1,1,170,0,0.2642924,"\int \frac{\sinh ^{-1}(c x)}{d+e x} \, dx","Int[ArcSinh[c*x]/(d + e*x),x]","\frac{\text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}+\frac{\text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}+\frac{\sinh ^{-1}(c x) \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}+1\right)}{e}+\frac{\sinh ^{-1}(c x) \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}+1\right)}{e}-\frac{\sinh ^{-1}(c x)^2}{2 e}","\frac{\text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}+\frac{\text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}+\frac{\sinh ^{-1}(c x) \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}+1\right)}{e}+\frac{\sinh ^{-1}(c x) \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}+1\right)}{e}-\frac{\sinh ^{-1}(c x)^2}{2 e}",1,"-ArcSinh[c*x]^2/(2*e) + (ArcSinh[c*x]*Log[1 + (e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2])])/e + (ArcSinh[c*x]*Log[1 + (e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2])])/e + PolyLog[2, -((e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2]))]/e + PolyLog[2, -((e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2]))]/e","A",8,5,12,0.4167,1,"{5799, 5561, 2190, 2279, 2391}"
2,1,260,0,0.4049466,"\int \frac{\sinh ^{-1}(c x)^2}{d+e x} \, dx","Int[ArcSinh[c*x]^2/(d + e*x),x]","\frac{2 \sinh ^{-1}(c x) \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}+\frac{2 \sinh ^{-1}(c x) \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}-\frac{2 \text{PolyLog}\left(3,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}-\frac{2 \text{PolyLog}\left(3,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}+\frac{\sinh ^{-1}(c x)^2 \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}+1\right)}{e}+\frac{\sinh ^{-1}(c x)^2 \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}+1\right)}{e}-\frac{\sinh ^{-1}(c x)^3}{3 e}","\frac{2 \sinh ^{-1}(c x) \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}+\frac{2 \sinh ^{-1}(c x) \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}-\frac{2 \text{PolyLog}\left(3,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}-\frac{2 \text{PolyLog}\left(3,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}+\frac{\sinh ^{-1}(c x)^2 \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}+1\right)}{e}+\frac{\sinh ^{-1}(c x)^2 \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}+1\right)}{e}-\frac{\sinh ^{-1}(c x)^3}{3 e}",1,"-ArcSinh[c*x]^3/(3*e) + (ArcSinh[c*x]^2*Log[1 + (e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2])])/e + (ArcSinh[c*x]^2*Log[1 + (e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2])])/e + (2*ArcSinh[c*x]*PolyLog[2, -((e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2]))])/e + (2*ArcSinh[c*x]*PolyLog[2, -((e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2]))])/e - (2*PolyLog[3, -((e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2]))])/e - (2*PolyLog[3, -((e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2]))])/e","A",10,6,14,0.4286,1,"{5799, 5561, 2190, 2531, 2282, 6589}"
3,1,348,0,0.4331447,"\int \frac{\sinh ^{-1}(c x)^3}{d+e x} \, dx","Int[ArcSinh[c*x]^3/(d + e*x),x]","\frac{3 \sinh ^{-1}(c x)^2 \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}+\frac{3 \sinh ^{-1}(c x)^2 \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}-\frac{6 \sinh ^{-1}(c x) \text{PolyLog}\left(3,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}-\frac{6 \sinh ^{-1}(c x) \text{PolyLog}\left(3,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}+\frac{6 \text{PolyLog}\left(4,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}+\frac{6 \text{PolyLog}\left(4,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}+\frac{\sinh ^{-1}(c x)^3 \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}+1\right)}{e}+\frac{\sinh ^{-1}(c x)^3 \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}+1\right)}{e}-\frac{\sinh ^{-1}(c x)^4}{4 e}","\frac{3 \sinh ^{-1}(c x)^2 \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}+\frac{3 \sinh ^{-1}(c x)^2 \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}-\frac{6 \sinh ^{-1}(c x) \text{PolyLog}\left(3,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}-\frac{6 \sinh ^{-1}(c x) \text{PolyLog}\left(3,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}+\frac{6 \text{PolyLog}\left(4,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}+\frac{6 \text{PolyLog}\left(4,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}+\frac{\sinh ^{-1}(c x)^3 \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}+1\right)}{e}+\frac{\sinh ^{-1}(c x)^3 \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}+1\right)}{e}-\frac{\sinh ^{-1}(c x)^4}{4 e}",1,"-ArcSinh[c*x]^4/(4*e) + (ArcSinh[c*x]^3*Log[1 + (e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2])])/e + (ArcSinh[c*x]^3*Log[1 + (e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2])])/e + (3*ArcSinh[c*x]^2*PolyLog[2, -((e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2]))])/e + (3*ArcSinh[c*x]^2*PolyLog[2, -((e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2]))])/e - (6*ArcSinh[c*x]*PolyLog[3, -((e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2]))])/e - (6*ArcSinh[c*x]*PolyLog[3, -((e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2]))])/e + (6*PolyLog[4, -((e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2]))])/e + (6*PolyLog[4, -((e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2]))])/e","A",12,7,14,0.5000,1,"{5799, 5561, 2190, 2531, 6609, 2282, 6589}"
4,1,176,0,0.1701854,"\int (d+e x)^3 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + e*x)^3*(a + b*ArcSinh[c*x]),x]","\frac{(d+e x)^4 \left(a+b \sinh ^{-1}(c x)\right)}{4 e}-\frac{b \sqrt{c^2 x^2+1} \left(e x \left(26 c^2 d^2-9 e^2\right)+4 d \left(19 c^2 d^2-16 e^2\right)\right)}{96 c^3}-\frac{b \left(-24 c^2 d^2 e^2+8 c^4 d^4+3 e^4\right) \sinh ^{-1}(c x)}{32 c^4 e}-\frac{b \sqrt{c^2 x^2+1} (d+e x)^3}{16 c}-\frac{7 b d \sqrt{c^2 x^2+1} (d+e x)^2}{48 c}","\frac{(d+e x)^4 \left(a+b \sinh ^{-1}(c x)\right)}{4 e}-\frac{b \sqrt{c^2 x^2+1} \left(e x \left(26 c^2 d^2-9 e^2\right)+4 d \left(19 c^2 d^2-16 e^2\right)\right)}{96 c^3}-\frac{b \left(-24 c^2 d^2 e^2+8 c^4 d^4+3 e^4\right) \sinh ^{-1}(c x)}{32 c^4 e}-\frac{b \sqrt{c^2 x^2+1} (d+e x)^3}{16 c}-\frac{7 b d \sqrt{c^2 x^2+1} (d+e x)^2}{48 c}",1,"(-7*b*d*(d + e*x)^2*Sqrt[1 + c^2*x^2])/(48*c) - (b*(d + e*x)^3*Sqrt[1 + c^2*x^2])/(16*c) - (b*(4*d*(19*c^2*d^2 - 16*e^2) + e*(26*c^2*d^2 - 9*e^2)*x)*Sqrt[1 + c^2*x^2])/(96*c^3) - (b*(8*c^4*d^4 - 24*c^2*d^2*e^2 + 3*e^4)*ArcSinh[c*x])/(32*c^4*e) + ((d + e*x)^4*(a + b*ArcSinh[c*x]))/(4*e)","A",5,5,16,0.3125,1,"{5801, 743, 833, 780, 215}"
5,1,124,0,0.0957302,"\int (d+e x)^2 \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + e*x)^2*(a + b*ArcSinh[c*x]),x]","\frac{(d+e x)^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 e}-\frac{b \sqrt{c^2 x^2+1} \left(4 \left(4 c^2 d^2-e^2\right)+5 c^2 d e x\right)}{18 c^3}-\frac{b d \left(2 d^2-\frac{3 e^2}{c^2}\right) \sinh ^{-1}(c x)}{6 e}-\frac{b \sqrt{c^2 x^2+1} (d+e x)^2}{9 c}","\frac{(d+e x)^3 \left(a+b \sinh ^{-1}(c x)\right)}{3 e}-\frac{b \sqrt{c^2 x^2+1} \left(4 \left(4 c^2 d^2-e^2\right)+5 c^2 d e x\right)}{18 c^3}-\frac{b d \left(2 d^2-\frac{3 e^2}{c^2}\right) \sinh ^{-1}(c x)}{6 e}-\frac{b \sqrt{c^2 x^2+1} (d+e x)^2}{9 c}",1,"-(b*(d + e*x)^2*Sqrt[1 + c^2*x^2])/(9*c) - (b*(4*(4*c^2*d^2 - e^2) + 5*c^2*d*e*x)*Sqrt[1 + c^2*x^2])/(18*c^3) - (b*d*(2*d^2 - (3*e^2)/c^2)*ArcSinh[c*x])/(6*e) + ((d + e*x)^3*(a + b*ArcSinh[c*x]))/(3*e)","A",4,4,16,0.2500,1,"{5801, 743, 780, 215}"
6,1,97,0,0.0521902,"\int (d+e x) \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + e*x)*(a + b*ArcSinh[c*x]),x]","\frac{(d+e x)^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 e}-\frac{b \left(2 d^2-\frac{e^2}{c^2}\right) \sinh ^{-1}(c x)}{4 e}-\frac{b \sqrt{c^2 x^2+1} (d+e x)}{4 c}-\frac{3 b d \sqrt{c^2 x^2+1}}{4 c}","\frac{(d+e x)^2 \left(a+b \sinh ^{-1}(c x)\right)}{2 e}-\frac{b \left(2 d^2-\frac{e^2}{c^2}\right) \sinh ^{-1}(c x)}{4 e}-\frac{b \sqrt{c^2 x^2+1} (d+e x)}{4 c}-\frac{3 b d \sqrt{c^2 x^2+1}}{4 c}",1,"(-3*b*d*Sqrt[1 + c^2*x^2])/(4*c) - (b*(d + e*x)*Sqrt[1 + c^2*x^2])/(4*c) - (b*(2*d^2 - e^2/c^2)*ArcSinh[c*x])/(4*e) + ((d + e*x)^2*(a + b*ArcSinh[c*x]))/(2*e)","A",4,4,14,0.2857,1,"{5801, 743, 641, 215}"
7,1,30,0,0.0132673,"\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}"
8,1,187,0,0.2586958,"\int \frac{a+b \sinh ^{-1}(c x)}{d+e x} \, dx","Int[(a + b*ArcSinh[c*x])/(d + e*x),x]","\frac{b \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}+\frac{b \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}+\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}+1\right)}{e}+\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}+1\right)}{e}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 b e}","\frac{b \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}+\frac{b \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}+\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}+1\right)}{e}+\frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}+1\right)}{e}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 b e}",1,"-(a + b*ArcSinh[c*x])^2/(2*b*e) + ((a + b*ArcSinh[c*x])*Log[1 + (e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2])])/e + ((a + b*ArcSinh[c*x])*Log[1 + (e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2])])/e + (b*PolyLog[2, -((e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2]))])/e + (b*PolyLog[2, -((e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2]))])/e","A",8,5,16,0.3125,1,"{5799, 5561, 2190, 2279, 2391}"
9,1,82,0,0.0545173,"\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{a+b \sinh ^{-1}(c x)}{e (d+e x)}-\frac{b c \tanh ^{-1}\left(\frac{e-c^2 d x}{\sqrt{c^2 x^2+1} \sqrt{c^2 d^2+e^2}}\right)}{e \sqrt{c^2 d^2+e^2}}","-\frac{a+b \sinh ^{-1}(c x)}{e (d+e x)}-\frac{b c \tanh ^{-1}\left(\frac{e-c^2 d x}{\sqrt{c^2 x^2+1} \sqrt{c^2 d^2+e^2}}\right)}{e \sqrt{c^2 d^2+e^2}}",1,"-((a + b*ArcSinh[c*x])/(e*(d + e*x))) - (b*c*ArcTanh[(e - c^2*d*x)/(Sqrt[c^2*d^2 + e^2]*Sqrt[1 + c^2*x^2])])/(e*Sqrt[c^2*d^2 + e^2])","A",3,3,16,0.1875,1,"{5801, 725, 206}"
10,1,128,0,0.0837947,"\int \frac{a+b \sinh ^{-1}(c x)}{(d+e x)^3} \, dx","Int[(a + b*ArcSinh[c*x])/(d + e*x)^3,x]","-\frac{a+b \sinh ^{-1}(c x)}{2 e (d+e x)^2}-\frac{b c \sqrt{c^2 x^2+1}}{2 \left(c^2 d^2+e^2\right) (d+e x)}-\frac{b c^3 d \tanh ^{-1}\left(\frac{e-c^2 d x}{\sqrt{c^2 x^2+1} \sqrt{c^2 d^2+e^2}}\right)}{2 e \left(c^2 d^2+e^2\right)^{3/2}}","-\frac{a+b \sinh ^{-1}(c x)}{2 e (d+e x)^2}-\frac{b c \sqrt{c^2 x^2+1}}{2 \left(c^2 d^2+e^2\right) (d+e x)}-\frac{b c^3 d \tanh ^{-1}\left(\frac{e-c^2 d x}{\sqrt{c^2 x^2+1} \sqrt{c^2 d^2+e^2}}\right)}{2 e \left(c^2 d^2+e^2\right)^{3/2}}",1,"-(b*c*Sqrt[1 + c^2*x^2])/(2*(c^2*d^2 + e^2)*(d + e*x)) - (a + b*ArcSinh[c*x])/(2*e*(d + e*x)^2) - (b*c^3*d*ArcTanh[(e - c^2*d*x)/(Sqrt[c^2*d^2 + e^2]*Sqrt[1 + c^2*x^2])])/(2*e*(c^2*d^2 + e^2)^(3/2))","A",4,4,16,0.2500,1,"{5801, 731, 725, 206}"
11,1,183,0,0.1380575,"\int \frac{a+b \sinh ^{-1}(c x)}{(d+e x)^4} \, dx","Int[(a + b*ArcSinh[c*x])/(d + e*x)^4,x]","-\frac{a+b \sinh ^{-1}(c x)}{3 e (d+e x)^3}-\frac{b c^3 d \sqrt{c^2 x^2+1}}{2 \left(c^2 d^2+e^2\right)^2 (d+e x)}-\frac{b c \sqrt{c^2 x^2+1}}{6 \left(c^2 d^2+e^2\right) (d+e x)^2}-\frac{b c^3 \left(2 c^2 d^2-e^2\right) \tanh ^{-1}\left(\frac{e-c^2 d x}{\sqrt{c^2 x^2+1} \sqrt{c^2 d^2+e^2}}\right)}{6 e \left(c^2 d^2+e^2\right)^{5/2}}","-\frac{a+b \sinh ^{-1}(c x)}{3 e (d+e x)^3}-\frac{b c^3 d \sqrt{c^2 x^2+1}}{2 \left(c^2 d^2+e^2\right)^2 (d+e x)}-\frac{b c \sqrt{c^2 x^2+1}}{6 \left(c^2 d^2+e^2\right) (d+e x)^2}-\frac{b c^3 \left(2 c^2 d^2-e^2\right) \tanh ^{-1}\left(\frac{e-c^2 d x}{\sqrt{c^2 x^2+1} \sqrt{c^2 d^2+e^2}}\right)}{6 e \left(c^2 d^2+e^2\right)^{5/2}}",1,"-(b*c*Sqrt[1 + c^2*x^2])/(6*(c^2*d^2 + e^2)*(d + e*x)^2) - (b*c^3*d*Sqrt[1 + c^2*x^2])/(2*(c^2*d^2 + e^2)^2*(d + e*x)) - (a + b*ArcSinh[c*x])/(3*e*(d + e*x)^3) - (b*c^3*(2*c^2*d^2 - e^2)*ArcTanh[(e - c^2*d*x)/(Sqrt[c^2*d^2 + e^2]*Sqrt[1 + c^2*x^2])])/(6*e*(c^2*d^2 + e^2)^(5/2))","A",5,5,16,0.3125,1,"{5801, 745, 807, 725, 206}"
12,1,368,0,0.7593838,"\int (d+e x)^3 \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)^3*(a + b*ArcSinh[c*x])^2,x]","-\frac{3 b d^2 e x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 c}+\frac{3 d^2 e \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^2}-\frac{2 b d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c}+\frac{4 b d e^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^3}-\frac{2 b d e^2 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 c}-\frac{b e^3 x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{8 c}+\frac{3 b e^3 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{16 c^3}-\frac{3 e^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{32 c^4}-\frac{d^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 e}+\frac{(d+e x)^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 e}-\frac{4 b^2 d e^2 x}{3 c^2}-\frac{3 b^2 e^3 x^2}{32 c^2}+\frac{3}{4} b^2 d^2 e x^2+2 b^2 d^3 x+\frac{2}{9} b^2 d e^2 x^3+\frac{1}{32} b^2 e^3 x^4","-\frac{3 b d^2 e x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 c}+\frac{3 d^2 e \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^2}-\frac{2 b d^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c}+\frac{4 b d e^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^3}-\frac{2 b d e^2 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{3 c}-\frac{b e^3 x^3 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{8 c}+\frac{3 b e^3 x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{16 c^3}-\frac{3 e^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{32 c^4}-\frac{d^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 e}+\frac{(d+e x)^4 \left(a+b \sinh ^{-1}(c x)\right)^2}{4 e}-\frac{4 b^2 d e^2 x}{3 c^2}-\frac{3 b^2 e^3 x^2}{32 c^2}+\frac{3}{4} b^2 d^2 e x^2+2 b^2 d^3 x+\frac{2}{9} b^2 d e^2 x^3+\frac{1}{32} b^2 e^3 x^4",1,"2*b^2*d^3*x - (4*b^2*d*e^2*x)/(3*c^2) + (3*b^2*d^2*e*x^2)/4 - (3*b^2*e^3*x^2)/(32*c^2) + (2*b^2*d*e^2*x^3)/9 + (b^2*e^3*x^4)/32 - (2*b*d^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/c + (4*b*d*e^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(3*c^3) - (3*b*d^2*e*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(2*c) + (3*b*e^3*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(16*c^3) - (2*b*d*e^2*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(3*c) - (b*e^3*x^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(8*c) - (d^4*(a + b*ArcSinh[c*x])^2)/(4*e) + (3*d^2*e*(a + b*ArcSinh[c*x])^2)/(4*c^2) - (3*e^3*(a + b*ArcSinh[c*x])^2)/(32*c^4) + ((d + e*x)^4*(a + b*ArcSinh[c*x])^2)/(4*e)","A",18,7,18,0.3889,1,"{5801, 5821, 5675, 5717, 8, 5758, 30}"
13,1,239,0,0.5118923,"\int (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{2 b d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c}-\frac{b d e x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c}+\frac{d e \left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^2}+\frac{4 b e^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^3}-\frac{2 b e^2 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c}-\frac{d^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 e}+\frac{(d+e x)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 e}-\frac{4 b^2 e^2 x}{9 c^2}+2 b^2 d^2 x+\frac{1}{2} b^2 d e x^2+\frac{2}{27} b^2 e^2 x^3","-\frac{2 b d^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c}-\frac{b d e x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c}+\frac{d e \left(a+b \sinh ^{-1}(c x)\right)^2}{2 c^2}+\frac{4 b e^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^3}-\frac{2 b e^2 x^2 \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{9 c}-\frac{d^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 e}+\frac{(d+e x)^3 \left(a+b \sinh ^{-1}(c x)\right)^2}{3 e}-\frac{4 b^2 e^2 x}{9 c^2}+2 b^2 d^2 x+\frac{1}{2} b^2 d e x^2+\frac{2}{27} b^2 e^2 x^3",1,"2*b^2*d^2*x - (4*b^2*e^2*x)/(9*c^2) + (b^2*d*e*x^2)/2 + (2*b^2*e^2*x^3)/27 - (2*b*d^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/c + (4*b*e^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(9*c^3) - (b*d*e*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/c - (2*b*e^2*x^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(9*c) - (d^3*(a + b*ArcSinh[c*x])^2)/(3*e) + (d*e*(a + b*ArcSinh[c*x])^2)/(2*c^2) + ((d + e*x)^3*(a + b*ArcSinh[c*x])^2)/(3*e)","A",13,7,18,0.3889,1,"{5801, 5821, 5675, 5717, 8, 5758, 30}"
14,1,140,0,0.3221865,"\int (d+e x) \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)*(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{b e x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 c}+\frac{e \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^2}-\frac{d^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 e}+\frac{(d+e x)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 e}+2 b^2 d x+\frac{1}{4} b^2 e x^2","-\frac{2 b d \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{c}-\frac{b e x \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{2 c}+\frac{e \left(a+b \sinh ^{-1}(c x)\right)^2}{4 c^2}-\frac{d^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 e}+\frac{(d+e x)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 e}+2 b^2 d x+\frac{1}{4} b^2 e x^2",1,"2*b^2*d*x + (b^2*e*x^2)/4 - (2*b*d*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/c - (b*e*x*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/(2*c) - (d^2*(a + b*ArcSinh[c*x])^2)/(2*e) + (e*(a + b*ArcSinh[c*x])^2)/(4*c^2) + ((d + e*x)^2*(a + b*ArcSinh[c*x])^2)/(2*e)","A",9,7,16,0.4375,1,"{5801, 5821, 5675, 5717, 8, 5758, 30}"
15,1,46,0,0.0633947,"\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}"
16,1,291,0,0.4694639,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{d+e x} \, dx","Int[(a + b*ArcSinh[c*x])^2/(d + e*x),x]","\frac{2 b \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}+\frac{2 b \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}-\frac{2 b^2 \text{PolyLog}\left(3,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}-\frac{2 b^2 \text{PolyLog}\left(3,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}+1\right)}{e}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}+1\right)}{e}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^3}{3 b e}","\frac{2 b \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}+\frac{2 b \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}-\frac{2 b^2 \text{PolyLog}\left(3,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e}-\frac{2 b^2 \text{PolyLog}\left(3,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}+1\right)}{e}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}+1\right)}{e}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^3}{3 b e}",1,"-(a + b*ArcSinh[c*x])^3/(3*b*e) + ((a + b*ArcSinh[c*x])^2*Log[1 + (e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2])])/e + ((a + b*ArcSinh[c*x])^2*Log[1 + (e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2])])/e + (2*b*(a + b*ArcSinh[c*x])*PolyLog[2, -((e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2]))])/e + (2*b*(a + b*ArcSinh[c*x])*PolyLog[2, -((e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2]))])/e - (2*b^2*PolyLog[3, -((e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2]))])/e - (2*b^2*PolyLog[3, -((e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2]))])/e","A",10,6,18,0.3333,1,"{5799, 5561, 2190, 2531, 2282, 6589}"
17,1,263,0,0.4715338,"\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{2 b^2 c \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e \sqrt{c^2 d^2+e^2}}-\frac{2 b^2 c \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e \sqrt{c^2 d^2+e^2}}+\frac{2 b c \left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}+1\right)}{e \sqrt{c^2 d^2+e^2}}-\frac{2 b c \left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}+1\right)}{e \sqrt{c^2 d^2+e^2}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{e (d+e x)}","\frac{2 b^2 c \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e \sqrt{c^2 d^2+e^2}}-\frac{2 b^2 c \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e \sqrt{c^2 d^2+e^2}}+\frac{2 b c \left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}+1\right)}{e \sqrt{c^2 d^2+e^2}}-\frac{2 b c \left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}+1\right)}{e \sqrt{c^2 d^2+e^2}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{e (d+e x)}",1,"-((a + b*ArcSinh[c*x])^2/(e*(d + e*x))) + (2*b*c*(a + b*ArcSinh[c*x])*Log[1 + (e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2])])/(e*Sqrt[c^2*d^2 + e^2]) - (2*b*c*(a + b*ArcSinh[c*x])*Log[1 + (e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2])])/(e*Sqrt[c^2*d^2 + e^2]) + (2*b^2*c*PolyLog[2, -((e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2]))])/(e*Sqrt[c^2*d^2 + e^2]) - (2*b^2*c*PolyLog[2, -((e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2]))])/(e*Sqrt[c^2*d^2 + e^2])","A",10,7,18,0.3889,1,"{5801, 5831, 3322, 2264, 2190, 2279, 2391}"
18,1,349,0,0.6089404,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{(d+e x)^3} \, dx","Int[(a + b*ArcSinh[c*x])^2/(d + e*x)^3,x]","\frac{b^2 c^3 d \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e \left(c^2 d^2+e^2\right)^{3/2}}-\frac{b^2 c^3 d \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e \left(c^2 d^2+e^2\right)^{3/2}}-\frac{b c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{\left(c^2 d^2+e^2\right) (d+e x)}+\frac{b c^3 d \left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}+1\right)}{e \left(c^2 d^2+e^2\right)^{3/2}}-\frac{b c^3 d \left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}+1\right)}{e \left(c^2 d^2+e^2\right)^{3/2}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 e (d+e x)^2}+\frac{b^2 c^2 \log (d+e x)}{e \left(c^2 d^2+e^2\right)}","\frac{b^2 c^3 d \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}\right)}{e \left(c^2 d^2+e^2\right)^{3/2}}-\frac{b^2 c^3 d \text{PolyLog}\left(2,-\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}\right)}{e \left(c^2 d^2+e^2\right)^{3/2}}-\frac{b c \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)}{\left(c^2 d^2+e^2\right) (d+e x)}+\frac{b c^3 d \left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2+e^2}}+1\right)}{e \left(c^2 d^2+e^2\right)^{3/2}}-\frac{b c^3 d \left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{e e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 d^2+e^2}+c d}+1\right)}{e \left(c^2 d^2+e^2\right)^{3/2}}-\frac{\left(a+b \sinh ^{-1}(c x)\right)^2}{2 e (d+e x)^2}+\frac{b^2 c^2 \log (d+e x)}{e \left(c^2 d^2+e^2\right)}",1,"-((b*c*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x]))/((c^2*d^2 + e^2)*(d + e*x))) - (a + b*ArcSinh[c*x])^2/(2*e*(d + e*x)^2) + (b*c^3*d*(a + b*ArcSinh[c*x])*Log[1 + (e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2])])/(e*(c^2*d^2 + e^2)^(3/2)) - (b*c^3*d*(a + b*ArcSinh[c*x])*Log[1 + (e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2])])/(e*(c^2*d^2 + e^2)^(3/2)) + (b^2*c^2*Log[d + e*x])/(e*(c^2*d^2 + e^2)) + (b^2*c^3*d*PolyLog[2, -((e*E^ArcSinh[c*x])/(c*d - Sqrt[c^2*d^2 + e^2]))])/(e*(c^2*d^2 + e^2)^(3/2)) - (b^2*c^3*d*PolyLog[2, -((e*E^ArcSinh[c*x])/(c*d + Sqrt[c^2*d^2 + e^2]))])/(e*(c^2*d^2 + e^2)^(3/2))","A",13,10,18,0.5556,1,"{5801, 5831, 3324, 3322, 2264, 2190, 2279, 2391, 2668, 31}"
19,1,394,0,1.1723668,"\int \frac{(d+e x)^3}{a+b \sinh ^{-1}(c x)} \, dx","Int[(d + e*x)^3/(a + b*ArcSinh[c*x]),x]","-\frac{3 d^2 e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{2 b c^2}-\frac{3 d e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b c^3}+\frac{3 d e^2 \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^3 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{4 b c^4}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{8 b c^4}+\frac{3 d^2 e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{2 b c^2}+\frac{3 d e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b c^3}-\frac{3 d e^2 \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{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{4 b c^4}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{8 b c^4}+\frac{d^3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b c}-\frac{d^3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b c}","-\frac{3 d^2 e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{2 b c^2}-\frac{3 d e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b c^3}+\frac{3 d e^2 \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^3 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{4 b c^4}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{8 b c^4}+\frac{3 d^2 e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{2 b c^2}+\frac{3 d e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b c^3}-\frac{3 d e^2 \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{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{4 b c^4}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c x)\right)}{8 b c^4}+\frac{d^3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b c}-\frac{d^3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b c}",1,"(d^3*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(b*c) - (3*d*e^2*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(4*b*c^3) + (3*d*e^2*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b*c^3) - (3*d^2*e*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]]*Sinh[(2*a)/b])/(2*b*c^2) + (e^3*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]]*Sinh[(2*a)/b])/(4*b*c^4) - (e^3*CoshIntegral[(4*a)/b + 4*ArcSinh[c*x]]*Sinh[(4*a)/b])/(8*b*c^4) - (d^3*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(b*c) + (3*d*e^2*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(4*b*c^3) + (3*d^2*e*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(2*b*c^2) - (e^3*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(4*b*c^4) - (3*d*e^2*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b*c^3) + (e^3*Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c*x]])/(8*b*c^4)","A",27,7,18,0.3889,1,"{5805, 6742, 3303, 3298, 3301, 5448, 12}"
20,1,245,0,0.7021104,"\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{d e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{b c^2}-\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b c^3}+\frac{e^2 \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{d e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{b c^2}+\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b c^3}-\frac{e^2 \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^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b c}-\frac{d^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b c}","-\frac{d e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{b c^2}-\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b c^3}+\frac{e^2 \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{d e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{b c^2}+\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{4 b c^3}-\frac{e^2 \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^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b c}-\frac{d^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b c}",1,"(d^2*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(b*c) - (e^2*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(4*b*c^3) + (e^2*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b*c^3) - (d*e*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]]*Sinh[(2*a)/b])/(b*c^2) - (d^2*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(b*c) + (e^2*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(4*b*c^3) + (d*e*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(b*c^2) - (e^2*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b*c^3)","A",17,6,18,0.3333,1,"{5805, 6742, 3303, 3298, 3301, 5448}"
21,1,116,0,0.3180026,"\int \frac{d+e x}{a+b \sinh ^{-1}(c x)} \, dx","Int[(d + e*x)/(a + b*ArcSinh[c*x]),x]","-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{2 b c^2}+\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{2 b c^2}+\frac{d \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b c}-\frac{d \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b c}","-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{2 b c^2}+\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{2 b c^2}+\frac{d \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b c}-\frac{d \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c x)\right)}{b c}",1,"(d*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c*x]])/(b*c) - (e*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]]*Sinh[(2*a)/b])/(2*b*c^2) - (d*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(b*c) + (e*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(2*b*c^2)","A",11,7,16,0.4375,1,"{5805, 6742, 3303, 3298, 3301, 5448, 12}"
22,1,54,0,0.073575,"\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}"
23,0,0,0,0.0419735,"\int \frac{1}{(d+e x) \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x)*(a + b*ArcSinh[c*x])),x]","\int \frac{1}{(d+e x) \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{(d+e x) \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/((d + e*x)*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
24,0,0,0,0.0392964,"\int \frac{1}{(d+e x)^2 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[1/((d + e*x)^2*(a + b*ArcSinh[c*x])),x]","\int \frac{1}{(d+e x)^2 \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{(d+e x)^2 \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,"{}"
25,1,351,0,0.6882324,"\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{2 d e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{b^2 c^2}+\frac{e^2 \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^2 \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{2 d e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{b^2 c^2}-\frac{e^2 \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^2 \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^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 \sqrt{c^2 x^2+1}}{b c \left(a+b \sinh ^{-1}(c x)\right)}-\frac{e^2 x^2 \sqrt{c^2 x^2+1}}{b c \left(a+b \sinh ^{-1}(c x)\right)}","\frac{2 d e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{b^2 c^2}+\frac{e^2 \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^2 \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{2 d e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{b^2 c^2}-\frac{e^2 \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^2 \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^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 \sqrt{c^2 x^2+1}}{b c \left(a+b \sinh ^{-1}(c x)\right)}-\frac{e^2 x^2 \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*Sqrt[1 + c^2*x^2])/(b*c*(a + b*ArcSinh[c*x])) - (e^2*x^2*Sqrt[1 + c^2*x^2])/(b*c*(a + b*ArcSinh[c*x])) + (2*d*e*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(b^2*c^2) - (d^2*CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(b^2*c) + (e^2*CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(4*b^2*c^3) - (3*e^2*CoshIntegral[(3*a)/b + 3*ArcSinh[c*x]]*Sinh[(3*a)/b])/(4*b^2*c^3) + (d^2*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(b^2*c) - (e^2*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(4*b^2*c^3) - (2*d*e*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(b^2*c^2) + (3*e^2*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c*x]])/(4*b^2*c^3)","A",19,7,18,0.3889,1,"{5803, 5655, 5779, 3303, 3298, 3301, 5665}"
26,1,176,0,0.3367297,"\int \frac{d+e x}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(d + e*x)/(a + b*ArcSinh[c*x])^2,x]","\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{b^2 c^2}-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c x)\right)}{b^2 c^2}-\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 \sqrt{c^2 x^2+1}}{b c \left(a+b \sinh ^{-1}(c x)\right)}","\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{b^2 c^2}-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c x)\right)}{b}\right)}{b^2 c^2}-\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 \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*Sqrt[1 + c^2*x^2])/(b*c*(a + b*ArcSinh[c*x])) + (e*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(b^2*c^2) - (d*CoshIntegral[a/b + ArcSinh[c*x]]*Sinh[a/b])/(b^2*c) + (d*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c*x]])/(b^2*c) - (e*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c*x]])/(b^2*c^2)","A",11,7,16,0.4375,1,"{5803, 5655, 5779, 3303, 3298, 3301, 5665}"
27,1,81,0,0.1794243,"\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}"
28,0,0,0,0.0314303,"\int \frac{1}{(d+e x) \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[1/((d + e*x)*(a + b*ArcSinh[c*x])^2),x]","\int \frac{1}{(d+e x) \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{(d+e x) \left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/((d + e*x)*(a + b*ArcSinh[c*x])^2), x]","A",0,0,0,0,-1,"{}"
29,0,0,0,0.0291871,"\int \frac{1}{(d+e x)^2 \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}{(d+e x)^2 \left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{(d+e x)^2 \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,"{}"
30,0,0,0,0.2612834,"\int (d+e x)^m \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","Int[(d + e*x)^m*(a + b*ArcSinh[c*x])^2,x]","\int (d+e x)^m \left(a+b \sinh ^{-1}(c x)\right)^2 \, dx","\frac{(d+e x)^{m+1} \left(a+b \sinh ^{-1}(c x)\right)^2}{e (m+1)}-\frac{2 b c \text{Int}\left(\frac{(d+e x)^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 x^2+1}},x\right)}{e (m+1)}",0,"((d + e*x)^(1 + m)*(a + b*ArcSinh[c*x])^2)/(e*(1 + m)) - (2*b*c*Defer[Int][((d + e*x)^(1 + m)*(a + b*ArcSinh[c*x]))/Sqrt[1 + c^2*x^2], x])/(e*(1 + m))","A",0,0,0,0,-1,"{}"
31,1,179,0,0.1006376,"\int (d+e x)^m \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(d + e*x)^m*(a + b*ArcSinh[c*x]),x]","\frac{(d+e x)^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{e (m+1)}-\frac{b c \sqrt{1-\frac{d+e x}{d-\frac{e}{\sqrt{-c^2}}}} \sqrt{1-\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}} (d+e x)^{m+2} F_1\left(m+2;\frac{1}{2},\frac{1}{2};m+3;\frac{d+e x}{d-\frac{e}{\sqrt{-c^2}}},\frac{d+e x}{d+\frac{e}{\sqrt{-c^2}}}\right)}{e^2 (m+1) (m+2) \sqrt{c^2 x^2+1}}","\frac{(d+e x)^{m+1} \left(a+b \sinh ^{-1}(c x)\right)}{e (m+1)}-\frac{b c \sqrt{1-\frac{d+e x}{d-\frac{e}{\sqrt{-c^2}}}} \sqrt{1-\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}} (d+e x)^{m+2} F_1\left(m+2;\frac{1}{2},\frac{1}{2};m+3;\frac{d+e x}{d-\frac{e}{\sqrt{-c^2}}},\frac{d+e x}{d+\frac{e}{\sqrt{-c^2}}}\right)}{e^2 (m+1) (m+2) \sqrt{c^2 x^2+1}}",1,"-((b*c*(d + e*x)^(2 + m)*Sqrt[1 - (d + e*x)/(d - e/Sqrt[-c^2])]*Sqrt[1 - (d + e*x)/(d + e/Sqrt[-c^2])]*AppellF1[2 + m, 1/2, 1/2, 3 + m, (d + e*x)/(d - e/Sqrt[-c^2]), (d + e*x)/(d + e/Sqrt[-c^2])])/(e^2*(1 + m)*(2 + m)*Sqrt[1 + c^2*x^2])) + ((d + e*x)^(1 + m)*(a + b*ArcSinh[c*x]))/(e*(1 + m))","A",3,3,16,0.1875,1,"{5801, 760, 133}"
32,0,0,0,0.0289984,"\int \frac{(d+e x)^m}{a+b \sinh ^{-1}(c x)} \, dx","Int[(d + e*x)^m/(a + b*ArcSinh[c*x]),x]","\int \frac{(d+e x)^m}{a+b \sinh ^{-1}(c x)} \, dx","\text{Int}\left(\frac{(d+e x)^m}{a+b \sinh ^{-1}(c x)},x\right)",0,"Defer[Int][(d + e*x)^m/(a + b*ArcSinh[c*x]), x]","A",0,0,0,0,-1,"{}"
33,0,0,0,0.0308005,"\int \frac{(d+e x)^m}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","Int[(d + e*x)^m/(a + b*ArcSinh[c*x])^2,x]","\int \frac{(d+e x)^m}{\left(a+b \sinh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{(d+e x)^m}{\left(a+b \sinh ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(d + e*x)^m/(a + b*ArcSinh[c*x])^2, x]","A",0,0,0,0,-1,"{}"
34,1,640,0,0.6867754,"\int (f+g x)^3 \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(f + g*x)^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]),x]","\frac{f^2 g \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{c^2}+\frac{1}{2} f^3 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{f^3 \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{3}{4} f g^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{3 f g^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 c^2}-\frac{3 f g^2 \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{g^3 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^4}-\frac{g^3 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^4}-\frac{b c f^2 g x^3 \sqrt{c^2 d x^2+d}}{3 \sqrt{c^2 x^2+1}}-\frac{b f^2 g x \sqrt{c^2 d x^2+d}}{c \sqrt{c^2 x^2+1}}-\frac{b c f^3 x^2 \sqrt{c^2 d x^2+d}}{4 \sqrt{c^2 x^2+1}}-\frac{3 b c f g^2 x^4 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{3 b f g^2 x^2 \sqrt{c^2 d x^2+d}}{16 c \sqrt{c^2 x^2+1}}-\frac{b c g^3 x^5 \sqrt{c^2 d x^2+d}}{25 \sqrt{c^2 x^2+1}}-\frac{b g^3 x^3 \sqrt{c^2 d x^2+d}}{45 c \sqrt{c^2 x^2+1}}+\frac{2 b g^3 x \sqrt{c^2 d x^2+d}}{15 c^3 \sqrt{c^2 x^2+1}}","\frac{f^2 g \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{c^2}+\frac{1}{2} f^3 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{f^3 \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{3}{4} f g^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{3 f g^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 c^2}-\frac{3 f g^2 \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{g^3 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^4}-\frac{g^3 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^4}-\frac{b c f^2 g x^3 \sqrt{c^2 d x^2+d}}{3 \sqrt{c^2 x^2+1}}-\frac{b f^2 g x \sqrt{c^2 d x^2+d}}{c \sqrt{c^2 x^2+1}}-\frac{b c f^3 x^2 \sqrt{c^2 d x^2+d}}{4 \sqrt{c^2 x^2+1}}-\frac{3 b c f g^2 x^4 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{3 b f g^2 x^2 \sqrt{c^2 d x^2+d}}{16 c \sqrt{c^2 x^2+1}}-\frac{b c g^3 x^5 \sqrt{c^2 d x^2+d}}{25 \sqrt{c^2 x^2+1}}-\frac{b g^3 x^3 \sqrt{c^2 d x^2+d}}{45 c \sqrt{c^2 x^2+1}}+\frac{2 b g^3 x \sqrt{c^2 d x^2+d}}{15 c^3 \sqrt{c^2 x^2+1}}",1,"-((b*f^2*g*x*Sqrt[d + c^2*d*x^2])/(c*Sqrt[1 + c^2*x^2])) + (2*b*g^3*x*Sqrt[d + c^2*d*x^2])/(15*c^3*Sqrt[1 + c^2*x^2]) - (b*c*f^3*x^2*Sqrt[d + c^2*d*x^2])/(4*Sqrt[1 + c^2*x^2]) - (3*b*f*g^2*x^2*Sqrt[d + c^2*d*x^2])/(16*c*Sqrt[1 + c^2*x^2]) - (b*c*f^2*g*x^3*Sqrt[d + c^2*d*x^2])/(3*Sqrt[1 + c^2*x^2]) - (b*g^3*x^3*Sqrt[d + c^2*d*x^2])/(45*c*Sqrt[1 + c^2*x^2]) - (3*b*c*f*g^2*x^4*Sqrt[d + c^2*d*x^2])/(16*Sqrt[1 + c^2*x^2]) - (b*c*g^3*x^5*Sqrt[d + c^2*d*x^2])/(25*Sqrt[1 + c^2*x^2]) + (f^3*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/2 + (3*f*g^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(8*c^2) + (3*f*g^2*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/4 + (f^2*g*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/c^2 - (g^3*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*c^4) + (g^3*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(5*c^4) + (f^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*c*Sqrt[1 + c^2*x^2]) - (3*f*g^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(16*b*c^3*Sqrt[1 + c^2*x^2])","A",16,12,30,0.4000,1,"{5835, 5821, 5682, 5675, 30, 5717, 5742, 5758, 266, 43, 5732, 12}"
35,1,431,0,0.5322569,"\int (f+g x)^2 \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(f + g*x)^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]),x]","\frac{1}{2} f^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{f^2 \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{2 f g \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2}+\frac{1}{4} g^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{g^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 c^2}-\frac{g^2 \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 f^2 x^2 \sqrt{c^2 d x^2+d}}{4 \sqrt{c^2 x^2+1}}-\frac{2 b c f g x^3 \sqrt{c^2 d x^2+d}}{9 \sqrt{c^2 x^2+1}}-\frac{2 b f g x \sqrt{c^2 d x^2+d}}{3 c \sqrt{c^2 x^2+1}}-\frac{b c g^2 x^4 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{b g^2 x^2 \sqrt{c^2 d x^2+d}}{16 c \sqrt{c^2 x^2+1}}","\frac{1}{2} f^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{f^2 \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{2 f g \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2}+\frac{1}{4} g^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{g^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{8 c^2}-\frac{g^2 \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 f^2 x^2 \sqrt{c^2 d x^2+d}}{4 \sqrt{c^2 x^2+1}}-\frac{2 b c f g x^3 \sqrt{c^2 d x^2+d}}{9 \sqrt{c^2 x^2+1}}-\frac{2 b f g x \sqrt{c^2 d x^2+d}}{3 c \sqrt{c^2 x^2+1}}-\frac{b c g^2 x^4 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{b g^2 x^2 \sqrt{c^2 d x^2+d}}{16 c \sqrt{c^2 x^2+1}}",1,"(-2*b*f*g*x*Sqrt[d + c^2*d*x^2])/(3*c*Sqrt[1 + c^2*x^2]) - (b*c*f^2*x^2*Sqrt[d + c^2*d*x^2])/(4*Sqrt[1 + c^2*x^2]) - (b*g^2*x^2*Sqrt[d + c^2*d*x^2])/(16*c*Sqrt[1 + c^2*x^2]) - (2*b*c*f*g*x^3*Sqrt[d + c^2*d*x^2])/(9*Sqrt[1 + c^2*x^2]) - (b*c*g^2*x^4*Sqrt[d + c^2*d*x^2])/(16*Sqrt[1 + c^2*x^2]) + (f^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/2 + (g^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(8*c^2) + (g^2*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/4 + (2*f*g*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*c^2) + (f^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*c*Sqrt[1 + c^2*x^2]) - (g^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(16*b*c^3*Sqrt[1 + c^2*x^2])","A",13,8,30,0.2667,1,"{5835, 5821, 5682, 5675, 30, 5717, 5742, 5758}"
36,1,227,0,0.2501435,"\int (f+g x) \sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(f + g*x)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]),x]","\frac{1}{2} f x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{f \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{g \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2}-\frac{b c f x^2 \sqrt{c^2 d x^2+d}}{4 \sqrt{c^2 x^2+1}}-\frac{b c g x^3 \sqrt{c^2 d x^2+d}}{9 \sqrt{c^2 x^2+1}}-\frac{b g x \sqrt{c^2 d x^2+d}}{3 c \sqrt{c^2 x^2+1}}","\frac{1}{2} f x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{f \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{g \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2}-\frac{b c f x^2 \sqrt{c^2 d x^2+d}}{4 \sqrt{c^2 x^2+1}}-\frac{b c g x^3 \sqrt{c^2 d x^2+d}}{9 \sqrt{c^2 x^2+1}}-\frac{b g x \sqrt{c^2 d x^2+d}}{3 c \sqrt{c^2 x^2+1}}",1,"-(b*g*x*Sqrt[d + c^2*d*x^2])/(3*c*Sqrt[1 + c^2*x^2]) - (b*c*f*x^2*Sqrt[d + c^2*d*x^2])/(4*Sqrt[1 + c^2*x^2]) - (b*c*g*x^3*Sqrt[d + c^2*d*x^2])/(9*Sqrt[1 + c^2*x^2]) + (f*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/2 + (g*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*c^2) + (f*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*c*Sqrt[1 + c^2*x^2])","A",8,6,28,0.2143,1,"{5835, 5821, 5682, 5675, 30, 5717}"
37,1,664,0,1.6495722,"\int \frac{\sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)}{f+g x} \, dx","Int[(Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(f + g*x),x]","\frac{b \sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2} \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{g^2 \sqrt{c^2 x^2+1}}-\frac{b \sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2} \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{g^2 \sqrt{c^2 x^2+1}}-\frac{\sqrt{c^2 d x^2+d} \left(\frac{c^2 f^2}{g^2}+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c \sqrt{c^2 x^2+1} (f+g x)}+\frac{\sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c (f+g x)}-\frac{c x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b g \sqrt{c^2 x^2+1}}-\frac{a \sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2} \tanh ^{-1}\left(\frac{g-c^2 f x}{\sqrt{c^2 x^2+1} \sqrt{c^2 f^2+g^2}}\right)}{g^2 \sqrt{c^2 x^2+1}}+\frac{a \sqrt{c^2 d x^2+d}}{g}+\frac{b \sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2} \sinh ^{-1}(c x) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{g^2 \sqrt{c^2 x^2+1}}-\frac{b \sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2} \sinh ^{-1}(c x) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}+1\right)}{g^2 \sqrt{c^2 x^2+1}}-\frac{b c x \sqrt{c^2 d x^2+d}}{g \sqrt{c^2 x^2+1}}+\frac{b \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{g}","\frac{b \sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2} \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{g^2 \sqrt{c^2 x^2+1}}-\frac{b \sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2} \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{g^2 \sqrt{c^2 x^2+1}}-\frac{\sqrt{c^2 d x^2+d} \left(\frac{c^2 f^2}{g^2}+1\right) \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c \sqrt{c^2 x^2+1} (f+g x)}+\frac{\sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c (f+g x)}-\frac{c x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b g \sqrt{c^2 x^2+1}}-\frac{a \sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2} \tanh ^{-1}\left(\frac{g-c^2 f x}{\sqrt{c^2 x^2+1} \sqrt{c^2 f^2+g^2}}\right)}{g^2 \sqrt{c^2 x^2+1}}+\frac{a \sqrt{c^2 d x^2+d}}{g}+\frac{b \sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2} \sinh ^{-1}(c x) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{g^2 \sqrt{c^2 x^2+1}}-\frac{b \sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2} \sinh ^{-1}(c x) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}+1\right)}{g^2 \sqrt{c^2 x^2+1}}-\frac{b c x \sqrt{c^2 d x^2+d}}{g \sqrt{c^2 x^2+1}}+\frac{b \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{g}",1,"(a*Sqrt[d + c^2*d*x^2])/g - (b*c*x*Sqrt[d + c^2*d*x^2])/(g*Sqrt[1 + c^2*x^2]) + (b*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/g - (c*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*g*Sqrt[1 + c^2*x^2]) - ((1 + (c^2*f^2)/g^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c*(f + g*x)*Sqrt[1 + c^2*x^2]) + (Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c*(f + g*x)) - (a*Sqrt[c^2*f^2 + g^2]*Sqrt[d + c^2*d*x^2]*ArcTanh[(g - c^2*f*x)/(Sqrt[c^2*f^2 + g^2]*Sqrt[1 + c^2*x^2])])/(g^2*Sqrt[1 + c^2*x^2]) + (b*Sqrt[c^2*f^2 + g^2]*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x]*Log[1 + (E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2])])/(g^2*Sqrt[1 + c^2*x^2]) - (b*Sqrt[c^2*f^2 + g^2]*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x]*Log[1 + (E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2])])/(g^2*Sqrt[1 + c^2*x^2]) + (b*Sqrt[c^2*f^2 + g^2]*Sqrt[d + c^2*d*x^2]*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2]))])/(g^2*Sqrt[1 + c^2*x^2]) - (b*Sqrt[c^2*f^2 + g^2]*Sqrt[d + c^2*d*x^2]*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2]))])/(g^2*Sqrt[1 + c^2*x^2])","A",22,20,30,0.6667,1,"{5835, 5823, 683, 5815, 6742, 261, 725, 206, 5859, 1654, 12, 5857, 5717, 8, 5831, 3322, 2264, 2190, 2279, 2391}"
38,1,781,0,2.5473488,"\int \frac{\sqrt{d+c^2 d x^2} \left(a+b \sinh ^{-1}(c x)\right)}{(f+g x)^2} \, dx","Int[(Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(f + g*x)^2,x]","-\frac{b c^2 f \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{g^2 \sqrt{c^2 x^2+1} \sqrt{c^2 f^2+g^2}}+\frac{b c^2 f \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{g^2 \sqrt{c^2 x^2+1} \sqrt{c^2 f^2+g^2}}-\frac{\sqrt{c^2 d x^2+d} \left(g-c^2 f x\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c \sqrt{c^2 x^2+1} \left(c^2 f^2+g^2\right) (f+g x)^2}+\frac{\sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c (f+g x)^2}+\frac{a c^3 f^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{g^2 \sqrt{c^2 x^2+1} \left(c^2 f^2+g^2\right)}+\frac{a c^2 f \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(\frac{g-c^2 f x}{\sqrt{c^2 x^2+1} \sqrt{c^2 f^2+g^2}}\right)}{g^2 \sqrt{c^2 x^2+1} \sqrt{c^2 f^2+g^2}}-\frac{a \sqrt{c^2 d x^2+d}}{g (f+g x)}+\frac{b c^3 f^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)^2}{2 g^2 \sqrt{c^2 x^2+1} \left(c^2 f^2+g^2\right)}-\frac{b c^2 f \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{g^2 \sqrt{c^2 x^2+1} \sqrt{c^2 f^2+g^2}}+\frac{b c^2 f \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}+1\right)}{g^2 \sqrt{c^2 x^2+1} \sqrt{c^2 f^2+g^2}}+\frac{b c \sqrt{c^2 d x^2+d} \log (f+g x)}{g^2 \sqrt{c^2 x^2+1}}-\frac{b \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{g (f+g x)}","-\frac{b c^2 f \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{g^2 \sqrt{c^2 x^2+1} \sqrt{c^2 f^2+g^2}}+\frac{b c^2 f \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{g^2 \sqrt{c^2 x^2+1} \sqrt{c^2 f^2+g^2}}-\frac{\sqrt{c^2 d x^2+d} \left(g-c^2 f x\right)^2 \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c \sqrt{c^2 x^2+1} \left(c^2 f^2+g^2\right) (f+g x)^2}+\frac{\sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b c (f+g x)^2}+\frac{a c^3 f^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{g^2 \sqrt{c^2 x^2+1} \left(c^2 f^2+g^2\right)}+\frac{a c^2 f \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(\frac{g-c^2 f x}{\sqrt{c^2 x^2+1} \sqrt{c^2 f^2+g^2}}\right)}{g^2 \sqrt{c^2 x^2+1} \sqrt{c^2 f^2+g^2}}-\frac{a \sqrt{c^2 d x^2+d}}{g (f+g x)}+\frac{b c^3 f^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)^2}{2 g^2 \sqrt{c^2 x^2+1} \left(c^2 f^2+g^2\right)}-\frac{b c^2 f \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{g^2 \sqrt{c^2 x^2+1} \sqrt{c^2 f^2+g^2}}+\frac{b c^2 f \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}+1\right)}{g^2 \sqrt{c^2 x^2+1} \sqrt{c^2 f^2+g^2}}+\frac{b c \sqrt{c^2 d x^2+d} \log (f+g x)}{g^2 \sqrt{c^2 x^2+1}}-\frac{b \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{g (f+g x)}",1,"-((a*Sqrt[d + c^2*d*x^2])/(g*(f + g*x))) - (b*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/(g*(f + g*x)) + (a*c^3*f^2*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/(g^2*(c^2*f^2 + g^2)*Sqrt[1 + c^2*x^2]) + (b*c^3*f^2*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x]^2)/(2*g^2*(c^2*f^2 + g^2)*Sqrt[1 + c^2*x^2]) - ((g - c^2*f*x)^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c*(c^2*f^2 + g^2)*(f + g*x)^2*Sqrt[1 + c^2*x^2]) + (Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c*(f + g*x)^2) + (a*c^2*f*Sqrt[d + c^2*d*x^2]*ArcTanh[(g - c^2*f*x)/(Sqrt[c^2*f^2 + g^2]*Sqrt[1 + c^2*x^2])])/(g^2*Sqrt[c^2*f^2 + g^2]*Sqrt[1 + c^2*x^2]) - (b*c^2*f*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x]*Log[1 + (E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2])])/(g^2*Sqrt[c^2*f^2 + g^2]*Sqrt[1 + c^2*x^2]) + (b*c^2*f*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x]*Log[1 + (E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2])])/(g^2*Sqrt[c^2*f^2 + g^2]*Sqrt[1 + c^2*x^2]) + (b*c*Sqrt[d + c^2*d*x^2]*Log[f + g*x])/(g^2*Sqrt[1 + c^2*x^2]) - (b*c^2*f*Sqrt[d + c^2*d*x^2]*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2]))])/(g^2*Sqrt[c^2*f^2 + g^2]*Sqrt[1 + c^2*x^2]) + (b*c^2*f*Sqrt[d + c^2*d*x^2]*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2]))])/(g^2*Sqrt[c^2*f^2 + g^2]*Sqrt[1 + c^2*x^2])","A",35,22,30,0.7333,1,"{5835, 5823, 37, 5813, 12, 1651, 844, 215, 725, 206, 5859, 5857, 5675, 5831, 3324, 3322, 2264, 2190, 2279, 2391, 2668, 31}"
39,1,918,0,0.9323965,"\int (f+g x)^3 \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(f + g*x)^3*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]),x]","-\frac{b c^3 d g^3 \sqrt{c^2 d x^2+d} x^7}{49 \sqrt{c^2 x^2+1}}-\frac{b c^3 d f g^2 \sqrt{c^2 d x^2+d} x^6}{12 \sqrt{c^2 x^2+1}}-\frac{8 b c d g^3 \sqrt{c^2 d x^2+d} x^5}{175 \sqrt{c^2 x^2+1}}-\frac{3 b c^3 d f^2 g \sqrt{c^2 d x^2+d} x^5}{25 \sqrt{c^2 x^2+1}}-\frac{b c^3 d f^3 \sqrt{c^2 d x^2+d} x^4}{16 \sqrt{c^2 x^2+1}}-\frac{7 b c d f g^2 \sqrt{c^2 d x^2+d} x^4}{32 \sqrt{c^2 x^2+1}}+\frac{3}{8} d f g^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^3+\frac{1}{2} d f g^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^3-\frac{b d g^3 \sqrt{c^2 d x^2+d} x^3}{105 c \sqrt{c^2 x^2+1}}-\frac{2 b c d f^2 g \sqrt{c^2 d x^2+d} x^3}{5 \sqrt{c^2 x^2+1}}-\frac{5 b c d f^3 \sqrt{c^2 d x^2+d} x^2}{16 \sqrt{c^2 x^2+1}}-\frac{3 b d f g^2 \sqrt{c^2 d x^2+d} x^2}{32 c \sqrt{c^2 x^2+1}}+\frac{3}{8} d f^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x+\frac{3 d f g^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x}{16 c^2}+\frac{1}{4} d f^3 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x+\frac{2 b d g^3 \sqrt{c^2 d x^2+d} x}{35 c^3 \sqrt{c^2 x^2+1}}-\frac{3 b d f^2 g \sqrt{c^2 d x^2+d} x}{5 c \sqrt{c^2 x^2+1}}+\frac{3 d f^3 \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{3 d f g^2 \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{d g^3 \left(c^2 x^2+1\right)^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^4}-\frac{d g^3 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^4}+\frac{3 d f^2 g \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^2}","-\frac{b c^3 d g^3 \sqrt{c^2 d x^2+d} x^7}{49 \sqrt{c^2 x^2+1}}-\frac{b c^3 d f g^2 \sqrt{c^2 d x^2+d} x^6}{12 \sqrt{c^2 x^2+1}}-\frac{8 b c d g^3 \sqrt{c^2 d x^2+d} x^5}{175 \sqrt{c^2 x^2+1}}-\frac{3 b c^3 d f^2 g \sqrt{c^2 d x^2+d} x^5}{25 \sqrt{c^2 x^2+1}}-\frac{b c^3 d f^3 \sqrt{c^2 d x^2+d} x^4}{16 \sqrt{c^2 x^2+1}}-\frac{7 b c d f g^2 \sqrt{c^2 d x^2+d} x^4}{32 \sqrt{c^2 x^2+1}}+\frac{3}{8} d f g^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^3+\frac{1}{2} d f g^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^3-\frac{b d g^3 \sqrt{c^2 d x^2+d} x^3}{105 c \sqrt{c^2 x^2+1}}-\frac{2 b c d f^2 g \sqrt{c^2 d x^2+d} x^3}{5 \sqrt{c^2 x^2+1}}-\frac{5 b c d f^3 \sqrt{c^2 d x^2+d} x^2}{16 \sqrt{c^2 x^2+1}}-\frac{3 b d f g^2 \sqrt{c^2 d x^2+d} x^2}{32 c \sqrt{c^2 x^2+1}}+\frac{3}{8} d f^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x+\frac{3 d f g^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x}{16 c^2}+\frac{1}{4} d f^3 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x+\frac{2 b d g^3 \sqrt{c^2 d x^2+d} x}{35 c^3 \sqrt{c^2 x^2+1}}-\frac{3 b d f^2 g \sqrt{c^2 d x^2+d} x}{5 c \sqrt{c^2 x^2+1}}+\frac{3 d f^3 \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{3 d f g^2 \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{d g^3 \left(c^2 x^2+1\right)^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^4}-\frac{d g^3 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^4}+\frac{3 d f^2 g \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^2}",1,"(-3*b*d*f^2*g*x*Sqrt[d + c^2*d*x^2])/(5*c*Sqrt[1 + c^2*x^2]) + (2*b*d*g^3*x*Sqrt[d + c^2*d*x^2])/(35*c^3*Sqrt[1 + c^2*x^2]) - (5*b*c*d*f^3*x^2*Sqrt[d + c^2*d*x^2])/(16*Sqrt[1 + c^2*x^2]) - (3*b*d*f*g^2*x^2*Sqrt[d + c^2*d*x^2])/(32*c*Sqrt[1 + c^2*x^2]) - (2*b*c*d*f^2*g*x^3*Sqrt[d + c^2*d*x^2])/(5*Sqrt[1 + c^2*x^2]) - (b*d*g^3*x^3*Sqrt[d + c^2*d*x^2])/(105*c*Sqrt[1 + c^2*x^2]) - (b*c^3*d*f^3*x^4*Sqrt[d + c^2*d*x^2])/(16*Sqrt[1 + c^2*x^2]) - (7*b*c*d*f*g^2*x^4*Sqrt[d + c^2*d*x^2])/(32*Sqrt[1 + c^2*x^2]) - (3*b*c^3*d*f^2*g*x^5*Sqrt[d + c^2*d*x^2])/(25*Sqrt[1 + c^2*x^2]) - (8*b*c*d*g^3*x^5*Sqrt[d + c^2*d*x^2])/(175*Sqrt[1 + c^2*x^2]) - (b*c^3*d*f*g^2*x^6*Sqrt[d + c^2*d*x^2])/(12*Sqrt[1 + c^2*x^2]) - (b*c^3*d*g^3*x^7*Sqrt[d + c^2*d*x^2])/(49*Sqrt[1 + c^2*x^2]) + (3*d*f^3*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/8 + (3*d*f*g^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(16*c^2) + (3*d*f*g^2*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/8 + (d*f^3*x*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/4 + (d*f*g^2*x^3*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/2 + (3*d*f^2*g*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(5*c^2) - (d*g^3*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(5*c^4) + (d*g^3*(1 + c^2*x^2)^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(7*c^4) + (3*d*f^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(16*b*c*Sqrt[1 + c^2*x^2]) - (3*d*f*g^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(32*b*c^3*Sqrt[1 + c^2*x^2])","A",24,17,30,0.5667,1,"{5835, 5821, 5684, 5682, 5675, 30, 14, 5717, 194, 5744, 5742, 5758, 266, 43, 5732, 12, 373}"
40,1,651,0,0.7308677,"\int (f+g x)^2 \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(f + g*x)^2*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]),x]","\frac{3}{8} d f^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{4} d f^2 x \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{3 d f^2 \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{2 d f g \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^2}+\frac{1}{8} d g^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{6} d g^2 x^3 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{d g^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{16 c^2}-\frac{d g^2 \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 f^2 x^4 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{5 b c d f^2 x^2 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{2 b c^3 d f g x^5 \sqrt{c^2 d x^2+d}}{25 \sqrt{c^2 x^2+1}}-\frac{4 b c d f g x^3 \sqrt{c^2 d x^2+d}}{15 \sqrt{c^2 x^2+1}}-\frac{2 b d f g x \sqrt{c^2 d x^2+d}}{5 c \sqrt{c^2 x^2+1}}-\frac{b c^3 d g^2 x^6 \sqrt{c^2 d x^2+d}}{36 \sqrt{c^2 x^2+1}}-\frac{7 b c d g^2 x^4 \sqrt{c^2 d x^2+d}}{96 \sqrt{c^2 x^2+1}}-\frac{b d g^2 x^2 \sqrt{c^2 d x^2+d}}{32 c \sqrt{c^2 x^2+1}}","\frac{3}{8} d f^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{4} d f^2 x \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{3 d f^2 \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{2 d f g \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^2}+\frac{1}{8} d g^2 x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{6} d g^2 x^3 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{d g^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{16 c^2}-\frac{d g^2 \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 f^2 x^4 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{5 b c d f^2 x^2 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{2 b c^3 d f g x^5 \sqrt{c^2 d x^2+d}}{25 \sqrt{c^2 x^2+1}}-\frac{4 b c d f g x^3 \sqrt{c^2 d x^2+d}}{15 \sqrt{c^2 x^2+1}}-\frac{2 b d f g x \sqrt{c^2 d x^2+d}}{5 c \sqrt{c^2 x^2+1}}-\frac{b c^3 d g^2 x^6 \sqrt{c^2 d x^2+d}}{36 \sqrt{c^2 x^2+1}}-\frac{7 b c d g^2 x^4 \sqrt{c^2 d x^2+d}}{96 \sqrt{c^2 x^2+1}}-\frac{b d g^2 x^2 \sqrt{c^2 d x^2+d}}{32 c \sqrt{c^2 x^2+1}}",1,"(-2*b*d*f*g*x*Sqrt[d + c^2*d*x^2])/(5*c*Sqrt[1 + c^2*x^2]) - (5*b*c*d*f^2*x^2*Sqrt[d + c^2*d*x^2])/(16*Sqrt[1 + c^2*x^2]) - (b*d*g^2*x^2*Sqrt[d + c^2*d*x^2])/(32*c*Sqrt[1 + c^2*x^2]) - (4*b*c*d*f*g*x^3*Sqrt[d + c^2*d*x^2])/(15*Sqrt[1 + c^2*x^2]) - (b*c^3*d*f^2*x^4*Sqrt[d + c^2*d*x^2])/(16*Sqrt[1 + c^2*x^2]) - (7*b*c*d*g^2*x^4*Sqrt[d + c^2*d*x^2])/(96*Sqrt[1 + c^2*x^2]) - (2*b*c^3*d*f*g*x^5*Sqrt[d + c^2*d*x^2])/(25*Sqrt[1 + c^2*x^2]) - (b*c^3*d*g^2*x^6*Sqrt[d + c^2*d*x^2])/(36*Sqrt[1 + c^2*x^2]) + (3*d*f^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/8 + (d*g^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(16*c^2) + (d*g^2*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/8 + (d*f^2*x*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/4 + (d*g^2*x^3*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/6 + (2*d*f*g*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(5*c^2) + (3*d*f^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(16*b*c*Sqrt[1 + c^2*x^2]) - (d*g^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(32*b*c^3*Sqrt[1 + c^2*x^2])","A",20,12,30,0.4000,1,"{5835, 5821, 5684, 5682, 5675, 30, 14, 5717, 194, 5744, 5742, 5758}"
