2 e^2+256 c^6 d^3 e+128 c^8 d^4+160 c^2 d e^3+35 e^4\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{1024 c^8 e \sqrt{c x-1} \sqrt{c x+1}}+\frac{b x \left(1-c^2 x^2\right) \left(d+e x^2\right)^3}{64 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{7 b x \left(1-c^2 x^2\right) \left(2 c^2 d+e\right) \left(d+e x^2\right)^2}{384 c^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(5*b*(2*c^2*d + e)*(40*c^4*d^2 + 40*c^2*d*e + 21*e^2)*x*(1 - c^2*x^2))/(3072*c^7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*(104*c^4*d^2 + 104*c^2*d*e + 35*e^2)*x*(1 - c^2*x^2)*(d + e*x^2))/(1536*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (7*b*(2*c^2*d + e)*x*(1 - c^2*x^2)*(d + e*x^2)^2)/(384*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*x*(1 - c^2*x^2)*(d + e*x^2)^3)/(64*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((d + e*x^2)^4*(a + b*ArcCosh[c*x]))/(8*e) - (b*(128*c^8*d^4 + 256*c^6*d^3*e + 288*c^4*d^2*e^2 + 160*c^2*d*e^3 + 35*e^4)*Sqrt[-1 + c^2*x^2]*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/(1024*c^8*e*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",8,7,19,0.3684,1,"{5788, 902, 416, 528, 388, 217, 206}"
483,1,287,0,0.3759196,"\int \left(d+e x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^3*(a + b*ArcCosh[c*x]),x]","d^2 e x^3 \left(a+b \cosh ^{-1}(c x)\right)+d^3 x \left(a+b \cosh ^{-1}(c x)\right)+\frac{3}{5} d e^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{7} e^3 x^7 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b e \left(1-c^2 x^2\right)^2 \left(35 c^4 d^2+42 c^2 d e+15 e^2\right)}{105 c^7 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \left(1-c^2 x^2\right) \left(35 c^4 d^2 e+35 c^6 d^3+21 c^2 d e^2+5 e^3\right)}{35 c^7 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b e^2 \left(1-c^2 x^2\right)^3 \left(7 c^2 d+5 e\right)}{175 c^7 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b e^3 \left(1-c^2 x^2\right)^4}{49 c^7 \sqrt{c x-1} \sqrt{c x+1}}","d^2 e x^3 \left(a+b \cosh ^{-1}(c x)\right)+d^3 x \left(a+b \cosh ^{-1}(c x)\right)+\frac{3}{5} d e^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{7} e^3 x^7 \left(a+b \cosh ^{-1}(c x)\right)-\frac{b e \left(1-c^2 x^2\right)^2 \left(35 c^4 d^2+42 c^2 d e+15 e^2\right)}{105 c^7 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \left(1-c^2 x^2\right) \left(35 c^4 d^2 e+35 c^6 d^3+21 c^2 d e^2+5 e^3\right)}{35 c^7 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b e^2 \left(1-c^2 x^2\right)^3 \left(7 c^2 d+5 e\right)}{175 c^7 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b e^3 \left(1-c^2 x^2\right)^4}{49 c^7 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*(35*c^6*d^3 + 35*c^4*d^2*e + 21*c^2*d*e^2 + 5*e^3)*(1 - c^2*x^2))/(35*c^7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*e*(35*c^4*d^2 + 42*c^2*d*e + 15*e^2)*(1 - c^2*x^2)^2)/(105*c^7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*b*e^2*(7*c^2*d + 5*e)*(1 - c^2*x^2)^3)/(175*c^7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*e^3*(1 - c^2*x^2)^4)/(49*c^7*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + d^3*x*(a + b*ArcCosh[c*x]) + d^2*e*x^3*(a + b*ArcCosh[c*x]) + (3*d*e^2*x^5*(a + b*ArcCosh[c*x]))/5 + (e^3*x^7*(a + b*ArcCosh[c*x]))/7","A",6,6,18,0.3333,1,"{194, 5705, 12, 1610, 1799, 1850}"
484,1,509,0,1.092016,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)^3*(a + b*ArcCosh[c*x]))/x,x]","-\frac{i b d^3 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3}{2} d^2 e x^2 \left(a+b \cosh ^{-1}(c x)\right)+d^3 \log (x) \left(a+b \cosh ^{-1}(c x)\right)+\frac{3}{4} d e^2 x^4 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{6} e^3 x^6 \left(a+b \cosh ^{-1}(c x)\right)-\frac{3 b d^2 e \cosh ^{-1}(c x)}{4 c^2}-\frac{i b d^3 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)^2}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^3 \sqrt{1-c^2 x^2} \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^3 \sqrt{1-c^2 x^2} \log (x) \sin ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{9 b d e^2 x \sqrt{c x-1} \sqrt{c x+1}}{32 c^3}-\frac{9 b d e^2 \cosh ^{-1}(c x)}{32 c^4}-\frac{5 b e^3 x^3 \sqrt{c x-1} \sqrt{c x+1}}{144 c^3}-\frac{5 b e^3 x \sqrt{c x-1} \sqrt{c x+1}}{96 c^5}-\frac{5 b e^3 \cosh ^{-1}(c x)}{96 c^6}-\frac{3 b d^2 e x \sqrt{c x-1} \sqrt{c x+1}}{4 c}-\frac{3 b d e^2 x^3 \sqrt{c x-1} \sqrt{c x+1}}{16 c}-\frac{b e^3 x^5 \sqrt{c x-1} \sqrt{c x+1}}{36 c}","-\frac{i b d^3 \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3}{2} d^2 e x^2 \left(a+b \cosh ^{-1}(c x)\right)+d^3 \log (x) \left(a+b \cosh ^{-1}(c x)\right)+\frac{3}{4} d e^2 x^4 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{6} e^3 x^6 \left(a+b \cosh ^{-1}(c x)\right)-\frac{3 b d^2 e \cosh ^{-1}(c x)}{4 c^2}-\frac{i b d^3 \sqrt{1-c^2 x^2} \sin ^{-1}(c x)^2}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^3 \sqrt{1-c^2 x^2} \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^3 \sqrt{1-c^2 x^2} \log (x) \sin ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{9 b d e^2 x \sqrt{c x-1} \sqrt{c x+1}}{32 c^3}-\frac{9 b d e^2 \cosh ^{-1}(c x)}{32 c^4}-\frac{5 b e^3 x^3 \sqrt{c x-1} \sqrt{c x+1}}{144 c^3}-\frac{5 b e^3 x \sqrt{c x-1} \sqrt{c x+1}}{96 c^5}-\frac{5 b e^3 \cosh ^{-1}(c x)}{96 c^6}-\frac{3 b d^2 e x \sqrt{c x-1} \sqrt{c x+1}}{4 c}-\frac{3 b d e^2 x^3 \sqrt{c x-1} \sqrt{c x+1}}{16 c}-\frac{b e^3 x^5 \sqrt{c x-1} \sqrt{c x+1}}{36 c}",1,"(-3*b*d^2*e*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*c) - (9*b*d*e^2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(32*c^3) - (5*b*e^3*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(96*c^5) - (3*b*d*e^2*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(16*c) - (5*b*e^3*x^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(144*c^3) - (b*e^3*x^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(36*c) - (3*b*d^2*e*ArcCosh[c*x])/(4*c^2) - (9*b*d*e^2*ArcCosh[c*x])/(32*c^4) - (5*b*e^3*ArcCosh[c*x])/(96*c^6) + (3*d^2*e*x^2*(a + b*ArcCosh[c*x]))/2 + (3*d*e^2*x^4*(a + b*ArcCosh[c*x]))/4 + (e^3*x^6*(a + b*ArcCosh[c*x]))/6 - ((I/2)*b*d^3*Sqrt[1 - c^2*x^2]*ArcSin[c*x]^2)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*d^3*Sqrt[1 - c^2*x^2]*ArcSin[c*x]*Log[1 - E^((2*I)*ArcSin[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + d^3*(a + b*ArcCosh[c*x])*Log[x] - (b*d^3*Sqrt[1 - c^2*x^2]*ArcSin[c*x]*Log[x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((I/2)*b*d^3*Sqrt[1 - c^2*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",23,15,21,0.7143,1,"{266, 43, 5790, 12, 6742, 90, 52, 100, 2328, 2326, 4625, 3717, 2190, 2279, 2391}"
485,1,265,0,0.4175728,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)^3*(a + b*ArcCosh[c*x]))/x^2,x]","3 d^2 e x \left(a+b \cosh ^{-1}(c x)\right)-\frac{d^3 \left(a+b \cosh ^{-1}(c x)\right)}{x}+d e^2 x^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{5} e^3 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b e \left(1-c^2 x^2\right) \left(15 c^4 d^2+5 c^2 d e+e^2\right)}{5 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d^3 \sqrt{c^2 x^2-1} \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b e^2 \left(1-c^2 x^2\right)^2 \left(5 c^2 d+2 e\right)}{15 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^3 \left(1-c^2 x^2\right)^3}{25 c^5 \sqrt{c x-1} \sqrt{c x+1}}","3 d^2 e x \left(a+b \cosh ^{-1}(c x)\right)-\frac{d^3 \left(a+b \cosh ^{-1}(c x)\right)}{x}+d e^2 x^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{5} e^3 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b e \left(1-c^2 x^2\right) \left(15 c^4 d^2+5 c^2 d e+e^2\right)}{5 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d^3 \sqrt{c^2 x^2-1} \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b e^2 \left(1-c^2 x^2\right)^2 \left(5 c^2 d+2 e\right)}{15 c^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^3 \left(1-c^2 x^2\right)^3}{25 c^5 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*e*(15*c^4*d^2 + 5*c^2*d*e + e^2)*(1 - c^2*x^2))/(5*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*e^2*(5*c^2*d + 2*e)*(1 - c^2*x^2)^2)/(15*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*e^3*(1 - c^2*x^2)^3)/(25*c^5*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d^3*(a + b*ArcCosh[c*x]))/x + 3*d^2*e*x*(a + b*ArcCosh[c*x]) + d*e^2*x^3*(a + b*ArcCosh[c*x]) + (e^3*x^5*(a + b*ArcCosh[c*x]))/5 + (b*c*d^3*Sqrt[-1 + c^2*x^2]*ArcTan[Sqrt[-1 + c^2*x^2]])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",7,7,21,0.3333,1,"{270, 5790, 1610, 1799, 1620, 63, 205}"
486,1,476,0,1.7602571,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)^3*(a + b*ArcCosh[c*x]))/x^3,x]","-\frac{3 i b d^2 e \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+3 d^2 e \log (x) \left(a+b \cosh ^{-1}(c x)\right)-\frac{d^3 \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}+\frac{3}{2} d e^2 x^2 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} e^3 x^4 \left(a+b \cosh ^{-1}(c x)\right)-\frac{3 i b d^2 e \sqrt{1-c^2 x^2} \sin ^{-1}(c x)^2}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b d^2 e \sqrt{1-c^2 x^2} \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b d^2 e \sqrt{1-c^2 x^2} \log (x) \sin ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^3 \left(1-c^2 x^2\right)}{2 x \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b e^2 x \left(1-c^2 x^2\right) \left(8 c^2 d+e\right)}{32 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b e^2 \sqrt{c^2 x^2-1} \left(8 c^2 d+e\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{32 c^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^3 x^3 \left(1-c^2 x^2\right)}{16 c \sqrt{c x-1} \sqrt{c x+1}}","-\frac{3 i b d^2 e \sqrt{1-c^2 x^2} \text{PolyLog}\left(2,e^{2 i \sin ^{-1}(c x)}\right)}{2 \sqrt{c x-1} \sqrt{c x+1}}+3 d^2 e \log (x) \left(a+b \cosh ^{-1}(c x)\right)-\frac{d^3 \left(a+b \cosh ^{-1}(c x)\right)}{2 x^2}+\frac{3}{2} d e^2 x^2 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} e^3 x^4 \left(a+b \cosh ^{-1}(c x)\right)-\frac{3 i b d^2 e \sqrt{1-c^2 x^2} \sin ^{-1}(c x)^2}{2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b d^2 e \sqrt{1-c^2 x^2} \sin ^{-1}(c x) \log \left(1-e^{2 i \sin ^{-1}(c x)}\right)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b d^2 e \sqrt{1-c^2 x^2} \log (x) \sin ^{-1}(c x)}{\sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^3 \left(1-c^2 x^2\right)}{2 x \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b e^2 x \left(1-c^2 x^2\right) \left(8 c^2 d+e\right)}{32 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b e^2 \sqrt{c^2 x^2-1} \left(8 c^2 d+e\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{32 c^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^3 x^3 \left(1-c^2 x^2\right)}{16 c \sqrt{c x-1} \sqrt{c x+1}}",1,"-(b*c*d^3*(1 - c^2*x^2))/(2*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*b*e^2*(8*c^2*d + e)*x*(1 - c^2*x^2))/(32*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*e^3*x^3*(1 - c^2*x^2))/(16*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d^3*(a + b*ArcCosh[c*x]))/(2*x^2) + (3*d*e^2*x^2*(a + b*ArcCosh[c*x]))/2 + (e^3*x^4*(a + b*ArcCosh[c*x]))/4 - (((3*I)/2)*b*d^2*e*Sqrt[1 - c^2*x^2]*ArcSin[c*x]^2)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (3*b*e^2*(8*c^2*d + e)*Sqrt[-1 + c^2*x^2]*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/(32*c^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*b*d^2*e*Sqrt[1 - c^2*x^2]*ArcSin[c*x]*Log[1 - E^((2*I)*ArcSin[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + 3*d^2*e*(a + b*ArcCosh[c*x])*Log[x] - (3*b*d^2*e*Sqrt[1 - c^2*x^2]*ArcSin[c*x]*Log[x])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (((3*I)/2)*b*d^2*e*Sqrt[1 - c^2*x^2]*PolyLog[2, E^((2*I)*ArcSin[c*x])])/(Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",18,19,21,0.9048,1,"{266, 43, 5790, 12, 6742, 1610, 1807, 1584, 459, 321, 217, 206, 2328, 2326, 4625, 3717, 2190, 2279, 2391}"
487,1,260,0,0.4620421,"\int \frac{\left(d+e x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)^3*(a + b*ArcCosh[c*x]))/x^4,x]","-\frac{3 d^2 e \left(a+b \cosh ^{-1}(c x)\right)}{x}-\frac{d^3 \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}+3 d e^2 x \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} e^3 x^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b c d^2 \sqrt{c^2 x^2-1} \left(c^2 d+18 e\right) \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^3 \left(1-c^2 x^2\right)}{6 x^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^2 \left(1-c^2 x^2\right) \left(9 c^2 d+e\right)}{3 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b e^3 \left(1-c^2 x^2\right)^2}{9 c^3 \sqrt{c x-1} \sqrt{c x+1}}","-\frac{3 d^2 e \left(a+b \cosh ^{-1}(c x)\right)}{x}-\frac{d^3 \left(a+b \cosh ^{-1}(c x)\right)}{3 x^3}+3 d e^2 x \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{3} e^3 x^3 \left(a+b \cosh ^{-1}(c x)\right)+\frac{b c d^2 \sqrt{c^2 x^2-1} \left(c^2 d+18 e\right) \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^3 \left(1-c^2 x^2\right)}{6 x^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^2 \left(1-c^2 x^2\right) \left(9 c^2 d+e\right)}{3 c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b e^3 \left(1-c^2 x^2\right)^2}{9 c^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*e^2*(9*c^2*d + e)*(1 - c^2*x^2))/(3*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*d^3*(1 - c^2*x^2))/(6*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*e^3*(1 - c^2*x^2)^2)/(9*c^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (d^3*(a + b*ArcCosh[c*x]))/(3*x^3) - (3*d^2*e*(a + b*ArcCosh[c*x]))/x + 3*d*e^2*x*(a + b*ArcCosh[c*x]) + (e^3*x^3*(a + b*ArcCosh[c*x]))/3 + (b*c*d^2*(c^2*d + 18*e)*Sqrt[-1 + c^2*x^2]*ArcTan[Sqrt[-1 + c^2*x^2]])/(6*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",9,9,21,0.4286,1,"{270, 5790, 12, 1610, 1799, 1621, 897, 1153, 205}"
488,1,395,0,0.4749495,"\int \left(d+e x^2\right)^4 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^4*(a + b*ArcCosh[c*x]),x]","\frac{6}{5} d^2 e^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{4}{3} d^3 e x^3 \left(a+b \cosh ^{-1}(c x)\right)+d^4 x \left(a+b \cosh ^{-1}(c x)\right)+\frac{4}{7} d e^3 x^7 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{9} e^4 x^9 \left(a+b \cosh ^{-1}(c x)\right)+\frac{2 b e^2 \left(1-c^2 x^2\right)^3 \left(63 c^4 d^2+90 c^2 d e+35 e^2\right)}{525 c^9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 b e \left(1-c^2 x^2\right)^2 \left(189 c^4 d^2 e+105 c^6 d^3+135 c^2 d e^2+35 e^3\right)}{945 c^9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \left(1-c^2 x^2\right) \left(378 c^4 d^2 e^2+420 c^6 d^3 e+315 c^8 d^4+180 c^2 d e^3+35 e^4\right)}{315 c^9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 b e^3 \left(1-c^2 x^2\right)^4 \left(9 c^2 d+7 e\right)}{441 c^9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^4 \left(1-c^2 x^2\right)^5}{81 c^9 \sqrt{c x-1} \sqrt{c x+1}}","\frac{6}{5} d^2 e^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)+\frac{4}{3} d^3 e x^3 \left(a+b \cosh ^{-1}(c x)\right)+d^4 x \left(a+b \cosh ^{-1}(c x)\right)+\frac{4}{7} d e^3 x^7 \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{9} e^4 x^9 \left(a+b \cosh ^{-1}(c x)\right)+\frac{2 b e^2 \left(1-c^2 x^2\right)^3 \left(63 c^4 d^2+90 c^2 d e+35 e^2\right)}{525 c^9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 b e \left(1-c^2 x^2\right)^2 \left(189 c^4 d^2 e+105 c^6 d^3+135 c^2 d e^2+35 e^3\right)}{945 c^9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \left(1-c^2 x^2\right) \left(378 c^4 d^2 e^2+420 c^6 d^3 e+315 c^8 d^4+180 c^2 d e^3+35 e^4\right)}{315 c^9 \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 b e^3 \left(1-c^2 x^2\right)^4 \left(9 c^2 d+7 e\right)}{441 c^9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^4 \left(1-c^2 x^2\right)^5}{81 c^9 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*(315*c^8*d^4 + 420*c^6*d^3*e + 378*c^4*d^2*e^2 + 180*c^2*d*e^3 + 35*e^4)*(1 - c^2*x^2))/(315*c^9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (4*b*e*(105*c^6*d^3 + 189*c^4*d^2*e + 135*c^2*d*e^2 + 35*e^3)*(1 - c^2*x^2)^2)/(945*c^9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (2*b*e^2*(63*c^4*d^2 + 90*c^2*d*e + 35*e^2)*(1 - c^2*x^2)^3)/(525*c^9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (4*b*e^3*(9*c^2*d + 7*e)*(1 - c^2*x^2)^4)/(441*c^9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*e^4*(1 - c^2*x^2)^5)/(81*c^9*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + d^4*x*(a + b*ArcCosh[c*x]) + (4*d^3*e*x^3*(a + b*ArcCosh[c*x]))/3 + (6*d^2*e^2*x^5*(a + b*ArcCosh[c*x]))/5 + (4*d*e^3*x^7*(a + b*ArcCosh[c*x]))/7 + (e^4*x^9*(a + b*ArcCosh[c*x]))/9","A",6,6,18,0.3333,1,"{194, 5705, 12, 1610, 1799, 1850}"
