1,1,124,0,0.1188491,"\int x^4 \left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^4*(d + c^2*d*x^2)*(a + b*ArcSinh[c*x]),x]","\frac{1}{7} c^2 d x^7 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{5} d x^5 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d \left(c^2 x^2+1\right)^{7/2}}{49 c^5}+\frac{8 b d \left(c^2 x^2+1\right)^{5/2}}{175 c^5}-\frac{b d \left(c^2 x^2+1\right)^{3/2}}{105 c^5}-\frac{2 b d \sqrt{c^2 x^2+1}}{35 c^5}","\frac{1}{7} c^2 d x^7 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{5} d x^5 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d \left(c^2 x^2+1\right)^{7/2}}{49 c^5}+\frac{8 b d \left(c^2 x^2+1\right)^{5/2}}{175 c^5}-\frac{b d \left(c^2 x^2+1\right)^{3/2}}{105 c^5}-\frac{2 b d \sqrt{c^2 x^2+1}}{35 c^5}",1,"(-2*b*d*Sqrt[1 + c^2*x^2])/(35*c^5) - (b*d*(1 + c^2*x^2)^(3/2))/(105*c^5) + (8*b*d*(1 + c^2*x^2)^(5/2))/(175*c^5) - (b*d*(1 + c^2*x^2)^(7/2))/(49*c^5) + (d*x^5*(a + b*ArcSinh[c*x]))/5 + (c^2*d*x^7*(a + b*ArcSinh[c*x]))/7","A",5,5,22,0.2273,1,"{14, 5730, 12, 446, 77}"
2,1,120,0,0.0981831,"\int x^3 \left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^3*(d + c^2*d*x^2)*(a + b*ArcSinh[c*x]),x]","\frac{1}{6} c^2 d x^6 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{4} d x^4 \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{36} b c d x^5 \sqrt{c^2 x^2+1}-\frac{b d x^3 \sqrt{c^2 x^2+1}}{36 c}+\frac{b d x \sqrt{c^2 x^2+1}}{24 c^3}-\frac{b d \sinh ^{-1}(c x)}{24 c^4}","\frac{1}{6} c^2 d x^6 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{4} d x^4 \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{36} b c d x^5 \sqrt{c^2 x^2+1}-\frac{b d x^3 \sqrt{c^2 x^2+1}}{36 c}+\frac{b d x \sqrt{c^2 x^2+1}}{24 c^3}-\frac{b d \sinh ^{-1}(c x)}{24 c^4}",1,"(b*d*x*Sqrt[1 + c^2*x^2])/(24*c^3) - (b*d*x^3*Sqrt[1 + c^2*x^2])/(36*c) - (b*c*d*x^5*Sqrt[1 + c^2*x^2])/36 - (b*d*ArcSinh[c*x])/(24*c^4) + (d*x^4*(a + b*ArcSinh[c*x]))/4 + (c^2*d*x^6*(a + b*ArcSinh[c*x]))/6","A",6,6,22,0.2727,1,"{14, 5730, 12, 459, 321, 215}"
3,1,102,0,0.1015881,"\int x^2 \left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^2*(d + c^2*d*x^2)*(a + b*ArcSinh[c*x]),x]","\frac{1}{5} c^2 d x^5 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{3} d x^3 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d \left(c^2 x^2+1\right)^{5/2}}{25 c^3}+\frac{b d \left(c^2 x^2+1\right)^{3/2}}{45 c^3}+\frac{2 b d \sqrt{c^2 x^2+1}}{15 c^3}","\frac{1}{5} c^2 d x^5 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{3} d x^3 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d \left(c^2 x^2+1\right)^{5/2}}{25 c^3}+\frac{b d \left(c^2 x^2+1\right)^{3/2}}{45 c^3}+\frac{2 b d \sqrt{c^2 x^2+1}}{15 c^3}",1,"(2*b*d*Sqrt[1 + c^2*x^2])/(15*c^3) + (b*d*(1 + c^2*x^2)^(3/2))/(45*c^3) - (b*d*(1 + c^2*x^2)^(5/2))/(25*c^3) + (d*x^3*(a + b*ArcSinh[c*x]))/3 + (c^2*d*x^5*(a + b*ArcSinh[c*x]))/5","A",5,5,22,0.2273,1,"{14, 5730, 12, 446, 77}"
4,1,87,0,0.0413919,"\int x \left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x*(d + c^2*d*x^2)*(a + b*ArcSinh[c*x]),x]","\frac{d \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{4 c^2}-\frac{b d x \left(c^2 x^2+1\right)^{3/2}}{16 c}-\frac{3 b d x \sqrt{c^2 x^2+1}}{32 c}-\frac{3 b d \sinh ^{-1}(c x)}{32 c^2}","\frac{d \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{4 c^2}-\frac{b d x \left(c^2 x^2+1\right)^{3/2}}{16 c}-\frac{3 b d x \sqrt{c^2 x^2+1}}{32 c}-\frac{3 b d \sinh ^{-1}(c x)}{32 c^2}",1,"(-3*b*d*x*Sqrt[1 + c^2*x^2])/(32*c) - (b*d*x*(1 + c^2*x^2)^(3/2))/(16*c) - (3*b*d*ArcSinh[c*x])/(32*c^2) + (d*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(4*c^2)","A",4,3,20,0.1500,1,"{5717, 195, 215}"
5,1,75,0,0.0599111,"\int \left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + c^2*d*x^2)*(a + b*ArcSinh[c*x]),x]","\frac{1}{3} c^2 d x^3 \left(a+b \sinh ^{-1}(c x)\right)+d x \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d \left(c^2 x^2+1\right)^{3/2}}{9 c}-\frac{2 b d \sqrt{c^2 x^2+1}}{3 c}","\frac{1}{3} c^2 d x^3 \left(a+b \sinh ^{-1}(c x)\right)+d x \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d \left(c^2 x^2+1\right)^{3/2}}{9 c}-\frac{2 b d \sqrt{c^2 x^2+1}}{3 c}",1,"(-2*b*d*Sqrt[1 + c^2*x^2])/(3*c) - (b*d*(1 + c^2*x^2)^(3/2))/(9*c) + d*x*(a + b*ArcSinh[c*x]) + (c^2*d*x^3*(a + b*ArcSinh[c*x]))/3","A",5,4,19,0.2105,1,"{5679, 12, 444, 43}"
6,1,111,0,0.1228607,"\int \frac{\left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right)}{x} \, dx","Int[((d + c^2*d*x^2)*(a + b*ArcSinh[c*x]))/x,x]","\frac{1}{2} b d \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)+\frac{1}{2} d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{d \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b}+d \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{4} b c d x \sqrt{c^2 x^2+1}-\frac{1}{4} b d \sinh ^{-1}(c x)","-\frac{1}{2} b d \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right)+\frac{1}{2} d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)+\frac{d \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b}+d \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{4} b c d x \sqrt{c^2 x^2+1}-\frac{1}{4} b d \sinh ^{-1}(c x)",1,"-(b*c*d*x*Sqrt[1 + c^2*x^2])/4 - (b*d*ArcSinh[c*x])/4 + (d*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/2 - (d*(a + b*ArcSinh[c*x])^2)/(2*b) + d*(a + b*ArcSinh[c*x])*Log[1 - E^(2*ArcSinh[c*x])] + (b*d*PolyLog[2, E^(2*ArcSinh[c*x])])/2","A",8,8,22,0.3636,0,"{5726, 5659, 3716, 2190, 2279, 2391, 195, 215}"
7,1,66,0,0.0814023,"\int \frac{\left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + c^2*d*x^2)*(a + b*ArcSinh[c*x]))/x^2,x]","c^2 d x \left(a+b \sinh ^{-1}(c x)\right)-\frac{d \left(a+b \sinh ^{-1}(c x)\right)}{x}-b c d \sqrt{c^2 x^2+1}-b c d \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)","c^2 d x \left(a+b \sinh ^{-1}(c x)\right)-\frac{d \left(a+b \sinh ^{-1}(c x)\right)}{x}-b c d \sqrt{c^2 x^2+1}-b c d \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)",1,"-(b*c*d*Sqrt[1 + c^2*x^2]) - (d*(a + b*ArcSinh[c*x]))/x + c^2*d*x*(a + b*ArcSinh[c*x]) - b*c*d*ArcTanh[Sqrt[1 + c^2*x^2]]","A",6,7,22,0.3182,1,"{14, 5730, 12, 446, 80, 63, 208}"
8,1,128,0,0.1263747,"\int \frac{\left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + c^2*d*x^2)*(a + b*ArcSinh[c*x]))/x^3,x]","\frac{1}{2} b c^2 d \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)-\frac{d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}-\frac{c^2 d \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b}+c^2 d \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{b c d \sqrt{c^2 x^2+1}}{2 x}+\frac{1}{2} b c^2 d \sinh ^{-1}(c x)","-\frac{1}{2} b c^2 d \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right)-\frac{d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}+\frac{c^2 d \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b}+c^2 d \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{b c d \sqrt{c^2 x^2+1}}{2 x}+\frac{1}{2} b c^2 d \sinh ^{-1}(c x)",1,"-(b*c*d*Sqrt[1 + c^2*x^2])/(2*x) + (b*c^2*d*ArcSinh[c*x])/2 - (d*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(2*x^2) - (c^2*d*(a + b*ArcSinh[c*x])^2)/(2*b) + c^2*d*(a + b*ArcSinh[c*x])*Log[1 - E^(2*ArcSinh[c*x])] + (b*c^2*d*PolyLog[2, E^(2*ArcSinh[c*x])])/2","A",8,8,22,0.3636,0,"{5728, 277, 215, 5659, 3716, 2190, 2279, 2391}"
9,1,80,0,0.0843184,"\int \frac{\left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + c^2*d*x^2)*(a + b*ArcSinh[c*x]))/x^4,x]","-\frac{c^2 d \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{d \left(a+b \sinh ^{-1}(c x)\right)}{3 x^3}-\frac{b c d \sqrt{c^2 x^2+1}}{6 x^2}-\frac{5}{6} b c^3 d \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)","-\frac{c^2 d \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{d \left(a+b \sinh ^{-1}(c x)\right)}{3 x^3}-\frac{b c d \sqrt{c^2 x^2+1}}{6 x^2}-\frac{5}{6} b c^3 d \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)",1,"-(b*c*d*Sqrt[1 + c^2*x^2])/(6*x^2) - (d*(a + b*ArcSinh[c*x]))/(3*x^3) - (c^2*d*(a + b*ArcSinh[c*x]))/x - (5*b*c^3*d*ArcTanh[Sqrt[1 + c^2*x^2]])/6","A",6,7,22,0.3182,1,"{14, 5730, 12, 446, 78, 63, 208}"
10,1,181,0,0.2081813,"\int x^4 \left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^4*(d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x]),x]","\frac{1}{9} c^4 d^2 x^9 \left(a+b \sinh ^{-1}(c x)\right)+\frac{2}{7} c^2 d^2 x^7 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{5} d^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d^2 \left(c^2 x^2+1\right)^{9/2}}{81 c^5}+\frac{10 b d^2 \left(c^2 x^2+1\right)^{7/2}}{441 c^5}-\frac{b d^2 \left(c^2 x^2+1\right)^{5/2}}{525 c^5}-\frac{4 b d^2 \left(c^2 x^2+1\right)^{3/2}}{945 c^5}-\frac{8 b d^2 \sqrt{c^2 x^2+1}}{315 c^5}","\frac{1}{9} c^4 d^2 x^9 \left(a+b \sinh ^{-1}(c x)\right)+\frac{2}{7} c^2 d^2 x^7 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{5} d^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d^2 \left(c^2 x^2+1\right)^{9/2}}{81 c^5}+\frac{10 b d^2 \left(c^2 x^2+1\right)^{7/2}}{441 c^5}-\frac{b d^2 \left(c^2 x^2+1\right)^{5/2}}{525 c^5}-\frac{4 b d^2 \left(c^2 x^2+1\right)^{3/2}}{945 c^5}-\frac{8 b d^2 \sqrt{c^2 x^2+1}}{315 c^5}",1,"(-8*b*d^2*Sqrt[1 + c^2*x^2])/(315*c^5) - (4*b*d^2*(1 + c^2*x^2)^(3/2))/(945*c^5) - (b*d^2*(1 + c^2*x^2)^(5/2))/(525*c^5) + (10*b*d^2*(1 + c^2*x^2)^(7/2))/(441*c^5) - (b*d^2*(1 + c^2*x^2)^(9/2))/(81*c^5) + (d^2*x^5*(a + b*ArcSinh[c*x]))/5 + (2*c^2*d^2*x^7*(a + b*ArcSinh[c*x]))/7 + (c^4*d^2*x^9*(a + b*ArcSinh[c*x]))/9","A",6,6,24,0.2500,1,"{270, 5730, 12, 1251, 897, 1153}"
11,1,180,0,0.1749304,"\int x^3 \left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^3*(d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x]),x]","\frac{1}{8} c^4 d^2 x^8 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{3} c^2 d^2 x^6 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{4} d^2 x^4 \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{64} b c^3 d^2 x^7 \sqrt{c^2 x^2+1}-\frac{43 b c d^2 x^5 \sqrt{c^2 x^2+1}}{1152}-\frac{73 b d^2 x^3 \sqrt{c^2 x^2+1}}{4608 c}+\frac{73 b d^2 x \sqrt{c^2 x^2+1}}{3072 c^3}-\frac{73 b d^2 \sinh ^{-1}(c x)}{3072 c^4}","\frac{1}{8} c^4 d^2 x^8 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{3} c^2 d^2 x^6 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{4} d^2 x^4 \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{64} b c^3 d^2 x^7 \sqrt{c^2 x^2+1}-\frac{43 b c d^2 x^5 \sqrt{c^2 x^2+1}}{1152}-\frac{73 b d^2 x^3 \sqrt{c^2 x^2+1}}{4608 c}+\frac{73 b d^2 x \sqrt{c^2 x^2+1}}{3072 c^3}-\frac{73 b d^2 \sinh ^{-1}(c x)}{3072 c^4}",1,"(73*b*d^2*x*Sqrt[1 + c^2*x^2])/(3072*c^3) - (73*b*d^2*x^3*Sqrt[1 + c^2*x^2])/(4608*c) - (43*b*c*d^2*x^5*Sqrt[1 + c^2*x^2])/1152 - (b*c^3*d^2*x^7*Sqrt[1 + c^2*x^2])/64 - (73*b*d^2*ArcSinh[c*x])/(3072*c^4) + (d^2*x^4*(a + b*ArcSinh[c*x]))/4 + (c^2*d^2*x^6*(a + b*ArcSinh[c*x]))/3 + (c^4*d^2*x^8*(a + b*ArcSinh[c*x]))/8","A",7,8,24,0.3333,1,"{266, 43, 5730, 12, 1267, 459, 321, 215}"
12,1,157,0,0.1689615,"\int x^2 \left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^2*(d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x]),x]","\frac{1}{7} c^4 d^2 x^7 \left(a+b \sinh ^{-1}(c x)\right)+\frac{2}{5} c^2 d^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{3} d^2 x^3 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d^2 \left(c^2 x^2+1\right)^{7/2}}{49 c^3}+\frac{b d^2 \left(c^2 x^2+1\right)^{5/2}}{175 c^3}+\frac{4 b d^2 \left(c^2 x^2+1\right)^{3/2}}{315 c^3}+\frac{8 b d^2 \sqrt{c^2 x^2+1}}{105 c^3}","\frac{1}{7} c^4 d^2 x^7 \left(a+b \sinh ^{-1}(c x)\right)+\frac{2}{5} c^2 d^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{3} d^2 x^3 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d^2 \left(c^2 x^2+1\right)^{7/2}}{49 c^3}+\frac{b d^2 \left(c^2 x^2+1\right)^{5/2}}{175 c^3}+\frac{4 b d^2 \left(c^2 x^2+1\right)^{3/2}}{315 c^3}+\frac{8 b d^2 \sqrt{c^2 x^2+1}}{105 c^3}",1,"(8*b*d^2*Sqrt[1 + c^2*x^2])/(105*c^3) + (4*b*d^2*(1 + c^2*x^2)^(3/2))/(315*c^3) + (b*d^2*(1 + c^2*x^2)^(5/2))/(175*c^3) - (b*d^2*(1 + c^2*x^2)^(7/2))/(49*c^3) + (d^2*x^3*(a + b*ArcSinh[c*x]))/3 + (2*c^2*d^2*x^5*(a + b*ArcSinh[c*x]))/5 + (c^4*d^2*x^7*(a + b*ArcSinh[c*x]))/7","A",5,5,24,0.2083,1,"{270, 5730, 12, 1251, 771}"
13,1,120,0,0.0646363,"\int x \left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x*(d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x]),x]","\frac{d^2 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)}{6 c^2}-\frac{b d^2 x \left(c^2 x^2+1\right)^{5/2}}{36 c}-\frac{5 b d^2 x \left(c^2 x^2+1\right)^{3/2}}{144 c}-\frac{5 b d^2 x \sqrt{c^2 x^2+1}}{96 c}-\frac{5 b d^2 \sinh ^{-1}(c x)}{96 c^2}","\frac{d^2 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)}{6 c^2}-\frac{b d^2 x \left(c^2 x^2+1\right)^{5/2}}{36 c}-\frac{5 b d^2 x \left(c^2 x^2+1\right)^{3/2}}{144 c}-\frac{5 b d^2 x \sqrt{c^2 x^2+1}}{96 c}-\frac{5 b d^2 \sinh ^{-1}(c x)}{96 c^2}",1,"(-5*b*d^2*x*Sqrt[1 + c^2*x^2])/(96*c) - (5*b*d^2*x*(1 + c^2*x^2)^(3/2))/(144*c) - (b*d^2*x*(1 + c^2*x^2)^(5/2))/(36*c) - (5*b*d^2*ArcSinh[c*x])/(96*c^2) + (d^2*(1 + c^2*x^2)^3*(a + b*ArcSinh[c*x]))/(6*c^2)","A",5,3,22,0.1364,1,"{5717, 195, 215}"
14,1,128,0,0.1019738,"\int \left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x]),x]","\frac{1}{5} c^4 d^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)+\frac{2}{3} c^2 d^2 x^3 \left(a+b \sinh ^{-1}(c x)\right)+d^2 x \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d^2 \left(c^2 x^2+1\right)^{5/2}}{25 c}-\frac{4 b d^2 \left(c^2 x^2+1\right)^{3/2}}{45 c}-\frac{8 b d^2 \sqrt{c^2 x^2+1}}{15 c}","\frac{1}{5} c^4 d^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)+\frac{2}{3} c^2 d^2 x^3 \left(a+b \sinh ^{-1}(c x)\right)+d^2 x \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d^2 \left(c^2 x^2+1\right)^{5/2}}{25 c}-\frac{4 b d^2 \left(c^2 x^2+1\right)^{3/2}}{45 c}-\frac{8 b d^2 \sqrt{c^2 x^2+1}}{15 c}",1,"(-8*b*d^2*Sqrt[1 + c^2*x^2])/(15*c) - (4*b*d^2*(1 + c^2*x^2)^(3/2))/(45*c) - (b*d^2*(1 + c^2*x^2)^(5/2))/(25*c) + d^2*x*(a + b*ArcSinh[c*x]) + (2*c^2*d^2*x^3*(a + b*ArcSinh[c*x]))/3 + (c^4*d^2*x^5*(a + b*ArcSinh[c*x]))/5","A",5,5,21,0.2381,1,"{194, 5679, 12, 1247, 698}"
15,1,172,0,0.2027393,"\int \frac{\left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{x} \, dx","Int[((d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x]))/x,x]","\frac{1}{2} b d^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)+\frac{1}{4} d^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{2} d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{d^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b}+d^2 \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{16} b c d^2 x \left(c^2 x^2+1\right)^{3/2}-\frac{11}{32} b c d^2 x \sqrt{c^2 x^2+1}-\frac{11}{32} b d^2 \sinh ^{-1}(c x)","-\frac{1}{2} b d^2 \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right)+\frac{1}{4} d^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{2} d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)+\frac{d^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b}+d^2 \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{16} b c d^2 x \left(c^2 x^2+1\right)^{3/2}-\frac{11}{32} b c d^2 x \sqrt{c^2 x^2+1}-\frac{11}{32} b d^2 \sinh ^{-1}(c x)",1,"(-11*b*c*d^2*x*Sqrt[1 + c^2*x^2])/32 - (b*c*d^2*x*(1 + c^2*x^2)^(3/2))/16 - (11*b*d^2*ArcSinh[c*x])/32 + (d^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/2 + (d^2*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/4 - (d^2*(a + b*ArcSinh[c*x])^2)/(2*b) + d^2*(a + b*ArcSinh[c*x])*Log[1 - E^(2*ArcSinh[c*x])] + (b*d^2*PolyLog[2, E^(2*ArcSinh[c*x])])/2","A",12,8,24,0.3333,0,"{5726, 5659, 3716, 2190, 2279, 2391, 195, 215}"
16,1,120,0,0.1572188,"\int \frac{\left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x]))/x^2,x]","\frac{1}{3} c^4 d^2 x^3 \left(a+b \sinh ^{-1}(c x)\right)+2 c^2 d^2 x \left(a+b \sinh ^{-1}(c x)\right)-\frac{d^2 \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{1}{9} b c d^2 \left(c^2 x^2+1\right)^{3/2}-\frac{5}{3} b c d^2 \sqrt{c^2 x^2+1}-b c d^2 \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)","\frac{1}{3} c^4 d^2 x^3 \left(a+b \sinh ^{-1}(c x)\right)+2 c^2 d^2 x \left(a+b \sinh ^{-1}(c x)\right)-\frac{d^2 \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{1}{9} b c d^2 \left(c^2 x^2+1\right)^{3/2}-\frac{5}{3} b c d^2 \sqrt{c^2 x^2+1}-b c d^2 \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)",1,"(-5*b*c*d^2*Sqrt[1 + c^2*x^2])/3 - (b*c*d^2*(1 + c^2*x^2)^(3/2))/9 - (d^2*(a + b*ArcSinh[c*x]))/x + 2*c^2*d^2*x*(a + b*ArcSinh[c*x]) + (c^4*d^2*x^3*(a + b*ArcSinh[c*x]))/3 - b*c*d^2*ArcTanh[Sqrt[1 + c^2*x^2]]","A",7,7,24,0.2917,1,"{270, 5730, 12, 1251, 897, 1153, 208}"
17,1,187,0,0.2109422,"\int \frac{\left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x]))/x^3,x]","b c^2 d^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)+c^2 d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{d^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}-\frac{c^2 d^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{b}+2 c^2 d^2 \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{4} b c^3 d^2 x \sqrt{c^2 x^2+1}-\frac{b c d^2 \left(c^2 x^2+1\right)^{3/2}}{2 x}+\frac{1}{4} b c^2 d^2 \sinh ^{-1}(c x)","-b c^2 d^2 \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right)+c^2 d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{d^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}+\frac{c^2 d^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{b}+2 c^2 d^2 \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{4} b c^3 d^2 x \sqrt{c^2 x^2+1}-\frac{b c d^2 \left(c^2 x^2+1\right)^{3/2}}{2 x}+\frac{1}{4} b c^2 d^2 \sinh ^{-1}(c x)",1,"(b*c^3*d^2*x*Sqrt[1 + c^2*x^2])/4 - (b*c*d^2*(1 + c^2*x^2)^(3/2))/(2*x) + (b*c^2*d^2*ArcSinh[c*x])/4 + c^2*d^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]) - (d^2*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(2*x^2) - (c^2*d^2*(a + b*ArcSinh[c*x])^2)/b + 2*c^2*d^2*(a + b*ArcSinh[c*x])*Log[1 - E^(2*ArcSinh[c*x])] + b*c^2*d^2*PolyLog[2, E^(2*ArcSinh[c*x])]","A",12,10,24,0.4167,0,"{5728, 277, 195, 215, 5726, 5659, 3716, 2190, 2279, 2391}"
18,1,126,0,0.1588752,"\int \frac{\left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x]))/x^4,x]","c^4 d^2 x \left(a+b \sinh ^{-1}(c x)\right)-\frac{2 c^2 d^2 \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{d^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 x^3}-b c^3 d^2 \sqrt{c^2 x^2+1}-\frac{b c d^2 \sqrt{c^2 x^2+1}}{6 x^2}-\frac{11}{6} b c^3 d^2 \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)","c^4 d^2 x \left(a+b \sinh ^{-1}(c x)\right)-\frac{2 c^2 d^2 \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{d^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 x^3}-b c^3 d^2 \sqrt{c^2 x^2+1}-\frac{b c d^2 \sqrt{c^2 x^2+1}}{6 x^2}-\frac{11}{6} b c^3 d^2 \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)",1,"-(b*c^3*d^2*Sqrt[1 + c^2*x^2]) - (b*c*d^2*Sqrt[1 + c^2*x^2])/(6*x^2) - (d^2*(a + b*ArcSinh[c*x]))/(3*x^3) - (2*c^2*d^2*(a + b*ArcSinh[c*x]))/x + c^4*d^2*x*(a + b*ArcSinh[c*x]) - (11*b*c^3*d^2*ArcTanh[Sqrt[1 + c^2*x^2]])/6","A",7,8,24,0.3333,1,"{270, 5730, 12, 1251, 897, 1157, 388, 208}"
19,1,226,0,0.2814837,"\int x^4 \left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^4*(d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x]),x]","\frac{1}{11} c^6 d^3 x^{11} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{3} c^4 d^3 x^9 \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{7} c^2 d^3 x^7 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{5} d^3 x^5 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d^3 \left(c^2 x^2+1\right)^{11/2}}{121 c^5}+\frac{4 b d^3 \left(c^2 x^2+1\right)^{9/2}}{297 c^5}-\frac{b d^3 \left(c^2 x^2+1\right)^{7/2}}{1617 c^5}-\frac{2 b d^3 \left(c^2 x^2+1\right)^{5/2}}{1925 c^5}-\frac{8 b d^3 \left(c^2 x^2+1\right)^{3/2}}{3465 c^5}-\frac{16 b d^3 \sqrt{c^2 x^2+1}}{1155 c^5}","\frac{1}{11} c^6 d^3 x^{11} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{3} c^4 d^3 x^9 \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{7} c^2 d^3 x^7 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{5} d^3 x^5 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d^3 \left(c^2 x^2+1\right)^{11/2}}{121 c^5}+\frac{4 b d^3 \left(c^2 x^2+1\right)^{9/2}}{297 c^5}-\frac{b d^3 \left(c^2 x^2+1\right)^{7/2}}{1617 c^5}-\frac{2 b d^3 \left(c^2 x^2+1\right)^{5/2}}{1925 c^5}-\frac{8 b d^3 \left(c^2 x^2+1\right)^{3/2}}{3465 c^5}-\frac{16 b d^3 \sqrt{c^2 x^2+1}}{1155 c^5}",1,"(-16*b*d^3*Sqrt[1 + c^2*x^2])/(1155*c^5) - (8*b*d^3*(1 + c^2*x^2)^(3/2))/(3465*c^5) - (2*b*d^3*(1 + c^2*x^2)^(5/2))/(1925*c^5) - (b*d^3*(1 + c^2*x^2)^(7/2))/(1617*c^5) + (4*b*d^3*(1 + c^2*x^2)^(9/2))/(297*c^5) - (b*d^3*(1 + c^2*x^2)^(11/2))/(121*c^5) + (d^3*x^5*(a + b*ArcSinh[c*x]))/5 + (3*c^2*d^3*x^7*(a + b*ArcSinh[c*x]))/7 + (c^4*d^3*x^9*(a + b*ArcSinh[c*x]))/3 + (c^6*d^3*x^11*(a + b*ArcSinh[c*x]))/11","A",5,5,24,0.2083,1,"{270, 5730, 12, 1799, 1620}"
20,1,199,0,0.1687059,"\int x^3 \left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^3*(d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x]),x]","\frac{d^3 \left(c^2 x^2+1\right)^5 \left(a+b \sinh ^{-1}(c x)\right)}{10 c^4}-\frac{d^3 \left(c^2 x^2+1\right)^4 \left(a+b \sinh ^{-1}(c x)\right)}{8 c^4}-\frac{b d^3 x \left(c^2 x^2+1\right)^{9/2}}{100 c^3}+\frac{7 b d^3 x \left(c^2 x^2+1\right)^{7/2}}{1600 c^3}+\frac{49 b d^3 x \left(c^2 x^2+1\right)^{5/2}}{9600 c^3}+\frac{49 b d^3 x \left(c^2 x^2+1\right)^{3/2}}{7680 c^3}+\frac{49 b d^3 x \sqrt{c^2 x^2+1}}{5120 c^3}+\frac{49 b d^3 \sinh ^{-1}(c x)}{5120 c^4}","\frac{d^3 \left(c^2 x^2+1\right)^5 \left(a+b \sinh ^{-1}(c x)\right)}{10 c^4}-\frac{d^3 \left(c^2 x^2+1\right)^4 \left(a+b \sinh ^{-1}(c x)\right)}{8 c^4}-\frac{b d^3 x \left(c^2 x^2+1\right)^{9/2}}{100 c^3}+\frac{7 b d^3 x \left(c^2 x^2+1\right)^{7/2}}{1600 c^3}+\frac{49 b d^3 x \left(c^2 x^2+1\right)^{5/2}}{9600 c^3}+\frac{49 b d^3 x \left(c^2 x^2+1\right)^{3/2}}{7680 c^3}+\frac{49 b d^3 x \sqrt{c^2 x^2+1}}{5120 c^3}+\frac{49 b d^3 \sinh ^{-1}(c x)}{5120 c^4}",1,"(49*b*d^3*x*Sqrt[1 + c^2*x^2])/(5120*c^3) + (49*b*d^3*x*(1 + c^2*x^2)^(3/2))/(7680*c^3) + (49*b*d^3*x*(1 + c^2*x^2)^(5/2))/(9600*c^3) + (7*b*d^3*x*(1 + c^2*x^2)^(7/2))/(1600*c^3) - (b*d^3*x*(1 + c^2*x^2)^(9/2))/(100*c^3) + (49*b*d^3*ArcSinh[c*x])/(5120*c^4) - (d^3*(1 + c^2*x^2)^4*(a + b*ArcSinh[c*x]))/(8*c^4) + (d^3*(1 + c^2*x^2)^5*(a + b*ArcSinh[c*x]))/(10*c^4)","A",8,7,24,0.2917,1,"{266, 43, 5730, 12, 388, 195, 215}"
21,1,202,0,0.2485804,"\int x^2 \left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^2*(d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x]),x]","\frac{1}{9} c^6 d^3 x^9 \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{7} c^4 d^3 x^7 \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{5} c^2 d^3 x^5 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{3} d^3 x^3 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d^3 \left(c^2 x^2+1\right)^{9/2}}{81 c^3}+\frac{b d^3 \left(c^2 x^2+1\right)^{7/2}}{441 c^3}+\frac{2 b d^3 \left(c^2 x^2+1\right)^{5/2}}{525 c^3}+\frac{8 b d^3 \left(c^2 x^2+1\right)^{3/2}}{945 c^3}+\frac{16 b d^3 \sqrt{c^2 x^2+1}}{315 c^3}","\frac{1}{9} c^6 d^3 x^9 \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{7} c^4 d^3 x^7 \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{5} c^2 d^3 x^5 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{3} d^3 x^3 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d^3 \left(c^2 x^2+1\right)^{9/2}}{81 c^3}+\frac{b d^3 \left(c^2 x^2+1\right)^{7/2}}{441 c^3}+\frac{2 b d^3 \left(c^2 x^2+1\right)^{5/2}}{525 c^3}+\frac{8 b d^3 \left(c^2 x^2+1\right)^{3/2}}{945 c^3}+\frac{16 b d^3 \sqrt{c^2 x^2+1}}{315 c^3}",1,"(16*b*d^3*Sqrt[1 + c^2*x^2])/(315*c^3) + (8*b*d^3*(1 + c^2*x^2)^(3/2))/(945*c^3) + (2*b*d^3*(1 + c^2*x^2)^(5/2))/(525*c^3) + (b*d^3*(1 + c^2*x^2)^(7/2))/(441*c^3) - (b*d^3*(1 + c^2*x^2)^(9/2))/(81*c^3) + (d^3*x^3*(a + b*ArcSinh[c*x]))/3 + (3*c^2*d^3*x^5*(a + b*ArcSinh[c*x]))/5 + (3*c^4*d^3*x^7*(a + b*ArcSinh[c*x]))/7 + (c^6*d^3*x^9*(a + b*ArcSinh[c*x]))/9","A",5,5,24,0.2083,1,"{270, 5730, 12, 1799, 1620}"
22,1,145,0,0.0697191,"\int x \left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x*(d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x]),x]","\frac{d^3 \left(c^2 x^2+1\right)^4 \left(a+b \sinh ^{-1}(c x)\right)}{8 c^2}-\frac{b d^3 x \left(c^2 x^2+1\right)^{7/2}}{64 c}-\frac{7 b d^3 x \left(c^2 x^2+1\right)^{5/2}}{384 c}-\frac{35 b d^3 x \left(c^2 x^2+1\right)^{3/2}}{1536 c}-\frac{35 b d^3 x \sqrt{c^2 x^2+1}}{1024 c}-\frac{35 b d^3 \sinh ^{-1}(c x)}{1024 c^2}","\frac{d^3 \left(c^2 x^2+1\right)^4 \left(a+b \sinh ^{-1}(c x)\right)}{8 c^2}-\frac{b d^3 x \left(c^2 x^2+1\right)^{7/2}}{64 c}-\frac{7 b d^3 x \left(c^2 x^2+1\right)^{5/2}}{384 c}-\frac{35 b d^3 x \left(c^2 x^2+1\right)^{3/2}}{1536 c}-\frac{35 b d^3 x \sqrt{c^2 x^2+1}}{1024 c}-\frac{35 b d^3 \sinh ^{-1}(c x)}{1024 c^2}",1,"(-35*b*d^3*x*Sqrt[1 + c^2*x^2])/(1024*c) - (35*b*d^3*x*(1 + c^2*x^2)^(3/2))/(1536*c) - (7*b*d^3*x*(1 + c^2*x^2)^(5/2))/(384*c) - (b*d^3*x*(1 + c^2*x^2)^(7/2))/(64*c) - (35*b*d^3*ArcSinh[c*x])/(1024*c^2) + (d^3*(1 + c^2*x^2)^4*(a + b*ArcSinh[c*x]))/(8*c^2)","A",6,3,22,0.1364,1,"{5717, 195, 215}"
23,1,170,0,0.16143,"\int \left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x]),x]","\frac{1}{7} c^6 d^3 x^7 \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{5} c^4 d^3 x^5 \left(a+b \sinh ^{-1}(c x)\right)+c^2 d^3 x^3 \left(a+b \sinh ^{-1}(c x)\right)+d^3 x \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d^3 \left(c^2 x^2+1\right)^{7/2}}{49 c}-\frac{6 b d^3 \left(c^2 x^2+1\right)^{5/2}}{175 c}-\frac{8 b d^3 \left(c^2 x^2+1\right)^{3/2}}{105 c}-\frac{16 b d^3 \sqrt{c^2 x^2+1}}{35 c}","\frac{1}{7} c^6 d^3 x^7 \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{5} c^4 d^3 x^5 \left(a+b \sinh ^{-1}(c x)\right)+c^2 d^3 x^3 \left(a+b \sinh ^{-1}(c x)\right)+d^3 x \left(a+b \sinh ^{-1}(c x)\right)-\frac{b d^3 \left(c^2 x^2+1\right)^{7/2}}{49 c}-\frac{6 b d^3 \left(c^2 x^2+1\right)^{5/2}}{175 c}-\frac{8 b d^3 \left(c^2 x^2+1\right)^{3/2}}{105 c}-\frac{16 b d^3 \sqrt{c^2 x^2+1}}{35 c}",1,"(-16*b*d^3*Sqrt[1 + c^2*x^2])/(35*c) - (8*b*d^3*(1 + c^2*x^2)^(3/2))/(105*c) - (6*b*d^3*(1 + c^2*x^2)^(5/2))/(175*c) - (b*d^3*(1 + c^2*x^2)^(7/2))/(49*c) + d^3*x*(a + b*ArcSinh[c*x]) + c^2*d^3*x^3*(a + b*ArcSinh[c*x]) + (3*c^4*d^3*x^5*(a + b*ArcSinh[c*x]))/5 + (c^6*d^3*x^7*(a + b*ArcSinh[c*x]))/7","A",5,5,21,0.2381,1,"{194, 5679, 12, 1799, 1850}"
24,1,221,0,0.2841603,"\int \frac{\left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right)}{x} \, dx","Int[((d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x]))/x,x]","\frac{1}{2} b d^3 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)+\frac{1}{6} d^3 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{4} d^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{2} d^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{d^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b}+d^3 \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{36} b c d^3 x \left(c^2 x^2+1\right)^{5/2}-\frac{7}{72} b c d^3 x \left(c^2 x^2+1\right)^{3/2}-\frac{19}{48} b c d^3 x \sqrt{c^2 x^2+1}-\frac{19}{48} b d^3 \sinh ^{-1}(c x)","-\frac{1}{2} b d^3 \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right)+\frac{1}{6} d^3 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{4} d^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{2} d^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)+\frac{d^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b}+d^3 \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{36} b c d^3 x \left(c^2 x^2+1\right)^{5/2}-\frac{7}{72} b c d^3 x \left(c^2 x^2+1\right)^{3/2}-\frac{19}{48} b c d^3 x \sqrt{c^2 x^2+1}-\frac{19}{48} b d^3 \sinh ^{-1}(c x)",1,"(-19*b*c*d^3*x*Sqrt[1 + c^2*x^2])/48 - (7*b*c*d^3*x*(1 + c^2*x^2)^(3/2))/72 - (b*c*d^3*x*(1 + c^2*x^2)^(5/2))/36 - (19*b*d^3*ArcSinh[c*x])/48 + (d^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/2 + (d^3*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/4 + (d^3*(1 + c^2*x^2)^3*(a + b*ArcSinh[c*x]))/6 - (d^3*(a + b*ArcSinh[c*x])^2)/(2*b) + d^3*(a + b*ArcSinh[c*x])*Log[1 - E^(2*ArcSinh[c*x])] + (b*d^3*PolyLog[2, E^(2*ArcSinh[c*x])])/2","A",17,8,24,0.3333,0,"{5726, 5659, 3716, 2190, 2279, 2391, 195, 215}"
25,1,160,0,0.2213444,"\int \frac{\left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x]))/x^2,x]","\frac{1}{5} c^6 d^3 x^5 \left(a+b \sinh ^{-1}(c x)\right)+c^4 d^3 x^3 \left(a+b \sinh ^{-1}(c x)\right)+3 c^2 d^3 x \left(a+b \sinh ^{-1}(c x)\right)-\frac{d^3 \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{1}{25} b c d^3 \left(c^2 x^2+1\right)^{5/2}-\frac{1}{5} b c d^3 \left(c^2 x^2+1\right)^{3/2}-\frac{11}{5} b c d^3 \sqrt{c^2 x^2+1}-b c d^3 \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)","\frac{1}{5} c^6 d^3 x^5 \left(a+b \sinh ^{-1}(c x)\right)+c^4 d^3 x^3 \left(a+b \sinh ^{-1}(c x)\right)+3 c^2 d^3 x \left(a+b \sinh ^{-1}(c x)\right)-\frac{d^3 \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{1}{25} b c d^3 \left(c^2 x^2+1\right)^{5/2}-\frac{1}{5} b c d^3 \left(c^2 x^2+1\right)^{3/2}-\frac{11}{5} b c d^3 \sqrt{c^2 x^2+1}-b c d^3 \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)",1,"(-11*b*c*d^3*Sqrt[1 + c^2*x^2])/5 - (b*c*d^3*(1 + c^2*x^2)^(3/2))/5 - (b*c*d^3*(1 + c^2*x^2)^(5/2))/25 - (d^3*(a + b*ArcSinh[c*x]))/x + 3*c^2*d^3*x*(a + b*ArcSinh[c*x]) + c^4*d^3*x^3*(a + b*ArcSinh[c*x]) + (c^6*d^3*x^5*(a + b*ArcSinh[c*x]))/5 - b*c*d^3*ArcTanh[Sqrt[1 + c^2*x^2]]","A",7,7,24,0.2917,1,"{270, 5730, 12, 1799, 1620, 63, 208}"
26,1,249,0,0.3033502,"\int \frac{\left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x]))/x^3,x]","\frac{3}{2} b c^2 d^3 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)-\frac{d^3 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}+\frac{3}{4} c^2 d^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{2} c^2 d^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{3 c^2 d^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b}+3 c^2 d^3 \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{b c d^3 \left(c^2 x^2+1\right)^{5/2}}{2 x}+\frac{7}{16} b c^3 d^3 x \left(c^2 x^2+1\right)^{3/2}-\frac{3}{32} b c^3 d^3 x \sqrt{c^2 x^2+1}-\frac{3}{32} b c^2 d^3 \sinh ^{-1}(c x)","-\frac{3}{2} b c^2 d^3 \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right)-\frac{d^3 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}+\frac{3}{4} c^2 d^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{2} c^2 d^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)+\frac{3 c^2 d^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b}+3 c^2 d^3 \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{b c d^3 \left(c^2 x^2+1\right)^{5/2}}{2 x}+\frac{7}{16} b c^3 d^3 x \left(c^2 x^2+1\right)^{3/2}-\frac{3}{32} b c^3 d^3 x \sqrt{c^2 x^2+1}-\frac{3}{32} b c^2 d^3 \sinh ^{-1}(c x)",1,"(-3*b*c^3*d^3*x*Sqrt[1 + c^2*x^2])/32 + (7*b*c^3*d^3*x*(1 + c^2*x^2)^(3/2))/16 - (b*c*d^3*(1 + c^2*x^2)^(5/2))/(2*x) - (3*b*c^2*d^3*ArcSinh[c*x])/32 + (3*c^2*d^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/2 + (3*c^2*d^3*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/4 - (d^3*(1 + c^2*x^2)^3*(a + b*ArcSinh[c*x]))/(2*x^2) - (3*c^2*d^3*(a + b*ArcSinh[c*x])^2)/(2*b) + 3*c^2*d^3*(a + b*ArcSinh[c*x])*Log[1 - E^(2*ArcSinh[c*x])] + (3*b*c^2*d^3*PolyLog[2, E^(2*ArcSinh[c*x])])/2","A",17,10,24,0.4167,0,"{5728, 277, 195, 215, 5726, 5659, 3716, 2190, 2279, 2391}"
27,1,174,0,0.2557752,"\int \frac{\left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x]))/x^4,x]","\frac{1}{3} c^6 d^3 x^3 \left(a+b \sinh ^{-1}(c x)\right)+3 c^4 d^3 x \left(a+b \sinh ^{-1}(c x)\right)-\frac{3 c^2 d^3 \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{d^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 x^3}-\frac{1}{9} b c^3 d^3 \left(c^2 x^2+1\right)^{3/2}-\frac{8}{3} b c^3 d^3 \sqrt{c^2 x^2+1}-\frac{b c d^3 \sqrt{c^2 x^2+1}}{6 x^2}-\frac{17}{6} b c^3 d^3 \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)","\frac{1}{3} c^6 d^3 x^3 \left(a+b \sinh ^{-1}(c x)\right)+3 c^4 d^3 x \left(a+b \sinh ^{-1}(c x)\right)-\frac{3 c^2 d^3 \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{d^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 x^3}-\frac{1}{9} b c^3 d^3 \left(c^2 x^2+1\right)^{3/2}-\frac{8}{3} b c^3 d^3 \sqrt{c^2 x^2+1}-\frac{b c d^3 \sqrt{c^2 x^2+1}}{6 x^2}-\frac{17}{6} b c^3 d^3 \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)",1,"(-8*b*c^3*d^3*Sqrt[1 + c^2*x^2])/3 - (b*c*d^3*Sqrt[1 + c^2*x^2])/(6*x^2) - (b*c^3*d^3*(1 + c^2*x^2)^(3/2))/9 - (d^3*(a + b*ArcSinh[c*x]))/(3*x^3) - (3*c^2*d^3*(a + b*ArcSinh[c*x]))/x + 3*c^4*d^3*x*(a + b*ArcSinh[c*x]) + (c^6*d^3*x^3*(a + b*ArcSinh[c*x]))/3 - (17*b*c^3*d^3*ArcTanh[Sqrt[1 + c^2*x^2]])/6","A",8,8,24,0.3333,1,"{270, 5730, 12, 1799, 1621, 897, 1153, 208}"
28,1,156,0,0.240951,"\int \frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)}{d+c^2 d x^2} \, dx","Int[(x^4*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2),x]","-\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c^5 d}+\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c^5 d}+\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2 d}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{c^4 d}+\frac{2 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d}-\frac{b \left(c^2 x^2+1\right)^{3/2}}{9 c^5 d}+\frac{4 b \sqrt{c^2 x^2+1}}{3 c^5 d}","-\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c^5 d}+\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c^5 d}+\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2 d}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{c^4 d}+\frac{2 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d}-\frac{b \left(c^2 x^2+1\right)^{3/2}}{9 c^5 d}+\frac{4 b \sqrt{c^2 x^2+1}}{3 c^5 d}",1,"(4*b*Sqrt[1 + c^2*x^2])/(3*c^5*d) - (b*(1 + c^2*x^2)^(3/2))/(9*c^5*d) - (x*(a + b*ArcSinh[c*x]))/(c^4*d) + (x^3*(a + b*ArcSinh[c*x]))/(3*c^2*d) + (2*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c^5*d) - (I*b*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^5*d) + (I*b*PolyLog[2, I*E^ArcSinh[c*x]])/(c^5*d)","A",12,8,24,0.3333,1,"{5767, 5693, 4180, 2279, 2391, 261, 266, 43}"
29,1,135,0,0.1954921,"\int \frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{d+c^2 d x^2} \, dx","Int[(x^3*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2),x]","-\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{2 c^4 d}+\frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 c^2 d}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c^4 d}-\frac{\log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^4 d}-\frac{b x \sqrt{c^2 x^2+1}}{4 c^3 d}+\frac{b \sinh ^{-1}(c x)}{4 c^4 d}","-\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{2 c^4 d}+\frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 c^2 d}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c^4 d}-\frac{\log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^4 d}-\frac{b x \sqrt{c^2 x^2+1}}{4 c^3 d}+\frac{b \sinh ^{-1}(c x)}{4 c^4 d}",1,"-(b*x*Sqrt[1 + c^2*x^2])/(4*c^3*d) + (b*ArcSinh[c*x])/(4*c^4*d) + (x^2*(a + b*ArcSinh[c*x]))/(2*c^2*d) + (a + b*ArcSinh[c*x])^2/(2*b*c^4*d) - ((a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(c^4*d) - (b*PolyLog[2, -E^(2*ArcSinh[c*x])])/(2*c^4*d)","A",8,8,24,0.3333,1,"{5767, 5714, 3718, 2190, 2279, 2391, 321, 215}"
30,1,108,0,0.1396531,"\int \frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)}{d+c^2 d x^2} \, dx","Int[(x^2*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2),x]","\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c^3 d}-\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c^3 d}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d}-\frac{2 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d}-\frac{b \sqrt{c^2 x^2+1}}{c^3 d}","\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c^3 d}-\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c^3 d}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d}-\frac{2 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d}-\frac{b \sqrt{c^2 x^2+1}}{c^3 d}",1,"-((b*Sqrt[1 + c^2*x^2])/(c^3*d)) + (x*(a + b*ArcSinh[c*x]))/(c^2*d) - (2*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c^3*d) + (I*b*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^3*d) - (I*b*PolyLog[2, I*E^ArcSinh[c*x]])/(c^3*d)","A",8,6,24,0.2500,1,"{5767, 5693, 4180, 2279, 2391, 261}"
31,1,73,0,0.1170855,"\int \frac{x \left(a+b \sinh ^{-1}(c x)\right)}{d+c^2 d x^2} \, dx","Int[(x*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2),x]","\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{2 c^2 d}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c^2 d}+\frac{\log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d}","\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{2 c^2 d}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c^2 d}+\frac{\log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d}",1,"-(a + b*ArcSinh[c*x])^2/(2*b*c^2*d) + ((a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(c^2*d) + (b*PolyLog[2, -E^(2*ArcSinh[c*x])])/(2*c^2*d)","A",5,5,22,0.2273,1,"{5714, 3718, 2190, 2279, 2391}"
32,1,70,0,0.0641422,"\int \frac{a+b \sinh ^{-1}(c x)}{d+c^2 d x^2} \, dx","Int[(a + b*ArcSinh[c*x])/(d + c^2*d*x^2),x]","-\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c d}+\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c d}+\frac{2 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c d}","-\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c d}+\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c d}+\frac{2 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c d}",1,"(2*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c*d) - (I*b*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c*d) + (I*b*PolyLog[2, I*E^ArcSinh[c*x]])/(c*d)","A",6,4,21,0.1905,1,"{5693, 4180, 2279, 2391}"
33,1,61,0,0.1167041,"\int \frac{a+b \sinh ^{-1}(c x)}{x \left(d+c^2 d x^2\right)} \, dx","Int[(a + b*ArcSinh[c*x])/(x*(d + c^2*d*x^2)),x]","-\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d}+\frac{b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{2 d}-\frac{2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}","-\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d}+\frac{b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{2 d}-\frac{2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}",1,"(-2*(a + b*ArcSinh[c*x])*ArcTanh[E^(2*ArcSinh[c*x])])/d - (b*PolyLog[2, -E^(2*ArcSinh[c*x])])/(2*d) + (b*PolyLog[2, E^(2*ArcSinh[c*x])])/(2*d)","A",7,5,24,0.2083,1,"{5720, 5461, 4182, 2279, 2391}"
34,1,101,0,0.1496394,"\int \frac{a+b \sinh ^{-1}(c x)}{x^2 \left(d+c^2 d x^2\right)} \, dx","Int[(a + b*ArcSinh[c*x])/(x^2*(d + c^2*d*x^2)),x]","\frac{i b c \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{d}-\frac{i b c \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{d}-\frac{a+b \sinh ^{-1}(c x)}{d x}-\frac{2 c \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}-\frac{b c \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{d}","\frac{i b c \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{d}-\frac{i b c \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{d}-\frac{a+b \sinh ^{-1}(c x)}{d x}-\frac{2 c \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}-\frac{b c \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{d}",1,"-((a + b*ArcSinh[c*x])/(d*x)) - (2*c*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/d - (b*c*ArcTanh[Sqrt[1 + c^2*x^2]])/d + (I*b*c*PolyLog[2, (-I)*E^ArcSinh[c*x]])/d - (I*b*c*PolyLog[2, I*E^ArcSinh[c*x]])/d","A",10,8,24,0.3333,1,"{5747, 5693, 4180, 2279, 2391, 266, 63, 208}"
35,1,113,0,0.1982183,"\int \frac{a+b \sinh ^{-1}(c x)}{x^3 \left(d+c^2 d x^2\right)} \, dx","Int[(a + b*ArcSinh[c*x])/(x^3*(d + c^2*d*x^2)),x]","\frac{b c^2 \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d}-\frac{b c^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{2 d}+\frac{2 c^2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}-\frac{a+b \sinh ^{-1}(c x)}{2 d x^2}-\frac{b c \sqrt{c^2 x^2+1}}{2 d x}","\frac{b c^2 \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d}-\frac{b c^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{2 d}+\frac{2 c^2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}-\frac{a+b \sinh ^{-1}(c x)}{2 d x^2}-\frac{b c \sqrt{c^2 x^2+1}}{2 d x}",1,"-(b*c*Sqrt[1 + c^2*x^2])/(2*d*x) - (a + b*ArcSinh[c*x])/(2*d*x^2) + (2*c^2*(a + b*ArcSinh[c*x])*ArcTanh[E^(2*ArcSinh[c*x])])/d + (b*c^2*PolyLog[2, -E^(2*ArcSinh[c*x])])/(2*d) - (b*c^2*PolyLog[2, E^(2*ArcSinh[c*x])])/(2*d)","A",9,7,24,0.2917,1,"{5747, 5720, 5461, 4182, 2279, 2391, 264}"
36,1,156,0,0.2465557,"\int \frac{a+b \sinh ^{-1}(c x)}{x^4 \left(d+c^2 d x^2\right)} \, dx","Int[(a + b*ArcSinh[c*x])/(x^4*(d + c^2*d*x^2)),x]","-\frac{i b c^3 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{d}+\frac{i b c^3 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{d}+\frac{c^2 \left(a+b \sinh ^{-1}(c x)\right)}{d x}+\frac{2 c^3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}-\frac{a+b \sinh ^{-1}(c x)}{3 d x^3}-\frac{b c \sqrt{c^2 x^2+1}}{6 d x^2}+\frac{7 b c^3 \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{6 d}","-\frac{i b c^3 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{d}+\frac{i b c^3 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{d}+\frac{c^2 \left(a+b \sinh ^{-1}(c x)\right)}{d x}+\frac{2 c^3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}-\frac{a+b \sinh ^{-1}(c x)}{3 d x^3}-\frac{b c \sqrt{c^2 x^2+1}}{6 d x^2}+\frac{7 b c^3 \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{6 d}",1,"-(b*c*Sqrt[1 + c^2*x^2])/(6*d*x^2) - (a + b*ArcSinh[c*x])/(3*d*x^3) + (c^2*(a + b*ArcSinh[c*x]))/(d*x) + (2*c^3*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/d + (7*b*c^3*ArcTanh[Sqrt[1 + c^2*x^2]])/(6*d) - (I*b*c^3*PolyLog[2, (-I)*E^ArcSinh[c*x]])/d + (I*b*c^3*PolyLog[2, I*E^ArcSinh[c*x]])/d","A",15,9,24,0.3750,1,"{5747, 5693, 4180, 2279, 2391, 266, 63, 208, 51}"
37,1,171,0,0.2407764,"\int \frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^2} \, dx","Int[(x^4*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^2,x]","\frac{3 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{2 c^5 d^2}-\frac{3 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{2 c^5 d^2}-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{2 c^2 d^2 \left(c^2 x^2+1\right)}+\frac{3 x \left(a+b \sinh ^{-1}(c x)\right)}{2 c^4 d^2}-\frac{3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d^2}-\frac{b \sqrt{c^2 x^2+1}}{c^5 d^2}+\frac{b}{2 c^5 d^2 \sqrt{c^2 x^2+1}}","\frac{3 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{2 c^5 d^2}-\frac{3 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{2 c^5 d^2}-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{2 c^2 d^2 \left(c^2 x^2+1\right)}+\frac{3 x \left(a+b \sinh ^{-1}(c x)\right)}{2 c^4 d^2}-\frac{3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d^2}-\frac{b \sqrt{c^2 x^2+1}}{c^5 d^2}+\frac{b}{2 c^5 d^2 \sqrt{c^2 x^2+1}}",1,"b/(2*c^5*d^2*Sqrt[1 + c^2*x^2]) - (b*Sqrt[1 + c^2*x^2])/(c^5*d^2) + (3*x*(a + b*ArcSinh[c*x]))/(2*c^4*d^2) - (x^3*(a + b*ArcSinh[c*x]))/(2*c^2*d^2*(1 + c^2*x^2)) - (3*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c^5*d^2) + (((3*I)/2)*b*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^5*d^2) - (((3*I)/2)*b*PolyLog[2, I*E^ArcSinh[c*x]])/(c^5*d^2)","A",12,9,24,0.3750,1,"{5751, 5767, 5693, 4180, 2279, 2391, 261, 266, 43}"
38,1,145,0,0.190549,"\int \frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^2} \, dx","Int[(x^3*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^2,x]","\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{2 c^4 d^2}-\frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 c^2 d^2 \left(c^2 x^2+1\right)}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c^4 d^2}+\frac{\log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^4 d^2}-\frac{b x}{2 c^3 d^2 \sqrt{c^2 x^2+1}}+\frac{b \sinh ^{-1}(c x)}{2 c^4 d^2}","\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{2 c^4 d^2}-\frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 c^2 d^2 \left(c^2 x^2+1\right)}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c^4 d^2}+\frac{\log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^4 d^2}-\frac{b x}{2 c^3 d^2 \sqrt{c^2 x^2+1}}+\frac{b \sinh ^{-1}(c x)}{2 c^4 d^2}",1,"-(b*x)/(2*c^3*d^2*Sqrt[1 + c^2*x^2]) + (b*ArcSinh[c*x])/(2*c^4*d^2) - (x^2*(a + b*ArcSinh[c*x]))/(2*c^2*d^2*(1 + c^2*x^2)) - (a + b*ArcSinh[c*x])^2/(2*b*c^4*d^2) + ((a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(c^4*d^2) + (b*PolyLog[2, -E^(2*ArcSinh[c*x])])/(2*c^4*d^2)","A",8,8,24,0.3333,1,"{5751, 5714, 3718, 2190, 2279, 2391, 288, 215}"
39,1,127,0,0.1337855,"\int \frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^2} \, dx","Int[(x^2*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^2,x]","-\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{2 c^3 d^2}+\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{2 c^3 d^2}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{2 c^2 d^2 \left(c^2 x^2+1\right)}+\frac{\tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d^2}-\frac{b}{2 c^3 d^2 \sqrt{c^2 x^2+1}}","-\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{2 c^3 d^2}+\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{2 c^3 d^2}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{2 c^2 d^2 \left(c^2 x^2+1\right)}+\frac{\tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d^2}-\frac{b}{2 c^3 d^2 \sqrt{c^2 x^2+1}}",1,"-b/(2*c^3*d^2*Sqrt[1 + c^2*x^2]) - (x*(a + b*ArcSinh[c*x]))/(2*c^2*d^2*(1 + c^2*x^2)) + ((a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c^3*d^2) - ((I/2)*b*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^3*d^2) + ((I/2)*b*PolyLog[2, I*E^ArcSinh[c*x]])/(c^3*d^2)","A",8,6,24,0.2500,1,"{5751, 5693, 4180, 2279, 2391, 261}"
40,1,55,0,0.0496438,"\int \frac{x \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^2} \, dx","Int[(x*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^2,x]","\frac{b x}{2 c d^2 \sqrt{c^2 x^2+1}}-\frac{a+b \sinh ^{-1}(c x)}{2 c^2 d^2 \left(c^2 x^2+1\right)}","\frac{b x}{2 c d^2 \sqrt{c^2 x^2+1}}-\frac{a+b \sinh ^{-1}(c x)}{2 c^2 d^2 \left(c^2 x^2+1\right)}",1,"(b*x)/(2*c*d^2*Sqrt[1 + c^2*x^2]) - (a + b*ArcSinh[c*x])/(2*c^2*d^2*(1 + c^2*x^2))","A",2,2,22,0.09091,1,"{5717, 191}"
41,1,124,0,0.0978521,"\int \frac{a+b \sinh ^{-1}(c x)}{\left(d+c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSinh[c*x])/(d + c^2*d*x^2)^2,x]","-\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{2 c d^2}+\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{2 c d^2}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{2 d^2 \left(c^2 x^2+1\right)}+\frac{\tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c d^2}+\frac{b}{2 c d^2 \sqrt{c^2 x^2+1}}","-\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{2 c d^2}+\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{2 c d^2}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{2 d^2 \left(c^2 x^2+1\right)}+\frac{\tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c d^2}+\frac{b}{2 c d^2 \sqrt{c^2 x^2+1}}",1,"b/(2*c*d^2*Sqrt[1 + c^2*x^2]) + (x*(a + b*ArcSinh[c*x]))/(2*d^2*(1 + c^2*x^2)) + ((a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c*d^2) - ((I/2)*b*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c*d^2) + ((I/2)*b*PolyLog[2, I*E^ArcSinh[c*x]])/(c*d^2)","A",8,6,21,0.2857,1,"{5690, 5693, 4180, 2279, 2391, 261}"
42,1,110,0,0.1769651,"\int \frac{a+b \sinh ^{-1}(c x)}{x \left(d+c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSinh[c*x])/(x*(d + c^2*d*x^2)^2),x]","-\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d^2}+\frac{b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{2 d^2}+\frac{a+b \sinh ^{-1}(c x)}{2 d^2 \left(c^2 x^2+1\right)}-\frac{2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}-\frac{b c x}{2 d^2 \sqrt{c^2 x^2+1}}","-\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d^2}+\frac{b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{2 d^2}+\frac{a+b \sinh ^{-1}(c x)}{2 d^2 \left(c^2 x^2+1\right)}-\frac{2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}-\frac{b c x}{2 d^2 \sqrt{c^2 x^2+1}}",1,"-(b*c*x)/(2*d^2*Sqrt[1 + c^2*x^2]) + (a + b*ArcSinh[c*x])/(2*d^2*(1 + c^2*x^2)) - (2*(a + b*ArcSinh[c*x])*ArcTanh[E^(2*ArcSinh[c*x])])/d^2 - (b*PolyLog[2, -E^(2*ArcSinh[c*x])])/(2*d^2) + (b*PolyLog[2, E^(2*ArcSinh[c*x])])/(2*d^2)","A",9,7,24,0.2917,1,"{5755, 5720, 5461, 4182, 2279, 2391, 191}"
43,1,168,0,0.1871808,"\int \frac{a+b \sinh ^{-1}(c x)}{x^2 \left(d+c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSinh[c*x])/(x^2*(d + c^2*d*x^2)^2),x]","\frac{3 i b c \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{2 d^2}-\frac{3 i b c \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{2 d^2}-\frac{3 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{2 d^2 \left(c^2 x^2+1\right)}-\frac{a+b \sinh ^{-1}(c x)}{d^2 x \left(c^2 x^2+1\right)}-\frac{3 c \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}-\frac{b c}{2 d^2 \sqrt{c^2 x^2+1}}-\frac{b c \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{d^2}","\frac{3 i b c \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{2 d^2}-\frac{3 i b c \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{2 d^2}-\frac{3 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{2 d^2 \left(c^2 x^2+1\right)}-\frac{a+b \sinh ^{-1}(c x)}{d^2 x \left(c^2 x^2+1\right)}-\frac{3 c \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}-\frac{b c}{2 d^2 \sqrt{c^2 x^2+1}}-\frac{b c \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{d^2}",1,"-(b*c)/(2*d^2*Sqrt[1 + c^2*x^2]) - (a + b*ArcSinh[c*x])/(d^2*x*(1 + c^2*x^2)) - (3*c^2*x*(a + b*ArcSinh[c*x]))/(2*d^2*(1 + c^2*x^2)) - (3*c*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/d^2 - (b*c*ArcTanh[Sqrt[1 + c^2*x^2]])/d^2 + (((3*I)/2)*b*c*PolyLog[2, (-I)*E^ArcSinh[c*x]])/d^2 - (((3*I)/2)*b*c*PolyLog[2, I*E^ArcSinh[c*x]])/d^2","A",13,11,24,0.4583,1,"{5747, 5690, 5693, 4180, 2279, 2391, 261, 266, 51, 63, 208}"
44,1,146,0,0.2597582,"\int \frac{a+b \sinh ^{-1}(c x)}{x^3 \left(d+c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSinh[c*x])/(x^3*(d + c^2*d*x^2)^2),x]","\frac{b c^2 \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{d^2}-\frac{b c^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{d^2}-\frac{c^2 \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \left(c^2 x^2+1\right)}-\frac{a+b \sinh ^{-1}(c x)}{2 d^2 x^2 \left(c^2 x^2+1\right)}+\frac{4 c^2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}-\frac{b c}{2 d^2 x \sqrt{c^2 x^2+1}}","\frac{b c^2 \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{d^2}-\frac{b c^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{d^2}-\frac{c^2 \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \left(c^2 x^2+1\right)}-\frac{a+b \sinh ^{-1}(c x)}{2 d^2 x^2 \left(c^2 x^2+1\right)}+\frac{4 c^2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}-\frac{b c}{2 d^2 x \sqrt{c^2 x^2+1}}",1,"-(b*c)/(2*d^2*x*Sqrt[1 + c^2*x^2]) - (c^2*(a + b*ArcSinh[c*x]))/(d^2*(1 + c^2*x^2)) - (a + b*ArcSinh[c*x])/(2*d^2*x^2*(1 + c^2*x^2)) + (4*c^2*(a + b*ArcSinh[c*x])*ArcTanh[E^(2*ArcSinh[c*x])])/d^2 + (b*c^2*PolyLog[2, -E^(2*ArcSinh[c*x])])/d^2 - (b*c^2*PolyLog[2, E^(2*ArcSinh[c*x])])/d^2","A",12,9,24,0.3750,1,"{5747, 5755, 5720, 5461, 4182, 2279, 2391, 191, 271}"
45,1,264,0,0.3090591,"\int \frac{a+b \sinh ^{-1}(c x)}{x^4 \left(d+c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSinh[c*x])/(x^4*(d + c^2*d*x^2)^2),x]","-\frac{5 i b c^3 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{2 d^2}+\frac{5 i b c^3 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{2 d^2}+\frac{5 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{2 d^2 \left(c^2 x^2+1\right)}+\frac{5 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 x \left(c^2 x^2+1\right)}-\frac{a+b \sinh ^{-1}(c x)}{3 d^2 x^3 \left(c^2 x^2+1\right)}+\frac{5 c^3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}+\frac{5 b c^3}{6 d^2 \sqrt{c^2 x^2+1}}-\frac{b c \sqrt{c^2 x^2+1}}{2 d^2 x^2}+\frac{b c}{3 d^2 x^2 \sqrt{c^2 x^2+1}}+\frac{13 b c^3 \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{6 d^2}","-\frac{5 i b c^3 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{2 d^2}+\frac{5 i b c^3 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{2 d^2}+\frac{5 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{2 d^2 \left(c^2 x^2+1\right)}+\frac{5 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 x \left(c^2 x^2+1\right)}-\frac{a+b \sinh ^{-1}(c x)}{3 d^2 x^3 \left(c^2 x^2+1\right)}+\frac{5 c^3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}+\frac{b c^3}{3 d^2 \sqrt{c^2 x^2+1}}-\frac{b c}{6 d^2 x^2 \sqrt{c^2 x^2+1}}+\frac{13 b c^3 \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{6 d^2}",1,"(5*b*c^3)/(6*d^2*Sqrt[1 + c^2*x^2]) + (b*c)/(3*d^2*x^2*Sqrt[1 + c^2*x^2]) - (b*c*Sqrt[1 + c^2*x^2])/(2*d^2*x^2) - (a + b*ArcSinh[c*x])/(3*d^2*x^3*(1 + c^2*x^2)) + (5*c^2*(a + b*ArcSinh[c*x]))/(3*d^2*x*(1 + c^2*x^2)) + (5*c^4*x*(a + b*ArcSinh[c*x]))/(2*d^2*(1 + c^2*x^2)) + (5*c^3*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/d^2 + (13*b*c^3*ArcTanh[Sqrt[1 + c^2*x^2]])/(6*d^2) - (((5*I)/2)*b*c^3*PolyLog[2, (-I)*E^ArcSinh[c*x]])/d^2 + (((5*I)/2)*b*c^3*PolyLog[2, I*E^ArcSinh[c*x]])/d^2","A",19,11,24,0.4583,1,"{5747, 5690, 5693, 4180, 2279, 2391, 261, 266, 51, 63, 208}"
46,1,186,0,0.2329014,"\int \frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^3} \, dx","Int[(x^4*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^3,x]","-\frac{3 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{8 c^5 d^3}+\frac{3 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{8 c^5 d^3}-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{4 c^2 d^3 \left(c^2 x^2+1\right)^2}-\frac{3 x \left(a+b \sinh ^{-1}(c x)\right)}{8 c^4 d^3 \left(c^2 x^2+1\right)}+\frac{3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c^5 d^3}-\frac{5 b}{8 c^5 d^3 \sqrt{c^2 x^2+1}}+\frac{b}{12 c^5 d^3 \left(c^2 x^2+1\right)^{3/2}}","-\frac{3 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{8 c^5 d^3}+\frac{3 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{8 c^5 d^3}-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{4 c^2 d^3 \left(c^2 x^2+1\right)^2}-\frac{3 x \left(a+b \sinh ^{-1}(c x)\right)}{8 c^4 d^3 \left(c^2 x^2+1\right)}+\frac{3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c^5 d^3}-\frac{5 b}{8 c^5 d^3 \sqrt{c^2 x^2+1}}+\frac{b}{12 c^5 d^3 \left(c^2 x^2+1\right)^{3/2}}",1,"b/(12*c^5*d^3*(1 + c^2*x^2)^(3/2)) - (5*b)/(8*c^5*d^3*Sqrt[1 + c^2*x^2]) - (x^3*(a + b*ArcSinh[c*x]))/(4*c^2*d^3*(1 + c^2*x^2)^2) - (3*x*(a + b*ArcSinh[c*x]))/(8*c^4*d^3*(1 + c^2*x^2)) + (3*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(4*c^5*d^3) - (((3*I)/8)*b*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^5*d^3) + (((3*I)/8)*b*PolyLog[2, I*E^ArcSinh[c*x]])/(c^5*d^3)","A",12,8,24,0.3333,1,"{5751, 5693, 4180, 2279, 2391, 261, 266, 43}"
47,1,97,0,0.0861107,"\int \frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^3} \, dx","Int[(x^3*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^3,x]","\frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3 \left(c^2 x^2+1\right)^2}+\frac{b x^3}{12 c d^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{b x}{4 c^3 d^3 \sqrt{c^2 x^2+1}}-\frac{b \sinh ^{-1}(c x)}{4 c^4 d^3}","\frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3 \left(c^2 x^2+1\right)^2}+\frac{b x^3}{12 c d^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{b x}{4 c^3 d^3 \sqrt{c^2 x^2+1}}-\frac{b \sinh ^{-1}(c x)}{4 c^4 d^3}",1,"(b*x^3)/(12*c*d^3*(1 + c^2*x^2)^(3/2)) + (b*x)/(4*c^3*d^3*Sqrt[1 + c^2*x^2]) - (b*ArcSinh[c*x])/(4*c^4*d^3) + (x^4*(a + b*ArcSinh[c*x]))/(4*d^3*(1 + c^2*x^2)^2)","A",4,3,24,0.1250,1,"{5723, 288, 215}"
48,1,184,0,0.1757429,"\int \frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^3} \, dx","Int[(x^2*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^3,x]","-\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{8 c^3 d^3}+\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{8 c^3 d^3}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{8 c^2 d^3 \left(c^2 x^2+1\right)}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{4 c^2 d^3 \left(c^2 x^2+1\right)^2}+\frac{\tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c^3 d^3}+\frac{b}{8 c^3 d^3 \sqrt{c^2 x^2+1}}-\frac{b}{12 c^3 d^3 \left(c^2 x^2+1\right)^{3/2}}","-\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{8 c^3 d^3}+\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{8 c^3 d^3}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{8 c^2 d^3 \left(c^2 x^2+1\right)}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{4 c^2 d^3 \left(c^2 x^2+1\right)^2}+\frac{\tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c^3 d^3}+\frac{b}{8 c^3 d^3 \sqrt{c^2 x^2+1}}-\frac{b}{12 c^3 d^3 \left(c^2 x^2+1\right)^{3/2}}",1,"-b/(12*c^3*d^3*(1 + c^2*x^2)^(3/2)) + b/(8*c^3*d^3*Sqrt[1 + c^2*x^2]) - (x*(a + b*ArcSinh[c*x]))/(4*c^2*d^3*(1 + c^2*x^2)^2) + (x*(a + b*ArcSinh[c*x]))/(8*c^2*d^3*(1 + c^2*x^2)) + ((a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(4*c^3*d^3) - ((I/8)*b*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^3*d^3) + ((I/8)*b*PolyLog[2, I*E^ArcSinh[c*x]])/(c^3*d^3)","A",10,7,24,0.2917,1,"{5751, 5690, 5693, 4180, 2279, 2391, 261}"
49,1,80,0,0.053746,"\int \frac{x \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^3} \, dx","Int[(x*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^3,x]","-\frac{a+b \sinh ^{-1}(c x)}{4 c^2 d^3 \left(c^2 x^2+1\right)^2}+\frac{b x}{6 c d^3 \sqrt{c^2 x^2+1}}+\frac{b x}{12 c d^3 \left(c^2 x^2+1\right)^{3/2}}","-\frac{a+b \sinh ^{-1}(c x)}{4 c^2 d^3 \left(c^2 x^2+1\right)^2}+\frac{b x}{6 c d^3 \sqrt{c^2 x^2+1}}+\frac{b x}{12 c d^3 \left(c^2 x^2+1\right)^{3/2}}",1,"(b*x)/(12*c*d^3*(1 + c^2*x^2)^(3/2)) + (b*x)/(6*c*d^3*Sqrt[1 + c^2*x^2]) - (a + b*ArcSinh[c*x])/(4*c^2*d^3*(1 + c^2*x^2)^2)","A",3,3,22,0.1364,1,"{5717, 192, 191}"
50,1,178,0,0.1407581,"\int \frac{a+b \sinh ^{-1}(c x)}{\left(d+c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSinh[c*x])/(d + c^2*d*x^2)^3,x]","-\frac{3 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{8 c d^3}+\frac{3 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{8 c d^3}+\frac{3 x \left(a+b \sinh ^{-1}(c x)\right)}{8 d^3 \left(c^2 x^2+1\right)}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3 \left(c^2 x^2+1\right)^2}+\frac{3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c d^3}+\frac{3 b}{8 c d^3 \sqrt{c^2 x^2+1}}+\frac{b}{12 c d^3 \left(c^2 x^2+1\right)^{3/2}}","-\frac{3 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{8 c d^3}+\frac{3 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{8 c d^3}+\frac{3 x \left(a+b \sinh ^{-1}(c x)\right)}{8 d^3 \left(c^2 x^2+1\right)}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3 \left(c^2 x^2+1\right)^2}+\frac{3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c d^3}+\frac{3 b}{8 c d^3 \sqrt{c^2 x^2+1}}+\frac{b}{12 c d^3 \left(c^2 x^2+1\right)^{3/2}}",1,"b/(12*c*d^3*(1 + c^2*x^2)^(3/2)) + (3*b)/(8*c*d^3*Sqrt[1 + c^2*x^2]) + (x*(a + b*ArcSinh[c*x]))/(4*d^3*(1 + c^2*x^2)^2) + (3*x*(a + b*ArcSinh[c*x]))/(8*d^3*(1 + c^2*x^2)) + (3*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(4*c*d^3) - (((3*I)/8)*b*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c*d^3) + (((3*I)/8)*b*PolyLog[2, I*E^ArcSinh[c*x]])/(c*d^3)","A",10,6,21,0.2857,1,"{5690, 5693, 4180, 2279, 2391, 261}"
51,1,159,0,0.2515795,"\int \frac{a+b \sinh ^{-1}(c x)}{x \left(d+c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSinh[c*x])/(x*(d + c^2*d*x^2)^3),x]","-\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d^3}+\frac{b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{2 d^3}+\frac{a+b \sinh ^{-1}(c x)}{2 d^3 \left(c^2 x^2+1\right)}+\frac{a+b \sinh ^{-1}(c x)}{4 d^3 \left(c^2 x^2+1\right)^2}-\frac{2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^3}-\frac{2 b c x}{3 d^3 \sqrt{c^2 x^2+1}}-\frac{b c x}{12 d^3 \left(c^2 x^2+1\right)^{3/2}}","-\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d^3}+\frac{b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{2 d^3}+\frac{a+b \sinh ^{-1}(c x)}{2 d^3 \left(c^2 x^2+1\right)}+\frac{a+b \sinh ^{-1}(c x)}{4 d^3 \left(c^2 x^2+1\right)^2}-\frac{2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^3}-\frac{2 b c x}{3 d^3 \sqrt{c^2 x^2+1}}-\frac{b c x}{12 d^3 \left(c^2 x^2+1\right)^{3/2}}",1,"-(b*c*x)/(12*d^3*(1 + c^2*x^2)^(3/2)) - (2*b*c*x)/(3*d^3*Sqrt[1 + c^2*x^2]) + (a + b*ArcSinh[c*x])/(4*d^3*(1 + c^2*x^2)^2) + (a + b*ArcSinh[c*x])/(2*d^3*(1 + c^2*x^2)) - (2*(a + b*ArcSinh[c*x])*ArcTanh[E^(2*ArcSinh[c*x])])/d^3 - (b*PolyLog[2, -E^(2*ArcSinh[c*x])])/(2*d^3) + (b*PolyLog[2, E^(2*ArcSinh[c*x])])/(2*d^3)","A",12,8,24,0.3333,1,"{5755, 5720, 5461, 4182, 2279, 2391, 191, 192}"
52,1,222,0,0.2383387,"\int \frac{a+b \sinh ^{-1}(c x)}{x^2 \left(d+c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSinh[c*x])/(x^2*(d + c^2*d*x^2)^3),x]","\frac{15 i b c \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{8 d^3}-\frac{15 i b c \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{8 d^3}-\frac{15 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{8 d^3 \left(c^2 x^2+1\right)}-\frac{5 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3 \left(c^2 x^2+1\right)^2}-\frac{a+b \sinh ^{-1}(c x)}{d^3 x \left(c^2 x^2+1\right)^2}-\frac{15 c \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3}-\frac{7 b c}{8 d^3 \sqrt{c^2 x^2+1}}-\frac{b c}{12 d^3 \left(c^2 x^2+1\right)^{3/2}}-\frac{b c \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{d^3}","\frac{15 i b c \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{8 d^3}-\frac{15 i b c \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{8 d^3}-\frac{15 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{8 d^3 \left(c^2 x^2+1\right)}-\frac{5 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3 \left(c^2 x^2+1\right)^2}-\frac{a+b \sinh ^{-1}(c x)}{d^3 x \left(c^2 x^2+1\right)^2}-\frac{15 c \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3}-\frac{7 b c}{8 d^3 \sqrt{c^2 x^2+1}}-\frac{b c}{12 d^3 \left(c^2 x^2+1\right)^{3/2}}-\frac{b c \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{d^3}",1,"-(b*c)/(12*d^3*(1 + c^2*x^2)^(3/2)) - (7*b*c)/(8*d^3*Sqrt[1 + c^2*x^2]) - (a + b*ArcSinh[c*x])/(d^3*x*(1 + c^2*x^2)^2) - (5*c^2*x*(a + b*ArcSinh[c*x]))/(4*d^3*(1 + c^2*x^2)^2) - (15*c^2*x*(a + b*ArcSinh[c*x]))/(8*d^3*(1 + c^2*x^2)) - (15*c*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(4*d^3) - (b*c*ArcTanh[Sqrt[1 + c^2*x^2]])/d^3 + (((15*I)/8)*b*c*PolyLog[2, (-I)*E^ArcSinh[c*x]])/d^3 - (((15*I)/8)*b*c*PolyLog[2, I*E^ArcSinh[c*x]])/d^3","A",16,11,24,0.4583,1,"{5747, 5690, 5693, 4180, 2279, 2391, 261, 266, 51, 63, 208}"
53,1,232,0,0.3437454,"\int \frac{a+b \sinh ^{-1}(c x)}{x^3 \left(d+c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSinh[c*x])/(x^3*(d + c^2*d*x^2)^3),x]","\frac{3 b c^2 \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d^3}-\frac{3 b c^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{2 d^3}-\frac{3 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 d^3 \left(c^2 x^2+1\right)}-\frac{3 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3 \left(c^2 x^2+1\right)^2}-\frac{a+b \sinh ^{-1}(c x)}{2 d^3 x^2 \left(c^2 x^2+1\right)^2}+\frac{6 c^2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^3}+\frac{2 b c^3 x}{3 d^3 \sqrt{c^2 x^2+1}}-\frac{5 b c^3 x}{12 d^3 \left(c^2 x^2+1\right)^{3/2}}-\frac{b c}{2 d^3 x \left(c^2 x^2+1\right)^{3/2}}","\frac{3 b c^2 \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d^3}-\frac{3 b c^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{2 d^3}-\frac{3 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 d^3 \left(c^2 x^2+1\right)}-\frac{3 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3 \left(c^2 x^2+1\right)^2}-\frac{a+b \sinh ^{-1}(c x)}{2 d^3 x^2 \left(c^2 x^2+1\right)^2}+\frac{6 c^2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^3}+\frac{2 b c^3 x}{3 d^3 \sqrt{c^2 x^2+1}}-\frac{5 b c^3 x}{12 d^3 \left(c^2 x^2+1\right)^{3/2}}-\frac{b c}{2 d^3 x \left(c^2 x^2+1\right)^{3/2}}",1,"-(b*c)/(2*d^3*x*(1 + c^2*x^2)^(3/2)) - (5*b*c^3*x)/(12*d^3*(1 + c^2*x^2)^(3/2)) + (2*b*c^3*x)/(3*d^3*Sqrt[1 + c^2*x^2]) - (3*c^2*(a + b*ArcSinh[c*x]))/(4*d^3*(1 + c^2*x^2)^2) - (a + b*ArcSinh[c*x])/(2*d^3*x^2*(1 + c^2*x^2)^2) - (3*c^2*(a + b*ArcSinh[c*x]))/(2*d^3*(1 + c^2*x^2)) + (6*c^2*(a + b*ArcSinh[c*x])*ArcTanh[E^(2*ArcSinh[c*x])])/d^3 + (3*b*c^2*PolyLog[2, -E^(2*ArcSinh[c*x])])/(2*d^3) - (3*b*c^2*PolyLog[2, E^(2*ArcSinh[c*x])])/(2*d^3)","A",16,10,24,0.4167,1,"{5747, 5755, 5720, 5461, 4182, 2279, 2391, 191, 192, 271}"
54,1,345,0,0.3671842,"\int \frac{a+b \sinh ^{-1}(c x)}{x^4 \left(d+c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSinh[c*x])/(x^4*(d + c^2*d*x^2)^3),x]","-\frac{35 i b c^3 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{8 d^3}+\frac{35 i b c^3 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{8 d^3}+\frac{35 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{8 d^3 \left(c^2 x^2+1\right)}+\frac{35 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{12 d^3 \left(c^2 x^2+1\right)^2}+\frac{7 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 d^3 x \left(c^2 x^2+1\right)^2}-\frac{a+b \sinh ^{-1}(c x)}{3 d^3 x^3 \left(c^2 x^2+1\right)^2}+\frac{35 c^3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3}+\frac{49 b c^3}{24 d^3 \sqrt{c^2 x^2+1}}+\frac{7 b c^3}{36 d^3 \left(c^2 x^2+1\right)^{3/2}}-\frac{5 b c \sqrt{c^2 x^2+1}}{6 d^3 x^2}+\frac{5 b c}{9 d^3 x^2 \sqrt{c^2 x^2+1}}+\frac{b c}{9 d^3 x^2 \left(c^2 x^2+1\right)^{3/2}}+\frac{19 b c^3 \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{6 d^3}","-\frac{35 i b c^3 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{8 d^3}+\frac{35 i b c^3 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{8 d^3}+\frac{35 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{8 d^3 \left(c^2 x^2+1\right)}+\frac{35 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{12 d^3 \left(c^2 x^2+1\right)^2}+\frac{7 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 d^3 x \left(c^2 x^2+1\right)^2}-\frac{a+b \sinh ^{-1}(c x)}{3 d^3 x^3 \left(c^2 x^2+1\right)^2}+\frac{35 c^3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3}+\frac{29 b c^3}{24 d^3 \sqrt{c^2 x^2+1}}-\frac{b c^3}{12 d^3 \left(c^2 x^2+1\right)^{3/2}}-\frac{b c}{6 d^3 x^2 \left(c^2 x^2+1\right)^{3/2}}+\frac{19 b c^3 \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{6 d^3}",1,"(7*b*c^3)/(36*d^3*(1 + c^2*x^2)^(3/2)) + (b*c)/(9*d^3*x^2*(1 + c^2*x^2)^(3/2)) + (49*b*c^3)/(24*d^3*Sqrt[1 + c^2*x^2]) + (5*b*c)/(9*d^3*x^2*Sqrt[1 + c^2*x^2]) - (5*b*c*Sqrt[1 + c^2*x^2])/(6*d^3*x^2) - (a + b*ArcSinh[c*x])/(3*d^3*x^3*(1 + c^2*x^2)^2) + (7*c^2*(a + b*ArcSinh[c*x]))/(3*d^3*x*(1 + c^2*x^2)^2) + (35*c^4*x*(a + b*ArcSinh[c*x]))/(12*d^3*(1 + c^2*x^2)^2) + (35*c^4*x*(a + b*ArcSinh[c*x]))/(8*d^3*(1 + c^2*x^2)) + (35*c^3*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(4*d^3) + (19*b*c^3*ArcTanh[Sqrt[1 + c^2*x^2]])/(6*d^3) - (((35*I)/8)*b*c^3*PolyLog[2, (-I)*E^ArcSinh[c*x]])/d^3 + (((35*I)/8)*b*c^3*PolyLog[2, I*E^ArcSinh[c*x]])/d^3","A",23,11,24,0.4583,1,"{5747, 5690, 5693, 4180, 2279, 2391, 261, 266, 51, 63, 208}"
55,1,111,0,0.1209056,"\int x^3 \sqrt{\pi +c^2 \pi  x^2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^3*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]),x]","\frac{\sqrt{\pi } \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^4}-\frac{\sqrt{\pi } \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^4}+\frac{2 \sqrt{\pi } b x}{15 c^3}-\frac{1}{25} \sqrt{\pi } b c x^5-\frac{\sqrt{\pi } b x^3}{45 c}","\frac{\left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 \pi ^2 c^4}-\frac{\left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  c^4}+\frac{2 \sqrt{\pi } b x}{15 c^3}-\frac{1}{25} \sqrt{\pi } b c x^5-\frac{\sqrt{\pi } b x^3}{45 c}",1,"(2*b*Sqrt[Pi]*x)/(15*c^3) - (b*Sqrt[Pi]*x^3)/(45*c) - (b*c*Sqrt[Pi]*x^5)/25 - (Sqrt[Pi]*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*c^4) + (Sqrt[Pi]*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(5*c^4)","A",3,4,26,0.1538,1,"{266, 43, 5732, 12}"
56,1,181,0,0.1978752,"\int x^2 \sqrt{\pi +c^2 \pi  x^2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]),x]","\frac{1}{4} x^3 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)+\frac{x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{8 c^2}-\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{c^2 x^2+1}}-\frac{b c x^4 \sqrt{\pi  c^2 x^2+\pi }}{16 \sqrt{c^2 x^2+1}}-\frac{b x^2 \sqrt{\pi  c^2 x^2+\pi }}{16 c \sqrt{c^2 x^2+1}}","\frac{1}{4} x^3 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)+\frac{\sqrt{\pi } x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{8 c^2}-\frac{\sqrt{\pi } \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c^3}-\frac{1}{16} \sqrt{\pi } b c x^4-\frac{\sqrt{\pi } b x^2}{16 c}",1,"-(b*x^2*Sqrt[Pi + c^2*Pi*x^2])/(16*c*Sqrt[1 + c^2*x^2]) - (b*c*x^4*Sqrt[Pi + c^2*Pi*x^2])/(16*Sqrt[1 + c^2*x^2]) + (x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(8*c^2) + (x^3*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/4 - (Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^2)/(16*b*c^3*Sqrt[1 + c^2*x^2])","A",5,4,26,0.1538,1,"{5742, 5758, 5675, 30}"
57,1,105,0,0.0678192,"\int x \sqrt{\pi +c^2 \pi  x^2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]),x]","\frac{\left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  c^2}-\frac{b c x^3 \sqrt{\pi  c^2 x^2+\pi }}{9 \sqrt{c^2 x^2+1}}-\frac{b x \sqrt{\pi  c^2 x^2+\pi }}{3 c \sqrt{c^2 x^2+1}}","\frac{\left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  c^2}-\frac{1}{9} \sqrt{\pi } b c x^3-\frac{\sqrt{\pi } b x}{3 c}",1,"-(b*x*Sqrt[Pi + c^2*Pi*x^2])/(3*c*Sqrt[1 + c^2*x^2]) - (b*c*x^3*Sqrt[Pi + c^2*Pi*x^2])/(9*Sqrt[1 + c^2*x^2]) + ((Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*c^2*Pi)","A",2,1,24,0.04167,1,"{5717}"
58,1,111,0,0.0593713,"\int \sqrt{\pi +c^2 \pi  x^2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]),x]","\frac{1}{2} x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)+\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{c^2 x^2+1}}-\frac{b c x^2 \sqrt{\pi  c^2 x^2+\pi }}{4 \sqrt{c^2 x^2+1}}","\frac{1}{2} x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)+\frac{\sqrt{\pi } \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c}-\frac{1}{4} \sqrt{\pi } b c x^2",1,"-(b*c*x^2*Sqrt[Pi + c^2*Pi*x^2])/(4*Sqrt[1 + c^2*x^2]) + (x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/2 + (Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*c*Sqrt[1 + c^2*x^2])","A",3,3,23,0.1304,1,"{5682, 5675, 30}"
59,1,177,0,0.1917504,"\int \frac{\sqrt{\pi +c^2 \pi  x^2} \left(a+b \sinh ^{-1}(c x)\right)}{x} \, dx","Int[(Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/x,x]","-\frac{b \sqrt{\pi  c^2 x^2+\pi } \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\frac{b \sqrt{\pi  c^2 x^2+\pi } \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)-\frac{2 \sqrt{\pi  c^2 x^2+\pi } \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}-\frac{b c x \sqrt{\pi  c^2 x^2+\pi }}{\sqrt{c^2 x^2+1}}","-\sqrt{\pi } b \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+\sqrt{\pi } b \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)+\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)-2 \sqrt{\pi } \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)+\sqrt{\pi } (-b) c x",1,"-((b*c*x*Sqrt[Pi + c^2*Pi*x^2])/Sqrt[1 + c^2*x^2]) + Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]) - (2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (b*Sqrt[Pi + c^2*Pi*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (b*Sqrt[Pi + c^2*Pi*x^2]*PolyLog[2, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2]","A",8,6,26,0.2308,1,"{5742, 5760, 4182, 2279, 2391, 8}"
60,1,105,0,0.1079239,"\int \frac{\sqrt{\pi +c^2 \pi  x^2} \left(a+b \sinh ^{-1}(c x)\right)}{x^2} \, dx","Int[(Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/x^2,x]","\frac{c \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b \sqrt{c^2 x^2+1}}-\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{x}+\frac{b c \sqrt{\pi  c^2 x^2+\pi } \log (x)}{\sqrt{c^2 x^2+1}}","-\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{x}+\frac{\sqrt{\pi } c \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b}+\sqrt{\pi } b c \log (x)",1,"-((Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/x) + (c*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*Sqrt[1 + c^2*x^2]) + (b*c*Sqrt[Pi + c^2*Pi*x^2]*Log[x])/Sqrt[1 + c^2*x^2]","A",3,3,26,0.1154,1,"{5737, 29, 5675}"
61,1,201,0,0.1954381,"\int \frac{\sqrt{\pi +c^2 \pi  x^2} \left(a+b \sinh ^{-1}(c x)\right)}{x^3} \, dx","Int[(Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/x^3,x]","-\frac{b c^2 \sqrt{\pi  c^2 x^2+\pi } \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}+\frac{b c^2 \sqrt{\pi  c^2 x^2+\pi } \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}-\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}-\frac{c^2 \sqrt{\pi  c^2 x^2+\pi } \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}-\frac{b c \sqrt{\pi  c^2 x^2+\pi }}{2 x \sqrt{c^2 x^2+1}}","-\frac{1}{2} \sqrt{\pi } b c^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+\frac{1}{2} \sqrt{\pi } b c^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)-\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}-\sqrt{\pi } c^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{\sqrt{\pi } b c}{2 x}",1,"-(b*c*Sqrt[Pi + c^2*Pi*x^2])/(2*x*Sqrt[1 + c^2*x^2]) - (Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(2*x^2) - (c^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (b*c^2*Sqrt[Pi + c^2*Pi*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/(2*Sqrt[1 + c^2*x^2]) + (b*c^2*Sqrt[Pi + c^2*Pi*x^2]*PolyLog[2, E^ArcSinh[c*x]])/(2*Sqrt[1 + c^2*x^2])","A",8,6,26,0.2308,1,"{5737, 30, 5760, 4182, 2279, 2391}"
62,1,106,0,0.0895466,"\int \frac{\sqrt{\pi +c^2 \pi  x^2} \left(a+b \sinh ^{-1}(c x)\right)}{x^4} \, dx","Int[(Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/x^4,x]","-\frac{\left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  x^3}-\frac{b c \sqrt{\pi  c^2 x^2+\pi }}{6 x^2 \sqrt{c^2 x^2+1}}+\frac{b c^3 \sqrt{\pi  c^2 x^2+\pi } \log (x)}{3 \sqrt{c^2 x^2+1}}","-\frac{\left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  x^3}+\frac{1}{3} \sqrt{\pi } b c^3 \log (x)-\frac{\sqrt{\pi } b c}{6 x^2}",1,"-(b*c*Sqrt[Pi + c^2*Pi*x^2])/(6*x^2*Sqrt[1 + c^2*x^2]) - ((Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*Pi*x^3) + (b*c^3*Sqrt[Pi + c^2*Pi*x^2]*Log[x])/(3*Sqrt[1 + c^2*x^2])","A",3,2,26,0.07692,1,"{5723, 14}"
63,1,127,0,0.1431252,"\int x^3 \left(\pi +c^2 \pi  x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^3*(Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]),x]","\frac{\pi ^{3/2} \left(c^2 x^2+1\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^4}-\frac{\pi ^{3/2} \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^4}-\frac{1}{49} \pi ^{3/2} b c^3 x^7+\frac{2 \pi ^{3/2} b x}{35 c^3}-\frac{8}{175} \pi ^{3/2} b c x^5-\frac{\pi ^{3/2} b x^3}{105 c}","\frac{\left(\pi  c^2 x^2+\pi \right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{7 \pi ^2 c^4}-\frac{\left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 \pi  c^4}-\frac{1}{49} \pi ^{3/2} b c^3 x^7+\frac{2 \pi ^{3/2} b x}{35 c^3}-\frac{8}{175} \pi ^{3/2} b c x^5-\frac{\pi ^{3/2} b x^3}{105 c}",1,"(2*b*Pi^(3/2)*x)/(35*c^3) - (b*Pi^(3/2)*x^3)/(105*c) - (8*b*c*Pi^(3/2)*x^5)/175 - (b*c^3*Pi^(3/2)*x^7)/49 - (Pi^(3/2)*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(5*c^4) + (Pi^(3/2)*(1 + c^2*x^2)^(7/2)*(a + b*ArcSinh[c*x]))/(7*c^4)","A",4,5,26,0.1923,1,"{266, 43, 5732, 12, 373}"
64,1,254,0,0.3211745,"\int x^2 \left(\pi +c^2 \pi  x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^2*(Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]),x]","\frac{1}{6} x^3 \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{8} \pi  x^3 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)+\frac{\pi  x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{16 c^2}-\frac{\pi  \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{c^2 x^2+1}}-\frac{\pi  b c^3 x^6 \sqrt{\pi  c^2 x^2+\pi }}{36 \sqrt{c^2 x^2+1}}-\frac{7 \pi  b c x^4 \sqrt{\pi  c^2 x^2+\pi }}{96 \sqrt{c^2 x^2+1}}-\frac{\pi  b x^2 \sqrt{\pi  c^2 x^2+\pi }}{32 c \sqrt{c^2 x^2+1}}","\frac{1}{6} x^3 \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{8} \pi  x^3 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)+\frac{\pi ^{3/2} x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{16 c^2}-\frac{\pi ^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{32 b c^3}-\frac{1}{36} \pi ^{3/2} b c^3 x^6-\frac{7}{96} \pi ^{3/2} b c x^4-\frac{\pi ^{3/2} b x^2}{32 c}",1,"-(b*Pi*x^2*Sqrt[Pi + c^2*Pi*x^2])/(32*c*Sqrt[1 + c^2*x^2]) - (7*b*c*Pi*x^4*Sqrt[Pi + c^2*Pi*x^2])/(96*Sqrt[1 + c^2*x^2]) - (b*c^3*Pi*x^6*Sqrt[Pi + c^2*Pi*x^2])/(36*Sqrt[1 + c^2*x^2]) + (Pi*x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(16*c^2) + (Pi*x^3*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/8 + (x^3*(Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/6 - (Pi*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^2)/(32*b*c^3*Sqrt[1 + c^2*x^2])","A",8,6,26,0.2308,1,"{5744, 5742, 5758, 5675, 30, 14}"
65,1,146,0,0.087301,"\int x \left(\pi +c^2 \pi  x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x*(Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]),x]","\frac{\left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 \pi  c^2}-\frac{\pi  b c^3 x^5 \sqrt{\pi  c^2 x^2+\pi }}{25 \sqrt{c^2 x^2+1}}-\frac{2 \pi  b c x^3 \sqrt{\pi  c^2 x^2+\pi }}{15 \sqrt{c^2 x^2+1}}-\frac{\pi  b x \sqrt{\pi  c^2 x^2+\pi }}{5 c \sqrt{c^2 x^2+1}}","\frac{\left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 \pi  c^2}-\frac{1}{25} \pi ^{3/2} b c^3 x^5-\frac{2}{15} \pi ^{3/2} b c x^3-\frac{\pi ^{3/2} b x}{5 c}",1,"-(b*Pi*x*Sqrt[Pi + c^2*Pi*x^2])/(5*c*Sqrt[1 + c^2*x^2]) - (2*b*c*Pi*x^3*Sqrt[Pi + c^2*Pi*x^2])/(15*Sqrt[1 + c^2*x^2]) - (b*c^3*Pi*x^5*Sqrt[Pi + c^2*Pi*x^2])/(25*Sqrt[1 + c^2*x^2]) + ((Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(5*c^2*Pi)","A",3,2,24,0.08333,1,"{5717, 194}"
66,1,180,0,0.1124838,"\int \left(\pi +c^2 \pi  x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]),x]","\frac{1}{4} x \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{8} \pi  x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)+\frac{3 \pi  \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c \sqrt{c^2 x^2+1}}-\frac{\pi  b c^3 x^4 \sqrt{\pi  c^2 x^2+\pi }}{16 \sqrt{c^2 x^2+1}}-\frac{5 \pi  b c x^2 \sqrt{\pi  c^2 x^2+\pi }}{16 \sqrt{c^2 x^2+1}}","\frac{1}{4} x \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{8} \pi  x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)+\frac{3 \pi ^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c}-\frac{1}{16} \pi ^{3/2} b c^3 x^4-\frac{5}{16} \pi ^{3/2} b c x^2",1,"(-5*b*c*Pi*x^2*Sqrt[Pi + c^2*Pi*x^2])/(16*Sqrt[1 + c^2*x^2]) - (b*c^3*Pi*x^4*Sqrt[Pi + c^2*Pi*x^2])/(16*Sqrt[1 + c^2*x^2]) + (3*Pi*x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/8 + (x*(Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/4 + (3*Pi*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^2)/(16*b*c*Sqrt[1 + c^2*x^2])","A",6,5,23,0.2174,1,"{5684, 5682, 5675, 30, 14}"
67,1,249,0,0.3041253,"\int \frac{\left(\pi +c^2 \pi  x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{x} \, dx","Int[((Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/x,x]","-\frac{\pi  b \sqrt{\pi  c^2 x^2+\pi } \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\frac{\pi  b \sqrt{\pi  c^2 x^2+\pi } \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\frac{1}{3} \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\pi  \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)-\frac{2 \pi  \sqrt{\pi  c^2 x^2+\pi } \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}-\frac{\pi  b c^3 x^3 \sqrt{\pi  c^2 x^2+\pi }}{9 \sqrt{c^2 x^2+1}}-\frac{4 \pi  b c x \sqrt{\pi  c^2 x^2+\pi }}{3 \sqrt{c^2 x^2+1}}","-\pi ^{3/2} b \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+\pi ^{3/2} b \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)+\frac{1}{3} \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\pi  \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)-2 \pi ^{3/2} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{9} \pi ^{3/2} b c^3 x^3-\frac{4}{3} \pi ^{3/2} b c x",1,"(-4*b*c*Pi*x*Sqrt[Pi + c^2*Pi*x^2])/(3*Sqrt[1 + c^2*x^2]) - (b*c^3*Pi*x^3*Sqrt[Pi + c^2*Pi*x^2])/(9*Sqrt[1 + c^2*x^2]) + Pi*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]) + ((Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/3 - (2*Pi*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (b*Pi*Sqrt[Pi + c^2*Pi*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (b*Pi*Sqrt[Pi + c^2*Pi*x^2]*PolyLog[2, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2]","A",10,7,26,0.2692,1,"{5744, 5742, 5760, 4182, 2279, 2391, 8}"
68,1,177,0,0.167999,"\int \frac{\left(\pi +c^2 \pi  x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{x^2} \, dx","Int[((Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/x^2,x]","\frac{3}{2} \pi  c^2 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)+\frac{3 \pi  c \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b \sqrt{c^2 x^2+1}}-\frac{\left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{\pi  b c^3 x^2 \sqrt{\pi  c^2 x^2+\pi }}{4 \sqrt{c^2 x^2+1}}+\frac{\pi  b c \sqrt{\pi  c^2 x^2+\pi } \log (x)}{\sqrt{c^2 x^2+1}}","\frac{3}{2} \pi  c^2 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)-\frac{\left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{x}+\frac{3 \pi ^{3/2} c \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b}-\frac{1}{4} \pi ^{3/2} b c^3 x^2+\pi ^{3/2} b c \log (x)",1,"-(b*c^3*Pi*x^2*Sqrt[Pi + c^2*Pi*x^2])/(4*Sqrt[1 + c^2*x^2]) + (3*c^2*Pi*x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/2 - ((Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/x + (3*c*Pi*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*Sqrt[1 + c^2*x^2]) + (b*c*Pi*Sqrt[Pi + c^2*Pi*x^2]*Log[x])/Sqrt[1 + c^2*x^2]","A",6,5,26,0.1923,1,"{5739, 5682, 5675, 30, 14}"
69,1,270,0,0.3022168,"\int \frac{\left(\pi +c^2 \pi  x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{x^3} \, dx","Int[((Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/x^3,x]","-\frac{3 \pi  b c^2 \sqrt{\pi  c^2 x^2+\pi } \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}+\frac{3 \pi  b c^2 \sqrt{\pi  c^2 x^2+\pi } \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}+\frac{3}{2} \pi  c^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)-\frac{\left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}-\frac{3 \pi  c^2 \sqrt{\pi  c^2 x^2+\pi } \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}-\frac{\pi  b c^3 x \sqrt{\pi  c^2 x^2+\pi }}{\sqrt{c^2 x^2+1}}-\frac{\pi  b c \sqrt{\pi  c^2 x^2+\pi }}{2 x \sqrt{c^2 x^2+1}}","-\frac{3}{2} \pi ^{3/2} b c^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+\frac{3}{2} \pi ^{3/2} b c^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)+\frac{3}{2} \pi  c^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)-\frac{\left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}-3 \pi ^{3/2} c^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)+\pi ^{3/2} (-b) c^3 x-\frac{\pi ^{3/2} b c}{2 x}",1,"-(b*c*Pi*Sqrt[Pi + c^2*Pi*x^2])/(2*x*Sqrt[1 + c^2*x^2]) - (b*c^3*Pi*x*Sqrt[Pi + c^2*Pi*x^2])/Sqrt[1 + c^2*x^2] + (3*c^2*Pi*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/2 - ((Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(2*x^2) - (3*c^2*Pi*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (3*b*c^2*Pi*Sqrt[Pi + c^2*Pi*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/(2*Sqrt[1 + c^2*x^2]) + (3*b*c^2*Pi*Sqrt[Pi + c^2*Pi*x^2]*PolyLog[2, E^ArcSinh[c*x]])/(2*Sqrt[1 + c^2*x^2])","A",11,8,26,0.3077,1,"{5739, 5742, 5760, 4182, 2279, 2391, 8, 14}"
70,1,184,0,0.2187107,"\int \frac{\left(\pi +c^2 \pi  x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{x^4} \, dx","Int[((Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/x^4,x]","\frac{\pi  c^3 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b \sqrt{c^2 x^2+1}}-\frac{\pi  c^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{\left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^3}-\frac{\pi  b c \sqrt{\pi  c^2 x^2+\pi }}{6 x^2 \sqrt{c^2 x^2+1}}+\frac{4 \pi  b c^3 \sqrt{\pi  c^2 x^2+\pi } \log (x)}{3 \sqrt{c^2 x^2+1}}","-\frac{\pi  c^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{\left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^3}+\frac{\pi ^{3/2} c^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b}+\frac{4}{3} \pi ^{3/2} b c^3 \log (x)-\frac{\pi ^{3/2} b c}{6 x^2}",1,"-(b*c*Pi*Sqrt[Pi + c^2*Pi*x^2])/(6*x^2*Sqrt[1 + c^2*x^2]) - (c^2*Pi*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/x - ((Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*x^3) + (c^3*Pi*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*Sqrt[1 + c^2*x^2]) + (4*b*c^3*Pi*Sqrt[Pi + c^2*Pi*x^2]*Log[x])/(3*Sqrt[1 + c^2*x^2])","A",6,5,26,0.1923,1,"{5739, 5737, 29, 5675, 14}"
71,1,143,0,0.1527812,"\int x^3 \left(\pi +c^2 \pi  x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^3*(Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x]),x]","\frac{\pi ^{5/2} \left(c^2 x^2+1\right)^{9/2} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^4}-\frac{\pi ^{5/2} \left(c^2 x^2+1\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^4}-\frac{1}{81} \pi ^{5/2} b c^5 x^9-\frac{19}{441} \pi ^{5/2} b c^3 x^7+\frac{2 \pi ^{5/2} b x}{63 c^3}-\frac{1}{21} \pi ^{5/2} b c x^5-\frac{\pi ^{5/2} b x^3}{189 c}","\frac{\left(\pi  c^2 x^2+\pi \right)^{9/2} \left(a+b \sinh ^{-1}(c x)\right)}{9 \pi ^2 c^4}-\frac{\left(\pi  c^2 x^2+\pi \right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{7 \pi  c^4}-\frac{1}{81} \pi ^{5/2} b c^5 x^9-\frac{19}{441} \pi ^{5/2} b c^3 x^7+\frac{2 \pi ^{5/2} b x}{63 c^3}-\frac{1}{21} \pi ^{5/2} b c x^5-\frac{\pi ^{5/2} b x^3}{189 c}",1,"(2*b*Pi^(5/2)*x)/(63*c^3) - (b*Pi^(5/2)*x^3)/(189*c) - (b*c*Pi^(5/2)*x^5)/21 - (19*b*c^3*Pi^(5/2)*x^7)/441 - (b*c^5*Pi^(5/2)*x^9)/81 - (Pi^(5/2)*(1 + c^2*x^2)^(7/2)*(a + b*ArcSinh[c*x]))/(7*c^4) + (Pi^(5/2)*(1 + c^2*x^2)^(9/2)*(a + b*ArcSinh[c*x]))/(9*c^4)","A",4,5,26,0.1923,1,"{266, 43, 5732, 12, 373}"
72,1,337,0,0.4577287,"\int x^2 \left(\pi +c^2 \pi  x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^2*(Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x]),x]","\frac{1}{8} x^3 \left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{48} \pi  x^3 \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{64} \pi ^2 x^3 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 \pi ^2 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{128 c^2}-\frac{5 \pi ^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{c^2 x^2+1}}-\frac{\pi ^2 b c^5 x^8 \sqrt{\pi  c^2 x^2+\pi }}{64 \sqrt{c^2 x^2+1}}-\frac{17 \pi ^2 b c^3 x^6 \sqrt{\pi  c^2 x^2+\pi }}{288 \sqrt{c^2 x^2+1}}-\frac{59 \pi ^2 b c x^4 \sqrt{\pi  c^2 x^2+\pi }}{768 \sqrt{c^2 x^2+1}}-\frac{5 \pi ^2 b x^2 \sqrt{\pi  c^2 x^2+\pi }}{256 c \sqrt{c^2 x^2+1}}","\frac{1}{8} x^3 \left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{48} \pi  x^3 \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{64} \pi ^2 x^3 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 \pi ^{5/2} x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{128 c^2}-\frac{5 \pi ^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{256 b c^3}-\frac{1}{64} \pi ^{5/2} b c^5 x^8-\frac{17}{288} \pi ^{5/2} b c^3 x^6-\frac{59}{768} \pi ^{5/2} b c x^4-\frac{5 \pi ^{5/2} b x^2}{256 c}",1,"(-5*b*Pi^2*x^2*Sqrt[Pi + c^2*Pi*x^2])/(256*c*Sqrt[1 + c^2*x^2]) - (59*b*c*Pi^2*x^4*Sqrt[Pi + c^2*Pi*x^2])/(768*Sqrt[1 + c^2*x^2]) - (17*b*c^3*Pi^2*x^6*Sqrt[Pi + c^2*Pi*x^2])/(288*Sqrt[1 + c^2*x^2]) - (b*c^5*Pi^2*x^8*Sqrt[Pi + c^2*Pi*x^2])/(64*Sqrt[1 + c^2*x^2]) + (5*Pi^2*x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(128*c^2) + (5*Pi^2*x^3*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/64 + (5*Pi*x^3*(Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/48 + (x^3*(Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/8 - (5*Pi^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^2)/(256*b*c^3*Sqrt[1 + c^2*x^2])","A",12,8,26,0.3077,1,"{5744, 5742, 5758, 5675, 30, 14, 266, 43}"
73,1,193,0,0.0868338,"\int x \left(\pi +c^2 \pi  x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x*(Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x]),x]","\frac{\left(\pi  c^2 x^2+\pi \right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{7 \pi  c^2}-\frac{\pi ^2 b c^5 x^7 \sqrt{\pi  c^2 x^2+\pi }}{49 \sqrt{c^2 x^2+1}}-\frac{3 \pi ^2 b c^3 x^5 \sqrt{\pi  c^2 x^2+\pi }}{35 \sqrt{c^2 x^2+1}}-\frac{\pi ^2 b c x^3 \sqrt{\pi  c^2 x^2+\pi }}{7 \sqrt{c^2 x^2+1}}-\frac{\pi ^2 b x \sqrt{\pi  c^2 x^2+\pi }}{7 c \sqrt{c^2 x^2+1}}","\frac{\left(\pi  c^2 x^2+\pi \right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{7 \pi  c^2}-\frac{1}{49} \pi ^{5/2} b c^5 x^7-\frac{3}{35} \pi ^{5/2} b c^3 x^5-\frac{1}{7} \pi ^{5/2} b c x^3-\frac{\pi ^{5/2} b x}{7 c}",1,"-(b*Pi^2*x*Sqrt[Pi + c^2*Pi*x^2])/(7*c*Sqrt[1 + c^2*x^2]) - (b*c*Pi^2*x^3*Sqrt[Pi + c^2*Pi*x^2])/(7*Sqrt[1 + c^2*x^2]) - (3*b*c^3*Pi^2*x^5*Sqrt[Pi + c^2*Pi*x^2])/(35*Sqrt[1 + c^2*x^2]) - (b*c^5*Pi^2*x^7*Sqrt[Pi + c^2*Pi*x^2])/(49*Sqrt[1 + c^2*x^2]) + ((Pi + c^2*Pi*x^2)^(7/2)*(a + b*ArcSinh[c*x]))/(7*c^2*Pi)","B",3,2,24,0.08333,1,"{5717, 194}"
74,1,254,0,0.1645082,"\int \left(\pi +c^2 \pi  x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x]),x]","\frac{1}{6} x \left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{24} \pi  x \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{16} \pi ^2 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 \pi ^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2}{32 b c \sqrt{c^2 x^2+1}}-\frac{5 \pi ^2 b c^3 x^4 \sqrt{\pi  c^2 x^2+\pi }}{96 \sqrt{c^2 x^2+1}}-\frac{25 \pi ^2 b c x^2 \sqrt{\pi  c^2 x^2+\pi }}{96 \sqrt{c^2 x^2+1}}-\frac{\pi ^2 b \left(c^2 x^2+1\right)^{5/2} \sqrt{\pi  c^2 x^2+\pi }}{36 c}","\frac{1}{6} x \left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{24} \pi  x \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{16} \pi ^2 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 \pi ^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{32 b c}-\frac{5}{96} \pi ^{5/2} b c^3 x^4-\frac{\pi ^{5/2} b \left(c^2 x^2+1\right)^3}{36 c}-\frac{25}{96} \pi ^{5/2} b c x^2",1,"(-25*b*c*Pi^2*x^2*Sqrt[Pi + c^2*Pi*x^2])/(96*Sqrt[1 + c^2*x^2]) - (5*b*c^3*Pi^2*x^4*Sqrt[Pi + c^2*Pi*x^2])/(96*Sqrt[1 + c^2*x^2]) - (b*Pi^2*(1 + c^2*x^2)^(5/2)*Sqrt[Pi + c^2*Pi*x^2])/(36*c) + (5*Pi^2*x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/16 + (5*Pi*x*(Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/24 + (x*(Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/6 + (5*Pi^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^2)/(32*b*c*Sqrt[1 + c^2*x^2])","A",8,6,23,0.2609,1,"{5684, 5682, 5675, 30, 14, 261}"
75,1,329,0,0.4296254,"\int \frac{\left(\pi +c^2 \pi  x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{x} \, dx","Int[((Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/x,x]","-\frac{\pi ^2 b \sqrt{\pi  c^2 x^2+\pi } \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\frac{\pi ^2 b \sqrt{\pi  c^2 x^2+\pi } \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\frac{1}{5} \left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{3} \pi  \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\pi ^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)-\frac{2 \pi ^2 \sqrt{\pi  c^2 x^2+\pi } \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}-\frac{\pi ^2 b c^5 x^5 \sqrt{\pi  c^2 x^2+\pi }}{25 \sqrt{c^2 x^2+1}}-\frac{11 \pi ^2 b c^3 x^3 \sqrt{\pi  c^2 x^2+\pi }}{45 \sqrt{c^2 x^2+1}}-\frac{23 \pi ^2 b c x \sqrt{\pi  c^2 x^2+\pi }}{15 \sqrt{c^2 x^2+1}}","-\pi ^{5/2} b \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+\pi ^{5/2} b \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)+\frac{1}{5} \left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{3} \pi  \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\pi ^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)-2 \pi ^{5/2} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{25} \pi ^{5/2} b c^5 x^5-\frac{11}{45} \pi ^{5/2} b c^3 x^3-\frac{23}{15} \pi ^{5/2} b c x",1,"(-23*b*c*Pi^2*x*Sqrt[Pi + c^2*Pi*x^2])/(15*Sqrt[1 + c^2*x^2]) - (11*b*c^3*Pi^2*x^3*Sqrt[Pi + c^2*Pi*x^2])/(45*Sqrt[1 + c^2*x^2]) - (b*c^5*Pi^2*x^5*Sqrt[Pi + c^2*Pi*x^2])/(25*Sqrt[1 + c^2*x^2]) + Pi^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]) + (Pi*(Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/3 + ((Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/5 - (2*Pi^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (b*Pi^2*Sqrt[Pi + c^2*Pi*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (b*Pi^2*Sqrt[Pi + c^2*Pi*x^2]*PolyLog[2, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2]","A",13,8,26,0.3077,1,"{5744, 5742, 5760, 4182, 2279, 2391, 8, 194}"
76,1,257,0,0.2358747,"\int \frac{\left(\pi +c^2 \pi  x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{x^2} \, dx","Int[((Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/x^2,x]","\frac{5}{4} \pi  c^2 x \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{15}{8} \pi ^2 c^2 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)+\frac{15 \pi ^2 c \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b \sqrt{c^2 x^2+1}}-\frac{\left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{\pi ^2 b c^5 x^4 \sqrt{\pi  c^2 x^2+\pi }}{16 \sqrt{c^2 x^2+1}}-\frac{9 \pi ^2 b c^3 x^2 \sqrt{\pi  c^2 x^2+\pi }}{16 \sqrt{c^2 x^2+1}}+\frac{\pi ^2 b c \sqrt{\pi  c^2 x^2+\pi } \log (x)}{\sqrt{c^2 x^2+1}}","\frac{5}{4} \pi  c^2 x \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{15}{8} \pi ^2 c^2 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)-\frac{\left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{x}+\frac{15 \pi ^{5/2} c \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b}-\frac{1}{16} \pi ^{5/2} b c^5 x^4-\frac{9}{16} \pi ^{5/2} b c^3 x^2+\pi ^{5/2} b c \log (x)",1,"(-9*b*c^3*Pi^2*x^2*Sqrt[Pi + c^2*Pi*x^2])/(16*Sqrt[1 + c^2*x^2]) - (b*c^5*Pi^2*x^4*Sqrt[Pi + c^2*Pi*x^2])/(16*Sqrt[1 + c^2*x^2]) + (15*c^2*Pi^2*x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/8 + (5*c^2*Pi*x*(Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/4 - ((Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/x + (15*c*Pi^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^2)/(16*b*Sqrt[1 + c^2*x^2]) + (b*c*Pi^2*Sqrt[Pi + c^2*Pi*x^2]*Log[x])/Sqrt[1 + c^2*x^2]","A",10,8,26,0.3077,1,"{5739, 5684, 5682, 5675, 30, 14, 266, 43}"
77,1,355,0,0.4309009,"\int \frac{\left(\pi +c^2 \pi  x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{x^3} \, dx","Int[((Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/x^3,x]","-\frac{5 \pi ^2 b c^2 \sqrt{\pi  c^2 x^2+\pi } \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}+\frac{5 \pi ^2 b c^2 \sqrt{\pi  c^2 x^2+\pi } \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}+\frac{5}{6} \pi  c^2 \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{2} \pi ^2 c^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)-\frac{\left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}-\frac{5 \pi ^2 c^2 \sqrt{\pi  c^2 x^2+\pi } \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}-\frac{\pi ^2 b c^5 x^3 \sqrt{\pi  c^2 x^2+\pi }}{9 \sqrt{c^2 x^2+1}}-\frac{7 \pi ^2 b c^3 x \sqrt{\pi  c^2 x^2+\pi }}{3 \sqrt{c^2 x^2+1}}-\frac{\pi ^2 b c \sqrt{\pi  c^2 x^2+\pi }}{2 x \sqrt{c^2 x^2+1}}","-\frac{5}{2} \pi ^{5/2} b c^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+\frac{5}{2} \pi ^{5/2} b c^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)+\frac{5}{6} \pi  c^2 \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{2} \pi ^2 c^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)-\frac{\left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}-5 \pi ^{5/2} c^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{9} \pi ^{5/2} b c^5 x^3-\frac{7}{3} \pi ^{5/2} b c^3 x-\frac{\pi ^{5/2} b c}{2 x}",1,"-(b*c*Pi^2*Sqrt[Pi + c^2*Pi*x^2])/(2*x*Sqrt[1 + c^2*x^2]) - (7*b*c^3*Pi^2*x*Sqrt[Pi + c^2*Pi*x^2])/(3*Sqrt[1 + c^2*x^2]) - (b*c^5*Pi^2*x^3*Sqrt[Pi + c^2*Pi*x^2])/(9*Sqrt[1 + c^2*x^2]) + (5*c^2*Pi^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/2 + (5*c^2*Pi*(Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/6 - ((Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(2*x^2) - (5*c^2*Pi^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (5*b*c^2*Pi^2*Sqrt[Pi + c^2*Pi*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/(2*Sqrt[1 + c^2*x^2]) + (5*b*c^2*Pi^2*Sqrt[Pi + c^2*Pi*x^2]*PolyLog[2, E^ArcSinh[c*x]])/(2*Sqrt[1 + c^2*x^2])","A",13,9,26,0.3462,1,"{5739, 5744, 5742, 5760, 4182, 2279, 2391, 8, 270}"
78,1,266,0,0.2939486,"\int \frac{\left(\pi +c^2 \pi  x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{x^4} \, dx","Int[((Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/x^4,x]","\frac{5}{2} \pi ^2 c^4 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 \pi ^2 c^3 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b \sqrt{c^2 x^2+1}}-\frac{5 \pi  c^2 \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 x}-\frac{\left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^3}-\frac{\pi ^2 b c^5 x^2 \sqrt{\pi  c^2 x^2+\pi }}{4 \sqrt{c^2 x^2+1}}-\frac{\pi ^2 b c \sqrt{\pi  c^2 x^2+\pi }}{6 x^2 \sqrt{c^2 x^2+1}}+\frac{7 \pi ^2 b c^3 \sqrt{\pi  c^2 x^2+\pi } \log (x)}{3 \sqrt{c^2 x^2+1}}","\frac{5}{2} \pi ^2 c^4 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)-\frac{5 \pi  c^2 \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 x}-\frac{\left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^3}+\frac{5 \pi ^{5/2} c^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b}-\frac{1}{4} \pi ^{5/2} b c^5 x^2+\frac{7}{3} \pi ^{5/2} b c^3 \log (x)-\frac{\pi ^{5/2} b c}{6 x^2}",1,"-(b*c*Pi^2*Sqrt[Pi + c^2*Pi*x^2])/(6*x^2*Sqrt[1 + c^2*x^2]) - (b*c^5*Pi^2*x^2*Sqrt[Pi + c^2*Pi*x^2])/(4*Sqrt[1 + c^2*x^2]) + (5*c^4*Pi^2*x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/2 - (5*c^2*Pi*(Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*x) - ((Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(3*x^3) + (5*c^3*Pi^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*Sqrt[1 + c^2*x^2]) + (7*b*c^3*Pi^2*Sqrt[Pi + c^2*Pi*x^2]*Log[x])/(3*Sqrt[1 + c^2*x^2])","A",10,7,26,0.2692,1,"{5739, 5682, 5675, 30, 14, 266, 43}"
79,1,32,0,0.0302964,"\int \sqrt{1+x^2} \sinh ^{-1}(x) \, dx","Int[Sqrt[1 + x^2]*ArcSinh[x],x]","-\frac{x^2}{4}+\frac{1}{2} \sqrt{x^2+1} x \sinh ^{-1}(x)+\frac{1}{4} \sinh ^{-1}(x)^2","-\frac{x^2}{4}+\frac{1}{2} \sqrt{x^2+1} x \sinh ^{-1}(x)+\frac{1}{4} \sinh ^{-1}(x)^2",1,"-x^2/4 + (x*Sqrt[1 + x^2]*ArcSinh[x])/2 + ArcSinh[x]^2/4","A",3,3,12,0.2500,1,"{5682, 5675, 30}"
80,1,215,0,0.2570346,"\int \frac{x^5 \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{\pi +c^2 \pi  x^2}} \, dx","Int[(x^5*(a + b*ArcSinh[c*x]))/Sqrt[Pi + c^2*Pi*x^2],x]","\frac{x^4 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{5 \pi  c^2}-\frac{4 x^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{15 \pi  c^4}+\frac{8 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{15 \pi  c^6}-\frac{b x^5 \sqrt{c^2 x^2+1}}{25 c \sqrt{\pi  c^2 x^2+\pi }}+\frac{4 b x^3 \sqrt{c^2 x^2+1}}{45 c^3 \sqrt{\pi  c^2 x^2+\pi }}-\frac{8 b x \sqrt{c^2 x^2+1}}{15 c^5 \sqrt{\pi  c^2 x^2+\pi }}","\frac{x^4 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{5 \pi  c^2}-\frac{4 x^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{15 \pi  c^4}+\frac{8 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{15 \pi  c^6}+\frac{4 b x^3}{45 \sqrt{\pi } c^3}-\frac{8 b x}{15 \sqrt{\pi } c^5}-\frac{b x^5}{25 \sqrt{\pi } c}",1,"(-8*b*x*Sqrt[1 + c^2*x^2])/(15*c^5*Sqrt[Pi + c^2*Pi*x^2]) + (4*b*x^3*Sqrt[1 + c^2*x^2])/(45*c^3*Sqrt[Pi + c^2*Pi*x^2]) - (b*x^5*Sqrt[1 + c^2*x^2])/(25*c*Sqrt[Pi + c^2*Pi*x^2]) + (8*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(15*c^6*Pi) - (4*x^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(15*c^4*Pi) + (x^4*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(5*c^2*Pi)","A",6,4,26,0.1538,1,"{5758, 5717, 8, 30}"
81,1,170,0,0.226495,"\int \frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{\pi +c^2 \pi  x^2}} \, dx","Int[(x^4*(a + b*ArcSinh[c*x]))/Sqrt[Pi + c^2*Pi*x^2],x]","\frac{x^3 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{4 \pi  c^2}-\frac{3 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{8 \pi  c^4}+\frac{3 \left(a+b \sinh ^{-1}(c x)\right)^2}{16 \sqrt{\pi } b c^5}-\frac{b x^4 \sqrt{c^2 x^2+1}}{16 c \sqrt{\pi  c^2 x^2+\pi }}+\frac{3 b x^2 \sqrt{c^2 x^2+1}}{16 c^3 \sqrt{\pi  c^2 x^2+\pi }}","\frac{x^3 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{4 \pi  c^2}-\frac{3 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{8 \pi  c^4}+\frac{3 \left(a+b \sinh ^{-1}(c x)\right)^2}{16 \sqrt{\pi } b c^5}+\frac{3 b x^2}{16 \sqrt{\pi } c^3}-\frac{b x^4}{16 \sqrt{\pi } c}",1,"(3*b*x^2*Sqrt[1 + c^2*x^2])/(16*c^3*Sqrt[Pi + c^2*Pi*x^2]) - (b*x^4*Sqrt[1 + c^2*x^2])/(16*c*Sqrt[Pi + c^2*Pi*x^2]) - (3*x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(8*c^4*Pi) + (x^3*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(4*c^2*Pi) + (3*(a + b*ArcSinh[c*x])^2)/(16*b*c^5*Sqrt[Pi])","A",5,3,26,0.1154,1,"{5758, 5675, 30}"
82,1,142,0,0.1572919,"\int \frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{\pi +c^2 \pi  x^2}} \, dx","Int[(x^3*(a + b*ArcSinh[c*x]))/Sqrt[Pi + c^2*Pi*x^2],x]","\frac{x^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  c^2}-\frac{2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  c^4}-\frac{b x^3 \sqrt{c^2 x^2+1}}{9 c \sqrt{\pi  c^2 x^2+\pi }}+\frac{2 b x \sqrt{c^2 x^2+1}}{3 c^3 \sqrt{\pi  c^2 x^2+\pi }}","\frac{x^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  c^2}-\frac{2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  c^4}+\frac{2 b x}{3 \sqrt{\pi } c^3}-\frac{b x^3}{9 \sqrt{\pi } c}",1,"(2*b*x*Sqrt[1 + c^2*x^2])/(3*c^3*Sqrt[Pi + c^2*Pi*x^2]) - (b*x^3*Sqrt[1 + c^2*x^2])/(9*c*Sqrt[Pi + c^2*Pi*x^2]) - (2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(3*c^4*Pi) + (x^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(3*c^2*Pi)","A",4,4,26,0.1538,1,"{5758, 5717, 8, 30}"
83,1,97,0,0.1214906,"\int \frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{\pi +c^2 \pi  x^2}} \, dx","Int[(x^2*(a + b*ArcSinh[c*x]))/Sqrt[Pi + c^2*Pi*x^2],x]","\frac{x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{2 \pi  c^2}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{4 \sqrt{\pi } b c^3}-\frac{b x^2 \sqrt{c^2 x^2+1}}{4 c \sqrt{\pi  c^2 x^2+\pi }}","\frac{x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{2 \pi  c^2}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{4 \sqrt{\pi } b c^3}-\frac{b x^2}{4 \sqrt{\pi } c}",1,"-(b*x^2*Sqrt[1 + c^2*x^2])/(4*c*Sqrt[Pi + c^2*Pi*x^2]) + (x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(2*c^2*Pi) - (a + b*ArcSinh[c*x])^2/(4*b*c^3*Sqrt[Pi])","A",3,3,26,0.1154,1,"{5758, 5675, 30}"
84,1,64,0,0.0646801,"\int \frac{x \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{\pi +c^2 \pi  x^2}} \, dx","Int[(x*(a + b*ArcSinh[c*x]))/Sqrt[Pi + c^2*Pi*x^2],x]","\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{\pi  c^2}-\frac{b x \sqrt{c^2 x^2+1}}{c \sqrt{\pi  c^2 x^2+\pi }}","\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{\pi  c^2}-\frac{b x}{\sqrt{\pi } c}",1,"-((b*x*Sqrt[1 + c^2*x^2])/(c*Sqrt[Pi + c^2*Pi*x^2])) + (Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(c^2*Pi)","A",2,2,24,0.08333,1,"{5717, 8}"
85,1,25,0,0.029716,"\int \frac{a+b \sinh ^{-1}(c x)}{\sqrt{\pi +c^2 \pi  x^2}} \, dx","Int[(a + b*ArcSinh[c*x])/Sqrt[Pi + c^2*Pi*x^2],x]","\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 \sqrt{\pi } b c}","\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 \sqrt{\pi } b c}",1,"(a + b*ArcSinh[c*x])^2/(2*b*c*Sqrt[Pi])","A",1,1,23,0.04348,1,"{5675}"
86,1,56,0,0.1190539,"\int \frac{a+b \sinh ^{-1}(c x)}{x \sqrt{\pi +c^2 \pi  x^2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x*Sqrt[Pi + c^2*Pi*x^2]),x]","-\frac{b \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{\pi }}+\frac{b \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{\pi }}-\frac{2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{\pi }}","-\frac{b \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{\pi }}+\frac{b \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{\pi }}-\frac{2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{\pi }}",1,"(-2*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Sqrt[Pi] - (b*PolyLog[2, -E^ArcSinh[c*x]])/Sqrt[Pi] + (b*PolyLog[2, E^ArcSinh[c*x]])/Sqrt[Pi]","A",6,4,26,0.1538,1,"{5760, 4182, 2279, 2391}"
87,1,63,0,0.0882457,"\int \frac{a+b \sinh ^{-1}(c x)}{x^2 \sqrt{\pi +c^2 \pi  x^2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^2*Sqrt[Pi + c^2*Pi*x^2]),x]","\frac{b c \sqrt{c^2 x^2+1} \log (x)}{\sqrt{\pi  c^2 x^2+\pi }}-\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{\pi  x}","\frac{b c \log (x)}{\sqrt{\pi }}-\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{\pi  x}",1,"-((Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(Pi*x)) + (b*c*Sqrt[1 + c^2*x^2]*Log[x])/Sqrt[Pi + c^2*Pi*x^2]","A",2,2,26,0.07692,1,"{5723, 29}"
88,1,137,0,0.2131718,"\int \frac{a+b \sinh ^{-1}(c x)}{x^3 \sqrt{\pi +c^2 \pi  x^2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^3*Sqrt[Pi + c^2*Pi*x^2]),x]","\frac{b c^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{\pi }}-\frac{b c^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{\pi }}-\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{2 \pi  x^2}+\frac{c^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{\pi }}-\frac{b c \sqrt{c^2 x^2+1}}{2 x \sqrt{\pi  c^2 x^2+\pi }}","\frac{b c^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{\pi }}-\frac{b c^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{\pi }}-\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{2 \pi  x^2}+\frac{c^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{\pi }}-\frac{b c}{2 \sqrt{\pi } x}",1,"-(b*c*Sqrt[1 + c^2*x^2])/(2*x*Sqrt[Pi + c^2*Pi*x^2]) - (Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(2*Pi*x^2) + (c^2*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Sqrt[Pi] + (b*c^2*PolyLog[2, -E^ArcSinh[c*x]])/(2*Sqrt[Pi]) - (b*c^2*PolyLog[2, E^ArcSinh[c*x]])/(2*Sqrt[Pi])","A",8,6,26,0.2308,1,"{5747, 5760, 4182, 2279, 2391, 30}"
89,1,141,0,0.181917,"\int \frac{a+b \sinh ^{-1}(c x)}{x^4 \sqrt{\pi +c^2 \pi  x^2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^4*Sqrt[Pi + c^2*Pi*x^2]),x]","\frac{2 c^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  x}-\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  x^3}-\frac{b c \sqrt{c^2 x^2+1}}{6 x^2 \sqrt{\pi  c^2 x^2+\pi }}-\frac{2 b c^3 \sqrt{c^2 x^2+1} \log (x)}{3 \sqrt{\pi  c^2 x^2+\pi }}","\frac{2 c^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  x}-\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  x^3}-\frac{2 b c^3 \log (x)}{3 \sqrt{\pi }}-\frac{b c}{6 \sqrt{\pi } x^2}",1,"-(b*c*Sqrt[1 + c^2*x^2])/(6*x^2*Sqrt[Pi + c^2*Pi*x^2]) - (Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(3*Pi*x^3) + (2*c^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(3*Pi*x) - (2*b*c^3*Sqrt[1 + c^2*x^2]*Log[x])/(3*Sqrt[Pi + c^2*Pi*x^2])","A",4,4,26,0.1538,1,"{5747, 5723, 29, 30}"
90,1,140,0,0.1723021,"\int \frac{x^5 \left(a+b \sinh ^{-1}(c x)\right)}{\left(\pi +c^2 \pi  x^2\right)^{3/2}} \, dx","Int[(x^5*(a + b*ArcSinh[c*x]))/(Pi + c^2*Pi*x^2)^(3/2),x]","\frac{\left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^{3/2} c^6}-\frac{2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^{3/2} c^6}-\frac{a+b \sinh ^{-1}(c x)}{\pi ^{3/2} c^6 \sqrt{c^2 x^2+1}}-\frac{b x^3}{9 \pi ^{3/2} c^3}+\frac{5 b x}{3 \pi ^{3/2} c^5}+\frac{b \tan ^{-1}(c x)}{\pi ^{3/2} c^6}","\frac{\left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^3 c^6}-\frac{2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^2 c^6}-\frac{a+b \sinh ^{-1}(c x)}{\pi  c^6 \sqrt{\pi  c^2 x^2+\pi }}-\frac{b x^3}{9 \pi ^{3/2} c^3}+\frac{5 b x}{3 \pi ^{3/2} c^5}+\frac{b \tan ^{-1}(c x)}{\pi ^{3/2} c^6}",1,"(5*b*x)/(3*c^5*Pi^(3/2)) - (b*x^3)/(9*c^3*Pi^(3/2)) - (a + b*ArcSinh[c*x])/(c^6*Pi^(3/2)*Sqrt[1 + c^2*x^2]) - (2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(c^6*Pi^(3/2)) + ((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*c^6*Pi^(3/2)) + (b*ArcTan[c*x])/(c^6*Pi^(3/2))","A",4,5,26,0.1923,1,"{266, 43, 5732, 1153, 205}"
91,1,181,0,0.2574673,"\int \frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)}{\left(\pi +c^2 \pi  x^2\right)^{3/2}} \, dx","Int[(x^4*(a + b*ArcSinh[c*x]))/(Pi + c^2*Pi*x^2)^(3/2),x]","-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{\pi  c^2 \sqrt{\pi  c^2 x^2+\pi }}+\frac{3 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{2 \pi ^2 c^4}-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 \pi ^{3/2} b c^5}-\frac{b x^2 \sqrt{c^2 x^2+1}}{4 \pi  c^3 \sqrt{\pi  c^2 x^2+\pi }}-\frac{b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{2 \pi  c^5 \sqrt{\pi  c^2 x^2+\pi }}","-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{\pi  c^2 \sqrt{\pi  c^2 x^2+\pi }}+\frac{3 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{2 \pi ^2 c^4}-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 \pi ^{3/2} b c^5}-\frac{b x^2}{4 \pi ^{3/2} c^3}-\frac{b \log \left(c^2 x^2+1\right)}{2 \pi ^{3/2} c^5}",1,"-(b*x^2*Sqrt[1 + c^2*x^2])/(4*c^3*Pi*Sqrt[Pi + c^2*Pi*x^2]) - (x^3*(a + b*ArcSinh[c*x]))/(c^2*Pi*Sqrt[Pi + c^2*Pi*x^2]) + (3*x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(2*c^4*Pi^2) - (3*(a + b*ArcSinh[c*x])^2)/(4*b*c^5*Pi^(3/2)) - (b*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(2*c^5*Pi*Sqrt[Pi + c^2*Pi*x^2])","A",7,6,26,0.2308,1,"{5751, 5758, 5675, 30, 266, 43}"
92,1,88,0,0.1424524,"\int \frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{\left(\pi +c^2 \pi  x^2\right)^{3/2}} \, dx","Int[(x^3*(a + b*ArcSinh[c*x]))/(Pi + c^2*Pi*x^2)^(3/2),x]","\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^{3/2} c^4}+\frac{a+b \sinh ^{-1}(c x)}{\pi ^{3/2} c^4 \sqrt{c^2 x^2+1}}-\frac{b x}{\pi ^{3/2} c^3}-\frac{b \tan ^{-1}(c x)}{\pi ^{3/2} c^4}","\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^2 c^4}+\frac{a+b \sinh ^{-1}(c x)}{\pi  c^4 \sqrt{\pi  c^2 x^2+\pi }}-\frac{b x}{\pi ^{3/2} c^3}-\frac{b \tan ^{-1}(c x)}{\pi ^{3/2} c^4}",1,"-((b*x)/(c^3*Pi^(3/2))) + (a + b*ArcSinh[c*x])/(c^4*Pi^(3/2)*Sqrt[1 + c^2*x^2]) + (Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(c^4*Pi^(3/2)) - (b*ArcTan[c*x])/(c^4*Pi^(3/2))","A",3,5,26,0.1923,1,"{266, 43, 5732, 388, 205}"
93,1,105,0,0.1395212,"\int \frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)}{\left(\pi +c^2 \pi  x^2\right)^{3/2}} \, dx","Int[(x^2*(a + b*ArcSinh[c*x]))/(Pi + c^2*Pi*x^2)^(3/2),x]","-\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{\pi  c^2 \sqrt{\pi  c^2 x^2+\pi }}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 \pi ^{3/2} b c^3}+\frac{b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{2 \pi  c^3 \sqrt{\pi  c^2 x^2+\pi }}","-\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{\pi  c^2 \sqrt{\pi  c^2 x^2+\pi }}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 \pi ^{3/2} b c^3}+\frac{b \log \left(c^2 x^2+1\right)}{2 \pi ^{3/2} c^3}",1,"-((x*(a + b*ArcSinh[c*x]))/(c^2*Pi*Sqrt[Pi + c^2*Pi*x^2])) + (a + b*ArcSinh[c*x])^2/(2*b*c^3*Pi^(3/2)) + (b*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(2*c^3*Pi*Sqrt[Pi + c^2*Pi*x^2])","A",3,3,26,0.1154,1,"{5751, 5675, 260}"
94,1,70,0,0.0723462,"\int \frac{x \left(a+b \sinh ^{-1}(c x)\right)}{\left(\pi +c^2 \pi  x^2\right)^{3/2}} \, dx","Int[(x*(a + b*ArcSinh[c*x]))/(Pi + c^2*Pi*x^2)^(3/2),x]","\frac{b \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{\pi  c^2 \sqrt{\pi  c^2 x^2+\pi }}-\frac{a+b \sinh ^{-1}(c x)}{\pi  c^2 \sqrt{\pi  c^2 x^2+\pi }}","\frac{b \tan ^{-1}(c x)}{\pi ^{3/2} c^2}-\frac{a+b \sinh ^{-1}(c x)}{\pi  c^2 \sqrt{\pi  c^2 x^2+\pi }}",1,"-((a + b*ArcSinh[c*x])/(c^2*Pi*Sqrt[Pi + c^2*Pi*x^2])) + (b*Sqrt[1 + c^2*x^2]*ArcTan[c*x])/(c^2*Pi*Sqrt[Pi + c^2*Pi*x^2])","A",2,2,24,0.08333,1,"{5717, 203}"
95,1,76,0,0.0388463,"\int \frac{a+b \sinh ^{-1}(c x)}{\left(\pi +c^2 \pi  x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(Pi + c^2*Pi*x^2)^(3/2),x]","\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{\pi  \sqrt{\pi  c^2 x^2+\pi }}-\frac{b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{2 \pi  c \sqrt{\pi  c^2 x^2+\pi }}","\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{\pi  \sqrt{\pi  c^2 x^2+\pi }}-\frac{b \log \left(c^2 x^2+1\right)}{2 \pi ^{3/2} c}",1,"(x*(a + b*ArcSinh[c*x]))/(Pi*Sqrt[Pi + c^2*Pi*x^2]) - (b*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(2*c*Pi*Sqrt[Pi + c^2*Pi*x^2])","A",2,2,23,0.08696,1,"{5687, 260}"
96,1,119,0,0.2219588,"\int \frac{a+b \sinh ^{-1}(c x)}{x \left(\pi +c^2 \pi  x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x*(Pi + c^2*Pi*x^2)^(3/2)),x]","-\frac{b \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\pi ^{3/2}}+\frac{b \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\pi ^{3/2}}+\frac{a+b \sinh ^{-1}(c x)}{\pi  \sqrt{\pi  c^2 x^2+\pi }}-\frac{2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^{3/2}}-\frac{b \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{\pi  \sqrt{\pi  c^2 x^2+\pi }}","-\frac{b \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\pi ^{3/2}}+\frac{b \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\pi ^{3/2}}+\frac{a+b \sinh ^{-1}(c x)}{\pi  \sqrt{\pi  c^2 x^2+\pi }}-\frac{2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^{3/2}}-\frac{b \tan ^{-1}(c x)}{\pi ^{3/2}}",1,"(a + b*ArcSinh[c*x])/(Pi*Sqrt[Pi + c^2*Pi*x^2]) - (b*Sqrt[1 + c^2*x^2]*ArcTan[c*x])/(Pi*Sqrt[Pi + c^2*Pi*x^2]) - (2*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Pi^(3/2) - (b*PolyLog[2, -E^ArcSinh[c*x]])/Pi^(3/2) + (b*PolyLog[2, E^ArcSinh[c*x]])/Pi^(3/2)","A",8,6,26,0.2308,1,"{5755, 5760, 4182, 2279, 2391, 203}"
97,1,95,0,0.1383607,"\int \frac{a+b \sinh ^{-1}(c x)}{x^2 \left(\pi +c^2 \pi  x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^2*(Pi + c^2*Pi*x^2)^(3/2)),x]","-\frac{2 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^{3/2} \sqrt{c^2 x^2+1}}-\frac{a+b \sinh ^{-1}(c x)}{\pi ^{3/2} x \sqrt{c^2 x^2+1}}+\frac{b c \log \left(c^2 x^2+1\right)}{2 \pi ^{3/2}}+\frac{b c \log (x)}{\pi ^{3/2}}","-\frac{2 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{\pi  \sqrt{\pi  c^2 x^2+\pi }}-\frac{a+b \sinh ^{-1}(c x)}{\pi  x \sqrt{\pi  c^2 x^2+\pi }}+\frac{b c \log \left(c^2 x^2+1\right)}{2 \pi ^{3/2}}+\frac{b c \log (x)}{\pi ^{3/2}}",1,"-((a + b*ArcSinh[c*x])/(Pi^(3/2)*x*Sqrt[1 + c^2*x^2])) - (2*c^2*x*(a + b*ArcSinh[c*x]))/(Pi^(3/2)*Sqrt[1 + c^2*x^2]) + (b*c*Log[x])/Pi^(3/2) + (b*c*Log[1 + c^2*x^2])/(2*Pi^(3/2))","A",4,5,26,0.1923,1,"{271, 191, 5732, 446, 72}"