41,1,353,0,0.3354571,"\int (f+g x) \left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(f + g*x)*(d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]),x]","\frac{3}{8} d f x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{4} d f x \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{3 d f \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{d g \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^2}-\frac{b c^3 d f x^4 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{5 b c d f x^2 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{b c^3 d g x^5 \sqrt{c^2 d x^2+d}}{25 \sqrt{c^2 x^2+1}}-\frac{2 b c d g x^3 \sqrt{c^2 d x^2+d}}{15 \sqrt{c^2 x^2+1}}-\frac{b d g x \sqrt{c^2 d x^2+d}}{5 c \sqrt{c^2 x^2+1}}","\frac{3}{8} d f x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{1}{4} d f x \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{3 d f \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{d g \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{5 c^2}-\frac{b c^3 d f x^4 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{5 b c d f x^2 \sqrt{c^2 d x^2+d}}{16 \sqrt{c^2 x^2+1}}-\frac{b c^3 d g x^5 \sqrt{c^2 d x^2+d}}{25 \sqrt{c^2 x^2+1}}-\frac{2 b c d g x^3 \sqrt{c^2 d x^2+d}}{15 \sqrt{c^2 x^2+1}}-\frac{b d g x \sqrt{c^2 d x^2+d}}{5 c \sqrt{c^2 x^2+1}}",1,"-(b*d*g*x*Sqrt[d + c^2*d*x^2])/(5*c*Sqrt[1 + c^2*x^2]) - (5*b*c*d*f*x^2*Sqrt[d + c^2*d*x^2])/(16*Sqrt[1 + c^2*x^2]) - (2*b*c*d*g*x^3*Sqrt[d + c^2*d*x^2])/(15*Sqrt[1 + c^2*x^2]) - (b*c^3*d*f*x^4*Sqrt[d + c^2*d*x^2])/(16*Sqrt[1 + c^2*x^2]) - (b*c^3*d*g*x^5*Sqrt[d + c^2*d*x^2])/(25*Sqrt[1 + c^2*x^2]) + (3*d*f*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/8 + (d*f*x*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/4 + (d*g*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(5*c^2) + (3*d*f*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(16*b*c*Sqrt[1 + c^2*x^2])","A",12,9,28,0.3214,1,"{5835, 5821, 5684, 5682, 5675, 30, 14, 5717, 194}"
42,1,984,0,1.8887872,"\int \frac{\left(d+c^2 d x^2\right)^{3/2} \left(a+b \sinh ^{-1}(c x)\right)}{f+g x} \, dx","Int[((d + c^2*d*x^2)^(3/2)*(a + b*ArcSinh[c*x]))/(f + g*x),x]","-\frac{b d x^3 \sqrt{c^2 d x^2+d} c^3}{9 g \sqrt{c^2 x^2+1}}+\frac{b d f x^2 \sqrt{c^2 d x^2+d} c^3}{4 g^2 \sqrt{c^2 x^2+1}}-\frac{d f x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) c^2}{2 g^2}-\frac{d \left(c^2 f^2+g^2\right) x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2 c}{2 b g^3 \sqrt{c^2 x^2+1}}-\frac{d f \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2 c}{4 b g^2 \sqrt{c^2 x^2+1}}-\frac{b d \left(c^2 f^2+g^2\right) x \sqrt{c^2 d x^2+d} c}{g^3 \sqrt{c^2 x^2+1}}-\frac{b d x \sqrt{c^2 d x^2+d} c}{3 g \sqrt{c^2 x^2+1}}+\frac{b d \left(c^2 f^2+g^2\right) \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{g^3}+\frac{d \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 g}-\frac{a d \left(c^2 f^2+g^2\right)^{3/2} \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(\frac{g-c^2 f x}{\sqrt{c^2 f^2+g^2} \sqrt{c^2 x^2+1}}\right)}{g^4 \sqrt{c^2 x^2+1}}+\frac{b d \left(c^2 f^2+g^2\right)^{3/2} \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x) \log \left(\frac{e^{\sinh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{g^4 \sqrt{c^2 x^2+1}}-\frac{b d \left(c^2 f^2+g^2\right)^{3/2} \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x) \log \left(\frac{e^{\sinh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2+g^2}}+1\right)}{g^4 \sqrt{c^2 x^2+1}}+\frac{b d \left(c^2 f^2+g^2\right)^{3/2} \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-\frac{e^{\sinh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2+g^2}}\right)}{g^4 \sqrt{c^2 x^2+1}}-\frac{b d \left(c^2 f^2+g^2\right)^{3/2} \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-\frac{e^{\sinh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2+g^2}}\right)}{g^4 \sqrt{c^2 x^2+1}}+\frac{a d \left(c^2 f^2+g^2\right) \sqrt{c^2 d x^2+d}}{g^3}+\frac{d \left(c^2 f^2+g^2\right) \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b g^2 (f+g x) c}-\frac{d \left(c^2 f^2+g^2\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b g^4 (f+g x) \sqrt{c^2 x^2+1} c}","-\frac{b d x^3 \sqrt{c^2 d x^2+d} c^3}{9 g \sqrt{c^2 x^2+1}}+\frac{b d f x^2 \sqrt{c^2 d x^2+d} c^3}{4 g^2 \sqrt{c^2 x^2+1}}-\frac{d f x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) c^2}{2 g^2}-\frac{d \left(c^2 f^2+g^2\right) x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2 c}{2 b g^3 \sqrt{c^2 x^2+1}}-\frac{d f \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2 c}{4 b g^2 \sqrt{c^2 x^2+1}}-\frac{b d \left(c^2 f^2+g^2\right) x \sqrt{c^2 d x^2+d} c}{g^3 \sqrt{c^2 x^2+1}}-\frac{b d x \sqrt{c^2 d x^2+d} c}{3 g \sqrt{c^2 x^2+1}}+\frac{b d \left(c^2 f^2+g^2\right) \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{g^3}+\frac{d \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 g}-\frac{a d \left(c^2 f^2+g^2\right)^{3/2} \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(\frac{g-c^2 f x}{\sqrt{c^2 f^2+g^2} \sqrt{c^2 x^2+1}}\right)}{g^4 \sqrt{c^2 x^2+1}}+\frac{b d \left(c^2 f^2+g^2\right)^{3/2} \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x) \log \left(\frac{e^{\sinh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{g^4 \sqrt{c^2 x^2+1}}-\frac{b d \left(c^2 f^2+g^2\right)^{3/2} \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x) \log \left(\frac{e^{\sinh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2+g^2}}+1\right)}{g^4 \sqrt{c^2 x^2+1}}+\frac{b d \left(c^2 f^2+g^2\right)^{3/2} \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-\frac{e^{\sinh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2+g^2}}\right)}{g^4 \sqrt{c^2 x^2+1}}-\frac{b d \left(c^2 f^2+g^2\right)^{3/2} \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-\frac{e^{\sinh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2+g^2}}\right)}{g^4 \sqrt{c^2 x^2+1}}+\frac{a d \left(c^2 f^2+g^2\right) \sqrt{c^2 d x^2+d}}{g^3}+\frac{d \left(c^2 f^2+g^2\right) \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b g^2 (f+g x) c}-\frac{d \left(c^2 f^2+g^2\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b g^4 (f+g x) \sqrt{c^2 x^2+1} c}",1,"(a*d*(c^2*f^2 + g^2)*Sqrt[d + c^2*d*x^2])/g^3 - (b*c*d*x*Sqrt[d + c^2*d*x^2])/(3*g*Sqrt[1 + c^2*x^2]) - (b*c*d*(c^2*f^2 + g^2)*x*Sqrt[d + c^2*d*x^2])/(g^3*Sqrt[1 + c^2*x^2]) + (b*c^3*d*f*x^2*Sqrt[d + c^2*d*x^2])/(4*g^2*Sqrt[1 + c^2*x^2]) - (b*c^3*d*x^3*Sqrt[d + c^2*d*x^2])/(9*g*Sqrt[1 + c^2*x^2]) + (b*d*(c^2*f^2 + g^2)*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/g^3 - (c^2*d*f*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(2*g^2) + (d*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*g) - (c*d*f*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*g^2*Sqrt[1 + c^2*x^2]) - (c*d*(c^2*f^2 + g^2)*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*g^3*Sqrt[1 + c^2*x^2]) - (d*(c^2*f^2 + g^2)^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c*g^4*(f + g*x)*Sqrt[1 + c^2*x^2]) + (d*(c^2*f^2 + g^2)*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c*g^2*(f + g*x)) - (a*d*(c^2*f^2 + g^2)^(3/2)*Sqrt[d + c^2*d*x^2]*ArcTanh[(g - c^2*f*x)/(Sqrt[c^2*f^2 + g^2]*Sqrt[1 + c^2*x^2])])/(g^4*Sqrt[1 + c^2*x^2]) + (b*d*(c^2*f^2 + g^2)^(3/2)*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x]*Log[1 + (E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2])])/(g^4*Sqrt[1 + c^2*x^2]) - (b*d*(c^2*f^2 + g^2)^(3/2)*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x]*Log[1 + (E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2])])/(g^4*Sqrt[1 + c^2*x^2]) + (b*d*(c^2*f^2 + g^2)^(3/2)*Sqrt[d + c^2*d*x^2]*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2]))])/(g^4*Sqrt[1 + c^2*x^2]) - (b*d*(c^2*f^2 + g^2)^(3/2)*Sqrt[d + c^2*d*x^2]*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2]))])/(g^4*Sqrt[1 + c^2*x^2])","A",29,24,30,0.8000,1,"{5835, 5825, 5682, 5675, 30, 5717, 5823, 683, 5815, 6742, 261, 725, 206, 5859, 1654, 12, 5857, 8, 5831, 3322, 2264, 2190, 2279, 2391}"
43,1,1228,0,1.13905,"\int (f+g x)^3 \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(f + g*x)^3*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]),x]","-\frac{b c^5 d^2 g^3 \sqrt{c^2 d x^2+d} x^9}{81 \sqrt{c^2 x^2+1}}-\frac{3 b c^5 d^2 f g^2 \sqrt{c^2 d x^2+d} x^8}{64 \sqrt{c^2 x^2+1}}-\frac{19 b c^3 d^2 g^3 \sqrt{c^2 d x^2+d} x^7}{441 \sqrt{c^2 x^2+1}}-\frac{3 b c^5 d^2 f^2 g \sqrt{c^2 d x^2+d} x^7}{49 \sqrt{c^2 x^2+1}}-\frac{17 b c^3 d^2 f g^2 \sqrt{c^2 d x^2+d} x^6}{96 \sqrt{c^2 x^2+1}}-\frac{b c d^2 g^3 \sqrt{c^2 d x^2+d} x^5}{21 \sqrt{c^2 x^2+1}}-\frac{9 b c^3 d^2 f^2 g \sqrt{c^2 d x^2+d} x^5}{35 \sqrt{c^2 x^2+1}}-\frac{5 b c^3 d^2 f^3 \sqrt{c^2 d x^2+d} x^4}{96 \sqrt{c^2 x^2+1}}-\frac{59 b c d^2 f g^2 \sqrt{c^2 d x^2+d} x^4}{256 \sqrt{c^2 x^2+1}}+\frac{15}{64} d^2 f g^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^3+\frac{3}{8} d^2 f g^2 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^3+\frac{5}{16} d^2 f g^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^3-\frac{b d^2 g^3 \sqrt{c^2 d x^2+d} x^3}{189 c \sqrt{c^2 x^2+1}}-\frac{3 b c d^2 f^2 g \sqrt{c^2 d x^2+d} x^3}{7 \sqrt{c^2 x^2+1}}-\frac{25 b c d^2 f^3 \sqrt{c^2 d x^2+d} x^2}{96 \sqrt{c^2 x^2+1}}-\frac{15 b d^2 f g^2 \sqrt{c^2 d x^2+d} x^2}{256 c \sqrt{c^2 x^2+1}}+\frac{5}{16} d^2 f^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x+\frac{15 d^2 f g^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^3 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^3 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x+\frac{2 b d^2 g^3 \sqrt{c^2 d x^2+d} x}{63 c^3 \sqrt{c^2 x^2+1}}-\frac{3 b d^2 f^2 g \sqrt{c^2 d x^2+d} x}{7 c \sqrt{c^2 x^2+1}}+\frac{5 d^2 f^3 \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{15 d^2 f g^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{d^2 g^3 \left(c^2 x^2+1\right)^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^4}-\frac{d^2 g^3 \left(c^2 x^2+1\right)^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^4}+\frac{3 d^2 f^2 g \left(c^2 x^2+1\right)^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^2}-\frac{b d^2 f^3 \left(c^2 x^2+1\right)^{5/2} \sqrt{c^2 d x^2+d}}{36 c}","-\frac{b c^5 d^2 g^3 \sqrt{c^2 d x^2+d} x^9}{81 \sqrt{c^2 x^2+1}}-\frac{3 b c^5 d^2 f g^2 \sqrt{c^2 d x^2+d} x^8}{64 \sqrt{c^2 x^2+1}}-\frac{19 b c^3 d^2 g^3 \sqrt{c^2 d x^2+d} x^7}{441 \sqrt{c^2 x^2+1}}-\frac{3 b c^5 d^2 f^2 g \sqrt{c^2 d x^2+d} x^7}{49 \sqrt{c^2 x^2+1}}-\frac{17 b c^3 d^2 f g^2 \sqrt{c^2 d x^2+d} x^6}{96 \sqrt{c^2 x^2+1}}-\frac{b c d^2 g^3 \sqrt{c^2 d x^2+d} x^5}{21 \sqrt{c^2 x^2+1}}-\frac{9 b c^3 d^2 f^2 g \sqrt{c^2 d x^2+d} x^5}{35 \sqrt{c^2 x^2+1}}-\frac{5 b c^3 d^2 f^3 \sqrt{c^2 d x^2+d} x^4}{96 \sqrt{c^2 x^2+1}}-\frac{59 b c d^2 f g^2 \sqrt{c^2 d x^2+d} x^4}{256 \sqrt{c^2 x^2+1}}+\frac{15}{64} d^2 f g^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^3+\frac{3}{8} d^2 f g^2 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^3+\frac{5}{16} d^2 f g^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^3-\frac{b d^2 g^3 \sqrt{c^2 d x^2+d} x^3}{189 c \sqrt{c^2 x^2+1}}-\frac{3 b c d^2 f^2 g \sqrt{c^2 d x^2+d} x^3}{7 \sqrt{c^2 x^2+1}}-\frac{25 b c d^2 f^3 \sqrt{c^2 d x^2+d} x^2}{96 \sqrt{c^2 x^2+1}}-\frac{15 b d^2 f g^2 \sqrt{c^2 d x^2+d} x^2}{256 c \sqrt{c^2 x^2+1}}+\frac{5}{16} d^2 f^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x+\frac{15 d^2 f g^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^3 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^3 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x+\frac{2 b d^2 g^3 \sqrt{c^2 d x^2+d} x}{63 c^3 \sqrt{c^2 x^2+1}}-\frac{3 b d^2 f^2 g \sqrt{c^2 d x^2+d} x}{7 c \sqrt{c^2 x^2+1}}+\frac{5 d^2 f^3 \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{15 d^2 f g^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{d^2 g^3 \left(c^2 x^2+1\right)^4 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{9 c^4}-\frac{d^2 g^3 \left(c^2 x^2+1\right)^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^4}+\frac{3 d^2 f^2 g \left(c^2 x^2+1\right)^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^2}-\frac{b d^2 f^3 \left(c^2 x^2+1\right)^{5/2} \sqrt{c^2 d x^2+d}}{36 c}",1,"(-3*b*d^2*f^2*g*x*Sqrt[d + c^2*d*x^2])/(7*c*Sqrt[1 + c^2*x^2]) + (2*b*d^2*g^3*x*Sqrt[d + c^2*d*x^2])/(63*c^3*Sqrt[1 + c^2*x^2]) - (25*b*c*d^2*f^3*x^2*Sqrt[d + c^2*d*x^2])/(96*Sqrt[1 + c^2*x^2]) - (15*b*d^2*f*g^2*x^2*Sqrt[d + c^2*d*x^2])/(256*c*Sqrt[1 + c^2*x^2]) - (3*b*c*d^2*f^2*g*x^3*Sqrt[d + c^2*d*x^2])/(7*Sqrt[1 + c^2*x^2]) - (b*d^2*g^3*x^3*Sqrt[d + c^2*d*x^2])/(189*c*Sqrt[1 + c^2*x^2]) - (5*b*c^3*d^2*f^3*x^4*Sqrt[d + c^2*d*x^2])/(96*Sqrt[1 + c^2*x^2]) - (59*b*c*d^2*f*g^2*x^4*Sqrt[d + c^2*d*x^2])/(256*Sqrt[1 + c^2*x^2]) - (9*b*c^3*d^2*f^2*g*x^5*Sqrt[d + c^2*d*x^2])/(35*Sqrt[1 + c^2*x^2]) - (b*c*d^2*g^3*x^5*Sqrt[d + c^2*d*x^2])/(21*Sqrt[1 + c^2*x^2]) - (17*b*c^3*d^2*f*g^2*x^6*Sqrt[d + c^2*d*x^2])/(96*Sqrt[1 + c^2*x^2]) - (3*b*c^5*d^2*f^2*g*x^7*Sqrt[d + c^2*d*x^2])/(49*Sqrt[1 + c^2*x^2]) - (19*b*c^3*d^2*g^3*x^7*Sqrt[d + c^2*d*x^2])/(441*Sqrt[1 + c^2*x^2]) - (3*b*c^5*d^2*f*g^2*x^8*Sqrt[d + c^2*d*x^2])/(64*Sqrt[1 + c^2*x^2]) - (b*c^5*d^2*g^3*x^9*Sqrt[d + c^2*d*x^2])/(81*Sqrt[1 + c^2*x^2]) - (b*d^2*f^3*(1 + c^2*x^2)^(5/2)*Sqrt[d + c^2*d*x^2])/(36*c) + (5*d^2*f^3*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/16 + (15*d^2*f*g^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(128*c^2) + (15*d^2*f*g^2*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/64 + (5*d^2*f^3*x*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/24 + (5*d^2*f*g^2*x^3*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/16 + (d^2*f^3*x*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/6 + (3*d^2*f*g^2*x^3*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/8 + (3*d^2*f^2*g*(1 + c^2*x^2)^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(7*c^2) - (d^2*g^3*(1 + c^2*x^2)^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(7*c^4) + (d^2*g^3*(1 + c^2*x^2)^4*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(9*c^4) + (5*d^2*f^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(32*b*c*Sqrt[1 + c^2*x^2]) - (15*d^2*f*g^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",30,18,30,0.6000,1,"{5835, 5821, 5684, 5682, 5675, 30, 14, 261, 5717, 194, 5744, 5742, 5758, 266, 43, 5732, 12, 373}"
44,1,901,0,0.9258637,"\int (f+g x)^2 \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(f + g*x)^2*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]),x]","-\frac{b c^5 d^2 g^2 \sqrt{c^2 d x^2+d} x^8}{64 \sqrt{c^2 x^2+1}}-\frac{2 b c^5 d^2 f g \sqrt{c^2 d x^2+d} x^7}{49 \sqrt{c^2 x^2+1}}-\frac{17 b c^3 d^2 g^2 \sqrt{c^2 d x^2+d} x^6}{288 \sqrt{c^2 x^2+1}}-\frac{6 b c^3 d^2 f g \sqrt{c^2 d x^2+d} x^5}{35 \sqrt{c^2 x^2+1}}-\frac{5 b c^3 d^2 f^2 \sqrt{c^2 d x^2+d} x^4}{96 \sqrt{c^2 x^2+1}}-\frac{59 b c d^2 g^2 \sqrt{c^2 d x^2+d} x^4}{768 \sqrt{c^2 x^2+1}}+\frac{5}{64} d^2 g^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^3+\frac{1}{8} d^2 g^2 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^3+\frac{5}{48} d^2 g^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^3-\frac{2 b c d^2 f g \sqrt{c^2 d x^2+d} x^3}{7 \sqrt{c^2 x^2+1}}-\frac{25 b c d^2 f^2 \sqrt{c^2 d x^2+d} x^2}{96 \sqrt{c^2 x^2+1}}-\frac{5 b d^2 g^2 \sqrt{c^2 d x^2+d} x^2}{256 c \sqrt{c^2 x^2+1}}+\frac{5}{16} d^2 f^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x+\frac{5 d^2 g^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^2 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x-\frac{2 b d^2 f g \sqrt{c^2 d x^2+d} x}{7 c \sqrt{c^2 x^2+1}}+\frac{5 d^2 f^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{5 d^2 g^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{2 d^2 f g \left(c^2 x^2+1\right)^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^2}-\frac{b d^2 f^2 \left(c^2 x^2+1\right)^{5/2} \sqrt{c^2 d x^2+d}}{36 c}","-\frac{b c^5 d^2 g^2 \sqrt{c^2 d x^2+d} x^8}{64 \sqrt{c^2 x^2+1}}-\frac{2 b c^5 d^2 f g \sqrt{c^2 d x^2+d} x^7}{49 \sqrt{c^2 x^2+1}}-\frac{17 b c^3 d^2 g^2 \sqrt{c^2 d x^2+d} x^6}{288 \sqrt{c^2 x^2+1}}-\frac{6 b c^3 d^2 f g \sqrt{c^2 d x^2+d} x^5}{35 \sqrt{c^2 x^2+1}}-\frac{5 b c^3 d^2 f^2 \sqrt{c^2 d x^2+d} x^4}{96 \sqrt{c^2 x^2+1}}-\frac{59 b c d^2 g^2 \sqrt{c^2 d x^2+d} x^4}{768 \sqrt{c^2 x^2+1}}+\frac{5}{64} d^2 g^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^3+\frac{1}{8} d^2 g^2 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^3+\frac{5}{48} d^2 g^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x^3-\frac{2 b c d^2 f g \sqrt{c^2 d x^2+d} x^3}{7 \sqrt{c^2 x^2+1}}-\frac{25 b c d^2 f^2 \sqrt{c^2 d x^2+d} x^2}{96 \sqrt{c^2 x^2+1}}-\frac{5 b d^2 g^2 \sqrt{c^2 d x^2+d} x^2}{256 c \sqrt{c^2 x^2+1}}+\frac{5}{16} d^2 f^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x+\frac{5 d^2 g^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^2 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) x-\frac{2 b d^2 f g \sqrt{c^2 d x^2+d} x}{7 c \sqrt{c^2 x^2+1}}+\frac{5 d^2 f^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{5 d^2 g^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{2 d^2 f g \left(c^2 x^2+1\right)^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^2}-\frac{b d^2 f^2 \left(c^2 x^2+1\right)^{5/2} \sqrt{c^2 d x^2+d}}{36 c}",1,"(-2*b*d^2*f*g*x*Sqrt[d + c^2*d*x^2])/(7*c*Sqrt[1 + c^2*x^2]) - (25*b*c*d^2*f^2*x^2*Sqrt[d + c^2*d*x^2])/(96*Sqrt[1 + c^2*x^2]) - (5*b*d^2*g^2*x^2*Sqrt[d + c^2*d*x^2])/(256*c*Sqrt[1 + c^2*x^2]) - (2*b*c*d^2*f*g*x^3*Sqrt[d + c^2*d*x^2])/(7*Sqrt[1 + c^2*x^2]) - (5*b*c^3*d^2*f^2*x^4*Sqrt[d + c^2*d*x^2])/(96*Sqrt[1 + c^2*x^2]) - (59*b*c*d^2*g^2*x^4*Sqrt[d + c^2*d*x^2])/(768*Sqrt[1 + c^2*x^2]) - (6*b*c^3*d^2*f*g*x^5*Sqrt[d + c^2*d*x^2])/(35*Sqrt[1 + c^2*x^2]) - (17*b*c^3*d^2*g^2*x^6*Sqrt[d + c^2*d*x^2])/(288*Sqrt[1 + c^2*x^2]) - (2*b*c^5*d^2*f*g*x^7*Sqrt[d + c^2*d*x^2])/(49*Sqrt[1 + c^2*x^2]) - (b*c^5*d^2*g^2*x^8*Sqrt[d + c^2*d*x^2])/(64*Sqrt[1 + c^2*x^2]) - (b*d^2*f^2*(1 + c^2*x^2)^(5/2)*Sqrt[d + c^2*d*x^2])/(36*c) + (5*d^2*f^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/16 + (5*d^2*g^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(128*c^2) + (5*d^2*g^2*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/64 + (5*d^2*f^2*x*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/24 + (5*d^2*g^2*x^3*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/48 + (d^2*f^2*x*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/6 + (d^2*g^2*x^3*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/8 + (2*d^2*f*g*(1 + c^2*x^2)^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(7*c^2) + (5*d^2*f^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(32*b*c*Sqrt[1 + c^2*x^2]) - (5*d^2*g^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",26,15,30,0.5000,1,"{5835, 5821, 5684, 5682, 5675, 30, 14, 261, 5717, 194, 5744, 5742, 5758, 266, 43}"
45,1,494,0,0.3972538,"\int (f+g x) \left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right) \, dx","Int[(f + g*x)*(d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]),x]","\frac{1}{6} d^2 f x \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{16} d^2 f x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{24} d^2 f x \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 d^2 f \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{d^2 g \left(c^2 x^2+1\right)^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^2}-\frac{5 b c^3 d^2 f x^4 \sqrt{c^2 d x^2+d}}{96 \sqrt{c^2 x^2+1}}-\frac{25 b c d^2 f x^2 \sqrt{c^2 d x^2+d}}{96 \sqrt{c^2 x^2+1}}-\frac{b d^2 f \left(c^2 x^2+1\right)^{5/2} \sqrt{c^2 d x^2+d}}{36 c}-\frac{b c^5 d^2 g x^7 \sqrt{c^2 d x^2+d}}{49 \sqrt{c^2 x^2+1}}-\frac{3 b c^3 d^2 g x^5 \sqrt{c^2 d x^2+d}}{35 \sqrt{c^2 x^2+1}}-\frac{b c d^2 g x^3 \sqrt{c^2 d x^2+d}}{7 \sqrt{c^2 x^2+1}}-\frac{b d^2 g x \sqrt{c^2 d x^2+d}}{7 c \sqrt{c^2 x^2+1}}","\frac{1}{6} d^2 f x \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{16} d^2 f x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5}{24} d^2 f x \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)+\frac{5 d^2 f \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{d^2 g \left(c^2 x^2+1\right)^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{7 c^2}-\frac{5 b c^3 d^2 f x^4 \sqrt{c^2 d x^2+d}}{96 \sqrt{c^2 x^2+1}}-\frac{25 b c d^2 f x^2 \sqrt{c^2 d x^2+d}}{96 \sqrt{c^2 x^2+1}}-\frac{b d^2 f \left(c^2 x^2+1\right)^{5/2} \sqrt{c^2 d x^2+d}}{36 c}-\frac{b c^5 d^2 g x^7 \sqrt{c^2 d x^2+d}}{49 \sqrt{c^2 x^2+1}}-\frac{3 b c^3 d^2 g x^5 \sqrt{c^2 d x^2+d}}{35 \sqrt{c^2 x^2+1}}-\frac{b c d^2 g x^3 \sqrt{c^2 d x^2+d}}{7 \sqrt{c^2 x^2+1}}-\frac{b d^2 g x \sqrt{c^2 d x^2+d}}{7 c \sqrt{c^2 x^2+1}}",1,"-(b*d^2*g*x*Sqrt[d + c^2*d*x^2])/(7*c*Sqrt[1 + c^2*x^2]) - (25*b*c*d^2*f*x^2*Sqrt[d + c^2*d*x^2])/(96*Sqrt[1 + c^2*x^2]) - (b*c*d^2*g*x^3*Sqrt[d + c^2*d*x^2])/(7*Sqrt[1 + c^2*x^2]) - (5*b*c^3*d^2*f*x^4*Sqrt[d + c^2*d*x^2])/(96*Sqrt[1 + c^2*x^2]) - (3*b*c^3*d^2*g*x^5*Sqrt[d + c^2*d*x^2])/(35*Sqrt[1 + c^2*x^2]) - (b*c^5*d^2*g*x^7*Sqrt[d + c^2*d*x^2])/(49*Sqrt[1 + c^2*x^2]) - (b*d^2*f*(1 + c^2*x^2)^(5/2)*Sqrt[d + c^2*d*x^2])/(36*c) + (5*d^2*f*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/16 + (5*d^2*f*x*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/24 + (d^2*f*x*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/6 + (d^2*g*(1 + c^2*x^2)^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(7*c^2) + (5*d^2*f*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(32*b*c*Sqrt[1 + c^2*x^2])","A",14,10,28,0.3571,1,"{5835, 5821, 5684, 5682, 5675, 30, 14, 261, 5717, 194}"
46,1,1536,0,2.4476238,"\int \frac{\left(d+c^2 d x^2\right)^{5/2} \left(a+b \sinh ^{-1}(c x)\right)}{f+g x} \, dx","Int[((d + c^2*d*x^2)^(5/2)*(a + b*ArcSinh[c*x]))/(f + g*x),x]","-\frac{b d^2 x^5 \sqrt{c^2 d x^2+d} c^5}{25 g \sqrt{c^2 x^2+1}}+\frac{b d^2 f x^4 \sqrt{c^2 d x^2+d} c^5}{16 g^2 \sqrt{c^2 x^2+1}}-\frac{d^2 f x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) c^4}{4 g^2}-\frac{b d^2 \left(c^2 f^2+2 g^2\right) x^3 \sqrt{c^2 d x^2+d} c^3}{9 g^3 \sqrt{c^2 x^2+1}}-\frac{b d^2 x^3 \sqrt{c^2 d x^2+d} c^3}{45 g \sqrt{c^2 x^2+1}}+\frac{b d^2 f \left(c^2 f^2+2 g^2\right) x^2 \sqrt{c^2 d x^2+d} c^3}{4 g^4 \sqrt{c^2 x^2+1}}+\frac{b d^2 f x^2 \sqrt{c^2 d x^2+d} c^3}{16 g^2 \sqrt{c^2 x^2+1}}-\frac{d^2 f \left(c^2 f^2+2 g^2\right) x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) c^2}{2 g^4}-\frac{d^2 f x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) c^2}{8 g^2}-\frac{d^2 f \left(c^2 f^2+2 g^2\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2 c}{4 b g^4 \sqrt{c^2 x^2+1}}-\frac{d^2 \left(c^2 f^2+g^2\right)^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2 c}{2 b g^5 \sqrt{c^2 x^2+1}}+\frac{d^2 f \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2 c}{16 b g^2 \sqrt{c^2 x^2+1}}-\frac{b d^2 \left(c^2 f^2+g^2\right)^2 x \sqrt{c^2 d x^2+d} c}{g^5 \sqrt{c^2 x^2+1}}-\frac{b d^2 \left(c^2 f^2+2 g^2\right) x \sqrt{c^2 d x^2+d} c}{3 g^3 \sqrt{c^2 x^2+1}}+\frac{2 b d^2 x \sqrt{c^2 d x^2+d} c}{15 g \sqrt{c^2 x^2+1}}+\frac{b d^2 \left(c^2 f^2+g^2\right)^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{g^5}+\frac{d^2 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{5 g}+\frac{d^2 \left(c^2 f^2+2 g^2\right) \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 g^3}-\frac{d^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 g}-\frac{a d^2 \left(c^2 f^2+g^2\right)^{5/2} \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(\frac{g-c^2 f x}{\sqrt{c^2 f^2+g^2} \sqrt{c^2 x^2+1}}\right)}{g^6 \sqrt{c^2 x^2+1}}+\frac{b d^2 \left(c^2 f^2+g^2\right)^{5/2} \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x) \log \left(\frac{e^{\sinh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{g^6 \sqrt{c^2 x^2+1}}-\frac{b d^2 \left(c^2 f^2+g^2\right)^{5/2} \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x) \log \left(\frac{e^{\sinh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2+g^2}}+1\right)}{g^6 \sqrt{c^2 x^2+1}}+\frac{b d^2 \left(c^2 f^2+g^2\right)^{5/2} \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-\frac{e^{\sinh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2+g^2}}\right)}{g^6 \sqrt{c^2 x^2+1}}-\frac{b d^2 \left(c^2 f^2+g^2\right)^{5/2} \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-\frac{e^{\sinh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2+g^2}}\right)}{g^6 \sqrt{c^2 x^2+1}}+\frac{a d^2 \left(c^2 f^2+g^2\right)^2 \sqrt{c^2 d x^2+d}}{g^5}+\frac{d^2 \left(c^2 f^2+g^2\right)^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b g^4 (f+g x) c}-\frac{d^2 \left(c^2 f^2+g^2\right)^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b g^6 (f+g x) \sqrt{c^2 x^2+1} c}","-\frac{b d^2 x^5 \sqrt{c^2 d x^2+d} c^5}{25 g \sqrt{c^2 x^2+1}}+\frac{b d^2 f x^4 \sqrt{c^2 d x^2+d} c^5}{16 g^2 \sqrt{c^2 x^2+1}}-\frac{d^2 f x^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) c^4}{4 g^2}-\frac{b d^2 \left(c^2 f^2+2 g^2\right) x^3 \sqrt{c^2 d x^2+d} c^3}{9 g^3 \sqrt{c^2 x^2+1}}-\frac{b d^2 x^3 \sqrt{c^2 d x^2+d} c^3}{45 g \sqrt{c^2 x^2+1}}+\frac{b d^2 f \left(c^2 f^2+2 g^2\right) x^2 \sqrt{c^2 d x^2+d} c^3}{4 g^4 \sqrt{c^2 x^2+1}}+\frac{b d^2 f x^2 \sqrt{c^2 d x^2+d} c^3}{16 g^2 \sqrt{c^2 x^2+1}}-\frac{d^2 f \left(c^2 f^2+2 g^2\right) x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) c^2}{2 g^4}-\frac{d^2 f x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right) c^2}{8 g^2}-\frac{d^2 f \left(c^2 f^2+2 g^2\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2 c}{4 b g^4 \sqrt{c^2 x^2+1}}-\frac{d^2 \left(c^2 f^2+g^2\right)^2 x \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2 c}{2 b g^5 \sqrt{c^2 x^2+1}}+\frac{d^2 f \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2 c}{16 b g^2 \sqrt{c^2 x^2+1}}-\frac{b d^2 \left(c^2 f^2+g^2\right)^2 x \sqrt{c^2 d x^2+d} c}{g^5 \sqrt{c^2 x^2+1}}-\frac{b d^2 \left(c^2 f^2+2 g^2\right) x \sqrt{c^2 d x^2+d} c}{3 g^3 \sqrt{c^2 x^2+1}}+\frac{2 b d^2 x \sqrt{c^2 d x^2+d} c}{15 g \sqrt{c^2 x^2+1}}+\frac{b d^2 \left(c^2 f^2+g^2\right)^2 \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x)}{g^5}+\frac{d^2 \left(c^2 x^2+1\right)^2 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{5 g}+\frac{d^2 \left(c^2 f^2+2 g^2\right) \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 g^3}-\frac{d^2 \left(c^2 x^2+1\right) \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)}{3 g}-\frac{a d^2 \left(c^2 f^2+g^2\right)^{5/2} \sqrt{c^2 d x^2+d} \tanh ^{-1}\left(\frac{g-c^2 f x}{\sqrt{c^2 f^2+g^2} \sqrt{c^2 x^2+1}}\right)}{g^6 \sqrt{c^2 x^2+1}}+\frac{b d^2 \left(c^2 f^2+g^2\right)^{5/2} \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x) \log \left(\frac{e^{\sinh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{g^6 \sqrt{c^2 x^2+1}}-\frac{b d^2 \left(c^2 f^2+g^2\right)^{5/2} \sqrt{c^2 d x^2+d} \sinh ^{-1}(c x) \log \left(\frac{e^{\sinh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2+g^2}}+1\right)}{g^6 \sqrt{c^2 x^2+1}}+\frac{b d^2 \left(c^2 f^2+g^2\right)^{5/2} \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-\frac{e^{\sinh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2+g^2}}\right)}{g^6 \sqrt{c^2 x^2+1}}-\frac{b d^2 \left(c^2 f^2+g^2\right)^{5/2} \sqrt{c^2 d x^2+d} \text{PolyLog}\left(2,-\frac{e^{\sinh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2+g^2}}\right)}{g^6 \sqrt{c^2 x^2+1}}+\frac{a d^2 \left(c^2 f^2+g^2\right)^2 \sqrt{c^2 d x^2+d}}{g^5}+\frac{d^2 \left(c^2 f^2+g^2\right)^2 \sqrt{c^2 x^2+1} \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b g^4 (f+g x) c}-\frac{d^2 \left(c^2 f^2+g^2\right)^3 \sqrt{c^2 d x^2+d} \left(a+b \sinh ^{-1}(c x)\right)^2}{2 b g^6 (f+g x) \sqrt{c^2 x^2+1} c}",1,"(a*d^2*(c^2*f^2 + g^2)^2*Sqrt[d + c^2*d*x^2])/g^5 + (2*b*c*d^2*x*Sqrt[d + c^2*d*x^2])/(15*g*Sqrt[1 + c^2*x^2]) - (b*c*d^2*(c^2*f^2 + g^2)^2*x*Sqrt[d + c^2*d*x^2])/(g^5*Sqrt[1 + c^2*x^2]) - (b*c*d^2*(c^2*f^2 + 2*g^2)*x*Sqrt[d + c^2*d*x^2])/(3*g^3*Sqrt[1 + c^2*x^2]) + (b*c^3*d^2*f*x^2*Sqrt[d + c^2*d*x^2])/(16*g^2*Sqrt[1 + c^2*x^2]) + (b*c^3*d^2*f*(c^2*f^2 + 2*g^2)*x^2*Sqrt[d + c^2*d*x^2])/(4*g^4*Sqrt[1 + c^2*x^2]) - (b*c^3*d^2*x^3*Sqrt[d + c^2*d*x^2])/(45*g*Sqrt[1 + c^2*x^2]) - (b*c^3*d^2*(c^2*f^2 + 2*g^2)*x^3*Sqrt[d + c^2*d*x^2])/(9*g^3*Sqrt[1 + c^2*x^2]) + (b*c^5*d^2*f*x^4*Sqrt[d + c^2*d*x^2])/(16*g^2*Sqrt[1 + c^2*x^2]) - (b*c^5*d^2*x^5*Sqrt[d + c^2*d*x^2])/(25*g*Sqrt[1 + c^2*x^2]) + (b*d^2*(c^2*f^2 + g^2)^2*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x])/g^5 - (c^2*d^2*f*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(8*g^2) - (c^2*d^2*f*(c^2*f^2 + 2*g^2)*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(2*g^4) - (c^4*d^2*f*x^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(4*g^2) - (d^2*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*g) + (d^2*(c^2*f^2 + 2*g^2)*(1 + c^2*x^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(3*g^3) + (d^2*(1 + c^2*x^2)^2*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x]))/(5*g) + (c*d^2*f*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(16*b*g^2*Sqrt[1 + c^2*x^2]) - (c*d^2*f*(c^2*f^2 + 2*g^2)*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*g^4*Sqrt[1 + c^2*x^2]) - (c*d^2*(c^2*f^2 + g^2)^2*x*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*g^5*Sqrt[1 + c^2*x^2]) - (d^2*(c^2*f^2 + g^2)^3*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c*g^6*(f + g*x)*Sqrt[1 + c^2*x^2]) + (d^2*(c^2*f^2 + g^2)^2*Sqrt[1 + c^2*x^2]*Sqrt[d + c^2*d*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c*g^4*(f + g*x)) - (a*d^2*(c^2*f^2 + g^2)^(5/2)*Sqrt[d + c^2*d*x^2]*ArcTanh[(g - c^2*f*x)/(Sqrt[c^2*f^2 + g^2]*Sqrt[1 + c^2*x^2])])/(g^6*Sqrt[1 + c^2*x^2]) + (b*d^2*(c^2*f^2 + g^2)^(5/2)*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x]*Log[1 + (E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2])])/(g^6*Sqrt[1 + c^2*x^2]) - (b*d^2*(c^2*f^2 + g^2)^(5/2)*Sqrt[d + c^2*d*x^2]*ArcSinh[c*x]*Log[1 + (E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2])])/(g^6*Sqrt[1 + c^2*x^2]) + (b*d^2*(c^2*f^2 + g^2)^(5/2)*Sqrt[d + c^2*d*x^2]*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2]))])/(g^6*Sqrt[1 + c^2*x^2]) - (b*d^2*(c^2*f^2 + g^2)^(5/2)*Sqrt[d + c^2*d*x^2]*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2]))])/(g^6*Sqrt[1 + c^2*x^2])","A",37,29,30,0.9667,1,"{5835, 5825, 5682, 5675, 30, 5717, 5742, 5758, 266, 43, 5732, 12, 5823, 683, 5815, 6742, 261, 725, 206, 5859, 1654, 5857, 8, 5831, 3322, 2264, 2190, 2279, 2391}"
47,1,430,0,0.575307,"\int \frac{(f+g x)^3 \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{d+c^2 d x^2}} \, dx","Int[((f + g*x)^3*(a + b*ArcSinh[c*x]))/Sqrt[d + c^2*d*x^2],x]","\frac{3 f^2 g \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^2 \sqrt{c^2 d x^2+d}}+\frac{f^3 \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{3 f g^2 \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{3 f g^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{2 c^2 \sqrt{c^2 d x^2+d}}-\frac{2 g^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c^4 \sqrt{c^2 d x^2+d}}+\frac{g^3 x^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2 \sqrt{c^2 d x^2+d}}-\frac{3 b f^2 g x \sqrt{c^2 x^2+1}}{c \sqrt{c^2 d x^2+d}}-\frac{3 b f g^2 x^2 \sqrt{c^2 x^2+1}}{4 c \sqrt{c^2 d x^2+d}}-\frac{b g^3 x^3 \sqrt{c^2 x^2+1}}{9 c \sqrt{c^2 d x^2+d}}+\frac{2 b g^3 x \sqrt{c^2 x^2+1}}{3 c^3 \sqrt{c^2 d x^2+d}}","\frac{3 f^2 g \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^2 \sqrt{c^2 d x^2+d}}+\frac{f^3 \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{3 f g^2 \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{3 f g^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{2 c^2 \sqrt{c^2 d x^2+d}}-\frac{2 g^3 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c^4 \sqrt{c^2 d x^2+d}}+\frac{g^3 x^2 \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{3 c^2 \sqrt{c^2 d x^2+d}}-\frac{3 b f^2 g x \sqrt{c^2 x^2+1}}{c \sqrt{c^2 d x^2+d}}-\frac{3 b f g^2 x^2 \sqrt{c^2 x^2+1}}{4 c \sqrt{c^2 d x^2+d}}-\frac{b g^3 x^3 \sqrt{c^2 x^2+1}}{9 c \sqrt{c^2 d x^2+d}}+\frac{2 b g^3 x \sqrt{c^2 x^2+1}}{3 c^3 \sqrt{c^2 d x^2+d}}",1,"(-3*b*f^2*g*x*Sqrt[1 + c^2*x^2])/(c*Sqrt[d + c^2*d*x^2]) + (2*b*g^3*x*Sqrt[1 + c^2*x^2])/(3*c^3*Sqrt[d + c^2*d*x^2]) - (3*b*f*g^2*x^2*Sqrt[1 + c^2*x^2])/(4*c*Sqrt[d + c^2*d*x^2]) - (b*g^3*x^3*Sqrt[1 + c^2*x^2])/(9*c*Sqrt[d + c^2*d*x^2]) + (3*f^2*g*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c^2*Sqrt[d + c^2*d*x^2]) - (2*g^3*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(3*c^4*Sqrt[d + c^2*d*x^2]) + (3*f*g^2*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(2*c^2*Sqrt[d + c^2*d*x^2]) + (g^3*x^2*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(3*c^2*Sqrt[d + c^2*d*x^2]) + (f^3*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c*Sqrt[d + c^2*d*x^2]) - (3*f*g^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*c^3*Sqrt[d + c^2*d*x^2])","A",13,7,30,0.2333,1,"{5835, 5821, 5675, 5717, 8, 5758, 30}"
48,1,258,0,0.4295508,"\int \frac{(f+g x)^2 \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{d+c^2 d x^2}} \, dx","Int[((f + g*x)^2*(a + b*ArcSinh[c*x]))/Sqrt[d + c^2*d*x^2],x]","\frac{f^2 \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{2 f g \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^2 \sqrt{c^2 d x^2+d}}-\frac{g^2 \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{g^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{2 c^2 \sqrt{c^2 d x^2+d}}-\frac{2 b f g x \sqrt{c^2 x^2+1}}{c \sqrt{c^2 d x^2+d}}-\frac{b g^2 x^2 \sqrt{c^2 x^2+1}}{4 c \sqrt{c^2 d x^2+d}}","\frac{f^2 \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{2 f g \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^2 \sqrt{c^2 d x^2+d}}-\frac{g^2 \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{g^2 x \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{2 c^2 \sqrt{c^2 d x^2+d}}-\frac{2 b f g x \sqrt{c^2 x^2+1}}{c \sqrt{c^2 d x^2+d}}-\frac{b g^2 x^2 \sqrt{c^2 x^2+1}}{4 c \sqrt{c^2 d x^2+d}}",1,"(-2*b*f*g*x*Sqrt[1 + c^2*x^2])/(c*Sqrt[d + c^2*d*x^2]) - (b*g^2*x^2*Sqrt[1 + c^2*x^2])/(4*c*Sqrt[d + c^2*d*x^2]) + (2*f*g*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c^2*Sqrt[d + c^2*d*x^2]) + (g^2*x*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(2*c^2*Sqrt[d + c^2*d*x^2]) + (f^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c*Sqrt[d + c^2*d*x^2]) - (g^2*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(4*b*c^3*Sqrt[d + c^2*d*x^2])","A",9,7,30,0.2333,1,"{5835, 5821, 5675, 5717, 8, 5758, 30}"
49,1,120,0,0.2171227,"\int \frac{(f+g x) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{d+c^2 d x^2}} \, dx","Int[((f + g*x)*(a + b*ArcSinh[c*x]))/Sqrt[d + c^2*d*x^2],x]","\frac{f \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{g \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^2 \sqrt{c^2 d x^2+d}}-\frac{b g x \sqrt{c^2 x^2+1}}{c \sqrt{c^2 d x^2+d}}","\frac{f \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{g \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{c^2 \sqrt{c^2 d x^2+d}}-\frac{b g x \sqrt{c^2 x^2+1}}{c \sqrt{c^2 d x^2+d}}",1,"-((b*g*x*Sqrt[1 + c^2*x^2])/(c*Sqrt[d + c^2*d*x^2])) + (g*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/(c^2*Sqrt[d + c^2*d*x^2]) + (f*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])^2)/(2*b*c*Sqrt[d + c^2*d*x^2])","A",6,5,28,0.1786,1,"{5835, 5821, 5675, 5717, 8}"
50,1,47,0,0.0567424,"\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}"
51,1,325,0,0.5480572,"\int \frac{a+b \sinh ^{-1}(c x)}{(f+g x) \sqrt{d+c^2 d x^2}} \, dx","Int[(a + b*ArcSinh[c*x])/((f + g*x)*Sqrt[d + c^2*d*x^2]),x]","\frac{b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{\sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2}}-\frac{b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{\sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2}}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{\sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2}}-\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}+1\right)}{\sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2}}","\frac{b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{\sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2}}-\frac{b \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{\sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2}}+\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{\sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2}}-\frac{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}+1\right)}{\sqrt{c^2 d x^2+d} \sqrt{c^2 f^2+g^2}}",1,"(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 + (E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2])])/(Sqrt[c^2*f^2 + g^2]*Sqrt[d + c^2*d*x^2]) - (Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 + (E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2])])/(Sqrt[c^2*f^2 + g^2]*Sqrt[d + c^2*d*x^2]) + (b*Sqrt[1 + c^2*x^2]*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2]))])/(Sqrt[c^2*f^2 + g^2]*Sqrt[d + c^2*d*x^2]) - (b*Sqrt[1 + c^2*x^2]*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2]))])/(Sqrt[c^2*f^2 + g^2]*Sqrt[d + c^2*d*x^2])","A",10,7,30,0.2333,1,"{5835, 5831, 3322, 2264, 2190, 2279, 2391}"
52,1,444,0,0.6607694,"\int \frac{a+b \sinh ^{-1}(c x)}{(f+g x)^2 \sqrt{d+c^2 d x^2}} \, dx","Int[(a + b*ArcSinh[c*x])/((f + g*x)^2*Sqrt[d + c^2*d*x^2]),x]","\frac{b c^2 f \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{\sqrt{c^2 d x^2+d} \left(c^2 f^2+g^2\right)^{3/2}}-\frac{b c^2 f \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{\sqrt{c^2 d x^2+d} \left(c^2 f^2+g^2\right)^{3/2}}-\frac{g \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 d x^2+d} \left(c^2 f^2+g^2\right) (f+g x)}+\frac{c^2 f \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{\sqrt{c^2 d x^2+d} \left(c^2 f^2+g^2\right)^{3/2}}-\frac{c^2 f \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}+1\right)}{\sqrt{c^2 d x^2+d} \left(c^2 f^2+g^2\right)^{3/2}}+\frac{b c \sqrt{c^2 x^2+1} \log (f+g x)}{\sqrt{c^2 d x^2+d} \left(c^2 f^2+g^2\right)}","\frac{b c^2 f \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{\sqrt{c^2 d x^2+d} \left(c^2 f^2+g^2\right)^{3/2}}-\frac{b c^2 f \sqrt{c^2 x^2+1} \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{\sqrt{c^2 d x^2+d} \left(c^2 f^2+g^2\right)^{3/2}}-\frac{g \left(c^2 x^2+1\right) \left(a+b \sinh ^{-1}(c x)\right)}{\sqrt{c^2 d x^2+d} \left(c^2 f^2+g^2\right) (f+g x)}+\frac{c^2 f \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{\sqrt{c^2 d x^2+d} \left(c^2 f^2+g^2\right)^{3/2}}-\frac{c^2 f \sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}+1\right)}{\sqrt{c^2 d x^2+d} \left(c^2 f^2+g^2\right)^{3/2}}+\frac{b c \sqrt{c^2 x^2+1} \log (f+g x)}{\sqrt{c^2 d x^2+d} \left(c^2 f^2+g^2\right)}",1,"-((g*(1 + c^2*x^2)*(a + b*ArcSinh[c*x]))/((c^2*f^2 + g^2)*(f + g*x)*Sqrt[d + c^2*d*x^2])) + (c^2*f*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 + (E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2])])/((c^2*f^2 + g^2)^(3/2)*Sqrt[d + c^2*d*x^2]) - (c^2*f*Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])*Log[1 + (E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2])])/((c^2*f^2 + g^2)^(3/2)*Sqrt[d + c^2*d*x^2]) + (b*c*Sqrt[1 + c^2*x^2]*Log[f + g*x])/((c^2*f^2 + g^2)*Sqrt[d + c^2*d*x^2]) + (b*c^2*f*Sqrt[1 + c^2*x^2]*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2]))])/((c^2*f^2 + g^2)^(3/2)*Sqrt[d + c^2*d*x^2]) - (b*c^2*f*Sqrt[1 + c^2*x^2]*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2]))])/((c^2*f^2 + g^2)^(3/2)*Sqrt[d + c^2*d*x^2])","A",13,10,30,0.3333,1,"{5835, 5831, 3324, 3322, 2264, 2190, 2279, 2391, 2668, 31}"
53,0,0,0,0.1859187,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^n \log \left(h (f+g x)^m\right)}{\sqrt{1+c^2 x^2}} \, dx","Int[((a + b*ArcSinh[c*x])^n*Log[h*(f + g*x)^m])/Sqrt[1 + c^2*x^2],x]","\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^n \log \left(h (f+g x)^m\right)}{\sqrt{1+c^2 x^2}} \, dx","\text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c x)\right)^n \log \left(h (f+g x)^m\right)}{\sqrt{c^2 x^2+1}},x\right)",0,"Defer[Int][((a + b*ArcSinh[c*x])^n*Log[h*(f + g*x)^m])/Sqrt[1 + c^2*x^2], x]","A",0,0,0,0,-1,"{}"
54,1,438,0,0.7265403,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(h (f+g x)^m\right)}{\sqrt{1+c^2 x^2}} \, dx","Int[((a + b*ArcSinh[c*x])^2*Log[h*(f + g*x)^m])/Sqrt[1 + c^2*x^2],x]","-\frac{m \left(a+b \sinh ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{c}-\frac{m \left(a+b \sinh ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{c}+\frac{2 b m \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(3,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{c}+\frac{2 b m \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(3,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{c}-\frac{2 b^2 m \text{PolyLog}\left(4,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{c}-\frac{2 b^2 m \text{PolyLog}\left(4,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{c}+\frac{m \left(a+b \sinh ^{-1}(c x)\right)^4}{12 b^2 c}-\frac{m \left(a+b \sinh ^{-1}(c x)\right)^3 \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{3 b c}-\frac{m \left(a+b \sinh ^{-1}(c x)\right)^3 \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}+1\right)}{3 b c}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^3 \log \left(h (f+g x)^m\right)}{3 b c}","-\frac{m \left(a+b \sinh ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{c}-\frac{m \left(a+b \sinh ^{-1}(c x)\right)^2 \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{c}+\frac{2 b m \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(3,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{c}+\frac{2 b m \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(3,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{c}-\frac{2 b^2 m \text{PolyLog}\left(4,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{c}-\frac{2 b^2 m \text{PolyLog}\left(4,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{c}+\frac{m \left(a+b \sinh ^{-1}(c x)\right)^4}{12 b^2 c}-\frac{m \left(a+b \sinh ^{-1}(c x)\right)^3 \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{3 b c}-\frac{m \left(a+b \sinh ^{-1}(c x)\right)^3 \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}+1\right)}{3 b c}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^3 \log \left(h (f+g x)^m\right)}{3 b c}",1,"(m*(a + b*ArcSinh[c*x])^4)/(12*b^2*c) - (m*(a + b*ArcSinh[c*x])^3*Log[1 + (E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2])])/(3*b*c) - (m*(a + b*ArcSinh[c*x])^3*Log[1 + (E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2])])/(3*b*c) + ((a + b*ArcSinh[c*x])^3*Log[h*(f + g*x)^m])/(3*b*c) - (m*(a + b*ArcSinh[c*x])^2*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2]))])/c - (m*(a + b*ArcSinh[c*x])^2*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2]))])/c + (2*b*m*(a + b*ArcSinh[c*x])*PolyLog[3, -((E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2]))])/c + (2*b*m*(a + b*ArcSinh[c*x])*PolyLog[3, -((E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2]))])/c - (2*b^2*m*PolyLog[4, -((E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2]))])/c - (2*b^2*m*PolyLog[4, -((E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2]))])/c","A",13,9,34,0.2647,1,"{5675, 5838, 5799, 5561, 2190, 2531, 6609, 2282, 6589}"
55,1,332,0,0.5587482,"\int \frac{\left(a+b \sinh ^{-1}(c x)\right) \log \left(h (f+g x)^m\right)}{\sqrt{1+c^2 x^2}} \, dx","Int[((a + b*ArcSinh[c*x])*Log[h*(f + g*x)^m])/Sqrt[1 + c^2*x^2],x]","-\frac{m \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{c}-\frac{m \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{c}+\frac{b m \text{PolyLog}\left(3,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{c}+\frac{b m \text{PolyLog}\left(3,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{c}+\frac{m \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b^2 c}-\frac{m \left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{2 b c}-\frac{m \left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}+1\right)}{2 b c}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(h (f+g x)^m\right)}{2 b c}","-\frac{m \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{c}-\frac{m \left(a+b \sinh ^{-1}(c x)\right) \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{c}+\frac{b m \text{PolyLog}\left(3,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{c}+\frac{b m \text{PolyLog}\left(3,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{c}+\frac{m \left(a+b \sinh ^{-1}(c x)\right)^3}{6 b^2 c}-\frac{m \left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{2 b c}-\frac{m \left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}+1\right)}{2 b c}+\frac{\left(a+b \sinh ^{-1}(c x)\right)^2 \log \left(h (f+g x)^m\right)}{2 b c}",1,"(m*(a + b*ArcSinh[c*x])^3)/(6*b^2*c) - (m*(a + b*ArcSinh[c*x])^2*Log[1 + (E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2])])/(2*b*c) - (m*(a + b*ArcSinh[c*x])^2*Log[1 + (E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2])])/(2*b*c) + ((a + b*ArcSinh[c*x])^2*Log[h*(f + g*x)^m])/(2*b*c) - (m*(a + b*ArcSinh[c*x])*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2]))])/c - (m*(a + b*ArcSinh[c*x])*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2]))])/c + (b*m*PolyLog[3, -((E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2]))])/c + (b*m*PolyLog[3, -((E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2]))])/c","A",11,8,32,0.2500,1,"{5675, 5838, 5799, 5561, 2190, 2531, 2282, 6589}"
56,1,197,0,0.3004691,"\int \frac{\log \left(h (f+g x)^m\right)}{\sqrt{1+c^2 x^2}} \, dx","Int[Log[h*(f + g*x)^m]/Sqrt[1 + c^2*x^2],x]","-\frac{m \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{c}-\frac{m \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{c}-\frac{m \sinh ^{-1}(c x) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{c}-\frac{m \sinh ^{-1}(c x) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}+1\right)}{c}+\frac{\sinh ^{-1}(c x) \log \left(h (f+g x)^m\right)}{c}+\frac{m \sinh ^{-1}(c x)^2}{2 c}","-\frac{m \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}\right)}{c}-\frac{m \text{PolyLog}\left(2,-\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}\right)}{c}-\frac{m \sinh ^{-1}(c x) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2+g^2}}+1\right)}{c}-\frac{m \sinh ^{-1}(c x) \log \left(\frac{g e^{\sinh ^{-1}(c x)}}{\sqrt{c^2 f^2+g^2}+c f}+1\right)}{c}+\frac{\sinh ^{-1}(c x) \log \left(h (f+g x)^m\right)}{c}+\frac{m \sinh ^{-1}(c x)^2}{2 c}",1,"(m*ArcSinh[c*x]^2)/(2*c) - (m*ArcSinh[c*x]*Log[1 + (E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2])])/c - (m*ArcSinh[c*x]*Log[1 + (E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2])])/c + (ArcSinh[c*x]*Log[h*(f + g*x)^m])/c - (m*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f - Sqrt[c^2*f^2 + g^2]))])/c - (m*PolyLog[2, -((E^ArcSinh[c*x]*g)/(c*f + Sqrt[c^2*f^2 + g^2]))])/c","A",9,7,24,0.2917,1,"{215, 2404, 5799, 5561, 2190, 2279, 2391}"
57,0,0,0,0.1949289,"\int \frac{\log \left(h (f+g x)^m\right)}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","Int[Log[h*(f + g*x)^m]/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])),x]","\int \frac{\log \left(h (f+g x)^m\right)}{\sqrt{1+c^2 x^2} \left(a+b \sinh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{\log \left(h (f+g x)^m\right)}{\sqrt{c^2 x^2+1} \left(a+b \sinh ^{-1}(c x)\right)},x\right)",0,"Defer[Int][Log[h*(f + g*x)^m]/(Sqrt[1 + c^2*x^2]*(a + b*ArcSinh[c*x])), x]","A",0,0,0,0,-1,"{}"
58,1,131,0,0.1721996,"\int x^3 \sinh ^{-1}(a+b x) \, dx","Int[x^3*ArcSinh[a + b*x],x]","-\frac{\left(4 a \left(16-19 a^2\right)-\left(9-26 a^2\right) (a+b x)\right) \sqrt{(a+b x)^2+1}}{96 b^4}-\frac{\left(8 a^4-24 a^2+3\right) \sinh ^{-1}(a+b x)}{32 b^4}+\frac{7 a x^2 \sqrt{(a+b x)^2+1}}{48 b^2}-\frac{x^3 \sqrt{(a+b x)^2+1}}{16 b}+\frac{1}{4} x^4 \sinh ^{-1}(a+b x)","-\frac{\left(4 a \left(16-19 a^2\right)-\left(9-26 a^2\right) (a+b x)\right) \sqrt{(a+b x)^2+1}}{96 b^4}-\frac{\left(8 a^4-24 a^2+3\right) \sinh ^{-1}(a+b x)}{32 b^4}+\frac{7 a x^2 \sqrt{(a+b x)^2+1}}{48 b^2}-\frac{x^3 \sqrt{(a+b x)^2+1}}{16 b}+\frac{1}{4} x^4 \sinh ^{-1}(a+b x)",1,"(7*a*x^2*Sqrt[1 + (a + b*x)^2])/(48*b^2) - (x^3*Sqrt[1 + (a + b*x)^2])/(16*b) - ((4*a*(16 - 19*a^2) - (9 - 26*a^2)*(a + b*x))*Sqrt[1 + (a + b*x)^2])/(96*b^4) - ((3 - 24*a^2 + 8*a^4)*ArcSinh[a + b*x])/(32*b^4) + (x^4*ArcSinh[a + b*x])/4","A",6,6,10,0.6000,1,"{5865, 5801, 743, 833, 780, 215}"
59,1,90,0,0.1125327,"\int x^2 \sinh ^{-1}(a+b x) \, dx","Int[x^2*ArcSinh[a + b*x],x]","\frac{\left(-11 a^2+5 a b x+4\right) \sqrt{(a+b x)^2+1}}{18 b^3}-\frac{a \left(3-2 a^2\right) \sinh ^{-1}(a+b x)}{6 b^3}-\frac{x^2 \sqrt{(a+b x)^2+1}}{9 b}+\frac{1}{3} x^3 \sinh ^{-1}(a+b x)","\frac{\left(-11 a^2+5 a b x+4\right) \sqrt{(a+b x)^2+1}}{18 b^3}-\frac{a \left(3-2 a^2\right) \sinh ^{-1}(a+b x)}{6 b^3}-\frac{x^2 \sqrt{(a+b x)^2+1}}{9 b}+\frac{1}{3} x^3 \sinh ^{-1}(a+b x)",1,"-(x^2*Sqrt[1 + (a + b*x)^2])/(9*b) + ((4 - 11*a^2 + 5*a*b*x)*Sqrt[1 + (a + b*x)^2])/(18*b^3) - (a*(3 - 2*a^2)*ArcSinh[a + b*x])/(6*b^3) + (x^3*ArcSinh[a + b*x])/3","A",5,5,10,0.5000,1,"{5865, 5801, 743, 780, 215}"
60,1,76,0,0.0661435,"\int x \sinh ^{-1}(a+b x) \, dx","Int[x*ArcSinh[a + b*x],x]","\frac{\left(1-2 a^2\right) \sinh ^{-1}(a+b x)}{4 b^2}+\frac{3 a \sqrt{(a+b x)^2+1}}{4 b^2}+\frac{1}{2} x^2 \sinh ^{-1}(a+b x)-\frac{x \sqrt{(a+b x)^2+1}}{4 b}","\frac{\left(1-2 a^2\right) \sinh ^{-1}(a+b x)}{4 b^2}+\frac{3 a \sqrt{(a+b x)^2+1}}{4 b^2}+\frac{1}{2} x^2 \sinh ^{-1}(a+b x)-\frac{x \sqrt{(a+b x)^2+1}}{4 b}",1,"(3*a*Sqrt[1 + (a + b*x)^2])/(4*b^2) - (x*Sqrt[1 + (a + b*x)^2])/(4*b) + ((1 - 2*a^2)*ArcSinh[a + b*x])/(4*b^2) + (x^2*ArcSinh[a + b*x])/2","A",5,5,8,0.6250,1,"{5865, 5801, 743, 641, 215}"
61,1,34,0,0.0139822,"\int \sinh ^{-1}(a+b x) \, dx","Int[ArcSinh[a + b*x],x]","\frac{(a+b x) \sinh ^{-1}(a+b x)}{b}-\frac{\sqrt{(a+b x)^2+1}}{b}","\frac{(a+b x) \sinh ^{-1}(a+b x)}{b}-\frac{\sqrt{(a+b x)^2+1}}{b}",1,"-(Sqrt[1 + (a + b*x)^2]/b) + ((a + b*x)*ArcSinh[a + b*x])/b","A",3,3,6,0.5000,1,"{5863, 5653, 261}"
62,1,131,0,0.2432666,"\int \frac{\sinh ^{-1}(a+b x)}{x} \, dx","Int[ArcSinh[a + b*x]/x,x]","\text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)+\text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)+\sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)+\sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)-\frac{1}{2} \sinh ^{-1}(a+b x)^2","\text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)+\text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)+\sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)+\sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)-\frac{1}{2} \sinh ^{-1}(a+b x)^2",1,"-ArcSinh[a + b*x]^2/2 + ArcSinh[a + b*x]*Log[1 - E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])] + ArcSinh[a + b*x]*Log[1 - E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])] + PolyLog[2, E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])] + PolyLog[2, E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])]","A",9,6,10,0.6000,1,"{5865, 5799, 5561, 2190, 2279, 2391}"
63,1,57,0,0.0704265,"\int \frac{\sinh ^{-1}(a+b x)}{x^2} \, dx","Int[ArcSinh[a + b*x]/x^2,x]","-\frac{b \tanh ^{-1}\left(\frac{a (a+b x)+1}{\sqrt{a^2+1} \sqrt{(a+b x)^2+1}}\right)}{\sqrt{a^2+1}}-\frac{\sinh ^{-1}(a+b x)}{x}","-\frac{b \tanh ^{-1}\left(\frac{a (a+b x)+1}{\sqrt{a^2+1} \sqrt{(a+b x)^2+1}}\right)}{\sqrt{a^2+1}}-\frac{\sinh ^{-1}(a+b x)}{x}",1,"-(ArcSinh[a + b*x]/x) - (b*ArcTanh[(1 + a*(a + b*x))/(Sqrt[1 + a^2]*Sqrt[1 + (a + b*x)^2])])/Sqrt[1 + a^2]","A",4,4,10,0.4000,1,"{5865, 5801, 725, 206}"
64,1,92,0,0.1020905,"\int \frac{\sinh ^{-1}(a+b x)}{x^3} \, dx","Int[ArcSinh[a + b*x]/x^3,x]","\frac{a b^2 \tanh ^{-1}\left(\frac{a (a+b x)+1}{\sqrt{a^2+1} \sqrt{(a+b x)^2+1}}\right)}{2 \left(a^2+1\right)^{3/2}}-\frac{b \sqrt{(a+b x)^2+1}}{2 \left(a^2+1\right) x}-\frac{\sinh ^{-1}(a+b x)}{2 x^2}","\frac{a b^2 \tanh ^{-1}\left(\frac{a (a+b x)+1}{\sqrt{a^2+1} \sqrt{(a+b x)^2+1}}\right)}{2 \left(a^2+1\right)^{3/2}}-\frac{b \sqrt{(a+b x)^2+1}}{2 \left(a^2+1\right) x}-\frac{\sinh ^{-1}(a+b x)}{2 x^2}",1,"-(b*Sqrt[1 + (a + b*x)^2])/(2*(1 + a^2)*x) - ArcSinh[a + b*x]/(2*x^2) + (a*b^2*ArcTanh[(1 + a*(a + b*x))/(Sqrt[1 + a^2]*Sqrt[1 + (a + b*x)^2])])/(2*(1 + a^2)^(3/2))","A",5,5,10,0.5000,1,"{5865, 5801, 731, 725, 206}"
65,1,129,0,0.1543252,"\int \frac{\sinh ^{-1}(a+b x)}{x^4} \, dx","Int[ArcSinh[a + b*x]/x^4,x]","\frac{a b^2 \sqrt{(a+b x)^2+1}}{2 \left(a^2+1\right)^2 x}+\frac{\left(1-2 a^2\right) b^3 \tanh ^{-1}\left(\frac{a (a+b x)+1}{\sqrt{a^2+1} \sqrt{(a+b x)^2+1}}\right)}{6 \left(a^2+1\right)^{5/2}}-\frac{b \sqrt{(a+b x)^2+1}}{6 \left(a^2+1\right) x^2}-\frac{\sinh ^{-1}(a+b x)}{3 x^3}","\frac{a b^2 \sqrt{(a+b x)^2+1}}{2 \left(a^2+1\right)^2 x}+\frac{\left(1-2 a^2\right) b^3 \tanh ^{-1}\left(\frac{a (a+b x)+1}{\sqrt{a^2+1} \sqrt{(a+b x)^2+1}}\right)}{6 \left(a^2+1\right)^{5/2}}-\frac{b \sqrt{(a+b x)^2+1}}{6 \left(a^2+1\right) x^2}-\frac{\sinh ^{-1}(a+b x)}{3 x^3}",1,"-(b*Sqrt[1 + (a + b*x)^2])/(6*(1 + a^2)*x^2) + (a*b^2*Sqrt[1 + (a + b*x)^2])/(2*(1 + a^2)^2*x) - ArcSinh[a + b*x]/(3*x^3) + ((1 - 2*a^2)*b^3*ArcTanh[(1 + a*(a + b*x))/(Sqrt[1 + a^2]*Sqrt[1 + (a + b*x)^2])])/(6*(1 + a^2)^(5/2))","A",6,6,10,0.6000,1,"{5865, 5801, 745, 807, 725, 206}"
66,1,167,0,0.2284286,"\int \frac{\sinh ^{-1}(a+b x)}{x^5} \, dx","Int[ArcSinh[a + b*x]/x^5,x]","\frac{5 a b^2 \sqrt{(a+b x)^2+1}}{24 \left(a^2+1\right)^2 x^2}+\frac{\left(4-11 a^2\right) b^3 \sqrt{(a+b x)^2+1}}{24 \left(a^2+1\right)^3 x}-\frac{a \left(3-2 a^2\right) b^4 \tanh ^{-1}\left(\frac{a (a+b x)+1}{\sqrt{a^2+1} \sqrt{(a+b x)^2+1}}\right)}{8 \left(a^2+1\right)^{7/2}}-\frac{b \sqrt{(a+b x)^2+1}}{12 \left(a^2+1\right) x^3}-\frac{\sinh ^{-1}(a+b x)}{4 x^4}","\frac{5 a b^2 \sqrt{(a+b x)^2+1}}{24 \left(a^2+1\right)^2 x^2}+\frac{\left(4-11 a^2\right) b^3 \sqrt{(a+b x)^2+1}}{24 \left(a^2+1\right)^3 x}-\frac{a \left(3-2 a^2\right) b^4 \tanh ^{-1}\left(\frac{a (a+b x)+1}{\sqrt{a^2+1} \sqrt{(a+b x)^2+1}}\right)}{8 \left(a^2+1\right)^{7/2}}-\frac{b \sqrt{(a+b x)^2+1}}{12 \left(a^2+1\right) x^3}-\frac{\sinh ^{-1}(a+b x)}{4 x^4}",1,"-(b*Sqrt[1 + (a + b*x)^2])/(12*(1 + a^2)*x^3) + (5*a*b^2*Sqrt[1 + (a + b*x)^2])/(24*(1 + a^2)^2*x^2) + ((4 - 11*a^2)*b^3*Sqrt[1 + (a + b*x)^2])/(24*(1 + a^2)^3*x) - ArcSinh[a + b*x]/(4*x^4) - (a*(3 - 2*a^2)*b^4*ArcTanh[(1 + a*(a + b*x))/(Sqrt[1 + a^2]*Sqrt[1 + (a + b*x)^2])])/(8*(1 + a^2)^(7/2))","A",7,7,10,0.7000,1,"{5865, 5801, 745, 835, 807, 725, 206}"
67,1,331,0,0.5467721,"\int x^3 \sinh ^{-1}(a+b x)^2 \, dx","Int[x^3*ArcSinh[a + b*x]^2,x]","-\frac{2 a^3 x}{b^3}+\frac{3 a^2 (a+b x)^2}{4 b^4}-\frac{a^4 \sinh ^{-1}(a+b x)^2}{4 b^4}+\frac{2 a^3 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{b^4}+\frac{3 a^2 \sinh ^{-1}(a+b x)^2}{4 b^4}-\frac{3 a^2 (a+b x) \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{2 b^4}-\frac{2 a (a+b x)^3}{9 b^4}+\frac{4 a x}{3 b^3}+\frac{(a+b x)^4}{32 b^4}-\frac{3 (a+b x)^2}{32 b^4}+\frac{2 a (a+b x)^2 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{3 b^4}-\frac{4 a \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{3 b^4}-\frac{3 \sinh ^{-1}(a+b x)^2}{32 b^4}-\frac{(a+b x)^3 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{8 b^4}+\frac{3 (a+b x) \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{16 b^4}+\frac{1}{4} x^4 \sinh ^{-1}(a+b x)^2","-\frac{2 a^3 x}{b^3}+\frac{3 a^2 (a+b x)^2}{4 b^4}-\frac{a^4 \sinh ^{-1}(a+b x)^2}{4 b^4}+\frac{2 a^3 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{b^4}+\frac{3 a^2 \sinh ^{-1}(a+b x)^2}{4 b^4}-\frac{3 a^2 (a+b x) \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{2 b^4}-\frac{2 a (a+b x)^3}{9 b^4}+\frac{4 a x}{3 b^3}+\frac{(a+b x)^4}{32 b^4}-\frac{3 (a+b x)^2}{32 b^4}+\frac{2 a (a+b x)^2 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{3 b^4}-\frac{4 a \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{3 b^4}-\frac{3 \sinh ^{-1}(a+b x)^2}{32 b^4}-\frac{(a+b x)^3 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{8 b^4}+\frac{3 (a+b x) \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{16 b^4}+\frac{1}{4} x^4 \sinh ^{-1}(a+b x)^2",1,"(4*a*x)/(3*b^3) - (2*a^3*x)/b^3 - (3*(a + b*x)^2)/(32*b^4) + (3*a^2*(a + b*x)^2)/(4*b^4) - (2*a*(a + b*x)^3)/(9*b^4) + (a + b*x)^4/(32*b^4) - (4*a*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/(3*b^4) + (2*a^3*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/b^4 + (3*(a + b*x)*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/(16*b^4) - (3*a^2*(a + b*x)*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/(2*b^4) + (2*a*(a + b*x)^2*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/(3*b^4) - ((a + b*x)^3*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/(8*b^4) - (3*ArcSinh[a + b*x]^2)/(32*b^4) + (3*a^2*ArcSinh[a + b*x]^2)/(4*b^4) - (a^4*ArcSinh[a + b*x]^2)/(4*b^4) + (x^4*ArcSinh[a + b*x]^2)/4","A",19,8,12,0.6667,1,"{5865, 5801, 5821, 5675, 5717, 8, 5758, 30}"