489,1,627,0,1.0515574,"\int \frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)}{d+e x^2} \, dx","Int[(x^4*(a + b*ArcCosh[c*x]))/(d + e*x^2),x]","-\frac{b (-d)^{3/2} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^{5/2}}+\frac{b (-d)^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^{5/2}}-\frac{b (-d)^{3/2} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^{5/2}}+\frac{b (-d)^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^{5/2}}+\frac{(-d)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^{5/2}}-\frac{(-d)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 e^{5/2}}+\frac{(-d)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^{5/2}}-\frac{(-d)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 e^{5/2}}+\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{3 e}-\frac{a d x}{e^2}-\frac{2 b \sqrt{c x-1} \sqrt{c x+1}}{9 c^3 e}+\frac{b d \sqrt{c x-1} \sqrt{c x+1}}{c e^2}-\frac{b d x \cosh ^{-1}(c x)}{e^2}-\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1}}{9 c e}","-\frac{b (-d)^{3/2} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^{5/2}}+\frac{b (-d)^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^{5/2}}-\frac{b (-d)^{3/2} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^{5/2}}+\frac{b (-d)^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^{5/2}}+\frac{(-d)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^{5/2}}-\frac{(-d)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 e^{5/2}}+\frac{(-d)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^{5/2}}-\frac{(-d)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 e^{5/2}}+\frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{3 e}-\frac{a d x}{e^2}-\frac{2 b \sqrt{c x-1} \sqrt{c x+1}}{9 c^3 e}+\frac{b d \sqrt{c x-1} \sqrt{c x+1}}{c e^2}-\frac{b d x \cosh ^{-1}(c x)}{e^2}-\frac{b x^2 \sqrt{c x-1} \sqrt{c x+1}}{9 c e}",1,"-((a*d*x)/e^2) + (b*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(c*e^2) - (2*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(9*c^3*e) - (b*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(9*c*e) - (b*d*x*ArcCosh[c*x])/e^2 + (x^3*(a + b*ArcCosh[c*x]))/(3*e) + ((-d)^(3/2)*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e^(5/2)) - ((-d)^(3/2)*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e^(5/2)) + ((-d)^(3/2)*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e^(5/2)) - ((-d)^(3/2)*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e^(5/2)) - (b*(-d)^(3/2)*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(2*e^(5/2)) + (b*(-d)^(3/2)*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e^(5/2)) - (b*(-d)^(3/2)*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(2*e^(5/2)) + (b*(-d)^(3/2)*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e^(5/2))","A",27,12,21,0.5714,1,"{5792, 5654, 74, 5662, 100, 12, 5707, 5800, 5562, 2190, 2279, 2391}"
490,1,521,0,0.9111542,"\int \frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{d+e x^2} \, dx","Int[(x^3*(a + b*ArcCosh[c*x]))/(d + e*x^2),x]","-\frac{b d \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^2}-\frac{b d \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^2}-\frac{b d \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^2}-\frac{b d \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^2}-\frac{d \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^2}-\frac{d \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 e^2}-\frac{d \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^2}-\frac{d \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 e^2}+\frac{d \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b e^2}+\frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 e}-\frac{b \cosh ^{-1}(c x)}{4 c^2 e}-\frac{b x \sqrt{c x-1} \sqrt{c x+1}}{4 c e}","-\frac{b d \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^2}-\frac{b d \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^2}-\frac{b d \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^2}-\frac{b d \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^2}-\frac{d \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^2}-\frac{d \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 e^2}-\frac{d \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^2}-\frac{d \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 e^2}+\frac{d \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b e^2}+\frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 e}-\frac{b \cosh ^{-1}(c x)}{4 c^2 e}-\frac{b x \sqrt{c x-1} \sqrt{c x+1}}{4 c e}",1,"-(b*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*c*e) - (b*ArcCosh[c*x])/(4*c^2*e) + (x^2*(a + b*ArcCosh[c*x]))/(2*e) + (d*(a + b*ArcCosh[c*x])^2)/(2*b*e^2) - (d*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e^2) - (d*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e^2) - (d*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e^2) - (d*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e^2) - (b*d*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(2*e^2) - (b*d*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e^2) - (b*d*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(2*e^2) - (b*d*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e^2)","A",23,9,21,0.4286,1,"{5792, 5662, 90, 52, 5800, 5562, 2190, 2279, 2391}"
491,1,544,0,0.901976,"\int \frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)}{d+e x^2} \, dx","Int[(x^2*(a + b*ArcCosh[c*x]))/(d + e*x^2),x]","-\frac{b \sqrt{-d} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^{3/2}}+\frac{b \sqrt{-d} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^{3/2}}-\frac{b \sqrt{-d} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^{3/2}}+\frac{b \sqrt{-d} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 e^{3/2}}+\frac{a x}{e}-\frac{b \sqrt{c x-1} \sqrt{c x+1}}{c e}+\frac{b x \cosh ^{-1}(c x)}{e}","-\frac{b \sqrt{-d} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^{3/2}}+\frac{b \sqrt{-d} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^{3/2}}-\frac{b \sqrt{-d} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^{3/2}}+\frac{b \sqrt{-d} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 e^{3/2}}+\frac{a x}{e}-\frac{b \sqrt{c x-1} \sqrt{c x+1}}{c e}+\frac{b x \cosh ^{-1}(c x)}{e}",1,"(a*x)/e - (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(c*e) + (b*x*ArcCosh[c*x])/e + (Sqrt[-d]*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e^(3/2)) - (Sqrt[-d]*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e^(3/2)) + (Sqrt[-d]*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e^(3/2)) - (Sqrt[-d]*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e^(3/2)) - (b*Sqrt[-d]*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(2*e^(3/2)) + (b*Sqrt[-d]*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e^(3/2)) - (b*Sqrt[-d]*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(2*e^(3/2)) + (b*Sqrt[-d]*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e^(3/2))","A",23,9,21,0.4286,1,"{5792, 5654, 74, 5707, 5800, 5562, 2190, 2279, 2391}"
492,1,449,0,0.7378322,"\int \frac{x \left(a+b \cosh ^{-1}(c x)\right)}{d+e x^2} \, dx","Int[(x*(a + b*ArcCosh[c*x]))/(d + e*x^2),x]","\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 e}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 e}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 b e}","\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 e}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 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 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e) + ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e) + ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e) + ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e) + (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(2*e) + (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e) + (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(2*e) + (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e)","A",18,6,19,0.3158,1,"{5792, 5800, 5562, 2190, 2279, 2391}"
493,1,501,0,0.7343635,"\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{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 \sqrt{-d} \sqrt{e}}","-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 \sqrt{-d} \sqrt{e}}",1,"((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*Sqrt[-d]*Sqrt[e]) + ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*Sqrt[-d]*Sqrt[e]) - (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(2*Sqrt[-d]*Sqrt[e]) + (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*Sqrt[-d]*Sqrt[e]) - (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(2*Sqrt[-d]*Sqrt[e]) + (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*Sqrt[-d]*Sqrt[e])","A",18,6,18,0.3333,1,"{5707, 5800, 5562, 2190, 2279, 2391}"
494,1,472,0,0.9248702,"\int \frac{a+b \cosh ^{-1}(c x)}{x \left(d+e x^2\right)} \, dx","Int[(a + b*ArcCosh[c*x])/(x*(d + e*x^2)),x]","-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d}+\frac{b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{2 d}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 d}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 d}+\frac{\log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{d}","-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)}{2 d}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 d}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 d}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{b d}+\frac{\log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{d}",1,"-((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*d) - ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*d) - ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*d) - ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*d) + ((a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])])/d - (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(2*d) - (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*d) - (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(2*d) - (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*d) + (b*PolyLog[2, -E^(2*ArcCosh[c*x])])/(2*d)","A",25,8,21,0.3810,0,"{5792, 5660, 3718, 2190, 2279, 2391, 5800, 5562}"
495,1,543,0,0.9064722,"\int \frac{a+b \cosh ^{-1}(c x)}{x^2 \left(d+e x^2\right)} \, dx","Int[(a + b*ArcCosh[c*x])/(x^2*(d + e*x^2)),x]","-\frac{b \sqrt{e} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 (-d)^{3/2}}+\frac{b \sqrt{e} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 (-d)^{3/2}}-\frac{b \sqrt{e} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 (-d)^{3/2}}+\frac{b \sqrt{e} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 (-d)^{3/2}}-\frac{a+b \cosh ^{-1}(c x)}{d x}+\frac{b c \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{d}","-\frac{b \sqrt{e} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 (-d)^{3/2}}+\frac{b \sqrt{e} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 (-d)^{3/2}}-\frac{b \sqrt{e} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 (-d)^{3/2}}+\frac{b \sqrt{e} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 (-d)^{3/2}}-\frac{a+b \cosh ^{-1}(c x)}{d x}+\frac{b c \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{d}",1,"-((a + b*ArcCosh[c*x])/(d*x)) + (b*c*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/d + (Sqrt[e]*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*(-d)^(3/2)) - (Sqrt[e]*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*(-d)^(3/2)) + (Sqrt[e]*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*(-d)^(3/2)) - (Sqrt[e]*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*(-d)^(3/2)) - (b*Sqrt[e]*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(2*(-d)^(3/2)) + (b*Sqrt[e]*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*(-d)^(3/2)) - (b*Sqrt[e]*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(2*(-d)^(3/2)) + (b*Sqrt[e]*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*(-d)^(3/2))","A",23,10,21,0.4762,1,"{5792, 5662, 92, 205, 5707, 5800, 5562, 2190, 2279, 2391}"
496,1,531,0,0.9548643,"\int \frac{a+b \cosh ^{-1}(c x)}{x^3 \left(d+e x^2\right)} \, dx","Int[(a + b*ArcCosh[c*x])/(x^3*(d + e*x^2)),x]","\frac{b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^2}+\frac{b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^2}+\frac{b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^2}+\frac{b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^2}-\frac{b e \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{2 d^2}+\frac{e \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^2}+\frac{e \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 d^2}+\frac{e \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^2}+\frac{e \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 d^2}-\frac{e \log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2}-\frac{a+b \cosh ^{-1}(c x)}{2 d x^2}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 d x}","\frac{b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^2}+\frac{b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^2}+\frac{b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^2}+\frac{b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^2}+\frac{b e \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)}{2 d^2}+\frac{e \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^2}+\frac{e \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 d^2}+\frac{e \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^2}+\frac{e \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 d^2}-\frac{e \left(a+b \cosh ^{-1}(c x)\right)^2}{b d^2}-\frac{e \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2}-\frac{a+b \cosh ^{-1}(c x)}{2 d x^2}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 d x}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*d*x) - (a + b*ArcCosh[c*x])/(2*d*x^2) + (e*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*d^2) + (e*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*d^2) + (e*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*d^2) + (e*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*d^2) - (e*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])])/d^2 + (b*e*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(2*d^2) + (b*e*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*d^2) + (b*e*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(2*d^2) + (b*e*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*d^2) - (b*e*PolyLog[2, -E^(2*ArcCosh[c*x])])/(2*d^2)","A",27,10,21,0.4762,0,"{5792, 5662, 95, 5660, 3718, 2190, 2279, 2391, 5800, 5562}"
497,1,624,0,0.981366,"\int \frac{a+b \cosh ^{-1}(c x)}{x^4 \left(d+e x^2\right)} \, dx","Int[(a + b*ArcCosh[c*x])/(x^4*(d + e*x^2)),x]","-\frac{b e^{3/2} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 (-d)^{5/2}}+\frac{b e^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 (-d)^{5/2}}-\frac{b e^{3/2} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 (-d)^{5/2}}+\frac{b e^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 (-d)^{5/2}}+\frac{e^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 (-d)^{5/2}}-\frac{e^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 (-d)^{5/2}}+\frac{e^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 (-d)^{5/2}}-\frac{e^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 (-d)^{5/2}}+\frac{e \left(a+b \cosh ^{-1}(c x)\right)}{d^2 x}-\frac{a+b \cosh ^{-1}(c x)}{3 d x^3}+\frac{b c^3 \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{6 d}-\frac{b c e \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{d^2}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{6 d x^2}","-\frac{b e^{3/2} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 (-d)^{5/2}}+\frac{b e^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 (-d)^{5/2}}-\frac{b e^{3/2} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 (-d)^{5/2}}+\frac{b e^{3/2} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 (-d)^{5/2}}+\frac{e^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 (-d)^{5/2}}-\frac{e^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 (-d)^{5/2}}+\frac{e^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 (-d)^{5/2}}-\frac{e^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 (-d)^{5/2}}+\frac{e \left(a+b \cosh ^{-1}(c x)\right)}{d^2 x}-\frac{a+b \cosh ^{-1}(c x)}{3 d x^3}+\frac{b c^3 \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{6 d}-\frac{b c e \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{d^2}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{6 d x^2}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(6*d*x^2) - (a + b*ArcCosh[c*x])/(3*d*x^3) + (e*(a + b*ArcCosh[c*x]))/(d^2*x) + (b*c^3*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/(6*d) - (b*c*e*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/d^2 + (e^(3/2)*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*(-d)^(5/2)) - (e^(3/2)*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*(-d)^(5/2)) + (e^(3/2)*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*(-d)^(5/2)) - (e^(3/2)*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*(-d)^(5/2)) - (b*e^(3/2)*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(2*(-d)^(5/2)) + (b*e^(3/2)*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*(-d)^(5/2)) - (b*e^(3/2)*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(2*(-d)^(5/2)) + (b*e^(3/2)*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*(-d)^(5/2))","A",28,12,21,0.5714,1,"{5792, 5662, 103, 12, 92, 205, 5707, 5800, 5562, 2190, 2279, 2391}"
498,1,562,0,0.9907435,"\int \frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^3*(a + b*ArcCosh[c*x]))/(d + e*x^2)^2,x]","\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^2}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^2}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 e^2}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^2}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 e^2}+\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{2 e^2 \left(d+e x^2\right)}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 b e^2}-\frac{b c \sqrt{d} \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{2 e^2 \sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d+e}}","\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^2}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^2}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 e^2}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^2}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 e^2}+\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{2 e^2 \left(d+e x^2\right)}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 b e^2}-\frac{b c \sqrt{d} \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{2 e^2 \sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d+e}}",1,"(d*(a + b*ArcCosh[c*x]))/(2*e^2*(d + e*x^2)) - (a + b*ArcCosh[c*x])^2/(2*b*e^2) - (b*c*Sqrt[d]*Sqrt[-1 + c^2*x^2]*ArcTanh[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(2*e^2*Sqrt[c^2*d + e]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e^2) + ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e^2) + ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e^2) + ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e^2) + (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(2*e^2) + (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e^2) + (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(2*e^2) + (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e^2)","A",24,10,21,0.4762,1,"{5792, 5788, 519, 377, 208, 5800, 5562, 2190, 2279, 2391}"