98,1,212,0,0.3503367,"\int \frac{a+b \sinh ^{-1}(c x)}{x^3 \left(\pi +c^2 \pi  x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^3*(Pi + c^2*Pi*x^2)^(3/2)),x]","\frac{3 b c^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \pi ^{3/2}}-\frac{3 b c^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \pi ^{3/2}}-\frac{3 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 \pi  \sqrt{\pi  c^2 x^2+\pi }}-\frac{a+b \sinh ^{-1}(c x)}{2 \pi  x^2 \sqrt{\pi  c^2 x^2+\pi }}+\frac{3 c^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^{3/2}}-\frac{b c \sqrt{c^2 x^2+1}}{2 \pi  x \sqrt{\pi  c^2 x^2+\pi }}+\frac{b c^2 \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{\pi  \sqrt{\pi  c^2 x^2+\pi }}","\frac{3 b c^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \pi ^{3/2}}-\frac{3 b c^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \pi ^{3/2}}-\frac{3 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 \pi  \sqrt{\pi  c^2 x^2+\pi }}-\frac{a+b \sinh ^{-1}(c x)}{2 \pi  x^2 \sqrt{\pi  c^2 x^2+\pi }}+\frac{3 c^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^{3/2}}+\frac{b c^2 \tan ^{-1}(c x)}{\pi ^{3/2}}-\frac{b c}{2 \pi ^{3/2} x}",1,"-(b*c*Sqrt[1 + c^2*x^2])/(2*Pi*x*Sqrt[Pi + c^2*Pi*x^2]) - (3*c^2*(a + b*ArcSinh[c*x]))/(2*Pi*Sqrt[Pi + c^2*Pi*x^2]) - (a + b*ArcSinh[c*x])/(2*Pi*x^2*Sqrt[Pi + c^2*Pi*x^2]) + (b*c^2*Sqrt[1 + c^2*x^2]*ArcTan[c*x])/(Pi*Sqrt[Pi + c^2*Pi*x^2]) + (3*c^2*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Pi^(3/2) + (3*b*c^2*PolyLog[2, -E^ArcSinh[c*x]])/(2*Pi^(3/2)) - (3*b*c^2*PolyLog[2, E^ArcSinh[c*x]])/(2*Pi^(3/2))","A",11,8,26,0.3077,1,"{5747, 5755, 5760, 4182, 2279, 2391, 203, 325}"
99,1,156,0,0.1750093,"\int \frac{a+b \sinh ^{-1}(c x)}{x^4 \left(\pi +c^2 \pi  x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^4*(Pi + c^2*Pi*x^2)^(3/2)),x]","\frac{8 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^{3/2} \sqrt{c^2 x^2+1}}+\frac{4 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^{3/2} x \sqrt{c^2 x^2+1}}-\frac{a+b \sinh ^{-1}(c x)}{3 \pi ^{3/2} x^3 \sqrt{c^2 x^2+1}}-\frac{b c^3 \log \left(c^2 x^2+1\right)}{2 \pi ^{3/2}}-\frac{5 b c^3 \log (x)}{3 \pi ^{3/2}}-\frac{b c}{6 \pi ^{3/2} x^2}","\frac{8 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  \sqrt{\pi  c^2 x^2+\pi }}+\frac{4 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  x \sqrt{\pi  c^2 x^2+\pi }}-\frac{a+b \sinh ^{-1}(c x)}{3 \pi  x^3 \sqrt{\pi  c^2 x^2+\pi }}-\frac{b c^3 \log \left(c^2 x^2+1\right)}{2 \pi ^{3/2}}-\frac{5 b c^3 \log (x)}{3 \pi ^{3/2}}-\frac{b c}{6 \pi ^{3/2} x^2}",1,"-(b*c)/(6*Pi^(3/2)*x^2) - (a + b*ArcSinh[c*x])/(3*Pi^(3/2)*x^3*Sqrt[1 + c^2*x^2]) + (4*c^2*(a + b*ArcSinh[c*x]))/(3*Pi^(3/2)*x*Sqrt[1 + c^2*x^2]) + (8*c^4*x*(a + b*ArcSinh[c*x]))/(3*Pi^(3/2)*Sqrt[1 + c^2*x^2]) - (5*b*c^3*Log[x])/(3*Pi^(3/2)) - (b*c^3*Log[1 + c^2*x^2])/(2*Pi^(3/2))","A",5,6,26,0.2308,1,"{271, 191, 5732, 12, 1251, 893}"
100,1,256,0,0.4252046,"\int \frac{x^6 \left(a+b \sinh ^{-1}(c x)\right)}{\left(\pi +c^2 \pi  x^2\right)^{5/2}} \, dx","Int[(x^6*(a + b*ArcSinh[c*x]))/(Pi + c^2*Pi*x^2)^(5/2),x]","-\frac{x^5 \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  c^2 \left(\pi  c^2 x^2+\pi \right)^{3/2}}-\frac{5 x^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^2 c^4 \sqrt{\pi  c^2 x^2+\pi }}+\frac{5 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{2 \pi ^3 c^6}-\frac{5 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 \pi ^{5/2} b c^7}-\frac{b x^2 \sqrt{c^2 x^2+1}}{4 \pi ^2 c^5 \sqrt{\pi  c^2 x^2+\pi }}-\frac{b}{6 \pi ^2 c^7 \sqrt{c^2 x^2+1} \sqrt{\pi  c^2 x^2+\pi }}-\frac{7 b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{6 \pi ^2 c^7 \sqrt{\pi  c^2 x^2+\pi }}","-\frac{x^5 \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  c^2 \left(\pi  c^2 x^2+\pi \right)^{3/2}}-\frac{5 x^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^2 c^4 \sqrt{\pi  c^2 x^2+\pi }}+\frac{5 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{2 \pi ^3 c^6}-\frac{5 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 \pi ^{5/2} b c^7}-\frac{b x^2}{4 \pi ^{5/2} c^5}-\frac{b}{6 \pi ^{5/2} c^7 \left(c^2 x^2+1\right)}-\frac{7 b \log \left(c^2 x^2+1\right)}{6 \pi ^{5/2} c^7}",1,"-b/(6*c^7*Pi^2*Sqrt[1 + c^2*x^2]*Sqrt[Pi + c^2*Pi*x^2]) - (b*x^2*Sqrt[1 + c^2*x^2])/(4*c^5*Pi^2*Sqrt[Pi + c^2*Pi*x^2]) - (x^5*(a + b*ArcSinh[c*x]))/(3*c^2*Pi*(Pi + c^2*Pi*x^2)^(3/2)) - (5*x^3*(a + b*ArcSinh[c*x]))/(3*c^4*Pi^2*Sqrt[Pi + c^2*Pi*x^2]) + (5*x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(2*c^6*Pi^3) - (5*(a + b*ArcSinh[c*x])^2)/(4*b*c^7*Pi^(5/2)) - (7*b*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(6*c^7*Pi^2*Sqrt[Pi + c^2*Pi*x^2])","A",11,6,26,0.2308,1,"{5751, 5758, 5675, 30, 266, 43}"
101,1,149,0,0.1814573,"\int \frac{x^5 \left(a+b \sinh ^{-1}(c x)\right)}{\left(\pi +c^2 \pi  x^2\right)^{5/2}} \, dx","Int[(x^5*(a + b*ArcSinh[c*x]))/(Pi + c^2*Pi*x^2)^(5/2),x]","\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^{5/2} c^6}+\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^{5/2} c^6 \sqrt{c^2 x^2+1}}-\frac{a+b \sinh ^{-1}(c x)}{3 \pi ^{5/2} c^6 \left(c^2 x^2+1\right)^{3/2}}+\frac{b x}{6 \pi ^{5/2} c^5 \left(c^2 x^2+1\right)}-\frac{b x}{\pi ^{5/2} c^5}-\frac{11 b \tan ^{-1}(c x)}{6 \pi ^{5/2} c^6}","\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^3 c^6}+\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^2 c^6 \sqrt{\pi  c^2 x^2+\pi }}-\frac{a+b \sinh ^{-1}(c x)}{3 \pi  c^6 \left(\pi  c^2 x^2+\pi \right)^{3/2}}+\frac{b x}{6 \pi ^{5/2} c^5 \left(c^2 x^2+1\right)}-\frac{b x}{\pi ^{5/2} c^5}-\frac{11 b \tan ^{-1}(c x)}{6 \pi ^{5/2} c^6}",1,"-((b*x)/(c^5*Pi^(5/2))) + (b*x)/(6*c^5*Pi^(5/2)*(1 + c^2*x^2)) - (a + b*ArcSinh[c*x])/(3*c^6*Pi^(5/2)*(1 + c^2*x^2)^(3/2)) + (2*(a + b*ArcSinh[c*x]))/(c^6*Pi^(5/2)*Sqrt[1 + c^2*x^2]) + (Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(c^6*Pi^(5/2)) - (11*b*ArcTan[c*x])/(6*c^6*Pi^(5/2))","A",5,7,26,0.2692,1,"{266, 43, 5732, 12, 1157, 388, 203}"
102,1,178,0,0.2828238,"\int \frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)}{\left(\pi +c^2 \pi  x^2\right)^{5/2}} \, dx","Int[(x^4*(a + b*ArcSinh[c*x]))/(Pi + c^2*Pi*x^2)^(5/2),x]","-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  c^2 \left(\pi  c^2 x^2+\pi \right)^{3/2}}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^2 c^4 \sqrt{\pi  c^2 x^2+\pi }}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 \pi ^{5/2} b c^5}+\frac{b}{6 \pi ^2 c^5 \sqrt{c^2 x^2+1} \sqrt{\pi  c^2 x^2+\pi }}+\frac{2 b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{3 \pi ^2 c^5 \sqrt{\pi  c^2 x^2+\pi }}","-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  c^2 \left(\pi  c^2 x^2+\pi \right)^{3/2}}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^2 c^4 \sqrt{\pi  c^2 x^2+\pi }}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 \pi ^{5/2} b c^5}+\frac{b}{6 \pi ^{5/2} c^5 \left(c^2 x^2+1\right)}+\frac{2 b \log \left(c^2 x^2+1\right)}{3 \pi ^{5/2} c^5}",1,"b/(6*c^5*Pi^2*Sqrt[1 + c^2*x^2]*Sqrt[Pi + c^2*Pi*x^2]) - (x^3*(a + b*ArcSinh[c*x]))/(3*c^2*Pi*(Pi + c^2*Pi*x^2)^(3/2)) - (x*(a + b*ArcSinh[c*x]))/(c^4*Pi^2*Sqrt[Pi + c^2*Pi*x^2]) + (a + b*ArcSinh[c*x])^2/(2*b*c^5*Pi^(5/2)) + (2*b*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(3*c^5*Pi^2*Sqrt[Pi + c^2*Pi*x^2])","A",7,5,26,0.1923,1,"{5751, 5675, 260, 266, 43}"
103,1,107,0,0.1465831,"\int \frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{\left(\pi +c^2 \pi  x^2\right)^{5/2}} \, dx","Int[(x^3*(a + b*ArcSinh[c*x]))/(Pi + c^2*Pi*x^2)^(5/2),x]","-\frac{a+b \sinh ^{-1}(c x)}{\pi ^{5/2} c^4 \sqrt{c^2 x^2+1}}+\frac{a+b \sinh ^{-1}(c x)}{3 \pi ^{5/2} c^4 \left(c^2 x^2+1\right)^{3/2}}-\frac{b x}{6 \pi ^{5/2} c^3 \left(c^2 x^2+1\right)}+\frac{5 b \tan ^{-1}(c x)}{6 \pi ^{5/2} c^4}","-\frac{a+b \sinh ^{-1}(c x)}{\pi ^2 c^4 \sqrt{\pi  c^2 x^2+\pi }}+\frac{a+b \sinh ^{-1}(c x)}{3 \pi  c^4 \left(\pi  c^2 x^2+\pi \right)^{3/2}}-\frac{b x}{6 \pi ^{5/2} c^3 \left(c^2 x^2+1\right)}+\frac{5 b \tan ^{-1}(c x)}{6 \pi ^{5/2} c^4}",1,"-(b*x)/(6*c^3*Pi^(5/2)*(1 + c^2*x^2)) + (a + b*ArcSinh[c*x])/(3*c^4*Pi^(5/2)*(1 + c^2*x^2)^(3/2)) - (a + b*ArcSinh[c*x])/(c^4*Pi^(5/2)*Sqrt[1 + c^2*x^2]) + (5*b*ArcTan[c*x])/(6*c^4*Pi^(5/2))","A",4,6,26,0.2308,1,"{266, 43, 5732, 12, 385, 203}"
104,1,119,0,0.1288638,"\int \frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)}{\left(\pi +c^2 \pi  x^2\right)^{5/2}} \, dx","Int[(x^2*(a + b*ArcSinh[c*x]))/(Pi + c^2*Pi*x^2)^(5/2),x]","\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  \left(\pi  c^2 x^2+\pi \right)^{3/2}}-\frac{b}{6 \pi ^2 c^3 \sqrt{c^2 x^2+1} \sqrt{\pi  c^2 x^2+\pi }}-\frac{b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{6 \pi ^2 c^3 \sqrt{\pi  c^2 x^2+\pi }}","\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  \left(\pi  c^2 x^2+\pi \right)^{3/2}}-\frac{b}{6 \pi ^{5/2} c^3 \left(c^2 x^2+1\right)}-\frac{b \log \left(c^2 x^2+1\right)}{6 \pi ^{5/2} c^3}",1,"-b/(6*c^3*Pi^2*Sqrt[1 + c^2*x^2]*Sqrt[Pi + c^2*Pi*x^2]) + (x^3*(a + b*ArcSinh[c*x]))/(3*Pi*(Pi + c^2*Pi*x^2)^(3/2)) - (b*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(6*c^3*Pi^2*Sqrt[Pi + c^2*Pi*x^2])","A",4,3,26,0.1154,1,"{5723, 266, 43}"
105,1,114,0,0.0802926,"\int \frac{x \left(a+b \sinh ^{-1}(c x)\right)}{\left(\pi +c^2 \pi  x^2\right)^{5/2}} \, dx","Int[(x*(a + b*ArcSinh[c*x]))/(Pi + c^2*Pi*x^2)^(5/2),x]","-\frac{a+b \sinh ^{-1}(c x)}{3 \pi  c^2 \left(\pi  c^2 x^2+\pi \right)^{3/2}}+\frac{b x}{6 \pi ^2 c \sqrt{c^2 x^2+1} \sqrt{\pi  c^2 x^2+\pi }}+\frac{b \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{6 \pi ^2 c^2 \sqrt{\pi  c^2 x^2+\pi }}","-\frac{a+b \sinh ^{-1}(c x)}{3 \pi  c^2 \left(\pi  c^2 x^2+\pi \right)^{3/2}}+\frac{b x}{6 \pi ^{5/2} c \left(c^2 x^2+1\right)}+\frac{b \tan ^{-1}(c x)}{6 \pi ^{5/2} c^2}",1,"(b*x)/(6*c*Pi^2*Sqrt[1 + c^2*x^2]*Sqrt[Pi + c^2*Pi*x^2]) - (a + b*ArcSinh[c*x])/(3*c^2*Pi*(Pi + c^2*Pi*x^2)^(3/2)) + (b*Sqrt[1 + c^2*x^2]*ArcTan[c*x])/(6*c^2*Pi^2*Sqrt[Pi + c^2*Pi*x^2])","A",3,3,24,0.1250,1,"{5717, 199, 203}"
106,1,147,0,0.0873414,"\int \frac{a+b \sinh ^{-1}(c x)}{\left(\pi +c^2 \pi  x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(Pi + c^2*Pi*x^2)^(5/2),x]","\frac{2 x \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^2 \sqrt{\pi  c^2 x^2+\pi }}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  \left(\pi  c^2 x^2+\pi \right)^{3/2}}+\frac{b}{6 \pi ^2 c \sqrt{c^2 x^2+1} \sqrt{\pi  c^2 x^2+\pi }}-\frac{b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{3 \pi ^2 c \sqrt{\pi  c^2 x^2+\pi }}","\frac{2 x \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^2 \sqrt{\pi  c^2 x^2+\pi }}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  \left(\pi  c^2 x^2+\pi \right)^{3/2}}+\frac{b}{6 \pi ^{5/2} c \left(c^2 x^2+1\right)}-\frac{b \log \left(c^2 x^2+1\right)}{3 \pi ^{5/2} c}",1,"b/(6*c*Pi^2*Sqrt[1 + c^2*x^2]*Sqrt[Pi + c^2*Pi*x^2]) + (x*(a + b*ArcSinh[c*x]))/(3*Pi*(Pi + c^2*Pi*x^2)^(3/2)) + (2*x*(a + b*ArcSinh[c*x]))/(3*Pi^2*Sqrt[Pi + c^2*Pi*x^2]) - (b*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(3*c*Pi^2*Sqrt[Pi + c^2*Pi*x^2])","A",4,4,23,0.1739,1,"{5690, 5687, 260, 261}"
107,1,187,0,0.3390606,"\int \frac{a+b \sinh ^{-1}(c x)}{x \left(\pi +c^2 \pi  x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x*(Pi + c^2*Pi*x^2)^(5/2)),x]","-\frac{b \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\pi ^{5/2}}+\frac{b \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\pi ^{5/2}}+\frac{a+b \sinh ^{-1}(c x)}{\pi ^2 \sqrt{\pi  c^2 x^2+\pi }}+\frac{a+b \sinh ^{-1}(c x)}{3 \pi  \left(\pi  c^2 x^2+\pi \right)^{3/2}}-\frac{2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^{5/2}}-\frac{b c x}{6 \pi ^2 \sqrt{c^2 x^2+1} \sqrt{\pi  c^2 x^2+\pi }}-\frac{7 b \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{6 \pi ^2 \sqrt{\pi  c^2 x^2+\pi }}","-\frac{b \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\pi ^{5/2}}+\frac{b \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\pi ^{5/2}}+\frac{a+b \sinh ^{-1}(c x)}{\pi ^2 \sqrt{\pi  c^2 x^2+\pi }}+\frac{a+b \sinh ^{-1}(c x)}{3 \pi  \left(\pi  c^2 x^2+\pi \right)^{3/2}}-\frac{2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^{5/2}}-\frac{b c x}{6 \pi ^{5/2} \left(c^2 x^2+1\right)}-\frac{7 b \tan ^{-1}(c x)}{6 \pi ^{5/2}}",1,"-(b*c*x)/(6*Pi^2*Sqrt[1 + c^2*x^2]*Sqrt[Pi + c^2*Pi*x^2]) + (a + b*ArcSinh[c*x])/(3*Pi*(Pi + c^2*Pi*x^2)^(3/2)) + (a + b*ArcSinh[c*x])/(Pi^2*Sqrt[Pi + c^2*Pi*x^2]) - (7*b*Sqrt[1 + c^2*x^2]*ArcTan[c*x])/(6*Pi^2*Sqrt[Pi + c^2*Pi*x^2]) - (2*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Pi^(5/2) - (b*PolyLog[2, -E^ArcSinh[c*x]])/Pi^(5/2) + (b*PolyLog[2, E^ArcSinh[c*x]])/Pi^(5/2)","A",11,7,26,0.2692,1,"{5755, 5760, 4182, 2279, 2391, 203, 199}"
108,1,153,0,0.1762809,"\int \frac{a+b \sinh ^{-1}(c x)}{x^2 \left(\pi +c^2 \pi  x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^2*(Pi + c^2*Pi*x^2)^(5/2)),x]","-\frac{8 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^{5/2} \sqrt{c^2 x^2+1}}-\frac{4 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^{5/2} \left(c^2 x^2+1\right)^{3/2}}-\frac{a+b \sinh ^{-1}(c x)}{\pi ^{5/2} x \left(c^2 x^2+1\right)^{3/2}}-\frac{b c}{6 \pi ^{5/2} \left(c^2 x^2+1\right)}+\frac{5 b c \log \left(c^2 x^2+1\right)}{6 \pi ^{5/2}}+\frac{b c \log (x)}{\pi ^{5/2}}","-\frac{8 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^2 \sqrt{\pi  c^2 x^2+\pi }}-\frac{4 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  \left(\pi  c^2 x^2+\pi \right)^{3/2}}-\frac{a+b \sinh ^{-1}(c x)}{\pi  x \left(\pi  c^2 x^2+\pi \right)^{3/2}}-\frac{b c}{6 \pi ^{5/2} \left(c^2 x^2+1\right)}+\frac{5 b c \log \left(c^2 x^2+1\right)}{6 \pi ^{5/2}}+\frac{b c \log (x)}{\pi ^{5/2}}",1,"-(b*c)/(6*Pi^(5/2)*(1 + c^2*x^2)) - (a + b*ArcSinh[c*x])/(Pi^(5/2)*x*(1 + c^2*x^2)^(3/2)) - (4*c^2*x*(a + b*ArcSinh[c*x]))/(3*Pi^(5/2)*(1 + c^2*x^2)^(3/2)) - (8*c^2*x*(a + b*ArcSinh[c*x]))/(3*Pi^(5/2)*Sqrt[1 + c^2*x^2]) + (b*c*Log[x])/Pi^(5/2) + (5*b*c*Log[1 + c^2*x^2])/(6*Pi^(5/2))","A",5,7,26,0.2692,1,"{271, 192, 191, 5732, 12, 1251, 893}"
109,1,325,0,0.4751303,"\int \frac{a+b \sinh ^{-1}(c x)}{x^3 \left(\pi +c^2 \pi  x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^3*(Pi + c^2*Pi*x^2)^(5/2)),x]","\frac{5 b c^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \pi ^{5/2}}-\frac{5 b c^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \pi ^{5/2}}-\frac{5 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 \pi ^2 \sqrt{\pi  c^2 x^2+\pi }}-\frac{5 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{6 \pi  \left(\pi  c^2 x^2+\pi \right)^{3/2}}-\frac{a+b \sinh ^{-1}(c x)}{2 \pi  x^2 \left(\pi  c^2 x^2+\pi \right)^{3/2}}+\frac{5 c^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^{5/2}}+\frac{5 b c^3 x}{12 \pi ^2 \sqrt{c^2 x^2+1} \sqrt{\pi  c^2 x^2+\pi }}-\frac{3 b c \sqrt{c^2 x^2+1}}{4 \pi ^2 x \sqrt{\pi  c^2 x^2+\pi }}+\frac{b c}{4 \pi ^2 x \sqrt{c^2 x^2+1} \sqrt{\pi  c^2 x^2+\pi }}+\frac{13 b c^2 \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{6 \pi ^2 \sqrt{\pi  c^2 x^2+\pi }}","\frac{5 b c^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \pi ^{5/2}}-\frac{5 b c^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \pi ^{5/2}}-\frac{5 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 \pi ^2 \sqrt{\pi  c^2 x^2+\pi }}-\frac{5 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{6 \pi  \left(\pi  c^2 x^2+\pi \right)^{3/2}}-\frac{a+b \sinh ^{-1}(c x)}{2 \pi  x^2 \left(\pi  c^2 x^2+\pi \right)^{3/2}}+\frac{5 c^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^{5/2}}+\frac{5 b c^3 x}{12 \pi ^{5/2} \left(c^2 x^2+1\right)}+\frac{b c}{4 \pi ^{5/2} x \left(c^2 x^2+1\right)}+\frac{13 b c^2 \tan ^{-1}(c x)}{6 \pi ^{5/2}}-\frac{3 b c}{4 \pi ^{5/2} x}",1,"(b*c)/(4*Pi^2*x*Sqrt[1 + c^2*x^2]*Sqrt[Pi + c^2*Pi*x^2]) + (5*b*c^3*x)/(12*Pi^2*Sqrt[1 + c^2*x^2]*Sqrt[Pi + c^2*Pi*x^2]) - (3*b*c*Sqrt[1 + c^2*x^2])/(4*Pi^2*x*Sqrt[Pi + c^2*Pi*x^2]) - (5*c^2*(a + b*ArcSinh[c*x]))/(6*Pi*(Pi + c^2*Pi*x^2)^(3/2)) - (a + b*ArcSinh[c*x])/(2*Pi*x^2*(Pi + c^2*Pi*x^2)^(3/2)) - (5*c^2*(a + b*ArcSinh[c*x]))/(2*Pi^2*Sqrt[Pi + c^2*Pi*x^2]) + (13*b*c^2*Sqrt[1 + c^2*x^2]*ArcTan[c*x])/(6*Pi^2*Sqrt[Pi + c^2*Pi*x^2]) + (5*c^2*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Pi^(5/2) + (5*b*c^2*PolyLog[2, -E^ArcSinh[c*x]])/(2*Pi^(5/2)) - (5*b*c^2*PolyLog[2, E^ArcSinh[c*x]])/(2*Pi^(5/2))","A",15,10,26,0.3846,1,"{5747, 5755, 5760, 4182, 2279, 2391, 203, 199, 290, 325}"
110,1,212,0,0.2398774,"\int \frac{a+b \sinh ^{-1}(c x)}{x^4 \left(\pi +c^2 \pi  x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^4*(Pi + c^2*Pi*x^2)^(5/2)),x]","\frac{16 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^{5/2} \sqrt{c^2 x^2+1}}+\frac{8 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^{5/2} \left(c^2 x^2+1\right)^{3/2}}+\frac{2 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^{5/2} x \left(c^2 x^2+1\right)^{3/2}}-\frac{a+b \sinh ^{-1}(c x)}{3 \pi ^{5/2} x^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{b c^3}{6 \pi ^{5/2} \left(c^2 x^2+1\right)}-\frac{4 b c^3 \log \left(c^2 x^2+1\right)}{3 \pi ^{5/2}}-\frac{8 b c^3 \log (x)}{3 \pi ^{5/2}}-\frac{b c}{6 \pi ^{5/2} x^2}","\frac{16 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^2 \sqrt{\pi  c^2 x^2+\pi }}+\frac{8 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi  \left(\pi  c^2 x^2+\pi \right)^{3/2}}+\frac{2 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{\pi  x \left(\pi  c^2 x^2+\pi \right)^{3/2}}-\frac{a+b \sinh ^{-1}(c x)}{3 \pi  x^3 \left(\pi  c^2 x^2+\pi \right)^{3/2}}+\frac{b c^3}{6 \pi ^{5/2} \left(c^2 x^2+1\right)}-\frac{4 b c^3 \log \left(c^2 x^2+1\right)}{3 \pi ^{5/2}}-\frac{8 b c^3 \log (x)}{3 \pi ^{5/2}}-\frac{b c}{6 \pi ^{5/2} x^2}",1,"-(b*c)/(6*Pi^(5/2)*x^2) + (b*c^3)/(6*Pi^(5/2)*(1 + c^2*x^2)) - (a + b*ArcSinh[c*x])/(3*Pi^(5/2)*x^3*(1 + c^2*x^2)^(3/2)) + (2*c^2*(a + b*ArcSinh[c*x]))/(Pi^(5/2)*x*(1 + c^2*x^2)^(3/2)) + (8*c^4*x*(a + b*ArcSinh[c*x]))/(3*Pi^(5/2)*(1 + c^2*x^2)^(3/2)) + (16*c^4*x*(a + b*ArcSinh[c*x]))/(3*Pi^(5/2)*Sqrt[1 + c^2*x^2]) - (8*b*c^3*Log[x])/(3*Pi^(5/2)) - (4*b*c^3*Log[1 + c^2*x^2])/(3*Pi^(5/2))","A",5,7,26,0.2692,1,"{271, 192, 191, 5732, 12, 1799, 1620}"
111,1,200,0,0.1229903,"\int \frac{\sinh ^{-1}(a x)}{\left(c+a^2 c x^2\right)^{7/2}} \, dx","Int[ArcSinh[a*x]/(c + a^2*c*x^2)^(7/2),x]","\frac{2}{15 a c^3 \sqrt{a^2 x^2+1} \sqrt{a^2 c x^2+c}}+\frac{1}{20 a c^3 \left(a^2 x^2+1\right)^{3/2} \sqrt{a^2 c x^2+c}}-\frac{4 \sqrt{a^2 x^2+1} \log \left(a^2 x^2+1\right)}{15 a c^3 \sqrt{a^2 c x^2+c}}+\frac{8 x \sinh ^{-1}(a x)}{15 c^3 \sqrt{a^2 c x^2+c}}+\frac{4 x \sinh ^{-1}(a x)}{15 c^2 \left(a^2 c x^2+c\right)^{3/2}}+\frac{x \sinh ^{-1}(a x)}{5 c \left(a^2 c x^2+c\right)^{5/2}}","\frac{2}{15 a c^3 \sqrt{a^2 x^2+1} \sqrt{a^2 c x^2+c}}+\frac{1}{20 a c^3 \left(a^2 x^2+1\right)^{3/2} \sqrt{a^2 c x^2+c}}-\frac{4 \sqrt{a^2 x^2+1} \log \left(a^2 x^2+1\right)}{15 a c^3 \sqrt{a^2 c x^2+c}}+\frac{8 x \sinh ^{-1}(a x)}{15 c^3 \sqrt{a^2 c x^2+c}}+\frac{4 x \sinh ^{-1}(a x)}{15 c^2 \left(a^2 c x^2+c\right)^{3/2}}+\frac{x \sinh ^{-1}(a x)}{5 c \left(a^2 c x^2+c\right)^{5/2}}",1,"1/(20*a*c^3*(1 + a^2*x^2)^(3/2)*Sqrt[c + a^2*c*x^2]) + 2/(15*a*c^3*Sqrt[1 + a^2*x^2]*Sqrt[c + a^2*c*x^2]) + (x*ArcSinh[a*x])/(5*c*(c + a^2*c*x^2)^(5/2)) + (4*x*ArcSinh[a*x])/(15*c^2*(c + a^2*c*x^2)^(3/2)) + (8*x*ArcSinh[a*x])/(15*c^3*Sqrt[c + a^2*c*x^2]) - (4*Sqrt[1 + a^2*x^2]*Log[1 + a^2*x^2])/(15*a*c^3*Sqrt[c + a^2*c*x^2])","A",6,4,19,0.2105,1,"{5690, 5687, 260, 261}"
112,1,86,0,0.1548757,"\int \frac{x^4 \sinh ^{-1}(a x)}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^4*ArcSinh[a*x])/Sqrt[1 + a^2*x^2],x]","\frac{3 x^2}{16 a^3}+\frac{x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{4 a^2}-\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{8 a^4}+\frac{3 \sinh ^{-1}(a x)^2}{16 a^5}-\frac{x^4}{16 a}","\frac{3 x^2}{16 a^3}+\frac{x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{4 a^2}-\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{8 a^4}+\frac{3 \sinh ^{-1}(a x)^2}{16 a^5}-\frac{x^4}{16 a}",1,"(3*x^2)/(16*a^3) - x^4/(16*a) - (3*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(8*a^4) + (x^3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(4*a^2) + (3*ArcSinh[a*x]^2)/(16*a^5)","A",5,3,21,0.1429,1,"{5758, 5675, 30}"
113,1,70,0,0.1110014,"\int \frac{x^3 \sinh ^{-1}(a x)}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^3*ArcSinh[a*x])/Sqrt[1 + a^2*x^2],x]","\frac{x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{3 a^2}-\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{3 a^4}+\frac{2 x}{3 a^3}-\frac{x^3}{9 a}","\frac{x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{3 a^2}-\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{3 a^4}+\frac{2 x}{3 a^3}-\frac{x^3}{9 a}",1,"(2*x)/(3*a^3) - x^3/(9*a) - (2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(3*a^4) + (x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(3*a^2)","A",4,4,21,0.1905,1,"{5758, 5717, 8, 30}"
114,1,49,0,0.1031162,"\int \frac{x^2 \sinh ^{-1}(a x)}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^2*ArcSinh[a*x])/Sqrt[1 + a^2*x^2],x]","\frac{x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{2 a^2}-\frac{\sinh ^{-1}(a x)^2}{4 a^3}-\frac{x^2}{4 a}","\frac{x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{2 a^2}-\frac{\sinh ^{-1}(a x)^2}{4 a^3}-\frac{x^2}{4 a}",1,"-x^2/(4*a) + (x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(2*a^2) - ArcSinh[a*x]^2/(4*a^3)","A",3,3,21,0.1429,1,"{5758, 5675, 30}"
115,1,28,0,0.0459697,"\int \frac{x \sinh ^{-1}(a x)}{\sqrt{1+a^2 x^2}} \, dx","Int[(x*ArcSinh[a*x])/Sqrt[1 + a^2*x^2],x]","\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{a^2}-\frac{x}{a}","\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{a^2}-\frac{x}{a}",1,"-(x/a) + (Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/a^2","A",2,2,19,0.1053,1,"{5717, 8}"
116,1,13,0,0.021915,"\int \frac{\sinh ^{-1}(a x)}{\sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]/Sqrt[1 + a^2*x^2],x]","\frac{\sinh ^{-1}(a x)^2}{2 a}","\frac{\sinh ^{-1}(a x)^2}{2 a}",1,"ArcSinh[a*x]^2/(2*a)","A",1,1,18,0.05556,1,"{5675}"
117,1,34,0,0.0916102,"\int \frac{\sinh ^{-1}(a x)}{x \sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]/(x*Sqrt[1 + a^2*x^2]),x]","-\text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+\text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-2 \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)","-\text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+\text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-2 \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)",1,"-2*ArcSinh[a*x]*ArcTanh[E^ArcSinh[a*x]] - PolyLog[2, -E^ArcSinh[a*x]] + PolyLog[2, E^ArcSinh[a*x]]","A",6,4,21,0.1905,1,"{5760, 4182, 2279, 2391}"
118,1,27,0,0.0636175,"\int \frac{\sinh ^{-1}(a x)}{x^2 \sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]/(x^2*Sqrt[1 + a^2*x^2]),x]","a \log (x)-\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{x}","a \log (x)-\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{x}",1,"-((Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/x) + a*Log[x]","A",2,2,21,0.09524,1,"{5723, 29}"
119,1,80,0,0.1483352,"\int \frac{\sinh ^{-1}(a x)}{x^3 \sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]/(x^3*Sqrt[1 + a^2*x^2]),x]","\frac{1}{2} a^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)-\frac{1}{2} a^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{2 x^2}+a^2 \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-\frac{a}{2 x}","\frac{1}{2} a^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)-\frac{1}{2} a^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{2 x^2}+a^2 \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-\frac{a}{2 x}",1,"-a/(2*x) - (Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(2*x^2) + a^2*ArcSinh[a*x]*ArcTanh[E^ArcSinh[a*x]] + (a^2*PolyLog[2, -E^ArcSinh[a*x]])/2 - (a^2*PolyLog[2, E^ArcSinh[a*x]])/2","A",8,6,21,0.2857,1,"{5747, 5760, 4182, 2279, 2391, 30}"
120,1,175,0,0.1609711,"\int x^3 \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]),x]","\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^4 d^2}-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^4 d}-\frac{b c x^5 \sqrt{c^2 d x^2+d}}{25 \sqrt{c^2 x^2+1}}-\frac{b x^3 \sqrt{c^2 d x^2+d}}{45 c \sqrt{c^2 x^2+1}}+\frac{2 b x \sqrt{c^2 d x^2+d}}{15 c^3 \sqrt{c^2 x^2+1}}","\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^4 d^2}-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^4 d}-\frac{b c x^5 \sqrt{c^2 d x^2+d}}{25 \sqrt{c^2 x^2+1}}-\frac{b x^3 \sqrt{c^2 d x^2+d}}{45 c \sqrt{c^2 x^2+1}}+\frac{2 b x \sqrt{c^2 d x^2+d}}{15 c^3 \sqrt{c^2 x^2+1}}",1,"(2*b*x*Sqrt[d + c^2*d*x^2])/(15*c^3*Sqrt[1 + c^2*x^2]) - (b*x^3*Sqrt[d + c^2*d*x^2])/(45*c*Sqrt[1 + c^2*x^2]) - (b*c*x^5*Sqrt[d + c^2*d*x^2])/(25*Sqrt[1 + c^2*x^2]) - ((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*c^4*d) + ((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(5*c^4*d^2)","A",6,4,26,0.1538,1,"{266, 43, 5734, 12}"
121,1,181,0,0.1941369,"\int x^2 \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]),x]","\frac{1}{4} x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 c^2}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{c^2 x^2+1}}-\frac{b c x^4 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{b x^2 \sqrt{c^2 d x^2+d}}{16 c \sqrt{c^2 x^2+1}}","\frac{1}{4} x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 c^2}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{c^2 x^2+1}}-\frac{b c x^4 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{b x^2 \sqrt{c^2 d x^2+d}}{16 c \sqrt{c^2 x^2+1}}",1,"-(b*x^2*Sqrt[d + c^2*d*x^2])/(16*c*Sqrt[1 + c^2*x^2]) - (b*c*x^4*Sqrt[d + c^2*d*x^2])/(16*Sqrt[1 + c^2*x^2]) + (x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(8*c^2) + (x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/4 - (Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(16*b*c^3*Sqrt[1 + c^2*x^2])","A",5,4,26,0.1538,1,"{5742, 5758, 5675, 30}"
122,1,105,0,0.0674952,"\int x \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]),x]","\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2 d}-\frac{b c x^3 \sqrt{c^2 d x^2+d}}{9 \sqrt{c^2 x^2+1}}-\frac{b x \sqrt{c^2 d x^2+d}}{3 c \sqrt{c^2 x^2+1}}","\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2 d}-\frac{b c x^3 \sqrt{c^2 d x^2+d}}{9 \sqrt{c^2 x^2+1}}-\frac{b x \sqrt{c^2 d x^2+d}}{3 c \sqrt{c^2 x^2+1}}",1,"-(b*x*Sqrt[d + c^2*d*x^2])/(3*c*Sqrt[1 + c^2*x^2]) - (b*c*x^3*Sqrt[d + c^2*d*x^2])/(9*Sqrt[1 + c^2*x^2]) + ((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*c^2*d)","A",2,1,24,0.04167,1,"{5717}"
123,1,111,0,0.0611233,"\int \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]),x]","\frac{1}{2} x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{c^2 x^2+1}}-\frac{b c x^2 \sqrt{c^2 d x^2+d}}{4 \sqrt{c^2 x^2+1}}","\frac{1}{2} x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{c^2 x^2+1}}-\frac{b c x^2 \sqrt{c^2 d x^2+d}}{4 \sqrt{c^2 x^2+1}}",1,"-(b*c*x^2*Sqrt[d + c^2*d*x^2])/(4*Sqrt[1 + c^2*x^2]) + (x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/2 + (Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*c*Sqrt[1 + c^2*x^2])","A",3,3,23,0.1304,1,"{5682, 5675, 30}"
124,1,177,0,0.1953022,"\int \frac{\sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)}{x} \, dx","Int[(Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/x,x]","-\frac{b \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\frac{b \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)-\frac{2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}-\frac{b c x \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}","-\frac{b \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\frac{b \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)-\frac{2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}-\frac{b c x \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}",1,"-((b*c*x*Sqrt[d + c^2*d*x^2])/Sqrt[1 + c^2*x^2]) + Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]) - (2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (b*Sqrt[d + c^2*d*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (b*Sqrt[d + c^2*d*x^2]*PolyLog[2, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2]","A",8,6,26,0.2308,1,"{5742, 5760, 4182, 2279, 2391, 8}"
125,1,105,0,0.1147125,"\int \frac{\sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)}{x^2} \, dx","Int[(Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/x^2,x]","\frac{c \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b \sqrt{c^2 x^2+1}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{x}+\frac{b c \log (x) \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}","\frac{c \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b \sqrt{c^2 x^2+1}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{x}+\frac{b c \log (x) \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}",1,"-((Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/x) + (c*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*Sqrt[1 + c^2*x^2]) + (b*c*Sqrt[d + c^2*d*x^2]*Log[x])/Sqrt[1 + c^2*x^2]","A",3,3,26,0.1154,1,"{5737, 29, 5675}"
126,1,201,0,0.1951662,"\int \frac{\sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)}{x^3} \, dx","Int[(Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/x^3,x]","-\frac{b c^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}+\frac{b c^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}-\frac{c^2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}-\frac{b c \sqrt{c^2 d x^2+d}}{2 x \sqrt{c^2 x^2+1}}","-\frac{b c^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}+\frac{b c^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}-\frac{c^2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}-\frac{b c \sqrt{c^2 d x^2+d}}{2 x \sqrt{c^2 x^2+1}}",1,"-(b*c*Sqrt[d + c^2*d*x^2])/(2*x*Sqrt[1 + c^2*x^2]) - (Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(2*x^2) - (c^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (b*c^2*Sqrt[d + c^2*d*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/(2*Sqrt[1 + c^2*x^2]) + (b*c^2*Sqrt[d + c^2*d*x^2]*PolyLog[2, E^ArcSinh[c*x]])/(2*Sqrt[1 + c^2*x^2])","A",8,6,26,0.2308,1,"{5737, 30, 5760, 4182, 2279, 2391}"
127,1,106,0,0.0945453,"\int \frac{\sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)}{x^4} \, dx","Int[(Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/x^4,x]","-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 d x^3}-\frac{b c \sqrt{c^2 d x^2+d}}{6 x^2 \sqrt{c^2 x^2+1}}+\frac{b c^3 \log (x) \sqrt{c^2 d x^2+d}}{3 \sqrt{c^2 x^2+1}}","-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 d x^3}-\frac{b c \sqrt{c^2 d x^2+d}}{6 x^2 \sqrt{c^2 x^2+1}}+\frac{b c^3 \log (x) \sqrt{c^2 d x^2+d}}{3 \sqrt{c^2 x^2+1}}",1,"-(b*c*Sqrt[d + c^2*d*x^2])/(6*x^2*Sqrt[1 + c^2*x^2]) - ((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*d*x^3) + (b*c^3*Sqrt[d + c^2*d*x^2]*Log[x])/(3*Sqrt[1 + c^2*x^2])","A",3,2,26,0.07692,1,"{5723, 14}"
128,1,217,0,0.1770404,"\int x^3 \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^3*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]),x]","\frac{\left(c^2 d x^2+d\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^4 d^2}-\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^4 d}-\frac{b c^3 d x^7 \sqrt{c^2 d x^2+d}}{49 \sqrt{c^2 x^2+1}}-\frac{8 b c d x^5 \sqrt{c^2 d x^2+d}}{175 \sqrt{c^2 x^2+1}}-\frac{b d x^3 \sqrt{c^2 d x^2+d}}{105 c \sqrt{c^2 x^2+1}}+\frac{2 b d x \sqrt{c^2 d x^2+d}}{35 c^3 \sqrt{c^2 x^2+1}}","\frac{\left(c^2 d x^2+d\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^4 d^2}-\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^4 d}-\frac{b c^3 d x^7 \sqrt{c^2 d x^2+d}}{49 \sqrt{c^2 x^2+1}}-\frac{8 b c d x^5 \sqrt{c^2 d x^2+d}}{175 \sqrt{c^2 x^2+1}}-\frac{b d x^3 \sqrt{c^2 d x^2+d}}{105 c \sqrt{c^2 x^2+1}}+\frac{2 b d x \sqrt{c^2 d x^2+d}}{35 c^3 \sqrt{c^2 x^2+1}}",1,"(2*b*d*x*Sqrt[d + c^2*d*x^2])/(35*c^3*Sqrt[1 + c^2*x^2]) - (b*d*x^3*Sqrt[d + c^2*d*x^2])/(105*c*Sqrt[1 + c^2*x^2]) - (8*b*c*d*x^5*Sqrt[d + c^2*d*x^2])/(175*Sqrt[1 + c^2*x^2]) - (b*c^3*d*x^7*Sqrt[d + c^2*d*x^2])/(49*Sqrt[1 + c^2*x^2]) - ((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(5*c^4*d) + ((d + c^2*d*x^2)^(7/2)*(a + b*ArcSinh[c*x]))/(7*c^4*d^2)","A",7,5,26,0.1923,1,"{266, 43, 5734, 12, 373}"
129,1,254,0,0.3100977,"\int x^2 \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^2*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]),x]","\frac{1}{6} x^3 \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{8} d x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{16 c^2}-\frac{d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{c^2 x^2+1}}-\frac{b c^3 d x^6 \sqrt{c^2 d x^2+d}}{36 \sqrt{c^2 x^2+1}}-\frac{7 b c d x^4 \sqrt{c^2 d x^2+d}}{96 \sqrt{c^2 x^2+1}}-\frac{b d x^2 \sqrt{c^2 d x^2+d}}{32 c \sqrt{c^2 x^2+1}}","\frac{1}{6} x^3 \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{8} d x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{16 c^2}-\frac{d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{c^2 x^2+1}}-\frac{b c^3 d x^6 \sqrt{c^2 d x^2+d}}{36 \sqrt{c^2 x^2+1}}-\frac{7 b c d x^4 \sqrt{c^2 d x^2+d}}{96 \sqrt{c^2 x^2+1}}-\frac{b d x^2 \sqrt{c^2 d x^2+d}}{32 c \sqrt{c^2 x^2+1}}",1,"-(b*d*x^2*Sqrt[d + c^2*d*x^2])/(32*c*Sqrt[1 + c^2*x^2]) - (7*b*c*d*x^4*Sqrt[d + c^2*d*x^2])/(96*Sqrt[1 + c^2*x^2]) - (b*c^3*d*x^6*Sqrt[d + c^2*d*x^2])/(36*Sqrt[1 + c^2*x^2]) + (d*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(16*c^2) + (d*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/8 + (x^3*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/6 - (d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(32*b*c^3*Sqrt[1 + c^2*x^2])","A",8,6,26,0.2308,1,"{5744, 5742, 5758, 5675, 30, 14}"
130,1,146,0,0.0740795,"\int x \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]),x]","\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^2 d}-\frac{b c^3 d x^5 \sqrt{c^2 d x^2+d}}{25 \sqrt{c^2 x^2+1}}-\frac{2 b c d x^3 \sqrt{c^2 d x^2+d}}{15 \sqrt{c^2 x^2+1}}-\frac{b d x \sqrt{c^2 d x^2+d}}{5 c \sqrt{c^2 x^2+1}}","\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^2 d}-\frac{b c^3 d x^5 \sqrt{c^2 d x^2+d}}{25 \sqrt{c^2 x^2+1}}-\frac{2 b c d x^3 \sqrt{c^2 d x^2+d}}{15 \sqrt{c^2 x^2+1}}-\frac{b d x \sqrt{c^2 d x^2+d}}{5 c \sqrt{c^2 x^2+1}}",1,"-(b*d*x*Sqrt[d + c^2*d*x^2])/(5*c*Sqrt[1 + c^2*x^2]) - (2*b*c*d*x^3*Sqrt[d + c^2*d*x^2])/(15*Sqrt[1 + c^2*x^2]) - (b*c^3*d*x^5*Sqrt[d + c^2*d*x^2])/(25*Sqrt[1 + c^2*x^2]) + ((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(5*c^2*d)","A",3,2,24,0.08333,1,"{5717, 194}"
131,1,180,0,0.1088961,"\int \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]),x]","\frac{1}{4} x \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{8} d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{3 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c \sqrt{c^2 x^2+1}}-\frac{b c^3 d x^4 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{5 b c d x^2 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}","\frac{1}{4} x \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{8} d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{3 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c \sqrt{c^2 x^2+1}}-\frac{b c^3 d x^4 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{5 b c d x^2 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}",1,"(-5*b*c*d*x^2*Sqrt[d + c^2*d*x^2])/(16*Sqrt[1 + c^2*x^2]) - (b*c^3*d*x^4*Sqrt[d + c^2*d*x^2])/(16*Sqrt[1 + c^2*x^2]) + (3*d*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/8 + (x*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/4 + (3*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(16*b*c*Sqrt[1 + c^2*x^2])","A",6,5,23,0.2174,1,"{5684, 5682, 5675, 30, 14}"
132,1,249,0,0.303196,"\int \frac{\left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{x} \, dx","Int[((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/x,x]","-\frac{b d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\frac{b d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\frac{1}{3} \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)-\frac{2 d \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}-\frac{b c^3 d x^3 \sqrt{c^2 d x^2+d}}{9 \sqrt{c^2 x^2+1}}-\frac{4 b c d x \sqrt{c^2 d x^2+d}}{3 \sqrt{c^2 x^2+1}}","-\frac{b d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\frac{b d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\frac{1}{3} \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)-\frac{2 d \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}-\frac{b c^3 d x^3 \sqrt{c^2 d x^2+d}}{9 \sqrt{c^2 x^2+1}}-\frac{4 b c d x \sqrt{c^2 d x^2+d}}{3 \sqrt{c^2 x^2+1}}",1,"(-4*b*c*d*x*Sqrt[d + c^2*d*x^2])/(3*Sqrt[1 + c^2*x^2]) - (b*c^3*d*x^3*Sqrt[d + c^2*d*x^2])/(9*Sqrt[1 + c^2*x^2]) + d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]) + ((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/3 - (2*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (b*d*Sqrt[d + c^2*d*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (b*d*Sqrt[d + c^2*d*x^2]*PolyLog[2, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2]","A",10,7,26,0.2692,1,"{5744, 5742, 5760, 4182, 2279, 2391, 8}"
133,1,177,0,0.1704622,"\int \frac{\left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/x^2,x]","\frac{3}{2} c^2 d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{3 c d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b \sqrt{c^2 x^2+1}}-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{b c^3 d x^2 \sqrt{c^2 d x^2+d}}{4 \sqrt{c^2 x^2+1}}+\frac{b c d \log (x) \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}","\frac{3}{2} c^2 d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{3 c d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b \sqrt{c^2 x^2+1}}-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{b c^3 d x^2 \sqrt{c^2 d x^2+d}}{4 \sqrt{c^2 x^2+1}}+\frac{b c d \log (x) \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}",1,"-(b*c^3*d*x^2*Sqrt[d + c^2*d*x^2])/(4*Sqrt[1 + c^2*x^2]) + (3*c^2*d*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/2 - ((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/x + (3*c*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*Sqrt[1 + c^2*x^2]) + (b*c*d*Sqrt[d + c^2*d*x^2]*Log[x])/Sqrt[1 + c^2*x^2]","A",6,5,26,0.1923,1,"{5739, 5682, 5675, 30, 14}"
134,1,270,0,0.3100304,"\int \frac{\left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/x^3,x]","-\frac{3 b c^2 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}+\frac{3 b c^2 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}+\frac{3}{2} c^2 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}-\frac{3 c^2 d \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}-\frac{b c^3 d x \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}-\frac{b c d \sqrt{c^2 d x^2+d}}{2 x \sqrt{c^2 x^2+1}}","-\frac{3 b c^2 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}+\frac{3 b c^2 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}+\frac{3}{2} c^2 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}-\frac{3 c^2 d \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}-\frac{b c^3 d x \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}-\frac{b c d \sqrt{c^2 d x^2+d}}{2 x \sqrt{c^2 x^2+1}}",1,"-(b*c*d*Sqrt[d + c^2*d*x^2])/(2*x*Sqrt[1 + c^2*x^2]) - (b*c^3*d*x*Sqrt[d + c^2*d*x^2])/Sqrt[1 + c^2*x^2] + (3*c^2*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/2 - ((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(2*x^2) - (3*c^2*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (3*b*c^2*d*Sqrt[d + c^2*d*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/(2*Sqrt[1 + c^2*x^2]) + (3*b*c^2*d*Sqrt[d + c^2*d*x^2]*PolyLog[2, E^ArcSinh[c*x]])/(2*Sqrt[1 + c^2*x^2])","A",11,8,26,0.3077,1,"{5739, 5742, 5760, 4182, 2279, 2391, 8, 14}"
135,1,184,0,0.2313545,"\int \frac{\left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/x^4,x]","\frac{c^3 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b \sqrt{c^2 x^2+1}}-\frac{c^2 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^3}-\frac{b c d \sqrt{c^2 d x^2+d}}{6 x^2 \sqrt{c^2 x^2+1}}+\frac{4 b c^3 d \log (x) \sqrt{c^2 d x^2+d}}{3 \sqrt{c^2 x^2+1}}","\frac{c^3 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b \sqrt{c^2 x^2+1}}-\frac{c^2 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^3}-\frac{b c d \sqrt{c^2 d x^2+d}}{6 x^2 \sqrt{c^2 x^2+1}}+\frac{4 b c^3 d \log (x) \sqrt{c^2 d x^2+d}}{3 \sqrt{c^2 x^2+1}}",1,"-(b*c*d*Sqrt[d + c^2*d*x^2])/(6*x^2*Sqrt[1 + c^2*x^2]) - (c^2*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/x - ((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*x^3) + (c^3*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*Sqrt[1 + c^2*x^2]) + (4*b*c^3*d*Sqrt[d + c^2*d*x^2]*Log[x])/(3*Sqrt[1 + c^2*x^2])","A",6,5,26,0.1923,1,"{5739, 5737, 29, 5675, 14}"
136,1,266,0,0.1920282,"\int x^3 \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^3*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]),x]","\frac{\left(c^2 d x^2+d\right)^{9/2} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^4 d^2}-\frac{\left(c^2 d x^2+d\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^4 d}-\frac{b c^5 d^2 x^9 \sqrt{c^2 d x^2+d}}{81 \sqrt{c^2 x^2+1}}-\frac{19 b c^3 d^2 x^7 \sqrt{c^2 d x^2+d}}{441 \sqrt{c^2 x^2+1}}-\frac{b c d^2 x^5 \sqrt{c^2 d x^2+d}}{21 \sqrt{c^2 x^2+1}}-\frac{b d^2 x^3 \sqrt{c^2 d x^2+d}}{189 c \sqrt{c^2 x^2+1}}+\frac{2 b d^2 x \sqrt{c^2 d x^2+d}}{63 c^3 \sqrt{c^2 x^2+1}}","\frac{\left(c^2 d x^2+d\right)^{9/2} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^4 d^2}-\frac{\left(c^2 d x^2+d\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^4 d}-\frac{b c^5 d^2 x^9 \sqrt{c^2 d x^2+d}}{81 \sqrt{c^2 x^2+1}}-\frac{19 b c^3 d^2 x^7 \sqrt{c^2 d x^2+d}}{441 \sqrt{c^2 x^2+1}}-\frac{b c d^2 x^5 \sqrt{c^2 d x^2+d}}{21 \sqrt{c^2 x^2+1}}-\frac{b d^2 x^3 \sqrt{c^2 d x^2+d}}{189 c \sqrt{c^2 x^2+1}}+\frac{2 b d^2 x \sqrt{c^2 d x^2+d}}{63 c^3 \sqrt{c^2 x^2+1}}",1,"(2*b*d^2*x*Sqrt[d + c^2*d*x^2])/(63*c^3*Sqrt[1 + c^2*x^2]) - (b*d^2*x^3*Sqrt[d + c^2*d*x^2])/(189*c*Sqrt[1 + c^2*x^2]) - (b*c*d^2*x^5*Sqrt[d + c^2*d*x^2])/(21*Sqrt[1 + c^2*x^2]) - (19*b*c^3*d^2*x^7*Sqrt[d + c^2*d*x^2])/(441*Sqrt[1 + c^2*x^2]) - (b*c^5*d^2*x^9*Sqrt[d + c^2*d*x^2])/(81*Sqrt[1 + c^2*x^2]) - ((d + c^2*d*x^2)^(7/2)*(a + b*ArcSinh[c*x]))/(7*c^4*d) + ((d + c^2*d*x^2)^(9/2)*(a + b*ArcSinh[c*x]))/(9*c^4*d^2)","A",7,5,26,0.1923,1,"{266, 43, 5734, 12, 373}"
137,1,337,0,0.4662631,"\int x^2 \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^2*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]),x]","\frac{5}{64} d^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{128 c^2}-\frac{5 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{c^2 x^2+1}}+\frac{1}{8} x^3 \left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{48} d x^3 \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{b c^5 d^2 x^8 \sqrt{c^2 d x^2+d}}{64 \sqrt{c^2 x^2+1}}-\frac{17 b c^3 d^2 x^6 \sqrt{c^2 d x^2+d}}{288 \sqrt{c^2 x^2+1}}-\frac{59 b c d^2 x^4 \sqrt{c^2 d x^2+d}}{768 \sqrt{c^2 x^2+1}}-\frac{5 b d^2 x^2 \sqrt{c^2 d x^2+d}}{256 c \sqrt{c^2 x^2+1}}","\frac{5}{64} d^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{128 c^2}-\frac{5 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{c^2 x^2+1}}+\frac{1}{8} x^3 \left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{48} d x^3 \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{b c^5 d^2 x^8 \sqrt{c^2 d x^2+d}}{64 \sqrt{c^2 x^2+1}}-\frac{17 b c^3 d^2 x^6 \sqrt{c^2 d x^2+d}}{288 \sqrt{c^2 x^2+1}}-\frac{59 b c d^2 x^4 \sqrt{c^2 d x^2+d}}{768 \sqrt{c^2 x^2+1}}-\frac{5 b d^2 x^2 \sqrt{c^2 d x^2+d}}{256 c \sqrt{c^2 x^2+1}}",1,"(-5*b*d^2*x^2*Sqrt[d + c^2*d*x^2])/(256*c*Sqrt[1 + c^2*x^2]) - (59*b*c*d^2*x^4*Sqrt[d + c^2*d*x^2])/(768*Sqrt[1 + c^2*x^2]) - (17*b*c^3*d^2*x^6*Sqrt[d + c^2*d*x^2])/(288*Sqrt[1 + c^2*x^2]) - (b*c^5*d^2*x^8*Sqrt[d + c^2*d*x^2])/(64*Sqrt[1 + c^2*x^2]) + (5*d^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(128*c^2) + (5*d^2*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/64 + (5*d*x^3*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/48 + (x^3*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/8 - (5*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(256*b*c^3*Sqrt[1 + c^2*x^2])","A",12,8,26,0.3077,1,"{5744, 5742, 5758, 5675, 30, 14, 266, 43}"
138,1,193,0,0.0881364,"\int x \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]),x]","\frac{\left(c^2 d x^2+d\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^2 d}-\frac{b c^5 d^2 x^7 \sqrt{c^2 d x^2+d}}{49 \sqrt{c^2 x^2+1}}-\frac{3 b c^3 d^2 x^5 \sqrt{c^2 d x^2+d}}{35 \sqrt{c^2 x^2+1}}-\frac{b c d^2 x^3 \sqrt{c^2 d x^2+d}}{7 \sqrt{c^2 x^2+1}}-\frac{b d^2 x \sqrt{c^2 d x^2+d}}{7 c \sqrt{c^2 x^2+1}}","\frac{\left(c^2 d x^2+d\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^2 d}-\frac{b c^5 d^2 x^7 \sqrt{c^2 d x^2+d}}{49 \sqrt{c^2 x^2+1}}-\frac{3 b c^3 d^2 x^5 \sqrt{c^2 d x^2+d}}{35 \sqrt{c^2 x^2+1}}-\frac{b c d^2 x^3 \sqrt{c^2 d x^2+d}}{7 \sqrt{c^2 x^2+1}}-\frac{b d^2 x \sqrt{c^2 d x^2+d}}{7 c \sqrt{c^2 x^2+1}}",1,"-(b*d^2*x*Sqrt[d + c^2*d*x^2])/(7*c*Sqrt[1 + c^2*x^2]) - (b*c*d^2*x^3*Sqrt[d + c^2*d*x^2])/(7*Sqrt[1 + c^2*x^2]) - (3*b*c^3*d^2*x^5*Sqrt[d + c^2*d*x^2])/(35*Sqrt[1 + c^2*x^2]) - (b*c^5*d^2*x^7*Sqrt[d + c^2*d*x^2])/(49*Sqrt[1 + c^2*x^2]) + ((d + c^2*d*x^2)^(7/2)*(a + b*ArcSinh[c*x]))/(7*c^2*d)","A",3,2,24,0.08333,1,"{5717, 194}"
139,1,254,0,0.1595221,"\int \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]),x]","\frac{5}{16} d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{32 b c \sqrt{c^2 x^2+1}}+\frac{1}{6} x \left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{24} d x \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{5 b c^3 d^2 x^4 \sqrt{c^2 d x^2+d}}{96 \sqrt{c^2 x^2+1}}-\frac{25 b c d^2 x^2 \sqrt{c^2 d x^2+d}}{96 \sqrt{c^2 x^2+1}}-\frac{b d^2 \left(c^2 x^2+1\right)^{5/2} \sqrt{c^2 d x^2+d}}{36 c}","\frac{5}{16} d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{32 b c \sqrt{c^2 x^2+1}}+\frac{1}{6} x \left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{24} d x \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{5 b c^3 d^2 x^4 \sqrt{c^2 d x^2+d}}{96 \sqrt{c^2 x^2+1}}-\frac{25 b c d^2 x^2 \sqrt{c^2 d x^2+d}}{96 \sqrt{c^2 x^2+1}}-\frac{b d^2 \left(c^2 x^2+1\right)^{5/2} \sqrt{c^2 d x^2+d}}{36 c}",1,"(-25*b*c*d^2*x^2*Sqrt[d + c^2*d*x^2])/(96*Sqrt[1 + c^2*x^2]) - (5*b*c^3*d^2*x^4*Sqrt[d + c^2*d*x^2])/(96*Sqrt[1 + c^2*x^2]) - (b*d^2*(1 + c^2*x^2)^(5/2)*Sqrt[d + c^2*d*x^2])/(36*c) + (5*d^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/16 + (5*d*x*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/24 + (x*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/6 + (5*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(32*b*c*Sqrt[1 + c^2*x^2])","A",8,6,23,0.2609,1,"{5684, 5682, 5675, 30, 14, 261}"
140,1,329,0,0.4390837,"\int \frac{\left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{x} \, dx","Int[((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/x,x]","-\frac{b d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\frac{b d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)-\frac{2 d^2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{1}{5} \left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{3} d \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{b c^5 d^2 x^5 \sqrt{c^2 d x^2+d}}{25 \sqrt{c^2 x^2+1}}-\frac{11 b c^3 d^2 x^3 \sqrt{c^2 d x^2+d}}{45 \sqrt{c^2 x^2+1}}-\frac{23 b c d^2 x \sqrt{c^2 d x^2+d}}{15 \sqrt{c^2 x^2+1}}","-\frac{b d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\frac{b d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)-\frac{2 d^2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{1}{5} \left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{3} d \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{b c^5 d^2 x^5 \sqrt{c^2 d x^2+d}}{25 \sqrt{c^2 x^2+1}}-\frac{11 b c^3 d^2 x^3 \sqrt{c^2 d x^2+d}}{45 \sqrt{c^2 x^2+1}}-\frac{23 b c d^2 x \sqrt{c^2 d x^2+d}}{15 \sqrt{c^2 x^2+1}}",1,"(-23*b*c*d^2*x*Sqrt[d + c^2*d*x^2])/(15*Sqrt[1 + c^2*x^2]) - (11*b*c^3*d^2*x^3*Sqrt[d + c^2*d*x^2])/(45*Sqrt[1 + c^2*x^2]) - (b*c^5*d^2*x^5*Sqrt[d + c^2*d*x^2])/(25*Sqrt[1 + c^2*x^2]) + d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]) + (d*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/3 + ((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/5 - (2*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (b*d^2*Sqrt[d + c^2*d*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (b*d^2*Sqrt[d + c^2*d*x^2]*PolyLog[2, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2]","A",13,8,26,0.3077,1,"{5744, 5742, 5760, 4182, 2279, 2391, 8, 194}"
141,1,257,0,0.2377195,"\int \frac{\left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/x^2,x]","\frac{15}{8} c^2 d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{15 c d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b \sqrt{c^2 x^2+1}}+\frac{5}{4} c^2 d x \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{b c^5 d^2 x^4 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{9 b c^3 d^2 x^2 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}+\frac{b c d^2 \log (x) \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}","\frac{15}{8} c^2 d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{15 c d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b \sqrt{c^2 x^2+1}}+\frac{5}{4} c^2 d x \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{b c^5 d^2 x^4 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{9 b c^3 d^2 x^2 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}+\frac{b c d^2 \log (x) \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}",1,"(-9*b*c^3*d^2*x^2*Sqrt[d + c^2*d*x^2])/(16*Sqrt[1 + c^2*x^2]) - (b*c^5*d^2*x^4*Sqrt[d + c^2*d*x^2])/(16*Sqrt[1 + c^2*x^2]) + (15*c^2*d^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/8 + (5*c^2*d*x*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/4 - ((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/x + (15*c*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(16*b*Sqrt[1 + c^2*x^2]) + (b*c*d^2*Sqrt[d + c^2*d*x^2]*Log[x])/Sqrt[1 + c^2*x^2]","A",10,8,26,0.3077,1,"{5739, 5684, 5682, 5675, 30, 14, 266, 43}"
142,1,355,0,0.4474022,"\int \frac{\left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/x^3,x]","-\frac{5 b c^2 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}+\frac{5 b c^2 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}+\frac{5}{2} c^2 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)-\frac{5 c^2 d^2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{5}{6} c^2 d \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}-\frac{b c^5 d^2 x^3 \sqrt{c^2 d x^2+d}}{9 \sqrt{c^2 x^2+1}}-\frac{7 b c^3 d^2 x \sqrt{c^2 d x^2+d}}{3 \sqrt{c^2 x^2+1}}-\frac{b c d^2 \sqrt{c^2 d x^2+d}}{2 x \sqrt{c^2 x^2+1}}","-\frac{5 b c^2 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}+\frac{5 b c^2 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 x^2+1}}+\frac{5}{2} c^2 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)-\frac{5 c^2 d^2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{5}{6} c^2 d \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{2 x^2}-\frac{b c^5 d^2 x^3 \sqrt{c^2 d x^2+d}}{9 \sqrt{c^2 x^2+1}}-\frac{7 b c^3 d^2 x \sqrt{c^2 d x^2+d}}{3 \sqrt{c^2 x^2+1}}-\frac{b c d^2 \sqrt{c^2 d x^2+d}}{2 x \sqrt{c^2 x^2+1}}",1,"-(b*c*d^2*Sqrt[d + c^2*d*x^2])/(2*x*Sqrt[1 + c^2*x^2]) - (7*b*c^3*d^2*x*Sqrt[d + c^2*d*x^2])/(3*Sqrt[1 + c^2*x^2]) - (b*c^5*d^2*x^3*Sqrt[d + c^2*d*x^2])/(9*Sqrt[1 + c^2*x^2]) + (5*c^2*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/2 + (5*c^2*d*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/6 - ((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(2*x^2) - (5*c^2*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (5*b*c^2*d^2*Sqrt[d + c^2*d*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/(2*Sqrt[1 + c^2*x^2]) + (5*b*c^2*d^2*Sqrt[d + c^2*d*x^2]*PolyLog[2, E^ArcSinh[c*x]])/(2*Sqrt[1 + c^2*x^2])","A",13,9,26,0.3462,1,"{5739, 5744, 5742, 5760, 4182, 2279, 2391, 8, 270}"
143,1,266,0,0.2997151,"\int \frac{\left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/x^4,x]","\frac{5}{2} c^4 d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 c^3 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b \sqrt{c^2 x^2+1}}-\frac{5 c^2 d \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 x}-\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^3}-\frac{b c^5 d^2 x^2 \sqrt{c^2 d x^2+d}}{4 \sqrt{c^2 x^2+1}}-\frac{b c d^2 \sqrt{c^2 d x^2+d}}{6 x^2 \sqrt{c^2 x^2+1}}+\frac{7 b c^3 d^2 \log (x) \sqrt{c^2 d x^2+d}}{3 \sqrt{c^2 x^2+1}}","\frac{5}{2} c^4 d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 c^3 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b \sqrt{c^2 x^2+1}}-\frac{5 c^2 d \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 x}-\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^3}-\frac{b c^5 d^2 x^2 \sqrt{c^2 d x^2+d}}{4 \sqrt{c^2 x^2+1}}-\frac{b c d^2 \sqrt{c^2 d x^2+d}}{6 x^2 \sqrt{c^2 x^2+1}}+\frac{7 b c^3 d^2 \log (x) \sqrt{c^2 d x^2+d}}{3 \sqrt{c^2 x^2+1}}",1,"-(b*c*d^2*Sqrt[d + c^2*d*x^2])/(6*x^2*Sqrt[1 + c^2*x^2]) - (b*c^5*d^2*x^2*Sqrt[d + c^2*d*x^2])/(4*Sqrt[1 + c^2*x^2]) + (5*c^4*d^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/2 - (5*c^2*d*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*x) - ((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(3*x^3) + (5*c^3*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*Sqrt[1 + c^2*x^2]) + (7*b*c^3*d^2*Sqrt[d + c^2*d*x^2]*Log[x])/(3*Sqrt[1 + c^2*x^2])","A",10,7,26,0.2692,1,"{5739, 5682, 5675, 30, 14, 266, 43}"
144,1,32,0,0.0290022,"\int \sqrt{1+x^2} \sinh ^{-1}(x) \, dx","Int[Sqrt[1 + x^2]*ArcSinh[x],x]","-\frac{x^2}{4}+\frac{1}{2} \sqrt{x^2+1} x \sinh ^{-1}(x)+\frac{1}{4} \sinh ^{-1}(x)^2","-\frac{x^2}{4}+\frac{1}{2} \sqrt{x^2+1} x \sinh ^{-1}(x)+\frac{1}{4} \sinh ^{-1}(x)^2",1,"-x^2/4 + (x*Sqrt[1 + x^2]*ArcSinh[x])/2 + ArcSinh[x]^2/4","A",3,3,12,0.2500,1,"{5682, 5675, 30}"
145,1,215,0,0.2643686,"\int \frac{x^5 \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{d+c^2 d x^2}} \, dx","Int[(x^5*(a + b*ArcSinh[c*x]))/Sqrt[d + c^2*d*x^2],x]","\frac{x^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^2 d}-\frac{4 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{15 c^4 d}+\frac{8 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{15 c^6 d}-\frac{b x^5 \sqrt{c^2 x^2+1}}{25 c \sqrt{c^2 d x^2+d}}+\frac{4 b x^3 \sqrt{c^2 x^2+1}}{45 c^3 \sqrt{c^2 d x^2+d}}-\frac{8 b x \sqrt{c^2 x^2+1}}{15 c^5 \sqrt{c^2 d x^2+d}}","\frac{x^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^2 d}-\frac{4 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{15 c^4 d}+\frac{8 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{15 c^6 d}-\frac{b x^5 \sqrt{c^2 x^2+1}}{25 c \sqrt{c^2 d x^2+d}}+\frac{4 b x^3 \sqrt{c^2 x^2+1}}{45 c^3 \sqrt{c^2 d x^2+d}}-\frac{8 b x \sqrt{c^2 x^2+1}}{15 c^5 \sqrt{c^2 d x^2+d}}",1,"(-8*b*x*Sqrt[1 + c^2*x^2])/(15*c^5*Sqrt[d + c^2*d*x^2]) + (4*b*x^3*Sqrt[1 + c^2*x^2])/(45*c^3*Sqrt[d + c^2*d*x^2]) - (b*x^5*Sqrt[1 + c^2*x^2])/(25*c*Sqrt[d + c^2*d*x^2]) + (8*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(15*c^6*d) - (4*x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(15*c^4*d) + (x^4*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(5*c^2*d)","A",6,4,26,0.1538,1,"{5758, 5717, 8, 30}"
146,1,192,0,0.2524667,"\int \frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{d+c^2 d x^2}} \, dx","Int[(x^4*(a + b*ArcSinh[c*x]))/Sqrt[d + c^2*d*x^2],x]","\frac{x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{4 c^2 d}-\frac{3 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 c^4 d}+\frac{3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c^5 \sqrt{c^2 d x^2+d}}-\frac{b x^4 \sqrt{c^2 x^2+1}}{16 c \sqrt{c^2 d x^2+d}}+\frac{3 b x^2 \sqrt{c^2 x^2+1}}{16 c^3 \sqrt{c^2 d x^2+d}}","\frac{x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{4 c^2 d}-\frac{3 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 c^4 d}+\frac{3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c^5 \sqrt{c^2 d x^2+d}}-\frac{b x^4 \sqrt{c^2 x^2+1}}{16 c \sqrt{c^2 d x^2+d}}+\frac{3 b x^2 \sqrt{c^2 x^2+1}}{16 c^3 \sqrt{c^2 d x^2+d}}",1,"(3*b*x^2*Sqrt[1 + c^2*x^2])/(16*c^3*Sqrt[d + c^2*d*x^2]) - (b*x^4*Sqrt[1 + c^2*x^2])/(16*c*Sqrt[d + c^2*d*x^2]) - (3*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(8*c^4*d) + (x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(4*c^2*d) + (3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(16*b*c^5*Sqrt[d + c^2*d*x^2])","A",6,4,26,0.1538,1,"{5758, 5677, 5675, 30}"
147,1,142,0,0.1582508,"\int \frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{d+c^2 d x^2}} \, dx","Int[(x^3*(a + b*ArcSinh[c*x]))/Sqrt[d + c^2*d*x^2],x]","\frac{x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2 d}-\frac{2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^4 d}-\frac{b x^3 \sqrt{c^2 x^2+1}}{9 c \sqrt{c^2 d x^2+d}}+\frac{2 b x \sqrt{c^2 x^2+1}}{3 c^3 \sqrt{c^2 d x^2+d}}","\frac{x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2 d}-\frac{2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^4 d}-\frac{b x^3 \sqrt{c^2 x^2+1}}{9 c \sqrt{c^2 d x^2+d}}+\frac{2 b x \sqrt{c^2 x^2+1}}{3 c^3 \sqrt{c^2 d x^2+d}}",1,"(2*b*x*Sqrt[1 + c^2*x^2])/(3*c^3*Sqrt[d + c^2*d*x^2]) - (b*x^3*Sqrt[1 + c^2*x^2])/(9*c*Sqrt[d + c^2*d*x^2]) - (2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*c^4*d) + (x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*c^2*d)","A",4,4,26,0.1538,1,"{5758, 5717, 8, 30}"
148,1,119,0,0.1457909,"\int \frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{d+c^2 d x^2}} \, dx","Int[(x^2*(a + b*ArcSinh[c*x]))/Sqrt[d + c^2*d*x^2],x]","\frac{x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{2 c^2 d}-\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c^3 \sqrt{c^2 d x^2+d}}-\frac{b x^2 \sqrt{c^2 x^2+1}}{4 c \sqrt{c^2 d x^2+d}}","\frac{x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{2 c^2 d}-\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c^3 \sqrt{c^2 d x^2+d}}-\frac{b x^2 \sqrt{c^2 x^2+1}}{4 c \sqrt{c^2 d x^2+d}}",1,"-(b*x^2*Sqrt[1 + c^2*x^2])/(4*c*Sqrt[d + c^2*d*x^2]) + (x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(2*c^2*d) - (Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*c^3*Sqrt[d + c^2*d*x^2])","A",4,4,26,0.1538,1,"{5758, 5677, 5675, 30}"
149,1,64,0,0.0609169,"\int \frac{x \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{d+c^2 d x^2}} \, dx","Int[(x*(a + b*ArcSinh[c*x]))/Sqrt[d + c^2*d*x^2],x]","\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d}-\frac{b x \sqrt{c^2 x^2+1}}{c \sqrt{c^2 d x^2+d}}","\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d}-\frac{b x \sqrt{c^2 x^2+1}}{c \sqrt{c^2 d x^2+d}}",1,"-((b*x*Sqrt[1 + c^2*x^2])/(c*Sqrt[d + c^2*d*x^2])) + (Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(c^2*d)","A",2,2,24,0.08333,1,"{5717, 8}"
150,1,47,0,0.0569614,"\int \frac{a+b \sinh ^{-1}(c x)}{\sqrt{d+c^2 d x^2}} \, dx","Int[(a + b*ArcSinh[c*x])/Sqrt[d + c^2*d*x^2],x]","\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c \sqrt{c^2 d x^2+d}}","\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c \sqrt{c^2 d x^2+d}}",1,"(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c*Sqrt[d + c^2*d*x^2])","A",2,2,23,0.08696,1,"{5677, 5675}"
151,1,122,0,0.1881665,"\int \frac{a+b \sinh ^{-1}(c x)}{x \sqrt{d+c^2 d x^2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x*Sqrt[d + c^2*d*x^2]),x]","-\frac{b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 d x^2+d}}+\frac{b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 d x^2+d}}-\frac{2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 d x^2+d}}","-\frac{b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 d x^2+d}}+\frac{b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 d x^2+d}}-\frac{2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 d x^2+d}}",1,"(-2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Sqrt[d + c^2*d*x^2] - (b*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/Sqrt[d + c^2*d*x^2] + (b*Sqrt[1 + c^2*x^2]*PolyLog[2, E^ArcSinh[c*x]])/Sqrt[d + c^2*d*x^2]","A",7,5,26,0.1923,1,"{5764, 5760, 4182, 2279, 2391}"
152,1,63,0,0.0891756,"\int \frac{a+b \sinh ^{-1}(c x)}{x^2 \sqrt{d+c^2 d x^2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^2*Sqrt[d + c^2*d*x^2]),x]","\frac{b c \sqrt{c^2 x^2+1} \log (x)}{\sqrt{c^2 d x^2+d}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{d x}","\frac{b c \sqrt{c^2 x^2+1} \log (x)}{\sqrt{c^2 d x^2+d}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{d x}",1,"-((Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(d*x)) + (b*c*Sqrt[1 + c^2*x^2]*Log[x])/Sqrt[d + c^2*d*x^2]","A",2,2,26,0.07692,1,"{5723, 29}"
153,1,203,0,0.2919355,"\int \frac{a+b \sinh ^{-1}(c x)}{x^3 \sqrt{d+c^2 d x^2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^3*Sqrt[d + c^2*d*x^2]),x]","\frac{b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 d x^2+d}}-\frac{b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 d x^2+d}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{2 d x^2}+\frac{c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1}}{2 x \sqrt{c^2 d x^2+d}}","\frac{b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 d x^2+d}}-\frac{b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 \sqrt{c^2 d x^2+d}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{2 d x^2}+\frac{c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1}}{2 x \sqrt{c^2 d x^2+d}}",1,"-(b*c*Sqrt[1 + c^2*x^2])/(2*x*Sqrt[d + c^2*d*x^2]) - (Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(2*d*x^2) + (c^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/Sqrt[d + c^2*d*x^2] + (b*c^2*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/(2*Sqrt[d + c^2*d*x^2]) - (b*c^2*Sqrt[1 + c^2*x^2]*PolyLog[2, E^ArcSinh[c*x]])/(2*Sqrt[d + c^2*d*x^2])","A",9,7,26,0.2692,1,"{5747, 5764, 5760, 4182, 2279, 2391, 30}"
154,1,141,0,0.1841898,"\int \frac{a+b \sinh ^{-1}(c x)}{x^4 \sqrt{d+c^2 d x^2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^4*Sqrt[d + c^2*d*x^2]),x]","\frac{2 c^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 d x}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 d x^3}-\frac{b c \sqrt{c^2 x^2+1}}{6 x^2 \sqrt{c^2 d x^2+d}}-\frac{2 b c^3 \sqrt{c^2 x^2+1} \log (x)}{3 \sqrt{c^2 d x^2+d}}","\frac{2 c^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 d x}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 d x^3}-\frac{b c \sqrt{c^2 x^2+1}}{6 x^2 \sqrt{c^2 d x^2+d}}-\frac{2 b c^3 \sqrt{c^2 x^2+1} \log (x)}{3 \sqrt{c^2 d x^2+d}}",1,"-(b*c*Sqrt[1 + c^2*x^2])/(6*x^2*Sqrt[d + c^2*d*x^2]) - (Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*d*x^3) + (2*c^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*d*x) - (2*b*c^3*Sqrt[1 + c^2*x^2]*Log[x])/(3*Sqrt[d + c^2*d*x^2])","A",4,4,26,0.1538,1,"{5747, 5723, 29, 30}"
155,1,220,0,0.2938353,"\int \frac{x^5 \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(x^5*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^(3/2),x]","\frac{4 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^4 d^2}-\frac{8 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^6 d^2}-\frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d \sqrt{c^2 d x^2+d}}-\frac{b x^3 \sqrt{c^2 x^2+1}}{9 c^3 d \sqrt{c^2 d x^2+d}}+\frac{5 b x \sqrt{c^2 x^2+1}}{3 c^5 d \sqrt{c^2 d x^2+d}}+\frac{b \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{c^6 d \sqrt{c^2 d x^2+d}}","\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^6 d^3}-\frac{2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{c^6 d^2}-\frac{a+b \sinh ^{-1}(c x)}{c^6 d \sqrt{c^2 d x^2+d}}-\frac{b x^3 \sqrt{c^2 d x^2+d}}{9 c^3 d^2 \sqrt{c^2 x^2+1}}+\frac{5 b x \sqrt{c^2 d x^2+d}}{3 c^5 d^2 \sqrt{c^2 x^2+1}}+\frac{b \sqrt{c^2 d x^2+d} \tan ^{-1}(c x)}{c^6 d^2 \sqrt{c^2 x^2+1}}",1,"(5*b*x*Sqrt[1 + c^2*x^2])/(3*c^5*d*Sqrt[d + c^2*d*x^2]) - (b*x^3*Sqrt[1 + c^2*x^2])/(9*c^3*d*Sqrt[d + c^2*d*x^2]) - (x^4*(a + b*ArcSinh[c*x]))/(c^2*d*Sqrt[d + c^2*d*x^2]) - (8*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*c^6*d^2) + (4*x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*c^4*d^2) + (b*Sqrt[1 + c^2*x^2]*ArcTan[c*x])/(c^6*d*Sqrt[d + c^2*d*x^2])","A",8,7,26,0.2692,1,"{5751, 5758, 5717, 8, 30, 302, 203}"
156,1,206,0,0.2822457,"\int \frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(x^4*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^(3/2),x]","\frac{3 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{2 c^4 d^2}-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d \sqrt{c^2 d x^2+d}}-\frac{3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c^5 d \sqrt{c^2 d x^2+d}}-\frac{b x^2 \sqrt{c^2 x^2+1}}{4 c^3 d \sqrt{c^2 d x^2+d}}-\frac{b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{2 c^5 d \sqrt{c^2 d x^2+d}}","\frac{3 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{2 c^4 d^2}-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d \sqrt{c^2 d x^2+d}}-\frac{3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c^5 d \sqrt{c^2 d x^2+d}}-\frac{b x^2 \sqrt{c^2 x^2+1}}{4 c^3 d \sqrt{c^2 d x^2+d}}-\frac{b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{2 c^5 d \sqrt{c^2 d x^2+d}}",1,"-(b*x^2*Sqrt[1 + c^2*x^2])/(4*c^3*d*Sqrt[d + c^2*d*x^2]) - (x^3*(a + b*ArcSinh[c*x]))/(c^2*d*Sqrt[d + c^2*d*x^2]) + (3*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(2*c^4*d^2) - (3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*c^5*d*Sqrt[d + c^2*d*x^2]) - (b*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(2*c^5*d*Sqrt[d + c^2*d*x^2])","A",8,7,26,0.2692,1,"{5751, 5758, 5677, 5675, 30, 266, 43}"
157,1,141,0,0.1817237,"\int \frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(x^3*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^(3/2),x]","\frac{2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{c^4 d^2}-\frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d \sqrt{c^2 d x^2+d}}-\frac{b x \sqrt{c^2 x^2+1}}{c^3 d \sqrt{c^2 d x^2+d}}-\frac{b \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{c^4 d \sqrt{c^2 d x^2+d}}","\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{c^4 d^2}+\frac{a+b \sinh ^{-1}(c x)}{c^4 d \sqrt{c^2 d x^2+d}}-\frac{b x \sqrt{c^2 d x^2+d}}{c^3 d^2 \sqrt{c^2 x^2+1}}-\frac{b \sqrt{c^2 d x^2+d} \tan ^{-1}(c x)}{c^4 d^2 \sqrt{c^2 x^2+1}}",1,"-((b*x*Sqrt[1 + c^2*x^2])/(c^3*d*Sqrt[d + c^2*d*x^2])) - (x^2*(a + b*ArcSinh[c*x]))/(c^2*d*Sqrt[d + c^2*d*x^2]) + (2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(c^4*d^2) - (b*Sqrt[1 + c^2*x^2]*ArcTan[c*x])/(c^4*d*Sqrt[d + c^2*d*x^2])","A",5,5,26,0.1923,1,"{5751, 5717, 8, 321, 203}"
158,1,130,0,0.1681882,"\int \frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(x^2*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^(3/2),x]","\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c^3 d \sqrt{c^2 d x^2+d}}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d \sqrt{c^2 d x^2+d}}+\frac{b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{2 c^3 d \sqrt{c^2 d x^2+d}}","\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c^3 d \sqrt{c^2 d x^2+d}}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d \sqrt{c^2 d x^2+d}}+\frac{b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{2 c^3 d \sqrt{c^2 d x^2+d}}",1,"-((x*(a + b*ArcSinh[c*x]))/(c^2*d*Sqrt[d + c^2*d*x^2])) + (Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c^3*d*Sqrt[d + c^2*d*x^2]) + (b*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(2*c^3*d*Sqrt[d + c^2*d*x^2])","A",4,4,26,0.1538,1,"{5751, 5677, 5675, 260}"
159,1,70,0,0.0703006,"\int \frac{x \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(x*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^(3/2),x]","\frac{b \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{c^2 d \sqrt{c^2 d x^2+d}}-\frac{a+b \sinh ^{-1}(c x)}{c^2 d \sqrt{c^2 d x^2+d}}","\frac{b \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{c^2 d \sqrt{c^2 d x^2+d}}-\frac{a+b \sinh ^{-1}(c x)}{c^2 d \sqrt{c^2 d x^2+d}}",1,"-((a + b*ArcSinh[c*x])/(c^2*d*Sqrt[d + c^2*d*x^2])) + (b*Sqrt[1 + c^2*x^2]*ArcTan[c*x])/(c^2*d*Sqrt[d + c^2*d*x^2])","A",2,2,24,0.08333,1,"{5717, 203}"
160,1,76,0,0.0382054,"\int \frac{a+b \sinh ^{-1}(c x)}{\left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(d + c^2*d*x^2)^(3/2),x]","\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{2 c d \sqrt{c^2 d x^2+d}}","\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{2 c d \sqrt{c^2 d x^2+d}}",1,"(x*(a + b*ArcSinh[c*x]))/(d*Sqrt[d + c^2*d*x^2]) - (b*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(2*c*d*Sqrt[d + c^2*d*x^2])","A",2,2,23,0.08696,1,"{5687, 260}"
161,1,194,0,0.3033397,"\int \frac{a+b \sinh ^{-1}(c x)}{x \left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x*(d + c^2*d*x^2)^(3/2)),x]","-\frac{b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}+\frac{b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}+\frac{a+b \sinh ^{-1}(c x)}{d \sqrt{c^2 d x^2+d}}-\frac{2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{b \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{d \sqrt{c^2 d x^2+d}}","-\frac{b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}+\frac{b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}+\frac{a+b \sinh ^{-1}(c x)}{d \sqrt{c^2 d x^2+d}}-\frac{2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{b \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{d \sqrt{c^2 d x^2+d}}",1,"(a + b*ArcSinh[c*x])/(d*Sqrt[d + c^2*d*x^2]) - (b*Sqrt[1 + c^2*x^2]*ArcTan[c*x])/(d*Sqrt[d + c^2*d*x^2]) - (2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) - (b*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) + (b*Sqrt[1 + c^2*x^2]*PolyLog[2, E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2])","A",9,7,26,0.2692,1,"{5755, 5764, 5760, 4182, 2279, 2391, 203}"
162,1,143,0,0.1536532,"\int \frac{a+b \sinh ^{-1}(c x)}{x^2 \left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^2*(d + c^2*d*x^2)^(3/2)),x]","-\frac{2 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{a+b \sinh ^{-1}(c x)}{d x \sqrt{c^2 d x^2+d}}+\frac{b c \sqrt{c^2 x^2+1} \log (x)}{d \sqrt{c^2 d x^2+d}}+\frac{b c \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{2 d \sqrt{c^2 d x^2+d}}","-\frac{2 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{a+b \sinh ^{-1}(c x)}{d x \sqrt{c^2 d x^2+d}}+\frac{b c \log (x) \sqrt{c^2 d x^2+d}}{d^2 \sqrt{c^2 x^2+1}}+\frac{b c \sqrt{c^2 d x^2+d} \log \left(c^2 x^2+1\right)}{2 d^2 \sqrt{c^2 x^2+1}}",1,"-((a + b*ArcSinh[c*x])/(d*x*Sqrt[d + c^2*d*x^2])) - (2*c^2*x*(a + b*ArcSinh[c*x]))/(d*Sqrt[d + c^2*d*x^2]) + (b*c*Sqrt[1 + c^2*x^2]*Log[x])/(d*Sqrt[d + c^2*d*x^2]) + (b*c*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(2*d*Sqrt[d + c^2*d*x^2])","A",7,7,26,0.2692,1,"{5747, 5687, 260, 266, 36, 29, 31}"
163,1,287,0,0.4305311,"\int \frac{a+b \sinh ^{-1}(c x)}{x^3 \left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^3*(d + c^2*d*x^2)^(3/2)),x]","\frac{3 b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 d \sqrt{c^2 d x^2+d}}-\frac{3 b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 d \sqrt{c^2 d x^2+d}}-\frac{3 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 d \sqrt{c^2 d x^2+d}}-\frac{a+b \sinh ^{-1}(c x)}{2 d x^2 \sqrt{c^2 d x^2+d}}+\frac{3 c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1}}{2 d x \sqrt{c^2 d x^2+d}}+\frac{b c^2 \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{d \sqrt{c^2 d x^2+d}}","\frac{3 b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 d \sqrt{c^2 d x^2+d}}-\frac{3 b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 d \sqrt{c^2 d x^2+d}}-\frac{3 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 d \sqrt{c^2 d x^2+d}}-\frac{a+b \sinh ^{-1}(c x)}{2 d x^2 \sqrt{c^2 d x^2+d}}+\frac{3 c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1}}{2 d x \sqrt{c^2 d x^2+d}}+\frac{b c^2 \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{d \sqrt{c^2 d x^2+d}}",1,"-(b*c*Sqrt[1 + c^2*x^2])/(2*d*x*Sqrt[d + c^2*d*x^2]) - (3*c^2*(a + b*ArcSinh[c*x]))/(2*d*Sqrt[d + c^2*d*x^2]) - (a + b*ArcSinh[c*x])/(2*d*x^2*Sqrt[d + c^2*d*x^2]) + (b*c^2*Sqrt[1 + c^2*x^2]*ArcTan[c*x])/(d*Sqrt[d + c^2*d*x^2]) + (3*c^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) + (3*b*c^2*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/(2*d*Sqrt[d + c^2*d*x^2]) - (3*b*c^2*Sqrt[1 + c^2*x^2]*PolyLog[2, E^ArcSinh[c*x]])/(2*d*Sqrt[d + c^2*d*x^2])","A",12,9,26,0.3462,1,"{5747, 5755, 5764, 5760, 4182, 2279, 2391, 203, 325}"
164,1,228,0,0.2888483,"\int \frac{a+b \sinh ^{-1}(c x)}{x^4 \left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^4*(d + c^2*d*x^2)^(3/2)),x]","\frac{8 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d \sqrt{c^2 d x^2+d}}+\frac{4 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 d x \sqrt{c^2 d x^2+d}}-\frac{a+b \sinh ^{-1}(c x)}{3 d x^3 \sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1}}{6 d x^2 \sqrt{c^2 d x^2+d}}-\frac{5 b c^3 \sqrt{c^2 x^2+1} \log (x)}{3 d \sqrt{c^2 d x^2+d}}-\frac{b c^3 \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{2 d \sqrt{c^2 d x^2+d}}","\frac{8 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d \sqrt{c^2 d x^2+d}}+\frac{4 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 d x \sqrt{c^2 d x^2+d}}-\frac{a+b \sinh ^{-1}(c x)}{3 d x^3 \sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 d x^2+d}}{6 d^2 x^2 \sqrt{c^2 x^2+1}}-\frac{5 b c^3 \log (x) \sqrt{c^2 d x^2+d}}{3 d^2 \sqrt{c^2 x^2+1}}-\frac{b c^3 \sqrt{c^2 d x^2+d} \log \left(c^2 x^2+1\right)}{2 d^2 \sqrt{c^2 x^2+1}}",1,"-(b*c*Sqrt[1 + c^2*x^2])/(6*d*x^2*Sqrt[d + c^2*d*x^2]) - (a + b*ArcSinh[c*x])/(3*d*x^3*Sqrt[d + c^2*d*x^2]) + (4*c^2*(a + b*ArcSinh[c*x]))/(3*d*x*Sqrt[d + c^2*d*x^2]) + (8*c^4*x*(a + b*ArcSinh[c*x]))/(3*d*Sqrt[d + c^2*d*x^2]) - (5*b*c^3*Sqrt[1 + c^2*x^2]*Log[x])/(3*d*Sqrt[d + c^2*d*x^2]) - (b*c^3*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(2*d*Sqrt[d + c^2*d*x^2])","A",11,8,26,0.3077,1,"{5747, 5687, 260, 266, 36, 29, 31, 44}"
165,1,281,0,0.4347985,"\int \frac{x^6 \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(x^6*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^(5/2),x]","-\frac{5 x^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}+\frac{5 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{2 c^6 d^3}-\frac{5 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c^7 d^2 \sqrt{c^2 d x^2+d}}-\frac{x^5 \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b x^2 \sqrt{c^2 x^2+1}}{4 c^5 d^2 \sqrt{c^2 d x^2+d}}-\frac{b}{6 c^7 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{7 b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{6 c^7 d^2 \sqrt{c^2 d x^2+d}}","-\frac{5 x^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}+\frac{5 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{2 c^6 d^3}-\frac{5 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c^7 d^2 \sqrt{c^2 d x^2+d}}-\frac{x^5 \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b x^2 \sqrt{c^2 x^2+1}}{4 c^5 d^2 \sqrt{c^2 d x^2+d}}-\frac{b}{6 c^7 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{7 b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{6 c^7 d^2 \sqrt{c^2 d x^2+d}}",1,"-b/(6*c^7*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) - (b*x^2*Sqrt[1 + c^2*x^2])/(4*c^5*d^2*Sqrt[d + c^2*d*x^2]) - (x^5*(a + b*ArcSinh[c*x]))/(3*c^2*d*(d + c^2*d*x^2)^(3/2)) - (5*x^3*(a + b*ArcSinh[c*x]))/(3*c^4*d^2*Sqrt[d + c^2*d*x^2]) + (5*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(2*c^6*d^3) - (5*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*c^7*d^2*Sqrt[d + c^2*d*x^2]) - (7*b*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(6*c^7*d^2*Sqrt[d + c^2*d*x^2])","A",12,7,26,0.2692,1,"{5751, 5758, 5677, 5675, 30, 266, 43}"
166,1,225,0,0.3086643,"\int \frac{x^5 \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(x^5*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^(5/2),x]","-\frac{4 x^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}+\frac{8 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^6 d^3}-\frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b x^3}{6 c^3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{5 b x \sqrt{c^2 x^2+1}}{6 c^5 d^2 \sqrt{c^2 d x^2+d}}-\frac{11 b \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{6 c^6 d^2 \sqrt{c^2 d x^2+d}}","\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{c^6 d^3}+\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{c^6 d^2 \sqrt{c^2 d x^2+d}}-\frac{a+b \sinh ^{-1}(c x)}{3 c^6 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b x \sqrt{c^2 d x^2+d}}{c^5 d^3 \sqrt{c^2 x^2+1}}+\frac{b x \sqrt{c^2 d x^2+d}}{6 c^5 d^3 \left(c^2 x^2+1\right)^{3/2}}-\frac{11 b \sqrt{c^2 d x^2+d} \tan ^{-1}(c x)}{6 c^6 d^3 \sqrt{c^2 x^2+1}}",1,"-(b*x^3)/(6*c^3*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) - (5*b*x*Sqrt[1 + c^2*x^2])/(6*c^5*d^2*Sqrt[d + c^2*d*x^2]) - (x^4*(a + b*ArcSinh[c*x]))/(3*c^2*d*(d + c^2*d*x^2)^(3/2)) - (4*x^2*(a + b*ArcSinh[c*x]))/(3*c^4*d^2*Sqrt[d + c^2*d*x^2]) + (8*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*c^6*d^3) - (11*b*Sqrt[1 + c^2*x^2]*ArcTan[c*x])/(6*c^6*d^2*Sqrt[d + c^2*d*x^2])","A",9,6,26,0.2308,1,"{5751, 5717, 8, 321, 203, 288}"
167,1,203,0,0.2963899,"\int \frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(x^4*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^(5/2),x]","-\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{c^4 d^2 \sqrt{c^2 d x^2+d}}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c^5 d^2 \sqrt{c^2 d x^2+d}}-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2 d \left(c^2 d x^2+d\right)^{3/2}}+\frac{b}{6 c^5 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{2 b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{3 c^5 d^2 \sqrt{c^2 d x^2+d}}","-\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{c^4 d^2 \sqrt{c^2 d x^2+d}}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c^5 d^2 \sqrt{c^2 d x^2+d}}-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2 d \left(c^2 d x^2+d\right)^{3/2}}+\frac{b}{6 c^5 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{2 b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{3 c^5 d^2 \sqrt{c^2 d x^2+d}}",1,"b/(6*c^5*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) - (x^3*(a + b*ArcSinh[c*x]))/(3*c^2*d*(d + c^2*d*x^2)^(3/2)) - (x*(a + b*ArcSinh[c*x]))/(c^4*d^2*Sqrt[d + c^2*d*x^2]) + (Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c^5*d^2*Sqrt[d + c^2*d*x^2]) + (2*b*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(3*c^5*d^2*Sqrt[d + c^2*d*x^2])","A",8,6,26,0.2308,1,"{5751, 5677, 5675, 260, 266, 43}"
168,1,149,0,0.1824644,"\int \frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(x^3*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^(5/2),x]","-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}-\frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b x}{6 c^3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{5 b \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{6 c^4 d^2 \sqrt{c^2 d x^2+d}}","-\frac{a+b \sinh ^{-1}(c x)}{c^4 d^2 \sqrt{c^2 d x^2+d}}+\frac{a+b \sinh ^{-1}(c x)}{3 c^4 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b x \sqrt{c^2 d x^2+d}}{6 c^3 d^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{5 b \sqrt{c^2 d x^2+d} \tan ^{-1}(c x)}{6 c^4 d^3 \sqrt{c^2 x^2+1}}",1,"-(b*x)/(6*c^3*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) - (x^2*(a + b*ArcSinh[c*x]))/(3*c^2*d*(d + c^2*d*x^2)^(3/2)) - (2*(a + b*ArcSinh[c*x]))/(3*c^4*d^2*Sqrt[d + c^2*d*x^2]) + (5*b*Sqrt[1 + c^2*x^2]*ArcTan[c*x])/(6*c^4*d^2*Sqrt[d + c^2*d*x^2])","A",5,4,26,0.1538,1,"{5751, 5717, 203, 288}"
169,1,119,0,0.1246165,"\int \frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(x^2*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^(5/2),x]","\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b}{6 c^3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{6 c^3 d^2 \sqrt{c^2 d x^2+d}}","\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b}{6 c^3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{6 c^3 d^2 \sqrt{c^2 d x^2+d}}",1,"-b/(6*c^3*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) + (x^3*(a + b*ArcSinh[c*x]))/(3*d*(d + c^2*d*x^2)^(3/2)) - (b*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(6*c^3*d^2*Sqrt[d + c^2*d*x^2])","A",4,3,26,0.1154,1,"{5723, 266, 43}"
170,1,114,0,0.0782282,"\int \frac{x \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(x*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^(5/2),x]","-\frac{a+b \sinh ^{-1}(c x)}{3 c^2 d \left(c^2 d x^2+d\right)^{3/2}}+\frac{b x}{6 c d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{b \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{6 c^2 d^2 \sqrt{c^2 d x^2+d}}","-\frac{a+b \sinh ^{-1}(c x)}{3 c^2 d \left(c^2 d x^2+d\right)^{3/2}}+\frac{b x}{6 c d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{b \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{6 c^2 d^2 \sqrt{c^2 d x^2+d}}",1,"(b*x)/(6*c*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) - (a + b*ArcSinh[c*x])/(3*c^2*d*(d + c^2*d*x^2)^(3/2)) + (b*Sqrt[1 + c^2*x^2]*ArcTan[c*x])/(6*c^2*d^2*Sqrt[d + c^2*d*x^2])","A",3,3,24,0.1250,1,"{5717, 199, 203}"
171,1,147,0,0.0794904,"\int \frac{a+b \sinh ^{-1}(c x)}{\left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(d + c^2*d*x^2)^(5/2),x]","\frac{2 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{3 d \left(c^2 d x^2+d\right)^{3/2}}+\frac{b}{6 c d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{3 c d^2 \sqrt{c^2 d x^2+d}}","\frac{2 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{3 d \left(c^2 d x^2+d\right)^{3/2}}+\frac{b}{6 c d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{b \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{3 c d^2 \sqrt{c^2 d x^2+d}}",1,"b/(6*c*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) + (x*(a + b*ArcSinh[c*x]))/(3*d*(d + c^2*d*x^2)^(3/2)) + (2*x*(a + b*ArcSinh[c*x]))/(3*d^2*Sqrt[d + c^2*d*x^2]) - (b*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(3*c*d^2*Sqrt[d + c^2*d*x^2])","A",4,4,23,0.1739,1,"{5690, 5687, 260, 261}"
172,1,262,0,0.4152737,"\int \frac{a+b \sinh ^{-1}(c x)}{x \left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x*(d + c^2*d*x^2)^(5/2)),x]","-\frac{b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{d^2 \sqrt{c^2 d x^2+d}}+\frac{b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{d^2 \sqrt{c^2 d x^2+d}}+\frac{a+b \sinh ^{-1}(c x)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 d x^2+d}}+\frac{a+b \sinh ^{-1}(c x)}{3 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b c x}{6 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{7 b \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{6 d^2 \sqrt{c^2 d x^2+d}}","-\frac{b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{d^2 \sqrt{c^2 d x^2+d}}+\frac{b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{d^2 \sqrt{c^2 d x^2+d}}+\frac{a+b \sinh ^{-1}(c x)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 d x^2+d}}+\frac{a+b \sinh ^{-1}(c x)}{3 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b c x}{6 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{7 b \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{6 d^2 \sqrt{c^2 d x^2+d}}",1,"-(b*c*x)/(6*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) + (a + b*ArcSinh[c*x])/(3*d*(d + c^2*d*x^2)^(3/2)) + (a + b*ArcSinh[c*x])/(d^2*Sqrt[d + c^2*d*x^2]) - (7*b*Sqrt[1 + c^2*x^2]*ArcTan[c*x])/(6*d^2*Sqrt[d + c^2*d*x^2]) - (2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2]) - (b*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2]) + (b*Sqrt[1 + c^2*x^2]*PolyLog[2, E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2])","A",12,8,26,0.3077,1,"{5755, 5764, 5760, 4182, 2279, 2391, 203, 199}"
173,1,214,0,0.2130781,"\int \frac{a+b \sinh ^{-1}(c x)}{x^2 \left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^2*(d + c^2*d*x^2)^(5/2)),x]","-\frac{8 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{4 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{a+b \sinh ^{-1}(c x)}{d x \left(c^2 d x^2+d\right)^{3/2}}-\frac{b c}{6 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{b c \sqrt{c^2 x^2+1} \log (x)}{d^2 \sqrt{c^2 d x^2+d}}+\frac{5 b c \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{6 d^2 \sqrt{c^2 d x^2+d}}","-\frac{8 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{4 c^2 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{a+b \sinh ^{-1}(c x)}{d x \left(c^2 d x^2+d\right)^{3/2}}-\frac{b c \sqrt{c^2 d x^2+d}}{6 d^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{b c \log (x) \sqrt{c^2 d x^2+d}}{d^3 \sqrt{c^2 x^2+1}}+\frac{5 b c \sqrt{c^2 d x^2+d} \log \left(c^2 x^2+1\right)}{6 d^3 \sqrt{c^2 x^2+1}}",1,"-(b*c)/(6*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) - (a + b*ArcSinh[c*x])/(d*x*(d + c^2*d*x^2)^(3/2)) - (4*c^2*x*(a + b*ArcSinh[c*x]))/(3*d*(d + c^2*d*x^2)^(3/2)) - (8*c^2*x*(a + b*ArcSinh[c*x]))/(3*d^2*Sqrt[d + c^2*d*x^2]) + (b*c*Sqrt[1 + c^2*x^2]*Log[x])/(d^2*Sqrt[d + c^2*d*x^2]) + (5*b*c*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(6*d^2*Sqrt[d + c^2*d*x^2])","A",8,7,26,0.2692,1,"{5747, 5690, 5687, 260, 261, 266, 44}"
174,1,400,0,0.5599308,"\int \frac{a+b \sinh ^{-1}(c x)}{x^3 \left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^3*(d + c^2*d*x^2)^(5/2)),x]","\frac{5 b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 d^2 \sqrt{c^2 d x^2+d}}-\frac{5 b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 d^2 \sqrt{c^2 d x^2+d}}-\frac{5 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 d^2 \sqrt{c^2 d x^2+d}}+\frac{5 c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{5 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{6 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{a+b \sinh ^{-1}(c x)}{2 d x^2 \left(c^2 d x^2+d\right)^{3/2}}+\frac{5 b c^3 x}{12 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{3 b c \sqrt{c^2 x^2+1}}{4 d^2 x \sqrt{c^2 d x^2+d}}+\frac{b c}{4 d^2 x \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{13 b c^2 \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{6 d^2 \sqrt{c^2 d x^2+d}}","\frac{5 b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{2 d^2 \sqrt{c^2 d x^2+d}}-\frac{5 b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{2 d^2 \sqrt{c^2 d x^2+d}}-\frac{5 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 d^2 \sqrt{c^2 d x^2+d}}+\frac{5 c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{5 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{6 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{a+b \sinh ^{-1}(c x)}{2 d x^2 \left(c^2 d x^2+d\right)^{3/2}}+\frac{5 b c^3 x}{12 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{3 b c \sqrt{c^2 x^2+1}}{4 d^2 x \sqrt{c^2 d x^2+d}}+\frac{b c}{4 d^2 x \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{13 b c^2 \sqrt{c^2 x^2+1} \tan ^{-1}(c x)}{6 d^2 \sqrt{c^2 d x^2+d}}",1,"(b*c)/(4*d^2*x*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) + (5*b*c^3*x)/(12*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) - (3*b*c*Sqrt[1 + c^2*x^2])/(4*d^2*x*Sqrt[d + c^2*d*x^2]) - (5*c^2*(a + b*ArcSinh[c*x]))/(6*d*(d + c^2*d*x^2)^(3/2)) - (a + b*ArcSinh[c*x])/(2*d*x^2*(d + c^2*d*x^2)^(3/2)) - (5*c^2*(a + b*ArcSinh[c*x]))/(2*d^2*Sqrt[d + c^2*d*x^2]) + (13*b*c^2*Sqrt[1 + c^2*x^2]*ArcTan[c*x])/(6*d^2*Sqrt[d + c^2*d*x^2]) + (5*c^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2]) + (5*b*c^2*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^ArcSinh[c*x]])/(2*d^2*Sqrt[d + c^2*d*x^2]) - (5*b*c^2*Sqrt[1 + c^2*x^2]*PolyLog[2, E^ArcSinh[c*x]])/(2*d^2*Sqrt[d + c^2*d*x^2])","A",16,11,26,0.4231,1,"{5747, 5755, 5764, 5760, 4182, 2279, 2391, 203, 199, 290, 325}"
175,1,297,0,0.3723791,"\int \frac{a+b \sinh ^{-1}(c x)}{x^4 \left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(x^4*(d + c^2*d*x^2)^(5/2)),x]","\frac{16 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{8 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d \left(c^2 d x^2+d\right)^{3/2}}+\frac{2 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{d x \left(c^2 d x^2+d\right)^{3/2}}-\frac{a+b \sinh ^{-1}(c x)}{3 d x^3 \left(c^2 d x^2+d\right)^{3/2}}+\frac{b c^3}{6 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1}}{6 d^2 x^2 \sqrt{c^2 d x^2+d}}-\frac{8 b c^3 \sqrt{c^2 x^2+1} \log (x)}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{4 b c^3 \sqrt{c^2 x^2+1} \log \left(c^2 x^2+1\right)}{3 d^2 \sqrt{c^2 d x^2+d}}","\frac{16 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{8 c^4 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d \left(c^2 d x^2+d\right)^{3/2}}+\frac{2 c^2 \left(a+b \sinh ^{-1}(c x)\right)}{d x \left(c^2 d x^2+d\right)^{3/2}}-\frac{a+b \sinh ^{-1}(c x)}{3 d x^3 \left(c^2 d x^2+d\right)^{3/2}}+\frac{b c^3 \sqrt{c^2 d x^2+d}}{6 d^3 \left(c^2 x^2+1\right)^{3/2}}-\frac{b c \sqrt{c^2 d x^2+d}}{6 d^3 x^2 \sqrt{c^2 x^2+1}}-\frac{8 b c^3 \log (x) \sqrt{c^2 d x^2+d}}{3 d^3 \sqrt{c^2 x^2+1}}-\frac{4 b c^3 \sqrt{c^2 d x^2+d} \log \left(c^2 x^2+1\right)}{3 d^3 \sqrt{c^2 x^2+1}}",1,"(b*c^3)/(6*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) - (b*c*Sqrt[1 + c^2*x^2])/(6*d^2*x^2*Sqrt[d + c^2*d*x^2]) - (a + b*ArcSinh[c*x])/(3*d*x^3*(d + c^2*d*x^2)^(3/2)) + (2*c^2*(a + b*ArcSinh[c*x]))/(d*x*(d + c^2*d*x^2)^(3/2)) + (8*c^4*x*(a + b*ArcSinh[c*x]))/(3*d*(d + c^2*d*x^2)^(3/2)) + (16*c^4*x*(a + b*ArcSinh[c*x]))/(3*d^2*Sqrt[d + c^2*d*x^2]) - (8*b*c^3*Sqrt[1 + c^2*x^2]*Log[x])/(3*d^2*Sqrt[d + c^2*d*x^2]) - (4*b*c^3*Sqrt[1 + c^2*x^2]*Log[1 + c^2*x^2])/(3*d^2*Sqrt[d + c^2*d*x^2])","A",12,7,26,0.2692,1,"{5747, 5690, 5687, 260, 261, 266, 44}"
176,1,200,0,0.112084,"\int \frac{\sinh ^{-1}(a x)}{\left(c+a^2 c x^2\right)^{7/2}} \, dx","Int[ArcSinh[a*x]/(c + a^2*c*x^2)^(7/2),x]","\frac{2}{15 a c^3 \sqrt{a^2 x^2+1} \sqrt{a^2 c x^2+c}}+\frac{1}{20 a c^3 \left(a^2 x^2+1\right)^{3/2} \sqrt{a^2 c x^2+c}}-\frac{4 \sqrt{a^2 x^2+1} \log \left(a^2 x^2+1\right)}{15 a c^3 \sqrt{a^2 c x^2+c}}+\frac{8 x \sinh ^{-1}(a x)}{15 c^3 \sqrt{a^2 c x^2+c}}+\frac{4 x \sinh ^{-1}(a x)}{15 c^2 \left(a^2 c x^2+c\right)^{3/2}}+\frac{x \sinh ^{-1}(a x)}{5 c \left(a^2 c x^2+c\right)^{5/2}}","\frac{2}{15 a c^3 \sqrt{a^2 x^2+1} \sqrt{a^2 c x^2+c}}+\frac{1}{20 a c^3 \left(a^2 x^2+1\right)^{3/2} \sqrt{a^2 c x^2+c}}-\frac{4 \sqrt{a^2 x^2+1} \log \left(a^2 x^2+1\right)}{15 a c^3 \sqrt{a^2 c x^2+c}}+\frac{8 x \sinh ^{-1}(a x)}{15 c^3 \sqrt{a^2 c x^2+c}}+\frac{4 x \sinh ^{-1}(a x)}{15 c^2 \left(a^2 c x^2+c\right)^{3/2}}+\frac{x \sinh ^{-1}(a x)}{5 c \left(a^2 c x^2+c\right)^{5/2}}",1,"1/(20*a*c^3*(1 + a^2*x^2)^(3/2)*Sqrt[c + a^2*c*x^2]) + 2/(15*a*c^3*Sqrt[1 + a^2*x^2]*Sqrt[c + a^2*c*x^2]) + (x*ArcSinh[a*x])/(5*c*(c + a^2*c*x^2)^(5/2)) + (4*x*ArcSinh[a*x])/(15*c^2*(c + a^2*c*x^2)^(3/2)) + (8*x*ArcSinh[a*x])/(15*c^3*Sqrt[c + a^2*c*x^2]) - (4*Sqrt[1 + a^2*x^2]*Log[1 + a^2*x^2])/(15*a*c^3*Sqrt[c + a^2*c*x^2])","A",6,4,19,0.2105,1,"{5690, 5687, 260, 261}"
177,1,86,0,0.1459458,"\int \frac{x^4 \sinh ^{-1}(a x)}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^4*ArcSinh[a*x])/Sqrt[1 + a^2*x^2],x]","\frac{3 x^2}{16 a^3}+\frac{x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{4 a^2}-\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{8 a^4}+\frac{3 \sinh ^{-1}(a x)^2}{16 a^5}-\frac{x^4}{16 a}","\frac{3 x^2}{16 a^3}+\frac{x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{4 a^2}-\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{8 a^4}+\frac{3 \sinh ^{-1}(a x)^2}{16 a^5}-\frac{x^4}{16 a}",1,"(3*x^2)/(16*a^3) - x^4/(16*a) - (3*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(8*a^4) + (x^3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(4*a^2) + (3*ArcSinh[a*x]^2)/(16*a^5)","A",5,3,21,0.1429,1,"{5758, 5675, 30}"
178,1,70,0,0.1029409,"\int \frac{x^3 \sinh ^{-1}(a x)}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^3*ArcSinh[a*x])/Sqrt[1 + a^2*x^2],x]","\frac{x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{3 a^2}-\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{3 a^4}+\frac{2 x}{3 a^3}-\frac{x^3}{9 a}","\frac{x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{3 a^2}-\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{3 a^4}+\frac{2 x}{3 a^3}-\frac{x^3}{9 a}",1,"(2*x)/(3*a^3) - x^3/(9*a) - (2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(3*a^4) + (x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(3*a^2)","A",4,4,21,0.1905,1,"{5758, 5717, 8, 30}"
179,1,49,0,0.0807102,"\int \frac{x^2 \sinh ^{-1}(a x)}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^2*ArcSinh[a*x])/Sqrt[1 + a^2*x^2],x]","\frac{x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{2 a^2}-\frac{\sinh ^{-1}(a x)^2}{4 a^3}-\frac{x^2}{4 a}","\frac{x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{2 a^2}-\frac{\sinh ^{-1}(a x)^2}{4 a^3}-\frac{x^2}{4 a}",1,"-x^2/(4*a) + (x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(2*a^2) - ArcSinh[a*x]^2/(4*a^3)","A",3,3,21,0.1429,1,"{5758, 5675, 30}"
180,1,28,0,0.0419967,"\int \frac{x \sinh ^{-1}(a x)}{\sqrt{1+a^2 x^2}} \, dx","Int[(x*ArcSinh[a*x])/Sqrt[1 + a^2*x^2],x]","\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{a^2}-\frac{x}{a}","\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{a^2}-\frac{x}{a}",1,"-(x/a) + (Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/a^2","A",2,2,19,0.1053,1,"{5717, 8}"
181,1,13,0,0.0198992,"\int \frac{\sinh ^{-1}(a x)}{\sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]/Sqrt[1 + a^2*x^2],x]","\frac{\sinh ^{-1}(a x)^2}{2 a}","\frac{\sinh ^{-1}(a x)^2}{2 a}",1,"ArcSinh[a*x]^2/(2*a)","A",1,1,18,0.05556,1,"{5675}"
182,1,34,0,0.0854683,"\int \frac{\sinh ^{-1}(a x)}{x \sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]/(x*Sqrt[1 + a^2*x^2]),x]","-\text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+\text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-2 \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)","-\text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+\text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-2 \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)",1,"-2*ArcSinh[a*x]*ArcTanh[E^ArcSinh[a*x]] - PolyLog[2, -E^ArcSinh[a*x]] + PolyLog[2, E^ArcSinh[a*x]]","A",6,4,21,0.1905,1,"{5760, 4182, 2279, 2391}"
183,1,27,0,0.058963,"\int \frac{\sinh ^{-1}(a x)}{x^2 \sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]/(x^2*Sqrt[1 + a^2*x^2]),x]","a \log (x)-\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{x}","a \log (x)-\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{x}",1,"-((Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/x) + a*Log[x]","A",2,2,21,0.09524,1,"{5723, 29}"
184,1,80,0,0.1439102,"\int \frac{\sinh ^{-1}(a x)}{x^3 \sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]/(x^3*Sqrt[1 + a^2*x^2]),x]","\frac{1}{2} a^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)-\frac{1}{2} a^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{2 x^2}+a^2 \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-\frac{a}{2 x}","\frac{1}{2} a^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)-\frac{1}{2} a^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{2 x^2}+a^2 \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-\frac{a}{2 x}",1,"-a/(2*x) - (Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(2*x^2) + a^2*ArcSinh[a*x]*ArcTanh[E^ArcSinh[a*x]] + (a^2*PolyLog[2, -E^ArcSinh[a*x]])/2 - (a^2*PolyLog[2, E^ArcSinh[a*x]])/2","A",8,6,21,0.2857,1,"{5747, 5760, 4182, 2279, 2391, 30}"
185,1,313,0,2.1722616,"\int x^m \left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^m*(d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x]),x]","\frac{3 c^2 d^3 x^{m+3} \left(a+b \sinh ^{-1}(c x)\right)}{m+3}+\frac{3 c^4 d^3 x^{m+5} \left(a+b \sinh ^{-1}(c x)\right)}{m+5}+\frac{c^6 d^3 x^{m+7} \left(a+b \sinh ^{-1}(c x)\right)}{m+7}+\frac{d^3 x^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{m+1}-\frac{3 b c d^3 \left(35 m^3+455 m^2+1813 m+2161\right) x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-c^2 x^2\right)}{(m+1) (m+2) (m+3)^2 (m+5)^2 (m+7)^2}-\frac{b c d^3 \left(m^4+27 m^3+284 m^2+1329 m+2271\right) \sqrt{c^2 x^2+1} x^{m+2}}{(m+3)^2 (m+5)^2 (m+7)^2}-\frac{b c^3 d^3 (m+9) (2 m+13) \sqrt{c^2 x^2+1} x^{m+4}}{(m+5)^2 (m+7)^2}-\frac{b c^5 d^3 \sqrt{c^2 x^2+1} x^{m+6}}{(m+7)^2}","\frac{3 c^2 d^3 x^{m+3} \left(a+b \sinh ^{-1}(c x)\right)}{m+3}+\frac{3 c^4 d^3 x^{m+5} \left(a+b \sinh ^{-1}(c x)\right)}{m+5}+\frac{c^6 d^3 x^{m+7} \left(a+b \sinh ^{-1}(c x)\right)}{m+7}+\frac{d^3 x^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{m+1}-\frac{3 b c d^3 \left(35 m^3+455 m^2+1813 m+2161\right) x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-c^2 x^2\right)}{(m+1) (m+2) (m+3)^2 (m+5)^2 (m+7)^2}-\frac{b c d^3 \left(m^4+27 m^3+284 m^2+1329 m+2271\right) \sqrt{c^2 x^2+1} x^{m+2}}{(m+3)^2 (m+5)^2 (m+7)^2}-\frac{b c^3 d^3 (m+9) (2 m+13) \sqrt{c^2 x^2+1} x^{m+4}}{(m+5)^2 (m+7)^2}-\frac{b c^5 d^3 \sqrt{c^2 x^2+1} x^{m+6}}{(m+7)^2}",1,"-((b*c*d^3*(2271 + 1329*m + 284*m^2 + 27*m^3 + m^4)*x^(2 + m)*Sqrt[1 + c^2*x^2])/((3 + m)^2*(5 + m)^2*(7 + m)^2)) - (b*c^3*d^3*(9 + m)*(13 + 2*m)*x^(4 + m)*Sqrt[1 + c^2*x^2])/((5 + m)^2*(7 + m)^2) - (b*c^5*d^3*x^(6 + m)*Sqrt[1 + c^2*x^2])/(7 + m)^2 + (d^3*x^(1 + m)*(a + b*ArcSinh[c*x]))/(1 + m) + (3*c^2*d^3*x^(3 + m)*(a + b*ArcSinh[c*x]))/(3 + m) + (3*c^4*d^3*x^(5 + m)*(a + b*ArcSinh[c*x]))/(5 + m) + (c^6*d^3*x^(7 + m)*(a + b*ArcSinh[c*x]))/(7 + m) - (3*b*c*d^3*(2161 + 1813*m + 455*m^2 + 35*m^3)*x^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, -(c^2*x^2)])/((1 + m)*(2 + m)*(3 + m)^2*(5 + m)^2*(7 + m)^2)","A",6,7,24,0.2917,1,"{270, 5730, 12, 1809, 1267, 459, 364}"
186,1,217,0,0.2966692,"\int x^m \left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^m*(d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x]),x]","\frac{2 c^2 d^2 x^{m+3} \left(a+b \sinh ^{-1}(c x)\right)}{m+3}+\frac{c^4 d^2 x^{m+5} \left(a+b \sinh ^{-1}(c x)\right)}{m+5}+\frac{d^2 x^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{m+1}-\frac{b c d^2 \left(15 m^2+100 m+149\right) x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-c^2 x^2\right)}{(m+1) (m+2) (m+3)^2 (m+5)^2}-\frac{b c d^2 \left(m^2+13 m+38\right) \sqrt{c^2 x^2+1} x^{m+2}}{(m+3)^2 (m+5)^2}-\frac{b c^3 d^2 \sqrt{c^2 x^2+1} x^{m+4}}{(m+5)^2}","\frac{2 c^2 d^2 x^{m+3} \left(a+b \sinh ^{-1}(c x)\right)}{m+3}+\frac{c^4 d^2 x^{m+5} \left(a+b \sinh ^{-1}(c x)\right)}{m+5}+\frac{d^2 x^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{m+1}-\frac{b c d^2 \left(15 m^2+100 m+149\right) x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-c^2 x^2\right)}{(m+1) (m+2) (m+3)^2 (m+5)^2}-\frac{b c d^2 \left(m^2+13 m+38\right) \sqrt{c^2 x^2+1} x^{m+2}}{(m+3)^2 (m+5)^2}-\frac{b c^3 d^2 \sqrt{c^2 x^2+1} x^{m+4}}{(m+5)^2}",1,"-((b*c*d^2*(38 + 13*m + m^2)*x^(2 + m)*Sqrt[1 + c^2*x^2])/((3 + m)^2*(5 + m)^2)) - (b*c^3*d^2*x^(4 + m)*Sqrt[1 + c^2*x^2])/(5 + m)^2 + (d^2*x^(1 + m)*(a + b*ArcSinh[c*x]))/(1 + m) + (2*c^2*d^2*x^(3 + m)*(a + b*ArcSinh[c*x]))/(3 + m) + (c^4*d^2*x^(5 + m)*(a + b*ArcSinh[c*x]))/(5 + m) - (b*c*d^2*(149 + 100*m + 15*m^2)*x^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, -(c^2*x^2)])/((1 + m)*(2 + m)*(3 + m)^2*(5 + m)^2)","A",5,6,24,0.2500,1,"{270, 5730, 12, 1267, 459, 364}"
187,1,128,0,0.1295716,"\int x^m \left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^m*(d + c^2*d*x^2)*(a + b*ArcSinh[c*x]),x]","\frac{c^2 d x^{m+3} \left(a+b \sinh ^{-1}(c x)\right)}{m+3}+\frac{d x^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{m+1}-\frac{b c d (3 m+7) x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-c^2 x^2\right)}{(m+1) (m+2) (m+3)^2}-\frac{b c d \sqrt{c^2 x^2+1} x^{m+2}}{(m+3)^2}","\frac{c^2 d x^{m+3} \left(a+b \sinh ^{-1}(c x)\right)}{m+3}+\frac{d x^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{m+1}-\frac{b c d (3 m+7) x^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-c^2 x^2\right)}{(m+1) (m+2) (m+3)^2}-\frac{b c d \sqrt{c^2 x^2+1} x^{m+2}}{(m+3)^2}",1,"-((b*c*d*x^(2 + m)*Sqrt[1 + c^2*x^2])/(3 + m)^2) + (d*x^(1 + m)*(a + b*ArcSinh[c*x]))/(1 + m) + (c^2*d*x^(3 + m)*(a + b*ArcSinh[c*x]))/(3 + m) - (b*c*d*(7 + 3*m)*x^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, -(c^2*x^2)])/((1 + m)*(2 + m)*(3 + m)^2)","A",4,5,22,0.2273,1,"{14, 5730, 12, 459, 364}"
188,0,0,0,0.0707081,"\int \frac{x^m \left(a+b \sinh ^{-1}(c x)\right)}{d+c^2 d x^2} \, dx","Int[(x^m*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2),x]","\int \frac{x^m \left(a+b \sinh ^{-1}(c x)\right)}{d+c^2 d x^2} \, dx","\text{Int}\left(\frac{x^m \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d x^2+d},x\right)",0,"Defer[Int][(x^m*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2), x]","A",0,0,0,0,-1,"{}"
189,0,0,0,0.1581763,"\int \frac{x^m \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^2} \, dx","Int[(x^m*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^2,x]","\int \frac{x^m \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^2} \, dx","\frac{(1-m) \text{Int}\left(\frac{x^m \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d x^2+d},x\right)}{2 d}+\frac{x^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 d^2 \left(c^2 x^2+1\right)}-\frac{b c 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 (m+2)}",0,"(x^(1 + m)*(a + b*ArcSinh[c*x]))/(2*d^2*(1 + c^2*x^2)) - (b*c*x^(2 + m)*Hypergeometric2F1[3/2, (2 + m)/2, (4 + m)/2, -(c^2*x^2)])/(2*d^2*(2 + m)) + ((1 - m)*Defer[Int][(x^m*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2), x])/(2*d)","A",0,0,0,0,-1,"{}"
190,0,0,0,0.2533052,"\int \frac{x^m \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^3} \, dx","Int[(x^m*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^3,x]","\int \frac{x^m \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^3} \, dx","\frac{(1-m) (3-m) \text{Int}\left(\frac{x^m \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d x^2+d},x\right)}{8 d^2}+\frac{(3-m) x^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{8 d^3 \left(c^2 x^2+1\right)}+\frac{x^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3 \left(c^2 x^2+1\right)^2}-\frac{b c (3-m) 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 (m+2)}-\frac{b c 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 (m+2)}",0,"(x^(1 + m)*(a + b*ArcSinh[c*x]))/(4*d^3*(1 + c^2*x^2)^2) + ((3 - m)*x^(1 + m)*(a + b*ArcSinh[c*x]))/(8*d^3*(1 + c^2*x^2)) - (b*c*(3 - m)*x^(2 + m)*Hypergeometric2F1[3/2, (2 + m)/2, (4 + m)/2, -(c^2*x^2)])/(8*d^3*(2 + m)) - (b*c*x^(2 + m)*Hypergeometric2F1[5/2, (2 + m)/2, (4 + m)/2, -(c^2*x^2)])/(4*d^3*(2 + m)) + ((1 - m)*(3 - m)*Defer[Int][(x^m*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2), x])/(8*d^2)","A",0,0,0,0,-1,"{}"
191,1,618,0,0.5561822,"\int x^m \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^m*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]),x]","-\frac{15 b c d^2 x^{m+2} \sqrt{c^2 d x^2+d} \, _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)}{(m+1) (m+2)^2 (m+4) (m+6) \sqrt{c^2 x^2+1}}+\frac{15 d^2 x^{m+1} \sqrt{c^2 d x^2+d} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-c^2 x^2\right) \left(a+b \sinh ^{-1}(c x)\right)}{(m+6) \left(m^3+7 m^2+14 m+8\right) \sqrt{c^2 x^2+1}}+\frac{15 d^2 x^{m+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{(m+6) \left(m^2+6 m+8\right)}+\frac{x^{m+1} \left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{m+6}+\frac{5 d x^{m+1} \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{(m+4) (m+6)}-\frac{5 b c d^2 x^{m+2} \sqrt{c^2 d x^2+d}}{(m+6) \left(m^2+6 m+8\right) \sqrt{c^2 x^2+1}}-\frac{b c d^2 x^{m+2} \sqrt{c^2 d x^2+d}}{\left(m^2+8 m+12\right) \sqrt{c^2 x^2+1}}-\frac{15 b c d^2 x^{m+2} \sqrt{c^2 d x^2+d}}{(m+2)^2 (m+4) (m+6) \sqrt{c^2 x^2+1}}-\frac{2 b c^3 d^2 x^{m+4} \sqrt{c^2 d x^2+d}}{(m+4) (m+6) \sqrt{c^2 x^2+1}}-\frac{5 b c^3 d^2 x^{m+4} \sqrt{c^2 d x^2+d}}{(m+4)^2 (m+6) \sqrt{c^2 x^2+1}}-\frac{b c^5 d^2 x^{m+6} \sqrt{c^2 d x^2+d}}{(m+6)^2 \sqrt{c^2 x^2+1}}","-\frac{15 b c d^2 x^{m+2} \sqrt{c^2 d x^2+d} \, _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)}{(m+1) (m+2)^2 (m+4) (m+6) \sqrt{c^2 x^2+1}}+\frac{15 d^2 x^{m+1} \sqrt{c^2 d x^2+d} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-c^2 x^2\right) \left(a+b \sinh ^{-1}(c x)\right)}{(m+6) \left(m^3+7 m^2+14 m+8\right) \sqrt{c^2 x^2+1}}+\frac{15 d^2 x^{m+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{(m+6) \left(m^2+6 m+8\right)}+\frac{x^{m+1} \left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{m+6}+\frac{5 d x^{m+1} \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{(m+4) (m+6)}-\frac{5 b c d^2 x^{m+2} \sqrt{c^2 d x^2+d}}{(m+6) \left(m^2+6 m+8\right) \sqrt{c^2 x^2+1}}-\frac{b c d^2 x^{m+2} \sqrt{c^2 d x^2+d}}{\left(m^2+8 m+12\right) \sqrt{c^2 x^2+1}}-\frac{15 b c d^2 x^{m+2} \sqrt{c^2 d x^2+d}}{(m+2)^2 (m+4) (m+6) \sqrt{c^2 x^2+1}}-\frac{2 b c^3 d^2 x^{m+4} \sqrt{c^2 d x^2+d}}{(m+4) (m+6) \sqrt{c^2 x^2+1}}-\frac{5 b c^3 d^2 x^{m+4} \sqrt{c^2 d x^2+d}}{(m+4)^2 (m+6) \sqrt{c^2 x^2+1}}-\frac{b c^5 d^2 x^{m+6} \sqrt{c^2 d x^2+d}}{(m+6)^2 \sqrt{c^2 x^2+1}}",1,"(-15*b*c*d^2*x^(2 + m)*Sqrt[d + c^2*d*x^2])/((2 + m)^2*(4 + m)*(6 + m)*Sqrt[1 + c^2*x^2]) - (5*b*c*d^2*x^(2 + m)*Sqrt[d + c^2*d*x^2])/((6 + m)*(8 + 6*m + m^2)*Sqrt[1 + c^2*x^2]) - (b*c*d^2*x^(2 + m)*Sqrt[d + c^2*d*x^2])/((12 + 8*m + m^2)*Sqrt[1 + c^2*x^2]) - (5*b*c^3*d^2*x^(4 + m)*Sqrt[d + c^2*d*x^2])/((4 + m)^2*(6 + m)*Sqrt[1 + c^2*x^2]) - (2*b*c^3*d^2*x^(4 + m)*Sqrt[d + c^2*d*x^2])/((4 + m)*(6 + m)*Sqrt[1 + c^2*x^2]) - (b*c^5*d^2*x^(6 + m)*Sqrt[d + c^2*d*x^2])/((6 + m)^2*Sqrt[1 + c^2*x^2]) + (15*d^2*x^(1 + m)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/((6 + m)*(8 + 6*m + m^2)) + (5*d*x^(1 + m)*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/((4 + m)*(6 + m)) + (x^(1 + m)*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(6 + m) + (15*d^2*x^(1 + m)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -(c^2*x^2)])/((6 + m)*(8 + 14*m + 7*m^2 + m^3)*Sqrt[1 + c^2*x^2]) - (15*b*c*d^2*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)])/((1 + m)*(2 + m)^2*(4 + m)*(6 + m)*Sqrt[1 + c^2*x^2])","A",9,6,26,0.2308,1,"{5744, 5742, 5762, 30, 14, 270}"
192,1,390,0,0.330163,"\int x^m \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^m*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]),x]","-\frac{3 b c d x^{m+2} \sqrt{c^2 d x^2+d} \, _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)}{(m+1) (m+2)^2 (m+4) \sqrt{c^2 x^2+1}}+\frac{3 d x^{m+1} \sqrt{c^2 d x^2+d} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-c^2 x^2\right) \left(a+b \sinh ^{-1}(c x)\right)}{\left(m^3+7 m^2+14 m+8\right) \sqrt{c^2 x^2+1}}+\frac{3 d x^{m+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{m^2+6 m+8}+\frac{x^{m+1} \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{m+4}-\frac{b c d x^{m+2} \sqrt{c^2 d x^2+d}}{\left(m^2+6 m+8\right) \sqrt{c^2 x^2+1}}-\frac{3 b c d x^{m+2} \sqrt{c^2 d x^2+d}}{(m+2)^2 (m+4) \sqrt{c^2 x^2+1}}-\frac{b c^3 d x^{m+4} \sqrt{c^2 d x^2+d}}{(m+4)^2 \sqrt{c^2 x^2+1}}","-\frac{3 b c d x^{m+2} \sqrt{c^2 d x^2+d} \, _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)}{(m+1) (m+2)^2 (m+4) \sqrt{c^2 x^2+1}}+\frac{3 d x^{m+1} \sqrt{c^2 d x^2+d} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-c^2 x^2\right) \left(a+b \sinh ^{-1}(c x)\right)}{\left(m^3+7 m^2+14 m+8\right) \sqrt{c^2 x^2+1}}+\frac{3 d x^{m+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{m^2+6 m+8}+\frac{x^{m+1} \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{m+4}-\frac{b c d x^{m+2} \sqrt{c^2 d x^2+d}}{\left(m^2+6 m+8\right) \sqrt{c^2 x^2+1}}-\frac{3 b c d x^{m+2} \sqrt{c^2 d x^2+d}}{(m+2)^2 (m+4) \sqrt{c^2 x^2+1}}-\frac{b c^3 d x^{m+4} \sqrt{c^2 d x^2+d}}{(m+4)^2 \sqrt{c^2 x^2+1}}",1,"(-3*b*c*d*x^(2 + m)*Sqrt[d + c^2*d*x^2])/((2 + m)^2*(4 + m)*Sqrt[1 + c^2*x^2]) - (b*c*d*x^(2 + m)*Sqrt[d + c^2*d*x^2])/((8 + 6*m + m^2)*Sqrt[1 + c^2*x^2]) - (b*c^3*d*x^(4 + m)*Sqrt[d + c^2*d*x^2])/((4 + m)^2*Sqrt[1 + c^2*x^2]) + (3*d*x^(1 + m)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(8 + 6*m + m^2) + (x^(1 + m)*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(4 + m) + (3*d*x^(1 + m)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -(c^2*x^2)])/((8 + 14*m + 7*m^2 + m^3)*Sqrt[1 + c^2*x^2]) - (3*b*c*d*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)])/((1 + m)*(2 + m)^2*(4 + m)*Sqrt[1 + c^2*x^2])","A",6,5,26,0.1923,1,"{5744, 5742, 5762, 30, 14}"
193,1,240,0,0.2027712,"\int x^m \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[x^m*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]),x]","-\frac{b c x^{m+2} \sqrt{c^2 d x^2+d} \, _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)}{(m+1) (m+2)^2 \sqrt{c^2 x^2+1}}+\frac{x^{m+1} \sqrt{c^2 d x^2+d} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-c^2 x^2\right) \left(a+b \sinh ^{-1}(c x)\right)}{\left(m^2+3 m+2\right) \sqrt{c^2 x^2+1}}+\frac{x^{m+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{m+2}-\frac{b c x^{m+2} \sqrt{c^2 d x^2+d}}{(m+2)^2 \sqrt{c^2 x^2+1}}","-\frac{b c x^{m+2} \sqrt{c^2 d x^2+d} \, _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)}{(m+1) (m+2)^2 \sqrt{c^2 x^2+1}}+\frac{x^{m+1} \sqrt{c^2 d x^2+d} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-c^2 x^2\right) \left(a+b \sinh ^{-1}(c x)\right)}{\left(m^2+3 m+2\right) \sqrt{c^2 x^2+1}}+\frac{x^{m+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{m+2}-\frac{b c x^{m+2} \sqrt{c^2 d x^2+d}}{(m+2)^2 \sqrt{c^2 x^2+1}}",1,"-((b*c*x^(2 + m)*Sqrt[d + c^2*d*x^2])/((2 + m)^2*Sqrt[1 + c^2*x^2])) + (x^(1 + m)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(2 + m) + (x^(1 + m)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -(c^2*x^2)])/((2 + 3*m + m^2)*Sqrt[1 + c^2*x^2]) - (b*c*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)])/((1 + m)*(2 + m)^2*Sqrt[1 + c^2*x^2])","A",3,3,26,0.1154,1,"{5742, 5762, 30}"
194,1,161,0,0.1922689,"\int \frac{x^m \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{d+c^2 d x^2}} \, dx","Int[(x^m*(a + b*ArcSinh[c*x]))/Sqrt[d + c^2*d*x^2],x]","\frac{\sqrt{c^2 x^2+1} 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 \sinh ^{-1}(c x)\right)}{(m+1) \sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1} 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)}{\left(m^2+3 m+2\right) \sqrt{c^2 d x^2+d}}","\frac{\sqrt{c^2 x^2+1} 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 \sinh ^{-1}(c x)\right)}{(m+1) \sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1} 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)}{\left(m^2+3 m+2\right) \sqrt{c^2 d x^2+d}}",1,"(x^(1 + m)*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -(c^2*x^2)])/((1 + m)*Sqrt[d + c^2*d*x^2]) - (b*c*x^(2 + m)*Sqrt[1 + c^2*x^2]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, -(c^2*x^2)])/((2 + 3*m + m^2)*Sqrt[d + c^2*d*x^2])","A",2,2,26,0.07692,1,"{5764, 5762}"
195,1,268,0,0.3307014,"\int \frac{x^m \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(x^m*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^(3/2),x]","\frac{b c m \sqrt{c^2 x^2+1} 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 \left(m^2+3 m+2\right) \sqrt{c^2 d x^2+d}}-\frac{m \sqrt{c^2 x^2+1} 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 \sinh ^{-1}(c x)\right)}{d (m+1) \sqrt{c^2 d x^2+d}}+\frac{x^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1} x^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-c^2 x^2\right)}{d (m+2) \sqrt{c^2 d x^2+d}}","\frac{b c m \sqrt{c^2 x^2+1} 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 \left(m^2+3 m+2\right) \sqrt{c^2 d x^2+d}}-\frac{m \sqrt{c^2 x^2+1} 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 \sinh ^{-1}(c x)\right)}{d (m+1) \sqrt{c^2 d x^2+d}}+\frac{x^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1} x^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-c^2 x^2\right)}{d (m+2) \sqrt{c^2 d x^2+d}}",1,"(x^(1 + m)*(a + b*ArcSinh[c*x]))/(d*Sqrt[d + c^2*d*x^2]) - (m*x^(1 + m)*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -(c^2*x^2)])/(d*(1 + m)*Sqrt[d + c^2*d*x^2]) - (b*c*x^(2 + m)*Sqrt[1 + c^2*x^2]*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -(c^2*x^2)])/(d*(2 + m)*Sqrt[d + c^2*d*x^2]) + (b*c*m*x^(2 + m)*Sqrt[1 + c^2*x^2]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, -(c^2*x^2)])/(d*(2 + 3*m + m^2)*Sqrt[d + c^2*d*x^2])","A",4,4,26,0.1538,1,"{5755, 5764, 5762, 364}"
196,1,402,0,0.4707454,"\int \frac{x^m \left(a+b \sinh ^{-1}(c x)\right)}{\left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(x^m*(a + b*ArcSinh[c*x]))/(d + c^2*d*x^2)^(5/2),x]","\frac{b c (2-m) m \sqrt{c^2 x^2+1} 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 \left(m^2+3 m+2\right) \sqrt{c^2 d x^2+d}}-\frac{(2-m) m \sqrt{c^2 x^2+1} 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 \sinh ^{-1}(c x)\right)}{3 d^2 (m+1) \sqrt{c^2 d x^2+d}}+\frac{(2-m) x^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{x^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b c (2-m) \sqrt{c^2 x^2+1} x^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-c^2 x^2\right)}{3 d^2 (m+2) \sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1} x^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};-c^2 x^2\right)}{3 d^2 (m+2) \sqrt{c^2 d x^2+d}}","\frac{b c (2-m) m \sqrt{c^2 x^2+1} 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 \left(m^2+3 m+2\right) \sqrt{c^2 d x^2+d}}-\frac{(2-m) m \sqrt{c^2 x^2+1} 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 \sinh ^{-1}(c x)\right)}{3 d^2 (m+1) \sqrt{c^2 d x^2+d}}+\frac{(2-m) x^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{x^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b c (2-m) \sqrt{c^2 x^2+1} x^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-c^2 x^2\right)}{3 d^2 (m+2) \sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1} x^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};-c^2 x^2\right)}{3 d^2 (m+2) \sqrt{c^2 d x^2+d}}",1,"(x^(1 + m)*(a + b*ArcSinh[c*x]))/(3*d*(d + c^2*d*x^2)^(3/2)) + ((2 - m)*x^(1 + m)*(a + b*ArcSinh[c*x]))/(3*d^2*Sqrt[d + c^2*d*x^2]) - ((2 - m)*m*x^(1 + m)*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -(c^2*x^2)])/(3*d^2*(1 + m)*Sqrt[d + c^2*d*x^2]) - (b*c*(2 - m)*x^(2 + m)*Sqrt[1 + c^2*x^2]*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -(c^2*x^2)])/(3*d^2*(2 + m)*Sqrt[d + c^2*d*x^2]) - (b*c*x^(2 + m)*Sqrt[1 + c^2*x^2]*Hypergeometric2F1[2, (2 + m)/2, (4 + m)/2, -(c^2*x^2)])/(3*d^2*(2 + m)*Sqrt[d + c^2*d*x^2]) + (b*c*(2 - m)*m*x^(2 + m)*Sqrt[1 + c^2*x^2]*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, -(c^2*x^2)])/(3*d^2*(2 + 3*m + m^2)*Sqrt[d + c^2*d*x^2])","A",6,4,26,0.1538,1,"{5755, 5764, 5762, 364}"