68,1,211,0,0.3748039,"\int x^2 \sinh ^{-1}(a+b x)^2 \, dx","Int[x^2*ArcSinh[a + b*x]^2,x]","\frac{2 a^2 x}{b^2}+\frac{a^3 \sinh ^{-1}(a+b x)^2}{3 b^3}-\frac{2 a^2 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{b^3}-\frac{a (a+b x)^2}{2 b^3}+\frac{2 (a+b x)^3}{27 b^3}-\frac{a \sinh ^{-1}(a+b x)^2}{2 b^3}+\frac{a (a+b x) \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{b^3}-\frac{2 (a+b x)^2 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{9 b^3}+\frac{4 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{9 b^3}+\frac{1}{3} x^3 \sinh ^{-1}(a+b x)^2-\frac{4 x}{9 b^2}","\frac{2 a^2 x}{b^2}+\frac{a^3 \sinh ^{-1}(a+b x)^2}{3 b^3}-\frac{2 a^2 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{b^3}-\frac{a (a+b x)^2}{2 b^3}+\frac{2 (a+b x)^3}{27 b^3}-\frac{a \sinh ^{-1}(a+b x)^2}{2 b^3}+\frac{a (a+b x) \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{b^3}-\frac{2 (a+b x)^2 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{9 b^3}+\frac{4 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{9 b^3}+\frac{1}{3} x^3 \sinh ^{-1}(a+b x)^2-\frac{4 x}{9 b^2}",1,"(-4*x)/(9*b^2) + (2*a^2*x)/b^2 - (a*(a + b*x)^2)/(2*b^3) + (2*(a + b*x)^3)/(27*b^3) + (4*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/(9*b^3) - (2*a^2*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/b^3 + (a*(a + b*x)*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/b^3 - (2*(a + b*x)^2*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/(9*b^3) - (a*ArcSinh[a + b*x]^2)/(2*b^3) + (a^3*ArcSinh[a + b*x]^2)/(3*b^3) + (x^3*ArcSinh[a + b*x]^2)/3","A",14,8,12,0.6667,1,"{5865, 5801, 5821, 5675, 5717, 8, 5758, 30}"
69,1,126,0,0.2364245,"\int x \sinh ^{-1}(a+b x)^2 \, dx","Int[x*ArcSinh[a + b*x]^2,x]","-\frac{a^2 \sinh ^{-1}(a+b x)^2}{2 b^2}+\frac{(a+b x)^2}{4 b^2}-\frac{\sqrt{(a+b x)^2+1} (a+b x) \sinh ^{-1}(a+b x)}{2 b^2}+\frac{\sinh ^{-1}(a+b x)^2}{4 b^2}+\frac{2 a \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{b^2}+\frac{1}{2} x^2 \sinh ^{-1}(a+b x)^2-\frac{2 a x}{b}","-\frac{a^2 \sinh ^{-1}(a+b x)^2}{2 b^2}+\frac{(a+b x)^2}{4 b^2}-\frac{\sqrt{(a+b x)^2+1} (a+b x) \sinh ^{-1}(a+b x)}{2 b^2}+\frac{\sinh ^{-1}(a+b x)^2}{4 b^2}+\frac{2 a \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{b^2}+\frac{1}{2} x^2 \sinh ^{-1}(a+b x)^2-\frac{2 a x}{b}",1,"(-2*a*x)/b + (a + b*x)^2/(4*b^2) + (2*a*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/b^2 - ((a + b*x)*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/(2*b^2) + ArcSinh[a + b*x]^2/(4*b^2) - (a^2*ArcSinh[a + b*x]^2)/(2*b^2) + (x^2*ArcSinh[a + b*x]^2)/2","A",10,8,10,0.8000,1,"{5865, 5801, 5821, 5675, 5717, 8, 5758, 30}"
70,1,45,0,0.0506684,"\int \sinh ^{-1}(a+b x)^2 \, dx","Int[ArcSinh[a + b*x]^2,x]","\frac{(a+b x) \sinh ^{-1}(a+b x)^2}{b}-\frac{2 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{b}+2 x","\frac{(a+b x) \sinh ^{-1}(a+b x)^2}{b}-\frac{2 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{b}+2 x",1,"2*x - (2*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/b + ((a + b*x)*ArcSinh[a + b*x]^2)/b","A",4,4,8,0.5000,1,"{5863, 5653, 5717, 8}"
71,1,205,0,0.350385,"\int \frac{\sinh ^{-1}(a+b x)^2}{x} \, dx","Int[ArcSinh[a + b*x]^2/x,x]","2 \sinh ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)+2 \sinh ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)-2 \text{PolyLog}\left(3,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)-2 \text{PolyLog}\left(3,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)+\sinh ^{-1}(a+b x)^2 \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)+\sinh ^{-1}(a+b x)^2 \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)-\frac{1}{3} \sinh ^{-1}(a+b x)^3","2 \sinh ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)+2 \sinh ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)-2 \text{PolyLog}\left(3,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)-2 \text{PolyLog}\left(3,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)+\sinh ^{-1}(a+b x)^2 \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)+\sinh ^{-1}(a+b x)^2 \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)-\frac{1}{3} \sinh ^{-1}(a+b x)^3",1,"-ArcSinh[a + b*x]^3/3 + ArcSinh[a + b*x]^2*Log[1 - E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])] + ArcSinh[a + b*x]^2*Log[1 - E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])] + 2*ArcSinh[a + b*x]*PolyLog[2, E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])] + 2*ArcSinh[a + b*x]*PolyLog[2, E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])] - 2*PolyLog[3, E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])] - 2*PolyLog[3, E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])]","A",11,7,12,0.5833,1,"{5865, 5799, 5561, 2190, 2531, 2282, 6589}"
72,1,178,0,0.3826594,"\int \frac{\sinh ^{-1}(a+b x)^2}{x^2} \, dx","Int[ArcSinh[a + b*x]^2/x^2,x]","-\frac{2 b \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\sqrt{a^2+1}}+\frac{2 b \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\sqrt{a^2+1}}-\frac{2 b \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\sqrt{a^2+1}}+\frac{2 b \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\sqrt{a^2+1}}-\frac{\sinh ^{-1}(a+b x)^2}{x}","-\frac{2 b \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\sqrt{a^2+1}}+\frac{2 b \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\sqrt{a^2+1}}-\frac{2 b \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\sqrt{a^2+1}}+\frac{2 b \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\sqrt{a^2+1}}-\frac{\sinh ^{-1}(a+b x)^2}{x}",1,"-(ArcSinh[a + b*x]^2/x) - (2*b*ArcSinh[a + b*x]*Log[1 - E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])])/Sqrt[1 + a^2] + (2*b*ArcSinh[a + b*x]*Log[1 - E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])])/Sqrt[1 + a^2] - (2*b*PolyLog[2, E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])])/Sqrt[1 + a^2] + (2*b*PolyLog[2, E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])])/Sqrt[1 + a^2]","A",11,8,12,0.6667,1,"{5865, 5801, 5831, 3322, 2264, 2190, 2279, 2391}"
73,1,235,0,0.4857573,"\int \frac{\sinh ^{-1}(a+b x)^2}{x^3} \, dx","Int[ArcSinh[a + b*x]^2/x^3,x]","\frac{a b^2 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\left(a^2+1\right)^{3/2}}-\frac{a b^2 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\left(a^2+1\right)^{3/2}}+\frac{b^2 \log (x)}{a^2+1}+\frac{a b^2 \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\left(a^2+1\right)^{3/2}}-\frac{a b^2 \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\left(a^2+1\right)^{3/2}}-\frac{b \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{\left(a^2+1\right) x}-\frac{\sinh ^{-1}(a+b x)^2}{2 x^2}","\frac{a b^2 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\left(a^2+1\right)^{3/2}}-\frac{a b^2 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\left(a^2+1\right)^{3/2}}+\frac{b^2 \log (x)}{a^2+1}+\frac{a b^2 \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\left(a^2+1\right)^{3/2}}-\frac{a b^2 \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\left(a^2+1\right)^{3/2}}-\frac{b \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{\left(a^2+1\right) x}-\frac{\sinh ^{-1}(a+b x)^2}{2 x^2}",1,"-((b*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/((1 + a^2)*x)) - ArcSinh[a + b*x]^2/(2*x^2) + (a*b^2*ArcSinh[a + b*x]*Log[1 - E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])])/(1 + a^2)^(3/2) - (a*b^2*ArcSinh[a + b*x]*Log[1 - E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])])/(1 + a^2)^(3/2) + (b^2*Log[x])/(1 + a^2) + (a*b^2*PolyLog[2, E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])])/(1 + a^2)^(3/2) - (a*b^2*PolyLog[2, E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])])/(1 + a^2)^(3/2)","A",14,11,12,0.9167,1,"{5865, 5801, 5831, 3324, 3322, 2264, 2190, 2279, 2391, 2668, 31}"
74,1,478,0,1.5732137,"\int \frac{\sinh ^{-1}(a+b x)^2}{x^4} \, dx","Int[ArcSinh[a + b*x]^2/x^4,x]","\frac{b^3 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{3 \left(a^2+1\right)^{3/2}}-\frac{a^2 b^3 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\left(a^2+1\right)^{5/2}}-\frac{b^3 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{3 \left(a^2+1\right)^{3/2}}+\frac{a^2 b^3 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\left(a^2+1\right)^{5/2}}-\frac{b^2}{3 \left(a^2+1\right) x}-\frac{a b^3 \log (x)}{\left(a^2+1\right)^2}+\frac{a b^2 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{\left(a^2+1\right)^2 x}+\frac{b^3 \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{3 \left(a^2+1\right)^{3/2}}-\frac{a^2 b^3 \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\left(a^2+1\right)^{5/2}}-\frac{b^3 \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{3 \left(a^2+1\right)^{3/2}}+\frac{a^2 b^3 \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\left(a^2+1\right)^{5/2}}-\frac{b \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{3 \left(a^2+1\right) x^2}-\frac{\sinh ^{-1}(a+b x)^2}{3 x^3}","\frac{b^3 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{3 \left(a^2+1\right)^{3/2}}-\frac{a^2 b^3 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\left(a^2+1\right)^{5/2}}-\frac{b^3 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{3 \left(a^2+1\right)^{3/2}}+\frac{a^2 b^3 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\left(a^2+1\right)^{5/2}}-\frac{b^2}{3 \left(a^2+1\right) x}-\frac{a b^3 \log (x)}{\left(a^2+1\right)^2}+\frac{a b^2 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{\left(a^2+1\right)^2 x}+\frac{b^3 \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{3 \left(a^2+1\right)^{3/2}}-\frac{a^2 b^3 \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\left(a^2+1\right)^{5/2}}-\frac{b^3 \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{3 \left(a^2+1\right)^{3/2}}+\frac{a^2 b^3 \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\left(a^2+1\right)^{5/2}}-\frac{b \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{3 \left(a^2+1\right) x^2}-\frac{\sinh ^{-1}(a+b x)^2}{3 x^3}",1,"-b^2/(3*(1 + a^2)*x) - (b*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/(3*(1 + a^2)*x^2) + (a*b^2*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/((1 + a^2)^2*x) - ArcSinh[a + b*x]^2/(3*x^3) - (a^2*b^3*ArcSinh[a + b*x]*Log[1 - E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])])/(1 + a^2)^(5/2) + (b^3*ArcSinh[a + b*x]*Log[1 - E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])])/(3*(1 + a^2)^(3/2)) + (a^2*b^3*ArcSinh[a + b*x]*Log[1 - E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])])/(1 + a^2)^(5/2) - (b^3*ArcSinh[a + b*x]*Log[1 - E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])])/(3*(1 + a^2)^(3/2)) - (a*b^3*Log[x])/(1 + a^2)^2 - (a^2*b^3*PolyLog[2, E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])])/(1 + a^2)^(5/2) + (b^3*PolyLog[2, E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])])/(3*(1 + a^2)^(3/2)) + (a^2*b^3*PolyLog[2, E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])])/(1 + a^2)^(5/2) - (b^3*PolyLog[2, E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])])/(3*(1 + a^2)^(3/2))","A",40,16,12,1.333,1,"{5865, 5801, 5831, 3325, 3324, 3322, 2264, 2190, 2279, 2391, 2668, 31, 6741, 12, 6742, 32}"
75,1,355,0,0.4497026,"\int x^2 \sinh ^{-1}(a+b x)^3 \, dx","Int[x^2*ArcSinh[a + b*x]^3,x]","-\frac{6 a^2 \sqrt{(a+b x)^2+1}}{b^3}+\frac{6 a^2 (a+b x) \sinh ^{-1}(a+b x)}{b^3}+\frac{a^3 \sinh ^{-1}(a+b x)^3}{3 b^3}-\frac{3 a^2 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{b^3}+\frac{3 a \sqrt{(a+b x)^2+1} (a+b x)}{4 b^3}-\frac{2 \left((a+b x)^2+1\right)^{3/2}}{27 b^3}+\frac{14 \sqrt{(a+b x)^2+1}}{9 b^3}+\frac{2 (a+b x)^3 \sinh ^{-1}(a+b x)}{9 b^3}-\frac{\sqrt{(a+b x)^2+1} (a+b x)^2 \sinh ^{-1}(a+b x)^2}{3 b^3}-\frac{3 a (a+b x)^2 \sinh ^{-1}(a+b x)}{2 b^3}+\frac{3 a \sqrt{(a+b x)^2+1} (a+b x) \sinh ^{-1}(a+b x)^2}{2 b^3}-\frac{4 (a+b x) \sinh ^{-1}(a+b x)}{3 b^3}-\frac{a \sinh ^{-1}(a+b x)^3}{2 b^3}+\frac{2 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{3 b^3}-\frac{3 a \sinh ^{-1}(a+b x)}{4 b^3}+\frac{1}{3} x^3 \sinh ^{-1}(a+b x)^3","-\frac{6 a^2 \sqrt{(a+b x)^2+1}}{b^3}+\frac{6 a^2 (a+b x) \sinh ^{-1}(a+b x)}{b^3}+\frac{a^3 \sinh ^{-1}(a+b x)^3}{3 b^3}-\frac{3 a^2 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{b^3}+\frac{3 a \sqrt{(a+b x)^2+1} (a+b x)}{4 b^3}-\frac{2 \left((a+b x)^2+1\right)^{3/2}}{27 b^3}+\frac{14 \sqrt{(a+b x)^2+1}}{9 b^3}+\frac{2 (a+b x)^3 \sinh ^{-1}(a+b x)}{9 b^3}-\frac{\sqrt{(a+b x)^2+1} (a+b x)^2 \sinh ^{-1}(a+b x)^2}{3 b^3}-\frac{3 a (a+b x)^2 \sinh ^{-1}(a+b x)}{2 b^3}+\frac{3 a \sqrt{(a+b x)^2+1} (a+b x) \sinh ^{-1}(a+b x)^2}{2 b^3}-\frac{4 (a+b x) \sinh ^{-1}(a+b x)}{3 b^3}-\frac{a \sinh ^{-1}(a+b x)^3}{2 b^3}+\frac{2 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{3 b^3}-\frac{3 a \sinh ^{-1}(a+b x)}{4 b^3}+\frac{1}{3} x^3 \sinh ^{-1}(a+b x)^3",1,"(14*Sqrt[1 + (a + b*x)^2])/(9*b^3) - (6*a^2*Sqrt[1 + (a + b*x)^2])/b^3 + (3*a*(a + b*x)*Sqrt[1 + (a + b*x)^2])/(4*b^3) - (2*(1 + (a + b*x)^2)^(3/2))/(27*b^3) - (3*a*ArcSinh[a + b*x])/(4*b^3) - (4*(a + b*x)*ArcSinh[a + b*x])/(3*b^3) + (6*a^2*(a + b*x)*ArcSinh[a + b*x])/b^3 - (3*a*(a + b*x)^2*ArcSinh[a + b*x])/(2*b^3) + (2*(a + b*x)^3*ArcSinh[a + b*x])/(9*b^3) + (2*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x]^2)/(3*b^3) - (3*a^2*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x]^2)/b^3 + (3*a*(a + b*x)*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x]^2)/(2*b^3) - ((a + b*x)^2*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x]^2)/(3*b^3) - (a*ArcSinh[a + b*x]^3)/(2*b^3) + (a^3*ArcSinh[a + b*x]^3)/(3*b^3) + (x^3*ArcSinh[a + b*x]^3)/3","A",18,11,12,0.9167,1,"{5865, 5801, 5831, 3317, 3296, 2638, 3311, 30, 2635, 8, 2633}"
76,1,203,0,0.3030595,"\int x \sinh ^{-1}(a+b x)^3 \, dx","Int[x*ArcSinh[a + b*x]^3,x]","-\frac{a^2 \sinh ^{-1}(a+b x)^3}{2 b^2}-\frac{3 (a+b x) \sqrt{(a+b x)^2+1}}{8 b^2}+\frac{6 a \sqrt{(a+b x)^2+1}}{b^2}+\frac{\sinh ^{-1}(a+b x)^3}{4 b^2}-\frac{3 (a+b x) \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{4 b^2}+\frac{3 a \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{b^2}+\frac{3 (a+b x)^2 \sinh ^{-1}(a+b x)}{4 b^2}-\frac{6 a (a+b x) \sinh ^{-1}(a+b x)}{b^2}+\frac{3 \sinh ^{-1}(a+b x)}{8 b^2}+\frac{1}{2} x^2 \sinh ^{-1}(a+b x)^3","-\frac{a^2 \sinh ^{-1}(a+b x)^3}{2 b^2}-\frac{3 (a+b x) \sqrt{(a+b x)^2+1}}{8 b^2}+\frac{6 a \sqrt{(a+b x)^2+1}}{b^2}+\frac{\sinh ^{-1}(a+b x)^3}{4 b^2}-\frac{3 (a+b x) \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{4 b^2}+\frac{3 a \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{b^2}+\frac{3 (a+b x)^2 \sinh ^{-1}(a+b x)}{4 b^2}-\frac{6 a (a+b x) \sinh ^{-1}(a+b x)}{b^2}+\frac{3 \sinh ^{-1}(a+b x)}{8 b^2}+\frac{1}{2} x^2 \sinh ^{-1}(a+b x)^3",1,"(6*a*Sqrt[1 + (a + b*x)^2])/b^2 - (3*(a + b*x)*Sqrt[1 + (a + b*x)^2])/(8*b^2) + (3*ArcSinh[a + b*x])/(8*b^2) - (6*a*(a + b*x)*ArcSinh[a + b*x])/b^2 + (3*(a + b*x)^2*ArcSinh[a + b*x])/(4*b^2) + (3*a*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x]^2)/b^2 - (3*(a + b*x)*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x]^2)/(4*b^2) + ArcSinh[a + b*x]^3/(4*b^2) - (a^2*ArcSinh[a + b*x]^3)/(2*b^2) + (x^2*ArcSinh[a + b*x]^3)/2","A",12,10,10,1.000,1,"{5865, 5801, 5831, 3317, 3296, 2638, 3311, 30, 2635, 8}"
77,1,78,0,0.0738137,"\int \sinh ^{-1}(a+b x)^3 \, dx","Int[ArcSinh[a + b*x]^3,x]","-\frac{6 \sqrt{(a+b x)^2+1}}{b}+\frac{(a+b x) \sinh ^{-1}(a+b x)^3}{b}-\frac{3 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{b}+\frac{6 (a+b x) \sinh ^{-1}(a+b x)}{b}","-\frac{6 \sqrt{(a+b x)^2+1}}{b}+\frac{(a+b x) \sinh ^{-1}(a+b x)^3}{b}-\frac{3 \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{b}+\frac{6 (a+b x) \sinh ^{-1}(a+b x)}{b}",1,"(-6*Sqrt[1 + (a + b*x)^2])/b + (6*(a + b*x)*ArcSinh[a + b*x])/b - (3*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x]^2)/b + ((a + b*x)*ArcSinh[a + b*x]^3)/b","A",5,4,8,0.5000,1,"{5863, 5653, 5717, 261}"
78,1,275,0,0.3983841,"\int \frac{\sinh ^{-1}(a+b x)^3}{x} \, dx","Int[ArcSinh[a + b*x]^3/x,x]","3 \sinh ^{-1}(a+b x)^2 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)+3 \sinh ^{-1}(a+b x)^2 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)-6 \sinh ^{-1}(a+b x) \text{PolyLog}\left(3,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)-6 \sinh ^{-1}(a+b x) \text{PolyLog}\left(3,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)+6 \text{PolyLog}\left(4,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)+6 \text{PolyLog}\left(4,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)+\sinh ^{-1}(a+b x)^3 \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)+\sinh ^{-1}(a+b x)^3 \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)-\frac{1}{4} \sinh ^{-1}(a+b x)^4","3 \sinh ^{-1}(a+b x)^2 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)+3 \sinh ^{-1}(a+b x)^2 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)-6 \sinh ^{-1}(a+b x) \text{PolyLog}\left(3,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)-6 \sinh ^{-1}(a+b x) \text{PolyLog}\left(3,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)+6 \text{PolyLog}\left(4,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)+6 \text{PolyLog}\left(4,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)+\sinh ^{-1}(a+b x)^3 \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)+\sinh ^{-1}(a+b x)^3 \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)-\frac{1}{4} \sinh ^{-1}(a+b x)^4",1,"-ArcSinh[a + b*x]^4/4 + ArcSinh[a + b*x]^3*Log[1 - E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])] + ArcSinh[a + b*x]^3*Log[1 - E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])] + 3*ArcSinh[a + b*x]^2*PolyLog[2, E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])] + 3*ArcSinh[a + b*x]^2*PolyLog[2, E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])] - 6*ArcSinh[a + b*x]*PolyLog[3, E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])] - 6*ArcSinh[a + b*x]*PolyLog[3, E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])] + 6*PolyLog[4, E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])] + 6*PolyLog[4, E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])]","A",13,8,12,0.6667,1,"{5865, 5799, 5561, 2190, 2531, 6609, 2282, 6589}"
79,1,268,0,0.5802184,"\int \frac{\sinh ^{-1}(a+b x)^3}{x^2} \, dx","Int[ArcSinh[a + b*x]^3/x^2,x]","-\frac{6 b \sinh ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\sqrt{a^2+1}}+\frac{6 b \sinh ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\sqrt{a^2+1}}+\frac{6 b \text{PolyLog}\left(3,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\sqrt{a^2+1}}-\frac{6 b \text{PolyLog}\left(3,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\sqrt{a^2+1}}-\frac{3 b \sinh ^{-1}(a+b x)^2 \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\sqrt{a^2+1}}+\frac{3 b \sinh ^{-1}(a+b x)^2 \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\sqrt{a^2+1}}-\frac{\sinh ^{-1}(a+b x)^3}{x}","-\frac{6 b \sinh ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\sqrt{a^2+1}}+\frac{6 b \sinh ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\sqrt{a^2+1}}+\frac{6 b \text{PolyLog}\left(3,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\sqrt{a^2+1}}-\frac{6 b \text{PolyLog}\left(3,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\sqrt{a^2+1}}-\frac{3 b \sinh ^{-1}(a+b x)^2 \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\sqrt{a^2+1}}+\frac{3 b \sinh ^{-1}(a+b x)^2 \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\sqrt{a^2+1}}-\frac{\sinh ^{-1}(a+b x)^3}{x}",1,"-(ArcSinh[a + b*x]^3/x) - (3*b*ArcSinh[a + b*x]^2*Log[1 - E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])])/Sqrt[1 + a^2] + (3*b*ArcSinh[a + b*x]^2*Log[1 - E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])])/Sqrt[1 + a^2] - (6*b*ArcSinh[a + b*x]*PolyLog[2, E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])])/Sqrt[1 + a^2] + (6*b*ArcSinh[a + b*x]*PolyLog[2, E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])])/Sqrt[1 + a^2] + (6*b*PolyLog[3, E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])])/Sqrt[1 + a^2] - (6*b*PolyLog[3, E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])])/Sqrt[1 + a^2]","A",13,9,12,0.7500,1,"{5865, 5801, 5831, 3322, 2264, 2190, 2531, 2282, 6589}"
80,1,514,0,0.8834128,"\int \frac{\sinh ^{-1}(a+b x)^3}{x^3} \, dx","Int[ArcSinh[a + b*x]^3/x^3,x]","\frac{3 a b^2 \sinh ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\left(a^2+1\right)^{3/2}}-\frac{3 a b^2 \sinh ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\left(a^2+1\right)^{3/2}}+\frac{3 b^2 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{a^2+1}+\frac{3 b^2 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{a^2+1}-\frac{3 a b^2 \text{PolyLog}\left(3,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\left(a^2+1\right)^{3/2}}+\frac{3 a b^2 \text{PolyLog}\left(3,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\left(a^2+1\right)^{3/2}}-\frac{3 b^2 \sinh ^{-1}(a+b x)^2}{2 \left(a^2+1\right)}+\frac{3 a b^2 \sinh ^{-1}(a+b x)^2 \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{2 \left(a^2+1\right)^{3/2}}-\frac{3 a b^2 \sinh ^{-1}(a+b x)^2 \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{2 \left(a^2+1\right)^{3/2}}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{a^2+1}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{a^2+1}-\frac{3 b \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{2 \left(a^2+1\right) x}-\frac{\sinh ^{-1}(a+b x)^3}{2 x^2}","\frac{3 a b^2 \sinh ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\left(a^2+1\right)^{3/2}}-\frac{3 a b^2 \sinh ^{-1}(a+b x) \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\left(a^2+1\right)^{3/2}}+\frac{3 b^2 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{a^2+1}+\frac{3 b^2 \text{PolyLog}\left(2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{a^2+1}-\frac{3 a b^2 \text{PolyLog}\left(3,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{\left(a^2+1\right)^{3/2}}+\frac{3 a b^2 \text{PolyLog}\left(3,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{\left(a^2+1\right)^{3/2}}-\frac{3 b^2 \sinh ^{-1}(a+b x)^2}{2 \left(a^2+1\right)}+\frac{3 a b^2 \sinh ^{-1}(a+b x)^2 \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{2 \left(a^2+1\right)^{3/2}}-\frac{3 a b^2 \sinh ^{-1}(a+b x)^2 \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{2 \left(a^2+1\right)^{3/2}}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right)}{a^2+1}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left(1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right)}{a^2+1}-\frac{3 b \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{2 \left(a^2+1\right) x}-\frac{\sinh ^{-1}(a+b x)^3}{2 x^2}",1,"(-3*b^2*ArcSinh[a + b*x]^2)/(2*(1 + a^2)) - (3*b*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x]^2)/(2*(1 + a^2)*x) - ArcSinh[a + b*x]^3/(2*x^2) + (3*b^2*ArcSinh[a + b*x]*Log[1 - E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])])/(1 + a^2) + (3*a*b^2*ArcSinh[a + b*x]^2*Log[1 - E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])])/(2*(1 + a^2)^(3/2)) + (3*b^2*ArcSinh[a + b*x]*Log[1 - E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])])/(1 + a^2) - (3*a*b^2*ArcSinh[a + b*x]^2*Log[1 - E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])])/(2*(1 + a^2)^(3/2)) + (3*b^2*PolyLog[2, E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])])/(1 + a^2) + (3*a*b^2*ArcSinh[a + b*x]*PolyLog[2, E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])])/(1 + a^2)^(3/2) + (3*b^2*PolyLog[2, E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])])/(1 + a^2) - (3*a*b^2*ArcSinh[a + b*x]*PolyLog[2, E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])])/(1 + a^2)^(3/2) - (3*a*b^2*PolyLog[3, E^ArcSinh[a + b*x]/(a - Sqrt[1 + a^2])])/(1 + a^2)^(3/2) + (3*a*b^2*PolyLog[3, E^ArcSinh[a + b*x]/(a + Sqrt[1 + a^2])])/(1 + a^2)^(3/2)","A",21,13,12,1.083,1,"{5865, 5801, 5831, 3324, 3322, 2264, 2190, 2531, 2282, 6589, 5561, 2279, 2391}"
81,1,60,0,0.5270692,"\int \frac{x^2}{\sinh ^{-1}(a+b x)} \, dx","Int[x^2/ArcSinh[a + b*x],x]","\frac{a^2 \text{Chi}\left(\sinh ^{-1}(a+b x)\right)}{b^3}-\frac{\text{Chi}\left(\sinh ^{-1}(a+b x)\right)}{4 b^3}+\frac{\text{Chi}\left(3 \sinh ^{-1}(a+b x)\right)}{4 b^3}-\frac{a \text{Shi}\left(2 \sinh ^{-1}(a+b x)\right)}{b^3}","\frac{a^2 \text{Chi}\left(\sinh ^{-1}(a+b x)\right)}{b^3}-\frac{\text{Chi}\left(\sinh ^{-1}(a+b x)\right)}{4 b^3}+\frac{\text{Chi}\left(3 \sinh ^{-1}(a+b x)\right)}{4 b^3}-\frac{a \text{Shi}\left(2 \sinh ^{-1}(a+b x)\right)}{b^3}",1,"-CoshIntegral[ArcSinh[a + b*x]]/(4*b^3) + (a^2*CoshIntegral[ArcSinh[a + b*x]])/b^3 + CoshIntegral[3*ArcSinh[a + b*x]]/(4*b^3) - (a*SinhIntegral[2*ArcSinh[a + b*x]])/b^3","A",14,8,12,0.6667,1,"{5865, 5805, 6741, 12, 6742, 3301, 5448, 3298}"
82,1,30,0,0.2113434,"\int \frac{x}{\sinh ^{-1}(a+b x)} \, dx","Int[x/ArcSinh[a + b*x],x]","\frac{\text{Shi}\left(2 \sinh ^{-1}(a+b x)\right)}{2 b^2}-\frac{a \text{Chi}\left(\sinh ^{-1}(a+b x)\right)}{b^2}","\frac{\text{Shi}\left(2 \sinh ^{-1}(a+b x)\right)}{2 b^2}-\frac{a \text{Chi}\left(\sinh ^{-1}(a+b x)\right)}{b^2}",1,"-((a*CoshIntegral[ArcSinh[a + b*x]])/b^2) + SinhIntegral[2*ArcSinh[a + b*x]]/(2*b^2)","A",10,8,10,0.8000,1,"{5865, 5805, 6741, 12, 6742, 3301, 5448, 3298}"
83,1,11,0,0.0233665,"\int \frac{1}{\sinh ^{-1}(a+b x)} \, dx","Int[ArcSinh[a + b*x]^(-1),x]","\frac{\text{Chi}\left(\sinh ^{-1}(a+b x)\right)}{b}","\frac{\text{Chi}\left(\sinh ^{-1}(a+b x)\right)}{b}",1,"CoshIntegral[ArcSinh[a + b*x]]/b","A",3,3,8,0.3750,1,"{5863, 5657, 3301}"
84,0,0,0,0.0440705,"\int \frac{1}{x \sinh ^{-1}(a+b x)} \, dx","Int[1/(x*ArcSinh[a + b*x]),x]","\int \frac{1}{x \sinh ^{-1}(a+b x)} \, dx","\text{Int}\left(\frac{1}{x \sinh ^{-1}(a+b x)},x\right)",0,"Defer[Subst][Defer[Int][1/((-(a/b) + x/b)*ArcSinh[x]), x], x, a + b*x]/b","A",0,0,0,0,-1,"{}"
85,1,154,0,0.2164963,"\int \frac{x^2}{\sinh ^{-1}(a+b x)^2} \, dx","Int[x^2/ArcSinh[a + b*x]^2,x]","\frac{a^2 \text{Shi}\left(\sinh ^{-1}(a+b x)\right)}{b^3}-\frac{a^2 \sqrt{(a+b x)^2+1}}{b^3 \sinh ^{-1}(a+b x)}-\frac{2 a \text{Chi}\left(2 \sinh ^{-1}(a+b x)\right)}{b^3}-\frac{\text{Shi}\left(\sinh ^{-1}(a+b x)\right)}{4 b^3}+\frac{3 \text{Shi}\left(3 \sinh ^{-1}(a+b x)\right)}{4 b^3}+\frac{2 a (a+b x) \sqrt{(a+b x)^2+1}}{b^3 \sinh ^{-1}(a+b x)}-\frac{(a+b x)^2 \sqrt{(a+b x)^2+1}}{b^3 \sinh ^{-1}(a+b x)}","\frac{a^2 \text{Shi}\left(\sinh ^{-1}(a+b x)\right)}{b^3}-\frac{a^2 \sqrt{(a+b x)^2+1}}{b^3 \sinh ^{-1}(a+b x)}-\frac{2 a \text{Chi}\left(2 \sinh ^{-1}(a+b x)\right)}{b^3}-\frac{\text{Shi}\left(\sinh ^{-1}(a+b x)\right)}{4 b^3}+\frac{3 \text{Shi}\left(3 \sinh ^{-1}(a+b x)\right)}{4 b^3}+\frac{2 a (a+b x) \sqrt{(a+b x)^2+1}}{b^3 \sinh ^{-1}(a+b x)}-\frac{(a+b x)^2 \sqrt{(a+b x)^2+1}}{b^3 \sinh ^{-1}(a+b x)}",1,"-((a^2*Sqrt[1 + (a + b*x)^2])/(b^3*ArcSinh[a + b*x])) + (2*a*(a + b*x)*Sqrt[1 + (a + b*x)^2])/(b^3*ArcSinh[a + b*x]) - ((a + b*x)^2*Sqrt[1 + (a + b*x)^2])/(b^3*ArcSinh[a + b*x]) - (2*a*CoshIntegral[2*ArcSinh[a + b*x]])/b^3 - SinhIntegral[ArcSinh[a + b*x]]/(4*b^3) + (a^2*SinhIntegral[ArcSinh[a + b*x]])/b^3 + (3*SinhIntegral[3*ArcSinh[a + b*x]])/(4*b^3)","A",12,7,12,0.5833,1,"{5865, 5803, 5655, 5779, 3298, 5665, 3301}"
86,1,84,0,0.1315849,"\int \frac{x}{\sinh ^{-1}(a+b x)^2} \, dx","Int[x/ArcSinh[a + b*x]^2,x]","\frac{\text{Chi}\left(2 \sinh ^{-1}(a+b x)\right)}{b^2}-\frac{a \text{Shi}\left(\sinh ^{-1}(a+b x)\right)}{b^2}+\frac{a \sqrt{(a+b x)^2+1}}{b^2 \sinh ^{-1}(a+b x)}-\frac{(a+b x) \sqrt{(a+b x)^2+1}}{b^2 \sinh ^{-1}(a+b x)}","\frac{\text{Chi}\left(2 \sinh ^{-1}(a+b x)\right)}{b^2}-\frac{a \text{Shi}\left(\sinh ^{-1}(a+b x)\right)}{b^2}+\frac{a \sqrt{(a+b x)^2+1}}{b^2 \sinh ^{-1}(a+b x)}-\frac{(a+b x) \sqrt{(a+b x)^2+1}}{b^2 \sinh ^{-1}(a+b x)}",1,"(a*Sqrt[1 + (a + b*x)^2])/(b^2*ArcSinh[a + b*x]) - ((a + b*x)*Sqrt[1 + (a + b*x)^2])/(b^2*ArcSinh[a + b*x]) + CoshIntegral[2*ArcSinh[a + b*x]]/b^2 - (a*SinhIntegral[ArcSinh[a + b*x]])/b^2","A",8,7,10,0.7000,1,"{5865, 5803, 5655, 5779, 3298, 5665, 3301}"
87,1,38,0,0.07259,"\int \frac{1}{\sinh ^{-1}(a+b x)^2} \, dx","Int[ArcSinh[a + b*x]^(-2),x]","\frac{\text{Shi}\left(\sinh ^{-1}(a+b x)\right)}{b}-\frac{\sqrt{(a+b x)^2+1}}{b \sinh ^{-1}(a+b x)}","\frac{\text{Shi}\left(\sinh ^{-1}(a+b x)\right)}{b}-\frac{\sqrt{(a+b x)^2+1}}{b \sinh ^{-1}(a+b x)}",1,"-(Sqrt[1 + (a + b*x)^2]/(b*ArcSinh[a + b*x])) + SinhIntegral[ArcSinh[a + b*x]]/b","A",4,4,8,0.5000,1,"{5863, 5655, 5779, 3298}"
88,0,0,0,0.0386165,"\int \frac{1}{x \sinh ^{-1}(a+b x)^2} \, dx","Int[1/(x*ArcSinh[a + b*x]^2),x]","\int \frac{1}{x \sinh ^{-1}(a+b x)^2} \, dx","\text{Int}\left(\frac{1}{x \sinh ^{-1}(a+b x)^2},x\right)",0,"Defer[Subst][Defer[Int][1/((-(a/b) + x/b)*ArcSinh[x]^2), x], x, a + b*x]/b","A",0,0,0,0,-1,"{}"
89,1,257,0,0.4970855,"\int \frac{x^2}{\sinh ^{-1}(a+b x)^3} \, dx","Int[x^2/ArcSinh[a + b*x]^3,x]","\frac{a^2 \text{Chi}\left(\sinh ^{-1}(a+b x)\right)}{2 b^3}-\frac{a^2 (a+b x)}{2 b^3 \sinh ^{-1}(a+b x)}-\frac{a^2 \sqrt{(a+b x)^2+1}}{2 b^3 \sinh ^{-1}(a+b x)^2}-\frac{\text{Chi}\left(\sinh ^{-1}(a+b x)\right)}{8 b^3}+\frac{9 \text{Chi}\left(3 \sinh ^{-1}(a+b x)\right)}{8 b^3}-\frac{2 a \text{Shi}\left(2 \sinh ^{-1}(a+b x)\right)}{b^3}-\frac{3 (a+b x)^3}{2 b^3 \sinh ^{-1}(a+b x)}+\frac{2 a (a+b x)^2}{b^3 \sinh ^{-1}(a+b x)}-\frac{\sqrt{(a+b x)^2+1} (a+b x)^2}{2 b^3 \sinh ^{-1}(a+b x)^2}-\frac{a+b x}{b^3 \sinh ^{-1}(a+b x)}+\frac{a \sqrt{(a+b x)^2+1} (a+b x)}{b^3 \sinh ^{-1}(a+b x)^2}+\frac{a}{b^3 \sinh ^{-1}(a+b x)}","\frac{a^2 \text{Chi}\left(\sinh ^{-1}(a+b x)\right)}{2 b^3}-\frac{a^2 (a+b x)}{2 b^3 \sinh ^{-1}(a+b x)}-\frac{a^2 \sqrt{(a+b x)^2+1}}{2 b^3 \sinh ^{-1}(a+b x)^2}-\frac{\text{Chi}\left(\sinh ^{-1}(a+b x)\right)}{8 b^3}+\frac{9 \text{Chi}\left(3 \sinh ^{-1}(a+b x)\right)}{8 b^3}-\frac{2 a \text{Shi}\left(2 \sinh ^{-1}(a+b x)\right)}{b^3}-\frac{3 (a+b x)^3}{2 b^3 \sinh ^{-1}(a+b x)}+\frac{2 a (a+b x)^2}{b^3 \sinh ^{-1}(a+b x)}-\frac{\sqrt{(a+b x)^2+1} (a+b x)^2}{2 b^3 \sinh ^{-1}(a+b x)^2}-\frac{a+b x}{b^3 \sinh ^{-1}(a+b x)}+\frac{a \sqrt{(a+b x)^2+1} (a+b x)}{b^3 \sinh ^{-1}(a+b x)^2}+\frac{a}{b^3 \sinh ^{-1}(a+b x)}",1,"-(a^2*Sqrt[1 + (a + b*x)^2])/(2*b^3*ArcSinh[a + b*x]^2) + (a*(a + b*x)*Sqrt[1 + (a + b*x)^2])/(b^3*ArcSinh[a + b*x]^2) - ((a + b*x)^2*Sqrt[1 + (a + b*x)^2])/(2*b^3*ArcSinh[a + b*x]^2) + a/(b^3*ArcSinh[a + b*x]) - (a + b*x)/(b^3*ArcSinh[a + b*x]) - (a^2*(a + b*x))/(2*b^3*ArcSinh[a + b*x]) + (2*a*(a + b*x)^2)/(b^3*ArcSinh[a + b*x]) - (3*(a + b*x)^3)/(2*b^3*ArcSinh[a + b*x]) - CoshIntegral[ArcSinh[a + b*x]]/(8*b^3) + (a^2*CoshIntegral[ArcSinh[a + b*x]])/(2*b^3) + (9*CoshIntegral[3*ArcSinh[a + b*x]])/(8*b^3) - (2*a*SinhIntegral[2*ArcSinh[a + b*x]])/b^3","A",24,12,12,1.000,1,"{5865, 5803, 5655, 5774, 5657, 3301, 5667, 5669, 5448, 12, 3298, 5675}"
90,1,147,0,0.2497323,"\int \frac{x}{\sinh ^{-1}(a+b x)^3} \, dx","Int[x/ArcSinh[a + b*x]^3,x]","-\frac{a \text{Chi}\left(\sinh ^{-1}(a+b x)\right)}{2 b^2}+\frac{\text{Shi}\left(2 \sinh ^{-1}(a+b x)\right)}{b^2}-\frac{(a+b x)^2}{b^2 \sinh ^{-1}(a+b x)}+\frac{a (a+b x)}{2 b^2 \sinh ^{-1}(a+b x)}-\frac{\sqrt{(a+b x)^2+1} (a+b x)}{2 b^2 \sinh ^{-1}(a+b x)^2}-\frac{1}{2 b^2 \sinh ^{-1}(a+b x)}+\frac{a \sqrt{(a+b x)^2+1}}{2 b^2 \sinh ^{-1}(a+b x)^2}","-\frac{a \text{Chi}\left(\sinh ^{-1}(a+b x)\right)}{2 b^2}+\frac{\text{Shi}\left(2 \sinh ^{-1}(a+b x)\right)}{b^2}-\frac{(a+b x)^2}{b^2 \sinh ^{-1}(a+b x)}+\frac{a (a+b x)}{2 b^2 \sinh ^{-1}(a+b x)}-\frac{\sqrt{(a+b x)^2+1} (a+b x)}{2 b^2 \sinh ^{-1}(a+b x)^2}-\frac{1}{2 b^2 \sinh ^{-1}(a+b x)}+\frac{a \sqrt{(a+b x)^2+1}}{2 b^2 \sinh ^{-1}(a+b x)^2}",1,"(a*Sqrt[1 + (a + b*x)^2])/(2*b^2*ArcSinh[a + b*x]^2) - ((a + b*x)*Sqrt[1 + (a + b*x)^2])/(2*b^2*ArcSinh[a + b*x]^2) - 1/(2*b^2*ArcSinh[a + b*x]) + (a*(a + b*x))/(2*b^2*ArcSinh[a + b*x]) - (a + b*x)^2/(b^2*ArcSinh[a + b*x]) - (a*CoshIntegral[ArcSinh[a + b*x]])/(2*b^2) + SinhIntegral[2*ArcSinh[a + b*x]]/b^2","A",14,12,10,1.200,1,"{5865, 5803, 5655, 5774, 5657, 3301, 5667, 5669, 5448, 12, 3298, 5675}"
91,1,63,0,0.0786598,"\int \frac{1}{\sinh ^{-1}(a+b x)^3} \, dx","Int[ArcSinh[a + b*x]^(-3),x]","\frac{\text{Chi}\left(\sinh ^{-1}(a+b x)\right)}{2 b}-\frac{a+b x}{2 b \sinh ^{-1}(a+b x)}-\frac{\sqrt{(a+b x)^2+1}}{2 b \sinh ^{-1}(a+b x)^2}","\frac{\text{Chi}\left(\sinh ^{-1}(a+b x)\right)}{2 b}-\frac{a+b x}{2 b \sinh ^{-1}(a+b x)}-\frac{\sqrt{(a+b x)^2+1}}{2 b \sinh ^{-1}(a+b x)^2}",1,"-Sqrt[1 + (a + b*x)^2]/(2*b*ArcSinh[a + b*x]^2) - (a + b*x)/(2*b*ArcSinh[a + b*x]) + CoshIntegral[ArcSinh[a + b*x]]/(2*b)","A",5,5,8,0.6250,1,"{5863, 5655, 5774, 5657, 3301}"
92,0,0,0,0.0395817,"\int \frac{1}{x \sinh ^{-1}(a+b x)^3} \, dx","Int[1/(x*ArcSinh[a + b*x]^3),x]","\int \frac{1}{x \sinh ^{-1}(a+b x)^3} \, dx","\text{Int}\left(\frac{1}{x \sinh ^{-1}(a+b x)^3},x\right)",0,"Defer[Subst][Defer[Int][1/((-(a/b) + x/b)*ArcSinh[x]^3), x], x, a + b*x]/b","A",0,0,0,0,-1,"{}"
93,0,0,0,0.0534858,"\int x^m \left(a+b \sinh ^{-1}(c+d x)\right)^n \, dx","Int[x^m*(a + b*ArcSinh[c + d*x])^n,x]","\int x^m \left(a+b \sinh ^{-1}(c+d x)\right)^n \, dx","\text{Int}\left(x^m \left(a+b \sinh ^{-1}(c+d x)\right)^n,x\right)",0,"Defer[Subst][Defer[Int][(-(c/d) + x/d)^m*(a + b*ArcSinh[x])^n, x], x, c + d*x]/d","A",0,0,0,0,-1,"{}"
94,1,545,0,1.1516194,"\int x^2 \left(a+b \sinh ^{-1}(c+d x)\right)^n \, dx","Int[x^2*(a + b*ArcSinh[c + d*x])^n,x]","\frac{c^2 e^{-\frac{a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{2 d^3}-\frac{c^2 e^{a/b} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{2 d^3}+\frac{3^{-n-1} e^{-\frac{3 a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{8 d^3}-\frac{c 2^{-n-2} e^{-\frac{2 a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{d^3}-\frac{e^{-\frac{a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{8 d^3}+\frac{e^{a/b} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{8 d^3}-\frac{c 2^{-n-2} e^{\frac{2 a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{d^3}-\frac{3^{-n-1} e^{\frac{3 a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{8 d^3}","\frac{c^2 e^{-\frac{a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{2 d^3}-\frac{c^2 e^{a/b} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{2 d^3}+\frac{3^{-n-1} e^{-\frac{3 a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{8 d^3}-\frac{c 2^{-n-2} e^{-\frac{2 a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{d^3}-\frac{e^{-\frac{a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{8 d^3}+\frac{e^{a/b} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{8 d^3}-\frac{c 2^{-n-2} e^{\frac{2 a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{d^3}-\frac{3^{-n-1} e^{\frac{3 a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{8 d^3}",1,"(3^(-1 - n)*(a + b*ArcSinh[c + d*x])^n*Gamma[1 + n, (-3*(a + b*ArcSinh[c + d*x]))/b])/(8*d^3*E^((3*a)/b)*(-((a + b*ArcSinh[c + d*x])/b))^n) - (2^(-2 - n)*c*(a + b*ArcSinh[c + d*x])^n*Gamma[1 + n, (-2*(a + b*ArcSinh[c + d*x]))/b])/(d^3*E^((2*a)/b)*(-((a + b*ArcSinh[c + d*x])/b))^n) - ((a + b*ArcSinh[c + d*x])^n*Gamma[1 + n, -((a + b*ArcSinh[c + d*x])/b)])/(8*d^3*E^(a/b)*(-((a + b*ArcSinh[c + d*x])/b))^n) + (c^2*(a + b*ArcSinh[c + d*x])^n*Gamma[1 + n, -((a + b*ArcSinh[c + d*x])/b)])/(2*d^3*E^(a/b)*(-((a + b*ArcSinh[c + d*x])/b))^n) + (E^(a/b)*(a + b*ArcSinh[c + d*x])^n*Gamma[1 + n, (a + b*ArcSinh[c + d*x])/b])/(8*d^3*((a + b*ArcSinh[c + d*x])/b)^n) - (c^2*E^(a/b)*(a + b*ArcSinh[c + d*x])^n*Gamma[1 + n, (a + b*ArcSinh[c + d*x])/b])/(2*d^3*((a + b*ArcSinh[c + d*x])/b)^n) - (2^(-2 - n)*c*E^((2*a)/b)*(a + b*ArcSinh[c + d*x])^n*Gamma[1 + n, (2*(a + b*ArcSinh[c + d*x]))/b])/(d^3*((a + b*ArcSinh[c + d*x])/b)^n) - (3^(-1 - n)*E^((3*a)/b)*(a + b*ArcSinh[c + d*x])^n*Gamma[1 + n, (3*(a + b*ArcSinh[c + d*x]))/b])/(8*d^3*((a + b*ArcSinh[c + d*x])/b)^n)","A",22,9,16,0.5625,1,"{5865, 5805, 6741, 12, 6742, 3307, 2181, 5448, 3308}"
95,1,267,0,0.483293,"\int x \left(a+b \sinh ^{-1}(c+d x)\right)^n \, dx","Int[x*(a + b*ArcSinh[c + d*x])^n,x]","\frac{2^{-n-3} e^{-\frac{2 a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{d^2}-\frac{c e^{-\frac{a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{2 d^2}+\frac{c e^{a/b} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{2 d^2}+\frac{2^{-n-3} e^{\frac{2 a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{d^2}","\frac{2^{-n-3} e^{-\frac{2 a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{d^2}-\frac{c e^{-\frac{a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{2 d^2}+\frac{c e^{a/b} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{2 d^2}+\frac{2^{-n-3} e^{\frac{2 a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{d^2}",1,"(2^(-3 - n)*(a + b*ArcSinh[c + d*x])^n*Gamma[1 + n, (-2*(a + b*ArcSinh[c + d*x]))/b])/(d^2*E^((2*a)/b)*(-((a + b*ArcSinh[c + d*x])/b))^n) - (c*(a + b*ArcSinh[c + d*x])^n*Gamma[1 + n, -((a + b*ArcSinh[c + d*x])/b)])/(2*d^2*E^(a/b)*(-((a + b*ArcSinh[c + d*x])/b))^n) + (c*E^(a/b)*(a + b*ArcSinh[c + d*x])^n*Gamma[1 + n, (a + b*ArcSinh[c + d*x])/b])/(2*d^2*((a + b*ArcSinh[c + d*x])/b)^n) + (2^(-3 - n)*E^((2*a)/b)*(a + b*ArcSinh[c + d*x])^n*Gamma[1 + n, (2*(a + b*ArcSinh[c + d*x]))/b])/(d^2*((a + b*ArcSinh[c + d*x])/b)^n)","A",14,9,14,0.6429,1,"{5865, 5805, 6741, 12, 6742, 3307, 2181, 5448, 3308}"
96,1,128,0,0.123552,"\int \left(a+b \sinh ^{-1}(c+d x)\right)^n \, dx","Int[(a + b*ArcSinh[c + d*x])^n,x]","\frac{e^{-\frac{a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{2 d}-\frac{e^{a/b} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{2 d}","\frac{e^{-\frac{a}{b}} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,-\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{2 d}-\frac{e^{a/b} \left(a+b \sinh ^{-1}(c+d x)\right)^n \left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)^{-n} \text{Gamma}\left(n+1,\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{2 d}",1,"((a + b*ArcSinh[c + d*x])^n*Gamma[1 + n, -((a + b*ArcSinh[c + d*x])/b)])/(2*d*E^(a/b)*(-((a + b*ArcSinh[c + d*x])/b))^n) - (E^(a/b)*(a + b*ArcSinh[c + d*x])^n*Gamma[1 + n, (a + b*ArcSinh[c + d*x])/b])/(2*d*((a + b*ArcSinh[c + d*x])/b)^n)","A",5,4,12,0.3333,1,"{5863, 5657, 3307, 2181}"
97,0,0,0,0.0595191,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^n}{x} \, dx","Int[(a + b*ArcSinh[c + d*x])^n/x,x]","\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^n}{x} \, dx","\text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^n}{x},x\right)",0,"Defer[Subst][Defer[Int][(a + b*ArcSinh[x])^n/(-(c/d) + x/d), x], x, c + d*x]/d","A",0,0,0,0,-1,"{}"
98,1,496,0,1.8468952,"\int x^2 \sqrt{a+b \sinh ^{-1}(c+d x)} \, dx","Int[x^2*Sqrt[a + b*ArcSinh[c + d*x]],x]","\frac{\sqrt{\pi } \sqrt{b} c^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d^3}-\frac{\sqrt{\pi } \sqrt{b} c^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d^3}+\frac{c^2 (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{d^3}-\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d^3}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} c e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d^3}+\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{48 d^3}+\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d^3}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} c e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d^3}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{48 d^3}+\frac{(c+d x)^3 \sqrt{a+b \sinh ^{-1}(c+d x)}}{3 d^3}-\frac{c \cosh \left(2 \sinh ^{-1}(c+d x)\right) \sqrt{a+b \sinh ^{-1}(c+d x)}}{2 d^3}","\frac{\sqrt{\pi } \sqrt{b} c^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d^3}-\frac{\sqrt{\pi } \sqrt{b} c^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d^3}+\frac{c^2 (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{d^3}-\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d^3}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} c e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d^3}+\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{48 d^3}+\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d^3}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} c e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d^3}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{48 d^3}+\frac{(c+d x)^3 \sqrt{a+b \sinh ^{-1}(c+d x)}}{3 d^3}-\frac{c \cosh \left(2 \sinh ^{-1}(c+d x)\right) \sqrt{a+b \sinh ^{-1}(c+d x)}}{2 d^3}",1,"(c^2*(c + d*x)*Sqrt[a + b*ArcSinh[c + d*x]])/d^3 + ((c + d*x)^3*Sqrt[a + b*ArcSinh[c + d*x]])/(3*d^3) - (c*Sqrt[a + b*ArcSinh[c + d*x]]*Cosh[2*ArcSinh[c + d*x]])/(2*d^3) - (Sqrt[b]*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(16*d^3) + (Sqrt[b]*c^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(4*d^3) + (Sqrt[b]*c*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(8*d^3) + (Sqrt[b]*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(48*d^3) + (Sqrt[b]*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(16*d^3*E^(a/b)) - (Sqrt[b]*c^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(4*d^3*E^(a/b)) + (Sqrt[b]*c*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(8*d^3*E^((2*a)/b)) - (Sqrt[b]*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(48*d^3*E^((3*a)/b))","A",23,12,18,0.6667,1,"{5865, 5805, 6741, 6742, 5325, 5298, 2205, 2204, 5324, 5299, 5372, 5300}"
99,1,259,0,0.6998551,"\int x \sqrt{a+b \sinh ^{-1}(c+d x)} \, dx","Int[x*Sqrt[a + b*ArcSinh[c + d*x]],x]","-\frac{\sqrt{\pi } \sqrt{b} c e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d^2}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d^2}+\frac{\sqrt{\pi } \sqrt{b} c e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d^2}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d^2}-\frac{c (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{d^2}+\frac{\cosh \left(2 \sinh ^{-1}(c+d x)\right) \sqrt{a+b \sinh ^{-1}(c+d x)}}{4 d^2}","-\frac{\sqrt{\pi } \sqrt{b} c e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d^2}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d^2}+\frac{\sqrt{\pi } \sqrt{b} c e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d^2}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d^2}-\frac{c (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{d^2}+\frac{\cosh \left(2 \sinh ^{-1}(c+d x)\right) \sqrt{a+b \sinh ^{-1}(c+d x)}}{4 d^2}",1,"-((c*(c + d*x)*Sqrt[a + b*ArcSinh[c + d*x]])/d^2) + (Sqrt[a + b*ArcSinh[c + d*x]]*Cosh[2*ArcSinh[c + d*x]])/(4*d^2) - (Sqrt[b]*c*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(4*d^2) - (Sqrt[b]*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(16*d^2) + (Sqrt[b]*c*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(4*d^2*E^(a/b)) - (Sqrt[b]*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(16*d^2*E^((2*a)/b))","A",14,10,16,0.6250,1,"{5865, 5805, 6741, 6742, 5325, 5298, 2205, 2204, 5324, 5299}"
100,1,115,0,0.2491196,"\int \sqrt{a+b \sinh ^{-1}(c+d x)} \, dx","Int[Sqrt[a + b*ArcSinh[c + d*x]],x]","\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}-\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}+\frac{(c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{d}","\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}-\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}+\frac{(c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{d}",1,"((c + d*x)*Sqrt[a + b*ArcSinh[c + d*x]])/d + (Sqrt[b]*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(4*d) - (Sqrt[b]*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(4*d*E^(a/b))","A",8,7,14,0.5000,1,"{5863, 5653, 5779, 3308, 2180, 2204, 2205}"
101,1,326,0,0.9647216,"\int x \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2} \, dx","Int[x*(a + b*ArcSinh[c + d*x])^(3/2),x]","-\frac{3 \sqrt{\pi } b^{3/2} c e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d^2}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d^2}-\frac{3 \sqrt{\pi } b^{3/2} c e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d^2}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d^2}-\frac{3 b \sinh \left(2 \sinh ^{-1}(c+d x)\right) \sqrt{a+b \sinh ^{-1}(c+d x)}}{16 d^2}+\frac{3 b c \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{2 d^2}-\frac{c (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{d^2}+\frac{\cosh \left(2 \sinh ^{-1}(c+d x)\right) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{4 d^2}","-\frac{3 \sqrt{\pi } b^{3/2} c e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d^2}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d^2}-\frac{3 \sqrt{\pi } b^{3/2} c e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d^2}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d^2}-\frac{3 b \sinh \left(2 \sinh ^{-1}(c+d x)\right) \sqrt{a+b \sinh ^{-1}(c+d x)}}{16 d^2}+\frac{3 b c \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{2 d^2}-\frac{c (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{d^2}+\frac{\cosh \left(2 \sinh ^{-1}(c+d x)\right) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{4 d^2}",1,"(3*b*c*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(2*d^2) - (c*(c + d*x)*(a + b*ArcSinh[c + d*x])^(3/2))/d^2 + ((a + b*ArcSinh[c + d*x])^(3/2)*Cosh[2*ArcSinh[c + d*x]])/(4*d^2) - (3*b^(3/2)*c*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(8*d^2) - (3*b^(3/2)*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(64*d^2) - (3*b^(3/2)*c*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(8*d^2*E^(a/b)) + (3*b^(3/2)*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(64*d^2*E^((2*a)/b)) - (3*b*Sqrt[a + b*ArcSinh[c + d*x]]*Sinh[2*ArcSinh[c + d*x]])/(16*d^2)","A",16,10,16,0.6250,1,"{5865, 5805, 6741, 6742, 5325, 5324, 5299, 2205, 2204, 5298}"
102,1,150,0,0.2486041,"\int \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2} \, dx","Int[(a + b*ArcSinh[c + d*x])^(3/2),x]","\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}+\frac{3 \sqrt{\pi } b^{3/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}-\frac{3 b \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{2 d}+\frac{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{d}","\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}+\frac{3 \sqrt{\pi } b^{3/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}-\frac{3 b \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{2 d}+\frac{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{d}",1,"(-3*b*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(2*d) + ((c + d*x)*(a + b*ArcSinh[c + d*x])^(3/2))/d + (3*b^(3/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(8*d) + (3*b^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(8*d*E^(a/b))","A",9,8,14,0.5714,1,"{5863, 5653, 5717, 5657, 3307, 2180, 2205, 2204}"
103,1,389,0,1.1263416,"\int x \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2} \, dx","Int[x*(a + b*ArcSinh[c + d*x])^(5/2),x]","-\frac{15 \sqrt{\pi } b^{5/2} c e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d^2}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d^2}+\frac{15 \sqrt{\pi } b^{5/2} c e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d^2}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d^2}-\frac{15 b^2 c (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{4 d^2}+\frac{15 b^2 \cosh \left(2 \sinh ^{-1}(c+d x)\right) \sqrt{a+b \sinh ^{-1}(c+d x)}}{64 d^2}+\frac{5 b c \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{2 d^2}-\frac{5 b \sinh \left(2 \sinh ^{-1}(c+d x)\right) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{16 d^2}-\frac{c (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{d^2}+\frac{\cosh \left(2 \sinh ^{-1}(c+d x)\right) \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{4 d^2}","-\frac{15 \sqrt{\pi } b^{5/2} c e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d^2}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d^2}+\frac{15 \sqrt{\pi } b^{5/2} c e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d^2}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d^2}-\frac{15 b^2 c (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{4 d^2}+\frac{15 b^2 \cosh \left(2 \sinh ^{-1}(c+d x)\right) \sqrt{a+b \sinh ^{-1}(c+d x)}}{64 d^2}+\frac{5 b c \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{2 d^2}-\frac{5 b \sinh \left(2 \sinh ^{-1}(c+d x)\right) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{16 d^2}-\frac{c (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{d^2}+\frac{\cosh \left(2 \sinh ^{-1}(c+d x)\right) \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{4 d^2}",1,"(-15*b^2*c*(c + d*x)*Sqrt[a + b*ArcSinh[c + d*x]])/(4*d^2) + (5*b*c*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(3/2))/(2*d^2) - (c*(c + d*x)*(a + b*ArcSinh[c + d*x])^(5/2))/d^2 + (15*b^2*Sqrt[a + b*ArcSinh[c + d*x]]*Cosh[2*ArcSinh[c + d*x]])/(64*d^2) + ((a + b*ArcSinh[c + d*x])^(5/2)*Cosh[2*ArcSinh[c + d*x]])/(4*d^2) - (15*b^(5/2)*c*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(16*d^2) - (15*b^(5/2)*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(256*d^2) + (15*b^(5/2)*c*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(16*d^2*E^(a/b)) - (15*b^(5/2)*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(256*d^2*E^((2*a)/b)) - (5*b*(a + b*ArcSinh[c + d*x])^(3/2)*Sinh[2*ArcSinh[c + d*x]])/(16*d^2)","A",18,10,16,0.6250,1,"{5865, 5805, 6741, 6742, 5325, 5324, 5298, 2205, 2204, 5299}"
104,1,179,0,0.3884615,"\int \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2} \, dx","Int[(a + b*ArcSinh[c + d*x])^(5/2),x]","\frac{15 \sqrt{\pi } b^{5/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{15 \sqrt{\pi } b^{5/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}+\frac{15 b^2 (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{4 d}-\frac{5 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{2 d}+\frac{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{d}","\frac{15 \sqrt{\pi } b^{5/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{15 \sqrt{\pi } b^{5/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}+\frac{15 b^2 (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{4 d}-\frac{5 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{2 d}+\frac{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{d}",1,"(15*b^2*(c + d*x)*Sqrt[a + b*ArcSinh[c + d*x]])/(4*d) - (5*b*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(3/2))/(2*d) + ((c + d*x)*(a + b*ArcSinh[c + d*x])^(5/2))/d + (15*b^(5/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(16*d) - (15*b^(5/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(16*d*E^(a/b))","A",10,8,14,0.5714,1,"{5863, 5653, 5717, 5779, 3308, 2180, 2204, 2205}"
105,1,411,0,0.8565151,"\int \frac{x^2}{\sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx","Int[x^2/Sqrt[a + b*ArcSinh[c + d*x]],x]","\frac{\sqrt{\pi } c^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^3}+\frac{\sqrt{\pi } c^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^3}+\frac{\sqrt{\frac{\pi }{2}} c e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^3}-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d^3}+\frac{\sqrt{\frac{\pi }{3}} e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d^3}-\frac{\sqrt{\frac{\pi }{2}} c e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^3}-\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d^3}+\frac{\sqrt{\frac{\pi }{3}} e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d^3}","\frac{\sqrt{\pi } c^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^3}+\frac{\sqrt{\pi } c^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^3}+\frac{\sqrt{\frac{\pi }{2}} c e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^3}-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d^3}+\frac{\sqrt{\frac{\pi }{3}} e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d^3}-\frac{\sqrt{\frac{\pi }{2}} c e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^3}-\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d^3}+\frac{\sqrt{\frac{\pi }{3}} e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d^3}",1,"-(E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(8*Sqrt[b]*d^3) + (c^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(2*Sqrt[b]*d^3) + (c*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(2*Sqrt[b]*d^3) + (E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(8*Sqrt[b]*d^3) - (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(8*Sqrt[b]*d^3*E^(a/b)) + (c^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(2*Sqrt[b]*d^3*E^(a/b)) - (c*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(2*Sqrt[b]*d^3*E^((2*a)/b)) + (Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(8*Sqrt[b]*d^3*E^((3*a)/b))","A",20,9,18,0.5000,1,"{5865, 5805, 6741, 6742, 5299, 2205, 2204, 5298, 5618}"
106,1,204,0,0.3918267,"\int \frac{x}{\sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx","Int[x/Sqrt[a + b*ArcSinh[c + d*x]],x]","-\frac{\sqrt{\pi } c e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^2}-\frac{\sqrt{\frac{\pi }{2}} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d^2}-\frac{\sqrt{\pi } c e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^2}+\frac{\sqrt{\frac{\pi }{2}} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d^2}","-\frac{\sqrt{\pi } c e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^2}-\frac{\sqrt{\frac{\pi }{2}} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d^2}-\frac{\sqrt{\pi } c e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d^2}+\frac{\sqrt{\frac{\pi }{2}} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d^2}",1,"-(c*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(2*Sqrt[b]*d^2) - (E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(4*Sqrt[b]*d^2) - (c*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(2*Sqrt[b]*d^2*E^(a/b)) + (Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(4*Sqrt[b]*d^2*E^((2*a)/b))","A",12,8,16,0.5000,1,"{5865, 5805, 6741, 6742, 5299, 2205, 2204, 5298}"
107,1,92,0,0.1289536,"\int \frac{1}{\sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx","Int[1/Sqrt[a + b*ArcSinh[c + d*x]],x]","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}",1,"(E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(2*Sqrt[b]*d) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(2*Sqrt[b]*d*E^(a/b))","A",7,6,14,0.4286,1,"{5863, 5657, 3307, 2180, 2205, 2204}"
108,1,269,0,0.5423652,"\int \frac{x}{\left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[x/(a + b*ArcSinh[c + d*x])^(3/2),x]","\frac{\sqrt{\pi } c e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d^2}+\frac{\sqrt{\frac{\pi }{2}} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d^2}-\frac{\sqrt{\pi } c e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d^2}+\frac{\sqrt{\frac{\pi }{2}} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d^2}+\frac{2 c \sqrt{(c+d x)^2+1}}{b d^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 (c+d x) \sqrt{(c+d x)^2+1}}{b d^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}","\frac{\sqrt{\pi } c e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d^2}+\frac{\sqrt{\frac{\pi }{2}} e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d^2}-\frac{\sqrt{\pi } c e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d^2}+\frac{\sqrt{\frac{\pi }{2}} e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d^2}+\frac{2 c \sqrt{(c+d x)^2+1}}{b d^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 (c+d x) \sqrt{(c+d x)^2+1}}{b d^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}",1,"(2*c*Sqrt[1 + (c + d*x)^2])/(b*d^2*Sqrt[a + b*ArcSinh[c + d*x]]) - (2*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(b*d^2*Sqrt[a + b*ArcSinh[c + d*x]]) + (c*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(b^(3/2)*d^2) + (E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(b^(3/2)*d^2) - (c*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(b^(3/2)*d^2*E^(a/b)) + (Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(b^(3/2)*d^2*E^((2*a)/b))","A",16,10,16,0.6250,1,"{5865, 5803, 5655, 5779, 3308, 2180, 2204, 2205, 5665, 3307}"
109,1,122,0,0.238905,"\int \frac{1}{\left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])^(-3/2),x]","-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 \sqrt{(c+d x)^2+1}}{b d \sqrt{a+b \sinh ^{-1}(c+d x)}}","-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 \sqrt{(c+d x)^2+1}}{b d \sqrt{a+b \sinh ^{-1}(c+d x)}}",1,"(-2*Sqrt[1 + (c + d*x)^2])/(b*d*Sqrt[a + b*ArcSinh[c + d*x]]) - (E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(b^(3/2)*d) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(b^(3/2)*d*E^(a/b))","A",8,7,14,0.5000,1,"{5863, 5655, 5779, 3308, 2180, 2204, 2205}"