499,1,113,0,0.0941429,"\int \frac{x \left(a+b \cosh ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x*(a + b*ArcCosh[c*x]))/(d + e*x^2)^2,x]","\frac{b c \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{2 \sqrt{d} e \sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d+e}}-\frac{a+b \cosh ^{-1}(c x)}{2 e \left(d+e x^2\right)}","\frac{b c \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{2 \sqrt{d} e \sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d+e}}-\frac{a+b \cosh ^{-1}(c x)}{2 e \left(d+e x^2\right)}",1,"-(a + b*ArcCosh[c*x])/(2*e*(d + e*x^2)) + (b*c*Sqrt[-1 + c^2*x^2]*ArcTanh[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(2*Sqrt[d]*e*Sqrt[c^2*d + e]*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",4,4,19,0.2105,1,"{5788, 519, 377, 208}"
500,1,581,0,1.061958,"\int \frac{a+b \cosh ^{-1}(c x)}{x \left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcCosh[c*x])/(x*(d + e*x^2)^2),x]","-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^2}+\frac{b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{2 d^2}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^2}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 d^2}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^2}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 d^2}+\frac{\log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2}+\frac{a+b \cosh ^{-1}(c x)}{2 d \left(d+e x^2\right)}-\frac{b c \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{2 d^{3/2} \sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d+e}}","-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)}{2 d^2}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^2}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 d^2}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^2}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 d^2}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{b d^2}+\frac{\log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^2}+\frac{a+b \cosh ^{-1}(c x)}{2 d \left(d+e x^2\right)}-\frac{b c \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{2 d^{3/2} \sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d+e}}",1,"(a + b*ArcCosh[c*x])/(2*d*(d + e*x^2)) - (b*c*Sqrt[-1 + c^2*x^2]*ArcTanh[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(2*d^(3/2)*Sqrt[c^2*d + e]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*d^2) - ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*d^2) - ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*d^2) - ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*d^2) + ((a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])])/d^2 - (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(2*d^2) - (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*d^2) - (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(2*d^2) - (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*d^2) + (b*PolyLog[2, -E^(2*ArcCosh[c*x])])/(2*d^2)","A",29,12,21,0.5714,0,"{5792, 5660, 3718, 2190, 2279, 2391, 5788, 519, 377, 208, 5800, 5562}"
501,1,616,0,1.0871755,"\int \frac{a+b \cosh ^{-1}(c x)}{x^3 \left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcCosh[c*x])/(x^3*(d + e*x^2)^2),x]","\frac{b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{d^3}+\frac{b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{d^3}+\frac{b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{d^3}+\frac{b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{d^3}-\frac{b e \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{d^3}+\frac{e \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{d^3}+\frac{e \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{d^3}+\frac{e \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{d^3}+\frac{e \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{d^3}-\frac{e \left(a+b \cosh ^{-1}(c x)\right)}{2 d^2 \left(d+e x^2\right)}-\frac{2 e \log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^3}-\frac{a+b \cosh ^{-1}(c x)}{2 d^2 x^2}+\frac{b c e \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{2 d^{5/2} \sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d+e}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 d^2 x}","\frac{b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{d^3}+\frac{b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{d^3}+\frac{b e \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{d^3}+\frac{b e \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{d^3}+\frac{b e \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)}{d^3}+\frac{e \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{d^3}+\frac{e \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{d^3}+\frac{e \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{d^3}+\frac{e \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{d^3}-\frac{e \left(a+b \cosh ^{-1}(c x)\right)}{2 d^2 \left(d+e x^2\right)}-\frac{2 e \left(a+b \cosh ^{-1}(c x)\right)^2}{b d^3}-\frac{2 e \log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^3}-\frac{a+b \cosh ^{-1}(c x)}{2 d^2 x^2}+\frac{b c e \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{2 d^{5/2} \sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d+e}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 d^2 x}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*d^2*x) - (a + b*ArcCosh[c*x])/(2*d^2*x^2) - (e*(a + b*ArcCosh[c*x]))/(2*d^2*(d + e*x^2)) + (b*c*e*Sqrt[-1 + c^2*x^2]*ArcTanh[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(2*d^(5/2)*Sqrt[c^2*d + e]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (e*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/d^3 + (e*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/d^3 + (e*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/d^3 + (e*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/d^3 - (2*e*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])])/d^3 + (b*e*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/d^3 + (b*e*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/d^3 + (b*e*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/d^3 + (b*e*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/d^3 - (b*e*PolyLog[2, -E^(2*ArcCosh[c*x])])/d^3","A",31,14,21,0.6667,0,"{5792, 5662, 95, 5660, 3718, 2190, 2279, 2391, 5788, 519, 377, 208, 5800, 5562}"
502,1,839,0,2.1877783,"\int \frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^4*(a + b*ArcCosh[c*x]))/(d + e*x^2)^2,x]","\frac{x \cosh ^{-1}(c x) b}{e^2}+\frac{c d \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right) b}{2 \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} e^{5/2}}-\frac{c d \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right) b}{2 \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} e^{5/2}}-\frac{3 \sqrt{-d} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right) b}{4 e^{5/2}}+\frac{3 \sqrt{-d} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right) b}{4 e^{5/2}}-\frac{3 \sqrt{-d} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right) b}{4 e^{5/2}}+\frac{3 \sqrt{-d} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right) b}{4 e^{5/2}}-\frac{\sqrt{c x-1} \sqrt{c x+1} b}{c e^2}+\frac{a x}{e^2}-\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{4 e^{5/2} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{4 e^{5/2} \left(\sqrt{e} x+\sqrt{-d}\right)}+\frac{3 \sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{c \sqrt{-d}-\sqrt{-d c^2-e}}+1\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{\sqrt{-d} c+\sqrt{-d c^2-e}}+1\right)}{4 e^{5/2}}","\frac{x \cosh ^{-1}(c x) b}{e^2}+\frac{c d \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right) b}{2 \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} e^{5/2}}-\frac{c d \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right) b}{2 \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} e^{5/2}}-\frac{3 \sqrt{-d} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right) b}{4 e^{5/2}}+\frac{3 \sqrt{-d} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right) b}{4 e^{5/2}}-\frac{3 \sqrt{-d} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right) b}{4 e^{5/2}}+\frac{3 \sqrt{-d} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right) b}{4 e^{5/2}}-\frac{\sqrt{c x-1} \sqrt{c x+1} b}{c e^2}+\frac{a x}{e^2}-\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{4 e^{5/2} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{4 e^{5/2} \left(\sqrt{e} x+\sqrt{-d}\right)}+\frac{3 \sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{c \sqrt{-d}-\sqrt{-d c^2-e}}+1\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{\sqrt{-d} c+\sqrt{-d c^2-e}}+1\right)}{4 e^{5/2}}",1,"(a*x)/e^2 - (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(c*e^2) + (b*x*ArcCosh[c*x])/e^2 - (d*(a + b*ArcCosh[c*x]))/(4*e^(5/2)*(Sqrt[-d] - Sqrt[e]*x)) + (d*(a + b*ArcCosh[c*x]))/(4*e^(5/2)*(Sqrt[-d] + Sqrt[e]*x)) + (b*c*d*ArcTanh[(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[-1 + c*x])])/(2*Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[c*Sqrt[-d] + Sqrt[e]]*e^(5/2)) - (b*c*d*ArcTanh[(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[-1 + c*x])])/(2*Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[c*Sqrt[-d] + Sqrt[e]]*e^(5/2)) + (3*Sqrt[-d]*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(4*e^(5/2)) - (3*Sqrt[-d]*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(4*e^(5/2)) + (3*Sqrt[-d]*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(4*e^(5/2)) - (3*Sqrt[-d]*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(4*e^(5/2)) - (3*b*Sqrt[-d]*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(4*e^(5/2)) + (3*b*Sqrt[-d]*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(4*e^(5/2)) - (3*b*Sqrt[-d]*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(4*e^(5/2)) + (3*b*Sqrt[-d]*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(4*e^(5/2))","A",49,12,21,0.5714,1,"{5792, 5654, 74, 5707, 5802, 93, 208, 5800, 5562, 2190, 2279, 2391}"
503,1,792,0,1.9686985,"\int \frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^2*(a + b*ArcCosh[c*x]))/(d + e*x^2)^2,x]","-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{4 \sqrt{-d} e^{3/2}}+\frac{a+b \cosh ^{-1}(c x)}{4 e^{3/2} \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{a+b \cosh ^{-1}(c x)}{4 e^{3/2} \left(\sqrt{-d}+\sqrt{e} x\right)}-\frac{b c \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c \sqrt{-d}-\sqrt{e}}}{\sqrt{c x-1} \sqrt{c \sqrt{-d}+\sqrt{e}}}\right)}{2 e^{3/2} \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c \sqrt{-d}+\sqrt{e}}}+\frac{b c \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c \sqrt{-d}+\sqrt{e}}}{\sqrt{c x-1} \sqrt{c \sqrt{-d}-\sqrt{e}}}\right)}{2 e^{3/2} \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c \sqrt{-d}+\sqrt{e}}}","-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{4 \sqrt{-d} e^{3/2}}+\frac{a+b \cosh ^{-1}(c x)}{4 e^{3/2} \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{a+b \cosh ^{-1}(c x)}{4 e^{3/2} \left(\sqrt{-d}+\sqrt{e} x\right)}-\frac{b c \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c \sqrt{-d}-\sqrt{e}}}{\sqrt{c x-1} \sqrt{c \sqrt{-d}+\sqrt{e}}}\right)}{2 e^{3/2} \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c \sqrt{-d}+\sqrt{e}}}+\frac{b c \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c \sqrt{-d}+\sqrt{e}}}{\sqrt{c x-1} \sqrt{c \sqrt{-d}-\sqrt{e}}}\right)}{2 e^{3/2} \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c \sqrt{-d}+\sqrt{e}}}",1,"(a + b*ArcCosh[c*x])/(4*e^(3/2)*(Sqrt[-d] - Sqrt[e]*x)) - (a + b*ArcCosh[c*x])/(4*e^(3/2)*(Sqrt[-d] + Sqrt[e]*x)) - (b*c*ArcTanh[(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[-1 + c*x])])/(2*Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[c*Sqrt[-d] + Sqrt[e]]*e^(3/2)) + (b*c*ArcTanh[(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[-1 + c*x])])/(2*Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[c*Sqrt[-d] + Sqrt[e]]*e^(3/2)) + ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(4*Sqrt[-d]*e^(3/2)) - ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(4*Sqrt[-d]*e^(3/2)) + ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(4*Sqrt[-d]*e^(3/2)) - ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(4*Sqrt[-d]*e^(3/2)) - (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(4*Sqrt[-d]*e^(3/2)) + (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(4*Sqrt[-d]*e^(3/2)) - (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(4*Sqrt[-d]*e^(3/2)) + (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(4*Sqrt[-d]*e^(3/2))","A",46,10,21,0.4762,1,"{5792, 5707, 5802, 93, 208, 5800, 5562, 2190, 2279, 2391}"
504,1,804,0,1.024227,"\int \frac{a+b \cosh ^{-1}(c x)}{\left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcCosh[c*x])/(d + e*x^2)^2,x]","-\frac{\log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{c \sqrt{-d}-\sqrt{-d c^2-e}}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{\sqrt{-d} c+\sqrt{-d c^2-e}}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{a+b \cosh ^{-1}(c x)}{4 d \sqrt{e} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{a+b \cosh ^{-1}(c x)}{4 d \sqrt{e} \left(\sqrt{e} x+\sqrt{-d}\right)}+\frac{b c \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right)}{2 d \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{e}}-\frac{b c \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right)}{2 d \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{4 (-d)^{3/2} \sqrt{e}}","-\frac{\log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{c \sqrt{-d}-\sqrt{-d c^2-e}}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{\sqrt{-d} c+\sqrt{-d c^2-e}}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{a+b \cosh ^{-1}(c x)}{4 d \sqrt{e} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{a+b \cosh ^{-1}(c x)}{4 d \sqrt{e} \left(\sqrt{e} x+\sqrt{-d}\right)}+\frac{b c \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right)}{2 d \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{e}}-\frac{b c \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right)}{2 d \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{4 (-d)^{3/2} \sqrt{e}}",1,"-(a + b*ArcCosh[c*x])/(4*d*Sqrt[e]*(Sqrt[-d] - Sqrt[e]*x)) + (a + b*ArcCosh[c*x])/(4*d*Sqrt[e]*(Sqrt[-d] + Sqrt[e]*x)) + (b*c*ArcTanh[(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[-1 + c*x])])/(2*d*Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[e]) - (b*c*ArcTanh[(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[-1 + c*x])])/(2*d*Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[e]) - ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(4*(-d)^(3/2)*Sqrt[e]) + ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(4*(-d)^(3/2)*Sqrt[e]) - ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(4*(-d)^(3/2)*Sqrt[e]) + ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(4*(-d)^(3/2)*Sqrt[e]) + (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(4*(-d)^(3/2)*Sqrt[e]) - (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(4*(-d)^(3/2)*Sqrt[e]) + (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(4*(-d)^(3/2)*Sqrt[e]) - (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(4*(-d)^(3/2)*Sqrt[e])","A",26,9,18,0.5000,1,"{5707, 5802, 93, 208, 5800, 5562, 2190, 2279, 2391}"
505,1,846,0,2.0219227,"\int \frac{a+b \cosh ^{-1}(c x)}{x^2 \left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcCosh[c*x])/(x^2*(d + e*x^2)^2),x]","-\frac{3 \sqrt{e} \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{c \sqrt{-d}-\sqrt{-d c^2-e}}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{\sqrt{-d} c+\sqrt{-d c^2-e}}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 (-d)^{5/2}}-\frac{a+b \cosh ^{-1}(c x)}{d^2 x}+\frac{\sqrt{e} \left(a+b \cosh ^{-1}(c x)\right)}{4 d^2 \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{\sqrt{e} \left(a+b \cosh ^{-1}(c x)\right)}{4 d^2 \left(\sqrt{e} x+\sqrt{-d}\right)}+\frac{b c \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{d^2}-\frac{b c \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right)}{2 d^2 \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}}}+\frac{b c \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right)}{2 d^2 \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}}}+\frac{3 b \sqrt{e} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{4 (-d)^{5/2}}-\frac{3 b \sqrt{e} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{4 (-d)^{5/2}}+\frac{3 b \sqrt{e} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{4 (-d)^{5/2}}-\frac{3 b \sqrt{e} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{4 (-d)^{5/2}}","-\frac{3 \sqrt{e} \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{c \sqrt{-d}-\sqrt{-d c^2-e}}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{\sqrt{-d} c+\sqrt{-d c^2-e}}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{4 (-d)^{5/2}}-\frac{a+b \cosh ^{-1}(c x)}{d^2 x}+\frac{\sqrt{e} \left(a+b \cosh ^{-1}(c x)\right)}{4 d^2 \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{\sqrt{e} \left(a+b \cosh ^{-1}(c x)\right)}{4 d^2 \left(\sqrt{e} x+\sqrt{-d}\right)}+\frac{b c \tan ^{-1}\left(\sqrt{c x-1} \sqrt{c x+1}\right)}{d^2}-\frac{b c \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right)}{2 d^2 \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}}}+\frac{b c \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right)}{2 d^2 \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}}}+\frac{3 b \sqrt{e} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{4 (-d)^{5/2}}-\frac{3 b \sqrt{e} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{4 (-d)^{5/2}}+\frac{3 b \sqrt{e} \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{4 (-d)^{5/2}}-\frac{3 b \sqrt{e} \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{4 (-d)^{5/2}}",1,"-((a + b*ArcCosh[c*x])/(d^2*x)) + (Sqrt[e]*(a + b*ArcCosh[c*x]))/(4*d^2*(Sqrt[-d] - Sqrt[e]*x)) - (Sqrt[e]*(a + b*ArcCosh[c*x]))/(4*d^2*(Sqrt[-d] + Sqrt[e]*x)) + (b*c*ArcTan[Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/d^2 - (b*c*Sqrt[e]*ArcTanh[(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[-1 + c*x])])/(2*d^2*Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[c*Sqrt[-d] + Sqrt[e]]) + (b*c*Sqrt[e]*ArcTanh[(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[-1 + c*x])])/(2*d^2*Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[c*Sqrt[-d] + Sqrt[e]]) - (3*Sqrt[e]*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(4*(-d)^(5/2)) + (3*Sqrt[e]*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(4*(-d)^(5/2)) - (3*Sqrt[e]*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(4*(-d)^(5/2)) + (3*Sqrt[e]*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(4*(-d)^(5/2)) + (3*b*Sqrt[e]*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(4*(-d)^(5/2)) - (3*b*Sqrt[e]*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(4*(-d)^(5/2)) + (3*b*Sqrt[e]*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(4*(-d)^(5/2)) - (3*b*Sqrt[e]*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(4*(-d)^(5/2))","A",49,13,21,0.6190,1,"{5792, 5662, 92, 205, 5707, 5802, 93, 208, 5800, 5562, 2190, 2279, 2391}"