197,1,102,0,0.0715032,"\int \frac{x^m \sinh ^{-1}(a x)}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^m*ArcSinh[a*x])/Sqrt[1 + a^2*x^2],x]","\frac{x^{m+1} \sinh ^{-1}(a x) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-a^2 x^2\right)}{m+1}-\frac{a 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)}{m^2+3 m+2}","\frac{x^{m+1} \sinh ^{-1}(a x) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-a^2 x^2\right)}{m+1}-\frac{a 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)}{m^2+3 m+2}",1,"(x^(1 + m)*ArcSinh[a*x]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -(a^2*x^2)])/(1 + m) - (a*x^(2 + m)*HypergeometricPFQ[{1, 1 + m/2, 1 + m/2}, {3/2 + m/2, 2 + m/2}, -(a^2*x^2)])/(2 + 3*m + m^2)","A",1,1,21,0.04762,1,"{5762}"
198,1,283,0,0.4767472,"\int x^4 \left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^4*(d + c^2*d*x^2)*(a + b*ArcSinh[c*x])^2,x]","\frac{1}{7} d x^5 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{4 b d x^4 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{175 c}+\frac{16 b d x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{525 c^3}-\frac{2 b d \left(c^2 x^2+1\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{49 c^5}+\frac{4 b d \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{35 c^5}-\frac{2 b d \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{21 c^5}-\frac{32 b d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{525 c^5}+\frac{2}{35} d x^5 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{343} b^2 c^2 d x^7-\frac{152 b^2 d x^3}{11025 c^2}+\frac{304 b^2 d x}{3675 c^4}+\frac{38 b^2 d x^5}{6125}","\frac{1}{7} d x^5 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{4 b d x^4 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{175 c}+\frac{16 b d x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{525 c^3}-\frac{2 b d \left(c^2 x^2+1\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{49 c^5}+\frac{4 b d \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{35 c^5}-\frac{2 b d \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{21 c^5}-\frac{32 b d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{525 c^5}+\frac{2}{35} d x^5 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{343} b^2 c^2 d x^7-\frac{152 b^2 d x^3}{11025 c^2}+\frac{304 b^2 d x}{3675 c^4}+\frac{38 b^2 d x^5}{6125}",1,"(304*b^2*d*x)/(3675*c^4) - (152*b^2*d*x^3)/(11025*c^2) + (38*b^2*d*x^5)/6125 + (2*b^2*c^2*d*x^7)/343 - (32*b*d*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(525*c^5) + (16*b*d*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(525*c^3) - (4*b*d*x^4*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(175*c) - (2*b*d*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(21*c^5) + (4*b*d*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(35*c^5) - (2*b*d*(1 + c^2*x^2)^(7/2)*(a + b*ArcSinh[c*x]))/(49*c^5) + (2*d*x^5*(a + b*ArcSinh[c*x])^2)/35 + (d*x^5*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/7","A",11,10,24,0.4167,1,"{5744, 5661, 5758, 5717, 8, 30, 266, 43, 5732, 12}"
199,1,198,0,0.5681749,"\int x^3 \left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^3*(d + c^2*d*x^2)*(a + b*ArcSinh[c*x])^2,x]","-\frac{1}{18} b c d x^5 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{6} d x^4 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b d x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{18 c}+\frac{b d x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{12 c^3}-\frac{d \left(a+b \sinh ^{-1}(c x)\right)^2}{24 c^4}+\frac{1}{12} d x^4 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{108} b^2 c^2 d x^6-\frac{b^2 d x^2}{24 c^2}+\frac{1}{72} b^2 d x^4","-\frac{1}{18} b c d x^5 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{6} d x^4 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b d x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{18 c}+\frac{b d x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{12 c^3}-\frac{d \left(a+b \sinh ^{-1}(c x)\right)^2}{24 c^4}+\frac{1}{12} d x^4 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{108} b^2 c^2 d x^6-\frac{b^2 d x^2}{24 c^2}+\frac{1}{72} b^2 d x^4",1,"-(b^2*d*x^2)/(24*c^2) + (b^2*d*x^4)/72 + (b^2*c^2*d*x^6)/108 + (b*d*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(12*c^3) - (b*d*x^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(18*c) - (b*c*d*x^5*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/18 - (d*(a + b*ArcSinh[c*x])^2)/(24*c^4) + (d*x^4*(a + b*ArcSinh[c*x])^2)/12 + (d*x^4*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/6","A",14,6,24,0.2500,1,"{5744, 5661, 5758, 5675, 30, 5742}"
200,1,206,0,0.3419958,"\int x^2 \left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^2*(d + c^2*d*x^2)*(a + b*ArcSinh[c*x])^2,x]","\frac{1}{5} d x^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{4 b d x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{45 c}-\frac{2 b d \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{25 c^3}+\frac{2 b d \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{15 c^3}+\frac{8 b d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{45 c^3}+\frac{2}{15} d x^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{125} b^2 c^2 d x^5-\frac{52 b^2 d x}{225 c^2}+\frac{26}{675} b^2 d x^3","\frac{1}{5} d x^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{4 b d x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{45 c}-\frac{2 b d \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{25 c^3}+\frac{2 b d \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{15 c^3}+\frac{8 b d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{45 c^3}+\frac{2}{15} d x^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{125} b^2 c^2 d x^5-\frac{52 b^2 d x}{225 c^2}+\frac{26}{675} b^2 d x^3",1,"(-52*b^2*d*x)/(225*c^2) + (26*b^2*d*x^3)/675 + (2*b^2*c^2*d*x^5)/125 + (8*b*d*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(45*c^3) - (4*b*d*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(45*c) + (2*b*d*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(15*c^3) - (2*b*d*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(25*c^3) + (2*d*x^3*(a + b*ArcSinh[c*x])^2)/15 + (d*x^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/5","A",9,10,24,0.4167,1,"{5744, 5661, 5758, 5717, 8, 30, 266, 43, 5732, 12}"
201,1,135,0,0.1342464,"\int x \left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x*(d + c^2*d*x^2)*(a + b*ArcSinh[c*x])^2,x]","-\frac{b d x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 c}-\frac{3 b d x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{16 c}+\frac{d \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^2}-\frac{3 d \left(a+b \sinh ^{-1}(c x)\right)^2}{32 c^2}+\frac{1}{32} b^2 c^2 d x^4+\frac{5}{32} b^2 d x^2","-\frac{b d x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 c}-\frac{3 b d x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{16 c}+\frac{d \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^2}-\frac{3 d \left(a+b \sinh ^{-1}(c x)\right)^2}{32 c^2}+\frac{1}{32} b^2 c^2 d x^4+\frac{5}{32} b^2 d x^2",1,"(5*b^2*d*x^2)/32 + (b^2*c^2*d*x^4)/32 - (3*b*d*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(16*c) - (b*d*x*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(8*c) - (3*d*(a + b*ArcSinh[c*x])^2)/(32*c^2) + (d*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/(4*c^2)","A",7,6,22,0.2727,1,"{5717, 5684, 5682, 5675, 30, 14}"
202,1,125,0,0.1442163,"\int \left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + c^2*d*x^2)*(a + b*ArcSinh[c*x])^2,x]","\frac{1}{3} d x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 b d \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{9 c}-\frac{4 b d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 c}+\frac{2}{3} d x \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{27} b^2 c^2 d x^3+\frac{14}{9} b^2 d x","\frac{1}{3} d x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 b d \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{9 c}-\frac{4 b d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 c}+\frac{2}{3} d x \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{27} b^2 c^2 d x^3+\frac{14}{9} b^2 d x",1,"(14*b^2*d*x)/9 + (2*b^2*c^2*d*x^3)/27 - (4*b*d*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(3*c) - (2*b*d*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(9*c) + (2*d*x*(a + b*ArcSinh[c*x])^2)/3 + (d*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/3","A",6,4,21,0.1905,1,"{5684, 5653, 5717, 8}"
203,1,165,0,0.2461141,"\int \frac{\left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{x} \, dx","Int[((d + c^2*d*x^2)*(a + b*ArcSinh[c*x])^2)/x,x]","b d \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{2} b^2 d \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)+\frac{1}{2} d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{1}{2} b c d x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)-\frac{d \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b}-\frac{1}{4} d \left(a+b \sinh ^{-1}(c x)\right)^2+d \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{4} b^2 c^2 d x^2","-b d \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{2} b^2 d \text{PolyLog}\left(3,e^{-2 \sinh ^{-1}(c x)}\right)+\frac{1}{2} d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{1}{2} b c d x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)+\frac{d \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b}-\frac{1}{4} d \left(a+b \sinh ^{-1}(c x)\right)^2+d \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{4} b^2 c^2 d x^2",1,"(b^2*c^2*d*x^2)/4 - (b*c*d*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/2 - (d*(a + b*ArcSinh[c*x])^2)/4 + (d*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/2 - (d*(a + b*ArcSinh[c*x])^3)/(3*b) + d*(a + b*ArcSinh[c*x])^2*Log[1 - E^(2*ArcSinh[c*x])] + b*d*(a + b*ArcSinh[c*x])*PolyLog[2, E^(2*ArcSinh[c*x])] - (b^2*d*PolyLog[3, E^(2*ArcSinh[c*x])])/2","A",10,10,24,0.4167,0,"{5744, 5659, 3716, 2190, 2531, 2282, 6589, 5682, 5675, 30}"
204,1,131,0,0.3184245,"\int \frac{\left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{x^2} \, dx","Int[((d + c^2*d*x^2)*(a + b*ArcSinh[c*x])^2)/x^2,x]","-2 b^2 c d \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+2 b^2 c d \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)-2 b c d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)-\frac{d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{x}+2 c^2 d x \left(a+b \sinh ^{-1}(c x)\right)^2-4 b c d \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)+2 b^2 c^2 d x","-2 b^2 c d \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+2 b^2 c d \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)-2 b c d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)-\frac{d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{x}+2 c^2 d x \left(a+b \sinh ^{-1}(c x)\right)^2-4 b c d \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)+2 b^2 c^2 d x",1,"2*b^2*c^2*d*x - 2*b*c*d*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]) + 2*c^2*d*x*(a + b*ArcSinh[c*x])^2 - (d*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/x - 4*b*c*d*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]] - 2*b^2*c*d*PolyLog[2, -E^ArcSinh[c*x]] + 2*b^2*c*d*PolyLog[2, E^ArcSinh[c*x]]","A",12,9,24,0.3750,1,"{5739, 5653, 5717, 8, 5742, 5760, 4182, 2279, 2391}"
205,1,179,0,0.3102789,"\int \frac{\left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{x^3} \, dx","Int[((d + c^2*d*x^2)*(a + b*ArcSinh[c*x])^2)/x^3,x]","b c^2 d \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{2} b^2 c^2 d \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)-\frac{d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{2 x^2}-\frac{b c d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{c^2 d \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b}+\frac{1}{2} c^2 d \left(a+b \sinh ^{-1}(c x)\right)^2+c^2 d \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2+b^2 c^2 d \log (x)","-b c^2 d \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{2} b^2 c^2 d \text{PolyLog}\left(3,e^{-2 \sinh ^{-1}(c x)}\right)-\frac{d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{2 x^2}-\frac{b c d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{x}+\frac{c^2 d \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b}+\frac{1}{2} c^2 d \left(a+b \sinh ^{-1}(c x)\right)^2+c^2 d \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2+b^2 c^2 d \log (x)",1,"-((b*c*d*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/x) + (c^2*d*(a + b*ArcSinh[c*x])^2)/2 - (d*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(2*x^2) - (c^2*d*(a + b*ArcSinh[c*x])^3)/(3*b) + c^2*d*(a + b*ArcSinh[c*x])^2*Log[1 - E^(2*ArcSinh[c*x])] + b^2*c^2*d*Log[x] + b*c^2*d*(a + b*ArcSinh[c*x])*PolyLog[2, E^(2*ArcSinh[c*x])] - (b^2*c^2*d*PolyLog[3, E^(2*ArcSinh[c*x])])/2","A",10,10,24,0.4167,0,"{5739, 5659, 3716, 2190, 2531, 2282, 6589, 5737, 29, 5675}"
206,1,158,0,0.3933786,"\int \frac{\left(d+c^2 d x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{x^4} \, dx","Int[((d + c^2*d*x^2)*(a + b*ArcSinh[c*x])^2)/x^4,x]","-\frac{5}{3} b^2 c^3 d \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+\frac{5}{3} b^2 c^3 d \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)-\frac{b c d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^2}-\frac{d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 x^3}-\frac{2 c^2 d \left(a+b \sinh ^{-1}(c x)\right)^2}{3 x}-\frac{10}{3} b c^3 d \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{b^2 c^2 d}{3 x}","-\frac{5}{3} b^2 c^3 d \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+\frac{5}{3} b^2 c^3 d \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)-\frac{b c d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^2}-\frac{d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 x^3}-\frac{2 c^2 d \left(a+b \sinh ^{-1}(c x)\right)^2}{3 x}-\frac{10}{3} b c^3 d \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{b^2 c^2 d}{3 x}",1,"-(b^2*c^2*d)/(3*x) - (b*c*d*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(3*x^2) - (2*c^2*d*(a + b*ArcSinh[c*x])^2)/(3*x) - (d*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(3*x^3) - (10*b*c^3*d*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/3 - (5*b^2*c^3*d*PolyLog[2, -E^ArcSinh[c*x]])/3 + (5*b^2*c^3*d*PolyLog[2, E^ArcSinh[c*x]])/3","A",16,8,24,0.3333,1,"{5739, 5661, 5760, 4182, 2279, 2391, 5737, 30}"
207,1,386,0,0.7389306,"\int x^4 \left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^4*(d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x])^2,x]","\frac{1}{9} d^2 x^5 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{4}{63} d^2 x^5 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{16 b d^2 x^4 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{1575 c}+\frac{64 b d^2 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{4725 c^3}-\frac{2 b d^2 \left(c^2 x^2+1\right)^{9/2} \left(a+b \sinh ^{-1}(c x)\right)}{81 c^5}+\frac{20 b d^2 \left(c^2 x^2+1\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{441 c^5}+\frac{2 b d^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{315 c^5}-\frac{8 b d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{189 c^5}-\frac{128 b d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{4725 c^5}+\frac{8}{315} d^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{729} b^2 c^4 d^2 x^9+\frac{212 b^2 c^2 d^2 x^7}{27783}-\frac{2104 b^2 d^2 x^3}{297675 c^2}+\frac{4208 b^2 d^2 x}{99225 c^4}+\frac{526 b^2 d^2 x^5}{165375}","\frac{1}{9} d^2 x^5 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{4}{63} d^2 x^5 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{16 b d^2 x^4 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{1575 c}+\frac{64 b d^2 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{4725 c^3}-\frac{2 b d^2 \left(c^2 x^2+1\right)^{9/2} \left(a+b \sinh ^{-1}(c x)\right)}{81 c^5}+\frac{20 b d^2 \left(c^2 x^2+1\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{441 c^5}+\frac{2 b d^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{315 c^5}-\frac{8 b d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{189 c^5}-\frac{128 b d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{4725 c^5}+\frac{8}{315} d^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{729} b^2 c^4 d^2 x^9+\frac{212 b^2 c^2 d^2 x^7}{27783}-\frac{2104 b^2 d^2 x^3}{297675 c^2}+\frac{4208 b^2 d^2 x}{99225 c^4}+\frac{526 b^2 d^2 x^5}{165375}",1,"(4208*b^2*d^2*x)/(99225*c^4) - (2104*b^2*d^2*x^3)/(297675*c^2) + (526*b^2*d^2*x^5)/165375 + (212*b^2*c^2*d^2*x^7)/27783 + (2*b^2*c^4*d^2*x^9)/729 - (128*b*d^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(4725*c^5) + (64*b*d^2*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(4725*c^3) - (16*b*d^2*x^4*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(1575*c) - (8*b*d^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(189*c^5) + (2*b*d^2*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(315*c^5) + (20*b*d^2*(1 + c^2*x^2)^(7/2)*(a + b*ArcSinh[c*x]))/(441*c^5) - (2*b*d^2*(1 + c^2*x^2)^(9/2)*(a + b*ArcSinh[c*x]))/(81*c^5) + (8*d^2*x^5*(a + b*ArcSinh[c*x])^2)/315 + (4*d^2*x^5*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/63 + (d^2*x^5*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/9","A",16,11,26,0.4231,1,"{5744, 5661, 5758, 5717, 8, 30, 266, 43, 5732, 12, 1153}"
208,1,296,0,1.0369759,"\int x^3 \left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^3*(d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x])^2,x]","-\frac{1}{32} b c d^2 x^5 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{25}{576} b c d^2 x^5 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{8} d^2 x^4 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{12} d^2 x^4 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{73 b d^2 x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2304 c}+\frac{73 b d^2 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{1536 c^3}-\frac{73 d^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3072 c^4}+\frac{1}{24} d^2 x^4 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{256} b^2 c^4 d^2 x^8+\frac{43 b^2 c^2 d^2 x^6}{3456}-\frac{73 b^2 d^2 x^2}{3072 c^2}+\frac{73 b^2 d^2 x^4}{9216}","-\frac{1}{32} b c d^2 x^5 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{25}{576} b c d^2 x^5 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{8} d^2 x^4 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{12} d^2 x^4 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{73 b d^2 x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2304 c}+\frac{73 b d^2 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{1536 c^3}-\frac{73 d^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3072 c^4}+\frac{1}{24} d^2 x^4 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{256} b^2 c^4 d^2 x^8+\frac{43 b^2 c^2 d^2 x^6}{3456}-\frac{73 b^2 d^2 x^2}{3072 c^2}+\frac{73 b^2 d^2 x^4}{9216}",1,"(-73*b^2*d^2*x^2)/(3072*c^2) + (73*b^2*d^2*x^4)/9216 + (43*b^2*c^2*d^2*x^6)/3456 + (b^2*c^4*d^2*x^8)/256 + (73*b*d^2*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(1536*c^3) - (73*b*d^2*x^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(2304*c) - (25*b*c*d^2*x^5*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/576 - (b*c*d^2*x^5*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/32 - (73*d^2*(a + b*ArcSinh[c*x])^2)/(3072*c^4) + (d^2*x^4*(a + b*ArcSinh[c*x])^2)/24 + (d^2*x^4*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/12 + (d^2*x^4*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/8","A",25,7,26,0.2692,1,"{5744, 5661, 5758, 5675, 30, 5742, 14}"
209,1,303,0,0.5941476,"\int x^2 \left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^2*(d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x])^2,x]","\frac{1}{7} d^2 x^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{4}{35} d^2 x^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{16 b d^2 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{315 c}-\frac{2 b d^2 \left(c^2 x^2+1\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{49 c^3}+\frac{2 b d^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{175 c^3}+\frac{8 b d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{105 c^3}+\frac{32 b d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{315 c^3}+\frac{8}{105} d^2 x^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{343} b^2 c^4 d^2 x^7+\frac{136 b^2 c^2 d^2 x^5}{6125}-\frac{1636 b^2 d^2 x}{11025 c^2}+\frac{818 b^2 d^2 x^3}{33075}","\frac{1}{7} d^2 x^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{4}{35} d^2 x^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{16 b d^2 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{315 c}-\frac{2 b d^2 \left(c^2 x^2+1\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{49 c^3}+\frac{2 b d^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{175 c^3}+\frac{8 b d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{105 c^3}+\frac{32 b d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{315 c^3}+\frac{8}{105} d^2 x^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{343} b^2 c^4 d^2 x^7+\frac{136 b^2 c^2 d^2 x^5}{6125}-\frac{1636 b^2 d^2 x}{11025 c^2}+\frac{818 b^2 d^2 x^3}{33075}",1,"(-1636*b^2*d^2*x)/(11025*c^2) + (818*b^2*d^2*x^3)/33075 + (136*b^2*c^2*d^2*x^5)/6125 + (2*b^2*c^4*d^2*x^7)/343 + (32*b*d^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(315*c^3) - (16*b*d^2*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(315*c) + (8*b*d^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(105*c^3) + (2*b*d^2*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(175*c^3) - (2*b*d^2*(1 + c^2*x^2)^(7/2)*(a + b*ArcSinh[c*x]))/(49*c^3) + (8*d^2*x^3*(a + b*ArcSinh[c*x])^2)/105 + (4*d^2*x^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/35 + (d^2*x^3*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/7","A",14,11,26,0.4231,1,"{5744, 5661, 5758, 5717, 8, 30, 266, 43, 5732, 12, 373}"
210,1,204,0,0.2059519,"\int x \left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x*(d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x])^2,x]","-\frac{b d^2 x \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{18 c}-\frac{5 b d^2 x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{72 c}-\frac{5 b d^2 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{48 c}+\frac{d^2 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{6 c^2}-\frac{5 d^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{96 c^2}+\frac{5}{288} b^2 c^2 d^2 x^4+\frac{b^2 d^2 \left(c^2 x^2+1\right)^3}{108 c^2}+\frac{25}{288} b^2 d^2 x^2","-\frac{b d^2 x \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{18 c}-\frac{5 b d^2 x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{72 c}-\frac{5 b d^2 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{48 c}+\frac{d^2 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{6 c^2}-\frac{5 d^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{96 c^2}+\frac{5}{288} b^2 c^2 d^2 x^4+\frac{b^2 d^2 \left(c^2 x^2+1\right)^3}{108 c^2}+\frac{25}{288} b^2 d^2 x^2",1,"(25*b^2*d^2*x^2)/288 + (5*b^2*c^2*d^2*x^4)/288 + (b^2*d^2*(1 + c^2*x^2)^3)/(108*c^2) - (5*b*d^2*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(48*c) - (5*b*d^2*x*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(72*c) - (b*d^2*x*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(18*c) - (5*d^2*(a + b*ArcSinh[c*x])^2)/(96*c^2) + (d^2*(1 + c^2*x^2)^3*(a + b*ArcSinh[c*x])^2)/(6*c^2)","A",9,7,24,0.2917,1,"{5717, 5684, 5682, 5675, 30, 14, 261}"
211,1,214,0,0.2558729,"\int \left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x])^2,x]","\frac{1}{5} d^2 x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{4}{15} d^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 b d^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{25 c}-\frac{8 b d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{45 c}-\frac{16 b d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{15 c}+\frac{8}{15} d^2 x \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{125} b^2 c^4 d^2 x^5+\frac{76}{675} b^2 c^2 d^2 x^3+\frac{298}{225} b^2 d^2 x","\frac{1}{5} d^2 x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{4}{15} d^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 b d^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{25 c}-\frac{8 b d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{45 c}-\frac{16 b d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{15 c}+\frac{8}{15} d^2 x \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{125} b^2 c^4 d^2 x^5+\frac{76}{675} b^2 c^2 d^2 x^3+\frac{298}{225} b^2 d^2 x",1,"(298*b^2*d^2*x)/225 + (76*b^2*c^2*d^2*x^3)/675 + (2*b^2*c^4*d^2*x^5)/125 - (16*b*d^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(15*c) - (8*b*d^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(45*c) - (2*b*d^2*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(25*c) + (8*d^2*x*(a + b*ArcSinh[c*x])^2)/15 + (4*d^2*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/15 + (d^2*x*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/5","A",10,5,23,0.2174,1,"{5684, 5653, 5717, 8, 194}"
212,1,256,0,0.4407168,"\int \frac{\left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{x} \, dx","Int[((d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x])^2)/x,x]","b d^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{2} b^2 d^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)-\frac{1}{8} b c d^2 x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{11}{16} b c d^2 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{4} d^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{2} d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{d^2 \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b}-\frac{11}{32} d^2 \left(a+b \sinh ^{-1}(c x)\right)^2+d^2 \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{32} b^2 c^4 d^2 x^4+\frac{13}{32} b^2 c^2 d^2 x^2","-b d^2 \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{2} b^2 d^2 \text{PolyLog}\left(3,e^{-2 \sinh ^{-1}(c x)}\right)-\frac{1}{8} b c d^2 x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{11}{16} b c d^2 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{4} d^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{2} d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{d^2 \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b}-\frac{11}{32} d^2 \left(a+b \sinh ^{-1}(c x)\right)^2+d^2 \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{32} b^2 c^4 d^2 x^4+\frac{13}{32} b^2 c^2 d^2 x^2",1,"(13*b^2*c^2*d^2*x^2)/32 + (b^2*c^4*d^2*x^4)/32 - (11*b*c*d^2*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/16 - (b*c*d^2*x*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/8 - (11*d^2*(a + b*ArcSinh[c*x])^2)/32 + (d^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/2 + (d^2*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/4 - (d^2*(a + b*ArcSinh[c*x])^3)/(3*b) + d^2*(a + b*ArcSinh[c*x])^2*Log[1 - E^(2*ArcSinh[c*x])] + b*d^2*(a + b*ArcSinh[c*x])*PolyLog[2, E^(2*ArcSinh[c*x])] - (b^2*d^2*PolyLog[3, E^(2*ArcSinh[c*x])])/2","A",17,12,26,0.4615,0,"{5744, 5659, 3716, 2190, 2531, 2282, 6589, 5682, 5675, 30, 5684, 14}"
213,1,229,0,0.5225047,"\int \frac{\left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{x^2} \, dx","Int[((d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x])^2)/x^2,x]","-2 b^2 c d^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+2 b^2 c d^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)+\frac{4}{3} c^2 d^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2}{9} b c d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{10}{3} b c d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)-\frac{d^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{x}+\frac{8}{3} c^2 d^2 x \left(a+b \sinh ^{-1}(c x)\right)^2-4 b c d^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)+\frac{2}{27} b^2 c^4 d^2 x^3+\frac{32}{9} b^2 c^2 d^2 x","-2 b^2 c d^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+2 b^2 c d^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)+\frac{4}{3} c^2 d^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2}{9} b c d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{10}{3} b c d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)-\frac{d^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{x}+\frac{8}{3} c^2 d^2 x \left(a+b \sinh ^{-1}(c x)\right)^2-4 b c d^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)+\frac{2}{27} b^2 c^4 d^2 x^3+\frac{32}{9} b^2 c^2 d^2 x",1,"(32*b^2*c^2*d^2*x)/9 + (2*b^2*c^4*d^2*x^3)/27 - (10*b*c*d^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/3 - (2*b*c*d^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/9 + (8*c^2*d^2*x*(a + b*ArcSinh[c*x])^2)/3 + (4*c^2*d^2*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/3 - (d^2*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/x - 4*b*c*d^2*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]] - 2*b^2*c*d^2*PolyLog[2, -E^ArcSinh[c*x]] + 2*b^2*c*d^2*PolyLog[2, E^ArcSinh[c*x]]","A",17,11,26,0.4231,1,"{5739, 5684, 5653, 5717, 8, 5744, 5742, 5760, 4182, 2279, 2391}"
214,1,272,0,0.5014331,"\int \frac{\left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{x^3} \, dx","Int[((d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x])^2)/x^3,x]","2 b c^2 d^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-b^2 c^2 d^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)+\frac{1}{2} b c^3 d^2 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)+c^2 d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b c d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{d^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 x^2}-\frac{2 c^2 d^2 \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b}+\frac{1}{4} c^2 d^2 \left(a+b \sinh ^{-1}(c x)\right)^2+2 c^2 d^2 \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{4} b^2 c^4 d^2 x^2+b^2 c^2 d^2 \log (x)","-2 b c^2 d^2 \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-b^2 c^2 d^2 \text{PolyLog}\left(3,e^{-2 \sinh ^{-1}(c x)}\right)+\frac{1}{2} b c^3 d^2 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)+c^2 d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b c d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{d^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 x^2}+\frac{2 c^2 d^2 \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b}+\frac{1}{4} c^2 d^2 \left(a+b \sinh ^{-1}(c x)\right)^2+2 c^2 d^2 \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{4} b^2 c^4 d^2 x^2+b^2 c^2 d^2 \log (x)",1,"(b^2*c^4*d^2*x^2)/4 + (b*c^3*d^2*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/2 - (b*c*d^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/x + (c^2*d^2*(a + b*ArcSinh[c*x])^2)/4 + c^2*d^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2 - (d^2*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/(2*x^2) - (2*c^2*d^2*(a + b*ArcSinh[c*x])^3)/(3*b) + 2*c^2*d^2*(a + b*ArcSinh[c*x])^2*Log[1 - E^(2*ArcSinh[c*x])] + b^2*c^2*d^2*Log[x] + 2*b*c^2*d^2*(a + b*ArcSinh[c*x])*PolyLog[2, E^(2*ArcSinh[c*x])] - b^2*c^2*d^2*PolyLog[3, E^(2*ArcSinh[c*x])]","A",17,12,26,0.4615,0,"{5739, 5744, 5659, 3716, 2190, 2531, 2282, 6589, 5682, 5675, 30, 14}"
215,1,248,0,0.706998,"\int \frac{\left(d+c^2 d x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{x^4} \, dx","Int[((d + c^2*d*x^2)^2*(a + b*ArcSinh[c*x])^2)/x^4,x]","-\frac{11}{3} b^2 c^3 d^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+\frac{11}{3} b^2 c^3 d^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)-\frac{5}{3} b c^3 d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)-\frac{4 c^2 d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 x}-\frac{b c d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^2}-\frac{d^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 x^3}+\frac{8}{3} c^4 d^2 x \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{22}{3} b c^3 d^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)+2 b^2 c^4 d^2 x-\frac{b^2 c^2 d^2}{3 x}","-\frac{11}{3} b^2 c^3 d^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+\frac{11}{3} b^2 c^3 d^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)-\frac{5}{3} b c^3 d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)-\frac{4 c^2 d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 x}-\frac{b c d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^2}-\frac{d^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 x^3}+\frac{8}{3} c^4 d^2 x \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{22}{3} b c^3 d^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)+2 b^2 c^4 d^2 x-\frac{b^2 c^2 d^2}{3 x}",1,"-(b^2*c^2*d^2)/(3*x) + 2*b^2*c^4*d^2*x - (5*b*c^3*d^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/3 - (b*c*d^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*x^2) + (8*c^4*d^2*x*(a + b*ArcSinh[c*x])^2)/3 - (4*c^2*d^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(3*x) - (d^2*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/(3*x^3) - (22*b*c^3*d^2*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/3 - (11*b^2*c^3*d^2*PolyLog[2, -E^ArcSinh[c*x]])/3 + (11*b^2*c^3*d^2*PolyLog[2, E^ArcSinh[c*x]])/3","A",24,10,26,0.3846,1,"{5739, 5653, 5717, 8, 5742, 5760, 4182, 2279, 2391, 14}"
216,1,465,0,1.0576539,"\int x^4 \left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^4*(d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x])^2,x]","\frac{1}{11} d^3 x^5 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{33} d^3 x^5 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{8}{231} d^3 x^5 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{32 b d^3 x^4 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{5775 c}+\frac{128 b d^3 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{17325 c^3}-\frac{2 b d^3 \left(c^2 x^2+1\right)^{11/2} \left(a+b \sinh ^{-1}(c x)\right)}{121 c^5}+\frac{8 b d^3 \left(c^2 x^2+1\right)^{9/2} \left(a+b \sinh ^{-1}(c x)\right)}{297 c^5}-\frac{2 b d^3 \left(c^2 x^2+1\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{1617 c^5}+\frac{4 b d^3 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{1155 c^5}-\frac{16 b d^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{693 c^5}-\frac{256 b d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{17325 c^5}+\frac{16 d^3 x^5 \left(a+b \sinh ^{-1}(c x)\right)^2}{1155}+\frac{2 b^2 c^6 d^3 x^{11}}{1331}+\frac{182 b^2 c^4 d^3 x^9}{29403}+\frac{9410 b^2 c^2 d^3 x^7}{1120581}-\frac{50488 b^2 d^3 x^3}{12006225 c^2}+\frac{100976 b^2 d^3 x}{4002075 c^4}+\frac{12622 b^2 d^3 x^5}{6670125}","\frac{1}{11} d^3 x^5 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{33} d^3 x^5 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{8}{231} d^3 x^5 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{32 b d^3 x^4 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{5775 c}+\frac{128 b d^3 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{17325 c^3}-\frac{2 b d^3 \left(c^2 x^2+1\right)^{11/2} \left(a+b \sinh ^{-1}(c x)\right)}{121 c^5}+\frac{8 b d^3 \left(c^2 x^2+1\right)^{9/2} \left(a+b \sinh ^{-1}(c x)\right)}{297 c^5}-\frac{2 b d^3 \left(c^2 x^2+1\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{1617 c^5}+\frac{4 b d^3 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{1155 c^5}-\frac{16 b d^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{693 c^5}-\frac{256 b d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{17325 c^5}+\frac{16 d^3 x^5 \left(a+b \sinh ^{-1}(c x)\right)^2}{1155}+\frac{2 b^2 c^6 d^3 x^{11}}{1331}+\frac{182 b^2 c^4 d^3 x^9}{29403}+\frac{9410 b^2 c^2 d^3 x^7}{1120581}-\frac{50488 b^2 d^3 x^3}{12006225 c^2}+\frac{100976 b^2 d^3 x}{4002075 c^4}+\frac{12622 b^2 d^3 x^5}{6670125}",1,"(100976*b^2*d^3*x)/(4002075*c^4) - (50488*b^2*d^3*x^3)/(12006225*c^2) + (12622*b^2*d^3*x^5)/6670125 + (9410*b^2*c^2*d^3*x^7)/1120581 + (182*b^2*c^4*d^3*x^9)/29403 + (2*b^2*c^6*d^3*x^11)/1331 - (256*b*d^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(17325*c^5) + (128*b*d^3*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(17325*c^3) - (32*b*d^3*x^4*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(5775*c) - (16*b*d^3*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(693*c^5) + (4*b*d^3*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(1155*c^5) - (2*b*d^3*(1 + c^2*x^2)^(7/2)*(a + b*ArcSinh[c*x]))/(1617*c^5) + (8*b*d^3*(1 + c^2*x^2)^(9/2)*(a + b*ArcSinh[c*x]))/(297*c^5) - (2*b*d^3*(1 + c^2*x^2)^(11/2)*(a + b*ArcSinh[c*x]))/(121*c^5) + (16*d^3*x^5*(a + b*ArcSinh[c*x])^2)/1155 + (8*d^3*x^5*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/231 + (2*d^3*x^5*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/33 + (d^3*x^5*(1 + c^2*x^2)^3*(a + b*ArcSinh[c*x])^2)/11","A",21,11,26,0.4231,1,"{5744, 5661, 5758, 5717, 8, 30, 266, 43, 5732, 12, 1153}"
217,1,376,0,1.657025,"\int x^3 \left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^3*(d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x])^2,x]","-\frac{1}{50} b c d^3 x^5 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{32} b c d^3 x^5 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{31}{960} b c d^3 x^5 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{10} d^3 x^4 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{3}{40} d^3 x^4 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{20} d^3 x^4 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{79 b d^3 x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3840 c}+\frac{79 b d^3 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2560 c^3}-\frac{79 d^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{5120 c^4}+\frac{1}{40} d^3 x^4 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{500} b^2 c^6 d^3 x^{10}+\frac{57 b^2 c^4 d^3 x^8}{6400}+\frac{401 b^2 c^2 d^3 x^6}{28800}-\frac{79 b^2 d^3 x^2}{5120 c^2}+\frac{79 b^2 d^3 x^4}{15360}","-\frac{1}{50} b c d^3 x^5 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{32} b c d^3 x^5 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{31}{960} b c d^3 x^5 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{10} d^3 x^4 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{3}{40} d^3 x^4 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{20} d^3 x^4 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{79 b d^3 x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3840 c}+\frac{79 b d^3 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2560 c^3}-\frac{79 d^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{5120 c^4}+\frac{1}{40} d^3 x^4 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{500} b^2 c^6 d^3 x^{10}+\frac{57 b^2 c^4 d^3 x^8}{6400}+\frac{401 b^2 c^2 d^3 x^6}{28800}-\frac{79 b^2 d^3 x^2}{5120 c^2}+\frac{79 b^2 d^3 x^4}{15360}",1,"(-79*b^2*d^3*x^2)/(5120*c^2) + (79*b^2*d^3*x^4)/15360 + (401*b^2*c^2*d^3*x^6)/28800 + (57*b^2*c^4*d^3*x^8)/6400 + (b^2*c^6*d^3*x^10)/500 + (79*b*d^3*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(2560*c^3) - (79*b*d^3*x^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(3840*c) - (31*b*c*d^3*x^5*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/960 - (b*c*d^3*x^5*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/32 - (b*c*d^3*x^5*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/50 - (79*d^3*(a + b*ArcSinh[c*x])^2)/(5120*c^4) + (d^3*x^4*(a + b*ArcSinh[c*x])^2)/40 + (d^3*x^4*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/20 + (3*d^3*x^4*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/40 + (d^3*x^4*(1 + c^2*x^2)^3*(a + b*ArcSinh[c*x])^2)/10","A",40,9,26,0.3462,1,"{5744, 5661, 5758, 5675, 30, 5742, 14, 266, 43}"
218,1,382,0,0.8613555,"\int x^2 \left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^2*(d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x])^2,x]","\frac{1}{9} d^3 x^3 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{21} d^3 x^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{8}{105} d^3 x^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{32 b d^3 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{945 c}-\frac{2 b d^3 \left(c^2 x^2+1\right)^{9/2} \left(a+b \sinh ^{-1}(c x)\right)}{81 c^3}+\frac{2 b d^3 \left(c^2 x^2+1\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{441 c^3}+\frac{4 b d^3 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{525 c^3}+\frac{16 b d^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{315 c^3}+\frac{64 b d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{945 c^3}+\frac{16}{315} d^3 x^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{729} b^2 c^6 d^3 x^9+\frac{374 b^2 c^4 d^3 x^7}{27783}+\frac{4198 b^2 c^2 d^3 x^5}{165375}-\frac{10516 b^2 d^3 x}{99225 c^2}+\frac{5258 b^2 d^3 x^3}{297675}","\frac{1}{9} d^3 x^3 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{21} d^3 x^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{8}{105} d^3 x^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{32 b d^3 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{945 c}-\frac{2 b d^3 \left(c^2 x^2+1\right)^{9/2} \left(a+b \sinh ^{-1}(c x)\right)}{81 c^3}+\frac{2 b d^3 \left(c^2 x^2+1\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{441 c^3}+\frac{4 b d^3 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{525 c^3}+\frac{16 b d^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{315 c^3}+\frac{64 b d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{945 c^3}+\frac{16}{315} d^3 x^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{729} b^2 c^6 d^3 x^9+\frac{374 b^2 c^4 d^3 x^7}{27783}+\frac{4198 b^2 c^2 d^3 x^5}{165375}-\frac{10516 b^2 d^3 x}{99225 c^2}+\frac{5258 b^2 d^3 x^3}{297675}",1,"(-10516*b^2*d^3*x)/(99225*c^2) + (5258*b^2*d^3*x^3)/297675 + (4198*b^2*c^2*d^3*x^5)/165375 + (374*b^2*c^4*d^3*x^7)/27783 + (2*b^2*c^6*d^3*x^9)/729 + (64*b*d^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(945*c^3) - (32*b*d^3*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(945*c) + (16*b*d^3*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(315*c^3) + (4*b*d^3*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(525*c^3) + (2*b*d^3*(1 + c^2*x^2)^(7/2)*(a + b*ArcSinh[c*x]))/(441*c^3) - (2*b*d^3*(1 + c^2*x^2)^(9/2)*(a + b*ArcSinh[c*x]))/(81*c^3) + (16*d^3*x^3*(a + b*ArcSinh[c*x])^2)/315 + (8*d^3*x^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/105 + (2*d^3*x^3*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/21 + (d^3*x^3*(1 + c^2*x^2)^3*(a + b*ArcSinh[c*x])^2)/9","A",19,11,26,0.4231,1,"{5744, 5661, 5758, 5717, 8, 30, 266, 43, 5732, 12, 373}"
219,1,261,0,0.2568256,"\int x \left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x*(d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x])^2,x]","-\frac{b d^3 x \left(c^2 x^2+1\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{32 c}-\frac{7 b d^3 x \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{192 c}-\frac{35 b d^3 x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{768 c}-\frac{35 b d^3 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{512 c}+\frac{d^3 \left(c^2 x^2+1\right)^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{8 c^2}-\frac{35 d^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{1024 c^2}+\frac{35 b^2 c^2 d^3 x^4}{3072}+\frac{b^2 d^3 \left(c^2 x^2+1\right)^4}{256 c^2}+\frac{7 b^2 d^3 \left(c^2 x^2+1\right)^3}{1152 c^2}+\frac{175 b^2 d^3 x^2}{3072}","-\frac{b d^3 x \left(c^2 x^2+1\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{32 c}-\frac{7 b d^3 x \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{192 c}-\frac{35 b d^3 x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{768 c}-\frac{35 b d^3 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{512 c}+\frac{d^3 \left(c^2 x^2+1\right)^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{8 c^2}-\frac{35 d^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{1024 c^2}+\frac{35 b^2 c^2 d^3 x^4}{3072}+\frac{b^2 d^3 \left(c^2 x^2+1\right)^4}{256 c^2}+\frac{7 b^2 d^3 \left(c^2 x^2+1\right)^3}{1152 c^2}+\frac{175 b^2 d^3 x^2}{3072}",1,"(175*b^2*d^3*x^2)/3072 + (35*b^2*c^2*d^3*x^4)/3072 + (7*b^2*d^3*(1 + c^2*x^2)^3)/(1152*c^2) + (b^2*d^3*(1 + c^2*x^2)^4)/(256*c^2) - (35*b*d^3*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(512*c) - (35*b*d^3*x*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(768*c) - (7*b*d^3*x*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(192*c) - (b*d^3*x*(1 + c^2*x^2)^(7/2)*(a + b*ArcSinh[c*x]))/(32*c) - (35*d^3*(a + b*ArcSinh[c*x])^2)/(1024*c^2) + (d^3*(1 + c^2*x^2)^4*(a + b*ArcSinh[c*x])^2)/(8*c^2)","A",11,7,24,0.2917,1,"{5717, 5684, 5682, 5675, 30, 14, 261}"
220,1,291,0,0.4030619,"\int \left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x])^2,x]","\frac{1}{7} d^3 x \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{6}{35} d^3 x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{8}{35} d^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 b d^3 \left(c^2 x^2+1\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{49 c}-\frac{12 b d^3 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{175 c}-\frac{16 b d^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{105 c}-\frac{32 b d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{35 c}+\frac{16}{35} d^3 x \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{343} b^2 c^6 d^3 x^7+\frac{234 b^2 c^4 d^3 x^5}{6125}+\frac{1514 b^2 c^2 d^3 x^3}{11025}+\frac{4322 b^2 d^3 x}{3675}","\frac{1}{7} d^3 x \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{6}{35} d^3 x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{8}{35} d^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 b d^3 \left(c^2 x^2+1\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)}{49 c}-\frac{12 b d^3 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{175 c}-\frac{16 b d^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{105 c}-\frac{32 b d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{35 c}+\frac{16}{35} d^3 x \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{343} b^2 c^6 d^3 x^7+\frac{234 b^2 c^4 d^3 x^5}{6125}+\frac{1514 b^2 c^2 d^3 x^3}{11025}+\frac{4322 b^2 d^3 x}{3675}",1,"(4322*b^2*d^3*x)/3675 + (1514*b^2*c^2*d^3*x^3)/11025 + (234*b^2*c^4*d^3*x^5)/6125 + (2*b^2*c^6*d^3*x^7)/343 - (32*b*d^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(35*c) - (16*b*d^3*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(105*c) - (12*b*d^3*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(175*c) - (2*b*d^3*(1 + c^2*x^2)^(7/2)*(a + b*ArcSinh[c*x]))/(49*c) + (16*d^3*x*(a + b*ArcSinh[c*x])^2)/35 + (8*d^3*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/35 + (6*d^3*x*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/35 + (d^3*x*(1 + c^2*x^2)^3*(a + b*ArcSinh[c*x])^2)/7","A",14,5,23,0.2174,1,"{5684, 5653, 5717, 8, 194}"
221,1,336,0,0.6840702,"\int \frac{\left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{x} \, dx","Int[((d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x])^2)/x,x]","b d^3 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{2} b^2 d^3 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)-\frac{1}{18} b c d^3 x \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{7}{36} b c d^3 x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{19}{24} b c d^3 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{6} d^3 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{4} d^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{2} d^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{d^3 \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b}-\frac{19}{48} d^3 \left(a+b \sinh ^{-1}(c x)\right)^2+d^3 \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{7}{144} b^2 c^4 d^3 x^4+\frac{71}{144} b^2 c^2 d^3 x^2+\frac{1}{108} b^2 d^3 \left(c^2 x^2+1\right)^3","-b d^3 \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{1}{2} b^2 d^3 \text{PolyLog}\left(3,e^{-2 \sinh ^{-1}(c x)}\right)-\frac{1}{18} b c d^3 x \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{7}{36} b c d^3 x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{19}{24} b c d^3 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{6} d^3 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{4} d^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{2} d^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{d^3 \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b}-\frac{19}{48} d^3 \left(a+b \sinh ^{-1}(c x)\right)^2+d^3 \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{7}{144} b^2 c^4 d^3 x^4+\frac{71}{144} b^2 c^2 d^3 x^2+\frac{1}{108} b^2 d^3 \left(c^2 x^2+1\right)^3",1,"(71*b^2*c^2*d^3*x^2)/144 + (7*b^2*c^4*d^3*x^4)/144 + (b^2*d^3*(1 + c^2*x^2)^3)/108 - (19*b*c*d^3*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/24 - (7*b*c*d^3*x*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/36 - (b*c*d^3*x*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/18 - (19*d^3*(a + b*ArcSinh[c*x])^2)/48 + (d^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/2 + (d^3*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/4 + (d^3*(1 + c^2*x^2)^3*(a + b*ArcSinh[c*x])^2)/6 - (d^3*(a + b*ArcSinh[c*x])^3)/(3*b) + d^3*(a + b*ArcSinh[c*x])^2*Log[1 - E^(2*ArcSinh[c*x])] + b*d^3*(a + b*ArcSinh[c*x])*PolyLog[2, E^(2*ArcSinh[c*x])] - (b^2*d^3*PolyLog[3, E^(2*ArcSinh[c*x])])/2","A",26,13,26,0.5000,0,"{5744, 5659, 3716, 2190, 2531, 2282, 6589, 5682, 5675, 30, 5684, 14, 261}"
222,1,307,0,0.7392509,"\int \frac{\left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{x^2} \, dx","Int[((d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x])^2)/x^2,x]","-2 b^2 c d^3 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+2 b^2 c d^3 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)+\frac{6}{5} c^2 d^3 x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{8}{5} c^2 d^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2}{25} b c d^3 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{2}{5} b c d^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{22}{5} b c d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)-\frac{d^3 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{x}+\frac{16}{5} c^2 d^3 x \left(a+b \sinh ^{-1}(c x)\right)^2-4 b c d^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)+\frac{2}{125} b^2 c^6 d^3 x^5+\frac{14}{75} b^2 c^4 d^3 x^3+\frac{122}{25} b^2 c^2 d^3 x","-2 b^2 c d^3 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+2 b^2 c d^3 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)+\frac{6}{5} c^2 d^3 x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{8}{5} c^2 d^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2}{25} b c d^3 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{2}{5} b c d^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{22}{5} b c d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)-\frac{d^3 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{x}+\frac{16}{5} c^2 d^3 x \left(a+b \sinh ^{-1}(c x)\right)^2-4 b c d^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)+\frac{2}{125} b^2 c^6 d^3 x^5+\frac{14}{75} b^2 c^4 d^3 x^3+\frac{122}{25} b^2 c^2 d^3 x",1,"(122*b^2*c^2*d^3*x)/25 + (14*b^2*c^4*d^3*x^3)/75 + (2*b^2*c^6*d^3*x^5)/125 - (22*b*c*d^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/5 - (2*b*c*d^3*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/5 - (2*b*c*d^3*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/25 + (16*c^2*d^3*x*(a + b*ArcSinh[c*x])^2)/5 + (8*c^2*d^3*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/5 + (6*c^2*d^3*x*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/5 - (d^3*(1 + c^2*x^2)^3*(a + b*ArcSinh[c*x])^2)/x - 4*b*c*d^3*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]] - 2*b^2*c*d^3*PolyLog[2, -E^ArcSinh[c*x]] + 2*b^2*c*d^3*PolyLog[2, E^ArcSinh[c*x]]","A",24,12,26,0.4615,1,"{5739, 5684, 5653, 5717, 8, 194, 5744, 5742, 5760, 4182, 2279, 2391}"
223,1,355,0,0.7498853,"\int \frac{\left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{x^3} \, dx","Int[((d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x])^2)/x^3,x]","3 b c^2 d^3 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{3}{2} b^2 c^2 d^3 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)+\frac{7}{8} b c^3 d^3 x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{3}{16} b c^3 d^3 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{4} c^2 d^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{3}{2} c^2 d^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b c d^3 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{d^3 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 x^2}-\frac{c^2 d^3 \left(a+b \sinh ^{-1}(c x)\right)^3}{b}-\frac{3}{32} c^2 d^3 \left(a+b \sinh ^{-1}(c x)\right)^2+3 c^2 d^3 \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{32} b^2 c^6 d^3 x^4+\frac{21}{32} b^2 c^4 d^3 x^2+b^2 c^2 d^3 \log (x)","-3 b c^2 d^3 \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)-\frac{3}{2} b^2 c^2 d^3 \text{PolyLog}\left(3,e^{-2 \sinh ^{-1}(c x)}\right)+\frac{7}{8} b c^3 d^3 x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{3}{16} b c^3 d^3 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{4} c^2 d^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{3}{2} c^2 d^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b c d^3 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{x}-\frac{d^3 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 x^2}+\frac{c^2 d^3 \left(a+b \sinh ^{-1}(c x)\right)^3}{b}-\frac{3}{32} c^2 d^3 \left(a+b \sinh ^{-1}(c x)\right)^2+3 c^2 d^3 \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{32} b^2 c^6 d^3 x^4+\frac{21}{32} b^2 c^4 d^3 x^2+b^2 c^2 d^3 \log (x)",1,"(21*b^2*c^4*d^3*x^2)/32 + (b^2*c^6*d^3*x^4)/32 - (3*b*c^3*d^3*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/16 + (7*b*c^3*d^3*x*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/8 - (b*c*d^3*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/x - (3*c^2*d^3*(a + b*ArcSinh[c*x])^2)/32 + (3*c^2*d^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/2 + (3*c^2*d^3*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/4 - (d^3*(1 + c^2*x^2)^3*(a + b*ArcSinh[c*x])^2)/(2*x^2) - (c^2*d^3*(a + b*ArcSinh[c*x])^3)/b + 3*c^2*d^3*(a + b*ArcSinh[c*x])^2*Log[1 - E^(2*ArcSinh[c*x])] + b^2*c^2*d^3*Log[x] + 3*b*c^2*d^3*(a + b*ArcSinh[c*x])*PolyLog[2, E^(2*ArcSinh[c*x])] - (3*b^2*c^2*d^3*PolyLog[3, E^(2*ArcSinh[c*x])])/2","A",28,15,26,0.5769,0,"{5739, 5744, 5659, 3716, 2190, 2531, 2282, 6589, 5682, 5675, 30, 5684, 14, 266, 43}"
224,1,326,0,1.0213699,"\int \frac{\left(d+c^2 d x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{x^4} \, dx","Int[((d + c^2*d*x^2)^3*(a + b*ArcSinh[c*x])^2)/x^4,x]","-\frac{17}{3} b^2 c^3 d^3 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+\frac{17}{3} b^2 c^3 d^3 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)+\frac{8}{3} c^4 d^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{9} b c^3 d^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-5 b c^3 d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)-\frac{2 c^2 d^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{x}-\frac{b c d^3 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^2}-\frac{d^3 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 x^3}+\frac{16}{3} c^4 d^3 x \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{34}{3} b c^3 d^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)+\frac{2}{27} b^2 c^6 d^3 x^3+\frac{50}{9} b^2 c^4 d^3 x-\frac{b^2 c^2 d^3}{3 x}","-\frac{17}{3} b^2 c^3 d^3 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)+\frac{17}{3} b^2 c^3 d^3 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)+\frac{8}{3} c^4 d^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{9} b c^3 d^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-5 b c^3 d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)-\frac{2 c^2 d^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{x}-\frac{b c d^3 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^2}-\frac{d^3 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 x^3}+\frac{16}{3} c^4 d^3 x \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{34}{3} b c^3 d^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)+\frac{2}{27} b^2 c^6 d^3 x^3+\frac{50}{9} b^2 c^4 d^3 x-\frac{b^2 c^2 d^3}{3 x}",1,"-(b^2*c^2*d^3)/(3*x) + (50*b^2*c^4*d^3*x)/9 + (2*b^2*c^6*d^3*x^3)/27 - 5*b*c^3*d^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]) + (b*c^3*d^3*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/9 - (b*c*d^3*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(3*x^2) + (16*c^4*d^3*x*(a + b*ArcSinh[c*x])^2)/3 + (8*c^4*d^3*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/3 - (2*c^2*d^3*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/x - (d^3*(1 + c^2*x^2)^3*(a + b*ArcSinh[c*x])^2)/(3*x^3) - (34*b*c^3*d^3*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/3 - (17*b^2*c^3*d^3*PolyLog[2, -E^ArcSinh[c*x]])/3 + (17*b^2*c^3*d^3*PolyLog[2, E^ArcSinh[c*x]])/3","A",31,12,26,0.4615,1,"{5739, 5684, 5653, 5717, 8, 5744, 5742, 5760, 4182, 2279, 2391, 270}"
225,1,277,0,0.5533912,"\int \frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{d+c^2 d x^2} \, dx","Int[(x^4*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2),x]","-\frac{2 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d}+\frac{2 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d}+\frac{2 i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{c^5 d}-\frac{2 i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{c^5 d}+\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^2 d}-\frac{2 b x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^3 d}+\frac{22 b \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^5 d}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{c^4 d}+\frac{2 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c^5 d}+\frac{2 b^2 x^3}{27 c^2 d}-\frac{22 b^2 x}{9 c^4 d}","-\frac{2 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d}+\frac{2 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d}+\frac{2 i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{c^5 d}-\frac{2 i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{c^5 d}+\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^2 d}-\frac{2 b x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^3 d}+\frac{22 b \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^5 d}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{c^4 d}+\frac{2 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c^5 d}+\frac{2 b^2 x^3}{27 c^2 d}-\frac{22 b^2 x}{9 c^4 d}",1,"(-22*b^2*x)/(9*c^4*d) + (2*b^2*x^3)/(27*c^2*d) + (22*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(9*c^5*d) - (2*b*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(9*c^3*d) - (x*(a + b*ArcSinh[c*x])^2)/(c^4*d) + (x^3*(a + b*ArcSinh[c*x])^2)/(3*c^2*d) + (2*(a + b*ArcSinh[c*x])^2*ArcTan[E^ArcSinh[c*x]])/(c^5*d) - ((2*I)*b*(a + b*ArcSinh[c*x])*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^5*d) + ((2*I)*b*(a + b*ArcSinh[c*x])*PolyLog[2, I*E^ArcSinh[c*x]])/(c^5*d) + ((2*I)*b^2*PolyLog[3, (-I)*E^ArcSinh[c*x]])/(c^5*d) - ((2*I)*b^2*PolyLog[3, I*E^ArcSinh[c*x]])/(c^5*d)","A",16,10,26,0.3846,1,"{5767, 5693, 4180, 2531, 2282, 6589, 5717, 8, 5758, 30}"
226,1,199,0,0.4079418,"\int \frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{d+c^2 d x^2} \, dx","Int[(x^3*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2),x]","-\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^4 d}+\frac{b^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{2 c^4 d}+\frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^2 d}-\frac{b x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 c^3 d}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c^4 d}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^4 d}-\frac{\log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c^4 d}+\frac{b^2 x^2}{4 c^2 d}","-\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^4 d}+\frac{b^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{2 c^4 d}+\frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^2 d}-\frac{b x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 c^3 d}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c^4 d}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^4 d}-\frac{\log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c^4 d}+\frac{b^2 x^2}{4 c^2 d}",1,"(b^2*x^2)/(4*c^2*d) - (b*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(2*c^3*d) + (a + b*ArcSinh[c*x])^2/(4*c^4*d) + (x^2*(a + b*ArcSinh[c*x])^2)/(2*c^2*d) + (a + b*ArcSinh[c*x])^3/(3*b*c^4*d) - ((a + b*ArcSinh[c*x])^2*Log[1 + E^(2*ArcSinh[c*x])])/(c^4*d) - (b*(a + b*ArcSinh[c*x])*PolyLog[2, -E^(2*ArcSinh[c*x])])/(c^4*d) + (b^2*PolyLog[3, -E^(2*ArcSinh[c*x])])/(2*c^4*d)","A",10,10,26,0.3846,1,"{5767, 5714, 3718, 2190, 2531, 2282, 6589, 5758, 5675, 30}"
227,1,198,0,0.293411,"\int \frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{d+c^2 d x^2} \, dx","Int[(x^2*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2),x]","\frac{2 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d}-\frac{2 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d}-\frac{2 i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{c^3 d}+\frac{2 i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{c^3 d}-\frac{2 b \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{c^2 d}-\frac{2 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c^3 d}+\frac{2 b^2 x}{c^2 d}","\frac{2 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d}-\frac{2 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d}-\frac{2 i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{c^3 d}+\frac{2 i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{c^3 d}-\frac{2 b \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{c^2 d}-\frac{2 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c^3 d}+\frac{2 b^2 x}{c^2 d}",1,"(2*b^2*x)/(c^2*d) - (2*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(c^3*d) + (x*(a + b*ArcSinh[c*x])^2)/(c^2*d) - (2*(a + b*ArcSinh[c*x])^2*ArcTan[E^ArcSinh[c*x]])/(c^3*d) + ((2*I)*b*(a + b*ArcSinh[c*x])*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^3*d) - ((2*I)*b*(a + b*ArcSinh[c*x])*PolyLog[2, I*E^ArcSinh[c*x]])/(c^3*d) - ((2*I)*b^2*PolyLog[3, (-I)*E^ArcSinh[c*x]])/(c^3*d) + ((2*I)*b^2*PolyLog[3, I*E^ArcSinh[c*x]])/(c^3*d)","A",11,8,26,0.3077,1,"{5767, 5693, 4180, 2531, 2282, 6589, 5717, 8}"
228,1,105,0,0.1837064,"\int \frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{d+c^2 d x^2} \, dx","Int[(x*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2),x]","\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{2 c^2 d}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c^2 d}+\frac{\log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c^2 d}","\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{2 c^2 d}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c^2 d}+\frac{\log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c^2 d}",1,"-(a + b*ArcSinh[c*x])^3/(3*b*c^2*d) + ((a + b*ArcSinh[c*x])^2*Log[1 + E^(2*ArcSinh[c*x])])/(c^2*d) + (b*(a + b*ArcSinh[c*x])*PolyLog[2, -E^(2*ArcSinh[c*x])])/(c^2*d) - (b^2*PolyLog[3, -E^(2*ArcSinh[c*x])])/(2*c^2*d)","A",6,6,24,0.2500,1,"{5714, 3718, 2190, 2531, 2282, 6589}"
229,1,138,0,0.1236862,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d+c^2 d x^2} \, dx","Int[(a + b*ArcSinh[c*x])^2/(d + c^2*d*x^2),x]","-\frac{2 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c d}+\frac{2 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c d}+\frac{2 i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{c d}-\frac{2 i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{c d}+\frac{2 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c d}","-\frac{2 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c d}+\frac{2 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c d}+\frac{2 i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{c d}-\frac{2 i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{c d}+\frac{2 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c d}",1,"(2*(a + b*ArcSinh[c*x])^2*ArcTan[E^ArcSinh[c*x]])/(c*d) - ((2*I)*b*(a + b*ArcSinh[c*x])*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c*d) + ((2*I)*b*(a + b*ArcSinh[c*x])*PolyLog[2, I*E^ArcSinh[c*x]])/(c*d) + ((2*I)*b^2*PolyLog[3, (-I)*E^ArcSinh[c*x]])/(c*d) - ((2*I)*b^2*PolyLog[3, I*E^ArcSinh[c*x]])/(c*d)","A",8,5,23,0.2174,1,"{5693, 4180, 2531, 2282, 6589}"
230,1,116,0,0.2075265,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x \left(d+c^2 d x^2\right)} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x*(d + c^2*d*x^2)),x]","-\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}+\frac{b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}+\frac{b^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d}-\frac{b^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)}{2 d}-\frac{2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d}","-\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}+\frac{b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}+\frac{b^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d}-\frac{b^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)}{2 d}-\frac{2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d}",1,"(-2*(a + b*ArcSinh[c*x])^2*ArcTanh[E^(2*ArcSinh[c*x])])/d - (b*(a + b*ArcSinh[c*x])*PolyLog[2, -E^(2*ArcSinh[c*x])])/d + (b*(a + b*ArcSinh[c*x])*PolyLog[2, E^(2*ArcSinh[c*x])])/d + (b^2*PolyLog[3, -E^(2*ArcSinh[c*x])])/(2*d) - (b^2*PolyLog[3, E^(2*ArcSinh[c*x])])/(2*d)","A",9,6,26,0.2308,1,"{5720, 5461, 4182, 2531, 2282, 6589}"
231,1,204,0,0.3352706,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^2 \left(d+c^2 d x^2\right)} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^2*(d + c^2*d*x^2)),x]","\frac{2 i b c \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}-\frac{2 i b c \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}-\frac{2 b^2 c \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{d}+\frac{2 b^2 c \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{d}-\frac{2 i b^2 c \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{d}+\frac{2 i b^2 c \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{d}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d x}-\frac{2 c \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d}-\frac{4 b c \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}","\frac{2 i b c \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}-\frac{2 i b c \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}-\frac{2 b^2 c \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{d}+\frac{2 b^2 c \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{d}-\frac{2 i b^2 c \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{d}+\frac{2 i b^2 c \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{d}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d x}-\frac{2 c \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d}-\frac{4 b c \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}",1,"-((a + b*ArcSinh[c*x])^2/(d*x)) - (2*c*(a + b*ArcSinh[c*x])^2*ArcTan[E^ArcSinh[c*x]])/d - (4*b*c*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/d - (2*b^2*c*PolyLog[2, -E^ArcSinh[c*x]])/d + ((2*I)*b*c*(a + b*ArcSinh[c*x])*PolyLog[2, (-I)*E^ArcSinh[c*x]])/d - ((2*I)*b*c*(a + b*ArcSinh[c*x])*PolyLog[2, I*E^ArcSinh[c*x]])/d + (2*b^2*c*PolyLog[2, E^ArcSinh[c*x]])/d - ((2*I)*b^2*c*PolyLog[3, (-I)*E^ArcSinh[c*x]])/d + ((2*I)*b^2*c*PolyLog[3, I*E^ArcSinh[c*x]])/d","A",15,10,26,0.3846,1,"{5747, 5693, 4180, 2531, 2282, 6589, 5760, 4182, 2279, 2391}"
232,1,194,0,0.3884487,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^3 \left(d+c^2 d x^2\right)} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^3*(d + c^2*d*x^2)),x]","\frac{b c^2 \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}-\frac{b c^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}-\frac{b^2 c^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d}+\frac{b^2 c^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)}{2 d}-\frac{b c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{d x}+\frac{2 c^2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 d x^2}+\frac{b^2 c^2 \log (x)}{d}","\frac{b c^2 \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}-\frac{b c^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}-\frac{b^2 c^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d}+\frac{b^2 c^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)}{2 d}-\frac{b c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{d x}+\frac{2 c^2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 d x^2}+\frac{b^2 c^2 \log (x)}{d}",1,"-((b*c*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(d*x)) - (a + b*ArcSinh[c*x])^2/(2*d*x^2) + (2*c^2*(a + b*ArcSinh[c*x])^2*ArcTanh[E^(2*ArcSinh[c*x])])/d + (b^2*c^2*Log[x])/d + (b*c^2*(a + b*ArcSinh[c*x])*PolyLog[2, -E^(2*ArcSinh[c*x])])/d - (b*c^2*(a + b*ArcSinh[c*x])*PolyLog[2, E^(2*ArcSinh[c*x])])/d - (b^2*c^2*PolyLog[3, -E^(2*ArcSinh[c*x])])/(2*d) + (b^2*c^2*PolyLog[3, E^(2*ArcSinh[c*x])])/(2*d)","A",12,9,26,0.3462,1,"{5747, 5720, 5461, 4182, 2531, 2282, 6589, 5723, 29}"
233,1,297,0,0.6388736,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^4 \left(d+c^2 d x^2\right)} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^4*(d + c^2*d*x^2)),x]","-\frac{2 i b c^3 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}+\frac{2 i b c^3 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}+\frac{7 b^2 c^3 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{3 d}-\frac{7 b^2 c^3 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{3 d}+\frac{2 i b^2 c^3 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{d}-\frac{2 i b^2 c^3 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{d}-\frac{b c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 d x^2}+\frac{c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{d x}+\frac{2 c^3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d}+\frac{14 b c^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{3 d x^3}-\frac{b^2 c^2}{3 d x}","-\frac{2 i b c^3 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}+\frac{2 i b c^3 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d}+\frac{7 b^2 c^3 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{3 d}-\frac{7 b^2 c^3 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{3 d}+\frac{2 i b^2 c^3 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{d}-\frac{2 i b^2 c^3 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{d}-\frac{b c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 d x^2}+\frac{c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{d x}+\frac{2 c^3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d}+\frac{14 b c^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{3 d x^3}-\frac{b^2 c^2}{3 d x}",1,"-(b^2*c^2)/(3*d*x) - (b*c*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(3*d*x^2) - (a + b*ArcSinh[c*x])^2/(3*d*x^3) + (c^2*(a + b*ArcSinh[c*x])^2)/(d*x) + (2*c^3*(a + b*ArcSinh[c*x])^2*ArcTan[E^ArcSinh[c*x]])/d + (14*b*c^3*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/(3*d) + (7*b^2*c^3*PolyLog[2, -E^ArcSinh[c*x]])/(3*d) - ((2*I)*b*c^3*(a + b*ArcSinh[c*x])*PolyLog[2, (-I)*E^ArcSinh[c*x]])/d + ((2*I)*b*c^3*(a + b*ArcSinh[c*x])*PolyLog[2, I*E^ArcSinh[c*x]])/d - (7*b^2*c^3*PolyLog[2, E^ArcSinh[c*x]])/(3*d) + ((2*I)*b^2*c^3*PolyLog[3, (-I)*E^ArcSinh[c*x]])/d - ((2*I)*b^2*c^3*PolyLog[3, I*E^ArcSinh[c*x]])/d","A",24,11,26,0.4231,1,"{5747, 5693, 4180, 2531, 2282, 6589, 5760, 4182, 2279, 2391, 30}"
234,1,279,0,0.5314132,"\int \frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^2} \, dx","Int[(x^4*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^2,x]","\frac{3 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d^2}-\frac{3 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d^2}-\frac{3 i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{c^5 d^2}+\frac{3 i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{c^5 d^2}-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^2 d^2 \left(c^2 x^2+1\right)}-\frac{2 b \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d^2}+\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d^2 \sqrt{c^2 x^2+1}}+\frac{3 x \left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^4 d^2}-\frac{3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c^5 d^2}+\frac{2 b^2 x}{c^4 d^2}-\frac{b^2 \tan ^{-1}(c x)}{c^5 d^2}","\frac{3 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d^2}-\frac{3 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d^2}-\frac{3 i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{c^5 d^2}+\frac{3 i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{c^5 d^2}-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^2 d^2 \left(c^2 x^2+1\right)}-\frac{2 b \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d^2}+\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d^2 \sqrt{c^2 x^2+1}}+\frac{3 x \left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^4 d^2}-\frac{3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c^5 d^2}+\frac{2 b^2 x}{c^4 d^2}-\frac{b^2 \tan ^{-1}(c x)}{c^5 d^2}",1,"(2*b^2*x)/(c^4*d^2) + (b*(a + b*ArcSinh[c*x]))/(c^5*d^2*Sqrt[1 + c^2*x^2]) - (2*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(c^5*d^2) + (3*x*(a + b*ArcSinh[c*x])^2)/(2*c^4*d^2) - (x^3*(a + b*ArcSinh[c*x])^2)/(2*c^2*d^2*(1 + c^2*x^2)) - (3*(a + b*ArcSinh[c*x])^2*ArcTan[E^ArcSinh[c*x]])/(c^5*d^2) - (b^2*ArcTan[c*x])/(c^5*d^2) + ((3*I)*b*(a + b*ArcSinh[c*x])*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^5*d^2) - ((3*I)*b*(a + b*ArcSinh[c*x])*PolyLog[2, I*E^ArcSinh[c*x]])/(c^5*d^2) - ((3*I)*b^2*PolyLog[3, (-I)*E^ArcSinh[c*x]])/(c^5*d^2) + ((3*I)*b^2*PolyLog[3, I*E^ArcSinh[c*x]])/(c^5*d^2)","A",15,14,26,0.5385,1,"{5751, 5767, 5693, 4180, 2531, 2282, 6589, 5717, 8, 266, 43, 5732, 388, 205}"
235,1,213,0,0.4047909,"\int \frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^2} \, dx","Int[(x^3*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^2,x]","\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^4 d^2}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{2 c^4 d^2}-\frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^2 d^2 \left(c^2 x^2+1\right)}-\frac{b x \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d^2 \sqrt{c^2 x^2+1}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c^4 d^2}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^4 d^2}+\frac{\log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c^4 d^2}+\frac{b^2 \log \left(c^2 x^2+1\right)}{2 c^4 d^2}","\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^4 d^2}-\frac{b^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{2 c^4 d^2}-\frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^2 d^2 \left(c^2 x^2+1\right)}-\frac{b x \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d^2 \sqrt{c^2 x^2+1}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c^4 d^2}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^4 d^2}+\frac{\log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c^4 d^2}+\frac{b^2 \log \left(c^2 x^2+1\right)}{2 c^4 d^2}",1,"-((b*x*(a + b*ArcSinh[c*x]))/(c^3*d^2*Sqrt[1 + c^2*x^2])) + (a + b*ArcSinh[c*x])^2/(2*c^4*d^2) - (x^2*(a + b*ArcSinh[c*x])^2)/(2*c^2*d^2*(1 + c^2*x^2)) - (a + b*ArcSinh[c*x])^3/(3*b*c^4*d^2) + ((a + b*ArcSinh[c*x])^2*Log[1 + E^(2*ArcSinh[c*x])])/(c^4*d^2) + (b^2*Log[1 + c^2*x^2])/(2*c^4*d^2) + (b*(a + b*ArcSinh[c*x])*PolyLog[2, -E^(2*ArcSinh[c*x])])/(c^4*d^2) - (b^2*PolyLog[3, -E^(2*ArcSinh[c*x])])/(2*c^4*d^2)","A",10,9,26,0.3462,1,"{5751, 5714, 3718, 2190, 2531, 2282, 6589, 5675, 260}"
236,1,213,0,0.2981986,"\int \frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^2} \, dx","Int[(x^2*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^2,x]","-\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d^2}+\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d^2}+\frac{i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{c^3 d^2}-\frac{i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{c^3 d^2}-\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d^2 \sqrt{c^2 x^2+1}}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^2 d^2 \left(c^2 x^2+1\right)}+\frac{\tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c^3 d^2}+\frac{b^2 \tan ^{-1}(c x)}{c^3 d^2}","-\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d^2}+\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d^2}+\frac{i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{c^3 d^2}-\frac{i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{c^3 d^2}-\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d^2 \sqrt{c^2 x^2+1}}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^2 d^2 \left(c^2 x^2+1\right)}+\frac{\tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c^3 d^2}+\frac{b^2 \tan ^{-1}(c x)}{c^3 d^2}",1,"-((b*(a + b*ArcSinh[c*x]))/(c^3*d^2*Sqrt[1 + c^2*x^2])) - (x*(a + b*ArcSinh[c*x])^2)/(2*c^2*d^2*(1 + c^2*x^2)) + ((a + b*ArcSinh[c*x])^2*ArcTan[E^ArcSinh[c*x]])/(c^3*d^2) + (b^2*ArcTan[c*x])/(c^3*d^2) - (I*b*(a + b*ArcSinh[c*x])*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^3*d^2) + (I*b*(a + b*ArcSinh[c*x])*PolyLog[2, I*E^ArcSinh[c*x]])/(c^3*d^2) + (I*b^2*PolyLog[3, (-I)*E^ArcSinh[c*x]])/(c^3*d^2) - (I*b^2*PolyLog[3, I*E^ArcSinh[c*x]])/(c^3*d^2)","A",11,8,26,0.3077,1,"{5751, 5693, 4180, 2531, 2282, 6589, 5717, 203}"
237,1,85,0,0.1068484,"\int \frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^2} \, dx","Int[(x*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^2,x]","\frac{b x \left(a+b \sinh ^{-1}(c x)\right)}{c d^2 \sqrt{c^2 x^2+1}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^2 d^2 \left(c^2 x^2+1\right)}-\frac{b^2 \log \left(c^2 x^2+1\right)}{2 c^2 d^2}","\frac{b x \left(a+b \sinh ^{-1}(c x)\right)}{c d^2 \sqrt{c^2 x^2+1}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^2 d^2 \left(c^2 x^2+1\right)}-\frac{b^2 \log \left(c^2 x^2+1\right)}{2 c^2 d^2}",1,"(b*x*(a + b*ArcSinh[c*x]))/(c*d^2*Sqrt[1 + c^2*x^2]) - (a + b*ArcSinh[c*x])^2/(2*c^2*d^2*(1 + c^2*x^2)) - (b^2*Log[1 + c^2*x^2])/(2*c^2*d^2)","A",3,3,24,0.1250,1,"{5717, 5687, 260}"
238,1,210,0,0.2450823,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSinh[c*x])^2/(d + c^2*d*x^2)^2,x]","-\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c d^2}+\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c d^2}+\frac{i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{c d^2}-\frac{i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{c d^2}+\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{c d^2 \sqrt{c^2 x^2+1}}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^2 \left(c^2 x^2+1\right)}+\frac{\tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c d^2}-\frac{b^2 \tan ^{-1}(c x)}{c d^2}","-\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c d^2}+\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c d^2}+\frac{i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{c d^2}-\frac{i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{c d^2}+\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{c d^2 \sqrt{c^2 x^2+1}}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^2 \left(c^2 x^2+1\right)}+\frac{\tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c d^2}-\frac{b^2 \tan ^{-1}(c x)}{c d^2}",1,"(b*(a + b*ArcSinh[c*x]))/(c*d^2*Sqrt[1 + c^2*x^2]) + (x*(a + b*ArcSinh[c*x])^2)/(2*d^2*(1 + c^2*x^2)) + ((a + b*ArcSinh[c*x])^2*ArcTan[E^ArcSinh[c*x]])/(c*d^2) - (b^2*ArcTan[c*x])/(c*d^2) - (I*b*(a + b*ArcSinh[c*x])*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c*d^2) + (I*b*(a + b*ArcSinh[c*x])*PolyLog[2, I*E^ArcSinh[c*x]])/(c*d^2) + (I*b^2*PolyLog[3, (-I)*E^ArcSinh[c*x]])/(c*d^2) - (I*b^2*PolyLog[3, I*E^ArcSinh[c*x]])/(c*d^2)","A",11,8,23,0.3478,1,"{5690, 5693, 4180, 2531, 2282, 6589, 5717, 203}"
239,1,193,0,0.34,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x \left(d+c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x*(d + c^2*d*x^2)^2),x]","-\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}+\frac{b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}+\frac{b^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d^2}-\frac{b^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)}{2 d^2}-\frac{b c x \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 x^2+1}}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^2 \left(c^2 x^2+1\right)}-\frac{2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d^2}+\frac{b^2 \log \left(c^2 x^2+1\right)}{2 d^2}","-\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}+\frac{b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}+\frac{b^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d^2}-\frac{b^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)}{2 d^2}-\frac{b c x \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 x^2+1}}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^2 \left(c^2 x^2+1\right)}-\frac{2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d^2}+\frac{b^2 \log \left(c^2 x^2+1\right)}{2 d^2}",1,"-((b*c*x*(a + b*ArcSinh[c*x]))/(d^2*Sqrt[1 + c^2*x^2])) + (a + b*ArcSinh[c*x])^2/(2*d^2*(1 + c^2*x^2)) - (2*(a + b*ArcSinh[c*x])^2*ArcTanh[E^(2*ArcSinh[c*x])])/d^2 + (b^2*Log[1 + c^2*x^2])/(2*d^2) - (b*(a + b*ArcSinh[c*x])*PolyLog[2, -E^(2*ArcSinh[c*x])])/d^2 + (b*(a + b*ArcSinh[c*x])*PolyLog[2, E^(2*ArcSinh[c*x])])/d^2 + (b^2*PolyLog[3, -E^(2*ArcSinh[c*x])])/(2*d^2) - (b^2*PolyLog[3, E^(2*ArcSinh[c*x])])/(2*d^2)","A",12,9,26,0.3462,1,"{5755, 5720, 5461, 4182, 2531, 2282, 6589, 5687, 260}"
240,1,287,0,0.5437789,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^2 \left(d+c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^2*(d + c^2*d*x^2)^2),x]","\frac{3 i b c \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}-\frac{3 i b c \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}-\frac{2 b^2 c \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{d^2}+\frac{2 b^2 c \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{d^2}-\frac{3 i b^2 c \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{d^2}+\frac{3 i b^2 c \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{d^2}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 x^2+1}}-\frac{3 c^2 x \left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^2 \left(c^2 x^2+1\right)}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d^2 x \left(c^2 x^2+1\right)}-\frac{3 c \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d^2}-\frac{4 b c \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}+\frac{b^2 c \tan ^{-1}(c x)}{d^2}","\frac{3 i b c \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}-\frac{3 i b c \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}-\frac{2 b^2 c \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{d^2}+\frac{2 b^2 c \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{d^2}-\frac{3 i b^2 c \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{d^2}+\frac{3 i b^2 c \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{d^2}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 x^2+1}}-\frac{3 c^2 x \left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^2 \left(c^2 x^2+1\right)}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d^2 x \left(c^2 x^2+1\right)}-\frac{3 c \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d^2}-\frac{4 b c \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}+\frac{b^2 c \tan ^{-1}(c x)}{d^2}",1,"-((b*c*(a + b*ArcSinh[c*x]))/(d^2*Sqrt[1 + c^2*x^2])) - (a + b*ArcSinh[c*x])^2/(d^2*x*(1 + c^2*x^2)) - (3*c^2*x*(a + b*ArcSinh[c*x])^2)/(2*d^2*(1 + c^2*x^2)) - (3*c*(a + b*ArcSinh[c*x])^2*ArcTan[E^ArcSinh[c*x]])/d^2 + (b^2*c*ArcTan[c*x])/d^2 - (4*b*c*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/d^2 - (2*b^2*c*PolyLog[2, -E^ArcSinh[c*x]])/d^2 + ((3*I)*b*c*(a + b*ArcSinh[c*x])*PolyLog[2, (-I)*E^ArcSinh[c*x]])/d^2 - ((3*I)*b*c*(a + b*ArcSinh[c*x])*PolyLog[2, I*E^ArcSinh[c*x]])/d^2 + (2*b^2*c*PolyLog[2, E^ArcSinh[c*x]])/d^2 - ((3*I)*b^2*c*PolyLog[3, (-I)*E^ArcSinh[c*x]])/d^2 + ((3*I)*b^2*c*PolyLog[3, I*E^ArcSinh[c*x]])/d^2","A",20,14,26,0.5385,1,"{5747, 5690, 5693, 4180, 2531, 2282, 6589, 5717, 203, 5755, 5760, 4182, 2279, 2391}"
241,1,253,0,0.5807806,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^3 \left(d+c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^3*(d + c^2*d*x^2)^2),x]","\frac{2 b c^2 \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}-\frac{2 b c^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}-\frac{b^2 c^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{d^2}+\frac{b^2 c^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)}{d^2}-\frac{c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{d^2 \left(c^2 x^2+1\right)}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{d^2 x \sqrt{c^2 x^2+1}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^2 x^2 \left(c^2 x^2+1\right)}+\frac{4 c^2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d^2}-\frac{b^2 c^2 \log \left(c^2 x^2+1\right)}{2 d^2}+\frac{b^2 c^2 \log (x)}{d^2}","\frac{2 b c^2 \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}-\frac{2 b c^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}-\frac{b^2 c^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{d^2}+\frac{b^2 c^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)}{d^2}-\frac{c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{d^2 \left(c^2 x^2+1\right)}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{d^2 x \sqrt{c^2 x^2+1}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^2 x^2 \left(c^2 x^2+1\right)}+\frac{4 c^2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d^2}-\frac{b^2 c^2 \log \left(c^2 x^2+1\right)}{2 d^2}+\frac{b^2 c^2 \log (x)}{d^2}",1,"-((b*c*(a + b*ArcSinh[c*x]))/(d^2*x*Sqrt[1 + c^2*x^2])) - (c^2*(a + b*ArcSinh[c*x])^2)/(d^2*(1 + c^2*x^2)) - (a + b*ArcSinh[c*x])^2/(2*d^2*x^2*(1 + c^2*x^2)) + (4*c^2*(a + b*ArcSinh[c*x])^2*ArcTanh[E^(2*ArcSinh[c*x])])/d^2 + (b^2*c^2*Log[x])/d^2 - (b^2*c^2*Log[1 + c^2*x^2])/(2*d^2) + (2*b*c^2*(a + b*ArcSinh[c*x])*PolyLog[2, -E^(2*ArcSinh[c*x])])/d^2 - (2*b*c^2*(a + b*ArcSinh[c*x])*PolyLog[2, E^(2*ArcSinh[c*x])])/d^2 - (b^2*c^2*PolyLog[3, -E^(2*ArcSinh[c*x])])/d^2 + (b^2*c^2*PolyLog[3, E^(2*ArcSinh[c*x])])/d^2","A",17,15,26,0.5769,1,"{5747, 5755, 5720, 5461, 4182, 2531, 2282, 6589, 5687, 260, 271, 191, 5732, 446, 72}"
242,1,401,0,0.9632927,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^4 \left(d+c^2 d x^2\right)^2} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^4*(d + c^2*d*x^2)^2),x]","-\frac{5 i b c^3 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}+\frac{5 i b c^3 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}+\frac{13 b^2 c^3 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{3 d^2}-\frac{13 b^2 c^3 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{3 d^2}+\frac{5 i b^2 c^3 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{d^2}-\frac{5 i b^2 c^3 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{d^2}+\frac{5 c^4 x \left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^2 \left(c^2 x^2+1\right)}+\frac{2 b c^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 x^2+1}}+\frac{5 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^2 x \left(c^2 x^2+1\right)}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 x^2 \sqrt{c^2 x^2+1}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^2 x^3 \left(c^2 x^2+1\right)}+\frac{5 c^3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d^2}+\frac{26 b c^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2}-\frac{b^2 c^2}{3 d^2 x}-\frac{b^2 c^3 \tan ^{-1}(c x)}{d^2}","-\frac{5 i b c^3 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}+\frac{5 i b c^3 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2}+\frac{13 b^2 c^3 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{3 d^2}-\frac{13 b^2 c^3 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{3 d^2}+\frac{5 i b^2 c^3 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{d^2}-\frac{5 i b^2 c^3 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{d^2}+\frac{5 c^4 x \left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^2 \left(c^2 x^2+1\right)}+\frac{2 b c^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 x^2+1}}+\frac{5 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^2 x \left(c^2 x^2+1\right)}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 x^2 \sqrt{c^2 x^2+1}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^2 x^3 \left(c^2 x^2+1\right)}+\frac{5 c^3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d^2}+\frac{26 b c^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2}-\frac{b^2 c^2}{3 d^2 x}-\frac{b^2 c^3 \tan ^{-1}(c x)}{d^2}",1,"-(b^2*c^2)/(3*d^2*x) + (2*b*c^3*(a + b*ArcSinh[c*x]))/(3*d^2*Sqrt[1 + c^2*x^2]) - (b*c*(a + b*ArcSinh[c*x]))/(3*d^2*x^2*Sqrt[1 + c^2*x^2]) - (a + b*ArcSinh[c*x])^2/(3*d^2*x^3*(1 + c^2*x^2)) + (5*c^2*(a + b*ArcSinh[c*x])^2)/(3*d^2*x*(1 + c^2*x^2)) + (5*c^4*x*(a + b*ArcSinh[c*x])^2)/(2*d^2*(1 + c^2*x^2)) + (5*c^3*(a + b*ArcSinh[c*x])^2*ArcTan[E^ArcSinh[c*x]])/d^2 - (b^2*c^3*ArcTan[c*x])/d^2 + (26*b*c^3*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/(3*d^2) + (13*b^2*c^3*PolyLog[2, -E^ArcSinh[c*x]])/(3*d^2) - ((5*I)*b*c^3*(a + b*ArcSinh[c*x])*PolyLog[2, (-I)*E^ArcSinh[c*x]])/d^2 + ((5*I)*b*c^3*(a + b*ArcSinh[c*x])*PolyLog[2, I*E^ArcSinh[c*x]])/d^2 - (13*b^2*c^3*PolyLog[2, E^ArcSinh[c*x]])/(3*d^2) + ((5*I)*b^2*c^3*PolyLog[3, (-I)*E^ArcSinh[c*x]])/d^2 - ((5*I)*b^2*c^3*PolyLog[3, I*E^ArcSinh[c*x]])/d^2","A",32,15,26,0.5769,1,"{5747, 5690, 5693, 4180, 2531, 2282, 6589, 5717, 203, 5755, 5760, 4182, 2279, 2391, 325}"
243,1,320,0,0.5451257,"\int \frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^3} \, dx","Int[(x^4*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^3,x]","-\frac{3 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c^5 d^3}+\frac{3 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c^5 d^3}+\frac{3 i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{4 c^5 d^3}-\frac{3 i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{4 c^5 d^3}-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^2 d^3 \left(c^2 x^2+1\right)^2}-\frac{3 x \left(a+b \sinh ^{-1}(c x)\right)^2}{8 c^4 d^3 \left(c^2 x^2+1\right)}-\frac{5 b \left(a+b \sinh ^{-1}(c x)\right)}{4 c^5 d^3 \sqrt{c^2 x^2+1}}+\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{6 c^5 d^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^5 d^3}-\frac{b^2 x}{12 c^4 d^3 \left(c^2 x^2+1\right)}+\frac{7 b^2 \tan ^{-1}(c x)}{6 c^5 d^3}","-\frac{3 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c^5 d^3}+\frac{3 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c^5 d^3}+\frac{3 i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{4 c^5 d^3}-\frac{3 i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{4 c^5 d^3}-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^2 d^3 \left(c^2 x^2+1\right)^2}-\frac{3 x \left(a+b \sinh ^{-1}(c x)\right)^2}{8 c^4 d^3 \left(c^2 x^2+1\right)}-\frac{5 b \left(a+b \sinh ^{-1}(c x)\right)}{4 c^5 d^3 \sqrt{c^2 x^2+1}}+\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{6 c^5 d^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^5 d^3}-\frac{b^2 x}{12 c^4 d^3 \left(c^2 x^2+1\right)}+\frac{7 b^2 \tan ^{-1}(c x)}{6 c^5 d^3}",1,"-(b^2*x)/(12*c^4*d^3*(1 + c^2*x^2)) + (b*(a + b*ArcSinh[c*x]))/(6*c^5*d^3*(1 + c^2*x^2)^(3/2)) - (5*b*(a + b*ArcSinh[c*x]))/(4*c^5*d^3*Sqrt[1 + c^2*x^2]) - (x^3*(a + b*ArcSinh[c*x])^2)/(4*c^2*d^3*(1 + c^2*x^2)^2) - (3*x*(a + b*ArcSinh[c*x])^2)/(8*c^4*d^3*(1 + c^2*x^2)) + (3*(a + b*ArcSinh[c*x])^2*ArcTan[E^ArcSinh[c*x]])/(4*c^5*d^3) + (7*b^2*ArcTan[c*x])/(6*c^5*d^3) - (((3*I)/4)*b*(a + b*ArcSinh[c*x])*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^5*d^3) + (((3*I)/4)*b*(a + b*ArcSinh[c*x])*PolyLog[2, I*E^ArcSinh[c*x]])/(c^5*d^3) + (((3*I)/4)*b^2*PolyLog[3, (-I)*E^ArcSinh[c*x]])/(c^5*d^3) - (((3*I)/4)*b^2*PolyLog[3, I*E^ArcSinh[c*x]])/(c^5*d^3)","A",16,13,26,0.5000,1,"{5751, 5693, 4180, 2531, 2282, 6589, 5717, 203, 266, 43, 5732, 12, 385}"
244,1,167,0,0.3367586,"\int \frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^3} \, dx","Int[(x^3*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^3,x]","\frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 d^3 \left(c^2 x^2+1\right)^2}+\frac{b x^3 \left(a+b \sinh ^{-1}(c x)\right)}{6 c d^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{b x \left(a+b \sinh ^{-1}(c x)\right)}{2 c^3 d^3 \sqrt{c^2 x^2+1}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^4 d^3}-\frac{b^2}{12 c^4 d^3 \left(c^2 x^2+1\right)}-\frac{b^2 \log \left(c^2 x^2+1\right)}{3 c^4 d^3}","\frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 d^3 \left(c^2 x^2+1\right)^2}+\frac{b x^3 \left(a+b \sinh ^{-1}(c x)\right)}{6 c d^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{b x \left(a+b \sinh ^{-1}(c x)\right)}{2 c^3 d^3 \sqrt{c^2 x^2+1}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^4 d^3}-\frac{b^2}{12 c^4 d^3 \left(c^2 x^2+1\right)}-\frac{b^2 \log \left(c^2 x^2+1\right)}{3 c^4 d^3}",1,"-b^2/(12*c^4*d^3*(1 + c^2*x^2)) + (b*x^3*(a + b*ArcSinh[c*x]))/(6*c*d^3*(1 + c^2*x^2)^(3/2)) + (b*x*(a + b*ArcSinh[c*x]))/(2*c^3*d^3*Sqrt[1 + c^2*x^2]) - (a + b*ArcSinh[c*x])^2/(4*c^4*d^3) + (x^4*(a + b*ArcSinh[c*x])^2)/(4*d^3*(1 + c^2*x^2)^2) - (b^2*Log[1 + c^2*x^2])/(3*c^4*d^3)","A",8,6,26,0.2308,1,"{5723, 5751, 5675, 260, 266, 43}"
245,1,318,0,0.4172525,"\int \frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^3} \, dx","Int[(x^2*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^3,x]","-\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c^3 d^3}+\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c^3 d^3}+\frac{i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{4 c^3 d^3}-\frac{i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{4 c^3 d^3}+\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{4 c^3 d^3 \sqrt{c^2 x^2+1}}-\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{6 c^3 d^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{8 c^2 d^3 \left(c^2 x^2+1\right)}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^2 d^3 \left(c^2 x^2+1\right)^2}+\frac{\tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^3 d^3}+\frac{b^2 x}{12 c^2 d^3 \left(c^2 x^2+1\right)}-\frac{b^2 \tan ^{-1}(c x)}{6 c^3 d^3}","-\frac{i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c^3 d^3}+\frac{i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c^3 d^3}+\frac{i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{4 c^3 d^3}-\frac{i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{4 c^3 d^3}+\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{4 c^3 d^3 \sqrt{c^2 x^2+1}}-\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{6 c^3 d^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{8 c^2 d^3 \left(c^2 x^2+1\right)}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^2 d^3 \left(c^2 x^2+1\right)^2}+\frac{\tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^3 d^3}+\frac{b^2 x}{12 c^2 d^3 \left(c^2 x^2+1\right)}-\frac{b^2 \tan ^{-1}(c x)}{6 c^3 d^3}",1,"(b^2*x)/(12*c^2*d^3*(1 + c^2*x^2)) - (b*(a + b*ArcSinh[c*x]))/(6*c^3*d^3*(1 + c^2*x^2)^(3/2)) + (b*(a + b*ArcSinh[c*x]))/(4*c^3*d^3*Sqrt[1 + c^2*x^2]) - (x*(a + b*ArcSinh[c*x])^2)/(4*c^2*d^3*(1 + c^2*x^2)^2) + (x*(a + b*ArcSinh[c*x])^2)/(8*c^2*d^3*(1 + c^2*x^2)) + ((a + b*ArcSinh[c*x])^2*ArcTan[E^ArcSinh[c*x]])/(4*c^3*d^3) - (b^2*ArcTan[c*x])/(6*c^3*d^3) - ((I/4)*b*(a + b*ArcSinh[c*x])*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^3*d^3) + ((I/4)*b*(a + b*ArcSinh[c*x])*PolyLog[2, I*E^ArcSinh[c*x]])/(c^3*d^3) + ((I/4)*b^2*PolyLog[3, (-I)*E^ArcSinh[c*x]])/(c^3*d^3) - ((I/4)*b^2*PolyLog[3, I*E^ArcSinh[c*x]])/(c^3*d^3)","A",15,10,26,0.3846,1,"{5751, 5690, 5693, 4180, 2531, 2282, 6589, 5717, 203, 199}"
246,1,145,0,0.1456544,"\int \frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^3} \, dx","Int[(x*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^3,x]","\frac{b x \left(a+b \sinh ^{-1}(c x)\right)}{3 c d^3 \sqrt{c^2 x^2+1}}+\frac{b x \left(a+b \sinh ^{-1}(c x)\right)}{6 c d^3 \left(c^2 x^2+1\right)^{3/2}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^2 d^3 \left(c^2 x^2+1\right)^2}+\frac{b^2}{12 c^2 d^3 \left(c^2 x^2+1\right)}-\frac{b^2 \log \left(c^2 x^2+1\right)}{6 c^2 d^3}","\frac{b x \left(a+b \sinh ^{-1}(c x)\right)}{3 c d^3 \sqrt{c^2 x^2+1}}+\frac{b x \left(a+b \sinh ^{-1}(c x)\right)}{6 c d^3 \left(c^2 x^2+1\right)^{3/2}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^2 d^3 \left(c^2 x^2+1\right)^2}+\frac{b^2}{12 c^2 d^3 \left(c^2 x^2+1\right)}-\frac{b^2 \log \left(c^2 x^2+1\right)}{6 c^2 d^3}",1,"b^2/(12*c^2*d^3*(1 + c^2*x^2)) + (b*x*(a + b*ArcSinh[c*x]))/(6*c*d^3*(1 + c^2*x^2)^(3/2)) + (b*x*(a + b*ArcSinh[c*x]))/(3*c*d^3*Sqrt[1 + c^2*x^2]) - (a + b*ArcSinh[c*x])^2/(4*c^2*d^3*(1 + c^2*x^2)^2) - (b^2*Log[1 + c^2*x^2])/(6*c^2*d^3)","A",5,5,24,0.2083,1,"{5717, 5690, 5687, 260, 261}"
247,1,309,0,0.3644105,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSinh[c*x])^2/(d + c^2*d*x^2)^3,x]","-\frac{3 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c d^3}+\frac{3 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c d^3}+\frac{3 i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{4 c d^3}-\frac{3 i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{4 c d^3}+\frac{3 b \left(a+b \sinh ^{-1}(c x)\right)}{4 c d^3 \sqrt{c^2 x^2+1}}+\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{6 c d^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{3 x \left(a+b \sinh ^{-1}(c x)\right)^2}{8 d^3 \left(c^2 x^2+1\right)}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{4 d^3 \left(c^2 x^2+1\right)^2}+\frac{3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c d^3}-\frac{b^2 x}{12 d^3 \left(c^2 x^2+1\right)}-\frac{5 b^2 \tan ^{-1}(c x)}{6 c d^3}","-\frac{3 i b \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c d^3}+\frac{3 i b \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 c d^3}+\frac{3 i b^2 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{4 c d^3}-\frac{3 i b^2 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{4 c d^3}+\frac{3 b \left(a+b \sinh ^{-1}(c x)\right)}{4 c d^3 \sqrt{c^2 x^2+1}}+\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{6 c d^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{3 x \left(a+b \sinh ^{-1}(c x)\right)^2}{8 d^3 \left(c^2 x^2+1\right)}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{4 d^3 \left(c^2 x^2+1\right)^2}+\frac{3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c d^3}-\frac{b^2 x}{12 d^3 \left(c^2 x^2+1\right)}-\frac{5 b^2 \tan ^{-1}(c x)}{6 c d^3}",1,"-(b^2*x)/(12*d^3*(1 + c^2*x^2)) + (b*(a + b*ArcSinh[c*x]))/(6*c*d^3*(1 + c^2*x^2)^(3/2)) + (3*b*(a + b*ArcSinh[c*x]))/(4*c*d^3*Sqrt[1 + c^2*x^2]) + (x*(a + b*ArcSinh[c*x])^2)/(4*d^3*(1 + c^2*x^2)^2) + (3*x*(a + b*ArcSinh[c*x])^2)/(8*d^3*(1 + c^2*x^2)) + (3*(a + b*ArcSinh[c*x])^2*ArcTan[E^ArcSinh[c*x]])/(4*c*d^3) - (5*b^2*ArcTan[c*x])/(6*c*d^3) - (((3*I)/4)*b*(a + b*ArcSinh[c*x])*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c*d^3) + (((3*I)/4)*b*(a + b*ArcSinh[c*x])*PolyLog[2, I*E^ArcSinh[c*x]])/(c*d^3) + (((3*I)/4)*b^2*PolyLog[3, (-I)*E^ArcSinh[c*x]])/(c*d^3) - (((3*I)/4)*b^2*PolyLog[3, I*E^ArcSinh[c*x]])/(c*d^3)","A",15,9,23,0.3913,1,"{5690, 5693, 4180, 2531, 2282, 6589, 5717, 203, 199}"
248,1,275,0,0.5069354,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x \left(d+c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x*(d + c^2*d*x^2)^3),x]","-\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^3}+\frac{b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^3}+\frac{b^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d^3}-\frac{b^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)}{2 d^3}-\frac{4 b c x \left(a+b \sinh ^{-1}(c x)\right)}{3 d^3 \sqrt{c^2 x^2+1}}-\frac{b c x \left(a+b \sinh ^{-1}(c x)\right)}{6 d^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^3 \left(c^2 x^2+1\right)}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{4 d^3 \left(c^2 x^2+1\right)^2}-\frac{2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d^3}-\frac{b^2}{12 d^3 \left(c^2 x^2+1\right)}+\frac{2 b^2 \log \left(c^2 x^2+1\right)}{3 d^3}","-\frac{b \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^3}+\frac{b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^3}+\frac{b^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d^3}-\frac{b^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)}{2 d^3}-\frac{4 b c x \left(a+b \sinh ^{-1}(c x)\right)}{3 d^3 \sqrt{c^2 x^2+1}}-\frac{b c x \left(a+b \sinh ^{-1}(c x)\right)}{6 d^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^3 \left(c^2 x^2+1\right)}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{4 d^3 \left(c^2 x^2+1\right)^2}-\frac{2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d^3}-\frac{b^2}{12 d^3 \left(c^2 x^2+1\right)}+\frac{2 b^2 \log \left(c^2 x^2+1\right)}{3 d^3}",1,"-b^2/(12*d^3*(1 + c^2*x^2)) - (b*c*x*(a + b*ArcSinh[c*x]))/(6*d^3*(1 + c^2*x^2)^(3/2)) - (4*b*c*x*(a + b*ArcSinh[c*x]))/(3*d^3*Sqrt[1 + c^2*x^2]) + (a + b*ArcSinh[c*x])^2/(4*d^3*(1 + c^2*x^2)^2) + (a + b*ArcSinh[c*x])^2/(2*d^3*(1 + c^2*x^2)) - (2*(a + b*ArcSinh[c*x])^2*ArcTanh[E^(2*ArcSinh[c*x])])/d^3 + (2*b^2*Log[1 + c^2*x^2])/(3*d^3) - (b*(a + b*ArcSinh[c*x])*PolyLog[2, -E^(2*ArcSinh[c*x])])/d^3 + (b*(a + b*ArcSinh[c*x])*PolyLog[2, E^(2*ArcSinh[c*x])])/d^3 + (b^2*PolyLog[3, -E^(2*ArcSinh[c*x])])/(2*d^3) - (b^2*PolyLog[3, E^(2*ArcSinh[c*x])])/(2*d^3)","A",17,11,26,0.4231,1,"{5755, 5720, 5461, 4182, 2531, 2282, 6589, 5687, 260, 5690, 261}"
249,1,389,0,0.7666484,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^2 \left(d+c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^2*(d + c^2*d*x^2)^3),x]","\frac{15 i b c \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3}-\frac{15 i b c \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3}-\frac{2 b^2 c \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{d^3}+\frac{2 b^2 c \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{d^3}-\frac{15 i b^2 c \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{4 d^3}+\frac{15 i b^2 c \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{4 d^3}-\frac{7 b c \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3 \sqrt{c^2 x^2+1}}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{6 d^3 \left(c^2 x^2+1\right)^{3/2}}-\frac{15 c^2 x \left(a+b \sinh ^{-1}(c x)\right)^2}{8 d^3 \left(c^2 x^2+1\right)}-\frac{5 c^2 x \left(a+b \sinh ^{-1}(c x)\right)^2}{4 d^3 \left(c^2 x^2+1\right)^2}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d^3 x \left(c^2 x^2+1\right)^2}-\frac{15 c \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{4 d^3}-\frac{4 b c \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^3}+\frac{b^2 c^2 x}{12 d^3 \left(c^2 x^2+1\right)}+\frac{11 b^2 c \tan ^{-1}(c x)}{6 d^3}","\frac{15 i b c \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3}-\frac{15 i b c \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3}-\frac{2 b^2 c \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{d^3}+\frac{2 b^2 c \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{d^3}-\frac{15 i b^2 c \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{4 d^3}+\frac{15 i b^2 c \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{4 d^3}-\frac{7 b c \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3 \sqrt{c^2 x^2+1}}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{6 d^3 \left(c^2 x^2+1\right)^{3/2}}-\frac{15 c^2 x \left(a+b \sinh ^{-1}(c x)\right)^2}{8 d^3 \left(c^2 x^2+1\right)}-\frac{5 c^2 x \left(a+b \sinh ^{-1}(c x)\right)^2}{4 d^3 \left(c^2 x^2+1\right)^2}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d^3 x \left(c^2 x^2+1\right)^2}-\frac{15 c \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{4 d^3}-\frac{4 b c \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^3}+\frac{b^2 c^2 x}{12 d^3 \left(c^2 x^2+1\right)}+\frac{11 b^2 c \tan ^{-1}(c x)}{6 d^3}",1,"(b^2*c^2*x)/(12*d^3*(1 + c^2*x^2)) - (b*c*(a + b*ArcSinh[c*x]))/(6*d^3*(1 + c^2*x^2)^(3/2)) - (7*b*c*(a + b*ArcSinh[c*x]))/(4*d^3*Sqrt[1 + c^2*x^2]) - (a + b*ArcSinh[c*x])^2/(d^3*x*(1 + c^2*x^2)^2) - (5*c^2*x*(a + b*ArcSinh[c*x])^2)/(4*d^3*(1 + c^2*x^2)^2) - (15*c^2*x*(a + b*ArcSinh[c*x])^2)/(8*d^3*(1 + c^2*x^2)) - (15*c*(a + b*ArcSinh[c*x])^2*ArcTan[E^ArcSinh[c*x]])/(4*d^3) + (11*b^2*c*ArcTan[c*x])/(6*d^3) - (4*b*c*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/d^3 - (2*b^2*c*PolyLog[2, -E^ArcSinh[c*x]])/d^3 + (((15*I)/4)*b*c*(a + b*ArcSinh[c*x])*PolyLog[2, (-I)*E^ArcSinh[c*x]])/d^3 - (((15*I)/4)*b*c*(a + b*ArcSinh[c*x])*PolyLog[2, I*E^ArcSinh[c*x]])/d^3 + (2*b^2*c*PolyLog[2, E^ArcSinh[c*x]])/d^3 - (((15*I)/4)*b^2*c*PolyLog[3, (-I)*E^ArcSinh[c*x]])/d^3 + (((15*I)/4)*b^2*c*PolyLog[3, I*E^ArcSinh[c*x]])/d^3","A",27,15,26,0.5769,1,"{5747, 5690, 5693, 4180, 2531, 2282, 6589, 5717, 203, 199, 5755, 5760, 4182, 2279, 2391}"
250,1,381,0,0.8029876,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^3 \left(d+c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^3*(d + c^2*d*x^2)^3),x]","\frac{3 b c^2 \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^3}-\frac{3 b c^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^3}-\frac{3 b^2 c^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d^3}+\frac{3 b^2 c^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)}{2 d^3}+\frac{4 b c^3 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d^3 \sqrt{c^2 x^2+1}}-\frac{5 b c^3 x \left(a+b \sinh ^{-1}(c x)\right)}{6 d^3 \left(c^2 x^2+1\right)^{3/2}}-\frac{3 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^3 \left(c^2 x^2+1\right)}-\frac{3 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 d^3 \left(c^2 x^2+1\right)^2}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{d^3 x \left(c^2 x^2+1\right)^{3/2}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^3 x^2 \left(c^2 x^2+1\right)^2}+\frac{6 c^2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d^3}+\frac{b^2 c^2}{12 d^3 \left(c^2 x^2+1\right)}-\frac{7 b^2 c^2 \log \left(c^2 x^2+1\right)}{6 d^3}+\frac{b^2 c^2 \log (x)}{d^3}","\frac{3 b c^2 \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^3}-\frac{3 b c^2 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^3}-\frac{3 b^2 c^2 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(c x)}\right)}{2 d^3}+\frac{3 b^2 c^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c x)}\right)}{2 d^3}+\frac{4 b c^3 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d^3 \sqrt{c^2 x^2+1}}-\frac{5 b c^3 x \left(a+b \sinh ^{-1}(c x)\right)}{6 d^3 \left(c^2 x^2+1\right)^{3/2}}-\frac{3 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^3 \left(c^2 x^2+1\right)}-\frac{3 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 d^3 \left(c^2 x^2+1\right)^2}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{d^3 x \left(c^2 x^2+1\right)^{3/2}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^3 x^2 \left(c^2 x^2+1\right)^2}+\frac{6 c^2 \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d^3}+\frac{b^2 c^2}{12 d^3 \left(c^2 x^2+1\right)}-\frac{7 b^2 c^2 \log \left(c^2 x^2+1\right)}{6 d^3}+\frac{b^2 c^2 \log (x)}{d^3}",1,"(b^2*c^2)/(12*d^3*(1 + c^2*x^2)) - (b*c*(a + b*ArcSinh[c*x]))/(d^3*x*(1 + c^2*x^2)^(3/2)) - (5*b*c^3*x*(a + b*ArcSinh[c*x]))/(6*d^3*(1 + c^2*x^2)^(3/2)) + (4*b*c^3*x*(a + b*ArcSinh[c*x]))/(3*d^3*Sqrt[1 + c^2*x^2]) - (3*c^2*(a + b*ArcSinh[c*x])^2)/(4*d^3*(1 + c^2*x^2)^2) - (a + b*ArcSinh[c*x])^2/(2*d^3*x^2*(1 + c^2*x^2)^2) - (3*c^2*(a + b*ArcSinh[c*x])^2)/(2*d^3*(1 + c^2*x^2)) + (6*c^2*(a + b*ArcSinh[c*x])^2*ArcTanh[E^(2*ArcSinh[c*x])])/d^3 + (b^2*c^2*Log[x])/d^3 - (7*b^2*c^2*Log[1 + c^2*x^2])/(6*d^3) + (3*b*c^2*(a + b*ArcSinh[c*x])*PolyLog[2, -E^(2*ArcSinh[c*x])])/d^3 - (3*b*c^2*(a + b*ArcSinh[c*x])*PolyLog[2, E^(2*ArcSinh[c*x])])/d^3 - (3*b^2*c^2*PolyLog[3, -E^(2*ArcSinh[c*x])])/(2*d^3) + (3*b^2*c^2*PolyLog[3, E^(2*ArcSinh[c*x])])/(2*d^3)","A",23,19,26,0.7308,1,"{5747, 5755, 5720, 5461, 4182, 2531, 2282, 6589, 5687, 260, 5690, 261, 271, 192, 191, 5732, 12, 1251, 893}"
251,1,529,0,1.3074241,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^4 \left(d+c^2 d x^2\right)^3} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^4*(d + c^2*d*x^2)^3),x]","-\frac{35 i b c^3 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3}+\frac{35 i b c^3 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3}+\frac{19 b^2 c^3 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{3 d^3}-\frac{19 b^2 c^3 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{3 d^3}+\frac{35 i b^2 c^3 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{4 d^3}-\frac{35 i b^2 c^3 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{4 d^3}+\frac{35 c^4 x \left(a+b \sinh ^{-1}(c x)\right)^2}{8 d^3 \left(c^2 x^2+1\right)}+\frac{35 c^4 x \left(a+b \sinh ^{-1}(c x)\right)^2}{12 d^3 \left(c^2 x^2+1\right)^2}+\frac{29 b c^3 \left(a+b \sinh ^{-1}(c x)\right)}{12 d^3 \sqrt{c^2 x^2+1}}-\frac{b c^3 \left(a+b \sinh ^{-1}(c x)\right)}{6 d^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{7 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^3 x \left(c^2 x^2+1\right)^2}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{3 d^3 x^2 \left(c^2 x^2+1\right)^{3/2}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^3 x^3 \left(c^2 x^2+1\right)^2}+\frac{35 c^3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{4 d^3}+\frac{38 b c^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d^3}+\frac{b^2 c^4 x}{12 d^3 \left(c^2 x^2+1\right)}+\frac{b^2 c^2}{6 d^3 x \left(c^2 x^2+1\right)}-\frac{b^2 c^2}{2 d^3 x}-\frac{17 b^2 c^3 \tan ^{-1}(c x)}{6 d^3}","-\frac{35 i b c^3 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3}+\frac{35 i b c^3 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{4 d^3}+\frac{19 b^2 c^3 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right)}{3 d^3}-\frac{19 b^2 c^3 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right)}{3 d^3}+\frac{35 i b^2 c^3 \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(c x)}\right)}{4 d^3}-\frac{35 i b^2 c^3 \text{PolyLog}\left(3,i e^{\sinh ^{-1}(c x)}\right)}{4 d^3}+\frac{35 c^4 x \left(a+b \sinh ^{-1}(c x)\right)^2}{8 d^3 \left(c^2 x^2+1\right)}+\frac{35 c^4 x \left(a+b \sinh ^{-1}(c x)\right)^2}{12 d^3 \left(c^2 x^2+1\right)^2}+\frac{29 b c^3 \left(a+b \sinh ^{-1}(c x)\right)}{12 d^3 \sqrt{c^2 x^2+1}}-\frac{b c^3 \left(a+b \sinh ^{-1}(c x)\right)}{6 d^3 \left(c^2 x^2+1\right)^{3/2}}+\frac{7 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^3 x \left(c^2 x^2+1\right)^2}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{3 d^3 x^2 \left(c^2 x^2+1\right)^{3/2}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^3 x^3 \left(c^2 x^2+1\right)^2}+\frac{35 c^3 \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{4 d^3}+\frac{38 b c^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d^3}+\frac{b^2 c^4 x}{12 d^3 \left(c^2 x^2+1\right)}+\frac{b^2 c^2}{6 d^3 x \left(c^2 x^2+1\right)}-\frac{b^2 c^2}{2 d^3 x}-\frac{17 b^2 c^3 \tan ^{-1}(c x)}{6 d^3}",1,"-(b^2*c^2)/(2*d^3*x) + (b^2*c^2)/(6*d^3*x*(1 + c^2*x^2)) + (b^2*c^4*x)/(12*d^3*(1 + c^2*x^2)) - (b*c^3*(a + b*ArcSinh[c*x]))/(6*d^3*(1 + c^2*x^2)^(3/2)) - (b*c*(a + b*ArcSinh[c*x]))/(3*d^3*x^2*(1 + c^2*x^2)^(3/2)) + (29*b*c^3*(a + b*ArcSinh[c*x]))/(12*d^3*Sqrt[1 + c^2*x^2]) - (a + b*ArcSinh[c*x])^2/(3*d^3*x^3*(1 + c^2*x^2)^2) + (7*c^2*(a + b*ArcSinh[c*x])^2)/(3*d^3*x*(1 + c^2*x^2)^2) + (35*c^4*x*(a + b*ArcSinh[c*x])^2)/(12*d^3*(1 + c^2*x^2)^2) + (35*c^4*x*(a + b*ArcSinh[c*x])^2)/(8*d^3*(1 + c^2*x^2)) + (35*c^3*(a + b*ArcSinh[c*x])^2*ArcTan[E^ArcSinh[c*x]])/(4*d^3) - (17*b^2*c^3*ArcTan[c*x])/(6*d^3) + (38*b*c^3*(a + b*ArcSinh[c*x])*ArcTanh[E^ArcSinh[c*x]])/(3*d^3) + (19*b^2*c^3*PolyLog[2, -E^ArcSinh[c*x]])/(3*d^3) - (((35*I)/4)*b*c^3*(a + b*ArcSinh[c*x])*PolyLog[2, (-I)*E^ArcSinh[c*x]])/d^3 + (((35*I)/4)*b*c^3*(a + b*ArcSinh[c*x])*PolyLog[2, I*E^ArcSinh[c*x]])/d^3 - (19*b^2*c^3*PolyLog[2, E^ArcSinh[c*x]])/(3*d^3) + (((35*I)/4)*b^2*c^3*PolyLog[3, (-I)*E^ArcSinh[c*x]])/d^3 - (((35*I)/4)*b^2*c^3*PolyLog[3, I*E^ArcSinh[c*x]])/d^3","A",43,17,26,0.6538,1,"{5747, 5690, 5693, 4180, 2531, 2282, 6589, 5717, 203, 199, 5755, 5760, 4182, 2279, 2391, 290, 325}"
252,1,420,0,0.3818035,"\int \left(\pi +c^2 \pi  x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2,x]","\frac{5 \pi ^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^3}{48 b c \sqrt{c^2 x^2+1}}+\frac{1}{6} x \left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{5}{24} \pi  x \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{5}{16} \pi ^2 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{\pi ^2 b \left(c^2 x^2+1\right)^{5/2} \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{18 c}-\frac{5 \pi ^2 b \left(c^2 x^2+1\right)^{3/2} \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{48 c}-\frac{5 \pi ^2 b c x^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{16 \sqrt{c^2 x^2+1}}+\frac{1}{108} \pi ^2 b^2 x \left(c^2 x^2+1\right)^2 \sqrt{\pi  c^2 x^2+\pi }+\frac{245 \pi ^2 b^2 x \sqrt{\pi  c^2 x^2+\pi }}{1152}+\frac{65 \pi ^2 b^2 x \left(c^2 x^2+1\right) \sqrt{\pi  c^2 x^2+\pi }}{1728}-\frac{115 \pi ^2 b^2 \sqrt{\pi  c^2 x^2+\pi } \sinh ^{-1}(c x)}{1152 c \sqrt{c^2 x^2+1}}","-\frac{\pi ^{5/2} b \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)}{18 c}-\frac{5 \pi ^{5/2} b \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{48 c}+\frac{1}{6} x \left(\pi  c^2 x^2+\pi \right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{5}{24} \pi  x \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{5}{16} \pi ^2 x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{5}{16} \pi ^{5/2} b c x^2 \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 \pi ^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{48 b c}+\frac{1}{108} \pi ^{5/2} b^2 x \left(c^2 x^2+1\right)^{5/2}+\frac{65 \pi ^{5/2} b^2 x \left(c^2 x^2+1\right)^{3/2}}{1728}+\frac{245 \pi ^{5/2} b^2 x \sqrt{c^2 x^2+1}}{1152}-\frac{115 \pi ^{5/2} b^2 \sinh ^{-1}(c x)}{1152 c}",1,"(245*b^2*Pi^2*x*Sqrt[Pi + c^2*Pi*x^2])/1152 + (65*b^2*Pi^2*x*(1 + c^2*x^2)*Sqrt[Pi + c^2*Pi*x^2])/1728 + (b^2*Pi^2*x*(1 + c^2*x^2)^2*Sqrt[Pi + c^2*Pi*x^2])/108 - (115*b^2*Pi^2*Sqrt[Pi + c^2*Pi*x^2]*ArcSinh[c*x])/(1152*c*Sqrt[1 + c^2*x^2]) - (5*b*c*Pi^2*x^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(16*Sqrt[1 + c^2*x^2]) - (5*b*Pi^2*(1 + c^2*x^2)^(3/2)*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(48*c) - (b*Pi^2*(1 + c^2*x^2)^(5/2)*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(18*c) + (5*Pi^2*x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^2)/16 + (5*Pi*x*(Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/24 + (x*(Pi + c^2*Pi*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/6 + (5*Pi^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^3)/(48*b*c*Sqrt[1 + c^2*x^2])","A",16,8,25,0.3200,1,"{5684, 5682, 5675, 5661, 321, 215, 5717, 195}"