110,1,365,0,0.8827858,"\int \frac{x}{\left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[x/(a + b*ArcSinh[c + d*x])^(5/2),x]","-\frac{2 \sqrt{\pi } c e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d^2}-\frac{2 \sqrt{2 \pi } e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d^2}-\frac{2 \sqrt{\pi } c e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d^2}+\frac{2 \sqrt{2 \pi } e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d^2}-\frac{8 (c+d x)^2}{3 b^2 d^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}+\frac{4 c (c+d x)}{3 b^2 d^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{4}{3 b^2 d^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 \sqrt{(c+d x)^2+1} (c+d x)}{3 b d^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}+\frac{2 c \sqrt{(c+d x)^2+1}}{3 b d^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}","-\frac{2 \sqrt{\pi } c e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d^2}-\frac{2 \sqrt{2 \pi } e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d^2}-\frac{2 \sqrt{\pi } c e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d^2}+\frac{2 \sqrt{2 \pi } e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d^2}-\frac{8 (c+d x)^2}{3 b^2 d^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}+\frac{4 c (c+d x)}{3 b^2 d^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{4}{3 b^2 d^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 \sqrt{(c+d x)^2+1} (c+d x)}{3 b d^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}+\frac{2 c \sqrt{(c+d x)^2+1}}{3 b d^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}",1,"(2*c*Sqrt[1 + (c + d*x)^2])/(3*b*d^2*(a + b*ArcSinh[c + d*x])^(3/2)) - (2*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(3*b*d^2*(a + b*ArcSinh[c + d*x])^(3/2)) - 4/(3*b^2*d^2*Sqrt[a + b*ArcSinh[c + d*x]]) + (4*c*(c + d*x))/(3*b^2*d^2*Sqrt[a + b*ArcSinh[c + d*x]]) - (8*(c + d*x)^2)/(3*b^2*d^2*Sqrt[a + b*ArcSinh[c + d*x]]) - (2*c*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(3*b^(5/2)*d^2) - (2*E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d^2) - (2*c*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(3*b^(5/2)*d^2*E^(a/b)) + (2*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d^2*E^((2*a)/b))","A",22,15,16,0.9375,1,"{5865, 5803, 5655, 5774, 5657, 3307, 2180, 2205, 2204, 5667, 5669, 5448, 12, 3308, 5675}"
111,1,158,0,0.2755834,"\int \frac{1}{\left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])^(-5/2),x]","\frac{2 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{4 (c+d x)}{3 b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 \sqrt{(c+d x)^2+1}}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}","\frac{2 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{4 (c+d x)}{3 b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 \sqrt{(c+d x)^2+1}}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}",1,"(-2*Sqrt[1 + (c + d*x)^2])/(3*b*d*(a + b*ArcSinh[c + d*x])^(3/2)) - (4*(c + d*x))/(3*b^2*d*Sqrt[a + b*ArcSinh[c + d*x]]) + (2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(3*b^(5/2)*d) + (2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(3*b^(5/2)*d*E^(a/b))","A",9,8,14,0.5714,1,"{5863, 5655, 5774, 5657, 3307, 2180, 2205, 2204}"
112,1,445,0,1.0467513,"\int \frac{x}{\left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[x/(a + b*ArcSinh[c + d*x])^(7/2),x]","\frac{4 \sqrt{\pi } c e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d^2}+\frac{8 \sqrt{2 \pi } e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d^2}-\frac{4 \sqrt{\pi } c e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d^2}+\frac{8 \sqrt{2 \pi } e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d^2}-\frac{8 (c+d x)^2}{15 b^2 d^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{32 \sqrt{(c+d x)^2+1} (c+d x)}{15 b^3 d^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}+\frac{4 c (c+d x)}{15 b^2 d^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}+\frac{8 c \sqrt{(c+d x)^2+1}}{15 b^3 d^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{4}{15 b^2 d^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{2 \sqrt{(c+d x)^2+1} (c+d x)}{5 b d^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}+\frac{2 c \sqrt{(c+d x)^2+1}}{5 b d^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}","\frac{4 \sqrt{\pi } c e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d^2}+\frac{8 \sqrt{2 \pi } e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d^2}-\frac{4 \sqrt{\pi } c e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d^2}+\frac{8 \sqrt{2 \pi } e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d^2}-\frac{8 (c+d x)^2}{15 b^2 d^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{32 \sqrt{(c+d x)^2+1} (c+d x)}{15 b^3 d^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}+\frac{4 c (c+d x)}{15 b^2 d^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}+\frac{8 c \sqrt{(c+d x)^2+1}}{15 b^3 d^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{4}{15 b^2 d^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{2 \sqrt{(c+d x)^2+1} (c+d x)}{5 b d^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}+\frac{2 c \sqrt{(c+d x)^2+1}}{5 b d^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}",1,"(2*c*Sqrt[1 + (c + d*x)^2])/(5*b*d^2*(a + b*ArcSinh[c + d*x])^(5/2)) - (2*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(5*b*d^2*(a + b*ArcSinh[c + d*x])^(5/2)) - 4/(15*b^2*d^2*(a + b*ArcSinh[c + d*x])^(3/2)) + (4*c*(c + d*x))/(15*b^2*d^2*(a + b*ArcSinh[c + d*x])^(3/2)) - (8*(c + d*x)^2)/(15*b^2*d^2*(a + b*ArcSinh[c + d*x])^(3/2)) + (8*c*Sqrt[1 + (c + d*x)^2])/(15*b^3*d^2*Sqrt[a + b*ArcSinh[c + d*x]]) - (32*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(15*b^3*d^2*Sqrt[a + b*ArcSinh[c + d*x]]) + (4*c*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(15*b^(7/2)*d^2) + (8*E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d^2) - (4*c*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(15*b^(7/2)*d^2*E^(a/b)) + (8*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d^2*E^((2*a)/b))","A",21,13,16,0.8125,1,"{5865, 5803, 5655, 5774, 5779, 3308, 2180, 2204, 2205, 5667, 5665, 3307, 5675}"
113,1,195,0,0.4111202,"\int \frac{1}{\left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])^(-7/2),x]","-\frac{4 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 \sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{4 (c+d x)}{15 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{8 \sqrt{(c+d x)^2+1}}{15 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 \sqrt{(c+d x)^2+1}}{5 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}","-\frac{4 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 \sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{4 (c+d x)}{15 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{8 \sqrt{(c+d x)^2+1}}{15 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 \sqrt{(c+d x)^2+1}}{5 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}",1,"(-2*Sqrt[1 + (c + d*x)^2])/(5*b*d*(a + b*ArcSinh[c + d*x])^(5/2)) - (4*(c + d*x))/(15*b^2*d*(a + b*ArcSinh[c + d*x])^(3/2)) - (8*Sqrt[1 + (c + d*x)^2])/(15*b^3*d*Sqrt[a + b*ArcSinh[c + d*x]]) - (4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(15*b^(7/2)*d) + (4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(15*b^(7/2)*d*E^(a/b))","A",10,8,14,0.5714,1,"{5863, 5655, 5774, 5779, 3308, 2180, 2204, 2205}"
114,1,91,0,0.0728582,"\int (c e+d e x)^m \left(a+b \sinh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^m*(a + b*ArcSinh[c + d*x]),x]","\frac{(e (c+d x))^{m+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{d e (m+1)}-\frac{b (e (c+d x))^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-(c+d x)^2\right)}{d e^2 (m+1) (m+2)}","\frac{(e (c+d x))^{m+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{d e (m+1)}-\frac{b (e (c+d x))^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-(c+d x)^2\right)}{d e^2 (m+1) (m+2)}",1,"((e*(c + d*x))^(1 + m)*(a + b*ArcSinh[c + d*x]))/(d*e*(1 + m)) - (b*(e*(c + d*x))^(2 + m)*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, -(c + d*x)^2])/(d*e^2*(1 + m)*(2 + m))","A",3,3,21,0.1429,1,"{5865, 5661, 364}"
115,1,100,0,0.0789751,"\int (c e+d e x)^4 \left(a+b \sinh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^4*(a + b*ArcSinh[c + d*x]),x]","\frac{e^4 (c+d x)^5 \left(a+b \sinh ^{-1}(c+d x)\right)}{5 d}-\frac{b e^4 \left((c+d x)^2+1\right)^{5/2}}{25 d}+\frac{2 b e^4 \left((c+d x)^2+1\right)^{3/2}}{15 d}-\frac{b e^4 \sqrt{(c+d x)^2+1}}{5 d}","\frac{e^4 (c+d x)^5 \left(a+b \sinh ^{-1}(c+d x)\right)}{5 d}-\frac{b e^4 \left((c+d x)^2+1\right)^{5/2}}{25 d}+\frac{2 b e^4 \left((c+d x)^2+1\right)^{3/2}}{15 d}-\frac{b e^4 \sqrt{(c+d x)^2+1}}{5 d}",1,"-(b*e^4*Sqrt[1 + (c + d*x)^2])/(5*d) + (2*b*e^4*(1 + (c + d*x)^2)^(3/2))/(15*d) - (b*e^4*(1 + (c + d*x)^2)^(5/2))/(25*d) + (e^4*(c + d*x)^5*(a + b*ArcSinh[c + d*x]))/(5*d)","A",6,5,21,0.2381,1,"{5865, 12, 5661, 266, 43}"
116,1,105,0,0.0699616,"\int (c e+d e x)^3 \left(a+b \sinh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcSinh[c + d*x]),x]","\frac{e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)}{4 d}-\frac{b e^3 \sqrt{(c+d x)^2+1} (c+d x)^3}{16 d}+\frac{3 b e^3 \sqrt{(c+d x)^2+1} (c+d x)}{32 d}-\frac{3 b e^3 \sinh ^{-1}(c+d x)}{32 d}","\frac{e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)}{4 d}-\frac{b e^3 \sqrt{(c+d x)^2+1} (c+d x)^3}{16 d}+\frac{3 b e^3 \sqrt{(c+d x)^2+1} (c+d x)}{32 d}-\frac{3 b e^3 \sinh ^{-1}(c+d x)}{32 d}",1,"(3*b*e^3*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(32*d) - (b*e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2])/(16*d) - (3*b*e^3*ArcSinh[c + d*x])/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcSinh[c + d*x]))/(4*d)","A",6,5,21,0.2381,1,"{5865, 12, 5661, 321, 215}"
117,1,76,0,0.0656067,"\int (c e+d e x)^2 \left(a+b \sinh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcSinh[c + d*x]),x]","\frac{e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)}{3 d}-\frac{b e^2 \left((c+d x)^2+1\right)^{3/2}}{9 d}+\frac{b e^2 \sqrt{(c+d x)^2+1}}{3 d}","\frac{e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)}{3 d}-\frac{b e^2 \left((c+d x)^2+1\right)^{3/2}}{9 d}+\frac{b e^2 \sqrt{(c+d x)^2+1}}{3 d}",1,"(b*e^2*Sqrt[1 + (c + d*x)^2])/(3*d) - (b*e^2*(1 + (c + d*x)^2)^(3/2))/(9*d) + (e^2*(c + d*x)^3*(a + b*ArcSinh[c + d*x]))/(3*d)","A",6,5,21,0.2381,1,"{5865, 12, 5661, 266, 43}"
118,1,68,0,0.0387322,"\int (c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)*(a + b*ArcSinh[c + d*x]),x]","\frac{e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)}{2 d}-\frac{b e \sqrt{(c+d x)^2+1} (c+d x)}{4 d}+\frac{b e \sinh ^{-1}(c+d x)}{4 d}","\frac{e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)}{2 d}-\frac{b e \sqrt{(c+d x)^2+1} (c+d x)}{4 d}+\frac{b e \sinh ^{-1}(c+d x)}{4 d}",1,"-(b*e*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(4*d) + (b*e*ArcSinh[c + d*x])/(4*d) + (e*(c + d*x)^2*(a + b*ArcSinh[c + d*x]))/(2*d)","A",5,5,19,0.2632,1,"{5865, 12, 5661, 321, 215}"
119,1,39,0,0.0227585,"\int \left(a+b \sinh ^{-1}(c+d x)\right) \, dx","Int[a + b*ArcSinh[c + d*x],x]","a x-\frac{b \sqrt{(c+d x)^2+1}}{d}+\frac{b (c+d x) \sinh ^{-1}(c+d x)}{d}","a x-\frac{b \sqrt{(c+d x)^2+1}}{d}+\frac{b (c+d x) \sinh ^{-1}(c+d x)}{d}",1,"a*x - (b*Sqrt[1 + (c + d*x)^2])/d + (b*(c + d*x)*ArcSinh[c + d*x])/d","A",4,3,10,0.3000,1,"{5863, 5653, 261}"
120,1,81,0,0.1117937,"\int \frac{a+b \sinh ^{-1}(c+d x)}{c e+d e x} \, dx","Int[(a + b*ArcSinh[c + d*x])/(c*e + d*e*x),x]","\frac{b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c+d x)}\right)}{2 d e}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{2 b d e}+\frac{\log \left(1-e^{2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e}","-\frac{b \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c+d x)}\right)}{2 d e}+\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{2 b d e}+\frac{\log \left(1-e^{-2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e}",1,"-(a + b*ArcSinh[c + d*x])^2/(2*b*d*e) + ((a + b*ArcSinh[c + d*x])*Log[1 - E^(2*ArcSinh[c + d*x])])/(d*e) + (b*PolyLog[2, E^(2*ArcSinh[c + d*x])])/(2*d*e)","A",7,7,21,0.3333,0,"{5865, 12, 5659, 3716, 2190, 2279, 2391}"
121,1,49,0,0.0540328,"\int \frac{a+b \sinh ^{-1}(c+d x)}{(c e+d e x)^2} \, dx","Int[(a + b*ArcSinh[c + d*x])/(c*e + d*e*x)^2,x]","-\frac{a+b \sinh ^{-1}(c+d x)}{d e^2 (c+d x)}-\frac{b \tanh ^{-1}\left(\sqrt{(c+d x)^2+1}\right)}{d e^2}","-\frac{a+b \sinh ^{-1}(c+d x)}{d e^2 (c+d x)}-\frac{b \tanh ^{-1}\left(\sqrt{(c+d x)^2+1}\right)}{d e^2}",1,"-((a + b*ArcSinh[c + d*x])/(d*e^2*(c + d*x))) - (b*ArcTanh[Sqrt[1 + (c + d*x)^2]])/(d*e^2)","A",6,6,21,0.2857,1,"{5865, 12, 5661, 266, 63, 207}"
122,1,59,0,0.0509626,"\int \frac{a+b \sinh ^{-1}(c+d x)}{(c e+d e x)^3} \, dx","Int[(a + b*ArcSinh[c + d*x])/(c*e + d*e*x)^3,x]","-\frac{a+b \sinh ^{-1}(c+d x)}{2 d e^3 (c+d x)^2}-\frac{b \sqrt{(c+d x)^2+1}}{2 d e^3 (c+d x)}","-\frac{a+b \sinh ^{-1}(c+d x)}{2 d e^3 (c+d x)^2}-\frac{b \sqrt{(c+d x)^2+1}}{2 d e^3 (c+d x)}",1,"-(b*Sqrt[1 + (c + d*x)^2])/(2*d*e^3*(c + d*x)) - (a + b*ArcSinh[c + d*x])/(2*d*e^3*(c + d*x)^2)","A",4,4,21,0.1905,1,"{5865, 12, 5661, 264}"
123,1,84,0,0.0709212,"\int \frac{a+b \sinh ^{-1}(c+d x)}{(c e+d e x)^4} \, dx","Int[(a + b*ArcSinh[c + d*x])/(c*e + d*e*x)^4,x]","-\frac{a+b \sinh ^{-1}(c+d x)}{3 d e^4 (c+d x)^3}-\frac{b \sqrt{(c+d x)^2+1}}{6 d e^4 (c+d x)^2}+\frac{b \tanh ^{-1}\left(\sqrt{(c+d x)^2+1}\right)}{6 d e^4}","-\frac{a+b \sinh ^{-1}(c+d x)}{3 d e^4 (c+d x)^3}-\frac{b \sqrt{(c+d x)^2+1}}{6 d e^4 (c+d x)^2}+\frac{b \tanh ^{-1}\left(\sqrt{(c+d x)^2+1}\right)}{6 d e^4}",1,"-(b*Sqrt[1 + (c + d*x)^2])/(6*d*e^4*(c + d*x)^2) - (a + b*ArcSinh[c + d*x])/(3*d*e^4*(c + d*x)^3) + (b*ArcTanh[Sqrt[1 + (c + d*x)^2]])/(6*d*e^4)","A",7,7,21,0.3333,1,"{5865, 12, 5661, 266, 51, 63, 207}"
124,1,90,0,0.0667661,"\int \frac{a+b \sinh ^{-1}(c+d x)}{(c e+d e x)^5} \, dx","Int[(a + b*ArcSinh[c + d*x])/(c*e + d*e*x)^5,x]","-\frac{a+b \sinh ^{-1}(c+d x)}{4 d e^5 (c+d x)^4}+\frac{b \sqrt{(c+d x)^2+1}}{6 d e^5 (c+d x)}-\frac{b \sqrt{(c+d x)^2+1}}{12 d e^5 (c+d x)^3}","-\frac{a+b \sinh ^{-1}(c+d x)}{4 d e^5 (c+d x)^4}+\frac{b \sqrt{(c+d x)^2+1}}{6 d e^5 (c+d x)}-\frac{b \sqrt{(c+d x)^2+1}}{12 d e^5 (c+d x)^3}",1,"-(b*Sqrt[1 + (c + d*x)^2])/(12*d*e^5*(c + d*x)^3) + (b*Sqrt[1 + (c + d*x)^2])/(6*d*e^5*(c + d*x)) - (a + b*ArcSinh[c + d*x])/(4*d*e^5*(c + d*x)^4)","A",5,5,21,0.2381,1,"{5865, 12, 5661, 271, 264}"
125,1,115,0,0.0862735,"\int \frac{a+b \sinh ^{-1}(c+d x)}{(c e+d e x)^6} \, dx","Int[(a + b*ArcSinh[c + d*x])/(c*e + d*e*x)^6,x]","-\frac{a+b \sinh ^{-1}(c+d x)}{5 d e^6 (c+d x)^5}+\frac{3 b \sqrt{(c+d x)^2+1}}{40 d e^6 (c+d x)^2}-\frac{b \sqrt{(c+d x)^2+1}}{20 d e^6 (c+d x)^4}-\frac{3 b \tanh ^{-1}\left(\sqrt{(c+d x)^2+1}\right)}{40 d e^6}","-\frac{a+b \sinh ^{-1}(c+d x)}{5 d e^6 (c+d x)^5}+\frac{3 b \sqrt{(c+d x)^2+1}}{40 d e^6 (c+d x)^2}-\frac{b \sqrt{(c+d x)^2+1}}{20 d e^6 (c+d x)^4}-\frac{3 b \tanh ^{-1}\left(\sqrt{(c+d x)^2+1}\right)}{40 d e^6}",1,"-(b*Sqrt[1 + (c + d*x)^2])/(20*d*e^6*(c + d*x)^4) + (3*b*Sqrt[1 + (c + d*x)^2])/(40*d*e^6*(c + d*x)^2) - (a + b*ArcSinh[c + d*x])/(5*d*e^6*(c + d*x)^5) - (3*b*ArcTanh[Sqrt[1 + (c + d*x)^2]])/(40*d*e^6)","A",8,7,21,0.3333,1,"{5865, 12, 5661, 266, 51, 63, 207}"
126,1,187,0,0.2065529,"\int (c e+d e x)^m \left(a+b \sinh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^m*(a + b*ArcSinh[c + d*x])^2,x]","\frac{2 b^2 (e (c+d x))^{m+3} \, _3F_2\left(1,\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};\frac{m}{2}+2,\frac{m}{2}+\frac{5}{2};-(c+d x)^2\right)}{d e^3 (m+1) (m+2) (m+3)}-\frac{2 b (e (c+d x))^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^2 (m+1) (m+2)}+\frac{(e (c+d x))^{m+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e (m+1)}","\frac{2 b^2 (e (c+d x))^{m+3} \, _3F_2\left(1,\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};\frac{m}{2}+2,\frac{m}{2}+\frac{5}{2};-(c+d x)^2\right)}{d e^3 (m+1) (m+2) (m+3)}-\frac{2 b (e (c+d x))^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^2 (m+1) (m+2)}+\frac{(e (c+d x))^{m+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e (m+1)}",1,"((e*(c + d*x))^(1 + m)*(a + b*ArcSinh[c + d*x])^2)/(d*e*(1 + m)) - (2*b*(e*(c + d*x))^(2 + m)*(a + b*ArcSinh[c + d*x])*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, -(c + d*x)^2])/(d*e^2*(1 + m)*(2 + m)) + (2*b^2*(e*(c + d*x))^(3 + m)*HypergeometricPFQ[{1, 3/2 + m/2, 3/2 + m/2}, {2 + m/2, 5/2 + m/2}, -(c + d*x)^2])/(d*e^3*(1 + m)*(2 + m)*(3 + m))","A",3,3,23,0.1304,1,"{5865, 5661, 5762}"
127,1,197,0,0.3068132,"\int (c e+d e x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^4*(a + b*ArcSinh[c + d*x])^2,x]","\frac{e^4 (c+d x)^5 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{5 d}-\frac{2 b e^4 \sqrt{(c+d x)^2+1} (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)}{25 d}+\frac{8 b e^4 \sqrt{(c+d x)^2+1} (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)}{75 d}-\frac{16 b e^4 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{75 d}+\frac{2 b^2 e^4 (c+d x)^5}{125 d}-\frac{8 b^2 e^4 (c+d x)^3}{225 d}+\frac{16}{75} b^2 e^4 x","\frac{e^4 (c+d x)^5 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{5 d}-\frac{2 b e^4 \sqrt{(c+d x)^2+1} (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)}{25 d}+\frac{8 b e^4 \sqrt{(c+d x)^2+1} (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)}{75 d}-\frac{16 b e^4 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{75 d}+\frac{2 b^2 e^4 (c+d x)^5}{125 d}-\frac{8 b^2 e^4 (c+d x)^3}{225 d}+\frac{16}{75} b^2 e^4 x",1,"(16*b^2*e^4*x)/75 - (8*b^2*e^4*(c + d*x)^3)/(225*d) + (2*b^2*e^4*(c + d*x)^5)/(125*d) - (16*b*e^4*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/(75*d) + (8*b*e^4*(c + d*x)^2*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/(75*d) - (2*b*e^4*(c + d*x)^4*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/(25*d) + (e^4*(c + d*x)^5*(a + b*ArcSinh[c + d*x])^2)/(5*d)","A",9,7,23,0.3043,1,"{5865, 12, 5661, 5758, 5717, 8, 30}"
128,1,172,0,0.2576494,"\int (c e+d e x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcSinh[c + d*x])^2,x]","\frac{e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{4 d}-\frac{b e^3 \sqrt{(c+d x)^2+1} (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)}{8 d}+\frac{3 b e^3 \sqrt{(c+d x)^2+1} (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)}{16 d}-\frac{3 e^3 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{32 d}+\frac{b^2 e^3 (c+d x)^4}{32 d}-\frac{3 b^2 e^3 (c+d x)^2}{32 d}","\frac{e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{4 d}-\frac{b e^3 \sqrt{(c+d x)^2+1} (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)}{8 d}+\frac{3 b e^3 \sqrt{(c+d x)^2+1} (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)}{16 d}-\frac{3 e^3 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{32 d}+\frac{b^2 e^3 (c+d x)^4}{32 d}-\frac{3 b^2 e^3 (c+d x)^2}{32 d}",1,"(-3*b^2*e^3*(c + d*x)^2)/(32*d) + (b^2*e^3*(c + d*x)^4)/(32*d) + (3*b*e^3*(c + d*x)*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/(16*d) - (b*e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/(8*d) - (3*e^3*(a + b*ArcSinh[c + d*x])^2)/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcSinh[c + d*x])^2)/(4*d)","A",8,6,23,0.2609,1,"{5865, 12, 5661, 5758, 5675, 30}"
129,1,136,0,0.2049607,"\int (c e+d e x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcSinh[c + d*x])^2,x]","\frac{e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{3 d}-\frac{2 b e^2 \sqrt{(c+d x)^2+1} (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)}{9 d}+\frac{4 b e^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{9 d}+\frac{2 b^2 e^2 (c+d x)^3}{27 d}-\frac{4}{9} b^2 e^2 x","\frac{e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{3 d}-\frac{2 b e^2 \sqrt{(c+d x)^2+1} (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)}{9 d}+\frac{4 b e^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{9 d}+\frac{2 b^2 e^2 (c+d x)^3}{27 d}-\frac{4}{9} b^2 e^2 x",1,"(-4*b^2*e^2*x)/9 + (2*b^2*e^2*(c + d*x)^3)/(27*d) + (4*b*e^2*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/(9*d) - (2*b*e^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/(9*d) + (e^2*(c + d*x)^3*(a + b*ArcSinh[c + d*x])^2)/(3*d)","A",7,7,23,0.3043,1,"{5865, 12, 5661, 5758, 5717, 8, 30}"
130,1,103,0,0.1448621,"\int (c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)*(a + b*ArcSinh[c + d*x])^2,x]","\frac{e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{2 d}-\frac{b e \sqrt{(c+d x)^2+1} (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)}{2 d}+\frac{e \left(a+b \sinh ^{-1}(c+d x)\right)^2}{4 d}+\frac{b^2 e (c+d x)^2}{4 d}","\frac{e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{2 d}-\frac{b e \sqrt{(c+d x)^2+1} (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)}{2 d}+\frac{e \left(a+b \sinh ^{-1}(c+d x)\right)^2}{4 d}+\frac{b^2 e (c+d x)^2}{4 d}",1,"(b^2*e*(c + d*x)^2)/(4*d) - (b*e*(c + d*x)*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/(2*d) + (e*(a + b*ArcSinh[c + d*x])^2)/(4*d) + (e*(c + d*x)^2*(a + b*ArcSinh[c + d*x])^2)/(2*d)","A",6,6,21,0.2857,1,"{5865, 12, 5661, 5758, 5675, 30}"
131,1,57,0,0.0701418,"\int \left(a+b \sinh ^{-1}(c+d x)\right)^2 \, dx","Int[(a + b*ArcSinh[c + d*x])^2,x]","-\frac{2 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{d}+\frac{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d}+2 b^2 x","-\frac{2 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{d}+\frac{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d}+2 b^2 x",1,"2*b^2*x - (2*b*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/d + ((c + d*x)*(a + b*ArcSinh[c + d*x])^2)/d","A",4,4,12,0.3333,1,"{5863, 5653, 5717, 8}"
132,1,115,0,0.1979954,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{c e+d e x} \, dx","Int[(a + b*ArcSinh[c + d*x])^2/(c*e + d*e*x),x]","\frac{b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e}-\frac{b^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c+d x)}\right)}{2 d e}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{3 b d e}+\frac{\log \left(1-e^{2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e}","-\frac{b \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e}-\frac{b^2 \text{PolyLog}\left(3,e^{-2 \sinh ^{-1}(c+d x)}\right)}{2 d e}+\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{3 b d e}+\frac{\log \left(1-e^{-2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e}",1,"-(a + b*ArcSinh[c + d*x])^3/(3*b*d*e) + ((a + b*ArcSinh[c + d*x])^2*Log[1 - E^(2*ArcSinh[c + d*x])])/(d*e) + (b*(a + b*ArcSinh[c + d*x])*PolyLog[2, E^(2*ArcSinh[c + d*x])])/(d*e) - (b^2*PolyLog[3, E^(2*ArcSinh[c + d*x])])/(2*d*e)","A",8,8,23,0.3478,0,"{5865, 12, 5659, 3716, 2190, 2531, 2282, 6589}"
133,1,100,0,0.1756779,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{(c e+d e x)^2} \, dx","Int[(a + b*ArcSinh[c + d*x])^2/(c*e + d*e*x)^2,x]","-\frac{2 b^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c+d x)}\right)}{d e^2}+\frac{2 b^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^2 (c+d x)}-\frac{4 b \tanh ^{-1}\left(e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^2}","-\frac{2 b^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c+d x)}\right)}{d e^2}+\frac{2 b^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^2 (c+d x)}-\frac{4 b \tanh ^{-1}\left(e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^2}",1,"-((a + b*ArcSinh[c + d*x])^2/(d*e^2*(c + d*x))) - (4*b*(a + b*ArcSinh[c + d*x])*ArcTanh[E^ArcSinh[c + d*x]])/(d*e^2) - (2*b^2*PolyLog[2, -E^ArcSinh[c + d*x]])/(d*e^2) + (2*b^2*PolyLog[2, E^ArcSinh[c + d*x]])/(d*e^2)","A",9,7,23,0.3043,1,"{5865, 12, 5661, 5760, 4182, 2279, 2391}"
134,1,85,0,0.136605,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{(c e+d e x)^3} \, dx","Int[(a + b*ArcSinh[c + d*x])^2/(c*e + d*e*x)^3,x]","-\frac{b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^3 (c+d x)}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)^2}+\frac{b^2 \log (c+d x)}{d e^3}","-\frac{b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^3 (c+d x)}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)^2}+\frac{b^2 \log (c+d x)}{d e^3}",1,"-((b*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/(d*e^3*(c + d*x))) - (a + b*ArcSinh[c + d*x])^2/(2*d*e^3*(c + d*x)^2) + (b^2*Log[c + d*x])/(d*e^3)","A",5,5,23,0.2174,1,"{5865, 12, 5661, 5723, 29}"
135,1,169,0,0.2466947,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{(c e+d e x)^4} \, dx","Int[(a + b*ArcSinh[c + d*x])^2/(c*e + d*e*x)^4,x]","\frac{b^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c+d x)}\right)}{3 d e^4}-\frac{b^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c+d x)}\right)}{3 d e^4}-\frac{b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{3 d e^4 (c+d x)^3}+\frac{2 b \tanh ^{-1}\left(e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{3 d e^4}-\frac{b^2}{3 d e^4 (c+d x)}","\frac{b^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c+d x)}\right)}{3 d e^4}-\frac{b^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c+d x)}\right)}{3 d e^4}-\frac{b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{3 d e^4 (c+d x)^3}+\frac{2 b \tanh ^{-1}\left(e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{3 d e^4}-\frac{b^2}{3 d e^4 (c+d x)}",1,"-b^2/(3*d*e^4*(c + d*x)) - (b*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/(3*d*e^4*(c + d*x)^2) - (a + b*ArcSinh[c + d*x])^2/(3*d*e^4*(c + d*x)^3) + (2*b*(a + b*ArcSinh[c + d*x])*ArcTanh[E^ArcSinh[c + d*x]])/(3*d*e^4) + (b^2*PolyLog[2, -E^ArcSinh[c + d*x]])/(3*d*e^4) - (b^2*PolyLog[2, E^ArcSinh[c + d*x]])/(3*d*e^4)","A",11,9,23,0.3913,1,"{5865, 12, 5661, 5747, 5760, 4182, 2279, 2391, 30}"
136,0,0,0,0.173323,"\int (c e+d e x)^m \left(a+b \sinh ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^m*(a + b*ArcSinh[c + d*x])^3,x]","\int (c e+d e x)^m \left(a+b \sinh ^{-1}(c+d x)\right)^3 \, dx","\frac{(e (c+d x))^{m+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d e (m+1)}-\frac{3 b \text{Int}\left(\frac{(e (c+d x))^{m+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{\sqrt{(c+d x)^2+1}},x\right)}{e (m+1)}",0,"((e*(c + d*x))^(1 + m)*(a + b*ArcSinh[c + d*x])^3)/(d*e*(1 + m)) - (3*b*Defer[Subst][Defer[Int][((e*x)^(1 + m)*(a + b*ArcSinh[x])^2)/Sqrt[1 + x^2], x], x, c + d*x])/(d*e*(1 + m))","A",0,0,0,0,-1,"{}"
137,1,326,0,0.4737405,"\int (c e+d e x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^4*(a + b*ArcSinh[c + d*x])^3,x]","\frac{6 b^2 e^4 (c+d x)^5 \left(a+b \sinh ^{-1}(c+d x)\right)}{125 d}-\frac{8 b^2 e^4 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)}{75 d}+\frac{16}{25} a b^2 e^4 x+\frac{e^4 (c+d x)^5 \left(a+b \sinh ^{-1}(c+d x)\right)^3}{5 d}-\frac{3 b e^4 \sqrt{(c+d x)^2+1} (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{25 d}+\frac{4 b e^4 \sqrt{(c+d x)^2+1} (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{25 d}-\frac{8 b e^4 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{25 d}-\frac{6 b^3 e^4 \left((c+d x)^2+1\right)^{5/2}}{625 d}+\frac{76 b^3 e^4 \left((c+d x)^2+1\right)^{3/2}}{1125 d}-\frac{298 b^3 e^4 \sqrt{(c+d x)^2+1}}{375 d}+\frac{16 b^3 e^4 (c+d x) \sinh ^{-1}(c+d x)}{25 d}","\frac{6 b^2 e^4 (c+d x)^5 \left(a+b \sinh ^{-1}(c+d x)\right)}{125 d}-\frac{8 b^2 e^4 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)}{75 d}+\frac{16}{25} a b^2 e^4 x+\frac{e^4 (c+d x)^5 \left(a+b \sinh ^{-1}(c+d x)\right)^3}{5 d}-\frac{3 b e^4 \sqrt{(c+d x)^2+1} (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{25 d}+\frac{4 b e^4 \sqrt{(c+d x)^2+1} (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{25 d}-\frac{8 b e^4 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{25 d}-\frac{6 b^3 e^4 \left((c+d x)^2+1\right)^{5/2}}{625 d}+\frac{76 b^3 e^4 \left((c+d x)^2+1\right)^{3/2}}{1125 d}-\frac{298 b^3 e^4 \sqrt{(c+d x)^2+1}}{375 d}+\frac{16 b^3 e^4 (c+d x) \sinh ^{-1}(c+d x)}{25 d}",1,"(16*a*b^2*e^4*x)/25 - (298*b^3*e^4*Sqrt[1 + (c + d*x)^2])/(375*d) + (76*b^3*e^4*(1 + (c + d*x)^2)^(3/2))/(1125*d) - (6*b^3*e^4*(1 + (c + d*x)^2)^(5/2))/(625*d) + (16*b^3*e^4*(c + d*x)*ArcSinh[c + d*x])/(25*d) - (8*b^2*e^4*(c + d*x)^3*(a + b*ArcSinh[c + d*x]))/(75*d) + (6*b^2*e^4*(c + d*x)^5*(a + b*ArcSinh[c + d*x]))/(125*d) - (8*b*e^4*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^2)/(25*d) + (4*b*e^4*(c + d*x)^2*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^2)/(25*d) - (3*b*e^4*(c + d*x)^4*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^2)/(25*d) + (e^4*(c + d*x)^5*(a + b*ArcSinh[c + d*x])^3)/(5*d)","A",17,9,23,0.3913,1,"{5865, 12, 5661, 5758, 5717, 5653, 261, 266, 43}"
138,1,279,0,0.3857156,"\int (c e+d e x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcSinh[c + d*x])^3,x]","\frac{3 b^2 e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)}{32 d}-\frac{9 b^2 e^3 (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)}{32 d}+\frac{e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^3}{4 d}-\frac{3 b e^3 \sqrt{(c+d x)^2+1} (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{16 d}+\frac{9 b e^3 \sqrt{(c+d x)^2+1} (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{32 d}-\frac{3 e^3 \left(a+b \sinh ^{-1}(c+d x)\right)^3}{32 d}-\frac{3 b^3 e^3 \sqrt{(c+d x)^2+1} (c+d x)^3}{128 d}+\frac{45 b^3 e^3 \sqrt{(c+d x)^2+1} (c+d x)}{256 d}-\frac{45 b^3 e^3 \sinh ^{-1}(c+d x)}{256 d}","\frac{3 b^2 e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)}{32 d}-\frac{9 b^2 e^3 (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)}{32 d}+\frac{e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^3}{4 d}-\frac{3 b e^3 \sqrt{(c+d x)^2+1} (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{16 d}+\frac{9 b e^3 \sqrt{(c+d x)^2+1} (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{32 d}-\frac{3 e^3 \left(a+b \sinh ^{-1}(c+d x)\right)^3}{32 d}-\frac{3 b^3 e^3 \sqrt{(c+d x)^2+1} (c+d x)^3}{128 d}+\frac{45 b^3 e^3 \sqrt{(c+d x)^2+1} (c+d x)}{256 d}-\frac{45 b^3 e^3 \sinh ^{-1}(c+d x)}{256 d}",1,"(45*b^3*e^3*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(256*d) - (3*b^3*e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2])/(128*d) - (45*b^3*e^3*ArcSinh[c + d*x])/(256*d) - (9*b^2*e^3*(c + d*x)^2*(a + b*ArcSinh[c + d*x]))/(32*d) + (3*b^2*e^3*(c + d*x)^4*(a + b*ArcSinh[c + d*x]))/(32*d) + (9*b*e^3*(c + d*x)*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^2)/(32*d) - (3*b*e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^2)/(16*d) - (3*e^3*(a + b*ArcSinh[c + d*x])^3)/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcSinh[c + d*x])^3)/(4*d)","A",13,7,23,0.3043,1,"{5865, 12, 5661, 5758, 5675, 321, 215}"
139,1,227,0,0.2999085,"\int (c e+d e x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcSinh[c + d*x])^3,x]","\frac{2 b^2 e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)}{9 d}-\frac{4}{3} a b^2 e^2 x+\frac{2 b e^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{3 d}-\frac{b e^2 (c+d x)^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{3 d}+\frac{e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^3}{3 d}-\frac{2 b^3 e^2 \left((c+d x)^2+1\right)^{3/2}}{27 d}+\frac{14 b^3 e^2 \sqrt{(c+d x)^2+1}}{9 d}-\frac{4 b^3 e^2 (c+d x) \sinh ^{-1}(c+d x)}{3 d}","\frac{2 b^2 e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)}{9 d}-\frac{4}{3} a b^2 e^2 x+\frac{2 b e^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{3 d}-\frac{b e^2 (c+d x)^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{3 d}+\frac{e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^3}{3 d}-\frac{2 b^3 e^2 \left((c+d x)^2+1\right)^{3/2}}{27 d}+\frac{14 b^3 e^2 \sqrt{(c+d x)^2+1}}{9 d}-\frac{4 b^3 e^2 (c+d x) \sinh ^{-1}(c+d x)}{3 d}",1,"(-4*a*b^2*e^2*x)/3 + (14*b^3*e^2*Sqrt[1 + (c + d*x)^2])/(9*d) - (2*b^3*e^2*(1 + (c + d*x)^2)^(3/2))/(27*d) - (4*b^3*e^2*(c + d*x)*ArcSinh[c + d*x])/(3*d) + (2*b^2*e^2*(c + d*x)^3*(a + b*ArcSinh[c + d*x]))/(9*d) + (2*b*e^2*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^2)/(3*d) - (b*e^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^2)/(3*d) + (e^2*(c + d*x)^3*(a + b*ArcSinh[c + d*x])^3)/(3*d)","A",12,9,23,0.3913,1,"{5865, 12, 5661, 5758, 5717, 5653, 261, 266, 43}"
140,1,161,0,0.2126066,"\int (c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)*(a + b*ArcSinh[c + d*x])^3,x]","\frac{3 b^2 e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)}{4 d}-\frac{3 b e (c+d x) \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{4 d}+\frac{e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^3}{2 d}+\frac{e \left(a+b \sinh ^{-1}(c+d x)\right)^3}{4 d}-\frac{3 b^3 e (c+d x) \sqrt{(c+d x)^2+1}}{8 d}+\frac{3 b^3 e \sinh ^{-1}(c+d x)}{8 d}","\frac{3 b^2 e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)}{4 d}-\frac{3 b e (c+d x) \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{4 d}+\frac{e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^3}{2 d}+\frac{e \left(a+b \sinh ^{-1}(c+d x)\right)^3}{4 d}-\frac{3 b^3 e (c+d x) \sqrt{(c+d x)^2+1}}{8 d}+\frac{3 b^3 e \sinh ^{-1}(c+d x)}{8 d}",1,"(-3*b^3*e*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(8*d) + (3*b^3*e*ArcSinh[c + d*x])/(8*d) + (3*b^2*e*(c + d*x)^2*(a + b*ArcSinh[c + d*x]))/(4*d) - (3*b*e*(c + d*x)*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^2)/(4*d) + (e*(a + b*ArcSinh[c + d*x])^3)/(4*d) + (e*(c + d*x)^2*(a + b*ArcSinh[c + d*x])^3)/(2*d)","A",8,7,21,0.3333,1,"{5865, 12, 5661, 5758, 5675, 321, 215}"
141,1,100,0,0.1082843,"\int \left(a+b \sinh ^{-1}(c+d x)\right)^3 \, dx","Int[(a + b*ArcSinh[c + d*x])^3,x]","6 a b^2 x-\frac{3 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d}+\frac{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d}-\frac{6 b^3 \sqrt{(c+d x)^2+1}}{d}+\frac{6 b^3 (c+d x) \sinh ^{-1}(c+d x)}{d}","6 a b^2 x-\frac{3 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d}+\frac{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d}-\frac{6 b^3 \sqrt{(c+d x)^2+1}}{d}+\frac{6 b^3 (c+d x) \sinh ^{-1}(c+d x)}{d}",1,"6*a*b^2*x - (6*b^3*Sqrt[1 + (c + d*x)^2])/d + (6*b^3*(c + d*x)*ArcSinh[c + d*x])/d - (3*b*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^2)/d + ((c + d*x)*(a + b*ArcSinh[c + d*x])^3)/d","A",6,4,12,0.3333,1,"{5863, 5653, 5717, 261}"
142,1,155,0,0.2235809,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{c e+d e x} \, dx","Int[(a + b*ArcSinh[c + d*x])^3/(c*e + d*e*x),x]","-\frac{3 b^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{2 d e}+\frac{3 b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{2 d e}+\frac{3 b^3 \text{PolyLog}\left(4,e^{2 \sinh ^{-1}(c+d x)}\right)}{4 d e}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{4 b d e}+\frac{\log \left(1-e^{2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d e}","-\frac{3 b^2 \text{PolyLog}\left(3,e^{-2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{2 d e}-\frac{3 b \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{2 d e}-\frac{3 b^3 \text{PolyLog}\left(4,e^{-2 \sinh ^{-1}(c+d x)}\right)}{4 d e}+\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{4 b d e}+\frac{\log \left(1-e^{-2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d e}",1,"-(a + b*ArcSinh[c + d*x])^4/(4*b*d*e) + ((a + b*ArcSinh[c + d*x])^3*Log[1 - E^(2*ArcSinh[c + d*x])])/(d*e) + (3*b*(a + b*ArcSinh[c + d*x])^2*PolyLog[2, E^(2*ArcSinh[c + d*x])])/(2*d*e) - (3*b^2*(a + b*ArcSinh[c + d*x])*PolyLog[3, E^(2*ArcSinh[c + d*x])])/(2*d*e) + (3*b^3*PolyLog[4, E^(2*ArcSinh[c + d*x])])/(4*d*e)","A",9,9,23,0.3913,0,"{5865, 12, 5659, 3716, 2190, 2531, 6609, 2282, 6589}"
143,1,166,0,0.2551478,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{(c e+d e x)^2} \, dx","Int[(a + b*ArcSinh[c + d*x])^3/(c*e + d*e*x)^2,x]","-\frac{6 b^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^2}+\frac{6 b^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^2}+\frac{6 b^3 \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c+d x)}\right)}{d e^2}-\frac{6 b^3 \text{PolyLog}\left(3,e^{\sinh ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{d e^2 (c+d x)}-\frac{6 b \tanh ^{-1}\left(e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^2}","-\frac{6 b^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^2}+\frac{6 b^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^2}+\frac{6 b^3 \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c+d x)}\right)}{d e^2}-\frac{6 b^3 \text{PolyLog}\left(3,e^{\sinh ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{d e^2 (c+d x)}-\frac{6 b \tanh ^{-1}\left(e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^2}",1,"-((a + b*ArcSinh[c + d*x])^3/(d*e^2*(c + d*x))) - (6*b*(a + b*ArcSinh[c + d*x])^2*ArcTanh[E^ArcSinh[c + d*x]])/(d*e^2) - (6*b^2*(a + b*ArcSinh[c + d*x])*PolyLog[2, -E^ArcSinh[c + d*x]])/(d*e^2) + (6*b^2*(a + b*ArcSinh[c + d*x])*PolyLog[2, E^ArcSinh[c + d*x]])/(d*e^2) + (6*b^3*PolyLog[3, -E^ArcSinh[c + d*x]])/(d*e^2) - (6*b^3*PolyLog[3, E^ArcSinh[c + d*x]])/(d*e^2)","A",11,8,23,0.3478,1,"{5865, 12, 5661, 5760, 4182, 2531, 2282, 6589}"
144,1,157,0,0.2605054,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{(c e+d e x)^3} \, dx","Int[(a + b*ArcSinh[c + d*x])^3/(c*e + d*e*x)^3,x]","\frac{3 b^3 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c+d x)}\right)}{2 d e^3}+\frac{3 b^2 \log \left(1-e^{2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^3}-\frac{3 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)}-\frac{3 b \left(a+b \sinh ^{-1}(c+d x)\right)^2}{2 d e^3}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{2 d e^3 (c+d x)^2}","-\frac{3 b^3 \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c+d x)}\right)}{2 d e^3}+\frac{3 b^2 \log \left(1-e^{-2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^3}-\frac{3 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)}+\frac{3 b \left(a+b \sinh ^{-1}(c+d x)\right)^2}{2 d e^3}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{2 d e^3 (c+d x)^2}",1,"(-3*b*(a + b*ArcSinh[c + d*x])^2)/(2*d*e^3) - (3*b*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^2)/(2*d*e^3*(c + d*x)) - (a + b*ArcSinh[c + d*x])^3/(2*d*e^3*(c + d*x)^2) + (3*b^2*(a + b*ArcSinh[c + d*x])*Log[1 - E^(2*ArcSinh[c + d*x])])/(d*e^3) + (3*b^3*PolyLog[2, E^(2*ArcSinh[c + d*x])])/(2*d*e^3)","A",9,9,23,0.3913,0,"{5865, 12, 5661, 5723, 5659, 3716, 2190, 2279, 2391}"
145,1,261,0,0.4100113,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{(c e+d e x)^4} \, dx","Int[(a + b*ArcSinh[c + d*x])^3/(c*e + d*e*x)^4,x]","\frac{b^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^4}-\frac{b^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^4}-\frac{b^3 \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c+d x)}\right)}{d e^4}+\frac{b^3 \text{PolyLog}\left(3,e^{\sinh ^{-1}(c+d x)}\right)}{d e^4}-\frac{b^2 \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^4 (c+d x)}-\frac{b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{2 d e^4 (c+d x)^2}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^3}+\frac{b \tanh ^{-1}\left(e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^4}-\frac{b^3 \tanh ^{-1}\left(\sqrt{(c+d x)^2+1}\right)}{d e^4}","\frac{b^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^4}-\frac{b^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^4}-\frac{b^3 \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c+d x)}\right)}{d e^4}+\frac{b^3 \text{PolyLog}\left(3,e^{\sinh ^{-1}(c+d x)}\right)}{d e^4}-\frac{b^2 \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^4 (c+d x)}-\frac{b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{2 d e^4 (c+d x)^2}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^3}+\frac{b \tanh ^{-1}\left(e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^4}-\frac{b^3 \tanh ^{-1}\left(\sqrt{(c+d x)^2+1}\right)}{d e^4}",1,"-((b^2*(a + b*ArcSinh[c + d*x]))/(d*e^4*(c + d*x))) - (b*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^2)/(2*d*e^4*(c + d*x)^2) - (a + b*ArcSinh[c + d*x])^3/(3*d*e^4*(c + d*x)^3) + (b*(a + b*ArcSinh[c + d*x])^2*ArcTanh[E^ArcSinh[c + d*x]])/(d*e^4) - (b^3*ArcTanh[Sqrt[1 + (c + d*x)^2]])/(d*e^4) + (b^2*(a + b*ArcSinh[c + d*x])*PolyLog[2, -E^ArcSinh[c + d*x]])/(d*e^4) - (b^2*(a + b*ArcSinh[c + d*x])*PolyLog[2, E^ArcSinh[c + d*x]])/(d*e^4) - (b^3*PolyLog[3, -E^ArcSinh[c + d*x]])/(d*e^4) + (b^3*PolyLog[3, E^ArcSinh[c + d*x]])/(d*e^4)","A",16,12,23,0.5217,1,"{5865, 12, 5661, 5747, 5760, 4182, 2531, 2282, 6589, 266, 63, 207}"
146,0,0,0,0.1788169,"\int (c e+d e x)^m \left(a+b \sinh ^{-1}(c+d x)\right)^4 \, dx","Int[(c*e + d*e*x)^m*(a + b*ArcSinh[c + d*x])^4,x]","\int (c e+d e x)^m \left(a+b \sinh ^{-1}(c+d x)\right)^4 \, dx","\frac{(e (c+d x))^{m+1} \left(a+b \sinh ^{-1}(c+d x)\right)^4}{d e (m+1)}-\frac{4 b \text{Int}\left(\frac{(e (c+d x))^{m+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{\sqrt{(c+d x)^2+1}},x\right)}{e (m+1)}",0,"((e*(c + d*x))^(1 + m)*(a + b*ArcSinh[c + d*x])^4)/(d*e*(1 + m)) - (4*b*Defer[Subst][Defer[Int][((e*x)^(1 + m)*(a + b*ArcSinh[x])^3)/Sqrt[1 + x^2], x], x, c + d*x])/(d*e*(1 + m))","A",0,0,0,0,-1,"{}"
147,1,349,0,0.6725201,"\int (c e+d e x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^4 \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcSinh[c + d*x])^4,x]","-\frac{3 b^3 e^3 (c+d x)^3 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{32 d}+\frac{45 b^3 e^3 (c+d x) \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{64 d}+\frac{3 b^2 e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{16 d}-\frac{45 b^2 e^3 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{128 d}-\frac{9 b^2 e^3 (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{16 d}-\frac{b e^3 (c+d x)^3 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{4 d}+\frac{3 b e^3 (c+d x) \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{8 d}+\frac{e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^4}{4 d}-\frac{3 e^3 \left(a+b \sinh ^{-1}(c+d x)\right)^4}{32 d}+\frac{3 b^4 e^3 (c+d x)^4}{128 d}-\frac{45 b^4 e^3 (c+d x)^2}{128 d}","-\frac{3 b^3 e^3 (c+d x)^3 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{32 d}+\frac{45 b^3 e^3 (c+d x) \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{64 d}+\frac{3 b^2 e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{16 d}-\frac{45 b^2 e^3 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{128 d}-\frac{9 b^2 e^3 (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{16 d}-\frac{b e^3 (c+d x)^3 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{4 d}+\frac{3 b e^3 (c+d x) \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{8 d}+\frac{e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^4}{4 d}-\frac{3 e^3 \left(a+b \sinh ^{-1}(c+d x)\right)^4}{32 d}+\frac{3 b^4 e^3 (c+d x)^4}{128 d}-\frac{45 b^4 e^3 (c+d x)^2}{128 d}",1,"(-45*b^4*e^3*(c + d*x)^2)/(128*d) + (3*b^4*e^3*(c + d*x)^4)/(128*d) + (45*b^3*e^3*(c + d*x)*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/(64*d) - (3*b^3*e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/(32*d) - (45*b^2*e^3*(a + b*ArcSinh[c + d*x])^2)/(128*d) - (9*b^2*e^3*(c + d*x)^2*(a + b*ArcSinh[c + d*x])^2)/(16*d) + (3*b^2*e^3*(c + d*x)^4*(a + b*ArcSinh[c + d*x])^2)/(16*d) + (3*b*e^3*(c + d*x)*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^3)/(8*d) - (b*e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^3)/(4*d) - (3*e^3*(a + b*ArcSinh[c + d*x])^4)/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcSinh[c + d*x])^4)/(4*d)","A",16,6,23,0.2609,1,"{5865, 12, 5661, 5758, 5675, 30}"
148,1,281,0,0.4849523,"\int (c e+d e x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^4 \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcSinh[c + d*x])^4,x]","\frac{160 b^3 e^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{27 d}-\frac{8 b^3 e^2 (c+d x)^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{27 d}+\frac{4 b^2 e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{9 d}-\frac{8 b^2 e^2 (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{3 d}+\frac{8 b e^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{9 d}-\frac{4 b e^2 (c+d x)^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{9 d}+\frac{e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^4}{3 d}+\frac{8 b^4 e^2 (c+d x)^3}{81 d}-\frac{160}{27} b^4 e^2 x","\frac{160 b^3 e^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{27 d}-\frac{8 b^3 e^2 (c+d x)^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{27 d}+\frac{4 b^2 e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{9 d}-\frac{8 b^2 e^2 (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{3 d}+\frac{8 b e^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{9 d}-\frac{4 b e^2 (c+d x)^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{9 d}+\frac{e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^4}{3 d}+\frac{8 b^4 e^2 (c+d x)^3}{81 d}-\frac{160}{27} b^4 e^2 x",1,"(-160*b^4*e^2*x)/27 + (8*b^4*e^2*(c + d*x)^3)/(81*d) + (160*b^3*e^2*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/(27*d) - (8*b^3*e^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/(27*d) - (8*b^2*e^2*(c + d*x)*(a + b*ArcSinh[c + d*x])^2)/(3*d) + (4*b^2*e^2*(c + d*x)^3*(a + b*ArcSinh[c + d*x])^2)/(9*d) + (8*b*e^2*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^3)/(9*d) - (4*b*e^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^3)/(9*d) + (e^2*(c + d*x)^3*(a + b*ArcSinh[c + d*x])^4)/(3*d)","A",13,8,23,0.3478,1,"{5865, 12, 5661, 5758, 5717, 5653, 8, 30}"
149,1,195,0,0.3208592,"\int (c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^4 \, dx","Int[(c*e + d*e*x)*(a + b*ArcSinh[c + d*x])^4,x]","-\frac{3 b^3 e (c+d x) \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{2 d}+\frac{3 b^2 e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{2 d}+\frac{3 b^2 e \left(a+b \sinh ^{-1}(c+d x)\right)^2}{4 d}-\frac{b e (c+d x) \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d}+\frac{e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^4}{2 d}+\frac{e \left(a+b \sinh ^{-1}(c+d x)\right)^4}{4 d}+\frac{3 b^4 e (c+d x)^2}{4 d}","-\frac{3 b^3 e (c+d x) \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{2 d}+\frac{3 b^2 e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{2 d}+\frac{3 b^2 e \left(a+b \sinh ^{-1}(c+d x)\right)^2}{4 d}-\frac{b e (c+d x) \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d}+\frac{e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^4}{2 d}+\frac{e \left(a+b \sinh ^{-1}(c+d x)\right)^4}{4 d}+\frac{3 b^4 e (c+d x)^2}{4 d}",1,"(3*b^4*e*(c + d*x)^2)/(4*d) - (3*b^3*e*(c + d*x)*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/(2*d) + (3*b^2*e*(a + b*ArcSinh[c + d*x])^2)/(4*d) + (3*b^2*e*(c + d*x)^2*(a + b*ArcSinh[c + d*x])^2)/(2*d) - (b*e*(c + d*x)*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^3)/d + (e*(a + b*ArcSinh[c + d*x])^4)/(4*d) + (e*(c + d*x)^2*(a + b*ArcSinh[c + d*x])^4)/(2*d)","A",9,6,21,0.2857,1,"{5865, 12, 5661, 5758, 5675, 30}"
150,1,115,0,0.1597422,"\int \left(a+b \sinh ^{-1}(c+d x)\right)^4 \, dx","Int[(a + b*ArcSinh[c + d*x])^4,x]","-\frac{24 b^3 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{d}+\frac{12 b^2 (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d}-\frac{4 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d}+\frac{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^4}{d}+24 b^4 x","-\frac{24 b^3 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)}{d}+\frac{12 b^2 (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d}-\frac{4 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d}+\frac{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^4}{d}+24 b^4 x",1,"24*b^4*x - (24*b^3*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x]))/d + (12*b^2*(c + d*x)*(a + b*ArcSinh[c + d*x])^2)/d - (4*b*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^3)/d + ((c + d*x)*(a + b*ArcSinh[c + d*x])^4)/d","A",6,4,12,0.3333,1,"{5863, 5653, 5717, 8}"
151,1,186,0,0.2585787,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{c e+d e x} \, dx","Int[(a + b*ArcSinh[c + d*x])^4/(c*e + d*e*x),x]","-\frac{3 b^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e}+\frac{3 b^3 \text{PolyLog}\left(4,e^{2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e}+\frac{2 b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d e}-\frac{3 b^4 \text{PolyLog}\left(5,e^{2 \sinh ^{-1}(c+d x)}\right)}{2 d e}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^5}{5 b d e}+\frac{\log \left(1-e^{2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^4}{d e}","-\frac{3 b^2 \text{PolyLog}\left(3,e^{-2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e}-\frac{3 b^3 \text{PolyLog}\left(4,e^{-2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e}-\frac{2 b \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d e}-\frac{3 b^4 \text{PolyLog}\left(5,e^{-2 \sinh ^{-1}(c+d x)}\right)}{2 d e}+\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^5}{5 b d e}+\frac{\log \left(1-e^{-2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^4}{d e}",1,"-(a + b*ArcSinh[c + d*x])^5/(5*b*d*e) + ((a + b*ArcSinh[c + d*x])^4*Log[1 - E^(2*ArcSinh[c + d*x])])/(d*e) + (2*b*(a + b*ArcSinh[c + d*x])^3*PolyLog[2, E^(2*ArcSinh[c + d*x])])/(d*e) - (3*b^2*(a + b*ArcSinh[c + d*x])^2*PolyLog[3, E^(2*ArcSinh[c + d*x])])/(d*e) + (3*b^3*(a + b*ArcSinh[c + d*x])*PolyLog[4, E^(2*ArcSinh[c + d*x])])/(d*e) - (3*b^4*PolyLog[5, E^(2*ArcSinh[c + d*x])])/(2*d*e)","A",10,9,23,0.3913,0,"{5865, 12, 5659, 3716, 2190, 2531, 6609, 2282, 6589}"
152,1,234,0,0.3171625,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{(c e+d e x)^2} \, dx","Int[(a + b*ArcSinh[c + d*x])^4/(c*e + d*e*x)^2,x]","\frac{24 b^3 \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^2}-\frac{24 b^3 \text{PolyLog}\left(3,e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^2}-\frac{12 b^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^2}+\frac{12 b^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^2}-\frac{24 b^4 \text{PolyLog}\left(4,-e^{\sinh ^{-1}(c+d x)}\right)}{d e^2}+\frac{24 b^4 \text{PolyLog}\left(4,e^{\sinh ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{d e^2 (c+d x)}-\frac{8 b \tanh ^{-1}\left(e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d e^2}","\frac{24 b^3 \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^2}-\frac{24 b^3 \text{PolyLog}\left(3,e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^2}-\frac{12 b^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^2}+\frac{12 b^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^2}-\frac{24 b^4 \text{PolyLog}\left(4,-e^{\sinh ^{-1}(c+d x)}\right)}{d e^2}+\frac{24 b^4 \text{PolyLog}\left(4,e^{\sinh ^{-1}(c+d x)}\right)}{d e^2}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{d e^2 (c+d x)}-\frac{8 b \tanh ^{-1}\left(e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d e^2}",1,"-((a + b*ArcSinh[c + d*x])^4/(d*e^2*(c + d*x))) - (8*b*(a + b*ArcSinh[c + d*x])^3*ArcTanh[E^ArcSinh[c + d*x]])/(d*e^2) - (12*b^2*(a + b*ArcSinh[c + d*x])^2*PolyLog[2, -E^ArcSinh[c + d*x]])/(d*e^2) + (12*b^2*(a + b*ArcSinh[c + d*x])^2*PolyLog[2, E^ArcSinh[c + d*x]])/(d*e^2) + (24*b^3*(a + b*ArcSinh[c + d*x])*PolyLog[3, -E^ArcSinh[c + d*x]])/(d*e^2) - (24*b^3*(a + b*ArcSinh[c + d*x])*PolyLog[3, E^ArcSinh[c + d*x]])/(d*e^2) - (24*b^4*PolyLog[4, -E^ArcSinh[c + d*x]])/(d*e^2) + (24*b^4*PolyLog[4, E^ArcSinh[c + d*x]])/(d*e^2)","A",13,9,23,0.3913,1,"{5865, 12, 5661, 5760, 4182, 2531, 6609, 2282, 6589}"
153,1,186,0,0.3280898,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{(c e+d e x)^3} \, dx","Int[(a + b*ArcSinh[c + d*x])^4/(c*e + d*e*x)^3,x]","\frac{6 b^3 \text{PolyLog}\left(2,e^{2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^3}-\frac{3 b^4 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}(c+d x)}\right)}{d e^3}+\frac{6 b^2 \log \left(1-e^{2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^3}-\frac{2 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d e^3 (c+d x)}-\frac{2 b \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d e^3}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{2 d e^3 (c+d x)^2}","-\frac{6 b^3 \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^3}-\frac{3 b^4 \text{PolyLog}\left(3,e^{-2 \sinh ^{-1}(c+d x)}\right)}{d e^3}+\frac{6 b^2 \log \left(1-e^{-2 \sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^3}-\frac{2 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d e^3 (c+d x)}+\frac{2 b \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d e^3}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{2 d e^3 (c+d x)^2}",1,"(-2*b*(a + b*ArcSinh[c + d*x])^3)/(d*e^3) - (2*b*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^3)/(d*e^3*(c + d*x)) - (a + b*ArcSinh[c + d*x])^4/(2*d*e^3*(c + d*x)^2) + (6*b^2*(a + b*ArcSinh[c + d*x])^2*Log[1 - E^(2*ArcSinh[c + d*x])])/(d*e^3) + (6*b^3*(a + b*ArcSinh[c + d*x])*PolyLog[2, E^(2*ArcSinh[c + d*x])])/(d*e^3) - (3*b^4*PolyLog[3, E^(2*ArcSinh[c + d*x])])/(d*e^3)","A",10,10,23,0.4348,0,"{5865, 12, 5661, 5723, 5659, 3716, 2190, 2531, 2282, 6589}"
154,1,385,0,0.5648923,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{(c e+d e x)^4} \, dx","Int[(a + b*ArcSinh[c + d*x])^4/(c*e + d*e*x)^4,x]","-\frac{4 b^3 \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^4}+\frac{4 b^3 \text{PolyLog}\left(3,e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^4}+\frac{2 b^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^4}-\frac{2 b^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^4}-\frac{4 b^4 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c+d x)}\right)}{d e^4}+\frac{4 b^4 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c+d x)}\right)}{d e^4}+\frac{4 b^4 \text{PolyLog}\left(4,-e^{\sinh ^{-1}(c+d x)}\right)}{d e^4}-\frac{4 b^4 \text{PolyLog}\left(4,e^{\sinh ^{-1}(c+d x)}\right)}{d e^4}-\frac{2 b^2 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^4 (c+d x)}-\frac{8 b^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^4}-\frac{2 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{3 d e^4 (c+d x)^3}+\frac{4 b \tanh ^{-1}\left(e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^3}{3 d e^4}","-\frac{4 b^3 \text{PolyLog}\left(3,-e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^4}+\frac{4 b^3 \text{PolyLog}\left(3,e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^4}+\frac{2 b^2 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^4}-\frac{2 b^2 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^4}-\frac{4 b^4 \text{PolyLog}\left(2,-e^{\sinh ^{-1}(c+d x)}\right)}{d e^4}+\frac{4 b^4 \text{PolyLog}\left(2,e^{\sinh ^{-1}(c+d x)}\right)}{d e^4}+\frac{4 b^4 \text{PolyLog}\left(4,-e^{\sinh ^{-1}(c+d x)}\right)}{d e^4}-\frac{4 b^4 \text{PolyLog}\left(4,e^{\sinh ^{-1}(c+d x)}\right)}{d e^4}-\frac{2 b^2 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e^4 (c+d x)}-\frac{8 b^3 \tanh ^{-1}\left(e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^4}-\frac{2 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{3 d e^4 (c+d x)^3}+\frac{4 b \tanh ^{-1}\left(e^{\sinh ^{-1}(c+d x)}\right) \left(a+b \sinh ^{-1}(c+d x)\right)^3}{3 d e^4}",1,"(-2*b^2*(a + b*ArcSinh[c + d*x])^2)/(d*e^4*(c + d*x)) - (2*b*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^3)/(3*d*e^4*(c + d*x)^2) - (a + b*ArcSinh[c + d*x])^4/(3*d*e^4*(c + d*x)^3) - (8*b^3*(a + b*ArcSinh[c + d*x])*ArcTanh[E^ArcSinh[c + d*x]])/(d*e^4) + (4*b*(a + b*ArcSinh[c + d*x])^3*ArcTanh[E^ArcSinh[c + d*x]])/(3*d*e^4) - (4*b^4*PolyLog[2, -E^ArcSinh[c + d*x]])/(d*e^4) + (2*b^2*(a + b*ArcSinh[c + d*x])^2*PolyLog[2, -E^ArcSinh[c + d*x]])/(d*e^4) + (4*b^4*PolyLog[2, E^ArcSinh[c + d*x]])/(d*e^4) - (2*b^2*(a + b*ArcSinh[c + d*x])^2*PolyLog[2, E^ArcSinh[c + d*x]])/(d*e^4) - (4*b^3*(a + b*ArcSinh[c + d*x])*PolyLog[3, -E^ArcSinh[c + d*x]])/(d*e^4) + (4*b^3*(a + b*ArcSinh[c + d*x])*PolyLog[3, E^ArcSinh[c + d*x]])/(d*e^4) + (4*b^4*PolyLog[4, -E^ArcSinh[c + d*x]])/(d*e^4) - (4*b^4*PolyLog[4, E^ArcSinh[c + d*x]])/(d*e^4)","A",21,12,23,0.5217,1,"{5865, 12, 5661, 5747, 5760, 4182, 2531, 6609, 2282, 6589, 2279, 2391}"
155,0,0,0,0.0603417,"\int \frac{(c e+d e x)^m}{a+b \sinh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^m/(a + b*ArcSinh[c + d*x]),x]","\int \frac{(c e+d e x)^m}{a+b \sinh ^{-1}(c+d x)} \, dx","\text{Int}\left(\frac{(e (c+d x))^m}{a+b \sinh ^{-1}(c+d x)},x\right)",0,"Defer[Subst][Defer[Int][(e*x)^m/(a + b*ArcSinh[x]), x], x, c + d*x]/d","A",0,0,0,0,-1,"{}"
156,1,209,0,0.4688928,"\int \frac{(c e+d e x)^4}{a+b \sinh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcSinh[c + d*x]),x]","\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{8 b d}-\frac{3 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c+d x)\right)}{16 b d}+\frac{e^4 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c+d x)\right)}{16 b d}-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{8 b d}+\frac{3 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c+d x)\right)}{16 b d}-\frac{e^4 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c+d x)\right)}{16 b d}","\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{8 b d}-\frac{3 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{16 b d}+\frac{e^4 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{16 b d}-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{8 b d}+\frac{3 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{16 b d}-\frac{e^4 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{16 b d}",1,"(e^4*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c + d*x]])/(8*b*d) - (3*e^4*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c + d*x]])/(16*b*d) + (e^4*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcSinh[c + d*x]])/(16*b*d) - (e^4*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c + d*x]])/(8*b*d) + (3*e^4*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c + d*x]])/(16*b*d) - (e^4*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c + d*x]])/(16*b*d)","A",14,7,23,0.3043,1,"{5865, 12, 5669, 5448, 3303, 3298, 3301}"
157,1,145,0,0.3402674,"\int \frac{(c e+d e x)^3}{a+b \sinh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcSinh[c + d*x]),x]","\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c+d x)\right)}{4 b d}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c+d x)\right)}{8 b d}-\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c+d x)\right)}{4 b d}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c+d x)\right)}{8 b d}","\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{4 b d}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{8 b d}-\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{4 b d}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{8 b d}",1,"(e^3*CoshIntegral[(2*a)/b + 2*ArcSinh[c + d*x]]*Sinh[(2*a)/b])/(4*b*d) - (e^3*CoshIntegral[(4*a)/b + 4*ArcSinh[c + d*x]]*Sinh[(4*a)/b])/(8*b*d) - (e^3*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c + d*x]])/(4*b*d) + (e^3*Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c + d*x]])/(8*b*d)","A",11,7,23,0.3043,1,"{5865, 12, 5669, 5448, 3303, 3298, 3301}"