506,1,737,0,1.1822369,"\int \frac{x^5 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^5*(a + b*ArcCosh[c*x]))/(d + e*x^2)^3,x]","\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^3}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^3}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 e^3}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^3}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 e^3}-\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)}{4 e^3 \left(d+e x^2\right)^2}+\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{e^3 \left(d+e x^2\right)}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 b e^3}+\frac{b c d x \left(1-c^2 x^2\right)}{8 e^2 \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right) \left(d+e x^2\right)}+\frac{b c \sqrt{d} \sqrt{c^2 x^2-1} \left(2 c^2 d+e\right) \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{8 e^3 \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right)^{3/2}}-\frac{b c \sqrt{d} \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{e^3 \sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d+e}}","\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^3}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 e^3}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 e^3}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 e^3}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 e^3}-\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)}{4 e^3 \left(d+e x^2\right)^2}+\frac{d \left(a+b \cosh ^{-1}(c x)\right)}{e^3 \left(d+e x^2\right)}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 b e^3}+\frac{b c d x \left(1-c^2 x^2\right)}{8 e^2 \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right) \left(d+e x^2\right)}+\frac{b c \sqrt{d} \sqrt{c^2 x^2-1} \left(2 c^2 d+e\right) \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{8 e^3 \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right)^{3/2}}-\frac{b c \sqrt{d} \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{e^3 \sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d+e}}",1,"(b*c*d*x*(1 - c^2*x^2))/(8*e^2*(c^2*d + e)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(d + e*x^2)) - (d^2*(a + b*ArcCosh[c*x]))/(4*e^3*(d + e*x^2)^2) + (d*(a + b*ArcCosh[c*x]))/(e^3*(d + e*x^2)) - (a + b*ArcCosh[c*x])^2/(2*b*e^3) - (b*c*Sqrt[d]*Sqrt[-1 + c^2*x^2]*ArcTanh[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(e^3*Sqrt[c^2*d + e]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c*Sqrt[d]*(2*c^2*d + e)*Sqrt[-1 + c^2*x^2]*ArcTanh[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(8*e^3*(c^2*d + e)^(3/2)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e^3) + ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e^3) + ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e^3) + ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e^3) + (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(2*e^3) + (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*e^3) + (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(2*e^3) + (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*e^3)","A",29,11,21,0.5238,1,"{5792, 5788, 519, 382, 377, 208, 5800, 5562, 2190, 2279, 2391}"
507,1,241,0,0.3616116,"\int \frac{x^3 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^3*(a + b*ArcCosh[c*x]))/(d + e*x^2)^3,x]","\frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)}{4 d \left(d+e x^2\right)^2}-\frac{b \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{4 d e^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c \sqrt{c^2 x^2-1} \left(2 c^2 d+3 e\right) \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{8 \sqrt{d} e^2 \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right)^{3/2}}-\frac{b c x \left(1-c^2 x^2\right)}{8 e \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right) \left(d+e x^2\right)}","\frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)}{4 d \left(d+e x^2\right)^2}-\frac{b \sqrt{1-c^2 x^2} \sin ^{-1}(c x)}{4 d e^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c \sqrt{1-c^2 x^2} \left(2 c^2 d+3 e\right) \tan ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{1-c^2 x^2}}\right)}{8 \sqrt{d} e^2 \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right)^{3/2}}-\frac{b c x \left(1-c^2 x^2\right)}{8 e \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right) \left(d+e x^2\right)}",1,"-(b*c*x*(1 - c^2*x^2))/(8*e*(c^2*d + e)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(d + e*x^2)) + (x^4*(a + b*ArcCosh[c*x]))/(4*d*(d + e*x^2)^2) - (b*Sqrt[-1 + c^2*x^2]*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/(4*d*e^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c*(2*c^2*d + 3*e)*Sqrt[-1 + c^2*x^2]*ArcTanh[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(8*Sqrt[d]*e^2*(c^2*d + e)^(3/2)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",9,10,21,0.4762,1,"{264, 5790, 12, 519, 470, 523, 217, 206, 377, 208}"
508,1,177,0,0.135168,"\int \frac{x \left(a+b \cosh ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x*(a + b*ArcCosh[c*x]))/(d + e*x^2)^3,x]","-\frac{a+b \cosh ^{-1}(c x)}{4 e \left(d+e x^2\right)^2}+\frac{b c \sqrt{c^2 x^2-1} \left(2 c^2 d+e\right) \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{8 d^{3/2} e \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right)^{3/2}}+\frac{b c x \left(1-c^2 x^2\right)}{8 d \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right) \left(d+e x^2\right)}","-\frac{a+b \cosh ^{-1}(c x)}{4 e \left(d+e x^2\right)^2}+\frac{b c \sqrt{c^2 x^2-1} \left(2 c^2 d+e\right) \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{8 d^{3/2} e \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right)^{3/2}}+\frac{b c x \left(1-c^2 x^2\right)}{8 d \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right) \left(d+e x^2\right)}",1,"(b*c*x*(1 - c^2*x^2))/(8*d*(c^2*d + e)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(d + e*x^2)) - (a + b*ArcCosh[c*x])/(4*e*(d + e*x^2)^2) + (b*c*(2*c^2*d + e)*Sqrt[-1 + c^2*x^2]*ArcTanh[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(8*d^(3/2)*e*(c^2*d + e)^(3/2)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",5,5,19,0.2632,1,"{5788, 519, 382, 377, 208}"
509,1,755,0,1.246143,"\int \frac{a+b \cosh ^{-1}(c x)}{x \left(d+e x^2\right)^3} \, dx","Int[(a + b*ArcCosh[c*x])/(x*(d + e*x^2)^3),x]","-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^3}+\frac{b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right)}{2 d^3}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^3}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 d^3}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^3}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 d^3}+\frac{a+b \cosh ^{-1}(c x)}{2 d^2 \left(d+e x^2\right)}+\frac{\log \left(e^{2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^3}+\frac{a+b \cosh ^{-1}(c x)}{4 d \left(d+e x^2\right)^2}-\frac{b c e x \left(1-c^2 x^2\right)}{8 d^2 \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right) \left(d+e x^2\right)}-\frac{b c \sqrt{c^2 x^2-1} \left(2 c^2 d+e\right) \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{8 d^{5/2} \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right)^{3/2}}-\frac{b c \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{2 d^{5/2} \sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d+e}}","-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right)}{2 d^3}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 d^3}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 d^3}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 d^3}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 d^3}+\frac{a+b \cosh ^{-1}(c x)}{2 d^2 \left(d+e x^2\right)}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{b d^3}+\frac{\log \left(e^{-2 \cosh ^{-1}(c x)}+1\right) \left(a+b \cosh ^{-1}(c x)\right)}{d^3}+\frac{a+b \cosh ^{-1}(c x)}{4 d \left(d+e x^2\right)^2}-\frac{b c e x \left(1-c^2 x^2\right)}{8 d^2 \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right) \left(d+e x^2\right)}-\frac{b c \sqrt{c^2 x^2-1} \left(2 c^2 d+e\right) \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{8 d^{5/2} \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right)^{3/2}}-\frac{b c \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{x \sqrt{c^2 d+e}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{2 d^{5/2} \sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d+e}}",1,"-(b*c*e*x*(1 - c^2*x^2))/(8*d^2*(c^2*d + e)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(d + e*x^2)) + (a + b*ArcCosh[c*x])/(4*d*(d + e*x^2)^2) + (a + b*ArcCosh[c*x])/(2*d^2*(d + e*x^2)) - (b*c*Sqrt[-1 + c^2*x^2]*ArcTanh[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(2*d^(5/2)*Sqrt[c^2*d + e]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (b*c*(2*c^2*d + e)*Sqrt[-1 + c^2*x^2]*ArcTanh[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(8*d^(5/2)*(c^2*d + e)^(3/2)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*d^3) - ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*d^3) - ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*d^3) - ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*d^3) + ((a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])])/d^3 - (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(2*d^3) - (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*d^3) - (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(2*d^3) - (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*d^3) + (b*PolyLog[2, -E^(2*ArcCosh[c*x])])/(2*d^3)","A",34,13,21,0.6190,0,"{5792, 5660, 3718, 2190, 2279, 2391, 5788, 519, 382, 377, 208, 5800, 5562}"
510,1,815,0,1.2953668,"\int \frac{a+b \cosh ^{-1}(c x)}{x^3 \left(d+e x^2\right)^3} \, dx","Int[(a + b*ArcCosh[c*x])/(x^3*(d + e*x^2)^3),x]","\frac{b c x \left(1-c^2 x^2\right) e^2}{8 d^3 \left(d c^2+e\right) \sqrt{c x-1} \sqrt{c x+1} \left(e x^2+d\right)}-\frac{\left(a+b \cosh ^{-1}(c x)\right) e}{d^3 \left(e x^2+d\right)}-\frac{\left(a+b \cosh ^{-1}(c x)\right) e}{4 d^2 \left(e x^2+d\right)^2}+\frac{b c \left(2 d c^2+e\right) \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{d c^2+e} x}{\sqrt{d} \sqrt{c^2 x^2-1}}\right) e}{8 d^{7/2} \left(d c^2+e\right)^{3/2} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{d c^2+e} x}{\sqrt{d} \sqrt{c^2 x^2-1}}\right) e}{d^{7/2} \sqrt{d c^2+e} \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right) e}{2 d^4}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{c \sqrt{-d}-\sqrt{-d c^2-e}}+1\right) e}{2 d^4}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right) e}{2 d^4}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{\sqrt{-d} c+\sqrt{-d c^2-e}}+1\right) e}{2 d^4}-\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(1+e^{2 \cosh ^{-1}(c x)}\right) e}{d^4}+\frac{3 b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right) e}{2 d^4}+\frac{3 b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right) e}{2 d^4}+\frac{3 b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right) e}{2 d^4}+\frac{3 b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right) e}{2 d^4}-\frac{3 b \text{PolyLog}\left(2,-e^{2 \cosh ^{-1}(c x)}\right) e}{2 d^4}-\frac{a+b \cosh ^{-1}(c x)}{2 d^3 x^2}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 d^3 x}","\frac{b c x \left(1-c^2 x^2\right) e^2}{8 d^3 \left(d c^2+e\right) \sqrt{c x-1} \sqrt{c x+1} \left(e x^2+d\right)}-\frac{3 \left(a+b \cosh ^{-1}(c x)\right)^2 e}{b d^4}-\frac{\left(a+b \cosh ^{-1}(c x)\right) e}{d^3 \left(e x^2+d\right)}-\frac{\left(a+b \cosh ^{-1}(c x)\right) e}{4 d^2 \left(e x^2+d\right)^2}+\frac{b c \left(2 d c^2+e\right) \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{d c^2+e} x}{\sqrt{d} \sqrt{c^2 x^2-1}}\right) e}{8 d^{7/2} \left(d c^2+e\right)^{3/2} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{d c^2+e} x}{\sqrt{d} \sqrt{c^2 x^2-1}}\right) e}{d^{7/2} \sqrt{d c^2+e} \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(1+e^{-2 \cosh ^{-1}(c x)}\right) e}{d^4}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right) e}{2 d^4}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{c \sqrt{-d}-\sqrt{-d c^2-e}}+1\right) e}{2 d^4}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right) e}{2 d^4}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{\sqrt{-d} c+\sqrt{-d c^2-e}}+1\right) e}{2 d^4}+\frac{3 b \text{PolyLog}\left(2,-e^{-2 \cosh ^{-1}(c x)}\right) e}{2 d^4}+\frac{3 b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right) e}{2 d^4}+\frac{3 b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right) e}{2 d^4}+\frac{3 b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right) e}{2 d^4}+\frac{3 b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right) e}{2 d^4}-\frac{a+b \cosh ^{-1}(c x)}{2 d^3 x^2}+\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 d^3 x}",1,"(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(2*d^3*x) + (b*c*e^2*x*(1 - c^2*x^2))/(8*d^3*(c^2*d + e)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(d + e*x^2)) - (a + b*ArcCosh[c*x])/(2*d^3*x^2) - (e*(a + b*ArcCosh[c*x]))/(4*d^2*(d + e*x^2)^2) - (e*(a + b*ArcCosh[c*x]))/(d^3*(d + e*x^2)) + (b*c*e*Sqrt[-1 + c^2*x^2]*ArcTanh[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(d^(7/2)*Sqrt[c^2*d + e]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*c*e*(2*c^2*d + e)*Sqrt[-1 + c^2*x^2]*ArcTanh[(Sqrt[c^2*d + e]*x)/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(8*d^(7/2)*(c^2*d + e)^(3/2)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (3*e*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*d^4) + (3*e*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*d^4) + (3*e*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*d^4) + (3*e*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*d^4) - (3*e*(a + b*ArcCosh[c*x])*Log[1 + E^(2*ArcCosh[c*x])])/d^4 + (3*b*e*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(2*d^4) + (3*b*e*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*d^4) + (3*b*e*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(2*d^4) + (3*b*e*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*d^4) - (3*b*e*PolyLog[2, -E^(2*ArcCosh[c*x])])/(2*d^4)","A",36,15,21,0.7143,0,"{5792, 5662, 95, 5660, 3718, 2190, 2279, 2391, 5788, 519, 382, 377, 208, 5800, 5562}"