253,1,294,0,0.2270461,"\int \left(\pi +c^2 \pi  x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2,x]","\frac{\pi  \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^3}{8 b c \sqrt{c^2 x^2+1}}+\frac{1}{4} x \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{3}{8} \pi  x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{\pi  b \left(c^2 x^2+1\right)^{3/2} \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{8 c}-\frac{3 \pi  b c x^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{8 \sqrt{c^2 x^2+1}}+\frac{15}{64} \pi  b^2 x \sqrt{\pi  c^2 x^2+\pi }+\frac{1}{32} \pi  b^2 x \left(c^2 x^2+1\right) \sqrt{\pi  c^2 x^2+\pi }-\frac{9 \pi  b^2 \sqrt{\pi  c^2 x^2+\pi } \sinh ^{-1}(c x)}{64 c \sqrt{c^2 x^2+1}}","\frac{1}{4} x \left(\pi  c^2 x^2+\pi \right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{3}{8} \pi  x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{\pi ^{3/2} b \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{8 c}-\frac{3}{8} \pi ^{3/2} b c x^2 \left(a+b \sinh ^{-1}(c x)\right)+\frac{\pi ^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{8 b c}+\frac{1}{32} \pi ^{3/2} b^2 x \left(c^2 x^2+1\right)^{3/2}+\frac{15}{64} \pi ^{3/2} b^2 x \sqrt{c^2 x^2+1}-\frac{9 \pi ^{3/2} b^2 \sinh ^{-1}(c x)}{64 c}",1,"(15*b^2*Pi*x*Sqrt[Pi + c^2*Pi*x^2])/64 + (b^2*Pi*x*(1 + c^2*x^2)*Sqrt[Pi + c^2*Pi*x^2])/32 - (9*b^2*Pi*Sqrt[Pi + c^2*Pi*x^2]*ArcSinh[c*x])/(64*c*Sqrt[1 + c^2*x^2]) - (3*b*c*Pi*x^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(8*Sqrt[1 + c^2*x^2]) - (b*Pi*(1 + c^2*x^2)^(3/2)*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(8*c) + (3*Pi*x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^2)/8 + (x*(Pi + c^2*Pi*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/4 + (Pi*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^3)/(8*b*c*Sqrt[1 + c^2*x^2])","A",10,8,25,0.3200,1,"{5684, 5682, 5675, 5661, 321, 215, 5717, 195}"
254,1,184,0,0.1129145,"\int \sqrt{\pi +c^2 \pi  x^2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^2,x]","\frac{\sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b c \sqrt{c^2 x^2+1}}+\frac{1}{2} x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b c x^2 \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{c^2 x^2+1}}+\frac{1}{4} b^2 x \sqrt{\pi  c^2 x^2+\pi }-\frac{b^2 \sqrt{\pi  c^2 x^2+\pi } \sinh ^{-1}(c x)}{4 c \sqrt{c^2 x^2+1}}","\frac{1}{2} x \sqrt{\pi  c^2 x^2+\pi } \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{1}{2} \sqrt{\pi } b c x^2 \left(a+b \sinh ^{-1}(c x)\right)+\frac{\sqrt{\pi } \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b c}+\frac{1}{4} \sqrt{\pi } b^2 x \sqrt{c^2 x^2+1}-\frac{\sqrt{\pi } b^2 \sinh ^{-1}(c x)}{4 c}",1,"(b^2*x*Sqrt[Pi + c^2*Pi*x^2])/4 - (b^2*Sqrt[Pi + c^2*Pi*x^2]*ArcSinh[c*x])/(4*c*Sqrt[1 + c^2*x^2]) - (b*c*x^2*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x]))/(2*Sqrt[1 + c^2*x^2]) + (x*Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^2)/2 + (Sqrt[Pi + c^2*Pi*x^2]*(a + b*ArcSinh[c*x])^3)/(6*b*c*Sqrt[1 + c^2*x^2])","A",5,5,25,0.2000,1,"{5682, 5675, 5661, 321, 215}"
255,1,25,0,0.0502889,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{\pi +c^2 \pi  x^2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/Sqrt[Pi + c^2*Pi*x^2],x]","\frac{\left(a+b \sinh ^{-1}(c x)\right)^3}{3 \sqrt{\pi } b c}","\frac{\left(a+b \sinh ^{-1}(c x)\right)^3}{3 \sqrt{\pi } b c}",1,"(a + b*ArcSinh[c*x])^3/(3*b*c*Sqrt[Pi])","A",1,1,25,0.04000,1,"{5675}"
256,1,179,0,0.1768431,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\left(\pi +c^2 \pi  x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(Pi + c^2*Pi*x^2)^(3/2),x]","-\frac{b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{\pi  c \sqrt{\pi  c^2 x^2+\pi }}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{\pi  \sqrt{\pi  c^2 x^2+\pi }}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{\pi  c \sqrt{\pi  c^2 x^2+\pi }}-\frac{2 b \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{\pi  c \sqrt{\pi  c^2 x^2+\pi }}","-\frac{b^2 \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{\pi ^{3/2} c}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{\pi  \sqrt{\pi  c^2 x^2+\pi }}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\pi ^{3/2} c}-\frac{2 b \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{\pi ^{3/2} c}",1,"(x*(a + b*ArcSinh[c*x])^2)/(Pi*Sqrt[Pi + c^2*Pi*x^2]) + (Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(c*Pi*Sqrt[Pi + c^2*Pi*x^2]) - (2*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(c*Pi*Sqrt[Pi + c^2*Pi*x^2]) - (b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^(2*ArcSinh[c*x])])/(c*Pi*Sqrt[Pi + c^2*Pi*x^2])","A",6,6,25,0.2400,1,"{5687, 5714, 3718, 2190, 2279, 2391}"
257,1,292,0,0.2815371,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\left(\pi +c^2 \pi  x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(Pi + c^2*Pi*x^2)^(5/2),x]","-\frac{2 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 \pi ^2 c \sqrt{\pi  c^2 x^2+\pi }}+\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^2 c \sqrt{c^2 x^2+1} \sqrt{\pi  c^2 x^2+\pi }}+\frac{2 x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \pi ^2 \sqrt{\pi  c^2 x^2+\pi }}+\frac{2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \pi ^2 c \sqrt{\pi  c^2 x^2+\pi }}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \pi  \left(\pi  c^2 x^2+\pi \right)^{3/2}}-\frac{4 b \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^2 c \sqrt{\pi  c^2 x^2+\pi }}-\frac{b^2 x}{3 \pi ^2 \sqrt{\pi  c^2 x^2+\pi }}","-\frac{2 b^2 \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 \pi ^{5/2} c}+\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^{5/2} c \left(c^2 x^2+1\right)}+\frac{2 x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \pi ^2 \sqrt{\pi  c^2 x^2+\pi }}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \pi  \left(\pi  c^2 x^2+\pi \right)^{3/2}}+\frac{2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \pi ^{5/2} c}-\frac{4 b \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 \pi ^{5/2} c}-\frac{b^2 x}{3 \pi ^{5/2} \sqrt{c^2 x^2+1}}",1,"-(b^2*x)/(3*Pi^2*Sqrt[Pi + c^2*Pi*x^2]) + (b*(a + b*ArcSinh[c*x]))/(3*c*Pi^2*Sqrt[1 + c^2*x^2]*Sqrt[Pi + c^2*Pi*x^2]) + (x*(a + b*ArcSinh[c*x])^2)/(3*Pi*(Pi + c^2*Pi*x^2)^(3/2)) + (2*x*(a + b*ArcSinh[c*x])^2)/(3*Pi^2*Sqrt[Pi + c^2*Pi*x^2]) + (2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(3*c*Pi^2*Sqrt[Pi + c^2*Pi*x^2]) - (4*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(3*c*Pi^2*Sqrt[Pi + c^2*Pi*x^2]) - (2*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^(2*ArcSinh[c*x])])/(3*c*Pi^2*Sqrt[Pi + c^2*Pi*x^2])","A",9,9,25,0.3600,1,"{5690, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 191}"
258,1,358,0,0.4788061,"\int x^3 \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2,x]","\frac{4 a b x \sqrt{c^2 d x^2+d}}{15 c^3 \sqrt{c^2 x^2+1}}-\frac{2 b c x^5 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{25 \sqrt{c^2 x^2+1}}+\frac{1}{5} x^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 b x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{45 c \sqrt{c^2 x^2+1}}+\frac{x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{15 c^2}-\frac{2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{15 c^4}+\frac{2 b^2 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d}}{125 c^4}-\frac{26 b^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}}{675 c^4}-\frac{52 b^2 \sqrt{c^2 d x^2+d}}{225 c^4}+\frac{4 b^2 x \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{15 c^3 \sqrt{c^2 x^2+1}}","\frac{4 a b x \sqrt{c^2 d x^2+d}}{15 c^3 \sqrt{c^2 x^2+1}}-\frac{2 b c x^5 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{25 \sqrt{c^2 x^2+1}}+\frac{1}{5} x^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 b x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{45 c \sqrt{c^2 x^2+1}}+\frac{x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{15 c^2}-\frac{2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{15 c^4}+\frac{2 b^2 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d}}{125 c^4}-\frac{26 b^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}}{675 c^4}-\frac{52 b^2 \sqrt{c^2 d x^2+d}}{225 c^4}+\frac{4 b^2 x \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{15 c^3 \sqrt{c^2 x^2+1}}",1,"(-52*b^2*Sqrt[d + c^2*d*x^2])/(225*c^4) + (4*a*b*x*Sqrt[d + c^2*d*x^2])/(15*c^3*Sqrt[1 + c^2*x^2]) - (26*b^2*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2])/(675*c^4) + (2*b^2*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2])/(125*c^4) + (4*b^2*x*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/(15*c^3*Sqrt[1 + c^2*x^2]) - (2*b*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(45*c*Sqrt[1 + c^2*x^2]) - (2*b*c*x^5*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(25*Sqrt[1 + c^2*x^2]) - (2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(15*c^4) + (x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(15*c^2) + (x^4*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/5","A",14,8,28,0.2857,1,"{5742, 5758, 5717, 5653, 261, 5661, 266, 43}"
259,1,291,0,0.372315,"\int x^2 \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2,x]","-\frac{b c x^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 \sqrt{c^2 x^2+1}}+\frac{1}{4} x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 c \sqrt{c^2 x^2+1}}+\frac{x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{8 c^2}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{24 b c^3 \sqrt{c^2 x^2+1}}+\frac{1}{32} b^2 x^3 \sqrt{c^2 d x^2+d}+\frac{b^2 x \sqrt{c^2 d x^2+d}}{64 c^2}-\frac{b^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{64 c^3 \sqrt{c^2 x^2+1}}","-\frac{b c x^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 \sqrt{c^2 x^2+1}}+\frac{1}{4} x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 c \sqrt{c^2 x^2+1}}+\frac{x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{8 c^2}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{24 b c^3 \sqrt{c^2 x^2+1}}+\frac{1}{32} b^2 x^3 \sqrt{c^2 d x^2+d}+\frac{b^2 x \sqrt{c^2 d x^2+d}}{64 c^2}-\frac{b^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{64 c^3 \sqrt{c^2 x^2+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]*ArcSinh[c*x])/(64*c^3*Sqrt[1 + c^2*x^2]) - (b*x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(8*c*Sqrt[1 + c^2*x^2]) - (b*c*x^4*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(8*Sqrt[1 + c^2*x^2]) + (x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(8*c^2) + (x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/4 - (Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^3)/(24*b*c^3*Sqrt[1 + c^2*x^2])","A",10,6,28,0.2143,1,"{5742, 5758, 5675, 5661, 321, 215}"
260,1,180,0,0.1522328,"\int x \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2,x]","-\frac{2 b c x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{c^2 x^2+1}}-\frac{2 b x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 c \sqrt{c^2 x^2+1}}+\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^2 d}+\frac{2 b^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}}{27 c^2}+\frac{4 b^2 \sqrt{c^2 d x^2+d}}{9 c^2}","-\frac{2 b c x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{c^2 x^2+1}}-\frac{2 b x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 c \sqrt{c^2 x^2+1}}+\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^2 d}+\frac{2 b^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}}{27 c^2}+\frac{4 b^2 \sqrt{c^2 d x^2+d}}{9 c^2}",1,"(4*b^2*Sqrt[d + c^2*d*x^2])/(9*c^2) + (2*b^2*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2])/(27*c^2) - (2*b*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*c*Sqrt[1 + c^2*x^2]) - (2*b*c*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(9*Sqrt[1 + c^2*x^2]) + ((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(3*c^2*d)","A",5,4,26,0.1538,1,"{5717, 5679, 444, 43}"
261,1,184,0,0.120337,"\int \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2,x]","\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b c \sqrt{c^2 x^2+1}}+\frac{1}{2} x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b c x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{c^2 x^2+1}}+\frac{1}{4} b^2 x \sqrt{c^2 d x^2+d}-\frac{b^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{4 c \sqrt{c^2 x^2+1}}","\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b c \sqrt{c^2 x^2+1}}+\frac{1}{2} x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b c x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{c^2 x^2+1}}+\frac{1}{4} b^2 x \sqrt{c^2 d x^2+d}-\frac{b^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{4 c \sqrt{c^2 x^2+1}}",1,"(b^2*x*Sqrt[d + c^2*d*x^2])/4 - (b^2*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/(4*c*Sqrt[1 + c^2*x^2]) - (b*c*x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(2*Sqrt[1 + c^2*x^2]) + (x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/2 + (Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^3)/(6*b*c*Sqrt[1 + c^2*x^2])","A",5,5,25,0.2000,1,"{5682, 5675, 5661, 321, 215}"
262,1,338,0,0.3425518,"\int \frac{\sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^2}{x} \, dx","Int[(Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/x,x]","-\frac{2 b \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{2 b \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{2 b^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{2 b^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{2 a b c x \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}+\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}+2 b^2 \sqrt{c^2 d x^2+d}-\frac{2 b^2 c x \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{\sqrt{c^2 x^2+1}}","-\frac{2 b \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{2 b \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{2 b^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{2 b^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{2 a b c x \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}+\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}+2 b^2 \sqrt{c^2 d x^2+d}-\frac{2 b^2 c x \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{\sqrt{c^2 x^2+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^2*x^2] - (2*b^2*c*x*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/Sqrt[1 + c^2*x^2] + Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2 - (2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (2*b*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (2*b*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (2*b^2*Sqrt[d + c^2*d*x^2]*PolyLog[3, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (2*b^2*Sqrt[d + c^2*d*x^2]*PolyLog[3, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2]","A",12,8,28,0.2857,1,"{5742, 5760, 4182, 2531, 2282, 6589, 5653, 261}"
263,1,209,0,0.2549244,"\int \frac{\sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^2}{x^2} \, dx","Int[(Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/x^2,x]","\frac{b^2 c \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\frac{c \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b \sqrt{c^2 x^2+1}}-\frac{c \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{x}+\frac{2 b c \sqrt{c^2 d x^2+d} \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}","-\frac{b^2 c \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}+\frac{c \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b \sqrt{c^2 x^2+1}}+\frac{c \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{x}+\frac{2 b c \sqrt{c^2 d x^2+d} \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}",1,"-((Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/x) - (c*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/Sqrt[1 + c^2*x^2] + (c*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^3)/(3*b*Sqrt[1 + c^2*x^2]) + (2*b*c*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*Log[1 - E^(2*ArcSinh[c*x])])/Sqrt[1 + c^2*x^2] + (b^2*c*Sqrt[d + c^2*d*x^2]*PolyLog[2, E^(2*ArcSinh[c*x])])/Sqrt[1 + c^2*x^2]","A",7,7,28,0.2500,0,"{5737, 5659, 3716, 2190, 2279, 2391, 5675}"
264,1,358,0,0.3826807,"\int \frac{\sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^2}{x^3} \, dx","Int[(Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/x^3,x]","-\frac{b c^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{b c^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{b^2 c^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{b^2 c^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{b c \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{x \sqrt{c^2 x^2+1}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 x^2}-\frac{c^2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}-\frac{b^2 c^2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{\sqrt{c^2 x^2+1}}","-\frac{b c^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{b c^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{b^2 c^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{b^2 c^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{b c \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{x \sqrt{c^2 x^2+1}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 x^2}-\frac{c^2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}-\frac{b^2 c^2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{\sqrt{c^2 x^2+1}}",1,"-((b*c*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(x*Sqrt[1 + c^2*x^2])) - (Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*x^2) - (c^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (b^2*c^2*Sqrt[d + c^2*d*x^2]*ArcTanh[Sqrt[1 + c^2*x^2]])/Sqrt[1 + c^2*x^2] - (b*c^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (b*c^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (b^2*c^2*Sqrt[d + c^2*d*x^2]*PolyLog[3, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (b^2*c^2*Sqrt[d + c^2*d*x^2]*PolyLog[3, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2]","A",13,10,28,0.3571,1,"{5737, 5661, 266, 63, 208, 5760, 4182, 2531, 2282, 6589}"
265,1,294,0,0.284515,"\int \frac{\sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^2}{x^4} \, dx","Int[(Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/x^4,x]","\frac{b^2 c^3 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{3 \sqrt{c^2 x^2+1}}-\frac{c^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \sqrt{c^2 x^2+1}}-\frac{b c \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^2}-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d x^3}+\frac{2 b c^3 \sqrt{c^2 d x^2+d} \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}-\frac{b^2 c^2 \sqrt{c^2 d x^2+d}}{3 x}+\frac{b^2 c^3 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{3 \sqrt{c^2 x^2+1}}","-\frac{b^2 c^3 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right)}{3 \sqrt{c^2 x^2+1}}+\frac{c^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \sqrt{c^2 x^2+1}}-\frac{b c \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^2}-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d x^3}+\frac{2 b c^3 \sqrt{c^2 d x^2+d} \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}-\frac{b^2 c^2 \sqrt{c^2 d x^2+d}}{3 x}+\frac{b^2 c^3 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{3 \sqrt{c^2 x^2+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]*ArcSinh[c*x])/(3*Sqrt[1 + c^2*x^2]) - (b*c*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*x^2) - (c^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(3*Sqrt[1 + c^2*x^2]) - ((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(3*d*x^3) + (2*b*c^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*Log[1 - E^(2*ArcSinh[c*x])])/(3*Sqrt[1 + c^2*x^2]) + (b^2*c^3*Sqrt[d + c^2*d*x^2]*PolyLog[2, E^(2*ArcSinh[c*x])])/(3*Sqrt[1 + c^2*x^2])","A",9,9,28,0.3214,0,"{5723, 5728, 277, 215, 5659, 3716, 2190, 2279, 2391}"
266,1,482,0,0.8110798,"\int x^3 \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^3*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2,x]","\frac{4 a b d x \sqrt{c^2 d x^2+d}}{35 c^3 \sqrt{c^2 x^2+1}}-\frac{2 b c^3 d x^7 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{49 \sqrt{c^2 x^2+1}}-\frac{16 b c d x^5 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{175 \sqrt{c^2 x^2+1}}+\frac{1}{7} x^4 \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{3}{35} d x^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 b d x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{105 c \sqrt{c^2 x^2+1}}+\frac{d x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{35 c^2}-\frac{2 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{35 c^4}+\frac{2 b^2 d \left(c^2 x^2+1\right)^3 \sqrt{c^2 d x^2+d}}{343 c^4}-\frac{38 b^2 d \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d}}{6125 c^4}-\frac{304 b^2 d \sqrt{c^2 d x^2+d}}{3675 c^4}-\frac{152 b^2 d \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}}{11025 c^4}+\frac{4 b^2 d x \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{35 c^3 \sqrt{c^2 x^2+1}}","\frac{4 a b d x \sqrt{c^2 d x^2+d}}{35 c^3 \sqrt{c^2 x^2+1}}-\frac{2 b c^3 d x^7 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{49 \sqrt{c^2 x^2+1}}-\frac{16 b c d x^5 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{175 \sqrt{c^2 x^2+1}}+\frac{1}{7} x^4 \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{3}{35} d x^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 b d x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{105 c \sqrt{c^2 x^2+1}}+\frac{d x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{35 c^2}-\frac{2 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{35 c^4}+\frac{2 b^2 d \left(c^2 x^2+1\right)^3 \sqrt{c^2 d x^2+d}}{343 c^4}-\frac{38 b^2 d \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d}}{6125 c^4}-\frac{304 b^2 d \sqrt{c^2 d x^2+d}}{3675 c^4}-\frac{152 b^2 d \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}}{11025 c^4}+\frac{4 b^2 d x \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{35 c^3 \sqrt{c^2 x^2+1}}",1,"(-304*b^2*d*Sqrt[d + c^2*d*x^2])/(3675*c^4) + (4*a*b*d*x*Sqrt[d + c^2*d*x^2])/(35*c^3*Sqrt[1 + c^2*x^2]) - (152*b^2*d*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2])/(11025*c^4) - (38*b^2*d*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2])/(6125*c^4) + (2*b^2*d*(1 + c^2*x^2)^3*Sqrt[d + c^2*d*x^2])/(343*c^4) + (4*b^2*d*x*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/(35*c^3*Sqrt[1 + c^2*x^2]) - (2*b*d*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(105*c*Sqrt[1 + c^2*x^2]) - (16*b*c*d*x^5*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(175*Sqrt[1 + c^2*x^2]) - (2*b*c^3*d*x^7*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(49*Sqrt[1 + c^2*x^2]) - (2*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(35*c^4) + (d*x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(35*c^2) + (3*d*x^4*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/35 + (x^4*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/7","A",20,14,28,0.5000,1,"{5744, 5742, 5758, 5717, 5653, 261, 5661, 266, 43, 14, 5730, 12, 446, 77}"
267,1,405,0,0.6639069,"\int x^2 \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^2*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2,x]","-\frac{b c^3 d x^6 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{18 \sqrt{c^2 x^2+1}}-\frac{7 b c d x^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{48 \sqrt{c^2 x^2+1}}+\frac{1}{6} x^3 \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{8} d x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b d x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{16 c \sqrt{c^2 x^2+1}}+\frac{d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 c^2}-\frac{d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{48 b c^3 \sqrt{c^2 x^2+1}}+\frac{1}{108} b^2 c^2 d x^5 \sqrt{c^2 d x^2+d}+\frac{43 b^2 d x^3 \sqrt{c^2 d x^2+d}}{1728}-\frac{7 b^2 d x \sqrt{c^2 d x^2+d}}{1152 c^2}+\frac{7 b^2 d \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{1152 c^3 \sqrt{c^2 x^2+1}}","-\frac{b c^3 d x^6 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{18 \sqrt{c^2 x^2+1}}-\frac{7 b c d x^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{48 \sqrt{c^2 x^2+1}}+\frac{1}{6} x^3 \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{8} d x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b d x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{16 c \sqrt{c^2 x^2+1}}+\frac{d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 c^2}-\frac{d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{48 b c^3 \sqrt{c^2 x^2+1}}+\frac{1}{108} b^2 c^2 d x^5 \sqrt{c^2 d x^2+d}+\frac{43 b^2 d x^3 \sqrt{c^2 d x^2+d}}{1728}-\frac{7 b^2 d x \sqrt{c^2 d x^2+d}}{1152 c^2}+\frac{7 b^2 d \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{1152 c^3 \sqrt{c^2 x^2+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]*ArcSinh[c*x])/(1152*c^3*Sqrt[1 + c^2*x^2]) - (b*d*x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(16*c*Sqrt[1 + c^2*x^2]) - (7*b*c*d*x^4*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(48*Sqrt[1 + c^2*x^2]) - (b*c^3*d*x^6*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(18*Sqrt[1 + c^2*x^2]) + (d*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(16*c^2) + (d*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/8 + (x^3*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/6 - (d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^3)/(48*b*c^3*Sqrt[1 + c^2*x^2])","A",17,11,28,0.3929,1,"{5744, 5742, 5758, 5675, 5661, 321, 215, 14, 5730, 12, 459}"
268,1,267,0,0.2185201,"\int x \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2,x]","-\frac{2 b c^3 d x^5 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{25 \sqrt{c^2 x^2+1}}-\frac{4 b c d x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{15 \sqrt{c^2 x^2+1}}-\frac{2 b d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{5 c \sqrt{c^2 x^2+1}}+\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{5 c^2 d}+\frac{2 b^2 d \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d}}{125 c^2}+\frac{16 b^2 d \sqrt{c^2 d x^2+d}}{75 c^2}+\frac{8 b^2 d \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}}{225 c^2}","-\frac{2 b c^3 d x^5 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{25 \sqrt{c^2 x^2+1}}-\frac{4 b c d x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{15 \sqrt{c^2 x^2+1}}-\frac{2 b d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{5 c \sqrt{c^2 x^2+1}}+\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{5 c^2 d}+\frac{2 b^2 d \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d}}{125 c^2}+\frac{16 b^2 d \sqrt{c^2 d x^2+d}}{75 c^2}+\frac{8 b^2 d \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}}{225 c^2}",1,"(16*b^2*d*Sqrt[d + c^2*d*x^2])/(75*c^2) + (8*b^2*d*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2])/(225*c^2) + (2*b^2*d*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2])/(125*c^2) - (2*b*d*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(5*c*Sqrt[1 + c^2*x^2]) - (4*b*c*d*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(15*Sqrt[1 + c^2*x^2]) - (2*b*c^3*d*x^5*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(25*Sqrt[1 + c^2*x^2]) + ((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/(5*c^2*d)","A",6,6,26,0.2308,1,"{5717, 194, 5679, 12, 1247, 698}"
269,1,294,0,0.2458639,"\int \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2,x]","\frac{d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{8 b c \sqrt{c^2 x^2+1}}+\frac{1}{4} x \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{3}{8} d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b d \left(c^2 x^2+1\right)^{3/2} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 c}-\frac{3 b c d x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 \sqrt{c^2 x^2+1}}+\frac{15}{64} b^2 d x \sqrt{c^2 d x^2+d}+\frac{1}{32} b^2 d x \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}-\frac{9 b^2 d \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{64 c \sqrt{c^2 x^2+1}}","\frac{d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{8 b c \sqrt{c^2 x^2+1}}+\frac{1}{4} x \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{3}{8} d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b d \left(c^2 x^2+1\right)^{3/2} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 c}-\frac{3 b c d x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 \sqrt{c^2 x^2+1}}+\frac{15}{64} b^2 d x \sqrt{c^2 d x^2+d}+\frac{1}{32} b^2 d x \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}-\frac{9 b^2 d \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{64 c \sqrt{c^2 x^2+1}}",1,"(15*b^2*d*x*Sqrt[d + c^2*d*x^2])/64 + (b^2*d*x*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2])/32 - (9*b^2*d*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/(64*c*Sqrt[1 + c^2*x^2]) - (3*b*c*d*x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(8*Sqrt[1 + c^2*x^2]) - (b*d*(1 + c^2*x^2)^(3/2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(8*c) + (3*d*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/8 + (x*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/4 + (d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^3)/(8*b*c*Sqrt[1 + c^2*x^2])","A",10,8,25,0.3200,1,"{5684, 5682, 5675, 5661, 321, 215, 5717, 195}"
270,1,498,0,0.5945878,"\int \frac{\left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{x} \, dx","Int[((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/x,x]","-\frac{2 b d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{2 b d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{2 b^2 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{2 b^2 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{2 a b c d x \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}-\frac{2 b c^3 d x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{c^2 x^2+1}}-\frac{2 b c d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}+\frac{1}{3} \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 d \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}+\frac{22}{9} b^2 d \sqrt{c^2 d x^2+d}+\frac{2}{27} b^2 d \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}-\frac{2 b^2 c d x \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{\sqrt{c^2 x^2+1}}","-\frac{2 b d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{2 b d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{2 b^2 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{2 b^2 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{2 a b c d x \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}-\frac{2 b c^3 d x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{c^2 x^2+1}}-\frac{2 b c d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}+\frac{1}{3} \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 d \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}+\frac{22}{9} b^2 d \sqrt{c^2 d x^2+d}+\frac{2}{27} b^2 d \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}-\frac{2 b^2 c d x \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{\sqrt{c^2 x^2+1}}",1,"(22*b^2*d*Sqrt[d + c^2*d*x^2])/9 - (2*a*b*c*d*x*Sqrt[d + c^2*d*x^2])/Sqrt[1 + c^2*x^2] + (2*b^2*d*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2])/27 - (2*b^2*c*d*x*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/Sqrt[1 + c^2*x^2] - (2*b*c*d*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*Sqrt[1 + c^2*x^2]) - (2*b*c^3*d*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(9*Sqrt[1 + c^2*x^2]) + d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2 + ((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/3 - (2*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (2*b*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (2*b*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (2*b^2*d*Sqrt[d + c^2*d*x^2]*PolyLog[3, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (2*b^2*d*Sqrt[d + c^2*d*x^2]*PolyLog[3, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2]","A",17,12,28,0.4286,1,"{5744, 5742, 5760, 4182, 2531, 2282, 6589, 5653, 261, 5679, 444, 43}"
271,1,398,0,0.4216308,"\int \frac{\left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{x^2} \, dx","Int[((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/x^2,x]","\frac{b^2 c d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{3 b c^3 d x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{c^2 x^2+1}}+\frac{3}{2} c^2 d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{c d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{2 b \sqrt{c^2 x^2+1}}-\frac{c d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}+b c d \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{x}+\frac{2 b c d \sqrt{c^2 d x^2+d} \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{1}{4} b^2 c^2 d x \sqrt{c^2 d x^2+d}-\frac{5 b^2 c d \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{4 \sqrt{c^2 x^2+1}}","-\frac{b^2 c d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{3 b c^3 d x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{c^2 x^2+1}}+\frac{3}{2} c^2 d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{c d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{2 b \sqrt{c^2 x^2+1}}+\frac{c d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}+b c d \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{x}+\frac{2 b c d \sqrt{c^2 d x^2+d} \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{1}{4} b^2 c^2 d x \sqrt{c^2 d x^2+d}-\frac{5 b^2 c d \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{4 \sqrt{c^2 x^2+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]*ArcSinh[c*x])/(4*Sqrt[1 + c^2*x^2]) - (3*b*c^3*d*x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(2*Sqrt[1 + c^2*x^2]) + b*c*d*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]) + (3*c^2*d*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/2 - (c*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/Sqrt[1 + c^2*x^2] - ((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/x + (c*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^3)/(2*b*Sqrt[1 + c^2*x^2]) + (2*b*c*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*Log[1 - E^(2*ArcSinh[c*x])])/Sqrt[1 + c^2*x^2] + (b^2*c*d*Sqrt[d + c^2*d*x^2]*PolyLog[2, E^(2*ArcSinh[c*x])])/Sqrt[1 + c^2*x^2]","A",14,13,28,0.4643,0,"{5739, 5682, 5675, 5661, 321, 215, 5726, 5659, 3716, 2190, 2279, 2391, 195}"
272,1,541,0,0.6543889,"\int \frac{\left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{x^3} \, dx","Int[((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/x^3,x]","-\frac{3 b c^2 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{3 b c^2 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{3 b^2 c^2 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{3 b^2 c^2 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{3 a b c^3 d x \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}+\frac{b c^3 d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{3}{2} c^2 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b c d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{x \sqrt{c^2 x^2+1}}-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 x^2}-\frac{3 c^2 d \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}+2 b^2 c^2 d \sqrt{c^2 d x^2+d}-\frac{3 b^2 c^3 d x \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{\sqrt{c^2 x^2+1}}-\frac{b^2 c^2 d \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{\sqrt{c^2 x^2+1}}","-\frac{3 b c^2 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{3 b c^2 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{3 b^2 c^2 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{3 b^2 c^2 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{3 a b c^3 d x \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}+\frac{b c^3 d x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{3}{2} c^2 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b c d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{x \sqrt{c^2 x^2+1}}-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 x^2}-\frac{3 c^2 d \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}+2 b^2 c^2 d \sqrt{c^2 d x^2+d}-\frac{3 b^2 c^3 d x \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{\sqrt{c^2 x^2+1}}-\frac{b^2 c^2 d \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{\sqrt{c^2 x^2+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^2*x^2] - (3*b^2*c^3*d*x*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/Sqrt[1 + c^2*x^2] - (b*c*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(x*Sqrt[1 + c^2*x^2]) + (b*c^3*d*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/Sqrt[1 + c^2*x^2] + (3*c^2*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/2 - ((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(2*x^2) - (3*c^2*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (b^2*c^2*d*Sqrt[d + c^2*d*x^2]*ArcTanh[Sqrt[1 + c^2*x^2]])/Sqrt[1 + c^2*x^2] - (3*b*c^2*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (3*b*c^2*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (3*b^2*c^2*d*Sqrt[d + c^2*d*x^2]*PolyLog[3, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (3*b^2*c^2*d*Sqrt[d + c^2*d*x^2]*PolyLog[3, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2]","A",18,15,28,0.5357,1,"{5739, 5742, 5760, 4182, 2531, 2282, 6589, 5653, 261, 14, 5730, 446, 80, 63, 208}"
273,1,378,0,0.5842956,"\int \frac{\left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{x^4} \, dx","Int[((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/x^4,x]","\frac{4 b^2 c^3 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{3 \sqrt{c^2 x^2+1}}+\frac{c^3 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b \sqrt{c^2 x^2+1}}-\frac{4 c^3 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \sqrt{c^2 x^2+1}}-\frac{c^2 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{x}-\frac{b c d \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^2}-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 x^3}+\frac{8 b c^3 d \sqrt{c^2 d x^2+d} \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}-\frac{b^2 c^2 d \sqrt{c^2 d x^2+d}}{3 x}+\frac{b^2 c^3 d \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{3 \sqrt{c^2 x^2+1}}","-\frac{4 b^2 c^3 d \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right)}{3 \sqrt{c^2 x^2+1}}+\frac{c^3 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b \sqrt{c^2 x^2+1}}+\frac{4 c^3 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \sqrt{c^2 x^2+1}}-\frac{c^2 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{x}-\frac{b c d \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^2}-\frac{\left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 x^3}+\frac{8 b c^3 d \sqrt{c^2 d x^2+d} \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}-\frac{b^2 c^2 d \sqrt{c^2 d x^2+d}}{3 x}+\frac{b^2 c^3 d \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{3 \sqrt{c^2 x^2+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]*ArcSinh[c*x])/(3*Sqrt[1 + c^2*x^2]) - (b*c*d*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*x^2) - (c^2*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/x - (4*c^3*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(3*Sqrt[1 + c^2*x^2]) - ((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(3*x^3) + (c^3*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^3)/(3*b*Sqrt[1 + c^2*x^2]) + (8*b*c^3*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*Log[1 - E^(2*ArcSinh[c*x])])/(3*Sqrt[1 + c^2*x^2]) + (4*b^2*c^3*d*Sqrt[d + c^2*d*x^2]*PolyLog[2, E^(2*ArcSinh[c*x])])/(3*Sqrt[1 + c^2*x^2])","A",16,11,28,0.3929,0,"{5739, 5737, 5659, 3716, 2190, 2279, 2391, 5675, 5728, 277, 215}"
274,1,625,0,1.2375448,"\int x^3 \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^3*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2,x]","\frac{4 a b d^2 x \sqrt{c^2 d x^2+d}}{63 c^3 \sqrt{c^2 x^2+1}}-\frac{2 b c^5 d^2 x^9 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{81 \sqrt{c^2 x^2+1}}-\frac{38 b c^3 d^2 x^7 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{441 \sqrt{c^2 x^2+1}}-\frac{2 b c d^2 x^5 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{21 \sqrt{c^2 x^2+1}}+\frac{1}{21} d^2 x^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 b d^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{189 c \sqrt{c^2 x^2+1}}+\frac{d^2 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{63 c^2}-\frac{2 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{63 c^4}+\frac{1}{9} x^4 \left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{5}{63} d x^4 \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2 b^2 d^2 \left(c^2 x^2+1\right)^4 \sqrt{c^2 d x^2+d}}{729 c^4}-\frac{50 b^2 d^2 \left(c^2 x^2+1\right)^3 \sqrt{c^2 d x^2+d}}{27783 c^4}-\frac{160 b^2 d^2 \sqrt{c^2 d x^2+d}}{3969 c^4}-\frac{4 b^2 d^2 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d}}{1323 c^4}-\frac{80 b^2 d^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}}{11907 c^4}+\frac{4 b^2 d^2 x \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{63 c^3 \sqrt{c^2 x^2+1}}","\frac{4 a b d^2 x \sqrt{c^2 d x^2+d}}{63 c^3 \sqrt{c^2 x^2+1}}-\frac{2 b c^5 d^2 x^9 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{81 \sqrt{c^2 x^2+1}}-\frac{38 b c^3 d^2 x^7 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{441 \sqrt{c^2 x^2+1}}-\frac{2 b c d^2 x^5 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{21 \sqrt{c^2 x^2+1}}+\frac{1}{21} d^2 x^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 b d^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{189 c \sqrt{c^2 x^2+1}}+\frac{d^2 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{63 c^2}-\frac{2 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{63 c^4}+\frac{1}{9} x^4 \left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{5}{63} d x^4 \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2 b^2 d^2 \left(c^2 x^2+1\right)^4 \sqrt{c^2 d x^2+d}}{729 c^4}-\frac{50 b^2 d^2 \left(c^2 x^2+1\right)^3 \sqrt{c^2 d x^2+d}}{27783 c^4}-\frac{160 b^2 d^2 \sqrt{c^2 d x^2+d}}{3969 c^4}-\frac{4 b^2 d^2 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d}}{1323 c^4}-\frac{80 b^2 d^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}}{11907 c^4}+\frac{4 b^2 d^2 x \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{63 c^3 \sqrt{c^2 x^2+1}}",1,"(-160*b^2*d^2*Sqrt[d + c^2*d*x^2])/(3969*c^4) + (4*a*b*d^2*x*Sqrt[d + c^2*d*x^2])/(63*c^3*Sqrt[1 + c^2*x^2]) - (80*b^2*d^2*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2])/(11907*c^4) - (4*b^2*d^2*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2])/(1323*c^4) - (50*b^2*d^2*(1 + c^2*x^2)^3*Sqrt[d + c^2*d*x^2])/(27783*c^4) + (2*b^2*d^2*(1 + c^2*x^2)^4*Sqrt[d + c^2*d*x^2])/(729*c^4) + (4*b^2*d^2*x*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/(63*c^3*Sqrt[1 + c^2*x^2]) - (2*b*d^2*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(189*c*Sqrt[1 + c^2*x^2]) - (2*b*c*d^2*x^5*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(21*Sqrt[1 + c^2*x^2]) - (38*b*c^3*d^2*x^7*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(441*Sqrt[1 + c^2*x^2]) - (2*b*c^5*d^2*x^9*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(81*Sqrt[1 + c^2*x^2]) - (2*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(63*c^4) + (d^2*x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(63*c^2) + (d^2*x^4*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/21 + (5*d*x^4*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/63 + (x^4*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/9","A",27,18,28,0.6429,1,"{5744, 5742, 5758, 5717, 5653, 261, 5661, 266, 43, 14, 5730, 12, 446, 77, 270, 1251, 897, 1153}"
275,1,536,0,1.0471705,"\int x^2 \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^2*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2,x]","-\frac{b c^5 d^2 x^8 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{32 \sqrt{c^2 x^2+1}}-\frac{17 b c^3 d^2 x^6 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{144 \sqrt{c^2 x^2+1}}-\frac{59 b c d^2 x^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{384 \sqrt{c^2 x^2+1}}+\frac{5}{64} d^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{5 b d^2 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{128 c \sqrt{c^2 x^2+1}}+\frac{5 d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{128 c^2}-\frac{5 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{384 b c^3 \sqrt{c^2 x^2+1}}+\frac{1}{8} x^3 \left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{5}{48} d x^3 \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{256} b^2 c^4 d^2 x^7 \sqrt{c^2 d x^2+d}+\frac{209 b^2 c^2 d^2 x^5 \sqrt{c^2 d x^2+d}}{13824}+\frac{1079 b^2 d^2 x^3 \sqrt{c^2 d x^2+d}}{55296}-\frac{359 b^2 d^2 x \sqrt{c^2 d x^2+d}}{36864 c^2}+\frac{359 b^2 d^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{36864 c^3 \sqrt{c^2 x^2+1}}","-\frac{b c^5 d^2 x^8 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{32 \sqrt{c^2 x^2+1}}-\frac{17 b c^3 d^2 x^6 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{144 \sqrt{c^2 x^2+1}}-\frac{59 b c d^2 x^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{384 \sqrt{c^2 x^2+1}}+\frac{5}{64} d^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{5 b d^2 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{128 c \sqrt{c^2 x^2+1}}+\frac{5 d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{128 c^2}-\frac{5 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{384 b c^3 \sqrt{c^2 x^2+1}}+\frac{1}{8} x^3 \left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{5}{48} d x^3 \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{256} b^2 c^4 d^2 x^7 \sqrt{c^2 d x^2+d}+\frac{209 b^2 c^2 d^2 x^5 \sqrt{c^2 d x^2+d}}{13824}+\frac{1079 b^2 d^2 x^3 \sqrt{c^2 d x^2+d}}{55296}-\frac{359 b^2 d^2 x \sqrt{c^2 d x^2+d}}{36864 c^2}+\frac{359 b^2 d^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{36864 c^3 \sqrt{c^2 x^2+1}}",1,"(-359*b^2*d^2*x*Sqrt[d + c^2*d*x^2])/(36864*c^2) + (1079*b^2*d^2*x^3*Sqrt[d + c^2*d*x^2])/55296 + (209*b^2*c^2*d^2*x^5*Sqrt[d + c^2*d*x^2])/13824 + (b^2*c^4*d^2*x^7*Sqrt[d + c^2*d*x^2])/256 + (359*b^2*d^2*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/(36864*c^3*Sqrt[1 + c^2*x^2]) - (5*b*d^2*x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(128*c*Sqrt[1 + c^2*x^2]) - (59*b*c*d^2*x^4*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(384*Sqrt[1 + c^2*x^2]) - (17*b*c^3*d^2*x^6*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(144*Sqrt[1 + c^2*x^2]) - (b*c^5*d^2*x^8*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(32*Sqrt[1 + c^2*x^2]) + (5*d^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(128*c^2) + (5*d^2*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/64 + (5*d*x^3*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/48 + (x^3*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/8 - (5*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^3)/(384*b*c^3*Sqrt[1 + c^2*x^2])","A",25,14,28,0.5000,1,"{5744, 5742, 5758, 5675, 5661, 321, 215, 14, 5730, 12, 459, 266, 43, 1267}"
276,1,366,0,0.2939567,"\int x \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2,x]","-\frac{2 b c^5 d^2 x^7 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{49 \sqrt{c^2 x^2+1}}-\frac{6 b c^3 d^2 x^5 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{35 \sqrt{c^2 x^2+1}}-\frac{2 b c d^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{7 \sqrt{c^2 x^2+1}}-\frac{2 b d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{7 c \sqrt{c^2 x^2+1}}+\frac{\left(c^2 d x^2+d\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{7 c^2 d}+\frac{2 b^2 d^2 \left(c^2 x^2+1\right)^3 \sqrt{c^2 d x^2+d}}{343 c^2}+\frac{32 b^2 d^2 \sqrt{c^2 d x^2+d}}{245 c^2}+\frac{12 b^2 d^2 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d}}{1225 c^2}+\frac{16 b^2 d^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}}{735 c^2}","-\frac{2 b c^5 d^2 x^7 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{49 \sqrt{c^2 x^2+1}}-\frac{6 b c^3 d^2 x^5 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{35 \sqrt{c^2 x^2+1}}-\frac{2 b c d^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{7 \sqrt{c^2 x^2+1}}-\frac{2 b d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{7 c \sqrt{c^2 x^2+1}}+\frac{\left(c^2 d x^2+d\right)^{7/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{7 c^2 d}+\frac{2 b^2 d^2 \left(c^2 x^2+1\right)^3 \sqrt{c^2 d x^2+d}}{343 c^2}+\frac{32 b^2 d^2 \sqrt{c^2 d x^2+d}}{245 c^2}+\frac{12 b^2 d^2 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d}}{1225 c^2}+\frac{16 b^2 d^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}}{735 c^2}",1,"(32*b^2*d^2*Sqrt[d + c^2*d*x^2])/(245*c^2) + (16*b^2*d^2*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2])/(735*c^2) + (12*b^2*d^2*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2])/(1225*c^2) + (2*b^2*d^2*(1 + c^2*x^2)^3*Sqrt[d + c^2*d*x^2])/(343*c^2) - (2*b*d^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(7*c*Sqrt[1 + c^2*x^2]) - (2*b*c*d^2*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(7*Sqrt[1 + c^2*x^2]) - (6*b*c^3*d^2*x^5*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(35*Sqrt[1 + c^2*x^2]) - (2*b*c^5*d^2*x^7*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(49*Sqrt[1 + c^2*x^2]) + ((d + c^2*d*x^2)^(7/2)*(a + b*ArcSinh[c*x])^2)/(7*c^2*d)","A",6,6,26,0.2308,1,"{5717, 194, 5679, 12, 1799, 1850}"
277,1,420,0,0.4035793,"\int \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2,x]","\frac{5 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{48 b c \sqrt{c^2 x^2+1}}+\frac{5}{16} d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b d^2 \left(c^2 x^2+1\right)^{5/2} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{18 c}-\frac{5 b d^2 \left(c^2 x^2+1\right)^{3/2} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{48 c}-\frac{5 b c d^2 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{16 \sqrt{c^2 x^2+1}}+\frac{1}{6} x \left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{5}{24} d x \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{108} b^2 d^2 x \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d}+\frac{245 b^2 d^2 x \sqrt{c^2 d x^2+d}}{1152}+\frac{65 b^2 d^2 x \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}}{1728}-\frac{115 b^2 d^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{1152 c \sqrt{c^2 x^2+1}}","\frac{5 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{48 b c \sqrt{c^2 x^2+1}}+\frac{5}{16} d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b d^2 \left(c^2 x^2+1\right)^{5/2} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{18 c}-\frac{5 b d^2 \left(c^2 x^2+1\right)^{3/2} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{48 c}-\frac{5 b c d^2 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{16 \sqrt{c^2 x^2+1}}+\frac{1}{6} x \left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{5}{24} d x \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{108} b^2 d^2 x \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d}+\frac{245 b^2 d^2 x \sqrt{c^2 d x^2+d}}{1152}+\frac{65 b^2 d^2 x \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}}{1728}-\frac{115 b^2 d^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{1152 c \sqrt{c^2 x^2+1}}",1,"(245*b^2*d^2*x*Sqrt[d + c^2*d*x^2])/1152 + (65*b^2*d^2*x*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2])/1728 + (b^2*d^2*x*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2])/108 - (115*b^2*d^2*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/(1152*c*Sqrt[1 + c^2*x^2]) - (5*b*c*d^2*x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(16*Sqrt[1 + c^2*x^2]) - (5*b*d^2*(1 + c^2*x^2)^(3/2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(48*c) - (b*d^2*(1 + c^2*x^2)^(5/2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(18*c) + (5*d^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/16 + (5*d*x*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/24 + (x*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/6 + (5*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^3)/(48*b*c*Sqrt[1 + c^2*x^2])","A",16,8,25,0.3200,1,"{5684, 5682, 5675, 5661, 321, 215, 5717, 195}"
278,1,635,0,0.9079395,"\int \frac{\left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{x} \, dx","Int[((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/x,x]","-\frac{2 b d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{2 b d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{2 b^2 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{2 b^2 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{2 a b c d^2 x \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}-\frac{2 b c^5 d^2 x^5 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{25 \sqrt{c^2 x^2+1}}-\frac{22 b c^3 d^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{45 \sqrt{c^2 x^2+1}}-\frac{16 b c d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{15 \sqrt{c^2 x^2+1}}+d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 d^2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}+\frac{1}{5} \left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{3} d \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{598}{225} b^2 d^2 \sqrt{c^2 d x^2+d}+\frac{2}{125} b^2 d^2 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d}+\frac{74}{675} b^2 d^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}-\frac{2 b^2 c d^2 x \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{\sqrt{c^2 x^2+1}}","-\frac{2 b d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{2 b d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{2 b^2 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{2 b^2 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{2 a b c d^2 x \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}-\frac{2 b c^5 d^2 x^5 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{25 \sqrt{c^2 x^2+1}}-\frac{22 b c^3 d^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{45 \sqrt{c^2 x^2+1}}-\frac{16 b c d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{15 \sqrt{c^2 x^2+1}}+d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 d^2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}+\frac{1}{5} \left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{3} d \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{598}{225} b^2 d^2 \sqrt{c^2 d x^2+d}+\frac{2}{125} b^2 d^2 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d}+\frac{74}{675} b^2 d^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}-\frac{2 b^2 c d^2 x \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{\sqrt{c^2 x^2+1}}",1,"(598*b^2*d^2*Sqrt[d + c^2*d*x^2])/225 - (2*a*b*c*d^2*x*Sqrt[d + c^2*d*x^2])/Sqrt[1 + c^2*x^2] + (74*b^2*d^2*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2])/675 + (2*b^2*d^2*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2])/125 - (2*b^2*c*d^2*x*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/Sqrt[1 + c^2*x^2] - (16*b*c*d^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(15*Sqrt[1 + c^2*x^2]) - (22*b*c^3*d^2*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(45*Sqrt[1 + c^2*x^2]) - (2*b*c^5*d^2*x^5*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(25*Sqrt[1 + c^2*x^2]) + d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2 + (d*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/3 + ((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/5 - (2*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (2*b*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (2*b*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (2*b^2*d^2*Sqrt[d + c^2*d*x^2]*PolyLog[3, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (2*b^2*d^2*Sqrt[d + c^2*d*x^2]*PolyLog[3, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2]","A",23,16,28,0.5714,1,"{5744, 5742, 5760, 4182, 2531, 2282, 6589, 5653, 261, 5679, 444, 43, 194, 12, 1247, 698}"
279,1,530,0,0.6126965,"\int \frac{\left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{x^2} \, dx","Int[((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/x^2,x]","\frac{b^2 c d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{15 b c^3 d^2 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 \sqrt{c^2 x^2+1}}+\frac{15}{8} c^2 d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{5 c d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{8 b \sqrt{c^2 x^2+1}}-\frac{c d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}-\frac{1}{8} b c d^2 \left(c^2 x^2+1\right)^{3/2} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+b c d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{2 b c d^2 \sqrt{c^2 d x^2+d} \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{5}{4} c^2 d x \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{x}+\frac{31}{64} b^2 c^2 d^2 x \sqrt{c^2 d x^2+d}+\frac{1}{32} b^2 c^2 d^2 x \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}-\frac{89 b^2 c d^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{64 \sqrt{c^2 x^2+1}}","-\frac{b^2 c d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{15 b c^3 d^2 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 \sqrt{c^2 x^2+1}}+\frac{15}{8} c^2 d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{5 c d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{8 b \sqrt{c^2 x^2+1}}+\frac{c d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}-\frac{1}{8} b c d^2 \left(c^2 x^2+1\right)^{3/2} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+b c d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{2 b c d^2 \sqrt{c^2 d x^2+d} \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{5}{4} c^2 d x \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{x}+\frac{31}{64} b^2 c^2 d^2 x \sqrt{c^2 d x^2+d}+\frac{1}{32} b^2 c^2 d^2 x \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}-\frac{89 b^2 c d^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{64 \sqrt{c^2 x^2+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^2*x^2)*Sqrt[d + c^2*d*x^2])/32 - (89*b^2*c*d^2*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/(64*Sqrt[1 + c^2*x^2]) - (15*b*c^3*d^2*x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(8*Sqrt[1 + c^2*x^2]) + b*c*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]) - (b*c*d^2*(1 + c^2*x^2)^(3/2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/8 + (15*c^2*d^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/8 - (c*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/Sqrt[1 + c^2*x^2] + (5*c^2*d*x*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/4 - ((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/x + (5*c*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^3)/(8*b*Sqrt[1 + c^2*x^2]) + (2*b*c*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*Log[1 - E^(2*ArcSinh[c*x])])/Sqrt[1 + c^2*x^2] + (b^2*c*d^2*Sqrt[d + c^2*d*x^2]*PolyLog[2, E^(2*ArcSinh[c*x])])/Sqrt[1 + c^2*x^2]","A",23,15,28,0.5357,0,"{5739, 5684, 5682, 5675, 5661, 321, 215, 5717, 195, 5726, 5659, 3716, 2190, 2279, 2391}"
280,1,687,0,0.9883362,"\int \frac{\left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{x^3} \, dx","Int[((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/x^3,x]","-\frac{5 b c^2 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{5 b c^2 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{5 b^2 c^2 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{5 b^2 c^2 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{5 a b c^3 d^2 x \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}-\frac{2 b c^5 d^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{c^2 x^2+1}}+\frac{b c^3 d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}+\frac{5}{2} c^2 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b c d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{x \sqrt{c^2 x^2+1}}-\frac{5 c^2 d^2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}+\frac{5}{6} c^2 d \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 x^2}+\frac{40}{9} b^2 c^2 d^2 \sqrt{c^2 d x^2+d}+\frac{2}{27} b^2 c^2 d^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}-\frac{5 b^2 c^3 d^2 x \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{\sqrt{c^2 x^2+1}}-\frac{b^2 c^2 d^2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{\sqrt{c^2 x^2+1}}","-\frac{5 b c^2 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{5 b c^2 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}}+\frac{5 b^2 c^2 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{5 b^2 c^2 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 x^2+1}}-\frac{5 a b c^3 d^2 x \sqrt{c^2 d x^2+d}}{\sqrt{c^2 x^2+1}}-\frac{2 b c^5 d^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{c^2 x^2+1}}+\frac{b c^3 d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}+\frac{5}{2} c^2 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b c d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{x \sqrt{c^2 x^2+1}}-\frac{5 c^2 d^2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 x^2+1}}+\frac{5}{6} c^2 d \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 x^2}+\frac{40}{9} b^2 c^2 d^2 \sqrt{c^2 d x^2+d}+\frac{2}{27} b^2 c^2 d^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}-\frac{5 b^2 c^3 d^2 x \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{\sqrt{c^2 x^2+1}}-\frac{b^2 c^2 d^2 \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{\sqrt{c^2 x^2+1}}",1,"(40*b^2*c^2*d^2*Sqrt[d + c^2*d*x^2])/9 - (5*a*b*c^3*d^2*x*Sqrt[d + c^2*d*x^2])/Sqrt[1 + c^2*x^2] + (2*b^2*c^2*d^2*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2])/27 - (5*b^2*c^3*d^2*x*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/Sqrt[1 + c^2*x^2] - (b*c*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(x*Sqrt[1 + c^2*x^2]) + (b*c^3*d^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*Sqrt[1 + c^2*x^2]) - (2*b*c^5*d^2*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(9*Sqrt[1 + c^2*x^2]) + (5*c^2*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/2 + (5*c^2*d*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/6 - ((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/(2*x^2) - (5*c^2*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2*ArcTanh[E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (b^2*c^2*d^2*Sqrt[d + c^2*d*x^2]*ArcTanh[Sqrt[1 + c^2*x^2]])/Sqrt[1 + c^2*x^2] - (5*b*c^2*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (5*b*c^2*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] + (5*b^2*c^2*d^2*Sqrt[d + c^2*d*x^2]*PolyLog[3, -E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2] - (5*b^2*c^2*d^2*Sqrt[d + c^2*d*x^2]*PolyLog[3, E^ArcSinh[c*x]])/Sqrt[1 + c^2*x^2]","A",25,20,28,0.7143,1,"{5739, 5744, 5742, 5760, 4182, 2531, 2282, 6589, 5653, 261, 5679, 444, 43, 270, 5730, 12, 1251, 897, 1153, 208}"
281,1,561,0,0.8505281,"\int \frac{\left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{x^4} \, dx","Int[((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/x^4,x]","\frac{7 b^2 c^3 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{3 \sqrt{c^2 x^2+1}}-\frac{5 b c^5 d^2 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{c^2 x^2+1}}+\frac{5}{2} c^4 d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{5 c^3 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b \sqrt{c^2 x^2+1}}-\frac{7 c^3 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \sqrt{c^2 x^2+1}}+\frac{7}{3} b c^3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)-\frac{b c d^2 \left(c^2 x^2+1\right)^{3/2} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^2}+\frac{14 b c^3 d^2 \sqrt{c^2 d x^2+d} \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}-\frac{5 c^2 d \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 x}-\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 x^3}+\frac{7}{12} b^2 c^4 d^2 x \sqrt{c^2 d x^2+d}-\frac{b^2 c^2 d^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}}{3 x}-\frac{23 b^2 c^3 d^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{12 \sqrt{c^2 x^2+1}}","-\frac{7 b^2 c^3 d^2 \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right)}{3 \sqrt{c^2 x^2+1}}-\frac{5 b c^5 d^2 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{c^2 x^2+1}}+\frac{5}{2} c^4 d^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{5 c^3 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b \sqrt{c^2 x^2+1}}+\frac{7 c^3 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \sqrt{c^2 x^2+1}}+\frac{7}{3} b c^3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)-\frac{b c d^2 \left(c^2 x^2+1\right)^{3/2} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^2}+\frac{14 b c^3 d^2 \sqrt{c^2 d x^2+d} \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}-\frac{5 c^2 d \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 x}-\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 x^3}+\frac{7}{12} b^2 c^4 d^2 x \sqrt{c^2 d x^2+d}-\frac{b^2 c^2 d^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d}}{3 x}-\frac{23 b^2 c^3 d^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{12 \sqrt{c^2 x^2+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^2*x^2)*Sqrt[d + c^2*d*x^2])/(3*x) - (23*b^2*c^3*d^2*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/(12*Sqrt[1 + c^2*x^2]) - (5*b*c^5*d^2*x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(2*Sqrt[1 + c^2*x^2]) + (7*b*c^3*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/3 - (b*c*d^2*(1 + c^2*x^2)^(3/2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*x^2) + (5*c^4*d^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/2 - (7*c^3*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(3*Sqrt[1 + c^2*x^2]) - (5*c^2*d*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(3*x) - ((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/(3*x^3) + (5*c^3*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^3)/(6*b*Sqrt[1 + c^2*x^2]) + (14*b*c^3*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])*Log[1 - E^(2*ArcSinh[c*x])])/(3*Sqrt[1 + c^2*x^2]) + (7*b^2*c^3*d^2*Sqrt[d + c^2*d*x^2]*PolyLog[2, E^(2*ArcSinh[c*x])])/(3*Sqrt[1 + c^2*x^2])","A",27,15,28,0.5357,0,"{5739, 5682, 5675, 5661, 321, 215, 5726, 5659, 3716, 2190, 2279, 2391, 195, 5728, 277}"
282,1,153,0,0.2896804,"\int \frac{x^4 \sinh ^{-1}(a x)^2}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^4*ArcSinh[a*x]^2)/Sqrt[1 + a^2*x^2],x]","\frac{x^3 \sqrt{a^2 x^2+1}}{32 a^2}-\frac{15 x \sqrt{a^2 x^2+1}}{64 a^4}+\frac{x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{4 a^2}+\frac{3 x^2 \sinh ^{-1}(a x)}{8 a^3}-\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{8 a^4}+\frac{\sinh ^{-1}(a x)^3}{8 a^5}+\frac{15 \sinh ^{-1}(a x)}{64 a^5}-\frac{x^4 \sinh ^{-1}(a x)}{8 a}","\frac{x^3 \sqrt{a^2 x^2+1}}{32 a^2}-\frac{15 x \sqrt{a^2 x^2+1}}{64 a^4}+\frac{x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{4 a^2}+\frac{3 x^2 \sinh ^{-1}(a x)}{8 a^3}-\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{8 a^4}+\frac{\sinh ^{-1}(a x)^3}{8 a^5}+\frac{15 \sinh ^{-1}(a x)}{64 a^5}-\frac{x^4 \sinh ^{-1}(a x)}{8 a}",1,"(-15*x*Sqrt[1 + a^2*x^2])/(64*a^4) + (x^3*Sqrt[1 + a^2*x^2])/(32*a^2) + (15*ArcSinh[a*x])/(64*a^5) + (3*x^2*ArcSinh[a*x])/(8*a^3) - (x^4*ArcSinh[a*x])/(8*a) - (3*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(8*a^4) + (x^3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(4*a^2) + ArcSinh[a*x]^3/(8*a^5)","A",10,5,23,0.2174,1,"{5758, 5675, 5661, 321, 215}"
283,1,122,0,0.2150106,"\int \frac{x^3 \sinh ^{-1}(a x)^2}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^3*ArcSinh[a*x]^2)/Sqrt[1 + a^2*x^2],x]","\frac{2 \left(a^2 x^2+1\right)^{3/2}}{27 a^4}-\frac{14 \sqrt{a^2 x^2+1}}{9 a^4}+\frac{x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{3 a^2}-\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{3 a^4}+\frac{4 x \sinh ^{-1}(a x)}{3 a^3}-\frac{2 x^3 \sinh ^{-1}(a x)}{9 a}","\frac{2 \left(a^2 x^2+1\right)^{3/2}}{27 a^4}-\frac{14 \sqrt{a^2 x^2+1}}{9 a^4}+\frac{x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{3 a^2}-\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{3 a^4}+\frac{4 x \sinh ^{-1}(a x)}{3 a^3}-\frac{2 x^3 \sinh ^{-1}(a x)}{9 a}",1,"(-14*Sqrt[1 + a^2*x^2])/(9*a^4) + (2*(1 + a^2*x^2)^(3/2))/(27*a^4) + (4*x*ArcSinh[a*x])/(3*a^3) - (2*x^3*ArcSinh[a*x])/(9*a) - (2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(3*a^4) + (x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(3*a^2)","A",8,7,23,0.3043,1,"{5758, 5717, 5653, 261, 5661, 266, 43}"
284,1,87,0,0.1539142,"\int \frac{x^2 \sinh ^{-1}(a x)^2}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^2*ArcSinh[a*x]^2)/Sqrt[1 + a^2*x^2],x]","\frac{x \sqrt{a^2 x^2+1}}{4 a^2}+\frac{x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{2 a^2}-\frac{\sinh ^{-1}(a x)^3}{6 a^3}-\frac{\sinh ^{-1}(a x)}{4 a^3}-\frac{x^2 \sinh ^{-1}(a x)}{2 a}","\frac{x \sqrt{a^2 x^2+1}}{4 a^2}+\frac{x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{2 a^2}-\frac{\sinh ^{-1}(a x)^3}{6 a^3}-\frac{\sinh ^{-1}(a x)}{4 a^3}-\frac{x^2 \sinh ^{-1}(a x)}{2 a}",1,"(x*Sqrt[1 + a^2*x^2])/(4*a^2) - ArcSinh[a*x]/(4*a^3) - (x^2*ArcSinh[a*x])/(2*a) + (x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(2*a^2) - ArcSinh[a*x]^3/(6*a^3)","A",5,5,23,0.2174,1,"{5758, 5675, 5661, 321, 215}"
285,1,52,0,0.0779984,"\int \frac{x \sinh ^{-1}(a x)^2}{\sqrt{1+a^2 x^2}} \, dx","Int[(x*ArcSinh[a*x]^2)/Sqrt[1 + a^2*x^2],x]","\frac{2 \sqrt{a^2 x^2+1}}{a^2}+\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{a^2}-\frac{2 x \sinh ^{-1}(a x)}{a}","\frac{2 \sqrt{a^2 x^2+1}}{a^2}+\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{a^2}-\frac{2 x \sinh ^{-1}(a x)}{a}",1,"(2*Sqrt[1 + a^2*x^2])/a^2 - (2*x*ArcSinh[a*x])/a + (Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/a^2","A",3,3,21,0.1429,1,"{5717, 5653, 261}"
286,1,13,0,0.0338568,"\int \frac{\sinh ^{-1}(a x)^2}{\sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]^2/Sqrt[1 + a^2*x^2],x]","\frac{\sinh ^{-1}(a x)^3}{3 a}","\frac{\sinh ^{-1}(a x)^3}{3 a}",1,"ArcSinh[a*x]^3/(3*a)","A",1,1,20,0.05000,1,"{5675}"
287,1,68,0,0.1485741,"\int \frac{\sinh ^{-1}(a x)^2}{x \sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]^2/(x*Sqrt[1 + a^2*x^2]),x]","-2 \sinh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+2 \sinh ^{-1}(a x) \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)+2 \text{PolyLog}\left(3,-e^{\sinh ^{-1}(a x)}\right)-2 \text{PolyLog}\left(3,e^{\sinh ^{-1}(a x)}\right)-2 \sinh ^{-1}(a x)^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)","-2 \sinh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+2 \sinh ^{-1}(a x) \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)+2 \text{PolyLog}\left(3,-e^{\sinh ^{-1}(a x)}\right)-2 \text{PolyLog}\left(3,e^{\sinh ^{-1}(a x)}\right)-2 \sinh ^{-1}(a x)^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)",1,"-2*ArcSinh[a*x]^2*ArcTanh[E^ArcSinh[a*x]] - 2*ArcSinh[a*x]*PolyLog[2, -E^ArcSinh[a*x]] + 2*ArcSinh[a*x]*PolyLog[2, E^ArcSinh[a*x]] + 2*PolyLog[3, -E^ArcSinh[a*x]] - 2*PolyLog[3, E^ArcSinh[a*x]]","A",8,5,23,0.2174,1,"{5760, 4182, 2531, 2282, 6589}"
288,1,66,0,0.1620826,"\int \frac{\sinh ^{-1}(a x)^2}{x^2 \sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]^2/(x^2*Sqrt[1 + a^2*x^2]),x]","a \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{x}-a \sinh ^{-1}(a x)^2+2 a \sinh ^{-1}(a x) \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)","a \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{x}-a \sinh ^{-1}(a x)^2+2 a \sinh ^{-1}(a x) \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)",1,"-(a*ArcSinh[a*x]^2) - (Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/x + 2*a*ArcSinh[a*x]*Log[1 - E^(2*ArcSinh[a*x])] + a*PolyLog[2, E^(2*ArcSinh[a*x])]","A",6,6,23,0.2609,1,"{5723, 5659, 3716, 2190, 2279, 2391}"
289,1,135,0,0.2624159,"\int \frac{\sinh ^{-1}(a x)^2}{x^3 \sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]^2/(x^3*Sqrt[1 + a^2*x^2]),x]","a^2 \sinh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)-a^2 \sinh ^{-1}(a x) \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-a^2 \text{PolyLog}\left(3,-e^{\sinh ^{-1}(a x)}\right)+a^2 \text{PolyLog}\left(3,e^{\sinh ^{-1}(a x)}\right)-\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{2 x^2}-a^2 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)+a^2 \sinh ^{-1}(a x)^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-\frac{a \sinh ^{-1}(a x)}{x}","a^2 \sinh ^{-1}(a x) \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)-a^2 \sinh ^{-1}(a x) \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-a^2 \text{PolyLog}\left(3,-e^{\sinh ^{-1}(a x)}\right)+a^2 \text{PolyLog}\left(3,e^{\sinh ^{-1}(a x)}\right)-\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{2 x^2}-a^2 \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)+a^2 \sinh ^{-1}(a x)^2 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-\frac{a \sinh ^{-1}(a x)}{x}",1,"-((a*ArcSinh[a*x])/x) - (Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(2*x^2) + a^2*ArcSinh[a*x]^2*ArcTanh[E^ArcSinh[a*x]] - a^2*ArcTanh[Sqrt[1 + a^2*x^2]] + a^2*ArcSinh[a*x]*PolyLog[2, -E^ArcSinh[a*x]] - a^2*ArcSinh[a*x]*PolyLog[2, E^ArcSinh[a*x]] - a^2*PolyLog[3, -E^ArcSinh[a*x]] + a^2*PolyLog[3, E^ArcSinh[a*x]]","A",13,10,23,0.4348,1,"{5747, 5760, 4182, 2531, 2282, 6589, 5661, 266, 63, 208}"
290,1,383,0,0.5542729,"\int \frac{x^5 \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+c^2 d x^2}} \, dx","Int[(x^5*(a + b*ArcSinh[c*x])^2)/Sqrt[d + c^2*d*x^2],x]","-\frac{16 a b x \sqrt{c^2 x^2+1}}{15 c^5 \sqrt{c^2 d x^2+d}}-\frac{2 b x^5 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{25 c \sqrt{c^2 d x^2+d}}+\frac{x^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{5 c^2 d}+\frac{8 b x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{45 c^3 \sqrt{c^2 d x^2+d}}-\frac{4 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{15 c^4 d}+\frac{8 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{15 c^6 d}+\frac{2 b^2 \left(c^2 x^2+1\right)^3}{125 c^6 \sqrt{c^2 d x^2+d}}-\frac{76 b^2 \left(c^2 x^2+1\right)^2}{675 c^6 \sqrt{c^2 d x^2+d}}+\frac{298 b^2 \left(c^2 x^2+1\right)}{225 c^6 \sqrt{c^2 d x^2+d}}-\frac{16 b^2 x \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{15 c^5 \sqrt{c^2 d x^2+d}}","-\frac{16 a b x \sqrt{c^2 x^2+1}}{15 c^5 \sqrt{c^2 d x^2+d}}-\frac{2 b x^5 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{25 c \sqrt{c^2 d x^2+d}}+\frac{x^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{5 c^2 d}+\frac{8 b x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{45 c^3 \sqrt{c^2 d x^2+d}}-\frac{4 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{15 c^4 d}+\frac{8 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{15 c^6 d}+\frac{2 b^2 \left(c^2 x^2+1\right)^3}{125 c^6 \sqrt{c^2 d x^2+d}}-\frac{76 b^2 \left(c^2 x^2+1\right)^2}{675 c^6 \sqrt{c^2 d x^2+d}}+\frac{298 b^2 \left(c^2 x^2+1\right)}{225 c^6 \sqrt{c^2 d x^2+d}}-\frac{16 b^2 x \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{15 c^5 \sqrt{c^2 d x^2+d}}",1,"(-16*a*b*x*Sqrt[1 + c^2*x^2])/(15*c^5*Sqrt[d + c^2*d*x^2]) + (298*b^2*(1 + c^2*x^2))/(225*c^6*Sqrt[d + c^2*d*x^2]) - (76*b^2*(1 + c^2*x^2)^2)/(675*c^6*Sqrt[d + c^2*d*x^2]) + (2*b^2*(1 + c^2*x^2)^3)/(125*c^6*Sqrt[d + c^2*d*x^2]) - (16*b^2*x*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(15*c^5*Sqrt[d + c^2*d*x^2]) + (8*b*x^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(45*c^3*Sqrt[d + c^2*d*x^2]) - (2*b*x^5*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(25*c*Sqrt[d + c^2*d*x^2]) + (8*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(15*c^6*d) - (4*x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(15*c^4*d) + (x^4*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(5*c^2*d)","A",14,7,28,0.2500,1,"{5758, 5717, 5653, 261, 5661, 266, 43}"
291,1,323,0,0.4788907,"\int \frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+c^2 d x^2}} \, dx","Int[(x^4*(a + b*ArcSinh[c*x])^2)/Sqrt[d + c^2*d*x^2],x]","-\frac{b x^4 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{8 c \sqrt{c^2 d x^2+d}}+\frac{x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^2 d}+\frac{3 b x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{8 c^3 \sqrt{c^2 d x^2+d}}-\frac{3 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{8 c^4 d}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{8 b c^5 \sqrt{c^2 d x^2+d}}+\frac{b^2 x^3 \left(c^2 x^2+1\right)}{32 c^2 \sqrt{c^2 d x^2+d}}-\frac{15 b^2 x \left(c^2 x^2+1\right)}{64 c^4 \sqrt{c^2 d x^2+d}}+\frac{15 b^2 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{64 c^5 \sqrt{c^2 d x^2+d}}","-\frac{b x^4 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{8 c \sqrt{c^2 d x^2+d}}+\frac{x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^2 d}+\frac{3 b x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{8 c^3 \sqrt{c^2 d x^2+d}}-\frac{3 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{8 c^4 d}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{8 b c^5 \sqrt{c^2 d x^2+d}}+\frac{b^2 x^3 \left(c^2 x^2+1\right)}{32 c^2 \sqrt{c^2 d x^2+d}}-\frac{15 b^2 x \left(c^2 x^2+1\right)}{64 c^4 \sqrt{c^2 d x^2+d}}+\frac{15 b^2 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{64 c^5 \sqrt{c^2 d x^2+d}}",1,"(-15*b^2*x*(1 + c^2*x^2))/(64*c^4*Sqrt[d + c^2*d*x^2]) + (b^2*x^3*(1 + c^2*x^2))/(32*c^2*Sqrt[d + c^2*d*x^2]) + (15*b^2*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(64*c^5*Sqrt[d + c^2*d*x^2]) + (3*b*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(8*c^3*Sqrt[d + c^2*d*x^2]) - (b*x^4*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(8*c*Sqrt[d + c^2*d*x^2]) - (3*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(8*c^4*d) + (x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(4*c^2*d) + (Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^3)/(8*b*c^5*Sqrt[d + c^2*d*x^2])","A",11,6,28,0.2143,1,"{5758, 5677, 5675, 5661, 321, 215}"
292,1,265,0,0.3296532,"\int \frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+c^2 d x^2}} \, dx","Int[(x^3*(a + b*ArcSinh[c*x])^2)/Sqrt[d + c^2*d*x^2],x]","\frac{4 a b x \sqrt{c^2 x^2+1}}{3 c^3 \sqrt{c^2 d x^2+d}}-\frac{2 b x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c \sqrt{c^2 d x^2+d}}+\frac{x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^2 d}-\frac{2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^4 d}+\frac{2 b^2 \left(c^2 x^2+1\right)^2}{27 c^4 \sqrt{c^2 d x^2+d}}-\frac{14 b^2 \left(c^2 x^2+1\right)}{9 c^4 \sqrt{c^2 d x^2+d}}+\frac{4 b^2 x \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{3 c^3 \sqrt{c^2 d x^2+d}}","\frac{4 a b x \sqrt{c^2 x^2+1}}{3 c^3 \sqrt{c^2 d x^2+d}}-\frac{2 b x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c \sqrt{c^2 d x^2+d}}+\frac{x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^2 d}-\frac{2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^4 d}+\frac{2 b^2 \left(c^2 x^2+1\right)^2}{27 c^4 \sqrt{c^2 d x^2+d}}-\frac{14 b^2 \left(c^2 x^2+1\right)}{9 c^4 \sqrt{c^2 d x^2+d}}+\frac{4 b^2 x \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{3 c^3 \sqrt{c^2 d x^2+d}}",1,"(4*a*b*x*Sqrt[1 + c^2*x^2])/(3*c^3*Sqrt[d + c^2*d*x^2]) - (14*b^2*(1 + c^2*x^2))/(9*c^4*Sqrt[d + c^2*d*x^2]) + (2*b^2*(1 + c^2*x^2)^2)/(27*c^4*Sqrt[d + c^2*d*x^2]) + (4*b^2*x*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(3*c^3*Sqrt[d + c^2*d*x^2]) - (2*b*x^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(9*c*Sqrt[d + c^2*d*x^2]) - (2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(3*c^4*d) + (x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(3*c^2*d)","A",9,7,28,0.2500,1,"{5758, 5717, 5653, 261, 5661, 266, 43}"
293,1,204,0,0.2754867,"\int \frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+c^2 d x^2}} \, dx","Int[(x^2*(a + b*ArcSinh[c*x])^2)/Sqrt[d + c^2*d*x^2],x]","-\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b c^3 \sqrt{c^2 d x^2+d}}+\frac{x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^2 d}-\frac{b x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 c \sqrt{c^2 d x^2+d}}+\frac{b^2 x \left(c^2 x^2+1\right)}{4 c^2 \sqrt{c^2 d x^2+d}}-\frac{b^2 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{4 c^3 \sqrt{c^2 d x^2+d}}","-\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b c^3 \sqrt{c^2 d x^2+d}}+\frac{x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^2 d}-\frac{b x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 c \sqrt{c^2 d x^2+d}}+\frac{b^2 x \left(c^2 x^2+1\right)}{4 c^2 \sqrt{c^2 d x^2+d}}-\frac{b^2 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{4 c^3 \sqrt{c^2 d x^2+d}}",1,"(b^2*x*(1 + c^2*x^2))/(4*c^2*Sqrt[d + c^2*d*x^2]) - (b^2*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(4*c^3*Sqrt[d + c^2*d*x^2]) - (b*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(2*c*Sqrt[d + c^2*d*x^2]) + (x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*c^2*d) - (Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^3)/(6*b*c^3*Sqrt[d + c^2*d*x^2])","A",6,6,28,0.2143,1,"{5758, 5677, 5675, 5661, 321, 215}"
294,1,138,0,0.1242071,"\int \frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+c^2 d x^2}} \, dx","Int[(x*(a + b*ArcSinh[c*x])^2)/Sqrt[d + c^2*d*x^2],x]","-\frac{2 a b x \sqrt{c^2 x^2+1}}{c \sqrt{c^2 d x^2+d}}+\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{c^2 d}+\frac{2 b^2 \left(c^2 x^2+1\right)}{c^2 \sqrt{c^2 d x^2+d}}-\frac{2 b^2 x \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{c \sqrt{c^2 d x^2+d}}","-\frac{2 a b x \sqrt{c^2 x^2+1}}{c \sqrt{c^2 d x^2+d}}+\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{c^2 d}+\frac{2 b^2 \left(c^2 x^2+1\right)}{c^2 \sqrt{c^2 d x^2+d}}-\frac{2 b^2 x \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{c \sqrt{c^2 d x^2+d}}",1,"(-2*a*b*x*Sqrt[1 + c^2*x^2])/(c*Sqrt[d + c^2*d*x^2]) + (2*b^2*(1 + c^2*x^2))/(c^2*Sqrt[d + c^2*d*x^2]) - (2*b^2*x*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(c*Sqrt[d + c^2*d*x^2]) + (Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(c^2*d)","A",4,3,26,0.1154,1,"{5717, 5653, 261}"
295,1,47,0,0.0947017,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+c^2 d x^2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/Sqrt[d + c^2*d*x^2],x]","\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c \sqrt{c^2 d x^2+d}}","\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c \sqrt{c^2 d x^2+d}}",1,"(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^3)/(3*b*c*Sqrt[d + c^2*d*x^2])","A",2,2,25,0.08000,1,"{5677, 5675}"
296,1,223,0,0.3423202,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x \sqrt{d+c^2 d x^2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x*Sqrt[d + c^2*d*x^2]),x]","-\frac{2 b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 d x^2+d}}+\frac{2 b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 d x^2+d}}+\frac{2 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 d x^2+d}}-\frac{2 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 d x^2+d}}-\frac{2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 d x^2+d}}","-\frac{2 b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 d x^2+d}}+\frac{2 b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 d x^2+d}}+\frac{2 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 d x^2+d}}-\frac{2 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 d x^2+d}}-\frac{2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 d x^2+d}}",1,"(-2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2*ArcTanh[E^ArcSinh[c*x]])/Sqrt[d + c^2*d*x^2] - (2*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, -E^ArcSinh[c*x]])/Sqrt[d + c^2*d*x^2] + (2*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, E^ArcSinh[c*x]])/Sqrt[d + c^2*d*x^2] + (2*b^2*Sqrt[1 + c^2*x^2]*PolyLog[3, -E^ArcSinh[c*x]])/Sqrt[d + c^2*d*x^2] - (2*b^2*Sqrt[1 + c^2*x^2]*PolyLog[3, E^ArcSinh[c*x]])/Sqrt[d + c^2*d*x^2]","A",9,6,28,0.2143,1,"{5764, 5760, 4182, 2531, 2282, 6589}"
297,1,167,0,0.2266589,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^2 \sqrt{d+c^2 d x^2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^2*Sqrt[d + c^2*d*x^2]),x]","\frac{b^2 c \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{\sqrt{c^2 d x^2+d}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{d x}-\frac{c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 d x^2+d}}+\frac{2 b c \sqrt{c^2 x^2+1} \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 d x^2+d}}","-\frac{b^2 c \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right)}{\sqrt{c^2 d x^2+d}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{d x}+\frac{c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 d x^2+d}}+\frac{2 b c \sqrt{c^2 x^2+1} \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 d x^2+d}}",1,"-((c*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/Sqrt[d + c^2*d*x^2]) - (Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(d*x) + (2*b*c*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 - E^(2*ArcSinh[c*x])])/Sqrt[d + c^2*d*x^2] + (b^2*c*Sqrt[1 + c^2*x^2]*PolyLog[2, E^(2*ArcSinh[c*x])])/Sqrt[d + c^2*d*x^2]","A",6,6,28,0.2143,0,"{5723, 5659, 3716, 2190, 2279, 2391}"
298,1,360,0,0.5703655,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^3 \sqrt{d+c^2 d x^2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^3*Sqrt[d + c^2*d*x^2]),x]","\frac{b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 d x^2+d}}-\frac{b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 d x^2+d}}-\frac{b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 d x^2+d}}+\frac{b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{x \sqrt{c^2 d x^2+d}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 d x^2}+\frac{c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 d x^2+d}}-\frac{b^2 c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{\sqrt{c^2 d x^2+d}}","\frac{b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 d x^2+d}}-\frac{b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 d x^2+d}}-\frac{b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 d x^2+d}}+\frac{b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{\sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{x \sqrt{c^2 d x^2+d}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 d x^2}+\frac{c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 d x^2+d}}-\frac{b^2 c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{\sqrt{c^2 d x^2+d}}",1,"-((b*c*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(x*Sqrt[d + c^2*d*x^2])) - (Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*d*x^2) + (c^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2*ArcTanh[E^ArcSinh[c*x]])/Sqrt[d + c^2*d*x^2] - (b^2*c^2*Sqrt[1 + c^2*x^2]*ArcTanh[Sqrt[1 + c^2*x^2]])/Sqrt[d + c^2*d*x^2] + (b*c^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, -E^ArcSinh[c*x]])/Sqrt[d + c^2*d*x^2] - (b*c^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, E^ArcSinh[c*x]])/Sqrt[d + c^2*d*x^2] - (b^2*c^2*Sqrt[1 + c^2*x^2]*PolyLog[3, -E^ArcSinh[c*x]])/Sqrt[d + c^2*d*x^2] + (b^2*c^2*Sqrt[1 + c^2*x^2]*PolyLog[3, E^ArcSinh[c*x]])/Sqrt[d + c^2*d*x^2]","A",14,11,28,0.3929,1,"{5747, 5764, 5760, 4182, 2531, 2282, 6589, 5661, 266, 63, 208}"
299,1,299,0,0.4273731,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^4 \sqrt{d+c^2 d x^2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^4*Sqrt[d + c^2*d*x^2]),x]","-\frac{2 b^2 c^3 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{3 \sqrt{c^2 d x^2+d}}+\frac{2 c^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \sqrt{c^2 d x^2+d}}+\frac{2 c^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d x}-\frac{b c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^2 \sqrt{c^2 d x^2+d}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d x^3}-\frac{4 b c^3 \sqrt{c^2 x^2+1} \log \left(1-e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 d x^2+d}}-\frac{b^2 c^2 \left(c^2 x^2+1\right)}{3 x \sqrt{c^2 d x^2+d}}","\frac{2 b^2 c^3 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c x)}\right)}{3 \sqrt{c^2 d x^2+d}}-\frac{2 c^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \sqrt{c^2 d x^2+d}}+\frac{2 c^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d x}-\frac{b c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 x^2 \sqrt{c^2 d x^2+d}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d x^3}-\frac{4 b c^3 \sqrt{c^2 x^2+1} \log \left(1-e^{-2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 d x^2+d}}-\frac{b^2 c^2 \left(c^2 x^2+1\right)}{3 x \sqrt{c^2 d x^2+d}}",1,"-(b^2*c^2*(1 + c^2*x^2))/(3*x*Sqrt[d + c^2*d*x^2]) - (b*c*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(3*x^2*Sqrt[d + c^2*d*x^2]) + (2*c^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(3*Sqrt[d + c^2*d*x^2]) - (Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(3*d*x^3) + (2*c^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(3*d*x) - (4*b*c^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 - E^(2*ArcSinh[c*x])])/(3*Sqrt[d + c^2*d*x^2]) - (2*b^2*c^3*Sqrt[1 + c^2*x^2]*PolyLog[2, E^(2*ArcSinh[c*x])])/(3*Sqrt[d + c^2*d*x^2])","A",9,9,28,0.3214,0,"{5747, 5723, 5659, 3716, 2190, 2279, 2391, 5661, 264}"
300,1,515,0,0.7925609,"\int \frac{x^5 \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(x^5*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^(3/2),x]","-\frac{2 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c^6 d \sqrt{c^2 d x^2+d}}+\frac{2 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c^6 d \sqrt{c^2 d x^2+d}}+\frac{4 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^4 d^2}-\frac{8 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^6 d^2}+\frac{16 a b x \sqrt{c^2 x^2+1}}{3 c^5 d \sqrt{c^2 d x^2+d}}-\frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{c^2 d \sqrt{c^2 d x^2+d}}-\frac{2 b x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^3 d \sqrt{c^2 d x^2+d}}-\frac{2 b x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d \sqrt{c^2 d x^2+d}}+\frac{4 b \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^6 d \sqrt{c^2 d x^2+d}}+\frac{2 b^2 \left(c^2 x^2+1\right)^2}{27 c^6 d \sqrt{c^2 d x^2+d}}-\frac{32 b^2 \left(c^2 x^2+1\right)}{9 c^6 d \sqrt{c^2 d x^2+d}}+\frac{16 b^2 x \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{3 c^5 d \sqrt{c^2 d x^2+d}}","-\frac{2 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c^6 d \sqrt{c^2 d x^2+d}}+\frac{2 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c^6 d \sqrt{c^2 d x^2+d}}+\frac{4 x^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^4 d^2}-\frac{8 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^6 d^2}+\frac{16 a b x \sqrt{c^2 x^2+1}}{3 c^5 d \sqrt{c^2 d x^2+d}}-\frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{c^2 d \sqrt{c^2 d x^2+d}}-\frac{2 b x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^3 d \sqrt{c^2 d x^2+d}}-\frac{2 b x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d \sqrt{c^2 d x^2+d}}+\frac{4 b \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^6 d \sqrt{c^2 d x^2+d}}+\frac{2 b^2 \left(c^2 x^2+1\right)^2}{27 c^6 d \sqrt{c^2 d x^2+d}}-\frac{32 b^2 \left(c^2 x^2+1\right)}{9 c^6 d \sqrt{c^2 d x^2+d}}+\frac{16 b^2 x \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{3 c^5 d \sqrt{c^2 d x^2+d}}",1,"(16*a*b*x*Sqrt[1 + c^2*x^2])/(3*c^5*d*Sqrt[d + c^2*d*x^2]) - (32*b^2*(1 + c^2*x^2))/(9*c^6*d*Sqrt[d + c^2*d*x^2]) + (2*b^2*(1 + c^2*x^2)^2)/(27*c^6*d*Sqrt[d + c^2*d*x^2]) + (16*b^2*x*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(3*c^5*d*Sqrt[d + c^2*d*x^2]) - (2*b*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(c^5*d*Sqrt[d + c^2*d*x^2]) - (2*b*x^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(9*c^3*d*Sqrt[d + c^2*d*x^2]) - (x^4*(a + b*ArcSinh[c*x])^2)/(c^2*d*Sqrt[d + c^2*d*x^2]) - (8*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(3*c^6*d^2) + (4*x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(3*c^4*d^2) + (4*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c^6*d*Sqrt[d + c^2*d*x^2]) - ((2*I)*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^6*d*Sqrt[d + c^2*d*x^2]) + ((2*I)*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, I*E^ArcSinh[c*x]])/(c^6*d*Sqrt[d + c^2*d*x^2])","A",22,13,28,0.4643,1,"{5751, 5758, 5717, 5653, 261, 5661, 266, 43, 5767, 5693, 4180, 2279, 2391}"
301,1,400,0,0.6649403,"\int \frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(x^4*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^(3/2),x]","-\frac{b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c^5 d \sqrt{c^2 d x^2+d}}+\frac{3 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^4 d^2}-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{c^2 d \sqrt{c^2 d x^2+d}}-\frac{b x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 c^3 d \sqrt{c^2 d x^2+d}}-\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{2 b c^5 d \sqrt{c^2 d x^2+d}}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{c^5 d \sqrt{c^2 d x^2+d}}-\frac{2 b \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d \sqrt{c^2 d x^2+d}}+\frac{b^2 x \left(c^2 x^2+1\right)}{4 c^4 d \sqrt{c^2 d x^2+d}}-\frac{b^2 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{4 c^5 d \sqrt{c^2 d x^2+d}}","-\frac{b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c^5 d \sqrt{c^2 d x^2+d}}+\frac{3 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^4 d^2}-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{c^2 d \sqrt{c^2 d x^2+d}}-\frac{b x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 c^3 d \sqrt{c^2 d x^2+d}}-\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{2 b c^5 d \sqrt{c^2 d x^2+d}}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{c^5 d \sqrt{c^2 d x^2+d}}-\frac{2 b \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^5 d \sqrt{c^2 d x^2+d}}+\frac{b^2 x \left(c^2 x^2+1\right)}{4 c^4 d \sqrt{c^2 d x^2+d}}-\frac{b^2 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{4 c^5 d \sqrt{c^2 d x^2+d}}",1,"(b^2*x*(1 + c^2*x^2))/(4*c^4*d*Sqrt[d + c^2*d*x^2]) - (b^2*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(4*c^5*d*Sqrt[d + c^2*d*x^2]) - (b*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(2*c^3*d*Sqrt[d + c^2*d*x^2]) - (x^3*(a + b*ArcSinh[c*x])^2)/(c^2*d*Sqrt[d + c^2*d*x^2]) + (Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(c^5*d*Sqrt[d + c^2*d*x^2]) + (3*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*c^4*d^2) - (Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^3)/(2*b*c^5*d*Sqrt[d + c^2*d*x^2]) - (2*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(c^5*d*Sqrt[d + c^2*d*x^2]) - (b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^(2*ArcSinh[c*x])])/(c^5*d*Sqrt[d + c^2*d*x^2])","A",15,13,28,0.4643,1,"{5751, 5758, 5677, 5675, 5661, 321, 215, 5767, 5714, 3718, 2190, 2279, 2391}"
302,1,383,0,0.4554926,"\int \frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(x^3*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^(3/2),x]","\frac{2 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c^4 d \sqrt{c^2 d x^2+d}}-\frac{2 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c^4 d \sqrt{c^2 d x^2+d}}+\frac{2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{c^4 d^2}-\frac{4 a b x \sqrt{c^2 x^2+1}}{c^3 d \sqrt{c^2 d x^2+d}}+\frac{2 b x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d \sqrt{c^2 d x^2+d}}-\frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{c^2 d \sqrt{c^2 d x^2+d}}-\frac{4 b \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^4 d \sqrt{c^2 d x^2+d}}+\frac{2 b^2 \left(c^2 x^2+1\right)}{c^4 d \sqrt{c^2 d x^2+d}}-\frac{4 b^2 x \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{c^3 d \sqrt{c^2 d x^2+d}}","\frac{2 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c^4 d \sqrt{c^2 d x^2+d}}-\frac{2 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c^4 d \sqrt{c^2 d x^2+d}}+\frac{2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{c^4 d^2}-\frac{4 a b x \sqrt{c^2 x^2+1}}{c^3 d \sqrt{c^2 d x^2+d}}+\frac{2 b x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d \sqrt{c^2 d x^2+d}}-\frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{c^2 d \sqrt{c^2 d x^2+d}}-\frac{4 b \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^4 d \sqrt{c^2 d x^2+d}}+\frac{2 b^2 \left(c^2 x^2+1\right)}{c^4 d \sqrt{c^2 d x^2+d}}-\frac{4 b^2 x \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{c^3 d \sqrt{c^2 d x^2+d}}",1,"(-4*a*b*x*Sqrt[1 + c^2*x^2])/(c^3*d*Sqrt[d + c^2*d*x^2]) + (2*b^2*(1 + c^2*x^2))/(c^4*d*Sqrt[d + c^2*d*x^2]) - (4*b^2*x*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(c^3*d*Sqrt[d + c^2*d*x^2]) + (2*b*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(c^3*d*Sqrt[d + c^2*d*x^2]) - (x^2*(a + b*ArcSinh[c*x])^2)/(c^2*d*Sqrt[d + c^2*d*x^2]) + (2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(c^4*d^2) - (4*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c^4*d*Sqrt[d + c^2*d*x^2]) + ((2*I)*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^4*d*Sqrt[d + c^2*d*x^2]) - ((2*I)*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, I*E^ArcSinh[c*x]])/(c^4*d*Sqrt[d + c^2*d*x^2])","A",13,9,28,0.3214,1,"{5751, 5717, 5653, 261, 5767, 5693, 4180, 2279, 2391}"
303,1,233,0,0.3834706,"\int \frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(x^2*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^(3/2),x]","\frac{b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c^3 d \sqrt{c^2 d x^2+d}}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c^3 d \sqrt{c^2 d x^2+d}}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{c^2 d \sqrt{c^2 d x^2+d}}-\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{c^3 d \sqrt{c^2 d x^2+d}}+\frac{2 b \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d \sqrt{c^2 d x^2+d}}","\frac{b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c^3 d \sqrt{c^2 d x^2+d}}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c^3 d \sqrt{c^2 d x^2+d}}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{c^2 d \sqrt{c^2 d x^2+d}}-\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{c^3 d \sqrt{c^2 d x^2+d}}+\frac{2 b \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^3 d \sqrt{c^2 d x^2+d}}",1,"-((x*(a + b*ArcSinh[c*x])^2)/(c^2*d*Sqrt[d + c^2*d*x^2])) - (Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(c^3*d*Sqrt[d + c^2*d*x^2]) + (Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^3)/(3*b*c^3*d*Sqrt[d + c^2*d*x^2]) + (2*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(c^3*d*Sqrt[d + c^2*d*x^2]) + (b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^(2*ArcSinh[c*x])])/(c^3*d*Sqrt[d + c^2*d*x^2])","A",8,8,28,0.2857,1,"{5751, 5677, 5675, 5714, 3718, 2190, 2279, 2391}"
304,1,188,0,0.1869865,"\int \frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(x*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^(3/2),x]","-\frac{2 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c^2 d \sqrt{c^2 d x^2+d}}+\frac{2 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c^2 d \sqrt{c^2 d x^2+d}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{c^2 d \sqrt{c^2 d x^2+d}}+\frac{4 b \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d \sqrt{c^2 d x^2+d}}","-\frac{2 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c^2 d \sqrt{c^2 d x^2+d}}+\frac{2 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c^2 d \sqrt{c^2 d x^2+d}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{c^2 d \sqrt{c^2 d x^2+d}}+\frac{4 b \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^2 d \sqrt{c^2 d x^2+d}}",1,"-((a + b*ArcSinh[c*x])^2/(c^2*d*Sqrt[d + c^2*d*x^2])) + (4*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c^2*d*Sqrt[d + c^2*d*x^2]) - ((2*I)*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^2*d*Sqrt[d + c^2*d*x^2]) + ((2*I)*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, I*E^ArcSinh[c*x]])/(c^2*d*Sqrt[d + c^2*d*x^2])","A",7,5,26,0.1923,1,"{5717, 5693, 4180, 2279, 2391}"
305,1,179,0,0.1835293,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(d + c^2*d*x^2)^(3/2),x]","-\frac{b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c d \sqrt{c^2 d x^2+d}}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{d \sqrt{c^2 d x^2+d}}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{c d \sqrt{c^2 d x^2+d}}-\frac{2 b \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c d \sqrt{c^2 d x^2+d}}","-\frac{b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c d \sqrt{c^2 d x^2+d}}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{d \sqrt{c^2 d x^2+d}}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{c d \sqrt{c^2 d x^2+d}}-\frac{2 b \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c d \sqrt{c^2 d x^2+d}}",1,"(x*(a + b*ArcSinh[c*x])^2)/(d*Sqrt[d + c^2*d*x^2]) + (Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(c*d*Sqrt[d + c^2*d*x^2]) - (2*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(c*d*Sqrt[d + c^2*d*x^2]) - (b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^(2*ArcSinh[c*x])])/(c*d*Sqrt[d + c^2*d*x^2])","A",6,6,25,0.2400,1,"{5687, 5714, 3718, 2190, 2279, 2391}"
306,1,412,0,0.5945303,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x \left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x*(d + c^2*d*x^2)^(3/2)),x]","-\frac{2 b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}+\frac{2 b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}+\frac{2 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}-\frac{2 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}+\frac{2 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}-\frac{2 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d \sqrt{c^2 d x^2+d}}-\frac{4 b \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d \sqrt{c^2 d x^2+d}}","-\frac{2 b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}+\frac{2 b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}+\frac{2 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}-\frac{2 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}+\frac{2 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}-\frac{2 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d \sqrt{c^2 d x^2+d}}-\frac{4 b \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d \sqrt{c^2 d x^2+d}}",1,"(a + b*ArcSinh[c*x])^2/(d*Sqrt[d + c^2*d*x^2]) - (4*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) - (2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2*ArcTanh[E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) - (2*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, -E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) + ((2*I)*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) - ((2*I)*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, I*E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) + (2*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) + (2*b^2*Sqrt[1 + c^2*x^2]*PolyLog[3, -E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) - (2*b^2*Sqrt[1 + c^2*x^2]*PolyLog[3, E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2])","A",16,11,28,0.3929,1,"{5755, 5764, 5760, 4182, 2531, 2282, 6589, 5693, 4180, 2279, 2391}"
307,1,305,0,0.4641999,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^2 \left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^2*(d + c^2*d*x^2)^(3/2)),x]","\frac{b^2 c \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}+\frac{b^2 c \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}-\frac{2 c^2 x \left(a+b \sinh ^{-1}(c x)\right)^2}{d \sqrt{c^2 d x^2+d}}-\frac{2 c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{d \sqrt{c^2 d x^2+d}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d x \sqrt{c^2 d x^2+d}}+\frac{4 b c \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{4 b c \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}","\frac{b^2 c \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}+\frac{b^2 c \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}-\frac{2 c^2 x \left(a+b \sinh ^{-1}(c x)\right)^2}{d \sqrt{c^2 d x^2+d}}-\frac{2 c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{d \sqrt{c^2 d x^2+d}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d x \sqrt{c^2 d x^2+d}}+\frac{4 b c \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{4 b c \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}",1,"-((a + b*ArcSinh[c*x])^2/(d*x*Sqrt[d + c^2*d*x^2])) - (2*c^2*x*(a + b*ArcSinh[c*x])^2)/(d*Sqrt[d + c^2*d*x^2]) - (2*c*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(d*Sqrt[d + c^2*d*x^2]) - (4*b*c*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^(2*ArcSinh[c*x])])/(d*Sqrt[d + c^2*d*x^2]) + (4*b*c*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(d*Sqrt[d + c^2*d*x^2]) + (b^2*c*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^(2*ArcSinh[c*x])])/(d*Sqrt[d + c^2*d*x^2]) + (b^2*c*Sqrt[1 + c^2*x^2]*PolyLog[2, E^(2*ArcSinh[c*x])])/(d*Sqrt[d + c^2*d*x^2])","A",14,10,28,0.3571,1,"{5747, 5687, 5714, 3718, 2190, 2279, 2391, 5720, 5461, 4182}"
308,1,573,0,0.925848,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^3 \left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^3*(d + c^2*d*x^2)^(3/2)),x]","\frac{3 b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{3 b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{2 i b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}+\frac{2 i b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}-\frac{3 b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}+\frac{3 b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}-\frac{3 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 d \sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{d x \sqrt{c^2 d x^2+d}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 d x^2 \sqrt{c^2 d x^2+d}}+\frac{4 b c^2 \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}+\frac{3 c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d \sqrt{c^2 d x^2+d}}-\frac{b^2 c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{d \sqrt{c^2 d x^2+d}}","\frac{3 b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{3 b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}-\frac{2 i b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}+\frac{2 i b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}-\frac{3 b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}+\frac{3 b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}-\frac{3 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 d \sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{d x \sqrt{c^2 d x^2+d}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 d x^2 \sqrt{c^2 d x^2+d}}+\frac{4 b c^2 \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{c^2 d x^2+d}}+\frac{3 c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d \sqrt{c^2 d x^2+d}}-\frac{b^2 c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{d \sqrt{c^2 d x^2+d}}",1,"-((b*c*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(d*x*Sqrt[d + c^2*d*x^2])) - (3*c^2*(a + b*ArcSinh[c*x])^2)/(2*d*Sqrt[d + c^2*d*x^2]) - (a + b*ArcSinh[c*x])^2/(2*d*x^2*Sqrt[d + c^2*d*x^2]) + (4*b*c^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) + (3*c^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2*ArcTanh[E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) - (b^2*c^2*Sqrt[1 + c^2*x^2]*ArcTanh[Sqrt[1 + c^2*x^2]])/(d*Sqrt[d + c^2*d*x^2]) + (3*b*c^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, -E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) - ((2*I)*b^2*c^2*Sqrt[1 + c^2*x^2]*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) + ((2*I)*b^2*c^2*Sqrt[1 + c^2*x^2]*PolyLog[2, I*E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) - (3*b*c^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) - (3*b^2*c^2*Sqrt[1 + c^2*x^2]*PolyLog[3, -E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2]) + (3*b^2*c^2*Sqrt[1 + c^2*x^2]*PolyLog[3, E^ArcSinh[c*x]])/(d*Sqrt[d + c^2*d*x^2])","A",27,15,28,0.5357,1,"{5747, 5755, 5764, 5760, 4182, 2531, 2282, 6589, 5693, 4180, 2279, 2391, 266, 63, 208}"
309,1,452,0,0.8409178,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^4 \left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^4*(d + c^2*d*x^2)^(3/2)),x]","-\frac{b^2 c^3 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}-\frac{5 b^2 c^3 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{3 d \sqrt{c^2 d x^2+d}}+\frac{8 c^4 x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d \sqrt{c^2 d x^2+d}}+\frac{8 c^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d \sqrt{c^2 d x^2+d}}+\frac{4 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d x \sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 d x^2 \sqrt{c^2 d x^2+d}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{3 d x^3 \sqrt{c^2 d x^2+d}}-\frac{16 b c^3 \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d \sqrt{c^2 d x^2+d}}+\frac{20 b c^3 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d \sqrt{c^2 d x^2+d}}-\frac{b^2 c^2 \left(c^2 x^2+1\right)}{3 d x \sqrt{c^2 d x^2+d}}","-\frac{b^2 c^3 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{d \sqrt{c^2 d x^2+d}}-\frac{5 b^2 c^3 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{3 d \sqrt{c^2 d x^2+d}}+\frac{8 c^4 x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d \sqrt{c^2 d x^2+d}}+\frac{8 c^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d \sqrt{c^2 d x^2+d}}+\frac{4 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d x \sqrt{c^2 d x^2+d}}-\frac{b c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 d x^2 \sqrt{c^2 d x^2+d}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{3 d x^3 \sqrt{c^2 d x^2+d}}-\frac{16 b c^3 \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d \sqrt{c^2 d x^2+d}}+\frac{20 b c^3 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d \sqrt{c^2 d x^2+d}}-\frac{b^2 c^2 \left(c^2 x^2+1\right)}{3 d x \sqrt{c^2 d x^2+d}}",1,"-(b^2*c^2*(1 + c^2*x^2))/(3*d*x*Sqrt[d + c^2*d*x^2]) - (b*c*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(3*d*x^2*Sqrt[d + c^2*d*x^2]) - (a + b*ArcSinh[c*x])^2/(3*d*x^3*Sqrt[d + c^2*d*x^2]) + (4*c^2*(a + b*ArcSinh[c*x])^2)/(3*d*x*Sqrt[d + c^2*d*x^2]) + (8*c^4*x*(a + b*ArcSinh[c*x])^2)/(3*d*Sqrt[d + c^2*d*x^2]) + (8*c^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(3*d*Sqrt[d + c^2*d*x^2]) + (20*b*c^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^(2*ArcSinh[c*x])])/(3*d*Sqrt[d + c^2*d*x^2]) - (16*b*c^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(3*d*Sqrt[d + c^2*d*x^2]) - (b^2*c^3*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^(2*ArcSinh[c*x])])/(d*Sqrt[d + c^2*d*x^2]) - (5*b^2*c^3*Sqrt[1 + c^2*x^2]*PolyLog[2, E^(2*ArcSinh[c*x])])/(3*d*Sqrt[d + c^2*d*x^2])","A",24,11,28,0.3929,1,"{5747, 5687, 5714, 3718, 2190, 2279, 2391, 5720, 5461, 4182, 264}"
310,1,512,0,0.8812227,"\int \frac{x^5 \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(x^5*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^(5/2),x]","\frac{11 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c^6 d^2 \sqrt{c^2 d x^2+d}}-\frac{11 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 c^6 d^2 \sqrt{c^2 d x^2+d}}-\frac{16 a b x \sqrt{c^2 x^2+1}}{3 c^5 d^2 \sqrt{c^2 d x^2+d}}-\frac{b x^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 c^3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{4 x^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}+\frac{11 b x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^5 d^2 \sqrt{c^2 d x^2+d}}+\frac{8 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^6 d^3}-\frac{22 b \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c^6 d^2 \sqrt{c^2 d x^2+d}}-\frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^2 d \left(c^2 d x^2+d\right)^{3/2}}+\frac{2 b^2 \left(c^2 x^2+1\right)}{c^6 d^2 \sqrt{c^2 d x^2+d}}+\frac{b^2}{3 c^6 d^2 \sqrt{c^2 d x^2+d}}-\frac{16 b^2 x \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{3 c^5 d^2 \sqrt{c^2 d x^2+d}}","\frac{11 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c^6 d^2 \sqrt{c^2 d x^2+d}}-\frac{11 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 c^6 d^2 \sqrt{c^2 d x^2+d}}-\frac{16 a b x \sqrt{c^2 x^2+1}}{3 c^5 d^2 \sqrt{c^2 d x^2+d}}-\frac{b x^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 c^3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{4 x^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}+\frac{11 b x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^5 d^2 \sqrt{c^2 d x^2+d}}+\frac{8 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^6 d^3}-\frac{22 b \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c^6 d^2 \sqrt{c^2 d x^2+d}}-\frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^2 d \left(c^2 d x^2+d\right)^{3/2}}+\frac{2 b^2 \left(c^2 x^2+1\right)}{c^6 d^2 \sqrt{c^2 d x^2+d}}+\frac{b^2}{3 c^6 d^2 \sqrt{c^2 d x^2+d}}-\frac{16 b^2 x \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{3 c^5 d^2 \sqrt{c^2 d x^2+d}}",1,"b^2/(3*c^6*d^2*Sqrt[d + c^2*d*x^2]) - (16*a*b*x*Sqrt[1 + c^2*x^2])/(3*c^5*d^2*Sqrt[d + c^2*d*x^2]) + (2*b^2*(1 + c^2*x^2))/(c^6*d^2*Sqrt[d + c^2*d*x^2]) - (16*b^2*x*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(3*c^5*d^2*Sqrt[d + c^2*d*x^2]) - (b*x^3*(a + b*ArcSinh[c*x]))/(3*c^3*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) + (11*b*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(3*c^5*d^2*Sqrt[d + c^2*d*x^2]) - (x^4*(a + b*ArcSinh[c*x])^2)/(3*c^2*d*(d + c^2*d*x^2)^(3/2)) - (4*x^2*(a + b*ArcSinh[c*x])^2)/(3*c^4*d^2*Sqrt[d + c^2*d*x^2]) + (8*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(3*c^6*d^3) - (22*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(3*c^6*d^2*Sqrt[d + c^2*d*x^2]) + (((11*I)/3)*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^6*d^2*Sqrt[d + c^2*d*x^2]) - (((11*I)/3)*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, I*E^ArcSinh[c*x]])/(c^6*d^2*Sqrt[d + c^2*d*x^2])","A",26,11,28,0.3929,1,"{5751, 5717, 5653, 261, 5767, 5693, 4180, 2279, 2391, 266, 43}"
311,1,398,0,0.761133,"\int \frac{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(x^4*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^(5/2),x]","\frac{4 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 c^5 d^2 \sqrt{c^2 d x^2+d}}-\frac{b x^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 c^3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{c^4 d^2 \sqrt{c^2 d x^2+d}}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c^5 d^2 \sqrt{c^2 d x^2+d}}-\frac{4 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^5 d^2 \sqrt{c^2 d x^2+d}}+\frac{8 b \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c^5 d^2 \sqrt{c^2 d x^2+d}}-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^2 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b^2 x}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}+\frac{b^2 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{3 c^5 d^2 \sqrt{c^2 d x^2+d}}","\frac{4 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 c^5 d^2 \sqrt{c^2 d x^2+d}}-\frac{b x^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 c^3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{c^4 d^2 \sqrt{c^2 d x^2+d}}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c^5 d^2 \sqrt{c^2 d x^2+d}}-\frac{4 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^5 d^2 \sqrt{c^2 d x^2+d}}+\frac{8 b \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c^5 d^2 \sqrt{c^2 d x^2+d}}-\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^2 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b^2 x}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}+\frac{b^2 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{3 c^5 d^2 \sqrt{c^2 d x^2+d}}",1,"-(b^2*x)/(3*c^4*d^2*Sqrt[d + c^2*d*x^2]) + (b^2*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(3*c^5*d^2*Sqrt[d + c^2*d*x^2]) - (b*x^2*(a + b*ArcSinh[c*x]))/(3*c^3*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) - (x^3*(a + b*ArcSinh[c*x])^2)/(3*c^2*d*(d + c^2*d*x^2)^(3/2)) - (x*(a + b*ArcSinh[c*x])^2)/(c^4*d^2*Sqrt[d + c^2*d*x^2]) - (4*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(3*c^5*d^2*Sqrt[d + c^2*d*x^2]) + (Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^3)/(3*b*c^5*d^2*Sqrt[d + c^2*d*x^2]) + (8*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(3*c^5*d^2*Sqrt[d + c^2*d*x^2]) + (4*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^(2*ArcSinh[c*x])])/(3*c^5*d^2*Sqrt[d + c^2*d*x^2])","A",17,10,28,0.3571,1,"{5751, 5677, 5675, 5714, 3718, 2190, 2279, 2391, 288, 215}"