158,1,137,0,0.292862,"\int \frac{(c e+d e x)^2}{a+b \sinh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcSinh[c + d*x]),x]","-\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{4 b d}+\frac{e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c+d x)\right)}{4 b d}+\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{4 b d}-\frac{e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c+d x)\right)}{4 b d}","-\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{4 b d}+\frac{e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{4 b d}+\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{4 b d}-\frac{e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{4 b d}",1,"-(e^2*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c + d*x]])/(4*b*d) + (e^2*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c + d*x]])/(4*b*d) + (e^2*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c + d*x]])/(4*b*d) - (e^2*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c + d*x]])/(4*b*d)","A",11,7,23,0.3043,1,"{5865, 12, 5669, 5448, 3303, 3298, 3301}"
159,1,69,0,0.1613347,"\int \frac{c e+d e x}{a+b \sinh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)/(a + b*ArcSinh[c + d*x]),x]","\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c+d x)\right)}{2 b d}-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c+d x)\right)}{2 b d}","\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{2 b d}-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{2 b d}",1,"-(e*CoshIntegral[(2*a)/b + 2*ArcSinh[c + d*x]]*Sinh[(2*a)/b])/(2*b*d) + (e*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c + d*x]])/(2*b*d)","A",8,7,21,0.3333,1,"{5865, 12, 5669, 5448, 3303, 3298, 3301}"
160,1,58,0,0.0889073,"\int \frac{1}{a+b \sinh ^{-1}(c+d x)} \, dx","Int[(a + b*ArcSinh[c + d*x])^(-1),x]","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{b d}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{b d}","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{b d}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{b d}",1,"(Cosh[a/b]*CoshIntegral[(a + b*ArcSinh[c + d*x])/b])/(b*d) - (Sinh[a/b]*SinhIntegral[(a + b*ArcSinh[c + d*x])/b])/(b*d)","A",5,5,12,0.4167,1,"{5863, 5657, 3303, 3298, 3301}"
161,0,0,0,0.066273,"\int \frac{1}{(c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcSinh[c + d*x])),x]","\int \frac{1}{(c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcSinh[x])), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
162,1,252,0,0.4090478,"\int \frac{(c e+d e x)^4}{\left(a+b \sinh ^{-1}(c+d x)\right)^2} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcSinh[c + d*x])^2,x]","-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{8 b^2 d}+\frac{9 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c+d x)\right)}{16 b^2 d}-\frac{5 e^4 \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c+d x)\right)}{16 b^2 d}+\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{8 b^2 d}-\frac{9 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c+d x)\right)}{16 b^2 d}+\frac{5 e^4 \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c+d x)\right)}{16 b^2 d}-\frac{e^4 (c+d x)^4 \sqrt{(c+d x)^2+1}}{b d \left(a+b \sinh ^{-1}(c+d x)\right)}","-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{8 b^2 d}+\frac{9 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{16 b^2 d}-\frac{5 e^4 \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{16 b^2 d}+\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{8 b^2 d}-\frac{9 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{16 b^2 d}+\frac{5 e^4 \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{16 b^2 d}-\frac{e^4 (c+d x)^4 \sqrt{(c+d x)^2+1}}{b d \left(a+b \sinh ^{-1}(c+d x)\right)}",1,"-((e^4*(c + d*x)^4*Sqrt[1 + (c + d*x)^2])/(b*d*(a + b*ArcSinh[c + d*x]))) - (e^4*CoshIntegral[a/b + ArcSinh[c + d*x]]*Sinh[a/b])/(8*b^2*d) + (9*e^4*CoshIntegral[(3*a)/b + 3*ArcSinh[c + d*x]]*Sinh[(3*a)/b])/(16*b^2*d) - (5*e^4*CoshIntegral[(5*a)/b + 5*ArcSinh[c + d*x]]*Sinh[(5*a)/b])/(16*b^2*d) + (e^4*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c + d*x]])/(8*b^2*d) - (9*e^4*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c + d*x]])/(16*b^2*d) + (5*e^4*Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c + d*x]])/(16*b^2*d)","A",13,6,23,0.2609,1,"{5865, 12, 5665, 3303, 3298, 3301}"
163,1,188,0,0.3107063,"\int \frac{(c e+d e x)^3}{\left(a+b \sinh ^{-1}(c+d x)\right)^2} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcSinh[c + d*x])^2,x]","-\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c+d x)\right)}{2 b^2 d}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c+d x)\right)}{2 b^2 d}+\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c+d x)\right)}{2 b^2 d}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c+d x)\right)}{2 b^2 d}-\frac{e^3 (c+d x)^3 \sqrt{(c+d x)^2+1}}{b d \left(a+b \sinh ^{-1}(c+d x)\right)}","-\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{2 b^2 d}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{2 b^2 d}+\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{2 b^2 d}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{2 b^2 d}-\frac{e^3 (c+d x)^3 \sqrt{(c+d x)^2+1}}{b d \left(a+b \sinh ^{-1}(c+d x)\right)}",1,"-((e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2])/(b*d*(a + b*ArcSinh[c + d*x]))) - (e^3*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSinh[c + d*x]])/(2*b^2*d) + (e^3*Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcSinh[c + d*x]])/(2*b^2*d) + (e^3*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c + d*x]])/(2*b^2*d) - (e^3*Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c + d*x]])/(2*b^2*d)","A",10,6,23,0.2609,1,"{5865, 12, 5665, 3303, 3298, 3301}"
164,1,180,0,0.2850502,"\int \frac{(c e+d e x)^2}{\left(a+b \sinh ^{-1}(c+d x)\right)^2} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcSinh[c + d*x])^2,x]","\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{4 b^2 d}-\frac{3 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c+d x)\right)}{4 b^2 d}-\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{4 b^2 d}+\frac{3 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c+d x)\right)}{4 b^2 d}-\frac{e^2 (c+d x)^2 \sqrt{(c+d x)^2+1}}{b d \left(a+b \sinh ^{-1}(c+d x)\right)}","\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{4 b^2 d}-\frac{3 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{4 b^2 d}-\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{4 b^2 d}+\frac{3 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{4 b^2 d}-\frac{e^2 (c+d x)^2 \sqrt{(c+d x)^2+1}}{b d \left(a+b \sinh ^{-1}(c+d x)\right)}",1,"-((e^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^2])/(b*d*(a + b*ArcSinh[c + d*x]))) + (e^2*CoshIntegral[a/b + ArcSinh[c + d*x]]*Sinh[a/b])/(4*b^2*d) - (3*e^2*CoshIntegral[(3*a)/b + 3*ArcSinh[c + d*x]]*Sinh[(3*a)/b])/(4*b^2*d) - (e^2*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c + d*x]])/(4*b^2*d) + (3*e^2*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c + d*x]])/(4*b^2*d)","A",10,6,23,0.2609,1,"{5865, 12, 5665, 3303, 3298, 3301}"
165,1,103,0,0.147562,"\int \frac{c e+d e x}{\left(a+b \sinh ^{-1}(c+d x)\right)^2} \, dx","Int[(c*e + d*e*x)/(a + b*ArcSinh[c + d*x])^2,x]","\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c+d x)\right)}{b^2 d}-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c+d x)\right)}{b^2 d}-\frac{e \sqrt{(c+d x)^2+1} (c+d x)}{b d \left(a+b \sinh ^{-1}(c+d x)\right)}","\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{b^2 d}-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{b^2 d}-\frac{e \sqrt{(c+d x)^2+1} (c+d x)}{b d \left(a+b \sinh ^{-1}(c+d x)\right)}",1,"-((e*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(b*d*(a + b*ArcSinh[c + d*x]))) + (e*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSinh[c + d*x]])/(b^2*d) - (e*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c + d*x]])/(b^2*d)","A",6,6,21,0.2857,1,"{5865, 12, 5665, 3303, 3298, 3301}"
166,1,87,0,0.1743561,"\int \frac{1}{\left(a+b \sinh ^{-1}(c+d x)\right)^2} \, dx","Int[(a + b*ArcSinh[c + d*x])^(-2),x]","-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{b^2 d}+\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{b^2 d}-\frac{\sqrt{(c+d x)^2+1}}{b d \left(a+b \sinh ^{-1}(c+d x)\right)}","-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{b^2 d}+\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{b^2 d}-\frac{\sqrt{(c+d x)^2+1}}{b d \left(a+b \sinh ^{-1}(c+d x)\right)}",1,"-(Sqrt[1 + (c + d*x)^2]/(b*d*(a + b*ArcSinh[c + d*x]))) - (CoshIntegral[a/b + ArcSinh[c + d*x]]*Sinh[a/b])/(b^2*d) + (Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c + d*x]])/(b^2*d)","A",6,6,12,0.5000,1,"{5863, 5655, 5779, 3303, 3298, 3301}"
167,0,0,0,0.0636682,"\int \frac{1}{(c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^2} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcSinh[c + d*x])^2),x]","\int \frac{1}{(c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^2} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^2},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcSinh[x])^2), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
168,1,316,0,0.8916973,"\int \frac{(c e+d e x)^4}{\left(a+b \sinh ^{-1}(c+d x)\right)^3} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcSinh[c + d*x])^3,x]","\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{16 b^3 d}-\frac{27 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c+d x)\right)}{32 b^3 d}+\frac{25 e^4 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c+d x)\right)}{32 b^3 d}-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{16 b^3 d}+\frac{27 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c+d x)\right)}{32 b^3 d}-\frac{25 e^4 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c+d x)\right)}{32 b^3 d}-\frac{5 e^4 (c+d x)^5}{2 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{2 e^4 (c+d x)^3}{b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^4 \sqrt{(c+d x)^2+1} (c+d x)^4}{2 b d \left(a+b \sinh ^{-1}(c+d x)\right)^2}","\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{16 b^3 d}-\frac{27 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{32 b^3 d}+\frac{25 e^4 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{32 b^3 d}-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{16 b^3 d}+\frac{27 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{32 b^3 d}-\frac{25 e^4 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{32 b^3 d}-\frac{5 e^4 (c+d x)^5}{2 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{2 e^4 (c+d x)^3}{b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^4 \sqrt{(c+d x)^2+1} (c+d x)^4}{2 b d \left(a+b \sinh ^{-1}(c+d x)\right)^2}",1,"-(e^4*(c + d*x)^4*Sqrt[1 + (c + d*x)^2])/(2*b*d*(a + b*ArcSinh[c + d*x])^2) - (2*e^4*(c + d*x)^3)/(b^2*d*(a + b*ArcSinh[c + d*x])) - (5*e^4*(c + d*x)^5)/(2*b^2*d*(a + b*ArcSinh[c + d*x])) + (e^4*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c + d*x]])/(16*b^3*d) - (27*e^4*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c + d*x]])/(32*b^3*d) + (25*e^4*Cosh[(5*a)/b]*CoshIntegral[(5*a)/b + 5*ArcSinh[c + d*x]])/(32*b^3*d) - (e^4*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c + d*x]])/(16*b^3*d) + (27*e^4*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c + d*x]])/(32*b^3*d) - (25*e^4*Sinh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c + d*x]])/(32*b^3*d)","A",26,9,23,0.3913,1,"{5865, 12, 5667, 5774, 5669, 5448, 3303, 3298, 3301}"
169,1,247,0,0.6819124,"\int \frac{(c e+d e x)^3}{\left(a+b \sinh ^{-1}(c+d x)\right)^3} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcSinh[c + d*x])^3,x]","\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c+d x)\right)}{2 b^3 d}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c+d x)\right)}{b^3 d}-\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c+d x)\right)}{2 b^3 d}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c+d x)\right)}{b^3 d}-\frac{2 e^3 (c+d x)^4}{b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{3 e^3 (c+d x)^2}{2 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^3 \sqrt{(c+d x)^2+1} (c+d x)^3}{2 b d \left(a+b \sinh ^{-1}(c+d x)\right)^2}","\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{2 b^3 d}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{b^3 d}-\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{2 b^3 d}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{b^3 d}-\frac{2 e^3 (c+d x)^4}{b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{3 e^3 (c+d x)^2}{2 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^3 \sqrt{(c+d x)^2+1} (c+d x)^3}{2 b d \left(a+b \sinh ^{-1}(c+d x)\right)^2}",1,"-(e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2])/(2*b*d*(a + b*ArcSinh[c + d*x])^2) - (3*e^3*(c + d*x)^2)/(2*b^2*d*(a + b*ArcSinh[c + d*x])) - (2*e^3*(c + d*x)^4)/(b^2*d*(a + b*ArcSinh[c + d*x])) + (e^3*CoshIntegral[(2*a)/b + 2*ArcSinh[c + d*x]]*Sinh[(2*a)/b])/(2*b^3*d) - (e^3*CoshIntegral[(4*a)/b + 4*ArcSinh[c + d*x]]*Sinh[(4*a)/b])/(b^3*d) - (e^3*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c + d*x]])/(2*b^3*d) + (e^3*Cosh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c + d*x]])/(b^3*d)","A",20,9,23,0.3913,1,"{5865, 12, 5667, 5774, 5669, 5448, 3303, 3298, 3301}"
170,1,305,0,0.6118276,"\int \frac{(c e+d e x)^2}{\left(a+b \sinh ^{-1}(c+d x)\right)^3} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcSinh[c + d*x])^3,x]","-\frac{9 e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{8 b^3 d}+\frac{9 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c+d x)\right)}{8 b^3 d}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{b^3 d}+\frac{9 e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{8 b^3 d}-\frac{9 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c+d x)\right)}{8 b^3 d}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{b^3 d}-\frac{3 e^2 (c+d x)^3}{2 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^2 (c+d x)}{b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^2 \sqrt{(c+d x)^2+1} (c+d x)^2}{2 b d \left(a+b \sinh ^{-1}(c+d x)\right)^2}","-\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{8 b^3 d}+\frac{9 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{8 b^3 d}+\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{8 b^3 d}-\frac{9 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{8 b^3 d}-\frac{3 e^2 (c+d x)^3}{2 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^2 (c+d x)}{b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^2 \sqrt{(c+d x)^2+1} (c+d x)^2}{2 b d \left(a+b \sinh ^{-1}(c+d x)\right)^2}",1,"-(e^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^2])/(2*b*d*(a + b*ArcSinh[c + d*x])^2) - (e^2*(c + d*x))/(b^2*d*(a + b*ArcSinh[c + d*x])) - (3*e^2*(c + d*x)^3)/(2*b^2*d*(a + b*ArcSinh[c + d*x])) - (9*e^2*Cosh[a/b]*CoshIntegral[a/b + ArcSinh[c + d*x]])/(8*b^3*d) + (9*e^2*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcSinh[c + d*x]])/(8*b^3*d) + (e^2*Cosh[a/b]*CoshIntegral[(a + b*ArcSinh[c + d*x])/b])/(b^3*d) + (9*e^2*Sinh[a/b]*SinhIntegral[a/b + ArcSinh[c + d*x]])/(8*b^3*d) - (9*e^2*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c + d*x]])/(8*b^3*d) - (e^2*Sinh[a/b]*SinhIntegral[(a + b*ArcSinh[c + d*x])/b])/(b^3*d)","A",18,10,23,0.4348,1,"{5865, 12, 5667, 5774, 5669, 5448, 3303, 3298, 3301, 5657}"
171,1,156,0,0.3312816,"\int \frac{c e+d e x}{\left(a+b \sinh ^{-1}(c+d x)\right)^3} \, dx","Int[(c*e + d*e*x)/(a + b*ArcSinh[c + d*x])^3,x]","-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c+d x)\right)}{b^3 d}+\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c+d x)\right)}{b^3 d}-\frac{e (c+d x)^2}{b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e}{2 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e \sqrt{(c+d x)^2+1} (c+d x)}{2 b d \left(a+b \sinh ^{-1}(c+d x)\right)^2}","-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{b^3 d}+\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{b^3 d}-\frac{e (c+d x)^2}{b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e}{2 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e \sqrt{(c+d x)^2+1} (c+d x)}{2 b d \left(a+b \sinh ^{-1}(c+d x)\right)^2}",1,"-(e*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(2*b*d*(a + b*ArcSinh[c + d*x])^2) - e/(2*b^2*d*(a + b*ArcSinh[c + d*x])) - (e*(c + d*x)^2)/(b^2*d*(a + b*ArcSinh[c + d*x])) - (e*CoshIntegral[(2*a)/b + 2*ArcSinh[c + d*x]]*Sinh[(2*a)/b])/(b^3*d) + (e*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c + d*x]])/(b^3*d)","A",11,10,21,0.4762,1,"{5865, 12, 5667, 5774, 5669, 5448, 3303, 3298, 3301, 5675}"
172,1,125,0,0.177495,"\int \frac{1}{\left(a+b \sinh ^{-1}(c+d x)\right)^3} \, dx","Int[(a + b*ArcSinh[c + d*x])^(-3),x]","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{2 b^3 d}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{2 b^3 d}-\frac{c+d x}{2 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{\sqrt{(c+d x)^2+1}}{2 b d \left(a+b \sinh ^{-1}(c+d x)\right)^2}","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{2 b^3 d}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{2 b^3 d}-\frac{c+d x}{2 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{\sqrt{(c+d x)^2+1}}{2 b d \left(a+b \sinh ^{-1}(c+d x)\right)^2}",1,"-Sqrt[1 + (c + d*x)^2]/(2*b*d*(a + b*ArcSinh[c + d*x])^2) - (c + d*x)/(2*b^2*d*(a + b*ArcSinh[c + d*x])) + (Cosh[a/b]*CoshIntegral[(a + b*ArcSinh[c + d*x])/b])/(2*b^3*d) - (Sinh[a/b]*SinhIntegral[(a + b*ArcSinh[c + d*x])/b])/(2*b^3*d)","A",7,7,12,0.5833,1,"{5863, 5655, 5774, 5657, 3303, 3298, 3301}"
173,0,0,0,0.0619979,"\int \frac{1}{(c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^3} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcSinh[c + d*x])^3),x]","\int \frac{1}{(c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^3} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^3},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcSinh[x])^3), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
174,1,406,0,0.8778484,"\int \frac{(c e+d e x)^4}{\left(a+b \sinh ^{-1}(c+d x)\right)^4} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcSinh[c + d*x])^4,x]","-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{48 b^4 d}+\frac{27 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c+d x)\right)}{32 b^4 d}-\frac{125 e^4 \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c+d x)\right)}{96 b^4 d}+\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{48 b^4 d}-\frac{27 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c+d x)\right)}{32 b^4 d}+\frac{125 e^4 \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 a}{b}+5 \sinh ^{-1}(c+d x)\right)}{96 b^4 d}-\frac{5 e^4 (c+d x)^5}{6 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{25 e^4 \sqrt{(c+d x)^2+1} (c+d x)^4}{6 b^3 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{2 e^4 (c+d x)^3}{3 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{2 e^4 \sqrt{(c+d x)^2+1} (c+d x)^2}{b^3 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^4 \sqrt{(c+d x)^2+1} (c+d x)^4}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^3}","-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{48 b^4 d}+\frac{27 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{32 b^4 d}-\frac{125 e^4 \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{96 b^4 d}+\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{48 b^4 d}-\frac{27 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{32 b^4 d}+\frac{125 e^4 \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{96 b^4 d}-\frac{5 e^4 (c+d x)^5}{6 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{25 e^4 \sqrt{(c+d x)^2+1} (c+d x)^4}{6 b^3 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{2 e^4 (c+d x)^3}{3 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{2 e^4 \sqrt{(c+d x)^2+1} (c+d x)^2}{b^3 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^4 \sqrt{(c+d x)^2+1} (c+d x)^4}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^3}",1,"-(e^4*(c + d*x)^4*Sqrt[1 + (c + d*x)^2])/(3*b*d*(a + b*ArcSinh[c + d*x])^3) - (2*e^4*(c + d*x)^3)/(3*b^2*d*(a + b*ArcSinh[c + d*x])^2) - (5*e^4*(c + d*x)^5)/(6*b^2*d*(a + b*ArcSinh[c + d*x])^2) - (2*e^4*(c + d*x)^2*Sqrt[1 + (c + d*x)^2])/(b^3*d*(a + b*ArcSinh[c + d*x])) - (25*e^4*(c + d*x)^4*Sqrt[1 + (c + d*x)^2])/(6*b^3*d*(a + b*ArcSinh[c + d*x])) - (e^4*CoshIntegral[a/b + ArcSinh[c + d*x]]*Sinh[a/b])/(48*b^4*d) + (27*e^4*CoshIntegral[(3*a)/b + 3*ArcSinh[c + d*x]]*Sinh[(3*a)/b])/(32*b^4*d) - (125*e^4*CoshIntegral[(5*a)/b + 5*ArcSinh[c + d*x]]*Sinh[(5*a)/b])/(96*b^4*d) + (e^4*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c + d*x]])/(48*b^4*d) - (27*e^4*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c + d*x]])/(32*b^4*d) + (125*e^4*Cosh[(5*a)/b]*SinhIntegral[(5*a)/b + 5*ArcSinh[c + d*x]])/(96*b^4*d)","A",24,8,23,0.3478,1,"{5865, 12, 5667, 5774, 5665, 3303, 3298, 3301}"
175,1,340,0,0.6959042,"\int \frac{(c e+d e x)^3}{\left(a+b \sinh ^{-1}(c+d x)\right)^4} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcSinh[c + d*x])^4,x]","-\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c+d x)\right)}{3 b^4 d}+\frac{4 e^3 \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c+d x)\right)}{3 b^4 d}+\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c+d x)\right)}{3 b^4 d}-\frac{4 e^3 \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \sinh ^{-1}(c+d x)\right)}{3 b^4 d}-\frac{2 e^3 (c+d x)^4}{3 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{8 e^3 \sqrt{(c+d x)^2+1} (c+d x)^3}{3 b^3 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^3 (c+d x)^2}{2 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{e^3 \sqrt{(c+d x)^2+1} (c+d x)}{b^3 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^3 \sqrt{(c+d x)^2+1} (c+d x)^3}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^3}","-\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}+\frac{4 e^3 \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}+\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}-\frac{4 e^3 \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}-\frac{2 e^3 (c+d x)^4}{3 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{8 e^3 \sqrt{(c+d x)^2+1} (c+d x)^3}{3 b^3 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^3 (c+d x)^2}{2 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{e^3 \sqrt{(c+d x)^2+1} (c+d x)}{b^3 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^3 \sqrt{(c+d x)^2+1} (c+d x)^3}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^3}",1,"-(e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2])/(3*b*d*(a + b*ArcSinh[c + d*x])^3) - (e^3*(c + d*x)^2)/(2*b^2*d*(a + b*ArcSinh[c + d*x])^2) - (2*e^3*(c + d*x)^4)/(3*b^2*d*(a + b*ArcSinh[c + d*x])^2) - (e^3*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(b^3*d*(a + b*ArcSinh[c + d*x])) - (8*e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2])/(3*b^3*d*(a + b*ArcSinh[c + d*x])) - (e^3*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSinh[c + d*x]])/(3*b^4*d) + (4*e^3*Cosh[(4*a)/b]*CoshIntegral[(4*a)/b + 4*ArcSinh[c + d*x]])/(3*b^4*d) + (e^3*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c + d*x]])/(3*b^4*d) - (4*e^3*Sinh[(4*a)/b]*SinhIntegral[(4*a)/b + 4*ArcSinh[c + d*x]])/(3*b^4*d)","A",17,8,23,0.3478,1,"{5865, 12, 5667, 5774, 5665, 3303, 3298, 3301}"
176,1,327,0,0.6745192,"\int \frac{(c e+d e x)^2}{\left(a+b \sinh ^{-1}(c+d x)\right)^4} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcSinh[c + d*x])^4,x]","\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{24 b^4 d}-\frac{9 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c+d x)\right)}{8 b^4 d}-\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{24 b^4 d}+\frac{9 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \sinh ^{-1}(c+d x)\right)}{8 b^4 d}-\frac{e^2 (c+d x)^3}{2 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{3 e^2 \sqrt{(c+d x)^2+1} (c+d x)^2}{2 b^3 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^2 (c+d x)}{3 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{e^2 \sqrt{(c+d x)^2+1}}{3 b^3 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^2 \sqrt{(c+d x)^2+1} (c+d x)^2}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^3}","\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{24 b^4 d}-\frac{9 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{8 b^4 d}-\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{24 b^4 d}+\frac{9 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{8 b^4 d}-\frac{e^2 (c+d x)^3}{2 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{3 e^2 \sqrt{(c+d x)^2+1} (c+d x)^2}{2 b^3 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^2 (c+d x)}{3 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{e^2 \sqrt{(c+d x)^2+1}}{3 b^3 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e^2 \sqrt{(c+d x)^2+1} (c+d x)^2}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^3}",1,"-(e^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^2])/(3*b*d*(a + b*ArcSinh[c + d*x])^3) - (e^2*(c + d*x))/(3*b^2*d*(a + b*ArcSinh[c + d*x])^2) - (e^2*(c + d*x)^3)/(2*b^2*d*(a + b*ArcSinh[c + d*x])^2) - (e^2*Sqrt[1 + (c + d*x)^2])/(3*b^3*d*(a + b*ArcSinh[c + d*x])) - (3*e^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^2])/(2*b^3*d*(a + b*ArcSinh[c + d*x])) + (e^2*CoshIntegral[a/b + ArcSinh[c + d*x]]*Sinh[a/b])/(24*b^4*d) - (9*e^2*CoshIntegral[(3*a)/b + 3*ArcSinh[c + d*x]]*Sinh[(3*a)/b])/(8*b^4*d) - (e^2*Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c + d*x]])/(24*b^4*d) + (9*e^2*Cosh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcSinh[c + d*x]])/(8*b^4*d)","A",18,10,23,0.4348,1,"{5865, 12, 5667, 5774, 5665, 3303, 3298, 3301, 5655, 5779}"
177,1,204,0,0.3414993,"\int \frac{c e+d e x}{\left(a+b \sinh ^{-1}(c+d x)\right)^4} \, dx","Int[(c*e + d*e*x)/(a + b*ArcSinh[c + d*x])^4,x]","\frac{2 e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c+d x)\right)}{3 b^4 d}-\frac{2 e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \sinh ^{-1}(c+d x)\right)}{3 b^4 d}-\frac{e (c+d x)^2}{3 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{2 e \sqrt{(c+d x)^2+1} (c+d x)}{3 b^3 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e}{6 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{e \sqrt{(c+d x)^2+1} (c+d x)}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^3}","\frac{2 e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}-\frac{2 e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}-\frac{e (c+d x)^2}{3 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{2 e \sqrt{(c+d x)^2+1} (c+d x)}{3 b^3 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{e}{6 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{e \sqrt{(c+d x)^2+1} (c+d x)}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^3}",1,"-(e*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(3*b*d*(a + b*ArcSinh[c + d*x])^3) - e/(6*b^2*d*(a + b*ArcSinh[c + d*x])^2) - (e*(c + d*x)^2)/(3*b^2*d*(a + b*ArcSinh[c + d*x])^2) - (2*e*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(3*b^3*d*(a + b*ArcSinh[c + d*x])) + (2*e*Cosh[(2*a)/b]*CoshIntegral[(2*a)/b + 2*ArcSinh[c + d*x]])/(3*b^4*d) - (2*e*Sinh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcSinh[c + d*x]])/(3*b^4*d)","A",9,9,21,0.4286,1,"{5865, 12, 5667, 5774, 5665, 3303, 3298, 3301, 5675}"
178,1,156,0,0.2674107,"\int \frac{1}{\left(a+b \sinh ^{-1}(c+d x)\right)^4} \, dx","Int[(a + b*ArcSinh[c + d*x])^(-4),x]","-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{6 b^4 d}+\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\sinh ^{-1}(c+d x)\right)}{6 b^4 d}-\frac{c+d x}{6 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{\sqrt{(c+d x)^2+1}}{6 b^3 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{\sqrt{(c+d x)^2+1}}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^3}","-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{6 b^4 d}+\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \sinh ^{-1}(c+d x)}{b}\right)}{6 b^4 d}-\frac{c+d x}{6 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^2}-\frac{\sqrt{(c+d x)^2+1}}{6 b^3 d \left(a+b \sinh ^{-1}(c+d x)\right)}-\frac{\sqrt{(c+d x)^2+1}}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^3}",1,"-Sqrt[1 + (c + d*x)^2]/(3*b*d*(a + b*ArcSinh[c + d*x])^3) - (c + d*x)/(6*b^2*d*(a + b*ArcSinh[c + d*x])^2) - Sqrt[1 + (c + d*x)^2]/(6*b^3*d*(a + b*ArcSinh[c + d*x])) - (CoshIntegral[a/b + ArcSinh[c + d*x]]*Sinh[a/b])/(6*b^4*d) + (Cosh[a/b]*SinhIntegral[a/b + ArcSinh[c + d*x]])/(6*b^4*d)","A",8,7,12,0.5833,1,"{5863, 5655, 5774, 5779, 3303, 3298, 3301}"
179,0,0,0,0.063398,"\int \frac{1}{(c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^4} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcSinh[c + d*x])^4),x]","\int \frac{1}{(c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^4} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^4},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcSinh[x])^4), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
180,1,361,0,0.8751084,"\int (c e+d e x)^4 \sqrt{a+b \sinh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^4*Sqrt[a + b*ArcSinh[c + d*x]],x]","\frac{\sqrt{\pi } \sqrt{b} e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{\sqrt{\frac{\pi }{5}} \sqrt{b} e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{320 d}-\frac{\sqrt{\pi } \sqrt{b} e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{\sqrt{\frac{\pi }{5}} \sqrt{b} e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{320 d}+\frac{e^4 (c+d x)^5 \sqrt{a+b \sinh ^{-1}(c+d x)}}{5 d}","\frac{\sqrt{\pi } \sqrt{b} e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{\sqrt{\frac{\pi }{5}} \sqrt{b} e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{320 d}-\frac{\sqrt{\pi } \sqrt{b} e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{\sqrt{\frac{\pi }{5}} \sqrt{b} e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{320 d}+\frac{e^4 (c+d x)^5 \sqrt{a+b \sinh ^{-1}(c+d x)}}{5 d}",1,"(e^4*(c + d*x)^5*Sqrt[a + b*ArcSinh[c + d*x]])/(5*d) + (Sqrt[b]*e^4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(32*d) - (Sqrt[b]*e^4*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(64*d) + (Sqrt[b]*e^4*E^((5*a)/b)*Sqrt[Pi/5]*Erf[(Sqrt[5]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(320*d) - (Sqrt[b]*e^4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(32*d*E^(a/b)) + (Sqrt[b]*e^4*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(64*d*E^((3*a)/b)) - (Sqrt[b]*e^4*Sqrt[Pi/5]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(320*d*E^((5*a)/b))","A",21,9,25,0.3600,1,"{5865, 12, 5663, 5779, 3312, 3308, 2180, 2204, 2205}"
181,1,272,0,0.6650035,"\int (c e+d e x)^3 \sqrt{a+b \sinh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^3*Sqrt[a + b*ArcSinh[c + d*x]],x]","-\frac{\sqrt{\pi } \sqrt{b} e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{\sqrt{\pi } \sqrt{b} e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{e^3 (c+d x)^4 \sqrt{a+b \sinh ^{-1}(c+d x)}}{4 d}-\frac{3 e^3 \sqrt{a+b \sinh ^{-1}(c+d x)}}{32 d}","-\frac{\sqrt{\pi } \sqrt{b} e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{\sqrt{\pi } \sqrt{b} e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{e^3 (c+d x)^4 \sqrt{a+b \sinh ^{-1}(c+d x)}}{4 d}-\frac{3 e^3 \sqrt{a+b \sinh ^{-1}(c+d x)}}{32 d}",1,"(-3*e^3*Sqrt[a + b*ArcSinh[c + d*x]])/(32*d) + (e^3*(c + d*x)^4*Sqrt[a + b*ArcSinh[c + d*x]])/(4*d) - (Sqrt[b]*e^3*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(256*d) + (Sqrt[b]*e^3*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(32*d) - (Sqrt[b]*e^3*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(256*d*E^((4*a)/b)) + (Sqrt[b]*e^3*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(32*d*E^((2*a)/b))","A",16,9,25,0.3600,1,"{5865, 12, 5663, 5779, 3312, 3307, 2180, 2204, 2205}"
182,1,245,0,0.6501808,"\int (c e+d e x)^2 \sqrt{a+b \sinh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)^2*Sqrt[a + b*ArcSinh[c + d*x]],x]","-\frac{\sqrt{\pi } \sqrt{b} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}+\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{48 d}+\frac{\sqrt{\pi } \sqrt{b} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{48 d}+\frac{e^2 (c+d x)^3 \sqrt{a+b \sinh ^{-1}(c+d x)}}{3 d}","-\frac{\sqrt{\pi } \sqrt{b} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}+\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{48 d}+\frac{\sqrt{\pi } \sqrt{b} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{48 d}+\frac{e^2 (c+d x)^3 \sqrt{a+b \sinh ^{-1}(c+d x)}}{3 d}",1,"(e^2*(c + d*x)^3*Sqrt[a + b*ArcSinh[c + d*x]])/(3*d) - (Sqrt[b]*e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(16*d) + (Sqrt[b]*e^2*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(48*d) + (Sqrt[b]*e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(16*d*E^(a/b)) - (Sqrt[b]*e^2*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(48*d*E^((3*a)/b))","A",16,9,25,0.3600,1,"{5865, 12, 5663, 5779, 3312, 3308, 2180, 2204, 2205}"
183,1,164,0,0.4292381,"\int (c e+d e x) \sqrt{a+b \sinh ^{-1}(c+d x)} \, dx","Int[(c*e + d*e*x)*Sqrt[a + b*ArcSinh[c + d*x]],x]","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}+\frac{e (c+d x)^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{2 d}+\frac{e \sqrt{a+b \sinh ^{-1}(c+d x)}}{4 d}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}+\frac{e (c+d x)^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{2 d}+\frac{e \sqrt{a+b \sinh ^{-1}(c+d x)}}{4 d}",1,"(e*Sqrt[a + b*ArcSinh[c + d*x]])/(4*d) + (e*(c + d*x)^2*Sqrt[a + b*ArcSinh[c + d*x]])/(2*d) - (Sqrt[b]*e*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(16*d) - (Sqrt[b]*e*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(16*d*E^((2*a)/b))","A",11,9,23,0.3913,1,"{5865, 12, 5663, 5779, 3312, 3307, 2180, 2204, 2205}"
184,1,115,0,0.2462218,"\int \sqrt{a+b \sinh ^{-1}(c+d x)} \, dx","Int[Sqrt[a + b*ArcSinh[c + d*x]],x]","\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}-\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}+\frac{(c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{d}","\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}-\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}+\frac{(c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{d}",1,"((c + d*x)*Sqrt[a + b*ArcSinh[c + d*x]])/d + (Sqrt[b]*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(4*d) - (Sqrt[b]*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(4*d*E^(a/b))","A",8,7,14,0.5000,1,"{5863, 5653, 5779, 3308, 2180, 2204, 2205}"
185,0,0,0,0.088093,"\int \frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{c e+d e x} \, dx","Int[Sqrt[a + b*ArcSinh[c + d*x]]/(c*e + d*e*x),x]","\int \frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{c e+d e x} \, dx","\frac{\text{Int}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{c+d x},x\right)}{e}",0,"Defer[Subst][Defer[Int][Sqrt[a + b*ArcSinh[x]]/x, x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
186,1,601,0,1.6616692,"\int (c e+d e x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2} \, dx","Int[(c*e + d*e*x)^4*(a + b*ArcSinh[c + d*x])^(3/2),x]","\frac{3 \sqrt{\pi } b^{3/2} e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{3 \sqrt{3 \pi } b^{3/2} e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3200 d}-\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{200 d}+\frac{3 \sqrt{\frac{\pi }{5}} b^{3/2} e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3200 d}+\frac{3 \sqrt{\pi } b^{3/2} e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{3 \sqrt{3 \pi } b^{3/2} e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3200 d}-\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{200 d}+\frac{3 \sqrt{\frac{\pi }{5}} b^{3/2} e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3200 d}+\frac{e^4 (c+d x)^5 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{5 d}-\frac{3 b e^4 \sqrt{(c+d x)^2+1} (c+d x)^4 \sqrt{a+b \sinh ^{-1}(c+d x)}}{50 d}+\frac{2 b e^4 \sqrt{(c+d x)^2+1} (c+d x)^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{25 d}-\frac{4 b e^4 \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{25 d}","\frac{3 \sqrt{\pi } b^{3/2} e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{3 \sqrt{3 \pi } b^{3/2} e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3200 d}-\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{200 d}+\frac{3 \sqrt{\frac{\pi }{5}} b^{3/2} e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3200 d}+\frac{3 \sqrt{\pi } b^{3/2} e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{3 \sqrt{3 \pi } b^{3/2} e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3200 d}-\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{200 d}+\frac{3 \sqrt{\frac{\pi }{5}} b^{3/2} e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3200 d}+\frac{e^4 (c+d x)^5 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{5 d}-\frac{3 b e^4 \sqrt{(c+d x)^2+1} (c+d x)^4 \sqrt{a+b \sinh ^{-1}(c+d x)}}{50 d}+\frac{2 b e^4 \sqrt{(c+d x)^2+1} (c+d x)^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{25 d}-\frac{4 b e^4 \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{25 d}",1,"(-4*b*e^4*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(25*d) + (2*b*e^4*(c + d*x)^2*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(25*d) - (3*b*e^4*(c + d*x)^4*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(50*d) + (e^4*(c + d*x)^5*(a + b*ArcSinh[c + d*x])^(3/2))/(5*d) + (3*b^(3/2)*e^4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(64*d) - (b^(3/2)*e^4*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(200*d) - (3*b^(3/2)*e^4*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(3200*d) + (3*b^(3/2)*e^4*E^((5*a)/b)*Sqrt[Pi/5]*Erf[(Sqrt[5]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(3200*d) + (3*b^(3/2)*e^4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(64*d*E^(a/b)) - (b^(3/2)*e^4*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(200*d*E^((3*a)/b)) - (3*b^(3/2)*e^4*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(3200*d*E^((3*a)/b)) + (3*b^(3/2)*e^4*Sqrt[Pi/5]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(3200*d*E^((5*a)/b))","A",43,12,25,0.4800,1,"{5865, 12, 5663, 5758, 5717, 5657, 3307, 2180, 2205, 2204, 5669, 5448}"
187,1,360,0,1.0585216,"\int (c e+d e x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2} \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcSinh[c + d*x])^(3/2),x]","-\frac{3 \sqrt{\pi } b^{3/2} e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2048 d}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{3 \sqrt{\pi } b^{3/2} e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2048 d}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{4 d}-\frac{3 b e^3 \sqrt{(c+d x)^2+1} (c+d x)^3 \sqrt{a+b \sinh ^{-1}(c+d x)}}{32 d}+\frac{9 b e^3 \sqrt{(c+d x)^2+1} (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{64 d}-\frac{3 e^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{32 d}","-\frac{3 \sqrt{\pi } b^{3/2} e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2048 d}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{3 \sqrt{\pi } b^{3/2} e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2048 d}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{4 d}-\frac{3 b e^3 \sqrt{(c+d x)^2+1} (c+d x)^3 \sqrt{a+b \sinh ^{-1}(c+d x)}}{32 d}+\frac{9 b e^3 \sqrt{(c+d x)^2+1} (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{64 d}-\frac{3 e^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{32 d}",1,"(9*b*e^3*(c + d*x)*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(64*d) - (3*b*e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(32*d) - (3*e^3*(a + b*ArcSinh[c + d*x])^(3/2))/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcSinh[c + d*x])^(3/2))/(4*d) - (3*b^(3/2)*e^3*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(2048*d) + (3*b^(3/2)*e^3*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(128*d) + (3*b^(3/2)*e^3*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(2048*d*E^((4*a)/b)) - (3*b^(3/2)*e^3*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(128*d*E^((2*a)/b))","A",27,11,25,0.4400,1,"{5865, 12, 5663, 5758, 5675, 5669, 5448, 3308, 2180, 2204, 2205}"
188,1,328,0,0.8820117,"\int (c e+d e x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2} \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcSinh[c + d*x])^(3/2),x]","-\frac{3 \sqrt{\pi } b^{3/2} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{96 d}-\frac{3 \sqrt{\pi } b^{3/2} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{96 d}+\frac{e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{3 d}-\frac{b e^2 \sqrt{(c+d x)^2+1} (c+d x)^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{6 d}+\frac{b e^2 \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{3 d}","-\frac{3 \sqrt{\pi } b^{3/2} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{96 d}-\frac{3 \sqrt{\pi } b^{3/2} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{96 d}+\frac{e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{3 d}-\frac{b e^2 \sqrt{(c+d x)^2+1} (c+d x)^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{6 d}+\frac{b e^2 \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{3 d}",1,"(b*e^2*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(3*d) - (b*e^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(6*d) + (e^2*(c + d*x)^3*(a + b*ArcSinh[c + d*x])^(3/2))/(3*d) - (3*b^(3/2)*e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(32*d) + (b^(3/2)*e^2*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(96*d) - (3*b^(3/2)*e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(32*d*E^(a/b)) + (b^(3/2)*e^2*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(96*d*E^((3*a)/b))","A",24,12,25,0.4800,1,"{5865, 12, 5663, 5758, 5717, 5657, 3307, 2180, 2205, 2204, 5669, 5448}"
189,1,205,0,0.4828888,"\int (c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2} \, dx","Int[(c*e + d*e*x)*(a + b*ArcSinh[c + d*x])^(3/2),x]","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{2 d}-\frac{3 b e \sqrt{(c+d x)^2+1} (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{8 d}+\frac{e \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{4 d}","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{2 d}-\frac{3 b e \sqrt{(c+d x)^2+1} (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{8 d}+\frac{e \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{4 d}",1,"(-3*b*e*(c + d*x)*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(8*d) + (e*(a + b*ArcSinh[c + d*x])^(3/2))/(4*d) + (e*(c + d*x)^2*(a + b*ArcSinh[c + d*x])^(3/2))/(2*d) - (3*b^(3/2)*e*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(64*d) + (3*b^(3/2)*e*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(64*d*E^((2*a)/b))","A",13,11,23,0.4783,1,"{5865, 12, 5663, 5758, 5675, 5669, 5448, 3308, 2180, 2204, 2205}"
190,1,150,0,0.253528,"\int \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2} \, dx","Int[(a + b*ArcSinh[c + d*x])^(3/2),x]","\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}+\frac{3 \sqrt{\pi } b^{3/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}-\frac{3 b \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{2 d}+\frac{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{d}","\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}+\frac{3 \sqrt{\pi } b^{3/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}-\frac{3 b \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{2 d}+\frac{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{d}",1,"(-3*b*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(2*d) + ((c + d*x)*(a + b*ArcSinh[c + d*x])^(3/2))/d + (3*b^(3/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(8*d) + (3*b^(3/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(8*d*E^(a/b))","A",9,8,14,0.5714,1,"{5863, 5653, 5717, 5657, 3307, 2180, 2205, 2204}"
191,0,0,0,0.1032108,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{c e+d e x} \, dx","Int[(a + b*ArcSinh[c + d*x])^(3/2)/(c*e + d*e*x),x]","\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{c e+d e x} \, dx","\frac{\text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{c+d x},x\right)}{e}",0,"Defer[Subst][Defer[Int][(a + b*ArcSinh[x])^(3/2)/x, x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
192,1,701,0,2.203125,"\int (c e+d e x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2} \, dx","Int[(c*e + d*e*x)^4*(a + b*ArcSinh[c + d*x])^(5/2),x]","\frac{15 \sqrt{\pi } b^{5/2} e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}-\frac{\sqrt{3 \pi } b^{5/2} e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{1280 d}-\frac{\sqrt{\frac{\pi }{3}} b^{5/2} e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{240 d}+\frac{3 \sqrt{\frac{\pi }{5}} b^{5/2} e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{6400 d}-\frac{15 \sqrt{\pi } b^{5/2} e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{\sqrt{3 \pi } b^{5/2} e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{1280 d}+\frac{\sqrt{\frac{\pi }{3}} b^{5/2} e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{240 d}-\frac{3 \sqrt{\frac{\pi }{5}} b^{5/2} e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{6400 d}+\frac{3 b^2 e^4 (c+d x)^5 \sqrt{a+b \sinh ^{-1}(c+d x)}}{100 d}-\frac{b^2 e^4 (c+d x)^3 \sqrt{a+b \sinh ^{-1}(c+d x)}}{15 d}+\frac{2 b^2 e^4 (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{5 d}+\frac{e^4 (c+d x)^5 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{5 d}-\frac{b e^4 \sqrt{(c+d x)^2+1} (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{10 d}+\frac{2 b e^4 \sqrt{(c+d x)^2+1} (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{15 d}-\frac{4 b e^4 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{15 d}","\frac{15 \sqrt{\pi } b^{5/2} e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}-\frac{\sqrt{3 \pi } b^{5/2} e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{1280 d}-\frac{\sqrt{\frac{\pi }{3}} b^{5/2} e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{240 d}+\frac{3 \sqrt{\frac{\pi }{5}} b^{5/2} e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{6400 d}-\frac{15 \sqrt{\pi } b^{5/2} e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{\sqrt{3 \pi } b^{5/2} e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{1280 d}+\frac{\sqrt{\frac{\pi }{3}} b^{5/2} e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{240 d}-\frac{3 \sqrt{\frac{\pi }{5}} b^{5/2} e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{6400 d}+\frac{3 b^2 e^4 (c+d x)^5 \sqrt{a+b \sinh ^{-1}(c+d x)}}{100 d}-\frac{b^2 e^4 (c+d x)^3 \sqrt{a+b \sinh ^{-1}(c+d x)}}{15 d}+\frac{2 b^2 e^4 (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{5 d}+\frac{e^4 (c+d x)^5 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{5 d}-\frac{b e^4 \sqrt{(c+d x)^2+1} (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{10 d}+\frac{2 b e^4 \sqrt{(c+d x)^2+1} (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{15 d}-\frac{4 b e^4 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{15 d}",1,"(2*b^2*e^4*(c + d*x)*Sqrt[a + b*ArcSinh[c + d*x]])/(5*d) - (b^2*e^4*(c + d*x)^3*Sqrt[a + b*ArcSinh[c + d*x]])/(15*d) + (3*b^2*e^4*(c + d*x)^5*Sqrt[a + b*ArcSinh[c + d*x]])/(100*d) - (4*b*e^4*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(3/2))/(15*d) + (2*b*e^4*(c + d*x)^2*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(3/2))/(15*d) - (b*e^4*(c + d*x)^4*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(3/2))/(10*d) + (e^4*(c + d*x)^5*(a + b*ArcSinh[c + d*x])^(5/2))/(5*d) + (15*b^(5/2)*e^4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(128*d) - (b^(5/2)*e^4*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(240*d) - (b^(5/2)*e^4*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(1280*d) + (3*b^(5/2)*e^4*E^((5*a)/b)*Sqrt[Pi/5]*Erf[(Sqrt[5]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(6400*d) - (15*b^(5/2)*e^4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(128*d*E^(a/b)) + (b^(5/2)*e^4*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(240*d*E^((3*a)/b)) + (b^(5/2)*e^4*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(1280*d*E^((3*a)/b)) - (3*b^(5/2)*e^4*Sqrt[Pi/5]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(6400*d*E^((5*a)/b))","A",46,12,25,0.4800,1,"{5865, 12, 5663, 5758, 5717, 5653, 5779, 3308, 2180, 2204, 2205, 3312}"
193,1,455,0,1.5196296,"\int (c e+d e x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2} \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcSinh[c + d*x])^(5/2),x]","-\frac{15 \sqrt{\pi } b^{5/2} e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16384 d}+\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{512 d}-\frac{15 \sqrt{\pi } b^{5/2} e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16384 d}+\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{512 d}+\frac{15 b^2 e^3 (c+d x)^4 \sqrt{a+b \sinh ^{-1}(c+d x)}}{256 d}-\frac{45 b^2 e^3 (c+d x)^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{256 d}-\frac{225 b^2 e^3 \sqrt{a+b \sinh ^{-1}(c+d x)}}{2048 d}+\frac{e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{4 d}-\frac{5 b e^3 \sqrt{(c+d x)^2+1} (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{32 d}+\frac{15 b e^3 \sqrt{(c+d x)^2+1} (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{64 d}-\frac{3 e^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{32 d}","-\frac{15 \sqrt{\pi } b^{5/2} e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16384 d}+\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{512 d}-\frac{15 \sqrt{\pi } b^{5/2} e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16384 d}+\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{512 d}+\frac{15 b^2 e^3 (c+d x)^4 \sqrt{a+b \sinh ^{-1}(c+d x)}}{256 d}-\frac{45 b^2 e^3 (c+d x)^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{256 d}-\frac{225 b^2 e^3 \sqrt{a+b \sinh ^{-1}(c+d x)}}{2048 d}+\frac{e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{4 d}-\frac{5 b e^3 \sqrt{(c+d x)^2+1} (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{32 d}+\frac{15 b e^3 \sqrt{(c+d x)^2+1} (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{64 d}-\frac{3 e^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{32 d}",1,"(-225*b^2*e^3*Sqrt[a + b*ArcSinh[c + d*x]])/(2048*d) - (45*b^2*e^3*(c + d*x)^2*Sqrt[a + b*ArcSinh[c + d*x]])/(256*d) + (15*b^2*e^3*(c + d*x)^4*Sqrt[a + b*ArcSinh[c + d*x]])/(256*d) + (15*b*e^3*(c + d*x)*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(3/2))/(64*d) - (5*b*e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(3/2))/(32*d) - (3*e^3*(a + b*ArcSinh[c + d*x])^(5/2))/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcSinh[c + d*x])^(5/2))/(4*d) - (15*b^(5/2)*e^3*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(16384*d) + (15*b^(5/2)*e^3*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(512*d) - (15*b^(5/2)*e^3*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(16384*d*E^((4*a)/b)) + (15*b^(5/2)*e^3*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(512*d*E^((2*a)/b))","A",29,11,25,0.4400,1,"{5865, 12, 5663, 5758, 5675, 5779, 3312, 3307, 2180, 2204, 2205}"
194,1,394,0,1.2444718,"\int (c e+d e x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2} \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcSinh[c + d*x])^(5/2),x]","-\frac{15 \sqrt{\pi } b^{5/2} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{5 \sqrt{\frac{\pi }{3}} b^{5/2} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{576 d}+\frac{15 \sqrt{\pi } b^{5/2} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{5 \sqrt{\frac{\pi }{3}} b^{5/2} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{576 d}+\frac{5 b^2 e^2 (c+d x)^3 \sqrt{a+b \sinh ^{-1}(c+d x)}}{36 d}-\frac{5 b^2 e^2 (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{6 d}+\frac{e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{3 d}-\frac{5 b e^2 \sqrt{(c+d x)^2+1} (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{18 d}+\frac{5 b e^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{9 d}","-\frac{15 \sqrt{\pi } b^{5/2} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{5 \sqrt{\frac{\pi }{3}} b^{5/2} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{576 d}+\frac{15 \sqrt{\pi } b^{5/2} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{5 \sqrt{\frac{\pi }{3}} b^{5/2} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{576 d}+\frac{5 b^2 e^2 (c+d x)^3 \sqrt{a+b \sinh ^{-1}(c+d x)}}{36 d}-\frac{5 b^2 e^2 (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{6 d}+\frac{e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{3 d}-\frac{5 b e^2 \sqrt{(c+d x)^2+1} (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{18 d}+\frac{5 b e^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{9 d}",1,"(-5*b^2*e^2*(c + d*x)*Sqrt[a + b*ArcSinh[c + d*x]])/(6*d) + (5*b^2*e^2*(c + d*x)^3*Sqrt[a + b*ArcSinh[c + d*x]])/(36*d) + (5*b*e^2*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(3/2))/(9*d) - (5*b*e^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(3/2))/(18*d) + (e^2*(c + d*x)^3*(a + b*ArcSinh[c + d*x])^(5/2))/(3*d) - (15*b^(5/2)*e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(64*d) + (5*b^(5/2)*e^2*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(576*d) + (15*b^(5/2)*e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(64*d*E^(a/b)) - (5*b^(5/2)*e^2*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(576*d*E^((3*a)/b))","A",26,12,25,0.4800,1,"{5865, 12, 5663, 5758, 5717, 5653, 5779, 3308, 2180, 2204, 2205, 3312}"
195,1,262,0,0.7313178,"\int (c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2} \, dx","Int[(c*e + d*e*x)*(a + b*ArcSinh[c + d*x])^(5/2),x]","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}+\frac{15 b^2 e (c+d x)^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{32 d}+\frac{15 b^2 e \sqrt{a+b \sinh ^{-1}(c+d x)}}{64 d}-\frac{5 b e (c+d x) \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{8 d}+\frac{e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{2 d}+\frac{e \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{4 d}","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}+\frac{15 b^2 e (c+d x)^2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{32 d}+\frac{15 b^2 e \sqrt{a+b \sinh ^{-1}(c+d x)}}{64 d}-\frac{5 b e (c+d x) \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{8 d}+\frac{e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{2 d}+\frac{e \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{4 d}",1,"(15*b^2*e*Sqrt[a + b*ArcSinh[c + d*x]])/(64*d) + (15*b^2*e*(c + d*x)^2*Sqrt[a + b*ArcSinh[c + d*x]])/(32*d) - (5*b*e*(c + d*x)*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(3/2))/(8*d) + (e*(a + b*ArcSinh[c + d*x])^(5/2))/(4*d) + (e*(c + d*x)^2*(a + b*ArcSinh[c + d*x])^(5/2))/(2*d) - (15*b^(5/2)*e*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(256*d) - (15*b^(5/2)*e*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(256*d*E^((2*a)/b))","A",14,11,23,0.4783,1,"{5865, 12, 5663, 5758, 5675, 5779, 3312, 3307, 2180, 2204, 2205}"
196,1,179,0,0.4024111,"\int \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2} \, dx","Int[(a + b*ArcSinh[c + d*x])^(5/2),x]","\frac{15 \sqrt{\pi } b^{5/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{15 \sqrt{\pi } b^{5/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}+\frac{15 b^2 (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{4 d}-\frac{5 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{2 d}+\frac{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{d}","\frac{15 \sqrt{\pi } b^{5/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{15 \sqrt{\pi } b^{5/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}+\frac{15 b^2 (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{4 d}-\frac{5 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{2 d}+\frac{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{d}",1,"(15*b^2*(c + d*x)*Sqrt[a + b*ArcSinh[c + d*x]])/(4*d) - (5*b*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(3/2))/(2*d) + ((c + d*x)*(a + b*ArcSinh[c + d*x])^(5/2))/d + (15*b^(5/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(16*d) - (15*b^(5/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(16*d*E^(a/b))","A",10,8,14,0.5714,1,"{5863, 5653, 5717, 5779, 3308, 2180, 2204, 2205}"
197,0,0,0,0.1052531,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{c e+d e x} \, dx","Int[(a + b*ArcSinh[c + d*x])^(5/2)/(c*e + d*e*x),x]","\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{c e+d e x} \, dx","\frac{\text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{c+d x},x\right)}{e}",0,"Defer[Subst][Defer[Int][(a + b*ArcSinh[x])^(5/2)/x, x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