511,1,1224,0,3.9616989,"\int \frac{x^4 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^4*(a + b*ArcCosh[c*x]))/(d + e*x^2)^3,x]","-\frac{b d \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right) c^3}{8 \left(c \sqrt{-d}-\sqrt{e}\right)^{3/2} \left(\sqrt{-d} c+\sqrt{e}\right)^{3/2} e^{5/2}}+\frac{b d \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right) c^3}{8 \left(c \sqrt{-d}-\sqrt{e}\right)^{3/2} \left(\sqrt{-d} c+\sqrt{e}\right)^{3/2} e^{5/2}}-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right) c}{8 \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} e^{5/2}}+\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right) c}{8 \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} e^{5/2}}-\frac{b \sqrt{-d} \sqrt{c x-1} \sqrt{c x+1} c}{16 e^2 \left(d c^2+e\right) \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{b \sqrt{-d} \sqrt{c x-1} \sqrt{c x+1} c}{16 e^2 \left(d c^2+e\right) \left(\sqrt{e} x+\sqrt{-d}\right)}+\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{16 e^{5/2} \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{16 e^{5/2} \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{\sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right)}{16 e^{5/2} \left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{\sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right)}{16 e^{5/2} \left(\sqrt{e} x+\sqrt{-d}\right)^2}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{c \sqrt{-d}-\sqrt{-d c^2-e}}+1\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{\sqrt{-d} c+\sqrt{-d c^2-e}}+1\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 \sqrt{-d} e^{5/2}}","-\frac{b d \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right) c^3}{8 \left(c \sqrt{-d}-\sqrt{e}\right)^{3/2} \left(\sqrt{-d} c+\sqrt{e}\right)^{3/2} e^{5/2}}+\frac{b d \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right) c^3}{8 \left(c \sqrt{-d}-\sqrt{e}\right)^{3/2} \left(\sqrt{-d} c+\sqrt{e}\right)^{3/2} e^{5/2}}-\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right) c}{8 \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} e^{5/2}}+\frac{5 b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right) c}{8 \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} e^{5/2}}-\frac{b \sqrt{-d} \sqrt{c x-1} \sqrt{c x+1} c}{16 e^2 \left(d c^2+e\right) \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{b \sqrt{-d} \sqrt{c x-1} \sqrt{c x+1} c}{16 e^2 \left(d c^2+e\right) \left(\sqrt{e} x+\sqrt{-d}\right)}+\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{16 e^{5/2} \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{16 e^{5/2} \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{\sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right)}{16 e^{5/2} \left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{\sqrt{-d} \left(a+b \cosh ^{-1}(c x)\right)}{16 e^{5/2} \left(\sqrt{e} x+\sqrt{-d}\right)^2}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{c \sqrt{-d}-\sqrt{-d c^2-e}}+1\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{\sqrt{-d} c+\sqrt{-d c^2-e}}+1\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 \sqrt{-d} e^{5/2}}",1,"-(b*c*Sqrt[-d]*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(16*e^2*(c^2*d + e)*(Sqrt[-d] - Sqrt[e]*x)) - (b*c*Sqrt[-d]*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(16*e^2*(c^2*d + e)*(Sqrt[-d] + Sqrt[e]*x)) - (Sqrt[-d]*(a + b*ArcCosh[c*x]))/(16*e^(5/2)*(Sqrt[-d] - Sqrt[e]*x)^2) + (5*(a + b*ArcCosh[c*x]))/(16*e^(5/2)*(Sqrt[-d] - Sqrt[e]*x)) + (Sqrt[-d]*(a + b*ArcCosh[c*x]))/(16*e^(5/2)*(Sqrt[-d] + Sqrt[e]*x)^2) - (5*(a + b*ArcCosh[c*x]))/(16*e^(5/2)*(Sqrt[-d] + Sqrt[e]*x)) - (b*c^3*d*ArcTanh[(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[-1 + c*x])])/(8*(c*Sqrt[-d] - Sqrt[e])^(3/2)*(c*Sqrt[-d] + Sqrt[e])^(3/2)*e^(5/2)) - (5*b*c*ArcTanh[(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[-1 + c*x])])/(8*Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[c*Sqrt[-d] + Sqrt[e]]*e^(5/2)) + (b*c^3*d*ArcTanh[(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[-1 + c*x])])/(8*(c*Sqrt[-d] - Sqrt[e])^(3/2)*(c*Sqrt[-d] + Sqrt[e])^(3/2)*e^(5/2)) + (5*b*c*ArcTanh[(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[-1 + c*x])])/(8*Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[c*Sqrt[-d] + Sqrt[e]]*e^(5/2)) + (3*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(16*Sqrt[-d]*e^(5/2)) - (3*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(16*Sqrt[-d]*e^(5/2)) + (3*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(16*Sqrt[-d]*e^(5/2)) - (3*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(16*Sqrt[-d]*e^(5/2)) - (3*b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(16*Sqrt[-d]*e^(5/2)) + (3*b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(16*Sqrt[-d]*e^(5/2)) - (3*b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(16*Sqrt[-d]*e^(5/2)) + (3*b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(16*Sqrt[-d]*e^(5/2))","A",80,11,21,0.5238,1,"{5792, 5707, 5802, 96, 93, 208, 5800, 5562, 2190, 2279, 2391}"
512,1,1234,0,2.9183495,"\int \frac{x^2 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^2*(a + b*ArcCosh[c*x]))/(d + e*x^2)^3,x]","\frac{b \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right) c^3}{8 \left(c \sqrt{-d}-\sqrt{e}\right)^{3/2} \left(\sqrt{-d} c+\sqrt{e}\right)^{3/2} e^{3/2}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right) c^3}{8 \left(c \sqrt{-d}-\sqrt{e}\right)^{3/2} \left(\sqrt{-d} c+\sqrt{e}\right)^{3/2} e^{3/2}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right) c}{8 d \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} e^{3/2}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right) c}{8 d \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} e^{3/2}}-\frac{b \sqrt{c x-1} \sqrt{c x+1} c}{16 \sqrt{-d} e \left(d c^2+e\right) \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{b \sqrt{c x-1} \sqrt{c x+1} c}{16 \sqrt{-d} e \left(d c^2+e\right) \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{a+b \cosh ^{-1}(c x)}{16 d e^{3/2} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{a+b \cosh ^{-1}(c x)}{16 d e^{3/2} \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{a+b \cosh ^{-1}(c x)}{16 \sqrt{-d} e^{3/2} \left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{a+b \cosh ^{-1}(c x)}{16 \sqrt{-d} e^{3/2} \left(\sqrt{e} x+\sqrt{-d}\right)^2}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{c \sqrt{-d}-\sqrt{-d c^2-e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{\sqrt{-d} c+\sqrt{-d c^2-e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 (-d)^{3/2} e^{3/2}}","\frac{b \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right) c^3}{8 \left(c \sqrt{-d}-\sqrt{e}\right)^{3/2} \left(\sqrt{-d} c+\sqrt{e}\right)^{3/2} e^{3/2}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right) c^3}{8 \left(c \sqrt{-d}-\sqrt{e}\right)^{3/2} \left(\sqrt{-d} c+\sqrt{e}\right)^{3/2} e^{3/2}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right) c}{8 d \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} e^{3/2}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right) c}{8 d \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} e^{3/2}}-\frac{b \sqrt{c x-1} \sqrt{c x+1} c}{16 \sqrt{-d} e \left(d c^2+e\right) \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{b \sqrt{c x-1} \sqrt{c x+1} c}{16 \sqrt{-d} e \left(d c^2+e\right) \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{a+b \cosh ^{-1}(c x)}{16 d e^{3/2} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{a+b \cosh ^{-1}(c x)}{16 d e^{3/2} \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{a+b \cosh ^{-1}(c x)}{16 \sqrt{-d} e^{3/2} \left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{a+b \cosh ^{-1}(c x)}{16 \sqrt{-d} e^{3/2} \left(\sqrt{e} x+\sqrt{-d}\right)^2}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{c \sqrt{-d}-\sqrt{-d c^2-e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{\sqrt{-d} c+\sqrt{-d c^2-e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 (-d)^{3/2} e^{3/2}}",1,"-(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(16*Sqrt[-d]*e*(c^2*d + e)*(Sqrt[-d] - Sqrt[e]*x)) - (b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(16*Sqrt[-d]*e*(c^2*d + e)*(Sqrt[-d] + Sqrt[e]*x)) - (a + b*ArcCosh[c*x])/(16*Sqrt[-d]*e^(3/2)*(Sqrt[-d] - Sqrt[e]*x)^2) - (a + b*ArcCosh[c*x])/(16*d*e^(3/2)*(Sqrt[-d] - Sqrt[e]*x)) + (a + b*ArcCosh[c*x])/(16*Sqrt[-d]*e^(3/2)*(Sqrt[-d] + Sqrt[e]*x)^2) + (a + b*ArcCosh[c*x])/(16*d*e^(3/2)*(Sqrt[-d] + Sqrt[e]*x)) + (b*c^3*ArcTanh[(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[-1 + c*x])])/(8*(c*Sqrt[-d] - Sqrt[e])^(3/2)*(c*Sqrt[-d] + Sqrt[e])^(3/2)*e^(3/2)) + (b*c*ArcTanh[(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[-1 + c*x])])/(8*d*Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[c*Sqrt[-d] + Sqrt[e]]*e^(3/2)) - (b*c^3*ArcTanh[(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[-1 + c*x])])/(8*(c*Sqrt[-d] - Sqrt[e])^(3/2)*(c*Sqrt[-d] + Sqrt[e])^(3/2)*e^(3/2)) - (b*c*ArcTanh[(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[-1 + c*x])])/(8*d*Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[c*Sqrt[-d] + Sqrt[e]]*e^(3/2)) - ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(16*(-d)^(3/2)*e^(3/2)) + ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(16*(-d)^(3/2)*e^(3/2)) - ((a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(16*(-d)^(3/2)*e^(3/2)) + ((a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(16*(-d)^(3/2)*e^(3/2)) + (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(16*(-d)^(3/2)*e^(3/2)) - (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(16*(-d)^(3/2)*e^(3/2)) + (b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(16*(-d)^(3/2)*e^(3/2)) - (b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(16*(-d)^(3/2)*e^(3/2))","A",62,11,21,0.5238,1,"{5792, 5707, 5802, 96, 93, 208, 5800, 5562, 2190, 2279, 2391}"
513,1,1234,0,1.4603437,"\int \frac{a+b \cosh ^{-1}(c x)}{\left(d+e x^2\right)^3} \, dx","Int[(a + b*ArcCosh[c*x])/(d + e*x^2)^3,x]","-\frac{b \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right) c^3}{8 d \left(c \sqrt{-d}-\sqrt{e}\right)^{3/2} \left(\sqrt{-d} c+\sqrt{e}\right)^{3/2} \sqrt{e}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right) c^3}{8 d \left(c \sqrt{-d}-\sqrt{e}\right)^{3/2} \left(\sqrt{-d} c+\sqrt{e}\right)^{3/2} \sqrt{e}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right) c}{8 d^2 \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{e}}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right) c}{8 d^2 \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{e}}-\frac{b \sqrt{c x-1} \sqrt{c x+1} c}{16 (-d)^{3/2} \left(d c^2+e\right) \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{b \sqrt{c x-1} \sqrt{c x+1} c}{16 (-d)^{3/2} \left(d c^2+e\right) \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{16 d^2 \sqrt{e} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{16 d^2 \sqrt{e} \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{a+b \cosh ^{-1}(c x)}{16 (-d)^{3/2} \sqrt{e} \left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{a+b \cosh ^{-1}(c x)}{16 (-d)^{3/2} \sqrt{e} \left(\sqrt{e} x+\sqrt{-d}\right)^2}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{c \sqrt{-d}-\sqrt{-d c^2-e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{\sqrt{-d} c+\sqrt{-d c^2-e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 (-d)^{5/2} \sqrt{e}}","-\frac{b \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right) c^3}{8 d \left(c \sqrt{-d}-\sqrt{e}\right)^{3/2} \left(\sqrt{-d} c+\sqrt{e}\right)^{3/2} \sqrt{e}}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right) c^3}{8 d \left(c \sqrt{-d}-\sqrt{e}\right)^{3/2} \left(\sqrt{-d} c+\sqrt{e}\right)^{3/2} \sqrt{e}}+\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x+1}}{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x-1}}\right) c}{8 d^2 \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{e}}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{c x+1}}{\sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{c x-1}}\right) c}{8 d^2 \sqrt{c \sqrt{-d}-\sqrt{e}} \sqrt{\sqrt{-d} c+\sqrt{e}} \sqrt{e}}-\frac{b \sqrt{c x-1} \sqrt{c x+1} c}{16 (-d)^{3/2} \left(d c^2+e\right) \left(\sqrt{-d}-\sqrt{e} x\right)}-\frac{b \sqrt{c x-1} \sqrt{c x+1} c}{16 (-d)^{3/2} \left(d c^2+e\right) \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{16 d^2 \sqrt{e} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{16 d^2 \sqrt{e} \left(\sqrt{e} x+\sqrt{-d}\right)}-\frac{a+b \cosh ^{-1}(c x)}{16 (-d)^{3/2} \sqrt{e} \left(\sqrt{-d}-\sqrt{e} x\right)^2}+\frac{a+b \cosh ^{-1}(c x)}{16 (-d)^{3/2} \sqrt{e} \left(\sqrt{e} x+\sqrt{-d}\right)^2}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{c \sqrt{-d}-\sqrt{-d c^2-e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e^{\cosh ^{-1}(c x)} \sqrt{e}}{\sqrt{-d} c+\sqrt{-d c^2-e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{-d c^2-e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{-d} c+\sqrt{-d c^2-e}}\right)}{16 (-d)^{5/2} \sqrt{e}}",1,"-(b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(16*(-d)^(3/2)*(c^2*d + e)*(Sqrt[-d] - Sqrt[e]*x)) - (b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(16*(-d)^(3/2)*(c^2*d + e)*(Sqrt[-d] + Sqrt[e]*x)) - (a + b*ArcCosh[c*x])/(16*(-d)^(3/2)*Sqrt[e]*(Sqrt[-d] - Sqrt[e]*x)^2) - (3*(a + b*ArcCosh[c*x]))/(16*d^2*Sqrt[e]*(Sqrt[-d] - Sqrt[e]*x)) + (a + b*ArcCosh[c*x])/(16*(-d)^(3/2)*Sqrt[e]*(Sqrt[-d] + Sqrt[e]*x)^2) + (3*(a + b*ArcCosh[c*x]))/(16*d^2*Sqrt[e]*(Sqrt[-d] + Sqrt[e]*x)) - (b*c^3*ArcTanh[(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[-1 + c*x])])/(8*d*(c*Sqrt[-d] - Sqrt[e])^(3/2)*(c*Sqrt[-d] + Sqrt[e])^(3/2)*Sqrt[e]) + (3*b*c*ArcTanh[(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[-1 + c*x])])/(8*d^2*Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[e]) + (b*c^3*ArcTanh[(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[-1 + c*x])])/(8*d*(c*Sqrt[-d] - Sqrt[e])^(3/2)*(c*Sqrt[-d] + Sqrt[e])^(3/2)*Sqrt[e]) - (3*b*c*ArcTanh[(Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[1 + c*x])/(Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[-1 + c*x])])/(8*d^2*Sqrt[c*Sqrt[-d] - Sqrt[e]]*Sqrt[c*Sqrt[-d] + Sqrt[e]]*Sqrt[e]) + (3*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(16*(-d)^(5/2)*Sqrt[e]) + (3*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(16*(-d)^(5/2)*Sqrt[e]) + (3*b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*b*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(16*(-d)^(5/2)*Sqrt[e]) + (3*b*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(16*(-d)^(5/2)*Sqrt[e])","A",34,10,18,0.5556,1,"{5707, 5802, 96, 93, 208, 5800, 5562, 2190, 2279, 2391}"
514,0,0,0,0.0330496,"\int \sqrt{d+e x^2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[Sqrt[d + e*x^2]*(a + b*ArcCosh[c*x]),x]","\int \sqrt{d+e x^2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","\text{Int}\left(\sqrt{d+e x^2} \left(a+b \cosh ^{-1}(c x)\right),x\right)",0,"Defer[Int][Sqrt[d + e*x^2]*(a + b*ArcCosh[c*x]), x]","A",0,0,0,0,-1,"{}"
515,0,0,0,0.0302334,"\int \frac{a+b \cosh ^{-1}(c x)}{\sqrt{d+e x^2}} \, dx","Int[(a + b*ArcCosh[c*x])/Sqrt[d + e*x^2],x]","\int \frac{a+b \cosh ^{-1}(c x)}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{a+b \cosh ^{-1}(c x)}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcCosh[c*x])/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
516,1,101,0,0.1917381,"\int \frac{a+b \cosh ^{-1}(c x)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])/(d + e*x^2)^(3/2),x]","\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d+e x^2}}-\frac{b \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{d \sqrt{e} \sqrt{c x-1} \sqrt{c x+1}}","\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{d \sqrt{d+e x^2}}-\frac{b \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{d \sqrt{e} \sqrt{c x-1} \sqrt{c x+1}}",1,"(x*(a + b*ArcCosh[c*x]))/(d*Sqrt[d + e*x^2]) - (b*Sqrt[-1 + c^2*x^2]*ArcTanh[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(d*Sqrt[e]*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",7,8,20,0.4000,1,"{191, 5705, 12, 519, 444, 63, 217, 206}"
517,1,190,0,0.182742,"\int \frac{a+b \cosh ^{-1}(c x)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCosh[c*x])/(d + e*x^2)^(5/2),x]","\frac{2 x \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \sqrt{d+e x^2}}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}-\frac{2 b \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{3 d^2 \sqrt{e} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c \left(1-c^2 x^2\right)}{3 d \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right) \sqrt{d+e x^2}}","\frac{2 x \left(a+b \cosh ^{-1}(c x)\right)}{3 d^2 \sqrt{d+e x^2}}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}+\frac{2 b \sqrt{1-c^2 x^2} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{1-c^2 x^2}}{c \sqrt{d+e x^2}}\right)}{3 d^2 \sqrt{e} \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{3 d \left(c^2 d+e\right) \sqrt{d+e x^2}}",1,"(b*c*(1 - c^2*x^2))/(3*d*(c^2*d + e)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Sqrt[d + e*x^2]) + (x*(a + b*ArcCosh[c*x]))/(3*d*(d + e*x^2)^(3/2)) + (2*x*(a + b*ArcCosh[c*x]))/(3*d^2*Sqrt[d + e*x^2]) - (2*b*Sqrt[-1 + c^2*x^2]*ArcTanh[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(3*d^2*Sqrt[e]*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",8,10,20,0.5000,1,"{192, 191, 5705, 12, 519, 571, 78, 63, 217, 206}"
518,1,284,0,0.8014084,"\int \frac{a+b \cosh ^{-1}(c x)}{\left(d+e x^2\right)^{7/2}} \, dx","Int[(a + b*ArcCosh[c*x])/(d + e*x^2)^(7/2),x]","\frac{8 x \left(a+b \cosh ^{-1}(c x)\right)}{15 d^3 \sqrt{d+e x^2}}+\frac{4 x \left(a+b \cosh ^{-1}(c x)\right)}{15 d^2 \left(d+e x^2\right)^{3/2}}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{5 d \left(d+e x^2\right)^{5/2}}+\frac{2 b c \left(1-c^2 x^2\right) \left(3 c^2 d+2 e\right)}{15 d^2 \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right)^2 \sqrt{d+e x^2}}-\frac{8 b \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{15 d^3 \sqrt{e} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c \left(1-c^2 x^2\right)}{15 d \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right) \left(d+e x^2\right)^{3/2}}","\frac{8 x \left(a+b \cosh ^{-1}(c x)\right)}{15 d^3 \sqrt{d+e x^2}}+\frac{4 x \left(a+b \cosh ^{-1}(c x)\right)}{15 d^2 \left(d+e x^2\right)^{3/2}}+\frac{x \left(a+b \cosh ^{-1}(c x)\right)}{5 d \left(d+e x^2\right)^{5/2}}+\frac{2 b c \left(1-c^2 x^2\right) \left(3 c^2 d+2 e\right)}{15 d^2 \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right)^2 \sqrt{d+e x^2}}-\frac{8 b \sqrt{c^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{15 d^3 \sqrt{e} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c \left(1-c^2 x^2\right)}{15 d \sqrt{c x-1} \sqrt{c x+1} \left(c^2 d+e\right) \left(d+e x^2\right)^{3/2}}",1,"(b*c*(1 - c^2*x^2))/(15*d*(c^2*d + e)*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(d + e*x^2)^(3/2)) + (2*b*c*(3*c^2*d + 2*e)*(1 - c^2*x^2))/(15*d^2*(c^2*d + e)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Sqrt[d + e*x^2]) + (x*(a + b*ArcCosh[c*x]))/(5*d*(d + e*x^2)^(5/2)) + (4*x*(a + b*ArcCosh[c*x]))/(15*d^2*(d + e*x^2)^(3/2)) + (8*x*(a + b*ArcCosh[c*x]))/(15*d^3*Sqrt[d + e*x^2]) - (8*b*Sqrt[-1 + c^2*x^2]*ArcTanh[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(15*d^3*Sqrt[e]*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",9,11,20,0.5500,1,"{192, 191, 5705, 12, 519, 6715, 949, 78, 63, 217, 206}"