312,1,307,0,0.504904,"\int \frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(x^3*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^(5/2),x]","-\frac{5 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}+\frac{5 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}-\frac{b x \left(a+b \sinh ^{-1}(c x)\right)}{3 c^3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}+\frac{10 b \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}-\frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^2 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b^2}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}","-\frac{5 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}+\frac{5 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}-\frac{b x \left(a+b \sinh ^{-1}(c x)\right)}{3 c^3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}+\frac{10 b \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}-\frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^2 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b^2}{3 c^4 d^2 \sqrt{c^2 d x^2+d}}",1,"-b^2/(3*c^4*d^2*Sqrt[d + c^2*d*x^2]) - (b*x*(a + b*ArcSinh[c*x]))/(3*c^3*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) - (x^2*(a + b*ArcSinh[c*x])^2)/(3*c^2*d*(d + c^2*d*x^2)^(3/2)) - (2*(a + b*ArcSinh[c*x])^2)/(3*c^4*d^2*Sqrt[d + c^2*d*x^2]) + (10*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(3*c^4*d^2*Sqrt[d + c^2*d*x^2]) - (((5*I)/3)*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^4*d^2*Sqrt[d + c^2*d*x^2]) + (((5*I)/3)*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, I*E^ArcSinh[c*x]])/(c^4*d^2*Sqrt[d + c^2*d*x^2])","A",16,7,28,0.2500,1,"{5751, 5717, 5693, 4180, 2279, 2391, 261}"
313,1,312,0,0.3643952,"\int \frac{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(x^2*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^(5/2),x]","-\frac{b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 c^3 d^2 \sqrt{c^2 d x^2+d}}+\frac{b x^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 c d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^3 d^2 \sqrt{c^2 d x^2+d}}-\frac{2 b \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c^3 d^2 \sqrt{c^2 d x^2+d}}+\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d \left(c^2 d x^2+d\right)^{3/2}}+\frac{b^2 x}{3 c^2 d^2 \sqrt{c^2 d x^2+d}}-\frac{b^2 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{3 c^3 d^2 \sqrt{c^2 d x^2+d}}","-\frac{b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 c^3 d^2 \sqrt{c^2 d x^2+d}}+\frac{b x^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 c d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^3 d^2 \sqrt{c^2 d x^2+d}}-\frac{2 b \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c^3 d^2 \sqrt{c^2 d x^2+d}}+\frac{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d \left(c^2 d x^2+d\right)^{3/2}}+\frac{b^2 x}{3 c^2 d^2 \sqrt{c^2 d x^2+d}}-\frac{b^2 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{3 c^3 d^2 \sqrt{c^2 d x^2+d}}",1,"(b^2*x)/(3*c^2*d^2*Sqrt[d + c^2*d*x^2]) - (b^2*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(3*c^3*d^2*Sqrt[d + c^2*d*x^2]) + (b*x^2*(a + b*ArcSinh[c*x]))/(3*c*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) + (x^3*(a + b*ArcSinh[c*x])^2)/(3*d*(d + c^2*d*x^2)^(3/2)) + (Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(3*c^3*d^2*Sqrt[d + c^2*d*x^2]) - (2*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(3*c^3*d^2*Sqrt[d + c^2*d*x^2]) - (b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^(2*ArcSinh[c*x])])/(3*c^3*d^2*Sqrt[d + c^2*d*x^2])","A",9,9,28,0.3214,1,"{5723, 5751, 5714, 3718, 2190, 2279, 2391, 288, 215}"
314,1,270,0,0.21746,"\int \frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(x*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^(5/2),x]","-\frac{i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{c^2 d x^2+d}}+\frac{i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{c^2 d x^2+d}}+\frac{b x \left(a+b \sinh ^{-1}(c x)\right)}{3 c d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{2 b \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2 d^2 \sqrt{c^2 d x^2+d}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^2 d \left(c^2 d x^2+d\right)^{3/2}}+\frac{b^2}{3 c^2 d^2 \sqrt{c^2 d x^2+d}}","-\frac{i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{c^2 d x^2+d}}+\frac{i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 c^2 d^2 \sqrt{c^2 d x^2+d}}+\frac{b x \left(a+b \sinh ^{-1}(c x)\right)}{3 c d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{2 b \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2 d^2 \sqrt{c^2 d x^2+d}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{3 c^2 d \left(c^2 d x^2+d\right)^{3/2}}+\frac{b^2}{3 c^2 d^2 \sqrt{c^2 d x^2+d}}",1,"b^2/(3*c^2*d^2*Sqrt[d + c^2*d*x^2]) + (b*x*(a + b*ArcSinh[c*x]))/(3*c*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) - (a + b*ArcSinh[c*x])^2/(3*c^2*d*(d + c^2*d*x^2)^(3/2)) + (2*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(3*c^2*d^2*Sqrt[d + c^2*d*x^2]) - ((I/3)*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c^2*d^2*Sqrt[d + c^2*d*x^2]) + ((I/3)*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, I*E^ArcSinh[c*x]])/(c^2*d^2*Sqrt[d + c^2*d*x^2])","A",9,7,26,0.2692,1,"{5717, 5690, 5693, 4180, 2279, 2391, 261}"
315,1,292,0,0.2944346,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(d + c^2*d*x^2)^(5/2),x]","-\frac{2 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 c d^2 \sqrt{c^2 d x^2+d}}+\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{3 c d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{2 x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c d^2 \sqrt{c^2 d x^2+d}}-\frac{4 b \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c d^2 \sqrt{c^2 d x^2+d}}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b^2 x}{3 d^2 \sqrt{c^2 d x^2+d}}","-\frac{2 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 c d^2 \sqrt{c^2 d x^2+d}}+\frac{b \left(a+b \sinh ^{-1}(c x)\right)}{3 c d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{2 x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c d^2 \sqrt{c^2 d x^2+d}}-\frac{4 b \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c d^2 \sqrt{c^2 d x^2+d}}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b^2 x}{3 d^2 \sqrt{c^2 d x^2+d}}",1,"-(b^2*x)/(3*d^2*Sqrt[d + c^2*d*x^2]) + (b*(a + b*ArcSinh[c*x]))/(3*c*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) + (x*(a + b*ArcSinh[c*x])^2)/(3*d*(d + c^2*d*x^2)^(3/2)) + (2*x*(a + b*ArcSinh[c*x])^2)/(3*d^2*Sqrt[d + c^2*d*x^2]) + (2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(3*c*d^2*Sqrt[d + c^2*d*x^2]) - (4*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(3*c*d^2*Sqrt[d + c^2*d*x^2]) - (2*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^(2*ArcSinh[c*x])])/(3*c*d^2*Sqrt[d + c^2*d*x^2])","A",9,9,25,0.3600,1,"{5690, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 191}"
316,1,518,0,0.8633784,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x \left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x*(d + c^2*d*x^2)^(5/2)),x]","-\frac{2 b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 d x^2+d}}+\frac{2 b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 d x^2+d}}+\frac{7 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{7 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{2 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{2 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{b c x \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d^2 \sqrt{c^2 d x^2+d}}-\frac{14 b \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d^2 \sqrt{c^2 d x^2+d}}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{3 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b^2}{3 d^2 \sqrt{c^2 d x^2+d}}","-\frac{2 b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 d x^2+d}}+\frac{2 b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 d x^2+d}}+\frac{7 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{7 i b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{2 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{2 b^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{b c x \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d^2 \sqrt{c^2 d x^2+d}}-\frac{14 b \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d^2 \sqrt{c^2 d x^2+d}}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{3 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{b^2}{3 d^2 \sqrt{c^2 d x^2+d}}",1,"-b^2/(3*d^2*Sqrt[d + c^2*d*x^2]) - (b*c*x*(a + b*ArcSinh[c*x]))/(3*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) + (a + b*ArcSinh[c*x])^2/(3*d*(d + c^2*d*x^2)^(3/2)) + (a + b*ArcSinh[c*x])^2/(d^2*Sqrt[d + c^2*d*x^2]) - (14*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(3*d^2*Sqrt[d + c^2*d*x^2]) - (2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2*ArcTanh[E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2]) - (2*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, -E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2]) + (((7*I)/3)*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2]) - (((7*I)/3)*b^2*Sqrt[1 + c^2*x^2]*PolyLog[2, I*E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2]) + (2*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2]) + (2*b^2*Sqrt[1 + c^2*x^2]*PolyLog[3, -E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2]) - (2*b^2*Sqrt[1 + c^2*x^2]*PolyLog[3, E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2])","A",25,13,28,0.4643,1,"{5755, 5764, 5760, 4182, 2531, 2282, 6589, 5693, 4180, 2279, 2391, 5690, 261}"
317,1,421,0,0.6550934,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^2 \left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^2*(d + c^2*d*x^2)^(5/2)),x]","\frac{5 b^2 c \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{b^2 c \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{8 c^2 x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{8 c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{16 b c \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{4 b c \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{4 c^2 x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d x \left(c^2 d x^2+d\right)^{3/2}}+\frac{b^2 c^2 x}{3 d^2 \sqrt{c^2 d x^2+d}}","\frac{5 b^2 c \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{b^2 c \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{8 c^2 x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{8 c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{16 b c \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{4 b c \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{4 c^2 x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d x \left(c^2 d x^2+d\right)^{3/2}}+\frac{b^2 c^2 x}{3 d^2 \sqrt{c^2 d x^2+d}}",1,"(b^2*c^2*x)/(3*d^2*Sqrt[d + c^2*d*x^2]) - (b*c*(a + b*ArcSinh[c*x]))/(3*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) - (a + b*ArcSinh[c*x])^2/(d*x*(d + c^2*d*x^2)^(3/2)) - (4*c^2*x*(a + b*ArcSinh[c*x])^2)/(3*d*(d + c^2*d*x^2)^(3/2)) - (8*c^2*x*(a + b*ArcSinh[c*x])^2)/(3*d^2*Sqrt[d + c^2*d*x^2]) - (8*c*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(3*d^2*Sqrt[d + c^2*d*x^2]) - (4*b*c*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^(2*ArcSinh[c*x])])/(d^2*Sqrt[d + c^2*d*x^2]) + (16*b*c*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(3*d^2*Sqrt[d + c^2*d*x^2]) + (5*b^2*c*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^(2*ArcSinh[c*x])])/(3*d^2*Sqrt[d + c^2*d*x^2]) + (b^2*c*Sqrt[1 + c^2*x^2]*PolyLog[2, E^(2*ArcSinh[c*x])])/(d^2*Sqrt[d + c^2*d*x^2])","A",19,14,28,0.5000,1,"{5747, 5690, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 191, 5755, 5720, 5461, 4182}"
318,1,687,0,1.2590011,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^3 \left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^3*(d + c^2*d*x^2)^(5/2)),x]","\frac{5 b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{5 b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{13 i b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{13 i b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{5 b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{d^2 \sqrt{c^2 d x^2+d}}+\frac{5 b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{2 b c^3 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{5 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^2 \sqrt{c^2 d x^2+d}}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{d^2 x \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{26 b c^2 \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{5 c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d^2 \sqrt{c^2 d x^2+d}}-\frac{5 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{6 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 d x^2 \left(c^2 d x^2+d\right)^{3/2}}+\frac{b^2 c^2}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{b^2 c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{d^2 \sqrt{c^2 d x^2+d}}","\frac{5 b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{5 b c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{13 i b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{13 i b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{5 b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c x)}\right)}{d^2 \sqrt{c^2 d x^2+d}}+\frac{5 b^2 c^2 \sqrt{c^2 x^2+1} \text{PolyLog}\left(3,e^{\sinh ^{-1}(c x)}\right)}{d^2 \sqrt{c^2 d x^2+d}}-\frac{2 b c^3 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{5 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 d^2 \sqrt{c^2 d x^2+d}}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{d^2 x \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}+\frac{26 b c^2 \sqrt{c^2 x^2+1} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{5 c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{d^2 \sqrt{c^2 d x^2+d}}-\frac{5 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{6 d \left(c^2 d x^2+d\right)^{3/2}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 d x^2 \left(c^2 d x^2+d\right)^{3/2}}+\frac{b^2 c^2}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{b^2 c^2 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{d^2 \sqrt{c^2 d x^2+d}}",1,"(b^2*c^2)/(3*d^2*Sqrt[d + c^2*d*x^2]) - (b*c*(a + b*ArcSinh[c*x]))/(d^2*x*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) - (2*b*c^3*x*(a + b*ArcSinh[c*x]))/(3*d^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) - (5*c^2*(a + b*ArcSinh[c*x])^2)/(6*d*(d + c^2*d*x^2)^(3/2)) - (a + b*ArcSinh[c*x])^2/(2*d*x^2*(d + c^2*d*x^2)^(3/2)) - (5*c^2*(a + b*ArcSinh[c*x])^2)/(2*d^2*Sqrt[d + c^2*d*x^2]) + (26*b*c^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(3*d^2*Sqrt[d + c^2*d*x^2]) + (5*c^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2*ArcTanh[E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2]) - (b^2*c^2*Sqrt[1 + c^2*x^2]*ArcTanh[Sqrt[1 + c^2*x^2]])/(d^2*Sqrt[d + c^2*d*x^2]) + (5*b*c^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, -E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2]) - (((13*I)/3)*b^2*c^2*Sqrt[1 + c^2*x^2]*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2]) + (((13*I)/3)*b^2*c^2*Sqrt[1 + c^2*x^2]*PolyLog[2, I*E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2]) - (5*b*c^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*PolyLog[2, E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2]) - (5*b^2*c^2*Sqrt[1 + c^2*x^2]*PolyLog[3, -E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2]) + (5*b^2*c^2*Sqrt[1 + c^2*x^2]*PolyLog[3, E^ArcSinh[c*x]])/(d^2*Sqrt[d + c^2*d*x^2])","A",39,18,28,0.6429,1,"{5747, 5755, 5764, 5760, 4182, 2531, 2282, 6589, 5693, 4180, 2279, 2391, 5690, 261, 266, 51, 63, 208}"
319,1,506,0,1.0941861,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{x^4 \left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(x^4*(d + c^2*d*x^2)^(5/2)),x]","-\frac{8 b^2 c^3 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{8 b^2 c^3 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{16 c^4 x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{16 c^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 x^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{32 b c^3 \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{32 b c^3 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{8 c^4 x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d \left(c^2 d x^2+d\right)^{3/2}}+\frac{2 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{d x \left(c^2 d x^2+d\right)^{3/2}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{3 d x^3 \left(c^2 d x^2+d\right)^{3/2}}-\frac{2 b^2 c^4 x}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{b^2 c^2}{3 d^2 x \sqrt{c^2 d x^2+d}}","-\frac{8 b^2 c^3 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{8 b^2 c^3 \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c x)}\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{16 c^4 x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{16 c^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{b c \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 x^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d}}-\frac{32 b c^3 \sqrt{c^2 x^2+1} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{32 b c^3 \sqrt{c^2 x^2+1} \tanh ^{-1}\left(e^{2 \sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{c^2 d x^2+d}}+\frac{8 c^4 x \left(a+b \sinh ^{-1}(c x)\right)^2}{3 d \left(c^2 d x^2+d\right)^{3/2}}+\frac{2 c^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{d x \left(c^2 d x^2+d\right)^{3/2}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{3 d x^3 \left(c^2 d x^2+d\right)^{3/2}}-\frac{2 b^2 c^4 x}{3 d^2 \sqrt{c^2 d x^2+d}}-\frac{b^2 c^2}{3 d^2 x \sqrt{c^2 d x^2+d}}",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*(a + b*ArcSinh[c*x]))/(3*d^2*x^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]) - (a + b*ArcSinh[c*x])^2/(3*d*x^3*(d + c^2*d*x^2)^(3/2)) + (2*c^2*(a + b*ArcSinh[c*x])^2)/(d*x*(d + c^2*d*x^2)^(3/2)) + (8*c^4*x*(a + b*ArcSinh[c*x])^2)/(3*d*(d + c^2*d*x^2)^(3/2)) + (16*c^4*x*(a + b*ArcSinh[c*x])^2)/(3*d^2*Sqrt[d + c^2*d*x^2]) + (16*c^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(3*d^2*Sqrt[d + c^2*d*x^2]) + (32*b*c^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*ArcTanh[E^(2*ArcSinh[c*x])])/(3*d^2*Sqrt[d + c^2*d*x^2]) - (32*b*c^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(3*d^2*Sqrt[d + c^2*d*x^2]) - (8*b^2*c^3*Sqrt[1 + c^2*x^2]*PolyLog[2, -E^(2*ArcSinh[c*x])])/(3*d^2*Sqrt[d + c^2*d*x^2]) - (8*b^2*c^3*Sqrt[1 + c^2*x^2]*PolyLog[2, E^(2*ArcSinh[c*x])])/(3*d^2*Sqrt[d + c^2*d*x^2])","A",32,15,28,0.5357,1,"{5747, 5690, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 191, 5755, 5720, 5461, 4182, 271}"
320,1,366,0,0.3528037,"\int \frac{\sinh ^{-1}(a x)^2}{\left(c+a^2 c x^2\right)^{7/2}} \, dx","Int[ArcSinh[a*x]^2/(c + a^2*c*x^2)^(7/2),x]","-\frac{8 \sqrt{a^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(a x)}\right)}{15 a c^3 \sqrt{a^2 c x^2+c}}-\frac{x}{3 c^3 \sqrt{a^2 c x^2+c}}-\frac{x}{30 c^3 \left(a^2 x^2+1\right) \sqrt{a^2 c x^2+c}}+\frac{8 x \sinh ^{-1}(a x)^2}{15 c^3 \sqrt{a^2 c x^2+c}}+\frac{8 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{15 a c^3 \sqrt{a^2 c x^2+c}}+\frac{4 x \sinh ^{-1}(a x)^2}{15 c^2 \left(a^2 c x^2+c\right)^{3/2}}+\frac{4 \sinh ^{-1}(a x)}{15 a c^3 \sqrt{a^2 x^2+1} \sqrt{a^2 c x^2+c}}+\frac{\sinh ^{-1}(a x)}{10 a c^3 \left(a^2 x^2+1\right)^{3/2} \sqrt{a^2 c x^2+c}}-\frac{16 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \log \left(e^{2 \sinh ^{-1}(a x)}+1\right)}{15 a c^3 \sqrt{a^2 c x^2+c}}+\frac{x \sinh ^{-1}(a x)^2}{5 c \left(a^2 c x^2+c\right)^{5/2}}","-\frac{8 \sqrt{a^2 x^2+1} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(a x)}\right)}{15 a c^3 \sqrt{a^2 c x^2+c}}-\frac{x}{3 c^3 \sqrt{a^2 c x^2+c}}-\frac{x}{30 c^3 \left(a^2 x^2+1\right) \sqrt{a^2 c x^2+c}}+\frac{8 x \sinh ^{-1}(a x)^2}{15 c^3 \sqrt{a^2 c x^2+c}}+\frac{8 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{15 a c^3 \sqrt{a^2 c x^2+c}}+\frac{4 x \sinh ^{-1}(a x)^2}{15 c^2 \left(a^2 c x^2+c\right)^{3/2}}+\frac{4 \sinh ^{-1}(a x)}{15 a c^3 \sqrt{a^2 x^2+1} \sqrt{a^2 c x^2+c}}+\frac{\sinh ^{-1}(a x)}{10 a c^3 \left(a^2 x^2+1\right)^{3/2} \sqrt{a^2 c x^2+c}}-\frac{16 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \log \left(e^{2 \sinh ^{-1}(a x)}+1\right)}{15 a c^3 \sqrt{a^2 c x^2+c}}+\frac{x \sinh ^{-1}(a x)^2}{5 c \left(a^2 c x^2+c\right)^{5/2}}",1,"-x/(3*c^3*Sqrt[c + a^2*c*x^2]) - x/(30*c^3*(1 + a^2*x^2)*Sqrt[c + a^2*c*x^2]) + ArcSinh[a*x]/(10*a*c^3*(1 + a^2*x^2)^(3/2)*Sqrt[c + a^2*c*x^2]) + (4*ArcSinh[a*x])/(15*a*c^3*Sqrt[1 + a^2*x^2]*Sqrt[c + a^2*c*x^2]) + (x*ArcSinh[a*x]^2)/(5*c*(c + a^2*c*x^2)^(5/2)) + (4*x*ArcSinh[a*x]^2)/(15*c^2*(c + a^2*c*x^2)^(3/2)) + (8*x*ArcSinh[a*x]^2)/(15*c^3*Sqrt[c + a^2*c*x^2]) + (8*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(15*a*c^3*Sqrt[c + a^2*c*x^2]) - (16*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]*Log[1 + E^(2*ArcSinh[a*x])])/(15*a*c^3*Sqrt[c + a^2*c*x^2]) - (8*Sqrt[1 + a^2*x^2]*PolyLog[2, -E^(2*ArcSinh[a*x])])/(15*a*c^3*Sqrt[c + a^2*c*x^2])","A",13,10,21,0.4762,1,"{5690, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 191, 192}"
321,0,0,0,0.1521915,"\int x^m \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^m*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2,x]","\int x^m \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","\frac{\left(c^2 d x^2+d\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2 x^{m+1}}{m+6}+\frac{5 d \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2 x^{m+1}}{(m+4) (m+6)}+\frac{15 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2 x^{m+1}}{(m+6) \left(m^2+6 m+8\right)}-\frac{30 b c d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^{m+2}}{(m+2)^2 (m+4) (m+6) \sqrt{c^2 x^2+1}}-\frac{10 b c d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^{m+2}}{(m+6) \left(m^2+6 m+8\right) \sqrt{c^2 x^2+1}}-\frac{2 b c d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^{m+2}}{\left(m^2+8 m+12\right) \sqrt{c^2 x^2+1}}+\frac{10 b^2 c^2 d^2 (3 m+10) \sqrt{c^2 d x^2+d} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};-c^2 x^2\right) x^{m+3}}{(m+2) (m+3) (m+4)^3 (m+6) \sqrt{c^2 x^2+1}}+\frac{2 b^2 c^2 d^2 \left(15 m^2+130 m+264\right) \sqrt{c^2 d x^2+d} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};-c^2 x^2\right) x^{m+3}}{(m+2) (m+3) (m+4)^2 (m+6)^3 \sqrt{c^2 x^2+1}}+\frac{30 b^2 c^2 d^2 \sqrt{c^2 d x^2+d} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};-c^2 x^2\right) x^{m+3}}{(m+2)^2 (m+3) (m+4) (m+6) \sqrt{c^2 x^2+1}}+\frac{2 b^2 c^2 d^2 \left(m^2+15 m+52\right) \sqrt{c^2 d x^2+d} x^{m+3}}{(m+4)^2 (m+6)^3}+\frac{10 b^2 c^2 d^2 \sqrt{c^2 d x^2+d} x^{m+3}}{(m+4)^3 (m+6)}-\frac{4 b c^3 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^{m+4}}{(m+4) (m+6) \sqrt{c^2 x^2+1}}-\frac{10 b c^3 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^{m+4}}{(m+4)^2 (m+6) \sqrt{c^2 x^2+1}}+\frac{2 b^2 c^4 d^2 \sqrt{c^2 d x^2+d} x^{m+5}}{(m+6)^3}-\frac{2 b c^5 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^{m+6}}{(m+6)^2 \sqrt{c^2 x^2+1}}+\frac{15 d^3 \text{Int}\left(\frac{x^m \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 d x^2+d}},x\right)}{(m+6) \left(m^2+6 m+8\right)}",0,"Defer[Int][x^m*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2, x]","A",0,0,0,0,-1,"{}"
322,0,0,0,0.1513213,"\int x^m \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^m*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2,x]","\int x^m \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","\frac{3 d^2 \text{Int}\left(\frac{x^m \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 d x^2+d}},x\right)}{m^2+6 m+8}+\frac{3 d x^{m+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{m^2+6 m+8}-\frac{2 b c d x^{m+2} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{\left(m^2+6 m+8\right) \sqrt{c^2 x^2+1}}+\frac{x^{m+1} \left(c^2 d x^2+d\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{m+4}-\frac{6 b c d x^{m+2} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{(m+2)^2 (m+4) \sqrt{c^2 x^2+1}}-\frac{2 b c^3 d x^{m+4} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{(m+4)^2 \sqrt{c^2 x^2+1}}+\frac{2 b^2 c^2 d (3 m+10) x^{m+3} \sqrt{c^2 d x^2+d} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};-c^2 x^2\right)}{(m+2) (m+3) (m+4)^3 \sqrt{c^2 x^2+1}}+\frac{6 b^2 c^2 d x^{m+3} \sqrt{c^2 d x^2+d} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};-c^2 x^2\right)}{(m+2)^2 (m+3) (m+4) \sqrt{c^2 x^2+1}}+\frac{2 b^2 c^2 d x^{m+3} \sqrt{c^2 d x^2+d}}{(m+4)^3}",0,"Defer[Int][x^m*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2, x]","A",0,0,0,0,-1,"{}"
323,0,0,0,0.1362418,"\int x^m \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[x^m*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2,x]","\int x^m \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","\frac{d \text{Int}\left(\frac{x^m \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 d x^2+d}},x\right)}{m+2}+\frac{x^{m+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{m+2}-\frac{2 b c x^{m+2} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{(m+2)^2 \sqrt{c^2 x^2+1}}+\frac{2 b^2 c^2 x^{m+3} \sqrt{c^2 d x^2+d} \, _2F_1\left(\frac{1}{2},\frac{m+3}{2};\frac{m+5}{2};-c^2 x^2\right)}{(m+2)^2 (m+3) \sqrt{c^2 x^2+1}}",0,"Defer[Int][x^m*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2, x]","A",0,0,0,0,-1,"{}"
324,0,0,0,0.1420207,"\int \frac{x^m \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+c^2 d x^2}} \, dx","Int[(x^m*(a + b*ArcSinh[c*x])^2)/Sqrt[d + c^2*d*x^2],x]","\int \frac{x^m \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+c^2 d x^2}} \, dx","\text{Int}\left(\frac{x^m \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{c^2 d x^2+d}},x\right)",0,"Defer[Int][(x^m*(a + b*ArcSinh[c*x])^2)/Sqrt[d + c^2*d*x^2], x]","A",0,0,0,0,-1,"{}"
325,0,0,0,0.1599242,"\int \frac{x^m \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^{3/2}} \, dx","Int[(x^m*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^(3/2),x]","\int \frac{x^m \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{x^m \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(c^2 d x^2+d\right)^{3/2}},x\right)",0,"Defer[Int][(x^m*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
326,0,0,0,0.1592737,"\int \frac{x^m \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^{5/2}} \, dx","Int[(x^m*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^(5/2),x]","\int \frac{x^m \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+c^2 d x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{x^m \left(a+b \sinh ^{-1}(c x)\right)^2}{\left(c^2 d x^2+d\right)^{5/2}},x\right)",0,"Defer[Int][(x^m*(a + b*ArcSinh[c*x])^2)/(d + c^2*d*x^2)^(5/2), x]","A",0,0,0,0,-1,"{}"
327,0,0,0,0.0917486,"\int \frac{x^m \sinh ^{-1}(a x)^2}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^m*ArcSinh[a*x]^2)/Sqrt[1 + a^2*x^2],x]","\int \frac{x^m \sinh ^{-1}(a x)^2}{\sqrt{1+a^2 x^2}} \, dx","\text{Int}\left(\frac{x^m \sinh ^{-1}(a x)^2}{\sqrt{a^2 x^2+1}},x\right)",0,"Defer[Int][(x^m*ArcSinh[a*x]^2)/Sqrt[1 + a^2*x^2], x]","A",0,0,0,0,-1,"{}"
328,1,359,0,0.7277174,"\int \left(c+a^2 c x^2\right)^3 \sinh ^{-1}(a x)^3 \, dx","Int[(c + a^2*c*x^2)^3*ArcSinh[a*x]^3,x]","-\frac{6 c^3 \left(a^2 x^2+1\right)^{7/2}}{2401 a}-\frac{2664 c^3 \left(a^2 x^2+1\right)^{5/2}}{214375 a}-\frac{30256 c^3 \left(a^2 x^2+1\right)^{3/2}}{385875 a}-\frac{413312 c^3 \sqrt{a^2 x^2+1}}{128625 a}+\frac{6}{343} a^6 c^3 x^7 \sinh ^{-1}(a x)+\frac{702 a^4 c^3 x^5 \sinh ^{-1}(a x)}{6125}+\frac{1514 a^2 c^3 x^3 \sinh ^{-1}(a x)}{3675}+\frac{1}{7} c^3 x \left(a^2 x^2+1\right)^3 \sinh ^{-1}(a x)^3+\frac{6}{35} c^3 x \left(a^2 x^2+1\right)^2 \sinh ^{-1}(a x)^3+\frac{8}{35} c^3 x \left(a^2 x^2+1\right) \sinh ^{-1}(a x)^3-\frac{3 c^3 \left(a^2 x^2+1\right)^{7/2} \sinh ^{-1}(a x)^2}{49 a}-\frac{18 c^3 \left(a^2 x^2+1\right)^{5/2} \sinh ^{-1}(a x)^2}{175 a}-\frac{8 c^3 \left(a^2 x^2+1\right)^{3/2} \sinh ^{-1}(a x)^2}{35 a}-\frac{48 c^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{35 a}+\frac{16}{35} c^3 x \sinh ^{-1}(a x)^3+\frac{4322 c^3 x \sinh ^{-1}(a x)}{1225}","-\frac{6 c^3 \left(a^2 x^2+1\right)^{7/2}}{2401 a}-\frac{2664 c^3 \left(a^2 x^2+1\right)^{5/2}}{214375 a}-\frac{30256 c^3 \left(a^2 x^2+1\right)^{3/2}}{385875 a}-\frac{413312 c^3 \sqrt{a^2 x^2+1}}{128625 a}+\frac{6}{343} a^6 c^3 x^7 \sinh ^{-1}(a x)+\frac{702 a^4 c^3 x^5 \sinh ^{-1}(a x)}{6125}+\frac{1514 a^2 c^3 x^3 \sinh ^{-1}(a x)}{3675}+\frac{1}{7} c^3 x \left(a^2 x^2+1\right)^3 \sinh ^{-1}(a x)^3+\frac{6}{35} c^3 x \left(a^2 x^2+1\right)^2 \sinh ^{-1}(a x)^3+\frac{8}{35} c^3 x \left(a^2 x^2+1\right) \sinh ^{-1}(a x)^3-\frac{3 c^3 \left(a^2 x^2+1\right)^{7/2} \sinh ^{-1}(a x)^2}{49 a}-\frac{18 c^3 \left(a^2 x^2+1\right)^{5/2} \sinh ^{-1}(a x)^2}{175 a}-\frac{8 c^3 \left(a^2 x^2+1\right)^{3/2} \sinh ^{-1}(a x)^2}{35 a}-\frac{48 c^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{35 a}+\frac{16}{35} c^3 x \sinh ^{-1}(a x)^3+\frac{4322 c^3 x \sinh ^{-1}(a x)}{1225}",1,"(-413312*c^3*Sqrt[1 + a^2*x^2])/(128625*a) - (30256*c^3*(1 + a^2*x^2)^(3/2))/(385875*a) - (2664*c^3*(1 + a^2*x^2)^(5/2))/(214375*a) - (6*c^3*(1 + a^2*x^2)^(7/2))/(2401*a) + (4322*c^3*x*ArcSinh[a*x])/1225 + (1514*a^2*c^3*x^3*ArcSinh[a*x])/3675 + (702*a^4*c^3*x^5*ArcSinh[a*x])/6125 + (6*a^6*c^3*x^7*ArcSinh[a*x])/343 - (48*c^3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(35*a) - (8*c^3*(1 + a^2*x^2)^(3/2)*ArcSinh[a*x]^2)/(35*a) - (18*c^3*(1 + a^2*x^2)^(5/2)*ArcSinh[a*x]^2)/(175*a) - (3*c^3*(1 + a^2*x^2)^(7/2)*ArcSinh[a*x]^2)/(49*a) + (16*c^3*x*ArcSinh[a*x]^3)/35 + (8*c^3*x*(1 + a^2*x^2)*ArcSinh[a*x]^3)/35 + (6*c^3*x*(1 + a^2*x^2)^2*ArcSinh[a*x]^3)/35 + (c^3*x*(1 + a^2*x^2)^3*ArcSinh[a*x]^3)/7","A",24,13,19,0.6842,1,"{5684, 5653, 5717, 261, 5679, 444, 43, 194, 12, 1247, 698, 1799, 1850}"
329,1,265,0,0.4214422,"\int \left(c+a^2 c x^2\right)^2 \sinh ^{-1}(a x)^3 \, dx","Int[(c + a^2*c*x^2)^2*ArcSinh[a*x]^3,x]","-\frac{6 c^2 \left(a^2 x^2+1\right)^{5/2}}{625 a}-\frac{272 c^2 \left(a^2 x^2+1\right)^{3/2}}{3375 a}-\frac{4144 c^2 \sqrt{a^2 x^2+1}}{1125 a}+\frac{6}{125} a^4 c^2 x^5 \sinh ^{-1}(a x)+\frac{76}{225} a^2 c^2 x^3 \sinh ^{-1}(a x)+\frac{1}{5} c^2 x \left(a^2 x^2+1\right)^2 \sinh ^{-1}(a x)^3+\frac{4}{15} c^2 x \left(a^2 x^2+1\right) \sinh ^{-1}(a x)^3-\frac{3 c^2 \left(a^2 x^2+1\right)^{5/2} \sinh ^{-1}(a x)^2}{25 a}-\frac{4 c^2 \left(a^2 x^2+1\right)^{3/2} \sinh ^{-1}(a x)^2}{15 a}-\frac{8 c^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{5 a}+\frac{8}{15} c^2 x \sinh ^{-1}(a x)^3+\frac{298}{75} c^2 x \sinh ^{-1}(a x)","-\frac{6 c^2 \left(a^2 x^2+1\right)^{5/2}}{625 a}-\frac{272 c^2 \left(a^2 x^2+1\right)^{3/2}}{3375 a}-\frac{4144 c^2 \sqrt{a^2 x^2+1}}{1125 a}+\frac{6}{125} a^4 c^2 x^5 \sinh ^{-1}(a x)+\frac{76}{225} a^2 c^2 x^3 \sinh ^{-1}(a x)+\frac{1}{5} c^2 x \left(a^2 x^2+1\right)^2 \sinh ^{-1}(a x)^3+\frac{4}{15} c^2 x \left(a^2 x^2+1\right) \sinh ^{-1}(a x)^3-\frac{3 c^2 \left(a^2 x^2+1\right)^{5/2} \sinh ^{-1}(a x)^2}{25 a}-\frac{4 c^2 \left(a^2 x^2+1\right)^{3/2} \sinh ^{-1}(a x)^2}{15 a}-\frac{8 c^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{5 a}+\frac{8}{15} c^2 x \sinh ^{-1}(a x)^3+\frac{298}{75} c^2 x \sinh ^{-1}(a x)",1,"(-4144*c^2*Sqrt[1 + a^2*x^2])/(1125*a) - (272*c^2*(1 + a^2*x^2)^(3/2))/(3375*a) - (6*c^2*(1 + a^2*x^2)^(5/2))/(625*a) + (298*c^2*x*ArcSinh[a*x])/75 + (76*a^2*c^2*x^3*ArcSinh[a*x])/225 + (6*a^4*c^2*x^5*ArcSinh[a*x])/125 - (8*c^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/(5*a) - (4*c^2*(1 + a^2*x^2)^(3/2)*ArcSinh[a*x]^2)/(15*a) - (3*c^2*(1 + a^2*x^2)^(5/2)*ArcSinh[a*x]^2)/(25*a) + (8*c^2*x*ArcSinh[a*x]^3)/15 + (4*c^2*x*(1 + a^2*x^2)*ArcSinh[a*x]^3)/15 + (c^2*x*(1 + a^2*x^2)^2*ArcSinh[a*x]^3)/5","A",17,11,19,0.5789,1,"{5684, 5653, 5717, 261, 5679, 444, 43, 194, 12, 1247, 698}"
330,1,153,0,0.2171834,"\int \left(c+a^2 c x^2\right) \sinh ^{-1}(a x)^3 \, dx","Int[(c + a^2*c*x^2)*ArcSinh[a*x]^3,x]","-\frac{2 c \left(a^2 x^2+1\right)^{3/2}}{27 a}-\frac{40 c \sqrt{a^2 x^2+1}}{9 a}+\frac{2}{9} a^2 c x^3 \sinh ^{-1}(a x)+\frac{1}{3} c x \left(a^2 x^2+1\right) \sinh ^{-1}(a x)^3-\frac{c \left(a^2 x^2+1\right)^{3/2} \sinh ^{-1}(a x)^2}{3 a}-\frac{2 c \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{a}+\frac{2}{3} c x \sinh ^{-1}(a x)^3+\frac{14}{3} c x \sinh ^{-1}(a x)","-\frac{2 c \left(a^2 x^2+1\right)^{3/2}}{27 a}-\frac{40 c \sqrt{a^2 x^2+1}}{9 a}+\frac{2}{9} a^2 c x^3 \sinh ^{-1}(a x)+\frac{1}{3} c x \left(a^2 x^2+1\right) \sinh ^{-1}(a x)^3-\frac{c \left(a^2 x^2+1\right)^{3/2} \sinh ^{-1}(a x)^2}{3 a}-\frac{2 c \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2}{a}+\frac{2}{3} c x \sinh ^{-1}(a x)^3+\frac{14}{3} c x \sinh ^{-1}(a x)",1,"(-40*c*Sqrt[1 + a^2*x^2])/(9*a) - (2*c*(1 + a^2*x^2)^(3/2))/(27*a) + (14*c*x*ArcSinh[a*x])/3 + (2*a^2*c*x^3*ArcSinh[a*x])/9 - (2*c*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2)/a - (c*(1 + a^2*x^2)^(3/2)*ArcSinh[a*x]^2)/(3*a) + (2*c*x*ArcSinh[a*x]^3)/3 + (c*x*(1 + a^2*x^2)*ArcSinh[a*x]^3)/3","A",10,7,17,0.4118,1,"{5684, 5653, 5717, 261, 5679, 444, 43}"
331,1,174,0,0.1300527,"\int \frac{\sinh ^{-1}(a x)^3}{c+a^2 c x^2} \, dx","Int[ArcSinh[a*x]^3/(c + a^2*c*x^2),x]","-\frac{3 i \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(a x)}\right)}{a c}+\frac{3 i \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(a x)}\right)}{a c}+\frac{6 i \sinh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(a x)}\right)}{a c}-\frac{6 i \sinh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\sinh ^{-1}(a x)}\right)}{a c}-\frac{6 i \text{PolyLog}\left(4,-i e^{\sinh ^{-1}(a x)}\right)}{a c}+\frac{6 i \text{PolyLog}\left(4,i e^{\sinh ^{-1}(a x)}\right)}{a c}+\frac{2 \sinh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)}{a c}","-\frac{3 i \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(a x)}\right)}{a c}+\frac{3 i \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(a x)}\right)}{a c}+\frac{6 i \sinh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(a x)}\right)}{a c}-\frac{6 i \sinh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\sinh ^{-1}(a x)}\right)}{a c}-\frac{6 i \text{PolyLog}\left(4,-i e^{\sinh ^{-1}(a x)}\right)}{a c}+\frac{6 i \text{PolyLog}\left(4,i e^{\sinh ^{-1}(a x)}\right)}{a c}+\frac{2 \sinh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)}{a c}",1,"(2*ArcSinh[a*x]^3*ArcTan[E^ArcSinh[a*x]])/(a*c) - ((3*I)*ArcSinh[a*x]^2*PolyLog[2, (-I)*E^ArcSinh[a*x]])/(a*c) + ((3*I)*ArcSinh[a*x]^2*PolyLog[2, I*E^ArcSinh[a*x]])/(a*c) + ((6*I)*ArcSinh[a*x]*PolyLog[3, (-I)*E^ArcSinh[a*x]])/(a*c) - ((6*I)*ArcSinh[a*x]*PolyLog[3, I*E^ArcSinh[a*x]])/(a*c) - ((6*I)*PolyLog[4, (-I)*E^ArcSinh[a*x]])/(a*c) + ((6*I)*PolyLog[4, I*E^ArcSinh[a*x]])/(a*c)","A",10,6,19,0.3158,1,"{5693, 4180, 2531, 6609, 2282, 6589}"
332,1,294,0,0.3061818,"\int \frac{\sinh ^{-1}(a x)^3}{\left(c+a^2 c x^2\right)^2} \, dx","Int[ArcSinh[a*x]^3/(c + a^2*c*x^2)^2,x]","-\frac{3 i \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(a x)}\right)}{2 a c^2}+\frac{3 i \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(a x)}\right)}{2 a c^2}+\frac{3 i \sinh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(a x)}\right)}{a c^2}-\frac{3 i \sinh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\sinh ^{-1}(a x)}\right)}{a c^2}+\frac{3 i \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(a x)}\right)}{a c^2}-\frac{3 i \text{PolyLog}\left(2,i e^{\sinh ^{-1}(a x)}\right)}{a c^2}-\frac{3 i \text{PolyLog}\left(4,-i e^{\sinh ^{-1}(a x)}\right)}{a c^2}+\frac{3 i \text{PolyLog}\left(4,i e^{\sinh ^{-1}(a x)}\right)}{a c^2}+\frac{x \sinh ^{-1}(a x)^3}{2 c^2 \left(a^2 x^2+1\right)}+\frac{3 \sinh ^{-1}(a x)^2}{2 a c^2 \sqrt{a^2 x^2+1}}+\frac{\sinh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)}{a c^2}-\frac{6 \sinh ^{-1}(a x) \tan ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)}{a c^2}","-\frac{3 i \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(a x)}\right)}{2 a c^2}+\frac{3 i \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(a x)}\right)}{2 a c^2}+\frac{3 i \sinh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(a x)}\right)}{a c^2}-\frac{3 i \sinh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\sinh ^{-1}(a x)}\right)}{a c^2}+\frac{3 i \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(a x)}\right)}{a c^2}-\frac{3 i \text{PolyLog}\left(2,i e^{\sinh ^{-1}(a x)}\right)}{a c^2}-\frac{3 i \text{PolyLog}\left(4,-i e^{\sinh ^{-1}(a x)}\right)}{a c^2}+\frac{3 i \text{PolyLog}\left(4,i e^{\sinh ^{-1}(a x)}\right)}{a c^2}+\frac{x \sinh ^{-1}(a x)^3}{2 c^2 \left(a^2 x^2+1\right)}+\frac{3 \sinh ^{-1}(a x)^2}{2 a c^2 \sqrt{a^2 x^2+1}}+\frac{\sinh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)}{a c^2}-\frac{6 \sinh ^{-1}(a x) \tan ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)}{a c^2}",1,"(3*ArcSinh[a*x]^2)/(2*a*c^2*Sqrt[1 + a^2*x^2]) + (x*ArcSinh[a*x]^3)/(2*c^2*(1 + a^2*x^2)) - (6*ArcSinh[a*x]*ArcTan[E^ArcSinh[a*x]])/(a*c^2) + (ArcSinh[a*x]^3*ArcTan[E^ArcSinh[a*x]])/(a*c^2) + ((3*I)*PolyLog[2, (-I)*E^ArcSinh[a*x]])/(a*c^2) - (((3*I)/2)*ArcSinh[a*x]^2*PolyLog[2, (-I)*E^ArcSinh[a*x]])/(a*c^2) - ((3*I)*PolyLog[2, I*E^ArcSinh[a*x]])/(a*c^2) + (((3*I)/2)*ArcSinh[a*x]^2*PolyLog[2, I*E^ArcSinh[a*x]])/(a*c^2) + ((3*I)*ArcSinh[a*x]*PolyLog[3, (-I)*E^ArcSinh[a*x]])/(a*c^2) - ((3*I)*ArcSinh[a*x]*PolyLog[3, I*E^ArcSinh[a*x]])/(a*c^2) - ((3*I)*PolyLog[4, (-I)*E^ArcSinh[a*x]])/(a*c^2) + ((3*I)*PolyLog[4, I*E^ArcSinh[a*x]])/(a*c^2)","A",18,10,19,0.5263,1,"{5690, 5693, 4180, 2531, 6609, 2282, 6589, 5717, 2279, 2391}"
333,1,409,0,0.5168482,"\int \frac{\sinh ^{-1}(a x)^3}{\left(c+a^2 c x^2\right)^3} \, dx","Int[ArcSinh[a*x]^3/(c + a^2*c*x^2)^3,x]","-\frac{9 i \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(a x)}\right)}{8 a c^3}+\frac{9 i \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(a x)}\right)}{8 a c^3}+\frac{9 i \sinh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(a x)}\right)}{4 a c^3}-\frac{9 i \sinh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\sinh ^{-1}(a x)}\right)}{4 a c^3}+\frac{5 i \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(a x)}\right)}{2 a c^3}-\frac{5 i \text{PolyLog}\left(2,i e^{\sinh ^{-1}(a x)}\right)}{2 a c^3}-\frac{9 i \text{PolyLog}\left(4,-i e^{\sinh ^{-1}(a x)}\right)}{4 a c^3}+\frac{9 i \text{PolyLog}\left(4,i e^{\sinh ^{-1}(a x)}\right)}{4 a c^3}-\frac{1}{4 a c^3 \sqrt{a^2 x^2+1}}+\frac{3 x \sinh ^{-1}(a x)^3}{8 c^3 \left(a^2 x^2+1\right)}+\frac{x \sinh ^{-1}(a x)^3}{4 c^3 \left(a^2 x^2+1\right)^2}+\frac{9 \sinh ^{-1}(a x)^2}{8 a c^3 \sqrt{a^2 x^2+1}}+\frac{\sinh ^{-1}(a x)^2}{4 a c^3 \left(a^2 x^2+1\right)^{3/2}}-\frac{x \sinh ^{-1}(a x)}{4 c^3 \left(a^2 x^2+1\right)}+\frac{3 \sinh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)}{4 a c^3}-\frac{5 \sinh ^{-1}(a x) \tan ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)}{a c^3}","-\frac{9 i \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(a x)}\right)}{8 a c^3}+\frac{9 i \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,i e^{\sinh ^{-1}(a x)}\right)}{8 a c^3}+\frac{9 i \sinh ^{-1}(a x) \text{PolyLog}\left(3,-i e^{\sinh ^{-1}(a x)}\right)}{4 a c^3}-\frac{9 i \sinh ^{-1}(a x) \text{PolyLog}\left(3,i e^{\sinh ^{-1}(a x)}\right)}{4 a c^3}+\frac{5 i \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(a x)}\right)}{2 a c^3}-\frac{5 i \text{PolyLog}\left(2,i e^{\sinh ^{-1}(a x)}\right)}{2 a c^3}-\frac{9 i \text{PolyLog}\left(4,-i e^{\sinh ^{-1}(a x)}\right)}{4 a c^3}+\frac{9 i \text{PolyLog}\left(4,i e^{\sinh ^{-1}(a x)}\right)}{4 a c^3}-\frac{1}{4 a c^3 \sqrt{a^2 x^2+1}}+\frac{3 x \sinh ^{-1}(a x)^3}{8 c^3 \left(a^2 x^2+1\right)}+\frac{x \sinh ^{-1}(a x)^3}{4 c^3 \left(a^2 x^2+1\right)^2}+\frac{9 \sinh ^{-1}(a x)^2}{8 a c^3 \sqrt{a^2 x^2+1}}+\frac{\sinh ^{-1}(a x)^2}{4 a c^3 \left(a^2 x^2+1\right)^{3/2}}-\frac{x \sinh ^{-1}(a x)}{4 c^3 \left(a^2 x^2+1\right)}+\frac{3 \sinh ^{-1}(a x)^3 \tan ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)}{4 a c^3}-\frac{5 \sinh ^{-1}(a x) \tan ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)}{a c^3}",1,"-1/(4*a*c^3*Sqrt[1 + a^2*x^2]) - (x*ArcSinh[a*x])/(4*c^3*(1 + a^2*x^2)) + ArcSinh[a*x]^2/(4*a*c^3*(1 + a^2*x^2)^(3/2)) + (9*ArcSinh[a*x]^2)/(8*a*c^3*Sqrt[1 + a^2*x^2]) + (x*ArcSinh[a*x]^3)/(4*c^3*(1 + a^2*x^2)^2) + (3*x*ArcSinh[a*x]^3)/(8*c^3*(1 + a^2*x^2)) - (5*ArcSinh[a*x]*ArcTan[E^ArcSinh[a*x]])/(a*c^3) + (3*ArcSinh[a*x]^3*ArcTan[E^ArcSinh[a*x]])/(4*a*c^3) + (((5*I)/2)*PolyLog[2, (-I)*E^ArcSinh[a*x]])/(a*c^3) - (((9*I)/8)*ArcSinh[a*x]^2*PolyLog[2, (-I)*E^ArcSinh[a*x]])/(a*c^3) - (((5*I)/2)*PolyLog[2, I*E^ArcSinh[a*x]])/(a*c^3) + (((9*I)/8)*ArcSinh[a*x]^2*PolyLog[2, I*E^ArcSinh[a*x]])/(a*c^3) + (((9*I)/4)*ArcSinh[a*x]*PolyLog[3, (-I)*E^ArcSinh[a*x]])/(a*c^3) - (((9*I)/4)*ArcSinh[a*x]*PolyLog[3, I*E^ArcSinh[a*x]])/(a*c^3) - (((9*I)/4)*PolyLog[4, (-I)*E^ArcSinh[a*x]])/(a*c^3) + (((9*I)/4)*PolyLog[4, I*E^ArcSinh[a*x]])/(a*c^3)","A",28,11,19,0.5789,1,"{5690, 5693, 4180, 2531, 6609, 2282, 6589, 5717, 2279, 2391, 261}"
334,1,509,0,0.5947541,"\int \left(c+a^2 c x^2\right)^{5/2} \sinh ^{-1}(a x)^3 \, dx","Int[(c + a^2*c*x^2)^(5/2)*ArcSinh[a*x]^3,x]","-\frac{65 a^3 c^2 x^4 \sqrt{a^2 c x^2+c}}{2304 \sqrt{a^2 x^2+1}}-\frac{865 a c^2 x^2 \sqrt{a^2 c x^2+c}}{2304 \sqrt{a^2 x^2+1}}-\frac{c^2 \left(a^2 x^2+1\right)^{5/2} \sqrt{a^2 c x^2+c}}{216 a}-\frac{15 a c^2 x^2 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{32 \sqrt{a^2 x^2+1}}+\frac{5}{16} c^2 x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^3+\frac{245}{384} c^2 x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)+\frac{1}{36} c^2 x \left(a^2 x^2+1\right)^2 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)+\frac{65}{576} c^2 x \left(a^2 x^2+1\right) \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)+\frac{5 c^2 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^4}{64 a \sqrt{a^2 x^2+1}}-\frac{c^2 \left(a^2 x^2+1\right)^{5/2} \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{12 a}-\frac{5 c^2 \left(a^2 x^2+1\right)^{3/2} \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{32 a}-\frac{115 c^2 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{768 a \sqrt{a^2 x^2+1}}+\frac{1}{6} x \left(a^2 c x^2+c\right)^{5/2} \sinh ^{-1}(a x)^3+\frac{5}{24} c x \left(a^2 c x^2+c\right)^{3/2} \sinh ^{-1}(a x)^3","-\frac{65 a^3 c^2 x^4 \sqrt{a^2 c x^2+c}}{2304 \sqrt{a^2 x^2+1}}-\frac{865 a c^2 x^2 \sqrt{a^2 c x^2+c}}{2304 \sqrt{a^2 x^2+1}}-\frac{c^2 \left(a^2 x^2+1\right)^{5/2} \sqrt{a^2 c x^2+c}}{216 a}-\frac{15 a c^2 x^2 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{32 \sqrt{a^2 x^2+1}}+\frac{5}{16} c^2 x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^3+\frac{245}{384} c^2 x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)+\frac{1}{36} c^2 x \left(a^2 x^2+1\right)^2 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)+\frac{65}{576} c^2 x \left(a^2 x^2+1\right) \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)+\frac{5 c^2 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^4}{64 a \sqrt{a^2 x^2+1}}-\frac{c^2 \left(a^2 x^2+1\right)^{5/2} \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{12 a}-\frac{5 c^2 \left(a^2 x^2+1\right)^{3/2} \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{32 a}-\frac{115 c^2 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{768 a \sqrt{a^2 x^2+1}}+\frac{1}{6} x \left(a^2 c x^2+c\right)^{5/2} \sinh ^{-1}(a x)^3+\frac{5}{24} c x \left(a^2 c x^2+c\right)^{3/2} \sinh ^{-1}(a x)^3",1,"(-865*a*c^2*x^2*Sqrt[c + a^2*c*x^2])/(2304*Sqrt[1 + a^2*x^2]) - (65*a^3*c^2*x^4*Sqrt[c + a^2*c*x^2])/(2304*Sqrt[1 + a^2*x^2]) - (c^2*(1 + a^2*x^2)^(5/2)*Sqrt[c + a^2*c*x^2])/(216*a) + (245*c^2*x*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x])/384 + (65*c^2*x*(1 + a^2*x^2)*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x])/576 + (c^2*x*(1 + a^2*x^2)^2*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x])/36 - (115*c^2*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^2)/(768*a*Sqrt[1 + a^2*x^2]) - (15*a*c^2*x^2*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^2)/(32*Sqrt[1 + a^2*x^2]) - (5*c^2*(1 + a^2*x^2)^(3/2)*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^2)/(32*a) - (c^2*(1 + a^2*x^2)^(5/2)*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^2)/(12*a) + (5*c^2*x*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^3)/16 + (5*c*x*(c + a^2*c*x^2)^(3/2)*ArcSinh[a*x]^3)/24 + (x*(c + a^2*c*x^2)^(5/2)*ArcSinh[a*x]^3)/6 + (5*c^2*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^4)/(64*a*Sqrt[1 + a^2*x^2])","A",24,9,21,0.4286,1,"{5684, 5682, 5675, 5661, 5758, 30, 5717, 14, 261}"
335,1,348,0,0.3479921,"\int \left(c+a^2 c x^2\right)^{3/2} \sinh ^{-1}(a x)^3 \, dx","Int[(c + a^2*c*x^2)^(3/2)*ArcSinh[a*x]^3,x]","-\frac{3 a^3 c x^4 \sqrt{a^2 c x^2+c}}{128 \sqrt{a^2 x^2+1}}-\frac{51 a c x^2 \sqrt{a^2 c x^2+c}}{128 \sqrt{a^2 x^2+1}}-\frac{9 a c x^2 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{16 \sqrt{a^2 x^2+1}}+\frac{1}{4} x \left(a^2 c x^2+c\right)^{3/2} \sinh ^{-1}(a x)^3+\frac{3}{8} c x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^3+\frac{45}{64} c x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)+\frac{3}{32} c x \left(a^2 x^2+1\right) \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)+\frac{3 c \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^4}{32 a \sqrt{a^2 x^2+1}}-\frac{3 c \left(a^2 x^2+1\right)^{3/2} \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{16 a}-\frac{27 c \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{128 a \sqrt{a^2 x^2+1}}","-\frac{3 a^3 c x^4 \sqrt{a^2 c x^2+c}}{128 \sqrt{a^2 x^2+1}}-\frac{51 a c x^2 \sqrt{a^2 c x^2+c}}{128 \sqrt{a^2 x^2+1}}-\frac{9 a c x^2 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{16 \sqrt{a^2 x^2+1}}+\frac{1}{4} x \left(a^2 c x^2+c\right)^{3/2} \sinh ^{-1}(a x)^3+\frac{3}{8} c x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^3+\frac{45}{64} c x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)+\frac{3}{32} c x \left(a^2 x^2+1\right) \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)+\frac{3 c \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^4}{32 a \sqrt{a^2 x^2+1}}-\frac{3 c \left(a^2 x^2+1\right)^{3/2} \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{16 a}-\frac{27 c \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{128 a \sqrt{a^2 x^2+1}}",1,"(-51*a*c*x^2*Sqrt[c + a^2*c*x^2])/(128*Sqrt[1 + a^2*x^2]) - (3*a^3*c*x^4*Sqrt[c + a^2*c*x^2])/(128*Sqrt[1 + a^2*x^2]) + (45*c*x*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x])/64 + (3*c*x*(1 + a^2*x^2)*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x])/32 - (27*c*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^2)/(128*a*Sqrt[1 + a^2*x^2]) - (9*a*c*x^2*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^2)/(16*Sqrt[1 + a^2*x^2]) - (3*c*(1 + a^2*x^2)^(3/2)*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^2)/(16*a) + (3*c*x*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^3)/8 + (x*(c + a^2*c*x^2)^(3/2)*ArcSinh[a*x]^3)/4 + (3*c*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^4)/(32*a*Sqrt[1 + a^2*x^2])","A",14,8,21,0.3810,1,"{5684, 5682, 5675, 5661, 5758, 30, 5717, 14}"
336,1,205,0,0.1764578,"\int \sqrt{c+a^2 c x^2} \sinh ^{-1}(a x)^3 \, dx","Int[Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^3,x]","-\frac{3 a x^2 \sqrt{a^2 c x^2+c}}{8 \sqrt{a^2 x^2+1}}+\frac{\sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^4}{8 a \sqrt{a^2 x^2+1}}+\frac{1}{2} x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^3-\frac{3 a x^2 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{4 \sqrt{a^2 x^2+1}}-\frac{3 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{8 a \sqrt{a^2 x^2+1}}+\frac{3}{4} x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)","-\frac{3 a x^2 \sqrt{a^2 c x^2+c}}{8 \sqrt{a^2 x^2+1}}+\frac{\sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^4}{8 a \sqrt{a^2 x^2+1}}+\frac{1}{2} x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^3-\frac{3 a x^2 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{4 \sqrt{a^2 x^2+1}}-\frac{3 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^2}{8 a \sqrt{a^2 x^2+1}}+\frac{3}{4} x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)",1,"(-3*a*x^2*Sqrt[c + a^2*c*x^2])/(8*Sqrt[1 + a^2*x^2]) + (3*x*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x])/4 - (3*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^2)/(8*a*Sqrt[1 + a^2*x^2]) - (3*a*x^2*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^2)/(4*Sqrt[1 + a^2*x^2]) + (x*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^3)/2 + (Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^4)/(8*a*Sqrt[1 + a^2*x^2])","A",6,5,21,0.2381,1,"{5682, 5675, 5661, 5758, 30}"
337,1,40,0,0.0784065,"\int \frac{\sinh ^{-1}(a x)^3}{\sqrt{c+a^2 c x^2}} \, dx","Int[ArcSinh[a*x]^3/Sqrt[c + a^2*c*x^2],x]","\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^4}{4 a \sqrt{a^2 c x^2+c}}","\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^4}{4 a \sqrt{a^2 c x^2+c}}",1,"(Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^4)/(4*a*Sqrt[c + a^2*c*x^2])","A",2,2,21,0.09524,1,"{5677, 5675}"
338,1,218,0,0.1880476,"\int \frac{\sinh ^{-1}(a x)^3}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[ArcSinh[a*x]^3/(c + a^2*c*x^2)^(3/2),x]","-\frac{3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(a x)}\right)}{a c \sqrt{a^2 c x^2+c}}+\frac{3 \sqrt{a^2 x^2+1} \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(a x)}\right)}{2 a c \sqrt{a^2 c x^2+c}}+\frac{x \sinh ^{-1}(a x)^3}{c \sqrt{a^2 c x^2+c}}+\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{a c \sqrt{a^2 c x^2+c}}-\frac{3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2 \log \left(e^{2 \sinh ^{-1}(a x)}+1\right)}{a c \sqrt{a^2 c x^2+c}}","-\frac{3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(a x)}\right)}{a c \sqrt{a^2 c x^2+c}}+\frac{3 \sqrt{a^2 x^2+1} \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(a x)}\right)}{2 a c \sqrt{a^2 c x^2+c}}+\frac{x \sinh ^{-1}(a x)^3}{c \sqrt{a^2 c x^2+c}}+\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{a c \sqrt{a^2 c x^2+c}}-\frac{3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2 \log \left(e^{2 \sinh ^{-1}(a x)}+1\right)}{a c \sqrt{a^2 c x^2+c}}",1,"(x*ArcSinh[a*x]^3)/(c*Sqrt[c + a^2*c*x^2]) + (Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(a*c*Sqrt[c + a^2*c*x^2]) - (3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2*Log[1 + E^(2*ArcSinh[a*x])])/(a*c*Sqrt[c + a^2*c*x^2]) - (3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]*PolyLog[2, -E^(2*ArcSinh[a*x])])/(a*c*Sqrt[c + a^2*c*x^2]) + (3*Sqrt[1 + a^2*x^2]*PolyLog[3, -E^(2*ArcSinh[a*x])])/(2*a*c*Sqrt[c + a^2*c*x^2])","A",7,7,21,0.3333,1,"{5687, 5714, 3718, 2190, 2531, 2282, 6589}"
339,1,363,0,0.3288105,"\int \frac{\sinh ^{-1}(a x)^3}{\left(c+a^2 c x^2\right)^{5/2}} \, dx","Int[ArcSinh[a*x]^3/(c + a^2*c*x^2)^(5/2),x]","-\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(a x)}\right)}{a c^2 \sqrt{a^2 c x^2+c}}+\frac{\sqrt{a^2 x^2+1} \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(a x)}\right)}{a c^2 \sqrt{a^2 c x^2+c}}+\frac{\sqrt{a^2 x^2+1} \log \left(a^2 x^2+1\right)}{2 a c^2 \sqrt{a^2 c x^2+c}}+\frac{2 x \sinh ^{-1}(a x)^3}{3 c^2 \sqrt{a^2 c x^2+c}}+\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{3 a c^2 \sqrt{a^2 c x^2+c}}+\frac{\sinh ^{-1}(a x)^2}{2 a c^2 \sqrt{a^2 x^2+1} \sqrt{a^2 c x^2+c}}-\frac{x \sinh ^{-1}(a x)}{c^2 \sqrt{a^2 c x^2+c}}-\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2 \log \left(e^{2 \sinh ^{-1}(a x)}+1\right)}{a c^2 \sqrt{a^2 c x^2+c}}+\frac{x \sinh ^{-1}(a x)^3}{3 c \left(a^2 c x^2+c\right)^{3/2}}","-\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(a x)}\right)}{a c^2 \sqrt{a^2 c x^2+c}}+\frac{\sqrt{a^2 x^2+1} \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(a x)}\right)}{a c^2 \sqrt{a^2 c x^2+c}}+\frac{\sqrt{a^2 x^2+1} \log \left(a^2 x^2+1\right)}{2 a c^2 \sqrt{a^2 c x^2+c}}+\frac{2 x \sinh ^{-1}(a x)^3}{3 c^2 \sqrt{a^2 c x^2+c}}+\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{3 a c^2 \sqrt{a^2 c x^2+c}}+\frac{\sinh ^{-1}(a x)^2}{2 a c^2 \sqrt{a^2 x^2+1} \sqrt{a^2 c x^2+c}}-\frac{x \sinh ^{-1}(a x)}{c^2 \sqrt{a^2 c x^2+c}}-\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2 \log \left(e^{2 \sinh ^{-1}(a x)}+1\right)}{a c^2 \sqrt{a^2 c x^2+c}}+\frac{x \sinh ^{-1}(a x)^3}{3 c \left(a^2 c x^2+c\right)^{3/2}}",1,"-((x*ArcSinh[a*x])/(c^2*Sqrt[c + a^2*c*x^2])) + ArcSinh[a*x]^2/(2*a*c^2*Sqrt[1 + a^2*x^2]*Sqrt[c + a^2*c*x^2]) + (x*ArcSinh[a*x]^3)/(3*c*(c + a^2*c*x^2)^(3/2)) + (2*x*ArcSinh[a*x]^3)/(3*c^2*Sqrt[c + a^2*c*x^2]) + (2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(3*a*c^2*Sqrt[c + a^2*c*x^2]) - (2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2*Log[1 + E^(2*ArcSinh[a*x])])/(a*c^2*Sqrt[c + a^2*c*x^2]) + (Sqrt[1 + a^2*x^2]*Log[1 + a^2*x^2])/(2*a*c^2*Sqrt[c + a^2*c*x^2]) - (2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]*PolyLog[2, -E^(2*ArcSinh[a*x])])/(a*c^2*Sqrt[c + a^2*c*x^2]) + (Sqrt[1 + a^2*x^2]*PolyLog[3, -E^(2*ArcSinh[a*x])])/(a*c^2*Sqrt[c + a^2*c*x^2])","A",11,10,21,0.4762,1,"{5690, 5687, 5714, 3718, 2190, 2531, 2282, 6589, 5717, 260}"
340,1,515,0,0.5259019,"\int \frac{\sinh ^{-1}(a x)^3}{\left(c+a^2 c x^2\right)^{7/2}} \, dx","Int[ArcSinh[a*x]^3/(c + a^2*c*x^2)^(7/2),x]","-\frac{8 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(a x)}\right)}{5 a c^3 \sqrt{a^2 c x^2+c}}+\frac{4 \sqrt{a^2 x^2+1} \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(a x)}\right)}{5 a c^3 \sqrt{a^2 c x^2+c}}-\frac{1}{20 a c^3 \sqrt{a^2 x^2+1} \sqrt{a^2 c x^2+c}}+\frac{\sqrt{a^2 x^2+1} \log \left(a^2 x^2+1\right)}{2 a c^3 \sqrt{a^2 c x^2+c}}+\frac{8 x \sinh ^{-1}(a x)^3}{15 c^3 \sqrt{a^2 c x^2+c}}+\frac{8 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{15 a c^3 \sqrt{a^2 c x^2+c}}+\frac{4 x \sinh ^{-1}(a x)^3}{15 c^2 \left(a^2 c x^2+c\right)^{3/2}}+\frac{2 \sinh ^{-1}(a x)^2}{5 a c^3 \sqrt{a^2 x^2+1} \sqrt{a^2 c x^2+c}}+\frac{3 \sinh ^{-1}(a x)^2}{20 a c^3 \left(a^2 x^2+1\right)^{3/2} \sqrt{a^2 c x^2+c}}-\frac{x \sinh ^{-1}(a x)}{c^3 \sqrt{a^2 c x^2+c}}-\frac{x \sinh ^{-1}(a x)}{10 c^3 \left(a^2 x^2+1\right) \sqrt{a^2 c x^2+c}}-\frac{8 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2 \log \left(e^{2 \sinh ^{-1}(a x)}+1\right)}{5 a c^3 \sqrt{a^2 c x^2+c}}+\frac{x \sinh ^{-1}(a x)^3}{5 c \left(a^2 c x^2+c\right)^{5/2}}","-\frac{8 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(a x)}\right)}{5 a c^3 \sqrt{a^2 c x^2+c}}+\frac{4 \sqrt{a^2 x^2+1} \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(a x)}\right)}{5 a c^3 \sqrt{a^2 c x^2+c}}-\frac{1}{20 a c^3 \sqrt{a^2 x^2+1} \sqrt{a^2 c x^2+c}}+\frac{\sqrt{a^2 x^2+1} \log \left(a^2 x^2+1\right)}{2 a c^3 \sqrt{a^2 c x^2+c}}+\frac{8 x \sinh ^{-1}(a x)^3}{15 c^3 \sqrt{a^2 c x^2+c}}+\frac{8 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{15 a c^3 \sqrt{a^2 c x^2+c}}+\frac{4 x \sinh ^{-1}(a x)^3}{15 c^2 \left(a^2 c x^2+c\right)^{3/2}}+\frac{2 \sinh ^{-1}(a x)^2}{5 a c^3 \sqrt{a^2 x^2+1} \sqrt{a^2 c x^2+c}}+\frac{3 \sinh ^{-1}(a x)^2}{20 a c^3 \left(a^2 x^2+1\right)^{3/2} \sqrt{a^2 c x^2+c}}-\frac{x \sinh ^{-1}(a x)}{c^3 \sqrt{a^2 c x^2+c}}-\frac{x \sinh ^{-1}(a x)}{10 c^3 \left(a^2 x^2+1\right) \sqrt{a^2 c x^2+c}}-\frac{8 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^2 \log \left(e^{2 \sinh ^{-1}(a x)}+1\right)}{5 a c^3 \sqrt{a^2 c x^2+c}}+\frac{x \sinh ^{-1}(a x)^3}{5 c \left(a^2 c x^2+c\right)^{5/2}}",1,"-1/(20*a*c^3*Sqrt[1 + a^2*x^2]*Sqrt[c + a^2*c*x^2]) - (x*ArcSinh[a*x])/(c^3*Sqrt[c + a^2*c*x^2]) - (x*ArcSinh[a*x])/(10*c^3*(1 + a^2*x^2)*Sqrt[c + a^2*c*x^2]) + (3*ArcSinh[a*x]^2)/(20*a*c^3*(1 + a^2*x^2)^(3/2)*Sqrt[c + a^2*c*x^2]) + (2*ArcSinh[a*x]^2)/(5*a*c^3*Sqrt[1 + a^2*x^2]*Sqrt[c + a^2*c*x^2]) + (x*ArcSinh[a*x]^3)/(5*c*(c + a^2*c*x^2)^(5/2)) + (4*x*ArcSinh[a*x]^3)/(15*c^2*(c + a^2*c*x^2)^(3/2)) + (8*x*ArcSinh[a*x]^3)/(15*c^3*Sqrt[c + a^2*c*x^2]) + (8*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(15*a*c^3*Sqrt[c + a^2*c*x^2]) - (8*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^2*Log[1 + E^(2*ArcSinh[a*x])])/(5*a*c^3*Sqrt[c + a^2*c*x^2]) + (Sqrt[1 + a^2*x^2]*Log[1 + a^2*x^2])/(2*a*c^3*Sqrt[c + a^2*c*x^2]) - (8*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]*PolyLog[2, -E^(2*ArcSinh[a*x])])/(5*a*c^3*Sqrt[c + a^2*c*x^2]) + (4*Sqrt[1 + a^2*x^2]*PolyLog[3, -E^(2*ArcSinh[a*x])])/(5*a*c^3*Sqrt[c + a^2*c*x^2])","A",17,11,21,0.5238,1,"{5690, 5687, 5714, 3718, 2190, 2531, 2282, 6589, 5717, 260, 261}"
341,0,0,0,0.0884131,"\int \frac{x^m \sinh ^{-1}(a x)^3}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^m*ArcSinh[a*x]^3)/Sqrt[1 + a^2*x^2],x]","\int \frac{x^m \sinh ^{-1}(a x)^3}{\sqrt{1+a^2 x^2}} \, dx","\text{Int}\left(\frac{x^m \sinh ^{-1}(a x)^3}{\sqrt{a^2 x^2+1}},x\right)",0,"Defer[Int][(x^m*ArcSinh[a*x]^3)/Sqrt[1 + a^2*x^2], x]","A",0,0,0,0,-1,"{}"
342,1,187,0,0.4984726,"\int \frac{x^4 \sinh ^{-1}(a x)^3}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^4*ArcSinh[a*x]^3)/Sqrt[1 + a^2*x^2],x]","\frac{45 x^2}{128 a^3}+\frac{x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{4 a^2}+\frac{3 x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{32 a^2}+\frac{9 x^2 \sinh ^{-1}(a x)^2}{16 a^3}-\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{8 a^4}-\frac{45 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{64 a^4}+\frac{3 \sinh ^{-1}(a x)^4}{32 a^5}+\frac{45 \sinh ^{-1}(a x)^2}{128 a^5}-\frac{3 x^4}{128 a}-\frac{3 x^4 \sinh ^{-1}(a x)^2}{16 a}","\frac{45 x^2}{128 a^3}+\frac{x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{4 a^2}+\frac{3 x^3 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{32 a^2}+\frac{9 x^2 \sinh ^{-1}(a x)^2}{16 a^3}-\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{8 a^4}-\frac{45 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{64 a^4}+\frac{3 \sinh ^{-1}(a x)^4}{32 a^5}+\frac{45 \sinh ^{-1}(a x)^2}{128 a^5}-\frac{3 x^4}{128 a}-\frac{3 x^4 \sinh ^{-1}(a x)^2}{16 a}",1,"(45*x^2)/(128*a^3) - (3*x^4)/(128*a) - (45*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(64*a^4) + (3*x^3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(32*a^2) + (45*ArcSinh[a*x]^2)/(128*a^5) + (9*x^2*ArcSinh[a*x]^2)/(16*a^3) - (3*x^4*ArcSinh[a*x]^2)/(16*a) - (3*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(8*a^4) + (x^3*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(4*a^2) + (3*ArcSinh[a*x]^4)/(32*a^5)","A",13,4,23,0.1739,1,"{5758, 5675, 5661, 30}"
343,1,153,0,0.3380494,"\int \frac{x^3 \sinh ^{-1}(a x)^3}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^3*ArcSinh[a*x]^3)/Sqrt[1 + a^2*x^2],x]","\frac{x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{3 a^2}+\frac{2 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{9 a^2}-\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{3 a^4}-\frac{40 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{9 a^4}+\frac{40 x}{9 a^3}+\frac{2 x \sinh ^{-1}(a x)^2}{a^3}-\frac{2 x^3}{27 a}-\frac{x^3 \sinh ^{-1}(a x)^2}{3 a}","\frac{x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{3 a^2}+\frac{2 x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{9 a^2}-\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{3 a^4}-\frac{40 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{9 a^4}+\frac{40 x}{9 a^3}+\frac{2 x \sinh ^{-1}(a x)^2}{a^3}-\frac{2 x^3}{27 a}-\frac{x^3 \sinh ^{-1}(a x)^2}{3 a}",1,"(40*x)/(9*a^3) - (2*x^3)/(27*a) - (40*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(9*a^4) + (2*x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(9*a^2) + (2*x*ArcSinh[a*x]^2)/a^3 - (x^3*ArcSinh[a*x]^2)/(3*a) - (2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(3*a^4) + (x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(3*a^2)","A",10,6,23,0.2609,1,"{5758, 5717, 5653, 8, 5661, 30}"
344,1,105,0,0.2245126,"\int \frac{x^2 \sinh ^{-1}(a x)^3}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^2*ArcSinh[a*x]^3)/Sqrt[1 + a^2*x^2],x]","\frac{x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{2 a^2}+\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{4 a^2}-\frac{\sinh ^{-1}(a x)^4}{8 a^3}-\frac{3 \sinh ^{-1}(a x)^2}{8 a^3}-\frac{3 x^2}{8 a}-\frac{3 x^2 \sinh ^{-1}(a x)^2}{4 a}","\frac{x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{2 a^2}+\frac{3 x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{4 a^2}-\frac{\sinh ^{-1}(a x)^4}{8 a^3}-\frac{3 \sinh ^{-1}(a x)^2}{8 a^3}-\frac{3 x^2}{8 a}-\frac{3 x^2 \sinh ^{-1}(a x)^2}{4 a}",1,"(-3*x^2)/(8*a) + (3*x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(4*a^2) - (3*ArcSinh[a*x]^2)/(8*a^3) - (3*x^2*ArcSinh[a*x]^2)/(4*a) + (x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(2*a^2) - ArcSinh[a*x]^4/(8*a^3)","A",6,4,23,0.1739,1,"{5758, 5675, 5661, 30}"
345,1,64,0,0.1097402,"\int \frac{x \sinh ^{-1}(a x)^3}{\sqrt{1+a^2 x^2}} \, dx","Int[(x*ArcSinh[a*x]^3)/Sqrt[1 + a^2*x^2],x]","\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{a^2}+\frac{6 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{a^2}-\frac{6 x}{a}-\frac{3 x \sinh ^{-1}(a x)^2}{a}","\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{a^2}+\frac{6 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{a^2}-\frac{6 x}{a}-\frac{3 x \sinh ^{-1}(a x)^2}{a}",1,"(-6*x)/a + (6*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/a^2 - (3*x*ArcSinh[a*x]^2)/a + (Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/a^2","A",4,3,21,0.1429,1,"{5717, 5653, 8}"
346,1,13,0,0.0310136,"\int \frac{\sinh ^{-1}(a x)^3}{\sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]^3/Sqrt[1 + a^2*x^2],x]","\frac{\sinh ^{-1}(a x)^4}{4 a}","\frac{\sinh ^{-1}(a x)^4}{4 a}",1,"ArcSinh[a*x]^4/(4*a)","A",1,1,20,0.05000,1,"{5675}"
347,1,102,0,0.162071,"\int \frac{\sinh ^{-1}(a x)^3}{x \sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]^3/(x*Sqrt[1 + a^2*x^2]),x]","-3 \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+3 \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)+6 \sinh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\sinh ^{-1}(a x)}\right)-6 \sinh ^{-1}(a x) \text{PolyLog}\left(3,e^{\sinh ^{-1}(a x)}\right)-6 \text{PolyLog}\left(4,-e^{\sinh ^{-1}(a x)}\right)+6 \text{PolyLog}\left(4,e^{\sinh ^{-1}(a x)}\right)-2 \sinh ^{-1}(a x)^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)","-3 \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+3 \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)+6 \sinh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\sinh ^{-1}(a x)}\right)-6 \sinh ^{-1}(a x) \text{PolyLog}\left(3,e^{\sinh ^{-1}(a x)}\right)-6 \text{PolyLog}\left(4,-e^{\sinh ^{-1}(a x)}\right)+6 \text{PolyLog}\left(4,e^{\sinh ^{-1}(a x)}\right)-2 \sinh ^{-1}(a x)^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)",1,"-2*ArcSinh[a*x]^3*ArcTanh[E^ArcSinh[a*x]] - 3*ArcSinh[a*x]^2*PolyLog[2, -E^ArcSinh[a*x]] + 3*ArcSinh[a*x]^2*PolyLog[2, E^ArcSinh[a*x]] + 6*ArcSinh[a*x]*PolyLog[3, -E^ArcSinh[a*x]] - 6*ArcSinh[a*x]*PolyLog[3, E^ArcSinh[a*x]] - 6*PolyLog[4, -E^ArcSinh[a*x]] + 6*PolyLog[4, E^ArcSinh[a*x]]","A",10,6,23,0.2609,1,"{5760, 4182, 2531, 6609, 2282, 6589}"
348,1,88,0,0.1887998,"\int \frac{\sinh ^{-1}(a x)^3}{x^2 \sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]^3/(x^2*Sqrt[1 + a^2*x^2]),x]","3 a \sinh ^{-1}(a x) \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-\frac{3}{2} a \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(a x)}\right)-\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{x}-a \sinh ^{-1}(a x)^3+3 a \sinh ^{-1}(a x)^2 \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)","3 a \sinh ^{-1}(a x) \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a x)}\right)-\frac{3}{2} a \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(a x)}\right)-\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{x}-a \sinh ^{-1}(a x)^3+3 a \sinh ^{-1}(a x)^2 \log \left(1-e^{2 \sinh ^{-1}(a x)}\right)",1,"-(a*ArcSinh[a*x]^3) - (Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/x + 3*a*ArcSinh[a*x]^2*Log[1 - E^(2*ArcSinh[a*x])] + 3*a*ArcSinh[a*x]*PolyLog[2, E^(2*ArcSinh[a*x])] - (3*a*PolyLog[3, E^(2*ArcSinh[a*x])])/2","A",7,7,23,0.3043,1,"{5723, 5659, 3716, 2190, 2531, 2282, 6589}"
349,1,210,0,0.3625821,"\int \frac{\sinh ^{-1}(a x)^3}{x^3 \sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]^3/(x^3*Sqrt[1 + a^2*x^2]),x]","\frac{3}{2} a^2 \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)-\frac{3}{2} a^2 \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-3 a^2 \sinh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\sinh ^{-1}(a x)}\right)+3 a^2 \sinh ^{-1}(a x) \text{PolyLog}\left(3,e^{\sinh ^{-1}(a x)}\right)-3 a^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+3 a^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)+3 a^2 \text{PolyLog}\left(4,-e^{\sinh ^{-1}(a x)}\right)-3 a^2 \text{PolyLog}\left(4,e^{\sinh ^{-1}(a x)}\right)-\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{2 x^2}+a^2 \sinh ^{-1}(a x)^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-6 a^2 \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-\frac{3 a \sinh ^{-1}(a x)^2}{2 x}","\frac{3}{2} a^2 \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)-\frac{3}{2} a^2 \sinh ^{-1}(a x)^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)-3 a^2 \sinh ^{-1}(a x) \text{PolyLog}\left(3,-e^{\sinh ^{-1}(a x)}\right)+3 a^2 \sinh ^{-1}(a x) \text{PolyLog}\left(3,e^{\sinh ^{-1}(a x)}\right)-3 a^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)+3 a^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)+3 a^2 \text{PolyLog}\left(4,-e^{\sinh ^{-1}(a x)}\right)-3 a^2 \text{PolyLog}\left(4,e^{\sinh ^{-1}(a x)}\right)-\frac{\sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^3}{2 x^2}+a^2 \sinh ^{-1}(a x)^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-6 a^2 \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)-\frac{3 a \sinh ^{-1}(a x)^2}{2 x}",1,"(-3*a*ArcSinh[a*x]^2)/(2*x) - (Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3)/(2*x^2) - 6*a^2*ArcSinh[a*x]*ArcTanh[E^ArcSinh[a*x]] + a^2*ArcSinh[a*x]^3*ArcTanh[E^ArcSinh[a*x]] - 3*a^2*PolyLog[2, -E^ArcSinh[a*x]] + (3*a^2*ArcSinh[a*x]^2*PolyLog[2, -E^ArcSinh[a*x]])/2 + 3*a^2*PolyLog[2, E^ArcSinh[a*x]] - (3*a^2*ArcSinh[a*x]^2*PolyLog[2, E^ArcSinh[a*x]])/2 - 3*a^2*ArcSinh[a*x]*PolyLog[3, -E^ArcSinh[a*x]] + 3*a^2*ArcSinh[a*x]*PolyLog[3, E^ArcSinh[a*x]] + 3*a^2*PolyLog[4, -E^ArcSinh[a*x]] - 3*a^2*PolyLog[4, E^ArcSinh[a*x]]","A",18,10,23,0.4348,1,"{5747, 5760, 4182, 2531, 6609, 2282, 6589, 5661, 2279, 2391}"
350,1,67,0,0.1149135,"\int \frac{\left(c+a^2 c x^2\right)^3}{\sinh ^{-1}(a x)} \, dx","Int[(c + a^2*c*x^2)^3/ArcSinh[a*x],x]","\frac{35 c^3 \text{Chi}\left(\sinh ^{-1}(a x)\right)}{64 a}+\frac{21 c^3 \text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{64 a}+\frac{7 c^3 \text{Chi}\left(5 \sinh ^{-1}(a x)\right)}{64 a}+\frac{c^3 \text{Chi}\left(7 \sinh ^{-1}(a x)\right)}{64 a}","\frac{35 c^3 \text{Chi}\left(\sinh ^{-1}(a x)\right)}{64 a}+\frac{21 c^3 \text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{64 a}+\frac{7 c^3 \text{Chi}\left(5 \sinh ^{-1}(a x)\right)}{64 a}+\frac{c^3 \text{Chi}\left(7 \sinh ^{-1}(a x)\right)}{64 a}",1,"(35*c^3*CoshIntegral[ArcSinh[a*x]])/(64*a) + (21*c^3*CoshIntegral[3*ArcSinh[a*x]])/(64*a) + (7*c^3*CoshIntegral[5*ArcSinh[a*x]])/(64*a) + (c^3*CoshIntegral[7*ArcSinh[a*x]])/(64*a)","A",7,3,19,0.1579,1,"{5699, 3312, 3301}"
351,1,50,0,0.1000213,"\int \frac{\left(c+a^2 c x^2\right)^2}{\sinh ^{-1}(a x)} \, dx","Int[(c + a^2*c*x^2)^2/ArcSinh[a*x],x]","\frac{5 c^2 \text{Chi}\left(\sinh ^{-1}(a x)\right)}{8 a}+\frac{5 c^2 \text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{16 a}+\frac{c^2 \text{Chi}\left(5 \sinh ^{-1}(a x)\right)}{16 a}","\frac{5 c^2 \text{Chi}\left(\sinh ^{-1}(a x)\right)}{8 a}+\frac{5 c^2 \text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{16 a}+\frac{c^2 \text{Chi}\left(5 \sinh ^{-1}(a x)\right)}{16 a}",1,"(5*c^2*CoshIntegral[ArcSinh[a*x]])/(8*a) + (5*c^2*CoshIntegral[3*ArcSinh[a*x]])/(16*a) + (c^2*CoshIntegral[5*ArcSinh[a*x]])/(16*a)","A",6,3,19,0.1579,1,"{5699, 3312, 3301}"
352,1,29,0,0.0705044,"\int \frac{c+a^2 c x^2}{\sinh ^{-1}(a x)} \, dx","Int[(c + a^2*c*x^2)/ArcSinh[a*x],x]","\frac{3 c \text{Chi}\left(\sinh ^{-1}(a x)\right)}{4 a}+\frac{c \text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{4 a}","\frac{3 c \text{Chi}\left(\sinh ^{-1}(a x)\right)}{4 a}+\frac{c \text{Chi}\left(3 \sinh ^{-1}(a x)\right)}{4 a}",1,"(3*c*CoshIntegral[ArcSinh[a*x]])/(4*a) + (c*CoshIntegral[3*ArcSinh[a*x]])/(4*a)","A",5,3,17,0.1765,1,"{5699, 3312, 3301}"
353,0,0,0,0.0262787,"\int \frac{1}{\left(c+a^2 c x^2\right) \sinh ^{-1}(a x)} \, dx","Int[1/((c + a^2*c*x^2)*ArcSinh[a*x]),x]","\int \frac{1}{\left(c+a^2 c x^2\right) \sinh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{\left(a^2 c x^2+c\right) \sinh ^{-1}(a x)},x\right)",0,"Defer[Int][1/((c + a^2*c*x^2)*ArcSinh[a*x]), x]","A",0,0,0,0,-1,"{}"
354,0,0,0,0.0292485,"\int \frac{1}{\left(c+a^2 c x^2\right)^2 \sinh ^{-1}(a x)} \, dx","Int[1/((c + a^2*c*x^2)^2*ArcSinh[a*x]),x]","\int \frac{1}{\left(c+a^2 c x^2\right)^2 \sinh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{\left(a^2 c x^2+c\right)^2 \sinh ^{-1}(a x)},x\right)",0,"Defer[Int][1/((c + a^2*c*x^2)^2*ArcSinh[a*x]), x]","A",0,0,0,0,-1,"{}"
355,1,206,0,0.5082864,"\int \frac{x^4 \sqrt{1+c^2 x^2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[(x^4*Sqrt[1 + c^2*x^2])/(a + b*ArcSinh[c*x]),x]","-\frac{\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{32 b c^5}-\frac{\cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{16 b c^5}+\frac{\cosh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 a}{b}+6 \sinh ^{-1}(c x)\right)}{32 b c^5}+\frac{\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{32 b c^5}+\frac{\sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{16 b c^5}-\frac{\sinh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 a}{b}+6 \sinh ^{-1}(c x)\right)}{32 b c^5}+\frac{\log \left(a+b \sinh ^{-1}(c x)\right)}{16 b c^5}","-\frac{\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c^5}-\frac{\cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^5}+\frac{\cosh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c^5}+\frac{\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c^5}+\frac{\sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^5}-\frac{\sinh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c^5}+\frac{\log \left(a+b \sinh ^{-1}(c x)\right)}{16 b c^5}",1,"-(Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(32*b*c^5) - (Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(16*b*c^5) + (Cosh[(6*a)/b]*CoshIntegral[(6*a)/b + 6*ArcSinh[c*x]])/(32*b*c^5) + Log[a + b*ArcSinh[c*x]]/(16*b*c^5) + (Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(32*b*c^5) + (Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(16*b*c^5) - (Sinh[(6*a)/b]*SinhIntegral[(6*a)/b + 6*ArcSinh[c*x]])/(32*b*c^5)","A",12,5,27,0.1852,1,"{5779, 5448, 3303, 3298, 3301}"
356,1,179,0,0.5318298,"\int \frac{x^3 \sqrt{1+c^2 x^2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[(x^3*Sqrt[1 + c^2*x^2])/(a + b*ArcSinh[c*x]),x]","\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b c^4}+\frac{\sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b c^4}-\frac{\sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b c^4}-\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b c^4}-\frac{\cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b c^4}+\frac{\cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b c^4}","\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b c^4}+\frac{\sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^4}-\frac{\sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^4}-\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b c^4}-\frac{\cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^4}+\frac{\cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^4}",1,"(CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(8*b*c^4) + (CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]]*Sinh[(3*a)/b])/(16*b*c^4) - (CoshIntegral[(5*a)/b + 5*ArcSinh[c*x]]*Sinh[(5*a)/b])/(16*b*c^4) - (Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(8*b*c^4) - (Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b*c^4) + (Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b*c^4)","A",12,5,27,0.1852,1,"{5779, 5448, 3303, 3298, 3301}"
357,1,82,0,0.2734933,"\int \frac{x^2 \sqrt{1+c^2 x^2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[(x^2*Sqrt[1 + c^2*x^2])/(a + b*ArcSinh[c*x]),x]","\frac{\cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{8 b c^3}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{8 b c^3}-\frac{\log \left(a+b \sinh ^{-1}(c x)\right)}{8 b c^3}","\frac{\cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 b c^3}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 b c^3}-\frac{\log \left(a+b \sinh ^{-1}(c x)\right)}{8 b c^3}",1,"(Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(8*b*c^3) - Log[a + b*ArcSinh[c*x]]/(8*b*c^3) - (Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(8*b*c^3)","A",6,5,27,0.1852,1,"{5779, 5448, 3303, 3298, 3301}"
358,1,117,0,0.3125239,"\int \frac{x \sqrt{1+c^2 x^2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[(x*Sqrt[1 + c^2*x^2])/(a + b*ArcSinh[c*x]),x]","-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b c^2}-\frac{\sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{4 b c^2}+\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b c^2}+\frac{\cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{4 b c^2}","-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b c^2}-\frac{\sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b c^2}+\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b c^2}+\frac{\cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b c^2}",1,"-(CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(4*b*c^2) - (CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]]*Sinh[(3*a)/b])/(4*b*c^2) + (Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(4*b*c^2) + (Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b*c^2)","A",9,5,25,0.2000,1,"{5779, 5448, 3303, 3298, 3301}"
359,1,82,0,0.182576,"\int \frac{\sqrt{1+c^2 x^2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[Sqrt[1 + c^2*x^2]/(a + b*ArcSinh[c*x]),x]","\frac{\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{2 b c}-\frac{\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{2 b c}+\frac{\log \left(a+b \sinh ^{-1}(c x)\right)}{2 b c}","\frac{\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b c}-\frac{\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b c}+\frac{\log \left(a+b \sinh ^{-1}(c x)\right)}{2 b c}",1,"(Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(2*b*c) + Log[a + b*ArcSinh[c*x]]/(2*b*c) - (Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(2*b*c)","A",6,5,24,0.2083,1,"{5699, 3312, 3303, 3298, 3301}"
360,0,0,0,0.4261396,"\int \frac{\sqrt{1+c^2 x^2}}{x \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[Sqrt[1 + c^2*x^2]/(x*(a + b*ArcSinh[c*x])),x]","\int \frac{\sqrt{1+c^2 x^2}}{x \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)},x\right)-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b}+\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b}",0,"-((CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/b) + (Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/b + Defer[Int][1/(x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
361,0,0,0,0.299652,"\int \frac{\sqrt{1+c^2 x^2}}{x^2 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[Sqrt[1 + c^2*x^2]/(x^2*(a + b*ArcSinh[c*x])),x]","\int \frac{\sqrt{1+c^2 x^2}}{x^2 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)},x\right)+\frac{c \log \left(a+b \sinh ^{-1}(c x)\right)}{b}",0,"(c*Log[a + b*ArcSinh[c*x]])/b + Defer[Int][1/(x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
362,0,0,0,0.126256,"\int \frac{\sqrt{1+c^2 x^2}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[Sqrt[1 + c^2*x^2]/(x^3*(a + b*ArcSinh[c*x])),x]","\int \frac{\sqrt{1+c^2 x^2}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\sqrt{c^2 x^2+1}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][Sqrt[1 + c^2*x^2]/(x^3*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
363,0,0,0,0.1247784,"\int \frac{\sqrt{1+c^2 x^2}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[Sqrt[1 + c^2*x^2]/(x^4*(a + b*ArcSinh[c*x])),x]","\int \frac{\sqrt{1+c^2 x^2}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\sqrt{c^2 x^2+1}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][Sqrt[1 + c^2*x^2]/(x^4*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
364,1,241,0,0.6156516,"\int \frac{x^3 \left(1+c^2 x^2\right)^{3/2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[(x^3*(1 + c^2*x^2)^(3/2))/(a + b*ArcSinh[c*x]),x]","\frac{3 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{64 b c^4}+\frac{3 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{64 b c^4}-\frac{\sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{64 b c^4}-\frac{\sinh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 a}{b}+7 \sinh ^{-1}(c x)\right)}{64 b c^4}-\frac{3 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{64 b c^4}-\frac{3 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{64 b c^4}+\frac{\cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{64 b c^4}+\frac{\cosh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 a}{b}+7 \sinh ^{-1}(c x)\right)}{64 b c^4}","\frac{3 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{64 b c^4}+\frac{3 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^4}-\frac{\sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^4}-\frac{\sinh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^4}-\frac{3 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{64 b c^4}-\frac{3 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^4}+\frac{\cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^4}+\frac{\cosh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^4}",1,"(3*CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(64*b*c^4) + (3*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]]*Sinh[(3*a)/b])/(64*b*c^4) - (CoshIntegral[(5*a)/b + 5*ArcSinh[c*x]]*Sinh[(5*a)/b])/(64*b*c^4) - (CoshIntegral[(7*a)/b + 7*ArcSinh[c*x]]*Sinh[(7*a)/b])/(64*b*c^4) - (3*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(64*b*c^4) - (3*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(64*b*c^4) + (Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(64*b*c^4) + (Cosh[(7*a)/b]*SinhIntegral[(7*a)/b + 7*ArcSinh[c*x]])/(64*b*c^4)","A",15,5,27,0.1852,1,"{5779, 5448, 3303, 3298, 3301}"
365,1,206,0,0.4947252,"\int \frac{x^2 \left(1+c^2 x^2\right)^{3/2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[(x^2*(1 + c^2*x^2)^(3/2))/(a + b*ArcSinh[c*x]),x]","-\frac{\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{32 b c^3}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{16 b c^3}+\frac{\cosh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 a}{b}+6 \sinh ^{-1}(c x)\right)}{32 b c^3}+\frac{\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{32 b c^3}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{16 b c^3}-\frac{\sinh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 a}{b}+6 \sinh ^{-1}(c x)\right)}{32 b c^3}-\frac{\log \left(a+b \sinh ^{-1}(c x)\right)}{16 b c^3}","-\frac{\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c^3}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^3}+\frac{\cosh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c^3}+\frac{\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c^3}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^3}-\frac{\sinh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c^3}-\frac{\log \left(a+b \sinh ^{-1}(c x)\right)}{16 b c^3}",1,"-(Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(32*b*c^3) + (Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(16*b*c^3) + (Cosh[(6*a)/b]*CoshIntegral[(6*a)/b + 6*ArcSinh[c*x]])/(32*b*c^3) - Log[a + b*ArcSinh[c*x]]/(16*b*c^3) + (Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(32*b*c^3) - (Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(16*b*c^3) - (Sinh[(6*a)/b]*SinhIntegral[(6*a)/b + 6*ArcSinh[c*x]])/(32*b*c^3)","A",12,5,27,0.1852,1,"{5779, 5448, 3303, 3298, 3301}"
366,1,179,0,0.4171735,"\int \frac{x \left(1+c^2 x^2\right)^{3/2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[(x*(1 + c^2*x^2)^(3/2))/(a + b*ArcSinh[c*x]),x]","-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b c^2}-\frac{3 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b c^2}-\frac{\sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b c^2}+\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b c^2}+\frac{3 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b c^2}+\frac{\cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b c^2}","-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b c^2}-\frac{3 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^2}-\frac{\sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^2}+\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b c^2}+\frac{3 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^2}+\frac{\cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^2}",1,"-(CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(8*b*c^2) - (3*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]]*Sinh[(3*a)/b])/(16*b*c^2) - (CoshIntegral[(5*a)/b + 5*ArcSinh[c*x]]*Sinh[(5*a)/b])/(16*b*c^2) + (Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(8*b*c^2) + (3*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b*c^2) + (Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b*c^2)","A",12,5,25,0.2000,1,"{5779, 5448, 3303, 3298, 3301}"
367,1,144,0,0.2866318,"\int \frac{\left(1+c^2 x^2\right)^{3/2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[(1 + c^2*x^2)^(3/2)/(a + b*ArcSinh[c*x]),x]","\frac{\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{2 b c}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{8 b c}-\frac{\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{2 b c}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{8 b c}+\frac{3 \log \left(a+b \sinh ^{-1}(c x)\right)}{8 b c}","\frac{\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b c}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 b c}-\frac{\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b c}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 b c}+\frac{3 \log \left(a+b \sinh ^{-1}(c x)\right)}{8 b c}",1,"(Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(2*b*c) + (Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(8*b*c) + (3*Log[a + b*ArcSinh[c*x]])/(8*b*c) - (Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(2*b*c) - (Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(8*b*c)","A",9,5,24,0.2083,1,"{5699, 3312, 3303, 3298, 3301}"
368,0,0,0,0.8531493,"\int \frac{\left(1+c^2 x^2\right)^{3/2}}{x \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[(1 + c^2*x^2)^(3/2)/(x*(a + b*ArcSinh[c*x])),x]","\int \frac{\left(1+c^2 x^2\right)^{3/2}}{x \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)},x\right)-\frac{5 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b}-\frac{\sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b}+\frac{5 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b}+\frac{\cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b}",0,"(-5*CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(4*b) - (CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]]*Sinh[(3*a)/b])/(4*b) + (5*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(4*b) + (Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b) + Defer[Int][1/(x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
369,0,0,0,0.6041613,"\int \frac{\left(1+c^2 x^2\right)^{3/2}}{x^2 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[(1 + c^2*x^2)^(3/2)/(x^2*(a + b*ArcSinh[c*x])),x]","\int \frac{\left(1+c^2 x^2\right)^{3/2}}{x^2 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)},x\right)+\frac{c \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b}-\frac{c \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b}+\frac{3 c \log \left(a+b \sinh ^{-1}(c x)\right)}{2 b}",0,"(c*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(2*b) + (3*c*Log[a + b*ArcSinh[c*x]])/(2*b) - (c*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(2*b) + Defer[Int][1/(x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
370,0,0,0,0.14518,"\int \frac{\left(1+c^2 x^2\right)^{3/2}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[(1 + c^2*x^2)^(3/2)/(x^3*(a + b*ArcSinh[c*x])),x]","\int \frac{\left(1+c^2 x^2\right)^{3/2}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\left(c^2 x^2+1\right)^{3/2}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][(1 + c^2*x^2)^(3/2)/(x^3*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
371,0,0,0,0.1413296,"\int \frac{\left(1+c^2 x^2\right)^{3/2}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[(1 + c^2*x^2)^(3/2)/(x^4*(a + b*ArcSinh[c*x])),x]","\int \frac{\left(1+c^2 x^2\right)^{3/2}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\left(c^2 x^2+1\right)^{3/2}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][(1 + c^2*x^2)^(3/2)/(x^4*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
372,1,241,0,0.5765326,"\int \frac{x^3 \left(1+c^2 x^2\right)^{5/2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[(x^3*(1 + c^2*x^2)^(5/2))/(a + b*ArcSinh[c*x]),x]","\frac{3 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{128 b c^4}+\frac{\sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{32 b c^4}-\frac{3 \sinh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 a}{b}+7 \sinh ^{-1}(c x)\right)}{256 b c^4}-\frac{\sinh \left(\frac{9 a}{b}\right) \text{Chi}\left(\frac{9 a}{b}+9 \sinh ^{-1}(c x)\right)}{256 b c^4}-\frac{3 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{128 b c^4}-\frac{\cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{32 b c^4}+\frac{3 \cosh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 a}{b}+7 \sinh ^{-1}(c x)\right)}{256 b c^4}+\frac{\cosh \left(\frac{9 a}{b}\right) \text{Shi}\left(\frac{9 a}{b}+9 \sinh ^{-1}(c x)\right)}{256 b c^4}","\frac{3 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{128 b c^4}+\frac{\sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c^4}-\frac{3 \sinh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{256 b c^4}-\frac{\sinh \left(\frac{9 a}{b}\right) \text{Chi}\left(\frac{9 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{256 b c^4}-\frac{3 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{128 b c^4}-\frac{\cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c^4}+\frac{3 \cosh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{256 b c^4}+\frac{\cosh \left(\frac{9 a}{b}\right) \text{Shi}\left(\frac{9 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{256 b c^4}",1,"(3*CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(128*b*c^4) + (CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]]*Sinh[(3*a)/b])/(32*b*c^4) - (3*CoshIntegral[(7*a)/b + 7*ArcSinh[c*x]]*Sinh[(7*a)/b])/(256*b*c^4) - (CoshIntegral[(9*a)/b + 9*ArcSinh[c*x]]*Sinh[(9*a)/b])/(256*b*c^4) - (3*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(128*b*c^4) - (Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(32*b*c^4) + (3*Cosh[(7*a)/b]*SinhIntegral[(7*a)/b + 7*ArcSinh[c*x]])/(256*b*c^4) + (Cosh[(9*a)/b]*SinhIntegral[(9*a)/b + 9*ArcSinh[c*x]])/(256*b*c^4)","A",15,5,27,0.1852,1,"{5779, 5448, 3303, 3298, 3301}"
373,1,268,0,0.6193479,"\int \frac{x^2 \left(1+c^2 x^2\right)^{5/2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[(x^2*(1 + c^2*x^2)^(5/2))/(a + b*ArcSinh[c*x]),x]","-\frac{\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{32 b c^3}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{32 b c^3}+\frac{\cosh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 a}{b}+6 \sinh ^{-1}(c x)\right)}{32 b c^3}+\frac{\cosh \left(\frac{8 a}{b}\right) \text{Chi}\left(\frac{8 a}{b}+8 \sinh ^{-1}(c x)\right)}{128 b c^3}+\frac{\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{32 b c^3}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{32 b c^3}-\frac{\sinh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 a}{b}+6 \sinh ^{-1}(c x)\right)}{32 b c^3}-\frac{\sinh \left(\frac{8 a}{b}\right) \text{Shi}\left(\frac{8 a}{b}+8 \sinh ^{-1}(c x)\right)}{128 b c^3}-\frac{5 \log \left(a+b \sinh ^{-1}(c x)\right)}{128 b c^3}","-\frac{\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c^3}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c^3}+\frac{\cosh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c^3}+\frac{\cosh \left(\frac{8 a}{b}\right) \text{Chi}\left(\frac{8 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{128 b c^3}+\frac{\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c^3}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c^3}-\frac{\sinh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c^3}-\frac{\sinh \left(\frac{8 a}{b}\right) \text{Shi}\left(\frac{8 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{128 b c^3}-\frac{5 \log \left(a+b \sinh ^{-1}(c x)\right)}{128 b c^3}",1,"-(Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(32*b*c^3) + (Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(32*b*c^3) + (Cosh[(6*a)/b]*CoshIntegral[(6*a)/b + 6*ArcSinh[c*x]])/(32*b*c^3) + (Cosh[(8*a)/b]*CoshIntegral[(8*a)/b + 8*ArcSinh[c*x]])/(128*b*c^3) - (5*Log[a + b*ArcSinh[c*x]])/(128*b*c^3) + (Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(32*b*c^3) - (Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(32*b*c^3) - (Sinh[(6*a)/b]*SinhIntegral[(6*a)/b + 6*ArcSinh[c*x]])/(32*b*c^3) - (Sinh[(8*a)/b]*SinhIntegral[(8*a)/b + 8*ArcSinh[c*x]])/(128*b*c^3)","A",15,5,27,0.1852,1,"{5779, 5448, 3303, 3298, 3301}"
374,1,241,0,0.4905016,"\int \frac{x \left(1+c^2 x^2\right)^{5/2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[(x*(1 + c^2*x^2)^(5/2))/(a + b*ArcSinh[c*x]),x]","-\frac{5 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{64 b c^2}-\frac{9 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{64 b c^2}-\frac{5 \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{64 b c^2}-\frac{\sinh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 a}{b}+7 \sinh ^{-1}(c x)\right)}{64 b c^2}+\frac{5 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{64 b c^2}+\frac{9 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{64 b c^2}+\frac{5 \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{64 b c^2}+\frac{\cosh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 a}{b}+7 \sinh ^{-1}(c x)\right)}{64 b c^2}","-\frac{5 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{64 b c^2}-\frac{9 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^2}-\frac{5 \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^2}-\frac{\sinh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^2}+\frac{5 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{64 b c^2}+\frac{9 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^2}+\frac{5 \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^2}+\frac{\cosh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^2}",1,"(-5*CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(64*b*c^2) - (9*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]]*Sinh[(3*a)/b])/(64*b*c^2) - (5*CoshIntegral[(5*a)/b + 5*ArcSinh[c*x]]*Sinh[(5*a)/b])/(64*b*c^2) - (CoshIntegral[(7*a)/b + 7*ArcSinh[c*x]]*Sinh[(7*a)/b])/(64*b*c^2) + (5*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(64*b*c^2) + (9*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(64*b*c^2) + (5*Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(64*b*c^2) + (Cosh[(7*a)/b]*SinhIntegral[(7*a)/b + 7*ArcSinh[c*x]])/(64*b*c^2)","A",15,5,25,0.2000,1,"{5779, 5448, 3303, 3298, 3301}"
375,1,206,0,0.3588407,"\int \frac{\left(1+c^2 x^2\right)^{5/2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[(1 + c^2*x^2)^(5/2)/(a + b*ArcSinh[c*x]),x]","\frac{15 \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{32 b c}+\frac{3 \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{16 b c}+\frac{\cosh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 a}{b}+6 \sinh ^{-1}(c x)\right)}{32 b c}-\frac{15 \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{32 b c}-\frac{3 \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{16 b c}-\frac{\sinh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 a}{b}+6 \sinh ^{-1}(c x)\right)}{32 b c}+\frac{5 \log \left(a+b \sinh ^{-1}(c x)\right)}{16 b c}","\frac{15 \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c}+\frac{3 \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c}+\frac{\cosh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c}-\frac{15 \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c}-\frac{3 \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c}-\frac{\sinh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b c}+\frac{5 \log \left(a+b \sinh ^{-1}(c x)\right)}{16 b c}",1,"(15*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(32*b*c) + (3*Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(16*b*c) + (Cosh[(6*a)/b]*CoshIntegral[(6*a)/b + 6*ArcSinh[c*x]])/(32*b*c) + (5*Log[a + b*ArcSinh[c*x]])/(16*b*c) - (15*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(32*b*c) - (3*Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(16*b*c) - (Sinh[(6*a)/b]*SinhIntegral[(6*a)/b + 6*ArcSinh[c*x]])/(32*b*c)","A",12,5,24,0.2083,1,"{5699, 3312, 3303, 3298, 3301}"
376,0,0,0,1.2796296,"\int \frac{\left(1+c^2 x^2\right)^{5/2}}{x \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[(1 + c^2*x^2)^(5/2)/(x*(a + b*ArcSinh[c*x])),x]","\int \frac{\left(1+c^2 x^2\right)^{5/2}}{x \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)},x\right)-\frac{11 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b}-\frac{7 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b}-\frac{\sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b}+\frac{11 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b}+\frac{7 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b}+\frac{\cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b}",0,"(-11*CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(8*b) - (7*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]]*Sinh[(3*a)/b])/(16*b) - (CoshIntegral[(5*a)/b + 5*ArcSinh[c*x]]*Sinh[(5*a)/b])/(16*b) + (11*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(8*b) + (7*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b) + (Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b) + Defer[Int][1/(x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
377,0,0,0,0.9667543,"\int \frac{\left(1+c^2 x^2\right)^{5/2}}{x^2 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[(1 + c^2*x^2)^(5/2)/(x^2*(a + b*ArcSinh[c*x])),x]","\int \frac{\left(1+c^2 x^2\right)^{5/2}}{x^2 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)},x\right)+\frac{c \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{b}+\frac{c \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 b}-\frac{c \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{b}-\frac{c \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 b}+\frac{15 c \log \left(a+b \sinh ^{-1}(c x)\right)}{8 b}",0,"(c*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]])/b + (c*Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(8*b) + (15*c*Log[a + b*ArcSinh[c*x]])/(8*b) - (c*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/b - (c*Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(8*b) + Defer[Int][1/(x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
378,0,0,0,0.139597,"\int \frac{\left(1+c^2 x^2\right)^{5/2}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[(1 + c^2*x^2)^(5/2)/(x^3*(a + b*ArcSinh[c*x])),x]","\int \frac{\left(1+c^2 x^2\right)^{5/2}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\left(c^2 x^2+1\right)^{5/2}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][(1 + c^2*x^2)^(5/2)/(x^3*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
379,0,0,0,0.140862,"\int \frac{\left(1+c^2 x^2\right)^{5/2}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[(1 + c^2*x^2)^(5/2)/(x^4*(a + b*ArcSinh[c*x])),x]","\int \frac{\left(1+c^2 x^2\right)^{5/2}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\left(c^2 x^2+1\right)^{5/2}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][(1 + c^2*x^2)^(5/2)/(x^4*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
380,1,41,0,0.1610554,"\int \frac{x^4}{\sqrt{1+a^2 x^2} \sinh ^{-1}(a x)} \, dx","Int[x^4/(Sqrt[1 + a^2*x^2]*ArcSinh[a*x]),x]","-\frac{\text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{2 a^5}+\frac{\text{Chi}\left(4 \sinh ^{-1}(a x)\right)}{8 a^5}+\frac{3 \log \left(\sinh ^{-1}(a x)\right)}{8 a^5}","-\frac{\text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{2 a^5}+\frac{\text{Chi}\left(4 \sinh ^{-1}(a x)\right)}{8 a^5}+\frac{3 \log \left(\sinh ^{-1}(a x)\right)}{8 a^5}",1,"-CoshIntegral[2*ArcSinh[a*x]]/(2*a^5) + CoshIntegral[4*ArcSinh[a*x]]/(8*a^5) + (3*Log[ArcSinh[a*x]])/(8*a^5)","A",5,3,23,0.1304,1,"{5779, 3312, 3301}"
381,1,27,0,0.1552885,"\int \frac{x^3}{\sqrt{1+a^2 x^2} \sinh ^{-1}(a x)} \, dx","Int[x^3/(Sqrt[1 + a^2*x^2]*ArcSinh[a*x]),x]","\frac{\text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{4 a^4}-\frac{3 \text{Shi}\left(\sinh ^{-1}(a x)\right)}{4 a^4}","\frac{\text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{4 a^4}-\frac{3 \text{Shi}\left(\sinh ^{-1}(a x)\right)}{4 a^4}",1,"(-3*SinhIntegral[ArcSinh[a*x]])/(4*a^4) + SinhIntegral[3*ArcSinh[a*x]]/(4*a^4)","A",5,3,23,0.1304,1,"{5779, 3312, 3298}"
382,1,27,0,0.1449558,"\int \frac{x^2}{\sqrt{1+a^2 x^2} \sinh ^{-1}(a x)} \, dx","Int[x^2/(Sqrt[1 + a^2*x^2]*ArcSinh[a*x]),x]","\frac{\text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{2 a^3}-\frac{\log \left(\sinh ^{-1}(a x)\right)}{2 a^3}","\frac{\text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{2 a^3}-\frac{\log \left(\sinh ^{-1}(a x)\right)}{2 a^3}",1,"CoshIntegral[2*ArcSinh[a*x]]/(2*a^3) - Log[ArcSinh[a*x]]/(2*a^3)","A",4,3,23,0.1304,1,"{5779, 3312, 3301}"
383,1,27,0,0.1439604,"\int \frac{x^2}{\sqrt{1+a^2 x^2} \sinh ^{-1}(a x)} \, dx","Int[x^2/(Sqrt[1 + a^2*x^2]*ArcSinh[a*x]),x]","\frac{\text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{2 a^3}-\frac{\log \left(\sinh ^{-1}(a x)\right)}{2 a^3}","\frac{\text{Chi}\left(2 \sinh ^{-1}(a x)\right)}{2 a^3}-\frac{\log \left(\sinh ^{-1}(a x)\right)}{2 a^3}",1,"CoshIntegral[2*ArcSinh[a*x]]/(2*a^3) - Log[ArcSinh[a*x]]/(2*a^3)","A",4,3,23,0.1304,1,"{5779, 3312, 3301}"
384,1,9,0,0.0801654,"\int \frac{x}{\sqrt{1+a^2 x^2} \sinh ^{-1}(a x)} \, dx","Int[x/(Sqrt[1 + a^2*x^2]*ArcSinh[a*x]),x]","\frac{\text{Shi}\left(\sinh ^{-1}(a x)\right)}{a^2}","\frac{\text{Shi}\left(\sinh ^{-1}(a x)\right)}{a^2}",1,"SinhIntegral[ArcSinh[a*x]]/a^2","A",2,2,21,0.09524,1,"{5779, 3298}"
385,1,9,0,0.0367984,"\int \frac{1}{\sqrt{1+a^2 x^2} \sinh ^{-1}(a x)} \, dx","Int[1/(Sqrt[1 + a^2*x^2]*ArcSinh[a*x]),x]","\frac{\log \left(\sinh ^{-1}(a x)\right)}{a}","\frac{\log \left(\sinh ^{-1}(a x)\right)}{a}",1,"Log[ArcSinh[a*x]]/a","A",1,1,20,0.05000,1,"{5673}"
386,0,0,0,0.0995991,"\int \frac{1}{x \sqrt{1+a^2 x^2} \sinh ^{-1}(a x)} \, dx","Int[1/(x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]),x]","\int \frac{1}{x \sqrt{1+a^2 x^2} \sinh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)},x\right)",0,"Defer[Int][1/(x*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]), x]","A",0,0,0,0,-1,"{}"
387,0,0,0,0.0981286,"\int \frac{1}{x^2 \sqrt{1+a^2 x^2} \sinh ^{-1}(a x)} \, dx","Int[1/(x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]),x]","\int \frac{1}{x^2 \sqrt{1+a^2 x^2} \sinh ^{-1}(a x)} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)},x\right)",0,"Defer[Int][1/(x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]), x]","A",0,0,0,0,-1,"{}"
388,1,179,0,0.4592181,"\int \frac{x^5}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[x^5/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])),x]","-\frac{5 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b c^6}+\frac{5 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b c^6}-\frac{\sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b c^6}+\frac{5 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b c^6}-\frac{5 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b c^6}+\frac{\cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b c^6}","-\frac{5 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b c^6}+\frac{5 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^6}-\frac{\sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^6}+\frac{5 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b c^6}-\frac{5 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^6}+\frac{\cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^6}",1,"(-5*CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(8*b*c^6) + (5*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]]*Sinh[(3*a)/b])/(16*b*c^6) - (CoshIntegral[(5*a)/b + 5*ArcSinh[c*x]]*Sinh[(5*a)/b])/(16*b*c^6) + (5*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(8*b*c^6) - (5*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b*c^6) + (Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b*c^6)","A",12,5,27,0.1852,1,"{5779, 3312, 3303, 3298, 3301}"
389,1,144,0,0.4029898,"\int \frac{x^4}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[x^4/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])),x]","-\frac{\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{2 b c^5}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{8 b c^5}+\frac{\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{2 b c^5}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{8 b c^5}+\frac{3 \log \left(a+b \sinh ^{-1}(c x)\right)}{8 b c^5}","-\frac{\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b c^5}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 b c^5}+\frac{\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b c^5}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 b c^5}+\frac{3 \log \left(a+b \sinh ^{-1}(c x)\right)}{8 b c^5}",1,"-(Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(2*b*c^5) + (Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(8*b*c^5) + (3*Log[a + b*ArcSinh[c*x]])/(8*b*c^5) + (Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(2*b*c^5) - (Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(8*b*c^5)","A",9,5,27,0.1852,1,"{5779, 3312, 3303, 3298, 3301}"
390,1,117,0,0.3864899,"\int \frac{x^3}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[x^3/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])),x]","\frac{3 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b c^4}-\frac{\sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{4 b c^4}-\frac{3 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b c^4}+\frac{\cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{4 b c^4}","\frac{3 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b c^4}-\frac{\sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b c^4}-\frac{3 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b c^4}+\frac{\cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b c^4}",1,"(3*CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(4*b*c^4) - (CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]]*Sinh[(3*a)/b])/(4*b*c^4) - (3*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(4*b*c^4) + (Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b*c^4)","A",9,5,27,0.1852,1,"{5779, 3312, 3303, 3298, 3301}"
391,1,82,0,0.2918694,"\int \frac{x^2}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[x^2/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])),x]","\frac{\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{2 b c^3}-\frac{\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{2 b c^3}-\frac{\log \left(a+b \sinh ^{-1}(c x)\right)}{2 b c^3}","\frac{\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b c^3}-\frac{\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b c^3}-\frac{\log \left(a+b \sinh ^{-1}(c x)\right)}{2 b c^3}",1,"(Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(2*b*c^3) - Log[a + b*ArcSinh[c*x]]/(2*b*c^3) - (Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(2*b*c^3)","A",6,5,27,0.1852,1,"{5779, 3312, 3303, 3298, 3301}"
392,1,50,0,0.1851909,"\int \frac{x}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[x/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])),x]","\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b c^2}-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b c^2}","\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c^2}-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c^2}",1,"-((CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(b*c^2)) + (Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(b*c^2)","A",4,4,25,0.1600,1,"{5779, 3303, 3298, 3301}"
393,1,16,0,0.0497027,"\int \frac{1}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[1/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])),x]","\frac{\log \left(a+b \sinh ^{-1}(c x)\right)}{b c}","\frac{\log \left(a+b \sinh ^{-1}(c x)\right)}{b c}",1,"Log[a + b*ArcSinh[c*x]]/(b*c)","A",1,1,24,0.04167,1,"{5673}"
394,0,0,0,0.1256657,"\int \frac{1}{x \sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[1/(x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])),x]","\int \frac{1}{x \sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
395,0,0,0,0.1330599,"\int \frac{1}{x^2 \sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[1/(x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])),x]","\int \frac{1}{x^2 \sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
396,0,0,0,0.1451222,"\int \frac{x^2}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[x^2/((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])),x]","\int \frac{x^2}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{x^2}{\left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][x^2/((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
397,0,0,0,0.1015085,"\int \frac{x}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[x/((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])),x]","\int \frac{x}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{x}{\left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][x/((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
398,0,0,0,0.0534405,"\int \frac{1}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[1/((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])),x]","\int \frac{1}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
399,0,0,0,0.1377281,"\int \frac{1}{x \left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[1/(x*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])),x]","\int \frac{1}{x \left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(x*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
400,0,0,0,0.1405163,"\int \frac{1}{x^2 \left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[1/(x^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])),x]","\int \frac{1}{x^2 \left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(x^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
401,0,0,0,0.1317459,"\int \frac{x^m \left(1+c^2 x^2\right)^{5/2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[(x^m*(1 + c^2*x^2)^(5/2))/(a + b*ArcSinh[c*x]),x]","\int \frac{x^m \left(1+c^2 x^2\right)^{5/2}}{a+b \sinh ^{-1}(c x)} \, dx","\text{Int}\left(\frac{\left(c^2 x^2+1\right)^{5/2} x^m}{a+b \sinh ^{-1}(c x)},x\right)",0,"Defer[Int][(x^m*(1 + c^2*x^2)^(5/2))/(a + b*ArcSinh[c*x]), x]","A",0,0,0,0,-1,"{}"
402,0,0,0,0.1306409,"\int \frac{x^m \left(1+c^2 x^2\right)^{3/2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[(x^m*(1 + c^2*x^2)^(3/2))/(a + b*ArcSinh[c*x]),x]","\int \frac{x^m \left(1+c^2 x^2\right)^{3/2}}{a+b \sinh ^{-1}(c x)} \, dx","\text{Int}\left(\frac{\left(c^2 x^2+1\right)^{3/2} x^m}{a+b \sinh ^{-1}(c x)},x\right)",0,"Defer[Int][(x^m*(1 + c^2*x^2)^(3/2))/(a + b*ArcSinh[c*x]), x]","A",0,0,0,0,-1,"{}"
403,0,0,0,0.1137536,"\int \frac{x^m \sqrt{1+c^2 x^2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[(x^m*Sqrt[1 + c^2*x^2])/(a + b*ArcSinh[c*x]),x]","\int \frac{x^m \sqrt{1+c^2 x^2}}{a+b \sinh ^{-1}(c x)} \, dx","\text{Int}\left(\frac{\sqrt{c^2 x^2+1} x^m}{a+b \sinh ^{-1}(c x)},x\right)",0,"Defer[Int][(x^m*Sqrt[1 + c^2*x^2])/(a + b*ArcSinh[c*x]), x]","A",0,0,0,0,-1,"{}"
404,0,0,0,0.1240433,"\int \frac{x^m}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[x^m/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])),x]","\int \frac{x^m}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{x^m}{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][x^m/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
405,0,0,0,0.1319088,"\int \frac{x^m}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[x^m/((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])),x]","\int \frac{x^m}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{x^m}{\left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][x^m/((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
406,1,94,0,0.1836764,"\int \frac{\left(c+a^2 c x^2\right)^3}{\sinh ^{-1}(a x)^2} \, dx","Int[(c + a^2*c*x^2)^3/ArcSinh[a*x]^2,x]","-\frac{c^3 \left(a^2 x^2+1\right)^{7/2}}{a \sinh ^{-1}(a x)}+\frac{35 c^3 \text{Shi}\left(\sinh ^{-1}(a x)\right)}{64 a}+\frac{63 c^3 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{64 a}+\frac{35 c^3 \text{Shi}\left(5 \sinh ^{-1}(a x)\right)}{64 a}+\frac{7 c^3 \text{Shi}\left(7 \sinh ^{-1}(a x)\right)}{64 a}","-\frac{c^3 \left(a^2 x^2+1\right)^{7/2}}{a \sinh ^{-1}(a x)}+\frac{35 c^3 \text{Shi}\left(\sinh ^{-1}(a x)\right)}{64 a}+\frac{63 c^3 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{64 a}+\frac{35 c^3 \text{Shi}\left(5 \sinh ^{-1}(a x)\right)}{64 a}+\frac{7 c^3 \text{Shi}\left(7 \sinh ^{-1}(a x)\right)}{64 a}",1,"-((c^3*(1 + a^2*x^2)^(7/2))/(a*ArcSinh[a*x])) + (35*c^3*SinhIntegral[ArcSinh[a*x]])/(64*a) + (63*c^3*SinhIntegral[3*ArcSinh[a*x]])/(64*a) + (35*c^3*SinhIntegral[5*ArcSinh[a*x]])/(64*a) + (7*c^3*SinhIntegral[7*ArcSinh[a*x]])/(64*a)","A",8,4,19,0.2105,1,"{5696, 5779, 5448, 3298}"
407,1,77,0,0.1695232,"\int \frac{\left(c+a^2 c x^2\right)^2}{\sinh ^{-1}(a x)^2} \, dx","Int[(c + a^2*c*x^2)^2/ArcSinh[a*x]^2,x]","-\frac{c^2 \left(a^2 x^2+1\right)^{5/2}}{a \sinh ^{-1}(a x)}+\frac{5 c^2 \text{Shi}\left(\sinh ^{-1}(a x)\right)}{8 a}+\frac{15 c^2 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{16 a}+\frac{5 c^2 \text{Shi}\left(5 \sinh ^{-1}(a x)\right)}{16 a}","-\frac{c^2 \left(a^2 x^2+1\right)^{5/2}}{a \sinh ^{-1}(a x)}+\frac{5 c^2 \text{Shi}\left(\sinh ^{-1}(a x)\right)}{8 a}+\frac{15 c^2 \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{16 a}+\frac{5 c^2 \text{Shi}\left(5 \sinh ^{-1}(a x)\right)}{16 a}",1,"-((c^2*(1 + a^2*x^2)^(5/2))/(a*ArcSinh[a*x])) + (5*c^2*SinhIntegral[ArcSinh[a*x]])/(8*a) + (15*c^2*SinhIntegral[3*ArcSinh[a*x]])/(16*a) + (5*c^2*SinhIntegral[5*ArcSinh[a*x]])/(16*a)","A",7,4,19,0.2105,1,"{5696, 5779, 5448, 3298}"
408,1,54,0,0.1350661,"\int \frac{c+a^2 c x^2}{\sinh ^{-1}(a x)^2} \, dx","Int[(c + a^2*c*x^2)/ArcSinh[a*x]^2,x]","-\frac{c \left(a^2 x^2+1\right)^{3/2}}{a \sinh ^{-1}(a x)}+\frac{3 c \text{Shi}\left(\sinh ^{-1}(a x)\right)}{4 a}+\frac{3 c \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{4 a}","-\frac{c \left(a^2 x^2+1\right)^{3/2}}{a \sinh ^{-1}(a x)}+\frac{3 c \text{Shi}\left(\sinh ^{-1}(a x)\right)}{4 a}+\frac{3 c \text{Shi}\left(3 \sinh ^{-1}(a x)\right)}{4 a}",1,"-((c*(1 + a^2*x^2)^(3/2))/(a*ArcSinh[a*x])) + (3*c*SinhIntegral[ArcSinh[a*x]])/(4*a) + (3*c*SinhIntegral[3*ArcSinh[a*x]])/(4*a)","A",6,4,17,0.2353,1,"{5696, 5779, 5448, 3298}"
409,0,0,0,0.1016915,"\int \frac{1}{\left(c+a^2 c x^2\right) \sinh ^{-1}(a x)^2} \, dx","Int[1/((c + a^2*c*x^2)*ArcSinh[a*x]^2),x]","\int \frac{1}{\left(c+a^2 c x^2\right) \sinh ^{-1}(a x)^2} \, dx","-\frac{a \text{Int}\left(\frac{x}{\left(a^2 x^2+1\right)^{3/2} \sinh ^{-1}(a x)},x\right)}{c}-\frac{1}{a c \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}",0,"-(1/(a*c*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])) - (a*Defer[Int][x/((1 + a^2*x^2)^(3/2)*ArcSinh[a*x]), x])/c","A",0,0,0,0,-1,"{}"
410,0,0,0,0.1012131,"\int \frac{1}{\left(c+a^2 c x^2\right)^2 \sinh ^{-1}(a x)^2} \, dx","Int[1/((c + a^2*c*x^2)^2*ArcSinh[a*x]^2),x]","\int \frac{1}{\left(c+a^2 c x^2\right)^2 \sinh ^{-1}(a x)^2} \, dx","-\frac{3 a \text{Int}\left(\frac{x}{\left(a^2 x^2+1\right)^{5/2} \sinh ^{-1}(a x)},x\right)}{c^2}-\frac{1}{a c^2 \left(a^2 x^2+1\right)^{3/2} \sinh ^{-1}(a x)}",0,"-(1/(a*c^2*(1 + a^2*x^2)^(3/2)*ArcSinh[a*x])) - (3*a*Defer[Int][x/((1 + a^2*x^2)^(5/2)*ArcSinh[a*x]), x])/c^2","A",0,0,0,0,-1,"{}"
411,1,209,0,0.7106904,"\int \frac{x^3 \sqrt{1+c^2 x^2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(x^3*Sqrt[1 + c^2*x^2])/(a + b*ArcSinh[c*x])^2,x]","-\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b^2 c^4}-\frac{3 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b^2 c^4}+\frac{5 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b^2 c^4}+\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b^2 c^4}+\frac{3 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b^2 c^4}-\frac{5 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b^2 c^4}-\frac{x^3 \left(c^2 x^2+1\right)}{b c \left(a+b \sinh ^{-1}(c x)\right)}","-\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b^2 c^4}-\frac{3 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^4}+\frac{5 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^4}+\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b^2 c^4}+\frac{3 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^4}-\frac{5 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^4}-\frac{x^3 \left(c^2 x^2+1\right)}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-((x^3*(1 + c^2*x^2))/(b*c*(a + b*ArcSinh[c*x]))) - (Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(8*b^2*c^4) - (3*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b^2*c^4) + (5*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b^2*c^4) + (Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(8*b^2*c^4) + (3*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b^2*c^4) - (5*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b^2*c^4)","A",22,6,27,0.2222,1,"{5777, 5669, 5448, 3303, 3298, 3301}"