198,1,835,0,3.2885048,"\int (c e+d e x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2} \, dx","Int[(c*e + d*e*x)^4*(a + b*ArcSinh[c + d*x])^(7/2),x]","\frac{e^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2} (c+d x)^5}{5 d}+\frac{7 b^2 e^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2} (c+d x)^5}{100 d}-\frac{7 b e^4 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2} (c+d x)^4}{50 d}-\frac{21 b^3 e^4 \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)} (c+d x)^4}{1000 d}-\frac{7 b^2 e^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2} (c+d x)^3}{45 d}+\frac{14 b e^4 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2} (c+d x)^2}{75 d}+\frac{119 b^3 e^4 \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)} (c+d x)^2}{1125 d}+\frac{14 b^2 e^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2} (c+d x)}{15 d}-\frac{28 b e^4 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{75 d}+\frac{105 b^{7/2} e^4 e^{a/b} \sqrt{\pi } \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}-\frac{21 b^{7/2} e^4 e^{\frac{3 a}{b}} \sqrt{3 \pi } \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64000 d}-\frac{119 b^{7/2} e^4 e^{\frac{3 a}{b}} \sqrt{\frac{\pi }{3}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{18000 d}+\frac{21 b^{7/2} e^4 e^{\frac{5 a}{b}} \sqrt{\frac{\pi }{5}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64000 d}+\frac{105 b^{7/2} e^4 e^{-\frac{a}{b}} \sqrt{\pi } \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}-\frac{21 b^{7/2} e^4 e^{-\frac{3 a}{b}} \sqrt{3 \pi } \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64000 d}-\frac{119 b^{7/2} e^4 e^{-\frac{3 a}{b}} \sqrt{\frac{\pi }{3}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{18000 d}+\frac{21 b^{7/2} e^4 e^{-\frac{5 a}{b}} \sqrt{\frac{\pi }{5}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64000 d}-\frac{1813 b^3 e^4 \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{1125 d}","\frac{e^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2} (c+d x)^5}{5 d}+\frac{7 b^2 e^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2} (c+d x)^5}{100 d}-\frac{7 b e^4 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2} (c+d x)^4}{50 d}-\frac{21 b^3 e^4 \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)} (c+d x)^4}{1000 d}-\frac{7 b^2 e^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2} (c+d x)^3}{45 d}+\frac{14 b e^4 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2} (c+d x)^2}{75 d}+\frac{119 b^3 e^4 \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)} (c+d x)^2}{1125 d}+\frac{14 b^2 e^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2} (c+d x)}{15 d}-\frac{28 b e^4 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{75 d}+\frac{105 b^{7/2} e^4 e^{a/b} \sqrt{\pi } \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}-\frac{21 b^{7/2} e^4 e^{\frac{3 a}{b}} \sqrt{3 \pi } \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64000 d}-\frac{119 b^{7/2} e^4 e^{\frac{3 a}{b}} \sqrt{\frac{\pi }{3}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{18000 d}+\frac{21 b^{7/2} e^4 e^{\frac{5 a}{b}} \sqrt{\frac{\pi }{5}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64000 d}+\frac{105 b^{7/2} e^4 e^{-\frac{a}{b}} \sqrt{\pi } \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}-\frac{21 b^{7/2} e^4 e^{-\frac{3 a}{b}} \sqrt{3 \pi } \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64000 d}-\frac{119 b^{7/2} e^4 e^{-\frac{3 a}{b}} \sqrt{\frac{\pi }{3}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{18000 d}+\frac{21 b^{7/2} e^4 e^{-\frac{5 a}{b}} \sqrt{\frac{\pi }{5}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64000 d}-\frac{1813 b^3 e^4 \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{1125 d}",1,"(-1813*b^3*e^4*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(1125*d) + (119*b^3*e^4*(c + d*x)^2*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(1125*d) - (21*b^3*e^4*(c + d*x)^4*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(1000*d) + (14*b^2*e^4*(c + d*x)*(a + b*ArcSinh[c + d*x])^(3/2))/(15*d) - (7*b^2*e^4*(c + d*x)^3*(a + b*ArcSinh[c + d*x])^(3/2))/(45*d) + (7*b^2*e^4*(c + d*x)^5*(a + b*ArcSinh[c + d*x])^(3/2))/(100*d) - (28*b*e^4*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(5/2))/(75*d) + (14*b*e^4*(c + d*x)^2*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(5/2))/(75*d) - (7*b*e^4*(c + d*x)^4*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(5/2))/(50*d) + (e^4*(c + d*x)^5*(a + b*ArcSinh[c + d*x])^(7/2))/(5*d) + (105*b^(7/2)*e^4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(256*d) - (119*b^(7/2)*e^4*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(18000*d) - (21*b^(7/2)*e^4*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(64000*d) + (21*b^(7/2)*e^4*E^((5*a)/b)*Sqrt[Pi/5]*Erf[(Sqrt[5]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(64000*d) + (105*b^(7/2)*e^4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(256*d*E^(a/b)) - (119*b^(7/2)*e^4*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(18000*d*E^((3*a)/b)) - (21*b^(7/2)*e^4*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(64000*d*E^((3*a)/b)) + (21*b^(7/2)*e^4*Sqrt[Pi/5]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(64000*d*E^((5*a)/b))","A",77,13,25,0.5200,1,"{5865, 12, 5663, 5758, 5717, 5653, 5657, 3307, 2180, 2205, 2204, 5669, 5448}"
199,1,547,0,2.143439,"\int (c e+d e x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2} \, dx","Int[(c*e + d*e*x)^3*(a + b*ArcSinh[c + d*x])^(7/2),x]","-\frac{105 \sqrt{\pi } b^{7/2} e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{131072 d}+\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2048 d}+\frac{105 \sqrt{\pi } b^{7/2} e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{131072 d}-\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2048 d}+\frac{35 b^2 e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{256 d}-\frac{105 b^3 e^3 \sqrt{(c+d x)^2+1} (c+d x)^3 \sqrt{a+b \sinh ^{-1}(c+d x)}}{2048 d}-\frac{105 b^2 e^3 (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{256 d}+\frac{1575 b^3 e^3 \sqrt{(c+d x)^2+1} (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{4096 d}-\frac{525 b^2 e^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{2048 d}+\frac{e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}}{4 d}-\frac{7 b e^3 \sqrt{(c+d x)^2+1} (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{32 d}+\frac{21 b e^3 \sqrt{(c+d x)^2+1} (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{64 d}-\frac{3 e^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}}{32 d}","-\frac{105 \sqrt{\pi } b^{7/2} e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{131072 d}+\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2048 d}+\frac{105 \sqrt{\pi } b^{7/2} e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{131072 d}-\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2048 d}+\frac{35 b^2 e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{256 d}-\frac{105 b^3 e^3 \sqrt{(c+d x)^2+1} (c+d x)^3 \sqrt{a+b \sinh ^{-1}(c+d x)}}{2048 d}-\frac{105 b^2 e^3 (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{256 d}+\frac{1575 b^3 e^3 \sqrt{(c+d x)^2+1} (c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}}{4096 d}-\frac{525 b^2 e^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{2048 d}+\frac{e^3 (c+d x)^4 \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}}{4 d}-\frac{7 b e^3 \sqrt{(c+d x)^2+1} (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{32 d}+\frac{21 b e^3 \sqrt{(c+d x)^2+1} (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{64 d}-\frac{3 e^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}}{32 d}",1,"(1575*b^3*e^3*(c + d*x)*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(4096*d) - (105*b^3*e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(2048*d) - (525*b^2*e^3*(a + b*ArcSinh[c + d*x])^(3/2))/(2048*d) - (105*b^2*e^3*(c + d*x)^2*(a + b*ArcSinh[c + d*x])^(3/2))/(256*d) + (35*b^2*e^3*(c + d*x)^4*(a + b*ArcSinh[c + d*x])^(3/2))/(256*d) + (21*b*e^3*(c + d*x)*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(5/2))/(64*d) - (7*b*e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(5/2))/(32*d) - (3*e^3*(a + b*ArcSinh[c + d*x])^(7/2))/(32*d) + (e^3*(c + d*x)^4*(a + b*ArcSinh[c + d*x])^(7/2))/(4*d) - (105*b^(7/2)*e^3*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(131072*d) + (105*b^(7/2)*e^3*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(2048*d) + (105*b^(7/2)*e^3*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(131072*d*E^((4*a)/b)) - (105*b^(7/2)*e^3*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(2048*d*E^((2*a)/b))","A",42,11,25,0.4400,1,"{5865, 12, 5663, 5758, 5675, 5669, 5448, 3308, 2180, 2204, 2205}"
200,1,481,0,1.6797683,"\int (c e+d e x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2} \, dx","Int[(c*e + d*e*x)^2*(a + b*ArcSinh[c + d*x])^(7/2),x]","-\frac{105 \sqrt{\pi } b^{7/2} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{35 \sqrt{\frac{\pi }{3}} b^{7/2} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3456 d}-\frac{105 \sqrt{\pi } b^{7/2} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{35 \sqrt{\frac{\pi }{3}} b^{7/2} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3456 d}+\frac{175 b^3 e^2 \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{54 d}-\frac{35 b^3 e^2 (c+d x)^2 \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{216 d}+\frac{35 b^2 e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{108 d}-\frac{35 b^2 e^2 (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{18 d}+\frac{7 b e^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{9 d}-\frac{7 b e^2 (c+d x)^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{18 d}+\frac{e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}}{3 d}","-\frac{105 \sqrt{\pi } b^{7/2} e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{35 \sqrt{\frac{\pi }{3}} b^{7/2} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3456 d}-\frac{105 \sqrt{\pi } b^{7/2} e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{35 \sqrt{\frac{\pi }{3}} b^{7/2} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3456 d}+\frac{175 b^3 e^2 \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{54 d}-\frac{35 b^3 e^2 (c+d x)^2 \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{216 d}+\frac{35 b^2 e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{108 d}-\frac{35 b^2 e^2 (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{18 d}+\frac{7 b e^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{9 d}-\frac{7 b e^2 (c+d x)^2 \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{18 d}+\frac{e^2 (c+d x)^3 \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}}{3 d}",1,"(175*b^3*e^2*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(54*d) - (35*b^3*e^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(216*d) - (35*b^2*e^2*(c + d*x)*(a + b*ArcSinh[c + d*x])^(3/2))/(18*d) + (35*b^2*e^2*(c + d*x)^3*(a + b*ArcSinh[c + d*x])^(3/2))/(108*d) + (7*b*e^2*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(5/2))/(9*d) - (7*b*e^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(5/2))/(18*d) + (e^2*(c + d*x)^3*(a + b*ArcSinh[c + d*x])^(7/2))/(3*d) - (105*b^(7/2)*e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(128*d) + (35*b^(7/2)*e^2*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(3456*d) - (105*b^(7/2)*e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(128*d*E^(a/b)) + (35*b^(7/2)*e^2*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(3456*d*E^((3*a)/b))","A",35,13,25,0.5200,1,"{5865, 12, 5663, 5758, 5717, 5653, 5657, 3307, 2180, 2205, 2204, 5669, 5448}"
201,1,305,0,0.7958432,"\int (c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2} \, dx","Int[(c*e + d*e*x)*(a + b*ArcSinh[c + d*x])^(7/2),x]","-\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{1024 d}+\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{1024 d}-\frac{105 b^3 e (c+d x) \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{128 d}+\frac{35 b^2 e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{32 d}+\frac{35 b^2 e \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{64 d}-\frac{7 b e (c+d x) \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{8 d}+\frac{e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}}{2 d}+\frac{e \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}}{4 d}","-\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{1024 d}+\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{1024 d}-\frac{105 b^3 e (c+d x) \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{128 d}+\frac{35 b^2 e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{32 d}+\frac{35 b^2 e \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{64 d}-\frac{7 b e (c+d x) \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{8 d}+\frac{e (c+d x)^2 \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}}{2 d}+\frac{e \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}}{4 d}",1,"(-105*b^3*e*(c + d*x)*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(128*d) + (35*b^2*e*(a + b*ArcSinh[c + d*x])^(3/2))/(64*d) + (35*b^2*e*(c + d*x)^2*(a + b*ArcSinh[c + d*x])^(3/2))/(32*d) - (7*b*e*(c + d*x)*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(5/2))/(8*d) + (e*(a + b*ArcSinh[c + d*x])^(7/2))/(4*d) + (e*(c + d*x)^2*(a + b*ArcSinh[c + d*x])^(7/2))/(2*d) - (105*b^(7/2)*e*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(1024*d) + (105*b^(7/2)*e*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(1024*d*E^((2*a)/b))","A",16,11,23,0.4783,1,"{5865, 12, 5663, 5758, 5675, 5669, 5448, 3308, 2180, 2204, 2205}"
202,1,216,0,0.4186276,"\int \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2} \, dx","Int[(a + b*ArcSinh[c + d*x])^(7/2),x]","\frac{105 \sqrt{\pi } b^{7/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{105 \sqrt{\pi } b^{7/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{105 b^3 \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{8 d}+\frac{35 b^2 (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{4 d}-\frac{7 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{2 d}+\frac{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}}{d}","\frac{105 \sqrt{\pi } b^{7/2} e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{105 \sqrt{\pi } b^{7/2} e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{105 b^3 \sqrt{(c+d x)^2+1} \sqrt{a+b \sinh ^{-1}(c+d x)}}{8 d}+\frac{35 b^2 (c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}{4 d}-\frac{7 b \sqrt{(c+d x)^2+1} \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}{2 d}+\frac{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}}{d}",1,"(-105*b^3*Sqrt[1 + (c + d*x)^2]*Sqrt[a + b*ArcSinh[c + d*x]])/(8*d) + (35*b^2*(c + d*x)*(a + b*ArcSinh[c + d*x])^(3/2))/(4*d) - (7*b*Sqrt[1 + (c + d*x)^2]*(a + b*ArcSinh[c + d*x])^(5/2))/(2*d) + ((c + d*x)*(a + b*ArcSinh[c + d*x])^(7/2))/d + (105*b^(7/2)*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(32*d) + (105*b^(7/2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(32*d*E^(a/b))","A",11,8,14,0.5714,1,"{5863, 5653, 5717, 5657, 3307, 2180, 2205, 2204}"
203,0,0,0,0.1017342,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}}{c e+d e x} \, dx","Int[(a + b*ArcSinh[c + d*x])^(7/2)/(c*e + d*e*x),x]","\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}}{c e+d e x} \, dx","\frac{\text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}}{c+d x},x\right)}{e}",0,"Defer[Subst][Defer[Int][(a + b*ArcSinh[x])^(7/2)/x, x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
204,1,326,0,0.6367857,"\int \frac{(c e+d e x)^4}{\sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx","Int[(c*e + d*e*x)^4/Sqrt[a + b*ArcSinh[c + d*x]],x]","\frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 \sqrt{b} d}-\frac{\sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{5}} e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 \sqrt{b} d}-\frac{\sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{5}} e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}","\frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 \sqrt{b} d}-\frac{\sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{5}} e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 \sqrt{b} d}-\frac{\sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{5}} e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}",1,"(e^4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(16*Sqrt[b]*d) - (e^4*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(32*Sqrt[b]*d) + (e^4*E^((5*a)/b)*Sqrt[Pi/5]*Erf[(Sqrt[5]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(32*Sqrt[b]*d) + (e^4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(16*Sqrt[b]*d*E^(a/b)) - (e^4*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(32*Sqrt[b]*d*E^((3*a)/b)) + (e^4*Sqrt[Pi/5]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(32*Sqrt[b]*d*E^((5*a)/b))","A",20,8,25,0.3200,1,"{5865, 12, 5669, 5448, 3307, 2180, 2204, 2205}"
205,1,217,0,0.4553712,"\int \frac{(c e+d e x)^3}{\sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx","Int[(c*e + d*e*x)^3/Sqrt[a + b*ArcSinh[c + d*x]],x]","-\frac{\sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{2}} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{2}} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}","-\frac{\sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{2}} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{2}} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}",1,"-(e^3*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(32*Sqrt[b]*d) + (e^3*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(8*Sqrt[b]*d) + (e^3*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(32*Sqrt[b]*d*E^((4*a)/b)) - (e^3*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(8*Sqrt[b]*d*E^((2*a)/b))","A",15,8,25,0.3200,1,"{5865, 12, 5669, 5448, 3308, 2180, 2204, 2205}"
206,1,214,0,0.4554155,"\int \frac{(c e+d e x)^2}{\sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx","Int[(c*e + d*e*x)^2/Sqrt[a + b*ArcSinh[c + d*x]],x]","-\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{3}} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}-\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{3}} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}","-\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{3}} e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}-\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{3}} e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}",1,"-(e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(8*Sqrt[b]*d) + (e^2*E^((3*a)/b)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(8*Sqrt[b]*d) - (e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(8*Sqrt[b]*d*E^(a/b)) + (e^2*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(8*Sqrt[b]*d*E^((3*a)/b))","A",15,8,25,0.3200,1,"{5865, 12, 5669, 5448, 3307, 2180, 2204, 2205}"
207,1,113,0,0.2429101,"\int \frac{c e+d e x}{\sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx","Int[(c*e + d*e*x)/Sqrt[a + b*ArcSinh[c + d*x]],x]","\frac{\sqrt{\frac{\pi }{2}} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{2}} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d}","\frac{\sqrt{\frac{\pi }{2}} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{2}} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d}",1,"-(e*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(4*Sqrt[b]*d) + (e*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(4*Sqrt[b]*d*E^((2*a)/b))","A",10,8,23,0.3478,1,"{5865, 12, 5669, 5448, 3308, 2180, 2204, 2205}"
208,1,92,0,0.1264799,"\int \frac{1}{\sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx","Int[1/Sqrt[a + b*ArcSinh[c + d*x]],x]","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}","\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}",1,"(E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(2*Sqrt[b]*d) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(2*Sqrt[b]*d*E^(a/b))","A",7,6,14,0.4286,1,"{5863, 5657, 3307, 2180, 2205, 2204}"
209,0,0,0,0.0979978,"\int \frac{1}{(c e+d e x) \sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx","Int[1/((c*e + d*e*x)*Sqrt[a + b*ArcSinh[c + d*x]]),x]","\int \frac{1}{(c e+d e x) \sqrt{a+b \sinh ^{-1}(c+d x)}} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \sqrt{a+b \sinh ^{-1}(c+d x)}},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*Sqrt[a + b*ArcSinh[x]]), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
210,1,367,0,0.6509104,"\int \frac{(c e+d e x)^4}{\left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcSinh[c + d*x])^(3/2),x]","-\frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{3/2} d}+\frac{3 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}-\frac{\sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{3/2} d}-\frac{3 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}+\frac{\sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}-\frac{2 e^4 (c+d x)^4 \sqrt{(c+d x)^2+1}}{b d \sqrt{a+b \sinh ^{-1}(c+d x)}}","-\frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{3/2} d}+\frac{3 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}-\frac{\sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{3/2} d}-\frac{3 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}+\frac{\sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}-\frac{2 e^4 (c+d x)^4 \sqrt{(c+d x)^2+1}}{b d \sqrt{a+b \sinh ^{-1}(c+d x)}}",1,"(-2*e^4*(c + d*x)^4*Sqrt[1 + (c + d*x)^2])/(b*d*Sqrt[a + b*ArcSinh[c + d*x]]) - (e^4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(8*b^(3/2)*d) + (3*e^4*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(16*b^(3/2)*d) - (e^4*E^((5*a)/b)*Sqrt[5*Pi]*Erf[(Sqrt[5]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(16*b^(3/2)*d) + (e^4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(8*b^(3/2)*d*E^(a/b)) - (3*e^4*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(16*b^(3/2)*d*E^((3*a)/b)) + (e^4*Sqrt[5*Pi]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(16*b^(3/2)*d*E^((5*a)/b))","A",19,7,25,0.2800,1,"{5865, 12, 5665, 3308, 2180, 2204, 2205}"
211,1,262,0,0.4531309,"\int \frac{(c e+d e x)^3}{\left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcSinh[c + d*x])^(3/2),x]","\frac{\sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{\sqrt{\frac{\pi }{2}} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{3/2} d}+\frac{\sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{\sqrt{\frac{\pi }{2}} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{3/2} d}-\frac{2 e^3 (c+d x)^3 \sqrt{(c+d x)^2+1}}{b d \sqrt{a+b \sinh ^{-1}(c+d x)}}","\frac{\sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{\sqrt{\frac{\pi }{2}} e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{3/2} d}+\frac{\sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{\sqrt{\frac{\pi }{2}} e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{3/2} d}-\frac{2 e^3 (c+d x)^3 \sqrt{(c+d x)^2+1}}{b d \sqrt{a+b \sinh ^{-1}(c+d x)}}",1,"(-2*e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2])/(b*d*Sqrt[a + b*ArcSinh[c + d*x]]) + (e^3*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(4*b^(3/2)*d) - (e^3*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(2*b^(3/2)*d) + (e^3*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(4*b^(3/2)*d*E^((4*a)/b)) - (e^3*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(2*b^(3/2)*d*E^((2*a)/b))","A",14,7,25,0.2800,1,"{5865, 12, 5665, 3307, 2180, 2204, 2205}"
212,1,255,0,0.4650205,"\int \frac{(c e+d e x)^2}{\left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcSinh[c + d*x])^(3/2),x]","\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{\sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{2 e^2 (c+d x)^2 \sqrt{(c+d x)^2+1}}{b d \sqrt{a+b \sinh ^{-1}(c+d x)}}","\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{\sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{2 e^2 (c+d x)^2 \sqrt{(c+d x)^2+1}}{b d \sqrt{a+b \sinh ^{-1}(c+d x)}}",1,"(-2*e^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^2])/(b*d*Sqrt[a + b*ArcSinh[c + d*x]]) + (e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(4*b^(3/2)*d) - (e^2*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(4*b^(3/2)*d) - (e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(4*b^(3/2)*d*E^(a/b)) + (e^2*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(4*b^(3/2)*d*E^((3*a)/b))","A",14,7,25,0.2800,1,"{5865, 12, 5665, 3308, 2180, 2204, 2205}"
213,1,148,0,0.2310143,"\int \frac{c e+d e x}{\left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(c*e + d*e*x)/(a + b*ArcSinh[c + d*x])^(3/2),x]","\frac{\sqrt{\frac{\pi }{2}} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\frac{\pi }{2}} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 e \sqrt{(c+d x)^2+1} (c+d x)}{b d \sqrt{a+b \sinh ^{-1}(c+d x)}}","\frac{\sqrt{\frac{\pi }{2}} e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\frac{\pi }{2}} e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 e \sqrt{(c+d x)^2+1} (c+d x)}{b d \sqrt{a+b \sinh ^{-1}(c+d x)}}",1,"(-2*e*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(b*d*Sqrt[a + b*ArcSinh[c + d*x]]) + (e*E^((2*a)/b)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(b^(3/2)*d) + (e*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(b^(3/2)*d*E^((2*a)/b))","A",8,7,23,0.3043,1,"{5865, 12, 5665, 3307, 2180, 2204, 2205}"
214,1,122,0,0.2549913,"\int \frac{1}{\left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])^(-3/2),x]","-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 \sqrt{(c+d x)^2+1}}{b d \sqrt{a+b \sinh ^{-1}(c+d x)}}","-\frac{\sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 \sqrt{(c+d x)^2+1}}{b d \sqrt{a+b \sinh ^{-1}(c+d x)}}",1,"(-2*Sqrt[1 + (c + d*x)^2])/(b*d*Sqrt[a + b*ArcSinh[c + d*x]]) - (E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(b^(3/2)*d) + (Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(b^(3/2)*d*E^(a/b))","A",8,7,14,0.5000,1,"{5863, 5655, 5779, 3308, 2180, 2204, 2205}"
215,0,0,0,0.1079897,"\int \frac{1}{(c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcSinh[c + d*x])^(3/2)),x]","\int \frac{1}{(c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcSinh[x])^(3/2)), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
216,1,437,0,1.5547382,"\int \frac{(c e+d e x)^4}{\left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcSinh[c + d*x])^(5/2),x]","\frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{5/2} d}-\frac{3 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{5/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{24 b^{5/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{5/2} d}-\frac{3 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{5/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{24 b^{5/2} d}-\frac{20 e^4 (c+d x)^5}{3 b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{16 e^4 (c+d x)^3}{3 b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 e^4 \sqrt{(c+d x)^2+1} (c+d x)^4}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}","\frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{5/2} d}-\frac{3 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{5/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{24 b^{5/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{5/2} d}-\frac{3 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{5/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{24 b^{5/2} d}-\frac{20 e^4 (c+d x)^5}{3 b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{16 e^4 (c+d x)^3}{3 b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 e^4 \sqrt{(c+d x)^2+1} (c+d x)^4}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}",1,"(-2*e^4*(c + d*x)^4*Sqrt[1 + (c + d*x)^2])/(3*b*d*(a + b*ArcSinh[c + d*x])^(3/2)) - (16*e^4*(c + d*x)^3)/(3*b^2*d*Sqrt[a + b*ArcSinh[c + d*x]]) - (20*e^4*(c + d*x)^5)/(3*b^2*d*Sqrt[a + b*ArcSinh[c + d*x]]) + (e^4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(12*b^(5/2)*d) - (3*e^4*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(8*b^(5/2)*d) + (5*e^4*E^((5*a)/b)*Sqrt[5*Pi]*Erf[(Sqrt[5]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(24*b^(5/2)*d) + (e^4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(12*b^(5/2)*d*E^(a/b)) - (3*e^4*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(8*b^(5/2)*d*E^((3*a)/b)) + (5*e^4*Sqrt[5*Pi]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(24*b^(5/2)*d*E^((5*a)/b))","A",36,10,25,0.4000,1,"{5865, 12, 5667, 5774, 5669, 5448, 3307, 2180, 2204, 2205}"
217,1,326,0,1.0957858,"\int \frac{(c e+d e x)^3}{\left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcSinh[c + d*x])^(5/2),x]","-\frac{2 \sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{\sqrt{2 \pi } e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{\sqrt{2 \pi } e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{16 e^3 (c+d x)^4}{3 b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{4 e^3 (c+d x)^2}{b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 e^3 \sqrt{(c+d x)^2+1} (c+d x)^3}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}","-\frac{2 \sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{\sqrt{2 \pi } e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{\sqrt{2 \pi } e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{16 e^3 (c+d x)^4}{3 b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{4 e^3 (c+d x)^2}{b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 e^3 \sqrt{(c+d x)^2+1} (c+d x)^3}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}",1,"(-2*e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2])/(3*b*d*(a + b*ArcSinh[c + d*x])^(3/2)) - (4*e^3*(c + d*x)^2)/(b^2*d*Sqrt[a + b*ArcSinh[c + d*x]]) - (16*e^3*(c + d*x)^4)/(3*b^2*d*Sqrt[a + b*ArcSinh[c + d*x]]) - (2*e^3*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d) + (e^3*E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d) + (2*e^3*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d*E^((4*a)/b)) - (e^3*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d*E^((2*a)/b))","A",26,10,25,0.4000,1,"{5865, 12, 5667, 5774, 5669, 5448, 3308, 2180, 2204, 2205}"
218,1,321,0,0.9599632,"\int \frac{(c e+d e x)^2}{\left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcSinh[c + d*x])^(5/2),x]","-\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{6 b^{5/2} d}+\frac{\sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{5/2} d}-\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{6 b^{5/2} d}+\frac{\sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{5/2} d}-\frac{4 e^2 (c+d x)^3}{b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{8 e^2 (c+d x)}{3 b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 e^2 \sqrt{(c+d x)^2+1} (c+d x)^2}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}","-\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{6 b^{5/2} d}+\frac{\sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{5/2} d}-\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{6 b^{5/2} d}+\frac{\sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{5/2} d}-\frac{4 e^2 (c+d x)^3}{b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{8 e^2 (c+d x)}{3 b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 e^2 \sqrt{(c+d x)^2+1} (c+d x)^2}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}",1,"(-2*e^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^2])/(3*b*d*(a + b*ArcSinh[c + d*x])^(3/2)) - (8*e^2*(c + d*x))/(3*b^2*d*Sqrt[a + b*ArcSinh[c + d*x]]) - (4*e^2*(c + d*x)^3)/(b^2*d*Sqrt[a + b*ArcSinh[c + d*x]]) - (e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(6*b^(5/2)*d) + (e^2*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(2*b^(5/2)*d) - (e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(6*b^(5/2)*d*E^(a/b)) + (e^2*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(2*b^(5/2)*d*E^((3*a)/b))","A",24,11,25,0.4400,1,"{5865, 12, 5667, 5774, 5669, 5448, 3307, 2180, 2204, 2205, 5657}"
219,1,209,0,0.5419296,"\int \frac{c e+d e x}{\left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[(c*e + d*e*x)/(a + b*ArcSinh[c + d*x])^(5/2),x]","-\frac{2 \sqrt{2 \pi } e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{2 \pi } e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{8 e (c+d x)^2}{3 b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{4 e}{3 b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 e \sqrt{(c+d x)^2+1} (c+d x)}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}","-\frac{2 \sqrt{2 \pi } e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{2 \pi } e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{8 e (c+d x)^2}{3 b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{4 e}{3 b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 e \sqrt{(c+d x)^2+1} (c+d x)}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}",1,"(-2*e*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(3*b*d*(a + b*ArcSinh[c + d*x])^(3/2)) - (4*e)/(3*b^2*d*Sqrt[a + b*ArcSinh[c + d*x]]) - (8*e*(c + d*x)^2)/(3*b^2*d*Sqrt[a + b*ArcSinh[c + d*x]]) - (2*e*E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d) + (2*e*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(3*b^(5/2)*d*E^((2*a)/b))","A",13,11,23,0.4783,1,"{5865, 12, 5667, 5774, 5669, 5448, 3308, 2180, 2204, 2205, 5675}"
220,1,158,0,0.2845276,"\int \frac{1}{\left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])^(-5/2),x]","\frac{2 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{4 (c+d x)}{3 b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 \sqrt{(c+d x)^2+1}}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}","\frac{2 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{4 (c+d x)}{3 b^2 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 \sqrt{(c+d x)^2+1}}{3 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}",1,"(-2*Sqrt[1 + (c + d*x)^2])/(3*b*d*(a + b*ArcSinh[c + d*x])^(3/2)) - (4*(c + d*x))/(3*b^2*d*Sqrt[a + b*ArcSinh[c + d*x]]) + (2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(3*b^(5/2)*d) + (2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(3*b^(5/2)*d*E^(a/b))","A",9,8,14,0.5714,1,"{5863, 5655, 5774, 5657, 3307, 2180, 2205, 2204}"
221,0,0,0,0.1085166,"\int \frac{1}{(c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcSinh[c + d*x])^(5/2)),x]","\int \frac{1}{(c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcSinh[x])^(5/2)), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
222,1,531,0,1.4674573,"\int \frac{(c e+d e x)^4}{\left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[(c*e + d*e*x)^4/(a + b*ArcSinh[c + d*x])^(7/2),x]","-\frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{30 b^{7/2} d}+\frac{9 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{20 b^{7/2} d}-\frac{5 \sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{7/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{30 b^{7/2} d}-\frac{9 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{20 b^{7/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{7/2} d}-\frac{4 e^4 (c+d x)^5}{3 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{40 e^4 \sqrt{(c+d x)^2+1} (c+d x)^4}{3 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{16 e^4 (c+d x)^3}{15 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{32 e^4 \sqrt{(c+d x)^2+1} (c+d x)^2}{5 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 e^4 \sqrt{(c+d x)^2+1} (c+d x)^4}{5 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}","-\frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{30 b^{7/2} d}+\frac{9 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{20 b^{7/2} d}-\frac{5 \sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{Erf}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{7/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{30 b^{7/2} d}-\frac{9 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{20 b^{7/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left(\frac{\sqrt{5} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{7/2} d}-\frac{4 e^4 (c+d x)^5}{3 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{40 e^4 \sqrt{(c+d x)^2+1} (c+d x)^4}{3 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{16 e^4 (c+d x)^3}{15 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{32 e^4 \sqrt{(c+d x)^2+1} (c+d x)^2}{5 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 e^4 \sqrt{(c+d x)^2+1} (c+d x)^4}{5 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}",1,"(-2*e^4*(c + d*x)^4*Sqrt[1 + (c + d*x)^2])/(5*b*d*(a + b*ArcSinh[c + d*x])^(5/2)) - (16*e^4*(c + d*x)^3)/(15*b^2*d*(a + b*ArcSinh[c + d*x])^(3/2)) - (4*e^4*(c + d*x)^5)/(3*b^2*d*(a + b*ArcSinh[c + d*x])^(3/2)) - (32*e^4*(c + d*x)^2*Sqrt[1 + (c + d*x)^2])/(5*b^3*d*Sqrt[a + b*ArcSinh[c + d*x]]) - (40*e^4*(c + d*x)^4*Sqrt[1 + (c + d*x)^2])/(3*b^3*d*Sqrt[a + b*ArcSinh[c + d*x]]) - (e^4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(30*b^(7/2)*d) + (9*e^4*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(20*b^(7/2)*d) - (5*e^4*E^((5*a)/b)*Sqrt[5*Pi]*Erf[(Sqrt[5]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(12*b^(7/2)*d) + (e^4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(30*b^(7/2)*d*E^(a/b)) - (9*e^4*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(20*b^(7/2)*d*E^((3*a)/b)) + (5*e^4*Sqrt[5*Pi]*Erfi[(Sqrt[5]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(12*b^(7/2)*d*E^((5*a)/b))","A",34,9,25,0.3600,1,"{5865, 12, 5667, 5774, 5665, 3308, 2180, 2204, 2205}"
223,1,420,0,1.0981875,"\int \frac{(c e+d e x)^3}{\left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[(c*e + d*e*x)^3/(a + b*ArcSinh[c + d*x])^(7/2),x]","\frac{16 \sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{4 \sqrt{2 \pi } e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{16 \sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{4 \sqrt{2 \pi } e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{16 e^3 (c+d x)^4}{15 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{128 e^3 \sqrt{(c+d x)^2+1} (c+d x)^3}{15 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{4 e^3 (c+d x)^2}{5 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{16 e^3 \sqrt{(c+d x)^2+1} (c+d x)}{5 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 e^3 \sqrt{(c+d x)^2+1} (c+d x)^3}{5 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}","\frac{16 \sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{Erf}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{4 \sqrt{2 \pi } e^3 e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{16 \sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{Erfi}\left(\frac{2 \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{4 \sqrt{2 \pi } e^3 e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{16 e^3 (c+d x)^4}{15 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{128 e^3 \sqrt{(c+d x)^2+1} (c+d x)^3}{15 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{4 e^3 (c+d x)^2}{5 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{16 e^3 \sqrt{(c+d x)^2+1} (c+d x)}{5 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 e^3 \sqrt{(c+d x)^2+1} (c+d x)^3}{5 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}",1,"(-2*e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2])/(5*b*d*(a + b*ArcSinh[c + d*x])^(5/2)) - (4*e^3*(c + d*x)^2)/(5*b^2*d*(a + b*ArcSinh[c + d*x])^(3/2)) - (16*e^3*(c + d*x)^4)/(15*b^2*d*(a + b*ArcSinh[c + d*x])^(3/2)) - (16*e^3*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(5*b^3*d*Sqrt[a + b*ArcSinh[c + d*x]]) - (128*e^3*(c + d*x)^3*Sqrt[1 + (c + d*x)^2])/(15*b^3*d*Sqrt[a + b*ArcSinh[c + d*x]]) + (16*e^3*E^((4*a)/b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d) - (4*e^3*E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d) + (16*e^3*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d*E^((4*a)/b)) - (4*e^3*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d*E^((2*a)/b))","A",23,9,25,0.3600,1,"{5865, 12, 5667, 5774, 5665, 3307, 2180, 2204, 2205}"
224,1,410,0,1.1097972,"\int \frac{(c e+d e x)^2}{\left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[(c*e + d*e*x)^2/(a + b*ArcSinh[c + d*x])^(7/2),x]","\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{3 \sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{5 b^{7/2} d}-\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{3 \sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{5 b^{7/2} d}-\frac{4 e^2 (c+d x)^3}{5 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{24 e^2 \sqrt{(c+d x)^2+1} (c+d x)^2}{5 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{8 e^2 (c+d x)}{15 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{16 e^2 \sqrt{(c+d x)^2+1}}{15 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 e^2 \sqrt{(c+d x)^2+1} (c+d x)^2}{5 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}","\frac{\sqrt{\pi } e^2 e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{3 \sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{Erf}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{5 b^{7/2} d}-\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{3 \sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{5 b^{7/2} d}-\frac{4 e^2 (c+d x)^3}{5 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{24 e^2 \sqrt{(c+d x)^2+1} (c+d x)^2}{5 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{8 e^2 (c+d x)}{15 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{16 e^2 \sqrt{(c+d x)^2+1}}{15 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 e^2 \sqrt{(c+d x)^2+1} (c+d x)^2}{5 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}",1,"(-2*e^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^2])/(5*b*d*(a + b*ArcSinh[c + d*x])^(5/2)) - (8*e^2*(c + d*x))/(15*b^2*d*(a + b*ArcSinh[c + d*x])^(3/2)) - (4*e^2*(c + d*x)^3)/(5*b^2*d*(a + b*ArcSinh[c + d*x])^(3/2)) - (16*e^2*Sqrt[1 + (c + d*x)^2])/(15*b^3*d*Sqrt[a + b*ArcSinh[c + d*x]]) - (24*e^2*(c + d*x)^2*Sqrt[1 + (c + d*x)^2])/(5*b^3*d*Sqrt[a + b*ArcSinh[c + d*x]]) + (e^2*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(15*b^(7/2)*d) - (3*e^2*E^((3*a)/b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(5*b^(7/2)*d) - (e^2*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(15*b^(7/2)*d*E^(a/b)) + (3*e^2*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(5*b^(7/2)*d*E^((3*a)/b))","A",24,11,25,0.4400,1,"{5865, 12, 5667, 5774, 5665, 3308, 2180, 2204, 2205, 5655, 5779}"
225,1,252,0,0.5622135,"\int \frac{c e+d e x}{\left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[(c*e + d*e*x)/(a + b*ArcSinh[c + d*x])^(7/2),x]","\frac{8 \sqrt{2 \pi } e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{8 \sqrt{2 \pi } e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{8 e (c+d x)^2}{15 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{32 e \sqrt{(c+d x)^2+1} (c+d x)}{15 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{4 e}{15 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{2 e \sqrt{(c+d x)^2+1} (c+d x)}{5 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}","\frac{8 \sqrt{2 \pi } e e^{\frac{2 a}{b}} \text{Erf}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{8 \sqrt{2 \pi } e e^{-\frac{2 a}{b}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{8 e (c+d x)^2}{15 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{32 e \sqrt{(c+d x)^2+1} (c+d x)}{15 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{4 e}{15 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{2 e \sqrt{(c+d x)^2+1} (c+d x)}{5 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}",1,"(-2*e*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(5*b*d*(a + b*ArcSinh[c + d*x])^(5/2)) - (4*e)/(15*b^2*d*(a + b*ArcSinh[c + d*x])^(3/2)) - (8*e*(c + d*x)^2)/(15*b^2*d*(a + b*ArcSinh[c + d*x])^(3/2)) - (32*e*(c + d*x)*Sqrt[1 + (c + d*x)^2])/(15*b^3*d*Sqrt[a + b*ArcSinh[c + d*x]]) + (8*e*E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d) + (8*e*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcSinh[c + d*x]])/Sqrt[b]])/(15*b^(7/2)*d*E^((2*a)/b))","A",11,10,23,0.4348,1,"{5865, 12, 5667, 5774, 5665, 3307, 2180, 2204, 2205, 5675}"
226,1,195,0,0.4653659,"\int \frac{1}{\left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])^(-7/2),x]","-\frac{4 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 \sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{4 (c+d x)}{15 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{8 \sqrt{(c+d x)^2+1}}{15 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 \sqrt{(c+d x)^2+1}}{5 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}","-\frac{4 \sqrt{\pi } e^{a/b} \text{Erf}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 \sqrt{\pi } e^{-\frac{a}{b}} \text{Erfi}\left(\frac{\sqrt{a+b \sinh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{4 (c+d x)}{15 b^2 d \left(a+b \sinh ^{-1}(c+d x)\right)^{3/2}}-\frac{8 \sqrt{(c+d x)^2+1}}{15 b^3 d \sqrt{a+b \sinh ^{-1}(c+d x)}}-\frac{2 \sqrt{(c+d x)^2+1}}{5 b d \left(a+b \sinh ^{-1}(c+d x)\right)^{5/2}}",1,"(-2*Sqrt[1 + (c + d*x)^2])/(5*b*d*(a + b*ArcSinh[c + d*x])^(5/2)) - (4*(c + d*x))/(15*b^2*d*(a + b*ArcSinh[c + d*x])^(3/2)) - (8*Sqrt[1 + (c + d*x)^2])/(15*b^3*d*Sqrt[a + b*ArcSinh[c + d*x]]) - (4*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(15*b^(7/2)*d) + (4*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcSinh[c + d*x]]/Sqrt[b]])/(15*b^(7/2)*d*E^(a/b))","A",10,8,14,0.5714,1,"{5863, 5655, 5774, 5779, 3308, 2180, 2204, 2205}"
227,0,0,0,0.1172965,"\int \frac{1}{(c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}} \, dx","Int[1/((c*e + d*e*x)*(a + b*ArcSinh[c + d*x])^(7/2)),x]","\int \frac{1}{(c e+d e x) \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \sinh ^{-1}(c+d x)\right)^{7/2}},x\right)}{e}",0,"Defer[Subst][Defer[Int][1/(x*(a + b*ArcSinh[x])^(7/2)), x], x, c + d*x]/(d*e)","A",0,0,0,0,-1,"{}"
228,1,298,0,0.3322066,"\int (c e+d e x)^{7/2} \left(a+b \sinh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^(7/2)*(a + b*ArcSinh[c + d*x]),x]","\frac{2 (e (c+d x))^{9/2} \left(a+b \sinh ^{-1}(c+d x)\right)}{9 d e}+\frac{28 b e^2 \sqrt{(c+d x)^2+1} (e (c+d x))^{3/2}}{405 d}-\frac{28 b e^3 \sqrt{(c+d x)^2+1} \sqrt{e (c+d x)}}{135 d (c+d x+1)}-\frac{14 b e^{7/2} (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{135 d \sqrt{(c+d x)^2+1}}+\frac{28 b e^{7/2} (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{135 d \sqrt{(c+d x)^2+1}}-\frac{4 b \sqrt{(c+d x)^2+1} (e (c+d x))^{7/2}}{81 d}","\frac{2 (e (c+d x))^{9/2} \left(a+b \sinh ^{-1}(c+d x)\right)}{9 d e}+\frac{28 b e^2 \sqrt{(c+d x)^2+1} (e (c+d x))^{3/2}}{405 d}-\frac{28 b e^3 \sqrt{(c+d x)^2+1} \sqrt{e (c+d x)}}{135 d (c+d x+1)}-\frac{14 b e^{7/2} (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{135 d \sqrt{(c+d x)^2+1}}+\frac{28 b e^{7/2} (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{135 d \sqrt{(c+d x)^2+1}}-\frac{4 b \sqrt{(c+d x)^2+1} (e (c+d x))^{7/2}}{81 d}",1,"(28*b*e^2*(e*(c + d*x))^(3/2)*Sqrt[1 + (c + d*x)^2])/(405*d) - (4*b*(e*(c + d*x))^(7/2)*Sqrt[1 + (c + d*x)^2])/(81*d) - (28*b*e^3*Sqrt[e*(c + d*x)]*Sqrt[1 + (c + d*x)^2])/(135*d*(1 + c + d*x)) + (2*(e*(c + d*x))^(9/2)*(a + b*ArcSinh[c + d*x]))/(9*d*e) + (28*b*e^(7/2)*(1 + c + d*x)*Sqrt[(1 + (c + d*x)^2)/(1 + c + d*x)^2]*EllipticE[2*ArcTan[Sqrt[e*(c + d*x)]/Sqrt[e]], 1/2])/(135*d*Sqrt[1 + (c + d*x)^2]) - (14*b*e^(7/2)*(1 + c + d*x)*Sqrt[(1 + (c + d*x)^2)/(1 + c + d*x)^2]*EllipticF[2*ArcTan[Sqrt[e*(c + d*x)]/Sqrt[e]], 1/2])/(135*d*Sqrt[1 + (c + d*x)^2])","A",8,7,23,0.3043,1,"{5865, 5661, 321, 329, 305, 220, 1196}"
229,1,177,0,0.1594049,"\int (c e+d e x)^{5/2} \left(a+b \sinh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^(5/2)*(a + b*ArcSinh[c + d*x]),x]","\frac{2 (e (c+d x))^{7/2} \left(a+b \sinh ^{-1}(c+d x)\right)}{7 d e}+\frac{20 b e^2 \sqrt{(c+d x)^2+1} \sqrt{e (c+d x)}}{147 d}-\frac{10 b e^{5/2} (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{147 d \sqrt{(c+d x)^2+1}}-\frac{4 b \sqrt{(c+d x)^2+1} (e (c+d x))^{5/2}}{49 d}","\frac{2 (e (c+d x))^{7/2} \left(a+b \sinh ^{-1}(c+d x)\right)}{7 d e}+\frac{20 b e^2 \sqrt{(c+d x)^2+1} \sqrt{e (c+d x)}}{147 d}-\frac{10 b e^{5/2} (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{147 d \sqrt{(c+d x)^2+1}}-\frac{4 b \sqrt{(c+d x)^2+1} (e (c+d x))^{5/2}}{49 d}",1,"(20*b*e^2*Sqrt[e*(c + d*x)]*Sqrt[1 + (c + d*x)^2])/(147*d) - (4*b*(e*(c + d*x))^(5/2)*Sqrt[1 + (c + d*x)^2])/(49*d) + (2*(e*(c + d*x))^(7/2)*(a + b*ArcSinh[c + d*x]))/(7*d*e) - (10*b*e^(5/2)*(1 + c + d*x)*Sqrt[(1 + (c + d*x)^2)/(1 + c + d*x)^2]*EllipticF[2*ArcTan[Sqrt[e*(c + d*x)]/Sqrt[e]], 1/2])/(147*d*Sqrt[1 + (c + d*x)^2])","A",6,5,23,0.2174,1,"{5865, 5661, 321, 329, 220}"
230,1,261,0,0.2426097,"\int (c e+d e x)^{3/2} \left(a+b \sinh ^{-1}(c+d x)\right) \, dx","Int[(c*e + d*e*x)^(3/2)*(a + b*ArcSinh[c + d*x]),x]","\frac{2 (e (c+d x))^{5/2} \left(a+b \sinh ^{-1}(c+d x)\right)}{5 d e}+\frac{6 b e^{3/2} (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{25 d \sqrt{(c+d x)^2+1}}-\frac{12 b e^{3/2} (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{25 d \sqrt{(c+d x)^2+1}}-\frac{4 b \sqrt{(c+d x)^2+1} (e (c+d x))^{3/2}}{25 d}+\frac{12 b e \sqrt{(c+d x)^2+1} \sqrt{e (c+d x)}}{25 d (c+d x+1)}","\frac{2 (e (c+d x))^{5/2} \left(a+b \sinh ^{-1}(c+d x)\right)}{5 d e}+\frac{6 b e^{3/2} (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{25 d \sqrt{(c+d x)^2+1}}-\frac{12 b e^{3/2} (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{25 d \sqrt{(c+d x)^2+1}}-\frac{4 b \sqrt{(c+d x)^2+1} (e (c+d x))^{3/2}}{25 d}+\frac{12 b e \sqrt{(c+d x)^2+1} \sqrt{e (c+d x)}}{25 d (c+d x+1)}",1,"(-4*b*(e*(c + d*x))^(3/2)*Sqrt[1 + (c + d*x)^2])/(25*d) + (12*b*e*Sqrt[e*(c + d*x)]*Sqrt[1 + (c + d*x)^2])/(25*d*(1 + c + d*x)) + (2*(e*(c + d*x))^(5/2)*(a + b*ArcSinh[c + d*x]))/(5*d*e) - (12*b*e^(3/2)*(1 + c + d*x)*Sqrt[(1 + (c + d*x)^2)/(1 + c + d*x)^2]*EllipticE[2*ArcTan[Sqrt[e*(c + d*x)]/Sqrt[e]], 1/2])/(25*d*Sqrt[1 + (c + d*x)^2]) + (6*b*e^(3/2)*(1 + c + d*x)*Sqrt[(1 + (c + d*x)^2)/(1 + c + d*x)^2]*EllipticF[2*ArcTan[Sqrt[e*(c + d*x)]/Sqrt[e]], 1/2])/(25*d*Sqrt[1 + (c + d*x)^2])","A",7,7,23,0.3043,1,"{5865, 5661, 321, 329, 305, 220, 1196}"
231,1,142,0,0.1263901,"\int \sqrt{c e+d e x} \left(a+b \sinh ^{-1}(c+d x)\right) \, dx","Int[Sqrt[c*e + d*e*x]*(a + b*ArcSinh[c + d*x]),x]","\frac{2 (e (c+d x))^{3/2} \left(a+b \sinh ^{-1}(c+d x)\right)}{3 d e}-\frac{4 b \sqrt{(c+d x)^2+1} \sqrt{e (c+d x)}}{9 d}+\frac{2 b \sqrt{e} (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{9 d \sqrt{(c+d x)^2+1}}","\frac{2 (e (c+d x))^{3/2} \left(a+b \sinh ^{-1}(c+d x)\right)}{3 d e}-\frac{4 b \sqrt{(c+d x)^2+1} \sqrt{e (c+d x)}}{9 d}+\frac{2 b \sqrt{e} (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{9 d \sqrt{(c+d x)^2+1}}",1,"(-4*b*Sqrt[e*(c + d*x)]*Sqrt[1 + (c + d*x)^2])/(9*d) + (2*(e*(c + d*x))^(3/2)*(a + b*ArcSinh[c + d*x]))/(3*d*e) + (2*b*Sqrt[e]*(1 + c + d*x)*Sqrt[(1 + (c + d*x)^2)/(1 + c + d*x)^2]*EllipticF[2*ArcTan[Sqrt[e*(c + d*x)]/Sqrt[e]], 1/2])/(9*d*Sqrt[1 + (c + d*x)^2])","A",5,5,23,0.2174,1,"{5865, 5661, 321, 329, 220}"
232,1,223,0,0.2116098,"\int \frac{a+b \sinh ^{-1}(c+d x)}{\sqrt{c e+d e x}} \, dx","Int[(a + b*ArcSinh[c + d*x])/Sqrt[c*e + d*e*x],x]","\frac{2 \sqrt{e (c+d x)} \left(a+b \sinh ^{-1}(c+d x)\right)}{d e}-\frac{4 b \sqrt{(c+d x)^2+1} \sqrt{e (c+d x)}}{d e (c+d x+1)}-\frac{2 b (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{d \sqrt{e} \sqrt{(c+d x)^2+1}}+\frac{4 b (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{d \sqrt{e} \sqrt{(c+d x)^2+1}}","\frac{2 \sqrt{e (c+d x)} \left(a+b \sinh ^{-1}(c+d x)\right)}{d e}-\frac{4 b \sqrt{(c+d x)^2+1} \sqrt{e (c+d x)}}{d e (c+d x+1)}-\frac{2 b (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{d \sqrt{e} \sqrt{(c+d x)^2+1}}+\frac{4 b (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{d \sqrt{e} \sqrt{(c+d x)^2+1}}",1,"(-4*b*Sqrt[e*(c + d*x)]*Sqrt[1 + (c + d*x)^2])/(d*e*(1 + c + d*x)) + (2*Sqrt[e*(c + d*x)]*(a + b*ArcSinh[c + d*x]))/(d*e) + (4*b*(1 + c + d*x)*Sqrt[(1 + (c + d*x)^2)/(1 + c + d*x)^2]*EllipticE[2*ArcTan[Sqrt[e*(c + d*x)]/Sqrt[e]], 1/2])/(d*Sqrt[e]*Sqrt[1 + (c + d*x)^2]) - (2*b*(1 + c + d*x)*Sqrt[(1 + (c + d*x)^2)/(1 + c + d*x)^2]*EllipticF[2*ArcTan[Sqrt[e*(c + d*x)]/Sqrt[e]], 1/2])/(d*Sqrt[e]*Sqrt[1 + (c + d*x)^2])","A",6,6,23,0.2609,1,"{5865, 5661, 329, 305, 220, 1196}"
233,1,106,0,0.1126148,"\int \frac{a+b \sinh ^{-1}(c+d x)}{(c e+d e x)^{3/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])/(c*e + d*e*x)^(3/2),x]","\frac{2 b (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{d e^{3/2} \sqrt{(c+d x)^2+1}}-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{d e \sqrt{e (c+d x)}}","\frac{2 b (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{d e^{3/2} \sqrt{(c+d x)^2+1}}-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{d e \sqrt{e (c+d x)}}",1,"(-2*(a + b*ArcSinh[c + d*x]))/(d*e*Sqrt[e*(c + d*x)]) + (2*b*(1 + c + d*x)*Sqrt[(1 + (c + d*x)^2)/(1 + c + d*x)^2]*EllipticF[2*ArcTan[Sqrt[e*(c + d*x)]/Sqrt[e]], 1/2])/(d*e^(3/2)*Sqrt[1 + (c + d*x)^2])","A",4,4,23,0.1739,1,"{5865, 5661, 329, 220}"
234,1,266,0,0.2376508,"\int \frac{a+b \sinh ^{-1}(c+d x)}{(c e+d e x)^{5/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])/(c*e + d*e*x)^(5/2),x]","-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{3 d e (e (c+d x))^{3/2}}-\frac{4 b \sqrt{(c+d x)^2+1}}{3 d e^2 \sqrt{e (c+d x)}}+\frac{4 b \sqrt{(c+d x)^2+1} \sqrt{e (c+d x)}}{3 d e^3 (c+d x+1)}+\frac{2 b (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{3 d e^{5/2} \sqrt{(c+d x)^2+1}}-\frac{4 b (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{3 d e^{5/2} \sqrt{(c+d x)^2+1}}","-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{3 d e (e (c+d x))^{3/2}}-\frac{4 b \sqrt{(c+d x)^2+1}}{3 d e^2 \sqrt{e (c+d x)}}+\frac{4 b \sqrt{(c+d x)^2+1} \sqrt{e (c+d x)}}{3 d e^3 (c+d x+1)}+\frac{2 b (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{3 d e^{5/2} \sqrt{(c+d x)^2+1}}-\frac{4 b (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{3 d e^{5/2} \sqrt{(c+d x)^2+1}}",1,"(-4*b*Sqrt[1 + (c + d*x)^2])/(3*d*e^2*Sqrt[e*(c + d*x)]) + (4*b*Sqrt[e*(c + d*x)]*Sqrt[1 + (c + d*x)^2])/(3*d*e^3*(1 + c + d*x)) - (2*(a + b*ArcSinh[c + d*x]))/(3*d*e*(e*(c + d*x))^(3/2)) - (4*b*(1 + c + d*x)*Sqrt[(1 + (c + d*x)^2)/(1 + c + d*x)^2]*EllipticE[2*ArcTan[Sqrt[e*(c + d*x)]/Sqrt[e]], 1/2])/(3*d*e^(5/2)*Sqrt[1 + (c + d*x)^2]) + (2*b*(1 + c + d*x)*Sqrt[(1 + (c + d*x)^2)/(1 + c + d*x)^2]*EllipticF[2*ArcTan[Sqrt[e*(c + d*x)]/Sqrt[e]], 1/2])/(3*d*e^(5/2)*Sqrt[1 + (c + d*x)^2])","A",7,7,23,0.3043,1,"{5865, 5661, 325, 329, 305, 220, 1196}"
235,1,145,0,0.135654,"\int \frac{a+b \sinh ^{-1}(c+d x)}{(c e+d e x)^{7/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])/(c*e + d*e*x)^(7/2),x]","-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{5 d e (e (c+d x))^{5/2}}-\frac{4 b \sqrt{(c+d x)^2+1}}{15 d e^2 (e (c+d x))^{3/2}}-\frac{2 b (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{15 d e^{7/2} \sqrt{(c+d x)^2+1}}","-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)}{5 d e (e (c+d x))^{5/2}}-\frac{4 b \sqrt{(c+d x)^2+1}}{15 d e^2 (e (c+d x))^{3/2}}-\frac{2 b (c+d x+1) \sqrt{\frac{(c+d x)^2+1}{(c+d x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)|\frac{1}{2}\right)}{15 d e^{7/2} \sqrt{(c+d x)^2+1}}",1,"(-4*b*Sqrt[1 + (c + d*x)^2])/(15*d*e^2*(e*(c + d*x))^(3/2)) - (2*(a + b*ArcSinh[c + d*x]))/(5*d*e*(e*(c + d*x))^(5/2)) - (2*b*(1 + c + d*x)*Sqrt[(1 + (c + d*x)^2)/(1 + c + d*x)^2]*EllipticF[2*ArcTan[Sqrt[e*(c + d*x)]/Sqrt[e]], 1/2])/(15*d*e^(7/2)*Sqrt[1 + (c + d*x)^2])","A",5,5,23,0.2174,1,"{5865, 5661, 325, 329, 220}"
236,1,134,0,0.2120176,"\int (c e+d e x)^{7/2} \left(a+b \sinh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^(7/2)*(a + b*ArcSinh[c + d*x])^2,x]","\frac{16 b^2 (e (c+d x))^{13/2} \, _3F_2\left(1,\frac{13}{4},\frac{13}{4};\frac{15}{4},\frac{17}{4};-(c+d x)^2\right)}{1287 d e^3}-\frac{8 b (e (c+d x))^{11/2} \, _2F_1\left(\frac{1}{2},\frac{11}{4};\frac{15}{4};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{99 d e^2}+\frac{2 (e (c+d x))^{9/2} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{9 d e}","\frac{16 b^2 (e (c+d x))^{13/2} \, _3F_2\left(1,\frac{13}{4},\frac{13}{4};\frac{15}{4},\frac{17}{4};-(c+d x)^2\right)}{1287 d e^3}-\frac{8 b (e (c+d x))^{11/2} \, _2F_1\left(\frac{1}{2},\frac{11}{4};\frac{15}{4};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{99 d e^2}+\frac{2 (e (c+d x))^{9/2} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{9 d e}",1,"(2*(e*(c + d*x))^(9/2)*(a + b*ArcSinh[c + d*x])^2)/(9*d*e) - (8*b*(e*(c + d*x))^(11/2)*(a + b*ArcSinh[c + d*x])*Hypergeometric2F1[1/2, 11/4, 15/4, -(c + d*x)^2])/(99*d*e^2) + (16*b^2*(e*(c + d*x))^(13/2)*HypergeometricPFQ[{1, 13/4, 13/4}, {15/4, 17/4}, -(c + d*x)^2])/(1287*d*e^3)","A",3,3,25,0.1200,1,"{5865, 5661, 5762}"
237,1,134,0,0.2212391,"\int (c e+d e x)^{5/2} \left(a+b \sinh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^(5/2)*(a + b*ArcSinh[c + d*x])^2,x]","\frac{16 b^2 (e (c+d x))^{11/2} \, _3F_2\left(1,\frac{11}{4},\frac{11}{4};\frac{13}{4},\frac{15}{4};-(c+d x)^2\right)}{693 d e^3}-\frac{8 b (e (c+d x))^{9/2} \, _2F_1\left(\frac{1}{2},\frac{9}{4};\frac{13}{4};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{63 d e^2}+\frac{2 (e (c+d x))^{7/2} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{7 d e}","\frac{16 b^2 (e (c+d x))^{11/2} \, _3F_2\left(1,\frac{11}{4},\frac{11}{4};\frac{13}{4},\frac{15}{4};-(c+d x)^2\right)}{693 d e^3}-\frac{8 b (e (c+d x))^{9/2} \, _2F_1\left(\frac{1}{2},\frac{9}{4};\frac{13}{4};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{63 d e^2}+\frac{2 (e (c+d x))^{7/2} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{7 d e}",1,"(2*(e*(c + d*x))^(7/2)*(a + b*ArcSinh[c + d*x])^2)/(7*d*e) - (8*b*(e*(c + d*x))^(9/2)*(a + b*ArcSinh[c + d*x])*Hypergeometric2F1[1/2, 9/4, 13/4, -(c + d*x)^2])/(63*d*e^2) + (16*b^2*(e*(c + d*x))^(11/2)*HypergeometricPFQ[{1, 11/4, 11/4}, {13/4, 15/4}, -(c + d*x)^2])/(693*d*e^3)","A",3,3,25,0.1200,1,"{5865, 5661, 5762}"
238,1,134,0,0.2166965,"\int (c e+d e x)^{3/2} \left(a+b \sinh ^{-1}(c+d x)\right)^2 \, dx","Int[(c*e + d*e*x)^(3/2)*(a + b*ArcSinh[c + d*x])^2,x]","\frac{16 b^2 (e (c+d x))^{9/2} \, _3F_2\left(1,\frac{9}{4},\frac{9}{4};\frac{11}{4},\frac{13}{4};-(c+d x)^2\right)}{315 d e^3}-\frac{8 b (e (c+d x))^{7/2} \, _2F_1\left(\frac{1}{2},\frac{7}{4};\frac{11}{4};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{35 d e^2}+\frac{2 (e (c+d x))^{5/2} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{5 d e}","\frac{16 b^2 (e (c+d x))^{9/2} \, _3F_2\left(1,\frac{9}{4},\frac{9}{4};\frac{11}{4},\frac{13}{4};-(c+d x)^2\right)}{315 d e^3}-\frac{8 b (e (c+d x))^{7/2} \, _2F_1\left(\frac{1}{2},\frac{7}{4};\frac{11}{4};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{35 d e^2}+\frac{2 (e (c+d x))^{5/2} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{5 d e}",1,"(2*(e*(c + d*x))^(5/2)*(a + b*ArcSinh[c + d*x])^2)/(5*d*e) - (8*b*(e*(c + d*x))^(7/2)*(a + b*ArcSinh[c + d*x])*Hypergeometric2F1[1/2, 7/4, 11/4, -(c + d*x)^2])/(35*d*e^2) + (16*b^2*(e*(c + d*x))^(9/2)*HypergeometricPFQ[{1, 9/4, 9/4}, {11/4, 13/4}, -(c + d*x)^2])/(315*d*e^3)","A",3,3,25,0.1200,1,"{5865, 5661, 5762}"