519,1,529,0,2.8091373,"\int (f x)^m \left(d+e x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^3*(a + b*ArcCosh[c*x]),x]","\frac{3 d^2 e (f x)^{m+3} \left(a+b \cosh ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{d^3 (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+1)}+\frac{3 d e^2 (f x)^{m+5} \left(a+b \cosh ^{-1}(c x)\right)}{f^5 (m+5)}+\frac{e^3 (f x)^{m+7} \left(a+b \cosh ^{-1}(c x)\right)}{f^7 (m+7)}-\frac{b c \sqrt{1-c^2 x^2} (f x)^{m+2} \left(\frac{e \left(3 c^4 d^2 \left(m^2+12 m+35\right)^2+3 c^2 d e (m+7)^2 \left(m^2+7 m+12\right)+e^2 \left(m^4+18 m^3+119 m^2+342 m+360\right)\right)}{c^6 (m+3)^2 (m+5)^2 (m+7)^2}+\frac{d^3}{m^2+3 m+2}\right) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{f^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e \left(1-c^2 x^2\right) (f x)^{m+2} \left(3 c^4 d^2 \left(m^2+12 m+35\right)^2+3 c^2 d e (m+7)^2 \left(m^2+7 m+12\right)+e^2 \left(m^4+18 m^3+119 m^2+342 m+360\right)\right)}{c^5 f^2 (m+3)^2 (m+5)^2 (m+7)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^2 \left(1-c^2 x^2\right) (f x)^{m+4} \left(3 c^2 d (m+7)^2+e \left(m^2+11 m+30\right)\right)}{c^3 f^4 (m+5)^2 (m+7)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^3 \left(1-c^2 x^2\right) (f x)^{m+6}}{c f^6 (m+7)^2 \sqrt{c x-1} \sqrt{c x+1}}","\frac{3 d^2 e (f x)^{m+3} \left(a+b \cosh ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{d^3 (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+1)}+\frac{3 d e^2 (f x)^{m+5} \left(a+b \cosh ^{-1}(c x)\right)}{f^5 (m+5)}+\frac{e^3 (f x)^{m+7} \left(a+b \cosh ^{-1}(c x)\right)}{f^7 (m+7)}-\frac{b \sqrt{1-c^2 x^2} (f x)^{m+2} \left(\frac{e (m+2) \left(3 c^4 d^2 \left(m^2+12 m+35\right)^2+3 c^2 d e (m+7)^2 \left(m^2+7 m+12\right)+e^2 \left(m^4+18 m^3+119 m^2+342 m+360\right)\right)}{(m+3) (m+5) (m+7)}+\frac{c^6 d^3 (m+3) (m+5) (m+7)}{m+1}\right) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{c^5 f^2 (m+2) (m+3) (m+5) (m+7) \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e \left(1-c^2 x^2\right) (f x)^{m+2} \left(3 c^4 d^2 \left(m^2+12 m+35\right)^2+3 c^2 d e (m+7)^2 \left(m^2+7 m+12\right)+e^2 \left(m^4+18 m^3+119 m^2+342 m+360\right)\right)}{c^5 f^2 (m+3)^2 (m+5)^2 (m+7)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^2 \left(1-c^2 x^2\right) (f x)^{m+4} \left(3 c^2 d (m+7)^2+e \left(m^2+11 m+30\right)\right)}{c^3 f^4 (m+5)^2 (m+7)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^3 \left(1-c^2 x^2\right) (f x)^{m+6}}{c f^6 (m+7)^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*e*(3*c^2*d*e*(7 + m)^2*(12 + 7*m + m^2) + 3*c^4*d^2*(35 + 12*m + m^2)^2 + e^2*(360 + 342*m + 119*m^2 + 18*m^3 + m^4))*(f*x)^(2 + m)*(1 - c^2*x^2))/(c^5*f^2*(3 + m)^2*(5 + m)^2*(7 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*e^2*(3*c^2*d*(7 + m)^2 + e*(30 + 11*m + m^2))*(f*x)^(4 + m)*(1 - c^2*x^2))/(c^3*f^4*(5 + m)^2*(7 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*e^3*(f*x)^(6 + m)*(1 - c^2*x^2))/(c*f^6*(7 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (d^3*(f*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(f*(1 + m)) + (3*d^2*e*(f*x)^(3 + m)*(a + b*ArcCosh[c*x]))/(f^3*(3 + m)) + (3*d*e^2*(f*x)^(5 + m)*(a + b*ArcCosh[c*x]))/(f^5*(5 + m)) + (e^3*(f*x)^(7 + m)*(a + b*ArcCosh[c*x]))/(f^7*(7 + m)) - (b*c*(d^3/(2 + 3*m + m^2) + (e*(3*c^2*d*e*(7 + m)^2*(12 + 7*m + m^2) + 3*c^4*d^2*(35 + 12*m + m^2)^2 + e^2*(360 + 342*m + 119*m^2 + 18*m^3 + m^4)))/(c^6*(3 + m)^2*(5 + m)^2*(7 + m)^2))*(f*x)^(2 + m)*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(f^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",8,9,23,0.3913,1,"{270, 5790, 12, 1610, 1809, 1267, 459, 365, 364}"
520,1,332,0,0.5601449,"\int (f x)^m \left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^2*(a + b*ArcCosh[c*x]),x]","\frac{d^2 (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+1)}+\frac{2 d e (f x)^{m+3} \left(a+b \cosh ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{e^2 (f x)^{m+5} \left(a+b \cosh ^{-1}(c x)\right)}{f^5 (m+5)}-\frac{b c \sqrt{1-c^2 x^2} (f x)^{m+2} \left(\frac{e \left(2 c^2 d (m+5)^2+e \left(m^2+7 m+12\right)\right)}{c^4 (m+3)^2 (m+5)^2}+\frac{d^2}{m^2+3 m+2}\right) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{f^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e \left(1-c^2 x^2\right) (f x)^{m+2} \left(2 c^2 d (m+5)^2+e \left(m^2+7 m+12\right)\right)}{c^3 f^2 (m+3)^2 (m+5)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^2 \left(1-c^2 x^2\right) (f x)^{m+4}}{c f^4 (m+5)^2 \sqrt{c x-1} \sqrt{c x+1}}","\frac{d^2 (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+1)}+\frac{2 d e (f x)^{m+3} \left(a+b \cosh ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{e^2 (f x)^{m+5} \left(a+b \cosh ^{-1}(c x)\right)}{f^5 (m+5)}-\frac{b \sqrt{1-c^2 x^2} (f x)^{m+2} \left(\frac{c^4 d^2 (m+3) (m+5)}{m+1}+\frac{e (m+2) \left(2 c^2 d (m+5)^2+e \left(m^2+7 m+12\right)\right)}{(m+3) (m+5)}\right) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{c^3 f^2 (m+2) (m+3) (m+5) \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e \left(1-c^2 x^2\right) (f x)^{m+2} \left(2 c^2 d (m+5)^2+e \left(m^2+7 m+12\right)\right)}{c^3 f^2 (m+3)^2 (m+5)^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b e^2 \left(1-c^2 x^2\right) (f x)^{m+4}}{c f^4 (m+5)^2 \sqrt{c x-1} \sqrt{c x+1}}",1,"(b*e*(2*c^2*d*(5 + m)^2 + e*(12 + 7*m + m^2))*(f*x)^(2 + m)*(1 - c^2*x^2))/(c^3*f^2*(3 + m)^2*(5 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (b*e^2*(f*x)^(4 + m)*(1 - c^2*x^2))/(c*f^4*(5 + m)^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (d^2*(f*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(f*(1 + m)) + (2*d*e*(f*x)^(3 + m)*(a + b*ArcCosh[c*x]))/(f^3*(3 + m)) + (e^2*(f*x)^(5 + m)*(a + b*ArcCosh[c*x]))/(f^5*(5 + m)) - (b*c*(d^2/(2 + 3*m + m^2) + (e*(2*c^2*d*(5 + m)^2 + e*(12 + 7*m + m^2)))/(c^4*(3 + m)^2*(5 + m)^2))*(f*x)^(2 + m)*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(f^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",7,8,23,0.3478,1,"{270, 5790, 12, 520, 1267, 459, 365, 364}"
521,1,187,0,0.2031704,"\int (f x)^m \left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)*(a + b*ArcCosh[c*x]),x]","\frac{d (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+1)}+\frac{e (f x)^{m+3} \left(a+b \cosh ^{-1}(c x)\right)}{f^3 (m+3)}-\frac{b \sqrt{1-c^2 x^2} (f x)^{m+2} \left(\frac{c^2 d}{m^2+3 m+2}+\frac{e}{(m+3)^2}\right) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{c f^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b e \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2}}{c f^2 (m+3)^2}","\frac{d (f x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{f (m+1)}+\frac{e (f x)^{m+3} \left(a+b \cosh ^{-1}(c x)\right)}{f^3 (m+3)}-\frac{b \sqrt{1-c^2 x^2} (f x)^{m+2} \left(c^2 d (m+3)^2+e (m+1) (m+2)\right) \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};c^2 x^2\right)}{c f^2 (m+1) (m+2) (m+3)^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b e \sqrt{c x-1} \sqrt{c x+1} (f x)^{m+2}}{c f^2 (m+3)^2}",1,"-((b*e*(f*x)^(2 + m)*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(c*f^2*(3 + m)^2)) + (d*(f*x)^(1 + m)*(a + b*ArcCosh[c*x]))/(f*(1 + m)) + (e*(f*x)^(3 + m)*(a + b*ArcCosh[c*x]))/(f^3*(3 + m)) - (b*(e/(3 + m)^2 + (c^2*d)/(2 + 3*m + m^2))*(f*x)^(2 + m)*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, c^2*x^2])/(c*f^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",5,5,21,0.2381,1,"{5786, 460, 126, 365, 364}"
522,0,0,0,0.0635233,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{d+e x^2} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x]))/(d + e*x^2),x]","\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{d+e x^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{d+e x^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcCosh[c*x]))/(d + e*x^2), x]","A",0,0,0,0,-1,"{}"
523,0,0,0,0.0620624,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x]))/(d + e*x^2)^2,x]","\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{\left(d+e x^2\right)^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcCosh[c*x]))/(d + e*x^2)^2, x]","A",0,0,0,0,-1,"{}"
524,0,0,0,0.0616717,"\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[((f*x)^m*(a + b*ArcCosh[c*x]))/(d + e*x^2)^3,x]","\int \frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \cosh ^{-1}(c x)\right)}{\left(d+e x^2\right)^3},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcCosh[c*x]))/(d + e*x^2)^3, x]","A",0,0,0,0,-1,"{}"
525,1,609,0,2.0991243,"\int \left(d+e x^2\right)^3 \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x^2)^3*(a + b*ArcCosh[c*x])^2,x]","-\frac{4 b d^2 e \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^3}-\frac{8 b d e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{25 c^3}-\frac{16 b d e^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{25 c^5}-\frac{12 b e^3 x^4 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{245 c^3}-\frac{16 b e^3 x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{245 c^5}-\frac{32 b e^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{245 c^7}+d^2 e x^3 \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 b d^2 e x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c}+d^3 x \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 b d^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}+\frac{3}{5} d e^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{6 b d e^2 x^4 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{25 c}+\frac{1}{7} e^3 x^7 \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 b e^3 x^6 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{49 c}+\frac{4 b^2 d^2 e x}{3 c^2}+\frac{8 b^2 d e^2 x^3}{75 c^2}+\frac{16 b^2 d e^2 x}{25 c^4}+\frac{12 b^2 e^3 x^5}{1225 c^2}+\frac{16 b^2 e^3 x^3}{735 c^4}+\frac{32 b^2 e^3 x}{245 c^6}+\frac{2}{9} b^2 d^2 e x^3+2 b^2 d^3 x+\frac{6}{125} b^2 d e^2 x^5+\frac{2}{343} b^2 e^3 x^7","-\frac{4 b d^2 e \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^3}-\frac{8 b d e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{25 c^3}-\frac{16 b d e^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{25 c^5}-\frac{12 b e^3 x^4 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{245 c^3}-\frac{16 b e^3 x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{245 c^5}-\frac{32 b e^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{245 c^7}+d^2 e x^3 \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 b d^2 e x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c}+d^3 x \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 b d^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}+\frac{3}{5} d e^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{6 b d e^2 x^4 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{25 c}+\frac{1}{7} e^3 x^7 \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 b e^3 x^6 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{49 c}+\frac{4 b^2 d^2 e x}{3 c^2}+\frac{8 b^2 d e^2 x^3}{75 c^2}+\frac{16 b^2 d e^2 x}{25 c^4}+\frac{12 b^2 e^3 x^5}{1225 c^2}+\frac{16 b^2 e^3 x^3}{735 c^4}+\frac{32 b^2 e^3 x}{245 c^6}+\frac{2}{9} b^2 d^2 e x^3+2 b^2 d^3 x+\frac{6}{125} b^2 d e^2 x^5+\frac{2}{343} b^2 e^3 x^7",1,"2*b^2*d^3*x + (4*b^2*d^2*e*x)/(3*c^2) + (16*b^2*d*e^2*x)/(25*c^4) + (32*b^2*e^3*x)/(245*c^6) + (2*b^2*d^2*e*x^3)/9 + (8*b^2*d*e^2*x^3)/(75*c^2) + (16*b^2*e^3*x^3)/(735*c^4) + (6*b^2*d*e^2*x^5)/125 + (12*b^2*e^3*x^5)/(1225*c^2) + (2*b^2*e^3*x^7)/343 - (2*b*d^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/c - (4*b*d^2*e*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*c^3) - (16*b*d*e^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(25*c^5) - (32*b*e^3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(245*c^7) - (2*b*d^2*e*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(3*c) - (8*b*d*e^2*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(25*c^3) - (16*b*e^3*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(245*c^5) - (6*b*d*e^2*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(25*c) - (12*b*e^3*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(245*c^3) - (2*b*e^3*x^6*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(49*c) + d^3*x*(a + b*ArcCosh[c*x])^2 + d^2*e*x^3*(a + b*ArcCosh[c*x])^2 + (3*d*e^2*x^5*(a + b*ArcCosh[c*x])^2)/5 + (e^3*x^7*(a + b*ArcCosh[c*x])^2)/7","A",26,7,20,0.3500,1,"{5707, 5654, 5718, 8, 5662, 5759, 30}"
526,1,359,0,1.1986155,"\int \left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x^2)^2*(a + b*ArcCosh[c*x])^2,x]","-\frac{8 b d e \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{9 c^3}-\frac{8 b e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{75 c^3}-\frac{16 b e^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{75 c^5}+d^2 x \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 b d^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}+\frac{2}{3} d e x^3 \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{4 b d e x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{9 c}+\frac{1}{5} e^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 b e^2 x^4 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{25 c}+\frac{8 b^2 d e x}{9 c^2}+\frac{8 b^2 e^2 x^3}{225 c^2}+\frac{16 b^2 e^2 x}{75 c^4}+2 b^2 d^2 x+\frac{4}{27} b^2 d e x^3+\frac{2}{125} b^2 e^2 x^5","-\frac{8 b d e \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{9 c^3}-\frac{8 b e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{75 c^3}-\frac{16 b e^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{75 c^5}+d^2 x \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 b d^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}+\frac{2}{3} d e x^3 \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{4 b d e x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{9 c}+\frac{1}{5} e^2 x^5 \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 b e^2 x^4 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{25 c}+\frac{8 b^2 d e x}{9 c^2}+\frac{8 b^2 e^2 x^3}{225 c^2}+\frac{16 b^2 e^2 x}{75 c^4}+2 b^2 d^2 x+\frac{4}{27} b^2 d e x^3+\frac{2}{125} b^2 e^2 x^5",1,"2*b^2*d^2*x + (8*b^2*d*e*x)/(9*c^2) + (16*b^2*e^2*x)/(75*c^4) + (4*b^2*d*e*x^3)/27 + (8*b^2*e^2*x^3)/(225*c^2) + (2*b^2*e^2*x^5)/125 - (2*b*d^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/c - (8*b*d*e*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(9*c^3) - (16*b*e^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(75*c^5) - (4*b*d*e*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(9*c) - (8*b*e^2*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(75*c^3) - (2*b*e^2*x^4*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(25*c) + d^2*x*(a + b*ArcCosh[c*x])^2 + (2*d*e*x^3*(a + b*ArcCosh[c*x])^2)/3 + (e^2*x^5*(a + b*ArcCosh[c*x])^2)/5","A",17,7,20,0.3500,1,"{5707, 5654, 5718, 8, 5662, 5759, 30}"
527,1,168,0,0.5734266,"\int \left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x^2)*(a + b*ArcCosh[c*x])^2,x]","-\frac{4 b e \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{9 c^3}+d x \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 b d \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}+\frac{1}{3} e x^3 \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 b e 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 x}{9 c^2}+2 b^2 d x+\frac{2}{27} b^2 e x^3","-\frac{4 b e \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{9 c^3}+d x \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 b d \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}+\frac{1}{3} e x^3 \left(a+b \cosh ^{-1}(c x)\right)^2-\frac{2 b e 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 x}{9 c^2}+2 b^2 d x+\frac{2}{27} b^2 e x^3",1,"2*b^2*d*x + (4*b^2*e*x)/(9*c^2) + (2*b^2*e*x^3)/27 - (2*b*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/c - (4*b*e*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(9*c^3) - (2*b*e*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/(9*c) + d*x*(a + b*ArcCosh[c*x])^2 + (e*x^3*(a + b*ArcCosh[c*x])^2)/3","A",10,7,18,0.3889,1,"{5707, 5654, 5718, 8, 5662, 5759, 30}"
528,1,51,0,0.1568149,"\int \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[(a + b*ArcCosh[c*x])^2,x]","-\frac{2 b \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}+x \left(a+b \cosh ^{-1}(c x)\right)^2+2 b^2 x","-\frac{2 b \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}+x \left(a+b \cosh ^{-1}(c x)\right)^2+2 b^2 x",1,"2*b^2*x - (2*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(a + b*ArcCosh[c*x]))/c + x*(a + b*ArcCosh[c*x])^2","A",3,3,10,0.3000,1,"{5654, 5718, 8}"
529,1,763,0,1.3079577,"\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{b \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{b \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{b \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{b \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{b^2 \text{PolyLog}\left(3,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{b^2 \text{PolyLog}\left(3,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{b^2 \text{PolyLog}\left(3,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{b^2 \text{PolyLog}\left(3,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 \sqrt{-d} \sqrt{e}}","-\frac{b \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{b \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{b \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{b \left(a+b \cosh ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{b^2 \text{PolyLog}\left(3,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{b^2 \text{PolyLog}\left(3,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{b^2 \text{PolyLog}\left(3,-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{b^2 \text{PolyLog}\left(3,\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{c^2 (-d)-e}}+1\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(1-\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{\sqrt{e} e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 (-d)-e}+c \sqrt{-d}}+1\right)}{2 \sqrt{-d} \sqrt{e}}",1,"((a + b*ArcCosh[c*x])^2*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcCosh[c*x])^2*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(2*Sqrt[-d]*Sqrt[e]) + ((a + b*ArcCosh[c*x])^2*Log[1 - (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcCosh[c*x])^2*Log[1 + (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(2*Sqrt[-d]*Sqrt[e]) - (b*(a + b*ArcCosh[c*x])*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(Sqrt[-d]*Sqrt[e]) + (b*(a + b*ArcCosh[c*x])*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(Sqrt[-d]*Sqrt[e]) - (b*(a + b*ArcCosh[c*x])*PolyLog[2, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(Sqrt[-d]*Sqrt[e]) + (b*(a + b*ArcCosh[c*x])*PolyLog[2, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(Sqrt[-d]*Sqrt[e]) + (b^2*PolyLog[3, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e]))])/(Sqrt[-d]*Sqrt[e]) - (b^2*PolyLog[3, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) - e])])/(Sqrt[-d]*Sqrt[e]) + (b^2*PolyLog[3, -((Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e]))])/(Sqrt[-d]*Sqrt[e]) - (b^2*PolyLog[3, (Sqrt[e]*E^ArcCosh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) - e])])/(Sqrt[-d]*Sqrt[e])","A",22,7,20,0.3500,1,"{5707, 5800, 5562, 2190, 2531, 2282, 6589}"