412,1,93,0,0.5615418,"\int \frac{x^2 \sqrt{1+c^2 x^2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(x^2*Sqrt[1 + c^2*x^2])/(a + b*ArcSinh[c*x])^2,x]","-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{2 b^2 c^3}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{2 b^2 c^3}-\frac{x^2 \left(c^2 x^2+1\right)}{b c \left(a+b \sinh ^{-1}(c x)\right)}","-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^3}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^3}-\frac{x^2 \left(c^2 x^2+1\right)}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-((x^2*(1 + c^2*x^2))/(b*c*(a + b*ArcSinh[c*x]))) - (CoshIntegral[(4*a)/b + 4*ArcSinh[c*x]]*Sinh[(4*a)/b])/(2*b^2*c^3) + (Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(2*b^2*c^3)","A",16,7,27,0.2593,1,"{5777, 5669, 5448, 12, 3303, 3298, 3301}"
413,1,198,0,0.4115575,"\int \frac{x \sqrt{1+c^2 x^2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(x*Sqrt[1 + c^2*x^2])/(a + b*ArcSinh[c*x])^2,x]","-\frac{3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b^2 c^2}+\frac{3 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{4 b^2 c^2}+\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b^2 c^2}+\frac{3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b^2 c^2}-\frac{3 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{4 b^2 c^2}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b^2 c^2}-\frac{x \left(c^2 x^2+1\right)}{b c \left(a+b \sinh ^{-1}(c x)\right)}","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b^2 c^2}+\frac{3 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^2}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b^2 c^2}-\frac{3 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^2}-\frac{x \left(c^2 x^2+1\right)}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-((x*(1 + c^2*x^2))/(b*c*(a + b*ArcSinh[c*x]))) - (3*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(4*b^2*c^2) + (3*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b^2*c^2) + (Cosh[a/b]*CoshIntegral[(a + b*ArcSinh[c*x])/b])/(b^2*c^2) + (3*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(4*b^2*c^2) - (3*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b^2*c^2) - (Sinh[a/b]*SinhIntegral[(a + b*ArcSinh[c*x])/b])/(b^2*c^2)","A",14,7,25,0.2800,1,"{5777, 5657, 3303, 3298, 3301, 5669, 5448}"
414,1,85,0,0.1808532,"\int \frac{\sqrt{1+c^2 x^2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[1 + c^2*x^2]/(a + b*ArcSinh[c*x])^2,x]","-\frac{\sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{b^2 c}+\frac{\cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{b^2 c}-\frac{c^2 x^2+1}{b c \left(a+b \sinh ^{-1}(c x)\right)}","-\frac{\sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{b^2 c}+\frac{\cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{b^2 c}-\frac{c^2 x^2+1}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-((1 + c^2*x^2)/(b*c*(a + b*ArcSinh[c*x]))) - (CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]]*Sinh[(2*a)/b])/(b^2*c) + (Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(b^2*c)","A",7,7,24,0.2917,1,"{5696, 5669, 5448, 12, 3303, 3298, 3301}"
415,0,0,0,0.2290776,"\int \frac{\sqrt{1+c^2 x^2}}{x \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[1 + c^2*x^2]/(x*(a + b*ArcSinh[c*x])^2),x]","\int \frac{\sqrt{1+c^2 x^2}}{x \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","-\frac{\text{Int}\left(\frac{1}{x^2 \left(a+b \sinh ^{-1}(c x)\right)},x\right)}{b c}+\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b^2}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b^2}-\frac{c^2 x^2+1}{b c x \left(a+b \sinh ^{-1}(c x)\right)}",0,"-((1 + c^2*x^2)/(b*c*x*(a + b*ArcSinh[c*x]))) + (Cosh[a/b]*CoshIntegral[(a + b*ArcSinh[c*x])/b])/b^2 - (Sinh[a/b]*SinhIntegral[(a + b*ArcSinh[c*x])/b])/b^2 - Defer[Int][1/(x^2*(a + b*ArcSinh[c*x])), x]/(b*c)","A",0,0,0,0,-1,"{}"
416,0,0,0,0.1543447,"\int \frac{\sqrt{1+c^2 x^2}}{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[1 + c^2*x^2]/(x^2*(a + b*ArcSinh[c*x])^2),x]","\int \frac{\sqrt{1+c^2 x^2}}{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","-\frac{2 \text{Int}\left(\frac{1}{x^3 \left(a+b \sinh ^{-1}(c x)\right)},x\right)}{b c}-\frac{c^2 x^2+1}{b c x^2 \left(a+b \sinh ^{-1}(c x)\right)}",0,"-((1 + c^2*x^2)/(b*c*x^2*(a + b*ArcSinh[c*x]))) - (2*Defer[Int][1/(x^3*(a + b*ArcSinh[c*x])), x])/(b*c)","A",0,0,0,0,-1,"{}"
417,0,0,0,0.1270292,"\int \frac{\sqrt{1+c^2 x^2}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[1 + c^2*x^2]/(x^3*(a + b*ArcSinh[c*x])^2),x]","\int \frac{\sqrt{1+c^2 x^2}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{c^2 x^2+1}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][Sqrt[1 + c^2*x^2]/(x^3*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
418,0,0,0,0.1309089,"\int \frac{\sqrt{1+c^2 x^2}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[1 + c^2*x^2]/(x^4*(a + b*ArcSinh[c*x])^2),x]","\int \frac{\sqrt{1+c^2 x^2}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{c^2 x^2+1}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][Sqrt[1 + c^2*x^2]/(x^4*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
419,1,273,0,1.0063822,"\int \frac{x^3 \left(1+c^2 x^2\right)^{3/2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(x^3*(1 + c^2*x^2)^(3/2))/(a + b*ArcSinh[c*x])^2,x]","-\frac{3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{64 b^2 c^4}-\frac{9 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{64 b^2 c^4}+\frac{5 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{64 b^2 c^4}+\frac{7 \cosh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 a}{b}+7 \sinh ^{-1}(c x)\right)}{64 b^2 c^4}+\frac{3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{64 b^2 c^4}+\frac{9 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{64 b^2 c^4}-\frac{5 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{64 b^2 c^4}-\frac{7 \sinh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 a}{b}+7 \sinh ^{-1}(c x)\right)}{64 b^2 c^4}-\frac{x^3 \left(c^2 x^2+1\right)^2}{b c \left(a+b \sinh ^{-1}(c x)\right)}","-\frac{3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{64 b^2 c^4}-\frac{9 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^4}+\frac{5 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^4}+\frac{7 \cosh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^4}+\frac{3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{64 b^2 c^4}+\frac{9 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^4}-\frac{5 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^4}-\frac{7 \sinh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^4}-\frac{x^3 \left(c^2 x^2+1\right)^2}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-((x^3*(1 + c^2*x^2)^2)/(b*c*(a + b*ArcSinh[c*x]))) - (3*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(64*b^2*c^4) - (9*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(64*b^2*c^4) + (5*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(64*b^2*c^4) + (7*Cosh[(7*a)/b]*CoshIntegral[(7*a)/b + 7*ArcSinh[c*x]])/(64*b^2*c^4) + (3*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(64*b^2*c^4) + (9*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(64*b^2*c^4) - (5*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(64*b^2*c^4) - (7*Sinh[(7*a)/b]*SinhIntegral[(7*a)/b + 7*ArcSinh[c*x]])/(64*b^2*c^4)","A",28,6,27,0.2222,1,"{5777, 5779, 5448, 3303, 3298, 3301}"
420,1,219,0,0.7157525,"\int \frac{x^2 \left(1+c^2 x^2\right)^{3/2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(x^2*(1 + c^2*x^2)^(3/2))/(a + b*ArcSinh[c*x])^2,x]","\frac{\sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{16 b^2 c^3}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{4 b^2 c^3}-\frac{3 \sinh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 a}{b}+6 \sinh ^{-1}(c x)\right)}{16 b^2 c^3}-\frac{\cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{16 b^2 c^3}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{4 b^2 c^3}+\frac{3 \cosh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 a}{b}+6 \sinh ^{-1}(c x)\right)}{16 b^2 c^3}-\frac{x^2 \left(c^2 x^2+1\right)^2}{b c \left(a+b \sinh ^{-1}(c x)\right)}","\frac{\sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^3}-\frac{3 \sinh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}-\frac{\cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^3}+\frac{3 \cosh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}-\frac{x^2 \left(c^2 x^2+1\right)^2}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-((x^2*(1 + c^2*x^2)^2)/(b*c*(a + b*ArcSinh[c*x]))) + (CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]]*Sinh[(2*a)/b])/(16*b^2*c^3) - (CoshIntegral[(4*a)/b + 4*ArcSinh[c*x]]*Sinh[(4*a)/b])/(4*b^2*c^3) - (3*CoshIntegral[(6*a)/b + 6*ArcSinh[c*x]]*Sinh[(6*a)/b])/(16*b^2*c^3) - (Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(16*b^2*c^3) + (Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(4*b^2*c^3) + (3*Cosh[(6*a)/b]*SinhIntegral[(6*a)/b + 6*ArcSinh[c*x]])/(16*b^2*c^3)","A",19,6,27,0.2222,1,"{5777, 5779, 5448, 3303, 3298, 3301}"
421,1,209,0,0.7322212,"\int \frac{x \left(1+c^2 x^2\right)^{3/2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(x*(1 + c^2*x^2)^(3/2))/(a + b*ArcSinh[c*x])^2,x]","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b^2 c^2}+\frac{9 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b^2 c^2}+\frac{5 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b^2 c^2}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b^2 c^2}-\frac{9 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b^2 c^2}-\frac{5 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b^2 c^2}-\frac{x \left(c^2 x^2+1\right)^2}{b c \left(a+b \sinh ^{-1}(c x)\right)}","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b^2 c^2}+\frac{9 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^2}+\frac{5 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^2}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b^2 c^2}-\frac{9 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^2}-\frac{5 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^2}-\frac{x \left(c^2 x^2+1\right)^2}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-((x*(1 + c^2*x^2)^2)/(b*c*(a + b*ArcSinh[c*x]))) + (Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(8*b^2*c^2) + (9*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b^2*c^2) + (5*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b^2*c^2) - (Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(8*b^2*c^2) - (9*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b^2*c^2) - (5*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b^2*c^2)","A",22,8,25,0.3200,1,"{5777, 5699, 3312, 3303, 3298, 3301, 5779, 5448}"
422,1,149,0,0.3178018,"\int \frac{\left(1+c^2 x^2\right)^{3/2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(1 + c^2*x^2)^(3/2)/(a + b*ArcSinh[c*x])^2,x]","-\frac{\sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{b^2 c}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{2 b^2 c}+\frac{\cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{b^2 c}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{2 b^2 c}-\frac{\left(c^2 x^2+1\right)^2}{b c \left(a+b \sinh ^{-1}(c x)\right)}","-\frac{\sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{b^2 c}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b^2 c}+\frac{\cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{b^2 c}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b^2 c}-\frac{\left(c^2 x^2+1\right)^2}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-((1 + c^2*x^2)^2/(b*c*(a + b*ArcSinh[c*x]))) - (CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]]*Sinh[(2*a)/b])/(b^2*c) - (CoshIntegral[(4*a)/b + 4*ArcSinh[c*x]]*Sinh[(4*a)/b])/(2*b^2*c) + (Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(b^2*c) + (Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(2*b^2*c)","A",10,6,24,0.2500,1,"{5696, 5779, 5448, 3303, 3298, 3301}"
423,0,0,0,0.4371084,"\int \frac{\left(1+c^2 x^2\right)^{3/2}}{x \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(1 + c^2*x^2)^(3/2)/(x*(a + b*ArcSinh[c*x])^2),x]","\int \frac{\left(1+c^2 x^2\right)^{3/2}}{x \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","-\frac{\text{Int}\left(\frac{c^2 x^2+1}{x^2 \left(a+b \sinh ^{-1}(c x)\right)},x\right)}{b c}+\frac{9 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b^2}+\frac{3 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b^2}-\frac{9 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b^2}-\frac{3 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b^2}-\frac{\left(c^2 x^2+1\right)^2}{b c x \left(a+b \sinh ^{-1}(c x)\right)}",0,"-((1 + c^2*x^2)^2/(b*c*x*(a + b*ArcSinh[c*x]))) + (9*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(4*b^2) + (3*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b^2) - (9*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(4*b^2) - (3*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b^2) - Defer[Int][(1 + c^2*x^2)/(x^2*(a + b*ArcSinh[c*x])), x]/(b*c)","A",0,0,0,0,-1,"{}"
424,0,0,0,0.2515911,"\int \frac{\left(1+c^2 x^2\right)^{3/2}}{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(1 + c^2*x^2)^(3/2)/(x^2*(a + b*ArcSinh[c*x])^2),x]","\int \frac{\left(1+c^2 x^2\right)^{3/2}}{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","-\frac{2 \text{Int}\left(\frac{c^2 x^2+1}{x^3 \left(a+b \sinh ^{-1}(c x)\right)},x\right)}{b c}+\frac{2 c \text{Int}\left(\frac{c^2 x^2+1}{x \left(a+b \sinh ^{-1}(c x)\right)},x\right)}{b}-\frac{\left(c^2 x^2+1\right)^2}{b c x^2 \left(a+b \sinh ^{-1}(c x)\right)}",0,"-((1 + c^2*x^2)^2/(b*c*x^2*(a + b*ArcSinh[c*x]))) - (2*Defer[Int][(1 + c^2*x^2)/(x^3*(a + b*ArcSinh[c*x])), x])/(b*c) + (2*c*Defer[Int][(1 + c^2*x^2)/(x*(a + b*ArcSinh[c*x])), x])/b","A",0,0,0,0,-1,"{}"
425,0,0,0,0.1394662,"\int \frac{\left(1+c^2 x^2\right)^{3/2}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(1 + c^2*x^2)^(3/2)/(x^3*(a + b*ArcSinh[c*x])^2),x]","\int \frac{\left(1+c^2 x^2\right)^{3/2}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\left(c^2 x^2+1\right)^{3/2}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(1 + c^2*x^2)^(3/2)/(x^3*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
426,0,0,0,0.1993512,"\int \frac{\left(1+c^2 x^2\right)^{3/2}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(1 + c^2*x^2)^(3/2)/(x^4*(a + b*ArcSinh[c*x])^2),x]","\int \frac{\left(1+c^2 x^2\right)^{3/2}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","-\frac{4 \text{Int}\left(\frac{c^2 x^2+1}{x^5 \left(a+b \sinh ^{-1}(c x)\right)},x\right)}{b c}-\frac{\left(c^2 x^2+1\right)^2}{b c x^4 \left(a+b \sinh ^{-1}(c x)\right)}",0,"-((1 + c^2*x^2)^2/(b*c*x^4*(a + b*ArcSinh[c*x]))) - (4*Defer[Int][(1 + c^2*x^2)/(x^5*(a + b*ArcSinh[c*x])), x])/(b*c)","A",0,0,0,0,-1,"{}"
427,1,273,0,1.2153852,"\int \frac{x^3 \left(1+c^2 x^2\right)^{5/2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(x^3*(1 + c^2*x^2)^(5/2))/(a + b*ArcSinh[c*x])^2,x]","-\frac{3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{128 b^2 c^4}-\frac{3 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{32 b^2 c^4}+\frac{21 \cosh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 a}{b}+7 \sinh ^{-1}(c x)\right)}{256 b^2 c^4}+\frac{9 \cosh \left(\frac{9 a}{b}\right) \text{Chi}\left(\frac{9 a}{b}+9 \sinh ^{-1}(c x)\right)}{256 b^2 c^4}+\frac{3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{128 b^2 c^4}+\frac{3 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{32 b^2 c^4}-\frac{21 \sinh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 a}{b}+7 \sinh ^{-1}(c x)\right)}{256 b^2 c^4}-\frac{9 \sinh \left(\frac{9 a}{b}\right) \text{Shi}\left(\frac{9 a}{b}+9 \sinh ^{-1}(c x)\right)}{256 b^2 c^4}-\frac{x^3 \left(c^2 x^2+1\right)^3}{b c \left(a+b \sinh ^{-1}(c x)\right)}","-\frac{3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{128 b^2 c^4}-\frac{3 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b^2 c^4}+\frac{21 \cosh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{256 b^2 c^4}+\frac{9 \cosh \left(\frac{9 a}{b}\right) \text{Chi}\left(\frac{9 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{256 b^2 c^4}+\frac{3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{128 b^2 c^4}+\frac{3 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 b^2 c^4}-\frac{21 \sinh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{256 b^2 c^4}-\frac{9 \sinh \left(\frac{9 a}{b}\right) \text{Shi}\left(\frac{9 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{256 b^2 c^4}-\frac{x^3 \left(c^2 x^2+1\right)^3}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-((x^3*(1 + c^2*x^2)^3)/(b*c*(a + b*ArcSinh[c*x]))) - (3*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(128*b^2*c^4) - (3*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(32*b^2*c^4) + (21*Cosh[(7*a)/b]*CoshIntegral[(7*a)/b + 7*ArcSinh[c*x]])/(256*b^2*c^4) + (9*Cosh[(9*a)/b]*CoshIntegral[(9*a)/b + 9*ArcSinh[c*x]])/(256*b^2*c^4) + (3*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(128*b^2*c^4) + (3*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(32*b^2*c^4) - (21*Sinh[(7*a)/b]*SinhIntegral[(7*a)/b + 7*ArcSinh[c*x]])/(256*b^2*c^4) - (9*Sinh[(9*a)/b]*SinhIntegral[(9*a)/b + 9*ArcSinh[c*x]])/(256*b^2*c^4)","A",34,6,27,0.2222,1,"{5777, 5779, 5448, 3303, 3298, 3301}"
428,1,281,0,1.071979,"\int \frac{x^2 \left(1+c^2 x^2\right)^{5/2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(x^2*(1 + c^2*x^2)^(5/2))/(a + b*ArcSinh[c*x])^2,x]","\frac{\sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{16 b^2 c^3}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{8 b^2 c^3}-\frac{3 \sinh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 a}{b}+6 \sinh ^{-1}(c x)\right)}{16 b^2 c^3}-\frac{\sinh \left(\frac{8 a}{b}\right) \text{Chi}\left(\frac{8 a}{b}+8 \sinh ^{-1}(c x)\right)}{16 b^2 c^3}-\frac{\cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{16 b^2 c^3}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{8 b^2 c^3}+\frac{3 \cosh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 a}{b}+6 \sinh ^{-1}(c x)\right)}{16 b^2 c^3}+\frac{\cosh \left(\frac{8 a}{b}\right) \text{Shi}\left(\frac{8 a}{b}+8 \sinh ^{-1}(c x)\right)}{16 b^2 c^3}-\frac{x^2 \left(c^2 x^2+1\right)^3}{b c \left(a+b \sinh ^{-1}(c x)\right)}","\frac{\sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 b^2 c^3}-\frac{3 \sinh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}-\frac{\sinh \left(\frac{8 a}{b}\right) \text{Chi}\left(\frac{8 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}-\frac{\cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 b^2 c^3}+\frac{3 \cosh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}+\frac{\cosh \left(\frac{8 a}{b}\right) \text{Shi}\left(\frac{8 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^3}-\frac{x^2 \left(c^2 x^2+1\right)^3}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-((x^2*(1 + c^2*x^2)^3)/(b*c*(a + b*ArcSinh[c*x]))) + (CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]]*Sinh[(2*a)/b])/(16*b^2*c^3) - (CoshIntegral[(4*a)/b + 4*ArcSinh[c*x]]*Sinh[(4*a)/b])/(8*b^2*c^3) - (3*CoshIntegral[(6*a)/b + 6*ArcSinh[c*x]]*Sinh[(6*a)/b])/(16*b^2*c^3) - (CoshIntegral[(8*a)/b + 8*ArcSinh[c*x]]*Sinh[(8*a)/b])/(16*b^2*c^3) - (Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(16*b^2*c^3) + (Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(8*b^2*c^3) + (3*Cosh[(6*a)/b]*SinhIntegral[(6*a)/b + 6*ArcSinh[c*x]])/(16*b^2*c^3) + (Cosh[(8*a)/b]*SinhIntegral[(8*a)/b + 8*ArcSinh[c*x]])/(16*b^2*c^3)","A",28,6,27,0.2222,1,"{5777, 5779, 5448, 3303, 3298, 3301}"
429,1,271,0,0.9695137,"\int \frac{x \left(1+c^2 x^2\right)^{5/2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(x*(1 + c^2*x^2)^(5/2))/(a + b*ArcSinh[c*x])^2,x]","\frac{5 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{64 b^2 c^2}+\frac{27 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{64 b^2 c^2}+\frac{25 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{64 b^2 c^2}+\frac{7 \cosh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 a}{b}+7 \sinh ^{-1}(c x)\right)}{64 b^2 c^2}-\frac{5 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{64 b^2 c^2}-\frac{27 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{64 b^2 c^2}-\frac{25 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{64 b^2 c^2}-\frac{7 \sinh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 a}{b}+7 \sinh ^{-1}(c x)\right)}{64 b^2 c^2}-\frac{x \left(c^2 x^2+1\right)^3}{b c \left(a+b \sinh ^{-1}(c x)\right)}","\frac{5 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{64 b^2 c^2}+\frac{27 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2}+\frac{25 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2}+\frac{7 \cosh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2}-\frac{5 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{64 b^2 c^2}-\frac{27 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2}-\frac{25 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2}-\frac{7 \sinh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b^2 c^2}-\frac{x \left(c^2 x^2+1\right)^3}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-((x*(1 + c^2*x^2)^3)/(b*c*(a + b*ArcSinh[c*x]))) + (5*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(64*b^2*c^2) + (27*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(64*b^2*c^2) + (25*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(64*b^2*c^2) + (7*Cosh[(7*a)/b]*CoshIntegral[(7*a)/b + 7*ArcSinh[c*x]])/(64*b^2*c^2) - (5*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(64*b^2*c^2) - (27*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(64*b^2*c^2) - (25*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(64*b^2*c^2) - (7*Sinh[(7*a)/b]*SinhIntegral[(7*a)/b + 7*ArcSinh[c*x]])/(64*b^2*c^2)","A",28,8,25,0.3200,1,"{5777, 5699, 3312, 3303, 3298, 3301, 5779, 5448}"
430,1,216,0,0.4463207,"\int \frac{\left(1+c^2 x^2\right)^{5/2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(1 + c^2*x^2)^(5/2)/(a + b*ArcSinh[c*x])^2,x]","-\frac{15 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{16 b^2 c}-\frac{3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{4 b^2 c}-\frac{3 \sinh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 a}{b}+6 \sinh ^{-1}(c x)\right)}{16 b^2 c}+\frac{15 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{16 b^2 c}+\frac{3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{4 b^2 c}+\frac{3 \cosh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 a}{b}+6 \sinh ^{-1}(c x)\right)}{16 b^2 c}-\frac{\left(c^2 x^2+1\right)^3}{b c \left(a+b \sinh ^{-1}(c x)\right)}","-\frac{15 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c}-\frac{3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c}-\frac{3 \sinh \left(\frac{6 a}{b}\right) \text{Chi}\left(\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c}+\frac{15 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c}+\frac{3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c}+\frac{3 \cosh \left(\frac{6 a}{b}\right) \text{Shi}\left(\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c}-\frac{\left(c^2 x^2+1\right)^3}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-((1 + c^2*x^2)^3/(b*c*(a + b*ArcSinh[c*x]))) - (15*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]]*Sinh[(2*a)/b])/(16*b^2*c) - (3*CoshIntegral[(4*a)/b + 4*ArcSinh[c*x]]*Sinh[(4*a)/b])/(4*b^2*c) - (3*CoshIntegral[(6*a)/b + 6*ArcSinh[c*x]]*Sinh[(6*a)/b])/(16*b^2*c) + (15*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(16*b^2*c) + (3*Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(4*b^2*c) + (3*Cosh[(6*a)/b]*SinhIntegral[(6*a)/b + 6*ArcSinh[c*x]])/(16*b^2*c)","A",13,6,24,0.2500,1,"{5696, 5779, 5448, 3303, 3298, 3301}"
431,0,0,0,0.5682576,"\int \frac{\left(1+c^2 x^2\right)^{5/2}}{x \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(1 + c^2*x^2)^(5/2)/(x*(a + b*ArcSinh[c*x])^2),x]","\int \frac{\left(1+c^2 x^2\right)^{5/2}}{x \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","-\frac{\text{Int}\left(\frac{\left(c^2 x^2+1\right)^2}{x^2 \left(a+b \sinh ^{-1}(c x)\right)},x\right)}{b c}+\frac{25 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b^2}+\frac{25 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2}+\frac{5 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2}-\frac{25 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b^2}-\frac{25 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2}-\frac{5 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2}-\frac{\left(c^2 x^2+1\right)^3}{b c x \left(a+b \sinh ^{-1}(c x)\right)}",0,"-((1 + c^2*x^2)^3/(b*c*x*(a + b*ArcSinh[c*x]))) + (25*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(8*b^2) + (25*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b^2) + (5*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b^2) - (25*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(8*b^2) - (25*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b^2) - (5*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b^2) - Defer[Int][(1 + c^2*x^2)^2/(x^2*(a + b*ArcSinh[c*x])), x]/(b*c)","A",0,0,0,0,-1,"{}"
432,0,0,0,0.3183608,"\int \frac{\left(1+c^2 x^2\right)^{5/2}}{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(1 + c^2*x^2)^(5/2)/(x^2*(a + b*ArcSinh[c*x])^2),x]","\int \frac{\left(1+c^2 x^2\right)^{5/2}}{x^2 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","-\frac{2 \text{Int}\left(\frac{\left(c^2 x^2+1\right)^2}{x^3 \left(a+b \sinh ^{-1}(c x)\right)},x\right)}{b c}+\frac{4 c \text{Int}\left(\frac{\left(c^2 x^2+1\right)^2}{x \left(a+b \sinh ^{-1}(c x)\right)},x\right)}{b}-\frac{\left(c^2 x^2+1\right)^3}{b c x^2 \left(a+b \sinh ^{-1}(c x)\right)}",0,"-((1 + c^2*x^2)^3/(b*c*x^2*(a + b*ArcSinh[c*x]))) - (2*Defer[Int][(1 + c^2*x^2)^2/(x^3*(a + b*ArcSinh[c*x])), x])/(b*c) + (4*c*Defer[Int][(1 + c^2*x^2)^2/(x*(a + b*ArcSinh[c*x])), x])/b","A",0,0,0,0,-1,"{}"
433,0,0,0,0.1437022,"\int \frac{\left(1+c^2 x^2\right)^{5/2}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(1 + c^2*x^2)^(5/2)/(x^3*(a + b*ArcSinh[c*x])^2),x]","\int \frac{\left(1+c^2 x^2\right)^{5/2}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\left(c^2 x^2+1\right)^{5/2}}{x^3 \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(1 + c^2*x^2)^(5/2)/(x^3*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
434,0,0,0,0.1443831,"\int \frac{\left(1+c^2 x^2\right)^{5/2}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(1 + c^2*x^2)^(5/2)/(x^4*(a + b*ArcSinh[c*x])^2),x]","\int \frac{\left(1+c^2 x^2\right)^{5/2}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\left(c^2 x^2+1\right)^{5/2}}{x^4 \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(1 + c^2*x^2)^(5/2)/(x^4*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
435,1,200,0,0.4801394,"\int \frac{x^5}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[x^5/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2),x]","\frac{5 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b^2 c^6}-\frac{15 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b^2 c^6}+\frac{5 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b^2 c^6}-\frac{5 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b^2 c^6}+\frac{15 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b^2 c^6}-\frac{5 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b^2 c^6}-\frac{x^5}{b c \left(a+b \sinh ^{-1}(c x)\right)}","\frac{5 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b^2 c^6}-\frac{15 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^6}+\frac{5 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^6}-\frac{5 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b^2 c^6}+\frac{15 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^6}-\frac{5 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^6}-\frac{x^5}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-(x^5/(b*c*(a + b*ArcSinh[c*x]))) + (5*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(8*b^2*c^6) - (15*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b^2*c^6) + (5*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b^2*c^6) - (5*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(8*b^2*c^6) + (15*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b^2*c^6) - (5*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b^2*c^6)","A",13,6,27,0.2222,1,"{5774, 5669, 5448, 3303, 3298, 3301}"
436,1,141,0,0.3954437,"\int \frac{x^4}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[x^4/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2),x]","\frac{\sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{b^2 c^5}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{2 b^2 c^5}-\frac{\cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{b^2 c^5}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{2 b^2 c^5}-\frac{x^4}{b c \left(a+b \sinh ^{-1}(c x)\right)}","\frac{\sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{b^2 c^5}-\frac{\sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^5}-\frac{\cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{b^2 c^5}+\frac{\cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^5}-\frac{x^4}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-(x^4/(b*c*(a + b*ArcSinh[c*x]))) + (CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]]*Sinh[(2*a)/b])/(b^2*c^5) - (CoshIntegral[(4*a)/b + 4*ArcSinh[c*x]]*Sinh[(4*a)/b])/(2*b^2*c^5) - (Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(b^2*c^5) + (Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(2*b^2*c^5)","A",10,6,27,0.2222,1,"{5774, 5669, 5448, 3303, 3298, 3301}"
437,1,138,0,0.3668075,"\int \frac{x^3}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[x^3/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2),x]","-\frac{3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b^2 c^4}+\frac{3 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{4 b^2 c^4}+\frac{3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b^2 c^4}-\frac{3 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{4 b^2 c^4}-\frac{x^3}{b c \left(a+b \sinh ^{-1}(c x)\right)}","-\frac{3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b^2 c^4}+\frac{3 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^4}+\frac{3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b^2 c^4}-\frac{3 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^4}-\frac{x^3}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-(x^3/(b*c*(a + b*ArcSinh[c*x]))) - (3*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(4*b^2*c^4) + (3*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b^2*c^4) + (3*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(4*b^2*c^4) - (3*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b^2*c^4)","A",10,6,27,0.2222,1,"{5774, 5669, 5448, 3303, 3298, 3301}"
438,1,79,0,0.2577862,"\int \frac{x^2}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[x^2/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2),x]","-\frac{\sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{b^2 c^3}+\frac{\cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{b^2 c^3}-\frac{x^2}{b c \left(a+b \sinh ^{-1}(c x)\right)}","-\frac{\sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{b^2 c^3}+\frac{\cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{b^2 c^3}-\frac{x^2}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-(x^2/(b*c*(a + b*ArcSinh[c*x]))) - (CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]]*Sinh[(2*a)/b])/(b^2*c^3) + (Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(b^2*c^3)","A",7,7,27,0.2593,1,"{5774, 5669, 5448, 12, 3303, 3298, 3301}"
439,1,73,0,0.160922,"\int \frac{x}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[x/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2),x]","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b^2 c^2}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b^2 c^2}-\frac{x}{b c \left(a+b \sinh ^{-1}(c x)\right)}","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b^2 c^2}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b^2 c^2}-\frac{x}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-(x/(b*c*(a + b*ArcSinh[c*x]))) + (Cosh[a/b]*CoshIntegral[(a + b*ArcSinh[c*x])/b])/(b^2*c^2) - (Sinh[a/b]*SinhIntegral[(a + b*ArcSinh[c*x])/b])/(b^2*c^2)","A",5,5,25,0.2000,1,"{5774, 5657, 3303, 3298, 3301}"
440,1,18,0,0.0447206,"\int \frac{1}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[1/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2),x]","-\frac{1}{b c \left(a+b \sinh ^{-1}(c x)\right)}","-\frac{1}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-(1/(b*c*(a + b*ArcSinh[c*x])))","A",1,1,24,0.04167,1,"{5675}"
441,0,0,0,0.1466164,"\int \frac{1}{x \sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[1/(x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2),x]","\int \frac{1}{x \sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","-\frac{\text{Int}\left(\frac{1}{x^2 \left(a+b \sinh ^{-1}(c x)\right)},x\right)}{b c}-\frac{1}{b c x \left(a+b \sinh ^{-1}(c x)\right)}",0,"-(1/(b*c*x*(a + b*ArcSinh[c*x]))) - Defer[Int][1/(x^2*(a + b*ArcSinh[c*x])), x]/(b*c)","A",0,0,0,0,-1,"{}"
442,0,0,0,0.1484094,"\int \frac{1}{x^2 \sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[1/(x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2),x]","\int \frac{1}{x^2 \sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","-\frac{2 \text{Int}\left(\frac{1}{x^3 \left(a+b \sinh ^{-1}(c x)\right)},x\right)}{b c}-\frac{1}{b c x^2 \left(a+b \sinh ^{-1}(c x)\right)}",0,"-(1/(b*c*x^2*(a + b*ArcSinh[c*x]))) - (2*Defer[Int][1/(x^3*(a + b*ArcSinh[c*x])), x])/(b*c)","A",0,0,0,0,-1,"{}"
443,0,0,0,0.1374392,"\int \frac{x^3}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[x^3/((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{x^3}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x^3}{\left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][x^3/((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
444,0,0,0,0.2006988,"\int \frac{x^2}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[x^2/((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{x^2}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\frac{2 \text{Int}\left(\frac{x}{\left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)},x\right)}{b c}-\frac{x^2}{b c \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}",0,"-(x^2/(b*c*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))) + (2*Defer[Int][x/((1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])), x])/(b*c)","A",0,0,0,0,-1,"{}"
445,0,0,0,0.0931618,"\int \frac{x}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[x/((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{x}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x}{\left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][x/((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
446,0,0,0,0.110704,"\int \frac{1}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[1/((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{1}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","-\frac{2 c \text{Int}\left(\frac{x}{\left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)},x\right)}{b}-\frac{1}{b c \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}",0,"-(1/(b*c*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))) - (2*c*Defer[Int][x/((1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])), x])/b","A",0,0,0,0,-1,"{}"
447,0,0,0,0.1319553,"\int \frac{1}{x \left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[1/(x*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{1}{x \left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/(x*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
448,0,0,0,0.130146,"\int \frac{1}{x^2 \left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[1/(x^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{1}{x^2 \left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/(x^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
449,0,0,0,0.1368406,"\int \frac{x^3}{\left(1+c^2 x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[x^3/((1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{x^3}{\left(1+c^2 x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x^3}{\left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][x^3/((1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
450,0,0,0,0.1359278,"\int \frac{x^2}{\left(1+c^2 x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[x^2/((1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{x^2}{\left(1+c^2 x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x^2}{\left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][x^2/((1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
451,0,0,0,0.0920734,"\int \frac{x}{\left(1+c^2 x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[x/((1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{x}{\left(1+c^2 x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x}{\left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][x/((1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
452,0,0,0,0.1099836,"\int \frac{1}{\left(1+c^2 x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[1/((1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{1}{\left(1+c^2 x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","-\frac{4 c \text{Int}\left(\frac{x}{\left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)},x\right)}{b}-\frac{1}{b c \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}",0,"-(1/(b*c*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))) - (4*c*Defer[Int][x/((1 + c^2*x^2)^3*(a + b*ArcSinh[c*x])), x])/b","A",0,0,0,0,-1,"{}"
453,0,0,0,0.1312267,"\int \frac{1}{x \left(1+c^2 x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[1/(x*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{1}{x \left(1+c^2 x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/(x*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
454,0,0,0,0.1318702,"\int \frac{1}{x^2 \left(1+c^2 x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[1/(x^2*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{1}{x^2 \left(1+c^2 x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/(x^2*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
455,0,0,0,0.1278306,"\int \frac{x^m \left(1+c^2 x^2\right)^{5/2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(x^m*(1 + c^2*x^2)^(5/2))/(a + b*ArcSinh[c*x])^2,x]","\int \frac{x^m \left(1+c^2 x^2\right)^{5/2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\left(c^2 x^2+1\right)^{5/2} x^m}{\left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(x^m*(1 + c^2*x^2)^(5/2))/(a + b*ArcSinh[c*x])^2, x]","A",0,0,0,0,-1,"{}"
456,0,0,0,0.1278192,"\int \frac{x^m \left(1+c^2 x^2\right)^{3/2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(x^m*(1 + c^2*x^2)^(3/2))/(a + b*ArcSinh[c*x])^2,x]","\int \frac{x^m \left(1+c^2 x^2\right)^{3/2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\left(c^2 x^2+1\right)^{3/2} x^m}{\left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(x^m*(1 + c^2*x^2)^(3/2))/(a + b*ArcSinh[c*x])^2, x]","A",0,0,0,0,-1,"{}"
457,0,0,0,0.1132618,"\int \frac{x^m \sqrt{1+c^2 x^2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(x^m*Sqrt[1 + c^2*x^2])/(a + b*ArcSinh[c*x])^2,x]","\int \frac{x^m \sqrt{1+c^2 x^2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{c^2 x^2+1} x^m}{\left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(x^m*Sqrt[1 + c^2*x^2])/(a + b*ArcSinh[c*x])^2, x]","A",0,0,0,0,-1,"{}"
458,0,0,0,0.1524045,"\int \frac{x^m}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[x^m/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2),x]","\int \frac{x^m}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\frac{m \text{Int}\left(\frac{x^{m-1}}{a+b \sinh ^{-1}(c x)},x\right)}{b c}-\frac{x^m}{b c \left(a+b \sinh ^{-1}(c x)\right)}",0,"-(x^m/(b*c*(a + b*ArcSinh[c*x]))) + (m*Defer[Int][x^(-1 + m)/(a + b*ArcSinh[c*x]), x])/(b*c)","A",0,0,0,0,-1,"{}"
459,0,0,0,0.1404311,"\int \frac{x^m}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[x^m/((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{x^m}{\left(1+c^2 x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x^m}{\left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][x^m/((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
460,0,0,0,0.1398875,"\int \frac{x^m}{\left(1+c^2 x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[x^m/((1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{x^m}{\left(1+c^2 x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x^m}{\left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][x^m/((1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
461,1,13,0,0.0354877,"\int \frac{1}{\sqrt{1+a^2 x^2} \sinh ^{-1}(a x)^3} \, dx","Int[1/(Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^3),x]","-\frac{1}{2 a \sinh ^{-1}(a x)^2}","-\frac{1}{2 a \sinh ^{-1}(a x)^2}",1,"-1/(2*a*ArcSinh[a*x]^2)","A",1,1,20,0.05000,1,"{5675}"
462,1,254,0,1.3078475,"\int \frac{x^3 \left(d+c^2 d x^2\right)}{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x^3*(d + c^2*d*x^2))/(a + b*ArcSinh[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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^4}-\frac{2 d x^3 \left(c^2 x^2+1\right)^{3/2}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}","-\frac{3 \sqrt{\frac{\pi }{2}} d e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^4}-\frac{2 d x^3 \left(c^2 x^2+1\right)^{3/2}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}",1,"(-2*d*x^3*(1 + c^2*x^2)^(3/2))/(b*c*Sqrt[a + b*ArcSinh[c*x]]) - (3*d*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[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*ArcSinh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^4) - (3*d*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[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*ArcSinh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^4*E^((6*a)/b))","A",27,7,26,0.2692,1,"{5777, 5779, 5448, 3307, 2180, 2204, 2205}"
463,1,335,0,1.3785866,"\int \frac{x^2 \left(d+c^2 d x^2\right)}{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x^2*(d + c^2*d*x^2))/(a + b*ArcSinh[c*x])^(3/2),x]","\frac{\sqrt{\pi } d e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{2 d x^2 \left(c^2 x^2+1\right)^{3/2}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}","\frac{\sqrt{\pi } d e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^3}-\frac{2 d x^2 \left(c^2 x^2+1\right)^{3/2}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}",1,"(-2*d*x^2*(1 + c^2*x^2)^(3/2))/(b*c*Sqrt[a + b*ArcSinh[c*x]]) + (d*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(8*b^(3/2)*c^3) - (d*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^3) - (d*E^((5*a)/b)*Sqrt[5*Pi]*Erf[(Sqrt[5]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^3) - (d*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(8*b^(3/2)*c^3*E^(a/b)) + (d*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^3*E^((3*a)/b)) + (d*Sqrt[5*Pi]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^3*E^((5*a)/b))","A",32,7,26,0.2692,1,"{5777, 5779, 5448, 3308, 2180, 2204, 2205}"
464,1,236,0,0.7666153,"\int \frac{x \left(d+c^2 d x^2\right)}{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x*(d + c^2*d*x^2))/(a + b*ArcSinh[c*x])^(3/2),x]","\frac{\sqrt{\pi } d e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2} c^2}-\frac{2 d x \left(c^2 x^2+1\right)^{3/2}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}","\frac{\sqrt{\pi } d e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2} c^2}-\frac{2 d x \left(c^2 x^2+1\right)^{3/2}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}",1,"(-2*d*x*(1 + c^2*x^2)^(3/2))/(b*c*Sqrt[a + b*ArcSinh[c*x]]) + (d*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c^2) + (d*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(2*b^(3/2)*c^2) + (d*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c^2*E^((4*a)/b)) + (d*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(2*b^(3/2)*c^2*E^((2*a)/b))","A",17,9,24,0.3750,1,"{5777, 5699, 3312, 3307, 2180, 2204, 2205, 5779, 5448}"
465,1,228,0,0.5250199,"\int \frac{d+c^2 d x^2}{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(d + c^2*d*x^2)/(a + b*ArcSinh[c*x])^(3/2),x]","-\frac{3 \sqrt{\pi } d e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}-\frac{2 d \left(c^2 x^2+1\right)^{3/2}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}","-\frac{3 \sqrt{\pi } d e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2} c}-\frac{2 d \left(c^2 x^2+1\right)^{3/2}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}",1,"(-2*d*(1 + c^2*x^2)^(3/2))/(b*c*Sqrt[a + b*ArcSinh[c*x]]) - (3*d*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(4*b^(3/2)*c) - (d*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c) + (3*d*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(4*b^(3/2)*c*E^(a/b)) + (d*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c*E^((3*a)/b))","A",14,7,23,0.3043,1,"{5696, 5779, 5448, 3308, 2180, 2204, 2205}"
466,0,0,0,0.7964112,"\int \frac{d+c^2 d x^2}{x \left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(d + c^2*d*x^2)/(x*(a + b*ArcSinh[c*x])^(3/2)),x]","\int \frac{d+c^2 d x^2}{x \left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","-\frac{2 d \text{Int}\left(\frac{1}{x^2 \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2}}-\frac{2 d \left(c^2 x^2+1\right)^{3/2}}{b c x \sqrt{a+b \sinh ^{-1}(c x)}}",0,"(-2*d*(1 + c^2*x^2)^(3/2))/(b*c*x*Sqrt[a + b*ArcSinh[c*x]]) + (d*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/b^(3/2) + (d*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(b^(3/2)*E^((2*a)/b)) - (2*d*Defer[Int][1/(x^2*Sqrt[1 + c^2*x^2]*Sqrt[a + b*ArcSinh[c*x]]), x])/(b*c)","A",0,0,0,0,-1,"{}"
467,1,474,0,1.5270895,"\int \frac{x^3 \left(d+c^2 d x^2\right)^2}{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x^3*(d + c^2*d*x^2)^2)/(a + b*ArcSinh[c*x])^(3/2),x]","-\frac{\sqrt{\pi } d^2 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}-\frac{2 d^2 x^3 \left(c^2 x^2+1\right)^{5/2}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}","-\frac{\sqrt{\pi } d^2 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{32 b^{3/2} c^4}-\frac{2 d^2 x^3 \left(c^2 x^2+1\right)^{5/2}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}",1,"(-2*d^2*x^3*(1 + c^2*x^2)^(5/2))/(b*c*Sqrt[a + b*ArcSinh[c*x]]) - (d^2*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcSinh[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*ArcSinh[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*ArcSinh[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*ArcSinh[c*x]])/Sqrt[b]])/(32*b^(3/2)*c^4) - (d^2*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcSinh[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*ArcSinh[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*ArcSinh[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*ArcSinh[c*x]])/Sqrt[b]])/(32*b^(3/2)*c^4*E^((6*a)/b))","A",32,7,28,0.2500,1,"{5777, 5779, 5448, 3307, 2180, 2204, 2205}"
468,1,457,0,1.7798206,"\int \frac{x^2 \left(d+c^2 d x^2\right)^2}{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x^2*(d + c^2*d*x^2)^2)/(a + b*ArcSinh[c*x])^(3/2),x]","\frac{5 \sqrt{\pi } d^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}-\frac{2 d^2 x^2 \left(c^2 x^2+1\right)^{5/2}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}","\frac{5 \sqrt{\pi } d^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{64 b^{3/2} c^3}-\frac{2 d^2 x^2 \left(c^2 x^2+1\right)^{5/2}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}",1,"(-2*d^2*x^2*(1 + c^2*x^2)^(5/2))/(b*c*Sqrt[a + b*ArcSinh[c*x]]) + (5*d^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[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*ArcSinh[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*ArcSinh[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*ArcSinh[c*x]])/Sqrt[b]])/(64*b^(3/2)*c^3) - (5*d^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(64*b^(3/2)*c^3*E^(a/b)) + (d^2*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[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*ArcSinh[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*ArcSinh[c*x]])/Sqrt[b]])/(64*b^(3/2)*c^3*E^((7*a)/b))","A",42,7,28,0.2500,1,"{5777, 5779, 5448, 3308, 2180, 2204, 2205}"
469,1,358,0,1.3302066,"\int \frac{x \left(d+c^2 d x^2\right)^2}{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(x*(d + c^2*d*x^2)^2)/(a + b*ArcSinh[c*x])^(3/2),x]","\frac{\sqrt{\pi } d^2 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^2}-\frac{2 d^2 x \left(c^2 x^2+1\right)^{5/2}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}","\frac{\sqrt{\pi } d^2 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c^2}-\frac{2 d^2 x \left(c^2 x^2+1\right)^{5/2}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}",1,"(-2*d^2*x*(1 + c^2*x^2)^(5/2))/(b*c*Sqrt[a + b*ArcSinh[c*x]]) + (d^2*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcSinh[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*ArcSinh[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*ArcSinh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^2) + (d^2*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcSinh[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*ArcSinh[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*ArcSinh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c^2*E^((6*a)/b))","A",32,9,26,0.3462,1,"{5777, 5699, 3312, 3307, 2180, 2204, 2205, 5779, 5448}"
470,1,346,0,0.7288436,"\int \frac{\left(d+c^2 d x^2\right)^2}{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(d + c^2*d*x^2)^2/(a + b*ArcSinh[c*x])^(3/2),x]","-\frac{5 \sqrt{\pi } d^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c}-\frac{2 d^2 \left(c^2 x^2+1\right)^{5/2}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}","-\frac{5 \sqrt{\pi } d^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{16 b^{3/2} c}-\frac{2 d^2 \left(c^2 x^2+1\right)^{5/2}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}",1,"(-2*d^2*(1 + c^2*x^2)^(5/2))/(b*c*Sqrt[a + b*ArcSinh[c*x]]) - (5*d^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[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*ArcSinh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c) - (d^2*E^((5*a)/b)*Sqrt[5*Pi]*Erf[(Sqrt[5]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c) + (5*d^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(8*b^(3/2)*c*E^(a/b)) + (5*d^2*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c*E^((3*a)/b)) + (d^2*Sqrt[5*Pi]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(16*b^(3/2)*c*E^((5*a)/b))","A",19,7,25,0.2800,1,"{5696, 5779, 5448, 3308, 2180, 2204, 2205}"
471,0,0,0,1.4410339,"\int \frac{\left(d+c^2 d x^2\right)^2}{x \left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(d + c^2*d*x^2)^2/(x*(a + b*ArcSinh[c*x])^(3/2)),x]","\int \frac{\left(d+c^2 d x^2\right)^2}{x \left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","-\frac{2 d^2 \text{Int}\left(\frac{1}{x^2 \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2}}+\frac{\sqrt{2 \pi } d^2 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} d^2 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 b^{3/2}}+\frac{\sqrt{2 \pi } d^2 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} d^2 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 b^{3/2}}-\frac{2 d^2 \left(c^2 x^2+1\right)^{5/2}}{b c x \sqrt{a+b \sinh ^{-1}(c x)}}",0,"(-2*d^2*(1 + c^2*x^2)^(5/2))/(b*c*x*Sqrt[a + b*ArcSinh[c*x]]) + (d^2*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(4*b^(3/2)) - (d^2*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(2*b^(3/2)) + (d^2*E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/b^(3/2) + (d^2*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(4*b^(3/2)*E^((4*a)/b)) - (d^2*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(2*b^(3/2)*E^((2*a)/b)) + (d^2*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(b^(3/2)*E^((2*a)/b)) - (2*d^2*Defer[Int][1/(x^2*Sqrt[1 + c^2*x^2]*Sqrt[a + b*ArcSinh[c*x]]), x])/(b*c)","A",0,0,0,0,-1,"{}"
472,1,319,0,0.4081086,"\int \left(c+a^2 c x^2\right)^{3/2} \sqrt{\sinh ^{-1}(a x)} \, dx","Int[(c + a^2*c*x^2)^(3/2)*Sqrt[ArcSinh[a*x]],x]","\frac{\sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{256 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a \sqrt{a^2 x^2+1}}-\frac{\sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{256 a \sqrt{a^2 x^2+1}}-\frac{\sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a \sqrt{a^2 x^2+1}}+\frac{1}{4} x \left(a^2 c x^2+c\right)^{3/2} \sqrt{\sinh ^{-1}(a x)}+\frac{c \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}}{4 a \sqrt{a^2 x^2+1}}+\frac{3}{8} c x \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}","\frac{\sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{256 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a \sqrt{a^2 x^2+1}}-\frac{\sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{256 a \sqrt{a^2 x^2+1}}-\frac{\sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a \sqrt{a^2 x^2+1}}+\frac{1}{4} x \left(a^2 c x^2+c\right)^{3/2} \sqrt{\sinh ^{-1}(a x)}+\frac{c \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}}{4 a \sqrt{a^2 x^2+1}}+\frac{3}{8} c x \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}",1,"(3*c*x*Sqrt[c + a^2*c*x^2]*Sqrt[ArcSinh[a*x]])/8 + (x*(c + a^2*c*x^2)^(3/2)*Sqrt[ArcSinh[a*x]])/4 + (c*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(3/2))/(4*a*Sqrt[1 + a^2*x^2]) + (c*Sqrt[Pi]*Sqrt[c + a^2*c*x^2]*Erf[2*Sqrt[ArcSinh[a*x]]])/(256*a*Sqrt[1 + a^2*x^2]) + (c*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(16*a*Sqrt[1 + a^2*x^2]) - (c*Sqrt[Pi]*Sqrt[c + a^2*c*x^2]*Erfi[2*Sqrt[ArcSinh[a*x]]])/(256*a*Sqrt[1 + a^2*x^2]) - (c*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(16*a*Sqrt[1 + a^2*x^2])","A",24,11,23,0.4783,1,"{5684, 5682, 5675, 5669, 5448, 12, 3308, 2180, 2204, 2205, 5779}"
473,1,186,0,0.1680286,"\int \sqrt{c+a^2 c x^2} \sqrt{\sinh ^{-1}(a x)} \, dx","Int[Sqrt[c + a^2*c*x^2]*Sqrt[ArcSinh[a*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a \sqrt{a^2 x^2+1}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}}{3 a \sqrt{a^2 x^2+1}}+\frac{1}{2} x \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a \sqrt{a^2 x^2+1}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}}{3 a \sqrt{a^2 x^2+1}}+\frac{1}{2} x \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}",1,"(x*Sqrt[c + a^2*c*x^2]*Sqrt[ArcSinh[a*x]])/2 + (Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(3/2))/(3*a*Sqrt[1 + a^2*x^2]) + (Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(16*a*Sqrt[1 + a^2*x^2]) - (Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(16*a*Sqrt[1 + a^2*x^2])","A",10,9,23,0.3913,1,"{5682, 5675, 5669, 5448, 12, 3308, 2180, 2204, 2205}"
474,1,42,0,0.0771497,"\int \frac{\sqrt{\sinh ^{-1}(a x)}}{\sqrt{c+a^2 c x^2}} \, dx","Int[Sqrt[ArcSinh[a*x]]/Sqrt[c + a^2*c*x^2],x]","\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{3 a \sqrt{a^2 c x^2+c}}","\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{3/2}}{3 a \sqrt{a^2 c x^2+c}}",1,"(2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^(3/2))/(3*a*Sqrt[c + a^2*c*x^2])","A",2,2,23,0.08696,1,"{5677, 5675}"
475,0,0,0,0.0963678,"\int \frac{\sqrt{\sinh ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[Sqrt[ArcSinh[a*x]]/(c + a^2*c*x^2)^(3/2),x]","\int \frac{\sqrt{\sinh ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","\frac{x \sqrt{\sinh ^{-1}(a x)}}{c \sqrt{a^2 c x^2+c}}-\frac{a \sqrt{a^2 x^2+1} \text{Int}\left(\frac{x}{\left(a^2 x^2+1\right) \sqrt{\sinh ^{-1}(a x)}},x\right)}{2 c \sqrt{a^2 c x^2+c}}",0,"(x*Sqrt[ArcSinh[a*x]])/(c*Sqrt[c + a^2*c*x^2]) - (a*Sqrt[1 + a^2*x^2]*Defer[Int][x/((1 + a^2*x^2)*Sqrt[ArcSinh[a*x]]), x])/(2*c*Sqrt[c + a^2*c*x^2])","A",0,0,0,0,-1,"{}"
476,0,0,0,0.1989648,"\int \frac{\sqrt{\sinh ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{5/2}} \, dx","Int[Sqrt[ArcSinh[a*x]]/(c + a^2*c*x^2)^(5/2),x]","\int \frac{\sqrt{\sinh ^{-1}(a x)}}{\left(c+a^2 c x^2\right)^{5/2}} \, dx","-\frac{a \sqrt{a^2 x^2+1} \text{Int}\left(\frac{x}{\left(a^2 x^2+1\right)^2 \sqrt{\sinh ^{-1}(a x)}},x\right)}{6 c^2 \sqrt{a^2 c x^2+c}}-\frac{a \sqrt{a^2 x^2+1} \text{Int}\left(\frac{x}{\left(a^2 x^2+1\right) \sqrt{\sinh ^{-1}(a x)}},x\right)}{3 c^2 \sqrt{a^2 c x^2+c}}+\frac{2 x \sqrt{\sinh ^{-1}(a x)}}{3 c^2 \sqrt{a^2 c x^2+c}}+\frac{x \sqrt{\sinh ^{-1}(a x)}}{3 c \left(a^2 c x^2+c\right)^{3/2}}",0,"(x*Sqrt[ArcSinh[a*x]])/(3*c*(c + a^2*c*x^2)^(3/2)) + (2*x*Sqrt[ArcSinh[a*x]])/(3*c^2*Sqrt[c + a^2*c*x^2]) - (a*Sqrt[1 + a^2*x^2]*Defer[Int][x/((1 + a^2*x^2)^2*Sqrt[ArcSinh[a*x]]), x])/(6*c^2*Sqrt[c + a^2*c*x^2]) - (a*Sqrt[1 + a^2*x^2]*Defer[Int][x/((1 + a^2*x^2)*Sqrt[ArcSinh[a*x]]), x])/(3*c^2*Sqrt[c + a^2*c*x^2])","A",0,0,0,0,-1,"{}"
477,1,449,0,0.5649764,"\int \left(c+a^2 c x^2\right)^{3/2} \sinh ^{-1}(a x)^{3/2} \, dx","Int[(c + a^2*c*x^2)^(3/2)*ArcSinh[a*x]^(3/2),x]","\frac{3 \sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{2048 a \sqrt{a^2 x^2+1}}+\frac{3 \sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{3 \sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{2048 a \sqrt{a^2 x^2+1}}+\frac{3 \sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{3 c \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{5/2}}{20 a \sqrt{a^2 x^2+1}}+\frac{1}{4} x \left(a^2 c x^2+c\right)^{3/2} \sinh ^{-1}(a x)^{3/2}+\frac{3}{8} c x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}-\frac{3 c \left(a^2 x^2+1\right)^{3/2} \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}{32 a}-\frac{9 a c x^2 \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}{32 \sqrt{a^2 x^2+1}}-\frac{27 c \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}{256 a \sqrt{a^2 x^2+1}}","\frac{3 \sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{2048 a \sqrt{a^2 x^2+1}}+\frac{3 \sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{3 \sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{2048 a \sqrt{a^2 x^2+1}}+\frac{3 \sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{3 c \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{5/2}}{20 a \sqrt{a^2 x^2+1}}+\frac{1}{4} x \left(a^2 c x^2+c\right)^{3/2} \sinh ^{-1}(a x)^{3/2}+\frac{3}{8} c x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}-\frac{3 c \left(a^2 x^2+1\right)^{3/2} \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}{32 a}-\frac{9 a c x^2 \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}{32 \sqrt{a^2 x^2+1}}-\frac{27 c \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}{256 a \sqrt{a^2 x^2+1}}",1,"(-27*c*Sqrt[c + a^2*c*x^2]*Sqrt[ArcSinh[a*x]])/(256*a*Sqrt[1 + a^2*x^2]) - (9*a*c*x^2*Sqrt[c + a^2*c*x^2]*Sqrt[ArcSinh[a*x]])/(32*Sqrt[1 + a^2*x^2]) - (3*c*(1 + a^2*x^2)^(3/2)*Sqrt[c + a^2*c*x^2]*Sqrt[ArcSinh[a*x]])/(32*a) + (3*c*x*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(3/2))/8 + (x*(c + a^2*c*x^2)^(3/2)*ArcSinh[a*x]^(3/2))/4 + (3*c*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(5/2))/(20*a*Sqrt[1 + a^2*x^2]) + (3*c*Sqrt[Pi]*Sqrt[c + a^2*c*x^2]*Erf[2*Sqrt[ArcSinh[a*x]]])/(2048*a*Sqrt[1 + a^2*x^2]) + (3*c*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(64*a*Sqrt[1 + a^2*x^2]) + (3*c*Sqrt[Pi]*Sqrt[c + a^2*c*x^2]*Erfi[2*Sqrt[ArcSinh[a*x]]])/(2048*a*Sqrt[1 + a^2*x^2]) + (3*c*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(64*a*Sqrt[1 + a^2*x^2])","A",26,12,23,0.5217,1,"{5684, 5682, 5675, 5663, 5779, 3312, 3307, 2180, 2204, 2205, 5717, 5699}"
478,1,271,0,0.2729767,"\int \sqrt{c+a^2 c x^2} \sinh ^{-1}(a x)^{3/2} \, dx","Int[Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(3/2),x]","\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{5/2}}{5 a \sqrt{a^2 x^2+1}}+\frac{1}{2} x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}-\frac{3 a x^2 \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}{8 \sqrt{a^2 x^2+1}}-\frac{3 \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}{16 a \sqrt{a^2 x^2+1}}","\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{5/2}}{5 a \sqrt{a^2 x^2+1}}+\frac{1}{2} x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}-\frac{3 a x^2 \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}{8 \sqrt{a^2 x^2+1}}-\frac{3 \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}{16 a \sqrt{a^2 x^2+1}}",1,"(-3*Sqrt[c + a^2*c*x^2]*Sqrt[ArcSinh[a*x]])/(16*a*Sqrt[1 + a^2*x^2]) - (3*a*x^2*Sqrt[c + a^2*c*x^2]*Sqrt[ArcSinh[a*x]])/(8*Sqrt[1 + a^2*x^2]) + (x*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(3/2))/2 + (Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(5/2))/(5*a*Sqrt[1 + a^2*x^2]) + (3*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(64*a*Sqrt[1 + a^2*x^2]) + (3*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(64*a*Sqrt[1 + a^2*x^2])","A",11,9,23,0.3913,1,"{5682, 5675, 5663, 5779, 3312, 3307, 2180, 2204, 2205}"
479,1,42,0,0.0742584,"\int \frac{\sinh ^{-1}(a x)^{3/2}}{\sqrt{c+a^2 c x^2}} \, dx","Int[ArcSinh[a*x]^(3/2)/Sqrt[c + a^2*c*x^2],x]","\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{5/2}}{5 a \sqrt{a^2 c x^2+c}}","\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{5/2}}{5 a \sqrt{a^2 c x^2+c}}",1,"(2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^(5/2))/(5*a*Sqrt[c + a^2*c*x^2])","A",2,2,23,0.08696,1,"{5677, 5675}"
480,0,0,0,0.0931448,"\int \frac{\sinh ^{-1}(a x)^{3/2}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[ArcSinh[a*x]^(3/2)/(c + a^2*c*x^2)^(3/2),x]","\int \frac{\sinh ^{-1}(a x)^{3/2}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","\frac{x \sinh ^{-1}(a x)^{3/2}}{c \sqrt{a^2 c x^2+c}}-\frac{3 a \sqrt{a^2 x^2+1} \text{Int}\left(\frac{x \sqrt{\sinh ^{-1}(a x)}}{a^2 x^2+1},x\right)}{2 c \sqrt{a^2 c x^2+c}}",0,"(x*ArcSinh[a*x]^(3/2))/(c*Sqrt[c + a^2*c*x^2]) - (3*a*Sqrt[1 + a^2*x^2]*Defer[Int][(x*Sqrt[ArcSinh[a*x]])/(1 + a^2*x^2), x])/(2*c*Sqrt[c + a^2*c*x^2])","A",0,0,0,0,-1,"{}"
481,1,514,0,0.7647223,"\int \left(c+a^2 c x^2\right)^{3/2} \sinh ^{-1}(a x)^{5/2} \, dx","Int[(c + a^2*c*x^2)^(3/2)*ArcSinh[a*x]^(5/2),x]","\frac{15 \sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{16384 a \sqrt{a^2 x^2+1}}+\frac{15 \sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{256 a \sqrt{a^2 x^2+1}}-\frac{15 \sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{16384 a \sqrt{a^2 x^2+1}}-\frac{15 \sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{256 a \sqrt{a^2 x^2+1}}+\frac{3 c \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{7/2}}{28 a \sqrt{a^2 x^2+1}}+\frac{1}{4} x \left(a^2 c x^2+c\right)^{3/2} \sinh ^{-1}(a x)^{5/2}+\frac{3}{8} c x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{5/2}-\frac{5 c \left(a^2 x^2+1\right)^{3/2} \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}}{32 a}-\frac{15 a c x^2 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}}{32 \sqrt{a^2 x^2+1}}-\frac{45 c \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}}{256 a \sqrt{a^2 x^2+1}}+\frac{225}{512} c x \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}+\frac{15}{256} c x \left(a^2 x^2+1\right) \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}","\frac{15 \sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{16384 a \sqrt{a^2 x^2+1}}+\frac{15 \sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{256 a \sqrt{a^2 x^2+1}}-\frac{15 \sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{16384 a \sqrt{a^2 x^2+1}}-\frac{15 \sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{256 a \sqrt{a^2 x^2+1}}+\frac{3 c \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{7/2}}{28 a \sqrt{a^2 x^2+1}}+\frac{1}{4} x \left(a^2 c x^2+c\right)^{3/2} \sinh ^{-1}(a x)^{5/2}+\frac{3}{8} c x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{5/2}-\frac{5 c \left(a^2 x^2+1\right)^{3/2} \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}}{32 a}-\frac{15 a c x^2 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}}{32 \sqrt{a^2 x^2+1}}-\frac{45 c \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}}{256 a \sqrt{a^2 x^2+1}}+\frac{225}{512} c x \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}+\frac{15}{256} c x \left(a^2 x^2+1\right) \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}",1,"(225*c*x*Sqrt[c + a^2*c*x^2]*Sqrt[ArcSinh[a*x]])/512 + (15*c*x*(1 + a^2*x^2)*Sqrt[c + a^2*c*x^2]*Sqrt[ArcSinh[a*x]])/256 - (45*c*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(3/2))/(256*a*Sqrt[1 + a^2*x^2]) - (15*a*c*x^2*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(3/2))/(32*Sqrt[1 + a^2*x^2]) - (5*c*(1 + a^2*x^2)^(3/2)*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(3/2))/(32*a) + (3*c*x*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(5/2))/8 + (x*(c + a^2*c*x^2)^(3/2)*ArcSinh[a*x]^(5/2))/4 + (3*c*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(7/2))/(28*a*Sqrt[1 + a^2*x^2]) + (15*c*Sqrt[Pi]*Sqrt[c + a^2*c*x^2]*Erf[2*Sqrt[ArcSinh[a*x]]])/(16384*a*Sqrt[1 + a^2*x^2]) + (15*c*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(256*a*Sqrt[1 + a^2*x^2]) - (15*c*Sqrt[Pi]*Sqrt[c + a^2*c*x^2]*Erfi[2*Sqrt[ArcSinh[a*x]]])/(16384*a*Sqrt[1 + a^2*x^2]) - (15*c*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(256*a*Sqrt[1 + a^2*x^2])","A",39,14,23,0.6087,1,"{5684, 5682, 5675, 5663, 5758, 5669, 5448, 12, 3308, 2180, 2204, 2205, 5717, 5779}"
482,1,298,0,0.3006586,"\int \sqrt{c+a^2 c x^2} \sinh ^{-1}(a x)^{5/2} \, dx","Int[Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(5/2),x]","\frac{15 \sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{256 a \sqrt{a^2 x^2+1}}-\frac{15 \sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{256 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{7/2}}{7 a \sqrt{a^2 x^2+1}}+\frac{1}{2} x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{5/2}-\frac{5 a x^2 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}}{8 \sqrt{a^2 x^2+1}}-\frac{5 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}}{16 a \sqrt{a^2 x^2+1}}+\frac{15}{32} x \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}","\frac{15 \sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{256 a \sqrt{a^2 x^2+1}}-\frac{15 \sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{256 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{7/2}}{7 a \sqrt{a^2 x^2+1}}+\frac{1}{2} x \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{5/2}-\frac{5 a x^2 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}}{8 \sqrt{a^2 x^2+1}}-\frac{5 \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}}{16 a \sqrt{a^2 x^2+1}}+\frac{15}{32} x \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}",1,"(15*x*Sqrt[c + a^2*c*x^2]*Sqrt[ArcSinh[a*x]])/32 - (5*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(3/2))/(16*a*Sqrt[1 + a^2*x^2]) - (5*a*x^2*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(3/2))/(8*Sqrt[1 + a^2*x^2]) + (x*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(5/2))/2 + (Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(7/2))/(7*a*Sqrt[1 + a^2*x^2]) + (15*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(256*a*Sqrt[1 + a^2*x^2]) - (15*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(256*a*Sqrt[1 + a^2*x^2])","A",13,11,23,0.4783,1,"{5682, 5675, 5663, 5758, 5669, 5448, 12, 3308, 2180, 2204, 2205}"
483,1,42,0,0.0720049,"\int \frac{\sinh ^{-1}(a x)^{5/2}}{\sqrt{c+a^2 c x^2}} \, dx","Int[ArcSinh[a*x]^(5/2)/Sqrt[c + a^2*c*x^2],x]","\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{7/2}}{7 a \sqrt{a^2 c x^2+c}}","\frac{2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)^{7/2}}{7 a \sqrt{a^2 c x^2+c}}",1,"(2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]^(7/2))/(7*a*Sqrt[c + a^2*c*x^2])","A",2,2,23,0.08696,1,"{5677, 5675}"
484,0,0,0,0.0894574,"\int \frac{\sinh ^{-1}(a x)^{5/2}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","Int[ArcSinh[a*x]^(5/2)/(c + a^2*c*x^2)^(3/2),x]","\int \frac{\sinh ^{-1}(a x)^{5/2}}{\left(c+a^2 c x^2\right)^{3/2}} \, dx","\frac{x \sinh ^{-1}(a x)^{5/2}}{c \sqrt{a^2 c x^2+c}}-\frac{5 a \sqrt{a^2 x^2+1} \text{Int}\left(\frac{x \sinh ^{-1}(a x)^{3/2}}{a^2 x^2+1},x\right)}{2 c \sqrt{a^2 c x^2+c}}",0,"(x*ArcSinh[a*x]^(5/2))/(c*Sqrt[c + a^2*c*x^2]) - (5*a*Sqrt[1 + a^2*x^2]*Defer[Int][(x*ArcSinh[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,"{}"
485,1,309,0,0.3600746,"\int \left(a^2+x^2\right)^{3/2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)} \, dx","Int[(a^2 + x^2)^(3/2)*Sqrt[ArcSinh[x/a]],x]","\frac{\sqrt{\pi } a^3 \sqrt{a^2+x^2} \text{Erf}\left(2 \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{256 \sqrt{\frac{x^2}{a^2}+1}}+\frac{\sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2+x^2} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{16 \sqrt{\frac{x^2}{a^2}+1}}-\frac{\sqrt{\pi } a^3 \sqrt{a^2+x^2} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{256 \sqrt{\frac{x^2}{a^2}+1}}-\frac{\sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2+x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{16 \sqrt{\frac{x^2}{a^2}+1}}+\frac{a^3 \sqrt{a^2+x^2} \sinh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{4 \sqrt{\frac{x^2}{a^2}+1}}+\frac{3}{8} a^2 x \sqrt{a^2+x^2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}+\frac{1}{4} x \left(a^2+x^2\right)^{3/2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}","\frac{\sqrt{\pi } a^3 \sqrt{a^2+x^2} \text{Erf}\left(2 \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{256 \sqrt{\frac{x^2}{a^2}+1}}+\frac{\sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2+x^2} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{16 \sqrt{\frac{x^2}{a^2}+1}}-\frac{\sqrt{\pi } a^3 \sqrt{a^2+x^2} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{256 \sqrt{\frac{x^2}{a^2}+1}}-\frac{\sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2+x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{16 \sqrt{\frac{x^2}{a^2}+1}}+\frac{a^3 \sqrt{a^2+x^2} \sinh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{4 \sqrt{\frac{x^2}{a^2}+1}}+\frac{3}{8} a^2 x \sqrt{a^2+x^2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}+\frac{1}{4} x \left(a^2+x^2\right)^{3/2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}",1,"(3*a^2*x*Sqrt[a^2 + x^2]*Sqrt[ArcSinh[x/a]])/8 + (x*(a^2 + x^2)^(3/2)*Sqrt[ArcSinh[x/a]])/4 + (a^3*Sqrt[a^2 + x^2]*ArcSinh[x/a]^(3/2))/(4*Sqrt[1 + x^2/a^2]) + (a^3*Sqrt[Pi]*Sqrt[a^2 + x^2]*Erf[2*Sqrt[ArcSinh[x/a]]])/(256*Sqrt[1 + x^2/a^2]) + (a^3*Sqrt[Pi/2]*Sqrt[a^2 + x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[x/a]]])/(16*Sqrt[1 + x^2/a^2]) - (a^3*Sqrt[Pi]*Sqrt[a^2 + x^2]*Erfi[2*Sqrt[ArcSinh[x/a]]])/(256*Sqrt[1 + x^2/a^2]) - (a^3*Sqrt[Pi/2]*Sqrt[a^2 + x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[x/a]]])/(16*Sqrt[1 + x^2/a^2])","A",24,11,22,0.5000,1,"{5684, 5682, 5675, 5669, 5448, 12, 3308, 2180, 2204, 2205, 5779}"
486,1,176,0,0.1481642,"\int \sqrt{a^2+x^2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)} \, dx","Int[Sqrt[a^2 + x^2]*Sqrt[ArcSinh[x/a]],x]","\frac{\sqrt{\frac{\pi }{2}} a \sqrt{a^2+x^2} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{16 \sqrt{\frac{x^2}{a^2}+1}}-\frac{\sqrt{\frac{\pi }{2}} a \sqrt{a^2+x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{16 \sqrt{\frac{x^2}{a^2}+1}}+\frac{a \sqrt{a^2+x^2} \sinh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{3 \sqrt{\frac{x^2}{a^2}+1}}+\frac{1}{2} x \sqrt{a^2+x^2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}","\frac{\sqrt{\frac{\pi }{2}} a \sqrt{a^2+x^2} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{16 \sqrt{\frac{x^2}{a^2}+1}}-\frac{\sqrt{\frac{\pi }{2}} a \sqrt{a^2+x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{16 \sqrt{\frac{x^2}{a^2}+1}}+\frac{a \sqrt{a^2+x^2} \sinh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{3 \sqrt{\frac{x^2}{a^2}+1}}+\frac{1}{2} x \sqrt{a^2+x^2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}",1,"(x*Sqrt[a^2 + x^2]*Sqrt[ArcSinh[x/a]])/2 + (a*Sqrt[a^2 + x^2]*ArcSinh[x/a]^(3/2))/(3*Sqrt[1 + x^2/a^2]) + (a*Sqrt[Pi/2]*Sqrt[a^2 + x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[x/a]]])/(16*Sqrt[1 + x^2/a^2]) - (a*Sqrt[Pi/2]*Sqrt[a^2 + x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[x/a]]])/(16*Sqrt[1 + x^2/a^2])","A",10,9,22,0.4091,1,"{5682, 5675, 5669, 5448, 12, 3308, 2180, 2204, 2205}"
487,1,39,0,0.0622118,"\int \frac{\sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{\sqrt{a^2+x^2}} \, dx","Int[Sqrt[ArcSinh[x/a]]/Sqrt[a^2 + x^2],x]","\frac{2 a \sqrt{\frac{x^2}{a^2}+1} \sinh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{3 \sqrt{a^2+x^2}}","\frac{2 a \sqrt{\frac{x^2}{a^2}+1} \sinh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{3 \sqrt{a^2+x^2}}",1,"(2*a*Sqrt[1 + x^2/a^2]*ArcSinh[x/a]^(3/2))/(3*Sqrt[a^2 + x^2])","A",2,2,22,0.09091,1,"{5677, 5675}"
488,0,0,0,0.0767944,"\int \frac{\sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{\left(a^2+x^2\right)^{3/2}} \, dx","Int[Sqrt[ArcSinh[x/a]]/(a^2 + x^2)^(3/2),x]","\int \frac{\sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{\left(a^2+x^2\right)^{3/2}} \, dx","\frac{x \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{a^2 \sqrt{a^2+x^2}}-\frac{\sqrt{\frac{x^2}{a^2}+1} \text{Int}\left(\frac{x}{\left(\frac{x^2}{a^2}+1\right) \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}},x\right)}{2 a^3 \sqrt{a^2+x^2}}",0,"(x*Sqrt[ArcSinh[x/a]])/(a^2*Sqrt[a^2 + x^2]) - (Sqrt[1 + x^2/a^2]*Defer[Int][x/((1 + x^2/a^2)*Sqrt[ArcSinh[x/a]]), x])/(2*a^3*Sqrt[a^2 + x^2])","A",0,0,0,0,-1,"{}"
489,0,0,0,0.1575423,"\int \frac{\sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{\left(a^2+x^2\right)^{5/2}} \, dx","Int[Sqrt[ArcSinh[x/a]]/(a^2 + x^2)^(5/2),x]","\int \frac{\sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{\left(a^2+x^2\right)^{5/2}} \, dx","-\frac{\sqrt{\frac{x^2}{a^2}+1} \text{Int}\left(\frac{x}{\left(\frac{x^2}{a^2}+1\right)^2 \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}},x\right)}{6 a^5 \sqrt{a^2+x^2}}-\frac{\sqrt{\frac{x^2}{a^2}+1} \text{Int}\left(\frac{x}{\left(\frac{x^2}{a^2}+1\right) \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}},x\right)}{3 a^5 \sqrt{a^2+x^2}}+\frac{2 x \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{3 a^4 \sqrt{a^2+x^2}}+\frac{x \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{3 a^2 \left(a^2+x^2\right)^{3/2}}",0,"(x*Sqrt[ArcSinh[x/a]])/(3*a^2*(a^2 + x^2)^(3/2)) + (2*x*Sqrt[ArcSinh[x/a]])/(3*a^4*Sqrt[a^2 + x^2]) - (Sqrt[1 + x^2/a^2]*Defer[Int][x/((1 + x^2/a^2)^2*Sqrt[ArcSinh[x/a]]), x])/(6*a^5*Sqrt[a^2 + x^2]) - (Sqrt[1 + x^2/a^2]*Defer[Int][x/((1 + x^2/a^2)*Sqrt[ArcSinh[x/a]]), x])/(3*a^5*Sqrt[a^2 + x^2])","A",0,0,0,0,-1,"{}"
490,1,433,0,0.5479819,"\int \left(a^2+x^2\right)^{3/2} \sinh ^{-1}\left(\frac{x}{a}\right)^{3/2} \, dx","Int[(a^2 + x^2)^(3/2)*ArcSinh[x/a]^(3/2),x]","\frac{3 \sqrt{\pi } a^3 \sqrt{a^2+x^2} \text{Erf}\left(2 \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{2048 \sqrt{\frac{x^2}{a^2}+1}}+\frac{3 \sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2+x^2} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{\frac{x^2}{a^2}+1}}+\frac{3 \sqrt{\pi } a^3 \sqrt{a^2+x^2} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{2048 \sqrt{\frac{x^2}{a^2}+1}}+\frac{3 \sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2+x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{\frac{x^2}{a^2}+1}}+\frac{3 a^3 \sqrt{a^2+x^2} \sinh ^{-1}\left(\frac{x}{a}\right)^{5/2}}{20 \sqrt{\frac{x^2}{a^2}+1}}-\frac{27 a^3 \sqrt{a^2+x^2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{256 \sqrt{\frac{x^2}{a^2}+1}}+\frac{3}{8} a^2 x \sqrt{a^2+x^2} \sinh ^{-1}\left(\frac{x}{a}\right)^{3/2}-\frac{9 a x^2 \sqrt{a^2+x^2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{32 \sqrt{\frac{x^2}{a^2}+1}}+\frac{1}{4} x \left(a^2+x^2\right)^{3/2} \sinh ^{-1}\left(\frac{x}{a}\right)^{3/2}-\frac{3 \left(a^2+x^2\right)^{5/2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{32 a \sqrt{\frac{x^2}{a^2}+1}}","\frac{3 \sqrt{\pi } a^3 \sqrt{a^2+x^2} \text{Erf}\left(2 \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{2048 \sqrt{\frac{x^2}{a^2}+1}}+\frac{3 \sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2+x^2} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{\frac{x^2}{a^2}+1}}+\frac{3 \sqrt{\pi } a^3 \sqrt{a^2+x^2} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{2048 \sqrt{\frac{x^2}{a^2}+1}}+\frac{3 \sqrt{\frac{\pi }{2}} a^3 \sqrt{a^2+x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{\frac{x^2}{a^2}+1}}+\frac{3 a^3 \sqrt{a^2+x^2} \sinh ^{-1}\left(\frac{x}{a}\right)^{5/2}}{20 \sqrt{\frac{x^2}{a^2}+1}}-\frac{27 a^3 \sqrt{a^2+x^2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{256 \sqrt{\frac{x^2}{a^2}+1}}+\frac{3}{8} a^2 x \sqrt{a^2+x^2} \sinh ^{-1}\left(\frac{x}{a}\right)^{3/2}-\frac{9 a x^2 \sqrt{a^2+x^2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{32 \sqrt{\frac{x^2}{a^2}+1}}+\frac{1}{4} x \left(a^2+x^2\right)^{3/2} \sinh ^{-1}\left(\frac{x}{a}\right)^{3/2}-\frac{3 \left(a^2+x^2\right)^{5/2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{32 a \sqrt{\frac{x^2}{a^2}+1}}",1,"(-27*a^3*Sqrt[a^2 + x^2]*Sqrt[ArcSinh[x/a]])/(256*Sqrt[1 + x^2/a^2]) - (9*a*x^2*Sqrt[a^2 + x^2]*Sqrt[ArcSinh[x/a]])/(32*Sqrt[1 + x^2/a^2]) - (3*(a^2 + x^2)^(5/2)*Sqrt[ArcSinh[x/a]])/(32*a*Sqrt[1 + x^2/a^2]) + (3*a^2*x*Sqrt[a^2 + x^2]*ArcSinh[x/a]^(3/2))/8 + (x*(a^2 + x^2)^(3/2)*ArcSinh[x/a]^(3/2))/4 + (3*a^3*Sqrt[a^2 + x^2]*ArcSinh[x/a]^(5/2))/(20*Sqrt[1 + x^2/a^2]) + (3*a^3*Sqrt[Pi]*Sqrt[a^2 + x^2]*Erf[2*Sqrt[ArcSinh[x/a]]])/(2048*Sqrt[1 + x^2/a^2]) + (3*a^3*Sqrt[Pi/2]*Sqrt[a^2 + x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[x/a]]])/(64*Sqrt[1 + x^2/a^2]) + (3*a^3*Sqrt[Pi]*Sqrt[a^2 + x^2]*Erfi[2*Sqrt[ArcSinh[x/a]]])/(2048*Sqrt[1 + x^2/a^2]) + (3*a^3*Sqrt[Pi/2]*Sqrt[a^2 + x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[x/a]]])/(64*Sqrt[1 + x^2/a^2])","A",26,12,22,0.5455,1,"{5684, 5682, 5675, 5663, 5779, 3312, 3307, 2180, 2204, 2205, 5717, 5699}"
491,1,259,0,0.2755629,"\int \sqrt{a^2+x^2} \sinh ^{-1}\left(\frac{x}{a}\right)^{3/2} \, dx","Int[Sqrt[a^2 + x^2]*ArcSinh[x/a]^(3/2),x]","\frac{3 \sqrt{\frac{\pi }{2}} a \sqrt{a^2+x^2} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{\frac{x^2}{a^2}+1}}+\frac{3 \sqrt{\frac{\pi }{2}} a \sqrt{a^2+x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{\frac{x^2}{a^2}+1}}+\frac{a \sqrt{a^2+x^2} \sinh ^{-1}\left(\frac{x}{a}\right)^{5/2}}{5 \sqrt{\frac{x^2}{a^2}+1}}+\frac{1}{2} x \sqrt{a^2+x^2} \sinh ^{-1}\left(\frac{x}{a}\right)^{3/2}-\frac{3 x^2 \sqrt{a^2+x^2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{8 a \sqrt{\frac{x^2}{a^2}+1}}-\frac{3 a \sqrt{a^2+x^2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{16 \sqrt{\frac{x^2}{a^2}+1}}","\frac{3 \sqrt{\frac{\pi }{2}} a \sqrt{a^2+x^2} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{\frac{x^2}{a^2}+1}}+\frac{3 \sqrt{\frac{\pi }{2}} a \sqrt{a^2+x^2} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}\right)}{64 \sqrt{\frac{x^2}{a^2}+1}}+\frac{a \sqrt{a^2+x^2} \sinh ^{-1}\left(\frac{x}{a}\right)^{5/2}}{5 \sqrt{\frac{x^2}{a^2}+1}}+\frac{1}{2} x \sqrt{a^2+x^2} \sinh ^{-1}\left(\frac{x}{a}\right)^{3/2}-\frac{3 x^2 \sqrt{a^2+x^2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{8 a \sqrt{\frac{x^2}{a^2}+1}}-\frac{3 a \sqrt{a^2+x^2} \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{16 \sqrt{\frac{x^2}{a^2}+1}}",1,"(-3*a*Sqrt[a^2 + x^2]*Sqrt[ArcSinh[x/a]])/(16*Sqrt[1 + x^2/a^2]) - (3*x^2*Sqrt[a^2 + x^2]*Sqrt[ArcSinh[x/a]])/(8*a*Sqrt[1 + x^2/a^2]) + (x*Sqrt[a^2 + x^2]*ArcSinh[x/a]^(3/2))/2 + (a*Sqrt[a^2 + x^2]*ArcSinh[x/a]^(5/2))/(5*Sqrt[1 + x^2/a^2]) + (3*a*Sqrt[Pi/2]*Sqrt[a^2 + x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[x/a]]])/(64*Sqrt[1 + x^2/a^2]) + (3*a*Sqrt[Pi/2]*Sqrt[a^2 + x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[x/a]]])/(64*Sqrt[1 + x^2/a^2])","A",11,9,22,0.4091,1,"{5682, 5675, 5663, 5779, 3312, 3307, 2180, 2204, 2205}"
492,1,39,0,0.0639839,"\int \frac{\sinh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{\sqrt{a^2+x^2}} \, dx","Int[ArcSinh[x/a]^(3/2)/Sqrt[a^2 + x^2],x]","\frac{2 a \sqrt{\frac{x^2}{a^2}+1} \sinh ^{-1}\left(\frac{x}{a}\right)^{5/2}}{5 \sqrt{a^2+x^2}}","\frac{2 a \sqrt{\frac{x^2}{a^2}+1} \sinh ^{-1}\left(\frac{x}{a}\right)^{5/2}}{5 \sqrt{a^2+x^2}}",1,"(2*a*Sqrt[1 + x^2/a^2]*ArcSinh[x/a]^(5/2))/(5*Sqrt[a^2 + x^2])","A",2,2,22,0.09091,1,"{5677, 5675}"
493,0,0,0,0.0756793,"\int \frac{\sinh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{\left(a^2+x^2\right)^{3/2}} \, dx","Int[ArcSinh[x/a]^(3/2)/(a^2 + x^2)^(3/2),x]","\int \frac{\sinh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{\left(a^2+x^2\right)^{3/2}} \, dx","\frac{x \sinh ^{-1}\left(\frac{x}{a}\right)^{3/2}}{a^2 \sqrt{a^2+x^2}}-\frac{3 \sqrt{\frac{x^2}{a^2}+1} \text{Int}\left(\frac{x \sqrt{\sinh ^{-1}\left(\frac{x}{a}\right)}}{\frac{x^2}{a^2}+1},x\right)}{2 a^3 \sqrt{a^2+x^2}}",0,"(x*ArcSinh[x/a]^(3/2))/(a^2*Sqrt[a^2 + x^2]) - (3*Sqrt[1 + x^2/a^2]*Defer[Int][(x*Sqrt[ArcSinh[x/a]])/(1 + x^2/a^2), x])/(2*a^3*Sqrt[a^2 + x^2])","A",0,0,0,0,-1,"{}"
494,1,33,0,0.0799689,"\int \frac{x}{\sqrt{1+x^2} \sqrt{\sinh ^{-1}(x)}} \, dx","Int[x/(Sqrt[1 + x^2]*Sqrt[ArcSinh[x]]),x]","\frac{1}{2} \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(x)}\right)-\frac{1}{2} \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(x)}\right)","\frac{1}{2} \sqrt{\pi } \text{Erfi}\left(\sqrt{\sinh ^{-1}(x)}\right)-\frac{1}{2} \sqrt{\pi } \text{Erf}\left(\sqrt{\sinh ^{-1}(x)}\right)",1,"-(Sqrt[Pi]*Erf[Sqrt[ArcSinh[x]]])/2 + (Sqrt[Pi]*Erfi[Sqrt[ArcSinh[x]]])/2","A",6,5,17,0.2941,1,"{5779, 3308, 2180, 2204, 2205}"
495,1,396,0,0.3080201,"\int \frac{\left(c+a^2 c x^2\right)^{5/2}}{\sqrt{\sinh ^{-1}(a x)}} \, dx","Int[(c + a^2*c*x^2)^(5/2)/Sqrt[ArcSinh[a*x]],x]","\frac{3 \sqrt{\pi } c^2 \sqrt{a^2 c x^2+c} \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{15 \sqrt{\frac{\pi }{2}} c^2 \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{\pi }{6}} c^2 \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{6} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{3 \sqrt{\pi } c^2 \sqrt{a^2 c x^2+c} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{15 \sqrt{\frac{\pi }{2}} c^2 \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{\pi }{6}} c^2 \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{6} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{5 c^2 \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}{8 a \sqrt{a^2 x^2+1}}","\frac{3 \sqrt{\pi } c^2 \sqrt{a^2 c x^2+c} \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{15 \sqrt{\frac{\pi }{2}} c^2 \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{\pi }{6}} c^2 \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{6} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{3 \sqrt{\pi } c^2 \sqrt{a^2 c x^2+c} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{15 \sqrt{\frac{\pi }{2}} c^2 \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{\pi }{6}} c^2 \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{6} \sqrt{\sinh ^{-1}(a x)}\right)}{64 a \sqrt{a^2 x^2+1}}+\frac{5 c^2 \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}{8 a \sqrt{a^2 x^2+1}}",1,"(5*c^2*Sqrt[c + a^2*c*x^2]*Sqrt[ArcSinh[a*x]])/(8*a*Sqrt[1 + a^2*x^2]) + (3*c^2*Sqrt[Pi]*Sqrt[c + a^2*c*x^2]*Erf[2*Sqrt[ArcSinh[a*x]]])/(64*a*Sqrt[1 + a^2*x^2]) + (15*c^2*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(64*a*Sqrt[1 + a^2*x^2]) + (c^2*Sqrt[Pi/6]*Sqrt[c + a^2*c*x^2]*Erf[Sqrt[6]*Sqrt[ArcSinh[a*x]]])/(64*a*Sqrt[1 + a^2*x^2]) + (3*c^2*Sqrt[Pi]*Sqrt[c + a^2*c*x^2]*Erfi[2*Sqrt[ArcSinh[a*x]]])/(64*a*Sqrt[1 + a^2*x^2]) + (15*c^2*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(64*a*Sqrt[1 + a^2*x^2]) + (c^2*Sqrt[Pi/6]*Sqrt[c + a^2*c*x^2]*Erfi[Sqrt[6]*Sqrt[ArcSinh[a*x]]])/(64*a*Sqrt[1 + a^2*x^2])","A",19,7,23,0.3043,1,"{5702, 5699, 3312, 3307, 2180, 2204, 2205}"
496,1,264,0,0.2265882,"\int \frac{\left(c+a^2 c x^2\right)^{3/2}}{\sqrt{\sinh ^{-1}(a x)}} \, dx","Int[(c + a^2*c*x^2)^(3/2)/Sqrt[ArcSinh[a*x]],x]","\frac{\sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{32 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{4 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{32 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{4 a \sqrt{a^2 x^2+1}}+\frac{3 c \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}{4 a \sqrt{a^2 x^2+1}}","\frac{\sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{32 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{4 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{32 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{4 a \sqrt{a^2 x^2+1}}+\frac{3 c \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}{4 a \sqrt{a^2 x^2+1}}",1,"(3*c*Sqrt[c + a^2*c*x^2]*Sqrt[ArcSinh[a*x]])/(4*a*Sqrt[1 + a^2*x^2]) + (c*Sqrt[Pi]*Sqrt[c + a^2*c*x^2]*Erf[2*Sqrt[ArcSinh[a*x]]])/(32*a*Sqrt[1 + a^2*x^2]) + (c*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(4*a*Sqrt[1 + a^2*x^2]) + (c*Sqrt[Pi]*Sqrt[c + a^2*c*x^2]*Erfi[2*Sqrt[ArcSinh[a*x]]])/(32*a*Sqrt[1 + a^2*x^2]) + (c*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(4*a*Sqrt[1 + a^2*x^2])","A",14,7,23,0.3043,1,"{5702, 5699, 3312, 3307, 2180, 2204, 2205}"
497,1,156,0,0.1636346,"\int \frac{\sqrt{c+a^2 c x^2}}{\sqrt{\sinh ^{-1}(a x)}} \, dx","Int[Sqrt[c + a^2*c*x^2]/Sqrt[ArcSinh[a*x]],x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{4 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{4 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}{a \sqrt{a^2 x^2+1}}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{4 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{4 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}{a \sqrt{a^2 x^2+1}}",1,"(Sqrt[c + a^2*c*x^2]*Sqrt[ArcSinh[a*x]])/(a*Sqrt[1 + a^2*x^2]) + (Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(4*a*Sqrt[1 + a^2*x^2]) + (Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(4*a*Sqrt[1 + a^2*x^2])","A",9,7,23,0.3043,1,"{5702, 5699, 3312, 3307, 2180, 2204, 2205}"
498,1,40,0,0.0724067,"\int \frac{1}{\sqrt{c+a^2 c x^2} \sqrt{\sinh ^{-1}(a x)}} \, dx","Int[1/(Sqrt[c + a^2*c*x^2]*Sqrt[ArcSinh[a*x]]),x]","\frac{2 \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{a \sqrt{a^2 c x^2+c}}","\frac{2 \sqrt{a^2 x^2+1} \sqrt{\sinh ^{-1}(a x)}}{a \sqrt{a^2 c x^2+c}}",1,"(2*Sqrt[1 + a^2*x^2]*Sqrt[ArcSinh[a*x]])/(a*Sqrt[c + a^2*c*x^2])","A",2,2,23,0.08696,1,"{5677, 5675}"
499,0,0,0,0.0418289,"\int \frac{1}{\left(c+a^2 c x^2\right)^{3/2} \sqrt{\sinh ^{-1}(a x)}} \, dx","Int[1/((c + a^2*c*x^2)^(3/2)*Sqrt[ArcSinh[a*x]]),x]","\int \frac{1}{\left(c+a^2 c x^2\right)^{3/2} \sqrt{\sinh ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{1}{\left(a^2 c x^2+c\right)^{3/2} \sqrt{\sinh ^{-1}(a x)}},x\right)",0,"Defer[Int][1/((c + a^2*c*x^2)^(3/2)*Sqrt[ArcSinh[a*x]]), x]","A",0,0,0,0,-1,"{}"
500,0,0,0,0.0424377,"\int \frac{1}{\left(c+a^2 c x^2\right)^{5/2} \sqrt{\sinh ^{-1}(a x)}} \, dx","Int[1/((c + a^2*c*x^2)^(5/2)*Sqrt[ArcSinh[a*x]]),x]","\int \frac{1}{\left(c+a^2 c x^2\right)^{5/2} \sqrt{\sinh ^{-1}(a x)}} \, dx","\text{Int}\left(\frac{1}{\left(a^2 c x^2+c\right)^{5/2} \sqrt{\sinh ^{-1}(a x)}},x\right)",0,"Defer[Int][1/((c + a^2*c*x^2)^(5/2)*Sqrt[ArcSinh[a*x]]), x]","A",0,0,0,0,-1,"{}"
501,1,391,0,0.3017314,"\int \frac{\left(c+a^2 c x^2\right)^{5/2}}{\sinh ^{-1}(a x)^{3/2}} \, dx","Int[(c + a^2*c*x^2)^(5/2)/ArcSinh[a*x]^(3/2),x]","-\frac{3 \sqrt{\pi } c^2 \sqrt{a^2 c x^2+c} \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{8 a \sqrt{a^2 x^2+1}}-\frac{15 \sqrt{\frac{\pi }{2}} c^2 \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a \sqrt{a^2 x^2+1}}-\frac{\sqrt{\frac{3 \pi }{2}} c^2 \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{6} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a \sqrt{a^2 x^2+1}}+\frac{3 \sqrt{\pi } c^2 \sqrt{a^2 c x^2+c} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{8 a \sqrt{a^2 x^2+1}}+\frac{15 \sqrt{\frac{\pi }{2}} c^2 \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{3 \pi }{2}} c^2 \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{6} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a \sqrt{a^2 x^2+1}}-\frac{2 \sqrt{a^2 x^2+1} \left(a^2 c x^2+c\right)^{5/2}}{a \sqrt{\sinh ^{-1}(a x)}}","-\frac{3 \sqrt{\pi } c^2 \sqrt{a^2 c x^2+c} \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{8 a \sqrt{a^2 x^2+1}}-\frac{15 \sqrt{\frac{\pi }{2}} c^2 \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a \sqrt{a^2 x^2+1}}-\frac{\sqrt{\frac{3 \pi }{2}} c^2 \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{6} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a \sqrt{a^2 x^2+1}}+\frac{3 \sqrt{\pi } c^2 \sqrt{a^2 c x^2+c} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{8 a \sqrt{a^2 x^2+1}}+\frac{15 \sqrt{\frac{\pi }{2}} c^2 \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{3 \pi }{2}} c^2 \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{6} \sqrt{\sinh ^{-1}(a x)}\right)}{16 a \sqrt{a^2 x^2+1}}-\frac{2 \sqrt{a^2 x^2+1} \left(a^2 c x^2+c\right)^{5/2}}{a \sqrt{\sinh ^{-1}(a x)}}",1,"(-2*Sqrt[1 + a^2*x^2]*(c + a^2*c*x^2)^(5/2))/(a*Sqrt[ArcSinh[a*x]]) - (3*c^2*Sqrt[Pi]*Sqrt[c + a^2*c*x^2]*Erf[2*Sqrt[ArcSinh[a*x]]])/(8*a*Sqrt[1 + a^2*x^2]) - (15*c^2*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(16*a*Sqrt[1 + a^2*x^2]) - (c^2*Sqrt[(3*Pi)/2]*Sqrt[c + a^2*c*x^2]*Erf[Sqrt[6]*Sqrt[ArcSinh[a*x]]])/(16*a*Sqrt[1 + a^2*x^2]) + (3*c^2*Sqrt[Pi]*Sqrt[c + a^2*c*x^2]*Erfi[2*Sqrt[ArcSinh[a*x]]])/(8*a*Sqrt[1 + a^2*x^2]) + (15*c^2*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(16*a*Sqrt[1 + a^2*x^2]) + (c^2*Sqrt[(3*Pi)/2]*Sqrt[c + a^2*c*x^2]*Erfi[Sqrt[6]*Sqrt[ArcSinh[a*x]]])/(16*a*Sqrt[1 + a^2*x^2])","A",19,7,23,0.3043,1,"{5696, 5779, 5448, 3308, 2180, 2204, 2205}"
502,1,256,0,0.2083309,"\int \frac{\left(c+a^2 c x^2\right)^{3/2}}{\sinh ^{-1}(a x)^{3/2}} \, dx","Int[(c + a^2*c*x^2)^(3/2)/ArcSinh[a*x]^(3/2),x]","-\frac{\sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{4 a \sqrt{a^2 x^2+1}}-\frac{\sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{4 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{a \sqrt{a^2 x^2+1}}-\frac{2 \sqrt{a^2 x^2+1} \left(a^2 c x^2+c\right)^{3/2}}{a \sqrt{\sinh ^{-1}(a x)}}","-\frac{\sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{4 a \sqrt{a^2 x^2+1}}-\frac{\sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{4 a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{\pi }{2}} c \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{a \sqrt{a^2 x^2+1}}-\frac{2 \sqrt{a^2 x^2+1} \left(a^2 c x^2+c\right)^{3/2}}{a \sqrt{\sinh ^{-1}(a x)}}",1,"(-2*Sqrt[1 + a^2*x^2]*(c + a^2*c*x^2)^(3/2))/(a*Sqrt[ArcSinh[a*x]]) - (c*Sqrt[Pi]*Sqrt[c + a^2*c*x^2]*Erf[2*Sqrt[ArcSinh[a*x]]])/(4*a*Sqrt[1 + a^2*x^2]) - (c*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(a*Sqrt[1 + a^2*x^2]) + (c*Sqrt[Pi]*Sqrt[c + a^2*c*x^2]*Erfi[2*Sqrt[ArcSinh[a*x]]])/(4*a*Sqrt[1 + a^2*x^2]) + (c*Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(a*Sqrt[1 + a^2*x^2])","A",14,7,23,0.3043,1,"{5696, 5779, 5448, 3308, 2180, 2204, 2205}"
503,1,152,0,0.1243014,"\int \frac{\sqrt{c+a^2 c x^2}}{\sinh ^{-1}(a x)^{3/2}} \, dx","Int[Sqrt[c + a^2*c*x^2]/ArcSinh[a*x]^(3/2),x]","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{a \sqrt{a^2 x^2+1}}-\frac{2 \sqrt{a^2 x^2+1} \sqrt{a^2 c x^2+c}}{a \sqrt{\sinh ^{-1}(a x)}}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{a \sqrt{a^2 x^2+1}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{a \sqrt{a^2 x^2+1}}-\frac{2 \sqrt{a^2 x^2+1} \sqrt{a^2 c x^2+c}}{a \sqrt{\sinh ^{-1}(a x)}}",1,"(-2*Sqrt[1 + a^2*x^2]*Sqrt[c + a^2*c*x^2])/(a*Sqrt[ArcSinh[a*x]]) - (Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(a*Sqrt[1 + a^2*x^2]) + (Sqrt[Pi/2]*Sqrt[c + a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(a*Sqrt[1 + a^2*x^2])","A",9,8,23,0.3478,1,"{5696, 5669, 5448, 12, 3308, 2180, 2204, 2205}"
504,1,40,0,0.0710817,"\int \frac{1}{\sqrt{c+a^2 c x^2} \sinh ^{-1}(a x)^{3/2}} \, dx","Int[1/(Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(3/2)),x]","-\frac{2 \sqrt{a^2 x^2+1}}{a \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}","-\frac{2 \sqrt{a^2 x^2+1}}{a \sqrt{a^2 c x^2+c} \sqrt{\sinh ^{-1}(a x)}}",1,"(-2*Sqrt[1 + a^2*x^2])/(a*Sqrt[c + a^2*c*x^2]*Sqrt[ArcSinh[a*x]])","A",2,2,23,0.08696,1,"{5677, 5675}"
505,0,0,0,0.089694,"\int \frac{1}{\left(c+a^2 c x^2\right)^{3/2} \sinh ^{-1}(a x)^{3/2}} \, dx","Int[1/((c + a^2*c*x^2)^(3/2)*ArcSinh[a*x]^(3/2)),x]","\int \frac{1}{\left(c+a^2 c x^2\right)^{3/2} \sinh ^{-1}(a x)^{3/2}} \, dx","-\frac{4 a \sqrt{a^2 x^2+1} \text{Int}\left(\frac{x}{\left(a^2 x^2+1\right)^2 \sqrt{\sinh ^{-1}(a x)}},x\right)}{c \sqrt{a^2 c x^2+c}}-\frac{2 \sqrt{a^2 x^2+1}}{a \left(a^2 c x^2+c\right)^{3/2} \sqrt{\sinh ^{-1}(a x)}}",0,"(-2*Sqrt[1 + a^2*x^2])/(a*(c + a^2*c*x^2)^(3/2)*Sqrt[ArcSinh[a*x]]) - (4*a*Sqrt[1 + a^2*x^2]*Defer[Int][x/((1 + a^2*x^2)^2*Sqrt[ArcSinh[a*x]]), x])/(c*Sqrt[c + a^2*c*x^2])","A",0,0,0,0,-1,"{}"
506,0,0,0,0.0884567,"\int \frac{1}{\left(c+a^2 c x^2\right)^{5/2} \sinh ^{-1}(a x)^{3/2}} \, dx","Int[1/((c + a^2*c*x^2)^(5/2)*ArcSinh[a*x]^(3/2)),x]","\int \frac{1}{\left(c+a^2 c x^2\right)^{5/2} \sinh ^{-1}(a x)^{3/2}} \, dx","-\frac{8 a \sqrt{a^2 x^2+1} \text{Int}\left(\frac{x}{\left(a^2 x^2+1\right)^3 \sqrt{\sinh ^{-1}(a x)}},x\right)}{c^2 \sqrt{a^2 c x^2+c}}-\frac{2 \sqrt{a^2 x^2+1}}{a \left(a^2 c x^2+c\right)^{5/2} \sqrt{\sinh ^{-1}(a x)}}",0,"(-2*Sqrt[1 + a^2*x^2])/(a*(c + a^2*c*x^2)^(5/2)*Sqrt[ArcSinh[a*x]]) - (8*a*Sqrt[1 + a^2*x^2]*Defer[Int][x/((1 + a^2*x^2)^3*Sqrt[ArcSinh[a*x]]), x])/(c^2*Sqrt[c + a^2*c*x^2])","A",0,0,0,0,-1,"{}"
507,1,296,0,0.3767074,"\int \frac{\left(c+a^2 c x^2\right)^{3/2}}{\sinh ^{-1}(a x)^{5/2}} \, dx","Int[(c + a^2*c*x^2)^(3/2)/ArcSinh[a*x]^(5/2),x]","\frac{2 \sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{3 a \sqrt{a^2 x^2+1}}+\frac{2 \sqrt{2 \pi } c \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{3 a \sqrt{a^2 x^2+1}}+\frac{2 \sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{3 a \sqrt{a^2 x^2+1}}+\frac{2 \sqrt{2 \pi } c \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{3 a \sqrt{a^2 x^2+1}}-\frac{2 \sqrt{a^2 x^2+1} \left(a^2 c x^2+c\right)^{3/2}}{3 a \sinh ^{-1}(a x)^{3/2}}-\frac{16 c x \left(a^2 x^2+1\right) \sqrt{a^2 c x^2+c}}{3 \sqrt{\sinh ^{-1}(a x)}}","\frac{2 \sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erf}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{3 a \sqrt{a^2 x^2+1}}+\frac{2 \sqrt{2 \pi } c \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{3 a \sqrt{a^2 x^2+1}}+\frac{2 \sqrt{\pi } c \sqrt{a^2 c x^2+c} \text{Erfi}\left(2 \sqrt{\sinh ^{-1}(a x)}\right)}{3 a \sqrt{a^2 x^2+1}}+\frac{2 \sqrt{2 \pi } c \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{3 a \sqrt{a^2 x^2+1}}-\frac{2 \sqrt{a^2 x^2+1} \left(a^2 c x^2+c\right)^{3/2}}{3 a \sinh ^{-1}(a x)^{3/2}}-\frac{16 c x \left(a^2 x^2+1\right) \sqrt{a^2 c x^2+c}}{3 \sqrt{\sinh ^{-1}(a x)}}",1,"(-2*Sqrt[1 + a^2*x^2]*(c + a^2*c*x^2)^(3/2))/(3*a*ArcSinh[a*x]^(3/2)) - (16*c*x*(1 + a^2*x^2)*Sqrt[c + a^2*c*x^2])/(3*Sqrt[ArcSinh[a*x]]) + (2*c*Sqrt[Pi]*Sqrt[c + a^2*c*x^2]*Erf[2*Sqrt[ArcSinh[a*x]]])/(3*a*Sqrt[1 + a^2*x^2]) + (2*c*Sqrt[2*Pi]*Sqrt[c + a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(3*a*Sqrt[1 + a^2*x^2]) + (2*c*Sqrt[Pi]*Sqrt[c + a^2*c*x^2]*Erfi[2*Sqrt[ArcSinh[a*x]]])/(3*a*Sqrt[1 + a^2*x^2]) + (2*c*Sqrt[2*Pi]*Sqrt[c + a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(3*a*Sqrt[1 + a^2*x^2])","A",18,10,23,0.4348,1,"{5696, 5777, 5699, 3312, 3307, 2180, 2204, 2205, 5779, 5448}"
508,1,182,0,0.1146105,"\int \frac{\sqrt{c+a^2 c x^2}}{\sinh ^{-1}(a x)^{5/2}} \, dx","Int[Sqrt[c + a^2*c*x^2]/ArcSinh[a*x]^(5/2),x]","\frac{2 \sqrt{2 \pi } \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{3 a \sqrt{a^2 x^2+1}}+\frac{2 \sqrt{2 \pi } \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{3 a \sqrt{a^2 x^2+1}}-\frac{8 x \sqrt{a^2 c x^2+c}}{3 \sqrt{\sinh ^{-1}(a x)}}-\frac{2 \sqrt{a^2 x^2+1} \sqrt{a^2 c x^2+c}}{3 a \sinh ^{-1}(a x)^{3/2}}","\frac{2 \sqrt{2 \pi } \sqrt{a^2 c x^2+c} \text{Erf}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{3 a \sqrt{a^2 x^2+1}}+\frac{2 \sqrt{2 \pi } \sqrt{a^2 c x^2+c} \text{Erfi}\left(\sqrt{2} \sqrt{\sinh ^{-1}(a x)}\right)}{3 a \sqrt{a^2 x^2+1}}-\frac{8 x \sqrt{a^2 c x^2+c}}{3 \sqrt{\sinh ^{-1}(a x)}}-\frac{2 \sqrt{a^2 x^2+1} \sqrt{a^2 c x^2+c}}{3 a \sinh ^{-1}(a x)^{3/2}}",1,"(-2*Sqrt[1 + a^2*x^2]*Sqrt[c + a^2*c*x^2])/(3*a*ArcSinh[a*x]^(3/2)) - (8*x*Sqrt[c + a^2*c*x^2])/(3*Sqrt[ArcSinh[a*x]]) + (2*Sqrt[2*Pi]*Sqrt[c + a^2*c*x^2]*Erf[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(3*a*Sqrt[1 + a^2*x^2]) + (2*Sqrt[2*Pi]*Sqrt[c + a^2*c*x^2]*Erfi[Sqrt[2]*Sqrt[ArcSinh[a*x]]])/(3*a*Sqrt[1 + a^2*x^2])","A",7,6,23,0.2609,1,"{5696, 5665, 3307, 2180, 2204, 2205}"
509,1,42,0,0.070311,"\int \frac{1}{\sqrt{c+a^2 c x^2} \sinh ^{-1}(a x)^{5/2}} \, dx","Int[1/(Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(5/2)),x]","-\frac{2 \sqrt{a^2 x^2+1}}{3 a \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}}","-\frac{2 \sqrt{a^2 x^2+1}}{3 a \sqrt{a^2 c x^2+c} \sinh ^{-1}(a x)^{3/2}}",1,"(-2*Sqrt[1 + a^2*x^2])/(3*a*Sqrt[c + a^2*c*x^2]*ArcSinh[a*x]^(3/2))","A",2,2,23,0.08696,1,"{5677, 5675}"
510,0,0,0,0.0913288,"\int \frac{1}{\left(c+a^2 c x^2\right)^{3/2} \sinh ^{-1}(a x)^{5/2}} \, dx","Int[1/((c + a^2*c*x^2)^(3/2)*ArcSinh[a*x]^(5/2)),x]","\int \frac{1}{\left(c+a^2 c x^2\right)^{3/2} \sinh ^{-1}(a x)^{5/2}} \, dx","-\frac{4 a \sqrt{a^2 x^2+1} \text{Int}\left(\frac{x}{\left(a^2 x^2+1\right)^2 \sinh ^{-1}(a x)^{3/2}},x\right)}{3 c \sqrt{a^2 c x^2+c}}-\frac{2 \sqrt{a^2 x^2+1}}{3 a \left(a^2 c x^2+c\right)^{3/2} \sinh ^{-1}(a x)^{3/2}}",0,"(-2*Sqrt[1 + a^2*x^2])/(3*a*(c + a^2*c*x^2)^(3/2)*ArcSinh[a*x]^(3/2)) - (4*a*Sqrt[1 + a^2*x^2]*Defer[Int][x/((1 + a^2*x^2)^2*ArcSinh[a*x]^(3/2)), x])/(3*c*Sqrt[c + a^2*c*x^2])","A",0,0,0,0,-1,"{}"
511,0,0,0,0.0905415,"\int \frac{1}{\left(c+a^2 c x^2\right)^{5/2} \sinh ^{-1}(a x)^{5/2}} \, dx","Int[1/((c + a^2*c*x^2)^(5/2)*ArcSinh[a*x]^(5/2)),x]","\int \frac{1}{\left(c+a^2 c x^2\right)^{5/2} \sinh ^{-1}(a x)^{5/2}} \, dx","-\frac{8 a \sqrt{a^2 x^2+1} \text{Int}\left(\frac{x}{\left(a^2 x^2+1\right)^3 \sinh ^{-1}(a x)^{3/2}},x\right)}{3 c^2 \sqrt{a^2 c x^2+c}}-\frac{2 \sqrt{a^2 x^2+1}}{3 a \left(a^2 c x^2+c\right)^{5/2} \sinh ^{-1}(a x)^{3/2}}",0,"(-2*Sqrt[1 + a^2*x^2])/(3*a*(c + a^2*c*x^2)^(5/2)*ArcSinh[a*x]^(3/2)) - (8*a*Sqrt[1 + a^2*x^2]*Defer[Int][x/((1 + a^2*x^2)^3*ArcSinh[a*x]^(3/2)), x])/(3*c^2*Sqrt[c + a^2*c*x^2])","A",0,0,0,0,-1,"{}"
512,1,235,0,0.4540662,"\int x^2 \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^n \, dx","Int[x^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n,x]","\frac{2^{-2 (n+3)} e^{-\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{2^{-2 (n+3)} e^{\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^{n+1}}{8 b c^3 (n+1) \sqrt{c^2 x^2+1}}","\frac{2^{-2 (n+3)} e^{-\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{2^{-2 (n+3)} e^{\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^{n+1}}{8 b c^3 (n+1) \sqrt{c^2 x^2+1}}",1,"-(Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^(1 + n))/(8*b*c^3*(1 + n)*Sqrt[1 + c^2*x^2]) + (Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-4*(a + b*ArcSinh[c*x]))/b])/(2^(2*(3 + n))*c^3*E^((4*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) - (E^((4*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (4*(a + b*ArcSinh[c*x]))/b])/(2^(2*(3 + n))*c^3*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n)","A",7,5,28,0.1786,1,"{5782, 5779, 5448, 3307, 2181}"
513,1,355,0,0.4730723,"\int x \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^n \, dx","Int[x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n,x]","\frac{3^{-n-1} e^{-\frac{3 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 c^2 \sqrt{c^2 x^2+1}}+\frac{e^{-\frac{a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 c^2 \sqrt{c^2 x^2+1}}+\frac{e^{a/b} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 c^2 \sqrt{c^2 x^2+1}}+\frac{3^{-n-1} e^{\frac{3 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 c^2 \sqrt{c^2 x^2+1}}","\frac{3^{-n-1} e^{-\frac{3 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 c^2 \sqrt{c^2 x^2+1}}+\frac{e^{-\frac{a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 c^2 \sqrt{c^2 x^2+1}}+\frac{e^{a/b} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 c^2 \sqrt{c^2 x^2+1}}+\frac{3^{-n-1} e^{\frac{3 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 c^2 \sqrt{c^2 x^2+1}}",1,"(3^(-1 - n)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-3*(a + b*ArcSinh[c*x]))/b])/(8*c^2*E^((3*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, -((a + b*ArcSinh[c*x])/b)])/(8*c^2*E^(a/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (E^(a/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (a + b*ArcSinh[c*x])/b])/(8*c^2*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n) + (3^(-1 - n)*E^((3*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (3*(a + b*ArcSinh[c*x]))/b])/(8*c^2*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n)","A",10,5,26,0.1923,1,"{5782, 5779, 5448, 3308, 2181}"
514,1,235,0,0.2980119,"\int \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^n \, dx","Int[Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n,x]","\frac{2^{-n-3} e^{-\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}-\frac{2^{-n-3} e^{\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}+\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^{n+1}}{2 b c (n+1) \sqrt{c^2 x^2+1}}","\frac{2^{-n-3} e^{-\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}-\frac{2^{-n-3} e^{\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}+\frac{\sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^{n+1}}{2 b c (n+1) \sqrt{c^2 x^2+1}}",1,"(Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^(1 + n))/(2*b*c*(1 + n)*Sqrt[1 + c^2*x^2]) + (2^(-3 - n)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-2*(a + b*ArcSinh[c*x]))/b])/(c*E^((2*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) - (2^(-3 - n)*E^((2*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (2*(a + b*ArcSinh[c*x]))/b])/(c*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n)","A",7,5,25,0.2000,1,"{5702, 5699, 3312, 3307, 2181}"
515,0,0,0,0.1417866,"\int \frac{\sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^n}{x} \, dx","Int[(Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n)/x,x]","\int \frac{\sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^n}{x} \, dx","d \text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c x)\right)^n}{x \sqrt{c^2 d x^2+d}},x\right)+\frac{d e^{-\frac{a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{2 \sqrt{c^2 d x^2+d}}+\frac{d e^{a/b} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{2 \sqrt{c^2 d x^2+d}}",0,"Defer[Int][(Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n)/x, x]","A",0,0,0,0,-1,"{}"
516,0,0,0,0.146752,"\int \frac{\sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^n}{x^2} \, dx","Int[(Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n)/x^2,x]","\int \frac{\sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)^n}{x^2} \, dx","d \text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c x)\right)^n}{x^2 \sqrt{c^2 d x^2+d}},x\right)+\frac{c d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^{n+1}}{b (n+1) \sqrt{c^2 d x^2+d}}",0,"Defer[Int][(Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n)/x^2, x]","A",0,0,0,0,-1,"{}"
517,1,616,0,0.8326718,"\int x^2 \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^n \, dx","Int[x^2*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^n,x]","\frac{d 2^{-n-7} 3^{-n-1} e^{-\frac{6 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}+\frac{d 2^{-2 n-7} e^{-\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{d 2^{-n-7} e^{-\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}+\frac{d 2^{-n-7} e^{\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{d 2^{-2 n-7} e^{\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{d 2^{-n-7} 3^{-n-1} e^{\frac{6 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^{n+1}}{16 b c^3 (n+1) \sqrt{c^2 x^2+1}}","\frac{d 2^{-n-7} 3^{-n-1} e^{-\frac{6 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}+\frac{d 2^{-2 n-7} e^{-\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{d 2^{-n-7} e^{-\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}+\frac{d 2^{-n-7} e^{\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{d 2^{-2 n-7} e^{\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{d 2^{-n-7} 3^{-n-1} e^{\frac{6 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^{n+1}}{16 b c^3 (n+1) \sqrt{c^2 x^2+1}}",1,"-(d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^(1 + n))/(16*b*c^3*(1 + n)*Sqrt[1 + c^2*x^2]) + (2^(-7 - n)*3^(-1 - n)*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-6*(a + b*ArcSinh[c*x]))/b])/(c^3*E^((6*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (2^(-7 - 2*n)*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-4*(a + b*ArcSinh[c*x]))/b])/(c^3*E^((4*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) - (2^(-7 - n)*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-2*(a + b*ArcSinh[c*x]))/b])/(c^3*E^((2*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (2^(-7 - n)*d*E^((2*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (2*(a + b*ArcSinh[c*x]))/b])/(c^3*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n) - (2^(-7 - 2*n)*d*E^((4*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (4*(a + b*ArcSinh[c*x]))/b])/(c^3*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n) - (2^(-7 - n)*3^(-1 - n)*d*E^((6*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (6*(a + b*ArcSinh[c*x]))/b])/(c^3*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n)","A",13,5,28,0.1786,1,"{5782, 5779, 5448, 3307, 2181}"
518,1,542,0,0.6309578,"\int x \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^n \, dx","Int[x*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^n,x]","\frac{d 5^{-n-1} e^{-\frac{5 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{c^2 x^2+1}}+\frac{d 3^{-n} e^{-\frac{3 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{c^2 x^2+1}}+\frac{d e^{-\frac{a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{16 c^2 \sqrt{c^2 x^2+1}}+\frac{d e^{a/b} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{16 c^2 \sqrt{c^2 x^2+1}}+\frac{d 3^{-n} e^{\frac{3 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{c^2 x^2+1}}+\frac{d 5^{-n-1} e^{\frac{5 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{c^2 x^2+1}}","\frac{d 5^{-n-1} e^{-\frac{5 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{c^2 x^2+1}}+\frac{d 3^{-n} e^{-\frac{3 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{c^2 x^2+1}}+\frac{d e^{-\frac{a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{16 c^2 \sqrt{c^2 x^2+1}}+\frac{d e^{a/b} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{16 c^2 \sqrt{c^2 x^2+1}}+\frac{d 3^{-n} e^{\frac{3 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{c^2 x^2+1}}+\frac{d 5^{-n-1} e^{\frac{5 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 c^2 \sqrt{c^2 x^2+1}}",1,"(5^(-1 - n)*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-5*(a + b*ArcSinh[c*x]))/b])/(32*c^2*E^((5*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-3*(a + b*ArcSinh[c*x]))/b])/(32*3^n*c^2*E^((3*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, -((a + b*ArcSinh[c*x])/b)])/(16*c^2*E^(a/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (d*E^(a/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (a + b*ArcSinh[c*x])/b])/(16*c^2*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n) + (d*E^((3*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (3*(a + b*ArcSinh[c*x]))/b])/(32*3^n*c^2*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n) + (5^(-1 - n)*d*E^((5*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (5*(a + b*ArcSinh[c*x]))/b])/(32*c^2*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n)","A",13,5,26,0.1923,1,"{5782, 5779, 5448, 3308, 2181}"
519,1,420,0,0.416662,"\int \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^n \, dx","Int[(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^n,x]","\frac{d 2^{-2 (n+3)} e^{-\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}+\frac{d 2^{-n-3} e^{-\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}-\frac{d 2^{-n-3} e^{\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}-\frac{d 2^{-2 (n+3)} e^{\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}+\frac{3 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^{n+1}}{8 b c (n+1) \sqrt{c^2 x^2+1}}","\frac{d 2^{-2 (n+3)} e^{-\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}+\frac{d 2^{-n-3} e^{-\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}-\frac{d 2^{-n-3} e^{\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}-\frac{d 2^{-2 (n+3)} e^{\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}+\frac{3 d \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^{n+1}}{8 b c (n+1) \sqrt{c^2 x^2+1}}",1,"(3*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^(1 + n))/(8*b*c*(1 + n)*Sqrt[1 + c^2*x^2]) + (d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-4*(a + b*ArcSinh[c*x]))/b])/(2^(2*(3 + n))*c*E^((4*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (2^(-3 - n)*d*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-2*(a + b*ArcSinh[c*x]))/b])/(c*E^((2*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) - (2^(-3 - n)*d*E^((2*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (2*(a + b*ArcSinh[c*x]))/b])/(c*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n) - (d*E^((4*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (4*(a + b*ArcSinh[c*x]))/b])/(2^(2*(3 + n))*c*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n)","A",10,5,25,0.2000,1,"{5702, 5699, 3312, 3307, 2181}"
520,0,0,0,0.1527639,"\int \frac{\left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^n}{x} \, dx","Int[((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^n)/x,x]","\int \frac{\left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^n}{x} \, dx","d^2 \text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c x)\right)^n}{x \sqrt{c^2 d x^2+d}},x\right)+\frac{d^2 3^{-n-1} e^{-\frac{3 a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 \sqrt{c^2 d x^2+d}}+\frac{5 d^2 e^{-\frac{a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 \sqrt{c^2 d x^2+d}}+\frac{5 d^2 e^{a/b} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 \sqrt{c^2 d x^2+d}}+\frac{d^2 3^{-n-1} e^{\frac{3 a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 \sqrt{c^2 d x^2+d}}",0,"Defer[Int][((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^n)/x, x]","A",0,0,0,0,-1,"{}"
521,0,0,0,0.1537822,"\int \frac{\left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^n}{x^2} \, dx","Int[((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^n)/x^2,x]","\int \frac{\left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^n}{x^2} \, dx","d^2 \text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c x)\right)^n}{x^2 \sqrt{c^2 d x^2+d}},x\right)+\frac{c d^2 2^{-n-3} e^{-\frac{2 a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{\sqrt{c^2 d x^2+d}}-\frac{c d^2 2^{-n-3} e^{\frac{2 a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{\sqrt{c^2 d x^2+d}}+\frac{3 c d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^{n+1}}{2 b (n+1) \sqrt{c^2 d x^2+d}}",0,"Defer[Int][((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x])^n)/x^2, x]","A",0,0,0,0,-1,"{}"
522,1,816,0,0.9746811,"\int x^2 \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^n \, dx","Int[x^2*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^n,x]","\frac{2^{-3 n-11} d^2 e^{-\frac{8 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{8 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n}}{c^3 \sqrt{c^2 x^2+1}}+\frac{2^{-n-7} 3^{-n-1} d^2 e^{-\frac{6 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n}}{c^3 \sqrt{c^2 x^2+1}}+\frac{2^{-2 (n+4)} d^2 e^{-\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n}}{c^3 \sqrt{c^2 x^2+1}}-\frac{2^{-n-7} d^2 e^{-\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n}}{c^3 \sqrt{c^2 x^2+1}}-\frac{5 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^{n+1}}{128 b c^3 (n+1) \sqrt{c^2 x^2+1}}+\frac{2^{-n-7} d^2 e^{\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{2^{-2 (n+4)} d^2 e^{\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{2^{-n-7} 3^{-n-1} d^2 e^{\frac{6 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{2^{-3 n-11} d^2 e^{\frac{8 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{8 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}","\frac{2^{-3 n-11} d^2 e^{-\frac{8 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{8 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n}}{c^3 \sqrt{c^2 x^2+1}}+\frac{2^{-n-7} 3^{-n-1} d^2 e^{-\frac{6 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n}}{c^3 \sqrt{c^2 x^2+1}}+\frac{2^{-2 (n+4)} d^2 e^{-\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n}}{c^3 \sqrt{c^2 x^2+1}}-\frac{2^{-n-7} d^2 e^{-\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \text{Gamma}\left(n+1,-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right) \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n}}{c^3 \sqrt{c^2 x^2+1}}-\frac{5 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^{n+1}}{128 b c^3 (n+1) \sqrt{c^2 x^2+1}}+\frac{2^{-n-7} d^2 e^{\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{2^{-2 (n+4)} d^2 e^{\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{2^{-n-7} 3^{-n-1} d^2 e^{\frac{6 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}-\frac{2^{-3 n-11} d^2 e^{\frac{8 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{8 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c^3 \sqrt{c^2 x^2+1}}",1,"(-5*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^(1 + n))/(128*b*c^3*(1 + n)*Sqrt[1 + c^2*x^2]) + (2^(-11 - 3*n)*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-8*(a + b*ArcSinh[c*x]))/b])/(c^3*E^((8*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (2^(-7 - n)*3^(-1 - n)*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-6*(a + b*ArcSinh[c*x]))/b])/(c^3*E^((6*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-4*(a + b*ArcSinh[c*x]))/b])/(2^(2*(4 + n))*c^3*E^((4*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) - (2^(-7 - n)*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-2*(a + b*ArcSinh[c*x]))/b])/(c^3*E^((2*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (2^(-7 - n)*d^2*E^((2*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (2*(a + b*ArcSinh[c*x]))/b])/(c^3*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n) - (d^2*E^((4*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (4*(a + b*ArcSinh[c*x]))/b])/(2^(2*(4 + n))*c^3*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[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*ArcSinh[c*x])^n*Gamma[1 + n, (6*(a + b*ArcSinh[c*x]))/b])/(c^3*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n) - (2^(-11 - 3*n)*d^2*E^((8*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (8*(a + b*ArcSinh[c*x]))/b])/(c^3*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n)","A",16,5,28,0.1786,1,"{5782, 5779, 5448, 3307, 2181}"