239,1,134,0,0.2094084,"\int \sqrt{c e+d e x} \left(a+b \sinh ^{-1}(c+d x)\right)^2 \, dx","Int[Sqrt[c*e + d*e*x]*(a + b*ArcSinh[c + d*x])^2,x]","\frac{16 b^2 (e (c+d x))^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};-(c+d x)^2\right)}{105 d e^3}-\frac{8 b (e (c+d x))^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{15 d e^2}+\frac{2 (e (c+d x))^{3/2} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{3 d e}","\frac{16 b^2 (e (c+d x))^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};-(c+d x)^2\right)}{105 d e^3}-\frac{8 b (e (c+d x))^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{15 d e^2}+\frac{2 (e (c+d x))^{3/2} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{3 d e}",1,"(2*(e*(c + d*x))^(3/2)*(a + b*ArcSinh[c + d*x])^2)/(3*d*e) - (8*b*(e*(c + d*x))^(5/2)*(a + b*ArcSinh[c + d*x])*Hypergeometric2F1[1/2, 5/4, 9/4, -(c + d*x)^2])/(15*d*e^2) + (16*b^2*(e*(c + d*x))^(7/2)*HypergeometricPFQ[{1, 7/4, 7/4}, {9/4, 11/4}, -(c + d*x)^2])/(105*d*e^3)","A",3,3,25,0.1200,1,"{5865, 5661, 5762}"
240,1,132,0,0.2026698,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{\sqrt{c e+d e x}} \, dx","Int[(a + b*ArcSinh[c + d*x])^2/Sqrt[c*e + d*e*x],x]","\frac{16 b^2 (e (c+d x))^{5/2} \, _3F_2\left(1,\frac{5}{4},\frac{5}{4};\frac{7}{4},\frac{9}{4};-(c+d x)^2\right)}{15 d e^3}-\frac{8 b (e (c+d x))^{3/2} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{3 d e^2}+\frac{2 \sqrt{e (c+d x)} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e}","\frac{16 b^2 (e (c+d x))^{5/2} \, _3F_2\left(1,\frac{5}{4},\frac{5}{4};\frac{7}{4},\frac{9}{4};-(c+d x)^2\right)}{15 d e^3}-\frac{8 b (e (c+d x))^{3/2} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{3 d e^2}+\frac{2 \sqrt{e (c+d x)} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e}",1,"(2*Sqrt[e*(c + d*x)]*(a + b*ArcSinh[c + d*x])^2)/(d*e) - (8*b*(e*(c + d*x))^(3/2)*(a + b*ArcSinh[c + d*x])*Hypergeometric2F1[1/2, 3/4, 7/4, -(c + d*x)^2])/(3*d*e^2) + (16*b^2*(e*(c + d*x))^(5/2)*HypergeometricPFQ[{1, 5/4, 5/4}, {7/4, 9/4}, -(c + d*x)^2])/(15*d*e^3)","A",3,3,25,0.1200,1,"{5865, 5661, 5762}"
241,1,130,0,0.2216975,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{(c e+d e x)^{3/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])^2/(c*e + d*e*x)^(3/2),x]","-\frac{16 b^2 (e (c+d x))^{3/2} \, _3F_2\left(\frac{3}{4},\frac{3}{4},1;\frac{5}{4},\frac{7}{4};-(c+d x)^2\right)}{3 d e^3}+\frac{8 b \sqrt{e (c+d x)} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^2}-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e \sqrt{e (c+d x)}}","-\frac{16 b^2 (e (c+d x))^{3/2} \, _3F_2\left(\frac{3}{4},\frac{3}{4},1;\frac{5}{4},\frac{7}{4};-(c+d x)^2\right)}{3 d e^3}+\frac{8 b \sqrt{e (c+d x)} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{d e^2}-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{d e \sqrt{e (c+d x)}}",1,"(-2*(a + b*ArcSinh[c + d*x])^2)/(d*e*Sqrt[e*(c + d*x)]) + (8*b*Sqrt[e*(c + d*x)]*(a + b*ArcSinh[c + d*x])*Hypergeometric2F1[1/4, 1/2, 5/4, -(c + d*x)^2])/(d*e^2) - (16*b^2*(e*(c + d*x))^(3/2)*HypergeometricPFQ[{3/4, 3/4, 1}, {5/4, 7/4}, -(c + d*x)^2])/(3*d*e^3)","A",3,3,25,0.1200,1,"{5865, 5661, 5762}"
242,1,134,0,0.2261325,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{(c e+d e x)^{5/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])^2/(c*e + d*e*x)^(5/2),x]","\frac{16 b^2 \sqrt{e (c+d x)} \, _3F_2\left(\frac{1}{4},\frac{1}{4},1;\frac{3}{4},\frac{5}{4};-(c+d x)^2\right)}{3 d e^3}-\frac{8 b \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{3 d e^2 \sqrt{e (c+d x)}}-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{3 d e (e (c+d x))^{3/2}}","\frac{16 b^2 \sqrt{e (c+d x)} \, _3F_2\left(\frac{1}{4},\frac{1}{4},1;\frac{3}{4},\frac{5}{4};-(c+d x)^2\right)}{3 d e^3}-\frac{8 b \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{3 d e^2 \sqrt{e (c+d x)}}-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{3 d e (e (c+d x))^{3/2}}",1,"(-2*(a + b*ArcSinh[c + d*x])^2)/(3*d*e*(e*(c + d*x))^(3/2)) - (8*b*(a + b*ArcSinh[c + d*x])*Hypergeometric2F1[-1/4, 1/2, 3/4, -(c + d*x)^2])/(3*d*e^2*Sqrt[e*(c + d*x)]) + (16*b^2*Sqrt[e*(c + d*x)]*HypergeometricPFQ[{1/4, 1/4, 1}, {3/4, 5/4}, -(c + d*x)^2])/(3*d*e^3)","A",3,3,25,0.1200,1,"{5865, 5661, 5762}"
243,1,134,0,0.229618,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{(c e+d e x)^{7/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])^2/(c*e + d*e*x)^(7/2),x]","-\frac{16 b^2 \, _3F_2\left(-\frac{1}{4},-\frac{1}{4},1;\frac{1}{4},\frac{3}{4};-(c+d x)^2\right)}{15 d e^3 \sqrt{e (c+d x)}}-\frac{8 b \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{15 d e^2 (e (c+d x))^{3/2}}-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{5 d e (e (c+d x))^{5/2}}","-\frac{16 b^2 \, _3F_2\left(-\frac{1}{4},-\frac{1}{4},1;\frac{1}{4},\frac{3}{4};-(c+d x)^2\right)}{15 d e^3 \sqrt{e (c+d x)}}-\frac{8 b \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};-(c+d x)^2\right) \left(a+b \sinh ^{-1}(c+d x)\right)}{15 d e^2 (e (c+d x))^{3/2}}-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)^2}{5 d e (e (c+d x))^{5/2}}",1,"(-2*(a + b*ArcSinh[c + d*x])^2)/(5*d*e*(e*(c + d*x))^(5/2)) - (8*b*(a + b*ArcSinh[c + d*x])*Hypergeometric2F1[-3/4, 1/2, 1/4, -(c + d*x)^2])/(15*d*e^2*(e*(c + d*x))^(3/2)) - (16*b^2*HypergeometricPFQ[{-1/4, -1/4, 1}, {1/4, 3/4}, -(c + d*x)^2])/(15*d*e^3*Sqrt[e*(c + d*x)])","A",3,3,25,0.1200,1,"{5865, 5661, 5762}"
244,0,0,0,0.2075658,"\int (c e+d e x)^{7/2} \left(a+b \sinh ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^(7/2)*(a + b*ArcSinh[c + d*x])^3,x]","\int (c e+d e x)^{7/2} \left(a+b \sinh ^{-1}(c+d x)\right)^3 \, dx","\frac{2 (e (c+d x))^{9/2} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{9 d e}-\frac{2 b \text{Int}\left(\frac{(e (c+d x))^{9/2} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{\sqrt{(c+d x)^2+1}},x\right)}{3 e}",0,"(2*(e*(c + d*x))^(9/2)*(a + b*ArcSinh[c + d*x])^3)/(9*d*e) - (2*b*Defer[Subst][Defer[Int][((e*x)^(9/2)*(a + b*ArcSinh[x])^2)/Sqrt[1 + x^2], x], x, c + d*x])/(3*d*e)","A",0,0,0,0,-1,"{}"
245,0,0,0,0.2033182,"\int (c e+d e x)^{5/2} \left(a+b \sinh ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^(5/2)*(a + b*ArcSinh[c + d*x])^3,x]","\int (c e+d e x)^{5/2} \left(a+b \sinh ^{-1}(c+d x)\right)^3 \, dx","\frac{2 (e (c+d x))^{7/2} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{7 d e}-\frac{6 b \text{Int}\left(\frac{(e (c+d x))^{7/2} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{\sqrt{(c+d x)^2+1}},x\right)}{7 e}",0,"(2*(e*(c + d*x))^(7/2)*(a + b*ArcSinh[c + d*x])^3)/(7*d*e) - (6*b*Defer[Subst][Defer[Int][((e*x)^(7/2)*(a + b*ArcSinh[x])^2)/Sqrt[1 + x^2], x], x, c + d*x])/(7*d*e)","A",0,0,0,0,-1,"{}"
246,0,0,0,0.209061,"\int (c e+d e x)^{3/2} \left(a+b \sinh ^{-1}(c+d x)\right)^3 \, dx","Int[(c*e + d*e*x)^(3/2)*(a + b*ArcSinh[c + d*x])^3,x]","\int (c e+d e x)^{3/2} \left(a+b \sinh ^{-1}(c+d x)\right)^3 \, dx","\frac{2 (e (c+d x))^{5/2} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{5 d e}-\frac{6 b \text{Int}\left(\frac{(e (c+d x))^{5/2} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{\sqrt{(c+d x)^2+1}},x\right)}{5 e}",0,"(2*(e*(c + d*x))^(5/2)*(a + b*ArcSinh[c + d*x])^3)/(5*d*e) - (6*b*Defer[Subst][Defer[Int][((e*x)^(5/2)*(a + b*ArcSinh[x])^2)/Sqrt[1 + x^2], x], x, c + d*x])/(5*d*e)","A",0,0,0,0,-1,"{}"
247,0,0,0,0.2024656,"\int \sqrt{c e+d e x} \left(a+b \sinh ^{-1}(c+d x)\right)^3 \, dx","Int[Sqrt[c*e + d*e*x]*(a + b*ArcSinh[c + d*x])^3,x]","\int \sqrt{c e+d e x} \left(a+b \sinh ^{-1}(c+d x)\right)^3 \, dx","\frac{2 (e (c+d x))^{3/2} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{3 d e}-\frac{2 b \text{Int}\left(\frac{(e (c+d x))^{3/2} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{\sqrt{(c+d x)^2+1}},x\right)}{e}",0,"(2*(e*(c + d*x))^(3/2)*(a + b*ArcSinh[c + d*x])^3)/(3*d*e) - (2*b*Defer[Subst][Defer[Int][((e*x)^(3/2)*(a + b*ArcSinh[x])^2)/Sqrt[1 + x^2], x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
248,0,0,0,0.183353,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{\sqrt{c e+d e x}} \, dx","Int[(a + b*ArcSinh[c + d*x])^3/Sqrt[c*e + d*e*x],x]","\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{\sqrt{c e+d e x}} \, dx","\frac{2 \sqrt{e (c+d x)} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d e}-\frac{6 b \text{Int}\left(\frac{\sqrt{e (c+d x)} \left(a+b \sinh ^{-1}(c+d x)\right)^2}{\sqrt{(c+d x)^2+1}},x\right)}{e}",0,"(2*Sqrt[e*(c + d*x)]*(a + b*ArcSinh[c + d*x])^3)/(d*e) - (6*b*Defer[Subst][Defer[Int][(Sqrt[e*x]*(a + b*ArcSinh[x])^2)/Sqrt[1 + x^2], x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
249,0,0,0,0.1927787,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{3/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])^3/(c*e + d*e*x)^(3/2),x]","\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{3/2}} \, dx","\frac{6 b \text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{\sqrt{(c+d x)^2+1} \sqrt{e (c+d x)}},x\right)}{e}-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)^3}{d e \sqrt{e (c+d x)}}",0,"(-2*(a + b*ArcSinh[c + d*x])^3)/(d*e*Sqrt[e*(c + d*x)]) + (6*b*Defer[Subst][Defer[Int][(a + b*ArcSinh[x])^2/(Sqrt[e*x]*Sqrt[1 + x^2]), x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
250,0,0,0,0.2088118,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{5/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])^3/(c*e + d*e*x)^(5/2),x]","\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{5/2}} \, dx","\frac{2 b \text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{\sqrt{(c+d x)^2+1} (e (c+d x))^{3/2}},x\right)}{e}-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)^3}{3 d e (e (c+d x))^{3/2}}",0,"(-2*(a + b*ArcSinh[c + d*x])^3)/(3*d*e*(e*(c + d*x))^(3/2)) + (2*b*Defer[Subst][Defer[Int][(a + b*ArcSinh[x])^2/((e*x)^(3/2)*Sqrt[1 + x^2]), x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
251,0,0,0,0.2167858,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{7/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])^3/(c*e + d*e*x)^(7/2),x]","\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{7/2}} \, dx","\frac{6 b \text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^2}{\sqrt{(c+d x)^2+1} (e (c+d x))^{5/2}},x\right)}{5 e}-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)^3}{5 d e (e (c+d x))^{5/2}}",0,"(-2*(a + b*ArcSinh[c + d*x])^3)/(5*d*e*(e*(c + d*x))^(5/2)) + (6*b*Defer[Subst][Defer[Int][(a + b*ArcSinh[x])^2/((e*x)^(5/2)*Sqrt[1 + x^2]), x], x, c + d*x])/(5*d*e)","A",0,0,0,0,-1,"{}"
252,0,0,0,0.2060396,"\int (c e+d e x)^{7/2} \left(a+b \sinh ^{-1}(c+d x)\right)^4 \, dx","Int[(c*e + d*e*x)^(7/2)*(a + b*ArcSinh[c + d*x])^4,x]","\int (c e+d e x)^{7/2} \left(a+b \sinh ^{-1}(c+d x)\right)^4 \, dx","\frac{2 (e (c+d x))^{9/2} \left(a+b \sinh ^{-1}(c+d x)\right)^4}{9 d e}-\frac{8 b \text{Int}\left(\frac{(e (c+d x))^{9/2} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{\sqrt{(c+d x)^2+1}},x\right)}{9 e}",0,"(2*(e*(c + d*x))^(9/2)*(a + b*ArcSinh[c + d*x])^4)/(9*d*e) - (8*b*Defer[Subst][Defer[Int][((e*x)^(9/2)*(a + b*ArcSinh[x])^3)/Sqrt[1 + x^2], x], x, c + d*x])/(9*d*e)","A",0,0,0,0,-1,"{}"
253,0,0,0,0.2069692,"\int (c e+d e x)^{5/2} \left(a+b \sinh ^{-1}(c+d x)\right)^4 \, dx","Int[(c*e + d*e*x)^(5/2)*(a + b*ArcSinh[c + d*x])^4,x]","\int (c e+d e x)^{5/2} \left(a+b \sinh ^{-1}(c+d x)\right)^4 \, dx","\frac{2 (e (c+d x))^{7/2} \left(a+b \sinh ^{-1}(c+d x)\right)^4}{7 d e}-\frac{8 b \text{Int}\left(\frac{(e (c+d x))^{7/2} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{\sqrt{(c+d x)^2+1}},x\right)}{7 e}",0,"(2*(e*(c + d*x))^(7/2)*(a + b*ArcSinh[c + d*x])^4)/(7*d*e) - (8*b*Defer[Subst][Defer[Int][((e*x)^(7/2)*(a + b*ArcSinh[x])^3)/Sqrt[1 + x^2], x], x, c + d*x])/(7*d*e)","A",0,0,0,0,-1,"{}"
254,0,0,0,0.2055505,"\int (c e+d e x)^{3/2} \left(a+b \sinh ^{-1}(c+d x)\right)^4 \, dx","Int[(c*e + d*e*x)^(3/2)*(a + b*ArcSinh[c + d*x])^4,x]","\int (c e+d e x)^{3/2} \left(a+b \sinh ^{-1}(c+d x)\right)^4 \, dx","\frac{2 (e (c+d x))^{5/2} \left(a+b \sinh ^{-1}(c+d x)\right)^4}{5 d e}-\frac{8 b \text{Int}\left(\frac{(e (c+d x))^{5/2} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{\sqrt{(c+d x)^2+1}},x\right)}{5 e}",0,"(2*(e*(c + d*x))^(5/2)*(a + b*ArcSinh[c + d*x])^4)/(5*d*e) - (8*b*Defer[Subst][Defer[Int][((e*x)^(5/2)*(a + b*ArcSinh[x])^3)/Sqrt[1 + x^2], x], x, c + d*x])/(5*d*e)","A",0,0,0,0,-1,"{}"
255,0,0,0,0.1940638,"\int \sqrt{c e+d e x} \left(a+b \sinh ^{-1}(c+d x)\right)^4 \, dx","Int[Sqrt[c*e + d*e*x]*(a + b*ArcSinh[c + d*x])^4,x]","\int \sqrt{c e+d e x} \left(a+b \sinh ^{-1}(c+d x)\right)^4 \, dx","\frac{2 (e (c+d x))^{3/2} \left(a+b \sinh ^{-1}(c+d x)\right)^4}{3 d e}-\frac{8 b \text{Int}\left(\frac{(e (c+d x))^{3/2} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{\sqrt{(c+d x)^2+1}},x\right)}{3 e}",0,"(2*(e*(c + d*x))^(3/2)*(a + b*ArcSinh[c + d*x])^4)/(3*d*e) - (8*b*Defer[Subst][Defer[Int][((e*x)^(3/2)*(a + b*ArcSinh[x])^3)/Sqrt[1 + x^2], x], x, c + d*x])/(3*d*e)","A",0,0,0,0,-1,"{}"
256,0,0,0,0.1816557,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{\sqrt{c e+d e x}} \, dx","Int[(a + b*ArcSinh[c + d*x])^4/Sqrt[c*e + d*e*x],x]","\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{\sqrt{c e+d e x}} \, dx","\frac{2 \sqrt{e (c+d x)} \left(a+b \sinh ^{-1}(c+d x)\right)^4}{d e}-\frac{8 b \text{Int}\left(\frac{\sqrt{e (c+d x)} \left(a+b \sinh ^{-1}(c+d x)\right)^3}{\sqrt{(c+d x)^2+1}},x\right)}{e}",0,"(2*Sqrt[e*(c + d*x)]*(a + b*ArcSinh[c + d*x])^4)/(d*e) - (8*b*Defer[Subst][Defer[Int][(Sqrt[e*x]*(a + b*ArcSinh[x])^3)/Sqrt[1 + x^2], x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
257,0,0,0,0.1940814,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{3/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])^4/(c*e + d*e*x)^(3/2),x]","\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{3/2}} \, dx","\frac{8 b \text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{\sqrt{(c+d x)^2+1} \sqrt{e (c+d x)}},x\right)}{e}-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)^4}{d e \sqrt{e (c+d x)}}",0,"(-2*(a + b*ArcSinh[c + d*x])^4)/(d*e*Sqrt[e*(c + d*x)]) + (8*b*Defer[Subst][Defer[Int][(a + b*ArcSinh[x])^3/(Sqrt[e*x]*Sqrt[1 + x^2]), x], x, c + d*x])/(d*e)","A",0,0,0,0,-1,"{}"
258,0,0,0,0.2061972,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{5/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])^4/(c*e + d*e*x)^(5/2),x]","\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{5/2}} \, dx","\frac{8 b \text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{\sqrt{(c+d x)^2+1} (e (c+d x))^{3/2}},x\right)}{3 e}-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)^4}{3 d e (e (c+d x))^{3/2}}",0,"(-2*(a + b*ArcSinh[c + d*x])^4)/(3*d*e*(e*(c + d*x))^(3/2)) + (8*b*Defer[Subst][Defer[Int][(a + b*ArcSinh[x])^3/((e*x)^(3/2)*Sqrt[1 + x^2]), x], x, c + d*x])/(3*d*e)","A",0,0,0,0,-1,"{}"
259,0,0,0,0.2070137,"\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{7/2}} \, dx","Int[(a + b*ArcSinh[c + d*x])^4/(c*e + d*e*x)^(7/2),x]","\int \frac{\left(a+b \sinh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{7/2}} \, dx","\frac{8 b \text{Int}\left(\frac{\left(a+b \sinh ^{-1}(c+d x)\right)^3}{\sqrt{(c+d x)^2+1} (e (c+d x))^{5/2}},x\right)}{5 e}-\frac{2 \left(a+b \sinh ^{-1}(c+d x)\right)^4}{5 d e (e (c+d x))^{5/2}}",0,"(-2*(a + b*ArcSinh[c + d*x])^4)/(5*d*e*(e*(c + d*x))^(5/2)) + (8*b*Defer[Subst][Defer[Int][(a + b*ArcSinh[x])^3/((e*x)^(5/2)*Sqrt[1 + x^2]), x], x, c + d*x])/(5*d*e)","A",0,0,0,0,-1,"{}"
260,1,131,0,0.1889933,"\int \sqrt{1+a^2+2 a b x+b^2 x^2} \sinh ^{-1}(a+b x)^3 \, dx","Int[Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2]*ArcSinh[a + b*x]^3,x]","-\frac{3 (a+b x)^2}{8 b}+\frac{\sinh ^{-1}(a+b x)^4}{8 b}+\frac{(a+b x) \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^3}{2 b}-\frac{3 (a+b x)^2 \sinh ^{-1}(a+b x)^2}{4 b}-\frac{3 \sinh ^{-1}(a+b x)^2}{8 b}+\frac{3 (a+b x) \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{4 b}","-\frac{3 (a+b x)^2}{8 b}+\frac{\sinh ^{-1}(a+b x)^4}{8 b}+\frac{(a+b x) \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^3}{2 b}-\frac{3 (a+b x)^2 \sinh ^{-1}(a+b x)^2}{4 b}-\frac{3 \sinh ^{-1}(a+b x)^2}{8 b}+\frac{3 (a+b x) \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)}{4 b}",1,"(-3*(a + b*x)^2)/(8*b) + (3*(a + b*x)*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/(4*b) - (3*ArcSinh[a + b*x]^2)/(8*b) - (3*(a + b*x)^2*ArcSinh[a + b*x]^2)/(4*b) + ((a + b*x)*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x]^3)/(2*b) + ArcSinh[a + b*x]^4/(8*b)","A",7,6,30,0.2000,1,"{5867, 5682, 5675, 5661, 5758, 30}"
261,1,107,0,0.1189779,"\int \sqrt{1+a^2+2 a b x+b^2 x^2} \sinh ^{-1}(a+b x)^2 \, dx","Int[Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2]*ArcSinh[a + b*x]^2,x]","\frac{(a+b x) \sqrt{(a+b x)^2+1}}{4 b}+\frac{\sinh ^{-1}(a+b x)^3}{6 b}+\frac{(a+b x) \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{2 b}-\frac{(a+b x)^2 \sinh ^{-1}(a+b x)}{2 b}-\frac{\sinh ^{-1}(a+b x)}{4 b}","\frac{(a+b x) \sqrt{(a+b x)^2+1}}{4 b}+\frac{\sinh ^{-1}(a+b x)^3}{6 b}+\frac{(a+b x) \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{2 b}-\frac{(a+b x)^2 \sinh ^{-1}(a+b x)}{2 b}-\frac{\sinh ^{-1}(a+b x)}{4 b}",1,"((a + b*x)*Sqrt[1 + (a + b*x)^2])/(4*b) - ArcSinh[a + b*x]/(4*b) - ((a + b*x)^2*ArcSinh[a + b*x])/(2*b) + ((a + b*x)*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x]^2)/(2*b) + ArcSinh[a + b*x]^3/(6*b)","A",6,6,30,0.2000,1,"{5867, 5682, 5675, 5661, 321, 215}"
262,1,61,0,0.0683636,"\int \sqrt{1+a^2+2 a b x+b^2 x^2} \sinh ^{-1}(a+b x) \, dx","Int[Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2]*ArcSinh[a + b*x],x]","-\frac{(a+b x)^2}{4 b}+\frac{\sqrt{(a+b x)^2+1} (a+b x) \sinh ^{-1}(a+b x)}{2 b}+\frac{\sinh ^{-1}(a+b x)^2}{4 b}","-\frac{(a+b x)^2}{4 b}+\frac{\sqrt{(a+b x)^2+1} (a+b x) \sinh ^{-1}(a+b x)}{2 b}+\frac{\sinh ^{-1}(a+b x)^2}{4 b}",1,"-(a + b*x)^2/(4*b) + ((a + b*x)*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/(2*b) + ArcSinh[a + b*x]^2/(4*b)","A",4,4,28,0.1429,1,"{5867, 5682, 5675, 30}"
263,1,31,0,0.1192854,"\int \frac{\sqrt{1+a^2+2 a b x+b^2 x^2}}{\sinh ^{-1}(a+b x)} \, dx","Int[Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2]/ArcSinh[a + b*x],x]","\frac{\text{Chi}\left(2 \sinh ^{-1}(a+b x)\right)}{2 b}+\frac{\log \left(\sinh ^{-1}(a+b x)\right)}{2 b}","\frac{\text{Chi}\left(2 \sinh ^{-1}(a+b x)\right)}{2 b}+\frac{\log \left(\sinh ^{-1}(a+b x)\right)}{2 b}",1,"CoshIntegral[2*ArcSinh[a + b*x]]/(2*b) + Log[ArcSinh[a + b*x]]/(2*b)","A",5,4,30,0.1333,1,"{5867, 5699, 3312, 3301}"
264,1,36,0,0.115471,"\int \frac{\sqrt{1+a^2+2 a b x+b^2 x^2}}{\sinh ^{-1}(a+b x)^2} \, dx","Int[Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2]/ArcSinh[a + b*x]^2,x]","\frac{\text{Shi}\left(2 \sinh ^{-1}(a+b x)\right)}{b}-\frac{(a+b x)^2+1}{b \sinh ^{-1}(a+b x)}","\frac{\text{Shi}\left(2 \sinh ^{-1}(a+b x)\right)}{b}-\frac{(a+b x)^2+1}{b \sinh ^{-1}(a+b x)}",1,"-((1 + (a + b*x)^2)/(b*ArcSinh[a + b*x])) + SinhIntegral[2*ArcSinh[a + b*x]]/b","A",6,6,30,0.2000,1,"{5867, 5696, 5669, 5448, 12, 3298}"
265,1,69,0,0.1063537,"\int \frac{\sqrt{1+a^2+2 a b x+b^2 x^2}}{\sinh ^{-1}(a+b x)^3} \, dx","Int[Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2]/ArcSinh[a + b*x]^3,x]","\frac{\text{Chi}\left(2 \sinh ^{-1}(a+b x)\right)}{b}-\frac{\sqrt{(a+b x)^2+1} (a+b x)}{b \sinh ^{-1}(a+b x)}-\frac{(a+b x)^2+1}{2 b \sinh ^{-1}(a+b x)^2}","\frac{\text{Chi}\left(2 \sinh ^{-1}(a+b x)\right)}{b}-\frac{\sqrt{(a+b x)^2+1} (a+b x)}{b \sinh ^{-1}(a+b x)}-\frac{(a+b x)^2+1}{2 b \sinh ^{-1}(a+b x)^2}",1,"-(1 + (a + b*x)^2)/(2*b*ArcSinh[a + b*x]^2) - ((a + b*x)*Sqrt[1 + (a + b*x)^2])/(b*ArcSinh[a + b*x]) + CoshIntegral[2*ArcSinh[a + b*x]]/b","A",4,4,30,0.1333,1,"{5867, 5696, 5665, 3301}"
266,1,235,0,0.3091312,"\int \left(1+a^2+2 a b x+b^2 x^2\right)^{3/2} \sinh ^{-1}(a+b x)^3 \, dx","Int[(1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2)*ArcSinh[a + b*x]^3,x]","-\frac{3 (a+b x)^4}{128 b}-\frac{51 (a+b x)^2}{128 b}-\frac{9 (a+b x)^2 \sinh ^{-1}(a+b x)^2}{16 b}+\frac{\left((a+b x)^2+1\right)^{3/2} (a+b x) \sinh ^{-1}(a+b x)^3}{4 b}+\frac{3 \sqrt{(a+b x)^2+1} (a+b x) \sinh ^{-1}(a+b x)^3}{8 b}+\frac{3 \left((a+b x)^2+1\right)^{3/2} (a+b x) \sinh ^{-1}(a+b x)}{32 b}+\frac{45 \sqrt{(a+b x)^2+1} (a+b x) \sinh ^{-1}(a+b x)}{64 b}+\frac{3 \sinh ^{-1}(a+b x)^4}{32 b}-\frac{3 \left((a+b x)^2+1\right)^2 \sinh ^{-1}(a+b x)^2}{16 b}-\frac{27 \sinh ^{-1}(a+b x)^2}{128 b}","-\frac{3 (a+b x)^4}{128 b}-\frac{51 (a+b x)^2}{128 b}-\frac{9 (a+b x)^2 \sinh ^{-1}(a+b x)^2}{16 b}+\frac{\left((a+b x)^2+1\right)^{3/2} (a+b x) \sinh ^{-1}(a+b x)^3}{4 b}+\frac{3 \sqrt{(a+b x)^2+1} (a+b x) \sinh ^{-1}(a+b x)^3}{8 b}+\frac{3 \left((a+b x)^2+1\right)^{3/2} (a+b x) \sinh ^{-1}(a+b x)}{32 b}+\frac{45 \sqrt{(a+b x)^2+1} (a+b x) \sinh ^{-1}(a+b x)}{64 b}+\frac{3 \sinh ^{-1}(a+b x)^4}{32 b}-\frac{3 \left((a+b x)^2+1\right)^2 \sinh ^{-1}(a+b x)^2}{16 b}-\frac{27 \sinh ^{-1}(a+b x)^2}{128 b}",1,"(-51*(a + b*x)^2)/(128*b) - (3*(a + b*x)^4)/(128*b) + (45*(a + b*x)*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/(64*b) + (3*(a + b*x)*(1 + (a + b*x)^2)^(3/2)*ArcSinh[a + b*x])/(32*b) - (27*ArcSinh[a + b*x]^2)/(128*b) - (9*(a + b*x)^2*ArcSinh[a + b*x]^2)/(16*b) - (3*(1 + (a + b*x)^2)^2*ArcSinh[a + b*x]^2)/(16*b) + (3*(a + b*x)*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x]^3)/(8*b) + ((a + b*x)*(1 + (a + b*x)^2)^(3/2)*ArcSinh[a + b*x]^3)/(4*b) + (3*ArcSinh[a + b*x]^4)/(32*b)","A",15,9,30,0.3000,1,"{5867, 5684, 5682, 5675, 5661, 5758, 30, 5717, 14}"
267,1,189,0,0.1904674,"\int \left(1+a^2+2 a b x+b^2 x^2\right)^{3/2} \sinh ^{-1}(a+b x)^2 \, dx","Int[(1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2)*ArcSinh[a + b*x]^2,x]","\frac{(a+b x) \left((a+b x)^2+1\right)^{3/2}}{32 b}+\frac{15 (a+b x) \sqrt{(a+b x)^2+1}}{64 b}+\frac{\sinh ^{-1}(a+b x)^3}{8 b}+\frac{(a+b x) \left((a+b x)^2+1\right)^{3/2} \sinh ^{-1}(a+b x)^2}{4 b}+\frac{3 (a+b x) \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{8 b}-\frac{3 (a+b x)^2 \sinh ^{-1}(a+b x)}{8 b}-\frac{\left((a+b x)^2+1\right)^2 \sinh ^{-1}(a+b x)}{8 b}-\frac{9 \sinh ^{-1}(a+b x)}{64 b}","\frac{(a+b x) \left((a+b x)^2+1\right)^{3/2}}{32 b}+\frac{15 (a+b x) \sqrt{(a+b x)^2+1}}{64 b}+\frac{\sinh ^{-1}(a+b x)^3}{8 b}+\frac{(a+b x) \left((a+b x)^2+1\right)^{3/2} \sinh ^{-1}(a+b x)^2}{4 b}+\frac{3 (a+b x) \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{8 b}-\frac{3 (a+b x)^2 \sinh ^{-1}(a+b x)}{8 b}-\frac{\left((a+b x)^2+1\right)^2 \sinh ^{-1}(a+b x)}{8 b}-\frac{9 \sinh ^{-1}(a+b x)}{64 b}",1,"(15*(a + b*x)*Sqrt[1 + (a + b*x)^2])/(64*b) + ((a + b*x)*(1 + (a + b*x)^2)^(3/2))/(32*b) - (9*ArcSinh[a + b*x])/(64*b) - (3*(a + b*x)^2*ArcSinh[a + b*x])/(8*b) - ((1 + (a + b*x)^2)^2*ArcSinh[a + b*x])/(8*b) + (3*(a + b*x)*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x]^2)/(8*b) + ((a + b*x)*(1 + (a + b*x)^2)^(3/2)*ArcSinh[a + b*x]^2)/(4*b) + ArcSinh[a + b*x]^3/(8*b)","A",11,9,30,0.3000,1,"{5867, 5684, 5682, 5675, 5661, 321, 215, 5717, 195}"
268,1,106,0,0.1036265,"\int \left(1+a^2+2 a b x+b^2 x^2\right)^{3/2} \sinh ^{-1}(a+b x) \, dx","Int[(1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2)*ArcSinh[a + b*x],x]","-\frac{(a+b x)^4}{16 b}-\frac{5 (a+b x)^2}{16 b}+\frac{\left((a+b x)^2+1\right)^{3/2} (a+b x) \sinh ^{-1}(a+b x)}{4 b}+\frac{3 \sqrt{(a+b x)^2+1} (a+b x) \sinh ^{-1}(a+b x)}{8 b}+\frac{3 \sinh ^{-1}(a+b x)^2}{16 b}","-\frac{(a+b x)^4}{16 b}-\frac{5 (a+b x)^2}{16 b}+\frac{\left((a+b x)^2+1\right)^{3/2} (a+b x) \sinh ^{-1}(a+b x)}{4 b}+\frac{3 \sqrt{(a+b x)^2+1} (a+b x) \sinh ^{-1}(a+b x)}{8 b}+\frac{3 \sinh ^{-1}(a+b x)^2}{16 b}",1,"(-5*(a + b*x)^2)/(16*b) - (a + b*x)^4/(16*b) + (3*(a + b*x)*Sqrt[1 + (a + b*x)^2]*ArcSinh[a + b*x])/(8*b) + ((a + b*x)*(1 + (a + b*x)^2)^(3/2)*ArcSinh[a + b*x])/(4*b) + (3*ArcSinh[a + b*x]^2)/(16*b)","A",7,6,28,0.2143,1,"{5867, 5684, 5682, 5675, 30, 14}"
269,1,47,0,0.1435196,"\int \frac{\left(1+a^2+2 a b x+b^2 x^2\right)^{3/2}}{\sinh ^{-1}(a+b x)} \, dx","Int[(1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2)/ArcSinh[a + b*x],x]","\frac{\text{Chi}\left(2 \sinh ^{-1}(a+b x)\right)}{2 b}+\frac{\text{Chi}\left(4 \sinh ^{-1}(a+b x)\right)}{8 b}+\frac{3 \log \left(\sinh ^{-1}(a+b x)\right)}{8 b}","\frac{\text{Chi}\left(2 \sinh ^{-1}(a+b x)\right)}{2 b}+\frac{\text{Chi}\left(4 \sinh ^{-1}(a+b x)\right)}{8 b}+\frac{3 \log \left(\sinh ^{-1}(a+b x)\right)}{8 b}",1,"CoshIntegral[2*ArcSinh[a + b*x]]/(2*b) + CoshIntegral[4*ArcSinh[a + b*x]]/(8*b) + (3*Log[ArcSinh[a + b*x]])/(8*b)","A",6,4,30,0.1333,1,"{5867, 5699, 3312, 3301}"
270,1,54,0,0.156555,"\int \frac{\left(1+a^2+2 a b x+b^2 x^2\right)^{3/2}}{\sinh ^{-1}(a+b x)^2} \, dx","Int[(1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2)/ArcSinh[a + b*x]^2,x]","\frac{\text{Shi}\left(2 \sinh ^{-1}(a+b x)\right)}{b}+\frac{\text{Shi}\left(4 \sinh ^{-1}(a+b x)\right)}{2 b}-\frac{\left((a+b x)^2+1\right)^2}{b \sinh ^{-1}(a+b x)}","\frac{\text{Shi}\left(2 \sinh ^{-1}(a+b x)\right)}{b}+\frac{\text{Shi}\left(4 \sinh ^{-1}(a+b x)\right)}{2 b}-\frac{\left((a+b x)^2+1\right)^2}{b \sinh ^{-1}(a+b x)}",1,"-((1 + (a + b*x)^2)^2/(b*ArcSinh[a + b*x])) + SinhIntegral[2*ArcSinh[a + b*x]]/b + SinhIntegral[4*ArcSinh[a + b*x]]/(2*b)","A",7,5,30,0.1667,1,"{5867, 5696, 5779, 5448, 3298}"
271,1,84,0,0.2807025,"\int \frac{\left(1+a^2+2 a b x+b^2 x^2\right)^{3/2}}{\sinh ^{-1}(a+b x)^3} \, dx","Int[(1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2)/ArcSinh[a + b*x]^3,x]","\frac{\text{Chi}\left(2 \sinh ^{-1}(a+b x)\right)}{b}+\frac{\text{Chi}\left(4 \sinh ^{-1}(a+b x)\right)}{b}-\frac{\left((a+b x)^2+1\right)^2}{2 b \sinh ^{-1}(a+b x)^2}-\frac{2 (a+b x) \left((a+b x)^2+1\right)^{3/2}}{b \sinh ^{-1}(a+b x)}","\frac{\text{Chi}\left(2 \sinh ^{-1}(a+b x)\right)}{b}+\frac{\text{Chi}\left(4 \sinh ^{-1}(a+b x)\right)}{b}-\frac{\left((a+b x)^2+1\right)^2}{2 b \sinh ^{-1}(a+b x)^2}-\frac{2 (a+b x) \left((a+b x)^2+1\right)^{3/2}}{b \sinh ^{-1}(a+b x)}",1,"-(1 + (a + b*x)^2)^2/(2*b*ArcSinh[a + b*x]^2) - (2*(a + b*x)*(1 + (a + b*x)^2)^(3/2))/(b*ArcSinh[a + b*x]) + CoshIntegral[2*ArcSinh[a + b*x]]/b + CoshIntegral[4*ArcSinh[a + b*x]]/b","A",11,8,30,0.2667,1,"{5867, 5696, 5777, 5699, 3312, 3301, 5779, 5448}"
272,1,15,0,0.0690976,"\int \frac{\sinh ^{-1}(a+b x)^3}{\sqrt{1+a^2+2 a b x+b^2 x^2}} \, dx","Int[ArcSinh[a + b*x]^3/Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2],x]","\frac{\sinh ^{-1}(a+b x)^4}{4 b}","\frac{\sinh ^{-1}(a+b x)^4}{4 b}",1,"ArcSinh[a + b*x]^4/(4*b)","A",2,2,30,0.06667,1,"{5867, 5675}"
273,1,15,0,0.0680001,"\int \frac{\sinh ^{-1}(a+b x)^2}{\sqrt{1+a^2+2 a b x+b^2 x^2}} \, dx","Int[ArcSinh[a + b*x]^2/Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2],x]","\frac{\sinh ^{-1}(a+b x)^3}{3 b}","\frac{\sinh ^{-1}(a+b x)^3}{3 b}",1,"ArcSinh[a + b*x]^3/(3*b)","A",2,2,30,0.06667,1,"{5867, 5675}"
274,1,15,0,0.042129,"\int \frac{\sinh ^{-1}(a+b x)}{\sqrt{1+a^2+2 a b x+b^2 x^2}} \, dx","Int[ArcSinh[a + b*x]/Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2],x]","\frac{\sinh ^{-1}(a+b x)^2}{2 b}","\frac{\sinh ^{-1}(a+b x)^2}{2 b}",1,"ArcSinh[a + b*x]^2/(2*b)","A",2,2,28,0.07143,1,"{5867, 5675}"
275,1,11,0,0.0751373,"\int \frac{1}{\sqrt{1+a^2+2 a b x+b^2 x^2} \sinh ^{-1}(a+b x)} \, dx","Int[1/(Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2]*ArcSinh[a + b*x]),x]","\frac{\log \left(\sinh ^{-1}(a+b x)\right)}{b}","\frac{\log \left(\sinh ^{-1}(a+b x)\right)}{b}",1,"Log[ArcSinh[a + b*x]]/b","A",2,2,30,0.06667,1,"{5867, 5673}"
276,1,13,0,0.0747208,"\int \frac{1}{\sqrt{1+a^2+2 a b x+b^2 x^2} \sinh ^{-1}(a+b x)^2} \, dx","Int[1/(Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2]*ArcSinh[a + b*x]^2),x]","-\frac{1}{b \sinh ^{-1}(a+b x)}","-\frac{1}{b \sinh ^{-1}(a+b x)}",1,"-(1/(b*ArcSinh[a + b*x]))","A",2,2,30,0.06667,1,"{5867, 5675}"
277,1,15,0,0.0702373,"\int \frac{1}{\sqrt{1+a^2+2 a b x+b^2 x^2} \sinh ^{-1}(a+b x)^3} \, dx","Int[1/(Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2]*ArcSinh[a + b*x]^3),x]","-\frac{1}{2 b \sinh ^{-1}(a+b x)^2}","-\frac{1}{2 b \sinh ^{-1}(a+b x)^2}",1,"-1/(2*b*ArcSinh[a + b*x]^2)","A",2,2,30,0.06667,1,"{5867, 5675}"
278,1,115,0,0.2061683,"\int \frac{\sinh ^{-1}(a+b x)^3}{\left(1+a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[ArcSinh[a + b*x]^3/(1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{3 \sinh ^{-1}(a+b x) \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(a+b x)}\right)}{b}+\frac{3 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(a+b x)}\right)}{2 b}+\frac{(a+b x) \sinh ^{-1}(a+b x)^3}{b \sqrt{(a+b x)^2+1}}+\frac{\sinh ^{-1}(a+b x)^3}{b}-\frac{3 \sinh ^{-1}(a+b x)^2 \log \left(e^{2 \sinh ^{-1}(a+b x)}+1\right)}{b}","-\frac{3 \sinh ^{-1}(a+b x) \text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(a+b x)}\right)}{b}+\frac{3 \text{PolyLog}\left(3,-e^{2 \sinh ^{-1}(a+b x)}\right)}{2 b}+\frac{(a+b x) \sinh ^{-1}(a+b x)^3}{b \sqrt{(a+b x)^2+1}}+\frac{\sinh ^{-1}(a+b x)^3}{b}-\frac{3 \sinh ^{-1}(a+b x)^2 \log \left(e^{2 \sinh ^{-1}(a+b x)}+1\right)}{b}",1,"ArcSinh[a + b*x]^3/b + ((a + b*x)*ArcSinh[a + b*x]^3)/(b*Sqrt[1 + (a + b*x)^2]) - (3*ArcSinh[a + b*x]^2*Log[1 + E^(2*ArcSinh[a + b*x])])/b - (3*ArcSinh[a + b*x]*PolyLog[2, -E^(2*ArcSinh[a + b*x])])/b + (3*PolyLog[3, -E^(2*ArcSinh[a + b*x])])/(2*b)","A",8,8,30,0.2667,1,"{5867, 5687, 5714, 3718, 2190, 2531, 2282, 6589}"
279,1,86,0,0.1600931,"\int \frac{\sinh ^{-1}(a+b x)^2}{\left(1+a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[ArcSinh[a + b*x]^2/(1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{\text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(a+b x)}\right)}{b}+\frac{(a+b x) \sinh ^{-1}(a+b x)^2}{b \sqrt{(a+b x)^2+1}}+\frac{\sinh ^{-1}(a+b x)^2}{b}-\frac{2 \sinh ^{-1}(a+b x) \log \left(e^{2 \sinh ^{-1}(a+b x)}+1\right)}{b}","-\frac{\text{PolyLog}\left(2,-e^{2 \sinh ^{-1}(a+b x)}\right)}{b}+\frac{(a+b x) \sinh ^{-1}(a+b x)^2}{b \sqrt{(a+b x)^2+1}}+\frac{\sinh ^{-1}(a+b x)^2}{b}-\frac{2 \sinh ^{-1}(a+b x) \log \left(e^{2 \sinh ^{-1}(a+b x)}+1\right)}{b}",1,"ArcSinh[a + b*x]^2/b + ((a + b*x)*ArcSinh[a + b*x]^2)/(b*Sqrt[1 + (a + b*x)^2]) - (2*ArcSinh[a + b*x]*Log[1 + E^(2*ArcSinh[a + b*x])])/b - PolyLog[2, -E^(2*ArcSinh[a + b*x])]/b","A",7,7,30,0.2333,1,"{5867, 5687, 5714, 3718, 2190, 2279, 2391}"
280,1,46,0,0.0575618,"\int \frac{\sinh ^{-1}(a+b x)}{\left(1+a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[ArcSinh[a + b*x]/(1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{(a+b x) \sinh ^{-1}(a+b x)}{b \sqrt{(a+b x)^2+1}}-\frac{\log \left((a+b x)^2+1\right)}{2 b}","\frac{(a+b x) \sinh ^{-1}(a+b x)}{b \sqrt{(a+b x)^2+1}}-\frac{\log \left((a+b x)^2+1\right)}{2 b}",1,"((a + b*x)*ArcSinh[a + b*x])/(b*Sqrt[1 + (a + b*x)^2]) - Log[1 + (a + b*x)^2]/(2*b)","A",3,3,28,0.1071,1,"{5867, 5687, 260}"
281,0,0,0,0.0821379,"\int \frac{1}{\left(1+a^2+2 a b x+b^2 x^2\right)^{3/2} \sinh ^{-1}(a+b x)} \, dx","Int[1/((1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2)*ArcSinh[a + b*x]),x]","\int \frac{1}{\left(1+a^2+2 a b x+b^2 x^2\right)^{3/2} \sinh ^{-1}(a+b x)} \, dx","\text{Int}\left(\frac{1}{\left((a+b x)^2+1\right)^{3/2} \sinh ^{-1}(a+b x)},x\right)",0,"Defer[Subst][Defer[Int][1/((1 + x^2)^(3/2)*ArcSinh[x]), x], x, a + b*x]/b","A",0,0,0,0,-1,"{}"
282,0,0,0,0.1165122,"\int \frac{1}{\left(1+a^2+2 a b x+b^2 x^2\right)^{3/2} \sinh ^{-1}(a+b x)^2} \, dx","Int[1/((1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2)*ArcSinh[a + b*x]^2),x]","\int \frac{1}{\left(1+a^2+2 a b x+b^2 x^2\right)^{3/2} \sinh ^{-1}(a+b x)^2} \, dx","-2 \text{Int}\left(\frac{a+b x}{\left((a+b x)^2+1\right)^2 \sinh ^{-1}(a+b x)},x\right)-\frac{1}{b \left((a+b x)^2+1\right) \sinh ^{-1}(a+b x)}",0,"-(1/(b*(1 + (a + b*x)^2)*ArcSinh[a + b*x])) - (2*Defer[Subst][Defer[Int][x/((1 + x^2)^2*ArcSinh[x]), x], x, a + b*x])/b","A",0,0,0,0,-1,"{}"
283,1,50,0,0.0365349,"\int x^3 \sinh ^{-1}\left(a x^2\right) \, dx","Int[x^3*ArcSinh[a*x^2],x]","-\frac{x^2 \sqrt{a^2 x^4+1}}{8 a}+\frac{\sinh ^{-1}\left(a x^2\right)}{8 a^2}+\frac{1}{4} x^4 \sinh ^{-1}\left(a x^2\right)","-\frac{x^2 \sqrt{a^2 x^4+1}}{8 a}+\frac{\sinh ^{-1}\left(a x^2\right)}{8 a^2}+\frac{1}{4} x^4 \sinh ^{-1}\left(a x^2\right)",1,"-(x^2*Sqrt[1 + a^2*x^4])/(8*a) + ArcSinh[a*x^2]/(8*a^2) + (x^4*ArcSinh[a*x^2])/4","A",5,5,10,0.5000,1,"{5902, 12, 275, 321, 215}"
284,1,101,0,0.043684,"\int x^2 \sinh ^{-1}\left(a x^2\right) \, dx","Int[x^2*ArcSinh[a*x^2],x]","-\frac{2 x \sqrt{a^2 x^4+1}}{9 a}+\frac{\left(a x^2+1\right) \sqrt{\frac{a^2 x^4+1}{\left(a x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{9 a^{3/2} \sqrt{a^2 x^4+1}}+\frac{1}{3} x^3 \sinh ^{-1}\left(a x^2\right)","-\frac{2 x \sqrt{a^2 x^4+1}}{9 a}+\frac{\left(a x^2+1\right) \sqrt{\frac{a^2 x^4+1}{\left(a x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{9 a^{3/2} \sqrt{a^2 x^4+1}}+\frac{1}{3} x^3 \sinh ^{-1}\left(a x^2\right)",1,"(-2*x*Sqrt[1 + a^2*x^4])/(9*a) + (x^3*ArcSinh[a*x^2])/3 + ((1 + a*x^2)*Sqrt[(1 + a^2*x^4)/(1 + a*x^2)^2]*EllipticF[2*ArcTan[Sqrt[a]*x], 1/2])/(9*a^(3/2)*Sqrt[1 + a^2*x^4])","A",4,4,10,0.4000,1,"{5902, 12, 321, 220}"
285,1,34,0,0.0224494,"\int x \sinh ^{-1}\left(a x^2\right) \, dx","Int[x*ArcSinh[a*x^2],x]","\frac{1}{2} x^2 \sinh ^{-1}\left(a x^2\right)-\frac{\sqrt{a^2 x^4+1}}{2 a}","\frac{1}{2} x^2 \sinh ^{-1}\left(a x^2\right)-\frac{\sqrt{a^2 x^4+1}}{2 a}",1,"-Sqrt[1 + a^2*x^4]/(2*a) + (x^2*ArcSinh[a*x^2])/2","A",3,3,8,0.3750,1,"{6715, 5653, 261}"
286,1,162,0,0.054459,"\int \sinh ^{-1}\left(a x^2\right) \, dx","Int[ArcSinh[a*x^2],x]","-\frac{2 x \sqrt{a^2 x^4+1}}{a x^2+1}-\frac{\left(a x^2+1\right) \sqrt{\frac{a^2 x^4+1}{\left(a x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{\sqrt{a} \sqrt{a^2 x^4+1}}+\frac{2 \left(a x^2+1\right) \sqrt{\frac{a^2 x^4+1}{\left(a x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{\sqrt{a} \sqrt{a^2 x^4+1}}+x \sinh ^{-1}\left(a x^2\right)","-\frac{2 x \sqrt{a^2 x^4+1}}{a x^2+1}-\frac{\left(a x^2+1\right) \sqrt{\frac{a^2 x^4+1}{\left(a x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{\sqrt{a} \sqrt{a^2 x^4+1}}+\frac{2 \left(a x^2+1\right) \sqrt{\frac{a^2 x^4+1}{\left(a x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{\sqrt{a} \sqrt{a^2 x^4+1}}+x \sinh ^{-1}\left(a x^2\right)",1,"(-2*x*Sqrt[1 + a^2*x^4])/(1 + a*x^2) + x*ArcSinh[a*x^2] + (2*(1 + a*x^2)*Sqrt[(1 + a^2*x^4)/(1 + a*x^2)^2]*EllipticE[2*ArcTan[Sqrt[a]*x], 1/2])/(Sqrt[a]*Sqrt[1 + a^2*x^4]) - ((1 + a*x^2)*Sqrt[(1 + a^2*x^4)/(1 + a*x^2)^2]*EllipticF[2*ArcTan[Sqrt[a]*x], 1/2])/(Sqrt[a]*Sqrt[1 + a^2*x^4])","A",5,5,6,0.8333,1,"{5900, 12, 305, 220, 1196}"
287,1,54,0,0.0622429,"\int \frac{\sinh ^{-1}\left(a x^2\right)}{x} \, dx","Int[ArcSinh[a*x^2]/x,x]","\frac{1}{4} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(a x^2\right)}\right)-\frac{1}{4} \sinh ^{-1}\left(a x^2\right)^2+\frac{1}{2} \sinh ^{-1}\left(a x^2\right) \log \left(1-e^{2 \sinh ^{-1}\left(a x^2\right)}\right)","\frac{1}{4} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(a x^2\right)}\right)-\frac{1}{4} \sinh ^{-1}\left(a x^2\right)^2+\frac{1}{2} \sinh ^{-1}\left(a x^2\right) \log \left(1-e^{2 \sinh ^{-1}\left(a x^2\right)}\right)",1,"-ArcSinh[a*x^2]^2/4 + (ArcSinh[a*x^2]*Log[1 - E^(2*ArcSinh[a*x^2])])/2 + PolyLog[2, E^(2*ArcSinh[a*x^2])]/4","A",5,5,10,0.5000,1,"{5890, 3716, 2190, 2279, 2391}"
288,1,75,0,0.0225441,"\int \frac{\sinh ^{-1}\left(a x^2\right)}{x^2} \, dx","Int[ArcSinh[a*x^2]/x^2,x]","\frac{\sqrt{a} \left(a x^2+1\right) \sqrt{\frac{a^2 x^4+1}{\left(a x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{\sqrt{a^2 x^4+1}}-\frac{\sinh ^{-1}\left(a x^2\right)}{x}","\frac{\sqrt{a} \left(a x^2+1\right) \sqrt{\frac{a^2 x^4+1}{\left(a x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{\sqrt{a^2 x^4+1}}-\frac{\sinh ^{-1}\left(a x^2\right)}{x}",1,"-(ArcSinh[a*x^2]/x) + (Sqrt[a]*(1 + a*x^2)*Sqrt[(1 + a^2*x^4)/(1 + a*x^2)^2]*EllipticF[2*ArcTan[Sqrt[a]*x], 1/2])/Sqrt[1 + a^2*x^4]","A",3,3,10,0.3000,1,"{5902, 12, 220}"
289,1,33,0,0.0264191,"\int \frac{\sinh ^{-1}\left(a x^2\right)}{x^3} \, dx","Int[ArcSinh[a*x^2]/x^3,x]","-\frac{1}{2} a \tanh ^{-1}\left(\sqrt{a^2 x^4+1}\right)-\frac{\sinh ^{-1}\left(a x^2\right)}{2 x^2}","-\frac{1}{2} a \tanh ^{-1}\left(\sqrt{a^2 x^4+1}\right)-\frac{\sinh ^{-1}\left(a x^2\right)}{2 x^2}",1,"-ArcSinh[a*x^2]/(2*x^2) - (a*ArcTanh[Sqrt[1 + a^2*x^4]])/2","A",5,5,10,0.5000,1,"{5902, 12, 266, 63, 208}"
290,1,197,0,0.0896105,"\int \frac{\sinh ^{-1}\left(a x^2\right)}{x^4} \, dx","Int[ArcSinh[a*x^2]/x^4,x]","\frac{2 a^2 x \sqrt{a^2 x^4+1}}{3 \left(a x^2+1\right)}-\frac{2 a \sqrt{a^2 x^4+1}}{3 x}+\frac{a^{3/2} \left(a x^2+1\right) \sqrt{\frac{a^2 x^4+1}{\left(a x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{3 \sqrt{a^2 x^4+1}}-\frac{2 a^{3/2} \left(a x^2+1\right) \sqrt{\frac{a^2 x^4+1}{\left(a x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{3 \sqrt{a^2 x^4+1}}-\frac{\sinh ^{-1}\left(a x^2\right)}{3 x^3}","\frac{2 a^2 x \sqrt{a^2 x^4+1}}{3 \left(a x^2+1\right)}-\frac{2 a \sqrt{a^2 x^4+1}}{3 x}+\frac{a^{3/2} \left(a x^2+1\right) \sqrt{\frac{a^2 x^4+1}{\left(a x^2+1\right)^2}} F\left(2 \tan ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{3 \sqrt{a^2 x^4+1}}-\frac{2 a^{3/2} \left(a x^2+1\right) \sqrt{\frac{a^2 x^4+1}{\left(a x^2+1\right)^2}} E\left(2 \tan ^{-1}\left(\sqrt{a} x\right)|\frac{1}{2}\right)}{3 \sqrt{a^2 x^4+1}}-\frac{\sinh ^{-1}\left(a x^2\right)}{3 x^3}",1,"(-2*a*Sqrt[1 + a^2*x^4])/(3*x) + (2*a^2*x*Sqrt[1 + a^2*x^4])/(3*(1 + a*x^2)) - ArcSinh[a*x^2]/(3*x^3) - (2*a^(3/2)*(1 + a*x^2)*Sqrt[(1 + a^2*x^4)/(1 + a*x^2)^2]*EllipticE[2*ArcTan[Sqrt[a]*x], 1/2])/(3*Sqrt[1 + a^2*x^4]) + (a^(3/2)*(1 + a*x^2)*Sqrt[(1 + a^2*x^4)/(1 + a*x^2)^2]*EllipticF[2*ArcTan[Sqrt[a]*x], 1/2])/(3*Sqrt[1 + a^2*x^4])","A",6,6,10,0.6000,1,"{5902, 12, 325, 305, 220, 1196}"
291,1,54,0,0.0621063,"\int \frac{\sinh ^{-1}\left(a x^5\right)}{x} \, dx","Int[ArcSinh[a*x^5]/x,x]","\frac{1}{10} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(a x^5\right)}\right)-\frac{1}{10} \sinh ^{-1}\left(a x^5\right)^2+\frac{1}{5} \sinh ^{-1}\left(a x^5\right) \log \left(1-e^{2 \sinh ^{-1}\left(a x^5\right)}\right)","\frac{1}{10} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(a x^5\right)}\right)-\frac{1}{10} \sinh ^{-1}\left(a x^5\right)^2+\frac{1}{5} \sinh ^{-1}\left(a x^5\right) \log \left(1-e^{2 \sinh ^{-1}\left(a x^5\right)}\right)",1,"-ArcSinh[a*x^5]^2/10 + (ArcSinh[a*x^5]*Log[1 - E^(2*ArcSinh[a*x^5])])/5 + PolyLog[2, E^(2*ArcSinh[a*x^5])]/10","A",5,5,10,0.5000,1,"{5890, 3716, 2190, 2279, 2391}"
292,1,72,0,0.0251364,"\int x^2 \sinh ^{-1}\left(\sqrt{x}\right) \, dx","Int[x^2*ArcSinh[Sqrt[x]],x]","-\frac{1}{18} \sqrt{x+1} x^{5/2}+\frac{5}{72} \sqrt{x+1} x^{3/2}+\frac{1}{3} x^3 \sinh ^{-1}\left(\sqrt{x}\right)-\frac{5}{48} \sqrt{x+1} \sqrt{x}+\frac{5}{48} \sinh ^{-1}\left(\sqrt{x}\right)","-\frac{1}{18} \sqrt{x+1} x^{5/2}+\frac{5}{72} \sqrt{x+1} x^{3/2}+\frac{1}{3} x^3 \sinh ^{-1}\left(\sqrt{x}\right)-\frac{5}{48} \sqrt{x+1} \sqrt{x}+\frac{5}{48} \sinh ^{-1}\left(\sqrt{x}\right)",1,"(-5*Sqrt[x]*Sqrt[1 + x])/48 + (5*x^(3/2)*Sqrt[1 + x])/72 - (x^(5/2)*Sqrt[1 + x])/18 + (5*ArcSinh[Sqrt[x]])/48 + (x^3*ArcSinh[Sqrt[x]])/3","A",7,5,10,0.5000,1,"{5902, 12, 50, 54, 215}"
293,1,56,0,0.0172571,"\int x \sinh ^{-1}\left(\sqrt{x}\right) \, dx","Int[x*ArcSinh[Sqrt[x]],x]","-\frac{1}{8} \sqrt{x+1} x^{3/2}+\frac{1}{2} x^2 \sinh ^{-1}\left(\sqrt{x}\right)+\frac{3}{16} \sqrt{x+1} \sqrt{x}-\frac{3}{16} \sinh ^{-1}\left(\sqrt{x}\right)","-\frac{1}{8} \sqrt{x+1} x^{3/2}+\frac{1}{2} x^2 \sinh ^{-1}\left(\sqrt{x}\right)+\frac{3}{16} \sqrt{x+1} \sqrt{x}-\frac{3}{16} \sinh ^{-1}\left(\sqrt{x}\right)",1,"(3*Sqrt[x]*Sqrt[1 + x])/16 - (x^(3/2)*Sqrt[1 + x])/8 - (3*ArcSinh[Sqrt[x]])/16 + (x^2*ArcSinh[Sqrt[x]])/2","A",6,5,8,0.6250,1,"{5902, 12, 50, 54, 215}"
294,1,35,0,0.0107196,"\int \sinh ^{-1}\left(\sqrt{x}\right) \, dx","Int[ArcSinh[Sqrt[x]],x]","-\frac{1}{2} \sqrt{x} \sqrt{x+1}+x \sinh ^{-1}\left(\sqrt{x}\right)+\frac{1}{2} \sinh ^{-1}\left(\sqrt{x}\right)","-\frac{1}{2} \sqrt{x} \sqrt{x+1}+x \sinh ^{-1}\left(\sqrt{x}\right)+\frac{1}{2} \sinh ^{-1}\left(\sqrt{x}\right)",1,"-(Sqrt[x]*Sqrt[1 + x])/2 + ArcSinh[Sqrt[x]]/2 + x*ArcSinh[Sqrt[x]]","A",6,6,6,1.000,1,"{5900, 12, 1958, 50, 54, 215}"
295,1,46,0,0.0643435,"\int \frac{\sinh ^{-1}\left(\sqrt{x}\right)}{x} \, dx","Int[ArcSinh[Sqrt[x]]/x,x]","\text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\sqrt{x}\right)}\right)-\sinh ^{-1}\left(\sqrt{x}\right)^2+2 \sinh ^{-1}\left(\sqrt{x}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\sqrt{x}\right)}\right)","\text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\sqrt{x}\right)}\right)-\sinh ^{-1}\left(\sqrt{x}\right)^2+2 \sinh ^{-1}\left(\sqrt{x}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\sqrt{x}\right)}\right)",1,"-ArcSinh[Sqrt[x]]^2 + 2*ArcSinh[Sqrt[x]]*Log[1 - E^(2*ArcSinh[Sqrt[x]])] + PolyLog[2, E^(2*ArcSinh[Sqrt[x]])]","A",5,5,10,0.5000,1,"{5890, 3716, 2190, 2279, 2391}"
296,1,26,0,0.0131465,"\int \frac{\sinh ^{-1}\left(\sqrt{x}\right)}{x^2} \, dx","Int[ArcSinh[Sqrt[x]]/x^2,x]","-\frac{\sqrt{x+1}}{\sqrt{x}}-\frac{\sinh ^{-1}\left(\sqrt{x}\right)}{x}","-\frac{\sqrt{x+1}}{\sqrt{x}}-\frac{\sinh ^{-1}\left(\sqrt{x}\right)}{x}",1,"-(Sqrt[1 + x]/Sqrt[x]) - ArcSinh[Sqrt[x]]/x","A",3,3,10,0.3000,1,"{5902, 12, 37}"
297,1,46,0,0.0170543,"\int \frac{\sinh ^{-1}\left(\sqrt{x}\right)}{x^3} \, dx","Int[ArcSinh[Sqrt[x]]/x^3,x]","-\frac{\sqrt{x+1}}{6 x^{3/2}}-\frac{\sinh ^{-1}\left(\sqrt{x}\right)}{2 x^2}+\frac{\sqrt{x+1}}{3 \sqrt{x}}","-\frac{\sqrt{x+1}}{6 x^{3/2}}-\frac{\sinh ^{-1}\left(\sqrt{x}\right)}{2 x^2}+\frac{\sqrt{x+1}}{3 \sqrt{x}}",1,"-Sqrt[1 + x]/(6*x^(3/2)) + Sqrt[1 + x]/(3*Sqrt[x]) - ArcSinh[Sqrt[x]]/(2*x^2)","A",4,4,10,0.4000,1,"{5902, 12, 45, 37}"
298,1,62,0,0.0215487,"\int \frac{\sinh ^{-1}\left(\sqrt{x}\right)}{x^4} \, dx","Int[ArcSinh[Sqrt[x]]/x^4,x]","\frac{4 \sqrt{x+1}}{45 x^{3/2}}-\frac{\sqrt{x+1}}{15 x^{5/2}}-\frac{\sinh ^{-1}\left(\sqrt{x}\right)}{3 x^3}-\frac{8 \sqrt{x+1}}{45 \sqrt{x}}","\frac{4 \sqrt{x+1}}{45 x^{3/2}}-\frac{\sqrt{x+1}}{15 x^{5/2}}-\frac{\sinh ^{-1}\left(\sqrt{x}\right)}{3 x^3}-\frac{8 \sqrt{x+1}}{45 \sqrt{x}}",1,"-Sqrt[1 + x]/(15*x^(5/2)) + (4*Sqrt[1 + x])/(45*x^(3/2)) - (8*Sqrt[1 + x])/(45*Sqrt[x]) - ArcSinh[Sqrt[x]]/(3*x^3)","A",5,4,10,0.4000,1,"{5902, 12, 45, 37}"
299,1,78,0,0.0273138,"\int \frac{\sinh ^{-1}\left(\sqrt{x}\right)}{x^5} \, dx","Int[ArcSinh[Sqrt[x]]/x^5,x]","-\frac{2 \sqrt{x+1}}{35 x^{3/2}}+\frac{3 \sqrt{x+1}}{70 x^{5/2}}-\frac{\sqrt{x+1}}{28 x^{7/2}}-\frac{\sinh ^{-1}\left(\sqrt{x}\right)}{4 x^4}+\frac{4 \sqrt{x+1}}{35 \sqrt{x}}","-\frac{2 \sqrt{x+1}}{35 x^{3/2}}+\frac{3 \sqrt{x+1}}{70 x^{5/2}}-\frac{\sqrt{x+1}}{28 x^{7/2}}-\frac{\sinh ^{-1}\left(\sqrt{x}\right)}{4 x^4}+\frac{4 \sqrt{x+1}}{35 \sqrt{x}}",1,"-Sqrt[1 + x]/(28*x^(7/2)) + (3*Sqrt[1 + x])/(70*x^(5/2)) - (2*Sqrt[1 + x])/(35*x^(3/2)) + (4*Sqrt[1 + x])/(35*Sqrt[x]) - ArcSinh[Sqrt[x]]/(4*x^4)","A",6,4,10,0.4000,1,"{5902, 12, 45, 37}"
300,1,56,0,0.039814,"\int x^2 \sinh ^{-1}\left(\frac{a}{x}\right) \, dx","Int[x^2*ArcSinh[a/x],x]","\frac{1}{6} a x^2 \sqrt{\frac{a^2}{x^2}+1}-\frac{1}{6} a^3 \tanh ^{-1}\left(\sqrt{\frac{a^2}{x^2}+1}\right)+\frac{1}{3} x^3 \text{csch}^{-1}\left(\frac{x}{a}\right)","\frac{1}{6} a x^2 \sqrt{\frac{a^2}{x^2}+1}-\frac{1}{6} a^3 \tanh ^{-1}\left(\sqrt{\frac{a^2}{x^2}+1}\right)+\frac{1}{3} x^3 \text{csch}^{-1}\left(\frac{x}{a}\right)",1,"(a*Sqrt[1 + a^2/x^2]*x^2)/6 + (x^3*ArcCsch[x/a])/3 - (a^3*ArcTanh[Sqrt[1 + a^2/x^2]])/6","A",6,6,10,0.6000,1,"{5892, 6284, 266, 51, 63, 208}"
301,1,33,0,0.0172917,"\int x \sinh ^{-1}\left(\frac{a}{x}\right) \, dx","Int[x*ArcSinh[a/x],x]","\frac{1}{2} a x \sqrt{\frac{a^2}{x^2}+1}+\frac{1}{2} x^2 \text{csch}^{-1}\left(\frac{x}{a}\right)","\frac{1}{2} a x \sqrt{\frac{a^2}{x^2}+1}+\frac{1}{2} x^2 \text{csch}^{-1}\left(\frac{x}{a}\right)",1,"(a*Sqrt[1 + a^2/x^2]*x)/2 + (x^2*ArcCsch[x/a])/2","A",3,3,8,0.3750,1,"{5892, 6284, 191}"
302,1,25,0,0.0172984,"\int \sinh ^{-1}\left(\frac{a}{x}\right) \, dx","Int[ArcSinh[a/x],x]","a \tanh ^{-1}\left(\sqrt{\frac{a^2}{x^2}+1}\right)+x \text{csch}^{-1}\left(\frac{x}{a}\right)","a \tanh ^{-1}\left(\sqrt{\frac{a^2}{x^2}+1}\right)+x \text{csch}^{-1}\left(\frac{x}{a}\right)",1,"x*ArcCsch[x/a] + a*ArcTanh[Sqrt[1 + a^2/x^2]]","A",5,5,6,0.8333,1,"{5892, 6278, 266, 63, 208}"
303,1,52,0,0.0619257,"\int \frac{\sinh ^{-1}\left(\frac{a}{x}\right)}{x} \, dx","Int[ArcSinh[a/x]/x,x]","-\frac{1}{2} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{a}{x}\right)}\right)+\frac{1}{2} \sinh ^{-1}\left(\frac{a}{x}\right)^2-\sinh ^{-1}\left(\frac{a}{x}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{a}{x}\right)}\right)","-\frac{1}{2} \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{a}{x}\right)}\right)+\frac{1}{2} \sinh ^{-1}\left(\frac{a}{x}\right)^2-\sinh ^{-1}\left(\frac{a}{x}\right) \log \left(1-e^{2 \sinh ^{-1}\left(\frac{a}{x}\right)}\right)",1,"ArcSinh[a/x]^2/2 - ArcSinh[a/x]*Log[1 - E^(2*ArcSinh[a/x])] - PolyLog[2, E^(2*ArcSinh[a/x])]/2","A",5,5,10,0.5000,1,"{5890, 3716, 2190, 2279, 2391}"
304,1,29,0,0.0241453,"\int \frac{\sinh ^{-1}\left(\frac{a}{x}\right)}{x^2} \, dx","Int[ArcSinh[a/x]/x^2,x]","\frac{\sqrt{\frac{a^2}{x^2}+1}}{a}-\frac{\text{csch}^{-1}\left(\frac{x}{a}\right)}{x}","\frac{\sqrt{\frac{a^2}{x^2}+1}}{a}-\frac{\text{csch}^{-1}\left(\frac{x}{a}\right)}{x}",1,"Sqrt[1 + a^2/x^2]/a - ArcCsch[x/a]/x","A",3,3,10,0.3000,1,"{5892, 6284, 261}"
305,1,50,0,0.034073,"\int \frac{\sinh ^{-1}\left(\frac{a}{x}\right)}{x^3} \, dx","Int[ArcSinh[a/x]/x^3,x]","\frac{\sqrt{\frac{a^2}{x^2}+1}}{4 a x}-\frac{\text{csch}^{-1}\left(\frac{x}{a}\right)}{4 a^2}-\frac{\text{csch}^{-1}\left(\frac{x}{a}\right)}{2 x^2}","\frac{\sqrt{\frac{a^2}{x^2}+1}}{4 a x}-\frac{\text{csch}^{-1}\left(\frac{x}{a}\right)}{4 a^2}-\frac{\text{csch}^{-1}\left(\frac{x}{a}\right)}{2 x^2}",1,"Sqrt[1 + a^2/x^2]/(4*a*x) - ArcCsch[x/a]/(4*a^2) - ArcCsch[x/a]/(2*x^2)","A",5,5,10,0.5000,1,"{5892, 6284, 335, 321, 215}"
306,1,54,0,0.0399537,"\int \frac{\sinh ^{-1}\left(\frac{a}{x}\right)}{x^4} \, dx","Int[ArcSinh[a/x]/x^4,x]","\frac{\left(\frac{a^2}{x^2}+1\right)^{3/2}}{9 a^3}-\frac{\sqrt{\frac{a^2}{x^2}+1}}{3 a^3}-\frac{\text{csch}^{-1}\left(\frac{x}{a}\right)}{3 x^3}","\frac{\left(\frac{a^2}{x^2}+1\right)^{3/2}}{9 a^3}-\frac{\sqrt{\frac{a^2}{x^2}+1}}{3 a^3}-\frac{\text{csch}^{-1}\left(\frac{x}{a}\right)}{3 x^3}",1,"-Sqrt[1 + a^2/x^2]/(3*a^3) + (1 + a^2/x^2)^(3/2)/(9*a^3) - ArcCsch[x/a]/(3*x^3)","A",5,4,10,0.4000,1,"{5892, 6284, 266, 43}"
307,1,77,0,0.044325,"\int x^m \sinh ^{-1}\left(a x^n\right) \, dx","Int[x^m*ArcSinh[a*x^n],x]","\frac{x^{m+1} \sinh ^{-1}\left(a x^n\right)}{m+1}-\frac{a n x^{m+n+1} \, _2F_1\left(\frac{1}{2},\frac{m+n+1}{2 n};\frac{m+3 n+1}{2 n};-a^2 x^{2 n}\right)}{(m+1) (m+n+1)}","\frac{x^{m+1} \sinh ^{-1}\left(a x^n\right)}{m+1}-\frac{a n x^{m+n+1} \, _2F_1\left(\frac{1}{2},\frac{m+n+1}{2 n};\frac{m+3 n+1}{2 n};-a^2 x^{2 n}\right)}{(m+1) (m+n+1)}",1,"(x^(1 + m)*ArcSinh[a*x^n])/(1 + m) - (a*n*x^(1 + m + n)*Hypergeometric2F1[1/2, (1 + m + n)/(2*n), (1 + m + 3*n)/(2*n), -(a^2*x^(2*n))])/((1 + m)*(1 + m + n))","A",3,3,10,0.3000,1,"{5902, 12, 364}"
308,1,64,0,0.0352749,"\int x^2 \sinh ^{-1}\left(a x^n\right) \, dx","Int[x^2*ArcSinh[a*x^n],x]","\frac{1}{3} x^3 \sinh ^{-1}\left(a x^n\right)-\frac{a n x^{n+3} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2 n};\frac{3 (n+1)}{2 n};-a^2 x^{2 n}\right)}{3 (n+3)}","\frac{1}{3} x^3 \sinh ^{-1}\left(a x^n\right)-\frac{a n x^{n+3} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2 n};\frac{3 (n+1)}{2 n};-a^2 x^{2 n}\right)}{3 (n+3)}",1,"(x^3*ArcSinh[a*x^n])/3 - (a*n*x^(3 + n)*Hypergeometric2F1[1/2, (3 + n)/(2*n), (3*(1 + n))/(2*n), -(a^2*x^(2*n))])/(3*(3 + n))","A",3,3,10,0.3000,1,"{5902, 12, 364}"
309,1,65,0,0.0297645,"\int x \sinh ^{-1}\left(a x^n\right) \, dx","Int[x*ArcSinh[a*x^n],x]","\frac{1}{2} x^2 \sinh ^{-1}\left(a x^n\right)-\frac{a n x^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2 n};\frac{1}{2} \left(3+\frac{2}{n}\right);-a^2 x^{2 n}\right)}{2 (n+2)}","\frac{1}{2} x^2 \sinh ^{-1}\left(a x^n\right)-\frac{a n x^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2 n};\frac{1}{2} \left(3+\frac{2}{n}\right);-a^2 x^{2 n}\right)}{2 (n+2)}",1,"(x^2*ArcSinh[a*x^n])/2 - (a*n*x^(2 + n)*Hypergeometric2F1[1/2, (2 + n)/(2*n), (3 + 2/n)/2, -(a^2*x^(2*n))])/(2*(2 + n))","A",3,3,8,0.3750,1,"{5902, 12, 364}"
310,1,56,0,0.0225214,"\int \sinh ^{-1}\left(a x^n\right) \, dx","Int[ArcSinh[a*x^n],x]","x \sinh ^{-1}\left(a x^n\right)-\frac{a n x^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2 n};\frac{1}{2} \left(3+\frac{1}{n}\right);-a^2 x^{2 n}\right)}{n+1}","x \sinh ^{-1}\left(a x^n\right)-\frac{a n x^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2 n};\frac{1}{2} \left(3+\frac{1}{n}\right);-a^2 x^{2 n}\right)}{n+1}",1,"x*ArcSinh[a*x^n] - (a*n*x^(1 + n)*Hypergeometric2F1[1/2, (1 + n)/(2*n), (3 + n^(-1))/2, -(a^2*x^(2*n))])/(1 + n)","A",3,3,6,0.5000,1,"{5900, 12, 364}"
311,1,60,0,0.0662234,"\int \frac{\sinh ^{-1}\left(a x^n\right)}{x} \, dx","Int[ArcSinh[a*x^n]/x,x]","\frac{\text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(a x^n\right)}\right)}{2 n}-\frac{\sinh ^{-1}\left(a x^n\right)^2}{2 n}+\frac{\sinh ^{-1}\left(a x^n\right) \log \left(1-e^{2 \sinh ^{-1}\left(a x^n\right)}\right)}{n}","\frac{\text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(a x^n\right)}\right)}{2 n}-\frac{\sinh ^{-1}\left(a x^n\right)^2}{2 n}+\frac{\sinh ^{-1}\left(a x^n\right) \log \left(1-e^{2 \sinh ^{-1}\left(a x^n\right)}\right)}{n}",1,"-ArcSinh[a*x^n]^2/(2*n) + (ArcSinh[a*x^n]*Log[1 - E^(2*ArcSinh[a*x^n])])/n + PolyLog[2, E^(2*ArcSinh[a*x^n])]/(2*n)","A",5,5,10,0.5000,1,"{5890, 3716, 2190, 2279, 2391}"
312,1,65,0,0.0331579,"\int \frac{\sinh ^{-1}\left(a x^n\right)}{x^2} \, dx","Int[ArcSinh[a*x^n]/x^2,x]","-\frac{a n x^{n-1} \, _2F_1\left(\frac{1}{2},-\frac{1-n}{2 n};\frac{1}{2} \left(3-\frac{1}{n}\right);-a^2 x^{2 n}\right)}{1-n}-\frac{\sinh ^{-1}\left(a x^n\right)}{x}","-\frac{a n x^{n-1} \, _2F_1\left(\frac{1}{2},-\frac{1-n}{2 n};\frac{1}{2} \left(3-\frac{1}{n}\right);-a^2 x^{2 n}\right)}{1-n}-\frac{\sinh ^{-1}\left(a x^n\right)}{x}",1,"-(ArcSinh[a*x^n]/x) - (a*n*x^(-1 + n)*Hypergeometric2F1[1/2, -(1 - n)/(2*n), (3 - n^(-1))/2, -(a^2*x^(2*n))])/(1 - n)","A",3,3,10,0.3000,1,"{5902, 12, 364}"
313,1,68,0,0.0390606,"\int \frac{\sinh ^{-1}\left(a x^n\right)}{x^3} \, dx","Int[ArcSinh[a*x^n]/x^3,x]","-\frac{a n x^{n-2} \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(1-\frac{2}{n}\right);\frac{1}{2} \left(3-\frac{2}{n}\right);-a^2 x^{2 n}\right)}{2 (2-n)}-\frac{\sinh ^{-1}\left(a x^n\right)}{2 x^2}","-\frac{a n x^{n-2} \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(1-\frac{2}{n}\right);\frac{1}{2} \left(3-\frac{2}{n}\right);-a^2 x^{2 n}\right)}{2 (2-n)}-\frac{\sinh ^{-1}\left(a x^n\right)}{2 x^2}",1,"-ArcSinh[a*x^n]/(2*x^2) - (a*n*x^(-2 + n)*Hypergeometric2F1[1/2, (1 - 2/n)/2, (3 - 2/n)/2, -(a^2*x^(2*n))])/(2*(2 - n))","A",3,3,10,0.3000,1,"{5902, 12, 364}"
314,1,153,0,0.0360296,"\int \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^4 \, dx","Int[(a + I*b*ArcSin[1 - I*d*x^2])^4,x]","-\frac{192 b^3 \sqrt{d^2 x^4+2 i d x^2} \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)}{d x}+48 b^2 x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^2-\frac{8 b \sqrt{d^2 x^4+2 i d x^2} \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^3}{d x}+x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^4+384 b^4 x","-\frac{192 b^3 \sqrt{d^2 x^4+2 i d x^2} \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)}{d x}+48 b^2 x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^2-\frac{8 b \sqrt{d^2 x^4+2 i d x^2} \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^3}{d x}+x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^4+384 b^4 x",1,"384*b^4*x - (192*b^3*Sqrt[(2*I)*d*x^2 + d^2*x^4]*(a + I*b*ArcSin[1 - I*d*x^2]))/(d*x) + 48*b^2*x*(a + I*b*ArcSin[1 - I*d*x^2])^2 - (8*b*Sqrt[(2*I)*d*x^2 + d^2*x^4]*(a + I*b*ArcSin[1 - I*d*x^2])^3)/(d*x) + x*(a + I*b*ArcSin[1 - I*d*x^2])^4","A",3,2,20,0.1000,1,"{4814, 8}"
315,1,129,0,0.0639983,"\int \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^3 \, dx","Int[(a + I*b*ArcSin[1 - I*d*x^2])^3,x]","24 a b^2 x-\frac{6 b \sqrt{d^2 x^4+2 i d x^2} \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^2}{d x}+x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^3-\frac{48 b^3 \sqrt{d^2 x^4+2 i d x^2}}{d x}+24 i b^3 x \sin ^{-1}\left(1-i d x^2\right)","24 a b^2 x-\frac{6 b \sqrt{d^2 x^4+2 i d x^2} \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^2}{d x}+x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^3-\frac{48 b^3 \sqrt{d^2 x^4+2 i d x^2}}{d x}+24 i b^3 x \sin ^{-1}\left(1-i d x^2\right)",1,"24*a*b^2*x - (48*b^3*Sqrt[(2*I)*d*x^2 + d^2*x^4])/(d*x) + (24*I)*b^3*x*ArcSin[1 - I*d*x^2] - (6*b*Sqrt[(2*I)*d*x^2 + d^2*x^4]*(a + I*b*ArcSin[1 - I*d*x^2])^2)/(d*x) + x*(a + I*b*ArcSin[1 - I*d*x^2])^3","A",5,4,20,0.2000,1,"{4814, 4840, 12, 1588}"
316,1,76,0,0.01526,"\int \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^2 \, dx","Int[(a + I*b*ArcSin[1 - I*d*x^2])^2,x]","-\frac{4 b \sqrt{d^2 x^4+2 i d x^2} \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)}{d x}+x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^2+8 b^2 x","-\frac{4 b \sqrt{d^2 x^4+2 i d x^2} \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)}{d x}+x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^2+8 b^2 x",1,"8*b^2*x - (4*b*Sqrt[(2*I)*d*x^2 + d^2*x^4]*(a + I*b*ArcSin[1 - I*d*x^2]))/(d*x) + x*(a + I*b*ArcSin[1 - I*d*x^2])^2","A",2,2,20,0.1000,1,"{4814, 8}"
317,1,50,0,0.04019,"\int \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right) \, dx","Int[a + I*b*ArcSin[1 - I*d*x^2],x]","a x-\frac{2 b \sqrt{d^2 x^4+2 i d x^2}}{d x}+i b x \sin ^{-1}\left(1-i d x^2\right)","a x-\frac{2 b \sqrt{d^2 x^4+2 i d x^2}}{d x}+i b x \sin ^{-1}\left(1-i d x^2\right)",1,"a*x - (2*b*Sqrt[(2*I)*d*x^2 + d^2*x^4])/(d*x) + I*b*x*ArcSin[1 - I*d*x^2]","A",4,3,18,0.1667,1,"{4840, 12, 1588}"
318,1,194,0,0.0478033,"\int \frac{1}{a+i b \sin ^{-1}\left(1-i d x^2\right)} \, dx","Int[(a + I*b*ArcSin[1 - I*d*x^2])^(-1),x]","\frac{x \left(-\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(-\frac{i \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)}{2 b}\right)}{2 b \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{i a}{2 b}-\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)}{2 b \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}","\frac{x \left(-\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(-\frac{i \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)}{2 b}\right)}{2 b \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{i a}{2 b}-\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)}{2 b \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}",1,"(x*CosIntegral[((-I/2)*(a + I*b*ArcSin[1 - I*d*x^2]))/b]*(I*Cosh[a/(2*b)] - Sinh[a/(2*b)]))/(2*b*(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2])) - (x*(I*Cosh[a/(2*b)] + Sinh[a/(2*b)])*SinIntegral[((I/2)*a)/b - ArcSin[1 - I*d*x^2]/2])/(2*b*(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2]))","A",1,1,20,0.05000,1,"{4816}"
319,1,245,0,0.0426255,"\int \frac{1}{\left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^2} \, dx","Int[(a + I*b*ArcSin[1 - I*d*x^2])^(-2),x]","\frac{x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(-\frac{i \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)}{2 b}\right)}{4 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}+\frac{x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{i a}{2 b}-\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)}{4 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{\sqrt{d^2 x^4+2 i d x^2}}{2 b d x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)}","\frac{x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(-\frac{i \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)}{2 b}\right)}{4 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}+\frac{x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{i a}{2 b}-\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)}{4 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{\sqrt{d^2 x^4+2 i d x^2}}{2 b d x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)}",1,"-Sqrt[(2*I)*d*x^2 + d^2*x^4]/(2*b*d*x*(a + I*b*ArcSin[1 - I*d*x^2])) + (x*CosIntegral[((-I/2)*(a + I*b*ArcSin[1 - I*d*x^2]))/b]*(Cosh[a/(2*b)] - I*Sinh[a/(2*b)]))/(4*b^2*(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2])) + (x*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)])*SinIntegral[((I/2)*a)/b - ArcSin[1 - I*d*x^2]/2])/(4*b^2*(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2]))","A",1,1,20,0.05000,1,"{4825}"