530,0,0,0,0.0405683,"\int \sqrt{d+e x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[d + e*x^2]*(a + b*ArcCosh[c*x])^2,x]","\int \sqrt{d+e x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","\text{Int}\left(\sqrt{d+e x^2} \left(a+b \cosh ^{-1}(c x)\right)^2,x\right)",0,"Defer[Int][Sqrt[d + e*x^2]*(a + b*ArcCosh[c*x])^2, x]","A",0,0,0,0,-1,"{}"
531,0,0,0,0.0431376,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d+e x^2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/Sqrt[d + e*x^2],x]","\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcCosh[c*x])^2/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
532,0,0,0,0.0471121,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/(d + e*x^2)^(3/2),x]","\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(a + b*ArcCosh[c*x])^2/(d + e*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
533,0,0,0,0.0469609,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCosh[c*x])^2/(d + e*x^2)^(5/2),x]","\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(a + b*ArcCosh[c*x])^2/(d + e*x^2)^(5/2), x]","A",0,0,0,0,-1,"{}"
534,1,380,0,0.7928526,"\int \frac{\left(d+e x^2\right)^2}{a+b \cosh ^{-1}(c x)} \, dx","Int[(d + e*x^2)^2/(a + b*ArcCosh[c*x]),x]","-\frac{d e \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{2 b c^3}-\frac{d e \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{2 b c^3}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{8 b c^5}-\frac{3 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{16 b c^5}-\frac{e^2 \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{16 b c^5}+\frac{d e \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{2 b c^3}+\frac{d e \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{2 b c^3}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{8 b c^5}+\frac{3 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{16 b c^5}+\frac{e^2 \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{16 b c^5}-\frac{d^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b c}+\frac{d^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b c}","-\frac{d e \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 b c^3}-\frac{d e \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b c^3}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b c^5}-\frac{3 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c^5}-\frac{e^2 \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c^5}+\frac{d e \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 b c^3}+\frac{d e \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b c^3}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b c^5}+\frac{3 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c^5}+\frac{e^2 \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b c^5}-\frac{d^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b c}+\frac{d^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b c}",1,"-(d*e*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b])/(2*b*c^3) - (e^2*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b])/(8*b*c^5) - (d^2*CoshIntegral[(a + b*ArcCosh[c*x])/b]*Sinh[a/b])/(b*c) - (d*e*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]]*Sinh[(3*a)/b])/(2*b*c^3) - (3*e^2*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]]*Sinh[(3*a)/b])/(16*b*c^5) - (e^2*CoshIntegral[(5*a)/b + 5*ArcCosh[c*x]]*Sinh[(5*a)/b])/(16*b*c^5) + (d*e*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(2*b*c^3) + (e^2*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(8*b*c^5) + (d*e*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(2*b*c^3) + (3*e^2*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(16*b*c^5) + (e^2*Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(16*b*c^5) + (d^2*Cosh[a/b]*SinhIntegral[(a + b*ArcCosh[c*x])/b])/(b*c)","A",27,7,20,0.3500,1,"{5707, 5658, 3303, 3298, 3301, 5670, 5448}"
535,1,176,0,0.3817527,"\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{e \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^3}-\frac{e \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 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^3}+\frac{e \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 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b c}+\frac{d \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b c}","-\frac{\sinh \left(\frac{a}{b}\right) \left(4 c^2 d+e\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b c^3}-\frac{e \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b c^3}+\frac{\cosh \left(\frac{a}{b}\right) \left(4 c^2 d+e\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b c^3}+\frac{e \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b c^3}",1,"-(e*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b])/(4*b*c^3) - (d*CoshIntegral[(a + b*ArcCosh[c*x])/b]*Sinh[a/b])/(b*c) - (e*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]]*Sinh[(3*a)/b])/(4*b*c^3) + (e*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(4*b*c^3) + (e*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(4*b*c^3) + (d*Cosh[a/b]*SinhIntegral[(a + b*ArcCosh[c*x])/b])/(b*c)","A",15,7,18,0.3889,1,"{5707, 5658, 3303, 3298, 3301, 5670, 5448}"
536,1,54,0,0.0704804,"\int \frac{1}{a+b \cosh ^{-1}(c x)} \, dx","Int[(a + b*ArcCosh[c*x])^(-1),x]","\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b c}-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b c}","\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b c}-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b c}",1,"-((CoshIntegral[(a + b*ArcCosh[c*x])/b]*Sinh[a/b])/(b*c)) + (Cosh[a/b]*SinhIntegral[(a + b*ArcCosh[c*x])/b])/(b*c)","A",4,4,10,0.4000,1,"{5658, 3303, 3298, 3301}"
537,0,0,0,0.0390261,"\int \frac{1}{\left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x^2)*(a + b*ArcCosh[c*x])),x]","\int \frac{1}{\left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right) \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,"{}"
538,0,0,0,0.0377451,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x^2)^2*(a + b*ArcCosh[c*x])),x]","\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d + e*x^2)^2*(a + b*ArcCosh[c*x])), x]","A",0,0,0,0,-1,"{}"
539,0,0,0,0.0461833,"\int \frac{\sqrt{d+e x^2}}{a+b \cosh ^{-1}(c x)} \, dx","Int[Sqrt[d + e*x^2]/(a + b*ArcCosh[c*x]),x]","\int \frac{\sqrt{d+e x^2}}{a+b \cosh ^{-1}(c x)} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2}}{a+b \cosh ^{-1}(c x)},x\right)",0,"Defer[Int][Sqrt[d + e*x^2]/(a + b*ArcCosh[c*x]), x]","A",0,0,0,0,-1,"{}"
540,0,0,0,0.0479128,"\int \frac{1}{\sqrt{d+e x^2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[1/(Sqrt[d + e*x^2]*(a + b*ArcCosh[c*x])),x]","\int \frac{1}{\sqrt{d+e x^2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\sqrt{d+e x^2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(Sqrt[d + e*x^2]*(a + b*ArcCosh[c*x])), x]","A",0,0,0,0,-1,"{}"
541,0,0,0,0.0513969,"\int \frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x^2)^(3/2)*(a + b*ArcCosh[c*x])),x]","\int \frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d + e*x^2)^(3/2)*(a + b*ArcCosh[c*x])), x]","A",0,0,0,0,-1,"{}"
542,0,0,0,0.0509137,"\int \frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x^2)^(5/2)*(a + b*ArcCosh[c*x])),x]","\int \frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d + e*x^2)^(5/2)*(a + b*ArcCosh[c*x])), x]","A",0,0,0,0,-1,"{}"
543,1,498,0,0.9509907,"\int \frac{\left(d+e x^2\right)^2}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(d + e*x^2)^2/(a + b*ArcCosh[c*x])^2,x]","\frac{d e \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{2 b^2 c^3}+\frac{3 d e \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{2 b^2 c^3}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{8 b^2 c^5}+\frac{9 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{16 b^2 c^5}+\frac{5 e^2 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{16 b^2 c^5}-\frac{d e \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{2 b^2 c^3}-\frac{3 d e \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{2 b^2 c^3}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{8 b^2 c^5}-\frac{9 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{16 b^2 c^5}-\frac{5 e^2 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \cosh ^{-1}(c x)\right)}{16 b^2 c^5}+\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^2 \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}-\frac{e^2 x^4 \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}","\frac{d e \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 b^2 c^3}+\frac{3 d e \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^3}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b^2 c^5}+\frac{9 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^5}+\frac{5 e^2 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^5}-\frac{d e \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 b^2 c^3}-\frac{3 d e \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^3}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{8 b^2 c^5}-\frac{9 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^5}-\frac{5 e^2 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^5}+\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^2 \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}-\frac{e^2 x^4 \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^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*(a + b*ArcCosh[c*x])) - (e^2*x^4*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) + (d*e*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(2*b^2*c^3) + (e^2*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(8*b^2*c^5) + (3*d*e*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(2*b^2*c^3) + (9*e^2*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(16*b^2*c^5) + (5*e^2*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(16*b^2*c^5) - (d^2*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(b^2*c) - (d*e*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(2*b^2*c^3) - (e^2*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(8*b^2*c^5) - (3*d*e*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(2*b^2*c^3) - (9*e^2*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(16*b^2*c^5) - (5*e^2*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcCosh[c*x]])/(16*b^2*c^5)","A",26,7,20,0.3500,1,"{5707, 5656, 5781, 3303, 3298, 3301, 5666}"
544,1,249,0,0.595345,"\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{e \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 \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{e \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 \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 \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^2 \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}","\frac{e \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 \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{e \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 \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 \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^2 \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^2*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[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(4*b^2*c^3) + (3*e*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(4*b^2*c^3) - (d*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(b^2*c) - (e*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(4*b^2*c^3) - (3*e*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCosh[c*x]])/(4*b^2*c^3)","A",15,7,18,0.3889,1,"{5707, 5656, 5781, 3303, 3298, 3301, 5666}"
545,1,86,0,0.3232342,"\int \frac{1}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[(a + b*ArcCosh[c*x])^(-2),x]","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b^2 c}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b^2 c}-\frac{\sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{\sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}",1,"-((Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*(a + b*ArcCosh[c*x]))) + (Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]])/(b^2*c) - (Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]])/(b^2*c)","A",5,5,10,0.5000,1,"{5656, 5781, 3303, 3298, 3301}"
546,0,0,0,0.0377301,"\int \frac{1}{\left(d+e x^2\right) \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}{\left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right) \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,"{}"
547,0,0,0,0.0367158,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[1/((d + e*x^2)^2*(a + b*ArcCosh[c*x])^2),x]","\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/((d + e*x^2)^2*(a + b*ArcCosh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
548,0,0,0,0.0450141,"\int \frac{\sqrt{d+e x^2}}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[d + e*x^2]/(a + b*ArcCosh[c*x])^2,x]","\int \frac{\sqrt{d+e x^2}}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2}}{\left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][Sqrt[d + e*x^2]/(a + b*ArcCosh[c*x])^2, x]","A",0,0,0,0,-1,"{}"
549,0,0,0,0.046372,"\int \frac{1}{\sqrt{d+e x^2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[1/(Sqrt[d + e*x^2]*(a + b*ArcCosh[c*x])^2),x]","\int \frac{1}{\sqrt{d+e x^2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\sqrt{d+e x^2} \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/(Sqrt[d + e*x^2]*(a + b*ArcCosh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
550,0,0,0,0.0503267,"\int \frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[1/((d + e*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/((d + e*x^2)^(3/2)*(a + b*ArcCosh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
551,0,0,0,0.0503068,"\int \frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Int[1/((d + e*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/((d + e*x^2)^(5/2)*(a + b*ArcCosh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
552,1,672,0,2.4021357,"\int \left(d+e x^2\right)^2 \sqrt{a+b \cosh ^{-1}(c x)} \, dx","Int[(d + e*x^2)^2*Sqrt[a + b*ArcCosh[c*x]],x]","-\frac{\sqrt{\pi } \sqrt{b} d e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c^3}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} d e e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{24 c^3}-\frac{\sqrt{\pi } \sqrt{b} d e e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c^3}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} d e e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{24 c^3}-\frac{\sqrt{\pi } \sqrt{b} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 c^5}-\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 x)}}{\sqrt{b}}\right)}{64 c^5}-\frac{\sqrt{\frac{\pi }{5}} \sqrt{b} e^2 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{320 c^5}-\frac{\sqrt{\pi } \sqrt{b} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 c^5}-\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 x)}}{\sqrt{b}}\right)}{64 c^5}-\frac{\sqrt{\frac{\pi }{5}} \sqrt{b} e^2 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{320 c^5}-\frac{\sqrt{\pi } \sqrt{b} d^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}-\frac{\sqrt{\pi } \sqrt{b} d^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+d^2 x \sqrt{a+b \cosh ^{-1}(c x)}+\frac{2}{3} d e x^3 \sqrt{a+b \cosh ^{-1}(c x)}+\frac{1}{5} e^2 x^5 \sqrt{a+b \cosh ^{-1}(c x)}","-\frac{\sqrt{\pi } \sqrt{b} d e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c^3}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} d e e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{24 c^3}-\frac{\sqrt{\pi } \sqrt{b} d e e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c^3}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} d e e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{24 c^3}-\frac{\sqrt{\pi } \sqrt{b} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 c^5}-\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 x)}}{\sqrt{b}}\right)}{64 c^5}-\frac{\sqrt{\frac{\pi }{5}} \sqrt{b} e^2 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{320 c^5}-\frac{\sqrt{\pi } \sqrt{b} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 c^5}-\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 x)}}{\sqrt{b}}\right)}{64 c^5}-\frac{\sqrt{\frac{\pi }{5}} \sqrt{b} e^2 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{320 c^5}-\frac{\sqrt{\pi } \sqrt{b} d^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}-\frac{\sqrt{\pi } \sqrt{b} d^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+d^2 x \sqrt{a+b \cosh ^{-1}(c x)}+\frac{2}{3} d e x^3 \sqrt{a+b \cosh ^{-1}(c x)}+\frac{1}{5} e^2 x^5 \sqrt{a+b \cosh ^{-1}(c x)}",1,"d^2*x*Sqrt[a + b*ArcCosh[c*x]] + (2*d*e*x^3*Sqrt[a + b*ArcCosh[c*x]])/3 + (e^2*x^5*Sqrt[a + b*ArcCosh[c*x]])/5 - (Sqrt[b]*d^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(4*c) - (Sqrt[b]*d*e*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(8*c^3) - (Sqrt[b]*e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(32*c^5) - (Sqrt[b]*d*e*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(24*c^3) - (Sqrt[b]*e^2*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(64*c^5) - (Sqrt[b]*e^2*E^((5*a)/b)*Sqrt[Pi/5]*Erf[(Sqrt[5]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(320*c^5) - (Sqrt[b]*d^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(4*c*E^(a/b)) - (Sqrt[b]*d*e*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(8*c^3*E^(a/b)) - (Sqrt[b]*e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(32*c^5*E^(a/b)) - (Sqrt[b]*d*e*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(24*c^3*E^((3*a)/b)) - (Sqrt[b]*e^2*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(64*c^5*E^((3*a)/b)) - (Sqrt[b]*e^2*Sqrt[Pi/5]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(320*c^5*E^((5*a)/b))","A",42,9,22,0.4091,1,"{5707, 5654, 5781, 3307, 2180, 2204, 2205, 5664, 3312}"