523,1,745,0,0.7851465,"\int x \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^n \, dx","Int[x*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^n,x]","\frac{d^2 7^{-n-1} e^{-\frac{7 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c^2 x^2+1}}+\frac{d^2 5^{-n} e^{-\frac{5 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c^2 x^2+1}}+\frac{d^2 3^{1-n} e^{-\frac{3 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c^2 x^2+1}}+\frac{5 d^2 e^{-\frac{a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{128 c^2 \sqrt{c^2 x^2+1}}+\frac{5 d^2 e^{a/b} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{128 c^2 \sqrt{c^2 x^2+1}}+\frac{d^2 3^{1-n} e^{\frac{3 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c^2 x^2+1}}+\frac{d^2 5^{-n} e^{\frac{5 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c^2 x^2+1}}+\frac{d^2 7^{-n-1} e^{\frac{7 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c^2 x^2+1}}","\frac{d^2 7^{-n-1} e^{-\frac{7 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c^2 x^2+1}}+\frac{d^2 5^{-n} e^{-\frac{5 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c^2 x^2+1}}+\frac{d^2 3^{1-n} e^{-\frac{3 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c^2 x^2+1}}+\frac{5 d^2 e^{-\frac{a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{128 c^2 \sqrt{c^2 x^2+1}}+\frac{5 d^2 e^{a/b} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{128 c^2 \sqrt{c^2 x^2+1}}+\frac{d^2 3^{1-n} e^{\frac{3 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c^2 x^2+1}}+\frac{d^2 5^{-n} e^{\frac{5 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c^2 x^2+1}}+\frac{d^2 7^{-n-1} e^{\frac{7 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{128 c^2 \sqrt{c^2 x^2+1}}",1,"(7^(-1 - n)*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-7*(a + b*ArcSinh[c*x]))/b])/(128*c^2*E^((7*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-5*(a + b*ArcSinh[c*x]))/b])/(128*5^n*c^2*E^((5*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (3^(1 - n)*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-3*(a + b*ArcSinh[c*x]))/b])/(128*c^2*E^((3*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (5*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, -((a + b*ArcSinh[c*x])/b)])/(128*c^2*E^(a/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (5*d^2*E^(a/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (a + b*ArcSinh[c*x])/b])/(128*c^2*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n) + (3^(1 - n)*d^2*E^((3*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (3*(a + b*ArcSinh[c*x]))/b])/(128*c^2*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n) + (d^2*E^((5*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (5*(a + b*ArcSinh[c*x]))/b])/(128*5^n*c^2*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n) + (7^(-1 - n)*d^2*E^((7*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (7*(a + b*ArcSinh[c*x]))/b])/(128*c^2*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n)","A",16,5,26,0.1923,1,"{5782, 5779, 5448, 3308, 2181}"
524,1,632,0,0.5999184,"\int \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^n \, dx","Int[(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^n,x]","\frac{d^2 2^{-n-7} 3^{-n-1} e^{-\frac{6 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}+\frac{3 d^2 2^{-2 n-7} e^{-\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}+\frac{15 d^2 2^{-n-7} e^{-\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}-\frac{15 d^2 2^{-n-7} e^{\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}-\frac{3 d^2 2^{-2 n-7} e^{\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}-\frac{d^2 2^{-n-7} 3^{-n-1} e^{\frac{6 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}+\frac{5 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^{n+1}}{16 b c (n+1) \sqrt{c^2 x^2+1}}","\frac{d^2 2^{-n-7} 3^{-n-1} e^{-\frac{6 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}+\frac{3 d^2 2^{-2 n-7} e^{-\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}+\frac{15 d^2 2^{-n-7} e^{-\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}-\frac{15 d^2 2^{-n-7} e^{\frac{2 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}-\frac{3 d^2 2^{-2 n-7} e^{\frac{4 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}-\frac{d^2 2^{-n-7} 3^{-n-1} e^{\frac{6 a}{b}} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{6 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{c \sqrt{c^2 x^2+1}}+\frac{5 d^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^{n+1}}{16 b c (n+1) \sqrt{c^2 x^2+1}}",1,"(5*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^(1 + n))/(16*b*c*(1 + n)*Sqrt[1 + c^2*x^2]) + (2^(-7 - n)*3^(-1 - n)*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-6*(a + b*ArcSinh[c*x]))/b])/(c*E^((6*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (3*2^(-7 - 2*n)*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-4*(a + b*ArcSinh[c*x]))/b])/(c*E^((4*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) + (15*2^(-7 - n)*d^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (-2*(a + b*ArcSinh[c*x]))/b])/(c*E^((2*a)/b)*Sqrt[1 + c^2*x^2]*(-((a + b*ArcSinh[c*x])/b))^n) - (15*2^(-7 - n)*d^2*E^((2*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (2*(a + b*ArcSinh[c*x]))/b])/(c*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n) - (3*2^(-7 - 2*n)*d^2*E^((4*a)/b)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^n*Gamma[1 + n, (4*(a + b*ArcSinh[c*x]))/b])/(c*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[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*ArcSinh[c*x])^n*Gamma[1 + n, (6*(a + b*ArcSinh[c*x]))/b])/(c*Sqrt[1 + c^2*x^2]*((a + b*ArcSinh[c*x])/b)^n)","A",13,5,25,0.2000,1,"{5702, 5699, 3312, 3307, 2181}"
525,0,0,0,0.1554392,"\int \frac{\left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^n}{x} \, dx","Int[((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^n)/x,x]","\int \frac{\left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^n}{x} \, dx","d^3 \text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c x)\right)^n}{x \sqrt{c^2 d x^2+d}},x\right)+\frac{d^3 5^{-n-1} e^{-\frac{5 a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 \sqrt{c^2 d x^2+d}}-\frac{5 d^3 3^{-n-1} e^{-\frac{3 a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 \sqrt{c^2 d x^2+d}}+\frac{d^3 3^{-n} e^{-\frac{3 a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 \sqrt{c^2 d x^2+d}}+\frac{11 d^3 e^{-\frac{a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{16 \sqrt{c^2 d x^2+d}}+\frac{11 d^3 e^{a/b} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{16 \sqrt{c^2 d x^2+d}}-\frac{5 d^3 3^{-n-1} e^{\frac{3 a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 \sqrt{c^2 d x^2+d}}+\frac{d^3 3^{-n} e^{\frac{3 a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{8 \sqrt{c^2 d x^2+d}}+\frac{d^3 5^{-n-1} e^{\frac{5 a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{32 \sqrt{c^2 d x^2+d}}",0,"Defer[Int][((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^n)/x, x]","A",0,0,0,0,-1,"{}"
526,0,0,0,0.1558035,"\int \frac{\left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^n}{x^2} \, dx","Int[((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^n)/x^2,x]","\int \frac{\left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^n}{x^2} \, dx","d^3 \text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c x)\right)^n}{x^2 \sqrt{c^2 d x^2+d}},x\right)+\frac{c d^3 2^{-2 (n+3)} e^{-\frac{4 a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{\sqrt{c^2 d x^2+d}}+\frac{c d^3 2^{-n-2} e^{-\frac{2 a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{\sqrt{c^2 d x^2+d}}-\frac{c d^3 2^{-n-2} e^{\frac{2 a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{\sqrt{c^2 d x^2+d}}-\frac{c d^3 2^{-2 (n+3)} e^{\frac{4 a}{b}} \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^n \left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{4 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{\sqrt{c^2 d x^2+d}}+\frac{15 c d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^{n+1}}{8 b (n+1) \sqrt{c^2 d x^2+d}}",0,"Defer[Int][((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x])^n)/x^2, x]","A",0,0,0,0,-1,"{}"
527,0,0,0,0.1036651,"\int \frac{x^m \sinh ^{-1}(a x)^n}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^m*ArcSinh[a*x]^n)/Sqrt[1 + a^2*x^2],x]","\int \frac{x^m \sinh ^{-1}(a x)^n}{\sqrt{1+a^2 x^2}} \, dx","\text{Int}\left(\frac{x^m \sinh ^{-1}(a x)^n}{\sqrt{a^2 x^2+1}},x\right)",0,"Defer[Int][(x^m*ArcSinh[a*x]^n)/Sqrt[1 + a^2*x^2], x]","A",0,0,0,0,-1,"{}"
528,1,113,0,0.2528606,"\int \frac{x^3 \sinh ^{-1}(a x)^n}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^3*ArcSinh[a*x]^n)/Sqrt[1 + a^2*x^2],x]","\frac{3^{-n-1} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-3 \sinh ^{-1}(a x)\right)}{8 a^4}-\frac{3 \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-\sinh ^{-1}(a x)\right)}{8 a^4}-\frac{3 \text{Gamma}\left(n+1,\sinh ^{-1}(a x)\right)}{8 a^4}+\frac{3^{-n-1} \text{Gamma}\left(n+1,3 \sinh ^{-1}(a x)\right)}{8 a^4}","\frac{3^{-n-1} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-3 \sinh ^{-1}(a x)\right)}{8 a^4}-\frac{3 \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-\sinh ^{-1}(a x)\right)}{8 a^4}-\frac{3 \text{Gamma}\left(n+1,\sinh ^{-1}(a x)\right)}{8 a^4}+\frac{3^{-n-1} \text{Gamma}\left(n+1,3 \sinh ^{-1}(a x)\right)}{8 a^4}",1,"(3^(-1 - n)*ArcSinh[a*x]^n*Gamma[1 + n, -3*ArcSinh[a*x]])/(8*a^4*(-ArcSinh[a*x])^n) - (3*ArcSinh[a*x]^n*Gamma[1 + n, -ArcSinh[a*x]])/(8*a^4*(-ArcSinh[a*x])^n) - (3*Gamma[1 + n, ArcSinh[a*x]])/(8*a^4) + (3^(-1 - n)*Gamma[1 + n, 3*ArcSinh[a*x]])/(8*a^4)","A",9,4,23,0.1739,1,"{5779, 3312, 3308, 2181}"
529,1,80,0,0.1932962,"\int \frac{x^2 \sinh ^{-1}(a x)^n}{\sqrt{1+a^2 x^2}} \, dx","Int[(x^2*ArcSinh[a*x]^n)/Sqrt[1 + a^2*x^2],x]","\frac{2^{-n-3} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-2 \sinh ^{-1}(a x)\right)}{a^3}-\frac{2^{-n-3} \text{Gamma}\left(n+1,2 \sinh ^{-1}(a x)\right)}{a^3}-\frac{\sinh ^{-1}(a x)^{n+1}}{2 a^3 (n+1)}","\frac{2^{-n-3} \sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-2 \sinh ^{-1}(a x)\right)}{a^3}-\frac{2^{-n-3} \text{Gamma}\left(n+1,2 \sinh ^{-1}(a x)\right)}{a^3}-\frac{\sinh ^{-1}(a x)^{n+1}}{2 a^3 (n+1)}",1,"-ArcSinh[a*x]^(1 + n)/(2*a^3*(1 + n)) + (2^(-3 - n)*ArcSinh[a*x]^n*Gamma[1 + n, -2*ArcSinh[a*x]])/(a^3*(-ArcSinh[a*x])^n) - (2^(-3 - n)*Gamma[1 + n, 2*ArcSinh[a*x]])/a^3","A",6,4,23,0.1739,1,"{5779, 3312, 3307, 2181}"
530,1,49,0,0.1170224,"\int \frac{x \sinh ^{-1}(a x)^n}{\sqrt{1+a^2 x^2}} \, dx","Int[(x*ArcSinh[a*x]^n)/Sqrt[1 + a^2*x^2],x]","\frac{\sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-\sinh ^{-1}(a x)\right)}{2 a^2}+\frac{\text{Gamma}\left(n+1,\sinh ^{-1}(a x)\right)}{2 a^2}","\frac{\sinh ^{-1}(a x)^n \left(-\sinh ^{-1}(a x)\right)^{-n} \text{Gamma}\left(n+1,-\sinh ^{-1}(a x)\right)}{2 a^2}+\frac{\text{Gamma}\left(n+1,\sinh ^{-1}(a x)\right)}{2 a^2}",1,"(ArcSinh[a*x]^n*Gamma[1 + n, -ArcSinh[a*x]])/(2*a^2*(-ArcSinh[a*x])^n) + Gamma[1 + n, ArcSinh[a*x]]/(2*a^2)","A",4,3,21,0.1429,1,"{5779, 3308, 2181}"
531,1,17,0,0.0380282,"\int \frac{\sinh ^{-1}(a x)^n}{\sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]^n/Sqrt[1 + a^2*x^2],x]","\frac{\sinh ^{-1}(a x)^{n+1}}{a (n+1)}","\frac{\sinh ^{-1}(a x)^{n+1}}{a (n+1)}",1,"ArcSinh[a*x]^(1 + n)/(a*(1 + n))","A",1,1,20,0.05000,1,"{5675}"
532,0,0,0,0.1022268,"\int \frac{\sinh ^{-1}(a x)^n}{x \sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]^n/(x*Sqrt[1 + a^2*x^2]),x]","\int \frac{\sinh ^{-1}(a x)^n}{x \sqrt{1+a^2 x^2}} \, dx","\text{Int}\left(\frac{\sinh ^{-1}(a x)^n}{x \sqrt{a^2 x^2+1}},x\right)",0,"Defer[Int][ArcSinh[a*x]^n/(x*Sqrt[1 + a^2*x^2]), x]","A",0,0,0,0,-1,"{}"
533,0,0,0,0.101782,"\int \frac{\sinh ^{-1}(a x)^n}{x^2 \sqrt{1+a^2 x^2}} \, dx","Int[ArcSinh[a*x]^n/(x^2*Sqrt[1 + a^2*x^2]),x]","\int \frac{\sinh ^{-1}(a x)^n}{x^2 \sqrt{1+a^2 x^2}} \, dx","\text{Int}\left(\frac{\sinh ^{-1}(a x)^n}{x^2 \sqrt{a^2 x^2+1}},x\right)",0,"Defer[Int][ArcSinh[a*x]^n/(x^2*Sqrt[1 + a^2*x^2]), x]","A",0,0,0,0,-1,"{}"
534,1,416,0,0.5973402,"\int (d+i c d x)^{5/2} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + I*c*d*x)^(5/2)*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]),x]","-\frac{1}{4} c^2 d^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 d^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c \sqrt{c^2 x^2+1}}+\frac{2 i d^2 \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{3 c}+\frac{3}{8} d^2 x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)+\frac{b c^3 d^2 x^4 \sqrt{d+i c d x} \sqrt{f-i c f x}}{16 \sqrt{c^2 x^2+1}}-\frac{2 i b c^2 d^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x}}{9 \sqrt{c^2 x^2+1}}-\frac{3 b c d^2 x^2 \sqrt{d+i c d x} \sqrt{f-i c f x}}{16 \sqrt{c^2 x^2+1}}-\frac{2 i b d^2 x \sqrt{d+i c d x} \sqrt{f-i c f x}}{3 \sqrt{c^2 x^2+1}}","-\frac{1}{4} c^2 d^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 d^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c \sqrt{c^2 x^2+1}}+\frac{2 i d^2 \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{3 c}+\frac{3}{8} d^2 x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)+\frac{b c^3 d^2 x^4 \sqrt{d+i c d x} \sqrt{f-i c f x}}{16 \sqrt{c^2 x^2+1}}-\frac{2 i b c^2 d^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x}}{9 \sqrt{c^2 x^2+1}}-\frac{3 b c d^2 x^2 \sqrt{d+i c d x} \sqrt{f-i c f x}}{16 \sqrt{c^2 x^2+1}}-\frac{2 i b d^2 x \sqrt{d+i c d x} \sqrt{f-i c f x}}{3 \sqrt{c^2 x^2+1}}",1,"(((-2*I)/3)*b*d^2*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/Sqrt[1 + c^2*x^2] - (3*b*c*d^2*x^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/(16*Sqrt[1 + c^2*x^2]) - (((2*I)/9)*b*c^2*d^2*x^3*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/Sqrt[1 + c^2*x^2] + (b*c^3*d^2*x^4*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/(16*Sqrt[1 + c^2*x^2]) + (3*d^2*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/8 - (c^2*d^2*x^3*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/4 + (((2*I)/3)*d^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/c + (5*d^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2)/(16*b*c*Sqrt[1 + c^2*x^2])","A",13,8,35,0.2286,1,"{5712, 5821, 5682, 5675, 30, 5717, 5742, 5758}"
535,1,304,0,0.3427162,"\int (d+i c d x)^{3/2} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + I*c*d*x)^(3/2)*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]),x]","\frac{d \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{c^2 x^2+1}}+\frac{i d \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{3 c}+\frac{1}{2} d x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)-\frac{i b c^2 d x^3 \sqrt{d+i c d x} \sqrt{f-i c f x}}{9 \sqrt{c^2 x^2+1}}-\frac{b c d x^2 \sqrt{d+i c d x} \sqrt{f-i c f x}}{4 \sqrt{c^2 x^2+1}}-\frac{i b d x \sqrt{d+i c d x} \sqrt{f-i c f x}}{3 \sqrt{c^2 x^2+1}}","\frac{d \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{c^2 x^2+1}}+\frac{i d \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{3 c}+\frac{1}{2} d x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)-\frac{i b c^2 d x^3 \sqrt{d+i c d x} \sqrt{f-i c f x}}{9 \sqrt{c^2 x^2+1}}-\frac{b c d x^2 \sqrt{d+i c d x} \sqrt{f-i c f x}}{4 \sqrt{c^2 x^2+1}}-\frac{i b d x \sqrt{d+i c d x} \sqrt{f-i c f x}}{3 \sqrt{c^2 x^2+1}}",1,"((-I/3)*b*d*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/Sqrt[1 + c^2*x^2] - (b*c*d*x^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/(4*Sqrt[1 + c^2*x^2]) - ((I/9)*b*c^2*d*x^3*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/Sqrt[1 + c^2*x^2] + (d*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/2 + ((I/3)*d*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/c + (d*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2)/(4*b*c*Sqrt[1 + c^2*x^2])","A",8,6,35,0.1714,1,"{5712, 5821, 5682, 5675, 30, 5717}"
536,1,147,0,0.1957253,"\int \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]),x]","\frac{\sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{c^2 x^2+1}}+\frac{1}{2} x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)-\frac{b c x^2 \sqrt{d+i c d x} \sqrt{f-i c f x}}{4 \sqrt{c^2 x^2+1}}","\frac{\sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{c^2 x^2+1}}+\frac{1}{2} x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)-\frac{b c x^2 \sqrt{d+i c d x} \sqrt{f-i c f x}}{4 \sqrt{c^2 x^2+1}}",1,"-(b*c*x^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/(4*Sqrt[1 + c^2*x^2]) + (x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/2 + (Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2)/(4*b*c*Sqrt[1 + c^2*x^2])","A",4,4,35,0.1143,1,"{5712, 5682, 5675, 30}"
537,1,158,0,0.2978354,"\int \frac{\sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{d+i c d x}} \, dx","Int[(Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/Sqrt[d + I*c*d*x],x]","\frac{f \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{i f \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{i b f x \sqrt{c^2 x^2+1}}{\sqrt{d+i c d x} \sqrt{f-i c f x}}","\frac{f \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{i f \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{i b f x \sqrt{c^2 x^2+1}}{\sqrt{d+i c d x} \sqrt{f-i c f x}}",1,"(I*b*f*x*Sqrt[1 + c^2*x^2])/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (I*f*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (f*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])","A",6,5,35,0.1429,1,"{5712, 5821, 5675, 5717, 8}"
538,1,181,0,0.40068,"\int \frac{\sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{(d+i c d x)^{3/2}} \, dx","Int[(Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/(d + I*c*d*x)^(3/2),x]","-\frac{f^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 i f^2 (1-i c x) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 b f^2 \left(c^2 x^2+1\right)^{3/2} \log (-c x+i)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}","-\frac{f^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 i f^2 (1-i c x) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 b f^2 \left(c^2 x^2+1\right)^{3/2} \log (-c x+i)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}",1,"((2*I)*f^2*(1 - I*c*x)*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (f^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(2*b*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (2*b*f^2*(1 + c^2*x^2)^(3/2)*Log[I - c*x])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",8,8,35,0.2286,1,"{5712, 5833, 637, 5819, 12, 627, 31, 5675}"
539,1,187,0,0.3064506,"\int \frac{\sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{(d+i c d x)^{5/2}} \, dx","Int[(Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/(d + I*c*d*x)^(5/2),x]","\frac{i f^3 (1-i c x)^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i b f^3 \left(c^2 x^2+1\right)^{5/2}}{3 c (-c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{b f^3 \left(c^2 x^2+1\right)^{5/2} \log (-c x+i)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","\frac{i f^3 (1-i c x)^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i b f^3 \left(c^2 x^2+1\right)^{5/2}}{3 c (-c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{b f^3 \left(c^2 x^2+1\right)^{5/2} \log (-c x+i)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"(((2*I)/3)*b*f^3*(1 + c^2*x^2)^(5/2))/(c*(I - c*x)*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + ((I/3)*f^3*(1 - I*c*x)^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (b*f^3*(1 + c^2*x^2)^(5/2)*Log[I - c*x])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",6,6,35,0.1714,1,"{5712, 651, 5819, 12, 627, 43}"
540,1,459,0,0.4413068,"\int (d+i c d x)^{5/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]),x]","\frac{3 d x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 \left(c^2 x^2+1\right)}+\frac{3 d (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c \left(c^2 x^2+1\right)^{3/2}}+\frac{i d \left(c^2 x^2+1\right) (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 c}+\frac{1}{4} d x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{i b c^4 d x^5 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{25 \left(c^2 x^2+1\right)^{3/2}}-\frac{b c^3 d x^4 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{16 \left(c^2 x^2+1\right)^{3/2}}-\frac{2 i b c^2 d x^3 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{15 \left(c^2 x^2+1\right)^{3/2}}-\frac{5 b c d x^2 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{16 \left(c^2 x^2+1\right)^{3/2}}-\frac{i b d x (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{5 \left(c^2 x^2+1\right)^{3/2}}","\frac{3 d x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 \left(c^2 x^2+1\right)}+\frac{3 d (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c \left(c^2 x^2+1\right)^{3/2}}+\frac{i d \left(c^2 x^2+1\right) (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 c}+\frac{1}{4} d x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{i b c^4 d x^5 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{25 \left(c^2 x^2+1\right)^{3/2}}-\frac{b c^3 d x^4 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{16 \left(c^2 x^2+1\right)^{3/2}}-\frac{2 i b c^2 d x^3 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{15 \left(c^2 x^2+1\right)^{3/2}}-\frac{5 b c d x^2 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{16 \left(c^2 x^2+1\right)^{3/2}}-\frac{i b d x (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{5 \left(c^2 x^2+1\right)^{3/2}}",1,"((-I/5)*b*d*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(1 + c^2*x^2)^(3/2) - (5*b*c*d*x^2*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(16*(1 + c^2*x^2)^(3/2)) - (((2*I)/15)*b*c^2*d*x^3*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(1 + c^2*x^2)^(3/2) - (b*c^3*d*x^4*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(16*(1 + c^2*x^2)^(3/2)) - ((I/25)*b*c^4*d*x^5*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(1 + c^2*x^2)^(3/2) + (d*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/4 + (3*d*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/(8*(1 + c^2*x^2)) + ((I/5)*d*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/c + (3*d*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^2)/(16*b*c*(1 + c^2*x^2)^(3/2))","A",12,9,35,0.2571,1,"{5712, 5821, 5684, 5682, 5675, 30, 14, 5717, 194}"
541,1,247,0,0.2522401,"\int (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]),x]","\frac{3 x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 \left(c^2 x^2+1\right)}+\frac{3 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c \left(c^2 x^2+1\right)^{3/2}}+\frac{1}{4} x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{b c^3 x^4 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{16 \left(c^2 x^2+1\right)^{3/2}}-\frac{5 b c x^2 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{16 \left(c^2 x^2+1\right)^{3/2}}","\frac{3 x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 \left(c^2 x^2+1\right)}+\frac{3 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c \left(c^2 x^2+1\right)^{3/2}}+\frac{1}{4} x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{b c^3 x^4 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{16 \left(c^2 x^2+1\right)^{3/2}}-\frac{5 b c x^2 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{16 \left(c^2 x^2+1\right)^{3/2}}",1,"(-5*b*c*x^2*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(16*(1 + c^2*x^2)^(3/2)) - (b*c^3*x^4*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(16*(1 + c^2*x^2)^(3/2)) + (x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/4 + (3*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/(8*(1 + c^2*x^2)) + (3*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^2)/(16*b*c*(1 + c^2*x^2)^(3/2))","A",7,6,35,0.1714,1,"{5712, 5684, 5682, 5675, 30, 14}"
542,1,304,0,0.3405406,"\int \sqrt{d+i c d x} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[Sqrt[d + I*c*d*x]*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]),x]","\frac{f \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{c^2 x^2+1}}-\frac{i f \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{3 c}+\frac{1}{2} f x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)+\frac{i b c^2 f x^3 \sqrt{d+i c d x} \sqrt{f-i c f x}}{9 \sqrt{c^2 x^2+1}}-\frac{b c f x^2 \sqrt{d+i c d x} \sqrt{f-i c f x}}{4 \sqrt{c^2 x^2+1}}+\frac{i b f x \sqrt{d+i c d x} \sqrt{f-i c f x}}{3 \sqrt{c^2 x^2+1}}","\frac{f \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{c^2 x^2+1}}-\frac{i f \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{3 c}+\frac{1}{2} f x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)+\frac{i b c^2 f x^3 \sqrt{d+i c d x} \sqrt{f-i c f x}}{9 \sqrt{c^2 x^2+1}}-\frac{b c f x^2 \sqrt{d+i c d x} \sqrt{f-i c f x}}{4 \sqrt{c^2 x^2+1}}+\frac{i b f x \sqrt{d+i c d x} \sqrt{f-i c f x}}{3 \sqrt{c^2 x^2+1}}",1,"((I/3)*b*f*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/Sqrt[1 + c^2*x^2] - (b*c*f*x^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/(4*Sqrt[1 + c^2*x^2]) + ((I/9)*b*c^2*f*x^3*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/Sqrt[1 + c^2*x^2] + (f*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/2 - ((I/3)*f*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/c + (f*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2)/(4*b*c*Sqrt[1 + c^2*x^2])","A",8,6,35,0.1714,1,"{5712, 5821, 5682, 5675, 30, 5717}"
543,1,266,0,0.4647717,"\int \frac{(f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{d+i c d x}} \, dx","Int[((f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/Sqrt[d + I*c*d*x],x]","\frac{3 f^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{f^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{2 i f^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{b c f^2 x^2 \sqrt{c^2 x^2+1}}{4 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{2 i b f^2 x \sqrt{c^2 x^2+1}}{\sqrt{d+i c d x} \sqrt{f-i c f x}}","\frac{3 f^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{f^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{2 i f^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{b c f^2 x^2 \sqrt{c^2 x^2+1}}{4 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{2 i b f^2 x \sqrt{c^2 x^2+1}}{\sqrt{d+i c d x} \sqrt{f-i c f x}}",1,"((2*I)*b*f^2*x*Sqrt[1 + c^2*x^2])/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (b*c*f^2*x^2*Sqrt[1 + c^2*x^2])/(4*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - ((2*I)*f^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (f^2*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (3*f^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])","A",9,7,35,0.2000,1,"{5712, 5821, 5675, 5717, 8, 5758, 30}"
544,1,284,0,0.4740881,"\int \frac{(f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{(d+i c d x)^{3/2}} \, dx","Int[((f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/(d + I*c*d*x)^(3/2),x]","-\frac{3 f^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{i f^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{4 i f^3 (1-i c x) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{i b f^3 x \left(c^2 x^2+1\right)^{3/2}}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 b f^3 \left(c^2 x^2+1\right)^{3/2} \log (-c x+i)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}","-\frac{3 f^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{i f^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{4 i f^3 (1-i c x) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{i b f^3 x \left(c^2 x^2+1\right)^{3/2}}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 b f^3 \left(c^2 x^2+1\right)^{3/2} \log (-c x+i)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}",1,"((-I)*b*f^3*x*(1 + c^2*x^2)^(3/2))/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + ((4*I)*f^3*(1 - I*c*x)*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (I*f^3*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (3*f^3*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(2*b*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (4*b*f^3*(1 + c^2*x^2)^(3/2)*Log[I - c*x])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",10,10,35,0.2857,1,"{5712, 5833, 637, 5819, 12, 627, 31, 5675, 5717, 8}"
545,1,364,0,0.383732,"\int \frac{(f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{(d+i c d x)^{5/2}} \, dx","Int[((f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/(d + I*c*d*x)^(5/2),x]","-\frac{2 i f^4 (1-i c x) \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i f^4 (1-i c x)^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{f^4 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{4 i b f^4 \left(c^2 x^2+1\right)^{5/2}}{3 c (-c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 b f^4 \left(c^2 x^2+1\right)^{5/2} \log (-c x+i)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b f^4 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x)^2}{2 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","-\frac{2 i f^4 (1-i c x) \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i f^4 (1-i c x)^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{f^4 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{4 i b f^4 \left(c^2 x^2+1\right)^{5/2}}{3 c (-c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 b f^4 \left(c^2 x^2+1\right)^{5/2} \log (-c x+i)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b f^4 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x)^2}{2 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"(((4*I)/3)*b*f^4*(1 + c^2*x^2)^(5/2))/(c*(I - c*x)*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (b*f^4*(1 + c^2*x^2)^(5/2)*ArcSinh[c*x]^2)/(2*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((2*I)/3)*f^4*(1 - I*c*x)^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - ((2*I)*f^4*(1 - I*c*x)*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (f^4*(1 + c^2*x^2)^(5/2)*ArcSinh[c*x]*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (8*b*f^4*(1 + c^2*x^2)^(5/2)*Log[I - c*x])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",9,9,35,0.2571,1,"{5712, 669, 653, 215, 5819, 627, 43, 31, 5675}"
546,1,344,0,0.3038691,"\int (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x]),x]","\frac{5 x (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{24 \left(c^2 x^2+1\right)}+\frac{5 x (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{16 \left(c^2 x^2+1\right)^2}+\frac{5 (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{32 b c \left(c^2 x^2+1\right)^{5/2}}+\frac{1}{6} x (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{5 b c^3 x^4 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}{96 \left(c^2 x^2+1\right)^{5/2}}-\frac{25 b c x^2 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}{96 \left(c^2 x^2+1\right)^{5/2}}-\frac{b \sqrt{c^2 x^2+1} (d+i c d x)^{5/2} (f-i c f x)^{5/2}}{36 c}","\frac{5 x (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{24 \left(c^2 x^2+1\right)}+\frac{5 x (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{16 \left(c^2 x^2+1\right)^2}+\frac{5 (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{32 b c \left(c^2 x^2+1\right)^{5/2}}+\frac{1}{6} x (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)-\frac{5 b c^3 x^4 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}{96 \left(c^2 x^2+1\right)^{5/2}}-\frac{25 b c x^2 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}{96 \left(c^2 x^2+1\right)^{5/2}}-\frac{b \sqrt{c^2 x^2+1} (d+i c d x)^{5/2} (f-i c f x)^{5/2}}{36 c}",1,"(-25*b*c*x^2*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))/(96*(1 + c^2*x^2)^(5/2)) - (5*b*c^3*x^4*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))/(96*(1 + c^2*x^2)^(5/2)) - (b*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)*Sqrt[1 + c^2*x^2])/(36*c) + (x*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x]))/6 + (5*x*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x]))/(16*(1 + c^2*x^2)^2) + (5*x*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x]))/(24*(1 + c^2*x^2)) + (5*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x])^2)/(32*b*c*(1 + c^2*x^2)^(5/2))","A",9,7,35,0.2000,1,"{5712, 5684, 5682, 5675, 30, 14, 261}"
547,1,459,0,0.4259818,"\int (d+i c d x)^{3/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x]),x]","\frac{3 f x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 \left(c^2 x^2+1\right)}+\frac{3 f (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c \left(c^2 x^2+1\right)^{3/2}}-\frac{i f \left(c^2 x^2+1\right) (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 c}+\frac{1}{4} f x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{i b c^4 f x^5 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{25 \left(c^2 x^2+1\right)^{3/2}}-\frac{b c^3 f x^4 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{16 \left(c^2 x^2+1\right)^{3/2}}+\frac{2 i b c^2 f x^3 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{15 \left(c^2 x^2+1\right)^{3/2}}-\frac{5 b c f x^2 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{16 \left(c^2 x^2+1\right)^{3/2}}+\frac{i b f x (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{5 \left(c^2 x^2+1\right)^{3/2}}","\frac{3 f x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 \left(c^2 x^2+1\right)}+\frac{3 f (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c \left(c^2 x^2+1\right)^{3/2}}-\frac{i f \left(c^2 x^2+1\right) (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 c}+\frac{1}{4} f x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)+\frac{i b c^4 f x^5 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{25 \left(c^2 x^2+1\right)^{3/2}}-\frac{b c^3 f x^4 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{16 \left(c^2 x^2+1\right)^{3/2}}+\frac{2 i b c^2 f x^3 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{15 \left(c^2 x^2+1\right)^{3/2}}-\frac{5 b c f x^2 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{16 \left(c^2 x^2+1\right)^{3/2}}+\frac{i b f x (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{5 \left(c^2 x^2+1\right)^{3/2}}",1,"((I/5)*b*f*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(1 + c^2*x^2)^(3/2) - (5*b*c*f*x^2*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(16*(1 + c^2*x^2)^(3/2)) + (((2*I)/15)*b*c^2*f*x^3*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(1 + c^2*x^2)^(3/2) - (b*c^3*f*x^4*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(16*(1 + c^2*x^2)^(3/2)) + ((I/25)*b*c^4*f*x^5*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(1 + c^2*x^2)^(3/2) + (f*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/4 + (3*f*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/(8*(1 + c^2*x^2)) - ((I/5)*f*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/c + (3*f*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^2)/(16*b*c*(1 + c^2*x^2)^(3/2))","A",12,9,35,0.2571,1,"{5712, 5821, 5684, 5682, 5675, 30, 14, 5717, 194}"
548,1,416,0,0.5714389,"\int \sqrt{d+i c d x} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[Sqrt[d + I*c*d*x]*(f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x]),x]","-\frac{1}{4} c^2 f^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 f^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c \sqrt{c^2 x^2+1}}-\frac{2 i f^2 \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{3 c}+\frac{3}{8} f^2 x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)+\frac{b c^3 f^2 x^4 \sqrt{d+i c d x} \sqrt{f-i c f x}}{16 \sqrt{c^2 x^2+1}}+\frac{2 i b c^2 f^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x}}{9 \sqrt{c^2 x^2+1}}-\frac{3 b c f^2 x^2 \sqrt{d+i c d x} \sqrt{f-i c f x}}{16 \sqrt{c^2 x^2+1}}+\frac{2 i b f^2 x \sqrt{d+i c d x} \sqrt{f-i c f x}}{3 \sqrt{c^2 x^2+1}}","-\frac{1}{4} c^2 f^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 f^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 b c \sqrt{c^2 x^2+1}}-\frac{2 i f^2 \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{3 c}+\frac{3}{8} f^2 x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)+\frac{b c^3 f^2 x^4 \sqrt{d+i c d x} \sqrt{f-i c f x}}{16 \sqrt{c^2 x^2+1}}+\frac{2 i b c^2 f^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x}}{9 \sqrt{c^2 x^2+1}}-\frac{3 b c f^2 x^2 \sqrt{d+i c d x} \sqrt{f-i c f x}}{16 \sqrt{c^2 x^2+1}}+\frac{2 i b f^2 x \sqrt{d+i c d x} \sqrt{f-i c f x}}{3 \sqrt{c^2 x^2+1}}",1,"(((2*I)/3)*b*f^2*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/Sqrt[1 + c^2*x^2] - (3*b*c*f^2*x^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/(16*Sqrt[1 + c^2*x^2]) + (((2*I)/9)*b*c^2*f^2*x^3*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/Sqrt[1 + c^2*x^2] + (b*c^3*f^2*x^4*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/(16*Sqrt[1 + c^2*x^2]) + (3*f^2*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/8 - (c^2*f^2*x^3*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/4 - (((2*I)/3)*f^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/c + (5*f^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2)/(16*b*c*Sqrt[1 + c^2*x^2])","A",13,8,35,0.2286,1,"{5712, 5821, 5682, 5675, 30, 5717, 5742, 5758}"
549,1,381,0,0.6275286,"\int \frac{(f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{d+i c d x}} \, dx","Int[((f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x]))/Sqrt[d + I*c*d*x],x]","\frac{5 f^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{i c f^3 x^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{3 f^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{11 i f^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{i b c^2 f^3 x^3 \sqrt{c^2 x^2+1}}{9 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{3 b c f^3 x^2 \sqrt{c^2 x^2+1}}{4 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{11 i b f^3 x \sqrt{c^2 x^2+1}}{3 \sqrt{d+i c d x} \sqrt{f-i c f x}}","\frac{5 f^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{i c f^3 x^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{3 f^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{11 i f^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{i b c^2 f^3 x^3 \sqrt{c^2 x^2+1}}{9 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{3 b c f^3 x^2 \sqrt{c^2 x^2+1}}{4 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{11 i b f^3 x \sqrt{c^2 x^2+1}}{3 \sqrt{d+i c d x} \sqrt{f-i c f x}}",1,"(((11*I)/3)*b*f^3*x*Sqrt[1 + c^2*x^2])/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (3*b*c*f^3*x^2*Sqrt[1 + c^2*x^2])/(4*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - ((I/9)*b*c^2*f^3*x^3*Sqrt[1 + c^2*x^2])/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (((11*I)/3)*f^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (3*f^3*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + ((I/3)*c*f^3*x^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (5*f^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])","A",13,7,35,0.2000,1,"{5712, 5821, 5675, 5717, 8, 5758, 30}"
550,1,518,0,0.4161297,"\int \frac{(f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{(d+i c d x)^{3/2}} \, dx","Int[((f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x]))/(d + I*c*d*x)^(3/2),x]","\frac{5 i f^4 (1-i c x) \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{15 i f^4 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 i f^4 (1-i c x)^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{15 f^4 \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x) \left(a+b \sinh ^{-1}(c x)\right)}{2 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{b c f^4 x^2 \left(c^2 x^2+1\right)^{3/2}}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{5 b f^4 (1-i c x)^2 \left(c^2 x^2+1\right)^{3/2}}{4 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{3 i b f^4 x \left(c^2 x^2+1\right)^{3/2}}{2 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{8 b f^4 \left(c^2 x^2+1\right)^{3/2} \log (-c x+i)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{15 b f^4 \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x)^2}{4 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}","\frac{5 i f^4 (1-i c x) \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{15 i f^4 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 i f^4 (1-i c x)^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{15 f^4 \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x) \left(a+b \sinh ^{-1}(c x)\right)}{2 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{b c f^4 x^2 \left(c^2 x^2+1\right)^{3/2}}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{5 b f^4 (1-i c x)^2 \left(c^2 x^2+1\right)^{3/2}}{4 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{3 i b f^4 x \left(c^2 x^2+1\right)^{3/2}}{2 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{8 b f^4 \left(c^2 x^2+1\right)^{3/2} \log (-c x+i)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{15 b f^4 \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x)^2}{4 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}",1,"(((-3*I)/2)*b*f^4*x*(1 + c^2*x^2)^(3/2))/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (b*c*f^4*x^2*(1 + c^2*x^2)^(3/2))/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (5*b*f^4*(1 - I*c*x)^2*(1 + c^2*x^2)^(3/2))/(4*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (15*b*f^4*(1 + c^2*x^2)^(3/2)*ArcSinh[c*x]^2)/(4*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + ((2*I)*f^4*(1 - I*c*x)^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (((15*I)/2)*f^4*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (((5*I)/2)*f^4*(1 - I*c*x)*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (15*f^4*(1 + c^2*x^2)^(3/2)*ArcSinh[c*x]*(a + b*ArcSinh[c*x]))/(2*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (8*b*f^4*(1 + c^2*x^2)^(3/2)*Log[I - c*x])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",7,9,35,0.2571,1,"{5712, 669, 671, 641, 215, 5819, 627, 43, 5675}"
551,1,472,0,0.4444645,"\int \frac{(f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{(d+i c d x)^{5/2}} \, dx","Int[((f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x]))/(d + I*c*d*x)^(5/2),x]","-\frac{5 i f^5 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{10 i f^5 (1-i c x)^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i f^5 (1-i c x)^4 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{5 f^5 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b f^5 x \left(c^2 x^2+1\right)^{5/2}}{(d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 i b f^5 \left(c^2 x^2+1\right)^{5/2}}{3 c (-c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{28 b f^5 \left(c^2 x^2+1\right)^{5/2} \log (-c x+i)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{5 b f^5 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x)^2}{2 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","-\frac{5 i f^5 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{10 i f^5 (1-i c x)^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i f^5 (1-i c x)^4 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{5 f^5 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b f^5 x \left(c^2 x^2+1\right)^{5/2}}{(d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 i b f^5 \left(c^2 x^2+1\right)^{5/2}}{3 c (-c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{28 b f^5 \left(c^2 x^2+1\right)^{5/2} \log (-c x+i)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{5 b f^5 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x)^2}{2 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"(I*b*f^5*x*(1 + c^2*x^2)^(5/2))/((d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((8*I)/3)*b*f^5*(1 + c^2*x^2)^(5/2))/(c*(I - c*x)*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (5*b*f^5*(1 + c^2*x^2)^(5/2)*ArcSinh[c*x]^2)/(2*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((2*I)/3)*f^5*(1 - I*c*x)^4*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (((10*I)/3)*f^5*(1 - I*c*x)^2*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - ((5*I)*f^5*(1 + c^2*x^2)^3*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (5*f^5*(1 + c^2*x^2)^(5/2)*ArcSinh[c*x]*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (28*b*f^5*(1 + c^2*x^2)^(5/2)*Log[I - c*x])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",10,8,35,0.2286,1,"{5712, 669, 641, 215, 5819, 627, 43, 5675}"
552,1,381,0,0.6293717,"\int \frac{(d+i c d x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{f-i c f x}} \, dx","Int[((d + I*c*d*x)^(5/2)*(a + b*ArcSinh[c*x]))/Sqrt[f - I*c*f*x],x]","\frac{5 d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{i c d^3 x^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{3 d^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{11 i d^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{i b c^2 d^3 x^3 \sqrt{c^2 x^2+1}}{9 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{3 b c d^3 x^2 \sqrt{c^2 x^2+1}}{4 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{11 i b d^3 x \sqrt{c^2 x^2+1}}{3 \sqrt{d+i c d x} \sqrt{f-i c f x}}","\frac{5 d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{i c d^3 x^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{3 d^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{11 i d^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{i b c^2 d^3 x^3 \sqrt{c^2 x^2+1}}{9 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{3 b c d^3 x^2 \sqrt{c^2 x^2+1}}{4 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{11 i b d^3 x \sqrt{c^2 x^2+1}}{3 \sqrt{d+i c d x} \sqrt{f-i c f x}}",1,"(((-11*I)/3)*b*d^3*x*Sqrt[1 + c^2*x^2])/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (3*b*c*d^3*x^2*Sqrt[1 + c^2*x^2])/(4*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + ((I/9)*b*c^2*d^3*x^3*Sqrt[1 + c^2*x^2])/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (((11*I)/3)*d^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (3*d^3*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - ((I/3)*c*d^3*x^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (5*d^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])","A",13,7,35,0.2000,1,"{5712, 5821, 5675, 5717, 8, 5758, 30}"
553,1,266,0,0.4659653,"\int \frac{(d+i c d x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{f-i c f x}} \, dx","Int[((d + I*c*d*x)^(3/2)*(a + b*ArcSinh[c*x]))/Sqrt[f - I*c*f*x],x]","\frac{3 d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{d^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{2 i d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{b c d^2 x^2 \sqrt{c^2 x^2+1}}{4 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{2 i b d^2 x \sqrt{c^2 x^2+1}}{\sqrt{d+i c d x} \sqrt{f-i c f x}}","\frac{3 d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{4 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{d^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{2 i d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{b c d^2 x^2 \sqrt{c^2 x^2+1}}{4 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{2 i b d^2 x \sqrt{c^2 x^2+1}}{\sqrt{d+i c d x} \sqrt{f-i c f x}}",1,"((-2*I)*b*d^2*x*Sqrt[1 + c^2*x^2])/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (b*c*d^2*x^2*Sqrt[1 + c^2*x^2])/(4*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + ((2*I)*d^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (d^2*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (3*d^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])","A",9,7,35,0.2000,1,"{5712, 5821, 5675, 5717, 8, 5758, 30}"
554,1,158,0,0.2903861,"\int \frac{\sqrt{d+i c d x} \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{f-i c f x}} \, dx","Int[(Sqrt[d + I*c*d*x]*(a + b*ArcSinh[c*x]))/Sqrt[f - I*c*f*x],x]","\frac{d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{i d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{i b d x \sqrt{c^2 x^2+1}}{\sqrt{d+i c d x} \sqrt{f-i c f x}}","\frac{d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{i d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{i b d x \sqrt{c^2 x^2+1}}{\sqrt{d+i c d x} \sqrt{f-i c f x}}",1,"((-I)*b*d*x*Sqrt[1 + c^2*x^2])/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (I*d*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (d*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])","A",6,5,35,0.1429,1,"{5712, 5821, 5675, 5717, 8}"
555,1,59,0,0.1695649,"\int \frac{a+b \sinh ^{-1}(c x)}{\sqrt{d+i c d x} \sqrt{f-i c f x}} \, dx","Int[(a + b*ArcSinh[c*x])/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]),x]","\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}","\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}",1,"(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])","A",2,2,35,0.05714,1,"{5712, 5675}"
556,1,111,0,0.2413069,"\int \frac{a+b \sinh ^{-1}(c x)}{(d+i c d x)^{3/2} \sqrt{f-i c f x}} \, dx","Int[(a + b*ArcSinh[c*x])/((d + I*c*d*x)^(3/2)*Sqrt[f - I*c*f*x]),x]","\frac{f (c x+i) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{b f \left(c^2 x^2+1\right)^{3/2} \log (-c x+i)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}","\frac{f (c x+i) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{b f \left(c^2 x^2+1\right)^{3/2} \log (-c x+i)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}",1,"(f*(I + c*x)*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (b*f*(1 + c^2*x^2)^(3/2)*Log[I - c*x])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",5,6,35,0.1714,1,"{5712, 637, 5819, 12, 627, 31}"
557,1,295,0,0.3371316,"\int \frac{a+b \sinh ^{-1}(c x)}{(d+i c d x)^{5/2} \sqrt{f-i c f x}} \, dx","Int[(a + b*ArcSinh[c*x])/((d + I*c*d*x)^(5/2)*Sqrt[f - I*c*f*x]),x]","\frac{f^2 x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i f^2 (1-i c x) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b f^2 \left(c^2 x^2+1\right)^{5/2}}{3 c (-c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b f^2 \left(c^2 x^2+1\right)^{5/2} \log \left(c^2 x^2+1\right)}{6 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i b f^2 \left(c^2 x^2+1\right)^{5/2} \tan ^{-1}(c x)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","\frac{f^2 x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i f^2 (1-i c x) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b f^2 \left(c^2 x^2+1\right)^{5/2}}{3 c (-c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b f^2 \left(c^2 x^2+1\right)^{5/2} \log \left(c^2 x^2+1\right)}{6 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i b f^2 \left(c^2 x^2+1\right)^{5/2} \tan ^{-1}(c x)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"((I/3)*b*f^2*(1 + c^2*x^2)^(5/2))/(c*(I - c*x)*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((2*I)/3)*f^2*(1 - I*c*x)*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (f^2*x*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - ((I/3)*b*f^2*(1 + c^2*x^2)^(5/2)*ArcTan[c*x])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (b*f^2*(1 + c^2*x^2)^(5/2)*Log[1 + c^2*x^2])/(6*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",8,8,35,0.2286,1,"{5712, 653, 191, 5819, 627, 44, 203, 260}"
558,1,517,0,0.4220321,"\int \frac{(d+i c d x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{(f-i c f x)^{3/2}} \, dx","Int[((d + I*c*d*x)^(5/2)*(a + b*ArcSinh[c*x]))/(f - I*c*f*x)^(3/2),x]","-\frac{5 i d^4 (1+i c x) \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{15 i d^4 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 i d^4 (1+i c x)^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{15 d^4 \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x) \left(a+b \sinh ^{-1}(c x)\right)}{2 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{b c d^4 x^2 \left(c^2 x^2+1\right)^{3/2}}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{5 b d^4 (1+i c x)^2 \left(c^2 x^2+1\right)^{3/2}}{4 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{3 i b d^4 x \left(c^2 x^2+1\right)^{3/2}}{2 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{8 b d^4 \left(c^2 x^2+1\right)^{3/2} \log (c x+i)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{15 b d^4 \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x)^2}{4 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}","-\frac{5 i d^4 (1+i c x) \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{15 i d^4 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 i d^4 (1+i c x)^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{15 d^4 \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x) \left(a+b \sinh ^{-1}(c x)\right)}{2 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{b c d^4 x^2 \left(c^2 x^2+1\right)^{3/2}}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{5 b d^4 (1+i c x)^2 \left(c^2 x^2+1\right)^{3/2}}{4 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{3 i b d^4 x \left(c^2 x^2+1\right)^{3/2}}{2 (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{8 b d^4 \left(c^2 x^2+1\right)^{3/2} \log (c x+i)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{15 b d^4 \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x)^2}{4 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}",1,"(((3*I)/2)*b*d^4*x*(1 + c^2*x^2)^(3/2))/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (b*c*d^4*x^2*(1 + c^2*x^2)^(3/2))/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (5*b*d^4*(1 + I*c*x)^2*(1 + c^2*x^2)^(3/2))/(4*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (15*b*d^4*(1 + c^2*x^2)^(3/2)*ArcSinh[c*x]^2)/(4*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - ((2*I)*d^4*(1 + I*c*x)^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (((15*I)/2)*d^4*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (((5*I)/2)*d^4*(1 + I*c*x)*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (15*d^4*(1 + c^2*x^2)^(3/2)*ArcSinh[c*x]*(a + b*ArcSinh[c*x]))/(2*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (8*b*d^4*(1 + c^2*x^2)^(3/2)*Log[I + c*x])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",7,9,35,0.2571,1,"{5712, 669, 671, 641, 215, 5819, 627, 43, 5675}"
559,1,283,0,0.4778031,"\int \frac{(d+i c d x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{(f-i c f x)^{3/2}} \, dx","Int[((d + I*c*d*x)^(3/2)*(a + b*ArcSinh[c*x]))/(f - I*c*f*x)^(3/2),x]","-\frac{3 d^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{i d^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 i d^3 (1+i c x) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{i b d^3 x \left(c^2 x^2+1\right)^{3/2}}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 b d^3 \left(c^2 x^2+1\right)^{3/2} \log (c x+i)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}","-\frac{3 d^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{i d^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 i d^3 (1+i c x) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{i b d^3 x \left(c^2 x^2+1\right)^{3/2}}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 b d^3 \left(c^2 x^2+1\right)^{3/2} \log (c x+i)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}",1,"(I*b*d^3*x*(1 + c^2*x^2)^(3/2))/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - ((4*I)*d^3*(1 + I*c*x)*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (I*d^3*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (3*d^3*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(2*b*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (4*b*d^3*(1 + c^2*x^2)^(3/2)*Log[I + c*x])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",10,10,35,0.2857,1,"{5712, 5833, 637, 5819, 12, 627, 31, 5675, 5717, 8}"
560,1,180,0,0.3999472,"\int \frac{\sqrt{d+i c d x} \left(a+b \sinh ^{-1}(c x)\right)}{(f-i c f x)^{3/2}} \, dx","Int[(Sqrt[d + I*c*d*x]*(a + b*ArcSinh[c*x]))/(f - I*c*f*x)^(3/2),x]","-\frac{d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 i d^2 (1+i c x) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 b d^2 \left(c^2 x^2+1\right)^{3/2} \log (c x+i)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}","-\frac{d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 i d^2 (1+i c x) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 b d^2 \left(c^2 x^2+1\right)^{3/2} \log (c x+i)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}",1,"((-2*I)*d^2*(1 + I*c*x)*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (d^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(2*b*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (2*b*d^2*(1 + c^2*x^2)^(3/2)*Log[I + c*x])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",8,8,35,0.2286,1,"{5712, 5833, 637, 5819, 12, 627, 31, 5675}"
561,1,112,0,0.2488493,"\int \frac{a+b \sinh ^{-1}(c x)}{\sqrt{d+i c d x} (f-i c f x)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(Sqrt[d + I*c*d*x]*(f - I*c*f*x)^(3/2)),x]","-\frac{d (-c x+i) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{b d \left(c^2 x^2+1\right)^{3/2} \log (c x+i)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}","-\frac{d (-c x+i) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{b d \left(c^2 x^2+1\right)^{3/2} \log (c x+i)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}",1,"-((d*(I - c*x)*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))) - (b*d*(1 + c^2*x^2)^(3/2)*Log[I + c*x])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",5,6,35,0.1714,1,"{5712, 637, 5819, 12, 627, 31}"
562,1,103,0,0.2054751,"\int \frac{a+b \sinh ^{-1}(c x)}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)),x]","\frac{x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{b \left(c^2 x^2+1\right)^{3/2} \log \left(c^2 x^2+1\right)}{2 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}","\frac{x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{b \left(c^2 x^2+1\right)^{3/2} \log \left(c^2 x^2+1\right)}{2 c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}",1,"(x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (b*(1 + c^2*x^2)^(3/2)*Log[1 + c^2*x^2])/(2*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",3,3,35,0.08571,1,"{5712, 5687, 260}"
563,1,282,0,0.3064029,"\int \frac{a+b \sinh ^{-1}(c x)}{(d+i c d x)^{5/2} (f-i c f x)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])/((d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(3/2)),x]","\frac{2 f x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{f (c x+i) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b f \left(c^2 x^2+1\right)^{5/2}}{6 c (-c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b f \left(c^2 x^2+1\right)^{5/2} \log \left(c^2 x^2+1\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i b f \left(c^2 x^2+1\right)^{5/2} \tan ^{-1}(c x)}{6 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","\frac{2 f x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{f (c x+i) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b f \left(c^2 x^2+1\right)^{5/2}}{6 c (-c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b f \left(c^2 x^2+1\right)^{5/2} \log \left(c^2 x^2+1\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i b f \left(c^2 x^2+1\right)^{5/2} \tan ^{-1}(c x)}{6 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"((I/6)*b*f*(1 + c^2*x^2)^(5/2))/(c*(I - c*x)*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (f*(I + c*x)*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (2*f*x*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - ((I/6)*b*f*(1 + c^2*x^2)^(5/2)*ArcTan[c*x])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (b*f*(1 + c^2*x^2)^(5/2)*Log[1 + c^2*x^2])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",8,8,35,0.2286,1,"{5712, 639, 191, 5819, 627, 44, 203, 260}"
564,1,470,0,0.4388584,"\int \frac{(d+i c d x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{(f-i c f x)^{5/2}} \, dx","Int[((d + I*c*d*x)^(5/2)*(a + b*ArcSinh[c*x]))/(f - I*c*f*x)^(5/2),x]","\frac{5 i d^5 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{10 i d^5 (1+i c x)^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i d^5 (1+i c x)^4 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{5 d^5 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i b d^5 x \left(c^2 x^2+1\right)^{5/2}}{(d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 i b d^5 \left(c^2 x^2+1\right)^{5/2}}{3 c (c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{28 b d^5 \left(c^2 x^2+1\right)^{5/2} \log (c x+i)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{5 b d^5 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x)^2}{2 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","\frac{5 i d^5 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{10 i d^5 (1+i c x)^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i d^5 (1+i c x)^4 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{5 d^5 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i b d^5 x \left(c^2 x^2+1\right)^{5/2}}{(d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 i b d^5 \left(c^2 x^2+1\right)^{5/2}}{3 c (c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{28 b d^5 \left(c^2 x^2+1\right)^{5/2} \log (c x+i)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{5 b d^5 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x)^2}{2 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"((-I)*b*d^5*x*(1 + c^2*x^2)^(5/2))/((d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((8*I)/3)*b*d^5*(1 + c^2*x^2)^(5/2))/(c*(I + c*x)*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (5*b*d^5*(1 + c^2*x^2)^(5/2)*ArcSinh[c*x]^2)/(2*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (((2*I)/3)*d^5*(1 + I*c*x)^4*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((10*I)/3)*d^5*(1 + I*c*x)^2*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + ((5*I)*d^5*(1 + c^2*x^2)^3*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (5*d^5*(1 + c^2*x^2)^(5/2)*ArcSinh[c*x]*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (28*b*d^5*(1 + c^2*x^2)^(5/2)*Log[I + c*x])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",10,8,35,0.2286,1,"{5712, 669, 641, 215, 5819, 627, 43, 5675}"
565,1,362,0,0.3922101,"\int \frac{(d+i c d x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{(f-i c f x)^{5/2}} \, dx","Int[((d + I*c*d*x)^(3/2)*(a + b*ArcSinh[c*x]))/(f - I*c*f*x)^(5/2),x]","\frac{2 i d^4 (1+i c x) \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i d^4 (1+i c x)^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{d^4 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{4 i b d^4 \left(c^2 x^2+1\right)^{5/2}}{3 c (c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 b d^4 \left(c^2 x^2+1\right)^{5/2} \log (c x+i)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b d^4 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x)^2}{2 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","\frac{2 i d^4 (1+i c x) \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i d^4 (1+i c x)^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{d^4 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{4 i b d^4 \left(c^2 x^2+1\right)^{5/2}}{3 c (c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 b d^4 \left(c^2 x^2+1\right)^{5/2} \log (c x+i)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b d^4 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x)^2}{2 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"(((4*I)/3)*b*d^4*(1 + c^2*x^2)^(5/2))/(c*(I + c*x)*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (b*d^4*(1 + c^2*x^2)^(5/2)*ArcSinh[c*x]^2)/(2*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (((2*I)/3)*d^4*(1 + I*c*x)^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + ((2*I)*d^4*(1 + I*c*x)*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (d^4*(1 + c^2*x^2)^(5/2)*ArcSinh[c*x]*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (8*b*d^4*(1 + c^2*x^2)^(5/2)*Log[I + c*x])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",9,9,35,0.2571,1,"{5712, 669, 653, 215, 5819, 627, 43, 31, 5675}"
566,1,185,0,0.3064741,"\int \frac{\sqrt{d+i c d x} \left(a+b \sinh ^{-1}(c x)\right)}{(f-i c f x)^{5/2}} \, dx","Int[(Sqrt[d + I*c*d*x]*(a + b*ArcSinh[c*x]))/(f - I*c*f*x)^(5/2),x]","-\frac{i d^3 (1+i c x)^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i b d^3 \left(c^2 x^2+1\right)^{5/2}}{3 c (c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{b d^3 \left(c^2 x^2+1\right)^{5/2} \log (c x+i)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","-\frac{i d^3 (1+i c x)^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i b d^3 \left(c^2 x^2+1\right)^{5/2}}{3 c (c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{b d^3 \left(c^2 x^2+1\right)^{5/2} \log (c x+i)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"(((2*I)/3)*b*d^3*(1 + c^2*x^2)^(5/2))/(c*(I + c*x)*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - ((I/3)*d^3*(1 + I*c*x)^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (b*d^3*(1 + c^2*x^2)^(5/2)*Log[I + c*x])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",6,6,35,0.1714,1,"{5712, 651, 5819, 12, 627, 43}"
567,1,294,0,0.3329122,"\int \frac{a+b \sinh ^{-1}(c x)}{\sqrt{d+i c d x} (f-i c f x)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(Sqrt[d + I*c*d*x]*(f - I*c*f*x)^(5/2)),x]","\frac{d^2 x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i d^2 (1+i c x) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b d^2 \left(c^2 x^2+1\right)^{5/2}}{3 c (c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b d^2 \left(c^2 x^2+1\right)^{5/2} \log \left(c^2 x^2+1\right)}{6 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b d^2 \left(c^2 x^2+1\right)^{5/2} \tan ^{-1}(c x)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","\frac{d^2 x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i d^2 (1+i c x) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b d^2 \left(c^2 x^2+1\right)^{5/2}}{3 c (c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b d^2 \left(c^2 x^2+1\right)^{5/2} \log \left(c^2 x^2+1\right)}{6 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b d^2 \left(c^2 x^2+1\right)^{5/2} \tan ^{-1}(c x)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"((I/3)*b*d^2*(1 + c^2*x^2)^(5/2))/(c*(I + c*x)*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (((2*I)/3)*d^2*(1 + I*c*x)*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (d^2*x*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + ((I/3)*b*d^2*(1 + c^2*x^2)^(5/2)*ArcTan[c*x])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (b*d^2*(1 + c^2*x^2)^(5/2)*Log[1 + c^2*x^2])/(6*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",8,8,35,0.2286,1,"{5712, 653, 191, 5819, 627, 44, 203, 260}"
568,1,282,0,0.2988187,"\int \frac{a+b \sinh ^{-1}(c x)}{(d+i c d x)^{3/2} (f-i c f x)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(5/2)),x]","\frac{2 d x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{d (-c x+i) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b d \left(c^2 x^2+1\right)^{5/2}}{6 c (c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b d \left(c^2 x^2+1\right)^{5/2} \log \left(c^2 x^2+1\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b d \left(c^2 x^2+1\right)^{5/2} \tan ^{-1}(c x)}{6 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","\frac{2 d x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{d (-c x+i) \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b d \left(c^2 x^2+1\right)^{5/2}}{6 c (c x+i) (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b d \left(c^2 x^2+1\right)^{5/2} \log \left(c^2 x^2+1\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b d \left(c^2 x^2+1\right)^{5/2} \tan ^{-1}(c x)}{6 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"((I/6)*b*d*(1 + c^2*x^2)^(5/2))/(c*(I + c*x)*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (d*(I - c*x)*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (2*d*x*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + ((I/6)*b*d*(1 + c^2*x^2)^(5/2)*ArcTan[c*x])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (b*d*(1 + c^2*x^2)^(5/2)*Log[1 + c^2*x^2])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",8,8,35,0.2286,1,"{5712, 639, 191, 5819, 627, 44, 203, 260}"
569,1,203,0,0.2445134,"\int \frac{a+b \sinh ^{-1}(c x)}{(d+i c d x)^{5/2} (f-i c f x)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])/((d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)),x]","\frac{2 x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{b \left(c^2 x^2+1\right)^{3/2}}{6 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b \left(c^2 x^2+1\right)^{5/2} \log \left(c^2 x^2+1\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","\frac{2 x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{b \left(c^2 x^2+1\right)^{3/2}}{6 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b \left(c^2 x^2+1\right)^{5/2} \log \left(c^2 x^2+1\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"(b*(1 + c^2*x^2)^(3/2))/(6*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (2*x*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x]))/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (b*(1 + c^2*x^2)^(5/2)*Log[1 + c^2*x^2])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",5,5,35,0.1429,1,"{5712, 5690, 5687, 260, 261}"
570,1,680,0,1.1076308,"\int (d+i c d x)^{5/2} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + I*c*d*x)^(5/2)*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2,x]","\frac{b c^3 d^2 x^4 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{8 \sqrt{c^2 x^2+1}}-\frac{1}{4} c^2 d^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{4 i b c^2 d^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{c^2 x^2+1}}-\frac{3 b c d^2 x^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{8 \sqrt{c^2 x^2+1}}-\frac{4 i b d^2 x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}+\frac{5 d^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^3}{24 b c \sqrt{c^2 x^2+1}}+\frac{2 i d^2 \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c}+\frac{3}{8} d^2 x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{1}{32} b^2 c^2 d^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x}+\frac{4 i b^2 d^2 \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x}}{27 c}-\frac{15 b^2 d^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \sinh ^{-1}(c x)}{64 c \sqrt{c^2 x^2+1}}+\frac{15}{64} b^2 d^2 x \sqrt{d+i c d x} \sqrt{f-i c f x}+\frac{8 i b^2 d^2 \sqrt{d+i c d x} \sqrt{f-i c f x}}{9 c}","\frac{b c^3 d^2 x^4 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{8 \sqrt{c^2 x^2+1}}-\frac{1}{4} c^2 d^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{4 i b c^2 d^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{c^2 x^2+1}}-\frac{3 b c d^2 x^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{8 \sqrt{c^2 x^2+1}}-\frac{4 i b d^2 x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}+\frac{5 d^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^3}{24 b c \sqrt{c^2 x^2+1}}+\frac{2 i d^2 \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c}+\frac{3}{8} d^2 x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{1}{32} b^2 c^2 d^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x}+\frac{4 i b^2 d^2 \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x}}{27 c}-\frac{15 b^2 d^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \sinh ^{-1}(c x)}{64 c \sqrt{c^2 x^2+1}}+\frac{15}{64} b^2 d^2 x \sqrt{d+i c d x} \sqrt{f-i c f x}+\frac{8 i b^2 d^2 \sqrt{d+i c d x} \sqrt{f-i c f x}}{9 c}",1,"(((8*I)/9)*b^2*d^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/c + (15*b^2*d^2*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/64 - (b^2*c^2*d^2*x^3*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/32 + (((4*I)/27)*b^2*d^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(1 + c^2*x^2))/c - (15*b^2*d^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*ArcSinh[c*x])/(64*c*Sqrt[1 + c^2*x^2]) - (((4*I)/3)*b*d^2*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/Sqrt[1 + c^2*x^2] - (3*b*c*d^2*x^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/(8*Sqrt[1 + c^2*x^2]) - (((4*I)/9)*b*c^2*d^2*x^3*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/Sqrt[1 + c^2*x^2] + (b*c^3*d^2*x^4*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/(8*Sqrt[1 + c^2*x^2]) + (3*d^2*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2)/8 - (c^2*d^2*x^3*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2)/4 + (((2*I)/3)*d^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/c + (5*d^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^3)/(24*b*c*Sqrt[1 + c^2*x^2])","A",23,13,37,0.3514,1,"{5712, 5821, 5682, 5675, 5661, 321, 215, 5717, 5679, 444, 43, 5742, 5758}"
571,1,508,0,0.6340309,"\int (d+i c d x)^{3/2} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + I*c*d*x)^(3/2)*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2,x]","-\frac{2 i b c^2 d x^3 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{c^2 x^2+1}}-\frac{b c d x^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{c^2 x^2+1}}-\frac{2 i b d x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}+\frac{d \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b c \sqrt{c^2 x^2+1}}+\frac{i d \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c}+\frac{1}{2} d x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2 i b^2 d \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x}}{27 c}-\frac{b^2 d \sqrt{d+i c d x} \sqrt{f-i c f x} \sinh ^{-1}(c x)}{4 c \sqrt{c^2 x^2+1}}+\frac{1}{4} b^2 d x \sqrt{d+i c d x} \sqrt{f-i c f x}+\frac{4 i b^2 d \sqrt{d+i c d x} \sqrt{f-i c f x}}{9 c}","-\frac{2 i b c^2 d x^3 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{c^2 x^2+1}}-\frac{b c d x^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{c^2 x^2+1}}-\frac{2 i b d x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}+\frac{d \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b c \sqrt{c^2 x^2+1}}+\frac{i d \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c}+\frac{1}{2} d x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2 i b^2 d \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x}}{27 c}-\frac{b^2 d \sqrt{d+i c d x} \sqrt{f-i c f x} \sinh ^{-1}(c x)}{4 c \sqrt{c^2 x^2+1}}+\frac{1}{4} b^2 d x \sqrt{d+i c d x} \sqrt{f-i c f x}+\frac{4 i b^2 d \sqrt{d+i c d x} \sqrt{f-i c f x}}{9 c}",1,"(((4*I)/9)*b^2*d*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/c + (b^2*d*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/4 + (((2*I)/27)*b^2*d*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(1 + c^2*x^2))/c - (b^2*d*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*ArcSinh[c*x])/(4*c*Sqrt[1 + c^2*x^2]) - (((2*I)/3)*b*d*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/Sqrt[1 + c^2*x^2] - (b*c*d*x^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/(2*Sqrt[1 + c^2*x^2]) - (((2*I)/9)*b*c^2*d*x^3*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/Sqrt[1 + c^2*x^2] + (d*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2)/2 + ((I/3)*d*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/c + (d*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^3)/(6*b*c*Sqrt[1 + c^2*x^2])","A",13,11,37,0.2973,1,"{5712, 5821, 5682, 5675, 5661, 321, 215, 5717, 5679, 444, 43}"
572,1,244,0,0.352603,"\int \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2,x]","\frac{\sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b c \sqrt{c^2 x^2+1}}-\frac{b c x^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{c^2 x^2+1}}+\frac{1}{2} x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \sinh ^{-1}(c x)}{4 c \sqrt{c^2 x^2+1}}+\frac{1}{4} b^2 x \sqrt{d+i c d x} \sqrt{f-i c f x}","\frac{\sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b c \sqrt{c^2 x^2+1}}-\frac{b c x^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{c^2 x^2+1}}+\frac{1}{2} x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{b^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \sinh ^{-1}(c x)}{4 c \sqrt{c^2 x^2+1}}+\frac{1}{4} b^2 x \sqrt{d+i c d x} \sqrt{f-i c f x}",1,"(b^2*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/4 - (b^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*ArcSinh[c*x])/(4*c*Sqrt[1 + c^2*x^2]) - (b*c*x^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/(2*Sqrt[1 + c^2*x^2]) + (x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2)/2 + (Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^3)/(6*b*c*Sqrt[1 + c^2*x^2])","A",6,6,37,0.1622,1,"{5712, 5682, 5675, 5661, 321, 215}"
573,1,259,0,0.5079026,"\int \frac{\sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+i c d x}} \, dx","Int[(Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2)/Sqrt[d + I*c*d*x],x]","\frac{2 i a b f x \sqrt{c^2 x^2+1}}{\sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{f \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{i f \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{2 i b^2 f \left(c^2 x^2+1\right)}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{2 i b^2 f x \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{\sqrt{d+i c d x} \sqrt{f-i c f x}}","\frac{2 i a b f x \sqrt{c^2 x^2+1}}{\sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{f \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{i f \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{2 i b^2 f \left(c^2 x^2+1\right)}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{2 i b^2 f x \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{\sqrt{d+i c d x} \sqrt{f-i c f x}}",1,"((2*I)*a*b*f*x*Sqrt[1 + c^2*x^2])/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - ((2*I)*b^2*f*(1 + c^2*x^2))/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + ((2*I)*b^2*f*x*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (I*f*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (f*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^3)/(3*b*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])","A",8,6,37,0.1622,1,"{5712, 5821, 5675, 5717, 5653, 261}"
574,1,544,0,1.0053757,"\int \frac{\sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2}} \, dx","Int[(Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2)/(d + I*c*d*x)^(3/2),x]","-\frac{4 b^2 f^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{4 b^2 f^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 b^2 f^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{f^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 f^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 i f^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 f^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 b f^2 \left(c^2 x^2+1\right)^{3/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{8 i b f^2 \left(c^2 x^2+1\right)^{3/2} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}","-\frac{4 b^2 f^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{4 b^2 f^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 b^2 f^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{f^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 f^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 i f^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 f^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 b f^2 \left(c^2 x^2+1\right)^{3/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{8 i b f^2 \left(c^2 x^2+1\right)^{3/2} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}",1,"((2*I)*f^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (2*f^2*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (2*f^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (f^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^3)/(3*b*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - ((8*I)*b*f^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (4*b*f^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (4*b^2*f^2*(1 + c^2*x^2)^(3/2)*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (4*b^2*f^2*(1 + c^2*x^2)^(3/2)*PolyLog[2, I*E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (2*b^2*f^2*(1 + c^2*x^2)^(3/2)*PolyLog[2, -E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",19,13,37,0.3514,1,"{5712, 5833, 5821, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 5693, 4180, 5675}"
575,1,518,0,1.1485595,"\int \frac{\sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{5/2}} \, dx","Int[(Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2)/(d + I*c*d*x)^(5/2),x]","\frac{4 b^2 f^3 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{f^3 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{4 b f^3 \left(c^2 x^2+1\right)^{5/2} \log \left(1+i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i f^3 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 b f^3 \left(c^2 x^2+1\right)^{5/2} \csc ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i f^3 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \csc ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{4 i b^2 f^3 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","\frac{4 b^2 f^3 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{f^3 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{4 b f^3 \left(c^2 x^2+1\right)^{5/2} \log \left(1+i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i f^3 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 b f^3 \left(c^2 x^2+1\right)^{5/2} \csc ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i f^3 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \csc ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{4 i b^2 f^3 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"-(f^3*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (((4*I)/3)*b^2*f^3*(1 + c^2*x^2)^(5/2)*Cot[Pi/4 + (I/2)*ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - ((I/3)*f^3*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2*Cot[Pi/4 + (I/2)*ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (2*b*f^3*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Csc[Pi/4 + (I/2)*ArcSinh[c*x]]^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + ((I/3)*f^3*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2*Cot[Pi/4 + (I/2)*ArcSinh[c*x]]*Csc[Pi/4 + (I/2)*ArcSinh[c*x]]^2)/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (4*b*f^3*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Log[1 + I*E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (4*b^2*f^3*(1 + c^2*x^2)^(5/2)*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",20,12,37,0.3243,1,"{5712, 5833, 5831, 3318, 4186, 3767, 8, 4184, 3716, 2190, 2279, 2391}"
576,1,774,0,0.857992,"\int (d+i c d x)^{5/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^2,x]","-\frac{2 i b c^4 d x^5 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{25 \left(c^2 x^2+1\right)^{3/2}}-\frac{4 i b c^2 d x^3 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{15 \left(c^2 x^2+1\right)^{3/2}}-\frac{3 b c d x^2 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 \left(c^2 x^2+1\right)^{3/2}}+\frac{3 d x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{8 \left(c^2 x^2+1\right)}-\frac{2 i b d x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 \left(c^2 x^2+1\right)^{3/2}}+\frac{d (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{8 b c \left(c^2 x^2+1\right)^{3/2}}+\frac{i d \left(c^2 x^2+1\right) (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{5 c}-\frac{b d \sqrt{c^2 x^2+1} (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 c}+\frac{1}{4} d x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{15 b^2 d x (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{64 \left(c^2 x^2+1\right)}+\frac{2 i b^2 d \left(c^2 x^2+1\right) (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{125 c}+\frac{16 i b^2 d (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{75 c \left(c^2 x^2+1\right)}-\frac{9 b^2 d (d+i c d x)^{3/2} (f-i c f x)^{3/2} \sinh ^{-1}(c x)}{64 c \left(c^2 x^2+1\right)^{3/2}}+\frac{1}{32} b^2 d x (d+i c d x)^{3/2} (f-i c f x)^{3/2}+\frac{8 i b^2 d (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{225 c}","-\frac{2 i b c^4 d x^5 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{25 \left(c^2 x^2+1\right)^{3/2}}-\frac{4 i b c^2 d x^3 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{15 \left(c^2 x^2+1\right)^{3/2}}-\frac{3 b c d x^2 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 \left(c^2 x^2+1\right)^{3/2}}+\frac{3 d x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{8 \left(c^2 x^2+1\right)}-\frac{2 i b d x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 \left(c^2 x^2+1\right)^{3/2}}+\frac{d (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{8 b c \left(c^2 x^2+1\right)^{3/2}}+\frac{i d \left(c^2 x^2+1\right) (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{5 c}-\frac{b d \sqrt{c^2 x^2+1} (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 c}+\frac{1}{4} d x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{15 b^2 d x (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{64 \left(c^2 x^2+1\right)}+\frac{2 i b^2 d \left(c^2 x^2+1\right) (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{125 c}+\frac{16 i b^2 d (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{75 c \left(c^2 x^2+1\right)}-\frac{9 b^2 d (d+i c d x)^{3/2} (f-i c f x)^{3/2} \sinh ^{-1}(c x)}{64 c \left(c^2 x^2+1\right)^{3/2}}+\frac{1}{32} b^2 d x (d+i c d x)^{3/2} (f-i c f x)^{3/2}+\frac{8 i b^2 d (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{225 c}",1,"(((8*I)/225)*b^2*d*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/c + (b^2*d*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/32 + (((16*I)/75)*b^2*d*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(c*(1 + c^2*x^2)) + (15*b^2*d*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(64*(1 + c^2*x^2)) + (((2*I)/125)*b^2*d*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(1 + c^2*x^2))/c - (9*b^2*d*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*ArcSinh[c*x])/(64*c*(1 + c^2*x^2)^(3/2)) - (((2*I)/5)*b*d*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/(1 + c^2*x^2)^(3/2) - (3*b*c*d*x^2*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/(8*(1 + c^2*x^2)^(3/2)) - (((4*I)/15)*b*c^2*d*x^3*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/(1 + c^2*x^2)^(3/2) - (((2*I)/25)*b*c^4*d*x^5*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/(1 + c^2*x^2)^(3/2) - (b*d*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(8*c) + (d*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^2)/4 + (3*d*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^2)/(8*(1 + c^2*x^2)) + ((I/5)*d*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/c + (d*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^3)/(8*b*c*(1 + c^2*x^2)^(3/2))","A",19,15,37,0.4054,1,"{5712, 5821, 5684, 5682, 5675, 5661, 321, 215, 5717, 195, 194, 5679, 12, 1247, 698}"
577,1,396,0,0.4819284,"\int (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^2,x]","\frac{(d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{8 b c \left(c^2 x^2+1\right)^{3/2}}+\frac{3 x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{8 \left(c^2 x^2+1\right)}-\frac{b \sqrt{c^2 x^2+1} (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 c}-\frac{3 b c x^2 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 \left(c^2 x^2+1\right)^{3/2}}+\frac{1}{4} x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{15 b^2 x (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{64 \left(c^2 x^2+1\right)}-\frac{9 b^2 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \sinh ^{-1}(c x)}{64 c \left(c^2 x^2+1\right)^{3/2}}+\frac{1}{32} b^2 x (d+i c d x)^{3/2} (f-i c f x)^{3/2}","\frac{(d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{8 b c \left(c^2 x^2+1\right)^{3/2}}+\frac{3 x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{8 \left(c^2 x^2+1\right)}-\frac{b \sqrt{c^2 x^2+1} (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 c}-\frac{3 b c x^2 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 \left(c^2 x^2+1\right)^{3/2}}+\frac{1}{4} x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{15 b^2 x (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{64 \left(c^2 x^2+1\right)}-\frac{9 b^2 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \sinh ^{-1}(c x)}{64 c \left(c^2 x^2+1\right)^{3/2}}+\frac{1}{32} b^2 x (d+i c d x)^{3/2} (f-i c f x)^{3/2}",1,"(b^2*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/32 + (15*b^2*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(64*(1 + c^2*x^2)) - (9*b^2*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*ArcSinh[c*x])/(64*c*(1 + c^2*x^2)^(3/2)) - (3*b*c*x^2*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/(8*(1 + c^2*x^2)^(3/2)) - (b*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(8*c) + (x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^2)/4 + (3*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^2)/(8*(1 + c^2*x^2)) + ((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^3)/(8*b*c*(1 + c^2*x^2)^(3/2))","A",11,9,37,0.2432,1,"{5712, 5684, 5682, 5675, 5661, 321, 215, 5717, 195}"
578,1,508,0,0.6490089,"\int \sqrt{d+i c d x} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[d + I*c*d*x]*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^2,x]","\frac{2 i b c^2 f x^3 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{c^2 x^2+1}}-\frac{b c f x^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{c^2 x^2+1}}+\frac{2 i b f x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}+\frac{f \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b c \sqrt{c^2 x^2+1}}-\frac{i f \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c}+\frac{1}{2} f x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 i b^2 f \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x}}{27 c}-\frac{b^2 f \sqrt{d+i c d x} \sqrt{f-i c f x} \sinh ^{-1}(c x)}{4 c \sqrt{c^2 x^2+1}}+\frac{1}{4} b^2 f x \sqrt{d+i c d x} \sqrt{f-i c f x}-\frac{4 i b^2 f \sqrt{d+i c d x} \sqrt{f-i c f x}}{9 c}","\frac{2 i b c^2 f x^3 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{c^2 x^2+1}}-\frac{b c f x^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{c^2 x^2+1}}+\frac{2 i b f x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}+\frac{f \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b c \sqrt{c^2 x^2+1}}-\frac{i f \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c}+\frac{1}{2} f x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{2 i b^2 f \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x}}{27 c}-\frac{b^2 f \sqrt{d+i c d x} \sqrt{f-i c f x} \sinh ^{-1}(c x)}{4 c \sqrt{c^2 x^2+1}}+\frac{1}{4} b^2 f x \sqrt{d+i c d x} \sqrt{f-i c f x}-\frac{4 i b^2 f \sqrt{d+i c d x} \sqrt{f-i c f x}}{9 c}",1,"(((-4*I)/9)*b^2*f*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/c + (b^2*f*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/4 - (((2*I)/27)*b^2*f*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(1 + c^2*x^2))/c - (b^2*f*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*ArcSinh[c*x])/(4*c*Sqrt[1 + c^2*x^2]) + (((2*I)/3)*b*f*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/Sqrt[1 + c^2*x^2] - (b*c*f*x^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/(2*Sqrt[1 + c^2*x^2]) + (((2*I)/9)*b*c^2*f*x^3*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/Sqrt[1 + c^2*x^2] + (f*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2)/2 - ((I/3)*f*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/c + (f*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^3)/(6*b*c*Sqrt[1 + c^2*x^2])","A",13,11,37,0.2973,1,"{5712, 5821, 5682, 5675, 5661, 321, 215, 5717, 5679, 444, 43}"
579,1,436,0,0.632811,"\int \frac{(f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+i c d x}} \, dx","Int[((f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^2)/Sqrt[d + I*c*d*x],x]","\frac{f^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{2 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{2 i f^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{f^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{b c f^2 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{4 i b f^2 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{4 i b^2 f^2 \left(c^2 x^2+1\right)}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{b^2 f^2 x \left(c^2 x^2+1\right)}{4 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{b^2 f^2 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{4 c \sqrt{d+i c d x} \sqrt{f-i c f x}}","\frac{f^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{2 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{2 i f^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{f^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{b c f^2 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{4 i b f^2 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{4 i b^2 f^2 \left(c^2 x^2+1\right)}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{b^2 f^2 x \left(c^2 x^2+1\right)}{4 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{b^2 f^2 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{4 c \sqrt{d+i c d x} \sqrt{f-i c f x}}",1,"((-4*I)*b^2*f^2*(1 + c^2*x^2))/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (b^2*f^2*x*(1 + c^2*x^2))/(4*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (b^2*f^2*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(4*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + ((4*I)*b*f^2*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (b*c*f^2*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - ((2*I)*f^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (f^2*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (f^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^3)/(2*b*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])","A",11,9,37,0.2432,1,"{5712, 5831, 3317, 3296, 2638, 3311, 32, 2635, 8}"
580,1,752,0,1.1280445,"\int \frac{(f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2}} \, dx","Int[((f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^2)/(d + I*c*d*x)^(3/2),x]","-\frac{8 b^2 f^3 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{8 b^2 f^3 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 b^2 f^3 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 i a b f^3 x \left(c^2 x^2+1\right)^{3/2}}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{f^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{b c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{i f^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{4 f^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{4 f^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{4 i f^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{8 b f^3 \left(c^2 x^2+1\right)^{3/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{16 i b f^3 \left(c^2 x^2+1\right)^{3/2} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 i b^2 f^3 \left(c^2 x^2+1\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 i b^2 f^3 x \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x)}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}","-\frac{8 b^2 f^3 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{8 b^2 f^3 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 b^2 f^3 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 i a b f^3 x \left(c^2 x^2+1\right)^{3/2}}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{f^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{b c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{i f^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{4 f^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{4 f^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{4 i f^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{8 b f^3 \left(c^2 x^2+1\right)^{3/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{16 i b f^3 \left(c^2 x^2+1\right)^{3/2} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 i b^2 f^3 \left(c^2 x^2+1\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 i b^2 f^3 x \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x)}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}",1,"((-2*I)*a*b*f^3*x*(1 + c^2*x^2)^(3/2))/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + ((2*I)*b^2*f^3*(1 + c^2*x^2)^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - ((2*I)*b^2*f^3*x*(1 + c^2*x^2)^(3/2)*ArcSinh[c*x])/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + ((4*I)*f^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (4*f^3*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (4*f^3*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (I*f^3*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (f^3*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^3)/(b*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - ((16*I)*b*f^3*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (8*b*f^3*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (8*b^2*f^3*(1 + c^2*x^2)^(3/2)*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (8*b^2*f^3*(1 + c^2*x^2)^(3/2)*PolyLog[2, I*E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (4*b^2*f^3*(1 + c^2*x^2)^(3/2)*PolyLog[2, -E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",23,15,37,0.4054,1,"{5712, 5833, 5821, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 5693, 4180, 5675, 5653, 261}"
581,1,580,0,1.2043399,"\int \frac{(f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{5/2}} \, dx","Int[((f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^2)/(d + I*c*d*x)^(5/2),x]","\frac{32 b^2 f^4 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{f^4 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{8 f^4 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{32 b f^4 \left(c^2 x^2+1\right)^{5/2} \log \left(1+i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{8 i f^4 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{4 b f^4 \left(c^2 x^2+1\right)^{5/2} \csc ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i f^4 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \csc ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{8 i b^2 f^4 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","\frac{32 b^2 f^4 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{f^4 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{8 f^4 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{32 b f^4 \left(c^2 x^2+1\right)^{5/2} \log \left(1+i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{8 i f^4 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{4 b f^4 \left(c^2 x^2+1\right)^{5/2} \csc ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i f^4 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \csc ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{8 i b^2 f^4 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"(-8*f^4*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (f^4*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^3)/(3*b*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (((8*I)/3)*b^2*f^4*(1 + c^2*x^2)^(5/2)*Cot[Pi/4 + (I/2)*ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (((8*I)/3)*f^4*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2*Cot[Pi/4 + (I/2)*ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (4*b*f^4*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Csc[Pi/4 + (I/2)*ArcSinh[c*x]]^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((2*I)/3)*f^4*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2*Cot[Pi/4 + (I/2)*ArcSinh[c*x]]*Csc[Pi/4 + (I/2)*ArcSinh[c*x]]^2)/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (32*b*f^4*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Log[1 + I*E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (32*b^2*f^4*(1 + c^2*x^2)^(5/2)*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",21,13,37,0.3514,1,"{5712, 5833, 5675, 5831, 3318, 4186, 3767, 8, 4184, 3716, 2190, 2279, 2391}"
582,1,548,0,0.6117434,"\int (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x])^2,x]","\frac{5 (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{48 b c \left(c^2 x^2+1\right)^{5/2}}+\frac{5 x (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{24 \left(c^2 x^2+1\right)}+\frac{5 x (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 \left(c^2 x^2+1\right)^2}-\frac{b \sqrt{c^2 x^2+1} (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{18 c}-\frac{5 b (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{48 c \sqrt{c^2 x^2+1}}-\frac{5 b c x^2 (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{16 \left(c^2 x^2+1\right)^{5/2}}+\frac{1}{6} x (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{65 b^2 x (d+i c d x)^{5/2} (f-i c f x)^{5/2}}{1728 \left(c^2 x^2+1\right)}+\frac{245 b^2 x (d+i c d x)^{5/2} (f-i c f x)^{5/2}}{1152 \left(c^2 x^2+1\right)^2}-\frac{115 b^2 (d+i c d x)^{5/2} (f-i c f x)^{5/2} \sinh ^{-1}(c x)}{1152 c \left(c^2 x^2+1\right)^{5/2}}+\frac{1}{108} b^2 x (d+i c d x)^{5/2} (f-i c f x)^{5/2}","\frac{5 (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{48 b c \left(c^2 x^2+1\right)^{5/2}}+\frac{5 x (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{24 \left(c^2 x^2+1\right)}+\frac{5 x (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{16 \left(c^2 x^2+1\right)^2}-\frac{b \sqrt{c^2 x^2+1} (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{18 c}-\frac{5 b (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{48 c \sqrt{c^2 x^2+1}}-\frac{5 b c x^2 (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{16 \left(c^2 x^2+1\right)^{5/2}}+\frac{1}{6} x (d+i c d x)^{5/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{65 b^2 x (d+i c d x)^{5/2} (f-i c f x)^{5/2}}{1728 \left(c^2 x^2+1\right)}+\frac{245 b^2 x (d+i c d x)^{5/2} (f-i c f x)^{5/2}}{1152 \left(c^2 x^2+1\right)^2}-\frac{115 b^2 (d+i c d x)^{5/2} (f-i c f x)^{5/2} \sinh ^{-1}(c x)}{1152 c \left(c^2 x^2+1\right)^{5/2}}+\frac{1}{108} b^2 x (d+i c d x)^{5/2} (f-i c f x)^{5/2}",1,"(b^2*x*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))/108 + (245*b^2*x*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))/(1152*(1 + c^2*x^2)^2) + (65*b^2*x*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))/(1728*(1 + c^2*x^2)) - (115*b^2*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)*ArcSinh[c*x])/(1152*c*(1 + c^2*x^2)^(5/2)) - (5*b*c*x^2*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x]))/(16*(1 + c^2*x^2)^(5/2)) - (5*b*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x]))/(48*c*Sqrt[1 + c^2*x^2]) - (b*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(18*c) + (x*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x])^2)/6 + (5*x*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x])^2)/(16*(1 + c^2*x^2)^2) + (5*x*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x])^2)/(24*(1 + c^2*x^2)) + (5*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x])^3)/(48*b*c*(1 + c^2*x^2)^(5/2))","A",17,9,37,0.2432,1,"{5712, 5684, 5682, 5675, 5661, 321, 215, 5717, 195}"
583,1,774,0,0.8334048,"\int (d+i c d x)^{3/2} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x])^2,x]","\frac{2 i b c^4 f x^5 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{25 \left(c^2 x^2+1\right)^{3/2}}+\frac{4 i b c^2 f x^3 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{15 \left(c^2 x^2+1\right)^{3/2}}-\frac{3 b c f x^2 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 \left(c^2 x^2+1\right)^{3/2}}+\frac{3 f x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{8 \left(c^2 x^2+1\right)}+\frac{2 i b f x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 \left(c^2 x^2+1\right)^{3/2}}+\frac{f (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{8 b c \left(c^2 x^2+1\right)^{3/2}}-\frac{i f \left(c^2 x^2+1\right) (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{5 c}-\frac{b f \sqrt{c^2 x^2+1} (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 c}+\frac{1}{4} f x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{15 b^2 f x (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{64 \left(c^2 x^2+1\right)}-\frac{2 i b^2 f \left(c^2 x^2+1\right) (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{125 c}-\frac{16 i b^2 f (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{75 c \left(c^2 x^2+1\right)}-\frac{9 b^2 f (d+i c d x)^{3/2} (f-i c f x)^{3/2} \sinh ^{-1}(c x)}{64 c \left(c^2 x^2+1\right)^{3/2}}+\frac{1}{32} b^2 f x (d+i c d x)^{3/2} (f-i c f x)^{3/2}-\frac{8 i b^2 f (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{225 c}","\frac{2 i b c^4 f x^5 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{25 \left(c^2 x^2+1\right)^{3/2}}+\frac{4 i b c^2 f x^3 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{15 \left(c^2 x^2+1\right)^{3/2}}-\frac{3 b c f x^2 (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 \left(c^2 x^2+1\right)^{3/2}}+\frac{3 f x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{8 \left(c^2 x^2+1\right)}+\frac{2 i b f x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{5 \left(c^2 x^2+1\right)^{3/2}}+\frac{f (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{8 b c \left(c^2 x^2+1\right)^{3/2}}-\frac{i f \left(c^2 x^2+1\right) (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{5 c}-\frac{b f \sqrt{c^2 x^2+1} (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{8 c}+\frac{1}{4} f x (d+i c d x)^{3/2} (f-i c f x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{15 b^2 f x (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{64 \left(c^2 x^2+1\right)}-\frac{2 i b^2 f \left(c^2 x^2+1\right) (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{125 c}-\frac{16 i b^2 f (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{75 c \left(c^2 x^2+1\right)}-\frac{9 b^2 f (d+i c d x)^{3/2} (f-i c f x)^{3/2} \sinh ^{-1}(c x)}{64 c \left(c^2 x^2+1\right)^{3/2}}+\frac{1}{32} b^2 f x (d+i c d x)^{3/2} (f-i c f x)^{3/2}-\frac{8 i b^2 f (d+i c d x)^{3/2} (f-i c f x)^{3/2}}{225 c}",1,"(((-8*I)/225)*b^2*f*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/c + (b^2*f*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/32 - (((16*I)/75)*b^2*f*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(c*(1 + c^2*x^2)) + (15*b^2*f*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))/(64*(1 + c^2*x^2)) - (((2*I)/125)*b^2*f*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(1 + c^2*x^2))/c - (9*b^2*f*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*ArcSinh[c*x])/(64*c*(1 + c^2*x^2)^(3/2)) + (((2*I)/5)*b*f*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/(1 + c^2*x^2)^(3/2) - (3*b*c*f*x^2*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/(8*(1 + c^2*x^2)^(3/2)) + (((4*I)/15)*b*c^2*f*x^3*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/(1 + c^2*x^2)^(3/2) + (((2*I)/25)*b*c^4*f*x^5*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x]))/(1 + c^2*x^2)^(3/2) - (b*f*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(8*c) + (f*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^2)/4 + (3*f*x*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^2)/(8*(1 + c^2*x^2)) - ((I/5)*f*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/c + (f*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)*(a + b*ArcSinh[c*x])^3)/(8*b*c*(1 + c^2*x^2)^(3/2))","A",19,15,37,0.4054,1,"{5712, 5821, 5684, 5682, 5675, 5661, 321, 215, 5717, 195, 194, 5679, 12, 1247, 698}"
584,1,680,0,1.0629045,"\int \sqrt{d+i c d x} (f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[d + I*c*d*x]*(f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x])^2,x]","\frac{b c^3 f^2 x^4 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{8 \sqrt{c^2 x^2+1}}-\frac{1}{4} c^2 f^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{4 i b c^2 f^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{c^2 x^2+1}}-\frac{3 b c f^2 x^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{8 \sqrt{c^2 x^2+1}}+\frac{4 i b f^2 x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}+\frac{5 f^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^3}{24 b c \sqrt{c^2 x^2+1}}-\frac{2 i f^2 \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c}+\frac{3}{8} f^2 x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{1}{32} b^2 c^2 f^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x}-\frac{4 i b^2 f^2 \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x}}{27 c}-\frac{15 b^2 f^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \sinh ^{-1}(c x)}{64 c \sqrt{c^2 x^2+1}}+\frac{15}{64} b^2 f^2 x \sqrt{d+i c d x} \sqrt{f-i c f x}-\frac{8 i b^2 f^2 \sqrt{d+i c d x} \sqrt{f-i c f x}}{9 c}","\frac{b c^3 f^2 x^4 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{8 \sqrt{c^2 x^2+1}}-\frac{1}{4} c^2 f^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{4 i b c^2 f^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{c^2 x^2+1}}-\frac{3 b c f^2 x^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{8 \sqrt{c^2 x^2+1}}+\frac{4 i b f^2 x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{c^2 x^2+1}}+\frac{5 f^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^3}{24 b c \sqrt{c^2 x^2+1}}-\frac{2 i f^2 \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c}+\frac{3}{8} f^2 x \sqrt{d+i c d x} \sqrt{f-i c f x} \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{1}{32} b^2 c^2 f^2 x^3 \sqrt{d+i c d x} \sqrt{f-i c f x}-\frac{4 i b^2 f^2 \left(c^2 x^2+1\right) \sqrt{d+i c d x} \sqrt{f-i c f x}}{27 c}-\frac{15 b^2 f^2 \sqrt{d+i c d x} \sqrt{f-i c f x} \sinh ^{-1}(c x)}{64 c \sqrt{c^2 x^2+1}}+\frac{15}{64} b^2 f^2 x \sqrt{d+i c d x} \sqrt{f-i c f x}-\frac{8 i b^2 f^2 \sqrt{d+i c d x} \sqrt{f-i c f x}}{9 c}",1,"(((-8*I)/9)*b^2*f^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/c + (15*b^2*f^2*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/64 - (b^2*c^2*f^2*x^3*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])/32 - (((4*I)/27)*b^2*f^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(1 + c^2*x^2))/c - (15*b^2*f^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*ArcSinh[c*x])/(64*c*Sqrt[1 + c^2*x^2]) + (((4*I)/3)*b*f^2*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/Sqrt[1 + c^2*x^2] - (3*b*c*f^2*x^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/(8*Sqrt[1 + c^2*x^2]) + (((4*I)/9)*b*c^2*f^2*x^3*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/Sqrt[1 + c^2*x^2] + (b*c^3*f^2*x^4*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x]))/(8*Sqrt[1 + c^2*x^2]) + (3*f^2*x*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2)/8 - (c^2*f^2*x^3*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^2)/4 - (((2*I)/3)*f^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/c + (5*f^2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]*(a + b*ArcSinh[c*x])^3)/(24*b*c*Sqrt[1 + c^2*x^2])","A",23,13,37,0.3514,1,"{5712, 5821, 5682, 5675, 5661, 321, 215, 5717, 5679, 444, 43, 5742, 5758}"
585,1,615,0,0.780721,"\int \frac{(f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+i c d x}} \, dx","Int[((f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x])^2)/Sqrt[d + I*c*d*x],x]","\frac{5 f^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{i c f^3 x^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{3 f^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{11 i f^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{2 i b c^2 f^3 x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{3 b c f^3 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{22 i b f^3 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{2 i b^2 f^3 \left(c^2 x^2+1\right)^2}{27 c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{3 b^2 f^3 x \left(c^2 x^2+1\right)}{4 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{68 i b^2 f^3 \left(c^2 x^2+1\right)}{9 c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{3 b^2 f^3 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{4 c \sqrt{d+i c d x} \sqrt{f-i c f x}}","\frac{5 f^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{i c f^3 x^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{3 f^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{11 i f^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{2 i b c^2 f^3 x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{3 b c f^3 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{22 i b f^3 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{2 i b^2 f^3 \left(c^2 x^2+1\right)^2}{27 c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{3 b^2 f^3 x \left(c^2 x^2+1\right)}{4 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{68 i b^2 f^3 \left(c^2 x^2+1\right)}{9 c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{3 b^2 f^3 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{4 c \sqrt{d+i c d x} \sqrt{f-i c f x}}",1,"(((-68*I)/9)*b^2*f^3*(1 + c^2*x^2))/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (3*b^2*f^3*x*(1 + c^2*x^2))/(4*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (((2*I)/27)*b^2*f^3*(1 + c^2*x^2)^2)/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (3*b^2*f^3*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(4*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (((22*I)/3)*b*f^3*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (3*b*c*f^3*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (((2*I)/9)*b*c^2*f^3*x^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (((11*I)/3)*f^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (3*f^3*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + ((I/3)*c*f^3*x^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (5*f^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^3)/(6*b*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])","A",17,10,37,0.2703,1,"{5712, 5831, 3317, 3296, 2638, 3311, 32, 2635, 8, 2633}"