320,1,275,0,0.0541483,"\int \frac{1}{\left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^3} \, dx","Int[(a + I*b*ArcSin[1 - I*d*x^2])^(-3),x]","\frac{x \left(-\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(-\frac{i \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)}{2 b}\right)}{16 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{i a}{2 b}-\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)}{16 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{x}{8 b^2 \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)}-\frac{\sqrt{d^2 x^4+2 i d x^2}}{4 b d x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^2}","\frac{x \left(-\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(-\frac{i \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)}{2 b}\right)}{16 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{Si}\left(\frac{i a}{2 b}-\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)}{16 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{x}{8 b^2 \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)}-\frac{\sqrt{d^2 x^4+2 i d x^2}}{4 b d x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^2}",1,"-Sqrt[(2*I)*d*x^2 + d^2*x^4]/(4*b*d*x*(a + I*b*ArcSin[1 - I*d*x^2])^2) - x/(8*b^2*(a + I*b*ArcSin[1 - I*d*x^2])) + (x*CosIntegral[((-I/2)*(a + I*b*ArcSin[1 - I*d*x^2]))/b]*(I*Cosh[a/(2*b)] - Sinh[a/(2*b)]))/(16*b^3*(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2])) - (x*(I*Cosh[a/(2*b)] + Sinh[a/(2*b)])*SinIntegral[((I/2)*a)/b - ArcSin[1 - I*d*x^2]/2])/(16*b^3*(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2]))","A",2,2,20,0.1000,1,"{4828, 4816}"
321,1,153,0,0.0318743,"\int \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^4 \, dx","Int[(a - I*b*ArcSin[1 + I*d*x^2])^4,x]","-\frac{192 b^3 \sqrt{d^2 x^4-2 i d x^2} \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)}{d x}+48 b^2 x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^2-\frac{8 b \sqrt{d^2 x^4-2 i d x^2} \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^3}{d x}+x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^4+384 b^4 x","-\frac{192 b^3 \sqrt{d^2 x^4-2 i d x^2} \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)}{d x}+48 b^2 x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^2-\frac{8 b \sqrt{d^2 x^4-2 i d x^2} \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^3}{d x}+x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^4+384 b^4 x",1,"384*b^4*x - (192*b^3*Sqrt[(-2*I)*d*x^2 + d^2*x^4]*(a - I*b*ArcSin[1 + I*d*x^2]))/(d*x) + 48*b^2*x*(a - I*b*ArcSin[1 + I*d*x^2])^2 - (8*b*Sqrt[(-2*I)*d*x^2 + d^2*x^4]*(a - I*b*ArcSin[1 + I*d*x^2])^3)/(d*x) + x*(a - I*b*ArcSin[1 + I*d*x^2])^4","A",3,2,20,0.1000,1,"{4814, 8}"
322,1,129,0,0.0588589,"\int \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^3 \, dx","Int[(a - I*b*ArcSin[1 + I*d*x^2])^3,x]","24 a b^2 x-\frac{6 b \sqrt{d^2 x^4-2 i d x^2} \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^2}{d x}+x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^3-\frac{48 b^3 \sqrt{d^2 x^4-2 i d x^2}}{d x}-24 i b^3 x \sin ^{-1}\left(1+i d x^2\right)","24 a b^2 x-\frac{6 b \sqrt{d^2 x^4-2 i d x^2} \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^2}{d x}+x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^3-\frac{48 b^3 \sqrt{d^2 x^4-2 i d x^2}}{d x}-24 i b^3 x \sin ^{-1}\left(1+i d x^2\right)",1,"24*a*b^2*x - (48*b^3*Sqrt[(-2*I)*d*x^2 + d^2*x^4])/(d*x) - (24*I)*b^3*x*ArcSin[1 + I*d*x^2] - (6*b*Sqrt[(-2*I)*d*x^2 + d^2*x^4]*(a - I*b*ArcSin[1 + I*d*x^2])^2)/(d*x) + x*(a - I*b*ArcSin[1 + I*d*x^2])^3","A",5,4,20,0.2000,1,"{4814, 4840, 12, 1588}"
323,1,76,0,0.0126438,"\int \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^2 \, dx","Int[(a - I*b*ArcSin[1 + I*d*x^2])^2,x]","-\frac{4 b \sqrt{d^2 x^4-2 i d x^2} \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)}{d x}+x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^2+8 b^2 x","-\frac{4 b \sqrt{d^2 x^4-2 i d x^2} \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)}{d x}+x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^2+8 b^2 x",1,"8*b^2*x - (4*b*Sqrt[(-2*I)*d*x^2 + d^2*x^4]*(a - I*b*ArcSin[1 + I*d*x^2]))/(d*x) + x*(a - I*b*ArcSin[1 + I*d*x^2])^2","A",2,2,20,0.1000,1,"{4814, 8}"
324,1,50,0,0.0387746,"\int \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right) \, dx","Int[a - I*b*ArcSin[1 + I*d*x^2],x]","a x-\frac{2 b \sqrt{d^2 x^4-2 i d x^2}}{d x}-i b x \sin ^{-1}\left(1+i d x^2\right)","a x-\frac{2 b \sqrt{d^2 x^4-2 i d x^2}}{d x}-i b x \sin ^{-1}\left(1+i d x^2\right)",1,"a*x - (2*b*Sqrt[(-2*I)*d*x^2 + d^2*x^4])/(d*x) - I*b*x*ArcSin[1 + I*d*x^2]","A",4,3,18,0.1667,1,"{4840, 12, 1588}"
325,1,191,0,0.0228964,"\int \frac{1}{a-i b \sin ^{-1}\left(1+i d x^2\right)} \, dx","Int[(a - I*b*ArcSin[1 + I*d*x^2])^(-1),x]","\frac{x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{Shi}\left(\frac{a-i b \sin ^{-1}\left(i d x^2+1\right)}{2 b}\right)}{2 b \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(\frac{i \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)}{2 b}\right)}{2 b \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}","\frac{x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{Shi}\left(\frac{a-i b \sin ^{-1}\left(i d x^2+1\right)}{2 b}\right)}{2 b \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(\frac{i \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)}{2 b}\right)}{2 b \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}",1,"-(x*CosIntegral[((I/2)*(a - I*b*ArcSin[1 + I*d*x^2]))/b]*(I*Cosh[a/(2*b)] + Sinh[a/(2*b)]))/(2*b*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2])) + (x*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)])*SinhIntegral[(a - I*b*ArcSin[1 + I*d*x^2])/(2*b)])/(2*b*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2]))","A",1,1,20,0.05000,1,"{4816}"
326,1,244,0,0.0286216,"\int \frac{1}{\left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^2} \, dx","Int[(a - I*b*ArcSin[1 + I*d*x^2])^(-2),x]","\frac{x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(\frac{i \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)}{2 b}\right)}{4 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{Shi}\left(\frac{a-i b \sin ^{-1}\left(i d x^2+1\right)}{2 b}\right)}{4 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{\sqrt{d^2 x^4-2 i d x^2}}{2 b d x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)}","\frac{x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(\frac{i \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)}{2 b}\right)}{4 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{Shi}\left(\frac{a-i b \sin ^{-1}\left(i d x^2+1\right)}{2 b}\right)}{4 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{\sqrt{d^2 x^4-2 i d x^2}}{2 b d x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)}",1,"-Sqrt[(-2*I)*d*x^2 + d^2*x^4]/(2*b*d*x*(a - I*b*ArcSin[1 + I*d*x^2])) + (x*CosIntegral[((I/2)*(a - I*b*ArcSin[1 + I*d*x^2]))/b]*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)]))/(4*b^2*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2])) - (x*(I*Cosh[a/(2*b)] + Sinh[a/(2*b)])*SinhIntegral[(a - I*b*ArcSin[1 + I*d*x^2])/(2*b)])/(4*b^2*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2]))","A",1,1,20,0.05000,1,"{4825}"
327,1,272,0,0.0508033,"\int \frac{1}{\left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^3} \, dx","Int[(a - I*b*ArcSin[1 + I*d*x^2])^(-3),x]","-\frac{x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(\frac{i \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)}{2 b}\right)}{16 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}+\frac{x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{Shi}\left(\frac{a-i b \sin ^{-1}\left(i d x^2+1\right)}{2 b}\right)}{16 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{x}{8 b^2 \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)}-\frac{\sqrt{d^2 x^4-2 i d x^2}}{4 b d x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^2}","-\frac{x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{CosIntegral}\left(\frac{i \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)}{2 b}\right)}{16 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}+\frac{x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{Shi}\left(\frac{a-i b \sin ^{-1}\left(i d x^2+1\right)}{2 b}\right)}{16 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{x}{8 b^2 \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)}-\frac{\sqrt{d^2 x^4-2 i d x^2}}{4 b d x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^2}",1,"-Sqrt[(-2*I)*d*x^2 + d^2*x^4]/(4*b*d*x*(a - I*b*ArcSin[1 + I*d*x^2])^2) - x/(8*b^2*(a - I*b*ArcSin[1 + I*d*x^2])) - (x*CosIntegral[((I/2)*(a - I*b*ArcSin[1 + I*d*x^2]))/b]*(I*Cosh[a/(2*b)] + Sinh[a/(2*b)]))/(16*b^3*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2])) + (x*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)])*SinhIntegral[(a - I*b*ArcSin[1 + I*d*x^2])/(2*b)])/(16*b^3*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2]))","A",2,2,20,0.1000,1,"{4828, 4816}"
328,1,348,0,0.1119111,"\int \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{5/2} \, dx","Int[(a + I*b*ArcSin[1 - I*d*x^2])^(5/2),x]","-\frac{15 \sqrt{\pi } \sqrt{-\frac{i}{b}} b^3 x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{-\frac{i}{b}} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)}+\frac{15 \sqrt{\pi } b^2 x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{-\frac{i}{b}} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi }}\right)}{\sqrt{-\frac{i}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}+15 b^2 x \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}-\frac{5 b \sqrt{d^2 x^4+2 i d x^2} \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{3/2}}{d x}+x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{5/2}","-\frac{15 \sqrt{\pi } \sqrt{-\frac{i}{b}} b^3 x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{-\frac{i}{b}} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)}+\frac{15 \sqrt{\pi } b^2 x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{-\frac{i}{b}} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi }}\right)}{\sqrt{-\frac{i}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}+15 b^2 x \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}-\frac{5 b \sqrt{d^2 x^4+2 i d x^2} \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{3/2}}{d x}+x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{5/2}",1,"15*b^2*x*Sqrt[a + I*b*ArcSin[1 - I*d*x^2]] - (5*b*Sqrt[(2*I)*d*x^2 + d^2*x^4]*(a + I*b*ArcSin[1 - I*d*x^2])^(3/2))/(d*x) + x*(a + I*b*ArcSin[1 - I*d*x^2])^(5/2) + (15*b^2*Sqrt[Pi]*x*FresnelS[(Sqrt[(-I)/b]*Sqrt[a + I*b*ArcSin[1 - I*d*x^2]])/Sqrt[Pi]]*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)]))/(Sqrt[(-I)/b]*(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2])) - (15*Sqrt[(-I)/b]*b^3*Sqrt[Pi]*x*FresnelC[(Sqrt[(-I)/b]*Sqrt[a + I*b*ArcSin[1 - I*d*x^2]])/Sqrt[Pi]]*(I*Cosh[a/(2*b)] + Sinh[a/(2*b)]))/(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2])","A",2,2,22,0.09091,1,"{4814, 4811}"
329,1,312,0,0.1050412,"\int \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{3/2} \, dx","Int[(a + I*b*ArcSin[1 - I*d*x^2])^(3/2),x]","-\frac{3 \sqrt{\pi } b^2 x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{i b} \sqrt{\pi }}\right)}{\sqrt{i b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{3 b \sqrt{d^2 x^4+2 i d x^2} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{d x}+\frac{3 \sqrt{\pi } \sqrt{i b} b x \left(-\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi } \sqrt{i b}}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)}+x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{3/2}","-\frac{3 \sqrt{\pi } b^2 x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{i b} \sqrt{\pi }}\right)}{\sqrt{i b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{3 b \sqrt{d^2 x^4+2 i d x^2} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{d x}+\frac{3 \sqrt{\pi } \sqrt{i b} b x \left(-\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi } \sqrt{i b}}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)}+x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{3/2}",1,"(-3*b*Sqrt[(2*I)*d*x^2 + d^2*x^4]*Sqrt[a + I*b*ArcSin[1 - I*d*x^2]])/(d*x) + x*(a + I*b*ArcSin[1 - I*d*x^2])^(3/2) + (3*Sqrt[I*b]*b*Sqrt[Pi]*x*FresnelC[Sqrt[a + I*b*ArcSin[1 - I*d*x^2]]/(Sqrt[I*b]*Sqrt[Pi])]*(I*Cosh[a/(2*b)] - Sinh[a/(2*b)]))/(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2]) - (3*b^2*Sqrt[Pi]*x*FresnelS[Sqrt[a + I*b*ArcSin[1 - I*d*x^2]]/(Sqrt[I*b]*Sqrt[Pi])]*(Cosh[a/(2*b)] - I*Sinh[a/(2*b)]))/(Sqrt[I*b]*(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2]))","A",2,2,22,0.09091,1,"{4814, 4819}"
330,1,263,0,0.0270555,"\int \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)} \, dx","Int[Sqrt[a + I*b*ArcSin[1 - I*d*x^2]],x]","-\frac{\sqrt{\pi } \sqrt{-\frac{i}{b}} b x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{-\frac{i}{b}} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)}+\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{-\frac{i}{b}} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi }}\right)}{\sqrt{-\frac{i}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}+x \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}","-\frac{\sqrt{\pi } \sqrt{-\frac{i}{b}} b x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{-\frac{i}{b}} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)}+\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{-\frac{i}{b}} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi }}\right)}{\sqrt{-\frac{i}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}+x \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}",1,"x*Sqrt[a + I*b*ArcSin[1 - I*d*x^2]] + (Sqrt[Pi]*x*FresnelS[(Sqrt[(-I)/b]*Sqrt[a + I*b*ArcSin[1 - I*d*x^2]])/Sqrt[Pi]]*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)]))/(Sqrt[(-I)/b]*(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2])) - (Sqrt[(-I)/b]*b*Sqrt[Pi]*x*FresnelC[(Sqrt[(-I)/b]*Sqrt[a + I*b*ArcSin[1 - I*d*x^2]])/Sqrt[Pi]]*(I*Cosh[a/(2*b)] + Sinh[a/(2*b)]))/(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2])","A",1,1,22,0.04545,1,"{4811}"
331,1,231,0,0.0299369,"\int \frac{1}{\sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}} \, dx","Int[1/Sqrt[a + I*b*ArcSin[1 - I*d*x^2]],x]","-\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi } \sqrt{i b}}\right)}{\sqrt{i b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{i b} \sqrt{\pi }}\right)}{\sqrt{i b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}","-\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi } \sqrt{i b}}\right)}{\sqrt{i b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{i b} \sqrt{\pi }}\right)}{\sqrt{i b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}",1,"-((Sqrt[Pi]*x*FresnelS[Sqrt[a + I*b*ArcSin[1 - I*d*x^2]]/(Sqrt[I*b]*Sqrt[Pi])]*(Cosh[a/(2*b)] - I*Sinh[a/(2*b)]))/(Sqrt[I*b]*(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2]))) - (Sqrt[Pi]*x*FresnelC[Sqrt[a + I*b*ArcSin[1 - I*d*x^2]]/(Sqrt[I*b]*Sqrt[Pi])]*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)]))/(Sqrt[I*b]*(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2]))","A",1,1,22,0.04545,1,"{4819}"
332,1,291,0,0.0524787,"\int \frac{1}{\left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{3/2}} \, dx","Int[(a + I*b*ArcSin[1 - I*d*x^2])^(-3/2),x]","-\frac{\sqrt{d^2 x^4+2 i d x^2}}{b d x \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}-\frac{\sqrt{\pi } \left(-\frac{i}{b}\right)^{3/2} x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{-\frac{i}{b}} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)}+\frac{\sqrt{\pi } \left(-\frac{i}{b}\right)^{3/2} x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{-\frac{i}{b}} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)}","-\frac{\sqrt{d^2 x^4+2 i d x^2}}{b d x \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}-\frac{\sqrt{\pi } \left(-\frac{i}{b}\right)^{3/2} x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{-\frac{i}{b}} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)}+\frac{\sqrt{\pi } \left(-\frac{i}{b}\right)^{3/2} x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{-\frac{i}{b}} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)}",1,"-(Sqrt[(2*I)*d*x^2 + d^2*x^4]/(b*d*x*Sqrt[a + I*b*ArcSin[1 - I*d*x^2]])) - (((-I)/b)^(3/2)*Sqrt[Pi]*x*FresnelC[(Sqrt[(-I)/b]*Sqrt[a + I*b*ArcSin[1 - I*d*x^2]])/Sqrt[Pi]]*(Cosh[a/(2*b)] - I*Sinh[a/(2*b)]))/(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2]) + (((-I)/b)^(3/2)*Sqrt[Pi]*x*FresnelS[(Sqrt[(-I)/b]*Sqrt[a + I*b*ArcSin[1 - I*d*x^2]])/Sqrt[Pi]]*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)]))/(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2])","A",1,1,22,0.04545,1,"{4822}"
333,1,326,0,0.0722763,"\int \frac{1}{\left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{5/2}} \, dx","Int[(a + I*b*ArcSin[1 - I*d*x^2])^(-5/2),x]","-\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi } \sqrt{i b}}\right)}{3 \sqrt{i b} b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{i b} \sqrt{\pi }}\right)}{3 \sqrt{i b} b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{x}{3 b^2 \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}-\frac{\sqrt{d^2 x^4+2 i d x^2}}{3 b d x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{3/2}}","-\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi } \sqrt{i b}}\right)}{3 \sqrt{i b} b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{i b} \sqrt{\pi }}\right)}{3 \sqrt{i b} b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{x}{3 b^2 \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}-\frac{\sqrt{d^2 x^4+2 i d x^2}}{3 b d x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{3/2}}",1,"-Sqrt[(2*I)*d*x^2 + d^2*x^4]/(3*b*d*x*(a + I*b*ArcSin[1 - I*d*x^2])^(3/2)) - x/(3*b^2*Sqrt[a + I*b*ArcSin[1 - I*d*x^2]]) - (Sqrt[Pi]*x*FresnelS[Sqrt[a + I*b*ArcSin[1 - I*d*x^2]]/(Sqrt[I*b]*Sqrt[Pi])]*(Cosh[a/(2*b)] - I*Sinh[a/(2*b)]))/(3*Sqrt[I*b]*b^2*(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2])) - (Sqrt[Pi]*x*FresnelC[Sqrt[a + I*b*ArcSin[1 - I*d*x^2]]/(Sqrt[I*b]*Sqrt[Pi])]*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)]))/(3*Sqrt[I*b]*b^2*(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2]))","A",2,2,22,0.09091,1,"{4828, 4819}"
334,1,389,0,0.0881781,"\int \frac{1}{\left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{7/2}} \, dx","Int[(a + I*b*ArcSin[1 - I*d*x^2])^(-7/2),x]","-\frac{\sqrt{d^2 x^4+2 i d x^2}}{15 b^3 d x \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}-\frac{\sqrt{\pi } \left(-\frac{i}{b}\right)^{3/2} x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{-\frac{i}{b}} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi }}\right)}{15 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}+\frac{\sqrt{\pi } \left(-\frac{i}{b}\right)^{3/2} x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{-\frac{i}{b}} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi }}\right)}{15 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{x}{15 b^2 \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{3/2}}-\frac{\sqrt{d^2 x^4+2 i d x^2}}{5 b d x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{5/2}}","-\frac{\sqrt{d^2 x^4+2 i d x^2}}{15 b^3 d x \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}-\frac{\sqrt{\pi } \left(-\frac{i}{b}\right)^{3/2} x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{-\frac{i}{b}} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi }}\right)}{15 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}+\frac{\sqrt{\pi } \left(-\frac{i}{b}\right)^{3/2} x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{-\frac{i}{b}} \sqrt{a+i b \sin ^{-1}\left(1-i d x^2\right)}}{\sqrt{\pi }}\right)}{15 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1-i d x^2\right)\right)\right)}-\frac{x}{15 b^2 \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{3/2}}-\frac{\sqrt{d^2 x^4+2 i d x^2}}{5 b d x \left(a+i b \sin ^{-1}\left(1-i d x^2\right)\right)^{5/2}}",1,"-Sqrt[(2*I)*d*x^2 + d^2*x^4]/(5*b*d*x*(a + I*b*ArcSin[1 - I*d*x^2])^(5/2)) - x/(15*b^2*(a + I*b*ArcSin[1 - I*d*x^2])^(3/2)) - Sqrt[(2*I)*d*x^2 + d^2*x^4]/(15*b^3*d*x*Sqrt[a + I*b*ArcSin[1 - I*d*x^2]]) - (((-I)/b)^(3/2)*Sqrt[Pi]*x*FresnelC[(Sqrt[(-I)/b]*Sqrt[a + I*b*ArcSin[1 - I*d*x^2]])/Sqrt[Pi]]*(Cosh[a/(2*b)] - I*Sinh[a/(2*b)]))/(15*b^2*(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2])) + (((-I)/b)^(3/2)*Sqrt[Pi]*x*FresnelS[(Sqrt[(-I)/b]*Sqrt[a + I*b*ArcSin[1 - I*d*x^2]])/Sqrt[Pi]]*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)]))/(15*b^2*(Cos[ArcSin[1 - I*d*x^2]/2] - Sin[ArcSin[1 - I*d*x^2]/2]))","A",2,2,22,0.09091,1,"{4828, 4822}"
335,1,348,0,0.0971646,"\int \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{5/2} \, dx","Int[(a - I*b*ArcSin[1 + I*d*x^2])^(5/2),x]","-\frac{15 \sqrt{\pi } b^2 x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{i}{b}} \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{i}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}+\frac{15 \sqrt{\pi } b^2 x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{\frac{i}{b}} \sqrt{a-i b \sin ^{-1}\left(i d x^2+1\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{i}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}+15 b^2 x \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}-\frac{5 b \sqrt{d^2 x^4-2 i d x^2} \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{3/2}}{d x}+x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{5/2}","-\frac{15 \sqrt{\pi } b^2 x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{i}{b}} \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{i}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}+\frac{15 \sqrt{\pi } b^2 x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{\frac{i}{b}} \sqrt{a-i b \sin ^{-1}\left(i d x^2+1\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{i}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}+15 b^2 x \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}-\frac{5 b \sqrt{d^2 x^4-2 i d x^2} \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{3/2}}{d x}+x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{5/2}",1,"15*b^2*x*Sqrt[a - I*b*ArcSin[1 + I*d*x^2]] - (5*b*Sqrt[(-2*I)*d*x^2 + d^2*x^4]*(a - I*b*ArcSin[1 + I*d*x^2])^(3/2))/(d*x) + x*(a - I*b*ArcSin[1 + I*d*x^2])^(5/2) + (15*b^2*Sqrt[Pi]*x*FresnelS[(Sqrt[I/b]*Sqrt[a - I*b*ArcSin[1 + I*d*x^2]])/Sqrt[Pi]]*(Cosh[a/(2*b)] - I*Sinh[a/(2*b)]))/(Sqrt[I/b]*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2])) - (15*b^2*Sqrt[Pi]*x*FresnelC[(Sqrt[I/b]*Sqrt[a - I*b*ArcSin[1 + I*d*x^2]])/Sqrt[Pi]]*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)]))/(Sqrt[I/b]*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2]))","A",2,2,22,0.09091,1,"{4814, 4811}"
336,1,310,0,0.0962973,"\int \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{3/2} \, dx","Int[(a - I*b*ArcSin[1 + I*d*x^2])^(3/2),x]","-\frac{3 \sqrt{\pi } b^2 x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a-i b \sin ^{-1}\left(i d x^2+1\right)}}{\sqrt{-i b} \sqrt{\pi }}\right)}{\sqrt{-i b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{3 b \sqrt{d^2 x^4-2 i d x^2} \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}{d x}-\frac{3 \sqrt{\pi } \sqrt{-i b} b x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}{\sqrt{\pi } \sqrt{-i b}}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)}+x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{3/2}","-\frac{3 \sqrt{\pi } b^2 x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a-i b \sin ^{-1}\left(i d x^2+1\right)}}{\sqrt{-i b} \sqrt{\pi }}\right)}{\sqrt{-i b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{3 b \sqrt{d^2 x^4-2 i d x^2} \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}{d x}-\frac{3 \sqrt{\pi } \sqrt{-i b} b x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}{\sqrt{\pi } \sqrt{-i b}}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)}+x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{3/2}",1,"(-3*b*Sqrt[(-2*I)*d*x^2 + d^2*x^4]*Sqrt[a - I*b*ArcSin[1 + I*d*x^2]])/(d*x) + x*(a - I*b*ArcSin[1 + I*d*x^2])^(3/2) - (3*b^2*Sqrt[Pi]*x*FresnelS[Sqrt[a - I*b*ArcSin[1 + I*d*x^2]]/(Sqrt[(-I)*b]*Sqrt[Pi])]*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)]))/(Sqrt[(-I)*b]*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2])) - (3*Sqrt[(-I)*b]*b*Sqrt[Pi]*x*FresnelC[Sqrt[a - I*b*ArcSin[1 + I*d*x^2]]/(Sqrt[(-I)*b]*Sqrt[Pi])]*(I*Cosh[a/(2*b)] + Sinh[a/(2*b)]))/(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2])","A",2,2,22,0.09091,1,"{4814, 4819}"
337,1,262,0,0.0275163,"\int \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)} \, dx","Int[Sqrt[a - I*b*ArcSin[1 + I*d*x^2]],x]","-\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{i}{b}} \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{i}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}+\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{\frac{i}{b}} \sqrt{a-i b \sin ^{-1}\left(i d x^2+1\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{i}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}+x \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}","-\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{i}{b}} \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{i}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}+\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{\frac{i}{b}} \sqrt{a-i b \sin ^{-1}\left(i d x^2+1\right)}}{\sqrt{\pi }}\right)}{\sqrt{\frac{i}{b}} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}+x \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}",1,"x*Sqrt[a - I*b*ArcSin[1 + I*d*x^2]] + (Sqrt[Pi]*x*FresnelS[(Sqrt[I/b]*Sqrt[a - I*b*ArcSin[1 + I*d*x^2]])/Sqrt[Pi]]*(Cosh[a/(2*b)] - I*Sinh[a/(2*b)]))/(Sqrt[I/b]*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2])) - (Sqrt[Pi]*x*FresnelC[(Sqrt[I/b]*Sqrt[a - I*b*ArcSin[1 + I*d*x^2]])/Sqrt[Pi]]*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)]))/(Sqrt[I/b]*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2]))","A",1,1,22,0.04545,1,"{4811}"
338,1,231,0,0.0276035,"\int \frac{1}{\sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}} \, dx","Int[1/Sqrt[a - I*b*ArcSin[1 + I*d*x^2]],x]","-\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}{\sqrt{\pi } \sqrt{-i b}}\right)}{\sqrt{-i b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a-i b \sin ^{-1}\left(i d x^2+1\right)}}{\sqrt{-i b} \sqrt{\pi }}\right)}{\sqrt{-i b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}","-\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}{\sqrt{\pi } \sqrt{-i b}}\right)}{\sqrt{-i b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a-i b \sin ^{-1}\left(i d x^2+1\right)}}{\sqrt{-i b} \sqrt{\pi }}\right)}{\sqrt{-i b} \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}",1,"-((Sqrt[Pi]*x*FresnelC[Sqrt[a - I*b*ArcSin[1 + I*d*x^2]]/(Sqrt[(-I)*b]*Sqrt[Pi])]*(Cosh[a/(2*b)] - I*Sinh[a/(2*b)]))/(Sqrt[(-I)*b]*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2]))) - (Sqrt[Pi]*x*FresnelS[Sqrt[a - I*b*ArcSin[1 + I*d*x^2]]/(Sqrt[(-I)*b]*Sqrt[Pi])]*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)]))/(Sqrt[(-I)*b]*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2]))","A",1,1,22,0.04545,1,"{4819}"
339,1,291,0,0.0486732,"\int \frac{1}{\left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{3/2}} \, dx","Int[(a - I*b*ArcSin[1 + I*d*x^2])^(-3/2),x]","-\frac{\sqrt{d^2 x^4-2 i d x^2}}{b d x \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}-\frac{\sqrt{\pi } \left(\frac{i}{b}\right)^{3/2} x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{i}{b}} \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)}+\frac{\sqrt{\pi } \left(\frac{i}{b}\right)^{3/2} x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{\frac{i}{b}} \sqrt{a-i b \sin ^{-1}\left(i d x^2+1\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)}","-\frac{\sqrt{d^2 x^4-2 i d x^2}}{b d x \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}-\frac{\sqrt{\pi } \left(\frac{i}{b}\right)^{3/2} x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{i}{b}} \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)}+\frac{\sqrt{\pi } \left(\frac{i}{b}\right)^{3/2} x \left(\cosh \left(\frac{a}{2 b}\right)-i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{\frac{i}{b}} \sqrt{a-i b \sin ^{-1}\left(i d x^2+1\right)}}{\sqrt{\pi }}\right)}{\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)}",1,"-(Sqrt[(-2*I)*d*x^2 + d^2*x^4]/(b*d*x*Sqrt[a - I*b*ArcSin[1 + I*d*x^2]])) + ((I/b)^(3/2)*Sqrt[Pi]*x*FresnelS[(Sqrt[I/b]*Sqrt[a - I*b*ArcSin[1 + I*d*x^2]])/Sqrt[Pi]]*(Cosh[a/(2*b)] - I*Sinh[a/(2*b)]))/(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2]) - ((I/b)^(3/2)*Sqrt[Pi]*x*FresnelC[(Sqrt[I/b]*Sqrt[a - I*b*ArcSin[1 + I*d*x^2]])/Sqrt[Pi]]*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)]))/(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2])","A",1,1,22,0.04545,1,"{4822}"
340,1,326,0,0.0725293,"\int \frac{1}{\left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{5/2}} \, dx","Int[(a - I*b*ArcSin[1 + I*d*x^2])^(-5/2),x]","-\frac{\sqrt{\pi } \sqrt{-i b} x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}{\sqrt{\pi } \sqrt{-i b}}\right)}{3 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a-i b \sin ^{-1}\left(i d x^2+1\right)}}{\sqrt{-i b} \sqrt{\pi }}\right)}{3 \sqrt{-i b} b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{x}{3 b^2 \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}-\frac{\sqrt{d^2 x^4-2 i d x^2}}{3 b d x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{3/2}}","-\frac{\sqrt{\pi } \sqrt{-i b} x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}{\sqrt{\pi } \sqrt{-i b}}\right)}{3 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{\sqrt{\pi } x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{a-i b \sin ^{-1}\left(i d x^2+1\right)}}{\sqrt{-i b} \sqrt{\pi }}\right)}{3 \sqrt{-i b} b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{x}{3 b^2 \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}-\frac{\sqrt{d^2 x^4-2 i d x^2}}{3 b d x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{3/2}}",1,"-Sqrt[(-2*I)*d*x^2 + d^2*x^4]/(3*b*d*x*(a - I*b*ArcSin[1 + I*d*x^2])^(3/2)) - x/(3*b^2*Sqrt[a - I*b*ArcSin[1 + I*d*x^2]]) - (Sqrt[Pi]*x*FresnelS[Sqrt[a - I*b*ArcSin[1 + I*d*x^2]]/(Sqrt[(-I)*b]*Sqrt[Pi])]*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)]))/(3*Sqrt[(-I)*b]*b^2*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2])) - (Sqrt[(-I)*b]*Sqrt[Pi]*x*FresnelC[Sqrt[a - I*b*ArcSin[1 + I*d*x^2]]/(Sqrt[(-I)*b]*Sqrt[Pi])]*(I*Cosh[a/(2*b)] + Sinh[a/(2*b)]))/(3*b^3*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2]))","A",2,2,22,0.09091,1,"{4828, 4819}"
341,1,389,0,0.0813284,"\int \frac{1}{\left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{7/2}} \, dx","Int[(a - I*b*ArcSin[1 + I*d*x^2])^(-7/2),x]","-\frac{\sqrt{d^2 x^4-2 i d x^2}}{15 b^3 d x \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}-\frac{\sqrt{\pi } \left(\frac{i}{b}\right)^{3/2} x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{i}{b}} \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}{\sqrt{\pi }}\right)}{15 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}+\frac{\sqrt{\pi } \sqrt{\frac{i}{b}} x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{\frac{i}{b}} \sqrt{a-i b \sin ^{-1}\left(i d x^2+1\right)}}{\sqrt{\pi }}\right)}{15 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{x}{15 b^2 \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{3/2}}-\frac{\sqrt{d^2 x^4-2 i d x^2}}{5 b d x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{5/2}}","-\frac{\sqrt{d^2 x^4-2 i d x^2}}{15 b^3 d x \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}-\frac{\sqrt{\pi } \left(\frac{i}{b}\right)^{3/2} x \left(\cosh \left(\frac{a}{2 b}\right)+i \sinh \left(\frac{a}{2 b}\right)\right) \text{FresnelC}\left(\frac{\sqrt{\frac{i}{b}} \sqrt{a-i b \sin ^{-1}\left(1+i d x^2\right)}}{\sqrt{\pi }}\right)}{15 b^2 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}+\frac{\sqrt{\pi } \sqrt{\frac{i}{b}} x \left(\sinh \left(\frac{a}{2 b}\right)+i \cosh \left(\frac{a}{2 b}\right)\right) S\left(\frac{\sqrt{\frac{i}{b}} \sqrt{a-i b \sin ^{-1}\left(i d x^2+1\right)}}{\sqrt{\pi }}\right)}{15 b^3 \left(\cos \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)-\sin \left(\frac{1}{2} \sin ^{-1}\left(1+i d x^2\right)\right)\right)}-\frac{x}{15 b^2 \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{3/2}}-\frac{\sqrt{d^2 x^4-2 i d x^2}}{5 b d x \left(a-i b \sin ^{-1}\left(1+i d x^2\right)\right)^{5/2}}",1,"-Sqrt[(-2*I)*d*x^2 + d^2*x^4]/(5*b*d*x*(a - I*b*ArcSin[1 + I*d*x^2])^(5/2)) - x/(15*b^2*(a - I*b*ArcSin[1 + I*d*x^2])^(3/2)) - Sqrt[(-2*I)*d*x^2 + d^2*x^4]/(15*b^3*d*x*Sqrt[a - I*b*ArcSin[1 + I*d*x^2]]) - ((I/b)^(3/2)*Sqrt[Pi]*x*FresnelC[(Sqrt[I/b]*Sqrt[a - I*b*ArcSin[1 + I*d*x^2]])/Sqrt[Pi]]*(Cosh[a/(2*b)] + I*Sinh[a/(2*b)]))/(15*b^2*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2])) + (Sqrt[I/b]*Sqrt[Pi]*x*FresnelS[(Sqrt[I/b]*Sqrt[a - I*b*ArcSin[1 + I*d*x^2]])/Sqrt[Pi]]*(I*Cosh[a/(2*b)] + Sinh[a/(2*b)]))/(15*b^3*(Cos[ArcSin[1 + I*d*x^2]/2] - Sin[ArcSin[1 + I*d*x^2]/2]))","A",2,2,22,0.09091,1,"{4828, 4822}"
342,0,0,0,0.0442882,"\int \frac{\left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^n}{1-c^2 x^2} \, dx","Int[(a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2),x]","\int \frac{\left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^n}{1-c^2 x^2} \, dx","\text{Int}\left(\frac{\left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^n}{1-c^2 x^2},x\right)",0,"Defer[Int][(a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2), x]","A",0,0,0,0,-1,"{}"
343,1,261,0,0.2257258,"\int \frac{\left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^3}{1-c^2 x^2} \, dx","Int[(a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3/(1 - c^2*x^2),x]","\frac{3 b^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}-\frac{3 b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}-\frac{3 b^3 \text{PolyLog}\left(4,e^{2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{4 c}+\frac{\left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^4}{4 b c}-\frac{\log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{c}","\frac{3 b^2 \text{PolyLog}\left(3,e^{-2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}+\frac{3 b \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}+\frac{3 b^3 \text{PolyLog}\left(4,e^{-2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{4 c}-\frac{\left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^4}{4 b c}-\frac{\log \left(1-e^{-2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{c}",1,"(a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^4/(4*b*c) - ((a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3*Log[1 - E^(2*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c - (3*b*(a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*PolyLog[2, E^(2*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/(2*c) + (3*b^2*(a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[3, E^(2*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/(2*c) - (3*b^3*PolyLog[4, E^(2*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/(4*c)","A",8,8,40,0.2000,0,"{6681, 5659, 3716, 2190, 2531, 6609, 2282, 6589}"
344,1,195,0,0.2156531,"\int \frac{\left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2}{1-c^2 x^2} \, dx","Int[(a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2/(1 - c^2*x^2),x]","-\frac{b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}+\frac{b^2 \text{PolyLog}\left(3,e^{2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}+\frac{\left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{3 b c}-\frac{\log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{c}","\frac{b \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}+\frac{b^2 \text{PolyLog}\left(3,e^{-2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}-\frac{\left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{3 b c}-\frac{\log \left(1-e^{-2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{c}",1,"(a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3/(3*b*c) - ((a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2*Log[1 - E^(2*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c - (b*(a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*PolyLog[2, E^(2*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c + (b^2*PolyLog[3, E^(2*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/(2*c)","A",7,7,40,0.1750,0,"{6681, 5659, 3716, 2190, 2531, 2282, 6589}"
345,1,133,0,0.1218322,"\int \frac{a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)}{1-c^2 x^2} \, dx","Int[(a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])/(1 - c^2*x^2),x]","-\frac{b \text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}+\frac{\left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 b c}-\frac{\log \left(1-e^{2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}","\frac{b \text{PolyLog}\left(2,e^{-2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}-\frac{\left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 b c}-\frac{\log \left(1-e^{-2 \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}",1,"(a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2/(2*b*c) - ((a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])*Log[1 - E^(2*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/c - (b*PolyLog[2, E^(2*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])])/(2*c)","A",6,7,38,0.1842,0,"{206, 6681, 5659, 3716, 2190, 2279, 2391}"
346,0,0,0,0.0492467,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)} \, dx","Int[1/((1 - c^2*x^2)*(a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])),x]","\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)} \, dx","\text{Int}\left(\frac{1}{\left(1-c^2 x^2\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)},x\right)",0,"Defer[Int][1/((1 - c^2*x^2)*(a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])), x]","A",0,0,0,0,-1,"{}"
347,0,0,0,0.0451338,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2} \, dx","Int[1/((1 - c^2*x^2)*(a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2),x]","\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(1-c^2 x^2\right) \left(a+b \sinh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2},x\right)",0,"Defer[Int][1/((1 - c^2*x^2)*(a + b*ArcSinh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2), x]","A",0,0,0,0,-1,"{}"
348,1,76,0,0.0756375,"\int \sinh ^{-1}\left(c e^{a+b x}\right) \, dx","Int[ArcSinh[c*E^(a + b*x)],x]","\frac{\text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(c e^{a+b x}\right)}\right)}{2 b}-\frac{\sinh ^{-1}\left(c e^{a+b x}\right)^2}{2 b}+\frac{\sinh ^{-1}\left(c e^{a+b x}\right) \log \left(1-e^{2 \sinh ^{-1}\left(c e^{a+b x}\right)}\right)}{b}","\frac{\text{PolyLog}\left(2,e^{2 \sinh ^{-1}\left(c e^{a+b x}\right)}\right)}{2 b}-\frac{\sinh ^{-1}\left(c e^{a+b x}\right)^2}{2 b}+\frac{\sinh ^{-1}\left(c e^{a+b x}\right) \log \left(1-e^{2 \sinh ^{-1}\left(c e^{a+b x}\right)}\right)}{b}",1,"-ArcSinh[c*E^(a + b*x)]^2/(2*b) + (ArcSinh[c*E^(a + b*x)]*Log[1 - E^(2*ArcSinh[c*E^(a + b*x)])])/b + PolyLog[2, E^(2*ArcSinh[c*E^(a + b*x)])]/(2*b)","A",6,6,10,0.6000,1,"{2282, 5659, 3716, 2190, 2279, 2391}"
349,1,165,0,0.1723548,"\int e^{\sinh ^{-1}(a+b x)} x^3 \, dx","Int[E^ArcSinh[a + b*x]*x^3,x]","\frac{\left(3-4 a^2\right) a e^{2 \sinh ^{-1}(a+b x)}}{16 b^4}+\frac{\left(3-4 a^2\right) a \sinh ^{-1}(a+b x)}{8 b^4}-\frac{\left(1-6 a^2\right) e^{-\sinh ^{-1}(a+b x)}}{8 b^4}-\frac{\left(1-6 a^2\right) e^{3 \sinh ^{-1}(a+b x)}}{24 b^4}+\frac{3 a e^{-2 \sinh ^{-1}(a+b x)}}{16 b^4}-\frac{3 a e^{4 \sinh ^{-1}(a+b x)}}{32 b^4}+\frac{e^{-3 \sinh ^{-1}(a+b x)}}{48 b^4}+\frac{e^{5 \sinh ^{-1}(a+b x)}}{80 b^4}","\frac{\left(3-4 a^2\right) a e^{2 \sinh ^{-1}(a+b x)}}{16 b^4}+\frac{\left(3-4 a^2\right) a \sinh ^{-1}(a+b x)}{8 b^4}-\frac{\left(1-6 a^2\right) e^{-\sinh ^{-1}(a+b x)}}{8 b^4}-\frac{\left(1-6 a^2\right) e^{3 \sinh ^{-1}(a+b x)}}{24 b^4}+\frac{3 a e^{-2 \sinh ^{-1}(a+b x)}}{16 b^4}-\frac{3 a e^{4 \sinh ^{-1}(a+b x)}}{32 b^4}+\frac{e^{-3 \sinh ^{-1}(a+b x)}}{48 b^4}+\frac{e^{5 \sinh ^{-1}(a+b x)}}{80 b^4}",1,"1/(48*b^4*E^(3*ArcSinh[a + b*x])) + (3*a)/(16*b^4*E^(2*ArcSinh[a + b*x])) - (1 - 6*a^2)/(8*b^4*E^ArcSinh[a + b*x]) + (a*(3 - 4*a^2)*E^(2*ArcSinh[a + b*x]))/(16*b^4) - ((1 - 6*a^2)*E^(3*ArcSinh[a + b*x]))/(24*b^4) - (3*a*E^(4*ArcSinh[a + b*x]))/(32*b^4) + E^(5*ArcSinh[a + b*x])/(80*b^4) + (a*(3 - 4*a^2)*ArcSinh[a + b*x])/(8*b^4)","A",5,4,12,0.3333,1,"{5898, 2282, 12, 1628}"
350,1,115,0,0.1252497,"\int e^{\sinh ^{-1}(a+b x)} x^2 \, dx","Int[E^ArcSinh[a + b*x]*x^2,x]","-\frac{\left(1-4 a^2\right) e^{2 \sinh ^{-1}(a+b x)}}{16 b^3}-\frac{\left(1-4 a^2\right) \sinh ^{-1}(a+b x)}{8 b^3}-\frac{a e^{-\sinh ^{-1}(a+b x)}}{2 b^3}-\frac{a e^{3 \sinh ^{-1}(a+b x)}}{6 b^3}-\frac{e^{-2 \sinh ^{-1}(a+b x)}}{16 b^3}+\frac{e^{4 \sinh ^{-1}(a+b x)}}{32 b^3}","-\frac{\left(1-4 a^2\right) e^{2 \sinh ^{-1}(a+b x)}}{16 b^3}-\frac{\left(1-4 a^2\right) \sinh ^{-1}(a+b x)}{8 b^3}-\frac{a e^{-\sinh ^{-1}(a+b x)}}{2 b^3}-\frac{a e^{3 \sinh ^{-1}(a+b x)}}{6 b^3}-\frac{e^{-2 \sinh ^{-1}(a+b x)}}{16 b^3}+\frac{e^{4 \sinh ^{-1}(a+b x)}}{32 b^3}",1,"-1/(16*b^3*E^(2*ArcSinh[a + b*x])) - a/(2*b^3*E^ArcSinh[a + b*x]) - ((1 - 4*a^2)*E^(2*ArcSinh[a + b*x]))/(16*b^3) - (a*E^(3*ArcSinh[a + b*x]))/(6*b^3) + E^(4*ArcSinh[a + b*x])/(32*b^3) - ((1 - 4*a^2)*ArcSinh[a + b*x])/(8*b^3)","A",5,4,12,0.3333,1,"{5898, 2282, 12, 1628}"
351,1,67,0,0.070877,"\int e^{\sinh ^{-1}(a+b x)} x \, dx","Int[E^ArcSinh[a + b*x]*x,x]","-\frac{a e^{2 \sinh ^{-1}(a+b x)}}{4 b^2}-\frac{a \sinh ^{-1}(a+b x)}{2 b^2}+\frac{e^{-\sinh ^{-1}(a+b x)}}{4 b^2}+\frac{e^{3 \sinh ^{-1}(a+b x)}}{12 b^2}","-\frac{a e^{2 \sinh ^{-1}(a+b x)}}{4 b^2}-\frac{a \sinh ^{-1}(a+b x)}{2 b^2}+\frac{e^{-\sinh ^{-1}(a+b x)}}{4 b^2}+\frac{e^{3 \sinh ^{-1}(a+b x)}}{12 b^2}",1,"1/(4*b^2*E^ArcSinh[a + b*x]) - (a*E^(2*ArcSinh[a + b*x]))/(4*b^2) + E^(3*ArcSinh[a + b*x])/(12*b^2) - (a*ArcSinh[a + b*x])/(2*b^2)","A",5,4,10,0.4000,1,"{5898, 2282, 12, 1628}"
352,1,31,0,0.0174833,"\int e^{\sinh ^{-1}(a+b x)} \, dx","Int[E^ArcSinh[a + b*x],x]","\frac{\sinh ^{-1}(a+b x)}{2 b}+\frac{e^{2 \sinh ^{-1}(a+b x)}}{4 b}","\frac{\sinh ^{-1}(a+b x)}{2 b}+\frac{e^{2 \sinh ^{-1}(a+b x)}}{4 b}",1,"E^(2*ArcSinh[a + b*x])/(4*b) + ArcSinh[a + b*x]/(2*b)","A",5,4,8,0.5000,1,"{5896, 2282, 12, 14}"
353,1,89,0,0.120651,"\int \frac{e^{\sinh ^{-1}(a+b x)}}{x} \, dx","Int[E^ArcSinh[a + b*x]/x,x]","\sqrt{a^2+2 a b x+b^2 x^2+1}-\sqrt{a^2+1} \tanh ^{-1}\left(\frac{a^2+a b x+1}{\sqrt{a^2+1} \sqrt{a^2+2 a b x+b^2 x^2+1}}\right)+a \sinh ^{-1}(a+b x)+a \log (x)+b x","\sqrt{a^2+2 a b x+b^2 x^2+1}-\sqrt{a^2+1} \tanh ^{-1}\left(\frac{a^2+a b x+1}{\sqrt{a^2+1} \sqrt{a^2+2 a b x+b^2 x^2+1}}\right)+a \sinh ^{-1}(a+b x)+a \log (x)+b x",1,"b*x + Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2] + a*ArcSinh[a + b*x] - Sqrt[1 + a^2]*ArcTanh[(1 + a^2 + a*b*x)/(Sqrt[1 + a^2]*Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2])] + a*Log[x]","A",9,8,12,0.6667,1,"{5907, 14, 734, 843, 619, 215, 724, 206}"
354,1,99,0,0.1053953,"\int \frac{e^{\sinh ^{-1}(a+b x)}}{x^2} \, dx","Int[E^ArcSinh[a + b*x]/x^2,x]","-\frac{\sqrt{a^2+2 a b x+b^2 x^2+1}}{x}-\frac{a b \tanh ^{-1}\left(\frac{a^2+a b x+1}{\sqrt{a^2+1} \sqrt{a^2+2 a b x+b^2 x^2+1}}\right)}{\sqrt{a^2+1}}+b \sinh ^{-1}(a+b x)-\frac{a}{x}+b \log (x)","-\frac{\sqrt{a^2+2 a b x+b^2 x^2+1}}{x}-\frac{a b \tanh ^{-1}\left(\frac{a^2+a b x+1}{\sqrt{a^2+1} \sqrt{a^2+2 a b x+b^2 x^2+1}}\right)}{\sqrt{a^2+1}}+b \sinh ^{-1}(a+b x)-\frac{a}{x}+b \log (x)",1,"-(a/x) - Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2]/x + b*ArcSinh[a + b*x] - (a*b*ArcTanh[(1 + a^2 + a*b*x)/(Sqrt[1 + a^2]*Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2])])/Sqrt[1 + a^2] + b*Log[x]","A",9,8,12,0.6667,1,"{5907, 14, 732, 843, 619, 215, 724, 206}"
355,1,116,0,0.0858755,"\int \frac{e^{\sinh ^{-1}(a+b x)}}{x^3} \, dx","Int[E^ArcSinh[a + b*x]/x^3,x]","-\frac{\left(a^2+a b x+1\right) \sqrt{a^2+2 a b x+b^2 x^2+1}}{2 \left(a^2+1\right) x^2}-\frac{b^2 \tanh ^{-1}\left(\frac{a^2+a b x+1}{\sqrt{a^2+1} \sqrt{a^2+2 a b x+b^2 x^2+1}}\right)}{2 \left(a^2+1\right)^{3/2}}-\frac{a}{2 x^2}-\frac{b}{x}","-\frac{\left(a^2+a b x+1\right) \sqrt{a^2+2 a b x+b^2 x^2+1}}{2 \left(a^2+1\right) x^2}-\frac{b^2 \tanh ^{-1}\left(\frac{a^2+a b x+1}{\sqrt{a^2+1} \sqrt{a^2+2 a b x+b^2 x^2+1}}\right)}{2 \left(a^2+1\right)^{3/2}}-\frac{a}{2 x^2}-\frac{b}{x}",1,"-a/(2*x^2) - b/x - ((1 + a^2 + a*b*x)*Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2])/(2*(1 + a^2)*x^2) - (b^2*ArcTanh[(1 + a^2 + a*b*x)/(Sqrt[1 + a^2]*Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2])])/(2*(1 + a^2)^(3/2))","A",6,5,12,0.4167,1,"{5907, 14, 720, 724, 206}"
356,1,156,0,0.108295,"\int \frac{e^{\sinh ^{-1}(a+b x)}}{x^4} \, dx","Int[E^ArcSinh[a + b*x]/x^4,x]","\frac{a b \left(a^2+a b x+1\right) \sqrt{a^2+2 a b x+b^2 x^2+1}}{2 \left(a^2+1\right)^2 x^2}-\frac{\left(a^2+2 a b x+b^2 x^2+1\right)^{3/2}}{3 \left(a^2+1\right) x^3}+\frac{a b^3 \tanh ^{-1}\left(\frac{a^2+a b x+1}{\sqrt{a^2+1} \sqrt{a^2+2 a b x+b^2 x^2+1}}\right)}{2 \left(a^2+1\right)^{5/2}}-\frac{a}{3 x^3}-\frac{b}{2 x^2}","\frac{a b \left(a^2+a b x+1\right) \sqrt{a^2+2 a b x+b^2 x^2+1}}{2 \left(a^2+1\right)^2 x^2}-\frac{\left(a^2+2 a b x+b^2 x^2+1\right)^{3/2}}{3 \left(a^2+1\right) x^3}+\frac{a b^3 \tanh ^{-1}\left(\frac{a^2+a b x+1}{\sqrt{a^2+1} \sqrt{a^2+2 a b x+b^2 x^2+1}}\right)}{2 \left(a^2+1\right)^{5/2}}-\frac{a}{3 x^3}-\frac{b}{2 x^2}",1,"-a/(3*x^3) - b/(2*x^2) + (a*b*(1 + a^2 + a*b*x)*Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2])/(2*(1 + a^2)^2*x^2) - (1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(3*(1 + a^2)*x^3) + (a*b^3*ArcTanh[(1 + a^2 + a*b*x)/(Sqrt[1 + a^2]*Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2])])/(2*(1 + a^2)^(5/2))","A",7,6,12,0.5000,1,"{5907, 14, 730, 720, 724, 206}"
357,1,207,0,0.1708808,"\int \frac{e^{\sinh ^{-1}(a+b x)}}{x^5} \, dx","Int[E^ArcSinh[a + b*x]/x^5,x]","\frac{\left(1-4 a^2\right) b^2 \left(a^2+a b x+1\right) \sqrt{a^2+2 a b x+b^2 x^2+1}}{8 \left(a^2+1\right)^3 x^2}+\frac{5 a b \left(a^2+2 a b x+b^2 x^2+1\right)^{3/2}}{12 \left(a^2+1\right)^2 x^3}-\frac{\left(a^2+2 a b x+b^2 x^2+1\right)^{3/2}}{4 \left(a^2+1\right) x^4}+\frac{\left(1-4 a^2\right) b^4 \tanh ^{-1}\left(\frac{a^2+a b x+1}{\sqrt{a^2+1} \sqrt{a^2+2 a b x+b^2 x^2+1}}\right)}{8 \left(a^2+1\right)^{7/2}}-\frac{a}{4 x^4}-\frac{b}{3 x^3}","\frac{\left(1-4 a^2\right) b^2 \left(a^2+a b x+1\right) \sqrt{a^2+2 a b x+b^2 x^2+1}}{8 \left(a^2+1\right)^3 x^2}+\frac{5 a b \left(a^2+2 a b x+b^2 x^2+1\right)^{3/2}}{12 \left(a^2+1\right)^2 x^3}-\frac{\left(a^2+2 a b x+b^2 x^2+1\right)^{3/2}}{4 \left(a^2+1\right) x^4}+\frac{\left(1-4 a^2\right) b^4 \tanh ^{-1}\left(\frac{a^2+a b x+1}{\sqrt{a^2+1} \sqrt{a^2+2 a b x+b^2 x^2+1}}\right)}{8 \left(a^2+1\right)^{7/2}}-\frac{a}{4 x^4}-\frac{b}{3 x^3}",1,"-a/(4*x^4) - b/(3*x^3) + ((1 - 4*a^2)*b^2*(1 + a^2 + a*b*x)*Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2])/(8*(1 + a^2)^3*x^2) - (1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(4*(1 + a^2)*x^4) + (5*a*b*(1 + a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(12*(1 + a^2)^2*x^3) + ((1 - 4*a^2)*b^4*ArcTanh[(1 + a^2 + a*b*x)/(Sqrt[1 + a^2]*Sqrt[1 + a^2 + 2*a*b*x + b^2*x^2])])/(8*(1 + a^2)^(7/2))","A",8,7,12,0.5833,1,"{5907, 14, 744, 806, 720, 724, 206}"
358,1,359,0,0.7429368,"\int e^{\sinh ^{-1}(a+b x)^2} x^3 \, dx","Int[E^ArcSinh[a + b*x]^2*x^3,x]","-\frac{\sqrt{\pi } a^3 \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b^4}-\frac{\sqrt{\pi } a^3 \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b^4}+\frac{3 \sqrt{\pi } a^2 \text{Erfi}\left(1-\sinh ^{-1}(a+b x)\right)}{8 e b^4}+\frac{3 \sqrt{\pi } a^2 \text{Erfi}\left(\sinh ^{-1}(a+b x)+1\right)}{8 e b^4}-\frac{3 \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)-3\right)\right)}{16 e^{9/4} b^4}+\frac{3 \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)-1\right)\right)}{16 \sqrt[4]{e} b^4}+\frac{3 \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)+1\right)\right)}{16 \sqrt[4]{e} b^4}-\frac{3 \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)+3\right)\right)}{16 e^{9/4} b^4}-\frac{\sqrt{\pi } \text{Erfi}\left(1-\sinh ^{-1}(a+b x)\right)}{16 e b^4}+\frac{\sqrt{\pi } \text{Erfi}\left(2-\sinh ^{-1}(a+b x)\right)}{32 e^4 b^4}-\frac{\sqrt{\pi } \text{Erfi}\left(\sinh ^{-1}(a+b x)+1\right)}{16 e b^4}+\frac{\sqrt{\pi } \text{Erfi}\left(\sinh ^{-1}(a+b x)+2\right)}{32 e^4 b^4}","-\frac{\sqrt{\pi } a^3 \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b^4}-\frac{\sqrt{\pi } a^3 \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b^4}+\frac{3 \sqrt{\pi } a^2 \text{Erfi}\left(1-\sinh ^{-1}(a+b x)\right)}{8 e b^4}+\frac{3 \sqrt{\pi } a^2 \text{Erfi}\left(\sinh ^{-1}(a+b x)+1\right)}{8 e b^4}-\frac{3 \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)-3\right)\right)}{16 e^{9/4} b^4}+\frac{3 \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)-1\right)\right)}{16 \sqrt[4]{e} b^4}+\frac{3 \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)+1\right)\right)}{16 \sqrt[4]{e} b^4}-\frac{3 \sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)+3\right)\right)}{16 e^{9/4} b^4}-\frac{\sqrt{\pi } \text{Erfi}\left(1-\sinh ^{-1}(a+b x)\right)}{16 e b^4}+\frac{\sqrt{\pi } \text{Erfi}\left(2-\sinh ^{-1}(a+b x)\right)}{32 e^4 b^4}-\frac{\sqrt{\pi } \text{Erfi}\left(\sinh ^{-1}(a+b x)+1\right)}{16 e b^4}+\frac{\sqrt{\pi } \text{Erfi}\left(\sinh ^{-1}(a+b x)+2\right)}{32 e^4 b^4}",1,"-(Sqrt[Pi]*Erfi[1 - ArcSinh[a + b*x]])/(16*b^4*E) + (3*a^2*Sqrt[Pi]*Erfi[1 - ArcSinh[a + b*x]])/(8*b^4*E) + (Sqrt[Pi]*Erfi[2 - ArcSinh[a + b*x]])/(32*b^4*E^4) - (Sqrt[Pi]*Erfi[1 + ArcSinh[a + b*x]])/(16*b^4*E) + (3*a^2*Sqrt[Pi]*Erfi[1 + ArcSinh[a + b*x]])/(8*b^4*E) + (Sqrt[Pi]*Erfi[2 + ArcSinh[a + b*x]])/(32*b^4*E^4) - (3*a*Sqrt[Pi]*Erfi[(-3 + 2*ArcSinh[a + b*x])/2])/(16*b^4*E^(9/4)) + (3*a*Sqrt[Pi]*Erfi[(-1 + 2*ArcSinh[a + b*x])/2])/(16*b^4*E^(1/4)) - (a^3*Sqrt[Pi]*Erfi[(-1 + 2*ArcSinh[a + b*x])/2])/(4*b^4*E^(1/4)) + (3*a*Sqrt[Pi]*Erfi[(1 + 2*ArcSinh[a + b*x])/2])/(16*b^4*E^(1/4)) - (a^3*Sqrt[Pi]*Erfi[(1 + 2*ArcSinh[a + b*x])/2])/(4*b^4*E^(1/4)) - (3*a*Sqrt[Pi]*Erfi[(3 + 2*ArcSinh[a + b*x])/2])/(16*b^4*E^(9/4))","A",37,8,14,0.5714,1,"{5898, 6741, 12, 6742, 5513, 2234, 2204, 5514}"
359,1,251,0,0.5160424,"\int e^{\sinh ^{-1}(a+b x)^2} x^2 \, dx","Int[E^ArcSinh[a + b*x]^2*x^2,x]","\frac{\sqrt{\pi } a^2 \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b^3}+\frac{\sqrt{\pi } a^2 \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b^3}-\frac{\sqrt{\pi } a \text{Erfi}\left(1-\sinh ^{-1}(a+b x)\right)}{4 e b^3}-\frac{\sqrt{\pi } a \text{Erfi}\left(\sinh ^{-1}(a+b x)+1\right)}{4 e b^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)-3\right)\right)}{16 e^{9/4} b^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)-1\right)\right)}{16 \sqrt[4]{e} b^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)+1\right)\right)}{16 \sqrt[4]{e} b^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)+3\right)\right)}{16 e^{9/4} b^3}","\frac{\sqrt{\pi } a^2 \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b^3}+\frac{\sqrt{\pi } a^2 \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b^3}-\frac{\sqrt{\pi } a \text{Erfi}\left(1-\sinh ^{-1}(a+b x)\right)}{4 e b^3}-\frac{\sqrt{\pi } a \text{Erfi}\left(\sinh ^{-1}(a+b x)+1\right)}{4 e b^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)-3\right)\right)}{16 e^{9/4} b^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)-1\right)\right)}{16 \sqrt[4]{e} b^3}-\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)+1\right)\right)}{16 \sqrt[4]{e} b^3}+\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)+3\right)\right)}{16 e^{9/4} b^3}",1,"-(a*Sqrt[Pi]*Erfi[1 - ArcSinh[a + b*x]])/(4*b^3*E) - (a*Sqrt[Pi]*Erfi[1 + ArcSinh[a + b*x]])/(4*b^3*E) + (Sqrt[Pi]*Erfi[(-3 + 2*ArcSinh[a + b*x])/2])/(16*b^3*E^(9/4)) - (Sqrt[Pi]*Erfi[(-1 + 2*ArcSinh[a + b*x])/2])/(16*b^3*E^(1/4)) + (a^2*Sqrt[Pi]*Erfi[(-1 + 2*ArcSinh[a + b*x])/2])/(4*b^3*E^(1/4)) - (Sqrt[Pi]*Erfi[(1 + 2*ArcSinh[a + b*x])/2])/(16*b^3*E^(1/4)) + (a^2*Sqrt[Pi]*Erfi[(1 + 2*ArcSinh[a + b*x])/2])/(4*b^3*E^(1/4)) + (Sqrt[Pi]*Erfi[(3 + 2*ArcSinh[a + b*x])/2])/(16*b^3*E^(9/4))","A",27,8,14,0.5714,1,"{5898, 6741, 12, 6742, 5513, 2234, 2204, 5514}"
360,1,117,0,0.2768394,"\int e^{\sinh ^{-1}(a+b x)^2} x \, dx","Int[E^ArcSinh[a + b*x]^2*x,x]","\frac{\sqrt{\pi } \text{Erfi}\left(1-\sinh ^{-1}(a+b x)\right)}{8 e b^2}+\frac{\sqrt{\pi } \text{Erfi}\left(\sinh ^{-1}(a+b x)+1\right)}{8 e b^2}-\frac{\sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b^2}-\frac{\sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b^2}","\frac{\sqrt{\pi } \text{Erfi}\left(1-\sinh ^{-1}(a+b x)\right)}{8 e b^2}+\frac{\sqrt{\pi } \text{Erfi}\left(\sinh ^{-1}(a+b x)+1\right)}{8 e b^2}-\frac{\sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b^2}-\frac{\sqrt{\pi } a \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b^2}",1,"(Sqrt[Pi]*Erfi[1 - ArcSinh[a + b*x]])/(8*b^2*E) + (Sqrt[Pi]*Erfi[1 + ArcSinh[a + b*x]])/(8*b^2*E) - (a*Sqrt[Pi]*Erfi[(-1 + 2*ArcSinh[a + b*x])/2])/(4*b^2*E^(1/4)) - (a*Sqrt[Pi]*Erfi[(1 + 2*ArcSinh[a + b*x])/2])/(4*b^2*E^(1/4))","A",17,8,12,0.6667,1,"{5898, 6741, 12, 6742, 5513, 2234, 2204, 5514}"
361,1,65,0,0.055106,"\int e^{\sinh ^{-1}(a+b x)^2} \, dx","Int[E^ArcSinh[a + b*x]^2,x]","\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b}+\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b}","\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b}+\frac{\sqrt{\pi } \text{Erfi}\left(\frac{1}{2} \left(2 \sinh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b}",1,"(Sqrt[Pi]*Erfi[(-1 + 2*ArcSinh[a + b*x])/2])/(4*b*E^(1/4)) + (Sqrt[Pi]*Erfi[(1 + 2*ArcSinh[a + b*x])/2])/(4*b*E^(1/4))","A",7,4,10,0.4000,1,"{5896, 5513, 2234, 2204}"
362,0,0,0,0.0382415,"\int \frac{e^{\sinh ^{-1}(a+b x)^2}}{x} \, dx","Int[E^ArcSinh[a + b*x]^2/x,x]","\int \frac{e^{\sinh ^{-1}(a+b x)^2}}{x} \, dx","\text{Int}\left(\frac{e^{\sinh ^{-1}(a+b x)^2}}{x},x\right)",0,"Defer[Int][E^ArcSinh[a + b*x]^2/x, x]","A",0,0,0,0,-1,"{}"
363,0,0,0,0.0373086,"\int \frac{e^{\sinh ^{-1}(a+b x)^2}}{x^2} \, dx","Int[E^ArcSinh[a + b*x]^2/x^2,x]","\int \frac{e^{\sinh ^{-1}(a+b x)^2}}{x^2} \, dx","\text{Int}\left(\frac{e^{\sinh ^{-1}(a+b x)^2}}{x^2},x\right)",0,"Defer[Int][E^ArcSinh[a + b*x]^2/x^2, x]","A",0,0,0,0,-1,"{}"
364,1,60,0,0.095525,"\int \frac{\sinh ^{-1}(a+b x)}{\frac{a d}{b}+d x} \, dx","Int[ArcSinh[a + b*x]/((a*d)/b + d*x),x]","\frac{\text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a+b x)}\right)}{2 d}-\frac{\sinh ^{-1}(a+b x)^2}{2 d}+\frac{\sinh ^{-1}(a+b x) \log \left(1-e^{2 \sinh ^{-1}(a+b x)}\right)}{d}","\frac{\text{PolyLog}\left(2,e^{2 \sinh ^{-1}(a+b x)}\right)}{2 d}-\frac{\sinh ^{-1}(a+b x)^2}{2 d}+\frac{\sinh ^{-1}(a+b x) \log \left(1-e^{2 \sinh ^{-1}(a+b x)}\right)}{d}",1,"-ArcSinh[a + b*x]^2/(2*d) + (ArcSinh[a + b*x]*Log[1 - E^(2*ArcSinh[a + b*x])])/d + PolyLog[2, E^(2*ArcSinh[a + b*x])]/(2*d)","A",7,7,19,0.3684,1,"{5865, 12, 5659, 3716, 2190, 2279, 2391}"
365,1,3,0,0.0595927,"\int \frac{x}{\sqrt{1+x^2} \sinh ^{-1}(x)} \, dx","Int[x/(Sqrt[1 + x^2]*ArcSinh[x]),x]","\text{Shi}\left(\sinh ^{-1}(x)\right)","\text{Shi}\left(\sinh ^{-1}(x)\right)",1,"SinhIntegral[ArcSinh[x]]","A",2,2,15,0.1333,1,"{5779, 3298}"
366,1,45,0,0.0485548,"\int x^3 \sinh ^{-1}\left(a+b x^4\right) \, dx","Int[x^3*ArcSinh[a + b*x^4],x]","\frac{\left(a+b x^4\right) \sinh ^{-1}\left(a+b x^4\right)}{4 b}-\frac{\sqrt{\left(a+b x^4\right)^2+1}}{4 b}","\frac{\left(a+b x^4\right) \sinh ^{-1}\left(a+b x^4\right)}{4 b}-\frac{\sqrt{\left(a+b x^4\right)^2+1}}{4 b}",1,"-Sqrt[1 + (a + b*x^4)^2]/(4*b) + ((a + b*x^4)*ArcSinh[a + b*x^4])/(4*b)","A",4,4,12,0.3333,1,"{6715, 5863, 5653, 261}"
367,1,46,0,0.0504628,"\int x^{-1+n} \sinh ^{-1}\left(a+b x^n\right) \, dx","Int[x^(-1 + n)*ArcSinh[a + b*x^n],x]","\frac{\left(a+b x^n\right) \sinh ^{-1}\left(a+b x^n\right)}{b n}-\frac{\sqrt{\left(a+b x^n\right)^2+1}}{b n}","\frac{\left(a+b x^n\right) \sinh ^{-1}\left(a+b x^n\right)}{b n}-\frac{\sqrt{\left(a+b x^n\right)^2+1}}{b n}",1,"-(Sqrt[1 + (a + b*x^n)^2]/(b*n)) + ((a + b*x^n)*ArcSinh[a + b*x^n])/(b*n)","A",4,4,14,0.2857,1,"{6715, 5863, 5653, 261}"
368,1,49,0,0.0322443,"\int \sinh ^{-1}\left(\frac{c}{a+b x}\right) \, dx","Int[ArcSinh[c/(a + b*x)],x]","\frac{c \tanh ^{-1}\left(\sqrt{\frac{1}{\left(\frac{a}{c}+\frac{b x}{c}\right)^2}+1}\right)}{b}+\frac{(a+b x) \text{csch}^{-1}\left(\frac{a}{c}+\frac{b x}{c}\right)}{b}","\frac{c \tanh ^{-1}\left(\sqrt{\frac{1}{\left(\frac{a}{c}+\frac{b x}{c}\right)^2}+1}\right)}{b}+\frac{(a+b x) \text{csch}^{-1}\left(\frac{a}{c}+\frac{b x}{c}\right)}{b}",1,"((a + b*x)*ArcCsch[a/c + (b*x)/c])/b + (c*ArcTanh[Sqrt[1 + (a/c + (b*x)/c)^(-2)]])/b","A",6,6,10,0.6000,1,"{5892, 6314, 372, 266, 63, 207}"
369,0,0,0,0.0393858,"\int \frac{x}{\sinh ^{-1}(\sinh (x))} \, dx","Int[x/ArcSinh[Sinh[x]],x]","\int \frac{x}{\sinh ^{-1}(\sinh (x))} \, dx","\sinh ^{-1}(\sinh (x))+\log \left(\sinh ^{-1}(\sinh (x))\right) \left(x \sqrt{\cosh ^2(x)} \text{sech}(x)-\sinh ^{-1}(\sinh (x))\right)",1,"Defer[Int][x/ArcSinh[Sinh[x]], x]","F",0,0,0,0,-1,"{}"
370,1,37,0,0.0665338,"\int \frac{\sinh ^{-1}\left(\sqrt{-1+b x^2}\right)^n}{\sqrt{-1+b x^2}} \, dx","Int[ArcSinh[Sqrt[-1 + b*x^2]]^n/Sqrt[-1 + b*x^2],x]","\frac{\sqrt{b x^2} \sinh ^{-1}\left(\sqrt{b x^2-1}\right)^{n+1}}{b (n+1) x}","\frac{\sqrt{b x^2} \sinh ^{-1}\left(\sqrt{b x^2-1}\right)^{n+1}}{b (n+1) x}",1,"(Sqrt[b*x^2]*ArcSinh[Sqrt[-1 + b*x^2]]^(1 + n))/(b*(1 + n)*x)","A",2,2,26,0.07692,1,"{5894, 5675}"
371,1,29,0,0.0615313,"\int \frac{1}{\sqrt{-1+b x^2} \sinh ^{-1}\left(\sqrt{-1+b x^2}\right)} \, dx","Int[1/(Sqrt[-1 + b*x^2]*ArcSinh[Sqrt[-1 + b*x^2]]),x]","\frac{\sqrt{b x^2} \log \left(\sinh ^{-1}\left(\sqrt{b x^2-1}\right)\right)}{b x}","\frac{\sqrt{b x^2} \log \left(\sinh ^{-1}\left(\sqrt{b x^2-1}\right)\right)}{b x}",1,"(Sqrt[b*x^2]*Log[ArcSinh[Sqrt[-1 + b*x^2]]])/(b*x)","A",2,2,26,0.07692,1,"{5894, 5673}"