553,1,322,0,1.2866238,"\int \left(d+e x^2\right) \sqrt{a+b \cosh ^{-1}(c x)} \, dx","Int[(d + e*x^2)*Sqrt[a + b*ArcCosh[c*x]],x]","-\frac{\sqrt{\pi } \sqrt{b} e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^3}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{48 c^3}-\frac{\sqrt{\pi } \sqrt{b} e e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^3}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{48 c^3}-\frac{\sqrt{\pi } \sqrt{b} d e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}-\frac{\sqrt{\pi } \sqrt{b} d e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+d x \sqrt{a+b \cosh ^{-1}(c x)}+\frac{1}{3} e x^3 \sqrt{a+b \cosh ^{-1}(c x)}","-\frac{\sqrt{\pi } \sqrt{b} e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^3}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{48 c^3}-\frac{\sqrt{\pi } \sqrt{b} e e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 c^3}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{48 c^3}-\frac{\sqrt{\pi } \sqrt{b} d e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}-\frac{\sqrt{\pi } \sqrt{b} d e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+d x \sqrt{a+b \cosh ^{-1}(c x)}+\frac{1}{3} e x^3 \sqrt{a+b \cosh ^{-1}(c x)}",1,"d*x*Sqrt[a + b*ArcCosh[c*x]] + (e*x^3*Sqrt[a + b*ArcCosh[c*x]])/3 - (Sqrt[b]*d*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(4*c) - (Sqrt[b]*e*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(16*c^3) - (Sqrt[b]*e*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(48*c^3) - (Sqrt[b]*d*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(4*c*E^(a/b)) - (Sqrt[b]*e*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(16*c^3*E^(a/b)) - (Sqrt[b]*e*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(48*c^3*E^((3*a)/b))","A",23,9,20,0.4500,1,"{5707, 5654, 5781, 3307, 2180, 2204, 2205, 5664, 3312}"
554,1,102,0,0.4203426,"\int \sqrt{a+b \cosh ^{-1}(c x)} \, dx","Int[Sqrt[a + b*ArcCosh[c*x]],x]","-\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}-\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+x \sqrt{a+b \cosh ^{-1}(c x)}","-\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}-\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+x \sqrt{a+b \cosh ^{-1}(c x)}",1,"x*Sqrt[a + b*ArcCosh[c*x]] - (Sqrt[b]*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(4*c) - (Sqrt[b]*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(4*c*E^(a/b))","A",7,6,12,0.5000,1,"{5654, 5781, 3307, 2180, 2204, 2205}"
555,0,0,0,0.0573845,"\int \frac{\sqrt{a+b \cosh ^{-1}(c x)}}{d+e x^2} \, dx","Int[Sqrt[a + b*ArcCosh[c*x]]/(d + e*x^2),x]","\int \frac{\sqrt{a+b \cosh ^{-1}(c x)}}{d+e x^2} \, dx","\text{Int}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{d+e x^2},x\right)",0,"Defer[Int][Sqrt[a + b*ArcCosh[c*x]]/(d + e*x^2), x]","A",0,0,0,0,-1,"{}"
556,0,0,0,0.0571904,"\int \frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\left(d+e x^2\right)^2} \, dx","Int[Sqrt[a + b*ArcCosh[c*x]]/(d + e*x^2)^2,x]","\int \frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\left(d+e x^2\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\left(d+e x^2\right)^2},x\right)",0,"Defer[Int][Sqrt[a + b*ArcCosh[c*x]]/(d + e*x^2)^2, x]","A",0,0,0,0,-1,"{}"
557,1,442,0,1.7316926,"\int \left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right)^{3/2} \, dx","Int[(d + e*x^2)*(a + b*ArcCosh[c*x])^(3/2),x]","-\frac{3 \sqrt{\pi } b^{3/2} e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 c^3}-\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{96 c^3}+\frac{3 \sqrt{\pi } b^{3/2} e e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 c^3}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{96 c^3}-\frac{3 \sqrt{\pi } b^{3/2} d e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}+\frac{3 \sqrt{\pi } b^{3/2} d e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}-\frac{b e \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}}{3 c^3}+d x \left(a+b \cosh ^{-1}(c x)\right)^{3/2}-\frac{3 b d \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}}{2 c}+\frac{1}{3} e x^3 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}-\frac{b e x^2 \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}}{6 c}","-\frac{3 \sqrt{\pi } b^{3/2} e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 c^3}-\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{96 c^3}+\frac{3 \sqrt{\pi } b^{3/2} e e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 c^3}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{96 c^3}-\frac{3 \sqrt{\pi } b^{3/2} d e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}+\frac{3 \sqrt{\pi } b^{3/2} d e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}-\frac{b e \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}}{3 c^3}+d x \left(a+b \cosh ^{-1}(c x)\right)^{3/2}-\frac{3 b d \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}}{2 c}+\frac{1}{3} e x^3 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}-\frac{b e x^2 \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}}{6 c}",1,"(-3*b*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Sqrt[a + b*ArcCosh[c*x]])/(2*c) - (b*e*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Sqrt[a + b*ArcCosh[c*x]])/(3*c^3) - (b*e*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Sqrt[a + b*ArcCosh[c*x]])/(6*c) + d*x*(a + b*ArcCosh[c*x])^(3/2) + (e*x^3*(a + b*ArcCosh[c*x])^(3/2))/3 - (3*b^(3/2)*d*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(8*c) - (3*b^(3/2)*e*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(32*c^3) - (b^(3/2)*e*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(96*c^3) + (3*b^(3/2)*d*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(8*c*E^(a/b)) + (3*b^(3/2)*e*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(32*c^3*E^(a/b)) + (b^(3/2)*e*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(96*c^3*E^((3*a)/b))","A",32,12,20,0.6000,1,"{5707, 5654, 5718, 5658, 3308, 2180, 2205, 2204, 5664, 5759, 5670, 5448}"
558,1,140,0,0.4019513,"\int \left(a+b \cosh ^{-1}(c x)\right)^{3/2} \, dx","Int[(a + b*ArcCosh[c*x])^(3/2),x]","-\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}+\frac{3 \sqrt{\pi } b^{3/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}-\frac{3 b \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}}{2 c}+x \left(a+b \cosh ^{-1}(c x)\right)^{3/2}","-\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}+\frac{3 \sqrt{\pi } b^{3/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}-\frac{3 b \sqrt{c x-1} \sqrt{c x+1} \sqrt{a+b \cosh ^{-1}(c x)}}{2 c}+x \left(a+b \cosh ^{-1}(c x)\right)^{3/2}",1,"(-3*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*Sqrt[a + b*ArcCosh[c*x]])/(2*c) + x*(a + b*ArcCosh[c*x])^(3/2) - (3*b^(3/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(8*c) + (3*b^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(8*c*E^(a/b))","A",8,7,12,0.5833,1,"{5654, 5718, 5658, 3308, 2180, 2205, 2204}"
559,0,0,0,0.0665648,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}}{d+e x^2} \, dx","Int[(a + b*ArcCosh[c*x])^(3/2)/(d + e*x^2),x]","\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}}{d+e x^2} \, dx","\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}}{d+e x^2},x\right)",0,"Defer[Int][(a + b*ArcCosh[c*x])^(3/2)/(d + e*x^2), x]","A",0,0,0,0,-1,"{}"
560,0,0,0,0.0613161,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}}{\left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcCosh[c*x])^(3/2)/(d + e*x^2)^2,x]","\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}}{\left(d+e x^2\right)^2} \, dx","\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}}{\left(d+e x^2\right)^2},x\right)",0,"Defer[Int][(a + b*ArcCosh[c*x])^(3/2)/(d + e*x^2)^2, x]","A",0,0,0,0,-1,"{}"
561,1,608,0,1.1477869,"\int \frac{\left(d+e x^2\right)^2}{\sqrt{a+b \cosh ^{-1}(c x)}} \, dx","Int[(d + e*x^2)^2/Sqrt[a + b*ArcCosh[c*x]],x]","-\frac{\sqrt{\pi } d e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{3}} d e e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^3}+\frac{\sqrt{\pi } d e e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^3}+\frac{\sqrt{\frac{\pi }{3}} d e e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^3}-\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 \sqrt{b} c^5}-\frac{\sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 \sqrt{b} c^5}-\frac{\sqrt{\frac{\pi }{5}} e^2 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 \sqrt{b} c^5}+\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 \sqrt{b} c^5}+\frac{\sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 \sqrt{b} c^5}+\frac{\sqrt{\frac{\pi }{5}} e^2 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 \sqrt{b} c^5}-\frac{\sqrt{\pi } d^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}+\frac{\sqrt{\pi } d^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}","-\frac{\sqrt{\pi } d e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{3}} d e e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^3}+\frac{\sqrt{\pi } d e e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^3}+\frac{\sqrt{\frac{\pi }{3}} d e e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 \sqrt{b} c^3}-\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 \sqrt{b} c^5}-\frac{\sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 \sqrt{b} c^5}-\frac{\sqrt{\frac{\pi }{5}} e^2 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 \sqrt{b} c^5}+\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 \sqrt{b} c^5}+\frac{\sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 \sqrt{b} c^5}+\frac{\sqrt{\frac{\pi }{5}} e^2 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 \sqrt{b} c^5}-\frac{\sqrt{\pi } d^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}+\frac{\sqrt{\pi } d^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}",1,"-(d^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(2*Sqrt[b]*c) - (d*e*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(4*Sqrt[b]*c^3) - (e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(16*Sqrt[b]*c^5) - (d*e*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(4*Sqrt[b]*c^3) - (e^2*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(32*Sqrt[b]*c^5) - (e^2*E^((5*a)/b)*Sqrt[Pi/5]*Erf[(Sqrt[5]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(32*Sqrt[b]*c^5) + (d^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(2*Sqrt[b]*c*E^(a/b)) + (d*e*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(4*Sqrt[b]*c^3*E^(a/b)) + (e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(16*Sqrt[b]*c^5*E^(a/b)) + (d*e*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(4*Sqrt[b]*c^3*E^((3*a)/b)) + (e^2*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(32*Sqrt[b]*c^5*E^((3*a)/b)) + (e^2*Sqrt[Pi/5]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(32*Sqrt[b]*c^5*E^((5*a)/b))","A",39,8,22,0.3636,1,"{5707, 5658, 3308, 2180, 2205, 2204, 5670, 5448}"
562,1,287,0,0.5347711,"\int \frac{d+e x^2}{\sqrt{a+b \cosh ^{-1}(c x)}} \, dx","Int[(d + e*x^2)/Sqrt[a + b*ArcCosh[c*x]],x]","-\frac{\sqrt{\pi } e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{3}} e e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}+\frac{\sqrt{\pi } e e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}+\frac{\sqrt{\frac{\pi }{3}} e e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}-\frac{\sqrt{\pi } d e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}+\frac{\sqrt{\pi } d e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}","-\frac{\sqrt{\pi } e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}-\frac{\sqrt{\frac{\pi }{3}} e e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}+\frac{\sqrt{\pi } e e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}+\frac{\sqrt{\frac{\pi }{3}} e e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 \sqrt{b} c^3}-\frac{\sqrt{\pi } d e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}+\frac{\sqrt{\pi } d e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}",1,"-(d*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(2*Sqrt[b]*c) - (e*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(8*Sqrt[b]*c^3) - (e*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(8*Sqrt[b]*c^3) + (d*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(2*Sqrt[b]*c*E^(a/b)) + (e*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(8*Sqrt[b]*c^3*E^(a/b)) + (e*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(8*Sqrt[b]*c^3*E^((3*a)/b))","A",21,8,20,0.4000,1,"{5707, 5658, 3308, 2180, 2205, 2204, 5670, 5448}"
563,1,88,0,0.1044391,"\int \frac{1}{\sqrt{a+b \cosh ^{-1}(c x)}} \, dx","Int[1/Sqrt[a + b*ArcCosh[c*x]],x]","\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}","\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}",1,"-(E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(2*Sqrt[b]*c) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(2*Sqrt[b]*c*E^(a/b))","A",6,5,12,0.4167,1,"{5658, 3308, 2180, 2205, 2204}"
564,0,0,0,0.0608199,"\int \frac{1}{\left(d+e x^2\right) \sqrt{a+b \cosh ^{-1}(c x)}} \, dx","Int[1/((d + e*x^2)*Sqrt[a + b*ArcCosh[c*x]]),x]","\int \frac{1}{\left(d+e x^2\right) \sqrt{a+b \cosh ^{-1}(c x)}} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right) \sqrt{a+b \cosh ^{-1}(c x)}},x\right)",0,"Defer[Int][1/((d + e*x^2)*Sqrt[a + b*ArcCosh[c*x]]), x]","A",0,0,0,0,-1,"{}"
565,0,0,0,0.0584369,"\int \frac{1}{\left(d+e x^2\right)^2 \sqrt{a+b \cosh ^{-1}(c x)}} \, dx","Int[1/((d + e*x^2)^2*Sqrt[a + b*ArcCosh[c*x]]),x]","\int \frac{1}{\left(d+e x^2\right)^2 \sqrt{a+b \cosh ^{-1}(c x)}} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^2 \sqrt{a+b \cosh ^{-1}(c x)}},x\right)",0,"Defer[Int][1/((d + e*x^2)^2*Sqrt[a + b*ArcCosh[c*x]]), x]","A",0,0,0,0,-1,"{}"
566,1,358,0,0.8314713,"\int \frac{d+e x^2}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(d + e*x^2)/(a + b*ArcCosh[c*x])^(3/2),x]","\frac{\sqrt{\pi } e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}+\frac{\sqrt{3 \pi } e e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}+\frac{\sqrt{\pi } e e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}+\frac{\sqrt{3 \pi } e e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}+\frac{\sqrt{\pi } d e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}+\frac{\sqrt{\pi } d e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 d \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{2 e x^2 \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}","\frac{\sqrt{\pi } e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}+\frac{\sqrt{3 \pi } e e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}+\frac{\sqrt{\pi } e e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}+\frac{\sqrt{3 \pi } e e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c^3}+\frac{\sqrt{\pi } d e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}+\frac{\sqrt{\pi } d e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 d \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}-\frac{2 e x^2 \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}",1,"(-2*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*Sqrt[a + b*ArcCosh[c*x]]) - (2*e*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*Sqrt[a + b*ArcCosh[c*x]]) + (d*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(b^(3/2)*c) + (e*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(4*b^(3/2)*c^3) + (e*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c^3) + (d*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(b^(3/2)*c*E^(a/b)) + (e*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(4*b^(3/2)*c^3*E^(a/b)) + (e*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c^3*E^((3*a)/b))","A",21,8,20,0.4000,1,"{5707, 5656, 5781, 3307, 2180, 2204, 2205, 5666}"
567,1,120,0,0.4163002,"\int \frac{1}{\left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(a + b*ArcCosh[c*x])^(-3/2),x]","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{c x-1} \sqrt{c x+1}}{b c \sqrt{a+b \cosh ^{-1}(c x)}}",1,"(-2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(b*c*Sqrt[a + b*ArcCosh[c*x]]) + (E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(b^(3/2)*c) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c*x]]/Sqrt[b]])/(b^(3/2)*c*E^(a/b))","A",7,6,12,0.5000,1,"{5656, 5781, 3307, 2180, 2204, 2205}"
568,0,0,0,0.0694119,"\int \frac{1}{\left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[1/((d + e*x^2)*(a + b*ArcCosh[c*x])^(3/2)),x]","\int \frac{1}{\left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right) \left(a+b \cosh ^{-1}(c x)\right)^{3/2}},x\right)",0,"Defer[Int][1/((d + e*x^2)*(a + b*ArcCosh[c*x])^(3/2)), x]","A",0,0,0,0,-1,"{}"
569,0,0,0,0.0641523,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","Int[1/((d + e*x^2)^2*(a + b*ArcCosh[c*x])^(3/2)),x]","\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^2 \left(a+b \cosh ^{-1}(c x)\right)^{3/2}},x\right)",0,"Defer[Int][1/((d + e*x^2)^2*(a + b*ArcCosh[c*x])^(3/2)), x]","A",0,0,0,0,-1,"{}"