586,1,972,0,1.3635125,"\int \frac{(f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2}} \, dx","Int[((f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x])^2)/(d + I*c*d*x)^(3/2),x]","-\frac{5 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3 f^4}{2 b c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{b^2 x \left(c^2 x^2+1\right)^2 f^4}{4 (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{8 i b^2 \left(c^2 x^2+1\right)^2 f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 f^4}{2 (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{4 i \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{8 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2 f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{8 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2 f^4}{(i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{8 i \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2 f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{8 i a b x \left(c^2 x^2+1\right)^{3/2} f^4}{(i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{8 i b^2 x \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x) f^4}{(i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{b^2 \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x) f^4}{4 c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{b c x^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) f^4}{2 (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{32 i b \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{16 b \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \log \left(1+e^{2 \sinh ^{-1}(c x)}\right) f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{16 b^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{16 b^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{8 b^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}","-\frac{5 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3 f^4}{2 b c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{b^2 x \left(c^2 x^2+1\right)^2 f^4}{4 (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{8 i b^2 \left(c^2 x^2+1\right)^2 f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 f^4}{2 (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{4 i \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{8 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2 f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{8 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2 f^4}{(i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{8 i \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2 f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{8 i a b x \left(c^2 x^2+1\right)^{3/2} f^4}{(i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{8 i b^2 x \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x) f^4}{(i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{b^2 \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x) f^4}{4 c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{b c x^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) f^4}{2 (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{32 i b \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{16 b \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \log \left(1+e^{2 \sinh ^{-1}(c x)}\right) f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{16 b^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{16 b^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{8 b^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) f^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}",1,"((-8*I)*a*b*f^4*x*(1 + c^2*x^2)^(3/2))/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + ((8*I)*b^2*f^4*(1 + c^2*x^2)^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (b^2*f^4*x*(1 + c^2*x^2)^2)/(4*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (b^2*f^4*(1 + c^2*x^2)^(3/2)*ArcSinh[c*x])/(4*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - ((8*I)*b^2*f^4*x*(1 + c^2*x^2)^(3/2)*ArcSinh[c*x])/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (b*c*f^4*x^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(2*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + ((8*I)*f^4*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (8*f^4*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (8*f^4*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + ((4*I)*f^4*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (f^4*x*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/(2*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (5*f^4*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^3)/(2*b*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - ((32*I)*b*f^4*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (16*b*f^4*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (16*b^2*f^4*(1 + c^2*x^2)^(3/2)*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (16*b^2*f^4*(1 + c^2*x^2)^(3/2)*PolyLog[2, I*E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (8*b^2*f^4*(1 + c^2*x^2)^(3/2)*PolyLog[2, -E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",28,19,37,0.5135,1,"{5712, 5833, 5821, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 5693, 4180, 5675, 5653, 261, 5758, 5661, 321, 215}"
587,1,790,0,1.3647751,"\int \frac{(f-i c f x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{5/2}} \, dx","Int[((f - I*c*f*x)^(5/2)*(a + b*ArcSinh[c*x])^2)/(d + I*c*d*x)^(5/2),x]","\frac{112 b^2 f^5 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i a b f^5 x \left(c^2 x^2+1\right)^{5/2}}{(d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{5 f^5 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i f^5 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{28 f^5 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{112 b f^5 \left(c^2 x^2+1\right)^{5/2} \log \left(1+i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{28 i f^5 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 b f^5 \left(c^2 x^2+1\right)^{5/2} \csc ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{4 i f^5 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \csc ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i b^2 f^5 \left(c^2 x^2+1\right)^3}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i b^2 f^5 x \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x)}{(d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{16 i b^2 f^5 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","\frac{112 b^2 f^5 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i a b f^5 x \left(c^2 x^2+1\right)^{5/2}}{(d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{5 f^5 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i f^5 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{28 f^5 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{112 b f^5 \left(c^2 x^2+1\right)^{5/2} \log \left(1+i e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{28 i f^5 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 b f^5 \left(c^2 x^2+1\right)^{5/2} \csc ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{4 i f^5 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \csc ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i b^2 f^5 \left(c^2 x^2+1\right)^3}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i b^2 f^5 x \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x)}{(d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{16 i b^2 f^5 \left(c^2 x^2+1\right)^{5/2} \cot \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"((2*I)*a*b*f^5*x*(1 + c^2*x^2)^(5/2))/((d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - ((2*I)*b^2*f^5*(1 + c^2*x^2)^3)/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + ((2*I)*b^2*f^5*x*(1 + c^2*x^2)^(5/2)*ArcSinh[c*x])/((d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (28*f^5*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (I*f^5*(1 + c^2*x^2)^3*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (5*f^5*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^3)/(3*b*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (((16*I)/3)*b^2*f^5*(1 + c^2*x^2)^(5/2)*Cot[Pi/4 + (I/2)*ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (((28*I)/3)*f^5*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2*Cot[Pi/4 + (I/2)*ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (8*b*f^5*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Csc[Pi/4 + (I/2)*ArcSinh[c*x]]^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((4*I)/3)*f^5*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2*Cot[Pi/4 + (I/2)*ArcSinh[c*x]]*Csc[Pi/4 + (I/2)*ArcSinh[c*x]]^2)/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (112*b*f^5*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Log[1 + I*E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (112*b^2*f^5*(1 + c^2*x^2)^(5/2)*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",25,16,37,0.4324,1,"{5712, 5833, 5675, 5717, 5653, 261, 5831, 3318, 4186, 3767, 8, 4184, 3716, 2190, 2279, 2391}"
588,1,615,0,0.7852626,"\int \frac{(d+i c d x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{f-i c f x}} \, dx","Int[((d + I*c*d*x)^(5/2)*(a + b*ArcSinh[c*x])^2)/Sqrt[f - I*c*f*x],x]","\frac{5 d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{i c d^3 x^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{3 d^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{11 i d^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{2 i b c^2 d^3 x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{3 b c d^3 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{22 i b d^3 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{2 i b^2 d^3 \left(c^2 x^2+1\right)^2}{27 c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{3 b^2 d^3 x \left(c^2 x^2+1\right)}{4 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{68 i b^2 d^3 \left(c^2 x^2+1\right)}{9 c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{3 b^2 d^3 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{4 c \sqrt{d+i c d x} \sqrt{f-i c f x}}","\frac{5 d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{i c d^3 x^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{3 d^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{11 i d^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{2 i b c^2 d^3 x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{3 b c d^3 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{22 i b d^3 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{2 i b^2 d^3 \left(c^2 x^2+1\right)^2}{27 c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{3 b^2 d^3 x \left(c^2 x^2+1\right)}{4 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{68 i b^2 d^3 \left(c^2 x^2+1\right)}{9 c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{3 b^2 d^3 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{4 c \sqrt{d+i c d x} \sqrt{f-i c f x}}",1,"(((68*I)/9)*b^2*d^3*(1 + c^2*x^2))/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (3*b^2*d^3*x*(1 + c^2*x^2))/(4*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (((2*I)/27)*b^2*d^3*(1 + c^2*x^2)^2)/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (3*b^2*d^3*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(4*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (((22*I)/3)*b*d^3*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (3*b*c*d^3*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (((2*I)/9)*b*c^2*d^3*x^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (((11*I)/3)*d^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (3*d^3*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - ((I/3)*c*d^3*x^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (5*d^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^3)/(6*b*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])","A",17,10,37,0.2703,1,"{5712, 5831, 3317, 3296, 2638, 3311, 32, 2635, 8, 2633}"
589,1,436,0,0.6685273,"\int \frac{(d+i c d x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{f-i c f x}} \, dx","Int[((d + I*c*d*x)^(3/2)*(a + b*ArcSinh[c*x])^2)/Sqrt[f - I*c*f*x],x]","\frac{d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{2 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{2 i d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{d^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{b c d^2 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{4 i b d^2 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{4 i b^2 d^2 \left(c^2 x^2+1\right)}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{b^2 d^2 x \left(c^2 x^2+1\right)}{4 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{b^2 d^2 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{4 c \sqrt{d+i c d x} \sqrt{f-i c f x}}","\frac{d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{2 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{2 i d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{d^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{b c d^2 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{4 i b d^2 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{4 i b^2 d^2 \left(c^2 x^2+1\right)}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{b^2 d^2 x \left(c^2 x^2+1\right)}{4 \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{b^2 d^2 \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{4 c \sqrt{d+i c d x} \sqrt{f-i c f x}}",1,"((4*I)*b^2*d^2*(1 + c^2*x^2))/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (b^2*d^2*x*(1 + c^2*x^2))/(4*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (b^2*d^2*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(4*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - ((4*I)*b*d^2*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (b*c*d^2*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + ((2*I)*d^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - (d^2*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(2*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (d^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^3)/(2*b*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])","A",11,9,37,0.2432,1,"{5712, 5831, 3317, 3296, 2638, 3311, 32, 2635, 8}"
590,1,259,0,0.5108421,"\int \frac{\sqrt{d+i c d x} \left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{f-i c f x}} \, dx","Int[(Sqrt[d + I*c*d*x]*(a + b*ArcSinh[c*x])^2)/Sqrt[f - I*c*f*x],x]","-\frac{2 i a b d x \sqrt{c^2 x^2+1}}{\sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{i d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{2 i b^2 d \left(c^2 x^2+1\right)}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{2 i b^2 d x \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{\sqrt{d+i c d x} \sqrt{f-i c f x}}","-\frac{2 i a b d x \sqrt{c^2 x^2+1}}{\sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{i d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}+\frac{2 i b^2 d \left(c^2 x^2+1\right)}{c \sqrt{d+i c d x} \sqrt{f-i c f x}}-\frac{2 i b^2 d x \sqrt{c^2 x^2+1} \sinh ^{-1}(c x)}{\sqrt{d+i c d x} \sqrt{f-i c f x}}",1,"((-2*I)*a*b*d*x*Sqrt[1 + c^2*x^2])/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + ((2*I)*b^2*d*(1 + c^2*x^2))/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) - ((2*I)*b^2*d*x*Sqrt[1 + c^2*x^2]*ArcSinh[c*x])/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (I*d*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]) + (d*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^3)/(3*b*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])","A",8,6,37,0.1622,1,"{5712, 5821, 5675, 5717, 5653, 261}"
591,1,59,0,0.2960791,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+i c d x} \sqrt{f-i c f x}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x]),x]","\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}","\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c \sqrt{d+i c d x} \sqrt{f-i c f x}}",1,"(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^3)/(3*b*c*Sqrt[d + I*c*d*x]*Sqrt[f - I*c*f*x])","A",2,2,37,0.05405,1,"{5712, 5675}"
592,1,464,0,0.7534957,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} \sqrt{f-i c f x}} \, dx","Int[(a + b*ArcSinh[c*x])^2/((d + I*c*d*x)^(3/2)*Sqrt[f - I*c*f*x]),x]","-\frac{2 b^2 f \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 b^2 f \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{b^2 f \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{f \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{i f \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{f x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 b f \left(c^2 x^2+1\right)^{3/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 i b f \left(c^2 x^2+1\right)^{3/2} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}","-\frac{2 b^2 f \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 b^2 f \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{b^2 f \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{f \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{i f \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{f x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 b f \left(c^2 x^2+1\right)^{3/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 i b f \left(c^2 x^2+1\right)^{3/2} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}",1,"(I*f*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (f*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (f*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - ((4*I)*b*f*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (2*b*f*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (2*b^2*f*(1 + c^2*x^2)^(3/2)*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (2*b^2*f*(1 + c^2*x^2)^(3/2)*PolyLog[2, I*E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (b^2*f*(1 + c^2*x^2)^(3/2)*PolyLog[2, -E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",16,11,37,0.2973,1,"{5712, 5821, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 5693, 4180}"
593,1,942,0,1.3318764,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{5/2} \sqrt{f-i c f x}} \, dx","Int[(a + b*ArcSinh[c*x])^2/((d + I*c*d*x)^(5/2)*Sqrt[f - I*c*f*x]),x]","-\frac{c^2 f^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2 x^3}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{b c f^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) x^2}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 b^2 f^2 \left(c^2 x^2+1\right)^2 x}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{2 f^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 x}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{f^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2 x}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i b f^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) x}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i b^2 f^2 \left(c^2 x^2+1\right)^2}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{f^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i f^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{b^2 f^2 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{b f^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{4 i b f^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 b f^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \log \left(1+e^{2 \sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 b^2 f^2 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{2 b^2 f^2 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{b^2 f^2 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}","-\frac{c^2 f^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2 x^3}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{b c f^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) x^2}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 b^2 f^2 \left(c^2 x^2+1\right)^2 x}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{2 f^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 x}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{f^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2 x}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i b f^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) x}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i b^2 f^2 \left(c^2 x^2+1\right)^2}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{f^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i f^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{b^2 f^2 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{b f^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{4 i b f^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 b f^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \log \left(1+e^{2 \sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 b^2 f^2 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{2 b^2 f^2 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{b^2 f^2 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}",1,"(((-2*I)/3)*b^2*f^2*(1 + c^2*x^2)^2)/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (2*b^2*f^2*x*(1 + c^2*x^2)^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (b^2*f^2*(1 + c^2*x^2)^(5/2)*ArcSinh[c*x])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (b*f^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (((2*I)/3)*b*f^2*x*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/((d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (b*c*f^2*x^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((2*I)/3)*f^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (f^2*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (c^2*f^2*x^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (2*f^2*x*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (f^2*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (((4*I)/3)*b*f^2*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (2*b*f^2*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (2*b^2*f^2*(1 + c^2*x^2)^(5/2)*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (2*b^2*f^2*(1 + c^2*x^2)^(5/2)*PolyLog[2, I*E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (b^2*f^2*(1 + c^2*x^2)^(5/2)*PolyLog[2, -E^(2*ArcSinh[c*x])])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",30,18,37,0.4865,1,"{5712, 5821, 5690, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 191, 5693, 4180, 261, 5723, 5751, 288, 215}"
594,1,972,0,1.3698747,"\int \frac{(d+i c d x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{(f-i c f x)^{3/2}} \, dx","Int[((d + I*c*d*x)^(5/2)*(a + b*ArcSinh[c*x])^2)/(f - I*c*f*x)^(3/2),x]","-\frac{5 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3 d^4}{2 b c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{b^2 x \left(c^2 x^2+1\right)^2 d^4}{4 (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{8 i b^2 \left(c^2 x^2+1\right)^2 d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 d^4}{2 (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{4 i \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{8 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2 d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{8 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2 d^4}{(i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{8 i \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2 d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{8 i a b x \left(c^2 x^2+1\right)^{3/2} d^4}{(i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{8 i b^2 x \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x) d^4}{(i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{b^2 \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x) d^4}{4 c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{b c x^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) d^4}{2 (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{32 i b \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{16 b \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \log \left(1+e^{2 \sinh ^{-1}(c x)}\right) d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{16 b^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{16 b^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{8 b^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}","-\frac{5 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3 d^4}{2 b c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{b^2 x \left(c^2 x^2+1\right)^2 d^4}{4 (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{8 i b^2 \left(c^2 x^2+1\right)^2 d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 d^4}{2 (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{4 i \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{8 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2 d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{8 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2 d^4}{(i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{8 i \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2 d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{8 i a b x \left(c^2 x^2+1\right)^{3/2} d^4}{(i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{8 i b^2 x \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x) d^4}{(i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{b^2 \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x) d^4}{4 c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{b c x^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) d^4}{2 (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{32 i b \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{16 b \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \log \left(1+e^{2 \sinh ^{-1}(c x)}\right) d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}+\frac{16 b^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right) d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{16 b^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right) d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}-\frac{8 b^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right) d^4}{c (i c x d+d)^{3/2} (f-i c f x)^{3/2}}",1,"((8*I)*a*b*d^4*x*(1 + c^2*x^2)^(3/2))/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - ((8*I)*b^2*d^4*(1 + c^2*x^2)^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (b^2*d^4*x*(1 + c^2*x^2)^2)/(4*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (b^2*d^4*(1 + c^2*x^2)^(3/2)*ArcSinh[c*x])/(4*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + ((8*I)*b^2*d^4*x*(1 + c^2*x^2)^(3/2)*ArcSinh[c*x])/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (b*c*d^4*x^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(2*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - ((8*I)*d^4*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (8*d^4*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (8*d^4*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - ((4*I)*d^4*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (d^4*x*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/(2*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (5*d^4*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^3)/(2*b*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + ((32*I)*b*d^4*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (16*b*d^4*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (16*b^2*d^4*(1 + c^2*x^2)^(3/2)*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (16*b^2*d^4*(1 + c^2*x^2)^(3/2)*PolyLog[2, I*E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (8*b^2*d^4*(1 + c^2*x^2)^(3/2)*PolyLog[2, -E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",28,19,37,0.5135,1,"{5712, 5833, 5821, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 5693, 4180, 5675, 5653, 261, 5758, 5661, 321, 215}"
595,1,752,0,1.1327737,"\int \frac{(d+i c d x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{(f-i c f x)^{3/2}} \, dx","Int[((d + I*c*d*x)^(3/2)*(a + b*ArcSinh[c*x])^2)/(f - I*c*f*x)^(3/2),x]","\frac{8 b^2 d^3 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{8 b^2 d^3 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 b^2 d^3 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 i a b d^3 x \left(c^2 x^2+1\right)^{3/2}}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{d^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{b c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{i d^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{4 d^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{4 d^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 i d^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{8 b d^3 \left(c^2 x^2+1\right)^{3/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{16 i b d^3 \left(c^2 x^2+1\right)^{3/2} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 i b^2 d^3 \left(c^2 x^2+1\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 i b^2 d^3 x \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x)}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}","\frac{8 b^2 d^3 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{8 b^2 d^3 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 b^2 d^3 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 i a b d^3 x \left(c^2 x^2+1\right)^{3/2}}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{d^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{b c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{i d^3 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{4 d^3 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{4 d^3 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 i d^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{8 b d^3 \left(c^2 x^2+1\right)^{3/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{16 i b d^3 \left(c^2 x^2+1\right)^{3/2} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 i b^2 d^3 \left(c^2 x^2+1\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 i b^2 d^3 x \left(c^2 x^2+1\right)^{3/2} \sinh ^{-1}(c x)}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}",1,"((2*I)*a*b*d^3*x*(1 + c^2*x^2)^(3/2))/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - ((2*I)*b^2*d^3*(1 + c^2*x^2)^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + ((2*I)*b^2*d^3*x*(1 + c^2*x^2)^(3/2)*ArcSinh[c*x])/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - ((4*I)*d^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (4*d^3*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (4*d^3*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (I*d^3*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (d^3*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^3)/(b*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + ((16*I)*b*d^3*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (8*b*d^3*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (8*b^2*d^3*(1 + c^2*x^2)^(3/2)*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (8*b^2*d^3*(1 + c^2*x^2)^(3/2)*PolyLog[2, I*E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (4*b^2*d^3*(1 + c^2*x^2)^(3/2)*PolyLog[2, -E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",23,15,37,0.4054,1,"{5712, 5833, 5821, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 5693, 4180, 5675, 5653, 261}"
596,1,544,0,0.9878799,"\int \frac{\sqrt{d+i c d x} \left(a+b \sinh ^{-1}(c x)\right)^2}{(f-i c f x)^{3/2}} \, dx","Int[(Sqrt[d + I*c*d*x]*(a + b*ArcSinh[c*x])^2)/(f - I*c*f*x)^(3/2),x]","\frac{4 b^2 d^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 b^2 d^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 b^2 d^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 i d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 d^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 b d^2 \left(c^2 x^2+1\right)^{3/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{8 i b d^2 \left(c^2 x^2+1\right)^{3/2} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}","\frac{4 b^2 d^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 b^2 d^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 b^2 d^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 i d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{2 d^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{4 b d^2 \left(c^2 x^2+1\right)^{3/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{8 i b d^2 \left(c^2 x^2+1\right)^{3/2} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}",1,"((-2*I)*d^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (2*d^2*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (2*d^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (d^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^3)/(3*b*c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + ((8*I)*b*d^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (4*b*d^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (4*b^2*d^2*(1 + c^2*x^2)^(3/2)*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (4*b^2*d^2*(1 + c^2*x^2)^(3/2)*PolyLog[2, I*E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (2*b^2*d^2*(1 + c^2*x^2)^(3/2)*PolyLog[2, -E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",19,13,37,0.3514,1,"{5712, 5833, 5821, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 5693, 4180, 5675}"
597,1,464,0,0.7038575,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+i c d x} (f-i c f x)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(Sqrt[d + I*c*d*x]*(f - I*c*f*x)^(3/2)),x]","\frac{2 b^2 d \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 b^2 d \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{b^2 d \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{d \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{i d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{d x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 b d \left(c^2 x^2+1\right)^{3/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{4 i b d \left(c^2 x^2+1\right)^{3/2} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}","\frac{2 b^2 d \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 b^2 d \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{b^2 d \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{d \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{i d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{d x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 b d \left(c^2 x^2+1\right)^{3/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{4 i b d \left(c^2 x^2+1\right)^{3/2} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}",1,"((-I)*d*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (d*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (d*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + ((4*I)*b*d*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (2*b*d*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + (2*b^2*d*(1 + c^2*x^2)^(3/2)*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (2*b^2*d*(1 + c^2*x^2)^(3/2)*PolyLog[2, I*E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (b^2*d*(1 + c^2*x^2)^(3/2)*PolyLog[2, -E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",16,11,37,0.2973,1,"{5712, 5821, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 5693, 4180}"
598,1,224,0,0.4233616,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)),x]","-\frac{b^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{\left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 b \left(c^2 x^2+1\right)^{3/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}","-\frac{b^2 \left(c^2 x^2+1\right)^{3/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{\left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}+\frac{x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} (f-i c f x)^{3/2}}-\frac{2 b \left(c^2 x^2+1\right)^{3/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c (d+i c d x)^{3/2} (f-i c f x)^{3/2}}",1,"(x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) + ((1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (2*b*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2)) - (b^2*(1 + c^2*x^2)^(3/2)*PolyLog[2, -E^(2*ArcSinh[c*x])])/(c*(d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(3/2))","A",7,7,37,0.1892,1,"{5712, 5687, 5714, 3718, 2190, 2279, 2391}"
599,1,743,0,0.9088607,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{5/2} (f-i c f x)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/((d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(3/2)),x]","-\frac{b^2 f \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{b^2 f \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 b^2 f \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 f \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 f x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{b f \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i b f x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i f \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{f x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{4 b f \left(c^2 x^2+1\right)^{5/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i b f \left(c^2 x^2+1\right)^{5/2} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i b^2 f \left(c^2 x^2+1\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b^2 f x \left(c^2 x^2+1\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","-\frac{b^2 f \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{b^2 f \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 b^2 f \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 f \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 f x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{b f \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i b f x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i f \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{f x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{4 b f \left(c^2 x^2+1\right)^{5/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i b f \left(c^2 x^2+1\right)^{5/2} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i b^2 f \left(c^2 x^2+1\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b^2 f x \left(c^2 x^2+1\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"((-I/3)*b^2*f*(1 + c^2*x^2)^2)/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (b^2*f*x*(1 + c^2*x^2)^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (b*f*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - ((I/3)*b*f*x*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/((d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + ((I/3)*f*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (f*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (2*f*x*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (2*f*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (((2*I)/3)*b*f*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (4*b*f*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (b^2*f*(1 + c^2*x^2)^(5/2)*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (b^2*f*(1 + c^2*x^2)^(5/2)*PolyLog[2, I*E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (2*b^2*f*(1 + c^2*x^2)^(5/2)*PolyLog[2, -E^(2*ArcSinh[c*x])])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",21,14,37,0.3784,1,"{5712, 5821, 5690, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 191, 5693, 4180, 261}"
600,1,794,0,1.3958854,"\int \frac{(d+i c d x)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{(f-i c f x)^{5/2}} \, dx","Int[((d + I*c*d*x)^(5/2)*(a + b*ArcSinh[c*x])^2)/(f - I*c*f*x)^(5/2),x]","-\frac{112 b^2 d^5 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{-\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i a b d^5 x \left(c^2 x^2+1\right)^{5/2}}{(d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{5 d^5 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i d^5 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{28 d^5 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{112 b d^5 \left(c^2 x^2+1\right)^{5/2} \log \left(1+i e^{-\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 b d^5 \left(c^2 x^2+1\right)^{5/2} \sec ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{28 i d^5 \left(c^2 x^2+1\right)^{5/2} \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{4 i d^5 \left(c^2 x^2+1\right)^{5/2} \sec ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i b^2 d^5 \left(c^2 x^2+1\right)^3}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i b^2 d^5 x \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x)}{(d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{16 i b^2 d^5 \left(c^2 x^2+1\right)^{5/2} \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","-\frac{112 b^2 d^5 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{-\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i a b d^5 x \left(c^2 x^2+1\right)^{5/2}}{(d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{5 d^5 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i d^5 \left(c^2 x^2+1\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{28 d^5 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{112 b d^5 \left(c^2 x^2+1\right)^{5/2} \log \left(1+i e^{-\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 b d^5 \left(c^2 x^2+1\right)^{5/2} \sec ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{28 i d^5 \left(c^2 x^2+1\right)^{5/2} \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{4 i d^5 \left(c^2 x^2+1\right)^{5/2} \sec ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i b^2 d^5 \left(c^2 x^2+1\right)^3}{c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i b^2 d^5 x \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x)}{(d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{16 i b^2 d^5 \left(c^2 x^2+1\right)^{5/2} \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"((-2*I)*a*b*d^5*x*(1 + c^2*x^2)^(5/2))/((d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + ((2*I)*b^2*d^5*(1 + c^2*x^2)^3)/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - ((2*I)*b^2*d^5*x*(1 + c^2*x^2)^(5/2)*ArcSinh[c*x])/((d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (28*d^5*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (I*d^5*(1 + c^2*x^2)^3*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (5*d^5*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^3)/(3*b*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (112*b*d^5*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Log[1 + I/E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (112*b^2*d^5*(1 + c^2*x^2)^(5/2)*PolyLog[2, (-I)/E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (8*b*d^5*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Sec[Pi/4 + (I/2)*ArcSinh[c*x]]^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((16*I)/3)*b^2*d^5*(1 + c^2*x^2)^(5/2)*Tan[Pi/4 + (I/2)*ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((28*I)/3)*d^5*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2*Tan[Pi/4 + (I/2)*ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (((4*I)/3)*d^5*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2*Sec[Pi/4 + (I/2)*ArcSinh[c*x]]^2*Tan[Pi/4 + (I/2)*ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",25,16,37,0.4324,1,"{5712, 5833, 5675, 5717, 5653, 261, 5831, 3318, 4186, 3767, 8, 4184, 3716, 2190, 2279, 2391}"
601,1,584,0,1.2054986,"\int \frac{(d+i c d x)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{(f-i c f x)^{5/2}} \, dx","Int[((d + I*c*d*x)^(3/2)*(a + b*ArcSinh[c*x])^2)/(f - I*c*f*x)^(5/2),x]","-\frac{32 b^2 d^4 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{-\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{d^4 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 d^4 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{32 b d^4 \left(c^2 x^2+1\right)^{5/2} \log \left(1+i e^{-\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{4 b d^4 \left(c^2 x^2+1\right)^{5/2} \sec ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 i d^4 \left(c^2 x^2+1\right)^{5/2} \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i d^4 \left(c^2 x^2+1\right)^{5/2} \sec ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 i b^2 d^4 \left(c^2 x^2+1\right)^{5/2} \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","-\frac{32 b^2 d^4 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{-\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{d^4 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^3}{3 b c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 d^4 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{32 b d^4 \left(c^2 x^2+1\right)^{5/2} \log \left(1+i e^{-\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{4 b d^4 \left(c^2 x^2+1\right)^{5/2} \sec ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 i d^4 \left(c^2 x^2+1\right)^{5/2} \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i d^4 \left(c^2 x^2+1\right)^{5/2} \sec ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{8 i b^2 d^4 \left(c^2 x^2+1\right)^{5/2} \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"(8*d^4*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (d^4*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^3)/(3*b*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (32*b*d^4*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Log[1 + I/E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (32*b^2*d^4*(1 + c^2*x^2)^(5/2)*PolyLog[2, (-I)/E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (4*b*d^4*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Sec[Pi/4 + (I/2)*ArcSinh[c*x]]^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((8*I)/3)*b^2*d^4*(1 + c^2*x^2)^(5/2)*Tan[Pi/4 + (I/2)*ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((8*I)/3)*d^4*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2*Tan[Pi/4 + (I/2)*ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (((2*I)/3)*d^4*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2*Sec[Pi/4 + (I/2)*ArcSinh[c*x]]^2*Tan[Pi/4 + (I/2)*ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",21,13,37,0.3514,1,"{5712, 5833, 5675, 5831, 3318, 4186, 3767, 8, 4184, 3716, 2190, 2279, 2391}"
602,1,522,0,1.1548267,"\int \frac{\sqrt{d+i c d x} \left(a+b \sinh ^{-1}(c x)\right)^2}{(f-i c f x)^{5/2}} \, dx","Int[(Sqrt[d + I*c*d*x]*(a + b*ArcSinh[c*x])^2)/(f - I*c*f*x)^(5/2),x]","-\frac{4 b^2 d^3 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{-\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{d^3 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{4 b d^3 \left(c^2 x^2+1\right)^{5/2} \log \left(1+i e^{-\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 b d^3 \left(c^2 x^2+1\right)^{5/2} \sec ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i d^3 \left(c^2 x^2+1\right)^{5/2} \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i d^3 \left(c^2 x^2+1\right)^{5/2} \sec ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{4 i b^2 d^3 \left(c^2 x^2+1\right)^{5/2} \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","-\frac{4 b^2 d^3 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{-\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{d^3 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{4 b d^3 \left(c^2 x^2+1\right)^{5/2} \log \left(1+i e^{-\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 b d^3 \left(c^2 x^2+1\right)^{5/2} \sec ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i d^3 \left(c^2 x^2+1\right)^{5/2} \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i d^3 \left(c^2 x^2+1\right)^{5/2} \sec ^2\left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{4 i b^2 d^3 \left(c^2 x^2+1\right)^{5/2} \tan \left(\frac{\pi }{4}+\frac{1}{2} i \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"(d^3*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (4*b*d^3*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Log[1 + I/E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (4*b^2*d^3*(1 + c^2*x^2)^(5/2)*PolyLog[2, (-I)/E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (2*b*d^3*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Sec[Pi/4 + (I/2)*ArcSinh[c*x]]^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((4*I)/3)*b^2*d^3*(1 + c^2*x^2)^(5/2)*Tan[Pi/4 + (I/2)*ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + ((I/3)*d^3*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2*Tan[Pi/4 + (I/2)*ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - ((I/3)*d^3*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2*Sec[Pi/4 + (I/2)*ArcSinh[c*x]]^2*Tan[Pi/4 + (I/2)*ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",20,12,37,0.3243,1,"{5712, 5833, 5831, 3318, 4186, 3767, 8, 4184, 3716, 2190, 2279, 2391}"
603,1,942,0,1.3011752,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+i c d x} (f-i c f x)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(Sqrt[d + I*c*d*x]*(f - I*c*f*x)^(5/2)),x]","-\frac{c^2 d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2 x^3}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{b c d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) x^2}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 b^2 d^2 \left(c^2 x^2+1\right)^2 x}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{2 d^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 x}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2 x}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i b d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) x}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i b^2 d^2 \left(c^2 x^2+1\right)^2}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{d^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{b^2 d^2 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{b d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{4 i b d^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 b d^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \log \left(1+e^{2 \sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{2 b^2 d^2 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 b^2 d^2 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{b^2 d^2 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}","-\frac{c^2 d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2 x^3}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{b c d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) x^2}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 b^2 d^2 \left(c^2 x^2+1\right)^2 x}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{2 d^2 \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 x}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2 x}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i b d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) x}{3 (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i b^2 d^2 \left(c^2 x^2+1\right)^2}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{d^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 i d^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{b^2 d^2 \left(c^2 x^2+1\right)^{5/2} \sinh ^{-1}(c x)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{b d^2 \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{4 i b d^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 b d^2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \log \left(1+e^{2 \sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}+\frac{2 b^2 d^2 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{2 b^2 d^2 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}-\frac{b^2 d^2 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 c (i c x d+d)^{5/2} (f-i c f x)^{5/2}}",1,"(((2*I)/3)*b^2*d^2*(1 + c^2*x^2)^2)/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (2*b^2*d^2*x*(1 + c^2*x^2)^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (b^2*d^2*(1 + c^2*x^2)^(5/2)*ArcSinh[c*x])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (b*d^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((2*I)/3)*b*d^2*x*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/((d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (b*c*d^2*x^2*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (((2*I)/3)*d^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (d^2*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (c^2*d^2*x^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (2*d^2*x*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (d^2*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((4*I)/3)*b*d^2*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (2*b*d^2*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (2*b^2*d^2*(1 + c^2*x^2)^(5/2)*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (2*b^2*d^2*(1 + c^2*x^2)^(5/2)*PolyLog[2, I*E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (b^2*d^2*(1 + c^2*x^2)^(5/2)*PolyLog[2, -E^(2*ArcSinh[c*x])])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",30,18,37,0.4865,1,"{5712, 5821, 5690, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 191, 5693, 4180, 261, 5723, 5751, 288, 215}"
604,1,743,0,0.8974441,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{3/2} (f-i c f x)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/((d + I*c*d*x)^(3/2)*(f - I*c*f*x)^(5/2)),x]","\frac{b^2 d \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b^2 d \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 b^2 d \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 d \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 d x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{b d \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b d x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{d x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{4 b d \left(c^2 x^2+1\right)^{5/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i b d \left(c^2 x^2+1\right)^{5/2} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b^2 d \left(c^2 x^2+1\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b^2 d x \left(c^2 x^2+1\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","\frac{b^2 d \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-i e^{\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b^2 d \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,i e^{\sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{2 b^2 d \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 d \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 d x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{b d \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b d x \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{i d \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{d x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{4 b d \left(c^2 x^2+1\right)^{5/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 i b d \left(c^2 x^2+1\right)^{5/2} \tan ^{-1}\left(e^{\sinh ^{-1}(c x)}\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{i b^2 d \left(c^2 x^2+1\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b^2 d x \left(c^2 x^2+1\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"((I/3)*b^2*d*(1 + c^2*x^2)^2)/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (b^2*d*x*(1 + c^2*x^2)^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (b*d*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + ((I/3)*b*d*x*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/((d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - ((I/3)*d*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (d*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (2*d*x*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (2*d*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (((2*I)/3)*b*d*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*ArcTan[E^ArcSinh[c*x]])/(c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (4*b*d*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (b^2*d*(1 + c^2*x^2)^(5/2)*PolyLog[2, (-I)*E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (b^2*d*(1 + c^2*x^2)^(5/2)*PolyLog[2, I*E^ArcSinh[c*x]])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (2*b^2*d*(1 + c^2*x^2)^(5/2)*PolyLog[2, -E^(2*ArcSinh[c*x])])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",21,14,37,0.3784,1,"{5712, 5821, 5690, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 191, 5693, 4180, 261}"
605,1,386,0,0.5312562,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{(d+i c d x)^{5/2} (f-i c f x)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/((d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)),x]","-\frac{2 b^2 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{b \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{4 b \left(c^2 x^2+1\right)^{5/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b^2 x \left(c^2 x^2+1\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}","-\frac{2 b^2 \left(c^2 x^2+1\right)^{5/2} \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(c x)}\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 \left(c^2 x^2+1\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{2 x \left(c^2 x^2+1\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{b \left(c^2 x^2+1\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}+\frac{x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{4 b \left(c^2 x^2+1\right)^{5/2} \log \left(e^{2 \sinh ^{-1}(c x)}+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c (d+i c d x)^{5/2} (f-i c f x)^{5/2}}-\frac{b^2 x \left(c^2 x^2+1\right)^2}{3 (d+i c d x)^{5/2} (f-i c f x)^{5/2}}",1,"-(b^2*x*(1 + c^2*x^2)^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (b*(1 + c^2*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x])^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (2*x*(1 + c^2*x^2)^2*(a + b*ArcSinh[c*x])^2)/(3*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) + (2*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2)/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (4*b*(1 + c^2*x^2)^(5/2)*(a + b*ArcSinh[c*x])*Log[1 + E^(2*ArcSinh[c*x])])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2)) - (2*b^2*(1 + c^2*x^2)^(5/2)*PolyLog[2, -E^(2*ArcSinh[c*x])])/(3*c*(d + I*c*d*x)^(5/2)*(f - I*c*f*x)^(5/2))","A",10,10,37,0.2703,1,"{5712, 5690, 5687, 5714, 3718, 2190, 2279, 2391, 5717, 191}"
606,1,312,0,0.3506491,"\int \left(d+e x^2\right)^4 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^4*(a + b*ArcSinh[c*x]),x]","\frac{6}{5} d^2 e^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)+\frac{4}{3} d^3 e x^3 \left(a+b \sinh ^{-1}(c x)\right)+d^4 x \left(a+b \sinh ^{-1}(c x)\right)+\frac{4}{7} d e^3 x^7 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{9} e^4 x^9 \left(a+b \sinh ^{-1}(c x)\right)-\frac{2 b e^2 \left(c^2 x^2+1\right)^{5/2} \left(63 c^4 d^2-90 c^2 d e+35 e^2\right)}{525 c^9}-\frac{4 b e \left(c^2 x^2+1\right)^{3/2} \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}-\frac{b \sqrt{c^2 x^2+1} \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}-\frac{4 b e^3 \left(c^2 x^2+1\right)^{7/2} \left(9 c^2 d-7 e\right)}{441 c^9}-\frac{b e^4 \left(c^2 x^2+1\right)^{9/2}}{81 c^9}","\frac{6}{5} d^2 e^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)+\frac{4}{3} d^3 e x^3 \left(a+b \sinh ^{-1}(c x)\right)+d^4 x \left(a+b \sinh ^{-1}(c x)\right)+\frac{4}{7} d e^3 x^7 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{9} e^4 x^9 \left(a+b \sinh ^{-1}(c x)\right)-\frac{2 b e^2 \left(c^2 x^2+1\right)^{5/2} \left(63 c^4 d^2-90 c^2 d e+35 e^2\right)}{525 c^9}-\frac{4 b e \left(c^2 x^2+1\right)^{3/2} \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}-\frac{b \sqrt{c^2 x^2+1} \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}-\frac{4 b e^3 \left(c^2 x^2+1\right)^{7/2} \left(9 c^2 d-7 e\right)}{441 c^9}-\frac{b e^4 \left(c^2 x^2+1\right)^{9/2}}{81 c^9}",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)*Sqrt[1 + c^2*x^2])/(315*c^9) - (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)^(3/2))/(945*c^9) - (2*b*e^2*(63*c^4*d^2 - 90*c^2*d*e + 35*e^2)*(1 + c^2*x^2)^(5/2))/(525*c^9) - (4*b*(9*c^2*d - 7*e)*e^3*(1 + c^2*x^2)^(7/2))/(441*c^9) - (b*e^4*(1 + c^2*x^2)^(9/2))/(81*c^9) + d^4*x*(a + b*ArcSinh[c*x]) + (4*d^3*e*x^3*(a + b*ArcSinh[c*x]))/3 + (6*d^2*e^2*x^5*(a + b*ArcSinh[c*x]))/5 + (4*d*e^3*x^7*(a + b*ArcSinh[c*x]))/7 + (e^4*x^9*(a + b*ArcSinh[c*x]))/9","A",5,5,18,0.2778,1,"{194, 5704, 12, 1799, 1850}"
607,1,221,0,0.2607275,"\int \left(d+e x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^3*(a + b*ArcSinh[c*x]),x]","d^2 e x^3 \left(a+b \sinh ^{-1}(c x)\right)+d^3 x \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{5} d e^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{7} e^3 x^7 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b e \left(c^2 x^2+1\right)^{3/2} \left(35 c^4 d^2-42 c^2 d e+15 e^2\right)}{105 c^7}-\frac{b \sqrt{c^2 x^2+1} \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}-\frac{3 b e^2 \left(c^2 x^2+1\right)^{5/2} \left(7 c^2 d-5 e\right)}{175 c^7}-\frac{b e^3 \left(c^2 x^2+1\right)^{7/2}}{49 c^7}","d^2 e x^3 \left(a+b \sinh ^{-1}(c x)\right)+d^3 x \left(a+b \sinh ^{-1}(c x)\right)+\frac{3}{5} d e^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{7} e^3 x^7 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b e \left(c^2 x^2+1\right)^{3/2} \left(35 c^4 d^2-42 c^2 d e+15 e^2\right)}{105 c^7}-\frac{b \sqrt{c^2 x^2+1} \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}-\frac{3 b e^2 \left(c^2 x^2+1\right)^{5/2} \left(7 c^2 d-5 e\right)}{175 c^7}-\frac{b e^3 \left(c^2 x^2+1\right)^{7/2}}{49 c^7}",1,"-(b*(35*c^6*d^3 - 35*c^4*d^2*e + 21*c^2*d*e^2 - 5*e^3)*Sqrt[1 + c^2*x^2])/(35*c^7) - (b*e*(35*c^4*d^2 - 42*c^2*d*e + 15*e^2)*(1 + c^2*x^2)^(3/2))/(105*c^7) - (3*b*(7*c^2*d - 5*e)*e^2*(1 + c^2*x^2)^(5/2))/(175*c^7) - (b*e^3*(1 + c^2*x^2)^(7/2))/(49*c^7) + d^3*x*(a + b*ArcSinh[c*x]) + d^2*e*x^3*(a + b*ArcSinh[c*x]) + (3*d*e^2*x^5*(a + b*ArcSinh[c*x]))/5 + (e^3*x^7*(a + b*ArcSinh[c*x]))/7","A",5,5,18,0.2778,1,"{194, 5704, 12, 1799, 1850}"
608,1,147,0,0.1430935,"\int \left(d+e x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^2*(a + b*ArcSinh[c*x]),x]","d^2 x \left(a+b \sinh ^{-1}(c x)\right)+\frac{2}{3} d e x^3 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{5} e^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b \sqrt{c^2 x^2+1} \left(15 c^4 d^2-10 c^2 d e+3 e^2\right)}{15 c^5}-\frac{2 b e \left(c^2 x^2+1\right)^{3/2} \left(5 c^2 d-3 e\right)}{45 c^5}-\frac{b e^2 \left(c^2 x^2+1\right)^{5/2}}{25 c^5}","d^2 x \left(a+b \sinh ^{-1}(c x)\right)+\frac{2}{3} d e x^3 \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{5} e^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b \sqrt{c^2 x^2+1} \left(15 c^4 d^2-10 c^2 d e+3 e^2\right)}{15 c^5}-\frac{2 b e \left(c^2 x^2+1\right)^{3/2} \left(5 c^2 d-3 e\right)}{45 c^5}-\frac{b e^2 \left(c^2 x^2+1\right)^{5/2}}{25 c^5}",1,"-(b*(15*c^4*d^2 - 10*c^2*d*e + 3*e^2)*Sqrt[1 + c^2*x^2])/(15*c^5) - (2*b*(5*c^2*d - 3*e)*e*(1 + c^2*x^2)^(3/2))/(45*c^5) - (b*e^2*(1 + c^2*x^2)^(5/2))/(25*c^5) + d^2*x*(a + b*ArcSinh[c*x]) + (2*d*e*x^3*(a + b*ArcSinh[c*x]))/3 + (e^2*x^5*(a + b*ArcSinh[c*x]))/5","A",5,5,18,0.2778,1,"{194, 5704, 12, 1247, 698}"
609,1,81,0,0.0697441,"\int \left(d+e x^2\right) \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)*(a + b*ArcSinh[c*x]),x]","d x \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{3} e x^3 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b \sqrt{c^2 x^2+1} \left(3 c^2 d-e\right)}{3 c^3}-\frac{b e \left(c^2 x^2+1\right)^{3/2}}{9 c^3}","d x \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{3} e x^3 \left(a+b \sinh ^{-1}(c x)\right)-\frac{b \sqrt{c^2 x^2+1} \left(3 c^2 d-e\right)}{3 c^3}-\frac{b e \left(c^2 x^2+1\right)^{3/2}}{9 c^3}",1,"-(b*(3*c^2*d - e)*Sqrt[1 + c^2*x^2])/(3*c^3) - (b*e*(1 + c^2*x^2)^(3/2))/(9*c^3) + d*x*(a + b*ArcSinh[c*x]) + (e*x^3*(a + b*ArcSinh[c*x]))/3","A",4,3,16,0.1875,1,"{5704, 444, 43}"
610,1,30,0,0.0141884,"\int \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[a + b*ArcSinh[c*x],x]","a x-\frac{b \sqrt{c^2 x^2+1}}{c}+b x \sinh ^{-1}(c x)","a x-\frac{b \sqrt{c^2 x^2+1}}{c}+b x \sinh ^{-1}(c x)",1,"a*x - (b*Sqrt[1 + c^2*x^2])/c + b*x*ArcSinh[c*x]","A",3,2,8,0.2500,1,"{5653, 261}"
611,1,485,0,0.8324937,"\int \frac{a+b \sinh ^{-1}(c x)}{d+e x^2} \, dx","Int[(a + b*ArcSinh[c*x])/(d + e*x^2),x]","-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}+1\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}+1\right)}{2 \sqrt{-d} \sqrt{e}}","-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}+1\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}+1\right)}{2 \sqrt{-d} \sqrt{e}}",1,"((a + b*ArcSinh[c*x])*Log[1 - (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) + e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcSinh[c*x])*Log[1 + (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) + e])])/(2*Sqrt[-d]*Sqrt[e]) + ((a + b*ArcSinh[c*x])*Log[1 - (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) + e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcSinh[c*x])*Log[1 + (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) + e])])/(2*Sqrt[-d]*Sqrt[e]) - (b*PolyLog[2, -((Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) + e]))])/(2*Sqrt[-d]*Sqrt[e]) + (b*PolyLog[2, (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) + e])])/(2*Sqrt[-d]*Sqrt[e]) - (b*PolyLog[2, -((Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) + e]))])/(2*Sqrt[-d]*Sqrt[e]) + (b*PolyLog[2, (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) + e])])/(2*Sqrt[-d]*Sqrt[e])","A",18,6,18,0.3333,1,"{5706, 5799, 5561, 2190, 2279, 2391}"
612,1,707,0,1.0748294,"\int \frac{a+b \sinh ^{-1}(c x)}{\left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcSinh[c*x])/(d + e*x^2)^2,x]","\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}+1\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}+1\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{a+b \sinh ^{-1}(c x)}{4 d \sqrt{e} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{a+b \sinh ^{-1}(c x)}{4 d \sqrt{e} \left(\sqrt{-d}+\sqrt{e} x\right)}-\frac{b c \tan ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{c^2 x^2+1} \sqrt{c^2 d-e}}\right)}{4 d \sqrt{e} \sqrt{c^2 d-e}}-\frac{b c \tan ^{-1}\left(\frac{c^2 \sqrt{-d} x+\sqrt{e}}{\sqrt{c^2 x^2+1} \sqrt{c^2 d-e}}\right)}{4 d \sqrt{e} \sqrt{c^2 d-e}}","\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}+1\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(1-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}+1\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{a+b \sinh ^{-1}(c x)}{4 d \sqrt{e} \left(\sqrt{-d}-\sqrt{e} x\right)}+\frac{a+b \sinh ^{-1}(c x)}{4 d \sqrt{e} \left(\sqrt{-d}+\sqrt{e} x\right)}-\frac{b c \tan ^{-1}\left(\frac{\sqrt{e}-c^2 \sqrt{-d} x}{\sqrt{c^2 x^2+1} \sqrt{c^2 d-e}}\right)}{4 d \sqrt{e} \sqrt{c^2 d-e}}-\frac{b c \tan ^{-1}\left(\frac{c^2 \sqrt{-d} x+\sqrt{e}}{\sqrt{c^2 x^2+1} \sqrt{c^2 d-e}}\right)}{4 d \sqrt{e} \sqrt{c^2 d-e}}",1,"-(a + b*ArcSinh[c*x])/(4*d*Sqrt[e]*(Sqrt[-d] - Sqrt[e]*x)) + (a + b*ArcSinh[c*x])/(4*d*Sqrt[e]*(Sqrt[-d] + Sqrt[e]*x)) - (b*c*ArcTan[(Sqrt[e] - c^2*Sqrt[-d]*x)/(Sqrt[c^2*d - e]*Sqrt[1 + c^2*x^2])])/(4*d*Sqrt[c^2*d - e]*Sqrt[e]) - (b*c*ArcTan[(Sqrt[e] + c^2*Sqrt[-d]*x)/(Sqrt[c^2*d - e]*Sqrt[1 + c^2*x^2])])/(4*d*Sqrt[c^2*d - e]*Sqrt[e]) - ((a + b*ArcSinh[c*x])*Log[1 - (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) + e])])/(4*(-d)^(3/2)*Sqrt[e]) + ((a + b*ArcSinh[c*x])*Log[1 + (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) + e])])/(4*(-d)^(3/2)*Sqrt[e]) - ((a + b*ArcSinh[c*x])*Log[1 - (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) + e])])/(4*(-d)^(3/2)*Sqrt[e]) + ((a + b*ArcSinh[c*x])*Log[1 + (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) + e])])/(4*(-d)^(3/2)*Sqrt[e]) + (b*PolyLog[2, -((Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) + e]))])/(4*(-d)^(3/2)*Sqrt[e]) - (b*PolyLog[2, (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) + e])])/(4*(-d)^(3/2)*Sqrt[e]) + (b*PolyLog[2, -((Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) + e]))])/(4*(-d)^(3/2)*Sqrt[e]) - (b*PolyLog[2, (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) + e])])/(4*(-d)^(3/2)*Sqrt[e])","A",26,9,18,0.5000,1,"{5706, 5801, 725, 204, 5799, 5561, 2190, 2279, 2391}"
613,1,559,0,0.9657648,"\int \left(d+e x^2\right)^3 \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x^2)^3*(a + b*ArcSinh[c*x])^2,x]","-\frac{2 b d^2 e x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 c}+\frac{4 b d^2 e \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^3}-\frac{2 b d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c}-\frac{6 b d e^2 x^4 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{25 c}+\frac{8 b d e^2 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{25 c^3}-\frac{16 b d e^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{25 c^5}-\frac{2 b e^3 x^6 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{49 c}+\frac{12 b e^3 x^4 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{245 c^3}-\frac{16 b e^3 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{245 c^5}+\frac{32 b e^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{245 c^7}+d^2 e x^3 \left(a+b \sinh ^{-1}(c x)\right)^2+d^3 x \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{3}{5} d e^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{7} e^3 x^7 \left(a+b \sinh ^{-1}(c x)\right)^2-\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{2 b d^2 e x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 c}+\frac{4 b d^2 e \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^3}-\frac{2 b d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c}-\frac{6 b d e^2 x^4 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{25 c}+\frac{8 b d e^2 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{25 c^3}-\frac{16 b d e^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{25 c^5}-\frac{2 b e^3 x^6 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{49 c}+\frac{12 b e^3 x^4 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{245 c^3}-\frac{16 b e^3 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{245 c^5}+\frac{32 b e^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{245 c^7}+d^2 e x^3 \left(a+b \sinh ^{-1}(c x)\right)^2+d^3 x \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{3}{5} d e^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{7} e^3 x^7 \left(a+b \sinh ^{-1}(c x)\right)^2-\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^2*x^2]*(a + b*ArcSinh[c*x]))/c + (4*b*d^2*e*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(3*c^3) - (16*b*d*e^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(25*c^5) + (32*b*e^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(245*c^7) - (2*b*d^2*e*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(3*c) + (8*b*d*e^2*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(25*c^3) - (16*b*e^3*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(245*c^5) - (6*b*d*e^2*x^4*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(25*c) + (12*b*e^3*x^4*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(245*c^3) - (2*b*e^3*x^6*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(49*c) + d^3*x*(a + b*ArcSinh[c*x])^2 + d^2*e*x^3*(a + b*ArcSinh[c*x])^2 + (3*d*e^2*x^5*(a + b*ArcSinh[c*x])^2)/5 + (e^3*x^7*(a + b*ArcSinh[c*x])^2)/7","A",26,7,20,0.3500,1,"{5706, 5653, 5717, 8, 5661, 5758, 30}"
614,1,329,0,0.5817805,"\int \left(d+e x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x^2)^2*(a + b*ArcSinh[c*x])^2,x]","-\frac{2 b d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c}-\frac{4 b d e x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c}+\frac{8 b d e \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^3}-\frac{2 b e^2 x^4 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{25 c}+\frac{8 b e^2 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{75 c^3}-\frac{16 b e^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{75 c^5}+d^2 x \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{3} d e x^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{5} e^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)^2-\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{2 b d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c}-\frac{4 b d e x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c}+\frac{8 b d e \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^3}-\frac{2 b e^2 x^4 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{25 c}+\frac{8 b e^2 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{75 c^3}-\frac{16 b e^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{75 c^5}+d^2 x \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{2}{3} d e x^3 \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{5} e^2 x^5 \left(a+b \sinh ^{-1}(c x)\right)^2-\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^2*x^2]*(a + b*ArcSinh[c*x]))/c + (8*b*d*e*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(9*c^3) - (16*b*e^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(75*c^5) - (4*b*d*e*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(9*c) + (8*b*e^2*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(75*c^3) - (2*b*e^2*x^4*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(25*c) + d^2*x*(a + b*ArcSinh[c*x])^2 + (2*d*e*x^3*(a + b*ArcSinh[c*x])^2)/3 + (e^2*x^5*(a + b*ArcSinh[c*x])^2)/5","A",17,7,20,0.3500,1,"{5706, 5653, 5717, 8, 5661, 5758, 30}"
615,1,153,0,0.2772058,"\int \left(d+e x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x^2)*(a + b*ArcSinh[c*x])^2,x]","-\frac{2 b d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c}-\frac{2 b e x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c}+\frac{4 b e \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^3}+d x \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{3} e x^3 \left(a+b \sinh ^{-1}(c x)\right)^2-\frac{4 b^2 e x}{9 c^2}+2 b^2 d x+\frac{2}{27} b^2 e x^3","-\frac{2 b d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c}-\frac{2 b e x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c}+\frac{4 b e \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^3}+d x \left(a+b \sinh ^{-1}(c x)\right)^2+\frac{1}{3} e x^3 \left(a+b \sinh ^{-1}(c x)\right)^2-\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^2*x^2]*(a + b*ArcSinh[c*x]))/c + (4*b*e*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(9*c^3) - (2*b*e*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(9*c) + d*x*(a + b*ArcSinh[c*x])^2 + (e*x^3*(a + b*ArcSinh[c*x])^2)/3","A",10,7,18,0.3889,1,"{5706, 5653, 5717, 8, 5661, 5758, 30}"
616,1,46,0,0.0636252,"\int \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(a + b*ArcSinh[c*x])^2,x]","-\frac{2 b \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c}+x \left(a+b \sinh ^{-1}(c x)\right)^2+2 b^2 x","-\frac{2 b \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c}+x \left(a+b \sinh ^{-1}(c x)\right)^2+2 b^2 x",1,"2*b^2*x - (2*b*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/c + x*(a + b*ArcSinh[c*x])^2","A",3,3,10,0.3000,1,"{5653, 5717, 8}"
617,1,739,0,1.3150715,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d+e x^2} \, dx","Int[(a + b*ArcSinh[c*x])^2/(d + e*x^2),x]","-\frac{b \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{b \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{b \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{b \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{b^2 \text{PolyLog}\left(3,-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{b^2 \text{PolyLog}\left(3,\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{b^2 \text{PolyLog}\left(3,-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{b^2 \text{PolyLog}\left(3,\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(1-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}+1\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(1-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}+1\right)}{2 \sqrt{-d} \sqrt{e}}","-\frac{b \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{b \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{b \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{b \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(2,\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{b^2 \text{PolyLog}\left(3,-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{b^2 \text{PolyLog}\left(3,\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{b^2 \text{PolyLog}\left(3,-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}-\frac{b^2 \text{PolyLog}\left(3,\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{\sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(1-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{c \sqrt{-d}-\sqrt{e-c^2 d}}+1\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(1-\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(\frac{\sqrt{e} e^{\sinh ^{-1}(c x)}}{\sqrt{e-c^2 d}+c \sqrt{-d}}+1\right)}{2 \sqrt{-d} \sqrt{e}}",1,"((a + b*ArcSinh[c*x])^2*Log[1 - (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) + e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcSinh[c*x])^2*Log[1 + (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) + e])])/(2*Sqrt[-d]*Sqrt[e]) + ((a + b*ArcSinh[c*x])^2*Log[1 - (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) + e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcSinh[c*x])^2*Log[1 + (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) + e])])/(2*Sqrt[-d]*Sqrt[e]) - (b*(a + b*ArcSinh[c*x])*PolyLog[2, -((Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) + e]))])/(Sqrt[-d]*Sqrt[e]) + (b*(a + b*ArcSinh[c*x])*PolyLog[2, (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) + e])])/(Sqrt[-d]*Sqrt[e]) - (b*(a + b*ArcSinh[c*x])*PolyLog[2, -((Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) + e]))])/(Sqrt[-d]*Sqrt[e]) + (b*(a + b*ArcSinh[c*x])*PolyLog[2, (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) + e])])/(Sqrt[-d]*Sqrt[e]) + (b^2*PolyLog[3, -((Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) + e]))])/(Sqrt[-d]*Sqrt[e]) - (b^2*PolyLog[3, (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] - Sqrt[-(c^2*d) + e])])/(Sqrt[-d]*Sqrt[e]) + (b^2*PolyLog[3, -((Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) + e]))])/(Sqrt[-d]*Sqrt[e]) - (b^2*PolyLog[3, (Sqrt[e]*E^ArcSinh[c*x])/(c*Sqrt[-d] + Sqrt[-(c^2*d) + e])])/(Sqrt[-d]*Sqrt[e])","A",22,7,20,0.3500,1,"{5706, 5799, 5561, 2190, 2531, 2282, 6589}"
618,1,658,0,1.3443224,"\int \frac{\left(d+e x^2\right)^3}{a+b \sinh ^{-1}(c x)} \, dx","Int[(d + e*x^2)^3/(a + b*ArcSinh[c*x]),x]","-\frac{3 d^2 e \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b c^3}+\frac{3 d^2 e \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{4 b c^3}+\frac{3 d e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b c^5}-\frac{9 d e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b c^5}+\frac{3 d e^2 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b c^5}-\frac{5 e^3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{64 b c^7}+\frac{9 e^3 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{64 b c^7}-\frac{5 e^3 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{64 b c^7}+\frac{e^3 \cosh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 a}{b}+7 \sinh ^{-1}(c x)\right)}{64 b c^7}+\frac{3 d^2 e \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b c^3}-\frac{3 d^2 e \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{4 b c^3}-\frac{3 d e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b c^5}+\frac{9 d e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b c^5}-\frac{3 d e^2 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b c^5}+\frac{5 e^3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{64 b c^7}-\frac{9 e^3 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{64 b c^7}+\frac{5 e^3 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{64 b c^7}-\frac{e^3 \sinh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 a}{b}+7 \sinh ^{-1}(c x)\right)}{64 b c^7}+\frac{d^3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c}-\frac{d^3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c}","-\frac{3 d^2 e \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b c^3}+\frac{3 d^2 e \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b c^3}+\frac{3 d e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b c^5}-\frac{9 d e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^5}+\frac{3 d e^2 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^5}-\frac{5 e^3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{64 b c^7}+\frac{9 e^3 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^7}-\frac{5 e^3 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^7}+\frac{e^3 \cosh \left(\frac{7 a}{b}\right) \text{Chi}\left(\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^7}+\frac{3 d^2 e \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b c^3}-\frac{3 d^2 e \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b c^3}-\frac{3 d e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b c^5}+\frac{9 d e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^5}-\frac{3 d e^2 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^5}+\frac{5 e^3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{64 b c^7}-\frac{9 e^3 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^7}+\frac{5 e^3 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^7}-\frac{e^3 \sinh \left(\frac{7 a}{b}\right) \text{Shi}\left(\frac{7 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{64 b c^7}+\frac{d^3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c}-\frac{d^3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c}",1,"(-3*d^2*e*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(4*b*c^3) + (3*d*e^2*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(8*b*c^5) - (5*e^3*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(64*b*c^7) + (3*d^2*e*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b*c^3) - (9*d*e^2*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b*c^5) + (9*e^3*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(64*b*c^7) + (3*d*e^2*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b*c^5) - (5*e^3*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(64*b*c^7) + (e^3*Cosh[(7*a)/b]*CoshIntegral[(7*a)/b + 7*ArcSinh[c*x]])/(64*b*c^7) + (d^3*Cosh[a/b]*CoshIntegral[(a + b*ArcSinh[c*x])/b])/(b*c) + (3*d^2*e*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(4*b*c^3) - (3*d*e^2*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(8*b*c^5) + (5*e^3*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(64*b*c^7) - (3*d^2*e*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b*c^3) + (9*d*e^2*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b*c^5) - (9*e^3*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(64*b*c^7) - (3*d*e^2*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b*c^5) + (5*e^3*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(64*b*c^7) - (e^3*Sinh[(7*a)/b]*SinhIntegral[(7*a)/b + 7*ArcSinh[c*x]])/(64*b*c^7) - (d^3*Sinh[a/b]*SinhIntegral[(a + b*ArcSinh[c*x])/b])/(b*c)","A",42,7,20,0.3500,1,"{5706, 5657, 3303, 3298, 3301, 5669, 5448}"
619,1,380,0,0.7862148,"\int \frac{\left(d+e x^2\right)^2}{a+b \sinh ^{-1}(c x)} \, dx","Int[(d + e*x^2)^2/(a + b*ArcSinh[c*x]),x]","-\frac{d e \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{2 b c^3}+\frac{d e \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{2 b c^3}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b c^5}-\frac{3 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b c^5}+\frac{e^2 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b c^5}+\frac{d e \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{2 b c^3}-\frac{d e \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{2 b c^3}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b c^5}+\frac{3 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b c^5}-\frac{e^2 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b c^5}+\frac{d^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c}-\frac{d^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c}","-\frac{d e \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{2 b c^3}+\frac{d e \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b c^3}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b c^5}-\frac{3 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^5}+\frac{e^2 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^5}+\frac{d e \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{2 b c^3}-\frac{d e \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b c^3}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b c^5}+\frac{3 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^5}-\frac{e^2 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b c^5}+\frac{d^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c}-\frac{d^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c}",1,"-(d*e*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(2*b*c^3) + (e^2*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(8*b*c^5) + (d*e*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(2*b*c^3) - (3*e^2*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b*c^5) + (e^2*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b*c^5) + (d^2*Cosh[a/b]*CoshIntegral[(a + b*ArcSinh[c*x])/b])/(b*c) + (d*e*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(2*b*c^3) - (e^2*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(8*b*c^5) - (d*e*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(2*b*c^3) + (3*e^2*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b*c^5) - (e^2*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b*c^5) - (d^2*Sinh[a/b]*SinhIntegral[(a + b*ArcSinh[c*x])/b])/(b*c)","A",27,7,20,0.3500,1,"{5706, 5657, 3303, 3298, 3301, 5669, 5448}"
620,1,176,0,0.3674189,"\int \frac{d+e x^2}{a+b \sinh ^{-1}(c x)} \, dx","Int[(d + e*x^2)/(a + b*ArcSinh[c*x]),x]","-\frac{e \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b c^3}+\frac{e \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{4 b c^3}+\frac{e \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b c^3}-\frac{e \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{4 b c^3}+\frac{d \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c}-\frac{d \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c}","-\frac{e \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b c^3}+\frac{e \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b c^3}+\frac{e \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b c^3}-\frac{e \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b c^3}+\frac{d \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c}-\frac{d \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c}",1,"-(e*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(4*b*c^3) + (e*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b*c^3) + (d*Cosh[a/b]*CoshIntegral[(a + b*ArcSinh[c*x])/b])/(b*c) + (e*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(4*b*c^3) - (e*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b*c^3) - (d*Sinh[a/b]*SinhIntegral[(a + b*ArcSinh[c*x])/b])/(b*c)","A",15,7,18,0.3889,1,"{5706, 5657, 3303, 3298, 3301, 5669, 5448}"
621,1,54,0,0.0699068,"\int \frac{1}{a+b \sinh ^{-1}(c x)} \, dx","Int[(a + b*ArcSinh[c*x])^(-1),x]","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c}","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b c}",1,"(Cosh[a/b]*CoshIntegral[(a + b*ArcSinh[c*x])/b])/(b*c) - (Sinh[a/b]*SinhIntegral[(a + b*ArcSinh[c*x])/b])/(b*c)","A",4,4,10,0.4000,1,"{5657, 3303, 3298, 3301}"
622,0,0,0,0.040101,"\int \frac{1}{\left(d+e x^2\right) \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x^2)*(a + b*ArcSinh[c*x])),x]","\int \frac{1}{\left(d+e x^2\right) \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right) \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d + e*x^2)*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
623,0,0,0,0.0401727,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x^2)^2*(a + b*ArcSinh[c*x])),x]","\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d + e*x^2)^2*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
624,1,483,0,0.8745665,"\int \frac{\left(d+e x^2\right)^2}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(d + e*x^2)^2/(a + b*ArcSinh[c*x])^2,x]","\frac{d e \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{2 b^2 c^3}-\frac{3 d e \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{2 b^2 c^3}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b^2 c^5}+\frac{9 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b^2 c^5}-\frac{5 e^2 \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b^2 c^5}-\frac{d e \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{2 b^2 c^3}+\frac{3 d e \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{2 b^2 c^3}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{8 b^2 c^5}-\frac{9 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{16 b^2 c^5}+\frac{5 e^2 \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c x)\right)}{16 b^2 c^5}-\frac{d^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b^2 c}+\frac{d^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b^2 c}-\frac{d^2 \sqrt{c^2 x^2+1}}{b c \left(a+b \sinh ^{-1}(c x)\right)}-\frac{2 d e x^2 \sqrt{c^2 x^2+1}}{b c \left(a+b \sinh ^{-1}(c x)\right)}-\frac{e^2 x^4 \sqrt{c^2 x^2+1}}{b c \left(a+b \sinh ^{-1}(c x)\right)}","\frac{d e \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{2 b^2 c^3}-\frac{3 d e \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^3}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b^2 c^5}+\frac{9 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^5}-\frac{5 e^2 \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^5}-\frac{d e \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{2 b^2 c^3}+\frac{3 d e \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{2 b^2 c^3}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{8 b^2 c^5}-\frac{9 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^5}+\frac{5 e^2 \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{16 b^2 c^5}-\frac{d^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b^2 c}+\frac{d^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{d^2 \sqrt{c^2 x^2+1}}{b c \left(a+b \sinh ^{-1}(c x)\right)}-\frac{2 d e x^2 \sqrt{c^2 x^2+1}}{b c \left(a+b \sinh ^{-1}(c x)\right)}-\frac{e^2 x^4 \sqrt{c^2 x^2+1}}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-((d^2*Sqrt[1 + c^2*x^2])/(b*c*(a + b*ArcSinh[c*x]))) - (2*d*e*x^2*Sqrt[1 + c^2*x^2])/(b*c*(a + b*ArcSinh[c*x])) - (e^2*x^4*Sqrt[1 + c^2*x^2])/(b*c*(a + b*ArcSinh[c*x])) - (d^2*CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(b^2*c) + (d*e*CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(2*b^2*c^3) - (e^2*CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(8*b^2*c^5) - (3*d*e*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]]*Sinh[(3*a)/b])/(2*b^2*c^3) + (9*e^2*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]]*Sinh[(3*a)/b])/(16*b^2*c^5) - (5*e^2*CoshIntegral[(5*a)/b + 5*ArcSinh[c*x]]*Sinh[(5*a)/b])/(16*b^2*c^5) + (d^2*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(b^2*c) - (d*e*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(2*b^2*c^3) + (e^2*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(8*b^2*c^5) + (3*d*e*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(2*b^2*c^3) - (9*e^2*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(16*b^2*c^5) + (5*e^2*Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c*x]])/(16*b^2*c^5)","A",26,7,20,0.3500,1,"{5706, 5655, 5779, 3303, 3298, 3301, 5665}"
625,1,239,0,0.47568,"\int \frac{d+e x^2}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(d + e*x^2)/(a + b*ArcSinh[c*x])^2,x]","\frac{e \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b^2 c^3}-\frac{3 e \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{4 b^2 c^3}-\frac{e \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b^2 c^3}+\frac{3 e \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c x)\right)}{4 b^2 c^3}-\frac{d \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b^2 c}+\frac{d \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b^2 c}-\frac{d \sqrt{c^2 x^2+1}}{b c \left(a+b \sinh ^{-1}(c x)\right)}-\frac{e x^2 \sqrt{c^2 x^2+1}}{b c \left(a+b \sinh ^{-1}(c x)\right)}","\frac{e \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b^2 c^3}-\frac{3 e \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^3}-\frac{e \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{4 b^2 c^3}+\frac{3 e \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^3}-\frac{d \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b^2 c}+\frac{d \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{d \sqrt{c^2 x^2+1}}{b c \left(a+b \sinh ^{-1}(c x)\right)}-\frac{e x^2 \sqrt{c^2 x^2+1}}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-((d*Sqrt[1 + c^2*x^2])/(b*c*(a + b*ArcSinh[c*x]))) - (e*x^2*Sqrt[1 + c^2*x^2])/(b*c*(a + b*ArcSinh[c*x])) - (d*CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(b^2*c) + (e*CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(4*b^2*c^3) - (3*e*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]]*Sinh[(3*a)/b])/(4*b^2*c^3) + (d*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(b^2*c) - (e*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(4*b^2*c^3) + (3*e*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b^2*c^3)","A",15,7,18,0.3889,1,"{5706, 5655, 5779, 3303, 3298, 3301, 5665}"
626,1,81,0,0.1880532,"\int \frac{1}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(a + b*ArcSinh[c*x])^(-2),x]","-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b^2 c}+\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b^2 c}-\frac{\sqrt{c^2 x^2+1}}{b c \left(a+b \sinh ^{-1}(c x)\right)}","-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b^2 c}+\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{\sqrt{c^2 x^2+1}}{b c \left(a+b \sinh ^{-1}(c x)\right)}",1,"-(Sqrt[1 + c^2*x^2]/(b*c*(a + b*ArcSinh[c*x]))) - (CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(b^2*c) + (Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(b^2*c)","A",5,5,10,0.5000,1,"{5655, 5779, 3303, 3298, 3301}"
627,0,0,0,0.0382917,"\int \frac{1}{\left(d+e x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[1/((d + e*x^2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{1}{\left(d+e x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/((d + e*x^2)*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
628,0,0,0,0.0372013,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[1/((d + e*x^2)^2*(a + b*ArcSinh[c*x])^2),x]","\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/((d + e*x^2)^2*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
629,1,672,0,1.8787994,"\int \left(d+e x^2\right)^2 \sqrt{a+b \sinh ^{-1}(c x)} \, dx","Int[(d + e*x^2)^2*Sqrt[a + b*ArcSinh[c*x]],x]","-\frac{\sqrt{\pi } \sqrt{b} d e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+d^2 x \sqrt{a+b \sinh ^{-1}(c x)}+\frac{2}{3} d e x^3 \sqrt{a+b \sinh ^{-1}(c x)}+\frac{1}{5} e^2 x^5 \sqrt{a+b \sinh ^{-1}(c x)}","-\frac{\sqrt{\pi } \sqrt{b} d e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+d^2 x \sqrt{a+b \sinh ^{-1}(c x)}+\frac{2}{3} d e x^3 \sqrt{a+b \sinh ^{-1}(c x)}+\frac{1}{5} e^2 x^5 \sqrt{a+b \sinh ^{-1}(c x)}",1,"d^2*x*Sqrt[a + b*ArcSinh[c*x]] + (2*d*e*x^3*Sqrt[a + b*ArcSinh[c*x]])/3 + (e^2*x^5*Sqrt[a + b*ArcSinh[c*x]])/5 + (Sqrt[b]*d^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(4*c) - (Sqrt[b]*d*e*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(8*c^3) + (Sqrt[b]*e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(32*c^5) + (Sqrt[b]*d*e*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(24*c^3) - (Sqrt[b]*e^2*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(64*c^5) + (Sqrt[b]*e^2*E^((5*a)/b)*Sqrt[Pi/5]*Erf[(Sqrt[5]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(320*c^5) - (Sqrt[b]*d^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(4*c*E^(a/b)) + (Sqrt[b]*d*e*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(8*c^3*E^(a/b)) - (Sqrt[b]*e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(32*c^5*E^(a/b)) - (Sqrt[b]*d*e*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(24*c^3*E^((3*a)/b)) + (Sqrt[b]*e^2*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(64*c^5*E^((3*a)/b)) - (Sqrt[b]*e^2*Sqrt[Pi/5]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(320*c^5*E^((5*a)/b))","A",42,9,22,0.4091,1,"{5706, 5653, 5779, 3308, 2180, 2204, 2205, 5663, 3312}"
630,1,322,0,0.9316099,"\int \left(d+e x^2\right) \sqrt{a+b \sinh ^{-1}(c x)} \, dx","Int[(d + e*x^2)*Sqrt[a + b*ArcSinh[c*x]],x]","-\frac{\sqrt{\pi } \sqrt{b} e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+d x \sqrt{a+b \sinh ^{-1}(c x)}+\frac{1}{3} e x^3 \sqrt{a+b \sinh ^{-1}(c x)}","-\frac{\sqrt{\pi } \sqrt{b} e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+d x \sqrt{a+b \sinh ^{-1}(c x)}+\frac{1}{3} e x^3 \sqrt{a+b \sinh ^{-1}(c x)}",1,"d*x*Sqrt[a + b*ArcSinh[c*x]] + (e*x^3*Sqrt[a + b*ArcSinh[c*x]])/3 + (Sqrt[b]*d*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(4*c) - (Sqrt[b]*e*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(16*c^3) + (Sqrt[b]*e*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(48*c^3) - (Sqrt[b]*d*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(4*c*E^(a/b)) + (Sqrt[b]*e*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(16*c^3*E^(a/b)) - (Sqrt[b]*e*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(48*c^3*E^((3*a)/b))","A",23,9,20,0.4500,1,"{5706, 5653, 5779, 3308, 2180, 2204, 2205, 5663, 3312}"
631,1,102,0,0.2601218,"\int \sqrt{a+b \sinh ^{-1}(c x)} \, dx","Int[Sqrt[a + b*ArcSinh[c*x]],x]","\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}-\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+x \sqrt{a+b \sinh ^{-1}(c x)}","\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}-\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{4 c}+x \sqrt{a+b \sinh ^{-1}(c x)}",1,"x*Sqrt[a + b*ArcSinh[c*x]] + (Sqrt[b]*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(4*c) - (Sqrt[b]*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(4*c*E^(a/b))","A",7,6,12,0.5000,1,"{5653, 5779, 3308, 2180, 2204, 2205}"
632,0,0,0,0.0564397,"\int \frac{\sqrt{a+b \sinh ^{-1}(c x)}}{d+e x^2} \, dx","Int[Sqrt[a + b*ArcSinh[c*x]]/(d + e*x^2),x]","\int \frac{\sqrt{a+b \sinh ^{-1}(c x)}}{d+e x^2} \, dx","\text{Int}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{d+e x^2},x\right)",0,"Defer[Int][Sqrt[a + b*ArcSinh[c*x]]/(d + e*x^2), x]","A",0,0,0,0,-1,"{}"
633,0,0,0,0.0539159,"\int \frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\left(d+e x^2\right)^2} \, dx","Int[Sqrt[a + b*ArcSinh[c*x]]/(d + e*x^2)^2,x]","\int \frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\left(d+e x^2\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\left(d+e x^2\right)^2},x\right)",0,"Defer[Int][Sqrt[a + b*ArcSinh[c*x]]/(d + e*x^2)^2, x]","A",0,0,0,0,-1,"{}"
634,1,427,0,1.2636959,"\int \left(d+e x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^{3/2} \, dx","Int[(d + e*x^2)*(a + b*ArcSinh[c*x])^(3/2),x]","-\frac{3 \sqrt{\pi } b^{3/2} e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}-\frac{3 b d \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-1}(c x)}}{2 c}-\frac{b e x^2 \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-1}(c x)}}{6 c}+\frac{b e \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-1}(c x)}}{3 c^3}+d x \left(a+b \sinh ^{-1}(c x)\right)^{3/2}+\frac{1}{3} e x^3 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}","-\frac{3 \sqrt{\pi } b^{3/2} e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}-\frac{3 b d \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-1}(c x)}}{2 c}-\frac{b e x^2 \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-1}(c x)}}{6 c}+\frac{b e \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-1}(c x)}}{3 c^3}+d x \left(a+b \sinh ^{-1}(c x)\right)^{3/2}+\frac{1}{3} e x^3 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}",1,"(-3*b*d*Sqrt[1 + c^2*x^2]*Sqrt[a + b*ArcSinh[c*x]])/(2*c) + (b*e*Sqrt[1 + c^2*x^2]*Sqrt[a + b*ArcSinh[c*x]])/(3*c^3) - (b*e*x^2*Sqrt[1 + c^2*x^2]*Sqrt[a + b*ArcSinh[c*x]])/(6*c) + d*x*(a + b*ArcSinh[c*x])^(3/2) + (e*x^3*(a + b*ArcSinh[c*x])^(3/2))/3 + (3*b^(3/2)*d*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(8*c) - (3*b^(3/2)*e*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(32*c^3) + (b^(3/2)*e*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(96*c^3) + (3*b^(3/2)*d*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(8*c*E^(a/b)) - (3*b^(3/2)*e*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(32*c^3*E^(a/b)) + (b^(3/2)*e*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(96*c^3*E^((3*a)/b))","A",32,12,20,0.6000,1,"{5706, 5653, 5717, 5657, 3307, 2180, 2205, 2204, 5663, 5758, 5669, 5448}"
635,1,135,0,0.2511941,"\int \left(a+b \sinh ^{-1}(c x)\right)^{3/2} \, dx","Int[(a + b*ArcSinh[c*x])^(3/2),x]","\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}-\frac{3 b \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-1}(c x)}}{2 c}+x \left(a+b \sinh ^{-1}(c x)\right)^{3/2}","\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{8 c}-\frac{3 b \sqrt{c^2 x^2+1} \sqrt{a+b \sinh ^{-1}(c x)}}{2 c}+x \left(a+b \sinh ^{-1}(c x)\right)^{3/2}",1,"(-3*b*Sqrt[1 + c^2*x^2]*Sqrt[a + b*ArcSinh[c*x]])/(2*c) + x*(a + b*ArcSinh[c*x])^(3/2) + (3*b^(3/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(8*c) + (3*b^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(8*c*E^(a/b))","A",8,7,12,0.5833,1,"{5653, 5717, 5657, 3307, 2180, 2205, 2204}"
636,0,0,0,0.0654058,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}}{d+e x^2} \, dx","Int[(a + b*ArcSinh[c*x])^(3/2)/(d + e*x^2),x]","\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}}{d+e x^2} \, dx","\text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}}{d+e x^2},x\right)",0,"Defer[Int][(a + b*ArcSinh[c*x])^(3/2)/(d + e*x^2), x]","A",0,0,0,0,-1,"{}"
637,0,0,0,0.0645926,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}}{\left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcSinh[c*x])^(3/2)/(d + e*x^2)^2,x]","\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}}{\left(d+e x^2\right)^2} \, dx","\text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}}{\left(d+e x^2\right)^2},x\right)",0,"Defer[Int][(a + b*ArcSinh[c*x])^(3/2)/(d + e*x^2)^2, x]","A",0,0,0,0,-1,"{}"
638,1,608,0,1.1951729,"\int \frac{\left(d+e x^2\right)^2}{\sqrt{a+b \sinh ^{-1}(c x)}} \, dx","Int[(d + e*x^2)^2/Sqrt[a + b*ArcSinh[c*x]],x]","-\frac{\sqrt{\pi } d e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}",1,"(d^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(2*Sqrt[b]*c) - (d*e*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(4*Sqrt[b]*c^3) + (e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(16*Sqrt[b]*c^5) + (d*e*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(4*Sqrt[b]*c^3) - (e^2*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(32*Sqrt[b]*c^5) + (e^2*E^((5*a)/b)*Sqrt[Pi/5]*Erf[(Sqrt[5]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(32*Sqrt[b]*c^5) + (d^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(2*Sqrt[b]*c*E^(a/b)) - (d*e*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(4*Sqrt[b]*c^3*E^(a/b)) + (e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(16*Sqrt[b]*c^5*E^(a/b)) + (d*e*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(4*Sqrt[b]*c^3*E^((3*a)/b)) - (e^2*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(32*Sqrt[b]*c^5*E^((3*a)/b)) + (e^2*Sqrt[Pi/5]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(32*Sqrt[b]*c^5*E^((5*a)/b))","A",39,8,22,0.3636,1,"{5706, 5657, 3307, 2180, 2205, 2204, 5669, 5448}"
639,1,287,0,0.5717432,"\int \frac{d+e x^2}{\sqrt{a+b \sinh ^{-1}(c x)}} \, dx","Int[(d + e*x^2)/Sqrt[a + b*ArcSinh[c*x]],x]","-\frac{\sqrt{\pi } e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}","-\frac{\sqrt{\pi } e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}",1,"(d*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(2*Sqrt[b]*c) - (e*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(8*Sqrt[b]*c^3) + (e*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(8*Sqrt[b]*c^3) + (d*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(2*Sqrt[b]*c*E^(a/b)) - (e*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(8*Sqrt[b]*c^3*E^(a/b)) + (e*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(8*Sqrt[b]*c^3*E^((3*a)/b))","A",21,8,20,0.4000,1,"{5706, 5657, 3307, 2180, 2205, 2204, 5669, 5448}"
640,1,88,0,0.1070282,"\int \frac{1}{\sqrt{a+b \sinh ^{-1}(c x)}} \, dx","Int[1/Sqrt[a + b*ArcSinh[c*x]],x]","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{2 \sqrt{b} c}",1,"(E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(2*Sqrt[b]*c) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(2*Sqrt[b]*c*E^(a/b))","A",6,5,12,0.4167,1,"{5657, 3307, 2180, 2205, 2204}"
641,0,0,0,0.0601469,"\int \frac{1}{\left(d+e x^2\right) \sqrt{a+b \sinh ^{-1}(c x)}} \, dx","Int[1/((d + e*x^2)*Sqrt[a + b*ArcSinh[c*x]]),x]","\int \frac{1}{\left(d+e x^2\right) \sqrt{a+b \sinh ^{-1}(c x)}} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right) \sqrt{a+b \sinh ^{-1}(c x)}},x\right)",0,"Defer[Int][1/((d + e*x^2)*Sqrt[a + b*ArcSinh[c*x]]), x]","A",0,0,0,0,-1,"{}"
642,0,0,0,0.0570992,"\int \frac{1}{\left(d+e x^2\right)^2 \sqrt{a+b \sinh ^{-1}(c x)}} \, dx","Int[1/((d + e*x^2)^2*Sqrt[a + b*ArcSinh[c*x]]),x]","\int \frac{1}{\left(d+e x^2\right)^2 \sqrt{a+b \sinh ^{-1}(c x)}} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^2 \sqrt{a+b \sinh ^{-1}(c x)}},x\right)",0,"Defer[Int][1/((d + e*x^2)^2*Sqrt[a + b*ArcSinh[c*x]]), x]","A",0,0,0,0,-1,"{}"
643,1,349,0,0.6912727,"\int \frac{d+e x^2}{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(d + e*x^2)/(a + b*ArcSinh[c*x])^(3/2),x]","\frac{\sqrt{\pi } e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 d \sqrt{c^2 x^2+1}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{2 e x^2 \sqrt{c^2 x^2+1}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}","\frac{\sqrt{\pi } e e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-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 \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 d \sqrt{c^2 x^2+1}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}-\frac{2 e x^2 \sqrt{c^2 x^2+1}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}",1,"(-2*d*Sqrt[1 + c^2*x^2])/(b*c*Sqrt[a + b*ArcSinh[c*x]]) - (2*e*x^2*Sqrt[1 + c^2*x^2])/(b*c*Sqrt[a + b*ArcSinh[c*x]]) - (d*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(b^(3/2)*c) + (e*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(4*b^(3/2)*c^3) - (e*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c^3) + (d*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(b^(3/2)*c*E^(a/b)) - (e*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(4*b^(3/2)*c^3*E^(a/b)) + (e*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c*x]])/Sqrt[b]])/(4*b^(3/2)*c^3*E^((3*a)/b))","A",21,8,20,0.4000,1,"{5706, 5655, 5779, 3308, 2180, 2204, 2205, 5665}"
644,1,116,0,0.2511649,"\int \frac{1}{\left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])^(-3/2),x]","-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{c^2 x^2+1}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}","-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c x)}}{\sqrt{b}}\right)}{b^{3/2} c}-\frac{2 \sqrt{c^2 x^2+1}}{b c \sqrt{a+b \sinh ^{-1}(c x)}}",1,"(-2*Sqrt[1 + c^2*x^2])/(b*c*Sqrt[a + b*ArcSinh[c*x]]) - (E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(b^(3/2)*c) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c*x]]/Sqrt[b]])/(b^(3/2)*c*E^(a/b))","A",7,6,12,0.5000,1,"{5655, 5779, 3308, 2180, 2204, 2205}"
645,0,0,0,0.0673352,"\int \frac{1}{\left(d+e x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[1/((d + e*x^2)*(a + b*ArcSinh[c*x])^(3/2)),x]","\int \frac{1}{\left(d+e x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right) \left(a+b \sinh ^{-1}(c x)\right)^{3/2}},x\right)",0,"Defer[Int][1/((d + e*x^2)*(a + b*ArcSinh[c*x])^(3/2)), x]","A",0,0,0,0,-1,"{}"
646,0,0,0,0.0652315,"\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","Int[1/((d + e*x^2)^2*(a + b*ArcSinh[c*x])^(3/2)),x]","\int \frac{1}{\left(d+e x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^{3/2}},x\right)",0,"Defer[Int][1/((d + e*x^2)^2*(a + b*ArcSinh[c*x])^(3/2)), x]","A",0,0,0,0,-1,"{}"
647,0,0,0,0.0231611,"\int \sqrt{d+e x^2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[Sqrt[d + e*x^2]*(a + b*ArcSinh[c*x]),x]","\int \sqrt{d+e x^2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","\text{Int}\left(\sqrt{d+e x^2} \left(a+b \sinh ^{-1}(c x)\right),x\right)",0,"Defer[Int][Sqrt[d + e*x^2]*(a + b*ArcSinh[c*x]), x]","A",0,0,0,0,-1,"{}"
648,0,0,0,0.0245021,"\int \frac{a+b \sinh ^{-1}(c x)}{\sqrt{d+e x^2}} \, dx","Int[(a + b*ArcSinh[c*x])/Sqrt[d + e*x^2],x]","\int \frac{a+b \sinh ^{-1}(c x)}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{a+b \sinh ^{-1}(c x)}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcSinh[c*x])/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
649,1,70,0,0.1010969,"\int \frac{a+b \sinh ^{-1}(c x)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(d + e*x^2)^(3/2),x]","\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{d+e x^2}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2+1}}{c \sqrt{d+e x^2}}\right)}{d \sqrt{e}}","\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{d \sqrt{d+e x^2}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2+1}}{c \sqrt{d+e x^2}}\right)}{d \sqrt{e}}",1,"(x*(a + b*ArcSinh[c*x]))/(d*Sqrt[d + e*x^2]) - (b*ArcTanh[(Sqrt[e]*Sqrt[1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(d*Sqrt[e])","A",6,7,20,0.3500,1,"{191, 5704, 12, 444, 63, 217, 206}"
650,1,146,0,0.1687816,"\int \frac{a+b \sinh ^{-1}(c x)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(d + e*x^2)^(5/2),x]","\frac{2 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{d+e x^2}}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}-\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2+1}}{c \sqrt{d+e x^2}}\right)}{3 d^2 \sqrt{e}}-\frac{b c \sqrt{c^2 x^2+1}}{3 d \left(c^2 d-e\right) \sqrt{d+e x^2}}","\frac{2 x \left(a+b \sinh ^{-1}(c x)\right)}{3 d^2 \sqrt{d+e x^2}}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}-\frac{2 b \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2+1}}{c \sqrt{d+e x^2}}\right)}{3 d^2 \sqrt{e}}-\frac{b c \sqrt{c^2 x^2+1}}{3 d \left(c^2 d-e\right) \sqrt{d+e x^2}}",1,"-(b*c*Sqrt[1 + c^2*x^2])/(3*d*(c^2*d - e)*Sqrt[d + e*x^2]) + (x*(a + b*ArcSinh[c*x]))/(3*d*(d + e*x^2)^(3/2)) + (2*x*(a + b*ArcSinh[c*x]))/(3*d^2*Sqrt[d + e*x^2]) - (2*b*ArcTanh[(Sqrt[e]*Sqrt[1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(3*d^2*Sqrt[e])","A",7,9,20,0.4500,1,"{192, 191, 5704, 12, 571, 78, 63, 217, 206}"
651,1,227,0,0.82047,"\int \frac{a+b \sinh ^{-1}(c x)}{\left(d+e x^2\right)^{7/2}} \, dx","Int[(a + b*ArcSinh[c*x])/(d + e*x^2)^(7/2),x]","\frac{8 x \left(a+b \sinh ^{-1}(c x)\right)}{15 d^3 \sqrt{d+e x^2}}+\frac{4 x \left(a+b \sinh ^{-1}(c x)\right)}{15 d^2 \left(d+e x^2\right)^{3/2}}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{5 d \left(d+e x^2\right)^{5/2}}-\frac{2 b c \sqrt{c^2 x^2+1} \left(3 c^2 d-2 e\right)}{15 d^2 \left(c^2 d-e\right)^2 \sqrt{d+e x^2}}-\frac{8 b \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2+1}}{c \sqrt{d+e x^2}}\right)}{15 d^3 \sqrt{e}}-\frac{b c \sqrt{c^2 x^2+1}}{15 d \left(c^2 d-e\right) \left(d+e x^2\right)^{3/2}}","\frac{8 x \left(a+b \sinh ^{-1}(c x)\right)}{15 d^3 \sqrt{d+e x^2}}+\frac{4 x \left(a+b \sinh ^{-1}(c x)\right)}{15 d^2 \left(d+e x^2\right)^{3/2}}+\frac{x \left(a+b \sinh ^{-1}(c x)\right)}{5 d \left(d+e x^2\right)^{5/2}}-\frac{2 b c \sqrt{c^2 x^2+1} \left(3 c^2 d-2 e\right)}{15 d^2 \left(c^2 d-e\right)^2 \sqrt{d+e x^2}}-\frac{8 b \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2+1}}{c \sqrt{d+e x^2}}\right)}{15 d^3 \sqrt{e}}-\frac{b c \sqrt{c^2 x^2+1}}{15 d \left(c^2 d-e\right) \left(d+e x^2\right)^{3/2}}",1,"-(b*c*Sqrt[1 + c^2*x^2])/(15*d*(c^2*d - e)*(d + e*x^2)^(3/2)) - (2*b*c*(3*c^2*d - 2*e)*Sqrt[1 + c^2*x^2])/(15*d^2*(c^2*d - e)^2*Sqrt[d + e*x^2]) + (x*(a + b*ArcSinh[c*x]))/(5*d*(d + e*x^2)^(5/2)) + (4*x*(a + b*ArcSinh[c*x]))/(15*d^2*(d + e*x^2)^(3/2)) + (8*x*(a + b*ArcSinh[c*x]))/(15*d^3*Sqrt[d + e*x^2]) - (8*b*ArcTanh[(Sqrt[e]*Sqrt[1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(15*d^3*Sqrt[e])","A",8,10,20,0.5000,1,"{192, 191, 5704, 12, 6715, 949, 78, 63, 217, 206}"
652,0,0,0,0.0420453,"\int \sqrt{d+e x^2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[Sqrt[d + e*x^2]*(a + b*ArcSinh[c*x])^2,x]","\int \sqrt{d+e x^2} \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","\text{Int}\left(\sqrt{d+e x^2} \left(a+b \sinh ^{-1}(c x)\right)^2,x\right)",0,"Defer[Int][Sqrt[d + e*x^2]*(a + b*ArcSinh[c*x])^2, x]","A",0,0,0,0,-1,"{}"
653,0,0,0,0.0448606,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+e x^2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/Sqrt[d + e*x^2],x]","\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcSinh[c*x])^2/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
654,0,0,0,0.0490404,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(d + e*x^2)^(3/2),x]","\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(a + b*ArcSinh[c*x])^2/(d + e*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
655,0,0,0,0.0475373,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c*x])^2/(d + e*x^2)^(5/2),x]","\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{\left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(a + b*ArcSinh[c*x])^2/(d + e*x^2)^(5/2), x]","A",0,0,0,0,-1,"{}"
656,0,0,0,0.0472286,"\int \frac{\sqrt{d+e x^2}}{a+b \sinh ^{-1}(c x)} \, dx","Int[Sqrt[d + e*x^2]/(a + b*ArcSinh[c*x]),x]","\int \frac{\sqrt{d+e x^2}}{a+b \sinh ^{-1}(c x)} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2}}{a+b \sinh ^{-1}(c x)},x\right)",0,"Defer[Int][Sqrt[d + e*x^2]/(a + b*ArcSinh[c*x]), x]","A",0,0,0,0,-1,"{}"
657,0,0,0,0.0498483,"\int \frac{1}{\sqrt{d+e x^2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[1/(Sqrt[d + e*x^2]*(a + b*ArcSinh[c*x])),x]","\int \frac{1}{\sqrt{d+e x^2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\sqrt{d+e x^2} \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(Sqrt[d + e*x^2]*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
658,0,0,0,0.0542436,"\int \frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x^2)^(3/2)*(a + b*ArcSinh[c*x])),x]","\int \frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d + e*x^2)^(3/2)*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
659,0,0,0,0.053293,"\int \frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x^2)^(5/2)*(a + b*ArcSinh[c*x])),x]","\int \frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d + e*x^2)^(5/2)*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
660,0,0,0,0.04383,"\int \frac{\sqrt{d+e x^2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[Sqrt[d + e*x^2]/(a + b*ArcSinh[c*x])^2,x]","\int \frac{\sqrt{d+e x^2}}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2}}{\left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][Sqrt[d + e*x^2]/(a + b*ArcSinh[c*x])^2, x]","A",0,0,0,0,-1,"{}"
661,0,0,0,0.0473418,"\int \frac{1}{\sqrt{d+e x^2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[1/(Sqrt[d + e*x^2]*(a + b*ArcSinh[c*x])^2),x]","\int \frac{1}{\sqrt{d+e x^2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\sqrt{d+e x^2} \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/(Sqrt[d + e*x^2]*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
662,0,0,0,0.0514789,"\int \frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[1/((d + e*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/((d + e*x^2)^(3/2)*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
663,0,0,0,0.0500434,"\int \frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[1/((d + e*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(d+e x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/((d + e*x^2)^(5/2)*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"